text stringlengths 14 5.77M | meta dict | __index_level_0__ int64 0 9.97k ⌀ |
|---|---|---|
\section{Summary and outlook}
We computed the ordinary static potential and the $\Pi_u$ and $\Sigma_u^-$ hybrid static potentials in $\text{SU(3)}$ lattice gauge theory at four different lattice spacings, where the smallest lattice spacing, $a = 0.04 \, \text{fm}$, is roughly half the size of lattice spacings previously used in similar computations.
Lattice discretization errors, which were found to be sizable in the bare lattice data points, were studied in detail.
We removed a large part of these discretization errors by using both perturbative tree-level improvement and a suitable simultaneous fit to the bare lattice data points from all our ensembles to identify the dominant $a^2$ contribution to the discretization errors.
Using the same fit we were also able to subtract the $a$-dependent unphysical self-energy.
For future reference these improved lattice data points are collected in Table~\ref{tab:latticedata_ABCD_tilde_all}.
Moreover, we investigated possibly existent systematic errors related to topological freezing, due to the finite spatial volume and because of glueball decays in detail and provided evidence that these errors are negligible compared to statistical errors.
We also provide parametrizations of the $\Sigma_g^+$, $\Pi_u$ and $\Sigma_u^-$ static potentials, which can e.g.\ be used for Born-Oppenheimer predictions of heavy hybrid meson masses.
The Born-Oppenheimer approach in the context of heavy hybrid mesons received considerable interest in the past couple of years, with many improvements and refinements, e.g.\ the derivation of coupled channel Schr\"odinger equations, which take into account mixing between different sectors \cite{Berwein:2015vca,Oncala:2017hop}, or the inclusion of effects due to the heavy quark spins \cite{Brambilla:2018pyn,Brambilla:2019jfi}.
These papers, however, use lattice data \cite{Juge:1997nc,Juge:1997ir,Juge:1999aw,Juge:2002br,Bali:2003jq,Juge:2003ge} generated around two decades ago at much coarser lattice spacing and partly without any dedicated investigation or removal of discretization errors.
Thus, it would be an interesting and important step towards higher precision to combine the refined Born-Oppenheimer approaches from Refs.\ \cite{Berwein:2015vca,Oncala:2017hop,Brambilla:2018pyn,Brambilla:2019jfi} with the lattice data points or the parametrizations presented in this work.
Since we performed computations at very small lattice spacings, we were able to reliably access quark-antiquark separations as small as $r = 0.08 \, \text{fm}$.
This, in turn, allowed to convincingly show the upward curvature at small $r$ of the $\Pi_u$ and $\Sigma_u^-$ hybrid static potentials predicted by perturbation theory, i.e.\ their repulsive nature at small quark-antiquark separations.
An interesting future direction with the aim to improve the precision of Born-Oppenheimer predictions even further could be to match higher order perturbation theory and the lattice results presented in this work.
For the ordinary static potential a possible method using next-to-next-to-next-to-leading order perturbation theory was discussed in Ref.\ \cite{Karbstein:2018mzo} and an approach based on leading order perturbation theory for hybrid static potentials can be found in Ref.\ \cite{Berwein:2015vca}.
\section*{Acknowledgements}
We thank Christian Reisinger for providing his multilevel code.
We acknowledge interesting and useful discussions with Eric Braaten, Nora Brambilla, Francesco Knechtli, Colin Morningstar, Lasse M\"uller, Christian Reisinger and Joan Soto.
M.W.\ acknowledges support by the Heisenberg Programme of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) -- project number 399217702.
Calculations on the GOETHE-HLR and on the on the FUCHS-CSC high-performance computers of the Frankfurt University were conducted for this research. We would like to thank HPC-Hessen, funded by the State Ministry of Higher Education, Research and the Arts, for programming advice.
\section{Excluding systematic errors}\label{sec:systematicerrors}
\subsection{Topological freezing}
In the continuum, gauge field configurations can be classified according to their integer topological charge $Q$. The corresponding topological sectors are separated by barriers of infinite action.
Topological freezing refers to the problem that a Monte Carlo simulation of a lattice gauge theory is trapped in one of the topological sectors, either during a significant part or the whole simulation.
Clearly, gauge link configurations generated in such a simulation do not form a representative set distributed according to $e^{-S}$.
Topological freezing is expected to appear, when using small lattice spacings $a \approx 0.05 \, \text{fm}$ \cite{Schaefer:2010hu}.
It becomes increasingly more problematic, when approaching the continuum, i.e.\ when further decreasing $a$.
If a simulation is fully trapped in a topological sector, observables exhibit specific finite volume corrections proportional to powers of $1/V$ ($V$ denotes the spacetime volume) \cite{Brower:2003yx,Aoki:2007ka,Dromard:2014ela,Bietenholz:2016ymo} in addition to finite volume corrections not related to topological freezing, which are discussed in Section~\ref{sec:finitevolume}.
Since our lattice spacings are as small as $0.04 \, \text{fm}$, we consider it important and neccessary, to check and compare the Monte Carlo histories of the topological charge for all our simulations.
We use a field strength definition of the topological charge on the lattice (for a discussion and comparison of various definitions see Refs.\ \cite{Cichy:2014qta,Alexandrou:2017hqw}),
\begin{equation}
Q = a^4\sum_x q(x)
\end{equation}
with the clover-leaf discretization of the topological charge density
\begin{eqnarray}
& & q(x) = \frac{1}{32\pi^2} \sum_{\mu,\nu,\sigma,\rho=0}^{3}\epsilon_{\mu \nu \rho \sigma} \Tr \left(C^{\textrm{clov}}_{\mu \nu}(x) C^{\textrm{clov}}_{\rho \sigma} (x)\right) \\
%
& & C^{\textrm{clov}}_{\mu \nu}(x) = \frac{1}{4} \Im \Big(P_{\mu \nu}(x)+ P_{\nu -\mu}(x)+P_{-\mu -\nu}(x)+P_{-\nu \mu}(x)\Big).
\end{eqnarray}
To eliminate UV-fluctuations, which do not contribute to the topological charge, but might cause strong distortions of the corresponding lattice results, a smoothing procedure needs to be applied to the gauge links.
We use 4-dimensional APE-smearing, similar to the 3-dimensional APE-smearing for the static potential operators, with $\alpha_{\text{APE}}=0.3$.
The number of smearing steps is chosen individually for each lattice spacing.
We stop smearing, as soon as $Q$ is stable for several smearing steps for the majority of gauge link configurations.
We computed the topological charge on all gauge link configurations of the four ensembles $A$, $B$, $C$ and $D$ given in Table~\ref{tab:latticesetups4}.
In Figure~\ref{fig:topcharge} we show exemplarily the Monte Carlo histories of the topological charge for a subset of gauge link configurations for ensemble $B$ ($a = 0.06 \, \text{fm}$) and $D$ ($a = 0.04 \, \text{fm}$).
At $a = 0.06 \, \text{fm}$ the topological charge changes frequently and topological freezing is clearly not a problem.
At $a = 0.04 \, \text{fm}$ the autocorrelation time of $Q$ is much longer, consistent with the expectation from Ref.\ \cite{Schaefer:2010hu}.
However, there are still sufficiently many changes, such that our statistical error analysis, based on four independent simulation runs and a suitable binning (see Appendix~\ref{APP012}), should provide realistic uncertainties for the static potentials.
In Figure~\ref{fig:topchargehistogram} we show normalized and symmetrized histograms reflecting the topological charge distribution for ensembles $B$ and $D$.
Both are consistent with Gaussian distributions, as expected at finite, large spacetime volume.
From their squared widths, $\expval{Q^2}$, we obtain estimates of the related topological susceptibilities via $\chi_{\text{top}}= \expval{Q^2}/V$, which are in reasonable agreement with results from the literature \cite{Athenodorou:2021qvs}.
This is another indication that our computations of static potentials do not suffer from the problem of topological freezing.
\begin{figure}
\begin{center}
\begin{minipage}{0.7\linewidth}
\includegraphics[width=\linewidth]{plots/Plot_toplogy}
\subcaption{}
\label{fig:topcharge}
\end{minipage} \\
\begin{minipage}{0.7\linewidth}
\includegraphics[width=\linewidth,page=3]{plots/Plot_toplogy}
\subcaption{}
\label{fig:topchargehistogram}
\end{minipage}
\end{center}
\caption{(a)~Monte Carlo histories of the topological charge for ensemble $B$ ($a = 0.06 \, \text{fm}$) and $D$ ($a = 0.04 \, \text{fm}$) for two independent simulation runs. (b)~Normalized and symmetrized histograms reflecting the topological charge distribution for ensemble $B$ and ensemble $D$.}
\end{figure}
\subsection{Finite volume corrections}\label{sec:finitevolume}
All static potential results discussed in Section~\ref{sec:latticeresults} and Section~\ref{sec:parametrization} were obtained from simulations with periodic spatial volume $L^3 \approx (1.2 \, \text{fm})^3 $.
Since this is a rather small volume, it is important to check that finite volume corrections to these results are negligible.
One source of finite volume corrections are virtual glueballs traveling around the far side of the periodic spacetime volume.
They cause a negative shift of energy levels, which is proportional to $\exp(-m_{0^{++}}L)$ at asymptotically large $L$\cite{Luscher:1985dn} ($m_{0^{++}}$ denotes the mass of the lightest glueball).
We observe a small negative shift for the ordinary static potential for $L \ll 1.0 \, \text{fm}$, which could be related to such glueball interactions.
Another type of finite volume correction will appear, when the (infinite volume) wave function of a state has a larger extent than the finite spacetime volume of the lattice.
Then this wave function is necessarily squeezed, which will lead to a positive shift of the corresponding energy level \cite{Fukugita:1992jj}.
For the $\Pi_u$ and $\Sigma_u^-$ hybrid static potentials we found sizable positive shifts for $L \ll 1.0 \, \text{fm}$.
Since their wave functions cover a significantly larger region than the ordinary static potential \cite{Muller:2019joq}, these positive shifts are also consistent with expectation.
In Figure~\ref{fig:FVE_potentialdifference_SU2} we show the difference between the $\Pi_u$ hybrid static potential and the ordinary static potential, $V_{\Pi_u} - V_{\Sigma_g^+}$, at fixed quark-antiquark separation $r=0.25 \, \text{fm}$ as function of the spatial lattice extent $L$ for gauge group $\text{SU(2)}$.
This difference is consistent with a constant, i.e.\ $L$-independent, for $L \raisebox{-0.5ex}{$\,\stackrel{>}{\scriptstyle\sim}\,$} 1.0 \, \text{fm}$.
For smaller $L$, however, the difference increases, which is consistent with the previously discussed expectation of a squeezed wave function for the $\Pi_u$ hybrid static potential.
\begin{figure}\centering
\includegraphics[width=0.5\linewidth,page=2]{plots/Plot_FVE_summary}
\caption{$(V_{\Pi_u}(0.25\,\text{fm}) - V_{\Sigma_g^+}(0.25\,\text{fm}))$ as function of the spatial lattice extent $L$ for gauge group $\text{SU(2)}$. Data points were obtained at several lattice spacings, but discretization errors were estimated to be smaller than statistical errors.}
\label{fig:FVE_potentialdifference_SU2}
\end{figure}
Additionally, for gauge group $\text{SU(3)}$ we compared results for the $\Sigma_g^+$, the $\Pi_u$ and the $\Sigma_u^-$ static potential from ensemble $A$ to results from an analogous computation with twice the spatial lattice extent, i.e.\ $L = 2.4 \, \text{fm}$.
We did not find statistically significant differences.
In summary, the investigations and checks discussed in this subsection strongly indicate that finite volume corrections at our preferred spacetime volume $L^3 \times T \approx (1.2 \, \text{fm})^3 \times 2.4 \, \text{fm}$ are small compared to current statistical errors and, thus, can be neglected.
\subsection{Glueball decay}\label{sec:glueballdecay}
At sufficiently small $r$, the energy difference between a hybrid static potential and the ordinary static potential is large enough such that the $\Lambda_\eta^\epsilon$ hybrid flux tube can decay into a glueball and the $\Sigma_g^+$ groundstate.
The threshold energy for a decay into the lightest glueball with quantum numbers $J^{PC}=0^{++}$ and mass $m_{0^{++}}=1.73(5) \,\text{GeV}$ \cite{Morningstar:1999rf} is shown as dashed line in Figure~\ref{fig:threshold} together with lattice results for hybrid static potentials from Ref.\ \cite{Capitani:2018rox}.
The critical separations $r^{\Lambda_\eta^\epsilon}_{\text{crit}}$, where the dashed line intersects the $\Lambda_\eta^\epsilon$ hybrid static potentials, are listed in Table \ref{tab:rcrit}. For $r \leq r^{\Lambda_\eta^\epsilon}_{\text{crit}}$ decays to a $0^{++}$ glueball are energetically allowed.
\begin{figure}\centering
\includegraphics[width=\linewidth]{plots/Plot_glueballdecaythreshold}
\caption{Threshold energy for decays of hybrid flux tubes into the $\Sigma_g^+$ ground state and a $0^{++}$ glueball (dashed line) and hybrid static potentials for various quantum numbers $\Lambda_\eta^\epsilon$. Static potentials are taken from Ref.\ \cite{Capitani:2018rox}, the $0^{++}$ glueball mass from Ref.\ \cite{Morningstar:1999rf}.}
\label{fig:threshold}
\end{figure}
\begin{table}[hbt]\centering
\renewcommand{1.2}{1.5}
\begin{tabular}{c|cccccc|cc}\hline
$\Lambda_{\eta}^{\epsilon}$ & $\Pi_u$ & $\Pi_g$ & $\Delta_g$ & $\Delta_u$ & ${{\Sigma}_g^+}^{\prime}$ & $\Sigma_u^+$ & $\Sigma_u^-$ & $\Sigma_g^-$\\ \hline
$r^{\Lambda_\eta^\epsilon}_{\text{crit}}\, [\text{fm}]$ & $0.11$ & $0.23 $ & $0.28 $ & $0.58 $ &$0.19 $ &$0.46 $ &$0.11 $ & $0.3 $ \\\hline
\end{tabular}
\caption{Maximal separation $r_{\text{crit}}^{\Lambda_\eta^\epsilon}$, where a decay of a $\Lambda_\eta^\epsilon$ hybrid flux tube into the $\Sigma_g^+$ ground state and a $0^{++}$ glueball is energetically possible. For $\Sigma_u^-$ and $\Sigma_g^-$ such decays are excluded, because of quantum numbers.
}
\label{tab:rcrit}
\renewcommand{1.2}{1.0}
\end{table}
However, such decays might be excluded, because of quantum numbers.
A comprehensive and general derivation of selection rules for both hybrids and tetraquarks can be found in Ref.\ \cite{Braaten:2014ita}.
Here we focus on hybrid static potentials with quantum numbers $\Lambda^\epsilon_\eta$ and discuss, whether decays to the $\Sigma_g^+$ groundstate and a $J^{PC} = 0^{++}$ glueball are possible.
Since $J = 0$ for the considered glueball, also $J_z = 0$.
Thus, the $z$-component of the orbital angular momentum of the glueball must be $L_z = \Lambda$ (as stated in Section~\ref{sec:theory_hybridstaticpotentials}, the static quark and antiquark are separated along the $z$ axis).
The quantum number $\eta$ does not protect a hybrid flux tube, because the distribution of the glueball in $z$-direction can be symmetric or antisymmetric.
There is, however, a constraint due to the quantum number $\epsilon$.
The $0^{++}$ glueball is symmetric with respect to $\mathcal{P}_x$.
Its orbital angular momentum wave function is also symmetric with respect to $\mathcal{P}_x$ for $L_z = \Lambda = \Sigma = 0$.
For $L_z = \Lambda > 0$ there are two independent possibilities for the wave function, one of them symmetric, the other antisymmetric.
From this one can conclude that a $0^{++}$ glueball decay is not possible for $\Sigma_u^-$ and for $\Sigma_g^-$, while it is allowed for all other hybrid flux tubes.
Decays into heavier glueballs with quantum numbers $J^{PC}$ different from $0^{++}$ (some of them are antisymmetric with respect to $\mathcal{P}_x$) are energetically only allowed for separations much smaller than those listed in Table~\ref{tab:rcrit}.
Thus, they are not relevant in the context of our work.
In Section~\ref{sec:latticeresults} and Section~\ref{sec:parametrization} we presented and used lattice results for separations as small as $r \approx 0.08 \, \text{fm}$. Since $r_{\text{crit}}^{\Pi_u} = 0.11 \, \text{fm}$, results for the $\Pi_u$ hybrid static potential below that separation might be contaminated by a ``$\Sigma_g^+$ + glueball'' scattering state.
However, we observe the expected upward curvature for the $\Pi_u$ hybrid static potential (see Figure~\ref{fig:parametrizedlatticedata1}).
Moreover, the $\Pi_u$ und $\Sigma_u^-$ hybrid static potentials approach each other for small $r$, consistent with the expected degeneracy in the limit $r \rightarrow 0$.
Thus, we conclude that a possible contamination of our results for the $\Pi_u$ hybrid static potential is negligible compared to statistical errors.
\section{Computational details}
\subsection{Gauge link ensembles}\label{sec:latticesetups}
We computed hybrid static potentials both on $\text{SU(2)}$ and $\text{SU(3)}$ gauge link configurations generated with the standard Wilson plaquette action without dynamical quarks.
Results for purely gluonic observables such as energies in the presence of a static quark-antiquark pair, possibly in a sector with hybrid quantum numbers, are expected to be similar in pure gauge theory and in QCD (for hybrid static potentials this is supported by lattice results from Ref.\ \cite{Bali:2000vr}). To study hybrid static potentials, it might even be advantageous to use pure gauge theory, because in that case an excited flux tube can only decay into multiparticle states, which include rather heavy glueballs, but not light pions. In Section~\ref{sec:glueballdecay} glueball decays are discussed in detail.
In the main part of this work we focus exclusively on computations and results for gauge group $\text{SU(3)}$. Corresponding results for gauge group $\text{SU(2)}$ are summarized in Appendix~\ref{Appendix:SU2results}.
We generated four ensembles of gauge link configurations with gauge couplings \\ $\beta = 6.594 \, , \, 6.451 \, , \, 6.284 \, , \, 6.000$ using the CL2QCD software package\cite{Philipsen:2014mra}.
We relate the corresponding lattice spacing $a$ to the Sommer scale $r_0$ via a parametrization of $\ln(a/r_0)$ provided in Ref.\ \cite{Necco:2001xg}, which is based on a precision determination of $r_0$ up to $\beta=6.92$.
We introduce physical units by setting $r_0 = 0.5 \, \text{fm}$, which is a simple and common choice in pure gauge theory, but is slightly larger than QCD results \cite{Sommer:2014mea}.
The details of our gauge link ensembles, which we label by $A$, $B$, $C$ and $D$, are collected in Table~\ref{tab:latticesetups4}.
The lattice volume for all four ensembles is $L^3 \times T \approx (1.2 \, \text{fm})^3 \times 2.4 \,\text{fm}$. This is sufficiently large to neglect finite volume corrections (see Section~\ref{sec:finitevolume} for a detailed investigation and discussion).
Each ensemble was generated by $N_{\text{sim}}$ independent Monte Carlo simulations, where each simulation comprises $N_{\text{total}}$ updates. An update is composed of a heatbath sweep and $N_{\text{or}}$ overrelaxation sweeps. $N_{\text{or}}$ is chosen roughly as $N_{\text{or}} \approx 1.5 \, r_0 / a$ following Ref.\ \cite{Guagnelli:1998ud}.
This is expected to minimize correlations between subsequent gauge link configurations.
The first $N_{\text{therm}}$ updates are considered as thermalization updates and the corresponding gauge link configurations were, thus, discarded. After thermalization, gauge link configurations separated by $N_{\text{sep}}$ updates were used to measure correlation functions. The total number of gauge link configurations used for measurements is thus $N_{\text{meas}} = N_{\text{sim}} (N_{\text{total}} - N_{\text{therm}}) / N_{\text{sep}}$.
To eliminate autocorrelations, we combined these $N_{\text{meas}}$ gauge link configurations into a much smaller number of bins. Statistical errors were determined using both the jackknife and the bootstrap method. Further details concerning data analysis are discussed in Appendix~\ref{APP012}.
\begin{table}[htb]
\begin{center}
\def1.2{1.2}
\begin{tabular}{cccccccccc}
\hline
ensemble & $\beta$ & $a$ in $\text{fm}$ \cite{Necco:2001xg} & $(L/a)^3 \times T/a$ & $N_{\text{sim}}$ & $N_{\text{total}}$ & $N_{\text{or}}$ & $N_{\text{therm}}$ & $N_{\text{sep}}$ & $N_{\text{meas}}$ \\
\hline
$A$ & $6.000$ & $0.093$ & $12^3\times 26$ & $2$ &
$60 000$ & $\phantom{0}4$ & $20 000$ & $\phantom{0}50$ & $1600$ \\
$B$ & $6.284$ & $0.060$ & $20^3\times 40$ & $2$ &
$60 000$ & $12$ & $20 000$ & $100$ & $\phantom{0}800$ \\
$C$ & $6.451$ & $0.048$ & $26^3\times 50$ & $4$ &
$80 000$ & $15$ & $40 000$ & $200$ & $\phantom{0}800$ \\
$D$ & $6.594$ & $0.040$ & $30^3\times 60$ & $4$ &
$80 000$ & $15$ & $40 000$ & $200$ & $\phantom{0}800$ \\
\hline
\end{tabular}
\end{center}
\caption{Gauge link ensembles.}
\label{tab:latticesetups4}
\end{table}
\subsection{Multilevel algorithm}\label{sec:multilevelalgorithm}
For the efficient computation of Wilson loop-like correlation functions (\ref{eq:CorrelationfunctionW}) we employ the multilevel algorithm \cite{Luscher:2001up}.
The starting point for a multilevel simulation is one of the sets of $N_{\text{meas}}$ thermalized gauge link configurations discussed in Section~\ref{sec:latticesetups}.
The lattice is partitioned into $n_{\text{ts}}$ time-slices with thicknesses $p_1,p_2, \dots, p_{n_{\text{ts}}}$.
In principle, time-slices can be partitioned more than once, but we use only a single level of partitioning.
For each time-slice $n_m$ sublattice configurations are generated using a standard heatbath algorithm. These sublattice configurations are separated by $n_u$ heatbath sweeps, where links in the interior of the time-slice are updated, while spatial links on the boundaries are fixed.
Two-link operators are defined via $\mathds{T}(x,r \hat{j})_{\alpha \beta \gamma \delta} = U_0^*(x)_{\alpha\beta} U_0(x+r \hat{j})_{\gamma\delta}$ ($\hat{j}$ denotes the spatial unit vector in $j$-direction, e.g.\ $\hat{1} = (0,1,0,0)$). They are multiplied according to
\begin{equation}
\mathds{P}_k = \{\mathds{T}(x+(d_k-p_k) a \hat{0},r \hat{j}) \mathds{T}(x+(d_k-p_k+1) a \hat{0},r \hat{j}) \dots \mathds{T}(x+(d_k-1) a \hat{0},r \hat{j})\}
\end{equation}
with the multiplication prescription $\{\mathds{T}_1 \mathds{T}_2\}_{\alpha \beta \gamma \delta} = \{\mathds{T}_1\}_{\alpha \sigma \gamma \rho} \{\mathds{T}_2\}_{\sigma \beta \rho \delta}$, i.e.\ such that the product $\mathds{P}_k$ connects the two boundaries of the time-slice $k$, i.e.\ extends from $t/a = d_{k-1}$ to $t/a = d_k$ with $d_k = \sum_{j=1}^k p_j$. The products $\mathds{P}_k$ are then averaged over the $n_m$ corresponding sublattice configurations with the results denoted as $[\mathds{P}_k]$.
Wilson loops are computed via
\begin{equation}
\label{EQN854} W_{S;\Lambda_\eta^\epsilon}(r,t) = a_{S;\Lambda_\eta^\epsilon}(\mathbf{x},\mathbf{x}+r \hat{j};x_0)_{\alpha \gamma} \{[\mathds{P}_{k}] [\mathds{P}_{k+1}] \dots [\mathds{P}_{k+n_t-1}]\}_{\alpha \beta \gamma \delta} \Big(a_{S;\Lambda_\eta^\epsilon}(\mathbf{x},\mathbf{x}+r \hat{j};x_0+t)\Big)^\ast_{\beta \delta} ,
\end{equation}
where the spatial parallel transporters $a_{S;\Lambda_\eta^\epsilon}$ (see Eq.\ (\ref{eq:a})) are both located on boundaries between time-slices.
$n_t$ denotes the number of time-slices traversed by the Wilson loop, i.e.\ $d_{k-1} = x_0$ and $\sum_{j=1}^{n_t} p_{k+j} = t/a$. Finally, the samples $W_{S;\Lambda_\eta^\epsilon}(r,t)$ from Eq.\ (\ref{EQN854}) are averaged over space-time, the three spatial directions and the $N_{\text{meas}}$ thermalized gauge link configurations.
Note that the time-slice partitioning might impose constraints on the temporal extent of Wilson loops, which can be computed.
For simplicity we choose a regular pattern, where all time-slices have thickness $2$, i.e.\ $p_1 = p_2 = \dots = p_{n_{\text{ts}}} = 2$.
This choice is not only simple but also efficient, because it allows to exploit translational invariance in temporal direction extensively.
Moreover, we use $n_m = 400$ and $n_u = 30$.
For a technically more detailed discussion of the multilevel algorithm see Section~3.2 of Ref.\ \cite{Brambilla:2021wqs}.
\subsection{Tree-level improvement for static potentials}\label{sec:treelevelimprovement}
To reduce lattice discretization errors for the ordinary and for hybrid static potentials, we apply a tree-level improvement similar as in Ref.\ \cite{Hasenfratz:2001tw}.
In the continuum in leading-order perturbation theory static potentials are proportional to $1/r$ due to one-gluon-exchange.
The ordinary static potential is attractive, while the $\Pi_u$ and $\Sigma_u^-$ hybrid static potentials exhibit a repulsive $1/r$ behavior, which is suppressed by the factor $1/8$.
On an infinite spacetime lattice the leading order perturbative result can be computed in a straightforward way as discussed in Appendix~\ref{Appendix:treelevelimprovement}. The difference to its $1/r$ continuum counterpart represents lattice discretization errors at tree-level.
These discretization errors can be subtracted from the non-perturbative lattice data points obtained from Wilson loop-like correlation functions (\ref{eq:CorrelationfunctionW}).
For this one needs to estimate the prefactor of the $1/r$ perturbative part, which is proportional to the strong coupling (see e.g.\ Ref.\ \cite{Jansen:2011vv} and references therein).
We do this in Section~\ref{sec:parametrization} with a suitable fit to the $\Sigma_g^+$ static potential.
We note that there is a related but slightly different method for tree-level improvement also common in the literature (see e.g.\ Refs.\ \cite{Necco:2001xg,Jansen:2011vv}). Instead of changing the lattice result for the value of the static potential at a given quark-antiquark separation, this separation is replaced by a so-called improved separation.
According to our numerical tests this method works well for the static force.
However, for static potentials it seems to be inferior to the method discussed in the previous paragraph, because of their linear behavior for large separations.
We plan to discuss this in detail in another publication.
\section{Lattice field theory results for the $\Pi_u$ and $\Sigma_u^-$ hybrid static potentials}\label{sec:latticeresults}
In the following we discuss our lattice field theory results $V^e_{\Lambda_\eta^\epsilon}(r)$ for static potentials with quantum numbers $\Lambda_\eta^\epsilon = \Sigma_g^+$ (the ordinary static potential) and $\Lambda_\eta^\epsilon = \Pi_u , \Sigma_u^-$ (the two lowest hybrid static potentials) for all four lattice ensembles $e \in \{A, B, C, D\}$ listed in Table~\ref{tab:latticesetups4}.
They correspond to the ground state energies in the sectors with quantum numbers $\Lambda_\eta^\epsilon$ and quark-antiquark separation $r$.
To extract these static potentials, we compute temporal correlation functions $W^e_{\Lambda_\eta^\epsilon}(r,t)$ (see Eq.~\eqref{eq:CorrelationfunctionW}) of suitably designed creation operators as discussed in Section~\ref{sec:theory_hybridstaticpotentials}.
We restrict the computations to temporal separations $t$, which are multiples of $2a$.
This allows the use of a single multilevel time-slice partitioning, which is simple as well as efficient (for details see Section~\ref{sec:multilevelalgorithm}).
Effective potentials are defined in terms of the correlation functions $W^e_{\Lambda_\eta^\epsilon}(r,t)$ via
\begin{equation}
V^e_{\text{eff};\Lambda_{\eta}^{\epsilon}}(r,t) = \frac{1}{2 a} \ln(\frac{W^e_{\Lambda_{\eta}^{\epsilon}}(r,t)}{W^e_{\Lambda_{\eta}^{\epsilon}}(r,t+2a)}) .
\end{equation}
These effective potentials approach plateaus at large $t$, which correspond to the ground state energies, i.e.\
\begin{equation}
\label{EQN833}
V^e_{\Lambda_\eta^\epsilon}(r) = \lim_{t \rightarrow \infty} V^e_{\text{eff};\Lambda_{\eta}^{\epsilon}}(r,t) .
\end{equation}
Numerically the plateau values and, thus, the static potentials are extracted by uncorrelated $\chi^2$ minimizing fits of constants to $a V^e_{\text{eff};\Lambda_\eta^\epsilon}(r,t)$ in the range $t^\prime_\text{min} \le t \le t^\prime_\text{max}$.
The fit range is chosen individually for each set of quantum numbers $\Lambda_\eta^\epsilon$ and each quark-antiquark separation $r$ by an algorithm used already in our preceding work \cite{Capitani:2018rox}:
\begin{itemize}
\item $t_{\text{min}}$ is defined as the minimal $t$, where the values of $a V^e_{\text{eff};\Lambda_\eta^\epsilon}(r,t-2a)$ and $a V^e_{\text{eff};\Lambda_\eta^\epsilon}(r,t)$ differ by less than $1 \, \sigma$.
\item $t_{\text{max}}$ is the maximal $t$, where $W^e_{\Lambda_\eta^\epsilon}(r,t+2a)$ has been computed, and where its statistical error is reasonably small.
\item Fits to $a V^e_{\text{eff};\Lambda_\eta^\epsilon}(r,t)$ are performed for all ranges $t^\prime_\text{min} \le t \le t^\prime_\text{max}$ with $t_\text{min} \le t^\prime_\text{min}$, $t^\prime_\text{max} \le t_\text{max}$ and $t^\prime_\text{max} - t^\prime_\text{min} \ge 6 \, a$.
\item The result of the fit with the longest plateau and $\chi_\text{red}^2 \le 1$ is taken as result for $V^e_{\Lambda_\eta^\epsilon}(r)$.
\end{itemize}
To illustrate the quality of our lattice data, we show exemplary effective potential plots in Figure~\ref{fig:effpotentials0}.
The final fit ranges $t^\prime_\text{min} \le t \le t^\prime_\text{max}$ and fit results are indicated by the horizontal lines.
\begin{figure}[htb]
\begin{minipage}{0.5\linewidth}
\includegraphics[width=\linewidth,page=1]{plots/Plot_Veff}
\end{minipage}
\begin{minipage}{0.5\linewidth}
\includegraphics[width=\linewidth,page=2]{plots/Plot_Veff}
\end{minipage}
\caption{Exemplary plots of effective potentials $a V^e_{\text{eff};\Lambda_{\eta}^{\epsilon}}(r,t)$ with $\Lambda_\eta^\epsilon = \Sigma_g^+,\Pi_u , \Sigma_u^-$ for $r= 4a$ (Left: ensemble $B$, i.e.\ $a=0.060 \, \text{fm}$; Right: ensemble $D$, i.e.\ $a=0.040 \, \text{fm}$).}
\label{fig:effpotentials0}
\end{figure}
The resulting static potentials
$V^e_{\Lambda_\eta^\epsilon}(r)$ for $\Lambda_\eta^\epsilon = \Sigma_g^+,\Pi_u , \Sigma_u^-$ and
separations $r \geq 2 a$ are collected in units of the lattice spacing in Appendix~\ref{Appendix:summarylatticedata}, Table~\ref{tab:latticedata_ABCD_all}.
Due to the regulator-dependent self-energy of static quarks, potentials computed at different lattice spacings $a$, i.e.\ on different ensembles $e$, are shifted relative to each other.
We will subtract these self-energies in Section~\ref{sec:parametrization}, where we also remove discretization errors at tree-level and partly proportional to $a^2$, before we show the results for all ensembles together in a common plot in Figure~\ref{fig:parametrizedlatticedata1} and list them in physical units in Table~\ref{tab:latticedata_ABCD_tilde_all}.
Note that in contrast to previous lattice field theory computations of hybrid static potentials \cite{Perantonis1989StaticPF,Michael:1990az,Perantonis:1990dy,Juge:1997nc,Juge:1997ir,Capitani:2018rox,Juge:2002br,Bali:2003jq,Juge:2003ge}, where lattice spacings $a \raisebox{-0.5ex}{$\,\stackrel{>}{\scriptstyle\sim}\,$} 0.07 \, \text{fm}$ were used \footnote{In Ref.\ \cite{Michael:1990az} hybrid static potentials were computed for gauge group SU(2) at very small lattice spacing $a \approx 0.022 \, \text{fm}$ (when setting the scale as in Ref.\ \cite{Hirakida:2018uoy}), but at the same time also at very small spatial volume, such that finite volume effects appear to be huge (see e.g.\ Figure~1 in Ref.\ \cite{Michael:1990az} and our our detailed discussion of finite volume effects in Section~\ref{sec:finitevolume}).}, our results are based on four ensembles with lattice spacings as small as $0.04 \, \text{fm}$.
Since lattice discretization errors in static potentials typically become large for $r \raisebox{-0.5ex}{$\,\stackrel{<}{\scriptstyle\sim}\,$} 2 \, a$, the lattice potentials presented in this work are trustworthy down to $r \approx 0.08 \, \text{fm}$, whereas existing works were limited to separations roughly twice as large.
A major goal of this work is to explore the small-$r$ region of the $\Pi_u$ and $\Sigma_u^-$ hybrid static potentials to make contact to perturbative calculations.
Using the framework of potential Non Relativistic QCD (pNRQCD) these hybrid static potentials have been predicted to be repulsive at very small $r$ \cite{Brambilla:1999xf,Bali:2003jq,Berwein:2015vca,Oncala:2017hop,Soto:2017one}, a behavior, which could not convincingly be confirmed by existing lattice computations, because of the use of rather coarse lattice spacings.
In contrast to that, our results from the ensembles with the fine lattice spacings $a \approx 0.048 \, \text{fm}$ and $a \approx 0.040 \, \text{fm}$ clearly show the predicted and expected upward curvature at small $r$ (see Table~\ref{tab:latticedata_ABCD_all}, Table~\ref{tab:latticedata_ABCD_tilde_all} and Figure~\ref{fig:parametrizedlatticedata1}).
This will be discussed in detail in Section~\ref{sec:parametrization}, where we parametrize our lattice data points by analytic functions based on pNRQCD predictions.
\section{Parametrization of lattice results for hybrid static potentials} \label{sec:parametrization}
In this section we parametrize the lattice data points for the ordinary static potential $V_{\Sigma_g^+}(r)$ and the two lowest hybrid static potentials $V_{\Pi_u}(r)$ and $V_{\Sigma_u^-}(r)$ computed in Section~\ref{sec:latticeresults} and collected in Table~\ref{tab:latticedata_ABCD_all}.
The resulting parametrizations allow to eliminate discretization errors to a large extent and can e.g.\ be used as input for Born-Oppenheimer predictions of heavy hybrid meson masses as previously done in Refs.\ \cite{Capitani:2018rox,Berwein:2015vca,Perantonis:1990dy,Juge:1997nc,Juge:1999ie,Braaten:2014qka,Oncala:2017hop,Guo:2008yz,Brambilla:2018pyn,Brambilla:2019jfi}.
In addition to the lattice data points specifically computed in the context of this work and discussed in Section~\ref{sec:latticeresults}, we use results from our previous computation \cite{Capitani:2018rox} for quark-antiquark separations $0.19 \, \text{fm} \raisebox{-0.5ex}{$\,\stackrel{<}{\scriptstyle\sim}\,$} r \raisebox{-0.5ex}{$\,\stackrel{<}{\scriptstyle\sim}\,$} 1.12 \, \text{fm}$ to constrain our parametrizations also at large separations.
This computation was performed at lattice spacing $a \approx 0.093\,\text{fm}$, which is identical to the largest lattice spacing used in this work,
i.e.\ to that of ensemble $A$.
However, in contrast to the computations discussed in Section~\ref{sec:latticeresults}, HYP2 smeared temporal links were used, which imply a significantly reduced self-energy and consequently smaller statistical errors, but possibly also larger discretization errors at small separations $r$.
For completeness, these previous lattice results $V^{A^\text{HYP2}}_{\Lambda_\eta^\epsilon}(r)$ are also listed in Table~\ref{tab:latticedata_ABCD_all}.
When combining the lattice results for the static potentials from the five ensembles \\ $e \in \{ A, B, C, D, A^\text{HYP2} \}$ ($A^\text{HYP2}$ denotes the ensemble generated in the context of Ref.\ \cite{Capitani:2018rox}), one needs to take into account that the self-energy is different for each ensemble.
It depends both on the lattice spacing $a$ and whether HYP2 smeared temporal links are used or not.
To eliminate both the self-energy and lattice discretization errors at tree-level, we first perform an 8-parameter uncorrelated $\chi^2$-minimizing fit of
\begin{equation}\label{eq:Cornellpotential_fitfunction}
V_{\Sigma_g^+}^{\text{fit},e}(r) = V_{\Sigma_g^+}(r) + C^e + \Delta V^{\text{lat},e}_{\Sigma_g^+}(r)
\end{equation}
with the Cornell ansatz
\begin{equation}\label{eq:Cornellpotential}
V_{\Sigma_g^+}(r) = -\frac{\alpha}{r} + \sigma r
\end{equation}
and
\begin{equation}\label{eq:latticeartifacts}
\Delta V^{\text{lat},e}_{\Sigma_g^+}(r) = \alpha' \bigg(\frac{1}{r} - \frac{G^e(r/a)}{a}\bigg)
\end{equation}
to all lattice data points $V_{\Sigma_g^+}^e(r)$ with $0.2 \, \text{fm} < r$. The fit parameters are the $1/r$ coefficient $\alpha$, the string tension $\sigma$, the coefficient $\alpha'$ and for each ensemble an additive constant $C^e$.
The constants $C^e$ absorb the ensemble dependent self energies. $\Delta V^{\text{lat},e}_{\Sigma_g^+}(r)$ reflects lattice discretization errors at tree level, where the continuum result for the ordinary static potential at tree level is proportional to $1/r$ and its lattice counterpart $G^e(r/a)/a$ can be calculated numerically (see Refs.\ \cite{Luscher:1995zz,Necco:2001xg,Hasenfratz:2001tw} and Appendix~\ref{Appendix:treelevelimprovement}).
The physically meaningful part of the parametrization (\ref{eq:Cornellpotential_fitfunction}) is $V_{\Sigma_g^+}(r)$ with the two parameters $\alpha$ and $\sigma$.
It is known that this Cornell ansatz provides an accurate description of the ordinary static potential for $0.2 \, \text{fm} \raisebox{-0.5ex}{$\,\stackrel{<}{\scriptstyle\sim}\,$} r$ (see e.g.\ Ref.\ \cite{Karbstein:2018mzo}).
The resulting fit parameters are collected in Table~\ref{tab:fitparameter}. In particular, we obtain \\ $\alpha = 0.289(2) = 0.0571(4) \, \text{GeV} \, \text{fm}$ and $\sigma = 1.064(4) \, \text{GeV}/\text{fm}$ in reasonable agreement with results from the literature \cite{Koma:2007jq}.
These fit parameters allow to define data points
\begin{equation}\label{eq:def_V_Sigmagplus_tilde}
\tilde{V}_{\Sigma_g^+}^e(r) = V_{\Sigma_g^+}^e(r) - C^e - \Delta V^{\text{lat},e}_{\Sigma_g^+}(r) ,
\end{equation}
where the self-energies and the lattice discretization errors at tree-level are subtracted. These data points are collected in Table~\ref{tab:latticedata_ABCD_tilde_all} and plotted in Figure~\ref{fig:parametrizedlatticedata1}. They are consistently parametrized by $V_{\Sigma_g^+}(r)$ for $0.2 \, \text{fm} \leq r$ as demonstrated in the same figure.
\begin{figure}[p]\centering
\includegraphics[width=\linewidth]{plots/Plot_latticeresults_impr_combined}
\caption{Lattice data points $\tilde{V}_{\Lambda_\eta^\epsilon}^e(r)$ in $\text{GeV}$ and corresponding parametrizations \eqref{eq:Cornellpotential}, \eqref{eq:parametrizationHybrid},\eqref{eq:extendedparametrizationHybrid_Piu} and \eqref{eq:extendedparametrizationHybrid_Sigmau} as functions of the quark-antiquark separation $r$ in $\text{fm}$.
The colors green, blue, yellow and red indicate different lattice spacings $a = 0.093 \, \text{fm}$, $a = 0.060 \, \text{fm}$, $a = 0.048 \, \text{fm}$ and $a = 0.040 \, \text{fm}$.}
\label{fig:parametrizedlatticedata1}
\end{figure}
\begin{table}\centering
\input{sections/tables/table_alpha_sigma}\vspace{0.3cm}
\input{sections/tables/table_As_Bs}\vspace{0.3cm}
\input{sections/tables/table_Ce_A2prime_all}
\caption{Resulting fit parameters.
Fit~1 and Fit~2 correspond to the parametrizations \eqref{eq:extendedparametrizationHybrid_Piu} and \eqref{eq:extendedparametrizationHybrid_Sigmau} and fit ranges $2a \leq r$ and $3a \leq r$, respectively.
Fit~3 corresponds to the parametrization \eqref{eq:parametrizationHybrid} and fit range $2a \leq r \leq 0.3 \, \text{fm}$, where $A_{3,\Pi_u}=A_3$ and $A_{3,\Sigma_u^-}=A_3 + B_1$.
}
\label{tab:fitparameter}
\end{table}
Our parametrization of the $\Pi_u$ and $\Sigma_u^-$ hybrid static potentials is based on the pNRQCD prediction for small separations $r \ll 1/\Lambda_{\text{QCD}}$,
\begin{equation}
V^{\text{pNRQCD}}_{\text{hybrid}} (r) = V_o (r) + \Lambda_H + \order{r^2}.
\end{equation}
(see Refs.\ \cite{Brambilla:1999xf,Berwein:2015vca}).
pNRQCD hybrid static energies are given through the perturbative octet potential $V_o(r)$ and a non-perturbative constant $\Lambda_H$ at leading order in a multipole expansion.
The next term in such a multipole expansion is proportional to $r^2$.
At leading order in perturbation theory, $V_o(r) \propto 1/r$.
Simple fit functions consistent with this pNRQCD prediction are
\begin{equation}
\label{eq:parametrizationHybrid}
V_{\Lambda_\eta^\epsilon}(r) = \frac{A_1}{r}+ A_2 + A_{3,\Lambda_\eta^\epsilon} r^2 ,
\end{equation}
where the parameters $A_1$ and $A_2$ are the same both for the $\Pi_u$ and the $\Sigma_u^-$ hybrid static potential, while the coefficients in front of the $r^2$ terms, $A_{3,\Pi_u}$ and $A_{3,\Sigma_u^-}$, are independent.
As in our preceding work \cite{Capitani:2018rox}, we found that Eq.\ \eqref{eq:parametrizationHybrid} is suited to parametrize the $\Pi_u$ potential in the $r$ range, where lattice data points are available, but not suited to parametrize the $\Sigma_u^-$ potential.
Because of that we use extended fit functions already proposed in Ref.\ \cite{Capitani:2018rox},
\begin{align}
\label{eq:extendedparametrizationHybrid_Piu}
V_{\Pi_u}(r) &= \frac{A_1}{r} + A_2 + A_3 r^2 \\
\label{eq:extendedparametrizationHybrid_Sigmau}
V_{\Sigma_u^-}(r) &= \frac{A_1}{r} + A_2 + A_3 r^2 + \frac{B_1 r^2}{1 + B_2 r + B_3 r^2} ,
\end{align}
which reduce to Eq.\ \eqref{eq:parametrizationHybrid} in the limit of small separations.
Note that, in principle, all fit parameters depend on the lattice spacing $a$.
In practice, however, only $A_2$ seems to have a sizable $a$ dependence, as indicated by a small ensemble dependent additive offset particularly prominent at large $a$.
We, thus, include the leading order lattice discretization error for $A_2$, which is proportional to $a^2$.
It can be different for the $\Pi_u$ and the $\Sigma_u^-$ hybrid static potential and when using HYP2 smeared temporal links or not, i.e.\ is represented by terms $A'^e_{2,\Lambda_\eta^\epsilon} a^2$ with $A'^A_{2,\Pi_u} = A'^B_{2,\Pi_u} = A'^C_{2,\Pi_u} = A'^D_{2,\Pi_u}$ and $A'^A_{2,\Sigma_u^-} = A'^B_{2,\Sigma_u^-} = A'^C_{2,\Sigma_u^-} = A'^D_{2,\Sigma_u^-}$.
As previously for the ordinary static potential, we also include in the fit functions the constants $C^e$ containing the self-energies. Moreover, we include a term reflecting discretization errors at tree level,
\begin{equation}\label{eq:latticeartifacts_hybrid}
\Delta V^{\text{lat},e}_\text{hybrid}(r) = -\frac{1}{8}\Delta V^{\text{lat},e}_{\Sigma_g^+}(r) = -\frac{\alpha'}{8} \bigg(\frac{1}{r} - \frac{G^e(r/a)}{a}\bigg) ,
\end{equation}
where the prefactor $-1 / 8$ relative to Eq.\ (\ref{eq:latticeartifacts}) is motivated by leading order perturbation theory.
In summary, this amounts to a $10$-parameter uncorrelated $\chi^2$ minimizing fit of
\begin{align}
\label{eq:extendedparametrizationHybrid_Piu_A2a}
V^{\text{fit},e}_{\Pi_u}(r) &= V_{\Pi_u}(r) + C^e +\Delta V^{\text{lat},e}_\text{hybrid} (r) + A'^e_{2,\Pi_u} a^2\\
\label{eq:extendedparametrizationHybrid_Sigmau_A2a}
V^{\text{fit},e}_{\Sigma_u^-}(r) &= V_{\Sigma_u^-}(r) + C^e+\Delta V^{\text{lat},e}_\text{hybrid} (r) + A'^e_{2,\Sigma_u^-} a^2
\end{align}
to the lattice data points $V^e_{\Pi_u}(r)$ and $V^e_{\Sigma_u^-}(r)$ of all five ensembles.
In Table~\ref{tab:fitparameter} we compare results obtained with two fit ranges, $2a \leq r$ (Fit~1) and $3a \leq r$ (Fit~2).
In analogy to Eq.~\eqref{eq:def_V_Sigmagplus_tilde} we define data points
\begin{align}\label{eq:def_V_hybrid_tilde}
\tilde{V}^e_{\Lambda_\eta^\epsilon}(r) = V^e_{\Lambda_\eta^\epsilon}(r) - C^e - \Delta V^{\text{lat},e}_\text{hybrid} (r) - A'^e_{2,\Lambda_\eta^\epsilon} a^2 ,
\end{align}
where the self-energy as well as lattice discretization errors at tree-level and proportional to $a^2$ in the difference to the ordinary static potential are removed. These data points are collected in Table~\ref{tab:latticedata_ABCD_tilde_all} and plotted in Figure~\ref{fig:parametrizedlatticedata1} together with the parametrizations \eqref{eq:extendedparametrizationHybrid_Piu} and \eqref{eq:extendedparametrizationHybrid_Sigmau}.
For larger separations, $r \raisebox{-0.5ex}{$\,\stackrel{>}{\scriptstyle\sim}\,$} 0.2 \, \text{fm}$, the parametrizations corresponding to $2a \leq r$ and to $3a \leq r$ are quite similar.
For separations $r \raisebox{-0.5ex}{$\,\stackrel{<}{\scriptstyle\sim}\,$} 0.15 \, \text{fm}$, however, there are clear deviations, which signal the importance of computing data points at small $r$.
This is also reflected by the difference in the results for the coefficient $A_1$ of the repulsive $1/r$ term, $A_1 = 0.0124(9)\,\text{GeV} \, \text{fm}$ versus \\ $A_1 = 0.0147(18)\,\text{GeV} \, \text{fm}$ for $2a \leq r$ and $3a \leq r$, respectively.
Since the corresponding reduced $\chi^2$ (listed in Table~\ref{tab:fitparameter}) indicate that both fits are of reasonable quality, we consider the parametrization obtained by taking into account a larger number of data points (i.e.\ Fit~1 with with $2a \leq r$) to be superior and recommend to use this parametrization in future applications, e.g.\ Born-Oppenheimer predictions of heavy hybrid meson masses.
To study hybrid static potentials at small separations in even more detail, we performed an additional fit, where we fixed $B_2 = B_3 = 0$.
The fit ansatz is then equivalent to Eq.\ (\ref{eq:parametrizationHybrid}), when identifying $A_{3,\Pi_u}$ in Eq.\ \eqref{eq:parametrizationHybrid} with $A_3$ in Eq.\ \eqref{eq:extendedparametrizationHybrid_Piu} and $A_{3,\Sigma_u^-}$ in Eq.\ \eqref{eq:parametrizationHybrid} with $A_3 + B_1$ in Eq.\ \eqref{eq:extendedparametrizationHybrid_Sigmau}.
Since the fit ansatz is then restricted to the perturbative prediction valid for small $r$, we use a reduced fit range, $2a \leq r \leq 0.3 \, \text{fm}$.
The fit is of reasonable quality and as before the fit results are collected in Table~\ref{tab:fitparameter} and the corresponding parametrization is shown in Figure~\ref{fig:parametrizedlatticedata1}.
The coefficient of the repulsive $1/r$ term is now significantly smaller, $A_1 = 0.0065(16) \,\text{GeV} \, \text{fm}$.
In summary, our lattice data points, both for the $\Pi_u$ and the $\Sigma_u^-$ hybrid static potential clearly show a repulsive behavior at small separations, as predicted perturbatively in pNRQCD.
We performed various fits with fit functions guided by these perturbative expansions, which are proportional to $1/r$ at small separations.
We find the coefficient $A_1$ of the $1/r$ term in the region $0.005 \, \text{GeV} \, \text{fm} \ldots 0.017 \, \text{GeV} \, \text{fm}$.
A more precise determination of a parametrization of the repulsive region of hybrid static potentials will require further data points at even smaller separations and possibly refined fit functions with additional terms contributing to the small-$r$ behavior.
Finally we compare to existing work, where the $1/r$ repulsion of the $\Pi_u$ and the $\Sigma_u^-$ hybrid static potentials was also quantified.
In Ref.\ \cite{Vairo:2009tn} the lattice data from Ref.\ \cite{Juge:2002br} for the $\Pi_u$ hybrid static potential was parametrized with a fit function similar to Eq.\ \eqref{eq:parametrizationHybrid} with $A_1=0.022 \, \text{GeV} \, \text{fm}$, which is larger than our results for $A_1$ from simultaneous fits to the $\Pi_u$ and $\Sigma_u^-$ potentials.
Ref.\ \cite{Oncala:2017hop} follows the prediction from perturbation theory at leading order in $\alpha_s$ and fixes the $1/r$-coefficient to $\alpha/8$, where $\alpha$ is obtained from a fit similar to Eq.~\eqref{eq:Cornellpotential} to lattice data from Ref.\ \cite{Juge:2002br} in the range $0.2\,\text{fm} \le r \le 2.4\,\text{fm}$.
The resulting $1/r$-coefficient for the hybrid potentials is $0.012 \, \text{GeV} \, \text{fm}$, which agrees with our fit results for the parameter $A_1$ for Fit~1 and Fit~2.
In Ref.\ \cite{Berwein:2015vca} hybrid static potential lattice data from Refs.\ \cite{Bali:2003jq,Juge:2002br} is parametrized consistently at small separations $0.08 \,\text{fm} \le r < 0.25\,\text{fm}$ by functions similar to Eq.~\eqref{eq:parametrizationHybrid}. There, the $1/r$-coefficient is not a fit parameter, but fixed to $\approx 0.01 \, \text{GeV} \, \text{fm}$ by the perturbative octet potential calculated in the Renormalon Subtracted scheme up to order $\alpha^3_s$. This value for the $1/r$-coefficient is in the ballpark of our fit results for $A_1$.
\subsection{Prediction of masses of heavy hybrid mesons}
In the following we estimate masses of $\bar c c$ and $\bar b b$ hybrid mesons following the same Born-Oppenheimer approach as in our previous work \cite{Capitani:2018rox}, this time, however, using the refined and more accurate parametrizations (\ref{eq:Cornellpotential}), (\ref{eq:extendedparametrizationHybrid_Piu}) and (\ref{eq:extendedparametrizationHybrid_Sigmau}) with parameters corresponding to Fit~1 (see Table~\ref{tab:fitparameter}). Our goal is to quantify the impact of our new lattice data (results for ensembles $A$, $B$, $C$ and $D$), which cover smaller separations as well as several smaller lattice spacings than our previous data from ensemble $A^\text{HYP2}$.
We solve the radial Schr\"odinger equation
\begin{eqnarray}\label{radialSchroedingerequation}
\bigg(-\frac{1}{2 \mu} \frac{d^2}{dr^2} + \frac{L (L+1) - 2 \Lambda^2 + J_{\Lambda_{\eta}^{\epsilon}} (J_{\Lambda_{\eta}^{\epsilon}}+1)}{2 \mu r^2} + V_{\Lambda_{\eta}^{\epsilon}}(r)\bigg) u_{\Lambda_{\eta}^{\epsilon};L,n}(r) \ \ = \ \ E_{\Lambda_{\eta}^{\epsilon};L,n} u_{\Lambda_{\eta}^{\epsilon};L,n}(r) ,
\end{eqnarray}
where $\mu = m_{\bar{Q}} m_Q / (m_{\bar{Q}} + m_Q)$ is the reduced mass of the heavy $\bar{Q} Q$ pair, $L$ is the orbital angular momentum and $V_{\Lambda_{\eta}^{\epsilon}}(r)$ is one of our parametrizations \eqref{eq:Cornellpotential}, \eqref{eq:extendedparametrizationHybrid_Piu} or \eqref{eq:extendedparametrizationHybrid_Sigmau} with parameters listed as Fit~1 in Table~\ref{tab:fitparameter}.
We use $ m_c = 1628 \, \textrm{MeV}$ and $ m_b = 4977 \, \textrm{MeV}$ from quark models \cite{PhysRevD.32.189}.
$J_{\Sigma_g^+} = 0$ and $J_{\Lambda_{\eta}^{\epsilon}} = 1$ for $\Lambda_{\eta}^{\epsilon} = \Pi_u , \Sigma_u^-$ following Ref.\ \cite{Braaten:2014qka}.
For further details on the numerical solution of the radial Schrödinger equation and the interpretation of the resulting energies in terms of hybrid meson multiplets we refer to Ref.\ \cite{Capitani:2018rox}.
In Table~\ref{tab:hybridmesonmasses} we provide our updated results for heavy hybrid meson masses, which are defined according to
\begin{eqnarray}
\label{EQN864} m_{\Lambda_{\eta}^{\epsilon};L,n} \ \ = \ \ E_{\Lambda_{\eta}^{\epsilon};L,n} - E_{\Lambda_{\eta}^{\epsilon}=\Sigma_g^+;n=1,L=0} + \overline{m} ,
\end{eqnarray}
where $\overline{m}$ is the spin averaged mass of the lightest quarkonium from experiments, either \\ $\overline{m} = (m_{\eta_c(1S),\textrm{exp}} + 3 m_{J/\Psi(1S),\textrm{exp}}) / 4 = 3.069(1) \, \textrm{GeV}$ or \\ $\overline{m} = (m_{\eta_b(1S),\textrm{exp}} + 3 m_{\Upsilon(1S),\textrm{exp}}) / 4 = 9.445(1) \, \textrm{GeV}$ \cite{ParticleDataGroup:2018ovx}.
In particular the masses obtained with $V_{\Sigma_u^-}(r)$ are around $55 \, \text{MeV}$ lower for $\bar c c$ and $35 \, \text{MeV}$ lower for $\bar b b$ compared to our previous results from Ref.\ \cite{Capitani:2018rox}. The masses related to $V_{\Pi_u}(r)$ are around $20 \, \text{MeV}$ lower for $\bar c c$ and almost unchanged for $\bar b b$.
These discrepancies are similar to our newly introduced term $A'^e_{2,\Lambda_\eta^\epsilon} a^2$ evaluated for $e = A^\text{HYP2}$, which is $43(4) \, \text{MeV}$ for $\Lambda_\eta^\epsilon = \Sigma_u^-$ and $9(6) \, \text{MeV}$ for $\Lambda_\eta^\epsilon = \Pi_u$.
The term $A'^e_{2,\Lambda_\eta^\epsilon} a^2$ represents lattice discretization errors, and can only be determined, when static potential lattice data is available for several lattice spacings.
This demonstrates that the lattice data and the corresponding parametrizations provided in this work constitute an important step towards higher precision in Born-Oppenheimer predictions of heavy hybrid meson masses.
The remaining discrepancies seem to be mostly related to the coefficient $\alpha$ in the parametrization (\ref{eq:Cornellpotential}) of $V_{\Sigma_g^+}(r)$, for which we quoted $\alpha = 0.0518(5) \, \text{GeV} \, \text{fm}$ in Ref.\ \cite{Capitani:2018rox} and which we updated to $\alpha = 0.0571(4) \, \text{GeV} \, \text{fm}$ in this work.
This change in $\alpha$ might also be a consequence of our careful identification and removal of lattice discretization errors, this time related to the tree level improvement represented by the term $\Delta V^{\text{lat},e}_{\Sigma_g^+}(r)$ defined in Eq.\ (\ref{eq:latticeartifacts}).
\begin{table}[htb]
\centering
\input{sections/tables/masses_table}
\caption{Predictions for heavy hybrid meson masses.}
\label{tab:hybridmesonmasses}
\end{table}
We note that our prediction of heavy hybrid meson masses within the Born-Oppenheimer approximation is based on several limiting assumptions (see the discussion in Section~$6.2$ in Ref.\ \cite{Capitani:2018rox}), e.g.\ the single-channel approximation, where mixing between static potentials is excluded, and the neglect of effects due to the heavy quark spins.
More sophisticated coupled channel Schrödinger equations were derived and used for Born-Oppenheimer predictions in Refs.\ \cite{Berwein:2015vca,Oncala:2017hop}.
Moreover, in Refs.\ \cite{Brambilla:2018pyn,Brambilla:2019jfi} first steps were taken to include corrections from the heavy quark spins.
These more advanced approaches also require lattice field theory results for the ordinary static potential and the $\Pi_u$ and $\Sigma_u^-$ hybrid static potentials.
However, the corresponding predictions of heavy hybrid meson masses are based on lattice field theory results obtained at significantly larger lattice spacing than our smallest lattice spacing and corresponding parametrizations trustworthy only at larger quark-antiquark separations and presumably suffering from sizable lattice discretization errors.
It would be interesting to repeat the Born-Oppenheimer computations from Refs.\ \cite{Berwein:2015vca,Oncala:2017hop,Brambilla:2018pyn,Brambilla:2019jfi} with the lattice field theory results for static potentials from this work provided in Table~\ref{tab:latticedata_ABCD_tilde_all}.
Finally we note that a precision determination of heavy hybrid meson masses in a Born-Oppenheimer framework also requires precise knowledge of static potentials for separations even smaller than $0.08 \, \text{fm}$, for which lattice computations were carried out in this work.
In this small-$r$ region higher order perturbation theory might be more suited than lattice QCD.
In Ref.\ \cite{Karbstein:2018mzo} the combination of NNNLO perturbation theory and lattice QCD is discussed for the $\Sigma_g^+$ potential.
It would be worthwhile to advance in the same direction for hybrid static potentials.
\section{\label{sec:theory_hybridstaticpotentials}Hybrid static potentials: quantum numbers, operators and correlation functions}
Hybrid static potentials represent the energy of the excited gluon field in the presence of a static quark and antiquark as a function of their separation.
Static potentials are characterized by the following three quantum numbers:
\begin{itemize}
\item $\Lambda = \Sigma (=0), \Pi (=1), \Delta (=2), \ldots$ denotes the total angular momentum with respect to the quark-antiquark separation axis, i.e.\ is a non-negative integer (w.l.o.g.\ we separate the static quark and antiquark along the $z$-axis).
\item $\eta = g (=+), u (=-)$ describes the even ($g$) or odd ($u$) behavior under the combined parity and charge conjugation transformation $\mathcal{P} \circ \mathcal{C}$.
\item $\epsilon = +,-$ is the eigenvalue of a reflection $\mathcal{P}_x$ along an axis perpendicular to the quark-antiquark separation axis (for definiteness we use the $x$-axis).
For $\Lambda \ge 1$, hybrid static potentials are degenerate with respect to $\epsilon$ and $\epsilon$ is typically omitted.
\end{itemize}
The ordinary static potential has quantum numbers $\Sigma_g^+$, while hybrid static potentials have quantum numbers different from $\Sigma_g^+$.
In this work we carry out a precise computation and parametrization of the two lowest hybrid static potentials, which have quantum numbers $\Pi_u$ and $\Sigma_u^-$, with particular focus on rather small quark-antiquark separations $r$.
Hybrid static potentials are computed from correlation functions similar to Wilson loops, where the straight spatial parallel transporters are replaced by more complicated gauge link combinations with non-trivial transformation properties,
\begin{eqnarray}\label{eq:CorrelationfunctionW}
\nonumber & & \hspace{-0.7cm} W_{S;\Lambda_{\eta}^{\epsilon}}(r,t) = \\
%
& & = \expval{
\Tr\left(
a_{S;\Lambda_{\eta}^{\epsilon}}(-r/2,+r/2;0) U(+r/2;0,t) \left(a_{S;\Lambda_{\eta}^{\epsilon}}(-r/2,+r/2;t)\right)^{\dagger} U(-r/2;t,0)
\right)
}_U .
\end{eqnarray}
$U(r;t_1,t_2)$ is a straight path of temporal gauge links from time $t_1$ to time $t_2$ at spatial position $\mathbf{r} = (0,0,r)$ and $\expval{\ldots}_U$ denotes the average on an ensemble of gauge link configurations.
$a_{S;\Lambda_{\eta}^{\epsilon}}$ is given by a sum of properly transformed spatial insertions $USU$, to probe the sector with quantum numbers $\Lambda_{\eta}^{\epsilon}$,
\begin{eqnarray}
\nonumber & & \hspace{-0.7cm} a_{S; \Lambda_{\eta}^{\epsilon}} (-r/2, +r/2) = \frac{1}{4} \sum_{k=0}^{3} \exp(\frac{i\pi \Lambda k}{2}) R\left( \frac{\pi k}{2}\right) \\
%
\nonumber & & \hspace{0.675cm} \Big(U(-r/2,r_1) \Big(S(r_1,r_2) + \epsilon S_{\mathcal{P}_x}(r_1,r_2)\Big) U(r_2,+r/2) \\
%
\label{eq:a} & & \hspace{0.675cm} + U(-r/2,-r_2) \Big(\eta S_{\mathcal{P} \circ \mathcal{C}}(-r_2,-r_1) + \eta \epsilon S_{(\mathcal{P} \circ \mathcal{C}) \mathcal{P}_x}(-r_2,-r_1)\Big) U(-r_1,+r/2)\Big).
\end{eqnarray}
The notation is explained in detail in Ref.\ \cite{Capitani:2018rox}. We employ operators $S$ from Ref.\ \cite{Capitani:2018rox}, where we have carried out a dedicated optimization to maximize the generated ground state overlaps. For the $\Pi_u$ hybrid static potential we use $S_{\RN{3},1}$ and for the $\Sigma_u^-$ hybrid static potential we use $S_{\RN{4},2}$. Detailed definitions can be found in Table~$3$ and Table~$5$ of Ref.\ \cite{Capitani:2018rox}. The operator extents in these tables are given in units of the lattice spacing for $a = 0.093 \, \text{fm}$. For computations at smaller values of $a$ we increase the operator extents in units of the lattice spacing such that they are approximately constant in physical units.
To further enhance the ground state overlaps, we apply APE smearing to the spatial gauge links appearing in $a_{S;\Lambda_{\eta}^{\epsilon}}$. The number of APE smearing steps is increased with decreasing lattice spacing to keep the smearing radius approximately constant in physical units.
Details can be found in Appendix~\ref{Appendix:optimization}.
\section{Introduction}
The constituent quark model is quite successful in explaining the properties of a variety of non-exotic hadrons, quark-antiquark pairs or triplets of quarks or antiquarks without gluonic excitations.
However, a particular class of exotic mesons, so-called hybrid mesons, contain such gluonic excitations and, thus, cannot be studied in a proper way using the constituent quark model. These systems require approaches closer to QCD, which contain gluons as degrees of freedom.
In this work we use lattice gauge theory and are interested in heavy hybrid mesons, which are composed of heavy $c$ or $b$ quarks and a surrounding excited gluon field.
The gluonic excitation contributes to the quantum numbers of the hybrid meson such that exotic combinations of $J^{PC}$ are allowed, which do not exist in the constituent quark model.
The experimental search for exotic states in existing and future facilities like the GlueX experiment at Jefferson Lab or the PANDA experiment at FAIR as well as the theoretical explanation of their internal structure and properties are currently hot research topics (for an experimental review see e.g.\ Ref.\ \cite{Olsen:2017bmm}, for theoretical reports we refer to Refs.\ \cite{Braaten:2014ita,Meyer:2015eta,Swanson:2015wgq,Lebed:2016hpi,Brambilla:2019esw}).
Concerning theoretical approaches, lattice gauge theory is an ideal non-perturbative first principles approach to investigate properties and masses of heavy hybrid mesons, either within the Born-Oppenheimer approximation~ \cite{Perantonis:1990dy,Juge:1997nc,Juge:1999ie,Guo:2008yz,Braaten:2014qka,Berwein:2015vca,Oncala:2017hop,Capitani:2018rox,Brambilla:2018pyn,Brambilla:2019jfi} or in full lattice QCD (see e.g.\ Refs.\ \cite{Bernard:2003jd,Bali:2011rd,Cheung:2016bym,Ray:2021nhe}).
We focus on hybrid mesons composed of heavy $c$ or $b$ quarks and use $\text{SU(3)}$ lattice gauge theory in combination with the Born-Oppenheimer approximation \cite{Born:1927}, which is a two-step approach.
In the first step, we fix the positions of the heavy quarks and compute so-called hybrid static potentials with lattice gauge theory. Hybrid static potentials correspond to energy levels of gluonic excitations in the presence of static quarks as functions of their separation.
In the second step of the Born-Oppenheimer approximation, the radial Schrödinger equation for the relative coordinate of the heavy quark-antiquark pair is solved with one of the hybrid static potentials obtained in the first step.
In recent years a lot of effort was invested to refine the second step of the Born-Oppenheimer approximation, e.g.\ by including the mixing of different sectors via coupled channel equations~\cite{Braaten:2014qka,Berwein:2015vca,Oncala:2017hop} and by taking heavy quark spin effects into account~\cite{Brambilla:2018pyn,Brambilla:2019jfi}.
These approaches require precise lattice results for hybrid static potentials, in particular at small quark-antiquark separations $r$ to combine them with perturbative predictions valid only at small $r$ or to fix matching coefficients in potential Non-Relativistic QCD (pNRQCD) \cite{Berwein:2015vca,Brambilla:2017uyf,Brambilla:2018pyn,Brambilla:2019jfi}. Thus, the main goal of this work is to use lattice gauge theory to investigate the small-$r$ region of the $\Pi_u$ and $\Sigma_u^-$ hybrid static potentials. We aim at extending the range of precise lattice field theory results to smaller quark-antiquark separations and improve existing investigations of hybrid static potentials \cite{Griffiths:1983ah,Campbell:1984fe,Campbell:1987nv,Perantonis1989StaticPF,
Michael:1990az,Perantonis:1990dy,Juge:1997nc,Peardon:1997jr,
Juge:1997ir,Morningstar:1998xh,Michael:1998tr,Michael:1999ge,
Juge:1999ie,Juge:1999aw,Bali:2000vr,
Morningstar:2001nu,Juge:2002br,Juge:2003qd,Michael:2003ai,
Michael:2003xg,Bali:2003jq,Juge:2003ge,
Wolf:2014tta,Reisinger:2017btr,Bicudo:2018yhk,Bicudo:2018jbb,Reisinger:2018lne,Capitani:2018rox}.
For this we perform computations at four different lattice spacings ranging from $a=0.040 \,\text{fm}$ to $a=0.093 \,\text{fm}$.
These computations at several small lattice spacings do not only allow to access smaller quark-antiquark separations than before, but also to explore and remove lattice discretization errors, such that our final results are expected to be consistent with the continuum limit within statistical errors. Moreover, we can convincingly confirm the repulsive behavior of hybrid static potentials at small $r$ predicted by perturbation theory.
To compute the ordinary static potential and the $\Pi_u$ and $\Sigma_u^-$ hybrid static potentials we employ optimized operators from our previous work \cite{Capitani:2018rox} as well as a multilevel algorithm \cite{Luscher:2001up}. In this way we obtain precise lattice results for these potentials on four ensembles for quark-antiquark separations as small as $0.08 \, \text{fm}$ (see Section~\ref{sec:theory_hybridstaticpotentials} to Section~\ref{sec:latticeresults}).
We also check that our lattice gauge theory computations are not contaminated by sizable systematic errors related to topological freezing, the finite spatial lattice volume or glueball decays of hybrid flux tubes, which are expected to be particularly prominent at small lattice spacings and small quark-antiquark separations (see Section~\ref{sec:systematicerrors}).
Moreover, we provide parametrizations describing the hybrid static potentials for quark-antiquark separations $0.08\,\text{fm} \raisebox{-0.5ex}{$\,\stackrel{<}{\scriptstyle\sim}\,$} r \raisebox{-0.5ex}{$\,\stackrel{<}{\scriptstyle\sim}\,$} 1.12\,\text{fm}$. We use these parameterizations to eliminate discretization errors and the $a$-dependent self-energy
(see Section~\ref{sec:parametrization}).
We also use the parametrizations to check the impact of including our new lattice data at small lattice spacings in Born-Oppenheimer predictions of $c \bar{c}$ and $b \bar{b}$ hybrid meson masses and find sizable differences to our previous work \cite{Capitani:2018rox}, where we have only considered a single lattice spacing $a = 0.093 \, \text{fm}$.
The numerical values of all lattice data points and their parametrizations are provided for straightforward use in future applications, e.g.\ for predictions of heavy hybrid meson masses in more refined Born-Oppenheimer approaches as proposed in Refs.\ \cite{Berwein:2015vca,Oncala:2017hop,Brambilla:2018pyn,Brambilla:2019jfi}. We also provide similar results for gauge group $\text{SU(2)}$, which were obtained at an early stage of this work.
\section{Optimization of operators} \label{Appendix:optimization}
The operators $S$ appearing in Eq.\ (\ref{eq:a}) were optimized in Ref.\ \cite{Capitani:2018rox} at lattice spacing $a=0.093 \, \text{fm}$ with respect to their generated ground state overlaps.
To retain this optimization also for smaller values of the lattice spacing, we adjust the operator extents in $x$- and $y$-direction in units of the lattice spacing, $E_x$ and $E_y$, such that the operator extents in physical units, $E_x a$ and $E_y a$, are almost independent of $a$.
Moreover, we select $N_\text{APE}$, the number of APE-smearing steps, individually for each lattice spacing, while keeping $\alpha_\text{APE} = 0.5$ constant (see e.g.\ Ref.\ \cite{Jansen:2008si} for detailed equations).
We do this in such a way that the effective potentials of the $\Pi_u$ and the $\Sigma_u^-$ hybrid static potentials at temporal separation $t/a = 2$ are small.
This amounts to increasing $N_\text{APE}$ for decreasing $a$. Our preferred values for $N_\text{APE}$ both for gauge group $\text{SU(2)}$ and $\text{SU(3)}$ are listed in Table~\ref{TAB500}.
\begin{table}[htb]
\begin{center}
\begin{tabular}{ccccc}
\toprule
$a$ in $\text{fm}$ & $0.078$ & $0.041$ & $0.026$ \\
\midrule
$N_\text{APE}$ for $\text{SU(2)}$ & $30$ & $100$ & $200$ \\
\bottomrule %
\end{tabular}
\vspace{0.3cm}
\begin{tabular}{ccccc}
\toprule
$a$ in $\text{fm}$ & $0.093$ & $0.060$ & $0.048$ & $0.040$ \\
\midrule
$N_\text{APE}$ for $\text{SU(3)}$ & $20$ & $50$ & $75$ & $100$ \\
\bottomrule %
\end{tabular}
\end{center}
\caption{\label{TAB500}Smearing parameter $N_\text{APE}$ for various lattice spacings for gauge group $\text{SU(2)}$ and $\text{SU(3)}$.}
\end{table}
\section{\label{APP012}Error analysis}
To eliminate correlations in Monte Carlo time, we combine consecutively generated gauge link configurations, which are used for the computation of static potentials, to $N^e$ bins.
For the data points $V^e_{\Lambda_\eta^\epsilon}(r)$ (see Section~\ref{sec:latticeresults}) statistical errors are determined via a standard jackknife analysis, i.e.\ from $N^e$ reduced jackknife samples $V^{e,\text{jackknife}}_{\Lambda_\eta^\epsilon,j}(r)$ according to
\begin{align}
\Delta V^e_{\Lambda_\eta^\epsilon}(r) = \bigg(\frac{N^e - 1}{N^e} \sum_{j=1}^{N^e} \Big(V^{e,\text{jackknife}}_{\Lambda_\eta^\epsilon,j}(r) - \bar{V}^e_{\Lambda_\eta^\epsilon}(r)\Big)^2\bigg)^{1/2}
\end{align}
($\bar{V}^e_{\Lambda_\eta^\epsilon}(r)$ denotes the result for the full sample).
The fits from Section~\ref{sec:parametrization}, where data points of all five ensembles are used at the same time, can in principle also be computed via the jackknife method.
The number of reduced jackknife samples, however, would be rather large, $N^A \times N^B \times N^C \times N^D \times N^{A^\text{HYP2}}$, and the corresponding computational effort huge.
Therefore, we use for these fits and all following analyses the bootstrap method.
To this end we first inflate the reduced jackknife samples,
\begin{align}
V^e_{\Lambda_\eta^\epsilon,j}(r) = \bar{V}^e_{\Lambda_\eta^\epsilon}(r) + (N^e - 1) \Big(V^{e,\text{jackknife}}_{\Lambda_\eta^\epsilon,j}(r) - \bar{V}^e_{\Lambda_\eta^\epsilon}(r)\Big) .
\end{align}
A bootstrap sample is then generated by randomly selecting $N^e$ of the inflated samples $V^e_{\Lambda_\eta^\epsilon,j}(r)$ for each ensemble, where the same inflated sample may be selected more than once.
As usual, the bootstrap error of a quantity $O$ is then the standard deviation of the results obtained on the bootstrap samples, i.e.\
\begin{align}
\Delta O = \bigg(\frac{1}{K} \sum_{j=1}^K \Big(O_j - \bar{O}\Big)^2\bigg)^{1/2} .
\end{align}
$O_j$ denotes the result on the $j$-th bootstrap sample and $\bar{O}$ the result on the full sample, where $O$ can be $\alpha$, $\sigma$, $\alpha'$, $C^e$, $A_1$, $A_2$, etc. $K$, the number of bootstrap samples, has to be chosen sufficiently large, such that $\Delta O$ is essentially independent of $K$.
For our computations we used $N^A = 320$, $ N^B = N^C = N^D = 160$, $N^{A^\text{HYP2}} = 5000$ and $K = 10000$.
\section{Tree-level improvement}\label{Appendix:treelevelimprovement}
In the continuum at tree-level of perturbation theory the ordinary static potential potential is attractive and proportional to $1/r$.
Its lattice counterpart for the standard Wilson plaquette gauge action and the Eichten-Hill static action is
\begin{equation}\label{eq:definition_rimproved}
\left(\frac{1}{r}\right)_\text{lat} = 4\pi G(r/a,0,0),
\end{equation}
where the Greens function
\begin{equation}\label{eq:latticepropagator1}
G(\textbf{R}) = \frac{1}{(2\pi)^3} \int_{-\pi}^{\pi} \dd[3]{k}
\frac{\prod_{j=1}^{3} \cos(k_j R_j)}{4 \sum_{j=1}^{3} \sin[2](k_j/2)},
\end{equation}
can be computed in an efficient way via a recursion relation \cite{Luscher:1995zz,Necco:2001xg}.
For the HYP2 static action \cite{DellaMorte:2005nwx,Hasenfratz:2001hp,DellaMorte:2003mn}, which was used for the computations on ensemble $A^\text{HYP2}$, the numerator of the integrand differs from Eq.\ \eqref{eq:latticepropagator1} by an additional factor,
\begin{equation}\label{eq:latticepropagator2}
G^\text{HYP}(\textbf{R}) = \frac{1}{(2\pi)^3} \int_{-\pi}^{\pi} \dd[3]{k}
\frac{\prod_{j=1}^{3} \cos(k_j R_j) \times \Big(
1- (\alpha_1 / 6) \sum_{i=1}^{3}4\sin[2](k_i)\Omega_{i0}
\Big)^2}{4 \sum_{j=1}^{3} \sin[2](k_j/2)},
\end{equation}
where $\Omega_{\mu \nu}$ is
\begin{align}
\Omega_{\mu \nu} = 1+ &\alpha_2(1+\alpha_3) - \frac{\alpha_2}{4}(1+2\alpha_3)\bigg(
\sum_{j=1}^{3}4\sin[2](p_j/2) - 4\sin[2](p_{\mu}/2) - 4\sin[2](p_{\nu}/2)\bigg) \\\nonumber
&+ \frac{\alpha_2 \alpha_3}{4}\prod_{\eta \neq \mu,\nu}^{} 4\sin[2](p_{\mu}/2).
\end{align}
(see Ref.\ \cite{Hasenfratz:2001tw}).
This integral can be solved e.g.\ by standard Monte Carlo integration techniques.
To eliminate lattice discretization errors at tree-level for the ordinary static potential, we subtract
\begin{equation}
\Delta V^{\text{lat},e}_{\Sigma_g^+}(r) = \alpha' \bigg(\frac{1}{r} - \frac{G^e(r/a)}{a}\bigg)
\end{equation}
from the lattice data points (see Section~\ref{sec:parametrization}, in particular Eq.\ (\ref{eq:def_V_Sigmagplus_tilde})), where $G^e(r/a) = 4 \pi G(r/a,0,0)$ for $e=A,B,C,D$ and $G^e(r/a) = 4 \pi G^\text{HYP}(r/a,0,0)$ for $e=A^{HYP2}$. $\alpha'$ is proportional to the strong coupling and determined by a fit to the lattice data (see again Section~\ref{sec:parametrization}).
Similarly, we subtract $\Delta V^{\text{lat},e}_\text{hybrid}(r) = -(1/8) \Delta V^{\text{lat},e}_{\Sigma_g^+}(r)$ from the lattice data points for the $\Pi_u$ and $\Sigma_u^-$ hybrid static potentials, which are repulsive and, in leading-order perturbation theory, suppressed by the factor $1/8$ relative to the ordinary static potential.
The benefit of applying tree-level improvement, when combining lattice field theory results obtained at different lattice spacings and with different static actions is demonstrated in Figure~\ref{fig:data_mi_para}, where we compare unimproved and improved data points for the $\Sigma_g^+$ potential from our five ensembles.
The two plots show that the majority of improved data points are consistent with a single curve, while unimproved data points from different ensembles exhibit strong discrepancies for $r \raisebox{-0.5ex}{$\,\stackrel{<}{\scriptstyle\sim}\,$} 0.4 \, \text{fm}$.
\begin{figure}[htb]
\centering
\includegraphics[width=\linewidth,page=1]{plots/Plot_latticeresults_minus_parametrization}
\caption{Comparison of unimproved (left) and improved (right) lattice data points for the $\Sigma_g^+$ static potential from our five ensembles $A$, $B$, $C$, $D$ and $A^\text{HYP2}$.
We subtract $V_{\Sigma_g^+}(r) + C^e$ with $V_{\Sigma_g^+}(r)$ defined in Eq.\ \eqref{eq:Cornellpotential} and parameters obtained by a fit to data points with $r \geq 0.2 \, \text{fm}$ (indicated by the vertical dashed line) as listed in Table~\ref{tab:fitparameter}.}
\label{fig:data_mi_para}
\end{figure}
\section{Summary of $\text{SU(3)}$ lattice field theory results for the $\Sigma_g^+$, $\Pi_u$ and $\Sigma_u^-$ static potentials}\label{Appendix:summarylatticedata}
In Table~\ref{tab:latticedata_ABCD_all} we list $V^e_{\Lambda_{\eta}^{\epsilon}}(r)a$, the bare lattice data points in units of the lattice spacing (see Section~\ref{sec:latticeresults}).
In Table~\ref{tab:latticedata_ABCD_tilde_all} we list $\tilde{V}^e_{\Lambda_\eta^\epsilon}(r)$, the lattice data points defined in Eqs.\ (\ref{eq:def_V_Sigmagplus_tilde}) and (\ref{eq:def_V_hybrid_tilde}), where the self energy as well as lattice discretization errors at tree-level and proportional to $a^2$ are removed.
\renewcommand{1.2}{1.1}
\begin{table}[h]\centering
\input{sections/tables/Va_all_tables}
\caption{Bare lattice data points for the $\Sigma_g^+$, $\Pi_u$ and $\Sigma_u^-$ static potentials in units of the lattice spacing (see Section~\ref{sec:latticeresults}).}
\label{tab:latticedata_ABCD_all}
\end{table}
\begin{table}[h]\centering
\input{sections/tables/Va_all_tables_tilde}
\caption{Lattice data points defined in Eqs.\ (\ref{eq:def_V_Sigmagplus_tilde}) and (\ref{eq:def_V_hybrid_tilde}), where the self energy as well as lattice discretization errors at tree-level and proportional to $a^2$ are removed (using Fit~1), for the $\Sigma_g^+$, $\Pi_u$ and $\Sigma_u^-$ static potentials in units of $\text{GeV}$ (physical units are introduced by setting $r_0 = 0.5 \, \text{fm}$).}
\label{tab:latticedata_ABCD_tilde_all}
\end{table}
\renewcommand{1.2}{1.0}
\section{$\text{SU(2)}$ lattice field theory results for the $\Sigma_g^+$, $\Pi_u$ and $\Sigma_u^-$ static potentials} \label{Appendix:SU2results}
We carried out computations for gauge group $\text{SU(2)}$ analogous to those for gauge group $\text{SU(3)}$ discussed and presented in the main sections of this work.
We generated three ensembles of gauge link configurations with gauge couplings $\beta = 2.85, \, 2.70, \, 2.50$.
We relate the lattice spacing $a$ to the scale $t_0$ using a parametrization of $\ln(t_0/a^2)$ determined in Ref.\ \cite{Hirakida:2018uoy} via the gradient flow.
Physical units are then introduced by setting $\sqrt{8 t_0} = 0.3010 \, \text{fm}$, which corresponds to $r_0 = 0.5 \, \text{fm}$.
The details of the gauge link ensembles are summarized in Table~\ref{tab:latticesetupsSU2}.
The three lattice volumes are quite similar, $L^3 \times T \approx (1.3 \, \text{fm})^3 \times (1.3 \, \text{fm})$.
For the investigation of finite volume effects in Section~\ref{sec:finitevolume}, additional ensembles with both smaller and larger lattice volumes at gauge couplings $\beta= 3.00 , \, 2.85 , \, 2.70 , \, 2.50$ were generated.
\begin{table}[htb]
\begin{center}
\def1.2{1.2}
\begin{tabular}{cccccccccc}
\hline
ensemble & $\beta$ & $a$ in $\text{fm}$ \cite{Hirakida:2018uoy} & $(L/a)^3 \times T/a$ & $N_{\text{sim}}$ & $N_{\text{total}}$ & $N_{\text{or}}$ & $N_{\text{therm}}$ & $N_{\text{sep}}$ & $N_{\text{meas}}$ \\
\hline
$a$ & $2.50$ & $0.078$ & $16^3\times 16$ & $20$ &
$40 000$ & $0$ & $10 000$ & $100$ & $6000$ \\
$b$ & $2.70$ & $0.041$ & $32^3\times 32$ & $20$ &
$25 000$ & $0$ & $10 000$ & $100$ & $3000$ \\
$c$ & $2.85$ & $0.026$ & $48^3\times 48$ & $20$ &
$25 000$ & $0$ & $10 000$ & $200$ & $1500$ \\
\hline
\end{tabular}
\end{center}
\caption{Gauge link ensembles for gauge group $\text{SU(2)}$.}
\label{tab:latticesetupsSU2}
\end{table}
\begin{table}[h]\centering
\input{sections/tables/Va_all_tables_SU2}
\caption{Bare lattice data points for the $\Sigma_g^+$, $\Pi_u$ and $\Sigma_u^-$ static potentials in units of the lattice spacing (see Table~\ref{tab:latticesetupsSU2}) for gauge group $\text{SU(2)}$.}
\label{tab:latticedata_SU2_all}
\end{table}
In Table~\ref{tab:latticedata_SU2_all} we list $V^e_{\Lambda_{\eta}^{\epsilon}}(r)a$, the bare lattice data points in units of the lattice spacing.
These can be used to generate parametrizations, using methods as e.g.\ discussed in Section~\ref{sec:parametrization}.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 76 |
\section{Introduction}\label{sec:intro}
The well-known \emph{constrained minimal supersymmetric standard
model} (CMSSM) \cite{Cmssm0, Cmssm,cmssm1,cmssm2}, which is a
highly predictive version of the \emph{minimal supersymmetric
standard model} (MSSM) based on universal boundary conditions for
the soft \emph{supersymmetry} (SUSY) breaking parameters, can be
further restricted by being embedded in a SUSY \emph{grand unified
theory} (GUT) with a gauge group containing $SU(4)_c$ and
$SU(2)_R$. This can lead \cite{pana} to `asymptotic' \emph{Yukawa
unification} (YU) \cite{als}, i.e. the exact unification of the
third generation Yukawa coupling constants $h_t$, $h_b$, and
$h_\tau$ of the top quark, the bottom quark, and the tau lepton,
respectively, at the SUSY GUT scale $M_{\rm GUT}$. The simplest
GUT gauge group which contains both $SU(4)_c$ and $SU(2)_R$ is the
\emph{Pati-Salam} (PS) group $G_{\rm PS}=SU(4)_c\times
SU(2)_L\times SU(2)_R$ \cite{leontaris,jean} -- for YU within
$SO(10)$, see Refs. \cite{baery,raby}.
However, given the experimental values of the top-quark and
tau-lepton masses (which, combined with YU, naturally restrict
$\tan\beta\sim50$), the CMSSM supplemented by the assumption of YU
yields unacceptable values of the $b$-quark mass $m_b$ for both signs
of the parameter $\mu$. This is due to the presence of sizable
SUSY corrections \cite{copw} to $m_b$ (about 20$\%$), which arise
\cite{copw,pierce} from sbottom-gluino (mainly) and stop-chargino
loops and have the sign of $\mu$ -- with the standard sign
convention of Ref.~\cite{sugra}. The predicted tree-level
$m_b(M_Z)$, which turns out to be close to the upper edge of its
$95\%$ \emph{confidence level} (c.l.) experimental range receives,
for $\mu>0$ [$\mu<0$], large positive [negative] corrections which
drive it well above [a little below] the allowed range.
Consequently, for both signs of $\mu$, YU leads to an unacceptable
$m_b(M_Z)$ with the $\mu<0$ case being much less disfavored.
The usual strategy to resolve this discrepancy is the introduction
of several kinds of nonuniversalities in the scalar \cite{baery,
raby} and/or gaugino \cite{nath,shafi} sector of MSSM with an
approximate preservation of YU. On the contrary, in
Ref.~\cite{qcdm}, concrete SUSY GUT models based on the PS gauge
group are constructed which naturally yield a moderate deviation
from exact YU and, thus, can allow acceptable values of the
$b$-quark mass for both signs of $\mu$ within the CMSSM. In
particular, the Higgs sector of the simplest PS model
\cite{leontaris, jean} is extended so that the electroweak Higgs
fields are not exclusively contained in a $SU(2)_L\times SU(2)_R$
bidoublet superfield but
receive subdominant contributions from other representations too.
As a consequence, a moderate violation of YU is naturally obtained,
which can allow an acceptable $b$-quark mass even with universal
boundary conditions. It is also remarkable that the resulting
extended SUSY PS models support new successful versions
\cite{axilleas} of hybrid inflation based solely on renormalizable
superpotential terms.
These models provide us with a set of `asymptotic' Yukawa
quasi-unification conditions which replace exact YU. However,
applying one of these conditions in the $\mu<0$ case does not
lead \cite{muneg,nova} to a viable scheme. This is due to the
fact that the parameter space allowed by the \emph{cold dark
matter} (CDM) requirements turns out \cite{muneg, nova} to lie
lower than the one allowed by the inclusive decay
$b\rightarrow s\gamma$ in the $m_{\rm LSP}-\Delta_{\tilde\tau_2}$
plane, where $m_{\rm LSP}$ is the mass of the lightest sparticle
(LSP), which, in our case, is the lightest neutralino $\tilde\chi$
and
$\Delta_{\tilde\tau_2}=(m_{\tilde\tau_2}-m_{\rm LSP})/m_{\rm LSP}$
is the relative mass splitting between the LSP and the lightest
stau mass eigenstate $\tilde\tau_2$. This result is
strengthened by the fact that $\mu<0$ is strongly disfavored by
the constraint arising from the deviation $\delta a_\mu$ of the
measured value of the muon anomalous magnetic moment $a_\mu$
from its predicted value $a^{\rm SM}_\mu$ in the
\emph{standard model} (SM). Indeed, $\mu<0$ is defended only
at 3$\sigma$ by
the calculation of $a^{\rm SM}_\mu$ based on the $\tau$-decay
data, whereas there is a stronger and stronger
tendency at present to prefer the $e^+e^-$-annihilation data for
the calculation of $a^{\rm SM}_\mu$, which favor the $\mu>0$
regime. Given the above situation, we focus here on the $\mu>0$
case.
Let us recall that, in this case, the suitable `asymptotic'
Yukawa quasi-unification condition applied \cite{qcdm, nova}
is
\begin{equation}
h_t:h_b:h_\tau=|1+c|:|1-c|:|1+3c|. \label{minimal}
\end{equation}
This relation depends on a single parameter $c$, which is
taken, for simplicity, to be real and lying in the range $0<c<1$.
With fixed masses for the fermions of the third generation, we
can determine the parameters $c$ and $\tan\beta$ so that
Eq.~(\ref{minimal}) is satisfied. In contrast to the original
version of the CMSSM \cite{Cmssm, cmssm1, cmssm2}, therefore,
$\tan\beta$ is not a free parameter but it can be restricted,
within our set-up, via \Eref{minimal} to relatively large values.
The remaining free parameters of our model are the universal soft
SUSY breaking parameters defined at $M_{\rm GUT}$, i.e.,
\begin{equation}
M_{1/2},~~m_0,~~\mbox{and}~~A_0, \label{param}
\end{equation}
where the symbols above denote the common gaugino mass, scalar
mass, and trilinear scalar coupling constant, respectively.
These parameters can be restricted by employing a number of
experimental and cosmological requirements as in Refs.~\cite{qcdm,
nova}. In view of the expected data from the \emph{Large Hadron
Collider} (LHC), it would be worth to retest our model
against observations using the most up-to-date version of the
available constraints.
We exhibit the cosmological and phenomenological
requirements which we considered in our investigation in
Sec.~\ref{sec:pheno} and we restrict the parameter space of our
model in Sec.~\ref{results}. Finally, we test our model from the
perspective of the CDM direct detection experiments in
Sec.~\ref{det} and summarize our conclusions in Sec.~\ref{con}.
\section{Cosmological and Phenomenological Constraints}
\label{sec:pheno}
In our investigation, we integrate the two-loop renormalization
group equations for the gauge and Yukawa coupling constants and
the one-loop ones for the soft SUSY breaking parameters between
$M_{\rm GUT}$ and a common SUSY threshold $M_{\rm SUSY}
\simeq(m_{\tilde t_1}m_{\tilde t_2})^{1/2}$ ($\tilde t_{1,2}$ are
the stop mass
eigenstates) determined in consistency with the SUSY spectrum. At
$M_{\rm SUSY}$, we impose radiative electroweak symmetry breaking,
evaluate the SUSY spectrum employing the publicly available
calculator {\tt SOFTSUSY} \cite{Softsusy}, and incorporate the SUSY
corrections to the $b$ and $\tau$ mass \cite{pierce}. The
corrections to the $\tau$-lepton mass $m_\tau$ (almost 4$\%$) lead
\cite{qcdm, muneg} to
a small decrease of $\tan\beta$. From $M_{\rm SUSY}$ to $M_Z$, the
running of gauge and Yukawa coupling constants is continued using
the SM renormalization group equations.
The parameter space of our model can be restricted by using a
number of phenomenological and cosmological constraints. We
calculate them using the latest version of the publicly available
code {\tt micrOMEGAs} \cite{micro}. We now briefly discuss these
requirements -- for similar recent analyses, see Ref.~\cite{lhc}
for CMSSM or Refs.~\cite{baerlhc, shafi} for MSSM with YU.
\paragraph{\hspace*{-0.3cm} SM Fermion Masses.} The masses of the
fermions of the third
generation play a crucial role in the determination of the
evolution of the Yukawa coupling constants. For the $b$-quark
mass, we adopt as an input parameter in our analysis the
$\overline{\rm MS}$ $b$-quark mass, which at 1$\sigma$ is
\cite{pdata}
\beq m_b \lf m_b\rg^{\overline{\rm MS}}=4.19^{+0.18}_{-0.06}~\GeV.
\eeq
This range is evolved up to $M_Z$ using the central value
$\alpha_s(M_Z)=0.1184$ \cite{pdata} of the strong fine structure
constant at $M_Z$ and then converted to the ${\rm \overline{DR}}$
scheme in accordance with the analysis of Ref.~\cite{baermb}. We
obtain, at $95\%$ c.l.,
\beq 2.745\lesssim m_b(M_Z)/{\rm GeV}\lesssim 3.13
\label{mbrg}\eeq
with the central value being $m_b(M_Z)=2.84~\GeV$. For the
top-quark mass, we use the central pole mass ($M_t$) as an input
parameter \cite{mtmt}:
\beq M_t=173~\GeV~~\Rightarrow~~m_t(m_t)=164.6~\GeV\eeq
with $m_t(m_t)$ being the running mass of the $t$ quark. We also
take the central value $m_{\tau}(M_Z) = 1.748~\GeV$ \cite{baermb}
of the ${\overline{\rm DR}}$ tau-lepton mass at $M_Z$.
\paragraph{\hspace*{-0.3cm} Cold Dark Matter Considerations.}
\label{phenoa}
According to the WMAP results \cite{wmap}, the $95\%$ c.l. range
for the CDM abundance is
\beq \Omega_{\rm CDM}h^2=0.1126\pm0.0072. \label{cdmba}\eeq
In the context of the CMSSM, the LSP can be the lightest
neutralino $\tilde\chi$ and naturally arises as a CDM
candidate. We require its relic abundance $\Omega_{\rm LSP}h^2$
in the universe
not to exceed the upper bound derived from Eq.~(\ref{cdmba}) --
the lower bound is not considered since other production
mechanisms \cite{scn} of LSPs may be present too and/or other
CDM candidates \cite{axino, Baerax} may also contribute to
$\Omega_{\rm CDM}h^2$. So, at $95\%$ c.l., we take
\beq \Omega_{\rm LSP}h^2\lesssim0.12.\label{cdmb}\eeq
An upper bound on $m_{\rm LSP}$ (or $m_{\tilde\chi}$) can be
derived from Eq.~(\ref{cdmb}) since, in general, $\Omx$ increases
with $\mx$. The calculation of $\Omx$ in \mcr\ includes accurately
thermally averaged exact tree-level cross sections of all the
possible (co)annihilation processes \cite{cmssm1, cdm}, treats
poles \cite{cmssm2, qcdm, nra} properly, and uses one-loop QCD and
SUSY QCD corrections \cite{copw, qcdm, pallis, microbsg} to the
Higgs decay widths and couplings to fermions.
\paragraph{\hspace*{-0.3cm}
The Branching Ratio $\bsg$ of $b\to s\gamma$.}
The most recent experimental world average for
${\rm BR}(b\rightarrow s\gamma)$ is known \cite{bsgexp} to be
$\lf3.52\pm0.23\pm0.09\rg\times10^{-4}$ and its updated SM
prediction is $\lf3.15\pm0.23\rg\times10^{-4}$ \cite{bsgSM}.
Combining in quadrature the experimental and theoretical errors
involved, we obtain the following constraints on this
branching ratio at $95\%$ c.l.:
\beq 2.84\times 10^{-4}\lesssim \bsg \lesssim 4.2\times 10^{-4}.
\label{bsgb} \eeq
The computation of $\bsg$ in the {\tt micrOMEGAs} package
presented in \cref{microbsg} includes \cite{nlobsg}
\emph{next-to-leading order} (NLO) QCD corrections to the charged
Higgs boson ($H^\pm$) contribution, the $\tan\beta$ enhanced
contributions, and resummed NLO SUSY QCD corrections. The $H^\pm$
contribution interferes constructively with the SM contribution,
whereas the SUSY contribution interferes destructively with the
other two contributions for $\mu>0$. The SM plus the $H^\pm$ and
SUSY contributions initially increases with $\mx$ and yields a
lower bound on $\mx$ from the lower bound in Eq.~(\ref{bsgb}).
(For higher values of $\mx$, it starts mildly decreasing.)
\paragraph{\hspace*{-0.3cm} The Branching Ratio $\bmm$ of
$B_s\to\mu^+\mu^-$.}
The rare decay $B_s\to \mu^+\mu^-$ occurs via $Z$ penguin and
box diagrams in the SM and, thus, its branching ratio is
highly suppressed. The SUSY contribution, though, originating
\cite{bsmm, mahmoudi} from neutral Higgs bosons in chargino-,
$H^\pm$-, and $W^\pm$-mediated penguins behaves as
$\tan^6\beta/m^4_A$ and hence is particularly important for large
$\tan\beta$'s. We impose the following $95\%$ c.l. upper bound:
\beq \bmm\lesssim5.8\times10^{-8} \label{bmmb} \eeq
as reported \cite{bmmexp} by the CDF collaboration. This bound
implies a lower bound on $\mx$ since $\bmm$ decreases as
$m_{\rm LSP}$ increases.
\paragraph{\hspace*{-0.3cm} The Branching Ratio
${\rm BR}\lf B_u\to \tau\nu\rg$ of $B_u\to \tau\nu$.}
The purely leptonic decay
$B_u\to \tau\nu$ proceeds via $W^\pm$- and $H^\pm$-mediated
annihilation processes. The SUSY contribution, contrary to the
SM one, is not helicity suppressed and depends on the mass
$m_{H^\pm}$ of the charged Higgs boson since it behaves
\cite{Btn, mahmoudi} as $\tan^4\beta/m^4_{H^\pm}$. The ratio
$\btn$ of the CMSSM to the SM branching ratio of
$B_u\to \tau\nu$ increases with $\mx$ and approaches unity. It
is to be consistent with the following $95\%$ c.l. range
\cite{bsgexp}:
\beq 0.52\lesssim\btn\lesssim2.04\ .\label{btnb} \eeq
A lower bound on $\mx$ can be derived from the lower bound in
this inequality.
\paragraph{\hspace*{-0.3cm} Muon Anomalous Magnetic Moment.}
\label{phenoc}
The quantity $\delta a_\mu$, which is defined in \Sref{sec:intro},
can be attributed to SUSY contributions arising from
chargino-sneutrino and neutralino-smuon loops. The relevant
calculation is based on the formulas of Ref.~\cite{gmuon}. The
absolute value of the result decreases as $m_{\rm LSP}$ increases
and its sign is positive for $\mu>0$. On the other hand, the
calculation of $a^{\rm SM}_\mu$ is not yet stabilized mainly
because of the ambiguities in the calculation of the hadronic
vacuum-polarization contribution. According to the most
up-to-date evaluation of this contribution in Ref.~\cite{g2davier},
there is still a discrepancy between the findings based on the
$e^+e^-$-annihilation data and the ones based on the
$\tau$-decay data. Taking into account the more reliable calculation
based on the $e^+e^-$ data and the experimental measurements
\cite{g2exp} of $a_\mu$, we obtain the following $95\%$ c.l. range:
\beq~12.7\times 10^{-10}\lesssim \delta a_\mu\lesssim 44.7\times 10^{-10}.
\label{g2b}\eeq
The $\tau$-decay based calculation, on the other hand, yields
the following $95\%$ c.l. range:
\beq~2.9\times 10^{-10}\lesssim \delta a_\mu\lesssim 36.1\times 10^{-10}.
\label{g2btau}\eeq
A lower [upper] bound on $\mx$ can be derived from the upper [lower]
bound in \Erefs{g2b}{g2btau}. As it turns out, only the upper bound
on $\mx$ is relevant in our case. Taking into account the
aforementioned computational instabilities, we will impose the less
stringent upper bound on $\mx$ from the $\tau$-decay based calculation.
However, we will also depict the more stringent bound from the
$e^+e^-$-annihilation data for comparison.
\paragraph{Collider Bounds.} For our analysis, the only relevant
collider bound is the $95\%$ c.l. LEP bound \cite{lepmh} on the
lightest CP-even neutral Higgs boson mass
\beq m_h\gtrsim114.4~{\rm GeV},\label{mhb} \eeq
which gives a lower bound on $m_{\rm LSP}$. The calculation of
$m_h$ in the package {\tt SOFTSUSY} \cite{Softsusy} includes the
full one-loop SUSY corrections and some zero-momentum two-loop
corrections \cite{2loops}. The results are well tested
\cite{comparisons} against other spectrum calculators.
\begin{figure}[!t]
\includegraphics[width=65mm,angle=-90]{Capg}
\caption{Summary of the conventions adopted in Figs.~\ref{Mmx} and
\ref{AMgx} for the various restrictions on the parameters of the
model.}
\label{Capgx}
\end{figure}
\begin{figure*}[!tb]
\centering
\includegraphics[width=65mm,angle=-90]{Mm0}
\includegraphics[width=65mm,angle=-90]{Mm1}\\
\includegraphics[width=65mm,angle=-90]{Mm1m}
\includegraphics[width=65mm,angle=-90]{Mm2m}
\caption{Restrictions in the $\Mg-m_{0}$ plane for
various values of $A_0/\Mg$ indicated in the graphs. The
conventions adopted are described in \Fref{Capgx}.}
\label{Mmx}
\end{figure*}
\section{Restrictions on the SUSY Parameters} \label{results}
Imposing the requirements described above, we can delineate the
allowed parameter space of our model. The predicted mass spectra
are possibly relevant for the LHC searches. Throughout our
investigation, we consider the central values for the SM
parameters $M_t$, $m_b(M_Z)$, $m_\tau(M_Z)$, and $\alpha_s(M_Z)$.
We adopt the following conventions for the various lines and
regions in the relevant figures (Figs.~\ref{Mmx} and \ref{AMgx})
-- see \Fref{Capgx}:
\begin{itemize}
\item on the solid black line, \Eref{cdmb} is saturated,
\item the light gray region is cosmologically excluded
since it predicts charged LSP,
\item the dark gray region is excluded by the lower bound
in \Eref{bsgb},
\item the gray region is excluded by \Eref{bmmb},
\item the yellow region is excluded by the lower bound
in \Eref{btnb},
\item the vertically hatched region is favored by
the lower bound in \Eref{g2b},
\item on the dotted black line, the lower bound in
\Eref{g2btau} is saturated,
\item the red region is excluded by \Eref{mhb},
\item the horizontally hatched region is allowed
by both \Eref{cdmb} and the lower bound in
\Eref{g2btau}.
\end{itemize}
Note that the upper bounds in Eqs.~(\ref{bsgb}), (\ref{btnb}),
(\ref{g2b}), and (\ref{g2btau}) do not restrict the parameters of
our model.
We present the restrictions from all the requirements imposed
in the $\Mg-m_0$ plane for $A_0/\Mg=0$, 1, $-1$, and $-2$ in
\Fref{Mmx}. We remark that the lower bound on $\Mg$ comes from
\Eref{bmmb} for $A_0/\Mg=0$, $-1$, and $-2$ and from the lower
bound in \Eref{btnb} for $A_0/\Mg=1$. Also, from the relevant
data, we observe that the lower bound in \Eref{btnb} is
fulfilled for the mass of the CP-odd Higgs boson
$m_A\simeq520~\GeV$ and almost independently of the other
parameters. Finally, note that, for $\AMg=-1$ and $-2$, the
bound in \Eref{mhb} is violated for $M_{1/2}<400~\GeV$ and,
consequently, does not appear in the relevant diagrams.
The constraint in \Eref{cdmb} is, in general, satisfied in
two well-defined distinct regions in the diagrams of
\Fref{Mmx}. In particular,
\begin{itemize}
\item the region to the left of the almost vertical part of
the line corresponding to the upper bound on $\Mg$ from
\Eref{cdmb}, where the LSP annihilation via the $s$-channel
exchange of a CP-odd Higgs boson $A$ is by far the dominant
(co)annihilation process. However, this region is excluded by
the constraints in Eqs.~(\ref{bmmb}) and (\ref{btnb}). On the
other hand, it is well known -- see e.g. Refs.~\cite{cmssm2, qcdm}
-- that this region is extremely sensitive to variations of
$m_b(M_Z)$. Indeed, we find that as $m_b(M_Z)$ decreases, the
$A$-boson mass $m_A$ increases and approaches $2m_{\rm LSP}$.
The $A$-pole neutralino annihilation is then enhanced and
$\Omega_{\rm LSP}h^2$ is drastically reduced causing an
increase of the upper bound on $\Mg$. However, even if we
reduce $m_b(M_Z)$, we do not find any $A$-pole annihilation
region which is allowed by the requirements of
Eqs.~(\ref{bmmb}) and (\ref{btnb}).
\item the narrow region which lies just above the light gray
area with charged LSP, where bino-stau coannihilations
\cite{cmssm1,cdm} take over
leading to a very pronounced reduction of $\Omx$. A large
portion of this region survives after the application of the
requirements in Eqs.~(\ref{bmmb}) and (\ref{btnb}) and
constitutes the overall allowed parameter range of our model
for the given $A_0$. To get a better understanding of this area,
we can replace the parameter $m_0$ by the relative mass
splitting $\Dst$ between the LSP and the lightest stau, defined
in Sec.~\ref{sec:intro}. We observe that the overall allowed
region requires $\Dst\lesssim0.025$. It is evident from
\Fref{Mmx} that the slope of the boundary line with $\Dst=0$
increases as $\AMg$ moves away from zero in both directions.
Note that this slope in our model turns out to be larger than
the one obtained in other versions of the CMSSM --
cf. \cref{cmssm1} -- with lower values of $\tan\beta$. As a
consequence, small variations of $m_0$ or $\Mg$ lead, in our
model, to more drastic variations in $\Dst$.
\end{itemize}
Finally, we note that the more stringent upper bound on $\Mg$ from
the lower bound in \Eref{g2b} is not satisfied for the values
taken for $\AMg$ in \Fref{Mmx}, with the values $\AMg=0$ and $1$
being much more favored. On the other hand, the lower bound in
\Eref{g2btau} is fulfilled in the whole allowed region for
$\AMg=0$ and $1$ whereas, for $\AMg=-1$ and $-2$, it imposes an
upper bound on $\Mg$ which overshadows the bound on $\Mg$ from
\Eref{cdmb}. Since the saturation of the lower bound in \Eref{g2btau}
occurs for $\Dst\lesssim 0.01$, the portion of the dotted black
line -- see Fig.~\ref{Capgx} -- which connects the black solid
line with the boundary of the gray area is not visible in the
relevant panels of \Fref{Mmx}.
\begin{figure}[!t]
\includegraphics[width=65mm,angle=-90]{AMg}
\caption{Restrictions in the
$M_{1/2}-A_{0}/M_{1/2}$ plane for $\Delta_{\tilde\tau_2}=0$
following the conventions of \Fref{Capgx}, but with the
horizontally hatched region not extended to areas excluded by
other constraints.}
\label{AMgx}
\end{figure}
To get a better idea of the allowed parameter space, we focus
on the coannihilation regime and construct the allowed region
in the $\Mg-A_0/\Mg$ plane. This is shown in \Fref{AMgx},
where we depict the restrictions on the parameters from the
various constraints for $\Dst=0$. This choice ensures the
maximal possible reduction of $\Omx$ due to the
$\tilde\chi-\tilde\tau_2$ coannihilation. So, for $\Dst=0$, we
find the maximal $\Mg$ or $\mx$ allowed by \Eref{cdmb} for a
given value of $A_0/\Mg$. We observe that, for $-0.8\lesssim
A_0/\Mg\lesssim3$ [$-2.55\lesssim A_0/\Mg\lesssim-0.8$ and
$3\lesssim A_0/\Mg\lesssim3.21$] the overall upper bound on
$\Mg$ or $\mx$ is derived from the bound in Eq.~(\ref{cdmb})
[lower bound in \Eref{g2btau}]. We find that, for $A_0/\Mg<0$,
processes with $\tilde\tau_2\tilde\tau_2^\ast$ in the initial
state and $W^\pm W^\mp$, $W^\pm H^\mp$ in the final one become
more efficient (with a total contribution to the effective cross
section of about $14$ to $21\%$ as $A_0/\Mg$ decreases from 0 to
-2.55) and so coannihilation is strengthened and $m_{\rm LSP}$'s
larger than in the $A_0/\Mg>0$ case are allowed. The overall
maximal $\Mg\simeq1495.4~\GeV$ or $\mx\simeq677~\GeV$ is
encountered at $A_0/\Mg\simeq-0.8$. On the other hand, for
$-2.55\lesssim A_0/\Mg\lesssim0.7$ [$0.7\lesssim A_0/\Mg
\lesssim3.21$] the lower bound on $\Mg$ or $\mx$ is derived
from the bound in Eq.~(\ref{bmmb}) [lower bound in \Eref{btnb}].
The overall allowed lowest $\Mg\simeq771.22~\GeV$ or
$\mx\simeq341~\GeV$ is encountered at $A_0/\Mg\simeq0.7$.
Let us remark that the more stringent upper bound on
$\Mg$ from the lower bound in \Eref{g2b} is not satisfied in
the allowed region of our model, since there is no common
region between the horizontally and the vertically hatched areas
for any $A_0/\Mg$. However, for $0\lesssim A_0/\Mg\lesssim1$,
these areas are quite close to each other. Note that
increasing $\Dst$ within its
allowed range $0-0.025$ does not alter the boundaries of the
various constraints in any essential way, except the solid line
which is displaced to the left so that the allowed area shrinks
considerably.
The deviation from YU can be estimated by defining \cite{nova}
the relative splittings $\delta h_{b}$ and $\delta h_{\tau}$ at
$M_{\rm GUT}$ through the relations:
\beq \delta h_{b}\equiv\frac{h_{b}-h_t}{h_t}=-\frac{2c}{1+c}=
-\delta h_{\tau}\equiv\frac{h_t-h_{\tau}}{h_t}\cdot\eeq
In the allowed (horizontally hatched) area of \Fref{AMgx}, the
ranges of the parameters $c,~\delta h_{\tau},~\delta h_{b}$, and
$\tan\beta$ are
\bea \nonumber 0.149\lesssim c\lesssim0.168,\\ \nonumber
0.26\lesssim\delta h_{\tau}=-\delta h_b \lesssim0.29,\\
56.3\lesssim \tan\beta\lesssim 57.7. \eea
Let us underline that, although the required deviation from YU
is not so small, the restrictions from YU are not completely lost
since $\tan\beta$ remains large -- close to 60 -- and the
deviation from YU is generated in a GUT-inspired well-motivated
way.
Taking into account the results depicted in \Fref{AMgx}, we can
make predictions for the sparticle and the Higgs boson spectrum
of our model, which may be observable at the LHC. In
\Tref{spectrum}, we list the model input and output parameters,
the masses in $\GeV$ of the sparticles -- neutralinos
$\tilde\chi$, $\tilde\chi_2^{0}$, $\tilde{\chi}_{3}^{0}$,
$\tilde{\chi}_{4}^{0}$, charginos $\tilde{\chi}_{1}^{\pm}$,
$\tilde{\chi}_{2}^{\pm}$, gluinos $\tilde{g}$, squarks
$\tilde{t}_1$, $\tilde{t}_2$, $\tilde{b}_1$, $\tilde{b}_2$,
$\tilde{u}_{L}$, $\tilde{u}_{R}$, $\tilde{d}_{L}$,
$\tilde{d}_{R}$, and sleptons $\tilde\tau_1$, $\tilde\tau_2$,
$\tilde\nu_\tau$, $\tilde{e}_L$, $\tilde{e}_R$, $\tilde{\nu}_{e}$
-- and the Higgs bosons ($h$, $H$, $H^\pm$, $A$), and the values
of the various low energy observables for $A_0/\Mg=0$, $\pm1$,
and $-2$ and for the lowest possible $\Mg$ in each case adjusting
$\Dst$ so as $\Omx\simeq 0.11$. Note that we consider the squarks
and sleptons of the two first generations as degenerate. From the
values of the various observable quantities, it is easy to
verify that all the relevant constraints are met. We also included
in \Tref{spectrum} predictions for the possible direct detection
of the LSP using central values for the hadronic inputs
$f_{{\rm T}q}^p$ or $\Delta_{q}^{p}$ -- see \Sref{det}.
\begin{table}[!t]
\caption{Input and output parameters, masses of the sparticles and
Higgs bosons, and values of the low energy observables of our
model for four values of $A_0/\Mg$. Recall that
$1~\pb\simeq2.6\times10^{-9}~\GeV^{-2}$.} \vspace*{1.mm}
\begin{tabular}{c@{\hspace{0.1cm}}c@{\hspace{0.3cm}}c@{\hspace{0.3cm}}c@{\hspace{0.3cm}}c}
\toprule \multicolumn{5}{c}{Input parameters}\\\colrule
$A_0/\Mg$ &$0$ &$1$&$-1$ &$-2$ \\
$c$ & $0.161$ &$156$&$0.165$ &$0.168$\\
$\Mg/\GeV$ & $825.7$ &$776.06$&$927.25$ &$1041.8$ \\
$m_0/\GeV$ &$665.4$ &$687.5$&$943.1$&$1466.8$ \\ \colrule
\multicolumn{5}{c}{Output parameters}\\\colrule
$\tan\beta$ & $57$ & $56.8$ & $57.4$ & $57.7$\\
$h_t(M_{\rm GUT})$ & $0.58$ & $0.58$ & $0.58$ & $0.58$\\
$100\delta h_\tau(M_{\rm GUT})$ & $27.7$ & $26.9$ & $28.3$ & $28.7$\\
$\mu/\GeV$ & $925.8$ & $804$ & $1170$ & $1505$\\
$\Dst (\%)$ & $2.46$ & $2.45$ & $2.13$ & $1.52$\\
\colrule
\multicolumn{5}{c}{Masses in ${\rm GeV}$ of sparticles and
Higgs bosons}\\\colrule
$\tilde\chi$& $365.7$ &$342.7$ &$413.2$ &$467.5$\\
$\tilde\chi_2^{0}$ &$705$&$656$ &$802$ &$909$\\
$\tilde{\chi}_{3}^{0}$ &$927$&$807$ &$1170$ &$1502$\\
$\tilde{\chi}_{4}^{0}$ &$940$ &$827$ &$1177$ &$1506$\\
$\tilde{\chi}_{1}^{\pm}$ &$940$ &$827$&$1177$ &$1506$\\
$\tilde{\chi}_{2}^{\pm}$ & $705$ &$656$ &$802$ &$909$ \\
$\tilde{g}$&$1916$&$1813$&$2145$&$2412$ \\ \colrule
$\tilde{t}_1$&$1585$&$1530$&$1752$&$1980$ \\
$\tilde{t}_2$ &$1383$ &$1352$ &$1506$&$1666$\\
$\tilde{b}_1$ &$1578$ &$1526$ &$1752$&$2008$\\
$\tilde{b}_2$ &$1498$ &$1454$&$1670$&$1916$ \\
$\tilde{u}_{L}$&$1052$&$1762$ &$2134$&$2585$ \\
$\tilde{u}_{R}$ &$1011$ &$1694$ &$2054$&$2503$ \\
$\tilde{d}_{L}$& $1055$ &$1764$ &$2135$ & $2586$\\
$\tilde{d}_{R}$&$1006$&$1764$&$2045$&$2494$\\\colrule
$\tilde\tau_1$&$777$&$754$&$956$&$1283$\\
$\tilde\tau_2$& $374.7$&$351.1$&$422$&$474.6$\\
$\tilde\nu_\tau$ &$756$&$738$&$939$&$1272$\\
$\tilde{e}_L$&$880$&$875$&$1142$&$1635$\\
$\tilde{e}_R$&$740$&$752$&$1010$&$1523$\\
$\tilde{\nu}_{e}$ &$876$ &$871$ &$1139$&$1633$\\\colrule
$h$ &$118.1$ &$117$ &$119.7$&$121.3$\\
$H$ &$584$ &$519$ &$668$&$747.6$\\
$H^{\pm}$ &$591$ &$527$ &$674$&$752.8$ \\
$A$ &$585$ & $520$&$669$ &$748$\\\colrule
\multicolumn{5}{c}{Low energy observables}\\\colrule
$10^4\bsg$ &$3.32$ &$3.41$ &$3.32$&$3.37$\\
$10^8\bmm$ &$5.76$ &$5.3$ &$5.78$&$5.8$\\
$\btn$ &$0.61$ &$0.52$ &$0.69$&$0.74$\\
$10^{10}\Dam$ &$10.6$&$11.6$ &$6.9$ &$3.9$\\\colrule
$\Omx$ &$0.11$&$0.11$&$0.11$&$0.11$\\[1mm]
$\ssi / 10^{-9} \pb$ &$0.536$&$1.1$ &$0.2$&$0.076$\\[1mm]
$\ssd / 10^{-7} \pb$ &$1.96$&$4.1$ &$0.6$&$0.2$\\[1mm]
\botrule
\end{tabular}
\label{spectrum}
\end{table}
\begin{figure}[t!]
\includegraphics[width=65mm,angle=-90]{mLSPh}
\caption{The allowed (horizontally hatched) region
in the $m_{\rm LSP}-m_h$ plane for $\Dst\simeq0$. We also depict the
curves corresponding to various values of $A_0/M_{1/2}$, indicated
on them. The dark points on the boundary correspond to
$A_0/M_{1/2}=-2.55$, -0.8, 3, 3.21, and 0.8 starting from the point
at the top of the allowed area and moving clockwise.}
\label{mLSPhx}
\end{figure}
For the lowest masses of the Higgs and sparticle spectrum ($m_h$
and $\mx$), we present even more explicit predictions in
\Fref{mLSPhx}, where we depict the allowed $m_h$'s versus $\mx$
for $\Dst\simeq0$ and $A_0/\Mg=0$, $\pm1$, and $\pm2$. As can be
seen from \Fref{AMgx},
the lower limits on the solid lines for $A_0/\Mg=0$, $-1$, and $-2$
[$A_0/\Mg=1$ and $2$] are found from the bound in \Eref{bmmb}
[lower bound in \Eref{btnb}] -- see also Table I. On the other
hand, the upper limits of the solid lines for $\AMg=0$, $1$,
and $2$ [$\AMg=-1$ and $-2$] are found from the bound in
\Eref{cdmb} [lower bound in \Eref{g2btau}]. The approximate
overall allowed area in the $\mx-m_h$ plane is hatched. Shown
are also the boundary points of this region at $\AMg\simeq-2.55$,
$-0.8$, $3$, $3.21$, and $0.7$ starting from the point at the
top of the allowed area and moving clockwise.
As one can see from \Fref{mLSPhx}, $m_h$ increases with $\mx$
and as $A_0$ decreases. Since the maximum allowed $\mx$ from
the bound in \Eref{cdmb} or the lower bound in \Eref{g2btau} is
achieved at $\Dst\simeq0$ for given $A_0$, we conclude that the
maximum
possible allowed $m_h$ can be obtained for $\Dst\simeq0$. On
the other hand, the minimum possible allowed $m_h$ practically
coincides with its value for $\Dst\simeq0$ since variation of
$\Dst$ within the values allowed by \Eref{cdmb} causes minor
modifications of $m_h$ for fixed $\Mg$. For $A_0=0$, we find
$826.4\lesssim\Mg/\GeV\lesssim1348.9$ or
$365.9\lesssim\mx/\GeV\lesssim607.4$ and $118.1\lesssim m_h/
\GeV\lesssim120.6$. The overall minimum [maximum] $m_h$ is
$117.03$ [$122.2$] obtained at
$A_0/\Mg\simeq1$ [$A_0/\Mg\simeq-2.55$] for
$\Mg=776.6~\GeV$ [$\Mg=1106.6~\GeV$] or $\mx\simeq343.1~\GeV$
[$\mx\simeq498.3~\GeV$].
\begin{figure*}[!tb]
\centering
\includegraphics[width=65mm,angle=-90]{SI}
\includegraphics[width=65mm,angle=-90]{SD}
\caption{The SI and SD $\tilde\chi-p$ cross sections
$\ssi$ and $\ssd$, respectively, versus $m_{\rm LSP}$ for various
$\AMg$'s indicated in the graphs. The bold solid lines in the
left panel are derived by fixing $\Omega_{\rm LSP}h^2$ and
$f_{{{\rm T}q}}^{p}$ to their central values
in Eqs.~(\ref{cdmba}) and (\ref{rgis4})-(\ref{rgis6}), whereas
the hatched bands in both panels by allowing the hadronic inputs
$f_{{{\rm T}q}}^{p}$ or $\Delta_{q}^{p}$ to vary in their ranges
in Eqs.~(\ref{rgis4})-(\ref{rgis6}) or
(\ref{Dqp1})-(\ref{Dqp3}). The
present and planned sensitivity limits of the various experimental
projects are also depicted by dashed and dotted lines,
respectively.}
\label{detx}
\end{figure*}
\section{CDM Direct Detection} \label{det}
As we have shown, our model possesses a limited and well-defined
range of parameters allowed by all the relevant cosmological and
phenomenological constraints. It would be, thus, interesting to
investigate whether the predicted LSPs in the universe could be
detected in the current or planned direct CDM searches
\cite{Cdms2,Xenon,icecube}, which look for evidence of
weakly-interacting massive particles through scattering on nuclei.
The quantities which are conventionally used in the recent
literature for comparing experimental results and theoretical
predictions are the spin-independent (SI) and spin-dependent (SD)
lightest neutralino-proton ($\tilde\chi-p$) scattering cross
sections $\ssi$ and $\ssd$, respectively.
These quantities are calculated by employing the relevant routine
of the {\tt micrOMEGAs} package \cite{Detmicro} based on the full
one-loop treatment of Ref.~\cite{drees}, which happens to agree
with the tree-level approximation \cite{Detellis} for the values
of the SUSY parameters encountered in our model. Following the
approach of Refs.~\cite{Detmicro,Detellis}, we calculate the
scalar form factors for light quarks in the proton
$f^p_{{{\rm T}_q}}$ (with $q=u,d,s$), needed for the calculation
of $\ssi$, via the formulas:
\beqs\bea && \label{rgis1} f_{{\rm T}d}^p= \frac{2\spn}{m_p\lf1 + \frac{m_u}
{m_d} \rg\lf1 + \frac{B_u}{B_d}\rg},\\
&& \label{rgis2} f_{{\rm T}u}^p=\frac{m_u}{m_d}\frac{B_u}{B_d}f_{{\rm
T}_d}^p,\\
&& f_{{\rm T}s}^p=\frac{y\spn}{m_p\lf1 + \frac{m_u}{m_d}\rg}
\frac{m_s}{m_d}.\label{rgis3}\eea\eeqs
Here we take for the mass of the proton $m_p=0.939~\GeV$ and for
the light quark mass ratios
\beq \frac{m_u}{m_d}=0.553\pm0.043~~\mbox{and}~~\frac{m_s}{
m_d}=18.9\pm0.8,
\eeq
whereas the ratio $B_u/B_d$ is evaluated from
\beq \frac{B_u}{B_d}=\frac{2z-(z-1)y}{2+(z-1)y}\eeq
with $z=1.49$. The uncertainties in $z$ and the quark mass ratios
are negligible compared to the uncertainties in the pion-nucleon
sigma term $\spn$ and the fractional strange quark content of the
nucleon $y$, for which recent lattice simulations suggest
\cite{lattice} that, at $68\%$ c.l.,
\beq \spn = 53^{+21.1}_{-7.3}~{\rm MeV} ~~\mbox{and}~~ y =
0.030^{+0.017}_{-0.018}.\eeq
Taking into account the relations above, we find the
following 1$\sigma$ ranges for the $f_{{\rm T}q}^p$'s:
\beqs\bea && \label{rgis4} f_{{\rm T}u}^p=0.024^{+0.0095}_{-0.0032},\\
&& \label{rgis5} f_{{\rm T}d}^p=0.029_{-0.0042}^{+0.012},\\
&& f_{{\rm T}s}^p=0.021^{+0.025}_{-0.013}. \label{rgis6}\eea\eeqs
Note that $f_{{\rm T}s}^p$ turns out to be considerably smaller
than its older value -- cf. \cref{nova} -- reducing thereby the
extracted $\ssi$.
For the calculation of $\ssd$, the relevant
axial-vector form factors for light quarks in the proton
$\Delta_q^{p}$ (with $q=u,d,s$) are taken to lie in their
1$\sigma$ ranges \cite{Dqpc}:
\beqs\begin{eqnarray}
&& \label{Dqp1} \Delta_{u}^{p}=+0.842\pm0.012,\\
&& \label{Dqp2} \Delta_{d}^{p}=-0.427\pm0.013, \\ &&
\Delta_{s}^{p}=-0.085\pm0.018.\label{Dqp3}
\end{eqnarray}\eeqs
Taking the central value of $\Omx$ in Eq.~(\ref{cdmba}), but
allowing the hadronic inputs $f_{{\rm T}q}^{p}$ or $\Delta_{q}^{p}$
to vary within their ranges in Eqs.~(\ref{rgis4})-(\ref{rgis6})
or (\ref{Dqp1})-(\ref{Dqp3}),
respectively, we derive the dark gray, gray, and light gray hatched
bands in the $\mx-\ssi$ or $\mx-\ssd$ plane corresponding to
$\AMg=0$, $0.7$, and $-0.8$, respectively -- Fig.~\ref{detx}. The
selected values of $\AMg$ allow us to cover the whole range of the
allowed $\mx$'s in our model -- cf. \Fref{mLSPhx}. The bold solid
lines in the middle of the bands of the left panel in Fig.~\ref{detx}
correspond to the central values of the $f_{{\rm T}q}^{p}$'s.
We used the central value of $\Omx$ since, as it turns out, for fixed
$\mx$, $\ssi$ and $\ssd$ are almost insensitive to the variation of
$\Omx$ within the range of Eq.~(\ref{cdmba}) -- or, equivalently, to
the required variation of $\Dst$. The width of the bands is almost
exclusively due to the variation of $f_{{\rm T}q}^{p}$ or
$\Delta_{q}^{p}$. As a consequence, the bands in the $\mx-\ssi$
plane are wider than those in the $\mx-\ssd$ plane due to the larger
uncertainties involved in the determination of the
$f_{{\rm T}q}^{p}$'s. In the left panel of \Fref{detx}, we
depict by a dashed green line the recently announced \cite{Xenon}
upper bound on $\ssi$ from XENON which is slightly lower than the
one from CDMSII \cite{Cdms2}, which is not included in the panel.
We also draw with dotted red lines the projected
sensitivities of SuperCDMS at Soudan and SNOLAB \cite{dmtools}
-- from top to bottom. Our model can be ultimately tested by
XENON-1 ton, whose planned sensitivity \cite{dmtools}, depicted by
a green dotted line, covers almost the whole available parameter
space of the model. On the contrary, as can be easily deduced from
the right panel of \Fref{detx}, $\ssd$ in our model lies well below
the sensitivity of IceCube \cite{icecube} (assuming neutralino
annihilation into
$W^+W^-$) -- depicted by a dashed red line -- and the expected
limit from the large DMTPC detector \cite{dmtools}, denoted by a
dotted green line. Therefore, the LSPs predicted by our model can
be detectable in the future projects which will release data on
$\ssi$. Furthermore, the overall upper bound on $m_{\rm LSP}$
found in \Sref{results} -- $\mx\lesssim677~\GeV$ -- implies
lower bounds on $\ssi$ and $\ssd$. Namely,
\beq \ssi\gtrsim
4.3~(3.6)\times10^{-11}~\pb~~\mbox{and}~~\ssd\gtrsim
1.5~(1.4)\times10^{-8}~\pb,
\label{sgmxp}\eeq
where the bounds in parentheses are derived by allowing
the $f_{{\rm T}q}^{p}$'s and $\Delta_q^p$'s to vary within
1$\sigma$. Needless to say that the low values of $\ssi$ and
$\ssd$ obtained here are due to the fact that we use universal
`asymptotic' gaugino masses and, thus, the LSP is an almost
pure bino, as in every version of the CMSSM.
\section{Conclusions} \label{con}
We performed a revised scan of the parameter space of the
CMSSM with $\mu>0$ applying a suitable Yukawa
quasi-unification condition predicted by the SUSY GUT model
of Ref.~\cite{qcdm}, which has been constructed in order
to remedy the $b$-quark mass problem arising from exact
Yukawa unification and universal boundary conditions. We
took into account updated constraints from collider and
cosmological data. These constraints originate from the
CDM abundance in the universe, $B$ physics
($b \rightarrow s\gamma$, $B_s\to \mu^+\mu^-$, and
$B_u\to\tau\nu$), $\delta\alpha_\mu$, and $m_h$. We showed
that our model possesses a limited but not unnaturally
small range of parameters which is consistent with all
these requirements. Namely, the constraint arising from CDM
considerations can be satisfied simultaneously with all the
other constraints thanks to the drastic reduction of the
LSP relic density by neutralino-stau coannihilations.
For $A_0=0$, we find $365.9\lesssim\mx/\GeV\lesssim607.4$
and $118.1\lesssim m_h/{\rm GeV}\lesssim120.6$, whereas, in the
overall allowed region of our model, we have
$-2.55\lesssim A_0/\Mg\lesssim3.21$ with
$341\lesssim\mx/\GeV\lesssim677$ and
$117\lesssim m_h/\GeV\lesssim 122.2$. Almost all the allowed
parameter space of our model will be accessible in future CDM
direct experiments which look for SI cross sections between
neutralino and proton.
It is worth mentioning that the present investigation constitutes
an improved version of the analysis in Ref.~\cite{qcdm}. The
consideration of the constraints from $\bmm$ and $\btn$, the
updated experimental results for all the other constraints, and
the evaluation of the particle spectrum employing {\tt SOFTSUSY}
are the main improvements in this work. The results obtained are
significantly different from the previous ones.
\section*{Note Added} While this work was under completion, we
became aware of \cref{Shafi11}, where the CMSSM with Yukawa
quasi-unification is also analyzed. Although our results as
regards $\tan\beta$, $c$, $\ssi$, and $\ssd$ are similar, there
are large discrepancies as regards the CMSSM mass parameters and,
consequently, the mass spectrum. In particular, the ratio
$(m_A-2\mx)/2\mx$, which determines the strength of the $A$-pole
effect in reducing $\Omx$, is not allowed to be lower than $0.2$
in our case and, thus, this effect is excluded. Indeed, the
portion of the parameter space allowed by \Eref{cdmb} due to
$A$-pole neutralino annihilations is excluded by the $B$-physics
constraints in our analysis -- contrary to the findings of
\cref{Shafi11}. These discrepancies can be possibly attributed to
the fact that we use different numerical routines for the
calculation of both the SUSY spectra and the low energy
observables. It is well known \cite{comparisons2} that the
predictions of the various SUSY spectrum calculators do not
coincide in the large $\tan\beta$ regime. Our results as regards
the implementation of the electroweak symmetry breaking are
consistent with our initial investigation in \cref{qcdm}.
\acknowledgments We would like to thank G.~B\'{e}langer,
M.E.~G\'omez, S.~Heinemeyer, A.~Pukhov, and P.~Slavich for
enlightening correspondence as well as I.~Gogoladze and Q.~Shafi
for useful discussions related to \cref{Shafi11}. This work was
supported by the European Union under the Marie Curie Initial
Training Network `UNILHC' PITN-GA-2009-237920 and also by the
European Union (European Social Fund - ESF) and Greek national
funds through the Operational Program ``Education and Lifelong
Learning'' of the National Strategic Reference Framework (NSRF) -
Research Funding Program: Heracleitus II. Investing in knowledge
society through the European Social Fund.
\def\ijmp#1#2#3{{Int. Jour. Mod. Phys.}
{\bf #1},~#3~(#2)}
\def\plb#1#2#3{{Phys. Lett. B }{\bf #1},~#3~(#2)}
\def\zpc#1#2#3{{Z. Phys. C }{\bf #1},~#3~(#2)}
\def\prl#1#2#3{{Phys. Rev. Lett.}
{\bf #1},~#3~(#2)}
\def\rmp#1#2#3{{Rev. Mod. Phys.}
{\bf #1},~#3~(#2)}
\def\prep#1#2#3{{Phys. Rep. }{\bf #1},~#3~(#2)}
\def\prd#1#2#3{{Phys. Rev. D }{\bf #1},~#3~(#2)}
\def\npb#1#2#3{{Nucl. Phys. }{\bf B#1},~#3~(#2)}
\def\npps#1#2#3{{Nucl. Phys. B (Proc. Sup.)}
{\bf #1},~#3~(#2)}
\def\mpl#1#2#3{{Mod. Phys. Lett.}
{\bf #1},~#3~(#2)}
\def\arnps#1#2#3{{Annu. Rev. Nucl. Part. Sci.}
{\bf #1},~#3~(#2)}
\def\sjnp#1#2#3{{Sov. J. Nucl. Phys.}
{\bf #1},~#3~(#2)}
\def\jetp#1#2#3{{JETP Lett. }{\bf #1},~#3~(#2)}
\def\app#1#2#3{{Acta Phys. Polon.}
{\bf #1},~#3~(#2)}
\def\rnc#1#2#3{{Riv. Nuovo Cim.}
{\bf #1},~#3~(#2)}
\def\ap#1#2#3{{Ann. Phys. }{\bf #1},~#3~(#2)}
\def\ptp#1#2#3{{Prog. Theor. Phys.}
{\bf #1},~#3~(#2)}
\def\apjl#1#2#3{{Astrophys. J. Lett.}
{\bf #1},~#3~(#2)}
\def\apjs#1#2#3{{Astrophys. J. Suppl.}
{\bf #1},~#3~(#2)}
\def\n#1#2#3{{Nature }{\bf #1},~#3~(#2)}
\def\apj#1#2#3{{Astrophys. J.}
{\bf #1},~#3~(#2)}
\def\anj#1#2#3{{Astron. J. }{\bf #1},~#3~(#2)}
\def\mnras#1#2#3{{MNRAS }{\bf #1},~#3~(#2)}
\def\grg#1#2#3{{Gen. Rel. Grav.}
{\bf #1},~#3~(#2)}
\def\s#1#2#3{{Science }{\bf #1},~#3~(#2)}
\def\baas#1#2#3{{Bull. Am. Astron. Soc.}
{\bf #1},~#3~(#2)}
\def\ibid#1#2#3{{\it ibid. }{\bf #1},~#3~(#2)}
\def\cpc#1#2#3{{Comput. Phys. Commun.}
{\bf #1},~#3~(#2)}
\def\astp#1#2#3{{Astropart. Phys.}
{\bf #1},~#3~(#2)}
\def\epjc#1#2#3{{Eur. Phys. J. C}
{\bf #1},~#3~(#2)}
\def\nima#1#2#3{{Nucl. Instrum. Meth. A}
{\bf #1},~#3~(#2)}
\def\jhep#1#2#3{{J. High Energy Phys.}
{\bf #1},~#3~(#2)}
\def\jcap#1#2#3{{J. Cosmol. Astropart. Phys.}
{\bf #1},~#3~(#2)}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 8,942 |
Antigonus III Doson () was king of Macedon from 229 BC to 221 BC. He was a member of the Antigonid dynasty.
Family background
Antigonus III Doson was a half-cousin of his predecessor, Demetrius II Aetolicus. Doson's father was Demetrius the Fair (briefly king of Cyrene), the son of Demetrius Poliorcetes and his third wife, Ptolemaïs, daughter of Ptolemy I Soter and Eurydice, daughter of Antipater. As such, Demetrius the Fair was, on his father's side, a younger half-brother of Demetrius II's father, Antigonus II Gonatas, the son of Poliorcetes by his first wife, Phila, another of Antipater's daughters; as well as a nephew of both Ptolemy Keraunos and Meleager on his mother's side. According to Eusebius, Doson's own mother was a Thessalian noblewoman, Olympias, daughter of Pauliclitus of Larissa. Antigonus also had a brother named Echecrates, whose son, named Antigonus after Doson himself, was put to death by Perseus on the latter's accession to the throne of Macedon.
Doson's father, Demetrius the Fair, died sometime around 250 BC, as a result of events that occurred after being summoned from Macedonia to Cyrene to marry Berenice II, the daughter and heir of Magas of Cyrene. Rather than contenting himself with his young bride, Demetrius openly became the lover of her powerful mother, Apama II. So the jealous bride took her revenge by having him assassinated. It is unclear whether Doson's mother had died before this time.
Antigonus' by-name, Doson, is Greek for "going to give." The meaning of this is uncertain. According to Plutarch it "implied that he was given to promising but did not perform his engagements", though even the exact meaning of this is unclear.
Regent of Macedonia
When Demetrius II died in battle in 229 BC, his son and would-be successor, the later Philip V, was only nine years old. According to Plutarch, both the Macedonian army and nobility thought the political situation too volatile to wait for Philip V to mature enough to assume command. As a consequence, the Macedonian nobility turned to Doson, who was subsequently made regent of the kingdom and then married his predecessor's widow and the mother of Philip, Chryseis. However, it was only after Doson demonstrated his leadership abilities by succeeding (where his cousin Demetrius had failed) in defeating the Dardanii invaders and also in putting down a rebellion by the Thessalians, and showing his rule to be generally moderate and good, that he was given the title of king. Unlike his Antigonid ancestors, he had no viable rivals to challenge his right to rule. Yet, even as king he apparently envisioned himself as caretaker for his cousin's son, Philip V.
King of Macedonia
As king, Antigonus III proved to be as much a master of tactical diplomacy as of military strategy. In less than a decade of rule he not only secured the borders of his nation, he also re-established Macedon as the dominant power in the region. Unlike previous Macedonian rulers who attempted direct dominion over their fiercely independent neighbours to the West and South, he formed alliances with Epirus and the Achaean League. When Sparta, under Cleomenes III, attempted to establish hegemony over the whole Peloponnese, Aratus of Sicyon - long the leader of Greek opposition to Macedonian domination - invited Antigonus to intervene (226 BC). Establishing his base on the heights above Corinth, Antigonus reconstituted a broad-based Hellenic league (224 BC) under his leadership before launching his attack on Sparta. The Spartan forces, outmatched by the larger, better equipped Macedonian army, were so overwhelmed in the Battle of Sellasia (222 BC) that Cleomenes only managed to escape with a few horsemen, and ultimately had to seek refuge in Egypt. However, in a magnanimous gesture, Antigonus restrained his soldiers from plundering Sparta, saying it was Cleomenes, not Sparta, that was his enemy.
Antigonus did not long survive this victory. For, while his forces were campaigning in the southern Peloponnese, Illyrians invaded Macedonia from the north. Antigonus had to rush north to repel this new threat. On his way, Antigonus passed through Tegea and Argos, his arrival at the latter coinciding with the beginning of the Nemean Games, where he was honoured by the Achaean League and various other cities. His death occurred soon after, when he returned to Macedon and engaged the Illyrian army; for though Macedonian forces were once again victorious, the commander became sick during the battle (possibly though not necessarily as a result of a ruptured blood vessel) and died.
Ancestry
References
External links
Antigonus III Doson entry in historical sourcebook by Mahlon H. Smith
|-
| width="30%" align="center" | Preceded by:Demetrius II
| width="40%" align="center" | Kings of Macedon229–221 BC
| width="30%" align="center" | Succeeded by:Philip V
263 BC births
221 BC deaths
3rd-century BC Macedonian monarchs
Ancient Macedonian monarchs
3rd-century BC rulers
Ancient Macedonian monarchs killed in battle
3rd-century BC Greek people
Antigonid dynasty | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,509 |
Q: How to add a legend to this histogram? I created a histogram:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
% matplotlib inline
#import csv
df = pd.read_csv('tmdb-movies.csv')
df_star_wars = df[df['original_title'].str.contains("Star Wars", na=False)]
df_star_trek = df[df['original_title'].str.contains("Star Trek", na=False)]
avg_starwars = df_star_wars ['vote_average'].hist(figsize = (8,8))
avg_startrek = df_star_trek ['vote_average'].hist(figsize = (8,8))
plt.xlabel("Bins_Vote", fontsize=16)
plt.ylabel("Vote_AVG", fontsize=16)
plt.xticks(fontsize=14)
plt.yticks(fontsize=14)
avg_starwars.legend()
avg_startrek.legend()
My problem is last two rows: I want to add a legend, but it doesn't work. Do you have any ideas?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 6,779 |
<?php
session_start();
if(isset($_SESSION['start']))
{
header("Location: account.php");
}
?>
<!Doctype html>
<html>
<head>
<title>Demo - Page</title>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<script type="text/javascript" src="js/jquery-3.0.0.min.js"></script>
<link rel="stylesheet" href="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/css/bootstrap.min.css">
<!-- Latest compiled JavaScript -->
<script src="http://maxcdn.bootstrapcdn.com/bootstrap/3.3.7/js/bootstrap.min.js"></script>
<style type="text/css">
.navbar {
border-radius: 0;
}
.heading {
padding: 10px;
}
input {
border-radius: 0px;
}
</style>
</head>
<body>
<!-- Navbar -->
<nav class="navbar navbar-inverse">
<div class="container-fluid">
<div class="navbar-header">
<button type="button" class="navbar-toggle" data-toggle="collapse" data-target="#myNavbar">
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<a class="navbar-brand" href="#">Registration-Module</a>
</div>
<div class="collapse navbar-collapse" id="myNavbar">
<ul class="nav navbar-nav">
<li class="active"><a href="#">Home</a></li>
</ul>
<ul class="nav navbar-nav navbar-right">
<li><a href="#Register"><span class="glyphicon glyphicon-user"></span> Sign Up</a></li>
<li><a href="#Login"><span class="glyphicon glyphicon-log-in"></span> Login</a></li>
</ul>
</div>
</div>
</nav>
<!-- Main Body -->
<div class="container"><br><br>
<div class="row">
<!-- Login -->
<div class="col-sm-4 col-sm-offset-1">
<div class="row">
<div class="col-sm-12 text-center">
<h2 class="heading">Login</h2>
</div>
<hr>
</div>
<form>
<div class="form-group">
<label for="login" id="loginLabel">Email or Username</label>
<input type="text" name="login" id="login" class="form-control" placeholder="Email or Username">
</div>
<div class="form-group">
<label for="passLogin" id="passLabelLogin">Password</label>
<input type="password" name="passLogin" id="passLogin" class="form-control" placeholder="Password">
</div>
<button type="button" class="btn btn-success" onclick="loginCheck()" value="Login">Submit</button>
</form>
</div>
<!-- Register -->
<div class="col-sm-4 col-sm-offset-2">
<div class="row">
<div class="col-sm-12 text-center">
<h2>Register</h2>
</div>
<hr>
</div>
<form>
<div class="form-group">
<label for="name" id="nameLabel">Your Name</label>
<input type="text" name="name" class="form-control" id="name" placeholder="Name">
</div>
<div class="form-group">
<label for="email" id="emailLabel">Email</label>
<input type="email" name="email" id="email" class="form-control" placeholder="Email id">
</div>
<div class="form-group">
<label id="userLabel">Username</label>
<input type="text" name="username" id="username" class="form-control" placeholder="Username">
</div>
<div class="form-group">
<label id="mobLabel">Mobile No.</label>
<input type="text" name="mob" id="mob" class="form-control" placeholder="99******00">
</div>
<div class="form-group">
<label for="passRegister" id="passLabelRegister">Password</label>
<input type="password" name="passRegister" id="passRegister" class="form-control" class="form-control" placeholder="Password">
</div>
<button type="button" class="btn btn-success" onclick="registerCheck()" value="Register">Register</button>
</form>
</div>
</div>
<br><br><br>
</div>
<!-- Modal -->
<div class="modal fade" id="myModal" role="dialog">
<div class="modal-dialog">
<!-- Modal content-->
<div class="modal-content">
<div class="modal-header">
<button type="button" class="close" data-dismiss="modal">×</button>
<h4 class="modal-title">Error</h4>
</div>
<div class="modal-body">
<p>Fill all the details that are required.</p>
</div>
<div class="modal-footer">
<button type="button" class="btn btn-default" data-dismiss="modal">Close</button>
</div>
</div>
</div>
</div>
<!-- Scripts -->
<script type="text/javascript" src="js/login_validate.js"></script>
<script type="text/javascript" src="js/register_validate.js"></script>
</body>
</html> | {
"redpajama_set_name": "RedPajamaGithub"
} | 789 |
\section{Introduction}
Large pre-trained language models, such as BERT \citep{devlin-etal-2019-bert}, GPT-3 \citep{gpt3}, T5 \citep{t5}, REALM \citep{realm} and ERNIE \citep{sun2021ernie} have become the state-of-the-art technology for many tasks. They are commonly pre-trained using unstructured text corpora, on tasks such as next word prediction, next sentence prediction (NSP) or masked language modelling (MLM). Especially for T5, self-supervised learning on unlabelled text corpus with MLM has been a common pre-training recipe \cite{roberts-etal-2020-much}. This is normally followed by a fine-tuning step on the task of interest \cite{ruder-etal-2019-transfer}, although large language models have also proved useful without this task-specific finetuning \cite{gpt3}.
Beyond the capacity of contextual understanding, human-level language understanding pivots on the knowledge about the world. The world knowledge is often expressed as factual triples \cite[c.f.][]{ji2020representation}, in the form of (\textit{subject entity}, \textit{relation}, \textit{object entity}). A knowledge graph (KG) defined by a set of factual triples consists of the subjects and objects as vertices/nodes, and the relations forming the edges connecting them. Most of the large scale KGs \cite[e.g. Wikidata,][]{wikidata} are stored in triple format.
LLMs demonstrate some capacity of learning world knowledge from the natural text corpus \cite{roberts-etal-2020-much}, but it is unclear to what degree they are also able to learn and memorize new knowledge directly from structured KG triples, or from text describing them explicitly.
In order to infuse knowledge into a LLM, one option is to generate a textual version of the knowledge base, and apply the standard training objectives, e.g. MLM. This is unfortunately highly nontrivial. One can either align sentences with KG triples, as done in ERNIE \cite{sun2021ernie}, or generate sentences from triples, as done in KELM \cite{agarwal-etal-2021-knowledge}. These approaches are unfortunately hard to port to knowledge graphs with different schemas. These processes are also lossy in that not every triple can be aligned or produce a valid sentence, and there is not a good understanding whether this can introduce unnecessary selection biases on top of biases existing in the original KG.
In this work, we propose a method of \textbf{Knowledge Infusion for Large Language Models (SKILL)}, where LLMs directly learns from knowledge triples. Experiment results shows the checkpoints trained with proposed method on Wikidata KG outperform the T5 baselines on four standard closed-book question-answering (QA) tasks. With a smaller KG, WikiMovies, the proposed method gain $3\times$ exact match score performance improvement on MetaQA task. The models learning directly from knowledge triples performs competitively with the ones with the aligned natural sentences that contain the same amount of knowledge. Being able to learn directly from knowledge triples enables easy addition of structured knowledge into language modeling pre-training.
\section{Related work}
Previous works that use knowledge graphs to enhance the quality of knowledge-intensive downstream tasks can be divided into two groups: using knowledge graphs at the inference time, and infusing knowledge into the model weights at the pre-training time. The proposed method falls in the latter group.
\paragraph{Explicit usage of knowledge graphs.}
A retrieval-augmented model is commonly used, in order to retrieve and apply the knowledge from external memories or sources. FILM \citep{verga-etal-2021-adaptable} and EaE \citep{fevry-etal-2020-entities} extend Transformer \citep{vaswani2017transformer} models with external entity (both FILM and EaE) and fact (FILM) memories. REALM \citep{realm} is pre-trained to perform reasoning over a large textual knowledge corpus on-the-fly during inference. UniK-QA \citep{oguz2020unik} combines the structured and unstructured information to improve the open-domain QA tasks with a retriever-reader framework. The main difference between the proposed method, SKILL, and retrieval-augmented models is that SKILL doesn't introduce retrieval system or external memories to the model, but it directly embeds knowledge into the model parameters, which introduces no extra cost at inference time.
\paragraph{Knowledge infusion.}
A common way of parameterized knowledge infusion is to map or convert structured knowledges into natural language text. ERNIE 3.0 \citep{sun2021ernie} trains a knowledge-enhanced model on a corpus combining triples and their aligned sentences, by randomly masking relation in a triple or words in a sentence. On the contrary, SKILL trains only on triples.
KnowBert \citep{peters-etal-2019-knowledge} incorporates knowledge from Wikipedia and WordNet \citep{miller1995wordnet} into a BERT model through entity embeddings with knowledge-attention and re-contextualization mechanism. BERT-MK \citep{he-etal-2020-bert} is a BERT-based model that integrates graph contextual knowledge of a medical KG, which demonstrates the utility of graph-level knowledge. These approaches requires entity linking and sentences contextualizing the knowledge graph information.
KG-FiD \citep{yu2021kg} extends the Fusion-in-Decoder model \citep{izacard-grave-2021-leveraging}, with a module that filters and re-ranks passages based on structural connections in knowledge graph between entities described in those passages. In contrast to the SKILL method that we propose, it requires the existence of natural text passages describing each knowledge graph entity, so Wikipedia corpus was used since it naturally provides articles that describe entities.
\citet{heinzerling-inui-2021-language} explored the ability of language models to memorize and understand information from knowledge graphs, but used natural language representation of triples based on predefined templates instead of structured representation. Usage of predefined templates significantly limits scalability and therefore only relatively small knowledge graphs were used, such as Google-RE\footnote{https://ai.googleblog.com/2013/04/50000-lessons-on-how-to-read-relation.html}.
In contrast to the new method presented in this paper, all of these approaches require an explicit mapping between the knowledge graph entities or facts and corresponding natural language sentences, which can limit applications to industry-scale knowledge graphs that don't have such a mapping.
\paragraph{Different goals of using knowledge graphs.}
Besides that, some papers embed knowledge into model weights but pursue different goals rather than improving performance on downstream tasks. COMET \citep{bosselut-etal-2019-comet} is most similar to our work and trains a commonsense-aware Transformer Language Model by learning to generate loosely structured commonsense descriptions in the natural language given the structured knowledge. Similar to us, it also uses KG triples in surface form as a source for training data, but in contrast to our research, the final goal of COMET is to generate new knowledge instead of utilizing existing ones. Another important difference is the scale: COMET uses Atomic \citep{sap2019atomic} and ConceptNet \citep{speer2017conceptnet} Knowledge Graphs that are much smaller than Wikidata \citep{wikidata}.
KELM \citep{agarwal-etal-2021-knowledge} fine-tunes a T5 model to convert KGs to synthetic natural language sentences to augment existing pre-training corpora. We build our research on top of it and use the KELM dataset to compare structured and natural language representations of knowledge.
\begin{table*}
\centering
\begin{adjustbox}{center}
{\footnotesize
\begin{tabular}{ccccc}
\hline
\textbf{Wikidata triple} & \textbf{KELM sentence} & \textbf{Wikidata input} & \textbf{KELM input} & \textbf{Target} \\ \hline
\makecell{("Pulp Fiction",\\ "award received",\\ "Palme d'Or")} & \makecell{Quentin Tarantino \\won the Palme d'Or in 1994\\ for Pulp Fiction.} & \makecell{Pulp Fiction,\\ award received,\\ {[}MASK{]}} & \makecell{Quentin Tarantino \\won the {[}MASK{]} in 1994\\ for Pulp Fiction.} & Palme d'Or \\ \hline
\end{tabular}}
\end{adjustbox}
\caption{
\label{table:inputs}
Example inputs for SKILL pre-training with Wikidata and KELM corpora.
}
\end{table*}
\section{Method}
\label{sec:method}
There are two components of knowledge infusion for LLMs (SKILL): the corpus and the training method. We introduce the method based on Wikidata KG, but it can be applied to any other KGs.
\paragraph{Training corpus.}
We use two corpora with different knowledge representations: Wikidata KG \cite{wikidata} in triple format, and KELM corpus\footnote{Data is available at https://github.com/google-research-datasets/KELM-corpus} \citep{agarwal-etal-2021-knowledge} as synthetic natural language sentences converted from Wikidata KG. The KELM corpus contains $15,628,486$ synthetic sentences. To ensure two corpora share the same knowledge, we take the snapshot of the Wikidata KG used to created the KELM corpus, which contains $35,697,715$ triples.
To prevent the degradation of model performance on natural language understanding, we mix the Wikidata corpus or KELM corpus with natural text from C4 \cite{t5}, $50:50$, for the knowledge infusion training data.
\paragraph{Training method.}
T5 \cite{t5} was trained through masked-language modelling with random span corruption on the C4 corpus. \citet{roberts-etal-2020-much} found that masking salient terms \cite{realm} in pre-training T5 models, instead of masking random token spans, could significantly improve the performance on downstream tasks, e.g. closed-book QA.
We apply salient span masking for unsupervised learning in our knowledge-infusing training. To mask the same amount of information is for both corpora, the following method is applied. For a knowledge triple, we mask either the subject or object entity. For a KELM sentence, we identify the aligned triple, with details in \Cref{sec:kelm-matching}, and mask the full spans corresponding to the subject or object in the triple. The \textit{relation} tokens are never masked, as there is no robust way to map the abstract relation in knowledge triples to natural language tokens in KELM sentences. Examples of the inputs for both corpora are in \Cref{table:inputs}.
\section{Experiments}
We assess SKILL by training and evaluating the knowledge infused models on closed-book QA tasks, where questions are provided without supporting context and external knowledge.
\subsection{Experiment Setup}
\paragraph{SKILL pre-training.}
We apply SKILL on three T5.1.1 pre-trained checkpoints\footnote{https://goo.gle/t5-checkpoints}, base, large, and XXL, with sizes of $\sim 250$M, $\sim 800$M and $\sim11$B parameters, respectively. For T5.1.1-base and -large, SKILL training is performed for $500$K steps with batch size $1024$, which translates to $\sim 7.17$ epochs on Wikidata KG and $\sim 16.38$ epochs in KELM sentences. For T5.1.1-XXL, the model is trained for $100$K steps to finish training in a feasible time.
As baseline we use pre-trained T5 checkpoints of the same size. To make sure that improvements come from knowledge infusion instead of from longer C4 pre-training, we use a second baseline by further training the T5 checkpoints on C4 for half of the aforementioned steps, to match the amount of C4 pre-training used in SKILL.
All the model variations are optimized by AdaFactor \cite{adafactor} with $10^{-3}$ learning rate and $0.1$ dropout rate, the same settings that were used for T5.
\paragraph{Fine-tuning on closed-book QA tasks.}
We evaluate the checkpoints by fine-tuning on the following QA benchmarks: FreebaseQA \citep{jiang-etal-2019-freebaseqa}, WikiHop \citep{welbl-etal-2018-constructing}, TriviaQA \citep{joshi-etal-2017-triviaqa} and NaturalQuestions \citep{kwiatkowski-etal-2019-natural}, with the aforementioned hyper-parameters for optimization and $128$ batch size. For the benchmarks without a \textit{test} split, we use the \textit{dev} split for test, and the last $10\%$ of \textit{train} as \textit{dev} split.
The Exact Match (EM) scores on the test sets are calculated after being fine-tuned for $50$K steps for T5.1.1-base and -large models, and $10$K steps for -XXL models. All models converged with no noticeable over-fitting according to the EM scores on validation sets.
\paragraph{Wikidata-answerable QA.}
\label{sec:wikidata-answerable-qa}
\begin{table*}[!ht]
\centering
\adjustbox{max width=\textwidth}{
\begin{tabular}{lcccccccccccc}
\hline
\textbf{Model} & \multicolumn{2}{c}{\textbf{FreebaseQA}} & \multicolumn{2}{c}{\textbf{WikiHop}} & \multicolumn{2}{c}{\textbf{TQA-matched}} & \multicolumn{2}{c}{\textbf{TQA}} & \multicolumn{2}{c}{\textbf{NQ-matched}} & \multicolumn{2}{c}{\textbf{NQ}} \\
& \multicolumn{1}{c}{\textbf{dev}} & \multicolumn{1}{c}{\textbf{test}} & \multicolumn{1}{c}{\textbf{dev}} & \multicolumn{1}{c}{\textbf{test}} & \multicolumn{1}{c}{\textbf{dev}} & \multicolumn{1}{c}{\textbf{test}} & \multicolumn{1}{c}{\textbf{dev}} & \multicolumn{1}{c}{\textbf{test}} & \multicolumn{1}{c}{\textbf{dev}} & \multicolumn{1}{c}{\textbf{test}} & \multicolumn{1}{c}{\textbf{dev}} & \multicolumn{1}{c}{\textbf{test}} \\ \hline
base & $25.24$ & $27.55$ & $19.09$ & $18.38$ & $31.24$ & $33.55$ & $22.64$ & $22.93$ & $36.64$ & $32.68$ & $25.04$ & $25.48$ \\
base + C4 & $26.19$ & $28.33$ & $19.57$ & $19.36$ & $32.9$ & $34.4$ & $24.54$ & $25.39$ & $36.98$ & $32.03$ & $\mathbf{25.88}$ & $25.84$ \\
base + WikiKG & $\mathbf{26.92}$ & $\mathbf{28.38}$ & $20.28$ & $\mathbf{20.22}$ & $\mathbf{34.21}$ & $35.08$ & $24.73$ & $\mathbf{25.77}$ & $\mathbf{37.41}$ & $\mathbf{33.33}$ & $25.51$ & $25.76$ \\
base + KELM & $26.64$ & $28.15$ & $\mathbf{20.62}$ & $19.81$ & $33.64$ & $\mathbf{35.54}$ & $\mathbf{25.22}$ & $25.75$ & $36.98$ & $32.9$ & $25.31$ & $\mathbf{26.2}$ \\ \hline
large & $30.22$ & $32.88$ & $20.92$ & $21.12$ & $36.7$ & $38.09$ & $29.24$ & $30.03$ & $39.22$ & $35.06$ & $27.12$ & $27.15$ \\
large + C4 & $32.55$ & $34.01$ & $22.5$ & $21.51$ & $38.78$ & $40.6$ & $30.32$ & $30.83$ & $39.74$ & $35.5$ & $27.46$ & $28.17$ \\
large + WikiKG & $\mathbf{33.22}$ & $\mathbf{35.29}$ & $\mathbf{23.5}$ & $\mathbf{23.4}$ & $39.19$ & $\mathbf{41.02}$ & $29.74$ & $30.47$ & $\mathbf{41.12}$ & $\mathbf{35.93}$ & $27.38$ & $27.89$ \\
large + KELM & $32.65$ & $34.16$ & $23.34$ & $22.91$ & $\mathbf{39.45}$ & $40.76$ & $\mathbf{30.51}$ & $\mathbf{30.65}$ & $40.95$ & $35.5$ & $\mathbf{27.67}$ & $\mathbf{28.56}$ \\ \hline
XXL & $43.67$ & $45.02$ & $24.76$ & $24.8$ & $51.73$ & $53.1$ & $42.44$ & $42.21$ & $46.47$ & $43.72$ & $31$ & $32.27$ \\
XXL + C4 & $42.01$ & $44.14$ & $23.34$ & $22.23$ & $50.59$ & $52.19$ & $40.66$ & $40.99$ & $45.43$ & $40.26$ & $30.35$ & $31.08$ \\
XXL + WikiKG & $45.22$ & $\mathbf{47.25}$ & $\mathbf{27.57}$ & $\mathbf{27.65}$ & $\mathbf{54.17}$ & $54.18$ & $42.55$ & $\mathbf{43.54}$ & $\mathbf{49.14}$ & $\mathbf{44.37}$ & $31.11$ & $\mathbf{32.74}$ \\
XXL + KELM & $\mathbf{45.42}$ & $45.9$ & $26.11$ & $26.26$ & $53.65$ & $\mathbf{54.21}$ & $\mathbf{42.68}$ & $42.95$ & $48.53$ & $44.16$ & $\mathbf{31.79}$ & $32.6$ \\ \hline
\end{tabular}
}
\caption{\label{table:wikidata}
Exact match scores achieved by fine-tuning the checkpoints on closed-book QA tasks. \texttt{base}, \texttt{large}, \texttt{XXL} represent the corresponding T5.1.1-* checkpoints. \texttt{*-C4} are the checkpoints additionally trained on C4 corpus as discussed in \Cref{sec:method}. \texttt{*-WikiKG} and \texttt{*-KELM} are the checkpoints trained on Wikidata KG triple corpus and KELM sentence corpus. The best performed checkpoints are in bold. Details about datasets are in \Cref{sec:dataset-sizes}.}
\end{table*}
We found that the majority of the questions in FreebaseQA and WikiHop can be answered directly from triples in Wikidata. This is because FreebaseQA was created by matching question-answer pairs with triples in Freebase \citep{freebase}, most of which was imported into Wikidata \citep{wikidata}. For WikiHop, the questions were generated from Wikidata triples.
However, TriviaQA and NaturalQuestions were created independently of Wikidata, and not every question can be answered using this knowledge base. We found frequent freshness issues, e.g. the golden answer for question "Who is the largest supermarket chain in the UK?" is "Aldi", while today it would be "Tesco". Some other questions can not be answered by WikiData, e.g. "Who, during a radio microphone test in 1984 said, 'I just signed legislation which outlaws Russia forever. The bombing begins in five minutes?'", with the golden answer "Ronald Reagan".
To mitigate this, we created subsets of TriviaQA (TQA) and NaturalQuestions (NQ) that were somewhat more likely to have answers in Wikidata. We selected all the items for which there exist a triple in Wikidata that has the answer either as subject or object, and the other entity in the triple is mentioned in the question. We match the entities by entity name, case-insensitive. We name the Wikidata-aligned version of TQA and NQ as TQA-matched and NQ-matched, respectively. The dataset sizes of all QA tasks are summarized in \Cref{sec:dataset-sizes}.
\subsection{Results}
\label{sec:results}
The results for closed-book QA tasks are summarized in \Cref{table:wikidata}. SKILL pre-trained models show improvements on FreebaseQA, WikiHop, and Wikidata-answerable versions of TriviaQA and NaturalQuestions, but no significant improvement on original TriviaQA and NaturalQuestions. As discussed in previous section, we believe this is due to the misalignment between the datasets and Wikidata.
Models pre-trained on Wikidata KG gives competitive results with ones on KELM sentences. It shows that the triple representation is as good as natural language representation, while being much easier to scale up for larger KG.
For T5.1.1-base and -large, additional pre-training on C4 boosts performance in comparison to the original baseline. For T5.1.1-XXL, this additional pre-training leads to a performance regress. In \citep{t5}, it is mentioned that training on C4 for multiple times may reduce the performance of a T5 model.
\paragraph{Impact of model size.}
As shown in \Cref{figure:delta-size}, SKILL pre-training introduces bigger improvements when applied on larger models. With more than $35$M triples in Wikidata KG, it is harder for smaller size models, e.g. T5.1.1.-base with $300$M parameters, to memorize them efficiently. We view this as an encouraging result, suggesting that as model size grows, gains from SKILL pre-training may increase further.
\begin{figure}
\centering
\includegraphics[width=0.85\columnwidth]{delta-size-WD-C4-average.png}
\caption{\label{figure:delta-size}
Performance improvements on closed-book QA tasks for different model sizes. The improvements are measured by the difference of exact match score ($\Delta$EM) between knowledge-infused model trained with Wikidata triples and the baseline trained with C4 corpus.
}
\end{figure}
\paragraph{Performance on a smaller KG.}
The WikiMovies KG \cite{miller-etal-2016-key} contains $134,741$ triples. T5.1.1-large should have enough parameters to memorize the KG. We train a T5.1.1-large model on the KG for $100$K steps, $\sim 380$ epochs, with the same hyperparameters as for Wikidata KG. We evaluate the checkpoints with MetaQA \citep{zhang2017variational} benchmark that was constructed over WikiMovies KG. The benchmark contains 3 different sub-tasks: 1-hop QA (e.g. "What films does Paresh Rawal appear in?"), 2-hop QA (e.g. "Who are the directors of the films written by Laura Kerr?"), 3-hop QA (e.g. "Who directed the movies written by the writer of Millennium Actress?").
The results in \Cref{table:metaqa} demonstrate the effectiveness of SKILL pre-training, when it's possible to memorize the whole knowledge graph.
\begin{table}
\centering
\begin{adjustbox}{center}
{\footnotesize
\begin{tabular}{llccc}
\hline
\textbf{Dataset} & \textbf{Split} & \textbf{Baseline} & \textbf{+ C4} & \textbf{+ KG} \\
\hline
\multirow{2}{*}{1-hop} & dev & $24.3$ & $23.12$ & $\mathbf{71.52}$ \\
& test & $24.5$ & $23.53$ & $\mathbf{71.47}$ \\
\multirow{2}{*}{2-hop} & dev & $32.05$ & $32.23$ & $\mathbf{33.49}$ \\
& test & $32.65$ & $32.78$ & $\mathbf{33.57}$ \\
\multirow{2}{*}{3-hop} & dev & $42.08$ & $39.22$ & $\mathbf{43.79}$ \\
& test & $42.31$ & $39.66$ & $\mathbf{43.41}$ \\
\hline
\end{tabular}}
\end{adjustbox}
\caption{\label{table:metaqa}
Exact match scores achieved by fine-tuning different T5.1.1-large checkpoints on MetaQA task.
}
\end{table}
As 1-hop questions are supported by single triples in the WikiMovies KG, a $3\times$ improvement on EM score is observed for the sub-task. In order to answer 2/3-hop questions it is not enough to memorize the triples, the model needs to be able to reason with them. This requires a better understanding of the graph structure. Training with single triples may not be enough, and the observed improvement is notably smaller. The performance could be further improved by representing more explicitly the graph structure in the training data, which we leave for future work.
\section{Conclusion}
We proposed a method to directly infuse knowledge from knowledge graphs into T5 models through pre-training. Empirical results show that T5 can learn directly from structured data and apply the learned knowledge to improve closed-book QA results. We also demonstrated that the models pre-trained on factual triples perform competitively with the ones on natural language sentences that contain the same knowledge. By enabling knowledge infusion directly from triples, this method can be very easily applied to industry-scale KGs.
\section{Ethical and Broader Impact}
In this work, we are introducing a new method to pre-train a well known natural language understanding model, T5, on the full corpora of public knowledge graphs. To the best of our knowledge, the method will not introduce extra bias to either the model or the dataset beyond the one potentially inherited from Wikidata \cite{wikidata} and WikiMovies \cite{miller-etal-2016-key} knowledge graphs. On the other hand, through knowledge fusion pre-training introduced in this work, a language model will be able to learn factual information to improve the quality of parameterized knowledge embedded in the model, which is demonstrated by improvements on various closed-book question-answering tasks. The proposed method and recipe will provide positive impact to the natural language processing community and help to improve the factualness in pre-trained large language model checkpoints.
\paragraph{Limitations.} A factual triple is the basic ingredient of a knowledge graph. However, as a semantic network, the graph structure of a knowledge graph describes how the factual triples are connected. This information is not easy to directly represent by random set of triples. We leave the exploration of how to infuse the information implied by the graph structure for future work. We expect that this will further improve the results, especially for multi-hop question-answering tasks.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,781 |
\section{Introduction}
Variable stars are key to investigating and testing stellar astrophysics, and the dynamics and structure of stellar systems. The detection, classification, and study of classes of variable stars is therefore an important pursuit. Typically, variable stars are detected through amplitude and period variations in their photometric light curve. Classifications of periodic variables based on their light curve are not always conclusive, but instead give a strong indication of variable type, and can be used to identify candidates for spectroscopic and photometric follow-up.
The full SuperWASP photometric archive contains $>$30 million light curves of relatively bright stars (V$\leq$15), observed with a high cadence (as short as 30 seconds) and long baseline ($\sim$11 years). A previous period search using the first few years of the SuperWASP archive enabled a significant amount of research in the field of stellar variability, including: the identification of 140 short-period eclipsing binaries close to the period cut-off \citep{lohr2013}; the identification of period change in post common-envelope eclipsing binary systems to search for circumbinary planets \citep{lohr2014}; the discovery of a doubly eclipsing quintuple system \citep{lohr2015}; the identification of period change in $\sim$1400 eclipsing binaries \citep{lohr2015b}; the discovery of a $\delta$ Sct star in an eclipsing binary \citep{norton2016}; the study of $\sim$5000 RR Lyrae stars and identification of $\sim$800 Blazhko effect systems \citep{greer2017}; and the study of rotationally modulated variables \citep{thiemann2020}. A more recent re-analysis of this archive detected $\sim$8 million potential periods in $\sim$3 million unique objects \citep{norton2018}.
There have been previous attempts at using machine learning algorithms and Artificial Neural Networks (ANNs), often called Neural Networks (NN), to automate the classification of SuperWASP variable stars from the raw data, including \citet{payne2013}, who made use of three NNs to process a range of parameters which defined the shape of the phase folded light curve. They processed over 4.3 million periods, giving $\sim$1.1 million preliminary classifications. However these NNs found only partial success, identifying 75 per cent of light curves correctly. As an alternative to machine learning, the SuperWASP Variable Stars (SVS) Zooniverse\footnote{\url{www.zooniverse.org/projects/ajnorton/superwasp-variable-stars}} project is instead using citizen science to classify the 1.6 million folded light curves referred to above. In this paper, we present the first analysis of SVS, containing over 1 million classifications, corresponding to over 500,000 unique object-period combinations.
\begin{figure}
\includegraphics[width=\columnwidth]{figures/hist_allflags.PNG}
\caption{Histogram of the identified periods in all objects in the \textit{SuperWASP Periodicity Catalogue}. There are significant numbers of excess periods close to integer multiples or fractions of a sidereal day or lunar month, indicated by coloured vertical lines (red lines correspond to fractions of a day; light blue corresponds to multiples of a day; dark blue corresponds to the monthly and linger cycles). All such periods are flagged and may be discarded. The upper panel shows the cumulative period histogram while the lower one, whose vertical axis is truncated, shows the regular histogram.}
\label{fig:hist_allflags}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{figures/hist_zeroflags.PNG}
\caption{Histogram of all un-flagged periods corresponding to objects in the \textit{SuperWASP Periodicity Catalogue}. The coloured vertical lines indicate where flagged periods have been removed (red lines correspond to fractions of a day; light blue corresponds to multiples of a day; dark blue corresponds to the monthly and linger cycles). The upper panel shows the cumulative period histogram while the lower one shows the regular histogram.}
\label{fig:hist_zeroflags}
\end{figure}
The SVS project was launched on 5th Sep 2018 and had engaged $\sim$4,500 volunteers at the time of this analysis. This analysis acts as a preliminary look at the Zooniverse classifications, demonstrating that SVS can be used for both population studies and for identifying rare and unique variables. This analysis will guide how we develop the project as it gains more volunteer and machine learning classifications. In Section \ref{sec:data} we describe the SuperWASP data; in Section \ref{sec:citsci} we describe the Zooniverse project; in Section \ref{sec:results} we summarise our results including the identification of new and unique stellar variables; in Section \ref{sec:conclusions} we draw our conclusions.
\section{SuperWASP Periodicity Catalogue}
\label{sec:data}
SuperWASP \citep{Pollacco2006} surveyed almost the entire night sky using two identical observatories in La Palma, Canary Islands, and Sutherland, South Africa. Each robotic observatory consisted of 8 cameras each with a 14 cm aperture and a 7.8 $\times$ 7.8 square degree field of view, allowing for a total sky coverage of $\sim$500 square degrees per exposure. The survey excludes the Galactic Plane where the large pixel scale of 16.7 arcsecond per pixel prevents separation of signals from individual stars in this dense stellar region. SuperWASP observations were reduced using the pipeline described in \citet{Pollacco2006}. Over the course of $\sim$2800 nights between 2004 - 2013, SuperWASP accumulated $\sim$16 million images containing $\sim$580 billion data points corresponding to $\sim$31 million unique stars \citep{norton2018}. The SuperWASP data set therefore provides a high cadence and long baseline of observations for more than 30 million stars with magnitudes between $V=8-15$.
For SuperWASP observations, 1 count $s^{-1}$ after background subtraction is roughly equivalent to V$\sim$15. Therefore the mean SuperWASP magnitude is defined as $V = -2.5 \log_{10}(\frac{F}{10^6})$ where $F$ is the mean SuperWASP flux and the pseudo-V magnitude is comparable to the Tycho V magnitude. A typical object in the SuperWASP archive will have $\sim$20,000 observations in its light curve. While the SuperWASP data can contain a significant level of noise, the long baseline of observations can often compensate for this in phase folded light curves.
SuperWASP photometry is carried out by placing apertures on the images at pre-defined positions identified using the USNO catalogue as an input. However, the large pixel size of the individual cameras means that it is possible that a single star can be associated with two or more different identifiers in the SuperWASP archive, and that light from multiple stars can appear within the same photometric aperture. Typically there is only a single (or dominant) star in the aperture, so association with a specific object is possible, but that is not always the case. Hence, in each case confirmatory photometry with a small PSF is necessary to confirm exactly which object is variable.
\begin{figure}
\includegraphics[width=\columnwidth]{figures/EW_example.png}
\caption{\textbf{Upper panel:} Volunteers are first tasked with classifying each light curve as a generic variable type. This example shows an EW folded at half the correct period. \textbf{Lower panel:} If a volunteer chooses a classification of EA/EB, EW, or pulsator, they are asked to choose whether the period is correct or not.}
\label{fig:EW_first}
\end{figure}
\citet{norton2018} recently performed a re-analysis of the entire SuperWASP archive with the aim of detecting all periodic variables. The re-analysis comprised a one-dimensional CLEAN power spectrum analysis (based on the technique outlined by \citet{roberts1987}) as well as a phase dispersion minimisation and folding analysis (following the method of \citet{davies1990}). Only periods that were significantly detected using \textit{both} methods were considered to be plausible. For each light curve, all periods that passed these criteria were recorded, with a significance value recorded from both the folding analysis and the Fourier analysis. The periods identified have an average uncertainty of $\sim\pm0.1$ per cent.
This re-analysis detected $\sim$8 million candidate periods of stellar variables in $\sim$3 million unique objects, shown in Figure \ref{fig:hist_allflags}. A significant number of period detections result from systematic effects in the SuperWASP photometric data, resulting in the detection of periods close to integer fractions or multiples of a sidereal day or lunar month (i.e. 1 day, 1/2 day, 1/4 day, etc.). Periods flagged as affected by one of these effects were removed from the data set, leaving 1,569,061 candidate periods in 767,199 unique objects, shown in Figure \ref{fig:hist_zeroflags}. Clearly some genuine periods will have been rejected by this method, but if we extrapolate across the gaps, the rejected genuine periods should amount to no more than 5 per cent of the total. The \textit{SuperWASP periodicity catalogue} is available on the Warwick SuperWASP archive\footnote{\url{http://wasp.warwick.ac.uk/archive/docs/index.shtml}} as the table \textit{period\_ajn5}.
To generate subjects for SVS \citep{norton2018}, light curve data for objects with one or more potentially genuine periods listed in the \textit{SuperWASP Periodicity Catalogue} were used. The data for each selected object were folded at each of its potential periods and then rendered to produce a set of one or more phase-folded light curve images. Each image displays the raw photometric data points, overlaid with the mean profile in 100 phase bins, an example of which is shown in Figure \ref{fig:EW_first}.
\section{Citizen Science}
\label{sec:citsci}
The Zooniverse\footnote{\url{www.zooniverse.org}} \citep{lintott2008} is the world's most popular platform for "people-powered research", where a community of volunteers, or "citizen scientists", can participate in real scientific research through simple tasks such as analysing and categorising large data sets. This approach, using the "wisdom of the crowd", can be used to greatly improve the accuracy and speed with which data can be analysed and classified. Despite minimal training and subject matter expertise, Zooniverse volunteers have proven time and time again that non-experts can achieve a good level of accuracy, and can identify unusual objects that automated algorithms will often miss.
SVS launched on 5th September 2018, with the aim of classifying the output of the \textit{SuperWASP Periodicity Catalogue} \citep{norton2018}. The aim of SVS is threefold: to identify rare variable stars; to identify populations of variable stars in order to probe the extremes and trends of each population; and to facilitate the future development of a web portal in order to give researchers and the public access to the output of this project.
We constructed the SVS project using the Zooniverse project builder platform\footnote{\url{www.zooniverse.org/lab}}, creating a classification task, tutorial, and "Field Guide" which provides example light curves and guidance for classification. There is also an option for volunteers to report their findings in the "Talk" section, where they can discuss individual light curves, highlight unusual and rare ones, and identify which objects have already been detected in other databases.
The classification of variable stars can be difficult, with 211 variable star types and sub-types listed in the International Variable Star Index\footnote{\url{www.aavso.org/vsx/index.php}} (VSX) \citep{2015watson}. The noise level of the SuperWASP light curves often makes it difficult to distinguish between similar types of variables. However, to be successful, Zooniverse, projects must be accessible to non-subject matter experts. We therefore ask volunteers to classify light curves into the following generic and overarching variable types:
\begin{itemize}
\item Pulsators: stars which display periodic changes in brightness due to changes in the star's size and luminosity as its outer layers expand and contract in a regular manner. This category includes RR Lyrae, $\delta$ Scuti, Cepheid variables, and Mira variables. Light curves are often asymmetric with a steeper rise and shallower fall in brightness.
\item EA/EB: detached and semi-detached eclipsing binary systems which display periodic changes in brightness. This category includes Algol (EA) and Beta Lyrae (EB) eclipsing binaries. Two eclipses per cycle may be distinguished, often of different depth, with clear boundaries to the eclipses.
\item EW: contact-eclipsing and near-contact eclipsing binary systems which display periodic changes in brightness. This category includes W Ursae Majoris (EW) type eclipsing binaries. Brightness variation is continuous and the eclipses are often of similar depth, resulting in half the orbital period often being identified instead of the true period.
\item Rotators: stars which display rotational modulation in their light curve. This category includes single stars with significant star spots and stars with ellipsoidal modulation from close binaries that do not eclipse but instead are distorted into non-spherical (ellipsoidal) shapes by gravity due to their proximity. Brightness variations are typically quasi-sinusoidal.
\item Unknown: stars displaying some degree of periodicity but which do not fall into any previous category. This category might include semi-regular stars and long period variables.
\item Junk: light curves which display no genuine periodicity, or apparent periodicity which is due only to data dropouts or remaining systematic artefacts.
\end{itemize}
Volunteers are presented with a phase-folded light curve and tasked with classifying it into one of the following options: pulsator, EA/EB, EW, rotator, unknown, or junk, shown in Figure \ref{fig:EW_first}. If the volunteer chooses either EA/EB, EW, or pulsator, they are presented with a second question which asks them to choose whether the folding period is: correct period, half period, or wrong period. The classification task itself is essentially a pattern matching task.
We collect multiple classifications of each phase-folded light curve, allowing us to take the most common classification as the true classification and "retire" it from the live project. Between 5th September 2018 -- 23rd September 2019, each light curve required 7 classifications from separate volunteers to "retire" it, meaning that if a light curve received 4 or more of the same classification, the light curve would be assigned to the corresponding category. On 24th September 2019, a variable retirement rate was implemented using Caesar\footnote{\url{https://caesar.zooniverse.org}} advanced retirement engine provided by the Zooniverse platform. As a result, a light curve is now retired if either the classification count reaches 7, the subject receives 4 of the same classification, or if the subject receives 3 junk classifications, since junk light curves are typically easier to identify. Following the introduction of the variable retirement rate with Caesar, junk classified subjects are retired more quickly, so we would expect to see a higher relative frequency of junk in the output, with the number of junk classifications eventually plateauing as they are retired from the live project.
In the period immediately following the project launch, the subject images presented to volunteers were selected randomly from the full pool of 1.6 million light curves. Even if all 4,500 volunteers that had so far engaged with the project classified one subject per minute, the expected time for any particular subject to accrue 7 classifications is almost 40 hours. In reality, the initial retirement rate was $\sim$3,000 subjects per month on average. Accordingly, a subject batching strategy was adopted which reduced the available subject pool size to 288,000 light curves at any one time. Following this change, the retirement rate increased to $\sim$17,000 subjects per month, peaking at $\sim$43,711 retirements in October 2019.
During peak times of activity (when SVS is promoted as a "featured project" on the Zooniverse front page), there is an average of $\sim$4,300 classifications per day, peaking at 11,442; outside of these intervals, there is an average of $\sim$1,100 classifications per day and a retirement rate of $\sim$5,000 per month. At this lower classification rate, it is estimated that it will take $\sim$4--5 years to complete each "live" set of 288,000 objects, or $\sim$25 years to complete the full set ($\sim$15 years at a higher classification rate). By comparison, one of the authors classified $\sim$5,000 light curves in a day without working on other research activities. Considering these timescales, machine learning will be vital to complete the classification of all 1.6 million phase-folded light curves within a reasonable time-frame.
We use the Gini coefficient to give a quantitative measure of the engagement of volunteers. The Gini coefficient ranges from 0 to 1, where 0 indicates that each volunteer contributes an equal number of classifications, and 1 indicates that there is an extreme difference in number of classifications from each volunteer. We find that the mean Gini coefficient for SVS is 0.92. By comparison, \citet{gini} finds that the mean Gini coefficient for astronomy projects on Zooniverse is 0.82, and \citet{Eisner} finds a similarly high Gini coefficient for \textit{Planet Hunters TESS} of 0.94. Whilst a higher Gini coefficient does not necessarily indicate project "success", it does indicate that SVS has a large number of prolific classifiers, which is often desirable for citizen science projects. Loyal classifiers spend more time engaging with the project, and hence are likely to have a strong understanding of the project aims and classification methods and make fewer mistakes.
For the project age, SVS has fewer total volunteers than other general astronomy projects on the Zooniverse, but a comparable number of total volunteers to other non-astronomy projects and variable star astronomy projects. A direct comparison is \textit{Variable Star Zoo}\footnote{\url{https://www.zooniverse.org/projects/ilacerna/variable-star-zoo}} (classifying $\sim$60,000 light curves), a project which aims to classify variable stars in the VVV survey. \textit{Variable Star Zoo} launched in July 2018 and has engaged with 5,305 volunteers to date, similar to SVS. Two upcoming variable star Zooniverse projects are \textit{Zwicky Stellar Sleuths}\footnote{\url{https://www.zooniverse.org/projects/adamamiller/zwickys-stellar-sleuths}}, and a new project by ASAS-SN, \textit{Citizen ASAS-SN}\footnote{\url{https://www.zooniverse.org/projects/tharinduj/citizen-asas-sn}}. SVS will complement these projects, and the increase in variable star Zooniverse projects may increase volunteer interest in this branch of astronomy.
\begin{figure}
\includegraphics[width=\columnwidth]{figures/time_series.png}
\caption{The number of classifications (black) and retirements (red) over the first 2 years of the project. The shallow increase shows pre-launch classifications from experts and beta testers. SVS was officially launched on 2nd September 2018, and since then has has a fairly consistent classification rate. Peaks of activity (such as being a "featured project") cause sudden rises in classifications. The change to a variable retirement limit and batching is clear in early 2019.}
\label{fig:class_timeseries}
\end{figure}
\subsection{Data Cleaning}
\label{sec:data_cleaning}
The classifications used in this analysis were downloaded on 2nd September 2020, giving almost 2 years of classification data. Although there have been 1,071,345 classifications corresponding to over 568,739 unique object-period combinations, the majority of light curves have not yet received a sufficient number of classifications for retirement.
Classifications from SVS are exported as a CSV file from the Zooniverse site. Before data cleaning, the SVS classification export is stripped of non-essential data, including time of classification and username of Zooniverse volunteers. In addition to the primary science analysis, an in-depth assessment of classification reliability, including detection of "spam" classifications was performed. For this secondary analysis, the full SVS classification export was used as is.
The likely classification for each subject is decided by a custom written script. This script looks at all the classifications of the same Subject ID (or same SuperWASP ID and Period ID) and finds the most popular (or only) classification. If two (or more) classifications are equally popular, then we allocate the classification as the first given classification from the following list: junk, pulsator, rotator, EW, EA/EB, unknown (ordered from most common to least common). The unfiltered SVS export has 1,071,345 rows corresponding to all classifications made up to that time. After processing and removing duplicated rows, 1,025,750 light curve classifications remain. After finding the top classification for each subject, the output had 568,739 rows corresponding to unique object-period combinations. Figure \ref{fig:number} shows a histogram of the number of classifications per object.
\begin{figure}
\includegraphics[width=\columnwidth]{figures/n_class_objects.png}
\caption{There are 5 objects with 9 classifications, 27 objects with 8 classifications, 1934 objects with 7 classifications, and 3510 objects with 6 classifications, 11,085 with 5 classifications, 35,298 with 4 classifications, 84,180 with 3 classifications, 109,034 with 2 classifications, 323,666 with 1 classification. At this stage, only 9 per cent of objects (7 per cent of non-junk objects) have received enough classifications for retirement.}
\label{fig:number}
\end{figure}
Additional catalogues are cross-matched with the output to identify additional parameters such as distance, colour, and previous classifications. This includes a 10 arcsecond spatial cross-match with Gaia-DR2 and the Gaia-DR2 Bailer-Jones distance catalogue (\citealt{GaiaB,bailer2018}), a 10 arcsecond cross-match with NOMAD \citep{nomad}, and a 2 arcminute cross-match to VSX \citep{2015watson}.
Light curves with fewer than 4 classifications are removed, and any remaining duplicates (both spatial and WASP ID) are retained, since these are plausibly multi-periodic or multi-classification objects. We complete an initial visual assessment of unrealistic periods, but at this stage, objects with such periods are not removed since these are plausibly extreme period objects which may be of interest. Table \ref{tab:initial_data_cleaning} shows a breakdown of the cleaned data set.
\begin{table*}
\caption{Breakdown of the first 1 million classifications corresponding to 568,739 unique object-period combinations, and the results of positional cross-matches to the Gaia-DR2 and \citet{bailer2018} catalogue, VSX, and SuperWASP catalogues of binaries \citep{payne2013} and pulsators \citep{greer2017}.}
\label{tab:initial_data_cleaning}
\begin{tabular}{lccccccc}
\hline
& Full output & EA/EB & EW & Pulsator & Rotator & Unknown & Junk \\
\hline
Classifications & 568739 & 29882 & 36328 & 25730 & 56582 & 41541 & 378,671 \\
$N_{class} \geq 4$ & 13390 & 2425 & 3187 & 1777 & 4402 & 1599 & N/A \\
$N_{class} \geq 4$ and correct period & 11322 & 1629 & 2672 & 1020 & 4402 & 1599 & N/A \\
In Gaia-DR2 & 10213 & 792 & 2599 & 1000 & 4275 & 1547 & N/A \\
In VSX & 5,283 & 665 & 1528 & 579 & 1939 & 572 & N/A \\
In Payne and/or Greer & 314 & 259 & 44 & 11 & N/A & N/A & N/A \\
\hline
\end{tabular}
\end{table*}
\subsection{Classification Reliability}
\label{sec:assessing}
A total of 7,478 volunteers made 1,071,345 classifications. SVS has $\sim$4,500 registered volunteers, indicating that $\sim$3000 volunteers engaged with the project but did not register on the Zooniverse platform. Registered volunteers made 93.9 per cent of classification, and 6.1 per cent of classifications (65,398) were made by unregistered or anonymous volunteers, making $\sim$20 classification each on average. Fig \ref{fig:volunteer_nclassification} shows the distribution of classifications made per volunteer. Just over half (52.6 per cent) of volunteers made 10 or fewer classifications, 36.0 per cent made 11--100, 9.6 per cent made 101--1000, and 1.6 per cent made over 1,000. 18 (0.2 per cent) "super-classifiers" made more than 10,000 classifications.
\begin{figure}
\includegraphics[width=\columnwidth]{figures/n_classification_per_volunteer.png}
\caption{The number of classifications per volunteer. Any classifications made by an anonymous volunteer over different days will be counted as multiple volunteers' inputs.}
\label{fig:volunteer_nclassification}
\end{figure}
To estimate the classification reliability, SVS classifications are compared existing variable classifications, such as VSX classifications or Gaia-DR2 variable types. Figure \ref{fig:confusion} shows the confusion matrix for volunteer classifications compared to the closest stellar variable within the VSX catalogue. While the SVS classification accuracy is high for binaries and pulsators, with $\sim$89 per cent of EA/EBs, $\sim$71 per cent of EWs, and $\sim$78 per cent of pulsators being correctly classified, rotators are a more challenging variable type with only $\sim$9 per cent of rotator classifications being "correct". The category of unknown easily categorised, but separating SVS classified objects into their corresponding classes from the VSX catalogue gives $\sim$24 per cent semi-regular variables, $\sim$23 per cent miscellaneous variables, and $\sim$15 per cent long period variables. Overall, we find a classification accuracy of 60 per cent for all variable types, excluding junk.
\begin{figure}
\includegraphics[width=\columnwidth]{figures/confusion.png}
\caption{The confusion matrix for volunteer classifications compared to VSX classifications. The category of unknown for VSX contains semi-regular stars and stars classified as miscellaneous. We find an overall classification accuracy of 60 per cent.}
\label{fig:confusion}
\end{figure}
Too few SVS variables have a Gaia-DR2 variability component to undertake a similar full assessment, using the \textit{Gaia-DR2 variability results} catalogue containing 363,369 classifications of pulsators from Cepheids to Mira variables. Only 1 EA/EB and 8 EW type SVS variables are classified as pulsating stars in Gaia-DR2. Of the 273 pulsators (27 per cent of 1020 identified) in \textit{Gaia-DR2 variability results}, 9 are classified as Type I or II Cepheids, 9 are Mira variables, 17 are $\delta$ Scuti stars, and 238 are RR Lyrae stars. 81 rotators and 47 unknown variables are classified as pulsators in \textit{Gaia-DR2 variability results}.
This assessment gives a rudimentary estimate on the probability that different classes of variables are classified correctly. When combined with the \textit{SuperWASP periodicity catalogue} likelihood statistics, we can use this to give us a good idea of the correct period and variability type. It is most likely that incorrect classifications arise from two causes. Some variable types, especially EA/EB, can appear to be another variable type when folded at the wrong period. It is therefore important that we have a robust method of identifying the true period of an object which may have multiple detected periods, see Section \ref{sec:multiple}. The other dominant cause of incorrect classifications will mostly likely be human error, and non-specialists may miss some of the nuances of a light curve that indicate a certain variability type. But a cohort of non-specialist volunteers is by no means a bad thing, since the combination of people-power and multiple classifications means that an accurate consensus is usually reached. Feedback from citizen scientist volunteers also suggests that confusion can arise from the overlaid binned red line, especially in instances where the binned line appears to show a different variable type from the actual data, due to data drop-outs or spikes. At this stage of the project, it is not possible to remove or edit this binned line, but it is something to be aware of in the analysis of the resultant classifications, and use of labelled data in machine learning. Other issues may arise if volunteers skip the training available to them through the Zooniverse interface, forget the training, or find the training is not written in their first language.
While highly unlikely, it is also possible that bots, spamming, or deliberate sabotage can influence the results. There are no in-built protections against this on the Zooniverse platform, so the only way of identifying "spam" classifications is by checking for a high number of classifications by the same user within an unrealistically short time-frame. All classifications were checked for a single user making multiple classifications per second and none were found. It is not possible to check this for users who are not logged in, so unexpected spikes in classifications ($>$100 classifications in $<$1 minute) were searched for. Only one spike in activity matching these parameters was detected by a single user, and their classifications were visually assessed by the authors and verified as non-spam.
Volunteer weightings have not yet been implemented in the classification pipeline, but will be an important part of the CNN, and will be used to improve classification reliability. We trialled two simple methods of calculating weightings: identifying overlap of classifications with "expert" or author classifications, and overlap with VSX classifications. With 6 possible variable types, a suitable number of classifications is needed for each variable type to calculate weightings. Unfortunately the overlap with "expert" classifications is too low to provide a conclusive weighting. Assessing against VSX, we take only those have made $>$100 classifications of each variable type, of which only 15 have an overlap of $>$100 with VSX, which also provides an inconclusive weighting system. Alternative methods will be explored in future work, for example through the use of individual volunteer confusion matrices, see Section \ref{sec:need_ML}.
\section{Results}
\label{sec:results}
\subsection{Overview}
\label{sec:overview}
Volunteer classifications indicate that this first analysis consists primarily of junk classifications (66.6 per cent of all classifications), which are discarded. The remainder of the classifications are made up of EA/EB (5.3 per cent), EW (6.4 per cent), pulsators (4.5 per cent), rotators (9.9 per cent), and unknown (7.3 per cent). As previously identified, the classification accuracy of rotators is low so the true proportion will be lower than this figure indicates. Figure \ref{fig:hist_mag} shows the distribution of V band magnitudes ranging from approximately 8$\geq$V$\geq$15, with a number of fainter sources. Genuine faint sources can be detected by the longest SuperWASP exposures, but contamination by nearby stars can sometimes mimic faint sources, resulting in spurious detections. Figure \ref{fig:distance} shows the distribution of distances of these typically near-by stellar variables. Each variable type has a similar distribution, with the exception of pulsators, showing a peak in distance at $\sim$4800 pc, with a fainter average V magnitude of $\sim$13.8, likely due to a greater number of more distant stellar variables of this type.
\begin{figure}
\includegraphics[width=\columnwidth]{figures/certain_hist_mag_full.png}
\caption{The distribution of NOMAD V magnitude of SVS stars with a variable type classification and correct period classification ranges between 8$\geq$V$\geq$18.}
\label{fig:hist_mag}
\end{figure}
\begin{figure}
\includegraphics[width=\columnwidth]{figures/hist_dist.png}
\caption{The distance (pc) distribution of SVS stars with a variable type classification and correct period classification. The full data set is shown in the solid line, while the pulsators are shown by the dashed line. Pulsators appear to have a different distribution to other variables.}
\label{fig:distance}
\end{figure}
The spatial distribution of the 568,739 unique object-period combinations is shown as a sky density plot in Figure \ref{fig:sky_map}. The classifications are not evenly distributed, since typically only a few degrees of sky are available for classification at any one time, and SuperWASP could not resolve objects in the dense regions of the Galactic Plane.
\begin{figure*}
\includegraphics[width=2\columnwidth]{figures/sky_map.png}
\caption{Map of SVS classifications. Red points indicate objects which have been retired from the live queue, grey points indicate objects which have received too few classifications for retirement. Classifications are not evenly distributed since only a few degrees of the sky are available to volunteers at any one time. As each data set is complete, more of the sky map will be filled.}
\label{fig:sky_map}
\end{figure*}
We have not yet accounted for the effects of interstellar extinction and reddening on magnitudes, colours, and variable classification. \citet{2018asasJ} make use of the reddening-free Wesenheit magnitudes (e.g. \citealt{1982madore,2018Lebzelter}), with Gaia DR2 and 2MASS passbands to improve variability classification for ASAS-SN, but do not account for the effects of extinction in colours. We aim to complete an analysis of the effect of both in future analyses of SVS classifications, making use of either the reddening-free Wesenheit magnitudes, the calculation of stellar extinction using the Binary and Stellar Evolution and Population Synthesis (BiSEPS) \citep{biseps} implementation of extinction given by \citet{drimmel}, or Gaia-DR2 reddening values and distances. Unlike ASAS-SN, magnitude and passband data does not feed into an automated classification pipeline, and our initial machine learning classification algorithm will not incorporate this data (Section \ref{sec:need_ML}). We expect that reddening would not be the cause of reclassification of the overarching variable types, however, for specific subsets of variable types (e.g. RR Lyrae stars), extinction correction may be necessary.
\subsection{New Variable Objects}
\label{sec:new}
\begin{table}
\centering
\begin{tabular}{c|c|c|c|c|c}
\hline
Type & EA/EB & EW & Pulsator & Rotator & Unknown \\
\hline
Number & 192 & 40 & 69 & 1,365 & 894 \\
\hline
\end{tabular}
\caption{Previously unidentified stellar variables by variable type. There are significantly more variables classified as rotator or unknown. Stars classified as rotators are unlikely to be true rotators and may be binaries and pulsators folded at the wrong period, and unknown variables are likely to be junk, semi-regular or long period variables.}
\label{tab:new}
\end{table}
\begin{table}
\centering
\begin{tabular}{c|c|c}
\hline
WASP ID & Type & Period (days) \\
\hline
1SWASPJ000005.14-755731.3 & EA/EB & 4.30 \\
1SWASPJ000026.84+393855.6 & EA/EB & 3.59 \\
1SWASPJ000028.05+041248.4 & EA/EB & 4.69 \\
1SWASPJ000039.60-191306.0 & EA/EB & 6.76 \\
1SWASPJ000047.05+353443.1 & EW & 1.22 \\
1SWASPJ000054.70+544425.6 & EA/EB & 3.19 \\
1SWASPJ000057.42-544520.1 & EA/EB & 0.75 \\
1SWASPJ000059.84+094404.5 & EA/EB & 0.65 \\
1SWASPJ000105.41-622920.6 & EA/EB & 1.48 \\
1SWASPJ000132.23-051917.6 & Pulsator & 1.62 \\
1SWASPJ000132.66-091513.7 & EA/EB & 4.19 \\
1SWASPJ000145.10+501843.4 & EA/EB & 1.69 \\
1SWASPJ000149.26+061830.8 & EA/EB & 0.32 \\
1SWASPJ000149.45-363918.1 & Pulsator & 0.64 \\
1SWASPJ000203.48-214746.0 & EA/EB & 0.86 \\
1SWASPJ000315.40+495750.8 & EA/EB & 3.65 \\
1SWASPJ000323.81+325049.7 & EA/EB & 8.25 \\
1SWASPJ000343.16+465244.0 & Pulsator & 1.31 \\
1SWASPJ000353.60+043503.0 & EW & 0.28 \\
1SWASPJ000410.77-525122.4 & EW & 0.24 \\
\hline
\end{tabular}
\caption{Sample from 301 previously unidentified stellar variables and related characteristics, not including rotators and unknown variables. The periods of each object have been assessed by the authors to correct for mis-classifications; whilst they have been corrected as much as possible, some periods remain best guesses. All periods have an uncertainty of $\pm$0.1 per cent. The full table, including rotators and unknown variables, can be found at \href{https://doi.org/10.5281/zenodo.4439383}{10.5281/zenodo.4439383}.
}
\label{tab:new_full}
\end{table}
We expect SVS to classify many known stellar variables, and identify several previously unknown stellar variables. Previously known variables are identified by a 2 arcminute cross-match with the VSX catalogue (retrieved on 20 October 2020), which contains classifications of 2,105,377 variable stars from surveys including e.g. OGLE \citep{ogle}, ASAS \citep{ASAS}, ASAS-SN (\citealt{Shappee,Kochanek,2018asasJ}), ROTSE \citep{rotse}, NSVS \citep{nsvs}, ZTF \citep{Bellm}. A secondary cross-match is performed with catalogues from \citet{payne2013} containing 12,884 EAs, 5,226 EBs, and 2,875 EWs, and \citet{greer2017} containing 4,963 RR Lyrae stars.
To select potentially new variable stars, objects with a known classification and period are removed; objects that are flagged as variable, but which have no classification or period, are not removed. All new stellar variables were assessed by eye by the authors to verify the classification type and correctness of the period. Duplicated objects were removed and objects were reclassified as required. We caution that the subset of remaining rotator and unknown objects may still contain binaries and pulsators at the incorrect period, despite the best efforts of the authors to identify them. Through this process, we are left with 2,560 unique candidate new variables, shown in Table \ref{tab:new}.
Using this approach, we have identified 301 previously unknown variable stars, not including rotators and unknown variables, a selection of which are shown in Table \ref{tab:new_full}, with a period distribution shown in Figure \ref{fig:new_hist_period}. Of particular interest are a short period cutoff eclipsing binary (with two SuperWASP IDs: 1SWASPJ004003.56+501501.9 and 1SWASPJ004008.54+501455.6), new $\delta$ Scuti stars (Section \ref{sec:extreme}), and binaries displaying the O'Connell effect. Based on the low classification accuracy of rotators, we caution that new variables classified as rotators or unknown may not have the correct classification.
\begin{figure}
\includegraphics[width=\columnwidth]{figures/new_hist_period.png}
\caption{The distribution of period of newly identified stellar variables (EA/EB, EW, and pulsator) by variable type. EA/EBs are shown by the dashed line; EWs by the dotted line; pulsators by the solid line.}
\label{fig:new_hist_period}
\end{figure}
Excluding rotators and unknown variables, these new variables are typically bright (V$\sim$13) stars. It is likely that these objects have not been detected due to either surveys not yet having enough epochs to provide a variability classification (e.g. ASAS-SN), focus on the Galactic Plane or specific specific fields (e.g. Kepler, OGLE), or can only observe one hemisphere (ZTF). Assuming that 66 per cent of the 1.6 million light curves in SVS are junk, we estimate that on completion of SVS, $\sim$5,000 new EA/EB, EW, and pulsating stellar variables could be identified.
\subsection{Multiple Periods and Multiple Classifications}
\label{sec:multiple}
Stars displaying two or more real periodic modulations in their light curve are of great interest, and multiply periodic systems can act as stellar laboratories. Targets of interest are pulsating stars in eclipsing binary systems. There are detections of only $\sim$100 $\delta$ Scuti stars in eclipsing binaries \citep{2017Kahraman}, and there are very few RR Lyrae stars known in eclipsing binaries, and no known Galactic Cepheids in eclipsing binaries with orbital periods of less than 1 year \citep{2011evans}.
A search identified 1,202 multi-periodic systems, including 229 EA/EBs, 362 EWs, 100 pulsators, 441 rotators, and 70 unknowns. A visual inspection by the authors revealed that none are convincing multi-periodic systems, but instead are objects with aliases of the true period. Initially, 1SWASPJ004859.70+172328.1 appeared to have multiple correct EA/EB classifications. Further investigation found this object has a true period of 3.11 d, discounting the alias periods. However, this object has previously been identified as an eclipseless rotator (with a period of 3.11 d), but the SuperWASP light curves show a clear primary eclipse and shallow secondary eclipse, shown in Figure \ref{fig:eaeb_multi}. While the primary eclipse depth remains constant, the out of eclipse light curve changes significantly over the 8 years of observation, possibly due to a tidally locked star spot on one of the stellar components.
\begin{figure*}
\includegraphics[width=2\columnwidth]{figures/004859.PNG}
\caption{1SWASPJ004859.70+172328.1, an object with multiple EA/EB classifications, with a true period of 3.11 d. The midpoint of each frame is as follows: field 1 (August 2004), field 2 (August 2006), field 8 (October 2011), field 9 (December 2012).}
\label{fig:eaeb_multi}
\end{figure*}
We are also interested in multi-classification systems. To identify such systems, we searched the SVS data set for subjects that have the same WASP ID but have multiple different, but by consensus "correct" period classifications. This search found 1,563 systems with 2 or more classifications, shown in Table \ref{tab:multi_class}. The classifications with the greatest overlap appear to be EA/EB and EW, and rotators with other classifications. Based on the low classification accuracy of rotators, we make the assumption that any multi-classification object in which one classification is rotator or unknown can be discounted as a true multiple classification.
Each of our candidate multi-classification systems were verified by eye (excluding rotators and unknown variables), ultimately yielding only apparently 1 real multi-classification system, 1SWASPJ000220.66-292933.8, shown in Figure \ref{fig:rscvn}. This object has both an EW and pulsator classification and SuperWASP periods of 3.15 d and 1.46 d respectively. On inspection, the EW classified light curve appears to be that of a RS Canum Venaticorum (RS CVn) binary. This object has a candidate RS CVn classification, with a period of 6.29 d or an eclipseless RS CVn classification with a period of 3.14 d in VSX. This object appears to have experienced significant surface spot coverage evolution over the 7 years of observations, and even hints at an eclipse in field 2.
\begin{figure*}
\includegraphics[width=2\columnwidth]{figures/000220.PNG}
\caption{The light curve of 1SWASPJ000220.66-292933.8, classified by volunteers both as an EW with a period of 3.15 d and a pulsator with a period of 1.46 d. It has previously been classified as an eclipseless RS CVn and a non-periodic rotator. The midpoint of each frame is as follows: field 1 (September 2006), field 2 (September 2007), field 4 (August 2012), field 5 (September 2013).}
\label{fig:rscvn}
\end{figure*}
Another object of particular interest was one which appeared to be a $\delta$ Scuti star in an eclipsing binary (1SWASPJ004811.15+473719.1), however this was found to be two separate systems, a binary (1SWASPJ004810.36+473747.7) and a $\delta$ Scuti star (1SWASPJ004811.15+473719.1), spatially separated by 30 arcseconds, shown in Fig \ref{fig:dscuti}.
\begin{table}
\centering
\begin{tabular}{c|c|c|c|c|c}
\hline
& EA/EB & EW & Rotator & Pulsator & Unknown \\
\hline
EA/EB & - & 246 & 128 & 5 & 75 \\
EW & 246 & - & 716 & 16 & 46 \\
Rotator & 128 & 716 & - & 99 & 202 \\
Pulsator & 5 & 16 & 99 & - & 30 \\
Unknown & 75 & 46 & 202 & 30 & - \\
\hline
\end{tabular}
\caption{The number of light curves with multiple classifications per classification type. Rotators have the greatest overlap with other variable classifications, likely due to the low classification accuracy of rotators, and the high number of alias period light curves per rotator object.}
\label{tab:multi_class}
\end{table}
\begin{figure}
\includegraphics[width=\columnwidth]{figures/scuti_ew.PNG}
\caption{\textbf{Upper:} The $\delta$ Scuti star 1SWASPJ004811.15+473719.1 with a period of 1.9 hours. \textbf{Lower:} The EW-type eclipsing binary 1SWASPJ004810.36+473747.7 with a period of 18.7 hours (0.78 d). These objects were classified as the singular object 1SWASPJ004811.15+473719.1 with both an EW and a $\delta$ Scuti star in the same photometric aperture.}
\label{fig:dscuti}
\end{figure}
\subsection{Extreme Variables}
\label{sec:extreme}
A valuable aspect of large catalogues of variable stars can be the identification of extremes of each class, i.e. those with extremely long or short periods, or extremely high or low amplitudes. SVS has the opportunity to increase the sample size of short period contact binaries, as well as identifying, for example, unusually long period contact binaries. For the full SVS data set, there are two peaks, at $\sim$0.3 days where we might expect to find short period binaries and aliases of binaries, and short period pulsators, and $\sim$30 days where we might expect to find semi-regular stars, currently classified as unknown.
We explore extremes of each variable type using the following criteria as standard definitions of periods, and visually inspect light curves at the extremes of each period:
\begin{itemize}
\item EA/EB: 0.3 d$\leq P \leq$10 d (e.g. \citealt{1995Stepien})
\item EW: 0.22 d$\leq P \leq$1 d (e.g. \citealt{1992Rucinski})
\item Pulsator: 0.3 d$\leq P \leq$8 d (e.g. \citealt{1912Leavitt,1979Breger,2006Matsunaga,2014Drake})
\item Rotator: P$\geq$0.5 d (periods range from hours to months (e.g. \citealt{2013Nielsen})
\item Unknown: N/A (semi-regular P $\geq$10 d) (e.g. \citealt{2009Soszy})
\end{itemize}
The class of pulsators has the widest range of possible periods, including $\delta$ Scuti ($\sim <$0.3d), RR Lyrae (0.44-0.82 d), Cepheid (with periods of weeks to months), Mira (P$\geq$100 d), and W Virginis (0.8 d$\leq P \leq$35 d). We chose a lower limit of P$\leq$0.3d to allow us to identify candidate $\delta$ Scuti and High Amplitude $\delta$ Scuti stars (HADS).
We have identified objects that appear to be long-period examples of near-contact eclipsing binary stars, with orbital periods of up to a month or more. To be in contact, or near contact, at such long periods requires the stellar components to be giants. Such objects have been proposed as the progenitors of red novae, but none have been conclusively identified pre-nova. The outbursts are believed to be due to stellar mergers, but only one progenitor of such an event has ever been studied, V1309 Sco, and that was only recognised retrospectively, after the merger occurred \citep{2011tylenda}. SVS volunteers have identified $\sim$10 candidates, with an example of one of these systems identified in SVS is shown in Figure \ref{fig:ncrgeb}. These candidate near-contact red giant eclipsing binaries are the subject of an ongoing follow-up campaign and the subject of an upcoming paper.
\begin{figure}
\includegraphics[width=\columnwidth]{figures/001521.PNG}
\caption{The first classification of a candidate near contact red giant eclipsing binary, 1SWASPJ000927.89+014542.1, with a period of 41.62 d, significantly longer than typical contact eclipsing binary periods.}
\label{fig:ncrgeb}
\end{figure}
We have also identified a new eclipsing binary (1SWASPJ004003.56+501501.9/1SWASPJ004008.54+501455.6) with a period of $\sim$0.23 days near the short-period cutoff of $\sim$0.22 days, shown in Figure \ref{fig:EW_short}. Such stars are of importance in the study of the evolution and structure of close binary systems.
\begin{figure}
\includegraphics[width=\columnwidth]{figures/004008.PNG}
\caption{A newly identified EW type binary (both 1SWASPJ004003.56+501501.9 and 1SWASPJ004008.54+501455.6) with a period of 0.23 d, close to the short-period cutoff.}
\label{fig:EW_short}
\end{figure}
\section{Discussion}
\label{sec:discussion}
In the full table of volunteer-classified light curves, we provide the SuperWASP ID, period (from the \textit{SuperWASP periodicity catalogue}), and best-guess variable type. We do not provide RA, Declination, or B, V, R magnitudes for any classified object. In most cases, there is only a single bright star in the photometric aperture and so this will usually be the source of the variability, so associations with other data are still possible most of the time. However. the large SuperWASP pixel size and possibility of contamination mean that we cannot confirm the association of a light curve with a specific stellar object without further follow up. We caution that anyone using this catalogue may need to confirm the variability type with their own follow up.
Although it is disappointing not to find many new multi-periodic or multi-classification systems at this stage, this analysis method can be applied to future analyses, especially for the identification of variables with evolving star spots. With a greater number of classifications, we expect to identify a significant number of extremely short and long period pulsators, including $\delta$ Scuti stars and Mira variables. Individual pulsator sub-types are not identified by citizen scientist volunteers, so would require the authors to visually inspect each pulsator light curve after making cuts using additional period, colour, and luminosity data. We also expect to identify more extreme binaries, including near-contact red giant eclipsing binaries, and binaries near the short-period cutoff. It is evident that if some form of machine learning is implemented, there may still be the need for some level of human interaction with multi-periodic and multi-classification systems to identify false positives.
We currently cannot estimate whether volunteer classifications have been biased. There is no identifying data on the image of each light curve, in an attempt to keep the classification task to a pattern matching exercise only. However, following the project launch, it was realised that some metadata for each light curve was visible to volunteers in the form of the SuperWASP ID. For volunteers who notice this, the ID gives information on the RA and Declination of each SuperWASP object, and hence the closest corresponding star from other catalogues. Subsequently, some users have used this ID to cross-match the light curve to existing classifications and surveys, using this knowledge to make a decision on the classification type. We do not have a way of identifying who has made use of this method and whether it can bias the results. Volunteer feedback has indicated that use of cross-matching has improved their knowledge of stellar variables and classification accuracy, and they value being able to investigate the light curves in more depth.
To that end, as of November 2020, we have added links to external catalogues (CERiT, ASAS-SN, and Simbad) to the metadata which is visible only after a classification has been completed. It is not intended to be a tool to influence classifications, but it has been developed in order to allow interested volunteers to engage with the project further.
\subsection{The Future of SuperWASP Variable Stars}
\label{sec:future}
To successfully complete all classifications in SVS and make the results public, we are now working on implementing machine learning techniques and building a platform through which the results can be accessed.
\subsubsection{The Need for Machine Learning}
\label{sec:need_ML}
We estimate that at the current classification rate it will take at least 15 years to classify all 1.6 million light curves in SVS. To this extent, we are developing a novel method for classifying these phase-folded light curves to speed up the classification process, which is the subject of an upcoming paper. In this new method we will train a Convolutional Neural Network (CNN) on the same \textit{images} of phase-folded light curves as those presented to SVS volunteers. We will make use of the $>$1 million volunteer-generated classifications, or labels, to train the CNNs. We will run an initial CNN using volunteer-generated labels, then use expert classified light curves to calculate further volunteer confusion matrices, deriving \textit{fuzzy} labels and weighting classifications to improve reliability. We will then use a custom Zooniverse project to allow for expert bulk classification of CNN predictions, and retrain the CNN using expert classifications.
There is also the scope to use volunteer comments from the "Talk" forum section of SVS. It is possible for a volunteer to create a discussion page for each light curve, where they might "tag" or comment on it, giving a further classification type (i.e. while the SVS classification might be pulsator, a volunteer might comment "RR Lyrae" which indicates that the light curve is a pulsator sub-type). This forum potentially holds another significant source of labelled data which may be explored in future work.
\subsubsection{A New User Interface}
\label{sec:new_UI}
One of the key aims of SVS is to make the classified \textit{SuperWASP periodicity catalogue} light curves publicly available and to create the first catalogue of variable stars in the SuperWASP archive. We have begun work on a new user interface (UI), similar to WASP-DR1\footnote{\url{https://wasp.cerit-sc.cz/form}} and the ASAS-SN Catalogue of Variable Stars\footnote{\url{https://asas-sn.osu.edu/variables}}.
This (UI) will take the form of a web portal, which will allow a user to easily and quickly search the classified light curves using a number of different parameters, including RA and Declination with a search radius, magnitude or flux, period, and variable type. A search of this UI will not only provide SuperWASP data and classifications, but also an automated cross-match to other catalogues, for example: SIMBAD, ASAS-SN, and VSX. Having selected an object, the user will be able to dynamically work with the data or download a FITS or CSV file. The dynamic interface will allow the user to fold the light curve at a different period, re-scale the plot, or convert between magnitude and flux, and more. This new UI will be updated with new SVS classifications or reclassifications every 6 months following its launch.
\section{Conclusions}
\label{sec:conclusions}
We present the preliminary results of the first analysis of the SuperWASP Variable Stars Zooniverse project, which consists of 1,025,750 classifications corresponding to 568,739 unique object-period combinations. Over 4,500 registered volunteers had engaged with the project between September 2018 and September 2020.
Each SuperWASP light curve has been classified by between 4 and 7 volunteers, classifying it as a broad type of stellar variable. We find that the majority (66.6 per cent) of classifications are junk and are therefore discarded, but the remainder (33.4 per cent) of the classifications corresponding to EA/EB, EW, pulsator, rotator, and unknown, are valuable for population studies and studies of unique stellar variables. We identified that variables with a rotational modulation are the most inconsistently classified by volunteers, with only $\sim$9 per cent of rotators being correctly classified, compared to $\sim$89 per cent of EA/EB type binaries. We caution that the classification of rotator should not be relied upon until there is a more reliable method of classification for this variable type.
As a result of SVS, 301 new variable stars have been identified. Extrapolating to the wider data set, we would expect that $\sim$5,000 new variable stars could be identified on completion of this project. We have identified extreme period variables, including long period contact binaries, and eclipsing contact binaries near the short-period cutoff, and $\delta$ Scuti stars. This project has the potential to expand the catalogue of $\delta$ Scuti stars in eclipsing binaries, and discover the first Cepheids in eclipsing binaries (if they exist), as well as to identify multi-periodic Cepheids and RR Lyrae stars. The high number of false-positive multiply periodic and multi-classification light curves identified by volunteers indicates that an expert must complete the final stage of classification by eye for the most extreme and unusual light curves.
This analysis is not conclusive, but it demonstrates that SVS is successful in its aims of identifying unique and extreme variables, and identifying populations of stellar variables for further study. This analysis and methods will guide the project in future analyses of volunteer and machine learning classifications. We are now working on using citizen scientist classified data to train CNNs to speed up the classification process, however humans are still skilled at picking out the rare and unique objects, and generating labelled data. Both volunteer classified light curves and CNN classified light curves will feed into a new public user interface which is currently under development.
\textbf{Data Availability:} The full catalogue of 301 new variables discovered in SVS is available via Zenodo.
\section*{Acknowledgements}
We would like to recognise and thank the thousands of Zooniverse volunteers for their contribution to the SuperWASP Variable Stars project. We would also like to thank the Zooniverse team for their help in developing and maintaining the Zooniverse platform. The SuperWASP Variable Stars project was developed with the help of the ASTERICS Horizon2020 project. This publication uses data generated via the Zooniverse.org platform, development of which is funded by generous support, including a Global Impact Award from Google, and by a grant from the Alfred P. Sloan Foundation. This work was supported by the Science and Technology Facilities Council [grant number ST/P006760/1] through the DISCnet Centre for Doctoral Training. The SuperWASP project is currently funded and operated by Warwick University and Keele University, and was originally set up by Queen's University Belfast, the Universities of Keele, St. Andrews and Leicester, the Open University, the ING, the IAC, SAAO and STFC. This research has made use of the International Variable Star Index (VSX) database, operated at AAVSO, Cambridge, Massachusetts, USA. This research has made use of the TOPCAT and STILTS software packages (written by Mark Taylor, University of Bristol). This research made use of the cross-match service provided by CDS, Strasbourg. This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France.
\bibliographystyle{mnras}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,516 |
\section{Introduction}
Pattern detection and recognition is a core task of image analysis in general~\cite{sonka2014image}, and of bioimage informatics in particular~\cite{Ran2004}.
Patterns of interest in biomedical images (\emph{e.g.}, vessel, elongated cells, bacteria, biomolecules) are often characterized by pronounced and characteristic directional components~\cite{frangi1998multiscale,depeursinge2017multiscale}.
Moreover, they can appear not only at any location in the image, but also at any orientation.
It follows that the major challenge for accurate pattern detection is to develop detectors that can sense discriminative directions with invariance/equivariance to translations and local rotations.
It is worth noting that, most often, no variation in terms of the scale of the pattern is expected in biomedical images and that the latter is a discriminative property~\cite{DFA2017}. For this reason, we shall consider that the sought-for patterns are all present at the same scale in the image.
This leads us to formulate the detection problem as follows.
We assume that the image to analyse $I$ can be written as
\begin{equation} \label{eq:detectionImageModelintro}
{I} = \sum_i {T} ( \mathbf{R}_{- \theta_i} ( \cdot - \boldsymbol{x}_i ) )+ {S},
\end{equation}
with $T$ a known template dispatched at unknown locations $\bm{x}_i$ and rotated at unknown orientations $\theta_i$, and $S$ the background signal, modeled as a Gaussian random field.
Our approach is to build a filter that allows for a convolution-based detection through the complete image, working in the Fourier domain.
We use steerable filters to efficiently test any possible orientation at any position, without reconvolving the image with oriented filters.
The filter is designed to be discriminative in the sense that it responds strongly to the template $T$, while being as insensitive as possible to the background signal $S$.
A strong constraint is that the detection filter can be learned from one unique training example (the template $T$ provided by the user) and from the background model (characterized by a single parameter quantifying its power-spectrum decay, as we shall describe later).
\subsection{Comparison with Previous Works}
Standard methods for pattern detection are based on handcrafted filters, transforms and criteria (\emph{e.g.}, Hough~\cite{Bal1981}, Laplacians of Gaussians~\cite{MaH1980}, Canny~\cite{Can1986}, Harris~\cite{HaS1988}).
These are targeting low-level image features such as lines, blobs, edges, lines or corners but are not rich enough to model higher-level templates such as complex biomolecules or cell mitosis.
Template matching allows detecting virtually any objects modeled by a template and to find image locations minimizing a given matching distance between the template and a local image neighborhood~\cite{OTM2012} (\emph{e.g.}, sum of absolute differences, normalized cross correlation).
However, template matching methods fulfilling the above-mentioned requirements in terms of invariance/equivariance to geometric transforms are computationally intensive since matching distances must potentially be evaluated for every positions and orientations of the pattern.
Several solutions were proposed to accelerate the matching process~\cite{KRT2017,MaE2007,BLR2018}.
A notable approach to allow efficient detection across pattern orientations is to use steerable detectors~\cite{Simoncelli1995steerable,Liu2012,muehlich2012design,puspoki2016design}.
The latter allow evaluating filter responses at any orientation using a simple angular-dependent linear combination of a small number of basis elements~\cite{Freeman1991design,Unser2013steerable}.
We also propose a detection method relying on steerable filters.
However, many approaches based on steerability focuse on the detection of polar separable patterns~\cite{Simoncelli1995steerable,puspoki2016design},
possibly relaxed with a multiscale wavelet-based approach~\cite{Puspoki2015template}.
Therefore, all these methods are adapted for a specific class of template, that is polar separable or sum of finitely many polar separable components.
As we shall see, a specificity of our method is to possibly consider any square-integrable template, with no restriction on polar separability, allowing to built detectors for any kind of patterns.
In addition, the strongest limitation of template matching approaches is their inability to include image background models.
For background models $S$ with non flat power spectrum, the goal is not only to match the template of interest but also to be as insensitive as possible to the statistical variations of the background.
Specifying the background signal $S$ is therefore useful to obtain discriminative detectors reducing the number of false positives.
The proposed method allows including a background model in the filter design criteria, which allows to dramatically improve the detection performance in practice and is one of the main novelty of our work.
Deep convolutional neural networks (CNN) allowed tremendous progress in biomedical image analysis~\cite{RFB2015,EKN2017}, including in pattern detection~\cite{RIZ2017,SRG2016}.
CNNs are able to learn a collection of detectors as deep image operators that are invariant to translations via convolutional operations.
However, CNNs have two main drawbacks, making them difficult to use when little labeled training data is available.
First, in their initial formulation, CNNs do not implement built-in invariance/equivariance to local rotations in most common designs, which is often palliated using rotational data augmentation~\cite{simard2003best}.
More advanced approaches exist including group equivariant and steerable CNNs~\cite{CoW2016b,WHS2018} but are not, to the best of our knowledge, designed for pattern detection.
More importantly, even when incorporating geometrical invariances,
CNNs need an enormous number of templates and background examples to adequately learn the deep image detectors. As an order of magnitude, CheXNet~\cite{RIZ2017} allowed radiologist-level pneumonia detection on chest x-rays but only when trained on more than 100,000 labeled examples~\cite{WPL2017}.
They cannot be trained on-the-fly from one or a few examples.
The problem tackled in this paper, in comparison, is to detect patterns of interest based on the knowledge of a \emph{single} example.
\subsection{Contributions}
The main contributions of the paper are summarized as follows.
\begin{itemize}
\item \emph{Steerable filter design:} We define a SNR criterion for the image model \eqref{eq:detectionImageModelintro}, from which we identify the optimal steerable filter for pattern detection. When the background has a flat power-spectrum (white noise model), the filter is the steerable function matching the template $T$ (Theorem \ref{subsec:optimalfilter}). We also consider a richer background model for self-similar and isotropic power-spectrum, for which we also identify the optimal steerable filter (Proposition \ref{prop:whitening}).
\item \emph{Radial B-spline expansion:} The optimal steerable filter is characterized by its Fourier domain angular/radial decomposition.
The angular dependency is controlled by the use of steerable filters, which is equivalent to an angular low-pass approximation of the optimal filter.
The discrete radial profile of the optimal filter is captured by developing an interpolation method based on radial B-splines, relying on the identification of the optimal B-spline-based steerable filter in Theorem \ref{subsec:splineharmonic}.
\item \emph{A complete detection algorithm:} The previous formulation allows for a practical implementation to design steerable filter. We also provide a complete algorithm for the detection process, that we carefully evaluate experimentally.
\end{itemize}
The paper is structured in the following way. The continuous-domain theory of SNR-based optimal steerable filter design
is presented in Section~\ref{sec:theory}.
The implementation of the proposed theory on discretized image grids and detection algorithm are detailed in Section~\ref{sec:OSFimplementation}.
In Section~\ref{sec:OSFpracticing}, we investigate the performance and parameter sensitivity of the proposed framework.
Discussions and conclusions are presented in Section~\ref{sec:discussandconclude}.
\section{Optimal Steerable Filters: Theory} \label{sec:theory}
This section is dedicated to our continuous-domain framework for the detection problem.
After introducing the main notations in Section \ref{subsec:notations}, we present the SNR criterion for which the optimal detectors will be constructed in Section \ref{subsec:SNR}.
One challenging aspect of the detection is that the pattern can be found at an unknown orientation. We address this problem by using steerable filters, introduced in Section \ref{subsec:steer}.
The main theoretical result of this paper is Theorem \ref{theo:optimalfilter} in Section \ref{subsec:optimalfilter}, which gives the formula for the optimal steerable detector considering the SNR criterion.
In Section \ref{subsec:whitening}, we present a refinement of this result for a richer class of background models that appears to be much more realistic than the white noise model in practice.
Finally, we show how to define response maps based on the optimal detector, that can be used for the detection procedure in Section~\ref{sec:detectionprocedure}.
\subsection{Notations} \label{subsec:notations}
Vectors in the plane are denoted in spatial domain by $\bm{x} = (x_1,x_2)$ and in Fourier domain by $\bm{\omega} = (\omega_1, \omega_2)$.
We write $(r,\theta)$ for the polar coordinates in Fourier domain where $r\geq 0$ and $\theta \in [0,2\pi)$.
We switch from Cartesian to polar coordinates according to $(\omega_1,\omega_2) = (r \cos\theta, r\sin\theta)$ and $(r,\theta)= \left( (\omega_1^2+\omega_2^2)^{1/2}, \arctan(\omega_2/ \omega_1)\right)$.
We consider functions $f$ from $ \mathbb{R}^2$ to $ \mathbb{R}$. The Fourier transform of $f$ is $\widehat{f}$. A function $f$ is square integrable and denoted by $f\in L_2( \mathbb{R}^2)$ if $\lVert f\rVert_2^2 = \int_{ \mathbb{R}^2} \lvert f(\bm{x})\rvert^2\mathrm{d} \bm{x} < \infty$.
We shall use repeatedly the Parseval relation $\langle f , g \rangle = \frac{1}{2\pi} \langle \widehat{f} , \widehat{g} \rangle$.
The usual scalar product between two square integrable functions in Fourier domain is then
\begin{align*}
\langle \widehat{f} , \widehat{g} \rangle & = \int_{ \mathbb{R}^2} \widehat{f}(\bm{\omega}) \overline{\widehat{g}(\bm{\omega})} \mathrm{d}\bm{\omega} = \int_{0}^{2\pi} \int_{0}^\infty \widehat{f}(r,\theta) \overline{\widehat{g}(r,\theta)} r \mathrm{d} r \mathrm{d} \theta.
\end{align*}
The rotation matrix of angle $\alpha$ is $\mathbf{R}_{\alpha} = \begin{pmatrix}
\cos \alpha & - \sin\alpha \\
\sin \alpha & \cos \alpha
\end{pmatrix}$.
Finally, $f\propto g$ means that the two functions $f$ and $g$ are proportional.
\subsection{SNR Criterion for Template Approximation} \label{subsec:SNR}
We start by assuming that the image $I_{0}$ is the sum of a template of interest $T$ and a background image $S$ as
\begin{equation} \label{eq:imageModel}
{I}_0 (\bm{x}) = {T} ( \bm{x} )+ {S} (\bm{x}).
\end{equation}
Mathematically, $T \in L_2( \mathbb{R}^2)$ is a square-integrable function and $S$ is modeled as a Gaussian field with zero mean.
We call \eqref{eq:imageModel} the local image model, for which we have only one template localized in the center of the image.
The goal is to design detection filters $f$ that
\begin{itemize}
\item strongly responds to the foreground template ${T}$,
\item responds as little as possible to the background signal ${S}$, and
\item can be used efficiently to determine the orientation of the template ${T}$ when it is unknown.
\end{itemize}
The third requirement will be achieved by using \emph{steerable} filters (see Section \ref{subsec:steer} below).
To tackle the two first point, we want $f$ to maximizes the \textit{signal-to-noise ratio} (SNR), defined as
\begin{equation} \label{eq:SNR}
\mathrm{SNR}(f) = \frac{\mathbb{E} [\langle I_0 , f \rangle ]^2}{\mathrm{Var} (\langle I_0, f \rangle)},
\end{equation}
which is a very classical criterion in detection theory \cite{Van2004}.
The template ${T}$ is deterministic and the background signal has zero mean, we therefore have that $\mathbb{E} [\langle I_0 , f \rangle ] = \langle T , f\rangle$ and $\mathrm{Var}( \langle I , f \rangle ) = \mathrm{Var}( \langle S , f\rangle)$.
\subsection{Steerable Filters and their Fourier Radial Profiles} \label{subsec:steer}
We aim at detecting patterns whose orientations are \emph{a priori} unknown in an image.
This can be performed using steerable filters, which can be rotated efficiently~\cite{Unser2013steerable}. \\
\begin{definition} \label{def:steerable}
A filter $f$ is \emph{steerable} if the span of its rotated versions $f(\mathbf{R}_{\alpha} \boldsymbol{x})$, with $\alpha\in [0,2\pi)$, is a finite-dimensional subspace of $L_2( \mathbb{R}^2)$. \\
\end{definition}
The main advantage of steerable filters is that their rotation by an arbitrary angle is reduced to a finite dimensional algebraic problem.
In Proposition \ref{theo:harmonicdecomposition}, we characterize steerable filters from their polar decomposition in terms of the circular harmonic functions $\theta \mapsto \mathrm{e}^{\mathrm{j} n \theta}$, where $n\in \mathbb{Z}$. \\
\begin{proposition} \label{theo:harmonicdecomposition}
A function $f \in L_2( \mathbb{R}^2)$ can be uniquely decomposed in polar coordinates in Fourier domain as
\begin{equation} \label{eq:ladecomposition}
\widehat{f}(r,\theta) = \sum_{n\in \mathbb{Z}} \widehat{f}_n(r) \mathrm{e}^{\mathrm{j} n \theta},
\end{equation}
where the $\widehat{f}_n$ jointly satisfy
$ \sum_{n\in \mathbb{Z}} \lVert \widehat{f}_n\rVert_2^2 < \infty.$
The functions $\widehat{f}_n$, called the \emph{Fourier radial profiles} of $f$, are given by
\begin{equation} \label{eq:fn}
\widehat{f}_n(r) = \frac{1}{2\pi} \int_0^{2\pi} \widehat{f}(r,\theta) \mathrm{e}^{- \mathrm{j} n \theta} {\rm d} \theta.
\end{equation}
Moreover, $f$ is steerable if and only if finitely many $\widehat{f}_n$ are non-zero. \\
\end{proposition}
The proof of Proposition \ref{theo:harmonicdecomposition} is presented in Appendix \ref{ProofDecomposition}.
As a consequence, the general form of a steerable filter in the Fourier domain is
$\widehat{f} (r,\theta) = \sum_{n\in H} \widehat{f}_n (r) \mathrm{e}^{\mathrm{j}n \theta}$,
where $H$ is a finite subset of $ \mathbb{Z}$ and $\widehat{f}_n \in L_2( \mathbb{R}^2)$ the non zero Fourier radial profiles. We have in that case that
\begin{equation} \label{eq:fsteerableRotation}
\widehat{f (\mathbf{R}_{\alpha} \cdot)} (\bm{\omega}) = \widehat{f}(\mathbf{R}_{\alpha} \boldsymbol{\omega}) = \widehat{f}(r, \theta + \alpha) = \sum_{n \in H} \mathrm{e}^{\mathrm{j} n \alpha} \widehat{f}_n(r) \mathrm{e}^{\mathrm{j} n \theta}.
\end{equation}
Hence, any rotated version of $f$ is a linear combination of the inverse Fourier transforms of the $\widehat{f}_n(r) \mathrm{e}^{\mathrm{j} n \theta}$ for $n\in H$, meaning that $f$ is steerable in the sense of Definition \ref{def:steerable}.
Finally, any function $f$ can be approximated by steerable functions at an arbitrary precision. Indeed, it is sufficient to consider the truncated sums $\sum_{\lvert n \rvert \leq N} \widehat{f}_n(r) \mathrm{e}^{\mathrm{j} n \theta}$ that converge to $\widehat{f}$ in $L_2( \mathbb{R}^2)$ when the number of harmonics $N$ increases.
\subsection{Optimal Steerable Filter Learning for White Background} \label{subsec:optimalfilter}
In this section, we assume that the background signal $S$ is a Gaussian white noise, which corresponds to a flat power spectrum.
This implies that $ \mathrm{Var}( \langle S , f\rangle) = \sigma^2 \lVert f \rVert_2^2$, with $\sigma^2$ the variance of $S$ (see Appendix \ref{app:randomModels}).
As a consequence, \eqref{eq:SNR} becomes
\begin{equation}\label{eq:SNR2}
\mathrm{SNR}(f) = \frac{1}{\sigma^2} \frac{ \lvert \langle {T} , f \rangle\rvert^2}{ \lVert f \rVert_2^2} = \frac{1}{\sigma^2} \frac{ \lvert\langle \widehat{T} , \widehat{f} \rangle\rvert^2}{ \lVert \widehat{f} \rVert_2^2},
\end{equation}
where we used the Parseval relation for the Fourier domain expression.
Note that the SNR is well-defined for any square-integrable filter, due to the assumption that $T \in L_2( \mathbb{R}^2)$.
In Section \ref{subsec:whitening}, we will also consider more evolved background models.
For a given finite set of harmonics $H$, it is then possible to specify the optimal steerable filter for the SNR criterion \eqref{eq:SNR2} associated to the image model \eqref{eq:imageModel}. \\
\begin{theorem} \label{theo:optimalfilter}
A filter $f$ maximizes the SNR criterion \eqref{eq:SNR2} among the space of steerable filters with harmonics in $H$ if and only if
\begin{equation} \label{eq:fSNR}
\widehat{f}(r,\theta) \propto \sum_{n \in H} \widehat{T}_n (r) \mathrm{e}^{\mathrm{j} n \theta},
\end{equation}
with $\widehat{T}_n$ the Fourier radial profiles of $T$ given for each harmonic $n$ by
\begin{equation} \label{eq:integralTn}
\widehat{T}_n(r) = \frac{1}{2\pi} \int_{0}^{2\pi} \widehat{T}(r,\theta) \mathrm{e}^{-\mathrm{j} n \theta} \mathrm{d} \theta.
\end{equation}
\end{theorem}
The optimal filter is defined up to a multiplicative constant since $\mathrm{SNR}(\lambda f) = \mathrm{SNR} (f)$ for every scalar $\lambda \neq 0$.
The proof of Theorem \ref{theo:optimalfilter} is given in Appendix \ref{ProofOptiFilter}.
The optimal filter is completely determined by the template to approximate $T$ and the set of harmonics $H$.
In practice, the main issue is to compute the integral \eqref{eq:integralTn} while knowing only $T$ on a finite cartesian grid in the Fourier domain.
This point will be discussed extensively in Section \ref{sec:OSFimplementation}.
\subsection{Isotropic Self-similar Background Model and Whitening} \label{subsec:whitening}
The SNR criterion \eqref{eq:SNR2} is based on the assumption that the background is adequately modeled as a Gaussian white noise, corresponding to the case where its power spectrum $P_S(\bm{\omega})$ is nearly constant.
In this section, we consider a richer model for the background signal.
Indeed, it has been shown in many signal and image processing applications that the power spectrum of the signal of interest follows a power law~\cite{Pentland1984fractal,Flandrin1992wavelet,Sage2005automatic,Unser2014sparse,Puspoki2015template},
and is therefore smoother than a white noise.
We moreover make the assumption that the background is statistically isotropic, which is equivalent to saying that the power spectrum is a radial function $P_S(\bm{\omega})=P_S(r)$.
Mathematically, this means that the background signal satisfies the equation
\begin{equation} \label{eq:DeltaS=W}
(-\Delta)^{\gamma/2} S = W
\end{equation}
with $W$ a Gaussian white noise and $(-\Delta)^{\gamma/2}$ the fractional Laplacian of order $\gamma \geq 0$.
Then, the background signal $S$ is an \emph{isotropic self-similar (ISS) Gaussian field}~\cite{Tafti2010brownian,Lodhia2016fractional}. In this case, $S$ can be \emph{whitened}, in the sense that it can be linearly transformed into a white noise. This is what we refer to as background model ``with whitening".
We call $\gamma$ the \emph{self-similarity parameter} of $S$.
It plays a crucial role in determining the smoothness properties of the background model.
The power spectrum of $S$ is then $P_S(\bm{\omega}) = P_S(r) = \sigma^2 / r^{2\gamma}$, with $\sigma^2$ the variance of the underlying white noise.
As a consequence, the higher $\gamma$, the smoother $S$.
For illustration purposes, we represent several ISS Gaussian fields in Figure~\ref{fig:seeprocess}.
\begin{figure}[t!]\label{fig:IM}
\centering
\includegraphics[scale=0.30]{3nuages}
\caption{Realizations of ISS Gaussian fields for different values of $\gamma$. From left to right: $\gamma = 0$ (white noise), $\gamma = 1$, $\gamma=2$.}
\label{fig:seeprocess}
\end{figure}
We now establish the general implications of this background model.
More technical details can be found in Appendix \ref{app:randomModels}.
First, we shall consider filters such that $\langle S , f\rangle$ is well-defined, which requires that $(-\Delta)^{\gamma/2} g = f$ for some $g \in L_2( \mathbb{R}^2)$, or equivalently,
$\widehat{f}(\bm{\omega}) / \lVert \bm{\omega} \rVert^{\gamma} \in L_2( \mathbb{R}^2)$.
Then, $\langle S, f \rangle$ is a well-defined Gaussian random variable with zero mean and variance
\begin{align} \label{eq:varianceS}
\mathrm{Var}(\langle S , f \rangle) &= \frac{\sigma^2 }{2\pi} \int_0^{\infty} r^{1-2\gamma} \int_0^{2\pi} \lvert \widehat{f}(r,\theta) \rvert^2 \mathrm{d}\theta \mathrm{d}r
\end{align}
as shown in Appendix \eqref{app:randomModels}.
Finally, the SNR criterion \eqref{eq:SNR} becomes, for this background model,
\begin{equation} \label{eq:SNR3}
\mathrm{SNR}(f) = \frac{1}{\sigma^2} \frac{ \lvert \langle \widehat{T} ,\widehat{f} \rangle\rvert^2}{\lVert \widehat{g} \rVert_2^2}. \\
\end{equation}
We now present how to maximize this new criterion. \\
\begin{proposition} \label{prop:whitening}
A steerable filter $f$ with finite set of harmonics $H$ maximizes the SNR criterion \eqref{eq:SNR3} for the self-similarity order $\gamma \geq 0$ if and only if
\begin{equation}\label{eq:fSNR2}
\widehat{f}(r,\theta) \,\propto\, r^{2\gamma} \sum_{n \in H} \widehat{T}_n (r) \mathrm{e}^{\mathrm{j} n \theta},
\end{equation}
where $\widehat{T}_n$ are the Fourier radial profiles of $T$ given by \eqref{eq:integralTn}. \\
\end{proposition}
Proposition \ref{prop:whitening} is proved in Appendix \ref{ProofWhitening}. The effect of the whitening is a multiplication in the Fourier domain of the optimal filter for the SNR criterion \eqref{eq:fSNR} by $ r^{2\gamma}$.
In practice, we do not necessarily know the self-similar parameter.
We can nevertheless estimate $\gamma$ from the background signal $S$ itself.
The principle is as follows.
For a test function $f$ and a scale $a>0$, we consider $a^{-1} f(\cdot /a)$ whose $L_2$-norm does not depend on $a$ and which allows analyzing the background signal $S$ at scale $a$.
Then, the variance of $X_a = \langle S , a^{-1} f( \cdot / a) \rangle$ is known to proportional to $a^{2\gamma}$~\cite[Proposition 5.6]{Fageot2015wavelet}.
We therefore perform a multiscale analysis at various $a>0$ to estimate the parameter $\gamma$ from the theoretical linear relation between $\log \mathrm{Var}(X_a)$ and $\log a$, namely
\begin{equation}
\log \langle S , a^{-1} f( \cdot / a) \rangle = 2\gamma \log a + b,
\end{equation}
where $b \in \mathbb{R}$.
This method has been implemented to analyse the statistics of natural images in~\cite{Fageot2015wavelet} and found to be robust.
Finally, we remark that one may have only access to $I_0 = T + S$ in \eqref{eq:imageModel}, and not to the template $T$ itself, to design the optimal steerable filter. In that case, one can use background substraction techniques to recover $T$ from $I_0$. We do not discuss this aspect further in the paper and we assume to have access to a good template representation.
\subsection{Detection Procedure}
\label{sec:detectionprocedure}
The objective of the detection process is to reveal the positions and orientations of patterns corresponding to a template $T(\bm{x})$ in a (larger) image $I(\bm{x})$.
We model $I$ as a sum of templates of interest $T_i$, positioned at locations $\bm{x}_i$ and rotated with an angle $\theta_i$, and a background image $S$.
Mathematically, $I$ is therefore a function from $ \mathbb{R}^2$ to $ \mathbb{R}$ such that
\begin{equation} \label{eq:detectionImageModel}
{I} (\bm{x}) = \sum_i {T} ( \mathbf{R}_{- \theta_i} ( \bm{x} - \boldsymbol{x}_i ) )+ {S} (\bm{x}),
\end{equation}
with $T \in L_2( \mathbb{R}^2)$, $\boldsymbol{x}_i \in \mathbb{R}^2$, $\theta_i \in [0,2 \pi)$, and ${S}$ is an ISS Gaussian field.
Here, we assume that the template ${T}$ and the variance of the background signal ${S}$ are known, while the $\boldsymbol{x}_i$ and $\theta_i$ are unknown.
In order to detect template locations $\bm{x}_i$ at the correct orientations $\theta_i$, we can efficiently compute the two following quantities using the steerability property~\eqref{eq:fsteerableRotation} of our detector $f$ as
\begin{align}
\label{eq:detectionArgmax}
I_{\text{ang}}(\bm{x}_0)&=\argmax_{\theta_0}\langle I(\cdot-\bm{x}_0), f(\mathbf{R}_{\theta_0}\cdot) \rangle, \\
\label{eq:detectionMax}
I_{\text{amp}}(\bm{x}_0)&=\max_{\theta_0}\langle I(\cdot-\bm{x}_0), f(\mathbf{R}_{\theta_0}\cdot) \rangle \\
&= \langle I(\cdot-\bm{x}_0), f(\mathbf{R}_{I_{\text{ang}}(\bm{x}_0)}\cdot) \rangle, \nonumber
\end{align}
where $I_{\text{ang}}(\bm{x}_0)$ is the estimated orientation of $T$ at $\bm{x}_0\in\mathbb{R}^2$ and $I_{\text{amp}}(\bm{x}_0)$ is the amplitude of the maximum response of $f$ at $\bm{x}_0$.
It is worth noting that $I_{\text{amp}}(\bm{x}_i)$ will be maximized when $I_{\text{ang}}(\bm{x}_i)\approx\theta_i$.
\section{Optimal Steerable Filters: Discretization} \label{sec:OSFimplementation}
We have now described how to deduce the optimal steerable filter associated to a template $T$ in a background signal $S$.
The formulation of Section \ref{sec:theory} is in the continuous-domain,
although images are in practice stored as discrete arrays in a computer.
The concrete design of detection algorithms therefore requires the discretization of the proposed theory.
Practically, one should compute the optimal steerable detector $f$ in \eqref{eq:fSNR} from a discretized version of the template of interest $T$.
Computing $f$ requires an angular averaging over the Fourier transform of the template in \eqref{eq:integralTn}.
The approximation of \eqref{eq:integralTn} on the Cartesian grid is challenging because it involves evaluating integrals over the angular polar coordinate $\theta$ for all values of $r$, where much less samples are available when $r$ is small.
The discretization we propose essentially relies on the expansion of the Fourier radial profiles in terms of radial B-splines, the latter being introduced in Section \ref{subsec:radialBsplines}.
We then combine the circular harmonics and the radial B-splines in Section \ref{subsec:splineharmonic}, and obtain the discretized optimal steerable filter in Theorem \ref{theo:Bsplineexpansion}. Finally, we summarize how to compute the discretized version of the optimal steerable filter in Section \ref{sec:integralInPractice}.
\subsection{B-Spline Expansion of the Radial Profiles} \label{subsec:radialBsplines}
Cardinal B-splines are well-known for the capability of approximating continuous-domain functions based on discrete measurements \cite{Unser2005think}. The theory is traditionally developed for one-dimensional functions from $ \mathbb{R}$ to $ \mathbb{R}$, and has to be slightly modified in our context, since we deal with \emph{radial} functions.
The B-spline of degree $0$ is $\beta_0 (x) = 1_{[0,1]} (x)$. The spline of degree $(M+1)$ is defined recursively as \mbox{$\beta_{M+1}(x) = \beta_M * \beta_0(x)$}. In our experiments, we use the quadratic B-spline $\beta_2$, which is supported over $[0,3]$ and is piecewise quadratic on the intervals $[k,k+1]$, $k \in \mathbb{Z}$. The closed form expression of the quadratic spline can be found for instance in \cite{Unser1999splines}. Thereafter, we write $\beta_2 = \beta$ to simplify the notation. \\
\subsubsection{Radial B-splines}
A radial B-spline is a radial function $\widehat{f}(r)$ in $L_2( \mathbb{R}^2)$ of the form
\begin{equation} \label{eq:formradialspline}
\widehat{f}(r) = \sum_{k \in \mathbb{Z}} \frac{c[k]}{r_0} \beta\left( \frac{r}{r_0} - k \right),
\end{equation}
with $r_0>0$ the discretization step and $c[k]$ the spline coefficients of $\widehat{f}$.
The function $\widehat{f}$ is defined for radius $r\geq 0$. One could therefore restrict the sum in \eqref{eq:formradialspline} to integers $k$ such that the support of $\beta(\cdot / r_0 - k)$ intersects $ \mathbb{R}^+$. For quadratic splines, this corresponds to $k \geq -2$.
However, we prefer to keep the summation over all integers, allowing to consider discrete convolutions between sequences indexed by $k \in \mathbb{Z}$.
In what follows, we approximate the Fourier radial profiles of the template $T$ using radial B-splines.
\\
\subsubsection{Approximation with Radial B-Splines}
A radial function $\widehat{f} \in L_2( \mathbb{R}^2)$ can be approximated by radial B-splines of the form \eqref{eq:formradialspline} at arbitrary precision by taking the discretization step $r_0 \rightarrow 0$.
This is well-known for classical B-splines \cite{Unser1999splines} and can be adapted to the case of radial B-splines.
The main difference between the usual B-splines expansion of 1D functions and the B-spline expansion of 2D radial functions is that one changes the scalar product. We recall that the 2D scalar product between two radial functions $\widehat{f}$ and $\widehat{g}$ is given by
\begin{align*}
\langle \widehat{f} , \widehat{g} \rangle &=
\int_0^\infty \int_0^{2\pi} \widehat{f}(r) \overline{ \widehat{g}(r)} r \mathrm{d} \theta \mathrm{d} r = 2 \pi \int_0^\infty \widehat{f}(r) \overline{ \widehat{g}(r)} r \mathrm{d} r.
\end{align*}
To facilitate computations, we identify a radial function $\widehat{f} : \mathbb{R}^+ \mapsto \mathbb{C}$ to its symmetrization $\widehat{f} : \mathbb{R} \mapsto \mathbb{C}$ such that $\widehat{f}(-r) = \widehat{f}(r)$. In particular, the scalar product between two radial functions becomes
$\langle \widehat{f} , \widehat{g} \rangle= \pi \int_{ \mathbb{R}} \widehat{f}(r) \overline{ \widehat{g}(r)} |r| \mathrm{d} r$.
All the scalar products between radial functions have to be understood with this symmetrization procedure.
The expansion of a radial function in the quadratic spline basis requires special attention since the family is not orthogonal. We can overcome this using classical techniques for B-splines that we adapt to the case of radial B-splines.
We set $h[k] = \langle \beta , \beta(\cdot - k) \rangle$ for each $k \in \mathbb{Z}$. The filter $h$ is nonzero only for $\lvert k \rvert\leq 2$ due to the support of $\beta$. The fact that $h$ differs from the Kronecker $\delta$ means precisely that the family of shifted B-spline is not orthonormal.
Since $g$ is compactly supported, there exists a unique discrete filter $h^{-1}=(h^{-1}[k])_{k\in \mathbb{Z}}$ such that $(h *h^{-1}) [k] = ( h^{-1} * h ) [k] = \delta[k]$~\cite{DeBoor1989,Fageot2017beyond}.
Then, $h^{-1}$ plays a crucial role to accurately identify the optimal B-spline coefficients to approximate a radial function. \\
For any radial function $\widehat{f} \in L_2( \mathbb{R}^2)$, its projection to the space of radial B-splines with discretization step $r_0$ is denoted by
\begin{equation} \label{eq:projectionBsplines}
\mathrm{P}_{r_0} \{\widehat{f}\}(r) = \sum_{k \in \mathbb{Z}} \frac{c[k]}{r_0} \beta\left( \frac{r}{r_0} - k \right),
\end{equation}
\begin{proposition} \label{prop:radialexpansion}
Let ${f} \in L_2( \mathbb{R}^2)$.
For $k\in \mathbb{Z}$, we set
\begin{equation} \label{eq:thedk}
d[k] = \frac{1}{2\pi} \left\langle \widehat{f} (r,\theta) , \frac{1}{r_0} \beta\left( \frac{r}{r_0} - k \right) \right\rangle.
\end{equation}
Then, the coefficients in the orthogonal projection \eqref{prop:radialexpansion} of $\widehat{f}$ are computed as
\begin{equation} \label{eq:cviad}
c[k] = (h^{-1} * d) [k].
\end{equation}
\end{proposition}
Proposition \ref{prop:radialexpansion} is proved in Appendix \ref{app:Bsplineprop}. It gives the optimal approximation of a radial function in terms of radial B-splines for a given discretization step. Note that the discrete filter $h^{-1}$ does not depend on the discretization step $r_0$.
\subsection{Combining Radial B-splines and Circular Harmonics} \label{subsec:splineharmonic}
We define the family of functions $\varphi_{n,k}$, $n,k \in \mathbb{Z}$, given in the Fourier domain by
\begin{equation}
\widehat{\varphi}_{n,k} ( r , \theta ) = \frac{1}{r_0} \beta\left( \frac{r}{r_0} - k \right) \mathrm{e}^{\mathrm{j} n \theta}.
\end{equation}
For a fixed finite set of harmonics $H \subset \mathbb{Z}$ and discretization step $r_0 > 0$, one denotes by $\mathrm{P}_{r_0,H} \{\widehat{f}\}$ the orthogonal projection of the function $\widehat{f}$ onto the space generated by the $\widehat{\varphi}_{n,k}$ for $n \in H, k \in \mathbb{Z}$.
We can combine Proposition \ref{theo:harmonicdecomposition} and Proposition \ref{prop:radialexpansion} to approximate any square-integrable function by steerable functions whose Fourier radial profiles are B-splines. \\
\begin{theorem} \label{theo:Bsplineexpansion}
Let $r_0 > 0$ and $H\subset \mathbb{Z}$.
For any function $T \in L_2( \mathbb{R}^2)$, the orthogonal projection of its Fourier transform on the $\widehat{\varphi}_{n,k}$, $n \in H, k \in \mathbb{Z}$
is
\begin{equation}
\mathrm{P}_{r_0,H} \{\widehat{T}\} (r , \theta ) = \sum_{n \in H} \sum_{k\in \mathbb{Z}} c_n[k] \widehat{\varphi}_{n,k} ( r, \theta),
\end{equation}
where $c_n[k] = (h^{-1} * d_n) [k] = \sum_{\ell \in \mathbb{Z}} h^{-1} [\ell] d_n [k -\ell]$ and
\begin{align} \label{eq:coeffsdn}
d_n[k] &= \frac{1}{2\pi} \left\langle \widehat{T} , \varphi_{n,k} \right\rangle= \frac{1}{2\pi} \left\langle \widehat{T}_n (r) , \frac{1}{r_0} \beta\left( \frac{r}{r_0} - k \right) \right\rangle.
\end{align}
Moreover, when $r_0 \rightarrow 0$ and $H \rightarrow \mathbb{Z}$, the orthogonal projection converges to any $T$ for the $L_2$-norm. \\
\end{theorem}
Theorem \ref{theo:Bsplineexpansion} is proved in Appendix \ref{app:Bsplineprop}. It allows to compute an approximation of any template $T$ from the B-spline coefficients $c_n[k]$ of the $n$th radial profile for each $n$. Moreover, this approximation can be as good as required by diminishing the step size $r_0$ and increasing the number of harmonics. These coefficients are obtained via the $d_n[k]$, computing a simple convolution. Note that this operation is necessary because the family $\varphi_{n,k}$ is not orthogonal.
In practice, one obtains the coefficients $d_n[k]$, and therefore $c_n[k]$, by computing scalar products of the form \eqref{eq:coeffsdn}.
Theorem \ref{theo:Bsplineexpansion} means that one can approximate the optimal steerable filter based on the integral \eqref{eq:coeffsdn}. This is a clear improvement since this 2D integral can be approximated from the knowledge of $T$ on a finite Cartesian grid. We develop this last point in the next section.
\subsection{Computing the Discretized Optimal Steerable Detector}\label{sec:integralInPractice}
In practice, we have access to the template $T$ in a finite square grid. The steps to compute the optimal steerable detector in Theorem \ref{theo:optimalfilter} are as follows.
\begin{itemize}
\item Fix the set of harmonics $H$ and the discretization step $r_0$.
\item Compute the discrete Fourier transform $\widehat{T}$ of $T$ via fast Fourier transform (FFT).
\item Compute the coefficients $d_n[k]$ for $n\in H$ and $k \in K$, where $K$ is the set of integers such that $r_0 k$ remains in the range of the image. To do so, we note that the scalar product \eqref{eq:coeffsdn} is expressed as an integral in Cartesian coordinates as
\begin{equation} \label{eq:dncartesian}
d_n[k] = \int_{ \mathbb{R}^2} \widehat{T} (\omega_x,\omega_y) \widehat{\varphi}_{n,k} (\omega_x, \omega_y) \mathrm{d} \omega_x \mathrm{d} \omega_y.
\end{equation}
This integral is approximated with its Riemann sum, from the knowledge of $\widehat{T}$ on the Cartesian grid. The expression of the basis functions $\widehat{\varphi}_{n,k}$ in Cartesian coordinates is
\begin{small}
\begin{equation}
\widehat{\varphi}_{n,k}(\omega_x,\omega_y) = \frac{1}{r_0} \beta \left(\frac{\sqrt{\omega_x^2 + \omega_y^2}}{r_0} - k\right) \mathrm{e}^{\mathrm{j} n \arctan(\omega_y / \omega_x)}.
\end{equation}
\end{small}
\item For every $n \in H$ and $k \in K$, we compute the $c_n[k]$ according to $c_n [k] = (h^{-1} * d_n)[k]$.
\item Finally, the optimal spline-based steerable filter $f_{\mathrm{opt}}$ is given in the Fourier domain by
\begin{equation} \label{eq:computefopt}
\widehat{f}_{\mathrm{opt}} (r,\theta) = \sum_{k \in K} \sum_{n \in H} c_n[k] \frac{1}{r_0} \beta( r / r_0 - k) \mathrm{e}^{\mathrm{j} n \theta}.
\end{equation}
\end{itemize}
We remark that the Riemann sum approximating the integral \eqref{eq:dncartesian} is obtained from a finite number of coefficients only. Indeed, it deals with the grid points lying in the area delineated by the radial function $\beta( r / r_0 - k)$. When the template is known only on a coarse grid, the quality of the estimation of $d_n[k]$ can therefore be insufficient. We remedy to this issue by zero-padding the template $T$ in space domain to increase the size of the image. This corresponds to a sinc interpolation in Fourier domain, increasing the number of points on which the integral \eqref{eq:dncartesian} is computed.
The relevance of our discretization method for the construction of the optimal steerable detector is investigated and illustrated in Section~\ref{sec:OSFpracticing}.
When the background signal $S$ is adequately modeled as an ISS Gaussian field of self-similar parameter $\gamma$ (see Section \ref{subsec:whitening}), the optimal detector is characterized in Proposition \ref{prop:whitening}.
It is simply obtained by multiplying \eqref{eq:computefopt} with $r^{2\gamma}$.
We recall that the estimation of $\gamma$ can be performed efficiently on a single realization of the background $S$ using the method developed in \cite{Fageot2015wavelet}.
\section{Results} \label{sec:OSFpracticing}
In this section, we evaluate the performance and parameter sensitivity of the proposed optimal steerable filter design.
We first focus on template approximation, and follow with pattern detection and orientation estimation.
\subsection{Template Approximation}\label{sec:templateApprox}
We first evaluate the template approximation ability of the proposed SNR-based filter design criterion under the hypothesis of Gaussian white noise (Theorem~\ref{theo:optimalfilter}).
The optimal steerable detector is computed following the steps described in Section~\ref{sec:integralInPractice}.
Both qualitative and quantitative results are showed in Figure~\ref{fig:approx} for a template containing (a) a hand-drawn ``three'' $T_{\text{three}}$ and (b) $T_{\text{DH}}$, a double helix (DH) point spread function~\cite{PTB2009}.
The approximation performance is measured in terms of root mean squared error (RMSE).
The dimensions of the templates are $200\times 200$.
The parameter $r_0$ in~(\ref{eq:computefopt}) is determined for each template independently as a trade-off between achieving a fine-grained resolution for the interpolation of $r$ as well as having a sufficient number of coefficients in the Riemann sum approximating the integral~(\ref{eq:dncartesian}).
In all experiments, $r_0$ of 0.033 and 0.041 were used for $T_{\text{three}}$ and $T_{\text{DH}}$, respectively.
Figure~\ref{fig:approx} shows that although using more harmonics consistently reduces the approximation error, only a small number of harmonics (\emph{e.g.}, $N\approx 6$) is required to achieve accurate template modeling.
Such as small amount of harmonics yields a low-pass approximation of the templates in terms of circular frequencies, which is striking for $T_{\text{three}}$ (see Figure~\ref{fig:approx}~(a)).
For $T_{\text{DH}}$, the decrease of RMSE with $N$ is less regular, where the second harmonic is of paramount importance to model the two characteristic diametrically opposed blobs of the DH.
The decrease of RMSE is much faster for $T_{\text{DH}}$, which is circularly smoother than $T_{\text{three}}$.
We observe in Figure~\ref{fig:approx} (c) that Fourier based approximation are better-suited for regular patterns.
\begin{figure}[t!]
\begin{minipage}{\columnwidth}
\centering
\includegraphics[scale=0.19]{3smo_200}\hspace{4pt}
\includegraphics[scale=0.19]{3smo_200_det_N=0}
\includegraphics[scale=0.19]{3smo_200_det_N=1}
\includegraphics[scale=0.19]{3smo_200_det_N=2}
\includegraphics[scale=0.19]{3smo_200_det_N=3}
\includegraphics[scale=0.19]{3smo_200_det_N=4}
\end{minipage}
\begin{minipage}{\columnwidth}
\centering
\vspace{4pt}
\subfloat[Three: original $T_{\text{three}}$ and approximations $f$ with $N=0,1,\dots,9$.]{
\hspace{39pt}
\includegraphics[scale=0.19]{3smo_200_det_N=5}
\includegraphics[scale=0.19]{3smo_200_det_N=6}
\includegraphics[scale=0.19]{3smo_200_det_N=7}
\includegraphics[scale=0.19]{3smo_200_det_N=8}
\includegraphics[scale=0.19]{3smo_200_det_N=9}
}
\end{minipage}
\begin{minipage}{\columnwidth}
\vspace{6pt}
\centering
\includegraphics[scale=0.19]{dh_200}\hspace{4pt}
\includegraphics[scale=0.19]{dh_200_det_N=0}
\includegraphics[scale=0.19]{dh_200_det_N=1}
\includegraphics[scale=0.19]{dh_200_det_N=2}
\includegraphics[scale=0.19]{dh_200_det_N=3}
\includegraphics[scale=0.19]{dh_200_det_N=4}
\end{minipage}
\begin{minipage}{\columnwidth}
\centering
\vspace{4pt}
\subfloat[DH: original $T_{\text{DH}}$ and approximations $f$ with $N=0,1,\dots,9$.]{
\hspace{39pt}
\includegraphics[scale=0.19]{dh_200_det_N=5}
\includegraphics[scale=0.19]{dh_200_det_N=6}
\includegraphics[scale=0.19]{dh_200_det_N=7}
\includegraphics[scale=0.19]{dh_200_det_N=8}
\includegraphics[scale=0.19]{dh_200_det_N=9}
}
\end{minipage}
\vspace{2pt}
\subfloat[Evolution of template approximation error (RMSE) with respect to $N$.]{
\includegraphics[scale=0.52]{RMSE_3_DH}
}
\caption{Influence of the number of harmonics $N$ for template approximation.}
\label{fig:approx}
\end{figure}
\subsection{Detection: Position and Orientation Estimation} \label{subsec:detect}
The images are generated following the mathematical model \eqref{eq:detectionImageModel}.
To evaluate the relevance of the proposed quantities for detection, we use semi-controlled experimental conditions by randomly positioning and orienting several occurrences of a template $T$ added to the background $S$ to form the image $I$ containing $S$ with a controlled noise level $\sigma$.
We aim at estimating the template locations $\bm{x}_i$ together with their orientation $\theta_i$. The orientation is estimated according to \eqref{eq:detectionArgmax}, while the amplitude of the maximum response of the filter $f$ at $\bm{x}_0$, defined in \eqref{eq:detectionMax}, is used as our detection score in the following experiments.
We consider the templates from Figure~\ref{fig:approx}, where $T_{\text{three}}$ and $T_{\text{DH}}$ are blended into various portions of histopathological images\footnote{$4422 \times 2934$ image of \emph{plasmodium falciparum}, courtesy of Dr. M. D. Hicklin, public domain.}
and distinct realizations of ISS Gaussian fields ($\gamma=1.2$), respectively (Figure~\ref{fig:templateBlending}).
\begin{figure}[t!]
\centering
\includegraphics[scale=0.09]{3smo_200_data1_ori_tapisInv_2_a=1_rea1_ori}
\includegraphics[scale=0.09]{dh_200_data1_gamma=1_2_a=0_5_rea1_ori}
\caption{Semi-controlled experimental conditions for evaluating the detection performance.
Left: $T_{\text{three}}$ in histopathological background ($1200 \times 1200$). Right: $T_{\text{DH}}$ in an ISS Gaussian field ($1200 \times 1200$, $\gamma=1.2$).}
\label{fig:templateBlending}
\end{figure}
We evaluate the position detection performance using precision-recall (PR) as well as receiver operating characteristic (ROC) analysis based on pixelwise scores from every positions in $I_{\text{amp}}$ and angles $I_{\text{ang}}$.
We use a severe detection criteria where only the unique pixel corresponding to the center of the template is considered a true positive.
Since the ratio of true positives over true negatives is very small in this setting (\emph{e.g.}, 1/500,000), ROC analysis is used to focus on the ability of the system to find the true positions of the template, whereas PR curves better reveal the system trend to generate false detections.
All experiments compare areas under the PR or ROC curve (AUC) when assuming that the background signal is either a white noise that does not require any whitening process (referred to as ``no whitening'') or a ISS Gaussian field whose self-similar parameter $\gamma$ is estimated (referred to as ``whitening'').
We explore the parameter sensitivity of the proposed approach in the following paragraphs.
Unless specifically studied, the parameters were fixed to a noise level of $\sigma=1$ and $M=30$ tested angles in $[0,2\pi)$.
The estimated whitening parameters $\gamma$ were of 1.35 and 1.21 for the histopathological images and the ISS Gaussian fields, respectively.
The latter were estimated using the method described in the last paragraph of Section~\ref{sec:integralInPractice} and was based on 10 realizations of $S(\bm{x})$.
The number $N$ of harmonics used to approximate the template were 20 and 8 for the $T_{\text{three}}$ and $T_{\text{DH}}$, respectively.
The robustness of detection performance for various noise levels is first investigated in Figure~\ref{fig:detectionNoiseLevel_Three} for $T_{\text{three}}$.
The use of whitening allows excellent robustness to noise, where an average ROC AUC of 0.98 and an angular error below 10 degrees are observed for a noise level $\sigma=5$ (the template can be hardly seen with such a noise variance).
This highlights the adequacy of the fractional Laplacian model for the histopathological background.
The evolution of the PR AUC and the corresponding cropped response maps suggest that most false positives occur in the vicinity of the true position.
The resulting false positive can subsequently be ruled out by enforcing a minimum distance between distinct detections.
A performance comparison based on a Laplacian of Gaussian (LoG) filter with optimized scale $\sigma_{\text{LoG}}\in[5,100]$ (with a step of 5) is provided as a baseline.
The LoG is a zero-mean band-pass handcrafted filter that is standard in several image analysis algorithms involving detection (\emph{e.g.}, scale-invariant feature transform (SIFT)~\cite{Low2004}, scale-space analysis~\cite{Lin2018}, Marr's theory on vision and detection~\cite{MaH1980}).
We observe that the detection performance obtained with the latter is very low and highlights the difficulty of the task when the considered templates are not isotropic and entangled in complex backgrounds.
Similar trends were observed for $T_{\text{DH}}$ in Figure~\ref{fig:detectionNoiseLevel_Three}.
The importance of the whitening operation is even more striking, which is explained by the fact that the background noise is the realization of an ISS Gaussian fields.
\begin{figure}[t!]
\centering
\includegraphics[trim = 120 330 120 325, clip, scale=0.63]{PR_3_noiseLevels}
\includegraphics[trim = 120 315 120 325, clip, scale=0.63]{ROC_3_noiseLevels}
\begin{minipage}{\columnwidth}
\hspace{51pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_ori_tapisInv_2_a=1_rea1_ori}
\hspace{-1pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_ori_tapisInv_2_a=2_rea1_ori}
\hspace{-1pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_ori_tapisInv_2_a=3_rea1_ori}
\hspace{-1pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_ori_tapisInv_2_a=4_rea1_ori}
\hspace{-1pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_ori_tapisInv_2_a=5_rea1_ori}
\put(-227,12){\small $I^{\text{loc}}(\bm{x})$}
\end{minipage}
\begin{minipage}{\columnwidth}
\vspace{4pt}
\hspace{51pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_ori_tapisInv_2_a=1_rea1_ori_amp_noWhite}
\hspace{-1pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_ori_tapisInv_2_a=2_rea1_ori_amp_noWhite}
\hspace{-1pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_ori_tapisInv_2_a=3_rea1_ori_amp_noWhite}
\hspace{-1pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_ori_tapisInv_2_a=4_rea1_ori_amp_noWhite}
\hspace{-1pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_ori_tapisInv_2_a=5_rea1_ori_amp_noWhite}
\put(-229,16){\small $I^{\text{loc}}_{\text{amp}}(\bm{x})$}
\put(-237,7){\scriptsize(no whitening)}
\end{minipage}
\begin{minipage}{\columnwidth}
\vspace{4pt}
\hspace{51pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_ori_tapisInv_2_a=1_rea1_ori_amp_white}
\hspace{-1pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_ori_tapisInv_2_a=2_rea1_ori_amp_white}
\hspace{-1pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_ori_tapisInv_2_a=3_rea1_ori_amp_white}
\hspace{-1pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_ori_tapisInv_2_a=4_rea1_ori_amp_white}
\hspace{-1pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_ori_tapisInv_2_a=4_rea1_ori_amp_white}
\put(-229,16){\small $I^{\text{loc}}_{\text{amp}}(\bm{x})$}
\put(-232,7){\scriptsize(whitening)}
\end{minipage}
\begin{minipage}{\columnwidth}
\vspace{4pt}
\hspace{51pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_sigma=60_tapisInv_2_a=1_rea1_LoG}
\hspace{-1pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_sigma=60_tapisInv_2_a=2_rea1_LoG}
\hspace{-1pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_sigma=60_tapisInv_2_a=3_rea1_LoG}
\hspace{-1pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_sigma=60_tapisInv_2_a=4_rea1_LoG}
\hspace{-1pt}
\includegraphics[trim = 292 368 170 99, clip, scale=0.32]{3smo_200_data1_sigma=60_tapisInv_2_a=5_rea1_LoG}
\put(-229,16){\small $I^{\text{loc}}_{\text{amp}}(\bm{x})$}
\put(-230.5,7){\scriptsize(opt. LoG)}
\vspace{8pt}
\end{minipage}
\includegraphics[trim = 120 320 120 325, clip, scale=0.63]{angularError_3_noiseLevels}
\caption{Robustness of detection of $T_{\text{three}}$ for various noise levels (histopathological background).
Cropped thumbnails of the image $I^{\text{loc}}$, and response $I^{\text{loc}}_{\text{amp}}(\bm{x})$ are shown to illustrate and compare the spatial distribution of the detection scores around a true positive for the corresponding noise levels $\sigma=1,\dots,5$.
The performance obtained with an optimized LoG filter ($\sigma_{\text{LoG}}=60$) is reported as a baseline (it does not appear in the last plot since it is isotropic and does not allow for angle estimation).}
\label{fig:detectionNoiseLevel_Three}
\end{figure}
\begin{figure}[t!]
\centering
\includegraphics[trim = 120 332 120 325, clip, scale=0.63]{PR_DH_noiseLevels}
\includegraphics[trim = 120 332 120 325, clip, scale=0.63]{ROC_DH_noiseLevels}
\includegraphics[trim = 120 320 120 325, clip, scale=0.63]{angularError_DH_noiseLevels}
\caption{Robustness of detection of $T_{\text{DH}}$ for various noise levels (ISS Gaussian fields).
The performance obtained with an optimized LoG filter ($\sigma_{\text{LoG}}=20$) is reported as a baseline (it does not appear for the last plot).}
\label{fig:detectionNoiseLevel_DH}
\end{figure}
The robustness of the estimation of the whitening parameter $\gamma$ and its influence on the detection performance is studied in Table~\ref{tab:gammaEstimate} and Figure~\ref{fig:gammaEstimateDetection}.
The estimated values $\tilde{\gamma}$ are found to be robust to the presence of templates for both types of background noise, which suggests that the whitening parameter can be directly estimated from $I(\bm{x})$ when the template density is relatively low.
A value of $\tilde{\gamma}=1.2$ corresponds to the ground truth for ISS Gaussian fields.
The optimal values for detection for $T_{\text{three}}$ and $T_{\text{DH}}$ were $\gamma_{\text{opt}} = 1.2$ and $\gamma_{\text{opt}} = 1.4$, respectively, which are close to $\tilde{\gamma}$.
Even if the correspondence between $\tilde{\gamma}$ and $\gamma_{\text{opt}}$ is remarkable, a precise estimation of $\gamma$ is not found to be critical as the PR AUC plateaus around $\gamma_{\text{opt}}$.
It is worth noting in Figure~\ref{fig:gammaEstimateDetection} that in the case of detecting $T_{\text{DH}}$ in the ISS Gaussian field, the assumption of white background noise (\emph{i.e.}, no whitening) leads to poor detection performance.
This is consistent with the findings in Figure~\ref{fig:detectionNoiseLevel_DH}:
the whitening operation becomes essential with this type of background (ISS Gaussian fields).
\begin{table
\caption{Estimated whitening parameter values $\tilde{\gamma}$ are compared when based on the pure background $S(\bm{x})$ versus $I(\bm{x})$ containing the templates~(\ref{eq:detectionImageModel}).
The values yielding optimal detection performance $\gamma_{\text{opt}}$ are compared.}
\label{tab:gammaEstimate}
\begin{center}
\begin{tabular}{c|c|c|c|}
$S(\bm{x})$ & $\tilde{\gamma}$ from $S(\bm{x})$ & $\tilde{\gamma}$ from $I(\bm{x})$ & $\gamma_{\text{opt}}$ \\
\hline
\begin{minipage}{60pt}
\vspace{3pt}
\centering
ISS
Gaussian fields ($\gamma=1.2$)\\
\vspace{3pt}
\end{minipage}
& 1.2 & 1.21 & 1.2 \\
\hline
\begin{minipage}{60pt}
\vspace{3pt}
\centering
histopathological\\
images\\
\vspace{3pt}
\end{minipage}
& 1.31 & 1.35 & 1.4 \\
\hline
\end{tabular}
\end{center}
\end{table}
\begin{figure}[t!]
\centering
\includegraphics[trim = 120 320 120 325, clip, scale=0.63]{gammaEstimateDetection}
\caption{Evolution PR AUC with the whitening parameter $\gamma$ for $T_{\text{three}}$ and the histopathological background as well as for $T_{\text{DH}}$ and the ISS Gaussian field.
$\gamma_{\text{opt}}$ values of 1.4 and 1.2 corresponds to the optimal PR AUC for $T_{\text{three}}$ and $T_{\text{DH}}$, respectively.
In both cases, a precise estimation is not critical as the AUC plateaus around $\gamma_{\text{opt}}$.}
\label{fig:gammaEstimateDetection}
\end{figure}
The importance of the number of harmonics $N$ for template modeling was investigated in Section~\ref{sec:templateApprox}.
The impact of the latter on detection performance is shown in Figure~\ref{fig:detectionNbHarmDH} for $T_{\text{DH}}$.
The observed AUC and angular errors are consistent with our previous observations, where the importance of harmonic $N=2$ is highlighted to capture the two blobs of $T_{\text{DH}}$.
The performance is stable for $N\geq 4$, and using more harmonics does not significantly improve the detection.
Similar observations are made on the influence of $N$ for detecting $T_{\text{three}}$.
\begin{figure}[t!]
\centering
\includegraphics[trim = 120 332 120 325, clip, scale=0.63]{PR_DH_nbHarm}
\includegraphics[trim = 120 332 120 325, clip, scale=0.63]{ROC_DH_nbHarm}
\includegraphics[trim = 120 320 120 325, clip, scale=0.63]{angularError_DH_nbHarm}
\caption{Impact of the number of harmonics $N$ on detection for $T_{\text{DH}}$. The findings are consistent with the study of template approximation error in Figure~\ref{fig:approx}, where the second harmonic is capturing the two distinctive blobs of the DH.}
\label{fig:detectionNbHarmDH}
\end{figure}
Finally, the influence of the number $M$ of tested angles in $[0,2\pi)$ for \eqref{eq:detectionArgmax} and~\eqref{eq:detectionMax} is studied in Figure~\ref{fig:detectionTestedAngles_three} for $T_{\text{three}}$.
we also report the \emph{baseline} angular error corresponding to the sampling step $\pi/M$.
Whereas the performance consistently increases with $M$, relatively coarse angular discretization (\emph{e.g.}, $M=12$) yields near to optimal detection rates.
When $M \leq 7$ the ROC AUC appears to be significantly higher for the non-whitened detector, which is contrasting with all other experiments.
This may indicate that the whitened detector must be aligned with increased precision (\emph{e.g.}, $M\geq10$) to provide optimal results when compared to the non-whitened one.
Once again, very similar trends were observed on the influence of $M$ for detecting $T_{\text{DH}}$ in ISS Gaussian fields.
\begin{figure}[t!]
\centering
\includegraphics[trim = 120 332 120 325, clip, scale=0.63]{PR_3_testedAngles}
\includegraphics[trim = 120 332 120 325, clip, scale=0.63]{ROC_3_testedAngles}
\includegraphics[trim = 120 320 120 325, clip, scale=0.63]{angularError_3_testedAngles}
\caption{Number $M$ of angles tested in $[0,2\pi)$ for the construction of $I_{\text{ang}}$ and $I_{\text{amp}}$.
The baseline angular error $\pi/M$ is reported.}
\label{fig:detectionTestedAngles_three}
\end{figure}
\section{Discussion and conclusion} \label{sec:discussandconclude}
The main goal of this paper was to provide a complete pipeline for the detection of specific patterns at unknown positions and orientations in an image.
The key ingredients of our approach are (a) a continuous-domain formulation of the detection problem based on steerable filters and the optimization of the SNR criterion (Section~\ref{sec:theory}),
(b) a B-spline based discretization scheme (Section~\ref{sec:OSFimplementation}),
and (c) an additional ``whitening" procedure to extract statistical information from the background (the self-similar parameter $\gamma$) and specify an appropriate image model.
We have demonstrated the abilities of our detection procedure in practice (Section \ref{sec:OSFpracticing}) and estimated adequately the position and orientation of the pattern of interest.
We briefly recap the main contributions of this paper.
\begin{itemize}
\item We approximate a template with steerable filters, which provides a low-pass approximation retaining only small angular frequencies.
In practice, we have seen that only few angular frequencies are required for good template approximation (Figure \ref{fig:approx}) or pattern detection (Figure \ref{fig:detectionNbHarmDH}).
\item In contrast to many other works~\cite{puspoki2016design}, we do not construct \emph{polar separable} steerable filters. This enables us to approximate any possible template $T$ at arbitrary precision (Proposition \ref{theo:harmonicdecomposition}), allowing for the precise detection of non-separable patterns such as the ones used in our experiments (three and double-helix).
\item Our method lies on the assumption that the patterns of interest in the image are adequately modeled by a common template $T$ provided by the user, as in \eqref{eq:detectionImageModel}.
Under this assumption, we are then able to precisely detect patterns featuring occurrences of this template (Section~\ref{subsec:detect}) with a strong robustness to noise (Figure~\ref{fig:detectionNoiseLevel_Three}).
\item The whitening procedure (Section \ref{subsec:whitening}) tremendously improves the detection performance (Figure~\ref{fig:gammaEstimateDetection}). This demonstrates the relevance of considering non-white background models. The proposed isotropic and self-similar model only requires the estimation of one parameter, $\gamma$,
for which we provide a theoretically justified procedure.
\item As a by-product of our method, we are not only able to recover the positions of the patterns, but also their a priori unknown orientation. This information is simply extracted from the angular map $I_{\text{ang}}$ in \eqref{eq:detectionArgmax}. To refine angular accuracy, one should consider enough tested angles. Higher values of $M$ do not significantly increase the detection performance but obviously affect the angular error (Figure \ref{fig:detectionTestedAngles_three}). This additional angular information could be exploited in segmentation~\cite{Uhlmann2016hermite} or to extract directional features of the object of interest.
\end{itemize}
Limitations of the current approach includes the modeling of one single template per detector.
However, this potential weakness is compensated by the ability of the model to approximate any template with high accuracy.
In addition, a collection of detectors can be obtained by repeating the learning process for each distinct template class.
Detection robustness with respect to pattern deformations was not specifically evaluated.
Nevertheless, we believe that using steerable models with a small number of harmonics results in regularized (i.e., low-pass) detectors capturing the global layout of the template with enhanced generalization abilities.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,576 |
{"url":"https:\/\/www.physicsforums.com\/threads\/how-to-solve-for-mass-given-gravitational-force-and-radius.622684\/","text":"# How to solve for mass given gravitational force and radius ?\n\n1. Jul 22, 2012\n\n### scientific_vi\n\nhow to solve for mass given gravitational force and radius ???\n\n1. The problem statement, all variables and given\/known data\nThe gravitational force between two identical objects 2.00m apart is 3.50x10^-6N. determine the mass of each object.\n\n2. Relevant equations\n\ni know that Fg= GmM\/r^2\nso gravitational force is equal to the gravitational constant times mass one and mass two over the radius squared\n\n3. The attempt at a solution\ni tried manipulating the formula to solve for the masses\ni went\nFgr^2\/G=mM\n\ni did (3.50x10^-6N)(2.oo^2m)\/(6.67x10^-11)\n\nwhich does not give me the answer of 458kg\n\n2. Jul 22, 2012\n\n### Villyer\n\nRe: how to solve for mass given gravitational force and radius ???\n\nYou calculated Fgr^2\/G, which you said was equal to mM.\n\nThey didn't ask for mM though, so you haven't finished the problem yet.\n\n3. Jul 22, 2012\n\n### scientific_vi\n\nRe: how to solve for mass given gravitational force and radius ???\n\nbut mM is the masses though.\nso would i need to solve for mass one in order to solve for mass two ?\n\n4. Jul 22, 2012\n\n### Villyer\n\nRe: how to solve for mass given gravitational force and radius ???\n\nmM is the product of the masses. You need to find each of them, m and M.\n\nWhat is the relationship between m and M?\n\n5. Jul 22, 2012\n\n### scientific_vi\n\nRe: how to solve for mass given gravitational force and radius ???\n\nim not sure on how to solve for each m individually.\nam i manipulating the formula incorrectly?\n\n6. Jul 22, 2012\n\n### Villyer\n\nRe: how to solve for mass given gravitational force and radius ???\n\nNo, it was correct to solve it for mM.\n\nWhat do they tell you in the problem about the two masses that might help you solve for one?\n\n7. Jul 22, 2012\n\n### scientific_vi\n\nRe: how to solve for mass given gravitational force and radius ???\n\nthey are both identical .\nhaha ohkay so if i calculate one they should both be the same.\n\n8. Jul 22, 2012\n\n### Villyer\n\nRe: how to solve for mass given gravitational force and radius ???\n\nExactly.\n\nMathematically, m = M.\n\n9. Jul 22, 2012\n\n### scientific_vi\n\nRe: how to solve for mass given gravitational force and radius ???\n\nThanks a million .\ni must read the questions more carefully hah.","date":"2017-12-12 16:57:17","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8294059038162231, \"perplexity\": 1787.1033910284386}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-51\/segments\/1512948517350.12\/warc\/CC-MAIN-20171212153808-20171212173808-00249.warc.gz\"}"} | null | null |
Armavir è una città della Russia, situata sulle rive del fiume Kuban' nella pianura a nord della catena montuosa del Caucaso; è una delle città più importanti del Territorio di Krasnodar e un importante centro industriale. Il centro abitato è attraversato dal 45º parallelo, la linea equidistante fra il Polo nord e l'Equatore.
Storia
La città venne fondata nel 1839 da alcuni coloni armeni con il nome di Armjanskij Aul; nel 1848 fu ribattezzata con l'attuale nome, in onore dell'antica capitale dell'Armenia. La città fu teatro di molte battaglie durante la guerra civile russa negli anni 1918-20; subì anche una lunga occupazione tedesca dal 1941 al 1943.
Società
Evoluzione demografica
Fonte: mojgorod.ru
1897: 6.100
1926: 74.400
1939: 83.700
1959: 111.000
1979: 161.500
1989: 161.000
2002: 193.964
2007: 190.000
Architetture
Nei pressi della città si trova una base militare che fornisce alla Russia copertura radar di tutto il Medio Oriente.
Amministrazione
Gemellaggi
Armavir è gemellata con:
Altri progetti
Collegamenti esterni | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,175 |
Inter-ethnic conflicts in Switzerland in the 16th century
I have come across this description in Paddy Ashdown's (excellent) autobiography A Fortunate Life:
I have often been struck by the similarities between those countries whose fortune (or misfortune) it is to find themselves at the junction of the tectonic plates of race, culture and religion. Countries like Switzerland, Afghanistan and Bosnia are all of them mountainous regions, incredibly beautiful, the battlegrounds of conquerors and the cockpits in which, from time to time, terrible inter-ethnic conflicts break out (before the Treaty of Ticino in 1516 the famously peaceful Switzerland of today was the Bosnia of the middle ages when it came to internal war and ethnic conflict).
What were the main inter-ethnic (racial, cultural, religious) dimensions of the 16th-century and perhaps earlier conflict in Switzerland that the author is referring to here?
I think he's off base about Switzerland, unless he is mischaracterizing the nature of the Swiss confederacy. I'm also not sure what he means about ethnic strife. He's probably talking about the Duchy of Savoy and France directly to the south, and the passes from France into Northwest Italy. It's a strategic point in Western Europe by which France was trying to expand into Italy, at the expense of the Holy Roman Empire and the Italian states. It's importance also made it a point of contest by the local nobility of Savoy and Milan.
Ticino is a region in Switzerland that juts into Milan, and was annexed to it in 1516.
In this case, 'ethnic-conflict' is presumably referring to ethnicity in the same way as it is defined in the Wikipedia article:
An ethnic group, or an ethnicity, is a category of people who identify with each other based on similarities such as common ancestry, language, society, culture or nation.
The group need not be based on race, culture, or religion.
The article on Swiss people states:
The traditional ethnic composition of the territories of modern Switzerland includes the following components:
The German-speaking Swiss (Deutschschweizer), i.e. Alemannic German, historically amalgamated from the Gallo-Roman population and the Alemanni and Burgundii, including subgroups such as the Walser. Closely related German-speaking peoples are the Alsatians, the Swabians and the Vorarlbergians.
The French-speaking Swiss (Romands), traditionally speaking Franco-Provençal dialects, today largely assimilated to the standard French language (Swiss French), amalgamated from the Gallo-Roman population and Burgundians (the historical Upper Burgundy). They are closely related to the French (especially those of Franche-Comté). They are occasionally referred to as Welsch in Swiss German.
The Italian-speaking Swiss (Svizzeri italiani), traditionally speakers of Lombard language (Ticinese variety) today partly assimilated to the standard Italian language, amalgamated from Raetians and Lombards. They are closely related to the Italians (especially Lombards and Piedmontese).
The Romansh, speakers of the Romansh language, settling in parts of the Grisons, historically of Raetic stock.
Now, Personally I don't know whether these groupings are generally agreed, or whether there is some dispute. That is not the point.
The point is that these groupings are accepted as ethnic groups by at least some people using that definition. Furthermore, by that definition conflict between these group is ethnic conflict, and Lord Ashdown's categorisation would seem reasonable.
At the beginning of the XVI th century the town of Geneva was an independent state. It was influenced by Luther's ideas from 1525 onwards and William Farel's sermons led to the setting up of the Commune, which was powerful in the town, establishing the Reform movement in 1536. The same year Jean Calvin, author of the already well-known Institution Chrétienne, was asked to come to Geneva to strengthen the Reform movement and to transform the town according to Scriptural principles. There were many factors which contributed to Geneva being called "protestant Rome" : the wave of incoming refugees from France, Italy, England or the Low Countries, the Academy, set up in 1559, which taught many foreign students, lastly, the activities of Théodore de Bèze, who worked with Calvin and later became his successor. The institutional model of the Genevan Church, with its ecclesiastical rule by a pastor, an elder and a deacon, became typical of all reformed churches.
During the same period, the Reform movement also became established in the largest Swiss cantons : Zurich, Bale and Berne (this included what is now the canton of Vaud with its capital Lausanne). In Zurich, Zwingli (1484-1531), who played an essential role in the Reform movement, developed a theological standpoint which differed from Lutheranism over the issue of the Last Supper in fact his theses were close to those of Calvin at a much later date in his doctrine of predestination.
On the whole, the Reform movement took hold in the towns, while the rural and mountain cantons remained catholic and, with the support of the pope and the emperor they formed a Christian union. The "first war of Kappel" (1529) ended in a compromise but Zwingli, ill pleased with the results, called for a second war this time, at the second battle of Kappel, the Zurich armies were badly defeated by the Catholics and Zwingli was killed (1531). The peace treaty which followed laid down the basis of religious division in Switzerland : on the one hand the four reformed cantons (Zurich, Berne, Bâle, Schaffhouse), on the other the seven catholic cantons (Uri, Schwyz, Unterwald, Lucerne, Zoug, Soleure and Fribourg). Glaris and Appenzell were of mixed religion. The catholic cantons, contrary to their protestant counterparts, were quite poor and with a relatively small population, but nonetheless they
had the majority of seats at the federal Diet and this catholic opposition would prevent the Confederation from expanding for a long time Geneva, an independent town, was only attached to it in 1815.
As for the Protestants, their religious structure differed from place to place : in Geneva, ecclesiastical rule was in the hands of the Consistory, in Zurich civil government had a certain amount of influence. Conflict came to an end with Heinrich Bullinger (1504-1575), the "patriarch of reformed Protestantism". The drawing-up of the New Helvitic Confession (Confession Hélvétique postérieure) (1566) was to be the definitive basis of Swiss Protestantism.
Hospitality of the cantons and the difficulties
The massive influx of refugees in the Vaud canton, required that the local authorities and the inhabitants participate in meeting the immediate needs of the displaced persons.
Lodging was ensured by "public housing", hostels (expenses paid for by the authorities( and hospitals, but also inhabitants who volunteered (refusals were rare) or were obliged to in case of massive influx. Transportation for the weakest ones was by boat or on wagons, and the transporters were generally paid. The extensive network of hospitals in the Vaud canton was opened to the refugees: lodging, food, health care, "passa ", i.e. alms given by a pastor, enabling the recipient to "pass" further to the next locality where the refugee could ask for another passage. This effort can be explained by the wish to hasten the conveyance of refugees from one stop-over to the next, and thus shorten their stay in localities.
Reformed Switzerland consisted of a transit route from a few weeks to a few months, for most refugees who were either waiting for relatives or help, or information, who did not want to get too far away from France in case Protestantism was restored. The refugees were mobile, often changed houses, were often poor, and the authorities had trouble curbing the roaming tramps and beggars.
A minority only settled permanently, notably those who could set up an economic activity, especially a factory. The authorities then awarded them a special status as "resident" without political rights, but established some agreement with the city, and they were registered in a special book. Only those who declared in writing that they came for religious reasons were accepted. Very few acceded to bourgeoisie.
Reformation and the 17th century
The 16th century in Western Europe was dominated by the Reformation, a movement which divided western Christianity into two camps.
Although the riots and destruction were fought on a religious level, this reflected, above all, the desire for social change and the social tensions that existed primarily between town and country. The 17th century saw three further landmarks in the development of modern-day Switzerland. All came as a result of the 30 Years' War (1618-48). While large parts of Europe were involved in this war, the Confederation remained neutral. An important consequence of the Thirty Years' War was Swiss independence from the Holy Roman Empire, which was formally recognised by the Treaty of Westphalia.
Two Reformers: Zwingli and Calvin
The Reformation in Switzerland involved various centres and reformers. A major role was played by Ulrich Zwingli, who was active from 1523 in Zurich, and John Calvin, who from 1536 transformed Geneva into what was called the "Protestant Rome".
Learn more Common.Of Two Reformers: Zwingli and Calvin
Conflict and religious wars
As elsewhere in Europe, the Reformation plunged the Confederation into religious wars. These often also led to renewals within the Catholic Church and its territories.
Learn more Common.Of Conflict and religious wars
Political structure in the 17th century
In the 17th century, the Confederation consisted of various territories whose inhabitants enjoyed greatly varying amounts of freedom depending on where they lived.
Learn more Common.Of Political structure in the 17th century
Thirty Years' War and independence
The Confederation stayed out of the war, with only the Associated Place of Graubünden being drawn into the hostilities. The Thirty Years' War ended for the Confederation with its separation from the Holy Roman Empire of the German Nation.
Learn more Common.Of Thirty Years' War and independence
Peasant revolts and religious peace
The conflicts between rulers and subjects in Lucerne, Bern, Solothurn and Basel culminated in 1653 in the Swiss Peasants' War. The religiously motivated Villmergen Wars of 1656 and 1702 led to the loss of Catholic supremacy.
Learn more Common.Of Peasant revolts and religious peace
Switzerland was originally inhabited by a Celtic population, who were named Helvetians by the Romans. Between the 3rd and 5th centuries, the Alemannen tribes swept down from the north and conquered the northern and eastern part of Switzerland. The southwestern part of Switzerland was ruled by the Burgundians, who had settled in France. In the 6th century, theFranks took control of the part of Switzerland that was part of the duchy of Swabia. The smaller south-western portion of the country remained under Burgundian domination at this time. The Burgundian Swiss spoke French, a language division that remains today.
In 1033, the kingdom of Burgundy joined the Holy Roman Empire, and when it became a part of France in the 14th century, the Helvetian part of Switzerland remained Swiss. The House of Hapsburg, the rulers of Austria, had their original seat in Switzerland, which they gained control of in 1278. Their policies provoked a rebellion among the Ur-cantons, or ancient cantons, of Schwyz, Uri, and Unterwalden. although they were free subjects of the Empire, according to tradition, they made a famous oath in 1291, to protect their freedom, refusing to "salute the governor's hat on a pole."
The governor, a local authority chosen by the emperor, demanded that all citizens salute his hat as they passed by, in order to assure that the Swiss would respect the authority of their ruler. According to Swiss folklore, William Tell refused to salute the symbol of the governor's authority and was forced to split the apple that had been placed on his son's head by the cruel governor, by shooting at his own son with an arrow from his own crossbow. he split the apple without harming his son, then turned on the governor and killed him. William thus began the successful Swiss battle for independence.
In 1315, the takers of the oath, or the Eidgenossen, defeated the emperor's forces and they also defeated a superior Austrian force in 1386. The mountains of Switzerland and Swiss military efficiency proved to be a major obstacle to a conquering army. By 1499, a further dozen cantons had joined the Swiss Confederacy, and Switzerland's already independent status was officially recognized by the Treaty of Westphalia in 1648.
After the glorious period known as the Renaissance, the forces of religious conflict, political transformation, and modernization shook the German states. However, by the end of the 15th century, the Swiss Confederacy had been established even though Switzerland's independence from the Holy Roman Empire was not officially recognized until after the Thirty Years' War.
In the 16th century, the Protestant Reformation shattered the unity that Western Christendom had experienced for over a thousand years. During the Reformation, Switzerland was not devastated by religious strife. On the contrary, it remained unified and strong. Cities such as Geneva, Lucerne, Zurich and Bern were centers of the Reformation. John Calvin achieved great prominence in Switzerland as a Protestant reformer and founded the branch of Protestantism that bears his name. This small country has remained united despite its four different languages: German, French, Raeto-Romanic, and Italian.
Switzerland is well known for its consistent political neutrality. With only seven percent its people involved in farming, Switzerland is a non-agricultural country whose main industries are tourism and banking. Swiss banks are world-famous for their discretion, hospitality, and efficiency. Other industries include chocolate and cheese manufacturing, as well as the traditional Swiss mastery of precision products, based on the watch-making tradition.
Switzerland has a highly developed market-oriented economy based on manufacturing and services such as international trade, shipping, banking, insurance, and tourism. The country has kept unemployment low and has achieved one of the highest per capita incomes in the world.
Despite Switzerland's limited supply of raw materials, its economy has prospered. This prosperity can be attributed to abundant hydroelectric power, a central position on international trade routes, and a skilled labor force.
Switzerland's rugged terrain limits the land available for growing crops. Agriculture accounts for only a very small portion of the country's income and jobs. The leading agricultural activity is cattle raising. Switzerland exports milk and other dairy products throughout Europe. There is considerable regional diversity in crops, ranging from the irrigated horticulture of the southwest to the modified Mediterranean crops of the south. The leading crops include sugar beets, wheat, potatoes, and hardy fruits. The production of wine is basically for domestic consumption. Food industries, based on the country's milk production, focus on cheese (Emmentaler and Gruyère) and chocolate products.
Manufacturing is an important part of Switzerland's economy. The country's transformation into an industrial state began during the late 19th century. Its major exports now include machinery, watches, pharmaceutical products, chemicals, and textiles. Many industries must import raw and semifinished materials by costly overland routes. Only the notable quality of its manufactured goods permits Switzerland to remain competitive. Leading manufacturing sectors include the production of turbines, generators, watches, precision instruments, textiles, chemicals, and foodstuffs. Zürich and Basel are the chief manufacturing centers, but industrial plants are scattered throughout the Mittelland—even within the rural countryside.
Mining and Energy
Switzerland's mineral resources are limited. There are small iron and manganese deposits in the Jura but no known deposits of coal. A variety of materials is worthy of commercial exploitation. Among them are lime, salt, sand, gravel, clay, and marble.
Switzerland's lack of mineral resources is largely counterbalanced by its greatest asset—waterpower—which is harnessed by huge dams that produce hydroelectricity for industry. Hydroelectric power supplies about a sixth of the country's energy needs. Nuclear power plants provide about a quarter of Switzerland's energy.. For much of its energy, however, Switzerland relies on thermal power plants that use imported fuels.
Switzerland has a large and highly developed service sector, which provides most of the country's income and jobs. High-tech and communications industries are at the forefront of Swiss economic development. Retail trade and business-related services are also important parts of the service sector. Switzerland's noted banking system and its reputation for financial secrecy have made it a key center of international finance. Foreign investors are drawn to Swiss banks by the country's economic stability, the solid Swiss franc, and the long experience of Swiss bankers. Many domestic and foreign fortunes are invested in Swiss banks.
Switzerland is one of the world's leading tourist centers. Its visitors bring in huge revenues to the economy. Tourism is a year-round industry, with a seasonal shift in activities from winter to summer. Winter sports include skiing, sledding, tobogganing, and ice skating. The leading winter resorts are St-Moritz, Gstaad, and Interlaken. All three are world renowned. Summers bring golf, boating, swimming, hiking, and climbing. Many people in Switzerland are employed in hotels, inns, spas, and restaurants. The Swiss are world famous for their hospitality and the quality of their cuisine.
For centuries land transportation routes have traversed Switzerland because it is an international crossroads. Because of the rugged terrain, hundreds of bridges and tunnels have had to be built, particularly through the Alps. Some of the tunnels are among the longest in Europe. The Gotthard Base Tunnel, which runs more than 35 miles (57 kilometers) under St. Gotthard Pass in the Swiss Alps, was the world's longest rail tunnel when it opened in 2016. Several international railways pass through Switzerland. All of the key rail lines are double-tracked, and since the 1960s the entire system has been electrified. Highways and highway tunnels are among the best in the world, connecting all key urban centers and roads that lead to Switzerland's neighbors. Basel, the country's chief port on the Rhine, handles millions of tons of goods, which are typically bulk imports that feed Swiss industries. The main international airports are in Geneva and Zürich.
Inter-ethnic conflicts in Switzerland in the 16th century - History
Go to Benin, Kingdom of in A Dictionary of World History (2 ed.)
See this event in other timelines:
Go to Realism in The Concise Oxford Dictionary of Art Terms (2 ed.)
Go to Machu Picchu, Peru in The Concise Oxford Dictionary of Archaeology (2 ed.)
Go to Augsburg in World Encyclopedia (1 ed.)
Go to Nanak (1469–1539) in The Oxford Dictionary of Phrase and Fable (2 ed.)
Go to clocks and watches in The Oxford Dictionary of the Renaissance (1 ed.)
Go to Leonardo da Vinci (1452–1519) in World Encyclopedia (1 ed.)
Go to majolica in The Concise Oxford Dictionary of Art Terms (2 ed.)
Go to Inca in A Dictionary of World History (2 ed.)
Go to Cabral, Pedro Álvares (1467–1520) in World Encyclopedia (1 ed.)
Go to Mozambique in A Dictionary of World History (2 ed.)
Go to Aboriginals and European diseases in The Oxford Companion to Canadian History (1 ed.)
Go to Salic law in A Dictionary of World History (2 ed.)
Go to istoriato in The Concise Oxford Dictionary of Art Terms (2 ed.)
Go to Ismail I, Shah of Iran (1487–1524) in The Oxford Companion to Military History (1 ed.)
Go to Michelangelo (1475–1564) in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to Vespucci, Amerigo (1454–1512) in The Oxford Companion to Ships and the Sea (2 ed.)
Go to da Gama, Vasco (c. 1469–1524) in A Dictionary of World History (2 ed.)
Go to James IV (b. 17 Mar. 1473) in The Kings and Queens of Britain (2 rev ed.)
Go to Bosch, Hieronymus (c.1450) in The Oxford Dictionary of Art and Artists (4 ed.)
Go to Zanzibar in World Encyclopedia (1 ed.)
Go to Mughal Empire in The Oxford Dictionary of Islam (1 ed.)
Go to Sri Lanka in A Dictionary of World History (2 ed.)
Go to Mona Lisa [Art] in The Oxford Dictionary of Reference and Allusion (3 ed.)
Go to Julius II (1443–1513) in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to sinister in The Oxford Dictionary of Phrase and Fable (2 ed.)
Go to Raphael (1483–1520) in World Encyclopedia (1 ed.)
Go to Henry VIII (1491–1547) in World Encyclopedia (1 ed.)
Go to humanism in The Oxford Dictionary of Philosophy (2 rev ed.)
Go to High Renaissance in The Concise Oxford Dictionary of Art Terms (2 ed.)
Go to Goa (India) in The Concise Dictionary of World Place-Names (2 ed.)
Go to Mannerism in The Concise Oxford Dictionary of Art Terms (2 ed.)
Go to Giorgione (c.1477) in The Oxford Dictionary of Art and Artists (4 ed.)
Go to curling in World Encyclopedia (1 ed.)
Go to Malacca in World Encyclopedia (1 ed.)
Go to Moluccas in World Encyclopedia (1 ed.)
Go to Balboa, Vasco Núñez de (1475–1519) in A Dictionary of World History (2 ed.)
Go to James V (b. 10 Apr. 1512) in The Kings and Queens of Britain (2 rev ed.)
Go to midwife in A Dictionary of Public Health (1 ed.)
Go to Hampton Court palace in A Dictionary of British History (1 rev ed.)
Go to Hormuz in The Oxford Encyclopedia of Maritime History (1 ed.)
Go to Francis I (1494–1547) in World Encyclopedia (1 ed.)
Go to Havana (Cuba, USA) in The Concise Dictionary of World Place-Names (2 ed.)
Go to Habsburg in A Dictionary of World History (2 ed.)
Go to Catherine of Aragon (1485–1536) in A Dictionary of World History (2 ed.)
Go to Ghetto in A Concise Companion to the Jewish Religion (1 rev ed.)
Go to Orlando Furioso in The Concise Oxford Companion to English Literature (3 ed.)
Go to Erasmus (d. c.300) in The Oxford Dictionary of Saints (5 rev ed.)
Go to Selim I (c. 1470–1520) in A Dictionary of World History (2 ed.)
Go to Caliph/Caliphate in The Oxford Dictionary of Islam (1 ed.)
Go to Ottoman empire in A Dictionary of World History (2 ed.)
Go to Tetzel, Johann (c.1464–1519) in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to Luther, Martin (1483–1546) in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to Melanchthon, Philipp (1497–1560) in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to Cortés, Hernando (1485–1547) in A Dictionary of World History (2 ed.)
Go to Magellan, Ferdinand (c. 1480–1521) in A Dictionary of World History (2 ed.)
Go to Charles V (1500–58) in World Encyclopedia (1 ed.)
Go to Tenochtitlán, Mexico in The Concise Oxford Dictionary of Archaeology (2 ed.)
Go to Cortés, Hernán (1485–1547) in World Encyclopedia (1 ed.)
Go to Holbein, Hans (1497–1543) in World Encyclopedia (1 ed.)
Go to Reformation in A Dictionary of World History (2 ed.)
Go to Field of Cloth of Gold (1520) in A Dictionary of British History (1 rev ed.)
Go to Stockholm Bloodbath in The Oxford Encyclopedia of the Reformation (1 ed.)
Go to Suleiman I (1494–1566) in World Encyclopedia (1 ed.)
Go to Loyola, Ignatius, St (1491–1556) in A Dictionary of World History (2 ed.)
Go to Zwingli, Ulrich (1484–1531) in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to d'Abbadie, Antoine (1810–1897) in The Oxford Companion to World Exploration (1 ed.)
Go to Gustavus I (Vasa) (1496–1560) in A Dictionary of World History (2 ed.)
Go to Tyndale, William (c.1494–1536) in A Dictionary of British History (1 rev ed.)
Go to smallpox in Concise Medical Dictionary (8 ed.)
Go to Atahualpa (1533) in A Dictionary of World History (2 ed.)
Go to Grebel, Conrad (c.1498–1526) in The Oxford Dictionary of the Renaissance (1 ed.)
Go to Peasants' War (1524–26) in A Dictionary of World History (2 ed.)
Go to Islam in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to conquistadores in A Dictionary of World History (2 ed.)
Go to Cranach, Lucas the Elder (1472) in The Oxford Dictionary of Art and Artists (4 ed.)
Go to Babur (1483–1530) in A Dictionary of World History (2 ed.)
Go to Protestant in The Oxford Dictionary of Phrase and Fable (2 ed.)
Go to Clement VII (1478–1534) in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to Fontainebleau School in World Encyclopedia (1 ed.)
Go to Gustavus I (1496–1560) in World Encyclopedia (1 ed.)
Go to Wolsey, Thomas (c. 1474–1530) in A Dictionary of World History (2 ed.)
Go to More, Sir Thomas (1478–1535) in A Dictionary of British History (1 rev ed.)
Go to Eucharist in The Oxford Dictionary of Phrase and Fable (2 ed.)
Go to Ethiopia in A Dictionary of World History (2 ed.)
Go to Pizarro, Francisco (c. 1478–1541) in A Dictionary of World History (2 ed.)
Go to Hospitallers in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to Augsburg, Confession of (1530) in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to Brunfels, Otto (c.1489–1534) in The Oxford Dictionary of the Renaissance (1 ed.)
Go to Virgin of Guadalupe in The Oxford Companion to World Mythology (1 ed.)
Go to Schmalkaldic League in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to Pizarro, Francisco (1471–1541) in World Encyclopedia (1 ed.)
Go to Rabelais, François in Oxford Dictionary of English (3 ed.)
Go to Henry VIII (1491–1547) in The Oxford Dictionary of the Renaissance (1 ed.)
Go to Cuzco in World Encyclopedia (1 ed.)
Go to Cranmer, Thomas (1489–1556) in World Encyclopedia (1 ed.)
Go to Elizabeth I (1533–1603) in The Oxford Dictionary of the Renaissance (1 ed.)
Go to Titian (1487) in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to Cartier, Jacques (1491–1557) in World Encyclopedia (1 ed.)
Go to Church of England in Oxford Dictionary of English (3 ed.)
Go to Bombay in A Dictionary of British History (1 rev ed.)
Go to Protestantism in World Encyclopedia (1 ed.)
Go to Montreal (Canada, France, USA) in The Concise Dictionary of World Place-Names (2 ed.)
Go to More, Thomas (1477) in The Oxford Dictionary of Philosophy (2 rev ed.)
Go to Wales, principality of in A Dictionary of British History (1 rev ed.)
Go to Christian III (1503–59) in The Oxford Dictionary of the Renaissance (1 ed.)
Go to Anne Boleyn (b. c.1501) in The Kings and Queens of Britain (2 rev ed.)
Go to Jane Seymour (b. c.1509) in The Kings and Queens of Britain (2 rev ed.)
Go to Peru (and USA) in The Concise Dictionary of World Place-Names (2 ed.)
Go to Edward VI (b. 12 Oct. 1537) in The Kings and Queens of Britain (2 rev ed.)
Go to Great Bible noun in Oxford Dictionary of English (3 ed.)
Go to Coronado, Francisco Vásquez de in New Oxford American Dictionary (3 ed.)
Go to Calvin, John (1509–64) in A Dictionary of World History (2 ed.)
Go to Suleiman I (c. 1494–1566) in A Dictionary of World History (2 ed.)
Go to Francis Xavier, St (1506–52) in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to encomiendas in The Oxford Dictionary of the Renaissance (1 ed.)
Go to Inquisition, Roman in The Oxford Dictionary of the Renaissance (1 ed.)
Go to Howard, Catherine (c. 1521–42) in A Dictionary of World History (2 ed.)
Go to Mary, Queen of Scots (1542–87) in World Encyclopedia (1 ed.)
Go to Deep Space 1 in A Dictionary of Astronomy (2 rev ed.)
Go to Japan in The Concise Dictionary of World Place-Names (2 ed.)
Go to Humayun (1508–56) in A Dictionary of World History (2 ed.)
Go to Potosí in Oxford Dictionary of English (3 ed.)
Go to Waldenses noun in Oxford Dictionary of English (3 ed.)
Go to Paré, Ambroise (c.1510–90) in The Oxford Companion to Military History (1 ed.)
Go to Beaton, David (c.1494–1546) in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to Ivan IV (1530–84) in A Dictionary of World History (2 ed.)
Go to draughts noun in Oxford Dictionary of English (3 ed.)
Go to Knox, John (1514–72) in World Encyclopedia (1 ed.)
Go to Brazil (and USA) in The Concise Dictionary of World Place-Names (2 ed.)
Go to Bahia (Brazil) in The Concise Dictionary of World Place-Names (2 ed.)
Go to Book of Common Prayer noun in Oxford Dictionary of English (3 ed.)
Go to Pléiade, Ia in The Oxford Dictionary of Literary Terms (3 ed.)
Go to slave trade, African in A Dictionary of World History (2 ed.)
Go to vassal noun in Oxford Dictionary of English (3 ed.)
Go to flint noun in Oxford Dictionary of English (3 ed.)
Go to Portobelo (Panama) in The Concise Dictionary of World Place-Names (2 ed.)
Go to Ronsard, Pierre de (1524–85) in The Oxford Companion to Shakespeare (1 ed.)
Go to Mary I (1516–58) in The Oxford Dictionary of the Renaissance (1 ed.)
Go to Philip II (1527–98) in A Dictionary of World History (2 ed.)
Go to Wyatt, Sir Thomas (c. 1521–54) in A Dictionary of British History (1 rev ed.)
Go to Wyatt's Rebellion (February 1554) in A Dictionary of World History (2 ed.)
Go to Russia Company in A Dictionary of British History (1 rev ed.)
Go to Augsburg, Peace of (1555) in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to Charles V (1500–58) in A Dictionary of World History (2 ed.)
Go to Akbar (b. 1542) in A Dictionary of Hinduism (1 ed.)
Go to Cranmer, Thomas (1489–1556) in A Dictionary of World History (2 ed.)
Go to Sinan Abdul Menan (1588) in The Oxford Dictionary of Islam (1 ed.)
Go to Macao in Oxford Dictionary of English (3 ed.)
Go to Elizabeth I (1533–1603) in A Dictionary of World History (2 ed.)
Go to Cecil, William (1520–98) in A Dictionary of World History (2 ed.)
Go to Mary, Queen of Scots (1542–87) in A Dictionary of World History (2 ed.)
Go to Stuart in A Dictionary of First Names (2 ed.)
Go to Huguenots in A Dictionary of British History (1 rev ed.)
Go to physic garden noun in Oxford Dictionary of English (3 ed.)
Go to Escorial in World Encyclopedia (1 ed.)
Go to Seven Years War of the North (1563–70) in A Dictionary of World History (2 ed.)
Go to Unitarianism in World Encyclopedia (1 ed.)
Go to Marlowe, Christopher in Oxford Dictionary of English (3 ed.)
Go to condom noun in Oxford Dictionary of English (3 ed.)
Go to Bruegel, Pieter (c.1525–69) [Art] in The Oxford Dictionary of Reference and Allusion (3 ed.)
Go to Darnley, Henry Stuart (1545–67) in The Oxford Dictionary of the Renaissance (1 ed.)
Go to Rizzio, David (c. 1533–66) in A Dictionary of British History (1 rev ed.)
Go to Bothwell, James Hepburn in Oxford Dictionary of English (3 ed.)
Go to Council of Blood (1567–8) in The Oxford Dictionary of the Renaissance (1 ed.)
Go to James I (1566–1625) in World Encyclopedia (1 ed.)
Go to Terra Australis Incognita in The Oxford Companion to Ships and the Sea (2 ed.)
Go to Mercator projection in The Oxford Dictionary of Phrase and Fable (2 ed.)
Go to privateers in A Dictionary of World History (2 ed.)
Go to Ashanti in World Encyclopedia (1 ed.)
Go to Palladio, Andrea in Oxford Dictionary of English (3 ed.)
Go to Philippines in The Concise Dictionary of World Place-Names (2 ed.)
Go to Fatehpur Sīkri (Uttar Pradesh/India) in The Concise Dictionary of World Place-Names (2 ed.)
Go to Ridolfi Plot (1571) in A Dictionary of World History (2 ed.)
Go to galley in A Dictionary of World History (2 ed.)
Go to Lepanto, Battle of in Oxford Dictionary of English (3 ed.)
Go to St Bartholomew's Day Massacre (23–24 August 1572) in A Dictionary of World History (2 ed.)
Go to Camões, Luis de (1524–80) in The Concise Oxford Companion to English Literature (3 ed.)
Go to William I (the Silent) (1533–84) in World Encyclopedia (1 ed.)
Go to Oda Nobunaga (1534–82) in A Dictionary of World History (2 ed.)
Go to Alkmaar (Suriname, The Netherlands) in The Concise Dictionary of World Place-Names (2 ed.)
Go to Ottoman Empire in Oxford Dictionary of English (3 ed.)
Go to Stefan Bátory (1533–86) in The Oxford Dictionary of the Renaissance (1 ed.)
Go to phalanx in The Oxford Dictionary of Phrase and Fable (2 ed.)
Go to Hawkins, Sir John (1532–95) in The Oxford Dictionary of the Renaissance (1 ed.)
Go to porcelain in World Encyclopedia (1 ed.)
Go to Ghent, Pacification of in The Oxford Dictionary of the Renaissance (1 ed.)
Go to Burbage, James (1530–97) in The Concise Oxford Companion to English Literature (3 ed.)
Go to Brahe, Tycho (1546–1601) in World Encyclopedia (1 ed.)
Go to Drake, Sir Francis in Oxford Dictionary of English (3 ed.)
Go to Establishment in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to Arras, Union of in The Oxford Dictionary of the Renaissance (1 ed.)
Go to Iroquois Confederacy in World Encyclopedia (1 ed.)
Go to Campion, Edmund, St (1540–81) in A Dictionary of World History (2 ed.)
Go to Montaigne, Michel de in Oxford Dictionary of English (3 ed.)
Go to forceps n. in A Dictionary of Nursing (5 ed.)
Go to ballet de cour in The Oxford Encyclopedia of Theatre and Performance (1 ed.)
Go to Tasso, Torquato (1544–95) in World Encyclopedia (1 ed.)
Go to grand duchy noun in Oxford Dictionary of English (3 ed.)
Go to Gregorian calendar in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to Shakespeare, William (1564–1616) in World Encyclopedia (1 ed.)
Go to Ricci, Matteo (1552–1610) in A Dictionary of World History (2 ed.)
Go to Gilbert, Sir Humphrey (c. 1539–83) in A Dictionary of World History (2 ed.)
Go to Raleigh, Sir Walter (c. 1552–1618) in A Dictionary of World History (2 ed.)
Go to Roanoke Island in A Dictionary of World History (2 ed.)
Go to martyr in Oxford Dictionary of English (3 ed.)
Go to White, John (1585–93) in The Oxford Companion to American Literature (6 ed.)
Go to Babington Plot (1586) in A Dictionary of World History (2 ed.)
Go to Venice in World Encyclopedia (1 ed.)
Go to Dare, Virginia in New Oxford American Dictionary (3 ed.)
Go to Hilliard, Nicholas (1547–1619) in A Dictionary of British History (1 rev ed.)
Go to Abbas I (1571–1629) in World Encyclopedia (1 ed.)
Go to Orange, House of in World Encyclopedia (1 ed.)
Go to raku in The Concise Oxford Dictionary of Art Terms (2 ed.)
Go to United Provinces of the Netherlands in A Dictionary of World History (2 ed.)
Go to Spanish Armada in A Dictionary of World History (2 ed.)
Go to framework knitting in The Oxford Companion to Family and Local History (2 ed.)
Go to real tennis noun in Oxford Dictionary of English (3 ed.)
Go to serfdom in A Dictionary of British History (1 rev ed.)
Go to gurdwara noun in Oxford Dictionary of English (3 ed.)
Go to Spenser, Edmund in Oxford Dictionary of English (3 ed.)
Go to Lippershey, Hans (c.1570–1619) in A Dictionary of Scientists (1 ed.)
Go to St Peter's, Rome in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to Henry IV in Oxford Dictionary of English (3 ed.)
Go to Barents, Willem (c. 1550–97) in A Dictionary of World History (2 ed.)
Go to Confucius in Oxford Dictionary of English (3 ed.)
Go to Mercator, Gerardus (1512–94) in World Encyclopedia (1 ed.)
Go to Java in World Encyclopedia (1 ed.)
Go to Bauhin, Gaspard (1550–1624) in A Dictionary of Plant Sciences (2 ed.)
Go to Harington, Sir John (1561–1612) in The Oxford Dictionary of the Renaissance (1 ed.)
Go to Daphne in World Encyclopedia (1 ed.)
Go to cricket in A Dictionary of British History (1 rev ed.)
Go to Shah Abbas I (1587–1629) in The Oxford Dictionary of Islam (1 ed.)
Go to James VI (1566–1625) in The Oxford Dictionary of the Renaissance (1 ed.)
Go to Nantes, Edict of (1598) in The Concise Oxford Dictionary of the Christian Church (2 rev ed.)
Go to Globe Theatre in Oxford Dictionary of English (3 ed.)
Go to Yoruba in World Encyclopedia (1 ed.)
Go to magnetic pole in A Dictionary of Environment and Conservation (1 ed.)
Go to oratorio noun in Oxford Dictionary of English (3 ed.)
Go to East Flanders in Oxford Dictionary of English (3 ed.)
Go to Gilbert, William (1540–1613) in A Dictionary of Earth Sciences (3 ed.)
Why Mostly Women Were Executed
Although men were also accused of witchcraft, about 75% to 80% of those executed during the witch hunts were women. Women were subject to cultural prejudices that framed them as inherently weaker than men and, thus, more susceptible to superstition and evil. In Europe, the idea of women's weakness was tied to Eve's temptation by the Devil in the Bible, but that story itself cannot be blamed for the proportion of women accused. Even in other cultures, witchcraft accusations have been more likely to be directed at women.
Some writers have also argued, with significant evidence, that many of those accused were single women or widows whose very existence delayed the full inheritance of property by male heirs. Dower rights, intended to protect widows, gave women in such circumstances power over property that they usually could not exercise. Witchcraft accusations were easy ways to remove the obstacle.
It was also true that most of those accused and executed were among the poorest, most marginal in society. Women's marginality compared to men added to their susceptibility to accusations.
33 Famous Swiss Castles to Visit
1. Aarburg Castle
Aarburg Castle is a medieval construction, first mentioned in a chronicle from the 13th-century. Although the story of the castle's origins is unknown, the place certainly had an important strategic value.
After a siege in 1415, the castle was finally renovated in the 16th-century, with new elements added throughout the years.
Located on an elevated rock above the Aare River, Aarburg Castle is a beautiful sight. Today the castle serves as a juvenile rehabilitation centre.
Where: Aarburg, Canton of Aarburg
When: 12th-century
Open for visit: Yes.
2. Bottmingen Castle
Dating back to the 13th-century, Bottmingen Castle is one of the most romantic castles in Switzerland and one of the few landmarks of its type left intact.
This moated castle was owned by the Kammerer family for three centuries, before being passed to Johaness Deucher in 1720. The new owner transformed the medieval structure into a Baroque country house based on the popular French style.
Both the original medieval structure and the later additions are visible today.
Where: Bottmingen, Canton of Basel-Land
Open for visit: Yes. Check here for more information.
3. Castelgrande (Castles of Bellinzona)
Castelgrande is the oldest and most impressive castle of the trio known as the Castles of Bellinzona. A fortification existed in the same place as early as the 4th-century, but the current construction dates back to medieval times.
Built on a hill near the city centre, the castle stands apart with its imposing towers. A recent restoration brought it to an excellent condition, and visitors can use an elevator to access the grounds of the castle.
Where: Bellinzona, Canton of Ticino
Open for visit: Yes,
4. Sasso Corbaro Castle (Castles of Bellinzona)
Located at the foothills of the Alps, the city of Bellinzona is famous for being the home of three stunning castles.
While Castelgrande is the oldest and the one that attracts the most attention, Castello Montebello and Castello Sasso Corbaro are also beautiful medieval structures of great historical and cultural value.
Built to protect the Ticino Valley and Bellinzona, the castles are now part of UNESCO World Heritage. All three castles are incredibly well-preserved. From the castles' grounds, visitors can enjoy stunning views of the city.
When: 13th- to 15th-century
5. Chillon Castle
One of the best castles in Switzerland, Chillon Castle is the quintessential castle located in a dreamlike location.
Built on a small rocky stretch of land on the shore of Lake Geneva, the castle is a spectacular sight that leaves visitors breathless. In fact, Chillon Castle is the most visited historic building in the entire country.
The castle has immense historical importance and is first mentioned in writing as early as 1150, although it was built much earlier. In the 13th-century, the original fortification underwent extensive renovations and became a residence for the Counts of Savoy.
It later served as a fortress and prison under the Bernese rule. In the 19th-century, intense renovation brought the courtyards, halls, and interiors to their original glory.
Where: Veytaux, Canton of Vaud
6. Lenzburg Castle
One of the oldest castles in Switzerland, Lenzburg Castle is an important part of the country's historic heritage. A legend says that the castle was built by two knights, Guntram and Wolfram.
Its position atop a hill suggests that the castle had strategic value for the Counts of Lenzburg. Over the centuries, the castle served as a royal residence, being passed among different ruling families. Today it belongs to the City of Lenzburg.
Where: Lenzburg
7. Marschlins Castle
Located in the village of Igis, in the Canton of Graubunden, Marschlins Castle was built in the 13th-century, although earlier structures existed on the site for at least two centuries.
The goal of the castle was to serve as a principal residence for the Bishop of Chur. Today the castle is a heritage site of great value and a popular sight.
Where: Igis, Graubunden
Open for visit: Yes
8. Oberhofen Castle
Nothing holds more charm than a castle on the water. The combination of old architecture and breathtaking scenery is what attracts people to Switzerland, and Oberhofen Castle does not disappoint.
Located on the shore of Lake Thun, the castle is considered a national treasure. The construction began as early as 13th-century, but numerous additions were made over the centuries, which led to a mix of architectural elements.
The present appearance dates back to the 19th-century when the castle was acquired by the Pourtàles family, who restored it. Today Oberhofen Castle is a museum.
Where: Oberhofen am Thunersee, Canton of Bern
Open for visit: Yes. Museum: check here for more information.
9. Tarasp Castle
Tarasp Castle is an impressive medieval castle built in an alpine area in eastern Switzerland, on a hilltop with sweeping views of the landscape.
Important parts of the structure, such as a ring wall and chapel, were built in the 11th-century, but the largest part of the castle was built in the 13th-century.
The castle served an important role in the protection of the area, but was also repeatedly attacked, especially in the 16th- and 17th- century. Tarasp Castle belonged to Austria until 1803.
Today it is private property, but the chapel and several restored rooms are open for visits.
Where: Tarasp, Canton of Graubünden
Open for visit: Yes. Only scheduled tours. Check here for more information.
10. Valere Basilica
Although not technically a castle, the Valere Basilica is an immense medieval structure and a heritage site of great significance for the Swiss.
This fortified church was built in the 13th-century in the town of Sion and has been active ever since as a church under the administration of the Roman Catholic Diocese of Sion.
Over the centuries, the construction was gradually expanded and in the 15th-century, an outstanding cathedral organ was brought in. The same organ can be heard today in the church.
Where: Sion, Canton of Valais
11. Vufflens Castle
Vufflens Castle took the place of an earlier medieval castle built at the beginning of the 15th-century by the Lords of Vufflens. After a hundred years of existence, this earlier castle was burned down by a Bernese army.
However, several features of the original structure, including towers, walls, and outbuildings, remained intact and the castle was rebuilt. Today it is regarded as an exquisite example of the late Middle Ages Vaud fortresses.
Located a short distance away from Lake Geneva and surrounded by vineyards, the castle is worth a visit just for its gorgeous architecture and charming location, even though the main structure is privately owned and not open to the public.
Where: Vufflens-le-Château, Canton of Vaud
Open for visit: No.
12. Aarwangen Castle
Aarwangen Castle was built in the 13th-century as a residence for the governors of Kyburg. Due to its location, the castle provided protection against enemies who used the nearby river to cross into the region.
For over six centuries, Aarwangen Castle maintained a significant political power as the seat of the Bernese authorities.
Architecturally, the castle combines the Gothic elements of its main tower with the Baroque features of its halls and interiors.
Where: Aarwangen, Canton of Bern
13. Aigle Castle
Aigle Castle is a beautiful castle built at the end of the 12th-century to serve as a residence for the Knights of Aigle.
In the following centuries, the castle underwent extensive construction work to include a massive circular wall and other important elements. At the end of the 18th-century, it was acquired by the local municipality.
Surrounded by endless rows of vineyards, Aigle Castle has been transformed into the Vine and Wine Museum in the 1970s.
Where: Aigle, Canton of Vaud
Open to visit: Yes. Check here for more information.
14. Aile Castle
Aile Castle can be found in the municipality of Vevey, Canton of Vaud. The construction of this gorgeous Neo-Gothic structure began in 1840 and ended four years later.
The new castle covered the site of an earlier 17th-century castle. For several decades, Aile Castle served as the private residence of Paul Morand, famous literary figure and traveller.
Although still privately owned, the castle is perfectly preserved and is considered part of Switzerland's historic heritage.
Where: Vevey, Canton of Vaud
15. Angenstein Castle
Located in the municipality of Duggingen, Angenstein Castle is a medieval castle perched on a rocky hill. Regarded as an important outpost of Basel, the castle ensured the control of the Jura region due to its strategic position.
Since the region was prone to conflicts, the castle suffered consistent damage over the centuries.
Additional fires and change of ownership led to severe neglect. After a tumultuous history, the castle was acquired by the city of Basel and went through extensive renovation work.
Where: Duggingen, Canton of Basel-Land
When: mid-13th-century
16. Bipp Castle
Bipp Castle is first mentioned in a document from 1268, which suggests that the castle dates back earlier than the 13th-century. According to historians, the castle changed ownership frequently, although it is unsure how many times it was sold or captured.
Many noble families resided in the Bipp Castle over the centuries. At the end of the 18th-century, the castle had been so neglected that it was no longer habitable. The ruins were bought by a family from Basel who built a private residence on the site.
Where: Oberbipp, Canton of Bern
When: 12th- or 13th- century
17. Birseck Castle
Located in Arlesheim, Birseck Castle was built around the 1240s, and it is one of the four castles on a slope above the River Birs. Although an important landmark, the castle was neglected for centuries.
In 1785, it was completely dilapidated, and in the 19th-century the ruins were integrated into a landscape garden. The circular tower, along with a small chapel and the courtyard were restored. Today Birseck Castle is a popular attraction.
Where: Alersheim, Canton of Basel
Open for visit: Yes, check here for more information.
18. Castle of Montebello
Montebello Castle is one of the three beautiful fortresses that once protected the city of Bellinzona. Built in the 14th-century, the castle suffered numerous attacks over the centuries and was brought to its original state at the beginning of the 20th-century.
Today, the castle is home to the Civic Museum, housing important archaeological exhibitions. Perched atop a hill, the castle also offers great panoramic views of the city and the surrounding landscape, including Lake Maggiore.
When: 13th- to 14th- centuries
19. Colombier Castle
Originally a fortified tower built in the 11th-century, Colombier Castle was further expanded in the 13th-century. Additions were also made in the following centuries.
The present appearance has remained intact since the 16th-century. This beautiful castle served as a military hospital in 1806 and was later used as barracks and arsenal by the militia. Today Colombier Castle is an infantry training centre.
Where: Colombier, Canton of Neuchâtel
20. Grandson Castle
The second-largest castle in the country, Grandson Castle is an impressive medieval structure that overlooks Lake Neuchâtel. The origins of the castle are the 11th-century fortress, but construction work continued over the next three centuries.
Otto I of Grandson requested the expansion of the castle as an attempt to enforce his political authority. This transformed the Grandson Castle is an important political hotspot. In the 15th-century, the castle was involved in the Battle of Grandson and several other wars.
Where: Grandson, Canton of Vaud
When: 11th- to 14th century
21. Gruyeres Castle
One of the most popular castles to visit in Switzerland, Gruyeres Castle was built at the end of the 13th-century by the Counts of Gruyeres. In 1544, a bankruptcy forced the Gruyeres family to sell the castle to two other noble families.
In 1938, the castle entered the possession of the Canton of Fribourg. Today it is considered the most important historic building in the region and houses a museum. Although not as imposing as other medieval fortifications, the castle has charming architecture, including towers, courtyards, and beautiful gardens.
Where: Fribourg
22. Hallwyl Castle
A simple, but captivating place, Hallwyl Castle was built in the 13th-century as a residence for the Lords of Hallwyl. The castle is located on an island on the River Aabach, north of Lake Hallwil.
Although neglected for centuries, the castle was finally renovated in the 19th-century according to the original architecture. Today the castle is part of the historic heritage of the Canton of Aargau.
Where: Seengen, Canton of Aargau
23. Hunegg Castle
Hunegg Castle is an important historical landmark built as a private residence for the family of the Prussian Baron Albert Otto von Parpart. The construction began in 1861 and took only two years.
The gorgeous construction was built in the Renaissance style prevalent at the time. After the death of the Baron in 1869, the castle changed owners several times. Due to its importance as a site of historic interest, the castle houses today the Renaissance Revival and Art Nouveau Museum.
Where: Hilterfingen, Canton of Bern
24. Meggenhorn Castle
Located on a hilly peninsula south of Lucerne, Meggenhorn Castle was built in 1868/1870 following a design inspired by the Chambord Castle in France.
Overlooking the lake and vineyards, the castle is a grandiose construction whose goal was to serve as a personal residence for wealthy industrialist Edouard Hofer-Grosjean.
After two other different owners, the castle was acquired by the municipality in 1974. The grounds are open to the public ever since.
Where: Lucerne, Canton of Bern
25. Mesocco Castle
Mesocco Castle is located in southern Mesolcina Valley, in the Italian-speaking region of Switzerland.
Built in the 13th-century, it had a central role in the region in the following two centuries, serving as the seat of the noble family von Sax. In the 15th-century, it was acquired by the Mesocco family.
The castle is still one of the most impressive fortifications in the country and it was never conquered, but fell into ruin for many centuries. Parts of the castle were excavated and restored in the 20th-century.
Where: Mesocco, Canton of Graubunden
26. Morges Castle
Morges Castle is a medieval fortress from the 13th-century, built by Louis de Savoy, the first ruler of Vaud. The castle has maintained its original medieval appearance over the years, with its impressive round towers intact.
It is one of the most gorgeous sights on Lake Geneva, and it is the home of four fascinating history museums on tin figures, military, police, and artillery.
Where: Morges, Canton of Vaud
27. Munot Fortress
Located in northern Switzerland, in the city of Schaffhausen, Munot is a circular medieval fortress dating back to the 16th-century. Rising above the city, the castle offers beautiful views of the Old Town and the Rhine River.
This panoramic location was an important strategic advantage over the centuries and helped ensure the protection of the city. Guards would notice from within the fortress any dangers that would threaten the city, not just foreign enemies but also fires.
Munot Castle is still intact and has suffered little modifications during its long history.
Where: Schaffhausen, Canton of Schaffhausen
28. Spiez Castle
Built-in 933 by the King of Burgundy, Spiez Castle is definitely one of the oldest castles on this list. In fact, at that time, a large part of the area was under Italian rule.
Over the centuries, Spiez Castle was expanded and many new elements were added gradually. As a consequence, the castle features different architectural styles.
The courtrooms are an exquisite example of the Renaissance style while the southern part has been redecorated with Baroque elements. Throughout its long history, the castle was owned by many royal and noble families.
In recent times, the castle was acquired by a foundation which opened the gardens to the public.
Where: Spiez, Canton of Bern
29. Rapperswil Castle
Rapperswil Castle is located on the shores of beautiful Lake Zurich, in the old town of Rapperswil. Built in the 13th-century on a rocky hilltop, the castle was meant to provide a vantage point for the control of passing ships.
For many centuries, the castle was in dire conditions due to neglect. In 1870, Polish Count Wladyslaw Broel-Plater purchased the property and restored the medieval look of the castle. After the renovation, it was opened to the public as the Polish National Museum.
Where: Rapperswil
Open for visit: No restrictions for the castle grounds. Inner castle: check here for more information.
30. Tourbillon Castle
Now in ruins, Tourbillon Castle has had a long and tumultuous history, starting from its construction in the 13th-century. It was built by the Bishop of Sion, Boniface de Challant, to serve as his residence and it ended up as a principal residence for many bishops from the Diocese of Sion.
Due to its political importance, the castle underwent many attacks and sieges. A large part was destroyed in 1417. Although it was immediately renovated, in 1788 a fire that affected the city of Sion completely destroyed the castle.
Only a chapel survived. Reconstruction work ensued in the second half of the 20th-century. The castle is located atop a hill on the opposite side from the Valere Basilica in the city of Sion.
31. Thun Castle
One of the most famous castles in Switzerland, Thun Castle has an imposing architecture, which combined with the beautiful scenery around it, makes it seem taken straight out of a storybook.
Offering gorgeous views of the city of Thun, Lake Thun and the surrounding mountains, the castle is considered a top tourist attraction.
Built-in the 12th-century, the castle was owned by various noble families who added a personal touch to the design, making various improvements. Today visitors can explore the donjon and the corner towers.
Where: Thun, Canton of Bern
32. Stockalper Palace
Stockalper Palace was built in the 17th-century by a wealthy Swiss politician and businessman named Kaspar Stockalper.
Due to its original design, the castle is regarded as one of the most unique buildings in the country. The imposing towers are the first element that stands out, but the entire complex is interesting to explore.
Where: Brig-Gils
33. Blonay Castle
Blonay Castle is a medieval construction in southwestern Switzerland. Built-in the 12th-century as a private residence for the Blonay family, the castle is still owned by the same family and has been in their ownership for all its history except a brief period in the 18th-century.
Throughout the centuries, the original construction suffered numerous changes. Only two of the four original towers can be seen today.
Where: Blonay, Canton of Vaud
Although Switzerland is not as famous as France or Germany when it comes to castles, Swiss castles have a particular charm of their own.
Usually set in scenic locations with views over the Alps or crystal-clear lakes, they can immediately draw you into a world of beauty, history, and charm.
Aarau, the capital of the Canton of Aargau in the Swiss Mittelland, is located on the River Aare to which the town and canton owe their name. The charming old town boasts the most beautiful eaves, the so-called «Dachhimmel», in Switzerland.
Aarau is located by the southern foot of the Jura foothills in the centre of the big city triangle of Zurich, Basel and Lucerne. The central location was recognised early on which is why Aarau for a brief few months in 1798 was Switzerland's first capital and home to Switzerland's first Houses of Parliament.
The many painted eaves, the so-called "Dachhimmel" which predominantly date from the 16th century when the town underwent considerable extension, are a special feature of the old town of Aarau. It's for this reason that Aarau is regarded as the town of beautiful gables.
And Aarau continues to display an appreciation of art: the Aargau Art Museum featuring an extension designed by the famous architects Herzog & de Meuron offers architecture and art exhibitions setting high standards. The «Naturama», Aargau nature museum, is not your run-of-the-mill museum: animals, plants, exciting video films highlight the interaction and areas of conflict between nature and man in Aargau.
The Roggenhausen Wildlife Park has wild animals in their natural habitat as well as a Nature Trail. Cycling and walking trails alongside the River Aare and the Jura slopes provide the perfect opportunity for some pleasant physical exercise. But to see the people of Aargau really enjoying themselves you need to come to one of the local and historic traditional events, such as the «Maienzug» in July, the «Bachfischet» or «Rüeblimärt».
The Canton of Aargau boasts a great many castles, including some of Switzerland's most impressive such as the Lenzburg, the Hallwyl Water Castle and the Habsburg Castle - main residence of the famous dynasty from the the 10th century onwards. And Brugg, Baden and Zurich are a very short journey away. The Vindonissa Museum offers an opportunity to discover traces of the Romans and Windish is home to the biggest and best-preserved amphitheatre in Switzerland. And there are also a lot of historic towns, such as Bremgarten, Zofingen and others, to visit in the Canton of Aargau.
Copyright © vwfuncup.be | Inter-ethnic conflicts in Switzerland in the 16th century... | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,619 |
\section{Introduction}
There are a lot of quasi-one dimensional compounds
whose behaviors can be adequately described within
the framework of interacting spin chains governed by the
Heisenberg model. Extensive studies on this model have shed
light on the quantum nature of spin dynamics. In 1983,
Haldane predicted that the one-dimensional Heisenberg
antiferromagnetic model with integer spin has an excitation
gap and a finite correlation length\cite{Haldane83}. Since then
a great amount of experimental and theoretical effort has been
made towards understanding the difference between half-integer
and integer spin chains.
In this paper we report results of a transfer-matrix
renormalization-group (TMRG)
\cite{Nishino95,Bursill96,Wang97} study for the
thermodynamics of quantum Heisenberg spin chains. We have
calculated the magnetic susceptibility, specific heat,
spin-spin correlation length, and other experimentally
relevant quantities as functions of temperature and applied
magnetic field for the S=1/2, 1, and 3/2 spin chains.
The Heisenberg model is defined by the Hamiltonian
\begin{equation}
{\hat H} = \sum_{i}^{N}h_i ;\quad
h_i = J {\bf S}_i \cdot {\bf S}_{i+1}
- {H\over 2} (S_{iz} + S_{i+1z}) ,\label{model}
\end{equation}
where $J$ is the spin exchange constant and $H$ is an applied
magnetic field\cite{model}. In this paper, we consider
antiferromagnetic spin chains only. We use units in which $J
=1$.
The spin-1/2 Heisenberg model is integrable by Bethe ansatz.
Many of its thermodynamic quantities, for example, the
specific heat and the spin susceptibility, can be calculated
by solving the Bethe ansatz equations. The conformal field
theory is also very useful in analysing the low temperature
low field thermodynamic properties, since the S=1/2 Heisenberg
model is equivalent to the k=1 Wess-Zumino-Witten nonlinear
$\sigma$ model.
Higher spin Heisenberg models are not at present
amenable to rigorous solution. The finite temperature properties of
the model were studied mainly through
transfer matrix \cite{Betsuyaku},
quantum Monte Carlo \cite{Yamamoto93,Kim97,Kashurnikov98},
and other approximate method \cite{Narayanan,Moukouri}.
At zero field, the ground state of ${\hat H}$ is a spin
singlet with zero spin magnetization. At finite
field, the magnetization of the ground state becomes finite
and increases with increasing $H$. There is a critical
field $H_{c2}$ beyond which all spins are fully polarized at
zero temperature. If we denote $E(N, S)$ as the lowest
eigenvalue of a $N$-site Heisenberg chain with total spin
$S$ at $H=0$, then it is straightforward to show that
$H_{c2} = E(N, S_{max}) - E(N, S_{max}-1) = 4S $,
independent on $N$. Below $H_{c2}$, a canted Neel order,
namely a state which has both ferromagnetic order along the
z-axis and antiferromagnetic order in the xy plane, exists
at sufficiently low temperature, and the pitch vector (i.e.
the value of the momenta at which the static structure
factor shows a peak) decreases continuously from $\pi$ to 0
with increasing $H$.
Integer spin chains can be described by the quantum
nonlinear $\sigma$ model. It is from the study of this
model that Haldane made the famous `Haldane conjecture'.
The ground state of the $O(3)$ $\sigma$ model has a finite
excitation gap and consequently a finite correlation length.
The application of a magnetic field causes a Zeeman
splitting of the triplet with one member crossing the ground
state at a critical field $H_{c1}$ whose value is equal to
the excitation gap $\Delta$. When $H<H_{c1}$, the Haldane
gap persists and the ground state is still a non-degenerate
spin singlet state. When $H_{c1}< H<H_{c2}$, the ground
state has a nonzero magnetization with gapless excitations.
Thus across $H_{c1}$, an integer spin system undergoes a
commensurate to incommensurate transition. This is an
interesting feature which is absent in a half odd integer
spin system. Evidence for such transitions has been used to
identify the Haldane gap in NENP\cite{nenp88} and other
quasi-1d spin compounds\cite{Granroth96}. Just above
$H_{c1}$, the ground state can be regarded as a Bose
condensate of the low energy boson. Varying the magnetic
field is equivalent to varying the chemical potential for
this boson and the (uniform) magnetization corresponds to the
boson number\cite{Affleck91}.
\section{TMRG} \label{sec2}
In this section, we discuss briefly the TMRG method. A more
detailed introduction to the method can be found from Refs.
\cite{Bursill96,Wang97}.
The TMRG method starts by mapping a 1d quantum system onto a
2d classical one with the Trotter-Suzuki decomposition and
represents the partition function as a trace of a power
function of virtual transfer matrix $T_M$:
\begin{equation}
Z = {\rm Tr} e^{-\beta H} =
\lim_{M\rightarrow \infty} {\rm Tr}T_M^{N/2},
\end{equation}
where $M$ is the Trotter number. $T_M$ is defined by
an inner product of 2M local transfer matrices
\begin{eqnarray}
&&
\langle \sigma_3^1...\sigma_3^{2M}| T_M |
\sigma_1^1...\sigma_1^{2M} \rangle
\nonumber\\
&=&
\sum_{\{\sigma_2^k\}} \prod_{k=1}^M t(\sigma_3^{2k-1}
\sigma_3^{2k} |\sigma_2^{2k-1}\sigma_2^{2k})
t(\sigma_2^{2k}\sigma_2^{2k+1} |\sigma_1^{2k}\sigma_1^{2k+1}),
\nonumber
\end{eqnarray}
where
$$t(\sigma_{i+1}^k \sigma_{i+1}^{k+1} |\sigma_i^k
\sigma_i^{k+1}) = \langle -\sigma_i^{k+1},
\sigma_{i+1}^{k+1}| e^{-\tau h_i} |\sigma_i^k,
-\sigma_{i+1}^k \rangle $$
and $\tau =\beta / M$. $|\sigma_i^k\rangle$ is an eigenstate
of $S_i^z$ and $\sigma_i^k$ is the corresponding eigenvalue:
$S_i^z |\sigma_i^k\rangle = \sigma_i^k |\sigma_i^k\rangle$.
The superscripts and subscripts in $ T_M$ and
$t$ represent the spin positions in the Trotter and real
space, respectively.
$T_M$ conserves the total spin in the Trotter space, i.e.
$\sum_k\sigma_i^k$. Thus $T_M$ is block diagonal according
to the value of $\sum_k\sigma_i^k$\cite{Wang97}. For the
S=1/2 Heisenberg model, it was shown rigorously that the
maximum eigenstate of $T_M$ is non-degenerate and in the
$\sum_k \sigma_i^k=0$ subspace, irrespective of the sign of
J and the value of $H$ \cite{Koma89}. When S $>$ 1/2, we found
numerically that the maximum eigenvectors of $T_M$ are also
in the $\sum_k \sigma_i^k=0$ subblock.
In the thermodynamic limit, the free energy per spin, is given by
\begin{equation}
F= - \lim_{N\rightarrow \infty}
{1\over N\beta} \ln Z =
-\frac 1{2\beta}\lim_{M\rightarrow \infty} \ln \lambda_{max} ,
\end{equation}
where $\lambda_{max}$ is the maximum eigenvalue of $T_M$.
From the derivatives of $F$ one can in principle calculate
all thermodynamic quantities. The internal energy $U$ and
the spin magnetization $M_z$ could, for example, be
calculated from the first derivative of $F$ with respect to
$H$ and $T$, respectively. However, numerically it is
better to calculate $U$ and $M_z$ directly from the
eigenvectors of $T_M$\cite{Wang97}. The spin susceptibility
$\chi=\partial M_z / \partial H$ and the specific heat $C =
\partial U / \partial T$ can then be calculated by numerical
derivatives. The specific heat such determined is generally
found to be less accurate than, for example, the
susceptibility data at low $T$. The reason for this is that
$U$ changes very slowly with $T$ (or equivalently $C$ is
very small) at low $T$, and a small error in $U$ would lead
to a relative large error in $C$.
The correlation length of the spin-spin correlation
functions, defined by $\xi_\alpha^{-1} = - {\rm lim}_{L
\rightarrow \infty } {\rm ln} \langle S_{i, \alpha}S_{i+L,
\alpha} \rangle$, can also be calculated from this method.
The longitudinal and transverse correlation lengthes are
determined by
\begin{eqnarray}
\xi_z^{-1} & = & {1\over 2} \lim_{M\rightarrow \infty}
{\rm ln} {\lambda_{max} \over
\lambda_2 } , \label{c_z} \\
\xi_x^{-1} & = & {1\over 2} \lim_{M\rightarrow \infty}
{\rm ln} {\lambda_{max} \over
\lambda_1 }, \label{c_x}
\end{eqnarray}
where $\lambda_2$ is the second largest eigenvalue of $T_M$
in the subspace $\sum_k \sigma_k^{i} = 0$ and $\lambda_1$ is
the largest eigenvalue of $T_M$ in the subspace $\sum_k
\sigma_k^{i} = \pm 1$.
Figure \ref{supblock} shows the configuration of superblock
used in our calculation. This configuration of superblock
is different from those used in Refs.
\cite{Bursill96,Wang97}. The advantage for forming
the superblock in such a way is that the transfer matrix
$T_M$ in this case can always be factorized as a product of
two sparse matrices (which are block diagonal with respect
to $n_s$ and $\sigma_3 \otimes n_e$, respectively). To
treat these two sparse matrices instead of $T_M$ itself
allows us to save both computer memory space and CPU time.
\begin{center}
\begin{figure}
\begin{picture}(160,145)
{\epsfig{file = tx_fig1.ps, height = 2.8cm, %
bbllx = 4.5cm, bblly=18.5cm, %
bburx = 10.65cm, bbury=21.8cm} }
\end{picture}
\caption{A pictorial representation of a superblock, which
consists of system and environment blocks connected by three
added spins to form a periodic chain. $n_s$ and $n_e$ are
indices for the system and environment blocks, respectively.
Initially the system block contains two spins and the
environment block contains only one spin. At each iteration
the system and environment blocks are augmented by adding
$\sigma^1$ to each of the blocks. The augmented system
${\tilde n}_s$ is formed by $n_e\oplus \sigma^1 $, and the
augmented environment ${\tilde n}_e$ is formed by $\sigma^1
\oplus n_s$.}
\label{supblock}
\end{figure}
\end{center}
We compute the maximum eigenvalue, $\lambda_{max}$, and the
corresponding right and left eigenvectors, $|\psi^R\rangle$
and $\langle \psi^L|$, of $T_M$ using an implicitly
restarted Arnoldi method\cite{Sorensen92}. This method is
more efficient than the power method which we used
before\cite{Bursill96,Wang97}. $\lambda_{1,2}$ can also be
calculated from this method, but their truncation errors
are generally larger than those of $\lambda_{max}$.
Thus the correlation lengthes determined from Eqs.
(\ref{c_z}, \ref{c_x}) are generally expected to be
less accurate than the free energy or other thermodynamic
quantities.
In the TMRG method, the density matrix for the augmented
system or environment block is non-symmetric, which is
different than in the zero-temperature DMRG method.
Numerically it is much more difficult to treat accurately a
nonsymmetric matrix than a symmetric one because the errors
in $|\psi^R \rangle$ and $\langle \psi^L |$ may affect the
the (semi-) positiveness of the density matrix and increase
the truncation error of the TMRG.
The TMRG treats directly an infinity spin chain. There is
therefore no finite size effect. The error caused by the
finiteness of the Trotter number (or $\tau$) is of order
$\tau^2$, which is generally very small. The error resulted
from the truncation of basis states is difficult to
estimate. A rough estimation for this type of error can be
obtained from the value of truncation error, which is
smaller than $10^{-3}$ in all our calculations. More
accurate results can be obtained simply by extrapolating the
results with respect to both $\tau$ and the number of states
retained $m$.
\section{Results} \label{sec3}
\subsection{S=1/2}
The S=1/2 Heisenberg model is by far the best understood
spin system. In the absence of field, the ground state is
massless and the Bethe ansatz result for the ground state
energy is $(1/4-\ln 2)$. The lowest excitatins states are
spin triplets with a spin wave spectrum \cite{Cloizeaux62}
$\varepsilon (k) = (\pi /2 ) |\sin k |$. Above this lower
boundary of excitations, there is a two-parameter continuum
of spin wave excitations with an upper boundary given by
\cite{Yamada69} $\varepsilon (k) = \pi |\sin (k/2) |$.
There are other excitations above this upper boundary.
The specific heat of the model was first calculated
numerically by Bonner and Fisher\cite{Bonner64}. They found
that at low temperature $C\sim 0.7T$ when $ H=0 $. Later,
Affleck\cite{Affleck86}, using the conformal field theory,
found that $C = (2/3) T$. The zero field zero temperature
magnetic susceptibility is $\chi = 1/ \pi^2$. This result
was first obtained by Griffiths with the Bethe ansatz and
numerics\cite{Griffiths64}. Recently, Eggert {\it et
al}\cite{Eggert94} found that the zero field susceptibility
approaches to its zero temperature value logarithmically
when $T< 0.01$,
\begin{equation}
\chi = {1\over 2\pi v} \left[ 1 + \left(2\ln {T_0 \over T}
\right)^{-1} \right],
\end{equation}
where $v= (\pi /2) $ is the spin wave velocity and
$T_0\approx 7.7$.
Figure \ref{half} shows the TMRG results for a number of
thermodynamic quantities of the S=1/2 antiferromagnetic
Heisenberg model in various magnetic fields with $m=81$ and
$\tau =0.1$. At zero field, the TMRG reproduces accurately
the results which were previously obtained by the Bethe
ansatz or conformal field theory. The extrapolated zero
field zero temperature values of the internal energy $U(T)$
(i.e. ground state energy), the spin susceptibility $\chi
(T)$ and the linear coefficient of the specific heat $C(T)$,
are -0.443, 0.109 and 0.66, respectively. In all the fields
which we studied, the peak position of $\chi (T)$ is located
at a temperature which is about twice of the peak
temperature of $C(T) / T$. This is due to the fact that
$\chi (T)$ is a measure of two-particle excitations and
$C(T)/T$ is only a measure of one-particle density of
states. The maximum of $\chi$ when $H=0$ is approximately
equal to $0.147$ at $T=0.64$, consistent with the Bethe
ansatz calculation\cite{Eggert94}.
There is a significant change in the temperature dependences
of $\chi$ and $C$ when $H$ is below and above a critical
field $H_{c2} = 2$. Below $H_{c2}$, both $C/T$ and $\chi$ are
finite at zero temperature, which shows that gapless spin
excitations with a finite low energy density of states exist
in this regime. When $H=H_{c2}$, both $\chi$ and $C/T$ vary as
$ 1/ \sqrt{T} $ at low temperature; the extrapolated value
of $\sqrt{T}\chi$ and $C/ \sqrt{T}$ at zero temperature are
$0.152$ and $0.22$, respectively. The divergency of $\chi$
and $C / T$ at $T=0$ implies that the density of states of
spin excitations is divergent at zero energy when $H = H_{c2}$.
Above $H_{c2}$, there is a gap in the excitation spectrum as
both $\chi$ and $C/T$ drop to zero exponentially at low
temperatures. The value of the gap estimated from the low
temperature behavior of $\chi$ and $C$ grows linearly with
$H-H_{c2}$.
\begin{figure}
\begin{center}
\leavevmode\epsfxsize=8.6cm
\epsfbox{tx_fig2.eps}
\caption{ (a) Free energy $F(T)$, (b) internal energy
$U(T)$, (c) ratio between the magnetization $M_z(T)$ and the
field $H$, (d) spin susceptibility $\chi (T)$, (e) specific
heat $C(T)$, and (f) $C(T)/T$, per lattice site, for the
spin-1/2 Heisenberg model in four applied fields, $H$ = 0
(or 0.05), 1, 2, and 2.5. When $H=2$,
$T^{1/2}\chi (T)$ and $2 C(T) /T^{1/2}$, instead of $\chi
(T)$ and $C(T)/T$, are shown in (d) and (f), respectively.
$\tau =0.1$ and $m=81$ are used in the TMRG calculations. }
\label{half}
\end{center}
\end{figure}
Figure (\ref{corrhalf}) shows the longitudinal and
transverse correlation lengthes of the S=1/2 model in
different applied fields. When $H=0$, $\xi_x=\xi_z$
diverges at zero temperature and the slope of $\xi_z^{-1}$
at low temperature is approximately equal to 2, in agreement
with the thermal Bethe ansatz as well as the k=1 WZW
$\sigma$ model result\cite{Nomura91}
\begin{equation}
\xi_z^{-1} = T\left[ 2 - \left( \ln {T_0\over T}\right)^{-1}
\right]
\end{equation}
In the presence of magnetic field, $\xi_z$ is substantially
suppressed and becomes finite at zero temperature. As the
correlation length is inversely proportional to the energy
gap of excitations, the finiteness of $\xi_z$ at $T=0$ means
that the longitudinal spin excitation modes are massive in a
field. There is a small dip in the curve of $\xi_z$ at
$T\sim 0.4$ when $H = 0.2$ or at $T\sim 0.6$ when $H=1$.
This dip feature of $\xi_z$, as will be shown later, appears
also in large $S$ systems.
The effect of the applied field on the transverse spin
excitation modes is weaker than the longitudinal modes. The
transverse spin excitations become massive only when $H >
H_{c2}$. Below $H_{c2}$, $\xi_x$ drops to zero linearly with $T$,
as for the case $H=0$. When $H = H_{c2}$, $\xi_x$ drops to
zero as $\sqrt{T}$. Clearly the thermodynamics of the
Heisenberg model in a field is mainly determined by the
transverse excitation modes at low temperatures.
\begin{figure}
\begin{center}
\leavevmode\epsfxsize=7cm
\epsfbox{tx_fig3.eps}
\caption {(a) $1/ \xi_x$ and (b) $\xi_z$ vs $T$ for the
spin-1/2 Heisenberg models. $\tau =0.1$
and $m=81$ are used in the TMRG calculations. The circles
and squares
are thermal Bethe ansatz results. }
\label{corrhalf}
\end{center}
\end{figure}
A simple understanding of the above results can be obtained
from an equivalent spinless fermion model of the S=1/2
Heisenberg model:
\begin{eqnarray} {\hat H}& =&
\sum_i\left[- {1\over 2} (c_{i+1}^\dagger c_i +c_i^\dagger
c_{i+1}) + (H-1)c_i^\dagger c_i \right. \nonumber \\ & &
\left. + ({1\over 4} - H) + c_i^\dagger c_i
c_{i+1}^\dagger c_{i+1}\right] , \label{fermion}
\end{eqnarray}
where $c_i$ a spinless fermion operator which
is linked to the $S=1/2$ spin operator by the Jordan-Wigner
transformation $c_i = S_i^+ \exp ( i \pi \sum_{l < i}
c_l^\dagger c_l ) $. The magnetic field is equivalent to a
chemical potential for the fermions. When H=0, the ground
state has zero uniform magnetization, corresponding to a
half filled fermion band. As $H$ increases, the ground
state is ferromagnetically polarized and the Fermi energy
shifts down. When $H$ is smaller than the critical field
$H_{c2}$, the ground state of this fermion model has no gap
but the spin orientation is canted, i.e. in an
incommensurate state. The pitch angle of this
incommensurate ground state, namely the wave vector at which
the maximum of the spin-spin correlation function appears,
can be estimated from the Fermi momentum of non-interacting
fermions as $2 k_F = [1 - 2 M_z(H)] \pi$. This value of
$k_F$ is not normalized by interactions according to the
Luttinger theorem.
Above $ H_{c2}$, there are no fermions at the ground state.
At low temperature, the number of fermions excited from the
ground state are rare. Thus, as a good approximation, the
interaction term in (\ref{fermion}) can be ignored at low
temperatures. For the non-interacting system, the energy
dispersion of fermion excitations from the ground state is
given by $\varepsilon_k = H - (1+ \cos k)$, which has a
gap of $H-H_{c2}$. When $H = H_{c2}$, $\varepsilon_k = (1
- \cos k)$, the density of states of excited fermions varies
as $ 1/ \sqrt{ \varepsilon }$ at low energy. From the
standard theory of noninteracting fermions, it is
straightforward to show that this singular density of states
will cause both $\chi$ and $C/T$ to diverge as $1/ \sqrt{T}$
at low temperature. When $H > H_{c2}$, there is a gap in
the fermion excitations, both $\chi $ and $C$ should
decrease exponentially at low temperature. These results
are just what we found in Figure \ref{half}.
\subsection{S=1}
As mentioned previously,
there are two critical fields in the spin-1 Heisenberg
model, $H_{c1}$ and $H_{c2}$: below $H_{c1}$, the ground
state is a massive spin singlet; above $H_{c2}$, the ground
state becomes a fully polarized ferromagnetic state; between
$H_{c1}$ and $H_{c2}$, the ground state is massless and has
a finite magnetization. The temperature dependence of
thermodynamic quantities of the S=1 model below, above and
(approximately) at these critical fields is shown in Fig.
\ref{one}.
At zero field both $\chi (T)$ and $C(T)$ drop exponentially
with decreasing $T$ at low temperatures duo to the opening
of the Haldane gap. In this case the ground state energy
extrapolated from the internal energy $U(T)$ is -1.4015, in
agreement with the zero-temperature DMRG result
\cite{White93}. The ground state excitation gap $\Delta$
can be determined from the temperature dependence of $\chi$
and $C$ at low temperatures. If we adapt the ansatz that
the low-lying excitation spectrum has approximately the form
\cite{Sorensen93}
\begin{equation}
\varepsilon (k) = \Delta + {v^2 \over 2\Delta} (k-\pi )^2 +O(|k-\pi|^3),
\end{equation}
where $v$ is the spin wave velocity, it is then
straightforward to show that, when $T \ll \Delta$, the spin
susceptibility and the specific heat are
\begin{eqnarray}
\chi (T) & \approx & {1\over v} \sqrt{2\Delta \over \pi T}
e^{-\Delta / T}, \label{sus1}
\\
C(T) & \approx &
{3 \Delta \over v \sqrt{ 2 \pi } } \left(
{\Delta \over T }\right)^{3/2} e^{-\Delta / T},
\end{eqnarray}
irrespective of the statistics of the excitations. Taking the
ratio between $\chi (T)$ and $C(T)$ gives
\begin{equation}
\Delta = \lim_{T\rightarrow 0} \sqrt{2TC(T)\over 3\chi (T)}.
\label{gapeq}
\end{equation}
This is a very useful equation for determining $\Delta$,
especially from the point of view of experiments, since both
$\chi (T)$ and $C (T)$ are experimentally measurable quantities.
\begin{figure}
\begin{center}
\leavevmode\epsfxsize=8.6cm
\epsfbox{tx_fig4.eps}
\caption{ Thermodynamic quantities for the spin-1 Heisenberg
model in five applied fields, $H$ = 0 (or 0.05), 0.4105, 2,
4, and 4.5. When $H=0$ and 0.4105, $F(T)$ and $U(T)$ are
almost indistinguishable in the figure. When $H=0.4105$ or
4, $T^{1/2}\chi (T)$ and $2 C(T) /T^{1/2}$ (dotted lines)
are shown in (d) and (f), respectively. $\tau =0.1$ and
$m=100$ are used in the TMRG calculations. }
\label{one}
\end{center}
\end{figure}
Fig. \ref{gap} shows $\sqrt{2TC(T)/ 3\chi (T)}$ as a
function of $T$ for the S=1 Heisenberg model at zero field.
By extrapolation, we find that $\Delta \sim 0.41$ in
agreement with the zero temperature DMRG \cite{White92} and
exact diagonalization \cite{Golinelli94} results. Given
$\Delta$, the value of $v$ can be found from Eq.
(\ref{sus1}) in the limit $T\rightarrow 0$. The value of
$v$ we found is $\sim 2.45$, consistent with other numerical
calculations \cite{Sorensen93}.
\begin{figure}
\begin{center}
\leavevmode\epsfxsize=8cm
\epsfbox{tx_fig5.eps}
\caption {$({2TC(T)/3\chi (T)})^{1/2}$ vs $T$ for the
S=1 Heisenberg model. ($m=100$ and $\tau =0.1$.)}
\label{gap}
\end{center}
\end{figure}
At the two critical fields, $H_{c1}\sim 0.4105$ and
$H_{c2}=4$, both $\chi (T)$ and $C(T)/T$ diverge as
$T^{-1/2}$ at low temperatures. This divergence, as for the
S=1/2 case, is due to the square-root divergence of the
density of states of the low-lying excitations. At
$H_{c1}$, one branch of the S=1 excitations becomes massless
and the low-energy excitation spectrum is approximately
given by
\begin{equation}
\varepsilon (k) \sim {v^2\over 2\Delta} (k-\pi)^2.
\end{equation}
If we assume that these excitations are fermion-like, i.e.
satisfy the Fermi statistics (a short-range interacting Bose
system is equivalent to a system of free fermions), then it
is simply to show that when $T\ll \Delta$
\begin{eqnarray}
\chi (T) & \approx & { 1 \over 3\pi v } \sqrt{2\Delta \over T},
\\
C (T) & \approx & {1 \over 2\pi v} \sqrt{2\Delta T} .
\end{eqnarray}
Thus in the limit $T\rightarrow 0$,
\begin{eqnarray}
T^{1/2}\chi (T) & = & { \sqrt{2\Delta} \over 3\pi v}
\sim 0.4 , \label{susT0} \\
T^{-1/2}C (T) & = & {\sqrt{2\Delta } \over 2\pi v} \sim 0.6.
\label{heatT0}
\end{eqnarray}
By extrapolation, the TMRG result gives $T^{1/2}\chi
|_{T\rightarrow 0} \sim 0.45$, which is close to that given by Eq.
(\ref{susT0}). The value of $T^{-1/2} C|_{T\rightarrow 0}$
is difficult to determine accurately from the TMRG result
since the error of $C(T)$ at low temperature is larger than
$C(T)$ itself.
\begin{figure}
\begin{center}
\leavevmode\epsfxsize=7cm
\epsfbox{tx_fig6.eps}
\caption {(a) $\xi_x^{-1}$ and (b) $\xi_z^{-1}$ vs $T$ for
the spin-1 Heisenberg models. $\xi_x^{-1}(H=0)$ and
$\xi_x^{-1}(H=0.4105)$ are almost indistinguishable when $T
> 0.6$. $\tau =0.1$ and $m=100$ are used in the TMRG
calculations. }
\label{corrone}
\end{center}
\end{figure}
Fig. \ref{corrone} shows $\xi^{-1}_x$ and $\xi_z^{-1}$ of
the S=1 model in different applied fields. Because of the
Haldane gap, the longitudinal correlation
length is finite even at zero field. Thus the longitudinal
excitation mode is always gapful. Above $H_{c1}$ but below
$H_{c2}$, the transverse correlation length
diverges at zero temperature. Thus the transverse mode is
massless in this field regime. We note, however, that
$\xi_{x,z}^{-1}$ at $H=0$ (similarly $\xi_z^{-1}$ at
$H=0.4105$) does not decrease monotonically at low
temperatures, actually it starts to raise
below a temperature $T^*$. This non-monotonic behavior
of $\xi^{-1}$ at $H=0$ seems only due to the truncation error.
Our preliminary calculation shows that $T^*$
decreases with increasing $m$. But by far we still do not
know if $T^*$ is zero in the limit $m\rightarrow \infty$.
Further investigation to the low temperature behavior of
$\xi$ is needed. If we do an extrapolation using
the TMRG data of $\xi^{-1}_x$ above $T^*$, we find that
$\xi_x (T=0) \sim 6.0$, which is consistent with the zero
temperature DMRG result \cite{White93}. If, however, the
TMRG data below $T^*$ are also included in the extrapolation,
we find that $\xi_x (T=0)$ is only $\sim 4.4$.
When $H > H_{c1}$, $\xi_{z}^{-1}$ drops rather sharply at
some temperatures. These sharp drops of $\xi^{-1}_z$ happen
when the second and third eigenvalues of the transfer matrix
with $\sum_k\sigma^k = 0$ cross each other. The physical
consequence of these sudden changes in the longitudinal
correlation length is still unknown.
\subsection{S=3/2}
The thermodynamic behaviors of the S=3/2 Heisenberg model,
as shown in Fig. \ref{half3}, are similar to those of the
S=1/2 model. When $H< H_{c2}=6$, $\chi$ is always finite at
zero temperature, indicating that the ground state is
massless; above $H_{c2}$, the ground state is fully
ferromagnetic polarized and a gap is open in the excitation
spectrum; at $H_{c2}$, both $\chi (T)$ and $C/T$ diverge as
$T^{-1/2}$. At zero field, the susceptibility data, extrapolated
to zero temperature, gives $\chi (0)\sim 0.67$, consistent
with recent numerical calculations \cite{Kim97,Moukouri}.
\begin{figure}
\begin{center}
\leavevmode\epsfxsize=8.6cm
\epsfbox{tx_fig7.eps}
\caption{ Thermodynamic quantities for the spin-3/2 Heisenberg
model in four applied fields, $H$ = 0 (or 0.05), 3,
6, and 6.5. When $H=6$,
$T^{1/2}\chi (T)$ and $2 C(T) /T^{1/2}$ (dotted lines)
are shown in (d) and
(f), respectively. $\tau =0.075$ and $m=81$ are used in the
TMRG calculations. }
\label{half3}
\end{center}
\end{figure}
The crossover from quantum to classical behavior can be
clearly seen (Fig. \ref{zerofield}) by comparing the zero
field susceptibility and specific heat of the S=1/2, 1 and
3/2 spin chains with the corresponding results of the
classical Heisenberg spin chain: \cite{Fisher64}
\begin{eqnarray}
\chi (T) &=& {1\over 3T} {1-u(T)\over 1+u(T)},
\quad u(T)=\coth {1\over T} - T ,\\
C(T) &= & 1 - {1\over T^2 \sinh^2 (1/T)} .
\end{eqnarray}
At high temperatures, $T/S(S+1) > 1$, the quantum results
approach asymptotically to the classical ones. The
agreement between the quantum and classical results persist
down to progressively lower temperatures as S increases. At
low temperatures, however, the difference between the
results of the S=3/2 system and those of the classical model
is still very large, indicating the importance of the
quantum effects in the study of quantum spin chains. (Note
for the classical Heisenberg model, $C(T)$ does not vanish
at zero temperature. This is a unrealistic feature of this
model.)
\begin{figure}
\begin{center}
\leavevmode\epsfxsize=8cm
\epsfbox{tx_fig8.eps}
\caption {The zero field specific heat and susceptibility vs
$T/|{\bf S}|^2$ for the S=1/2, 1, and 3/2 spin chains
($|{\bf S}|^2 = {\rm S(S+1)}$). The corresponding results
for the classical Heisenberg model ($|{\bf S}|^2=1$) are
also shown for comparison. }
\label{zerofield}
\end{center}
\end{figure}
\subsection{Zero temperature magnetization}
Figure \ref{MT0} shows $M_z (T=0)$, extrapolated from the
finite temperature TMRG data of $M_z(T)$, for the S=1/2, 1,
and 3/2 systems. For comparison the Bethe ansatz
result\cite{Griffiths64} for the S=1/2 Heisenberg model is
also shown in the figure. With increasing S,
we found that $M_z$ tends to approach to its classical
limit ($S \rightarrow \infty$) where $M_z$ increases
linearly with $H$, i.e. $M_z / S = H / H_{c2}$.
\begin{figure}
\begin{center}
\leavevmode\epsfxsize=8cm
\epsfbox{tx_fig9.eps}
\caption {Normalized zero temperature magnetization $M_z$ as
a function of $H / H_{c2}$. The TMRG results for S=1/2
(circles), S=1 (solid line), and S=3/2 (dashed line) are
obtained by extrapolation from the low $T$ values of $M_z$
with $(m, \tau) = (81, 0.1)$, (81, 0.1), and (60, 0.75),
respectively. Dotted line is the Bethe ansatz result for
the S=1/2 system.
}
\label{MT0}
\end{center}
\end{figure}
For the S=1/2 system, the TMRG result agrees well with the
Bethe ansatz one. A least square fit to the curve of $M_z$
up to the fourth order term of $\sqrt{H_{c2} -H}$ gives $M =
M_c - a_1 \sqrt{ H_{c2}-H} + a_2 (H_{c2}-H) -
a_3(H_{c2}-H)^{3/2} + a_4 (H_{c2}-H)^2$, with $a_1\approx
0.448$, $a_2 \approx 0.123$, $a_3 = 0.05$ and $a_4=0.00744$.
$a_1$ agrees very accurately with the exact value $\sqrt{2}/
\pi$. In the weak field limit, the asymptotic behavior of
$M_z$ is
\begin{equation}
M_z\approx {H \over \pi^2} \left( 1 -{1 \over 2 \ln
(H/H_{c2}) } \right),
\end{equation}
as predicted by the Bethe Ansatz theory \cite{Yang66,Babujian83}.
For the S=1 model, $M_z(T=0)$ becomes finite when
$H>H_{c1}$. In a very narrow regime of field near $H_{c1}$,
$M_z (0)$ varies approximately as $\sqrt{H - H_{c1}}$, in
agreement with the prediction of the Bose condensation
theory \cite{Affleck91}. But the difference between the
result of the Bose condensation theory
\begin{equation}
M_z (T=0) \approx {\sqrt{2 (H - H_{c1}) \Delta }\over \pi v}
\end{equation}
and that of the TMRG becomes already significant when
$H-H_{c1} = 0.04$.
Near $H_{c2}$, $M_z$ approaches to its saturation value
$M_c=S$ as a function of $\sqrt{H_{c2} - H}$ for the three
spin systems we study. For the S=1/2 and 1 systems, the
TMRG results agree very accurately with the Bethe ansatz
result \cite{Yang66,Parkinson85}
\begin{equation}
{M_z \over S} = 1 -{2 \over \pi S} \sqrt{ 1 - {H \over H_{c2}}}.
\label{MzT=0}
\end{equation}
For the S=3/2 system, the asymptotic regime of $H$ is
very narrow, we cannot do a detailed comparison between
the TMRG result and Eq. (\ref{MzT=0}). The magnetization
curve does not show a plateaus at $M_z = 1/2$,
in agreement with other studies \cite{Oshikawa97}.
\subsection{Staggered susceptibility}
To calculate the staggered susceptibility, we add a
staggered magnetic field $H_s$ to the Hamiltonian ${\hat
H}$. The staggered magnetization is then calculated in a
way similarly to the calculation of the uniform
magnetization. The staggered susceptibility $\chi_s$ is
obtained by differentiating the staggered magnetization with
respect to $H_s$. For half-odd-integer spin chains $\chi_s$
diverges as $T^{-1}$ at low temperatures. Thus the
staggered magnetization becomes saturated at low temperatures
when $\chi_s (T) H_s > S$, since the maximum value of the
staggered magnetization per spin is S. This means that to
estimate accurately the zero field staggered susceptibility
the staggered field used should satisfy the condition $H_s
\ll S/\chi_s(T_{min})$, where $T_{min}$ is the lowest
temperature to study.
\begin{figure}
\begin{center}
\leavevmode\epsfxsize=8cm
\epsfbox{tx_fig10.eps}
\caption {the staggered
susceptibility $\chi_s (T)$ at zero field. The parameters
used for the S=1/2, 1, and 3/2 chains are ($H_s$,
$\tau$, m) = (0.0001, 0.1, 140), (0.0001, 0.05, 100), and
(0.0001, 0.025, 81), respectively. }
\label{stagger}
\end{center}
\end{figure}
Fig. \ref{stagger} shows the temperature dependence of
$\chi_s$ for the S=1/2, 1, and 3/2 spin chains. At low
temperatures, $\chi_s$ for the S=1/2 model is expected to
have the following asymptotic form
\begin{equation}
\chi_s = {D_\chi \over T} \sqrt{ \ln {T_\chi \over T} } \label{stag}
\end{equation}
according to a scaling argument \cite{Starykh97}.
Our TMRG result agrees well with this equation at low
temperatures. By plotting $(T \chi_s)^2$ against $\ln T$,
we find that $D_\chi \approx 0.30$ and $T_\chi \approx 10.5$,
in agreement with a Monte Carlo calculation \cite{Kim97}.
For the S=1 model, $\chi_s$ is finite at zero temperature.
The extrapolated zero temperature value of $\chi_s$ for the
S=1 model is 18.55, in agreement with other numerical
calculations \cite{Kim97,Sakai90}.
\section{Conclusion} \label{sec4}
In conclusion, the temperature dependence of the
susceptibility, specific heat, and several other quantities
of the quantum Heisenberg spin chains with spin ranging from
1/2 to 3/2 in a finite or zero applied magnetic field are
studied using the TMRG method. At high temperatures, the
quantum results for the specific heat as well as other
thermodynamic quantities approach asymptotically to the
classical ones for both the integer and half-integer spin
systems. At low temperatures, however, the quantum effect
is strong and the integer spin chains behave very
differently than the half-integer spin chains. For the S=1
model, both $\chi$ and $C$ decay exponentially at low
temperatures due to the opening the Haldane gap. For the
S=1/2 and 3/2 spin chains, there is no gap in the excitation
spectrum and both $\chi$ and $C/T$ are finite at zero
temperature. The thermodynamics of the Heisenberg spin
chains in an applied field is mainly determined by the
transverse excitation modes. At low temperatures, $\chi$,
$C/T$, and the transverse correlation length $\xi_x$ diverge
as $T^{-1/2}$ at $H_{c2}$ for the S=1/2 and 3/2 models and
at both $H_{c1}$ and $H_{c2}$ for the S=1 model. This
square-root divergence indicates that the low energy spin
excitations have a square-root divergent density of states
at these critical fields. Our data agree well with the
Bethe ansatz, quantum Monte Carlo, and other analytic or
numerical results.
\section*{Acknowledgments}
I would like to thank R. J. Bursill, G. A. Gehring,
S. J. Qin and X. Wang for stimulating discussions.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 31 |
OECD Statistics Working Papers
Can Increasing Inequality Be a Steady State?
The OECD Statistics Working Paper Series - managed by the OECD Statistics and Data Directorate – is designed to make available in a timely fashion and to a wider readership selected studies prepared by staff in the Secretariat or by outside consultants working on OECD projects. The papers included are of a technical, methodological or statistical policy nature and relate to statistical work relevant to the organisation. The Working Papers are generally available only in their original language - English or French - with a summary in the other.
Joint Working Papers:
Testing the evidence, how good are public sector responsiveness measures and how to improve them? (with OECD Public Governance Directorate)
Measuring Well-being and Progress in Countries at Different Stages of Development: Towards a More Universal Conceptual Framework (with OECD Development Centre)
Measuring and Assessing Job Quality: The OECD Job Quality Framework (with OECD Directorate for Employment, Labour and Social Affairs)
Forecasting GDP during and after the Great Recession: A contest between small-scale bridge and large-scale dynamic factor models (with OECD Economics Directorate)
Decoupling of wages from productivity: Macro-level facts (with OECD Economics Directorate)
Which policies increase value for money in health care? (with OECD Directorate for Employment, Labour and Social Affairs)
Compiling mineral and energy resource accounts according to the System of Environmental-Economic Accounting (SEEA) 2012 (with OECD Environment Directorate)
Historically, discussions of income inequality have emphasised cross-sectional comparisons of levels of inequality of income. These comparisons have been used to argue that countries with more inequality are less healthy, less democratic, more crime-infested, less happy, less mobile and less equal in economic opportunity, but such comparisons implicitly presume that current levels of inequality are steady state outcomes. However, the income distribution can only remain stable if the growth rate of income is equal at all percentiles of the distribution. This paper compares long-run levels of real income growth at the very top, and for the bottom 90% and bottom 99% in the United States, Canada and Australia to illustrate the uniqueness of the post-WWII period of balanced growth (and consequent stability in the income distribution). The 'new normal' of the United States, Canada and Australia is 'unbalanced' growth – specifically, over the last thirty years the incomes of the top 1% have grown significantly more rapidly than those of everyone else. The paper asks if auto-equilibrating market mechanisms will spontaneously equalise income growth rates and stabilise inequality. It concludes that the more likely scenario is continued unbalanced income growth. This, in turn, implies, on the economic side, consumption and savings flows which accumulate to changed stocks of indebtedness, financial fragility, and periodic macroeconomic crises; and, on the social side, to increasing inequality of opportunity and political influence. Greater economic and socio-political instabilities are therefore the most likely consequence of increasing income inequality over time.
Lars Osbergi iDalhousie University
https://doi.org/10.1787/5jz2bxc80xq6-en
http://instance.metastore.ingenta.com/content/paper/5jz2bxc80xq6-en | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,711 |
{"url":"http:\/\/mathhelpforum.com\/calculus\/160659-integration-parts-help-plz.html","text":"# Math Help - Integration by parts? help plz\n\n1. ## Integration by parts? help plz\n\nintegral 0 to infinite (x^ 3)(e^-8x) cos(5x) dx\n\nshould I do integrate by part?\nhelp me\n\nIs it: $\\displaystyle \\int_{0}^{\\infty} x^3 \\cdot e^{-8x} \\cdot \\cos (5x) dx$\n\nOr is it: $\\displaystyle \\int_{0}^{\\infty} x^{3e^{-8x}} \\cdot \\cos (5x) dx$\n\n3. 1st one. ! thanks. how did you do it?\n\n4. To type equations like I did, you use LaTeX to do it. LaTeX Tutorial.\n\nYes, you would use integration by parts. For the $\\cos (5x)$ part you would also need to use integration by u-substitution as well as integration by parts.\n\n$\\displaystyle \\int f'(x)g(x)h(x)dx = f(x)g(x)h(x) - \\int f(x)g'(x)h(x)dx - \\int f(x)g(x)h'(x)dx$\n\n5. Originally Posted by ddcamp\nintegral 0 to infinite (x^ 3)(e^-8x) cos(5x) dx\n\nshould I do integrate by part?\ndo you have to find the actual value of the improper definite integral, or do you just have to show that it converges?\n\n6. I have to find the actual value :S :S thanks!","date":"2014-10-21 14:43:24","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 4, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.9686053395271301, \"perplexity\": 1670.7401414505205}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-42\/segments\/1413507444465.10\/warc\/CC-MAIN-20141017005724-00063-ip-10-16-133-185.ec2.internal.warc.gz\"}"} | null | null |
Q: Can't configure ngx-ui-loader from app.module.ts file I am using the ngx ui loader for my angular 7 project.
In the app.module.ts file, I have imported the ngx-ui-loader package like this:-
import { NgxUiLoaderModule, NgxUiLoaderHttpModule, NgxUiLoaderConfig, SPINNER, POSITION, PB_DIRECTION } from 'ngx-ui-loader';
Then I created a constant like this to define the configuration parameters:-
const ngxUiLoaderConfig: NgxUiLoaderConfig = {
bgsColor: 'red',
bgsPosition: POSITION.bottomCenter,
bgsSize: 40,
bgsType: SPINNER.rectangleBounce,
pbDirection: PB_DIRECTION.leftToRight, // progress bar direction
pbThickness: 5, // progress bar thickness
};
Then added the NgxUiLoaderModule.forRoot(ngxUiLoaderConfig) in the imports array of the @NgModule
In the app.component.html file, I have added the <ngx-ui-loader></ngx-ui-loader> tag just above the <router-outlet></router-outlet> tag.
In the app.component.ts file, I kept the following code
import { NgxUiLoaderService } from 'ngx-ui-loader';
export class AppComponent implements OnInit{
title = 'medico';
constructor(private ngxService: NgxUiLoaderService) { }
ngOnInit() {
this.ngxService.start(); // start foreground spinner of the master loader with 'default' taskId
// Stop the foreground loading after 5s
setTimeout(() => {
this.ngxService.stop(); // stop foreground spinner of the master loader with 'default' taskId
}, 300);
}
}
When I am running the page, I can see the loader. The issue is, even after changing the configuration data in the app.module.ts, the loader property doesn't change.
What am I doing wrong?
Note: Please don't give suggestions like "why don't you use other loader like http-loader, etc". The question is about why the ngx ui loader isn't working as expected.
A: You need to change all instances of bgs to fgs, so bgsColor should be fgsColor.
By default, the only spinner viewable appears to be the forground spinner and the progress bar.
Hope that helps
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,132 |
\section{Introduction}
Magnetic single atoms and molecules are the pinnacle of ever-increasing demands for information storage density \cite{Bogani2008,Natterer2017} and quantum information processing \cite{doi:10.1126/science.1249802,doi:10.1126/science.aay6779}. Reaching the ultimate spatial limit requires the technical capabilities to achieve the single spin sensitivity and control. The scanning tunneling microscopy (STM) provides a particularly high spatial resolution that allows it to image single atoms and molecules, characterize their electronic and magnetic states, and manipulate their positions on a surface \cite{PhysRevLett.49.57,Bian2021}. Despite its exclusively high sensitivity with atomic resolution, the spectral resolution of STM is often limited by temperature due to the thermal Fermi-Dirac broadening of the energy of tunneling electrons \cite{PhysRev.165.821, Song2010, Ast2016, PhysRevLett.107.076804}. Even when the spin systems are cooled down below 1 K temperatures at a high cost, achieving spectral resolution of tens of nano-eV in the conventional spectroscopy of STM, such as inelastic electron tunneling spectroscopy (IETS), is impossible. In contrast, the detection of spin transitions with a few nano-eV energy resolution is easily attainable in electron spin resonance (ESR). Conventional ensemble ESR, however, requires at least $10^7$ spins ($10^{12}$ for nuclear spins) to get strong enough signals\cite{BLANK2003116,Assig2013, Ciobanu2002}, while its spectroscopic resolution is not limited by temperature. The integration of ESR with STM maximizes the powerful benefits of both approaches, and the single spin ESR detection with atomic resolution has been exclusively achieved by ESR spectroscopy in STM \cite{Baumann417,https://doi.org/10.1002/adma.202107534}.
\begin{figure*}
\includegraphics[width=170mm]{Figure1.pdf
\caption{\label{fig:structures} Design of the home-built ESR-STM. (a) Overview of the whole system including a cryostat, a vector magnet, a mechanical damping system, a cooling system, an STM, and a preparation chamber. The preparation chamber and the ultrahigh vacuum (UHV) insert are connected to the top flange of an exchange gas can (EGC) via a flexible bellows. The UHV insert is supported by three arms connected to the system via three flexible bellows (labelled as `Pendulum'). (b) ESR-STM setup on a massive concrete block. The cryostat rests on a concrete block floated by four air springs in a sound-proof room. (c) Velocity spectrum measured on the floor of the sound-proof room (purple, QNS floor) and on top of the floating concrete block (magenta, QNS block) in comparison with other precision laboratories (blue, IBM Almaden; green, IBM Zurich; light blue, MPI Stuttgart). (d) Power spectral density (PSD) of the tunnel current measured with pendulum on (magenta) and off (blue) ($V_{\mathrm{DC}}$ = 10 mV, $I$ = 1 nA, Integral-gain = 1 nm/s). (e) Schematics showing pendulum operation. The UHV insert is suspended by three welded bellows, while schematics shows only two bellows for simplicity. When the pendulum is in the `off' state (top), the UHV insert is misaligned and thus in mechanical contact with EGC. In the `on' state (bottom), the pendulum is aligned inside the EGC without touching the EGC and, thus, mechanically isolated from the rest of the system.}
\end{figure*}
ESR measurements in STM require the use of specialized cables for the injection of radio-frequency (RF) electric fields into the tunnel junction \cite{doi:10.1063/1.4955446,PhysRevResearch.2.013032}. However, adding RF cables or replacing existing cables with RF cables to a low-temperature STM for ESR capability is not so trivial since most STMs are already compactly wired and semi-rigid RF cables may cause vibration and heat transmissions to the tunnel junction \cite{doi:10.1063/1.5065384,doi:10.1063/1.5104317,doi:10.1063/1.5109721, Weerdenburg2021, drost2021combining}. Furthermore, to obtain strong ESR signals from a single atom/molecule, it is important to sufficiently polarize the spin state, which imposes a strict requirement on temperature of the system. Given that many existing STMs operate in the 2--4 K temperature range or above, an external magnetic field greater than 1 T facilitates the polarization of surface spins, necessitating RF fields with frequencies higher than 30 GHz at the tunnel junction.
In this work, we introduce an extremely stable, home-built ESR-STM which operates at temperatures ranging from 1 K to at least 10 K. We use RF cables for the STM tip and an antenna parallel to the sample plane, which enables us to examine RF signal transmission to the tunnel junction through two different cabling schemes. The RF cable going directly to the STM tip allows for a high transmission to the STM junction, where the STM tip apex is positioned within a nanometer scale from an atom or a molecule on a surface. However, the resonance frequency available at the tunnel junction is limited to around 35 GHz due to the requirement for a flexible coaxial cable for the coarse motion of the STM tip. In contrast, for the antenna placed about 4 mm distant from the tunnel junction, we observe that a larger frequency window than the direct wiring to the STM tip is available at the tunnel junction, enabling us to perform high temperature ESR measurements up to 10 K. While the ESR intensities exponentially decrease at elevated temperatures, our ESR-STM enables us to detect weak ESR signals such as sub-fA. Extending the temperature range accessible for the ESR spectroscopy in STM and providing the sensitivity without incurring large costs to modify existing STMs for a lower temperature operation will hasten the spread of this technique for the phase-sensitive control and detection of spins on a surface.
\section{Instrument design}
We present the design of an ultrahigh vacuum (UHV) ESR-STM operational at a broad range of temperatures with high mechanical stability. The ESR-STM system comprises a cryostat (MAXes\textsuperscript{TM} 6T/4T vector magnet, American Magnetics Inc.), a cooling system, a UHV insert with an STM, and a UHV preparation chamber [Fig.~\ref{fig:structures}(a)]. The liquid \textsuperscript{4}He (LHe) bath cryostat contains a commercially available two-axis vector magnet (American Magnetics Inc., maximum 6 T in-plane and 4 T out-of-plane of a sample) and an exchange gas can (EGC) which is filled with \textsuperscript{4}He exchange gas. The UHV insert, which includes the transfer neck with baffles, `5K-flange', `1K-pot', and STM, is positioned inside of the EGC and cooled by \textsuperscript{4}He exchange gas without direct contact with the LHe reservoir. The 1K-pot contains a home-built Joule-Thomson (JT) refrigerator which serves as the system's coldest location. The STM is rigidly attached to the 1K-pot by materials having high mechanical stiffness and high thermal conductivity. Samples are prepared \textit{in-situ} in a separate preparation chamber and transferred to the STM sample stage using a home-built vertical manipulator with a travel length of about 2 m. In the following sections, we describe each part in detail.
\subsection{Mechanical dampers}
The STM measurement relies on the precise placement of a metallic tip a nanometer apart from the surface \cite{PhysRevLett.49.57,Bian2021}. The extremely high spatial resolution is predicated on the exponential sensitivity of tunnel current on the separation between the STM tip and a sample. For the same reason, ambient vibrations reaching the tunnel junction are exponentially amplified in the tunnel current signals. Constructing high-performance STM with atomic-scale spatial precision, thus, necessitates mitigating the impact of external vibration sources on the tunnel junction. Ambient vibration sources include mechanical vibrations and acoustic noise.
To avoid such noise sources from being transmitted to the tunnel junction, we installed the entire STM system on a floating concrete block, which weighs 80 tons, in a sound-proof room. The room is located in a low vibration facility built on a 1.4 m thick concrete foundation which is separated from the rest of the building [Fig.~\ref{fig:structures}(a) and (b)]. The massive concrete block is placed in the center of the sound-proof room, separated by about 1 m from the acoustically absorptive wall, and lifted up by four air springs (BiAir-ED-HE-MAX, Bilz Vibration Technology AG) to further isolate the block from floor vibrations.
Figure~\ref{fig:structures}(c) compares the facility's velocity spectrum to that of other facilities \cite{Loertscher2013,Bian2021}, which was measured using an accelerometer (731A/P31, Wilcoxon) on the floor of the sound-proof room and on the concrete block under ambient vibration conditions. The measured linear acceleration is integrated to obtain linear velocity, which is then converted to an A-weighted one-third octave band spectrum after Fourier transform. The floor noises higher than 3 Hz are significantly suppressed by the massive inertia block, resulting in a one order of magnitude reduction in noise on the block. Given that the lowest fundamental acoustic mode is at 11.16 Hz in the 5.69 m $\times$ 7.68 m $\times$ 6.28 m size room, the feature appearing at around 12 Hz in the noise spectrum [Fig.~\ref{fig:structures}(c), QNS block] is presumably the result of acoustic stimulation of the concrete block motion\cite{MacLeod2016}. The noise level we attained in the overall frequency range relevant to STM performance is comparable to or even better than noise levels measured in the world's leading precision laboratories [Fig.~\ref{fig:structures}(c)]. At considerably higher frequencies, where the STM stage's resonances are located, little environmental vibrations are transmitted.
While the entire system is rigidly mounted on the floating concrete block, we provide one more damping stage for the STM. To reduce vibration transfer and provide flexibility to adjust alignment, the UHV insert, which includes the STM unit near its lower end, is connected to the top flange using one central bellows for the connection of the preparation chamber and three side bellows for three supporting arms [Fig.~\ref{fig:structures}(a) and (e)]. The UHV insert can be floated by controlling the pressure in the three side bellows and lifting three supporting arms, which suspends the STM like a pendulum. The 1.5 m tall UHV insert has a 1--2 mm gap with the EGC. Mechanical deformation and misalignment, thus, might cause the mechanical contact of the UHV insert to the EGC. Controlling the pressure of the three side bellows allows us to adjust the alignment of the UHV insert with respect to the EGC. The idea for this design stems from the first low-temperature STM built by Don Eigler at IBM \cite{Eigler1990}. As shown by the power spectral density of the tunnel current [Fig.~\ref{fig:structures}(d)], which is measured at a setpoint of $V_{\mathrm{DC}}$ = 10 mV and $I$ = 1 nA using 10\textsuperscript{9} V/A gain preamplifier (SA-606F2, NF corp), we observed significant noise transfer from the environment to the tunnel junction when the pendulum is not adequately operational [upper in Fig.~\ref{fig:structures}(e)]. When the pendulum is well isolated [lower in Fig.~\ref{fig:structures}(e)], the noise level at the tunnel junction is significantly reduced. The combination of the floating concrete block and the internal pendulum results in a remarkable mechanical stability of the system.
\subsection{Joule-Thomson refrigerator}
\begin{figure}[t]
\includegraphics[width=85mm]{Figure2.pdf}
\caption{\label{fig:JT} Joule-Thomson (JT) refrigerator. (a) Overview of the cooling system including JT refrigerator, 5K-flange, and 1K-pot. For the JT refrigerator, the \textsuperscript{4}He gas is cooled through cooling posts and inserted to the capillary at the 1K-pot. The liquefied He is accumulated to the lower Cu part of 1K-pot, where the whole STM structure is attached by Cu rods. The 1K-pot is pumped through the EGC. At the pumping port, the cooling post and baffle cover are located, which cool the He gas and electrical feedthroughs, respectively. (b) Photographs of the UHV insert with baffle cover on 5K-flange, the UHV chamber made of stainless steel and BeCu, 5K-flange with feedthroughs and a cooling post, and 1K-pot. (c) Temperature of STM controlled by a heater installed on the 1K-pot during the operation of JT refrigerator. By adjusting the heating power, the system can stably operate at different temperatures. Inset: STM temperature during the operation of JT refrigerator without heating the STM stage, which can run continuously at 1.3 K.}
\end{figure}
The LHe bath cryostat, containing the superconducting magnets, provides a LHe reservoir (maximum 133 L of LHe) with a hold time of around 140 hours allowing for the operation of magnets. The EGC is housed in the cryostat and is in direct contact with LHe. The EGC is composed of three different segments [Fig.~\ref{fig:structures}(a)]. The top part from room temperature (RT) top flange to the end of the cryostat's neck is made of stainless steel with a small wall thickness ($\sim$7 mm) to minimize thermal conduction. The choice of materials for the middle section is oxygen-free, high conductivity (OFHC) copper (Cu) for better cooling of the UHV insert regardless of the level of LHe in the cryostat. The last part is the tail of the EGC, which is placed in the magnet's center. To avoid the creation of eddy currents while ramping the magnet, the tail is made of stainless steel. The EGC is filled with He exchange gas (0.01--3 mbar). The work shown in this manuscript uses \textsuperscript{4}He as exchange gas, which can be replaced with \textsuperscript{3}He to achieve lower base temperatures.
The UHV insert is situated inside the EGC and cooled by the exchange gas without direct contact with LHe, which lowers the vibration transfer stemming from the boiling of LHe and external vibration sources. The UHV insert includes the transfer neck with baffles, 5K-flange, 1K-pot, and STM [Fig.~\ref{fig:structures}(a) and \ref{fig:JT}(a)]. The transfer neck is a 750 mm long nipple with DN35CF, made of stainless steel, with an outer diameter of 40 mm and a wall thickness of 1.4 mm. We installed six baffles outside the transfer neck with a diameter close to the inner diameter of the EGC, to prevent thermal radiation from reaching the bottom of the UHV insert and to provide a thermal gradient from the RT top flange to the 5K-flange. The baffles are made of gold-plated Cu without Ni plating. All six baffles are located in the top stainless steel part of the EGC except the last one, which is located in the Cu section of the EGC. The 5K-flange maintains a gap of about 2 mm to the EGC, allowing the exchange gas to effectively transfer heat between the EGC and the 5K-flange. All electrical feedthroughs are installed on the 5K-flange to cool electrical cables before entering the STM stage. We additionally installed a baffle cover made of OFHC Cu to help cooling all feedthroughs on the 5K-flange [labelled as `Baffle cover' in Fig.~\ref{fig:JT}(a) and (b)].
To achieve STM operation at temperatures below 5 K, the UHV insert is equipped with a JT refrigerator in the 1K-pot. The 1K-pot is made of two different materials: stainless steel for the upper section and Cu for the lower section [Fig.~\ref{fig:JT}(b) lower right corner]. The 1K-pot with a volume of $\sim$0.1 L is mounted on the UHV side of the 5K-flange above the magnet and thermally isolated from the surrounding UHV chamber. The 1K-pot is continuously fed with cold, compressed He gas through a thin capillary [Fig.~\ref{fig:JT}(a)]. Through the JT effect, some of this gas is liquefied in the 1K-pot. The liquefied He is accumulated in the lower Cu part of the 1K-pot, where the STM is rigidly attached through three rods made of OFHC Cu. The capillary inside the 1K-pot is 0.3 m long and is coiled three times and partially submerged in the LHe in the 1K-pot [Fig.~\ref{fig:JT}(a)]. The capillary is composed of Inconel tube with an inner diameter of 500 $\mu$m. We create a flow impedance by fitting a tungsten wire with a nominal diameter of 500 $\mu$m inside the Inconel tube. In steady-state flow, the phase transition of He happens via the JT effect in the 1K-pot, liquefying some of the exchange gas and making the 1K-pot the coldest place in the entire system \cite{doi:10.1063/1.3520482}. We installed a heater on the 1K-pot to control STM temperatures (see Table \ref{tab:table1} for wiring). As shown in Fig.~\ref{fig:JT}(c), we can accurately and reliably adjust the STM temperature by varying the power applied to the heater.
The boil-off from the LHe in the 1K-pot goes through a pumping line (a 0.15 m long nipple with DN16CF), where it cools the incoming gas in a counter-flow heat exchanger [Fig.~\ref{fig:JT}(a)]. We used a customized gasket with a reduced inner diameter (12 mm) to avoid additional noise production caused by pumping liquefied He at around the $\lambda$-point of He ($\sim$2.18 K). The pumped gas then exits into the EGC at the 5K-flange. The exchange gas (\textsuperscript{4}He) is pumped out at the RT side using a turbo pump (HiPace 450, Pfeiffer Vacuum) and a roots pump (A100L, Pfeiffer Vacuum), compressed using a customized diaphragm pump (N186.1.2AN/V.12E, KNF), cleaned by a cold trap, and injected back into the capillary located at the 1K-pot [Fig.~\ref{fig:structures}(a)]. Prior to entering the 1K-pot, the compressed gas passes two precooling stages, on one of baffles and the 5K-flange, where the 1/8 inch diameter stainless steel tube for the insert gas is brazed around Cu rods [Fig.~\ref{fig:JT}(a) and (b)]. Continuous operation of the JT refrigerator has no perceptive effect on the hold time of LHe in the cryostat or the noise level at the tunnel junction, which allows us to keep the JT refrigerator running during STM operation. To minimize heat input from thermal radiation, the 1K-pot and STM are protected by a radiation shutter at the end of the transfer neck [Fig.~\ref{fig:JT}(a)].
\subsection{Design of RF antenna}
\begin{figure}
\includegraphics[width=85mm]{Figure3.pdf
\caption{\label{fig:antenna} RF signal transmission of two different antennas. (a) Experimental setup for RF transmission test of the PT- (upper) and PS-antennas (lower). Using a network analyzer, RF signals are applied to the antenna and the transmitted signals to the tip are measured. The PT- and PS-antennas are made of stripped parts of coaxial cables which run parallel to the tip and to the sample, respectively. The PS-antenna is terminated with a 50-Ohm load and held in place with the help of an antenna mount. (b) Signal transmission for the PT-antenna (blue) and PS-antenna with (magenta) and without (yellow) a 50-Ohm terminator. (c) Signal transmission for the PT-antenna (blue) and PS-antenna (magenta) without the sample. While the transmission for the PT-antenna remains nearly identical, we observed a considerable loss in transmission between the PS-antenna and the tip when the sample was removed.
}
\end{figure}
The first demonstration of ESR of single atoms on a surface was achieved by applying RF voltages into the tunnel junction via the STM tip (referred to as the "original ESR-STM design"), where the RF voltages are combined with the DC bias voltage at RT using a bias tee\cite{Baumann417, doi:10.1063/1.4955446}. Due to the complex modifications to the RF cablings of STM in the early design, Seifert et al.\cite{PhysRevResearch.2.013032} introduced one simple antenna capacitively coupled to the tip, where the antenna was installed as parallel as possible to the tip (PT-antenna). The PT-antenna offers larger signal transmission to the tunnel junction at high frequency than the original ESR-STM design. Here, we introduce a new design of an antenna parallel to the sample (PS-antenna) and compare two different antennas (PT- and PS-antennas) by measuring and simulating their signal transmission to the tip and simultaneously to the sample. We provide a universal approach to integrating RF cables into the STM, while the antenna design was dedicated based on the geometry of our STM by considering three aspects: i) stable transmission while allowing for the coarse motion of the tip, ii) mechanical stability, and iii) suppression of standing waves.
Figure~\ref{fig:antenna}(a) shows the experimental setup for the characterization of signal transmission from two different antennas (PT- and PS-antennas) to the tip-sample junction using a network analyzer (N5224B, Keysight). We set the tip and each antenna using semi-rigid coaxial cables (UT-085C-LL, Carlisle Interconnect Tech.) and the sample using a Cu foil. The PT-antenna and the tip are made of coaxial cables with unshielded inner conductors at the ends, while the PS-antenna is made by stripping the outer conductor in the middle of a coaxial cable and terminating it with a 50-Ohm load [Fig.~\ref{fig:antenna}(a)]. We used an antenna mount to hold two sides of the PS-antenna's outer conductors to rigidly support the antenna and thus provide better mechanical stability [lower in Fig.~\ref{fig:antenna}(a)]. Note that the metallic antenna mount may behave like a signal receiver when it is less than 50 mm away from the antenna. The tip and each antenna are connected to the network analyzer for transmission (S21) measurements using flexible cables (FLC-1M-SMSM+, Mini-Circuits), and calibrations are performed using an electronic calibration module (Ecal N4693A (4693-60003), Keysight) to eliminate the systematic errors from the flexible cables.
Despite their different designs, both PT- and PS-antennas exhibit a uniform decrease over the whole frequency range, with sharp dips at frequencies lower than 10 GHz. We ascribe such sharp attenuations to interferences of incident and reflected signals at unshielded parts of the semi-rigid cables. The transmission of an antenna often has a strong frequency dependence where the resonance frequency is determined by its size and shape. RF signals with wavelengths longer than the dimensions of an antenna are difficult to transmit through capacitive coupling\cite{RFandMICROWAVE_ENGINEERING}. Such losses at low frequencies remained even after we removed the sample [Fig~.\ref{fig:antenna}(c)], supporting our hypothesis.
While the signal transmissions through two different antennas are comparable, we found distinct transmission paths between two antennas. The shape and dimension of the PT-antenna are chosen to be similar to those of the tip and, thus, we expect maximum transmission between the two by a capacitive coupling as the antenna is placed parallel to the tip. In the range of 10 to 30 GHz, we indeed observe less loss from the PT-antenna compared to the PS-antenna [Fig.~\ref{fig:antenna}(b)]. The PS-antenna, on the other hand, is less coupled to the tip since it is designed to be parallel to the sample and thus practically perpendicular to the tip. We also note that there is a considerable change in the transmission for the PS-antenna when the sample was removed, indicating significant coupling of the PS-antenna to the sample [Fig.~\ref{fig:antenna}(b) and (c)]. Despite rather drastic changes in the design, these results qualify that the PS-antenna is an adequate alternate to the PT-antenna, particularly at frequencies above 30 GHz as we see better transmission properties. Note that we have a 20 mm long unshielded part of the cable for the PT-antenna. Adjusting the stripped area possibly provides additional room to improve the signal transmission.
We briefly discuss the role of the 50-Ohm terminator in the PS-antenna. A proper termination of an RF cable is essential to reduce the creation of standing waves. Ideally, if the load impedance at the cable's end is matched to the characteristic impedance of the transmission cable, no reflections appear\cite{RFandMICROWAVE_ENGINEERING}. However, in reality, the impedance mismatch between the cable (50 Ohm) and the STM junction (typically 1 GOhm) causes significant reflections and thus the creation of standing waves. To suppress reflections, we put a 50-Ohm terminator (BM11132, Bracke) rated up to 40 GHz at the end of the transmission cable [Fig.~\ref{fig:antenna}(a)]. Figure~\ref{fig:antenna}(b) shows signal transmissions from the PS-antenna to the tip with and without the 50-Ohm terminator, designated as PS and PS open, respectively. We observed that adding the 50-Ohm terminator helps reducing some abrupt features in the transmission.
\begin{figure}
\includegraphics[width=85mm]{Figure4.pdf
\caption{\label{fig:COMSOL} COMSOL simulations of electric field distribution. (a) Schematics of the simulation setup and the simulated images of electric fields around the antenna, tip, and sample for the PT- and (b) PS-antenna when oscillating voltage signals are applied through the antennas. Three selected simulation results are shown when the frequency of the incident oscillating voltage is set to 14.5, 24, and 30 GHz.}
\end{figure}
The signal transmissions of each antenna to the tip-sample junction are further investigated using COMSOL multiphysics to simulate the electric field in space. In the simulation, we provide an oscillating voltage of 1 V to the transmission line of the antenna, which is then transmitted to the junction. Figures~\ref{fig:COMSOL}(a) and (b) show simulated results calculated at incident electric field frequencies of 14.5, 24, and 30 GHz for the PT- and PS-antennas. The simulation results reveal that for both PT- and PS-antennas a strong localized electric field is generated at the tip-sample junction.
On average, the PS-antenna transmits somewhat less to the junction than the PT-antenna across all frequencies (5--35 GHz). However, we observed that at some frequencies (for example at 14.5 GHz), the PT-antenna barely transmits signals. Because the tip and the PT-antenna have similar dimensions, the transmission might change drastically at particular frequencies where a half of a wavelength ($\sim$10 mm) is comparable to the length of the PT-antenna or the tip. The PS-antenna, on the other hand, is less frequency-sensitive due to its highly distinct dimensions from the sample. Furthermore, the PS-antenna partially transmits signals through the tip, which allows it to transmit the RF signals without considerable frequency dependence by transmitting the signals through alternative paths. We note that moving the tip laterally along the antenna results in no significant change of the localized electric field at the tip-sample junction.
The simulation results support the practical replacement of the PT-antenna with the PS-antenna, particularly for STMs where the sample is fixed while the tip moves in large coarse steps. In the later sections, we will demonstrate that this newly-designed antenna is indeed competitive with the PT-antenna for ESR-STM measurement.
\begin{figure}
\includegraphics[width=85mm]{Figure5.pdf
\caption{\label{fig:wiremap} STM stage and cabling schemes. (a) Overview of the STM stage including the tip, antenna, sample stage, and piezo stacks. Coaxial cables (orange and cyan) are used for connections to the tip and the antenna. The sample holder is clamped by BeCu springs (light orange) with sapphire wheels (light gray). A molybdenum (Mo) bolt of the sample holder is in contact with the BeCu spring (light orange), which is connected to the inner conductor of a flexible coaxial cable (cyan) as a tunnel current signal line. The PtIr tip is in a tin plated BeCu pin spring socket (2-330808-7, AMP-TE connectivity) as a tip holder which is mounted in the Macor tip plate on the sapphire plate sitting on three piezo stacks for the tip's coarse and scan motions (below). Only two stacks are shown in the side view. (b) Wiring schemes for ESR-STM measurement. The same RF cable schemes are used for the tip and antenna except for the cables between the 1K-pot to STM stage. For the tip side, a flexible coaxial cable is used between the semi-rigid Cu cable and the tip. For the antenna, the semi-rigid Cu cable is partially stripped near the sample, then returned back to the 1K-pot, and followed by NbTi cable with a 50-Ohm terminator.}
\end{figure}
\subsection{Scanning tunneling microscope with RF cabling}
\begin{table*}
\caption{\label{tab:table1}Summary of electrical cables used in the system}
\begin{tabular}{|m{2.4cm}||m{4.7cm}|m{4.7cm}|m{5.2cm}|}
\hline
\textbf{ } & \textbf{RT top flange to 5K-flange} & \textbf{5K-flange to 1K-pot} & \textbf{1K-pot to STM}\\
\hline
\textbf{Piezo stacks} & CC-SS, Lake Shore Cryotronics & CC-SS, Lake Shore Cryotronics & TYP3-2TW-15, Accu-Glass Products\\
\hline
\textbf{Sample current} & N12-36M-131, New England Wire & N23-44M-100-0, New England Wire & CW-2040-3650P, Cooner Wire\\
\hline
\textbf{Tip bias} & SCA49141-09, Fairview; & SC-160/50-NbTi-NbTi, Coax Japan & UT-085C-LL, Carlisle Interconnect Tech;\\
& SC-119/50-SSS-SS, Coax Japan & & CW2040-3650P, Cooner Wire\\
\hline
\textbf{Antenna} & SCA49141-09, Fairview;& SC-160/50-NbTi-NbTi, Coax Japan & UT-085C-LL, Carlisle Interconnect Tech\\
& SC-119/50-SSS-SS, Coax Japan& & \\
\hline
\textbf{Temperature} & Silicon diodes / Cernox& Cernox & \\
\textbf{Sensors}& with Quad-Lead$\textsuperscript{TM}$ cryogenic wires, &with Quad-twist$\textsuperscript{TM}$ cryogenic wire,& -\\
& Lake Shore Cryotronics&Lake Shore Cryotronics& \\
\hline
\textbf{Heaters}&WMW-32, Lake Shore Cryotronics&SS 304 insulated with HNY,& -\\
& &California Fine Wire company& \\
\hline
\end{tabular}
\end{table*}
Our STM is relatively simple in design [Fig.~\ref{fig:wiremap}(a)] and comprises the tip, sample stage, and cables for RF signal transmission, electrical control, and STM signal. Our sample is vertically loaded and held in place by two BeCu springs with sapphire wheels [Fig.~\ref{fig:wiremap}(a)]. The sapphire wheels allow us to transfer samples without producing excessive friction and hold the sample in the STM stage without electrical contact to the stage. The sample holder is electrically isolated from the STM stage made of silicon phosphorus copper (SiPCu) by sapphire pieces between them. These sapphire pieces are glued to the rest of STM stage using epoxy (T7110, EPO-TEK). For better thermal coupling, the bottom part of sample holder is contacted to the SiPCu stage without sapphire but covered by a Kepton tape for electrical insulation.
While the sample stays in place, we move the tip for both coarse and fine motion. The coarse motion of the tip is given in two directions, parallel ($x$) and perpendicular ($z$) to the sample surface for lateral coarse positioning and coarse approaching, respectively [Fig.~\ref{fig:wiremap}(a)]. For each direction, we used two shear piezoelectric actuators. The same shear piezo actuators are used for the fine scanning motions in $x$ and $z$. For fine motion in the other in-plane direction ($y$), we used four linear piezo actuators. The total 8 piezo actuators (PAXZ+0063, PI) are thus stacked together, where an alumina plate is inserted between actuators responsible for motion in different directions to prevent electrical interference. A sapphire plate is mounted on top of three sets of these piezo stacks [Fig.~\ref{fig:wiremap}(a)]. A tip mount made of Macor is glued to the sapphire plate and at present, the tip cannot be changed \textit{in-situ}. The tip is made of PtIr wire. If the tip is contaminated and, thus, the tunnel current does not show an exponential dependence on the tip-sample distance, we clean the tip by applying a high bias voltage ($\sim$100 V) between the tip and the sample as part of field emission process while using a preamp with low gain ($10^7-10^8 $ V/A). To protect the STM wire from damage caused by excessively high current flow, we insert a resistor between the high voltage power supply and the tip during field emission. A 50 mm long BeCu spring pulls the sapphire plate against the piezo stacks. The spring is designed in such a way that the normal force exerted by the spring results in right amount of friction for the coarse motion of the slip-stick mechanism without mechanical instability during scanning.
The electrical cables used for STM operation are carefully selected in consideration of the electrical noise transfer, signal loss, and heat transfer for each section [Fig.~\ref{fig:wiremap}(b)]: i) from RT top flange to 5K-flange, ii) from 5K-flange to 1K-pot, and iii) from 1K-pot to STM. The choice of cables for each component is summarized in Table \ref{tab:table1}. From the RT flange to the 5K-flange, all cables are thermalized by the exchange gas in the EGC. For further thermalization, flexible cables are wrapped around gold-plated Cu posts located at baffles. All cables are connected to the UHV side using electric feedthroughs. Since unshielded parts of high voltage cables can cause an electric arc in the EGC filled with He gas at a pressure of 0.01–3 mbar, we paid special attention to the high voltage multi-pin feedthroughs (9132004, MDC) at the RT top flange a
nd the 5K-flange. To protect high voltage cables from the electric arc, we used Teflon tubes to cover the cable ends and connectors, and a hand-strippable coating compound (TURCO5580-G, AeroBase Group) to cover the metallic part of feedthroughs between pins.
We used coaxial cables both for the tip bias line and for the antenna to inject RF signals to the tunnel junction [Fig.~\ref{fig:wiremap}(b) and Table \ref{tab:table1}]. We used stainless steel semi-rigid coaxial cables (SC-119/50-SSS-SS, Coax Japan) between the RT top flange and the 5K-flange [Fig.~\ref{fig:wiremap}(b) light gray]. The cables are connected to the RT top flange using hand-formable coaxial cables (SCA49141-09, Fairview) [Fig.~\ref{fig:wiremap}(b) purple] to permit pendulum adjustment. Through electrical feedthroughs (242-SMAD27G-C16, Allectra), the cables are connected to semi-rigid NbTi coaxial cables [Fig.~\ref{fig:wiremap}(b) gray] on the UHV side. From 1K-pot, we used different cabling schemes for the tip and antenna. For both, we installed semi-rigid Cu coaxial cables [Fig.~\ref{fig:wiremap}(b) orange]. For the tip, the Cu cable is connected to the PtIr tip by a flexible Cu cable (CW2040-3650p, Cooner Wire), using a tin-plated BeCu pin spring socket (2-330808-7, AMP-TE connectivity) as an adapter. While the RF cable for the STM tip terminates with an open end at the STM stage, the RF cable for the antenna passes the STM stage parallel to the sample surface and terminates with a 50-Ohm terminator near the 5K-flange [Fig.~\ref{fig:wiremap}(b)]. Note that in an earlier work \cite{PhysRevResearch.2.013032}, an antenna was positioned parallel to the tip, which is not ideal in our design due to changing distance between the antenna and the tunnel junction during coarse motion of the tip. Instead, we installed an antenna parallel to the sample plane as introduced in the previous section (Fig.~\ref{fig:antenna}). For the antenna, the outer conductor of the coaxial cable is stripped off by $\sim$20~mm around the tip and the exposed inner conductor acts as the antenna to transfer RF signals to the STM junction. The inner conductor is $\sim$ 2 mm above the tip and $\sim$ 3 mm away from the sample, ensuring that the RF cable does not interrupt the tip's coarse motion or sample transfer. Both sides of the stripped cable are rigidly fixed, which makes the antenna robust against mechanical vibration.
\subsection{UHV chamber and sample preparation}
In our ESR-STM system, the preparation chamber and the UHV insert are in UHV. The preparation chamber is equipped with several e-beam and thermal evaporators, a heating stage, a manipulator, a sputter gun (IQE 11/35, SPECS), an Auger electron spectrometer (ESA 100, STAIB), leak valves for inserting gases (such as Ar, O\textsubscript{2}, and N\textsubscript{2}), a residual gas analyzer (RGA100, Stanford Research Systems), a turbo molecular pump (HiPace 700 H, Pfeiffer Vacuum), and an ion pump (VacIon Plus 500 Starcell, Agilent). In the preparation chamber, we prepare atomically clean substrates and grow ultra-thin insulating layers on metallic substrates, e.g., MgO(100) on Ag(100). After the sample preparation, the sample is transferred from the preparation chamber to the STM stage in the UHV insert using a manipulator with the travel length of $\sim$2 m.
Access to the UHV insert from the preparation chamber is given by shutter mechanisms. There is no visual access to the scan head during the sample transfer procedure. To ensure a safe sample transfer, we installed a transfer guiding ring near the STM stage, which guides the manipulator to reach the STM stage. furthermore, we are able to adjust the pendulum to align the UHV insert (thus, the STM stage) with the manipulator. We have indicators which monitor the movement of the pendulum. During the sample transfer, the indicators show any change of pendulum positions caused by misalignment between the manipulator and the STM stage.
Our UHV insert does not require bake-out and is pumped through the preparation chamber before cooling the system. Once we start cooling the UHV insert and its pressure becomes lower than the preparation chamber due to cryogenic pumping effect, we close the gate valve between the preparation chamber and the UHV insert. We observed no perceptible degradation of the clean sample for at least 5 months.
Many STMs require samples to be taken out in order to deposit atoms or molecules on surfaces. This leads to an unavoidable heating of the samples, which often causes unwanted diffusion of adsorbates. It can also lead to intrusion of hydrogen into the STM stage. Our STM design allows direct deposition of atoms and molecules onto the sample surface without removing the sample from the STM stage. As shown in Fig.~\ref{fig:structures}(a), we installed evaporators on the rotary platform. While the manipulator is aligned with the UHV insert during the sample transfer, we rotate the platform to align evaporators with the STM stage for the evaporation of atoms or molecules. Our sample holder made of molybdenum (Mo) is machined to have an $\sim8^{\circ}$ slope. This ensures that some atoms, which are evaporated in the preparation chamber at a distance of $\sim$2 m from the sample, land on the sample surface. Together with a mechanically actuated shutter located at the 5K-flange [Fig.~\ref{fig:JT}(a)], this permits \textit{in-situ} deposition of atoms/molecules on our sample which remains at a temperature of about 10 K during deposition.
\section{System operation and performance characterization}
Using this home-built ESR-STM, we implement ESR spectroscopy of hydrogenated titanium (TiH) atoms on two monolayers (MLs) of MgO on Ag(100) \cite{doi:10.1103/PhysRevLett.122.227203, Baeeaau4159}.
We characterize frequency-dependent transmission to the tunnel junction through the tip and the newly introduced antenna (Fig.~\ref{fig:wiremap}), which allows us to compare available frequency windows and transmission efficiency. We perform the side-by-side comparison of the two ESR measurements using the same tip and atomic species and ultimately present ESR spectra measured at elevated temperature (10 K) without losing energy resolution.
\subsection{Transfer function}
\begin{figure}
\includegraphics[width=85mm]{Figure6.pdf
\caption{\label{fig:tf} Experimental setup for ESR measurement. (a) A constant current STM image of Fe and TiH on MgO/Ag(100) ($V_{\mathrm{DC}}$ = 100 mV, $I$ = 20 pA, T = 1.3 K). (b) Characteristic STM d$I$/d$V$ spectra of Fe and TiH. The Fe and different TiH species (TiH\textsubscript{O}/TiH\textsubscript{B}) are easily identified by their distinct d$I$/d$V$ spectra and apparent heights. Successive curves are shifted by 0.4 and 1.2 nS, respectively, for clarity ($V_{\mathrm{DC}}$ = 100 mV, $I$ = 100 pA, $V_{\mathrm{mod}}$ = 1 mV, $T$ = 1.3 K). (c) Quantifying RF transmission to the tunnel junction. The IETS step of Fe is broadened while applying RF voltages, which is used to quantify the effective RF amplitudes at the tunnel junction ($V_{\mathrm{DC}}$ = 14.3 mV, $I$ = 100 pA, $V_{\mathrm{mod}}$ = 1 mV, $T$ = 1.3 K, $f$ = 16.21 GHz, $P_{\mathrm{RF}}$ = --16 dBm). (d) Transfer functions measured by applying RF voltages through the tip (blue) and the antenna (magenta). Both curves are shifted by --50 dB to have 0 dB correspondent to the zero attenuation of the transmission line.
}
\end{figure}
Figure~\ref{fig:tf}(a) shows a constant current STM image of Fe and TiH on 2 MLs of MgO on Ag(100). We deposited Fe and Ti \textit{in-situ} while the sample was kept below 10 K. The Ti tends to be hydrogenated during the deposition by the residual hydrogen in the UHV chamber. The thickness of the MgO layer was determined from the point-contact measurement and IETS steps of Fe\cite{10.1038/nphys3965}. Spin-polarized tips were made by picking up Fe atoms. TiH, as the simplest spin system\cite{doi:10.1103/PhysRevLett.122.227203, Baeeaau4159}, is chosen for the ESR measurement. While Fe absorbs on top of the oxygen atoms in the MgO lattice, TiH is found at two different binding sites, a bridge between oxygen atoms (TiH\textsubscript{B}) \cite{Baeeaau4159} or atop oxygen atoms (TiH\textsubscript{O}) \cite{doi:10.1103/PhysRevLett.122.227203}. The d$I$/d$V$ spectra [Fig.~\ref{fig:tf}(b)] and apparent heights in constant current STM images [Fig.~\ref{fig:tf}(a)] readily identify Fe and TiH on MgO/Ag(100).
As a crucial step towards frequency-sweep ESR measurements, we characterize the frequency-dependent transfer function\cite{doi:10.1063/1.4955446} of both RF transmission lines (the tip and the antenna) using IETS steps of Fe at around 14.5 meV [Fig.~\ref{fig:tf}(c)]\cite{10.1038/nphys3965}. Note that IETS steps of TiH\textsubscript{O} are also available\cite{PhysRevResearch.2.013032,drost2021combining,Weerdenburg2021}. The IETS steps are broadened while applying RF power to the tunnel junction. The IETS step broadening, which follows an arcsine distribution, is used as a reference to convert the effective RF voltage at the tunnel junction to a voltage measured by a lock-in amplifier (SR865A, SRS). The lock-in amplifier detects variations in effective RF voltages in the tunnel junction caused by frequency-dependent transmission. Figure~\ref{fig:tf}(d) shows transfer functions in the frequency range of 5--45 GHz. While the transfer functions of the two cabling schemes are comparable over a wide frequency range, the prominent difference is manifested at frequencies higher than 37 GHz and frequencies lower than 15 GHz. Due to the existence of a flexible cable (CW2040-3650p, Cooner Wire) for coarse movement of the tip and a bare wire as the tip, considerable signal loss occurs at frequencies greater than 37 GHz. This limitation is circumvented by using an antenna, which does not require the use of lossy lines and thus enables for transmission at frequencies greater than 37 GHz. At frequencies lower than 15 GHz, however, the antenna transmits less than the tip, which is presumably related to resonances of the antenna ($\sim$20 mm in length) and its surroundings, such as the sample ($\sim$5 mm in diameter) and the tip ($\sim$10 mm in length).
Based on the Fourier analysis of transfer functions in Fig.~\ref{fig:tf}(d), we found no prominent standing waves for both transmission lines, which indicates all cables are properly connected. Standing wave features from the Fourier transform for the antenna are scarcely visible, which corresponds to the length of the stripped part ($\sim$20 mm). Given the huge impedance mismatch of the stripped cable, the standing waves created for the antenna's transmission line are negligibly small. We ascribe this suppression of standing waves to the effects of a 50-Ohm terminator, which is further supported by the antenna test shown in Fig.~\ref{fig:antenna}(b). Employing the measured transfer functions, we are able to apply RF voltages with constant amplitudes at the tunnel junction throughout a large frequency range (5--40 GHz) by adjusting the power output of the generator. Once calibrated after an iterative optimization procedure of transmission measurements, we observed no significant change in the transfer function for at least several weeks (even possibly several months if there is no change of cables), which implies that the RF cables are well thermalized to fixed temperature points, and that the temperature of these points is not dependent on the LHe level in the cryostat.
\subsection{Single atom ESR spectroscopy}
\begin{figure}
\includegraphics[width=85mm]{Figure7.pdf
\caption{\label{fig:expsetup} Characterization of the TiH and the spin-polarized tip for ESR measurement. (a) d$I$/d$V$ spectra of TiH\textsubscript{B} at different magnetic fields ($B_{\mathrm{ext}}=$0, 2, and 6 T in the in-plane direction, $V_{\mathrm{DC}}$~=~4~mV, $I$ = 70 pA, $V_{\mathrm{mod}}$ = 50 $\mu$V, $T$ = 1.3 K). (b) d$I$/d$V$ spectra of TiH\textsubscript{B} with different spin polarization of the tip. The spin-averaging tip corresponds to the Ag-coated STM tip. The STM tip is spin-polarized by picking up Fe atoms on the surface. Each spectrum was measured after picking up Fe atom one-by-one (5 spectra measured with 0 (spin-averaging tip, light blue) to 4 Fe atoms (spin-polarized tip, dark blue) at the tip apex) ($B_{\mathrm{ext}} = 0.9$ T, in-plane direction, $V_{\mathrm{DC}}$ = 10 mV, $I$ = 100 pA, $V_{\mathrm{mod}}$ = 1 mV, $T$ = 1.3 K).}
\end{figure}
We implement the frequency-sweep ESR spectroscopy on a single TiH by applying RF voltages through the tip or the antenna. TiH is a well-known spin-1/2 system\cite{Baeeaau4159,doi:10.1103/PhysRevLett.122.227203}. In a typical spectroscopy of STM, the energy splitting between two spin states of TiH by Zeeman energy is only visible if large external magnetic fields are applied [Fig.~\ref{fig:expsetup}(a)] since the spectral resolution is restricted by the thermal broadening of the tunneling electrons' energy and electrical noises. The spectral resolution can be significantly enhanced by ESR spectroscopy in STM. In ESR-STM, the energy is measured with respect to the frequency of an applied RF field and thus the energy resolution is limited only by the spin dynamics of the objects such as spin relaxation and coherence times\cite{https://doi.org/10.1002/adma.202107534}. For the ESR measurement, a spin-polarized tip is prepared by picking up several Fe atoms to the tip (typically 3--10 Fe atoms) and checking its polarization by d$I$/d$V$ curves of TiH\textsubscript{O} or TiH\textsubscript{B} that show an asymmetric feature near the zero bias voltage [Fig.~\ref{fig:expsetup}(b)]. Larger spin polarization facilitates ESR measurement but does not guarantee ESR signals since detection and driving of ESR require spin-polarization of the tip and simultaneously inhomogeneous transverse (or longitudinal depending on transitions) magnetic fields from the tip \cite{Baeeaau4159,doi:10.1103/PhysRevLett.122.227203,DOI:10.1126/sciadv.abc5511}.
\begin{figure}
\includegraphics[width=85mm]{Figure8.pdf
\caption{\label{fig:ESR1} Comparison of ESR spectra measured using the tip and the antenna for RF transmission. (a) ESR of TiH\textsubscript{B} measured using the tip for RF transmission ($V_{\mathrm{DC}}$~=~50~mV, $I$ = 20 pA, $V_{\mathrm{RF}}$ = 21 mV, $B_{\mathrm{ext}}$ = 1 T, $T$ = 1.3 K). (b) ESR spectrum of the same TiH\textsubscript{B} atom measured using the same microtip but the antenna for RF transmission ($V_{\mathrm{DC}}$ = 50 mV, $I$ = 20 pA, $V_{\mathrm{RF}}$ = 22 mV, $B_{\mathrm{ext}}$ = 1 T, and $T$ = 1.3 K). (c) ESR spectra of TiH\textsubscript{B} at different magnetic fields measured using the antenna. Curves are shifted for clarity ($V_{\mathrm{DC}}$ = 50 mV, $I$ = 20 pA, $V_{\mathrm{RF}}$ = 20 mV, and $T$ = 1.3 K). (d) Resonance frequencies and (e) intensities of ESR signals at different magnitudes of magnetic fields. The values are extracted from the fit to eq. \ref{eq:Fano} of the data in (c) (Antenna; $V_{\mathrm{DC}}$ = 50 mV, $I$ = 20 pA, $V_{\mathrm{RF}}$ = 20 mV, and $T$ = 1.3 K) (Tip; $V_{\mathrm{DC}}$ = 50 mV, $I$ = 20 pA, $V_{\mathrm{RF}}$ = 21 mV, and $T$ = 1.3 K). The solid lines in (d) are linear fits, which gives the TiH\textsubscript{B} magnetic moments, $\mu$. The solid line in (e) corresponds to the estimated ESR intensity based on the Boltzman distribution of spin state populations.}
\end{figure}
We compare the ESR spectra of TiH\textsubscript{B} measured using the tip or the antenna for RF voltage transmission. For RF transmission through the tip, the RF voltages are combined with the DC bias voltage by a bias-tee at RT [Fig.~\ref{fig:wiremap}(b)]. For the ESR measurement using the antenna, we just apply DC bias voltages to the tip, while the RF voltages are applied separately to the antenna. During ESR measurements, transfer functions calibrated for each RF cabling are used to compensate for frequency-dependent RF transmissions. Both measurements use the same signal detection scheme, which detects RF-induced current using a lock-in amplifier while modulating RF power\cite{doi:10.1063/1.4955446}. Figures~\ref{fig:ESR1}(a) and (b) show ESR spectra obtained by applying RF voltages to the tip and the antenna, respectively. Note that we used the same spin-polarized tip and atomic species to measure the change in dc current ($\Delta I$) caused by the population change of Zeeman states and the precession of the transverse magnetization at the resonance frequency\cite{Baeeaau4159}. The ESR spectra are fit to the equation\cite{Baeeaau4159}:
\begin{equation}
\Delta I =I\textsubscript{0} + I\textsubscript{p}\cdot \frac{1+\alpha\delta}{1+{\delta}^2}
\label{eq:Fano}
\end{equation}
with $\alpha$ asymmetry factor, $I\textsubscript{p}$ ESR intensity, and $\delta$ normalized frequency ($\delta = \Delta f/{\pi\Gamma}$, where $\Delta f$ is the difference of RF frequency and resonance frequency and $\Gamma$ is the full width at half-maximum of the signal). As analyzed using eq. \ref{eq:Fano}, with well-calibrated transfer functions in two different schemes, we observed ESR spectra with comparable ESR intensity, line-shape, and resonance frequency, which reflects that the underlying mechanism of ESR driving and detection is the same for these two different methods of ESR spectroscopy in STM.
The ESR signal intensity increases with increasing the population differences between two states. The thermal population can be controlled by changing temperature or energy splitting, where the Zeeman splitting stems from the applied magnetic fields. As shown in Fig.~\ref{fig:ESR1}(c), the ESR spectra were measured at different magnetic fields using the antenna. We observed no spurious features in a large frequency window (24--40 GHz) which might be caused due to miscalibrations of the transfer function. With increasing magnetic field, the resonance frequency of ESR signals linearly increases [Fig.~\ref{fig:ESR1}(c) and (d)], where the slope reflects the magnetic moments of TiH\textsubscript{B}, $\mu = \sim 0.83 \mu_{\mathrm{B}}$, in the in-plane field\cite{10.1103/PhysRevB.104.174408,Baeeaau4159}. With increasing resonance frequencies and thus Zeeman energies, the signal intensity tends to increase (the solid lines in Fig.~\ref{fig:ESR1}(e) show the expected ESR intensities based on the Boltzmann distribution).
\subsection{ESR spectroscopy at variable temperatures}
\begin{figure}
\includegraphics[width=85mm]{Figure9.pdf
\caption{\label{fig:ESR2} Temperature dependence of ESR signals. (a) ESR signals of TiH\textsubscript{B} measured at different temperatures from 1.3 K to 10 K ($V_{\mathrm{DC}}$ = 40 mV, $I$ = 40 pA, $V_{\mathrm{RF}}$ = 20 mV, and $B_{\mathrm{ext}}$ = 1.59 T). (b) d$I$/d$V$ spectra measured at different temperatures ($V_{\mathrm{DC}}$ = 10 mV, $I$ = 100 pA, $V_{\mathrm{mod}}$ = 1 mV, and $B_{\mathrm{ext}}$ = 1.59 T). The spectra were measured using the same tip and atom with (a). The assymetric step at zero bias is observable at 1.3 K, while the feature is indistinguishable at 9 K. (c) The ESR signal intensities and (d) linewidths for ESR spectra in (a), as extracted using eq.~\ref{eq:Fano}. (e) The smallest ESR signal measured using our ESR-STM system ($V_{\mathrm{DC}}$ = 32 mV, $I$ = 0.8 pA, $V_{\mathrm{RF}}$ = 30 mV, and $B_{\mathrm{ext}}$ = 1 T, and $T$ = 1.3 K)}
\end{figure}
Taking advantage of large transmission through the antenna at high frequencies, we implement the ESR spectroscopy at higher temperatures which have not been explored before in ESR-STM. We maximize the population difference by increasing the Zeeman energy splitting so that the ESR signals appear at the largest frequency ($\sim$40 GHz) in our frequency window. Figure~\ref{fig:ESR2}(a) shows the ESR spectra at different temperatures. Our STM enables us to conduct experiments at elevated temperatures in the range from 1.3 K to at least 10 K. Using a spin-polarized tip, which shows very strong ESR signals of 3 pA at 1.3 K (out of 40 pA setpoint current), we succeeded in detecting the ESR signal at 10 K, which is $\sim$10 times weaker than the one at 1.3 K. As shown in Fig.~\ref{fig:ESR2}(c), the ESR signal intensity falls exponentially with rising temperature, which is consistent with the exponential dependence of Boltzmann distribution on temperature. While the peak intensity varies dramatically with temperature, there is no discernible trend in the ESR peak broadening [Fig.~\ref{fig:ESR2}(d)], which indicates that there is no major change in the energy resolution of ESR in STM with temperature. In comparison, the spin-dependent feature at zero bias is smeared out in the d$I$/d$V$ curve [Fig.~\ref{fig:ESR2}(b)] since the spectral resolution of the d$I$/d$V$ spectroscopy is limited by the thermal broadening of tunneling electrons' energy. The strength of ESR spectroscopy in STM, thus, becomes more evident for experiments at higher temperatures. In addition, the highly stable operation of ESR-STM allows for the extremely sensitive measurement of single-spin ESR spectroscopy with the corresponding change in tunnel current by sub-fA [Fig.~\ref{fig:ESR2}(e)].
\section{Conclusion}
To summarize, we have presented the design and performance of ESR-STM operating at temperatures of 1--10 K. We for the first time demonstrated ESR of a single atom at elevated temperatures up to 10 K, which was realized by introducing an antenna positioned parallel to the sample and optimizing the operation of ESR-STM. We demonstrated the characterization of the newly introduced antenna in comparison with the early design RF cablings, which provides varieties in designs of RF antennas for integrating ESR in STM and easy modifications of existing STMs for ESR applications. A planned future upgrade will replace the \textsuperscript{4}He gas in the JT refrigerator with \textsuperscript{3}He gas, which should enable stable performance below 0.5 K.
\begin{acknowledgments}
We thank Alexander F. Otte and Alexandre Artaud for their initiative works and fruitful discussions on COMSOL simulations. All authors acknowledge
support from the Institute for Basic Science (IBS-R027-D1).
\end{acknowledgments}
\section*{Data Availability Statement}
The data that support the findings of this study are available from the corresponding author upon reasonable request.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,272 |
\section*{Introduction}
All rings considered in this paper are nontrivial rings with identity; homomorphisms need not be unitary, unless otherwise stated.
All chains considered are chains with respect to containment.
The symbol $\subset$ means proper inclusion and the symbol $\subseteq$ means inclusion
or equality. For a ring $R$ we denote the center of $R$ by $Z(R)$.
We start with some background on the notions we consider.
In his highly respected paper from 1937, in which Krull (see [Kr]) proved his basic theorems regarding the behavior of prime ideals under integral extensions, and defined the notions LO, GU, GD and INC, he proposed the following question: assuming $S \subseteq R$ are integral domains with $R$ integral over $S$ and $S$ integrally closed; do adjacent prime ideals
in $R$ contract to adjacent prime ideals in $S$? In 1972 Kaplansky (see [Ka]) answered the question negatively. In 1977, Ratliff (see [Ra]) made another step; he defined and studied the notion GB (going between): let $S \subseteq R$ be commutative rings. $S \subseteq R$ is said to satisfy GB if whenever $Q_1 \subset Q_2$ are prime ideals of $R$ and there exists a prime ideal $Q_1 \cap S \subset P' \subset Q_2 \cap S$, then there exists a prime ideal $Q' $ in $R$ such that
$Q_1 \subset Q' \subset Q_2$. Later, in 2003, G. Picavet (see [Pi])
introduced the notion SGB (strong going between), to be presented later.
In 2003, Kang and Oh (cf. [KO]) defined the notion of an SCLO extension: let $S \subseteq R$ be commutative rings. $S \subseteq R$ is called an
SCLO extension if, for every chain of prime ideals $\mathcal D$ of $S$ with an initial element $P$ and $Q$ a prime ideal of $R$ lying over $P$, there exists a chain of prime ideals $\mathcal C$ of $R$ lying over $\mathcal D$ whose initial element is $Q$. They proved that $S \subseteq R$ is
an SCLO extension iff it is a GU extension (cf. [KO, Corollary 12]). In particular, if $S \subseteq R$ is a GU extension, then for every chain of prime ideals $\mathcal D$ of $S$ there exists a chain of prime ideals of $R$ covering $\mathcal D$. We note that when considering a unitary homomorphism $f:S \rightarrow R$, some authors call
$f$ a chain morphism if every chain in $\text{Spec}(S)$ can be covered by a chain in $\text{Spec}(R)$. Also, some authors call an SCLO extension a GGU (generalized going up) extension. It follows that, in the commutative case, GU implies GGU for unitary ring homomorphisms. In 2005 Dobbs and Hetzel (cf. [DH]) proved that, in the commutative case,
GD implies GGD (generalized going down) for unitary ring homomorphisms. GGD is defined analogously to GGU.
We consider a more general setting. Namely, {\it In this paper $S$ and $R$ are rings (not necessarily commutative) and $f:S \rightarrow R$ is a homomorphism
(not necessarily unitary) such that $f[S] \subseteq Z(R)$.} We study the connections between chains of prime ideals of $S$ and chains of prime ideals of $R$.
For $I \vartriangleleft R$ and $J \vartriangleleft S$ we say that $I$ is lying over $J$ if $J=f^{-1}[I]$.
Note that if $Q$ is a prime ideal of $R$ then $f^{-1}[Q]$ is a prime ideal of $S$ or $f^{-1}[Q]=S$.
It is not difficult to see that $f$ is unitary if and only if for all $Q \in \text{Spec} (R)$, $f^{-1}[Q] \in \text{Spec} (S)$.
Indeed, $(\Rightarrow)$ is easy to check and as for $(\Leftarrow)$, if $f$ is not unitary then $f(1)$ is a central idempotent$\neq 1$. Thus, there exists a prime ideal
$Q \in \text {Spec} (R)$ containing $f(1)$; clearly, $f^{-1}[Q]=S$.
For the reader's convenience, we now define the five basic properties we consider.
We say that $f$ satisfies LO (lying over) if for all $P \in \text {Spec} (S)$ there exists $Q \in \text {Spec}(R)$ lying over $P$.
We say that $f$
satisfies GD (going down) if for any $P_{1} \subset
P_{2}$ in $\text{Spec} (S)$ and for every $Q_{2} \in \text{Spec} (R)$
lying over $P_{2}$, there exists $Q_{1} \subset Q_{2}$ in
$\text{Spec} (R)$ lying over $P_{1}$.
We say that $f$
satisfies GU (going up) if for any $P_{1} \subset
P_{2}$ in $\text{Spec} (S)$ and for every $Q_{1} \in \text{Spec} (R)$
lying over $P_{1}$, there exists $Q_{1} \subset Q_{2}$ in
$\text{Spec} (R)$ lying over $P_{2}$.
We say that $f$
satisfies SGB (strong going between) if for any $P_{1} \subset
P_{2} \subset
P_{3}$ in $\text{Spec} (S)$ and for every $Q_{1} \subset
Q_{3}$ in $\text{Spec} (R)$ such that $Q_{1}$ is lying over $P_{1}$ and
$Q_{3}$ is lying over $P_{3}$, there exists $Q_{1} \subset Q_{2} \subset Q_{3}$ in
$\text{Spec} (R)$ lying over $P_{2}$.
We note that the "standard" definition of INC is as follows: $f$ is said to satisfy INC (incomparability) if
whenever $Q_{1} \subset Q_{2}$ in $\text{Spec}(R)$, we have $f^{-1}[Q_{1}]
\subset f^{-1}[Q_{2}] $. However, in order for us to be able to discuss non-unitary homomorphisms we make the following modification and
define INC as follows: we say that $f$ satisfies INC if
whenever $Q_{1} \subset Q_{2}$ in $\text{Spec}(R)$ and $f^{-1}[Q_{2}] \neq S$, we have $f^{-1}[Q_{1}]
\subset f^{-1}[Q_{2}] $.
We note that the case in which $R$ is an algebra over $S$ can be considered as a special case (of the case we consider). In particular, the case in which $S \subseteq R$ are rings and $S \subseteq Z(R)$ (and thus $S$ is a commutative ring) can be considered as a special case. Also, in this special case, one can show that, as in the commutative case, GU implies LO. However, in our case, GU does not necessarily imply LO. As an easy example, let $p \in \Bbb N$ be a prime number and let $2 \leq n \in \Bbb N$ such that $n$ is not a power of $p$. Let $f: \Bbb Z_{np} \rightarrow \Bbb Z_{p}$ be the homomorphism defined by $x$mod$(np)$ $\rightarrow x$mod$(p)$ . Then $f$ satisfies GU (in a trivial way, because k-dim $\Bbb Z_{np}=0$) but there is no prime ideal in $\Bbb Z_p$ lying over $q\Bbb Z_{np}$, where $p \neq q \in \Bbb N$ is any prime number dividing $n$.
\section{Maximal chains in Spec$(R)$ that cover maximal chains in Spec$(S)$}
In this section we prove that every maximal chain of
prime ideals of $R$ covers a maximal chain of prime ideals of $S$,
under the assumptions GU, GD and SGB. We also present an example from quasi-valuation theory.
We start with some basic definitions.
\begin{defn} Let $\mathcal D$ denote a set
of prime ideals of $S$. We say that a chain $\mathcal
C$ of prime ideals of $R$ is a {\it
$\mathcal D$-chain} if $f^{-1}[Q] \in \mathcal D$ for
every $Q \in \mathcal
C$.\end{defn}
\begin{defn} Let $\mathcal D \subseteq \text {Spec}(S)$ be a chain of prime ideals
and let $\mathcal C \subseteq \text {Spec}(R)$ be a $\mathcal D$-chain. We say that $\mathcal C$ is a {\it cover} of
$\mathcal D$ (or that $\mathcal C$ covers $\mathcal D$) if for all $P \in \mathcal D$ there exists
$Q \in \mathcal C$ lying over $P$; i.e. the map $Q \rightarrow f^{-1}[Q]$ from $\mathcal C$ to $\mathcal D$ is surjective.
We say that $\mathcal C$ is a {\it perfect cover} of
$\mathcal D$ if $\mathcal C$ is a cover of $\mathcal D$ and the map $Q \rightarrow f^{-1}[Q]$ from $\mathcal C$ to $\mathcal D$ is injective. In other words, $\mathcal C$ is a perfect cover of
$\mathcal D$ if the map $Q \rightarrow f^{-1}[Q]$ from $\mathcal C$ to $\mathcal D$ is bijective. \end{defn}
The following lemma is well known.
\begin{lem} \label{alphar in Q implies one is in Q} Let $R$ be a ring. Let $\alpha \in Z(R)$, $r \in R$ and $Q \in \text{Spec}(R)$. If
$\alpha r \in Q$ then $\alpha \in Q$ or $r \in Q$.
\end{lem}
\begin{proof} $\alpha R r= R \alpha r \subseteq Q$. Thus $\alpha \in Q$ or $r \in Q$.
\end{proof}
We recall now the notion of a weak zero divisor, introduced in [BLM].
For a ring $R$, $a \in R$ is called a weak zero-divisor if there
are $r_1,r_2 \in R$ with $r_1ar_2 = 0$ and $r_1r_2 \neq 0$. In [BLM] it is shown that in any ring R,
the elements of a minimal prime ideal are weak zero-divisors. Explicitly, the following is proven (see [BLM, Theorem 2.2]).
\begin{lem} Let $R$ be a ring and let $Q \in \text{Spec}(R)$ denote a minimal prime of $R$.
Then for every $q \in Q$, $q$ is a weak zero divisor.
\end{lem}
It will be more convenient for us to use the following version of the previous lemma.
\begin{lem} \label{elements of a minimal prime ideal are weak zero-divisors}
Let $R$ be a ring, let $I \vartriangleleft R$ and let $Q \in \text{Spec}(R)$ denote a minimal prime ideal over $I$.
Then for every $q \in Q$ there exist $r_1,r_2 \in R$ such that $r_1qr_2 \in I$ and $r_1r_2 \notin I$.
\end{lem}
We return now to our discussion. But before proving the next proposition, we note that $R$ is not necessarily commutative.
Therefore, a union of prime ideals of a chain in $\text{Spec}(R)$ is not necessarily a prime ideal of $R$.
\begin{prop} \label{minimal prime over union of chain intersection is the same} Let $\mathcal C \subseteq \text{Spec}(R)$ denote a chain of prime ideals of $R$. Let $\bigcup_{Q \in \mathcal C} Q \subseteq Q' \in \text{Spec}(R)$
denote a minimal prime ideal over $\bigcup_{Q \in \mathcal C} Q $. Then $f^{-1}[\bigcup_{Q \in \mathcal C} Q]=f^{-1}[Q']$.
In particular, if $f$ is unitary then $f^{-1}[\bigcup_{Q \in \mathcal C} Q]$ is a prime ideal of $S$.
\end{prop}
\begin{proof} Assume to the contrary that $f^{-1}[\bigcup_{Q \in \mathcal C} Q] \subset f^{-1}[Q']$ and let
$s \in f^{-1}[Q'] \setminus f^{-1}[\bigcup_{Q \in \mathcal C} Q]$. By Lemma \ref{elements of a minimal prime ideal are weak zero-divisors}, there exist $r_1,r_2 \in R$ such that $r_1f(s)r_2 \in \bigcup_{Q \in \mathcal C} Q$
and $r_1r_2 \notin \bigcup_{Q \in \mathcal C} Q$. However, $f(s) \in f[S] \subseteq Z(R)$ and thus $f(s)r_1r_2=r_1f(s)r_2 \in \bigcup_{Q \in \mathcal C} Q$.
So, there exists $Q \in \mathcal C$ such that $f(s)r_1r_2 \in Q$. Note that $f(s) \notin \bigcup_{Q \in \mathcal C} Q$; hence,
by Lemma \ref{alphar in Q implies one is in Q}, $r_1r_2 \in Q$. That is,
$r_1r_2 \in \bigcup_{Q \in \mathcal C} Q$, a contradiction.
\end{proof}
As shown, a union of prime ideals of a chain in $\text{Spec}(R)$ and a minimal prime ideal over it, are lying over the same prime ideal of $S$ (or over $S$).
Now, given an ideal $I$ of $R$ that is contained in an arbitrary prime ideal $Q_2$ of $R$,
we prove the existence of a minimal prime ideal over $I$, contained in $Q_2$.
\begin {lem} \label{there exists a minimal prime} Let $I$ be an ideal of $R$ and let $Q_{2}$ be any prime ideal of
$R$ containing $I$. Then there exists $I \subseteq Q' \subseteq Q_{2}$,
a minimal prime ideal over $I$. In particular, if $J$ is any ideal of $R$ then there exists a minimal prime ideal over $J$.
\end {lem}
\begin {proof} By Zorn's Lemma there exists a maximal chain
of prime ideals, say $\mathcal C'$, between $I$ and $Q_{2}$. So, $I \subseteq \bigcap_{Q \in \mathcal C'} Q \subseteq Q_{2}$ is a minimal prime ideal over $I$. The last assertion is clear.
\end {proof}
We have proven the following: let $\mathcal C \subseteq \text{Spec}(R)$ denote a chain of prime ideals of $R$
and let $Q_2$ be a prime ideal of $R$ containing $\bigcup_{Q \in \mathcal C} Q$. Then there exists a prime ideal
$\bigcup_{Q \in \mathcal C} Q \subseteq Q' \subseteq Q_{2}$ such that $Q'$ is lying over $f^{-1}[\bigcup_{Q \in \mathcal C} Q]$, which is a prime ideal of $S$ or equals $S$.
One may ask whether this fact can be generalized as follows:
let $I$ be an ideal of $R$ lying over a prime ideal of $S$ and let $I \subseteq Q_{2}$ be any prime ideal of $R$.
Must there be a prime ideal $I \subseteq Q' \subseteq Q_{2}$ in $R$ such that $Q'$ is lying over the prime ideal $f^{-1}[I]$?
The answer to this question is: "no", even in the case where $S \subseteq R$ are commutative rings and $R$ is integral over $S$. As shown in the following example.
\begin{ex} \label{ex GU LO but no GD} Let $S \subseteq R$ be rings such that $R$ satisfies LO over $S$ but not GD (in our terminology, assume that the map $f: S \rightarrow R$, defined by $f(s)=s$ for all $s \in S$, satisfies LO but not GD). Let $P_{1} \subset P_{2}$ be prime ideals of $S$ and let $Q_{2}$ be a prime ideal of $R$ lying over $P_{2}$ such that
there is no prime ideal $Q_{1} \subset Q_{2}$ lying over $P_{1}$. Let $Q_{3}$ be a prime ideal of $R$ lying over $P_{1}$. Denote $I= Q_{3} \cap Q_{2}$ and note that $I$ is clearly not a prime ideal of $R$; then, $I$ is an ideal of $R$ lying over the prime ideal $P_{1}$ and $I \subset Q_{2}$, but there is no prime ideal $I \subseteq Q' \subset Q_{2}$ of $R$ lying over $P_{1}$.
\end{ex}
The following two remarks are obvious.
\begin{rem} \label{order preserving} Let $\mathcal C$ denote a chain of prime ideals of $R$. Then the map
$Q \rightarrow f^{-1}[Q]$ from $\mathcal C$ to $\text {Spec}(S)$ is order preserving.
\end{rem}
\begin{rem} \label{mini inc} Assume that $f$ satisfies INC. Let $\mathcal C$ denote a chain of prime ideals of $R$ and let
$\mathcal C'=\{ Q \in \mathcal C \mid f^{-1}[Q] \neq S\}$. Then the map
$Q \rightarrow f^{-1}[Q]$ from $\mathcal C'$ to $\text{Spec}(S)$ is injective.
\end{rem}
For the reader's convenience, in order to establish the following results in a clearer way, we briefly present here the notion of cuts.
Let $T$ denote a totally ordered set. A subset $X$ of $T$ is called {\it initial} (resp.
{\it final}) if for every $\gamma \in X$ and $\alpha \in T$, if $\alpha
\leq \gamma$ (resp. $\alpha \geq \gamma$), then $\alpha \in
X$. A cut $\mathcal A=(\mathcal A^{L}, \mathcal A^{R})$ of
$T$ is a partition of $T$ into two subsets $\mathcal A^{L}$ and $\mathcal
A^{R}$, such that, for every $\alpha \in \mathcal A^{L}$ and $\beta
\in \mathcal A^{R}$, $\alpha<\beta$. To define a cut, one often writes $\mathcal A^{L}=X$, meaning that
$\mathcal A$ is defined as $(X, T \setminus X)$ when $X$ is an initial
subset of $T$. For more information about cuts see, for example, [FKK] or [Weh].
\begin{lem} \label{QsbsetQ} Let $\mathcal C=\{X_{\alpha}\}_{\alpha \in I}$ be a chain of subsets
of $R$. Let $\mathcal D=\{f^{-1}[X_{\alpha } ] \}_{\alpha \in I}$
and let $Y \subseteq S$, $Y \notin \mathcal D$. Let $A=\{X \in
\mathcal C \mid f^{-1}[X] \subset Y\}$ and $B=\{X \in \mathcal C
\mid f^{-1}[X] \supset Y\}$. If $X \in A$ and $X' \in \mathcal C
\setminus A$ then $X \subset X'$. If $X \in B$ and $X' \in
\mathcal C \setminus B$ then $X \supset X'$. In particular,
assuming $A,B \neq \emptyset$ and denoting $X_{1}=\bigcup_{X \in
A} X$ and $X_{2}=\bigcap_{X \in B} X$, one has $X_{1} \subseteq
X_{2}$.
\end{lem}
\begin{proof} Clearly, $A$ is an initial subset of $\mathcal C$ and $B$ is a final subset of $\mathcal C$.
The assertions are now obvious.
\end{proof}
We shall freely use Lemma \ref{QsbsetQ} without reference.
We note that a maximal chain of prime ideals exists by Zorn's
Lemma and is nonempty, since every ring has a maximal ideal. Also
note that if $\mathcal C=\{Q_{\alpha}\}_{\alpha \in I}$ is a chain
of prime ideals of $R$ then $\mathcal D=\{f^{-1}[Q_{\alpha}]\}_{\alpha \in I} \subseteq \text {Spec}(S) \cup \{ S \}$ is a chain;
if $f$ is unitary then $\mathcal D$ is a chain of prime ideals of $S$. Our
immediate objective (to be reached in theorem \ref{D is a maximal chain}) is to prove that, under certain assumptions, if
$\mathcal C$ is a maximal chain in $\text {Spec}(R)$ then $\mathcal D$ is a
maximal chain in $\text {Spec}(S)$.
\begin{rem} \label{Q2 in C} Let $\mathcal C$ be a maximal
chain of prime ideals of $R$, let $A \neq \emptyset$ be an initial subset of $\mathcal C$ and let $B \neq \emptyset$ be a final subset of $\mathcal C$.
Then $\bigcap_{Q \in B} Q \in \mathcal C$. Moreover, if $\bigcup_{Q \in A} Q $ is a prime ideal of $R$ then $\bigcup_{Q \in A} Q \in \mathcal C$.
\end{rem}
\begin{proof} $\bigcap_{Q \in B} Q \in \text {Spec}(R)$ and $\mathcal C \cup \{ \bigcap_{Q \in B} Q \}$ is a chain; thus
$\bigcap_{Q \in B} Q \in \mathcal C$. In a similar way, if $\bigcup_{Q \in A} Q $ is prime then $\mathcal C \cup \{ \bigcup_{Q \in A} Q \}$ is a chain
of prime ideals in $\text {Spec}(R)$; thus
$\bigcup_{Q \in A} Q \in \mathcal C$.
\end{proof}
\begin{lem} \label{Q1 in A Q2 in B} Let $\mathcal C=\{Q_{\alpha}\}_{\alpha \in I}$ be a maximal chain of prime ideals of $R$,
$\mathcal D=\{f^{-1}[Q_{\alpha }] \}_{\alpha \in I}$, $P \in
\text {Spec}(S) \setminus \mathcal D$, $A=\{Q \in \mathcal C \mid f^{-1}[Q]
\subset P\}$ and $B=\{Q \in \mathcal C \mid f^{-1}[Q] \supset P\}$.
Assume that $A,B \neq \emptyset$ and denote $Q_{1}=\bigcup_{Q \in A} Q$ and
$Q_{2}=\bigcap_{Q \in B} Q$. Then $Q_{2} \in B$ and $Q_{1} \in A$.
\end{lem}
\begin{proof}
We start by proving that $Q_{2} \in B$. First note that $f^{-1}[Q_{2}] \supseteq P$. By Remark \ref{Q2 in C}, $Q_{2} \in \mathcal C$.
Since $P \in \text {Spec}(S) \setminus \mathcal D$, one cannot have $f^{-1}[Q_{2}] = P$. Thus, $Q_{2} \in B$.
We shall prove now that $Q_{1}$ is a prime ideal of $R$. Assume to the contrary and let
$Q_{3}=\bigcap_{Q \in \mathcal C \setminus A} Q$. By Remark \ref{Q2 in C}, $Q_{3} \in \mathcal C$. Since $\mathcal C$ is a maximal chain
in $\text {Spec}(R)$, $Q_{3}$ is a minimal prime ideal over $Q_{1}$, strictly containing it.
Clearly $f^{-1}[Q_{1}] \subseteq P$ and by Proposition \ref{minimal prime over union of chain intersection is the same}, $f^{-1}[Q_{1}]=f^{-1}[Q_{3}]$. Since $P \in \text {Spec}(S) \setminus \mathcal D$, one cannot have $f^{-1}[Q_{3}] = P$.
Therefore, $f^{-1}[Q_{3}] \subset P$, i.e., $Q_{3} \in A$, a contradiction (to the fact that $Q_{3}$ strictly contains $Q_{1}$). So, $Q_{1}$ is a prime ideal of $R$. We conclude by Remark \ref{Q2 in C} that $Q_{1} \in \mathcal C$. Thus, $Q_{1} \in A$.
\end{proof}
\begin{comment}
\begin{lem} \label{Q_2inB,Q_1prime} Let $\mathcal C=\{Q_{\alpha}\}_{\alpha \in I}$ be a maximal
chain of prime ideals of $R$. Let $\mathcal D=\{f^{-1}[Q_{\alpha }]
\}_{\alpha \in I}$ and let $P \in {\text Spec}(S) \setminus \mathcal D$.
Let $A=\{Q \in \mathcal C \mid f^{-1}[Q] \subset P\}$ and $B=\{Q
\in \mathcal C \mid f^{-1}[Q] \supset P\}$. Assume that $A,B \neq
\emptyset$ and denote $Q_{1}=\bigcup_{Q \in A} Q$ and
$Q_{2}=\bigcap_{Q \in B} Q$. Then $Q_{2} \in B$; moreover, If
$Q_{1}$ is a prime ideal of $R$ then $Q_{1} \in A$.
\end{lem}
\begin{proof} It is easy to see that $Q_{2} \in {\text Spec}(R)$ and $f^{-1}[Q_{2}]
\supseteq P$; thus $Q_{2} \notin \mathcal C \setminus B$. By Lemma
\ref{QsbsetQ}, $Q_{2} \supseteq Q'$ for every $Q' \in \mathcal C
\setminus B$. Also note that $Q_{2} \subseteq Q$ for every $Q \in
B$. Thus, assuming $Q_{2} \notin B$ we get a chain $\mathcal C
\cup \{Q_{2}\}$ strictly containing $\mathcal C$, a contradiction
to the maximality of $\mathcal C$. Hence, $Q_{2} \in B$; in
particular $f^{-1}[Q_{2}] \supset P$.
As for $Q_{1}$, it is easy to see that $P_{1}=f^{-1}[Q_{1}]
\subseteq P$; thus one cannot have $Q_{1} \in \mathcal C \setminus
A$. Assume now that $Q_{1}$ is prime. By the definition of $Q_{1}$
and Lemma \ref{QsbsetQ}, $Q \subseteq Q_{1} \subseteq Q'$ for
every $Q \in A$ and $Q' \in \mathcal C \setminus A$. Thus,
assuming $Q_{1} \notin A$ we get a chain $\mathcal C \cup
\{Q_{1}\}$ strictly containing $\mathcal C$, a contradiction to
the maximality of $\mathcal C$. Hence, $Q_{1} \in A$.
\end{proof}
\begin{lem} \label{Q_1inA} Assume that $S$ is commutative. Let $\mathcal C=\{Q_{\alpha}\}_{\alpha \in I}$ be a maximal chain of prime ideals of $R$,
$\mathcal D=\{f^{-1}[Q_{\alpha }] \}_{\alpha \in I}$, $P \in
{\text Spec}(S) \setminus \mathcal D$, $A=\{Q \in \mathcal C \mid f^{-1}[Q]
\subset P\}$ and $B=\{Q \in \mathcal C \mid f^{-1}[Q] \supset P\}$.
Assume that $A,B \neq \emptyset$ and let $Q_{1}=\bigcup_{Q \in A}
Q$ then $Q_{1} \in A$.
\end{lem}
\begin{proof}
Let $Q_{3}=\bigcap_{Q \in \mathcal C \setminus A} Q$. It is easy
to see that $Q_{3}$ is a prime ideal of $R$. We denote
$P_{3}=f^{-1}[Q_{3}]$ and deduce by Lemma \ref{QsbsetQ} that $Q_{1}
\subseteq Q_{3}$.
Assuming $Q_{1}=Q_{3}$ we get that $Q_{1}$ is a prime ideal of
$R$. Thus, by Lemma \ref{Q_2inB,Q_1prime}, $Q_{1} \in A$ and the
Lemma is proved.
So, we may assume that $Q_{1} \subset Q_{3}$. Thus $Q_{3} \notin
A$. Note that by the definition of $Q_{3}$ and Lemma
\ref{QsbsetQ}, $Q \subseteq Q_{3} \subseteq Q'$ for every $Q \in
A$ and $Q' \in \mathcal C \setminus A$. Thus, assuming $Q_{3}
\notin \mathcal C \setminus A$, we get a chain $\mathcal C \cup \{
Q_{3} \}$ strictly containing $\mathcal C$, a contradiction.
Hence, $Q_{3} \in \mathcal C \setminus A$; in particular, $P_{3}
\nsubseteq P$.
It is obvious that $P_{1}=f^{-1}[Q_{1}] \subseteq P$. Note that
$$f^{-1}[Q_{1}]=f^{-1}[\bigcup_{Q \in A} Q] = \bigcup_{Q \in A} (f^{-1}[Q]),$$ which is a union of prime ideals of a chain in a
commutative ring and thus $P_{1}=f^{-1}[Q_{1}]$ is a prime ideal of
$S$.
Therefore, By Lemma \ref{zorn double containment}, there exists a
prime ideal $Q_{1} \subseteq Q'' \subseteq Q_{3}$ such that $f^{-1}[Q'']
=P_{1}$.
Note that $P_{1} \subseteq P \nsupseteq P_{3}$.
Thus $Q'' \neq Q_{3}$. Assuming $Q'' \neq Q_{1}$ we get, by the
definition of $Q_{1}$ and $Q_{3}$, $Q \subseteq Q_{1} \subset Q''
\subset Q_{3} \subseteq Q'$ for every $Q \in A$ and $Q' \in
\mathcal C \setminus A$. Hence, $\mathcal C \cup \{Q''\}$ is a
chain strictly containing $\mathcal C$, a contradiction to the
maximality of $\mathcal C$. Therefore, $Q_{1}=Q''$ is a prime
ideal of $R$. We conclude by Lemma \ref{Q_2inB,Q_1prime} that
$Q_{1} \in A$.
\end{proof}
\end{comment}
Note that by the previous lemma, $Q_{1}$ is the greatest member of
$A$ and $Q_{2}$ is the smallest member of $B$.
\begin{thm} \label{D is a maximal chain} Assume that $f$ is unitary and satisfies GU, GD and SGB. Let $\mathcal C=\{Q_{\alpha}\}_{\alpha \in
I}$ be a maximal chain of prime ideals in $\text {Spec}(R)$. Then $\mathcal
D=\{f^{-1}[Q_{\alpha}]\}_{\alpha \in I}$ is a maximal chain of
prime ideals in $\text {Spec}(S)$. In other words, every maximal chain in $\text {Spec}(R)$ is a cover of some \textbf{maximal} chain in $\text {Spec}(S)$.
\end{thm}
\begin{proof} First note that since $f$ is unitary, every prime ideal of $R$ is lying over some prime ideal of $S$.
Now, since $\mathcal C$ is a maximal chain in $\text {Spec}(R)$, $\bigcup_{\alpha \in I}
Q_{\alpha}$ is a maximal ideal of $R$ containing each $Q_{\alpha}
\in \mathcal C$ and thus $\bigcup_{\alpha \in I} Q_{\alpha} \in
\mathcal C$. In a similar way, since $\bigcap_{\alpha \in I}
Q_{\alpha}$ is a prime ideal of $R$ contained in each $Q_{\alpha}
\in \mathcal C$, $\bigcap_{\alpha \in I} Q_{\alpha} \in \mathcal
C$. We prove that $\bigcap_{\alpha \in I} Q_{\alpha}$ is lying
over a minimal prime ideal of $S$. Indeed, $\bigcap_{\alpha \in I}
Q_{\alpha}$ is lying over a prime ideal $P$ of $S$; assume to the
contrary that there exists a prime ideal $P_{0} \subset P$. Then
by GD, there exists $Q_{0} \subset \bigcap_{\alpha \in I}
Q_{\alpha}$ lying over $P_{0}$. Thus, $\mathcal C \cup \{ Q_{0}\}$
is chain of prime ideals strictly containing $\mathcal C$, a contradiction.
Similarly, we prove that $\bigcup_{\alpha \in I} Q_{\alpha}$ is
lying over a maximal ideal of $S$. Indeed, $\bigcup_{\alpha \in I}
Q_{\alpha}$ is lying over a prime ideal $P$ of $S$;
assume to the contrary that there exists a prime ideal $P \subset P'$. Then by
GU, there exists $\bigcup_{\alpha \in I} Q_{\alpha} \subset Q' $
lying over $P'$. Thus, $\mathcal C \cup \{ Q'\}$ is a chain of prime ideals strictly
containing $\mathcal C$, a contradiction.
We prove now that $\mathcal D=\{f^{-1}[Q_{\alpha}]\}_{\alpha \in
I}$ is a maximal chain of prime ideals of $S$. Assume to the
contrary that there exists $P \in \text {Spec}(S)$ such that $\mathcal D
\cup \{ P\}$ is a chain of prime ideals strictly containing
$\mathcal D$. Denote $A=\{Q \in \mathcal C \mid f^{-1}[Q] \subset
P\}$ and $B=\{Q \in \mathcal C \mid f^{-1}[Q] \supset P\}$. Note
that by the previous paragraph $P$ cannot be the greatest element
nor the smallest element in $\mathcal D \cup \{ P\}$; therefore
$A,B \neq \emptyset$. Denote $Q_{1}=\bigcup_{Q \in A} Q$ and
$Q_{2}=\bigcap_{Q \in B} Q$ and let $P_{1}=f^{-1}[Q_{1}]$ and
$P_{2}=f^{-1}[Q_{2}]$; by Lemma \ref{Q1 in A Q2 in B}, $Q_{1} \in A$ and $Q_{2} \in B$.
Hence, $P_{1} \subset P \subset P_{2}$. Therefore, by SGB, there exists a prime ideal
$Q_{1} \subset Q \subset Q_{2}$ lying over $P$. It is easy to see
that $\mathcal C$ is a disjoint union of $A$ and $B$ because
$\mathcal D \cup \{ P \}$ is a chain. Now, by the definition of
$Q_{1}$ and $Q_{2}$, we get $Q' \subseteq Q_{1} \subset Q \subset
Q_{2} \subseteq Q''$ for every $Q' \in A$ and $Q'' \in \mathcal C
\setminus A=B$. Thus, $\mathcal C \cup \{ Q\}$ is a chain strictly
containing $\mathcal C$, a contradiction to the maximality of
$\mathcal C$.
\end{proof}
It is easy to see that if $f$ is not unitary then Theorem \ref{D is a maximal chain} is not valid. As a trivial example, take $f$
as the zero map. Obviously, $f$ satisfies GU, GD and SGB, in a trivial way. Here is a less trivial example: let $R$ be a ring and consider the homomorphism $f: R \rightarrow R \oplus R$ sending each $r \in R$ to $(r,0) \in R \oplus R$. It is easy to see that $f$ satisfies GU, GD and SGB. Now, let $\{Q_{\alpha}\}_{\alpha \in
I}$ be a maximal chain of prime ideals in $\text {Spec}(R)$; then $\mathcal C=\{R \oplus Q_{\alpha}\}_{\alpha \in
I}$ is a maximal chain of prime ideals in $\text {Spec}(R \oplus R)$. However $ \{ f^{-1}[R \oplus Q_{\alpha}]\}_{\alpha \in
I} =\{ R \}$, which is clearly not a maximal chain of prime ideals of $R$.
\begin{cor} \label{one to one} Assume that $f$ is unitary and satisfies INC, GU, GD and SGB. Let $\mathcal C=\{Q_{\alpha}\}_{\alpha \in
I}$ be a maximal chain of prime ideals in $\text {Spec}(R)$. Then $\mathcal C$ is a perfect cover of
the \textbf {maximal} chain $\mathcal D=\{f^{-1}[Q_{\alpha}]\}_{\alpha \in I}$.
\end{cor}
\begin{proof} By Lemma \ref{mini inc} and Theorem \ref{D is a maximal chain}.
\end{proof}
\begin{ex} \label{example from qv theory} Suppose $F$ is a field with valuation $v$ and valuation ring $O_{v}$, $E/F$ is a finite dimensional field extension
and $R \subseteq E$ is a subring of $E$ lying over $O_{v}$. By [Sa1, Theorem 9.34] there exists a quasi-valuation $w$ on $RF$ extending the valuation $v$, with $R$ as its quasi-valuation ring; in this case $R$ satisfies LO (although we do not need this property here), INC, and GD over $O_{v}$ (see [Sa1, Theorem 9.38, 3]). By [Sa3, Theorem 3.7]
$R$ satisfies SGB over $O_{v}$. Moreover,
if there exists a quasi-valuation extending $v$, having a value group, and such that $R$ is the quasi-valuation ring,
then $R$ satisfies GU over $O_{v}$ (see [Sa1, Theorem 9.38, 6a]). Now, let $\mathcal
C=\{Q_{\alpha} \}_{\alpha \in I}$ be \textbf {any maximal
chain} of prime ideals of $R$. By Corollary \ref{one to one}, the map $Q
\rightarrow Q \cap O_{v}$ is a bijective order preserving
correspondence between $\mathcal C$ and \textbf {the maximal
chain} $\mathcal D=\{Q_{\alpha} \cap S\}_{\alpha \in I}$ of prime
ideals of $O_{v}$, namely, $\mathcal D=\text {Spec}(O_{v})$. In other words, any maximal chain in $\text {Spec}(R)$
covers the maximal chain $\text {Spec}(O_{v})$ in a one-to-one correspondence. In particular, for any chain in $\text {Spec}(O_{v})$
there exists a chain in $\text {Spec}(R)$ covering it, in a one-to-one correspondence.
\end{ex}
For more information on quasi-valuations see [Sa1], [Sa2] and [Sa3].
Let $S$ be a ring
such that $\text {Spec}(S)$ is totally ordered by inclusion, let $R$ be a ring, and let $f:S \rightarrow R$ be a unitary homomorphism with $f[S] \subseteq Z(R)$.
In light of Theorem \ref{D is a maximal chain} and Example \ref{example from qv theory}, if $f$ satisfies GU, GD, and SGB, then $f$ satisfies LO. Compare this example with Lemma
\ref{GU + f^-1[0] contained in P implies LO} and Lemma \ref{GD + f[P]R neq R implies LO}.
\section {Maximal $\mathcal D$-chains}
We shall now study the subject from the opposite point of view: we
take $\mathcal D$, a chain of prime ideals of $S$ and
study $\mathcal D$-chains; in particular, maximal $\mathcal D$-chains.
we start with the definition of a maximal $\mathcal D$-chain.
\begin{defn} Let $\mathcal D$
be a chain of prime ideals of $S$ and let $\mathcal C$ be a $\mathcal D$-chain.
We say that $\mathcal C$ is a {\it maximal $\mathcal D$-chain} (not to be confused with a maximal chain) if
whenever $\mathcal C'$ is a chain of prime ideals of $R$ strictly containing $\mathcal C$ then
there exists $Q \in \mathcal C'$ such that $f^{-1}[Q]\notin \mathcal
D$. Namely, $\mathcal C$ is a $\mathcal D$-chain which is maximal with respect to containment.
\end{defn}
We shall now prove a basic lemma, the existence of maximal $\mathcal D$-chains.
\begin{lem} \label{there exists C maximal over D} $f$ satisfies LO if and only if for every nonempty chain
$\mathcal D \subseteq \text {Spec} (S)$, there exists a
nonempty maximal $\mathcal D$-chain
\end{lem}
\begin{proof} $(\Rightarrow)$ Let $\mathcal D \subseteq \text {Spec} (S)$ be a nonempty chain, let $P \in
\mathcal D$,
and let $$\mathcal Z= \{ \mathcal E \subseteq \text {Spec} (R) \mid \mathcal E \text{ is a nonempty } \mathcal D \text{ -chain} \}.$$ By LO there exists $Q \in \text {Spec} (R)$ such that $f^{-1}[Q]=P$;
hence $\{ Q\} \in \mathcal Z$. Therefore, $\mathcal Z \neq
\emptyset$. Now, $\mathcal Z$ with the partial order of
containment satisfies the conditions of Zorn's Lemma and thus
there exists $\mathcal C \in \mathcal Z$ maximal with
respect to containment.
$(\Leftarrow)$ It is obvious.
\end{proof}
Note that one can prove a similar version of $(\Rightarrow)$ of Lemma \ref{there exists C maximal over D} without the LO assumption. However, in this case a maximal $\mathcal D$-chain might be empty. Also note that similarly, one can prove that for any $\mathcal D$-chain $\mathcal C'$ there exists a maximal $\mathcal D$-chain $\mathcal C$ containing $\mathcal C'$.
Our immediate goal is to provide a preliminary connection between the properties LO, INC, GU, GD and SGB and maximal $\mathcal D$-chains. In order to do that, we define the following definition.
\begin{defn} \label{def_layers} Let $n \in \Bbb N$. We say that $f$ satisfies the {\it layer $n$ property} if for every
chain $\mathcal D \subseteq \text {Spec}(S)$ of cardinality $n$, every maximal $\mathcal D$-chain is of cardinality $n$.
\end{defn}
We shall prove that if $f$ satisfies layers $1$, $2$ and $3$ properties then for every
chain $\mathcal D \subseteq \text {Spec}(S)$ of arbitrary cardinality, every maximal $\mathcal D$-chain is of the same cardinality.
The following proposition is seen by an easy inspection.
\begin{prop} \label{layers iff properties}
1. $f$ satisfies the layer $1$ property if and only if $f$ satisfies LO and INC.
2. $f$ satisfies layers $1$ and $2$ properties if and only if $f$ satisfies LO, INC, GU and GD.
3. $f$ satisfies layers $1$, $2$ and $3$ properties if and only if $f$ satisfies LO, INC, GU, GD and SGB.
\end{prop}
For each of the properties GD, GU and SGB we present now necessary and sufficient conditions in terms of maximal $\mathcal D$-chains.
\begin{prop} \label{mini GD} $f$ satisfies GD iff
for every nonempty chain $\mathcal D \subseteq \text {Spec}(S)$ and for every nonempty maximal $\mathcal D$-chain, $C \subseteq \text {Spec}(R)$,
the following holds: for every $P \in
\mathcal D$ there exists $Q \in \mathcal C$ such that $f^{-1}[Q]
\subseteq P$.
\end{prop}
\begin{proof} $(\Rightarrow)$ Let $\mathcal D \subseteq \text {Spec}(S)$ be a nonempty chain, let
$C \subseteq \text {Spec}(R)$ be a nonempty maximal $\mathcal D$-chain, and let $P \in \mathcal
D$. Note that $f^{-1}[Q] \in D$ for every $Q \in \mathcal C$ and
since $\mathcal D$ is a chain, for every $Q \in \mathcal C$ we
have $f^{-1}[Q] \subseteq P$ or $P \subseteq f^{-1}[Q]$. Assume to
the contrary that $P \subset f^{-1}[Q]$ for all $Q \in \mathcal C$.
Thus, $$P \subseteq \bigcap_{Q \in \mathcal C} (f^{-1}[Q])=f^{-1}[\bigcap_{Q \in \mathcal C} Q].$$ Obviously, $\bigcap_{Q
\in \mathcal C} Q \subseteq Q$ for every $Q \in \mathcal C$ and
$\bigcap_{Q \in \mathcal C} Q \in \text {Spec}(R)$ (note that
$\mathcal C$ is not empty). Therefore, it is impossible that $P = f^{-1}[\bigcap_{Q \in \mathcal C} Q]$, since then
$\mathcal C \cup \{ \bigcap_{Q \in \mathcal C} Q \}$ is a $\mathcal D$-chain strictly containing $\mathcal C$.
Hence, we may assume that $P \subset f^{-1}[\bigcap_{Q \in \mathcal C} Q]$. Now, $\bigcap_{Q \in \mathcal C} Q$ is a prime ideal of $R$ lying over $f^{-1}[\bigcap_{Q \in \mathcal C} Q] \in \text {Spec}(S)$ (note that $f^{-1}[\bigcap_{Q \in \mathcal C} Q] \subseteq f^{-1}[Q]$ for all $Q \in \mathcal C$ and $\mathcal C$ is a nonempty $\mathcal D$-chain; thus $f^{-1}[\bigcap_{Q \in \mathcal C} Q] \neq S$). Therefore, by GD there exists a prime ideal $Q' \subset \bigcap_{Q \in \mathcal C} Q$ that is lying over $P$. We then get a $\mathcal D$-chain $\mathcal C \cup
\{ Q' \} $ that strictly contains $\mathcal C$, which is again
impossible.
$(\Leftarrow)$ Let $P_{1} \subset P_{2} \in \text {Spec}(S)$ and let $Q_{2} \in \text {Spec}(R)$ lying over $P_{2}$.
Assume to the contrary that there is no prime ideal $Q_{1} \subset Q_{2}$ lying over $P_{1}$.
Let $\mathcal C$ denote a maximal $\{ P_{1}, P_{2}\}$-chain containing $Q_{2}$.
Hence, for all $Q \in \mathcal C$, $P_{1} \subset f^{-1}[Q](=P_{2})$, a contradiction.
\end{proof}
We shall now prove the dual of Proposition \ref{mini GD}.
\begin{prop} \label{mini GU} $f$ satisfies GU iff
for every nonempty chain $\mathcal D \subseteq \text {Spec}(S)$ and for every nonempty maximal $\mathcal D$-chain, $C \subseteq \text {Spec}(R)$,
the following holds: for every $P \in
\mathcal D$ there exists $Q \in \mathcal C$ such that $P
\subseteq f^{-1}[Q]$.
\end{prop}
\begin{proof} $(\Rightarrow)$
Let $\mathcal D \subseteq \text {Spec}(S)$ be a nonempty chain and let
$C \subseteq \text {Spec}(R)$ be a nonempty maximal $\mathcal D$-chain.
Let $P \in \mathcal
D$ and assume to the contrary that $P \supset f^{-1}[Q] $ for all $Q \in \mathcal
C$. Then,
$$ P \supseteq \bigcup_{Q \in \mathcal C} (f^{-1}[Q])=f^{-1}[\bigcup_{Q
\in \mathcal C} Q].$$
Note that $Q \subseteq \bigcup_{Q
\in \mathcal C} Q$ for every $Q \in \mathcal C$ (although $\bigcup_{Q
\in \mathcal C} Q$ is not necessarily a prime ideal of $R$). Now, by Lemma \ref{there exists a minimal prime},
there exists a minimal prime ideal $Q'$ over $\bigcup_{Q
\in \mathcal C} Q$ and by Proposition \ref{minimal prime over union of chain intersection is the same}, $f^{-1}[ \bigcup_{Q \in \mathcal C} Q])=f^{-1}[Q']$, which is a prime ideal of $S$ (note that $f^{-1}[ \bigcup_{Q \in \mathcal C} Q] \subseteq P$, so one cannot have $f^{-1}[ \bigcup_{Q \in \mathcal C} Q])=S$).
Now, if $ P = f^{-1}[ \bigcup_{Q \in \mathcal C} Q])$ then $\mathcal C \cup \{ Q' \}$ is a $\mathcal D$-chain strictly containing $\mathcal C$, a contradiction. If $f^{-1}[ \bigcup_{Q \in \mathcal C} Q]) \subset P$ then by GU, there
exists a prime ideal of $R$, $Q' \subset Q''$ lying over $P$. So,
we get a $\mathcal D$-chain, $\mathcal C \cup \{Q''\}$ strictly
containing $\mathcal C$, which is again impossible.
$(\Leftarrow)$ The proof is almost identical to the proof of $(\Leftarrow)$ in Proposition \ref{mini GD}.
\end{proof}
\begin{prop} \label{mini SGB} $f$ satisfies SGB iff
for every nonempty chain $\mathcal D \subseteq \text {Spec}(S)$, for every nonempty maximal $\mathcal D$-chain, $C \subseteq \text {Spec}(R)$,
and for every cut $\mathcal A$ of
$\mathcal C$ such that $\mathcal A \neq (\emptyset, \mathcal C)$ and $\mathcal A \neq
(\mathcal C,\emptyset )$ (thus $|\mathcal C| \geq 2$), the following holds:
for every $P \in
\mathcal D$ there exists $Q_{1} \in \mathcal A^{L}$ such that $P
\subseteq f^{-1}[Q_{1}]$ or there exists $Q_{2} \in \mathcal A^{R}$ such
that $f^{-1}[Q_{2}] \subseteq P$.
\end{prop}
\begin{proof} $(\Rightarrow)$ Let $\mathcal D \subseteq \text {Spec}(S)$ be a nonempty chain, let
$C \subseteq \text {Spec}(R)$ be a nonempty maximal $\mathcal D$-chain,
and let $\mathcal A$ be a cut of
$\mathcal C$ such that $\mathcal A \neq (\emptyset, \mathcal C)$ and $\mathcal A \neq
(\mathcal C,\emptyset )$.
Assume to the contrary that there exists $P \in \mathcal
D$ such that $$f^{-1}[ Q_{l}] \subset P \subset f^{-1}[ Q_{r}]$$ for
all $Q_{l} \in \mathcal A^{L}$ and $Q_{r} \in \mathcal A^{R}$. Thus,
$$f^{-1}[\bigcup_{Q \in \mathcal A^{L}} Q]=\bigcup_{Q \in \mathcal A^{L}} f^{-1}[Q] \subseteq P \subseteq
\bigcap_{Q \in \mathcal A^{R}} f^{-1}[Q]=f^{-1}[\bigcap_{Q \in \mathcal A^{R}} Q].$$
Now, $\bigcap_{Q \in \mathcal A^{R}} Q \in \text {Spec}(R)$ and $\mathcal C \cup \{ \bigcap_{Q \in \mathcal A^{R}} Q \}$
is a chain of prime ideals of $R$. Thus, since $\mathcal C$ is a maximal $\mathcal D$-chain, $\bigcap_{Q \in \mathcal A^{R}} Q$ is not lying over $P$. Hence,
$$P \subset f^{-1}[\bigcap_{Q \in \mathcal A^{R}} Q)].$$
On the other hand, $\bigcup_{Q \in \mathcal A^{L}} Q$ is an ideal of $R$ lying over $f^{-1}[ \bigcup_{Q \in \mathcal A^{L}} Q] $
and is contained in the prime ideal $\bigcap_{Q \in \mathcal A^{R}} Q$.
Thus, by Lemma \ref{there exists a minimal prime}, there exists a minimal prime ideal $\bigcup_{Q \in \mathcal A^{L}} Q \subseteq Q' \subseteq \bigcap_{Q \in \mathcal A^{R}} Q$ over $\bigcup_{Q \in \mathcal A^{L}} Q$, and by Proposition \ref{minimal prime over union of chain intersection is the same}, $Q'$ is lying over $f^{-1}[ \bigcup_{Q \in \mathcal A^{L}} Q] \in \text {Spec}(S)$ (note that, as in Proposition \ref{mini GU}, $f^{-1}[ \bigcup_{Q \in \mathcal A^{L}} Q] \subseteq P$, so one cannot have $f^{-1}[ \bigcup_{Q \in \mathcal C} Q])=S$). Now, since $\mathcal C \cup \{ Q' \}$ is a chain of prime ideals and $\mathcal C$ is a maximal $\mathcal D$-chain,
one cannot have $Q'$ lying over $P$. Thus, $$ f^{-1}[\bigcup_{Q \in \mathcal A^{L}} Q] \subset P.$$
So we have a chain of prime ideals $ f^{-1}[\bigcup_{Q \in \mathcal A^{L}} Q] \subset P \subset f^{-1}[\bigcap_{Q \in \mathcal A^{R}} Q)]$ in $\text {Spec}(S)$
(note that, as in Proposition \ref{mini GD}, $f^{-1}[\bigcap_{Q \in \mathcal A^{R}} Q)] \neq S$); we have
$Q' \subset \bigcap_{Q \in \mathcal A^{R}} Q \in \text {Spec}(R)$ lying over $f^{-1}[\bigcup_{Q \in \mathcal A^{L}} Q]$ and $f^{-1}[\bigcap_{Q \in \mathcal A^{R}} Q]$
respectively, such that $\mathcal C \cup \{ Q' , \bigcap_{Q \in \mathcal A^{R}} Q\} $ is a chain in $\text {Spec}(R)$. Thus,
by SGB, there exists $Q'' \in \text {Spec}(R)$ such that
$$ Q' \subset Q'' \subset \bigcap_{Q \in
\mathcal A^{R}} Q$$ and $f^{-1}[Q'']=P$. But then $\mathcal C \cup \{ Q''\}$
is a $\mathcal D$-chain strictly containing $\mathcal C$, a
contradiction.
$(\Leftarrow)$ Let $P_{1} \subset P_{2} \subset P_{3} \in \text {Spec}(S)$ and let $Q_{1} \subset Q_{3} \in \text {Spec}(R)$ such that $Q_{1}$ is lying over $P_{1}$
and $Q_{3}$ is lying over $P_{3}$.
Assume to the contrary that there is no prime ideal $Q_{1} \subset Q_{2} \subset Q_{3}$ lying over $P_{2}$.
Let $\mathcal C$ denote a maximal $\{ P_{1}, P_{2}, P_{3}\}$-chain containing $\{ Q_{1},Q_{3}\}$.
Let $\mathcal A$ be the cut defined by $\mathcal A^{L} =\{ Q \in \mathcal C \mid f^{-1}[Q] =P_{1}\}$ and
$\mathcal A^{R} =\{ Q \in \mathcal C \mid f^{-1}[Q] =P_{3} \}$ (note that, by our assumption, for all $Q \in \mathcal C, f^{-1}[Q] \neq P_{2})$.
Note that $\mathcal A^{L} \neq \emptyset$ and $\mathcal A^{R} \neq \emptyset$.
Hence, $ f^{-1}[Q_{l}] \subset P_{2} \subset f^{-1}[Q_{r}]$ for all $Q_{l} \in \mathcal A^{L}$ and $Q_{r} \in \mathcal A^{R}$, a contradiction.
\end{proof}
Using Propositions \ref{mini GD} and \ref{mini SGB} the following corollary is obvious.
\begin{cor} Assume that $f$ satisfies GD and SGB; then $f$ satisfies GGD (generalized going down).
Moreover, if $\mathcal D \subseteq \text {Spec}(S)$ is a chain of prime ideals whose final element is $P$
and $Q \in \text {Spec}(R)$ lying over $P$, then every maximal $\mathcal D$-chain
containing $Q$ (and in particular if $Q$ is its final element) is a cover of $\mathcal D$.
\end{cor}
Note that the dual of the previous corollary is also valid.
We shall now present sufficient conditions for a GU (and GD) homomorphism to satisfy LO.
\begin{lem} \label{GU + f^-1[0] contained in P implies LO} Assume that $f$ satisfies GU and let $P \in \text {Spec}(S)$ such that
$f^{-1}[\{ 0 \} ] \subseteq P$. Then there exists $Q \in \text {Spec}(R)$ lying over $P$; in particular, if $f^{-1}[\{ 0 \} ] \subseteq P$ for all $P \in \text {Spec}(S)$,
then $f$ satisfies LO.
\end{lem}
\begin{proof} The set $\mathcal Z=\{ I \lhd R \mid f^{-1} [ I] \subseteq P\}$ is not empty and satisfies the conditions of Zorn's Lemma.
Thus, there exists a maximal element $Q' \in \mathcal Z $; it is standard to check that $Q'$ is a prime ideal of $R$.
Now, $Q'$ must be lying over $P$; since otherwise, by GU there exists $Q' \subset Q \in \text {Spec}(R)$ lying over $P$.
\end{proof}
\begin{lem} \label{GD + f[P]R neq R implies LO} Assume that $f$ is unitary and satisfies GD.
Let $P \in \text {Spec}(S)$ such that
$f[P]R \neq R$. Then there exists $Q \in \text {Spec}(R)$ lying over $P$; in particular, $f^{-1}[f[P]R]=P$. Moreover, if $f[P]R \neq R$ for all $P \in \text {Spec}(S)$,
then $f$ satisfies LO.
\end{lem}
\begin{proof} Let $Q' \in \text {Spec}(R)$ be any prime ideal containing $f[P]R$. It is obvious that $P \subseteq f^{-1}[f[P]R]$;
so, $Q'$ is lying over a prime ideal $P'$ (note that $f$ is unitary) such that $P \subseteq P'$. By GD, there exists
a prime ideal $Q \subseteq Q'$ lying over $P$. Clearly, $f[P]R \subseteq Q$; hence, $f^{-1}[f[P]R]=P$. The last assertion is clear. \end{proof}
\begin{defn} Let $\mathcal D \subseteq \text {Spec}(S)$ be a chain of prime ideals
and let $\mathcal C \subseteq \text {Spec}(R)$ be a $\mathcal D$-chain. We say that $\mathcal C$ is a {\it maximal cover} of
$\mathcal D$ if $\mathcal C$ is a cover of
$\mathcal D$, which is maximal with respect to containment.
\end{defn}
\begin{thm} \label{maximal D-chain covers D} $f$
satisfies GD, GU and SGB if and only if for every nonempty chain $\mathcal D \subseteq \text {Spec}(S)$ and for every
nonempty maximal $\mathcal D$-chain $\mathcal C \subseteq \text {Spec}(R)$, $\mathcal C$ is a (maximal) cover of
$\mathcal D$.
\end{thm}
\begin{proof} $(\Rightarrow)$ Let $\mathcal D \subseteq \text {Spec}(S)$ be a nonempty chain and
let $\mathcal C \subseteq \text {Spec}(R)$ be a nonempty maximal $\mathcal D$-chain.
Assume to the contrary that $\mathcal C$ is
not a cover of $\mathcal D$. So there
exists a prime ideal $P \in \mathcal D \setminus \{f^{-1}[Q]\}_{Q \in \mathcal C}$.
Obviously $\{f^{-1}[Q]\}_{Q \in \mathcal C} \cup \{ P\}$ is a chain. We have the following three possibilities:
1. $P \subset f^{-1}[Q]$ for all $Q \in \mathcal C$. However, by assumption $f$ satisfies GD and thus by Proposition \ref{mini GD},
this situation is impossible.
2. $f^{-1}[Q] \subset P$ for all $Q \in \mathcal C$. However, by assumption $f$ satisfies GU and thus by Proposition \ref{mini GU},
this situation is impossible.
3. There exist $Q', Q'' \in \mathcal C$ such that $f^{-1}[Q'] \subset P
\subset f^{-1}[Q'']$. So, let $\mathcal A$ be the cut defined by $\mathcal A^{L} =\{ Q \in \mathcal C \mid f^{-1}[Q] \subset P \}$ and
$\mathcal A^{R} =\{ Q \in \mathcal C \mid P \subset f^{-1}[Q] \}$. Note that $\mathcal A^{L} \neq \emptyset$ and $\mathcal A^{R} \neq \emptyset$.
Thus $f^{-1}[ Q_{l}] \subset P \subset f^{-1}[ Q_{r}]$ for
all $Q_{l} \in \mathcal A^{L}$ and $Q_{r} \in \mathcal A^{R}$. However, by assumption $f$ satisfies SGB and thus by Proposition \ref{mini SGB},
this situation is impossible.
Finally, it is obvious that $\mathcal C$ is a maximal cover of $\mathcal D$, since $\mathcal C$ is a cover of $\mathcal D$ and a maximal $\mathcal D$-chain.
$(\Leftarrow)$ It is obvious.
\end{proof}
We note that by [KO, Proposition 4 and Corollary 11], if $S \subseteq R$ are commutative rings such that $R$ satisfies GU over $S$, then for
every chain of prime ideals $\mathcal D \subseteq \text {Spec}(S)$ there exists
a chain of prime ideals in $\text {Spec}(R)$ covering it. However, if for example $R$ does not satisfy GD over $S$, then one can find
a chain $\mathcal D \subseteq \text {Spec}(S)$ such that not \textbf{every} maximal $\mathcal D$-chain is a cover of $\mathcal D$.
See Example \ref{ex GU LO but no GD}.
We shall now present one of the main results of this paper.
\begin{thm} \label{LO, INC, GD, GU and SGB imply perfect cover} Assume that $f$
satisfies LO, INC, GD, GU and SGB. Let $\mathcal D$ denote a chain of prime ideals in $\text {Spec} (S)$. Then there
exists a perfect maximal cover of $\mathcal D$. Moreover, any maximal $\mathcal
D$-chain is a perfect maximal cover.
\end{thm}
\begin{proof} If $\mathcal D$ is empty then a maximal $\mathcal D$-chain must be empty and the assertion is clear.
We may therefore assume that $\mathcal D$ is not empty. $f$ satisfies LO; thus by Lemma \ref{there exists C maximal over D} there exists a nonempty maximal $\mathcal D$-chain.
Now, let $\mathcal C$ be any maximal $\mathcal D$-chain.
$f$ satisfies GD, GU and SGB and therefore by Theorem \ref{maximal D-chain covers D}, $\mathcal C$ is a maximal cover of $\mathcal D$.
Finally, $f$ satisfies INC; hence by Lemma \ref{mini inc}, $\mathcal C$ is a perfect maximal cover of $\mathcal D$.
\end{proof}
We can now present another main result of this paper. The following corollary closes the circle.
\begin{cor} \label{equivalent conditions} The following conditions are equivalent:
1. $f$ satisfies layers 1,2 and 3 properties.
2. $f$ satisfies LO, INC, GD, GU and SGB.
3. For every chain $\mathcal D \subseteq \text {Spec} (S)$ and for every maximal $\mathcal
D$-chain $\mathcal C \subseteq \text {Spec} (R)$, $\mathcal C$ is a perfect maximal cover of $\mathcal D$.
4. For every chain $\mathcal D \subseteq \text {Spec} (S)$ and for every maximal $\mathcal
D$-chain $\mathcal C \subseteq \text {Spec} (R)$, $|C|=|D|$.
\end{cor}
\begin{proof} $(1) \Rightarrow (2)$: By Proposition \ref{layers iff properties}. $(2) \Rightarrow (3)$: By Theorem \ref{LO, INC, GD, GU and SGB imply perfect cover}.
$(3) \Rightarrow (4)$ and $(4) \Rightarrow (1)$ are obvious.
\end{proof}
\begin{ex} Notation and assumptions as in Example \ref{example from qv theory}. Then $R$ satisfies
LO, INC, GU, GD, and SGB over $O_{v}$. Therefore, for every chain $\mathcal D \subseteq \text {Spec} (O_{v})$ and for every maximal $\mathcal
D$-chain $\mathcal C \subseteq \text {Spec} (R)$, $\mathcal C$ is a perfect maximal cover of $\mathcal D$.
\end{ex}
We note that one can easily construct examples of functions that satisfy some of the properties. We shall present now an example in
which the cardinality of the set of all chains in $ \text {Spec} (S)$ that satisfy property 4 of Corollary \ref{equivalent conditions} is equal to
the cardinality of $ P(\text {Spec} (S))$, the power set of $ \text {Spec} (S)$, still without $f$ satisfying the equivalent conditions of Corollary \ref{equivalent conditions} (because property 4 is not fully satisfied).
\begin{ex} Let $A$ be a valuation ring of a field $F$ with $ |\text {Spec} (A)|=a$, an infinite cardinal. Let $Q_{0}$ denote the maximal ideal of $A$ and assume that
$Q_{0}$ has an immediate predecessor, namely, a prime ideal $Q_{1} \subset Q_{0}$, such that there is no prime ideal between $ Q_{0}$ and $Q_{1}$.
Let $B=A_{Q_{1}}$, a valuation ring of $F$ with maximal ideal $Q_{1}$. Consider $A$ as a subring of $B$ and let $f : A \rightarrow B$ be the map defined by $f(a)=a$ for all $a \in A$. It is well known that there is a bijective map $Q \rightarrow Q \cap A$ from $\text {Spec} (B)$ to $\text {Spec} (A) \setminus \{ Q_{0}\}$.
Let $$T=\{ \mathcal D \subseteq \text {Spec} (A) \mid \text { for every maximal } \mathcal
D \text {-chain } \mathcal C \subseteq \text {Spec} (B), \ |C|=|D| \};$$
It is not difficult to see that
$$P(\text {Spec} (A)) \setminus T= \{ \mathcal E \subseteq \text {Spec} (A) \mid Q_{0} \in \mathcal E, |\mathcal E|=n \text { for some } n \in \Bbb N \}.$$
It is obvious that $|P(\text {Spec} (A)) \setminus T|=a$ and thus
$|T|=|P(\text {Spec} (A))|=2^{a}$.
Note that $f$ does not satisfy LO and GU, although it does satisfy INC, GD and SGB.
Finally, denote $T'=\{ \mathcal D \subseteq \text {Spec} (A) \mid \text { for every maximal } \mathcal
D \text {-chain } \mathcal C \subseteq \text {Spec} (B), \ \mathcal C \text { is a perfect maximal cover of } \mathcal D \}$. Then
$T' \subset T$; in fact, $T'=P(\text {Spec} (A) \setminus \{ Q_{0}\} ) $. In other words, the set of chains in $\text {Spec} (A)$ that satisfy
property 3 of Corollary \ref{equivalent conditions} is strictly contained in the set of chains in $\text {Spec} (A)$ that satisfy
property 4 of Corollary \ref{equivalent conditions}.
\end{ex}
We close this paper by presenting some results regarding maximal chains in $\text {Spec}(S)$.
We shall need to assume that $f$ is unitary.
\begin{lem} \label{maximal cover over maximal is maximal} Assume that $f$ is unitary. Let $\mathcal D \subseteq \text {Spec}(S)$ be a maximal chain
and let $\mathcal C \subseteq \text {Spec}(R)$ be a maximal cover of $\mathcal D$. Then $\mathcal C$ is a maximal chain in $\text {Spec}(R)$.
\end{lem}
\begin{proof} Assume to the contrary that $\mathcal C$ is
not a maximal chain in $\text {Spec}(R)$. Then there exists a prime ideal $Q' $
of $R$ such that $\mathcal C \cup \{ Q' \}$ is a chain of prime
ideals of $R$ strictly containing $\mathcal C$. However, since $\mathcal C$ is a cover of $\mathcal D$, we have
$\mathcal D = \{ f^{-1}[Q]\}_{Q \in \mathcal C}$ and since $\mathcal C$ is a maximal cover of $\mathcal D$, we have
$f^{-1}[Q'] \notin \mathcal D$. Note that, since $f$ is unitary, $f^{-1}[Q'] \in \text {Spec}(S)$. Therefore, $$ \{ f^{-1}[Q]\}_{Q \in \mathcal C} \cup \{ f^{-1}[Q']\}$$ is a chain in
$\text {Spec}(S)$ strictly containing $\mathcal D$, a contradiction.
\end{proof}
We are now able to prove that, assuming $f$ is unitary and
satisfies GD, GU and SGB, if $\mathcal
D$ is a maximal chain in $\text {Spec}(S)$ and $\mathcal C$ is any maximal $\mathcal D$-chain, then
$\mathcal C$ must be a maximal chain in $\text {Spec}(R)$.
\begin{cor} \label{maximal D-chain implies maximal} Assume that $f$ is unitary and
satisfies GD, GU and SGB. Let $\mathcal
D$ be a maximal chain in $\text {Spec}(S)$ (so $\mathcal
D$ is not empty) and let $\mathcal C \subseteq \text {Spec}(R)$
be a nonempty maximal $\mathcal D$-chain. Then $\mathcal C$ is
a maximal cover of $\mathcal
D$ and a maximal chain in $\text {Spec}(R)$.
\end{cor}
\begin{proof} By Theorem \ref{maximal D-chain covers D}, $\mathcal C$ is a maximal cover of $\mathcal D$. By Lemma \ref{maximal cover over maximal is maximal}, $\mathcal C$ is a maximal chain in $\text {Spec}(R)$
\end{proof}
\begin{cor} \label{there exists maximal D-chain which is maximal} Assume that $f$ is unitary and
satisfies LO, GD, GU and SGB. Let $\mathcal D$ denote a maximal chain of prime ideals in $\text {Spec}(S)$. Then there
exists a maximal cover of $\mathcal D$, which is a maximal chain of
prime ideals in $\text {Spec}(R)$.
\end{cor}
\begin{proof} By Lemma \ref{there exists C maximal over D} there exists a nonempty maximal $\mathcal
D$-chain, and by Corollary \ref{maximal D-chain implies maximal} it
is a maximal chain of prime ideals in $\text {Spec}(R)$, covering $\mathcal D$.
\end{proof}
Note: it is not difficult to see that if $f$ is not unitary then the results presented in \ref{maximal cover over maximal is maximal},
\ref{maximal D-chain implies maximal} and \ref{there exists maximal D-chain which is maximal} are no longer valid.
\begin{comment}
*********************************************************************PROBLEM WITH WHAT"S WRRITEN BELOW.
In order to obtain an easy result, we define now a weaker definition than definition \ref{def_layers}.
\begin{defn} Let $n \in \Bbb N$. We say that $f$ satisfies the {\it layer $n^{+}$ property} if for every
chain $\mathcal D \subseteq \text {Spec}(S)$ of cardinality $n$, every maximal $\mathcal D$-chain is of cardinality $ \geq n$.
\end{defn}
It is not difficult to find examples of rings that satisfy some of the properties.
In fact, one can weaken a bit the assumptions of Theorem \ref{equivalent conditions} and get the following corollary.
\begin{cor} Assume that $S$ is commutative. The following conditions are equivalent:NOT GOOD
1. $f$ satisfies layers $ 1^{+}, 2^{+}$ and $ 3^{+}$ properties.
2. $f$ satisfies LO, GD, GU and SGB.
3. For every chain $\mathcal D \subseteq \text {Spec} (S)$ and for every maximal $\mathcal
D$-chain $\mathcal C \subseteq \text {Spec} (R)$, $\mathcal C$ is a maximal cover of $\mathcal D$.
4. For every chain $\mathcal D \subseteq \text {Spec} (S)$ and for every maximal $\mathcal
D$-chain $\mathcal C \subseteq \text {Spec} (R)$, $|C| \leq |D|$.
\end{cor}
******************************************************************
\begin{thm} Assume that $S$ is commutative. Assume that $f$
satisfies LO, INC, GD, GU and SGB. Let $\mathcal D$ denote a chain of prime ideals in $\text {Spec} (S)$. Then there
exists a maximal $\mathcal D$-chain, $\mathcal
C$, such that the map $Q \rightarrow f^{-1}[Q]$ is a bijective
order preserving correspondence between $\mathcal C$ and
$\mathcal D$. Moreover, if $\mathcal C'$ is a any maximal $\mathcal
D$-chain then the map $Q \rightarrow f^{-1}[Q]$ is a bijective
order preserving correspondence between $\mathcal C'$ and
$\mathcal D$.
\end{thm}
\begin{thm} Assume that $R$ satisfies LO, INC, GU, GD and SGB over $S$ and let $\mathcal D=\{P_{\alpha}\}_{\alpha \in
I}$ denote a maximal chain of prime ideals in $S$. Then there
exists a maximal $\mathcal D$-chain, $\mathcal
C=\{Q_{\alpha}\}_{\alpha \in I}$ (note that $|\mathcal
C|=|\mathcal D|$), which is a maximal chain of prime ideals in
$R$. Moreover, if $\mathcal C'$ is a any maximal $\mathcal
D$-chain then the map $Q \rightarrow Q \cap S$ is a bijective
order preserving correspondence between $\mathcal C'$ and
$\mathcal D$.
\end{thm}
\begin{proof} By the previous Corollary there exists a maximal $\mathcal D$-chain which is a maximal chain
of prime ideals in $R$. Let $\mathcal C'=\{Q_{\beta} \}_{\beta \in
J}$ be any maximal $\mathcal D$-chain. Then by Lemma \ref{maximal
D-chain implies maximal}, $\mathcal C'$ is a maximal chain of
prime ideals in $R$. By assumption $R$ satisfies INC, GU, GD and
SGB over $S$; thus by Theorem \ref{one to one}, the map $Q
\rightarrow Q \cap S$ is a bijective order preserving
correspondence between $\mathcal C'$ and the maximal chain
$\mathcal E=\{Q_{\beta} \cap S\}_{\beta \in J} \subseteq \mathcal
D$ of prime ideals in $S$. Since $\mathcal E$ is a maximal chain
one must have $\mathcal E= \mathcal D$ and the theorem is proved.
\end{proof}
\begin{cor} Assume that $R$ satisfies LO, INC, GU, GD and SGB over $S$ and let $\mathcal D'=\{P_{\beta}\}_{\beta \in
J}$ denote \textbf{any chain} of prime ideals in $S$. Then there
exists a maximal $\mathcal D'$-chain, $\mathcal
C'=\{Q_{\beta}\}_{\beta \in J}$ such that the map $Q \rightarrow Q
\cap S$ is a bijective order preserving correspondence between
$\mathcal C'$ and $\mathcal D'$.
\end{cor}
\begin{proof} Let $\mathcal D=\{P_{\alpha}\}_{\alpha \in I}$ denote a
maximal chain of prime ideals in $S$ containing $ \mathcal D'$. By
the previous Theorem, there exists a maximal chain of prime ideals
in $R$, $\mathcal C=\{Q_{\alpha}\}_{\alpha \in I}$ such that the
map $Q \rightarrow Q \cap S$ is a bijective order preserving
correspondence between $\mathcal C$ and $\mathcal D$. Define
$$\mathcal C'=\{ Q \in \mathcal C \mid Q \cap S \in \mathcal
D'\}.$$ By Lemma \ref{mini inc} the map $Q \rightarrow Q \cap S$
between $\mathcal C'$ and $\mathcal D'$ is injective. Now, let $P
\in \mathcal D'$; then $P \in \mathcal D$. Thus, there exists $Q
\in \mathcal C$ satisfying $Q \cap S =P$; hence $Q \in \mathcal
C'$. So the map above is surjective. It remains to prove that
$\mathcal C'$ is a maximal $\mathcal D'$-chain. Indeed, assume to
the contrary that there exists a prime ideal $K$ of $R$ such that
$\mathcal C' \cup \{K\}$ is a $\mathcal D'$-chain strictly
containing $\mathcal C'$. Then $K \cap S =P_{0}\in \mathcal D'$.
However, as note above, the map $Q \rightarrow Q \cap S$ between
$\mathcal C'$ and $\mathcal D'$ is surjective; thus there exists
$Q_{0} \in \mathcal C'$ such that $Q_{0} \cap S=P_{0}$. Now, since
$\mathcal C' \cup \{K\}$ is a chain, we have $Q_{0} \subset K$ or
$K \subset Q_{0}$, in contradiction to INC.
\end{proof}
We return now to our general discussion i.e., $(F,v)$ is a valued
field with valuation ring $O_{v}$, $A$ is a finite dimensional
$F-$algebra and $R \subseteq A$ is a subring of $A$ lying over
$O_{v}$; we do not assume that $R$ is an $O_{v}-$nice subring of
$A$.
\begin{thm} Assume that $R=O_{w}$ where $O_{w}$ is a \qv ring with $w$
extending $v$ (on $RF$) and $M_{w}$ is cancellative. Let $\mathcal
C=\{Q_{\alpha} \}_{\alpha \in I}$ denote \textbf {any maximal
chain} of prime ideals in $R$. Then the map $Q_{\alpha}
\rightarrow Q_{\alpha} \cap O_{v}$ is a bijective order preserving
correspondence between $\mathcal C$ and \textbf {the maximal
chain} $\mathcal D=\{Q_{\alpha} \cap S\}_{\alpha \in I}$ of prime
ideals in $O_{v}$.
\end{thm}
\begin{proof} By Theorem \ref{LO} $R$ satisfies LO over $O_{v}$, by Theorem \ref{GD} $R$
satisfies GD over $O_{v}$ and by Theorem \ref{INC} $R$ satisfies
INC over $O_{v}$ (note that LO, GD and INC are valid without the
assumption that $M_{w}$ is cancellative). Now, using the
assumption that $M_{w}$ is cancellative, we deduce by Theorem
\ref{SGB} that $R$ satisfies SGB over $O_{v}$ and by Theorem
\ref{GU} that $R$ satisfies GU over $O_{v}$. The Theorem now
follows from Theorem \ref{one to one}.
\end{proof}
In particular, if $R $ is finitely generated as an $O_{v}$ module
then by Corollary \ref{R be a subring of A finitely generated
implies M_w cancellative} there exists a \qv $w$ on $RF$ extending
$v$ on $F$ with $R=O_{w}$ and $M_{w}$ cancellative. So, the
results of the previous Theorem applies on $R$.
\end{comment}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,277 |
Two Major Factors Impacting Most SC Workers' Comp Claims | Holland & Usry, P.A.
Do you know the two things that can make the difference in your worker's compensation settlement? Spartanburg worker's compensation lawyer Rob Usry explains in this video.
Let's talk for a minute about two things that you, or your workers compensation lawyer, if you have one, can negotiate that might have the biggest impact on you in your workers compensation case. The first is medical care. You may be able to negotiate with the insurance company to get them to continue to pay your future medical care as long as it makes you better. You might also be able to negotiate with the insurance company to give you the right to come back for future medical care, for one year after your last comp check. And finally you might just decide to let the insurance company off the hook entirely for future medical care. We call that a clincher. It sounds like a bad idea but it works in a lot of cases, especially if you don't think you're going to have to come back to get any more medical treatment.
The reason it works out better is you can convince the compensation carrier to pay you a little more money and they might. The reason for it is you end their risk of having to pay for future medical care. so if you sign a clincher and you come back for more medical care from the carrier, they're going to tell you "I'm sorry you clinched your case and it's over." that's something to keep in mind.
The second thing that can really change the value of your case that might be negotiated is your disability rating. Your workers compensation disability rating is based on the impairment rating you get from your doctor. The impairment rating measures your loss of mobility, that's motion, and strength that's permanent as a result of your work injury. Then, the parties try to negotiate the amount of your disability rating. your disability rating measures how much that impairment rating hurts your ability to work and it's different for just about everybody. For example, a ten percent medical impairment to your arm is going to result in a much bigger work disability for a bricklayer than an office worker. Bricklayers got a lift and carry heavy loads all the time, while an office worker just doesn't.
So those are two things that can really impact the value of your claim and affect you in the future for your injury. I thank you for thinking about this with me and listening to me. | {
"redpajama_set_name": "RedPajamaC4"
} | 8,089 |
\section{Introduction}
In the Standard Model (SM), weak transitions between quark
flavours are described by the elements $V_{ij}$ of the Cabibbo
Kobayashi Maskawa (CKM)\cite{CKM}
matrix. Theory does not predict the magnitude of the elements which
therefore must be determined experimentally. The matrix is unitary
by construction and one of the unitarity conditions,
$V_{ud}V^*_{ub}+V_{cd}V_{cb}^*+V_{td}V_{tb}^*=0$, can be
geometrically represented as a triangle in the complex plane
$(\bar\rho,\bar\eta)$\footnote{$\bar{\rho}=(1-\lambda^2/2)\rho$,
$\bar{\eta}=(1-\lambda^2/2)\eta$, where $\lambda=V_{us}$ and
$A\lambda^3(\rho-i\eta)=V_{ub}$. $\rho$, $\eta$ and $A$ are defined
in the Wolfenstein's CKM parametrization~\cite{WOLF}.}, the well
known Unitarity Triangle (UT). Any non zero value of the $\bar\eta$
parameter is an indication of $CP$ violation. The angles and sides of
the UT can be measured by studying $B$ meson decays.
The Unitarity Triangle analysis shows an impressive success of the
CKM picture in describing $CP$ violation in the SM, but, as the
experimental results become increasingly precise, a slight
disagreement between the angle $\beta$, characterising indirect $CP$
violation in $b\rightarrow\bar{c}cs$ transitions and currently known at
the 4\% level, and $|V_{ub}|/|V_{cb}|$ has appeared in the UT fit. This
disagreement could be due to some problems with theoretical
calculations impacting on $|V_{ub}|$ determinations. Tree-level
processes are essentially immune to contributions from new physics, so
studying semileptonic $B$ decays and therefore determining $|V_{cb}|$ and
$|V_{ub}|$ is a way to test the electroweak sector of the SM. While
the determination of $|V_{cb}|$ is at the 2\% level~\cite{BUCH}, the
uncertainty on $|V_{ub}|$ is still at the 8\% level. The need for an
improvement in the precision on $|V_{ub}|$ is therefore evident.
In the following we will present the current status and outlook
regarding experimental determinations of $|V_{ub}|$.
\section{Semileptonic $B$ Decays}
The theoretical description of charmless semileptonic $B$ decays is at
a mature stage. $\bar{B}\rightarrow X_u\ell\bar\nu$ decays provide the
cleanest way to measure $|V_{ub}|$ since the leptonic and hadronic
part of the weak current factorize into two terms not interacting
between each other, resulting in an easy theoretical description at
the parton level, even though uncertainties arise when introducing QCD
calculations to describe the hadronization process. Given the fact
that the $b$ quark mass is considerably larger than the scale
$\Lambda_{QCD}$ that determines the low energy hadron physics, the
total rate can be expanded in powers of $\Lambda_{QCD}/m_b$ and
$\alpha_S$, separating non-perturbative and perturbative physics.
Two main experimental approaches are used to measure $|V_{ub}|$ from
$\bar{B}\rightarrow X_u\ell\bar\nu$ decays, depending on the choice
being made between integrating over all possible charmless final
states or selecting a particular one: inclusive and exclusive. The
first approach provides higher signal efficiency while the second
gives a better background rejection. Theoretical inputs are needed by
both approaches to model the hadronization, but since they rely on
independent calculations, they provide two complementary
determinations of $|V_{ub}|$.
\section{Experimental Techniques}
The most recent measurements of charmless semileptonic $B$ decays have
been performed by the \babar, Belle and CLEO experiments. These
experiments record $e^+e^-$ collisions at the energy of the
$\Upsilon(4S)$, a $b\bar{b}$ bound state that decays predominantly to
$B^0\bar{B}^0$ or $B^+B^-$ mesons. The main backgrounds for
$b\rightarrow u\ell\bar\nu$ transitions are the more abundant
$b\rightarrow c\ell\bar\nu$
(rate $\sim50$ times larger), the continuum background coming from
$e^+e^-\rightarrow q\bar{q},\ q = (u,d,s,c)$ and, where applicable,
combinatorial background due to random association of tracks in the
reconstruction of a $B$ meson. There are three established
experimental techniques employed to select signal events, that differ
on the reconstruction of the second $B$ in the event ({\it tag} side),
and are described below.
\subsection{Untagged Method}
In the untagged method the $B$ recoiling against the signal $B$ is not
explicitly reconstructed. With this technique, the neutrino
four-momentum is inferred from the difference between the
four-momentum of the colliding beam particles and the sum of the
four-momenta of all the charged and neutral particles detected in a
single event. The kinematic consistency of a $B_{tag}$ candidate with
a $B$ meson decay is evaluated using two variables: the beam-energy
substituted mass $m_{ES} \equiv \sqrt{s/4-|p^*_B|^2}$, and the energy
difference $\Delta E \equiv E^*_B -\sqrt{s}/2$. Here $ \sqrt{s}$ is
the total CM energy, and $p^*_B$ and $E^*_B$ denote the magnitude of
the 3-momentum and energy of the $B_{tag}$ candidate in the CM
frame. For correctly identified $B_{tag}$ decays, the $m_{ES}$
distribution peaks at the $B$ meson mass, while $\Delta E$ is
consistent with zero.
The untagged method offers higher signal efficiency ($\sim5\%$) with
respect to the other two methods but due to the poor resolution on the
neutrino 4-momentum has lower purity.
\subsection{Semileptonic Tag Method}
In the semileptonic method, a $B\rightarrow \bar{D}^{(*)}\ell\nu$ decay is
reconstructed in the tag side. Several $\bar{D}$ and $\bar{D}^*$ decay
modes are used for tagging. The presence of two neutrinos requires other
kinematical constraints in order to separate signal events from
backgrounds. With respect to the untagged method, the semileptonic tag
provides lower efficiency ($\sim 1\%$) but higher purity.
\subsection{Hadronic Tag Method}
In this method the tag side is reconstructed as a decay of the type
$B\rightarrow \bar{D}^{(*)}Y$, where $Y$ represents a linear
combination of charged and neutral pions and kaons. Several decay
combinations are taken into account. $\Delta E$ and $m_{ES}$ variables
are used to check the consistency of the reconstructed $B$
candidate. Since the $B_{tag}$ is fully reconstructed, the kinematics
of the event is completely constrained and charge and flavour of the
signal $B$ can be inferred. Given the good neutrino 4-momentum
resolution provided by this method, other kinematical variables, such
as the leptonic squared invariant mass $q^2$, the missing mass squared
$mm^2$ or the hadronic invariant mass $m_X$ can be exploited to
separate the background from the $b\rightarrow u$ signal events. The
fallback of this method is the very low tag efficiency (at the order
of $10^{-3}$).
\section{Exclusive $|V_{ub}|$ Determinations}
In the exclusive approach, the measured branching fraction for a
specific charmless decay channel,
e.g. $\bar{B}\rightarrow\pi\ell\bar\nu$, is converted into $|V_{ub}|$
using theoretical calculations of the form factors (FF) which
parametrize QCD effects. In particular, for
$\bar{B}\rightarrow\pi\ell\bar\nu$ decays, the differential branching
fraction as function of $q^2$ is proportional to $|V_{ub}||f_+(q^2)|$,
the latter term of the product being the FF. Experiments measure
$|V_{ub}||f_+(q^2)|$ and information on the shape and normalization of
$f_+(q^2)$ must come from theory. Several FF calculations are
available, based on quark models~\cite{ISGW}, lattice
QCD~\cite{HPQCD,FNAL} and Light Cone Sum Rules
(LCSR)~\cite{LCSR}. Lattice QCD and LCSR calculations have validity in
complementary $q^2$ ranges, giving predictions for
$q^2>16$~GeV$^2$/$c^4$ and $q^2<14$~GeV$^2$/$c^4$ respectively.
With more and more statistics provided by the $B$-Factories, it has become
possible to measure branching ratios in different $q^2$ intervals and
compare the predicted FF shapes to experimental
data. Figure~\ref{FF_figure} shows the differential partial branching
ratio spectrum as function of $q^2$ for $B^0\rightarrow\pi^-\ell^+\nu$
decays measured with an untagged analysis performed
by~\babar~\cite{unt}. This analysis has shown that FF calculations
based on quark models are not consistent with data distributions.
Table~\ref{excl_table} lists a summary of published branching ratio
determinations for $B\rightarrow\pi\ell^+\nu$ decays. All the
measurements are consistent within the experimental
uncertainties. Among all the methods, the untagged one provides the
most precise measurement, having an uncertainty of approximately 7\% in
the branching ratio determination.
\begin{table}[h]
\begin{center}
\caption{$\mathcal{B}(B\rightarrow\pi\ell^+\nu)$ measurements for
different experiments and tagging techniques. U, SL and Had indicate
untagged, semileptonic tag and hadronic tag methods respectively. Errors
on branching ratios are statistical and systematic.}
\begin{tabular}{|c|c|c|l|}
\hline
\textbf{Mode} & \textbf{$B\bar{B}$} & \textbf{Branching
Ratio} & \textbf{Exp./Tag}\\
& $[10^6]$ & $[10^{-4}]$ & \\
\hline
$B^0\rightarrow\pi^-\ell^+\nu$ & 227 & $1.46\pm0.07\pm0.08$ &
\babar~\cite{unt} U\\
\cline{2-4}
& 15.4 & $1.37\pm0.15\pm0.11$ & CLEO~\cite{CLEOunt} U\\
\cline{2-4}
& 232 & $1.12\pm0.25\pm0.10$ & \babar~\cite{babarsl} SL\\
\cline{2-4}
& 275 & $1.38\pm0.19\pm0.14$ & Belle~\cite{bellesl} SL\\
\cline{2-4}
& 232 & $1.07\pm0.27\pm0.15$ & \babar~\cite{babarsl} Had\\
\hline
$B^+\rightarrow\pi^0\ell^+\nu$ & 232 & $0.73\pm0.18\pm0.08$ &
\babar~\cite{babarsl} SL\\
\cline{2-4}
& 275 & $0.77\pm0.14\pm0.08$ & Belle~\cite{bellesl} SL\\
\cline{2-4}
& 232 & $0.82\pm0.22\pm0.11$ & \babar~\cite{babarsl} Had\\
\hline
\end{tabular}
\label{excl_table}
\end{center}
\end{table}
The world average computed by the HFAG~\cite{HFAG} group is
$\mathcal{B}(B^0\rightarrow\pi^-\ell^+\nu)=(1.38\pm0.06\pm0.07)\times10^{-4}$,
where the first error is statistical and the second due to systematic
uncertainties.
\begin{figure}[ht]
\centering
\includegraphics[width=70mm]{FF.eps}
\caption{$\Delta\mathcal{B}(B^0\rightarrow\pi^-\ell^+\nu)$ as function of
$q^2$ measured by \babar~\cite{unt}. The solid black curve shows the
result of the fit of the BK parametrization~\cite{BK} to the
data. Other FF calculations~\cite{HPQCD,FNAL,LCSR,ISGW} are
also compared to data.} \label{FF_figure}
\end{figure}
According to the various FF calculations, different $|V_{ub}|$ values
can be computed and are shown in Fig.~\ref{VubExcl_figure}, for the
full $q^2$ range. With the exclusive approach, the central value for
$|V_{ub}|$ lies in the interval $[3.11,3.80]\times10^{-3}$, in good
agreement with the indirect determination of $|V_{ub}|$ performed by
UT fit collaboration:
$|V_{ub}|_{UTfit}=(3.44\pm0.16)\times10^{-3}$~\cite{UTFIT}. The exclusive
determinations are still limited by the theoretical uncertainties on
the knowledge of the FF, which contribute up to 23\% to the total
error.
Branching ratio measurements of a $B$ meson decaying into other
charmless semileptonic final state ($\rho$, $\eta/\eta'$, $\omega$)
have been performed (world averages can be found on HFAG
website~\cite{HFAG}); however theory calculations necessary to convert
these measurements into $|V_{ub}|$ values are not yet mature.
\begin{figure}[ht]
\centering
\includegraphics[width=80mm]{vubexcl.eps}
\caption{Comparison of exclusive $|V_{ub}|$ determinations for
different form factor calculations for the full $q^2$
range.} \label{VubExcl_figure}
\end{figure}
\section{Inclusive $|V_{ub}|$ Determinations}
The full rate of inclusive charmless $B$ decays is computed within the
Operator Product Expansion (OPE) with a theory uncertainty
of $\sim 5\%$, mainly due to uncertainty on the $b$ quark mass. In
practice the accessible rate is reduced since it is necessary to
exploit kinematical variables that describe the semileptonic decays in
order to suppress the overwhelming background from $b\rightarrow c$
transitions; this restricts the measurement to phase space regions
where particles containing charm cannot be produced. The drawback of
this approach is on the theory side since calculating partial widths
in regions of phase space where $\bar{B}\rightarrow X_c\ell\bar\nu$
are suppressed is very challenging, as the HQE convergence in these
regions is spoiled and a non-perturbative distribution function,
the shape function (SF)\cite{SF1,SF2}, whose form is unknown, needs to
be introduced. Weak annihilation and other non-perturbative effects
need to be modeled too.
The shape function is a universal property of $B$ mesons at leading
order, however sub-leading shape functions arise at each order in the
$1/m_b$ expansion. SF parameters can be constrained by measuring
moments of inclusive distributions from $\bar{B}\rightarrow
X_c\ell\bar\nu$ and $\bar{B}\rightarrow X_s\gamma$ decays which are related
to the same heavy quark parameters ($m_b$, the $b$ quark mass and
$\mu_\pi^2$, the square of the kinetic energy of the $b$ quark in the
$B$ meson).
In recent years, many theoretical calculations have become
available, either based on the OPE approach~\cite{BLNP,LNR,BLL,GGOU}
or on models of non-perturbative QCD~\cite{DGE,AC}.
Several kinematical variables are used to separate signal from
$b\rightarrow c$ background, each having its own advantage. The
lepton energy $E_\ell$ is the simplest to measure but the cut applied
to reduce the charmed background restricts the total accessible signal
rate to $\sim10\%$ of the total; moreover the dependence on leading
and subleading SF and weak annihilation corrections may be
substantial. The squared leptonic invariant mass $q^2$ is weakly
sensitive to SF effects, has higher accessible $b\rightarrow u$
fraction, $\sim 20\%$, but is sensitive to weak annihilation
corrections. Much higher signal rate is provided by the hadronic
invariant mass $m_X$ and the light cone momentum
$P_+=E_X-|\vec{p}_X|$, $\sim80\%$ and $\sim70\%$ respectively, but
both depend on SF and subleading SF corrections.
\begin{figure*}[t]
\centering
\includegraphics[totalheight=8.5cm]{mx.eps}
\includegraphics[totalheight=8.5cm]{pplus.eps}
\includegraphics[totalheight=8.5cm]{2D.eps}
\caption{Upper row: $m_X$ (a), $P_+$ (b) and $q^2$ with $m_X<1.7$
GeV/$c^2$ (c) measured spectra (data points)~\cite{babarhad}. The
result of the fit to the sum of three Monte Carlo contributions is
shown in the histograms: $\bar{B}\rightarrow X_u\ell\bar\nu$
decays generated inside (white) and outside (gray) the signal
region, and $\bar{B}\rightarrow X_c\ell\bar\nu$ and other
background (blue). Lower row: corresponding spectra
for $\bar{B}\rightarrow X_u\ell\bar\nu$ after $\bar{B}\rightarrow
X_c\ell\bar\nu$ and other background subtraction, rebinned to show
the shape of the kinematical variables. } \label{babarHad_figure}
\end{figure*}
The most recent inclusive $|V_{ub}|$ determinations have been
performed by the \babar\ experiment using the hadronig tag
technique~\cite{babarhad}. In this analysis, inclusive $m_X$, $P_+$
and $(m_X,q^2)$ distributions have been reconstructed for semileptonic
$B$ decays and measurements of charmless partial branching fractions
have been performed in regions of phase space where the $b\rightarrow
c$ transitions are highly suppressed. Continuum and combinatoric
backgrounds have been subtracted with fits to $m_{ES}$
distributions. Figure~\ref{babarHad_figure} shows the fits of Monte
Carlo $b\rightarrow c$ (blue), $b\rightarrow u$ (white) and other
background (gray) shapes to the measured data (points) from which
partial branching fractions for the signal enhanced region have been
determined. $|V_{ub}|$ values have then been calculated using the
relation
\begin{equation}
|V_{ub}|=\sqrt{\frac{\Delta\mathcal{B}(\bar{B}\rightarrow
X_u\ell\bar\nu)}{\tau_B\tilde{\Gamma}_{thy}}}\label{vub_formula}
\end{equation}
where $\tau_B$ is the $B$ lifetime and $\tilde{\Gamma}_{thy}$ are the
theoretical acceptances provided by the cited models. The $|V_{ub}|$
determinations obtained are in good agreement with the ones provided
in a similar analysis by Belle~\cite{Bellehad}, and show
that the measurements based on $m_X$ and $(m_X,q^2)$ are compatible
with theory calculations, while there is a hint that results based on
$P_+$ are somewhat lower than theory predictions and closer to
$|V_{ub}|$ determinations which use exclusive charmless semileptonic
decays.
HFAG~\cite{HFAG} provides world averages of $|V_{ub}|$ values
obtained within the
currently available theoretical frameworks and these are listed in
Fig.~\ref{inclVub_figure}. Inclusive charmless semileptonic decays
give $|V_{ub}|$ determinations that are compatible with exclusive
ones, even though with higher values. As is the case for the exclusive
measurements, the dominant uncertainty is due to theory ($\sim7\%$).
\begin{figure}[ht]
\centering
\includegraphics[width=80mm]{inclvub.eps}
\caption{Comparison of inclusive $|V_{ub}|$ values obtained using different
theoretical calculations.}\label{inclVub_figure}
\end{figure}
\section{Weak Annihilation}
{\it Weak annihilation} denotes a $B^+\rightarrow X_u\ell^+\nu$ decay in which
the $\bar{b}$ and the spectator $u$ quark forming the $B^+$ meson
annihilate into a $W^+$ boson, and a soft gluon emitted in the
interaction materializes into a charmless final state. The
contribution to the total charmless semileptonic rate is expected to
be small, of the order of 3\%, but can be
relevant when selecting large $q^2$ regions. Weak
annihilation can be experimentally observed as a difference in
the partial decay rates of $B^0\rightarrow X_u^-\ell^+\nu$ and
$B^+\rightarrow X^0_u\ell^+\nu$ at high $q^2$ since it occurs only for
charged $B$ mesons. Measurements performed by \babar~\cite{babarWA}
and CLEO~\cite{CLEOWA} have provided no evidence of weak annihilation
so far, placing the upper limit: $\Gamma_{WA}/\Gamma_{b\rightarrow
u\ell\nu}<8\%$ at $90\%$ CL.
\section{Conclusion}
The large datasets collected at the $B$-Factories, and the increased
precision of theoretical calculations have allowed an improvement in the
determination of $|V_{ub}|$. However, there are still significant
uncertainties. In the exclusive approach, the most precise measurement
of the pion channel branching ratio is obtained by an untagged
analysis. This very good precision can be reached by tagged analyses
with more data. The problem with exclusive decays is that the strong
hadron dynamics can not be calculated from first principles and the
determination of the form factor has to rely on light-cone sum rules or
lattice QCD calculations. The current data samples allow a comparison
of different FF models with data distributions. With
further developments on lattice calculations, the theoretical error
should shrink to reach the experimental one.
The inclusive approach still provides the most precise $|V_{ub}|$
determinations. With new theoretical calculations, the mild ($2.5\sigma$)
discrepancy with respect to the $|V_{ub}|$ value determined from the
global UT fit has been reduced. As in the exclusive approach,
theoretical uncertainties represent the limiting factor to the precision
of the measurement. Reducing the theoretical uncertainties
to a level comparable with the statistical error is challenging. New
measurements in semileptonic decays of charm mesons could increase the
confidence in theoretical calculations and related uncertainties.
\bigskip
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,235 |
{"url":"https:\/\/geocompr.robinlovelace.net\/eco.html","text":"# Chapter 14 Ecology\n\n## Prerequisites\n\nThis chapter assumes you have a strong grasp of geographic data analysis and processing, covered in Chapters 2 to 5. In it you will also make use of R\u2019s interfaces to dedicated GIS software, and spatial cross-validation, topics covered in Chapters 9 and 11, respectively.\n\nThe chapter uses the following packages:\n\n## 14.1 Introduction\n\nIn this chapter we will model the floristic gradient of fog oases to reveal distinctive vegetation belts that are clearly controlled by water availability. To do so, we will bring together concepts presented in previous chapters and even extend them (Chapters 2 to 5 and Chapters 9 and 11).\n\nFog oases are one of the most fascinating vegetation formations we have ever encountered. These formations, locally termed lomas, develop on mountains along the coastal deserts of Peru and Chile.76 The deserts\u2019 extreme conditions and remoteness provide the habitat for a unique ecosystem, including species endemic to the fog oases. Despite the arid conditions and low levels of precipitation of around 30-50 mm per year on average, fog deposition increases the amount of water available to plants during austal winter. This results in green southern-facing mountain slopes along the coastal strip of Peru (Figure 14.1). This fog, which develops below the temperature inversion caused by the cold Humboldt current in austral winter, provides the name for this habitat. Every few years, the El Ni\u00f1o phenomenon brings torrential rainfall to this sun-baked environment (Dillon, Nakazawa, and Leiva 2003). This causes the desert to bloom, and provides tree seedlings a chance to develop roots long enough to survive the following arid conditions.\n\nUnfortunately, fog oases are heavily endangered. This is mostly due to human activity (agriculture and climate change). To effectively protect the last remnants of this unique vegetation ecosystem, evidence is needed on the composition and spatial distribution of the native flora (J. Muenchow, Br\u00e4uning, et al. 2013; J. Muenchow, Hauenstein, et al. 2013). Lomas mountains also have economic value as a tourist destination, and can contribute to the well-being of local people via recreation. For example, most Peruvians live in the coastal desert, and lomas mountains are frequently the closest \u201cgreen\u201d destination.\n\nIn this chapter we will demonstrate ecological applications of some of the techniques learned in the previous chapters. This case study will involve analyzing the composition and the spatial distribution of the vascular plants on the southern slope of Mt. Mong\u00f3n, a lomas mountain near Casma on the central northern coast of Peru (Figure 14.1).\n\nDuring a field study to Mt. Mong\u00f3n, we recorded all vascular plants living in 100 randomly sampled 4x4 m2 plots in the austral winter of 2011 (J. Muenchow, Br\u00e4uning, et al. 2013). The sampling coincided with a strong La Ni\u00f1a event that year (see ENSO monitoring of the NOASS Climate Prediction Center). This led to even higher levels of aridity than usual in the coastal desert. On the other hand, it also increased fog activity on the southern slopes of Peruvian lomas mountains.\n\nOrdinations are dimension-reducing techniques which allow the extraction of the main gradients from a (noisy) dataset, in our case the floristic gradient developing along the southern mountain slope (see next section). In this chapter we will model the first ordination axis, i.e., the floristic gradient, as a function of environmental predictors such as altitude, slope, catchment area and NDVI. For this, we will make use of a random forest model - a very popular machine learning algorithm (Breiman 2001). The model will allow us to make spatial predictions of the floristic composition anywhere in the study area. To guarantee an optimal prediction, it is advisable to tune beforehand the hyperparameters with the help of spatial cross-validation (see Section 11.5.2).\n\n## 14.2 Data and data preparation\n\nAll the data needed for the subsequent analyses is available via the RQGIS package.\n\nstudy_area is an sf polygon representing the outlines of the study area. random_points is an sf object, and contains the 100 randomly chosen sites. comm is a community matrix of the wide data format (Wickham 2014b) where the rows represent the visited sites in the field and the columns the observed species.77\n\nThe values represent species cover per site, and were recorded as the area covered by a species in proportion to the site area in percentage points (%; please note that one site can have >100% due to overlapping cover between individual plants). The rownames of comm correspond to the id column of random_points. dem is the digital elevation model (DEM) for the study area, and ndvi is the Normalized Difference Vegetation Index (NDVI) computed from the red and near-infrared channels of a Landsat scene (see Section 4.3.3 and ?ndvi). Visualizing the data helps to get more familiar with it, as shown in Figure 14.2 where the dem is overplotted by the random_points and the study_area.\n\nThe next step is to compute variables which we will not only need for the modeling and predictive mapping (see Section 14.4.2) but also for aligning the Non-metric multidimensional scaling (NMDS) axes with the main gradient in the study area, altitude and humidity, respectively (see Section 14.3).\n\nSpecifically, we will compute catchment slope and catchment area from a digital elevation model using R-GIS bridges (see Chapter 9). Curvatures might also represent valuable predictors, in the Exercise section you can find out how they would change the modeling result.\n\nTo compute catchment area and catchment slope, we will make use of the saga:sagawetnessindex function.78 get_usage() returns all function parameters and default values of a specific geoalgorithm. Here, we present only a selection of the complete output.\n\nSubsequently, we can specify the needed parameters using R named arguments (see Section 9.2). Remember that we can use a RasterLayer living in R\u2019s global environment to specify the input raster DEM (see Section 9.2). Specifying 1 as the SLOPE_TYPE makes sure that the algorithm will return the catchment slope. The resulting output rasters should be saved to temporary files with an .sdat extension which is a SAGA raster format. Setting load_output to TRUE ensures that the resulting rasters will be imported into R.\n\nThis returns a list named ep consisting of two elements: AREA and SLOPE. Let us add two more raster objects to the list, namely dem and ndvi, and convert it into a raster stack (see Section 2.3.3).\n\n### 14.4.2 Predictive mapping\n\nThe tuned hyperparameters can now be used for the prediction. We simply have to modify our learner using the result of the hyperparameter tuning, and run the corresponding model.\n\nThe last step is to apply the model to the spatially available predictors, i.e., to the raster stack. So far, raster::predict() does not support the output of ranger models, hence, we will have to program the prediction ourselves. First, we convert ep into a prediction data frame which secondly serves as input for the predict.ranger() function. Thirdly, we put the predicted values back into a RasterLayer (see Section 3.3.1 and Figure 14.5).\n\nThe predictive mapping clearly reveals distinct vegetation belts (Figure 14.5). Please refer to J. Muenchow, Hauenstein, et al. (2013) for a detailed description of vegetation belts on lomas mountains. The blue color tones represent the so-called Tillandsia-belt. Tillandsia is a highly adapted genus especially found in high quantities at the sandy and quite desertic foot of lomas mountains. The yellow color tones refer to a herbaceous vegetation belt with a much higher plant cover compared to the Tillandsia-belt. The orange colors represent the bromeliad belt, which features the highest species richness and plant cover. It can be found directly beneath the temperature inversion (ca. 750-850 m asl) where humidity due to fog is highest. Water availability naturally decreases above the temperature inversion, and the landscape becomes desertic again with only a few succulent species (succulent belt; red colors). Interestingly, the spatial prediction clearly reveals that the bromeliad belt is interrupted which is a very interesting finding we would have not detected without the predictive mapping.\n\n## 14.5 Conclusions\n\nIn this chapter we have ordinated the community matrix of the lomas Mt. Mong\u00f3n with the help of a NMDS (Section 14.3). The first axis, representing the main floristic gradient in the study area, was modeled as a function of environmental predictors which partly were derived through R-GIS bridges (Section 14.2). The mlr package provided the building blocks to spatially tune the hyperparameters mtry, sample.fraction and min.node.size (Section 14.4.1). The tuned hyperparameters served as input for the final model which in turn was applied to the environmental predictors for a spatial representation of the floristic gradient (Section 14.4.2). The result demonstrates spatially the astounding biodiversity in the middle of the desert. Since lomas mountains are heavily endangered, the prediction map can serve as basis for informed decision-making on delineating protection zones, and making the local population aware of the uniqueness found in their immediate neighborhood.\n\n\u2022 It would be interesting to also model the second ordination axis, and to subsequently find an innovative way of visualizing jointly the modeled scores of the two axes in one prediction map.\n\u2022 If we were interested in interpreting the model in an ecologically meaningful way, we should probably use (semi-)parametric models (J. Muenchow, Br\u00e4uning, et al. 2013; Zuur et al. 2009, 2017). However, there are at least approaches that help to interpret machine learning models such as random forests (see, e.g., https:\/\/mlr-org.github.io\/interpretable-machine-learning-iml-and-mlr\/).\n\u2022 A sequential model-based optimization (SMBO) might be preferable to the random search for hyperparameter optimization used in this chapter (Probst, Wright, and Boulesteix 2018).\n\nFinally, please note that random forest and other machine learning models are frequently used in a setting with lots of observations and many predictors, much more than used in this chapter, and where it is unclear which variables and variable interactions contribute to explaining the response. Additionally, the relationships might be highly non-linear. In our use case, the relationship between response and predictors are pretty clear, there is only a slight amount of non-linearity and the number of observations and predictors is low. Hence, it might be worth trying a linear model. A linear model is much easier to explain and understand than a random forest model, and therefore to be preferred (law of parsimony), additionally it is computationally less demanding (see Exercises). If the linear model cannot cope with the degree of non-linearity present in the data, one could also try a generalized additive model (GAM). The point here is that the toolbox of a data scientist consists of more than one tool, and it is your responsibility to select the tool best suited for the task or purpose at hand. Here, we wanted to introduce the reader to random forest modeling and how to use the corresponding results for spatial predictions. For this purpose, a well-studied dataset with known relationships between response and predictors, is appropriate. However, this does not imply that the random forest model has returned the best result in terms of predictive performance (see Exercises).\n\n## 14.6 Exercises\n\n1. Run a NMDS using the percentage data of the community matrix. Report the stress value and compare it to the stress value as retrieved from the NMDS using presence-absence data. What might explain the observed difference?\n\n2. Compute all the predictor rasters we have used in the chapter (catchment slope, catchment area), and put them into a raster stack. Add dem and ndvi to the raster stack. Next, compute profile and tangential curvature as additional predictor rasters and add them to the raster stack (hint: grass7:r.slope.aspect). Finally, construct a response-predictor matrix. The scores of the first NMDS axis (which were the result when using the presence-absence community matrix) rotated in accordance with elevation represent the response variable, and should be joined to random_points (use an inner join). To complete the response-predictor matrix, extract the values of the environmental predictor raster stack to random_points.\n\n3. Use the response-predictor matrix of the previous exercise to fit a random forest model. Find the optimal hyperparameters and use them for making a prediction map.\n\n4. Retrieve the bias-reduced RMSE of a random forest model using spatial cross-validation including the estimation of optimal hyperparameter combinations (random search with 50 iterations) in an inner tuning loop (see Section 11.5.2). Parallelize the tuning level (see Section 11.5.2). Report the mean RMSE and use a boxplot to visualize all retrieved RMSEs.\n\n5. Retrieve the bias-reduced RMSE of a simple linear model using spatial cross-validation. Compare the result to the result of the random forest model by making RMSE boxplots for each modeling approach.\n\n### References\n\nBorcard, Daniel, Fran\u00e7ois Gillet, and Pierre Legendre. 2011. Numerical Ecology with R. Use R! New York: Springer.\n\nBreiman, Leo. 2001. \u201cRandom Forests.\u201d Machine Learning 45 (1): 5\u201332. https:\/\/doi.org\/10.1023\/A:1010933404324.\n\nDillon, M. O., M. Nakazawa, and S. G. Leiva. 2003. \u201cThe Lomas Formations of Coastal Peru: Composition and Biogeographic History.\u201d In El Ni\u00f1o in Peru: Biology and Culture over 10,000 Years, edited by J. Haas and M. O. Dillon, 1\u20139. Chicago: Field Museum of Natural History.\n\nHengl, Tomislav, Madlene Nussbaum, Marvin N. Wright, Gerard B.M. Heuvelink, and Benedikt Gr\u00e4ler. 2018. \u201cRandom Forest as a Generic Framework for Predictive Modeling of Spatial and Spatio-Temporal Variables.\u201d PeerJ 6 (August): e5518. https:\/\/doi.org\/10.7717\/peerj.5518.\n\nJames, Gareth, Daniela Witten, Trevor Hastie, and Robert Tibshirani, eds. 2013. An Introduction to Statistical Learning: With Applications in R. Springer Texts in Statistics 103. New York: Springer.\n\nMcCune, Bruce, James B. Grace, and Dean L. Urban. 2002. Analysis of Ecological Communities. Second. Gleneden Beach, OR: MjM Software Design.\n\nMuenchow, Jannes, Achim Br\u00e4uning, Eric Frank Rodr\u00edguez, and Henrik von Wehrden. 2013. \u201cPredictive Mapping of Species Richness and Plant Species\u2019 Distributions of a Peruvian Fog Oasis Along an Altitudinal Gradient.\u201d Biotropica 45 (5): 557\u201366. https:\/\/doi.org\/10.1111\/btp.12049.\n\nMuenchow, Jannes, Simon Hauenstein, Achim Br\u00e4uning, Rupert B\u00e4umler, Eric Frank Rodr\u00edguez, and Henrik von Wehrden. 2013. \u201cSoil Texture and Altitude, Respectively, Largely Determine the Floristic Gradient of the Most Diverse Fog Oasis in the Peruvian Desert.\u201d Journal of Tropical Ecology 29 (05): 427\u201338. https:\/\/doi.org\/10.1017\/S0266467413000436.\n\nMuenchow, Jannes, Patrick Schratz, and Alexander Brenning. 2017. \u201cRQGIS: Integrating R with QGIS for Statistical Geocomputing.\u201d The R Journal 9 (2): 409\u201328.\n\nProbst, Philipp, Marvin Wright, and Anne-Laure Boulesteix. 2018. \u201cHyperparameters and Tuning Strategies for Random Forest.\u201d arXiv:1804.03515 [Cs, Stat], April. http:\/\/arxiv.org\/abs\/1804.03515.\n\nSchratz, Patrick, J. Muenchow, Eugenia Iturritxa, Jakob Richter, and A. Brenning. 2018. \u201cPerformance Evaluation and Hyperparameter Tuning of Statistical and Machine-Learning Models Using Spatial Data.\u201d\n\nvon Wehrden, Henrik, Jan Hanspach, Helge Bruelheide, and Karsten Wesche. 2009. \u201cPluralism and Diversity: Trends in the Use and Application of Ordination Methods 1990-2007.\u201d Journal of Vegetation Science 20 (4): 695\u2013705. https:\/\/doi.org\/10.1111\/j.1654-1103.2009.01063.x.\n\nWickham, Hadley. 2014b. \u201cTidy Data.\u201d Journal of Statistical Software 59 (10). https:\/\/doi.org\/10.18637\/jss.v059.i10.\n\nZuur, Alain F., Elena N. Ieno, Anatoly A. Saveliev, and Alain F. Zuur. 2017. Beginner\u2019s Guide to Spatial, Temporal and Spatial-Temporal Ecological Data Analysis with R-INLA. Vol. 1. Newburgh, United Kingdom: Highland Statistics Ltd.\n\nZuur, Alain, Elena N. Ieno, Neil Walker, Anatoly A. Saveliev, and Graham M. Smith. 2009. Mixed Effects Models and Extensions in Ecology with R. Statistics for Biology and Health. New York: Springer-Verlag.\n\n1. Similar vegetation formations develop also in other parts of the world, e.g., in Namibia and along the coasts of Yemen and Oman (Galletti, Turner, and Myint 2016).\n\n2. In statistics, this is also called a contingency table or cross-table.\n\n3. Admittedly, it is a bit unsatisfying that the only way of knowing that sagawetnessindex computes the desired terrain attributes is to be familiar with SAGA.\n\n4. One way of choosing k is to try k values between 1 and 6 and then using the result which yields the best stress value (McCune, Grace, and Urban 2002).","date":"2020-02-20 10:44:56","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6092162728309631, \"perplexity\": 3785.8076251546786}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-10\/segments\/1581875144722.77\/warc\/CC-MAIN-20200220100914-20200220130914-00257.warc.gz\"}"} | null | null |
extec screens amp crushers ltd - dcscbedscreens amp crushers ltd de - quantumtutorials. screens amp crushers ltd de anggroup. mobile crusher of amp amp Extec Screens and Crushers Ltd Crunchbase Extec Screens and Crushers Ltd is manufactures mobile crushers, screeners, and shredders for quarrying, mining, and recycling applications.
See Extec Screens And Crushers Ltd. 's products and customers Thousands of companies like you use Panjiva to research suppliers and competitors. Sign Up 1 min video. Easy access to trade data . Extec Ltd. Shipper Address. HEARTHCOTE ROAD, SWADLINCOTE DE11 9DU GB. Consignee Name. Mining & Construction.
extec screens and crushers ltd padmahotel. EXTEC Screen Aggregate Equipment For Sale Machinery Trader. buy 2005 extec 5x16, extec 5000, extec double screen, 1998 extec robotrac, 2008 extec s5, 2006 extec s5, 2005 extec s5, 2008 extec s6, 2003 extec 5x10, extec 5x16 . Check price.
Extec Screens And Crushers Ltd., Hearthcote Road . Extec Screens And Crushers Ltd. at Hearthcote Road, Swadlincote, Derbyshire DE11, UK. Find their customers, contact information, and details on 276 shipments.
About Crush & Screen Parts. Crush & Screen Parts supplies high quality low priced parts for all major brands of Crushing and Screening Plants. Powerscreen, , , Extec, Fintec, , Keestrack, Eagle, Finlay and . Contact Crush & Screen Parts for your replacement wear item or screen media needs. Screens, Belting, Bearings .
extec screens crusher ltd Mobile Crushers all over the World. Jan 14, 2015 extec screens crusher ltd heavy industry is specialized in the design, manufacture and supply of crushing equipment used in mining industry.
extec screens amp crushers ni ltd - hetmonaster.nl. 2 extec screensamp crushers ltd . extec screens 26amp 3b crushers ltd office at . 2 extec screens amp amp crushers ltd 2 extec screens the asphalt works 26amp 3b crushers co ltd the asphalt works 26amp 3b picture of washing 26amp 3 Read More .
ImportGenius has the complete import/export history of Extec Screens And Crushers Limited. Their June 17, 2010 shipment to Mining Construction De Me in the USA contained 46080KG of Portable Mch F/crush Earth, etcone(1)mobile Tracke.
Crushing Screening Parts Ltd. Home; Visit Our Shop Manufactures. Brands . We are a growing force in the supply of quality products for an increasing list of Crushing & Screening machines.Located in Northern Ireland, the hub of manufacturing for Crushing & Screening machines, we have the ability to supply many of the replacement products .
Extec Screens & Crushers Ltd - Manufacturers Of Mobile .
Desc: Manufacturers of mobile crushers, screeners and shredders. Manufacturers of mobile crushers, jaw crushers, screeners and shredders, serving the quarry, recycling and mineral extraction industries. Specialists in jaw crushers, cone crushers and doublescreen boxes, experts in crusher, screen, shredder technology.
Extec Screen & Crushers Ltd Company and Product Info from . zenith acquired Extec and Fintec, and have incorporated the brands into the zenith . Extec Screen & Crushers Ltd .. Extec introduces C-10+ jaw crusher. Get Price. Extec Screens & Crushers Ltd v David Rice- 3 Hare Court.
extec screens and crushers ltd - gigsgh. Extec Screens & Crushers Ltd. - Recycling Product News. Recycling Product News covers the latest industry news, product information and new equipment technologies for the solid waste and recycling industry. Chat Online.
JianYe Machinery Manufacturing Co., Ltd. . Extec C10 Extec C12 Jaw Plate Spare Parts. Jaw plate spare parts for extec c10, . Jaw plate extec c10 is widely used as a main wear part of extec jaw crusher and the service life of jaw crusher relate a lot to jaw plate. Jianye Machinery Jaw plate is manufactured with super high manganese steel .
Oct 08, 2018 · Find Extec, Powerscreen,, Deutz-Fahr,, Rubble master for sale on Machinio.Extec Screens & Crushers Ltd Crusher Mills, Cone Crusher .Extec Screen & Crushers Ltd Company and Product Info from .
Northern Crusher Spares are mobile crushing and screening parts specialists offering spares for , Extec, Finlay & Fintec machinery & Optibelt dealer. . Instant crusher spares, Parker crusher spares, Extec Crusher parts and Finley parts for crushers. We have jaw crusher parts, . Northern Crusher Spares Ltd Unit 9a Enterprise Park .
Extec Screens & Crushers Ltd Competitors and Products in .
Extec Screens & Crushers Ltd From humble beginnings Extec has achieved its position today as the world's leading manufacturer of mobile screening and crushing equipment with . | {
"redpajama_set_name": "RedPajamaC4"
} | 1,862 |
Indianola police try to stay warm while patrolling in polar vortex
Lt. Rob Hawkins said Wednesday was the coldest day in his 21 years on the police force.
Indianola police try to stay warm while patrolling in polar vortex Lt. Rob Hawkins said Wednesday was the coldest day in his 21 years on the police force. Check out this story on desmoinesregister.com: https://www.desmoinesregister.com/story/news/local/indianola/2019/01/30/polar-vortex-indianola-police-try-stay-warm-dangerous-cold-temperatures-in-iowa-weather/2726124002/
Teresa Kay Albertson, Des Moines Register Published 6:30 p.m. CT Jan. 30, 2019
Indianola police Lt. Rob Hawkins tucked his gloves and stocking cap into his pocket before heading to his cruiser to patrol the city's nearly deserted streets.
Staying warm was a top priority for officers Wednesday as temperatures dipped to minus 15 before pushing to a high of -8 by the afternoon.
Hawkins said it was the coldest day he could remember in his 21 years with the department.
► Iowa weather: Overnight cold broke multiple decades-old records. See if your city came close
An hour into his afternoon patrol shift, he had yet to come across anyone walking outside.
Indianola police Lt. Rob Hawkins patrols the city's nearly deserted streets Wednesday afternoon. (Photo: Teresa Kay Albertson)
"The highway here in the middle of town over the lunch hour is nearly deserted," he said. "And that's good. We want people home and warm and safe on a day like today."
His job Wednesday mostly involved patrolling the streets, looking for anyone who might need assistance.
► 'Above and beyond': After 24-hour shift, firefighters volunteer to help Iowa mom in need
"I had a domestic issue to deal with earlier today, but otherwise, it's been very quiet," he said.
The worst case scenario on a day like this? A fire or another emergency that would require an officer to be outside for more than a few minutes, he said.
"We are just like you," he said. "I want my car to start in the cold. I want my family to be safe.
"I'm a citizen of Indianola, and when I'm not on duty, my family is policed by the department just like everyone else."
Photos: Deep freeze hits Des Moines
A woman bundled in a coat and boots walks into the East Village store Raygun, past their sign poking fun at midwestern weather on Wednesday, Jan. 30, 2019, in Des Moines. The National Weather Service reported a new record low temperature of -19 in Des Moines on Wednesday morning. Kelsey Kremer/The Register
A flock of geese seek refuge on a patch of ice over the Des Moines River on Wednesday, Jan. 30, 2019, in downtown Des Moines. Steam rolls off the river as it's warmer than the sub-zero air temperature. Kelsey Kremer/The Register
Des Moines Water Works crews fix a water main break in Des Moines' East Village on Wednesday, Jan. 30, 2019. The National Weather Service reported a new record low temperature of -19 in Des Moines on Wednesday morning. Kelsey Kremer/The Register
Icicles cling to power lines above where Des Moines Water Works crews are working to fix a water main break in Des Moines' East Village on Wednesday, Jan. 30, 2019. The National Weather Service reported a new record low temperature of -19 in Des Moines on Wednesday morning. Kelsey Kremer/The Register
A pair of people brave the cold in Des Moines' East Village on Wednesday, Jan. 30, 2019. The National Weather Service reported a new record low temperature of -19 in Des Moines on Wednesday morning. Kelsey Kremer/The Register
Steam rises into the air off of a building in downtown Des Moines on Wednesday, Jan. 30, 2019. The National Weather Service reported a new record low temperature of -19 in Des Moines on Wednesday morning. Kelsey Kremer/The Register
Read or Share this story: https://www.desmoinesregister.com/story/news/local/indianola/2019/01/30/polar-vortex-indianola-police-try-stay-warm-dangerous-cold-temperatures-in-iowa-weather/2726124002/
Joe Biden: I won't make a deal to require Senate testimony
Sanders, Biden accuse each other of going negative
Former Ames business owner faces fraud, tax evasion charges | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 590 |
\section{Introduction}
\IEEEPARstart{N}{onlinear} system identification is now a mature field. For the last three decades,
much attention has been paid to the problem of building nonlinear models from data
\cite{isermann2010identification,billings2013nonlinear,nelles2013nonlinear,schoukens2019}.
A natural next step is the use of such identified models in more specific applications, such as
compensation and control, which is the aim of this work.
The presence of nonlinear effects can impose significant performance limitations in a wide range of
applications, such as actuators \cite{Rakotondrabe2011,li2018position}, sensors \cite{cao2018temperature},
pH neutralization \cite{hong1996control}, and power systems \cite{singh2007neural}, among others
\cite{chernous2008control,morris2012,castillo2012soft}. A natural solution would be to mitigate such
effects by making the systems more linear -- by using a compensator -- and, consequently, more amenable to control.
A dynamical model with simple structure is quite useful to design a compensator.
Compensation approaches aim to design a compensation input that reduces nonlinearity
allowing for more accurate control and tracking. Many of these approaches start with an
appropriate model that represents the most fundamental aspects of the system, especially the static
nonlinearity \cite{agu_eal/02iee}. In the literature, there
is a vast number of works devoted to the modeling and compensation for nonlinear systems ranging from those based
on phenomenological models \cite{Rakotondrabe2011,Lin_etal2013, liu2011intrachannel} to those that use
computational intelligence \cite{Quaranta_etal2020} such as Radial Basis Functions (RBFs)
\cite{cao2018temperature,zhou2020dynamic,li2018position} and Neural Networks (NNs) \cite{singh2007neural,zhang2010neural,guo2018composite,meng2020neural},
among others.
The identification of phenomenological models tends to be a challenging task that requires sophisticated
algorithms based often on heuristics techniques. Therefore, satisfactory results depend largely on the proper design
of these algorithms, including the tuning of meta-parameters, which is usually an empiric task \cite{Quaranta_etal2020}.
In addition, the achievement of compensators for such models is not usually simple or even possible, because it depends
on the analytical inversion of these models. For methods based on universal approximation of functions, such as RBFs and NNs,
it is more difficult to provide a physics-based interpretation \cite{Quaranta_etal2020}. A particular type of neural network
that has been often used in the literature for identification and compensation of nonlinear systems is the Nonlinear
AutoRegressive with eXogenous inputs Neural Networks, i.e., NARX NNs \cite{zhang2010neural,meng2020neural}.
Despite the benefits of NARX NNs due to the fair generality presented by NARX structures, these frameworks are
based on a black-box philosophy that complicates the use of constraints related to the structure or parameters,
which can be elegantly accommodated in gray-box approaches \cite{Abreu_etal2020}. Also, their compensators present low or no degree of interpretability which limits the analysis of these types of models and their compensators.
An alternative framework is based on NARX polynomial models, adopted in this paper. For this class of models,
if the structure is carefully chosen \cite{bil_eal/89,agu_bil/94b,pir_spi/03}, besides being quite general \cite{leo_bil/85a},
such models can encode nonlinear information in a simple and recognizable way \cite{agu_eal/02iee,Martins_Aguirre2016}, which
allows using them to derive explicitly compensation laws \cite{Abreu_etal2020}. In addition, NARX polynomials are amenable to
gray-box techniques \cite{Aguirre_2019} that allow the encoding relevant features from nonlinear systems, which is usually not
possible with purely black-box strategies. From now on, the term NARX models must be understood strictly as NARX polynomial
models, and form the basis of this work. Although these models can represent a variety of phenomena, few works
in the literature apply NARX polynomials for compensation since the most common applications take NARX NNs as a basis.
In the context of hysteresis compensation, \cite{Lacerda_etal2019} has presented a strategy based on an analytical
inversion of NARX models. For this purpose, somewhat restrictive assumptions must be satisfied by the model structure.
Also, as pointed out in \cite{Abreu_etal2020}, the
methodology developed by \cite{Lacerda_etal2019} may suffer from singularity problems when the velocity variable equals zero.
Two ways to design compensators have been presented in \cite{Abreu_etal2020}:
the first one is similar to what was done in \cite{Lacerda_etal2019} and the second seeks compensators directly
from the data. Both strategies have overcome the singularity problem because the restrictions on the models' structure prevent a division by the velocity variable in the compensator. However, as the former also needs to isolate
the input explicitly, such a method uses with more specific structures than those used in the present paper.
The second strategy requires careful data processing, such as filtering the output signals. Also, some algebraic
tricks are required to overcome potential causality problems \cite{Abreu_etal2020}.
The main contributions of this work are the proposed approaches to find compensation inputs iteratively for nonlinear
systems in static and dynamical contexts through identified NARX models. Besides, an adaptation of the dynamical strategy
is presented for hysteretic systems. In both strategies, an algebraic polynomial of the compensation input is formulated,
which is achieved by manipulating the identified model. Thus, the compensation input signal is calculated iteratively,
which confers an adaptive feature to the approaches. The proposed compensators are compared with one well-established
\cite{Rakotondrabe2011} and two recent \cite{Abreu_etal2020} ones. The comparison is not performed with \cite{Lacerda_etal2019} due to the similarity with the first method of \cite{Abreu_etal2020}.
This work is organized as follows. In Section~\ref{back} background is provided. The statement of the compensation problem is
introduced in Sec.~\ref{sp}. Section \ref{Methodology} presents the compensation strategy proposed and formulated for static
(\ref{sub_comp_stat}), dynamical (\ref{sub_comp_dyn}) and adapted specifically for hysteresis (\ref{sub_comp_hys}) contexts. Numerical and experimental results are discussed in Sec.~\ref{NumericalExamples}. Finally, concluding remarks are given in Sec.~\ref{Conclusion}.
\vspace{-0.4cm}
\section{Background}\label{back}
A NARX (Nonlinear Autoregressive model with eXogenous inputs) polynomial model
${\cal M}$ for a single-input single-output system is given by \cite{leo_bil/85a}:
\begin{eqnarray}
\label{eq_model}
y(k) {=} f^\ell\big(y(k{-}1), \ldots ,y(k{-}n_y),u(k{-}\tau_{\rm d}), \ldots ,u(k{-}n_u)\big) \nonumber \\
{+}e(k),
\end{eqnarray}
\noindent
where $u(k),\,y(k) \in \mathbb{R}$ are respectively the input and output signals sampled at instant
$k \in \mathbb{N}$, and $f^\ell(\cdot)$ is a nonlinear polynomial function with degree
$\ell \in \mathbb{N}^+$. $n_u,\,n_y \in \mathbb{N}^+$ are the maximum lags for $u$ and $y$,
respectively, $\tau_{\rm d} \in \mathbb{N}^+$ is the pure time delay, and $e(k)$ accounts for the
uncertainties and possible noise.
Model (\ref{eq_model}) is a parsimonious polynomial model in the sense that it contains
only a small group of regressors chosen from an usually large set of candidate regressors
by means of some structure selection procedure \cite{bil_eal/89,agu_bil/94b,pir_spi/03,fal_eal/15,ret_agu/19}.
Each regressor of ${\cal M}$, which can be any linear and nonlinear combination up to degree
$\ell$, is multiplied by a constant parameter, indicated by $\theta_i$. Hence,
a NARX polynomial model is linear-in-the-parameters and classic least squares (LS) procedures
can be used \cite{Norton_1986}. In the presence of noise, however, it is common to add moving average (MA)
terms to the model, which will no longer be linear-in-the-parameters. Fortunately, extended least
squares estimators (ELS) can be used to circumvent noise-induced bias \cite{Ljung_1987,bil_eal/89}.
\subsection{Steady-state analysis}\label{sub_steady_state_analysis}
The steady-state relation of model (\ref{eq_model}) is obtained by taking
$u(k)=\bar{u}$ and $y(k)=\bar{y}, ~\forall k$, thus yielding:
\begin{equation}
\bar{\cal M}: ~ \bar{y} = \bar{f}^{\ell}(\bar{u},\bar{y}),
\nonumber
\end{equation}
\noindent
which, {\it for a known value of $\bar{u}$}, can be rewritten as:
\begin{equation}
\label{eq_model_stat}
c_{y,\,\ell_y}(\bar{u})\bar{y}^{\ell_y}+c_{y,\,\ell_y{-}1}(\bar{u})\bar{y}^{\ell_y{-}1}+\ldots+c_{y,1}(\bar{u})\bar{y}+ c_{y,0}(\bar{u}) = 0,
\end{equation}
\noindent
where $1 \leq \ell_y \leq \ell$ is the degree of the static model $\bar{\cal M}$, whose coefficients
$c_{y,i},~i=0,\ldots,\ell_y$ usually depend on $\bar{u}$. Solving (\ref{eq_model_stat}) for the unknown
$\bar{y}$ is achieved by finding the $\ell_y$ roots of this polynomial. The roots of (\ref{eq_model_stat})
will yield the fixed points of model (\ref{eq_model}) for $\bar{u}$, whose definition is presented below.
\begin{defin}{\rm(Fixed points \cite{Aguirre_Mendes1996})}.
\label{Definition:Fixed_Points}
The steady-state analysis of model (\ref{eq_model}) is computed by taking $y(k){=}\bar{y},\,\forall k$
and $u(k){=}\bar{u},\,\forall k$, yielding $\bar{y} = \bar{f}^{\ell}(\bar{y},\bar{u})$, whose
solution/root(s) $\bar{y}$ (\ref{eq_model_stat}) for a given constant value of input $\bar{u}$
is defined as the fixed point(s), or equilibria, of model (\ref{eq_model}) for $\bar{u}$.
\end{defin}
The condition for (local) stability of the fixed points is obtained by finding the eigenvalues
of the Jacobian matrix of model $\cal M$ (\ref{eq_model}) evaluated at each fixed point, as follows:
\begin{equation}
\label{eq_stab_fix_point}
\bigg|{\rm{eig}} \left(\frac{\partial f^{\ell}}{\partial \bm{y}} \Big|_{\bar{u},\bar{y}} \right) \bigg| < 1,
\end{equation}
\noindent
where $\bm{y}=[y(k-1)\, \ldots y(k-n_y)]^T$, $T$ is the transpose and ${\rm eig}(\cdot)$ indicates the
eigenvalues.
\begin{example}\label{ex_1}
Consider model ${\cal M}$ given by:
%
\begin{eqnarray}
\label{Eq:Example_Model_Stat}
y(k) & {=} & \hat{\theta}_1y(k-1)+\hat{\theta}_2u(k-1)+\hat{\theta}_3u(k-1)u(k-2) \nonumber \\
& {~} & +\hat{\theta}_4u(k-1)^2+\hat{\theta}_5u(k-1)^3,
\end{eqnarray}
\noindent
for which $\tau_{\rm d} {=} 1$, $n_y{=}1$, $n_u{=}2$, and $\ell{=}3$. Its static form $\bar{\cal M}$ is obtained taking
$u(k-1){=}u(k-2){=}\bar{u}$ and $y(k-1){=}y(k){=}\bar{y}$, such that:
%
\begin{equation}\label{eq_model_ss}
\bar{y} = \hat{\theta}_1\bar{y} +\hat{\theta}_2 \bar{u}+\hat{\theta}_3\bar{u}^2 +\hat{\theta}_4\bar{u}^2+\hat{\theta}_5\bar{u}^3,
\end{equation}
\noindent
which can be written in the format of (\ref{eq_model_stat}) as:
%
\begin{equation}
0 = \underbrace{\big[\hat{\theta}_1-1\big]}_{c_{y,1}}\bar{y} + \underbrace{\hat{\theta}_5\bar{u}^3 +\big[\hat{\theta}_3+\hat{\theta}_4\big]\bar{u}^2 + \hat{\theta}_2 \bar{u}}_{c_{y,0}(\bar{u})}.
\end{equation}
\noindent
Hence, model (\ref{Eq:Example_Model_Stat}) only has one fixed point for each value of $\bar{u}$, given by:
%
\begin{equation}
\label{fp1}
\bar{y} = -\dfrac{c_{y,0}(\bar{u})}{c_{y,1}} = \dfrac{\hat{\theta}_5\bar{u}^3+\big[\hat{\theta}_3+\hat{\theta}_4\big]\bar{u}^2+\hat{\theta}_2\bar{u}}{1-\hat{\theta}_1}.
\end{equation}
\noindent
For the first-order model (\ref{Eq:Example_Model_Stat}),
the Jacobian ``matrix'' will be a scalar and condition (\ref{eq_stab_fix_point})
becomes:
%
\begin{eqnarray}
\label{Eq:example1}
\left| \frac{\partial f^{\ell}}{\partial y(k-1)} \Big|_{\bar{u},\bar{y}} \right| & < & 1, \nonumber \\
\left|\hat{\theta}_1 \Big|_{\bar{u},\bar{y}} \right| & < & 1, \nonumber \\
-1 ~<~ \hat{\theta}_1 & < & 1.
\end{eqnarray}
\noindent
Therefore, if (\ref{Eq:example1}) is satisfied, then (\ref{fp1}) is a stable fixed point.
\flushright{$\square$}
\end{example}
\section{Statement of the Problem}
\label{sp}
It is assumed that a NARX model $\cal{M}$ (\ref{eq_model}) is available for a
given nonlinear dynamical system $\cal{S}$, estimated
from input-output data $Z^N=\{u(k),\,y_{\rm s}(k)\}_{k=1}^N$ collected from $\cal{S}$.
Based on ${\cal M}$, the aim is to design a compensator ${\cal M}_r$ such that
the open-loop combination of ${\cal M}_r$ followed by
$\cal{S}$ (see Fig.\,\ref{block_diagram}) is more linear and therefore more amenable
for control. Specifically, ${\cal M}_r$ should compensate the nonlinearity in $\cal{S}$.
\begin{figure}[h
\centering{
\centering
\includegraphics[width=1\columnwidth]{fig_1.pdf}
\vspace{-0.8cm}
\caption{Block diagram of the compensated system.}
\label{block_diagram}
}
\end{figure}
Mathematically, we require that the reference $r(k)$ and output $y_{\rm c}(k)$ of the
compensated system should be closer than the input $u(k)$ and output $y_{\rm s}(k)$
of the uncompensated system. Hence $J[r(k),\,y_{\rm c}(k)]<J[u(k),\,y_{\rm s}(k)]$,
where $J$ is some proximity cost function, like the mean squared value.
\section{Methodology}
\label{Methodology}
This section presents the methodology developed to design compensators based on
NARX polynomial models. First, in Sec.\,\ref{sub_comp_stat}, we present the static
compensation that is simpler to understand and serves as a basis for the main result,
which is the dynamical compensation detailed in Sec.\,\ref{sub_comp_dyn}. In the sequel,
this approach is applied to systems with hysteresis in Sec.\,\ref{sub_comp_hys}.
The identification of model ${\cal M}$ is not described in this paper. The interested
reader is referred to \cite{Aguirre_2019}, and references therein.
\subsection{Static Compensation}
\label{sub_comp_stat}
It is assumed that the input and output signals are bounded, thus
$u(k) \in [u_{\rm min},\, u_{\rm max}], \forall k$ and $y_{\rm s}(k) \in [y_{{\rm min}},\, y_{{\rm max}}], \forall k$.
As for model $\cal{M}$(\ref{eq_model}), the following assumptions will be needed:
\begin{assump}
\label{Assump1}
$\cal{M}$ is valid, that is, $y(k) \approx y_{\rm s}(k)$ for the same input.
\end{assump}
\begin{assump}
\label{Assump2}
For any $\bar{u} \in [u_{\rm min},u_{\rm max}]$, the model
${\cal M}$ has at least one local stable fixed point such that
$\bar{y} \in [y_{\rm min}, y_{\rm max}]$.
\end{assump}
In order to obtain a static compensator $\bar{\cal M}_r$, an {\it inverse problem} in steady-state has to be solved.
In other words, we seek the system input values $\bar{m}$ that will drive the output to the reference at steady-state,
$\bar{y} \approx \bar{r}$. Considering the model $\cal{M}$ expressed as $\bar{y} = \bar{f}^{\ell}(\bar{u},\bar{y})$,
$\bar{y}$ is replaced by $\bar{r}$ and $\bar{u}$ by $\bar{m}$ so that $\bar{\cal M}_r$ is $\bar{r} = \bar{f}^{\ell}(\bar{m},\bar{r})$.
Consequently, it is possible to rewrite (\ref{eq_model_stat}) by grouping its terms in such a way that it yields a
polynomial in the unknown variable $\bar{m}$, $\cal {\bar M}_{\rm r}$:
\begin{eqnarray}
\label{eq_comp_stat}
c_{m,\,\ell_m}({\bar{r}}){\bar{m}}^{\ell_m} {+} c_{m,\,\ell_m{-}1}({\bar{r}}){\bar{m}}^{\ell_m{-}1}{+} \ldots{+}c_{m,\,1}({\bar{r}})\bar{m}\nonumber \\
{+} c_{m,\,0}({\bar{r}}) {=} 0.
\end{eqnarray}
Although each of the $\ell_m$ roots of (\ref{eq_comp_stat}) is a solution to the inverse problem,
not all are appropriate to be used in practice. For this reason, two constraints are considered. The used root:
\begin{cons}
\label{c1}
must be real, ${m} \in \mathbb{R}$; and
\end{cons}
\begin{cons}
\label{c2}
must be within the data range, namely ${m} \in [u_{\rm min},\, u_{\rm max}]$.
\end{cons}
Assumption\,\ref{Assump2} ensures that any root $\bar{m}$ (\ref{eq_comp_stat}) that satisfies the above
constrains will drive the system to a stable fixed point.
Also, because of Assumption~\ref{Assump1}, such a steady-state will satisfy $\bar{y}_{\rm c} \approx {\bar{r}}$.
The algebraic procedure is illustrated below with a simple example. Then, in the sequel, a dynamical version of
this procedure will be discussed in Sec.\,\ref{sub_comp_dyn}.
\begin{example}\label{ex_3}
For the model in Example\,\ref{ex_1}, it was seen that:
%
\begin{equation*}
\bar{y} = \hat{\theta}_1\bar{y} +\hat{\theta}_2 \bar{u}+\hat{\theta}_3\bar{u}^2 +\hat{\theta}_4\bar{u}^2+\hat{\theta}_5\bar{u}^3,
\end{equation*}
\noindent
which can be written in the format of (\ref{eq_comp_stat}) as:
\begin{eqnarray}
\label{pol_ex3}
\!\!\!\!\!\!\bar{r} & {=} & \hat{\theta}_1\bar{r} +\hat{\theta}_2 \bar{m}+\hat{\theta}_3\bar{m}^2 +\hat{\theta}_4\bar{m}^2+\hat{\theta}_5\bar{m}^3, \nonumber \\
\!\!\!\!\!\!0 & {=} & \underbrace{\hat{\theta}_5}_{c_{m,3}}\bar{m}^3 +\underbrace{\big[\hat{\theta}_3+\hat{\theta}_4\big]}_{c_{m,2}}\bar{m}^2 + \underbrace{\hat{\theta}_2}_{c_{m,1}}\bar{m} +\underbrace{\big[\hat{\theta}_1\bar{r}-\bar{r}\big]}_{c_{m,0}(\bar{r})}.
\end{eqnarray}
\noindent
Hence, for a given reference value $\bar{r}$, the roots of (\ref{pol_ex3}) provide potential
compensation inputs that in steady-state would drive the system to the target. A practical problem
is to decide which of the three roots in this example should be used. If there is only one real root,
then it is chosen as the compensation input. However, if there are three real roots, a more general
decision-making process is required. \hfill $\square$
\end{example}
For the sake of clarity, the roots of \eqref{eq_comp_stat} will be placed in a
vector $\bm{\bar{m}}(\bar{r}) \triangleq [\bar{m}_{1}~\cdots~\bar{m}_{\ell_m}]^T$.
Although the $\ell_m$ values of $\bar{m}$ are solutions to the
inverse problem, only those that satisfy C\ref{c1} and C\ref{c2} should be considered as potential
compensation inputs. This reasoning underlies the main algorithm that will be used in the dynamical
context. The practical issue of {\it how}\, to choose from two potential inputs that satisfy
C\ref{c1} and C\ref{c2} will be discussed in the dynamical setting below.
\subsection{Dynamical Compensation}
\label{sub_comp_dyn}
The main difference between the framework developed in this subsection and the basis laid down
in the previous one is that here the reference is a sequence of values $r(k)$, and not a
constant value $\bar{r}$. The same is true for the compensation input $m(k)$ and the compensated
output $y_{\rm c}(k)$.
The aim now is to achieve $y(k) \approx r(k)$ by solving
an inverse problem dynamically. Replacing variables as in Sec.\,\ref{sub_comp_stat} and
omitting the noise term, (\ref{eq_model}) can be written as:
\begin{equation}
r(k) {=} f^\ell\big(r(k-1), \ldots , r(k-n_y), m(k-\tau_{\rm d}), \ldots , m(k-n_u)\big). \nonumber
\end{equation}
As will become clear, it is convenient to introduce the time-shift $k \leftarrow k+\tau_{\rm d}$ --
meaning that $k$ will be replaced with $k+\tau_{\rm d}$ --
hence the last equation becomes:
\begin{eqnarray}
\label{eq_compensator_1}
r(k{+}\tau_{\rm d}) &{=}& f^\ell\big(r(k{+}\tau_{\rm d}{-}1),\ldots,r(k{+}\tau_{\rm d}{-}n_y), \nonumber \\
&~& \hspace{1.4cm} m(k),\ldots, m(k{+}\tau_{\rm d}{-}n_u)\big).
\end{eqnarray}
The aim is to find $m(k)$ that will drive the system to the desired target $r(k)$.
Consequently, as before, (\ref{eq_compensator_1}) will be expressed in terms of a
polynomial in the unknown $m(k)$ as:
\begin{eqnarray}
\label{eq_compensator_2}
0 {=} c_{{\ell_m}}(k)m(k)^{\ell_{m}} {+} c_{{\ell_m{-}1}}(k)m(k)^{\ell_m{-}1} +\ldots \!\!&\!\!+\!\!&\!\! c_{1}(k)m(k) \nonumber \\
\!\!&\!\!+\!\!&\!\! c_{0}(k),
\end{eqnarray}
\noindent
where the time-varying coefficients $c_{j}(k)$, $j = 0,\ldots,\ell_m$, can depend on past values of $m$ up to time $k-1$,
and on past and future values of $r$ up to time $k+\tau_{\rm d}$. Hence, the following additional assumption
is required in the dynamical case.
\begin{assump}
\label{Assump3}
The reference signal must be known up to time $k+\tau_{\rm d}$.
\end{assump}
The following example illustrates this procedure.
\begin{example}
\label{example4}
Consider the same model used in Example\,\ref{ex_1}, replacing $y(k)$ with $r(k)$ and $u(k)$ with $m(k)$, yields:
%
\begin{eqnarray}
r(k) & {=} & \hat{\theta}_1r(k-1)+\hat{\theta}_2m(k-1)+\hat{\theta}_3m(k-1)m(k-2) \nonumber \\
& {~} & + \hat{\theta}_4m(k-1)^2+\hat{\theta}_5m(k-1)^3, \nonumber
\end{eqnarray}
\noindent
for which $\tau_{\rm d}=1$. Next, taking the time-shift $k \leftarrow k+1$, the last equation
can be expressed in the form of (\ref{eq_compensator_2}):
%
\begin{eqnarray}
\label{mr1}
\!\!\!\!\!\!0 &{=}& \hat{\theta}_5m(k)^3{+}\hat{\theta}_4m(k)^2{+}\big[\hat{\theta}_2{+}\hat{\theta}_3m(k{-}1)\big]m(k)\nonumber \\
\!\!\!\!\!\!&{~}&{+}[\hat{\theta}_1r(k){-}r(k{+}1)], \nonumber \\
\!\!\!\!\!\!0 &{=}& c_{3}(k)m(k)^3{+}c_{2}(k)m(k)^2{+}c_{1}(k)m(k)+c_{0}(k),
\end{eqnarray}
\noindent
where all the values of $r$ are known (see Assumption\,\ref{Assump3}) and also all past values of $m$.
Hence, at each time step $k$ the solutions to (\ref{mr1}), that is, the three values of $m(k)$ are the potential
compensation inputs. \hfill
$\square$
\end{example}
In what follows, some important recommendations on initialization and the decision-making process adopted
to choose the root to be used as compensation input are stated.
\begin{remark}(Initial compensator conditions).
\label{Rem1}
From Assumption~\ref{Assump3}, $r(k+\tau_{\rm d})$ is known in compensator (\ref{eq_compensator_2}). Call that
value $\bar{r}$. Using the calibration curve of ${\cal S}$ or the static nonlinearity of ${\cal M}$, find the
respective $\bar{m}$ and take $m(j)=\bar{m},~j=k-1,\ldots,k{+}\tau_{\rm d}{-}n_u$. If the calibration curve is
not available, this value can be obtained through the static nonlinearity of model ${\cal M}$ or by solving the
static compensator $\bar{{\cal M}}_r$ (\ref{eq_comp_stat}), $\bar{r}{=}\bar{f}^{\ell}(\bar{m},\bar{r})$, for
$\bar{m}$. If there is more than one solution
to $\bar{r} = \bar{f}^{\ell}(\bar{m},\bar{r})$ use the one that: i)~stabilizes the model output and ii)~satisfies
constraints C\ref{c1} and C\ref{c2}. Items i) and ii) are automatically taken into account by using the calibration
curve or static nonlinearity. \hfill $\square$
\end{remark}
\begin{remark}(The decision-making process).
\label{Rem2}
Let $\bm{m}_k \triangleq [m_{1}^k~\cdots~m_{\ell_m}^k]^T$ be the set of roots of (\ref{eq_compensator_2}).
If only one element of $\bm{m}_k$
satisfies C\ref{c1} and C\ref{c2} , then this will be the compensation input at
time $k$, otherwise we choose the appropriate root according to:
%
\begin{alignat}{1}
\label{c3}
m(k)=\underset{m_j^k,~\forall j\in \{1,\ldots,\ell_m\}}{\arg\min} & \Big(|m_j^k-m(k-1)|\Big) . \\
\text{subject to:} ~C\ref{c1},\,C\ref{c2}\nonumber
\end{alignat}
\noindent
The use of (\ref{c3}) selects the solution that is closest to the
compensation value used in the previous time step. This simple criterion results in smoother signals $m(k)$
and, consequently, in less compensation effort \cite{Abreu_etal2020}. \hfill $\square$
\end{remark}
If $\ell_m$ is even and composed only of complex conjugate values, then take $m(k){=}m(k-1)$.
This situation is not common for models that satisfy Assumption\,\ref{Assump1}.
Algorithm\,\ref{sel_root} summarizes the method to select the appropriate root.
\begin{algorithm}
\label{sel_root}
\SetAlgoLined\SetArgSty{}
\KwIn{$m(k-1); \quad \bm{m}_k \triangleq [m_{1}^k~\cdots~m_{\ell_m}^k]^T$}
$v \leftarrow \infty$ \\
$a \leftarrow 0$ \\
\For{$j=1$ \KwTo $\ell_m$}{
\If{$m_j^k \in \mathbb{R}$ (C1) \textbf{and} $ u_{\min} \leq m_j^k \leq u_{\max}$ (C2)}
{
$e \leftarrow |m_j^k-m(k-1)|$\\
\If{$e < v$}
{
$v \leftarrow e$\\
$a \leftarrow 1$\\
$m(k) \leftarrow m_j^k$\\
}
}
}
\If{$a = 0$}
{
$m(k) \leftarrow m(k-1)$
}
\KwOut{$m(k)$}
\caption{Selecting the Appropriate Solution for \eqref{eq_compensator_2}}
\end{algorithm}
\vspace{-0.3cm}
\subsection{Compensation for Systems with Hysteresis}
\label{sub_comp_hys}
The inclusion of the first difference of the input $u(k)$ and the corresponding
sign function as regressors is a sufficient condition for NARX models to mimic
hysteresis loop \cite{Martins_Aguirre2016}. A general NARX model set
\cite{bil_che/89} extended with these regressors
will be referred to as ${\cal{M}}_{\rm h}$:
\begin{eqnarray}
\label{m_narx_hys}
\!\!\!\!\!y(k) &{=}& g^{\ell}\big(y({k-1}),\cdots,y(k-n_{y}), \,u(k-\tau_{\rm d}),\cdots, \nonumber \\
&{~}& \hspace{3mm} u(k-n_u), \phi_{1}(k-1), \,\phi_{2}(k-1) \big) +e(k),
\end{eqnarray}
\noindent
where $\phi_{1}(k){=}u(k){-}u(k{-}1)$, $\phi_{2}(k) {=} {\rm sign}(\phi_{1}(k))$, $g^{\ell}(\cdot)$
is a polynomial function of the regressor variables up to degree $\ell$, and the other parameters are
the same as defined in \eqref{eq_model}. For models such as \eqref{m_narx_hys}, there are two sets of
equilibria for the deterministic part (omitting the noise) under loading-unloading inputs: one for
loading with $\phi_{2}(k){=}1$, and one for unloading with $\phi_{2}(k){=}{-}1$ \cite{Abreu_etal2020}. A constrained approach is proposed and detailed by \cite{Abreu_etal2020} to ensure that the model can describe the dynamic behaviour and also features in steady-state.
Therefore, to deal specifically with hysteresis compensation, the general compensation method proposed
in Sec.\,\ref{sub_comp_dyn} will be adapted. Considering non-constant inputs, the following simplification
will be used:
\begin{eqnarray}
\label{eq_product_simp}
\phi_1(k-1)\phi_2(k-1) & = & \phi_1(k-1)\dfrac{|\phi_1(k-1)|}{\phi_1(k-1)}, \nonumber \\
& = & |u(k-1)-u(k-2)|,
\end{eqnarray}
\noindent
for $u(k-1) \neq u(k-2)$.
The compensator is developed following the {\it steps} below:
\begin{enumerate}
\item Rewrite ${\cal M}_{\rm h}$ as:\label{step_1}
%
\begin{eqnarray}
\label{mr_hys_gen_1}
0 &{=}& g^{\ell}\big(y({k-1}),\cdots,y(k-n_{y}), \,u(k-\tau_{\rm d}),\cdots, \nonumber \\
&{~}& u(k\!-\!n_u),\phi_{1}(k\!-\!1), \,\phi_{2}(k\!-\!1) \big) - y(k);
\end{eqnarray}
\item if $\phi_1(k-1)\phi_2(k-1)$ appears in any regressor of \eqref{mr_hys_gen_1}, use the result in \eqref{eq_product_simp}; \label{step_2}
\item if $\phi_1(k\!-\!1)$ and $\phi_2(k\!-\!1)$ still appear, replace them with $u(k\!-\!1)\!-\!u(k\!-\!2)$ and
$|u(k\!-\!1)\!-\!u(k-2)|/[u(k\!-\!1)\!-\!u(k-2)]$, respectively; \label{step_3}
\item if $[u(k-1)-u(k-2)]$ appears in any denominator, multiply the equation by $[u(k-1)-u(k-2)]$; \label{step_4}
\item replace $y(k)$ with $r(k)$, $u(k)$ with $m(k)$, perform the time shift $k \leftarrow k + \tau_{\rm d}$, and
rewrite this equation like (\ref{eq_compensator_2}); \label{step_5}
\item split the equation with $|\cdot|$ into two polynomials in $m(k)$: \label{step_6}
%
\begin{eqnarray}
\label{mr_hys_load}
0&{=}& c_{\ell_m}^{\rm L}(k)m(k)^{\ell_m}+c_{\ell_m-1}^{\rm L}(k)m(k)^{\ell_m-1}\nonumber \\
&{~}&+\ldots+c_{1}^{\rm L}(k)m(k)+ c_{0}^{\rm L}(k) \\
&{~}& \text{for} \quad m(k)>m(k-1), \nonumber
\end{eqnarray}
%
\begin{eqnarray}
\label{mr_hys_unload}
0 &{=}& c_{\ell_m}^{\rm U}(k)m(k)^{\ell_m}+c_{\ell_m-1}^{\rm U}(k)m(k)^{\ell_m-1}\nonumber \\
&{~}&+\ldots+c_{1}^{\rm U}(k)m(k)+ c_{0}^{\rm U}(k) \\
&{~}& \text{for} \quad m(k)<m(k-1), \nonumber
\end{eqnarray}
\end{enumerate}
\noindent
where the superscripts $\rm L$ and $\rm U$ refer to loading and unloading regimes, respectively.
Note that, as we are now dealing with a hysteretic system, (\ref{eq_compensator_2}) has two
counterparts: one for loading (\ref{mr_hys_load}), and one for unloading (\ref{mr_hys_unload}).
In this case, the compensation input $m(k)$ will be a feasible root of (\ref{mr_hys_load}) or (\ref{mr_hys_unload}).
Before detailing the decision-making process to compensate for such systems, the previous steps will be illustrated
below.
\begin{example}
\label{example5}
Suppose that the model ${\cal M}_{\rm h}$ is:
%
\begin{eqnarray}
\label{m_hys_1}
y(k) \!\!\!&\!\!\! = \!\!\!&\!\!\! \hat{\theta}_1y(k\!-\!1)\!+\! \hat{\theta}_2u(k\!-\!1)^3
\!+\! \hat{\theta}_3\phi_1(k\!-\!1)\phi_2(k\!-\!1)u(k\!-\!1) \nonumber \\ & & +\hat{\theta}_4\phi_1(k-1)\phi_2(k-1)y(k-1).
\end{eqnarray}
\noindent
Following steps\,\ref{step_1} and \ref{step_2}, \eqref{m_hys_1} is rewritten as:
%
\begin{eqnarray}
\label{m_hys_ex1}
0 \!\!\!&\!\!\! = \!\!\!&\!\!\! \hat{\theta}_1y(k\!-\!1)\!+\! \hat{\theta}_2u(k\!-\!1)^3
\!+\! \hat{\theta}_3|u(k\!-\!1)-u(k\!-\!2)|u(k\!-\!1) \nonumber \\ & & +\hat{\theta}_4|u(k\!-\!1)-u(k\!-\!2)|y(k-1) - y(k).
\end{eqnarray}
\noindent
In this model, steps\,\ref{step_3} and \ref{step_4} do not apply. By means of step\,\ref{step_5},
we get the following equation (remember that $\tau_{\rm d}=1$):
\begin{eqnarray}
\label{m_hys_ex2}
0 \!\!\!&\!\!\! = \!\!\!&\!\!\! \hat{\theta}_1r(k)\!+\! \hat{\theta}_2m(k)^3
\!+\! \hat{\theta}_3|m(k)-m(k\!-\!1)|m(k) \nonumber \\ & & +\hat{\theta}_4|m(k)-m(k\!-\!1)|r(k) - r(k+1),
\end{eqnarray}
\noindent
which can be split into two polynomials (step\,\ref{step_6}) as:
%
\begin{eqnarray}
0 & = & \hat{\theta}_2m(k)^3 + \hat{\theta}_3m(k)^2+ \nonumber \\
&~&[-\hat{\theta}_3m(k-1)+\hat{\theta}_4r(k)]m(k)+\nonumber \\
&~& [\hat{\theta}_1r(k)-\hat{\theta}_4m(k-1)r(k)-r(k+1)] \nonumber \\
&~& \text{for} \quad m(k)>m(k-1),
\label{mr_hys_load_ex}
\end{eqnarray}
%
\begin{eqnarray}
0 & = & \hat{\theta}_2m(k)^3 -\hat{\theta}_3m(k)^2+ \nonumber \\
&~&[\hat{\theta}_3m(k-1)-\hat{\theta}_4r(k)]m(k)+\nonumber \\
&~& [\hat{\theta}_1r(k)+\hat{\theta}_4m(k-1)r(k)-r(k+1)] \nonumber \\
&~& \text{for} \quad m(k)<m(k-1).
\label{mr_hys_unload_ex}
\end{eqnarray}
\noindent
Here, \eqref{mr_hys_load_ex} refers to loading regime similar to form \eqref{mr_hys_load} with
$c_{3}^{\rm L}(k) =\hat{\theta}_2$, $c_{2}^{\rm L}(k)=\hat{\theta}_3$,
$c_{1}^{\rm L}(k)=-\hat{\theta}_3m(k-1)+\hat{\theta}_4r(k)$, and
$c_{0}^{\rm L}(k)=\hat{\theta}_1r(k)-\hat{\theta}_4m(k-1)r(k)-r(k+1)$; while, in an analogous way,
\eqref{mr_hys_unload_ex} refers to unloading regime in form \eqref{mr_hys_unload} with coefficients
$c_{3}^{\rm U}(k) =\hat{\theta}_2$, $c_{2}^{\rm U}(k)=-\hat{\theta}_3$,
$c_{1}^{\rm U}(k)=\hat{\theta}_3m(k-1)-\hat{\theta}_4r(k)$, and
$c_{0}^{\rm U}(k)=\hat{\theta}_1r(k)+\hat{\theta}_4m(k-1)r(k)-r(k+1)$.
The polynomials \eqref{mr_hys_load_ex} and \eqref{mr_hys_unload_ex}, which are
valid for $k \geq 1$, can be initialized, at $k=0$, using an estimate of the hysteresis loop,
as will be illustrated in Example~\ref{example6}. \hfill $\square$
\end{example}
In addition to Assumption\,\ref{Assump3}, C\ref{c1} and C\ref{c2}, the following must also
be true for hysteretic systems:
\begin{cons}
$m(k)>m(k-1)$, if \eqref{mr_hys_load} is used at time $k$; {\rm OR}
\end{cons}
\begin{cons}
$m(k)<m(k-1)$, if \eqref{mr_hys_unload} is used at time $k$.
\end{cons}
Constraints C3 and C4 are needed to ensure that the root is consistent with the regime
for which it was calculated. Therefore, the decision-making process for hysteretic systems
is similar to that explained in Remark\,\ref{Rem2} with the addition of these new constraints.
Hence:
\begin{alignat}{1}
\label{c4}
m(k)=\underset{m_{j}^k,~\forall j\in \{1,\ldots,\ell_m\}}{\arg\min} & \Big(|m_{j}^k-m(k-1)|\Big), \\
\text{subject to:} ~C1,\,C2,\,Cq\nonumber
\end{alignat}
\noindent
where $q \in \{3,4\}$. The step-by-step procedure is analogous to Algorithm\,\ref{sel_root},
but now using \eqref{c4} instead of \eqref{c3}.
\subsection{Initialization of Compensators for Systems with Hysteresis}
\label{icsh}
If any parameter of compensators \eqref{mr_hys_load} and \eqref{mr_hys_unload} depends on
previous values of the compensation input $m(k)$, i.e. $\{m(k{-}1),\,\ldots,m(k{+}\tau_{\rm d}{-}n_u)\}$,
such values must be determined for initialization. In Sec.\,\ref{sub_comp_dyn}, we can use the
static curve to estimate these initial values, as described in Remark\,\ref{Rem1}. Here,
a hysteresis loop ${\cal H}$ behavior displayed on the input-output plane will be used.
In what follows, a procedure is described to obtain ${\cal H}$ for a given
model ${\cal M}_{\rm h}$ (\ref{m_narx_hys}).
Consider the following sinusoidal input signal with period $T = 1/f_{\rm min}$:
\begin{equation}
\label{eq_u_quasi_static}
\tilde{u}(k) = A \sin\left(2\pi f_{\rm min}k\right) + \tilde{u}_0,
\end{equation}
\noindent
where $f_{\rm min}=1/T$ is the lowest frequency of interest,
$\tilde{u}_0 {=} (u_{\rm min} {+} u_{\rm max})/2$ is the mean, and
$A = u_{\rm max} - \tilde{u}_0$ is the amplitude. Using $\tilde{u}(k)$ in the model \eqref{m_narx_hys},
after the transient, the resulting data set $\{\tilde{u}(k), \tilde{y}(k)\}^{N_e}_{k=N_i}$, where $N_i > T$ and $N_e = N_i + T$,
correspond to a hysteresis loop $\cal{H}$. The use of $\cal{H}$ to initialize the compensator is illustrated in the
next example.
\begin{example}
\label{example6}
Consider model\,(\ref{m_hys_1}) of Example\,\ref{example5}, whose parameter
values are $\hat{\theta}_1=0.8$, $\hat{\theta}_2=0.4$, $\hat{\theta}_3=0.2$, and
$\hat{\theta}_4 = 0.1$. In order to initialize the compensator, at $k=0$, $m(-1)$
is needed in \eqref{mr_hys_load_ex} and \eqref{mr_hys_unload_ex}. For this purpose,
suppose that the excitation input signal $\tilde{u}$ \eqref{eq_u_quasi_static}
is defined with $A = 1$, $f_{\rm min} = 1 \text{ } {\rm Hz}$, and $\tilde{u}_0 = 1$ for
which the resulting $\cal{H}$ is shown in Fig.\,\ref{fig_ini_hys_ex}.
\begin{figure}[!h]
\centering
\includegraphics[width=0.8\columnwidth]{fig_2.pdf}
\vspace{-0.3cm}
\caption{Loop $\cal H$ is obtained from the simulation of model \eqref{m_hys_1} with
the input described in Example\,\ref{example6}. Blue dots (\textcolor{blue}{$\vdot$}) refer to loading regime,
while those in red (\textcolor{red}{$\vdot$}) refer to unloading. For a given output or reference,
say $r(1)$, there are two possible inputs indicated by triangles (\textcolor{blue}{$\blacktriangle$})
blue and red (\textcolor{red}{$\blacktriangle$}) that correspond to $m_{\rm L}(0)$ and $m_{\rm U}(0)$,
respectively. Which of these to use to start computing the compensator is determined by the regime at initialization time.}
\label{fig_ini_hys_ex}
\end{figure}
From Assumption\,\ref{Assump3}, we have that the reference is known up to time $r(k{+}1)$.
Suppose that $r(1)=2$ and that $\tilde{y}=r(1)$, there are two possible values for the input $\tilde{u}$,
namely of, $ m_{\rm L}(0)$ and $m_{\rm U}(0)$, which can be obtained from $\cal{H}$ (Fig.\,\ref{fig_ini_hys_ex}).
The selection between these values is made based on the current regime of the reference signal, i.e., loading $(r(1)-r(0)>0)$
or unloading $(r(1)-r(0)<0)$. In this example, at $k=0$, the reference is in the loading regime and, therefore, $m(0)=m_{\rm L}(0)$
is chosen to initialize equations \eqref{mr_hys_load_ex} and \eqref{mr_hys_unload_ex}. \hfill $\square$
\vspace{-0.3cm}
\end{example}
\section{Results}
\label{NumericalExamples}
This section illustrates the compensator design
proposed in Sec.\,\ref{Methodology} for two simulated benchmark systems and for a pilot plant starting from the identified models.
The input design and other identification procedures are detailed in \cite{Tavares_2020_arxiv}. To evaluate the performance of the compensation achieved, the static nonlinearity of the compensated and uncompensated systems are compared and their time
evolution is evaluated using
the mean absolute percentage error ({\rm MAPE}) index is computed as follows:
\begin{equation}
\label{Eq:MAPE}
{\rm{MAPE}} = \dfrac{\sum_{k=1}^{N}|y_s(k) - y(k)|}{N|{\max}({\bm y_s})-{\min}({\bm y_s})|}.
\end{equation}
\vspace{-0.1cm}
\subsection{A Heating System}
\label{sec_hs_sys}
The bench test system is a small electrical heater modeled by the following
Hammerstein model \cite{agu_eal/05iee}:
\begin{align}
\label{heat_sys_s}
y(k) = & \beta_1 y(k-1) + \beta_2 v(k-1) + \beta_3 y(k-2) + \beta_4 v(k-2), \nonumber \\
v(k) = & p_1 u(k)^2+ p_2 u(k),
\end{align}
\noindent
where $y(k)$ is the normalized temperature, and $u(k)$ is the electric power applied to the heater within the range
$ 0{ \leq} u(k) {\leq} 1$. The data set has been presented in \cite{agu_eal/02iee}, and is
available at \lucas{\textcolor{black}{\url{https://bit.ly/3iQ6rCF}}}.
The operation region of the model is $u(k) \in [0,~1]$ and $y(k) \in [0,~0.5]$. As described in \cite{Tavares_2020_arxiv}, the obtained parameters of (\ref{heat_sys_s}) are: $p_1 = 4.639331 \times 10^{-1}$, $p_2 = 5.435865 \times 10^{-2}$; while $\beta_1=1.205445$, $\beta_2 = 8.985133 \times 10^{-2}$, $\beta_3= -3.0877507 \times 10^{-1}$ and $\beta_4 = 9.462358 \times 10^{-3}$. From now on, the Hammerstein model (\ref{heat_sys_s}) will be treated as the system $\cal{S}$ to be compensated.
To compensate the nonlinearities in $\cal S$, the following three-term model $\cal M$ was obtained according to the procedure detailed in \cite{Tavares_2020_arxiv}:
\begin{equation}
\label{hs_model}
y(k) = \hat{\theta}_1y(k-1)+\hat{\theta}_2 u(k-2)^2 + \hat{\theta}_3y(k-2),
\end{equation}
\noindent
where $\hat{\theta}_1 = 8.958185 \times 10^{-1}$, $ \hat{\theta}_2 = 6.393347 \times 10^{-2}$, and
$\hat{\theta}_3 = -1.746750 \times 10^{-2}$. The validation results are shown in Table\,\ref{hs_tab_mape_model}, which indicate some degradation at higher frequencies and at points of
operation close to the origin.
\vspace{-0.2cm}
\begin{table}[htb]
\centering
\caption{${\rm MAPE}$ for model \eqref{hs_model} with sinusoidal inputs $u(k) = u_0 + 0.2 {\rm{sin}}(2\pi f k) $.
Free-run simulation was used.}
\setlength\tabcolsep{10pt}
\begin{tabular}{c | c c c}
\multirow{2}{*}{$f$ [Hz]}
& \multicolumn{3}{c}{$u_0$ [{\rm V}]} \\
& \textbf{$0.3$} & \textbf{$0.5$} & $0.7$ \\ \hline
0.0005 & 5.5\% & 3.0\% & 2.9\% \\
0.001 & 5.8\% & 2.9\% & 2.8\% \\
0.002 & 7.0\% & 4.0\% & 3.1\%
\label{hs_tab_mape_model}
\end{tabular}
\vspace{-0.1cm}
\end{table}
The static function of $\cal {M}$ (\ref{hs_model}) is:
\begin{equation}
\label{hs_m_stab}
\bar{y} = \dfrac{\hat{\theta}_2 \bar{u}^2}{1-\hat{\theta}_1-\hat{\theta}_3},
\end{equation}
\noindent
from where it is seen that for each value of the input, there is only one fixed point.
Because $\cal {M}$ is second-order, there are two eigenvalues at each fixed point $\bar{y}$.
The Jacobian matrix in this case does not depend on $\bar{u}$ or $\bar{y}$.
Using (\ref{eq_stab_fix_point}) the condition for stability is:
\begin{equation}
\begin{matrix}
\left| \rm{eig} \left(
\begin{bmatrix} 0 & 1 \\ \theta_3 & \theta_1 \end{bmatrix}
\right)
\right|< 1,
\end{matrix} \nonumber
\end{equation}
\noindent
where the eigenvalues of the Jacobian matrix are the algebraic solutions of
$\lambda^2-\theta_1\lambda-\theta_3 = 0$, which yields $|\lambda_1| = 0.8759$
and $|\lambda_2| = 0.0199$. Therefore, the fixed point for each input value is stable and, consequently, Assumption \ref{Assump2} is satisfied.
To illustrate the static compensation method presented in Sec.\,\ref{sub_comp_stat},
$\bar{y}$ is replaced with $\bar{r}$ and $\bar{u}$ with $\bar{m}$ in \eqref{hs_m_stab} to find
a polynomial in the unknown $\bar{m}$, that can be expressed like \eqref{eq_comp_stat}:
\begin{eqnarray}
\label{hs_bar_m}
\bar{r} & \!\!\! = \!\!\! &\dfrac{\hat{\theta}_2 \bar{m}^2}{1-\hat{\theta}_1-\hat{\theta}_3}, \nonumber \\
0 & \!\!\!=\!\!\! & \underbrace{[\hat{\theta}_2]}_{c_{m,2}}\bar{m}^2+\underbrace{[(\hat{\theta}_1+\hat{\theta}_3-1)\bar{r}]}_{c_{m,0}(\bar{r})}.
\end{eqnarray}
Since \eqref{hs_bar_m} is an incomplete quadratic equation and the operation region is limited to
$0 \leq \bar{m} \leq 1$, the algebraic solution is given by:
\begin{equation}
\label{hs_bar_m_2}
\bar{m} = \sqrt{\dfrac{-c_{m,0}(\bar{r})}{ c_{m,2}}} = \sqrt{\dfrac{(1-\hat{\theta}_1-\hat{\theta}_3)\bar{r}}{\hat{\theta}_2}}.
\end{equation}
Also, as $\bar{r} \geq 0$, $\hat{\theta}_2 > 0$ and $1-\hat{\theta}_1-\hat{\theta}_3> 0$,
the result of the square root in \eqref{hs_bar_m_2} is always real. In Fig.\,\ref{fig_hs_val_comp_stat_y},
the static compensation results are shown for a reference that is a sequence of steps.
As expected, the compensated system is approximately linear (see Fig. \ref{fig_hs_val_comp_stat_y}-b).
The static compensation can be used to find the initial values for the dynamical compensator when needed.
\begin{figure}[htb]
\centering
\includegraphics[width=0.88\columnwidth]{fig_3.pdf}
\normalsize \vspace{-0.3cm}
\caption{Validation results for static compensation:
(\textcolor{blue}{\hbox{--}}) is the reference; (\textcolor{red}{\hbox{-$\cdot$-}}), output of the compensated system; (\textcolor{green}{- -}), output of the uncompensated system. In (a), temporal evolution of the outputs and the reference; (b), the
$r \times y$ plane.}
\label{fig_hs_val_comp_stat_y}
\vspace{-0cm}
\end{figure}
For dynamical compensation, using model $\cal M$ (\ref{hs_model})
the procedure put forward in Sec.\,\ref{sub_comp_dyn} yields
(see Eq.\,\ref{eq_compensator_1}):
\begin{equation}
r(k+1) = \hat{\theta}_1 r(k)+\hat{\theta}_2m(k)^2+\hat{\theta}_3r(k-1) \nonumber
\end{equation}
\noindent
and (see Eq.\,\ref{eq_compensator_2}):
\begin{eqnarray}
\label{hs_mr_2}
\!\!\!\!0 & \!\!\!=\!\!\! & \underbrace{[\hat{\theta}_2]}_{c_{2}}m(k)^2+\underbrace{[\hat{\theta}_1r(k)+\hat{\theta}_3r(k-1)-r(k+1)]}_{c_{0}(k)}.
\end{eqnarray}
Solving \eqref{hs_mr_2} at each iteration yields the compensation input $m(k)$. Because
\eqref{hs_mr_2} is quadratic, there are two possibilities. Either both roots are real,
and then Algorithm\,\ref{sel_root} is used to select which one to use, or the roots are complex
conjugate in which case the previous value is used, i.e., $m(k)=m(k-1)$.
The algebraic solution of \eqref{hs_mr_2} gives the compensator $\cal M_{\rm r}$:
\begin{equation}
m(k) = \sqrt{\dfrac{-c_{0}(k)}{c_{2}}} = \sqrt{\dfrac{r(k+1)-\hat{\theta}_1r(k)-\hat{\theta}_3r(k-1)}{\hat{\theta}_2}}. \label{hs_mr_3}
\end{equation}
\noindent
Because $m(k)$ does not depend on its previous values, in order to initialize \eqref{hs_mr_3},
it is sufficient to make $r(-1)=r(0)$ in (\ref{hs_mr_3}) at $k=0$.
In Fig.\,\ref{fig_hs_val_comp_sin_y} and in Table~\ref{hs_tab_mape_comp}, the results obtained with $\cal M_{\rm r}$ (\ref{hs_mr_3}) is compared to the uncompensated system for different reference signals. The uncompensated results are performed using $r(k)$ as the input for $\cal S$. From Table~\ref{hs_tab_mape_comp},
it is seen that as the frequency increases, the compensation becomes somewhat less effective, as would be expected for most control systems. Also for small values of $r(k)$ (see Fig. \ref{fig_hs_val_comp_sin_y}-b), complex roots appear, and according to Algorithm\,\ref{sel_root}, the last computed value will be used, that is, $m(k) = m(k-1)$.
\begin{figure}[htb]
\centering
\includegraphics[width=0.88\columnwidth]{fig_4.pdf}
\normalsize \vspace{-0.3cm}
\caption{Compensation results. (a)~temporal evolution; (b)~the applied inputs. In (a),
(\textcolor{blue}{\hbox{--}}) is the reference $r(k) = 0.2 {\rm{sin}}(2\pi (0.002) k+\pi/2) + 0.15$;
(\textcolor{red}{\hbox{-$\cdot$-}}) is the output of the compensated system $y_{\rm c}(k)$ and
(\textcolor{green}{\hbox{- -}}) is the output of the system $y_{\rm s}(k)$ without compensation. In (b),
(\textcolor{red}{\hbox{-$\cdot$-}}) is the compensation input $m(k)$, while (\textcolor{green}{- -}) is the input applied in the uncompensated system.}
\label{fig_hs_val_comp_sin_y}
\vspace{-0.3cm}
\end{figure}
\begin{table}[htb]
\centering
\caption{${\rm MAPE}$ for compensated and uncompensated systems with $r(k) = r_0 {\rm{sin}}(2\pi f k+\pi/2) + r_0$.}
\setlength\tabcolsep{10pt}
\begin{tabular}{c | c | c c c c}
\multirow{2}{*}{} &\multirow{2}{*}{$f$ [Hz]}
& \multicolumn{3}{c}{$r_0$ [{\rm V}]} \\
& & \textbf{$0.05$} & \textbf{$0.10$} & $0.20$ \\ \hline
\multirow{4}{*}{Compensated}
& 0.0005 & 7.8\% & 4.1\% & 3.4\% \\
& 0.001 & 9.4\% & 6.4\% & 5.6\% \\
& 0.002 & 15.5\% & 12.2\% & 10.2\% \\
& 0.004 & 29.5\% & 25.8\% & 20.2\%
\\ \hline
\multirow{4}{*}{Uncompensated}
& 0.0005 & 45.6\% & 44.0\% & 40.8\% \\
& 0.001 & 45.5\% & 44.0\% & 40.9\% \\
& 0.002 & 45.3\% & 44.0\% & 41.4\% \\
& 0.004 & 44.8\% & 43.7\% & \text{ }41.8\%
\label{hs_tab_mape_comp}
\end{tabular}
\vspace{-0.6cm}
\end{table}
Figure\,\ref{fig_hs_monte_carlo} shows the results for a Monte Carlo test of $10000$ runs.
During each run, a perturbed model $\cal M$ (\ref{hs_model}) is obtained by taking parameters
from a Gaussian distribution centered at the original parameters and with the covariance matrix
of the estimator. The black dashed lines indicate the region determined by $\mu(\bar{r}) \pm 2\sigma(\bar{r})$,
where $\mu(\bar{r})$ is the output mean and $\sigma(\bar{r})$ is the standard deviation.
The compensation performance is considerably effective on average for $\bar{r}{<}0.3$, and then it degrades a bit.
\begin{figure}[htb]
\centering
\includegraphics[width=0.8\columnwidth]{fig_5.pdf}
\vspace{-0.4cm}
\caption{Results of a Monte Carlo test.
(\textcolor{green}{-$\ast$-}) static curve of the uncompensated system, (\textcolor{blue}{-$\ast$-}) is the reference and
(\textcolor{red}{-$\ast$-}) is $\mu(\bar{r})$, the mean calculated for the 10000 runs at each value $\bar{r}$, (\textcolor{black}{- -}) represent the error bars of $\pm 2\sigma(\bar{r})$.}
\label{fig_hs_monte_carlo}
\vspace{-0.8cm}
\end{figure}
\subsection{A Hysteretic System}
\label{sec_bw}
In this example, the following Bouc-Wen model was used to describe the hysteretic behavior of a
piezoelectric actuator (PZT) that is an unimorph cantilever \cite{Rakotondrabe2011}:
\begin{align}
\dot{h}(t) =& \alpha_{\rm bw}\dot{u}(t)-\beta_{\rm bw}|\dot{u}(t)|h(t)-\gamma_{\rm bw} \dot{u}(t)|h(t)|, \nonumber\\
y(t) =& \nu_{y}u(t) - h(t),
\label{eq_bw}
\end{align}
\noindent
where $u(t)$[V] is the voltage input, $y(t)$[$\rm{\mu}m$] is the position output,
the parameters $\alpha_{\rm bw} = 0.9 [\mu\rm{ m}/\rm{V}]$ and
$\beta_{\rm bw}=\gamma_{\rm bw} = 0.008[\rm{V}^{-1}]$ determine the hysteresis loop, while
$\nu_{y}=1.6 [\mu\rm{ m}/\rm{V}]$ is a weight factor for the output. Here,
\eqref{eq_bw} is referred as the system $\cal S$ to be compensated, which is simulated
with a fourth-order Runge-Kutta method considering the integration step $\delta_t=5 \rm{ms}$.
The following NARX polynomial model ${\cal M}_{\rm h}$ (\ref{m_narx_hys}) to represent $\cal S$ was obtained as detailed in \cite{Tavares_2020_arxiv}:
\begin{eqnarray}
\label{bw_model}
y(k)\!\!\!\! &{=}&\!\!\!\!\hat{\theta}_1y(k{-}1){+}\hat{\theta}_2\phi_{2}(k{-}1)\phi_{3}(k{-}1)u(k{-}1) \nonumber \\
& & {+}\hat{\theta}_3\phi_{2}(k{-}1)\phi_{3}(k{-}1)y(k{-}1){+}\hat{\theta}_4\phi_{2}(k{-}1),
\end{eqnarray}
\noindent
where $\hat{\theta}_1 = 1.000099$, $ \hat{\theta}_2 = 6.630567 \times 10^{-3}$, $\hat{\theta}_3 = -6.247018 \times 10^{-3}$, and $\hat{\theta}_4=7.892915$. The validation results are shown in Table\,\ref{bw_tab_mape_model}, which indicate some degradation at higher frequencies and amplitudes.
\begin{table}[htb]
\centering
\caption{${\rm MAPE}$ for model (\ref{bw_model}) with sinusoidal inputs $u(k) = {\rm{Gsin}}(2\pi f k)$.
Free-run simulation was used.}
\setlength\tabcolsep{10pt}
\begin{tabular}{c | c c c}
\multirow{2}{*}{$f$ [Hz]}
& \multicolumn{3}{c}{$\rm G$ [{\rm V}]} \\
& \textbf{$10$} & \textbf{$30$} & $50$ \\ \hline
0.2 & 2.6\% & 2.0\% & 4.7\% \\
1.0 & 2.7\% & 1.3\% & 4.1\% \\
5.0 & 7.7\% & 5.0\% & \text{ }3.6\%
\label{bw_tab_mape_model}
\end{tabular}
\vspace{-0.2cm}
\end{table}
Following steps \ref{step_1}, \ref{step_2}, \ref{step_3} and \ref{step_5} for the
procedure presented in Sec.\,\ref{sub_comp_hys}, the compensator obtained is ${\cal M}_{\rm h, r}$ given by:
\begin{eqnarray}
\label{hs_mr_hys_1}
0 \!\!&\!\!\!\! {=} \!\!\!\!&\!\! \hat{\theta}_1r(k){-}r(k{+}1){+}\hat{\theta}_2|m(k){-}m(k{-}1)|m(k) \nonumber \\
& &{+}\hat{\theta}_3|m(k){-}m(k{-}1)|r(k){+}\hat{\theta}_4|m(k){-}m(k{-}1)|,
\end{eqnarray}
\noindent
for which is assumed that $m(k) {\neq} m(k-1)$, and it can be split into two polynomials
in $m(k)$, like (\ref{mr_hys_load}) and (\ref{mr_hys_unload}) in step\,\ref{step_6}, as:
\begin{equation}
\label{mr_hys_2}
\!\!0 {=} c_{2}^{\rm L}m(k)^2{+}c_{1}^{\rm L}(k)m(k){+} c_{0}^{\rm L}(k),~~ \text{for}~~ m(k){>}m(k{-}1);
\end{equation}
and
\begin{equation}
\label{mr_hys_3}
\!\!0{=} c_{2}^{\rm U}m(k)^2{+}c_{1}^{\rm U}(k)m(k){+} c_{0}^{\rm U}(k),~~ \text{for} ~~ m(k){<}m(k{-}1),
\end{equation}
\noindent
where $c_{2}^{\rm L}=\hat{\theta}_2$, $c_{1}^{\rm L}(k)=-\hat{\theta}_2m(k-1)+\hat{\theta}_3r(k)+\hat{\theta}_4$, $c_{0}^{\rm L}(k)=\hat{\theta}_1r(k)-\hat{\theta}_3m(k-1)r(k)-\hat{\theta}_4m(k-1)-r(k+1)$, $c_{2}^{\rm U}=-\hat{\theta}_2$, $c_{1}^{\rm U}(k)=\hat{\theta}_2m(k-1)-\hat{\theta}_3r(k)-\hat{\theta}_4$, and $c_{0}^{\rm U}(k)=\hat{\theta}_1r(k)+\hat{\theta}_3m(k-1)r(k)+\hat{\theta}_4m(k-1)-r(k+1).$
As some parameters of (\ref{mr_hys_2}) and (\ref{mr_hys_3}) depend on $m(k-1)$,
the initialization of the compensator is required at $k=0$. Applying
$\tilde{u} = 50{\rm{sin}}(2\pi0.2k)$ to model ${\cal M}_{\rm h}$ (\ref{bw_model}),
the loop ${\cal{H}}(\tilde{u}, \tilde{y})$ is determined. Making
$\tilde{y} = r(k + 1)$, $m(k-1)$ can be determined directly from
loop $\cal H$ similarly to Example\,\ref{example6}.
The validation results for compensation with (\ref{mr_hys_2}) and (\ref{mr_hys_3}) are shown in
Fig.\,\ref{fig_bw_comp_valid} and in Table\,\ref{bw_tab_mape_comp}. These results
indicate that the compensated system presents better tracking performance than the
uncompensated in all evaluated scenarios. In addition, the worst results occur
at higher frequencies and amplitudes.
\begin{figure}[htb]
\centering
\includegraphics[width=0.88\columnwidth]{fig_6.pdf}
\vspace{-0.35cm}
\caption{Compensation results for system \eqref{eq_bw}. (a)~temporal evolution of outputs; (b) the $r \times y$ plane and (c)~temporal evolution of inputs. (\textcolor{blue}{--}) represents the reference $r(k) = 30{\rm{sin}}(2\pi (2) k+\pi/2)$;
(\textcolor{red}{-$\cdot$-}), results for compensator given by (\ref{mr_hys_2}) and (\ref{mr_hys_3}) and (\textcolor{green}{- -}), uncompensated system.}
\label{fig_bw_comp_valid}
\end{figure}
\begin{table}[htb]
\centering
\caption{${\rm MAPE}$ for compensated and uncompensated systems with $r(k) = G_0 {\rm{sin}}(2\pi f k+\pi/2)$.}
\setlength\tabcolsep{10pt}
\begin{tabular}{c | c | c c c c}
\multirow{2}{*}{} &\multirow{2}{*}{$f$ [Hz]}
& \multicolumn{3}{c}{$G_0$ [$\mu${\rm m}]} \\
& & \textbf{$20$} & \textbf{$30$} & $40$ \\ \hline
\multirow{4}{*}{Compensated}
& 0.2 & 1.4\% & 3.2\% & 5.2\% \\
& 1.0 & 0.9\% & 2.5\% & 4.5\% \\
& 2.0 & 1.0\% & 1.4\% & 3.4\% \\
& 5.0 & 5.4\% & 4.5\% & 3.9\%
\\ \hline
\multirow{4}{*}{Uncompensated}
& 0.2 & 7.8\% & 7.1\% & 6.4\% \\
& 1.0 & 7.8\% & 7.0\% & 6.3\% \\
& 2.0 & 7.7\% & 6.9\% & 6.1\% \\
& 5.0 & 7.6\% & 6.6\% & \text{ }5.8\%
\label{bw_tab_mape_comp}
\end{tabular}
\vspace{-0.2cm}
\end{table}
Finally, Fig.\,\ref{fig_bw_monte_carlo} shows the results for $10000$ Monte Carlo runs,
where $r(k) = 20 {\rm{sin}}(2\pi(2) k+\pi/2)$ is used in 5 cycles. A perturbed model ${\cal M}_{\rm h}$ (\ref{bw_model})
is obtained, as before. The Monte Carlo test presents a region determined by $\mu(k) \pm 2\sigma(k)$,
where $\mu(k)$ and $\sigma(k)$ are analogous to those described in Sec.~\ref{sec_hs_sys}, now for
each $k$, instead of $\bar{r}$. Comparing with Fig. \ref{fig_hs_monte_carlo}, the error bars determine a wider region. It is explained due to the sensitiviy of $\cal{M}_{\rm h}$ on variations in $\hat{\theta}_2$.
\begin{figure}[htb]
\centering
\includegraphics[width=0.88\columnwidth]{fig_7.pdf}
\vspace{-0.5cm}
\caption{Results for 10000 Monte Carlo runs. (a) temporal evolution of the outputs in the last cycle; (b) plane $r(k) \times y(k)$. (\textcolor{green}{-$\ast$-}) refers to the uncompensated system, (\textcolor{blue}{-$\ast$-}) refers to the reference and (\textcolor{red}{-$\ast$-}) is the average $\mu(k)$ of the 10000 Monte Carlo runs for the compensated system. (\textcolor{black}{- -}) represent the error bars of $\pm 2\sigma(k)$.}
\label{fig_bw_monte_carlo}
\vspace{-0.35cm}
\end{figure}
It should be mentioned that the constraint $\Sigma_y=1$ presented by \cite{Abreu_etal2020} is not fulfilled, where $\Sigma_y=1$ is the sum of all linear output's regressors. In order to show how this constraint affects the behavior of the model and compensator, we use a constrained least squares estimator to impose $\Sigma_y=1$ on the parameters of (\ref{bw_model}). The model obtained with constraints,
${\cal M}_{\rm h, cns}$, has the same structure of $\cal M_{\rm h}$ (\ref{bw_model}) with parameters: $\Sigma_y=\hat{\theta}_{1, \rm cns}= 1$, $\hat{\theta}_{2, \rm cns} = 6.630913 \times 10^{-3}$, $\hat{\theta}_{3, \rm cns} = -6.157515 \times 10^{-3}$, and $\hat{\rho}_{4, \rm cns}=7.893146$.
Because the equal framework of ${\cal M}_{\rm h}$ and ${\cal M}_{\rm h, cns}$, their compensators
also have a same polynomial structure. The compensator ${\cal M}_{\rm h, cns,r }$ is obtained when we replace each corresponding parameter of ${\cal M}_{\rm h, cns}$ in (\ref{mr_hys_2}) and (\ref{mr_hys_3}). Since the results obtained for modeling and compensation are similar to those presented by Tables\,\ref{bw_tab_mape_model} and \,\ref{bw_tab_mape_comp}, these results are omitted.
A more relevant comparison for these two models and compensators is shown in Fig.\,\ref{fig_bw_constant}.
In this figure, the performance of the models and compensators is verified when an input/reference sinusoidal signal
becomes constant. Note that the validation and compensation results for ${\cal M}_{\rm h}$ (\ref{bw_model})
do not converge at steady-state. As $\bar{\phi}_1=\bar{\phi}_2=0$, both models become $\bar{y} = \Sigma_y\bar{y}$ that
have a single eigenvalue equal to $\Sigma_y$. Consequently, as $\Sigma_y=\hat{\theta}_1>1$, ${\cal M}_{\rm h}$ is unstable
in steady-state while the constraint $\Sigma_y=\hat{\theta}_{1,\rm cns}=1$, makes ${\cal M}_{\rm h, cns}$ remains in the last state. The compensation methods work in an open-loop, hence steady-state errors are expected, but they tend to be less
significant for more precise models.
For the current example, it was found that model ${\cal M}_{\rm h}$ has a steady-state error that tends to infinity over time, while the constrained model ${\cal M}_{\rm h, cns}$ provides a steady-state error of approximately 0,26$\mu$m in Fig. \ref{fig_bw_constant}-(b). Such errors are reflected in the
compensation performance since ${\cal M}_{\rm h, cns, r}$ presents an offset error of 0.83$\mu$m in Fig. \ref{fig_bw_constant}-(d) while the other, ${\cal M}_{\rm h, r}$, has a steady-state error which tends to infinity similarly to its model.
\begin{figure}[htb]
\centering
\includegraphics[width=1\columnwidth]{fig_8.pdf}
\vspace{-0.4cm}
\caption{Validation and compensation results for models ${\cal M}_{\rm h}$ and ${\cal M}_{\rm h, cns}$ when a sinusoidal input or reference become constant. In (a), we have the temporal evolution of the input $u(k)=30{\rm sin}(2\pi(2)k)$ that becomes constant at $k=920$. This input determines the outputs in (b) when applied to the system $\cal S$ (\textcolor{blue}{\hbox{--}}), to ${\cal M}_{\rm h}$ (\textcolor{red}{\hbox{-$\cdot$-}}) and to ${\cal M}_{\rm h, cns}$ (\textcolor{black}{\hbox{- -}}). In (c), $m(k)$ for ${\cal M}_{\rm h}$ (\textcolor{red}{\hbox{-$\cdot$-}}) and ${\cal M}_{\rm h, cns}$ (\textcolor{black}{\hbox{- -}}) that were calculated for $r(k)=u(30{\rm sin}(2\pi(2)k)$) Finally, (d) shows the respective outputs for (c) where $r(k)$ is (\textcolor{blue}{\hbox{--}}).}
\label{fig_bw_constant}
\vspace{-0.3cm}
\end{figure}
\subsection{Experimental Results}
\label{sec_exp_results}
\definecolor{cms}{HTML}{ff00ff}
\definecolor{cci}{HTML}{94a0a0}
\definecolor{inv}{HTML}{6cbbe7}
In this section, the compensation strategy is applied to an experimental pneumatic control valve,
which is a type of actuator widely used in industrial processes. For this type of actuator, the
control performance can degrade significantly due to
friction, dead-zone, dead-band, and hysteresis \cite{Choudhury_etal2008,rom_gar/11}.
The present valve is the same used in \cite{Abreu_etal2020}, where the measured output is its
stem position and the input is a pressure signal applied to the valve after passing V/I and I/P conversion.
The sampling time is $T_{\rm s}=0.01\,{\rm s}$ and, for details of the identification of this system the reader is
referred to \cite{Abreu_etal2020,Tavares_2020_arxiv}. The following models will be considered in this
case study.
\vspace{0.2cm}
\noindent 1) ${\cal M}_{\rm h}$ is the model identified with the inclusion of $\phi_{1}(k)$ and $\phi_{2}(k)$ as
candidate regressors \cite{Martins_Aguirre2016}, and with the gray-box restrictions proposed by \cite{Abreu_etal2020}. As shown in Fig. \ref{fig_bw_constant}, the use of such constraints is important to describe the behavior in steady-state. The estimated model is
\begin{eqnarray}\label{mh_cns_valve}
y(k) & = & \hat{\theta}_1y(k-1)+\hat{\theta}_2y(k-2) + \hat{\theta}_3\phi_1(k-1) \nonumber \\
& + & \hat{\theta}_4u(k-1)\phi_{1}(k-1)\phi_{2}(k-1) \nonumber \\
& + & \hat{\theta}_5y(k-2)\phi_{1}(k-1)\phi_2(k-1),
\end{eqnarray}
with $\hat{\theta}_1=9.76\times 10^{-1}$, $\hat{\theta}_2=2.40 \times 10^{-2}$, $\hat{\theta}_3=1.19 \times 10^{-1}$,
$\hat{\theta}_4=3.76$ and $\hat{\theta}_5=-4.73$. Note that, $\Sigma_y = \hat{\theta}_1 + \hat{\theta}_2 = 1$.
The following models are found in the literature.
\vspace{0.2cm}
\noindent 2) ${\cal M}_{\rm bw}$ is used to represent a BW model (\ref{eq_bw}). To estimate the valve output, its parameters were re-estimated using an evolutionary approach based on
niches, which is formulated in \cite{tavares2019}. These parameters are: $\alpha_{\rm bw} = 7.54 \times 10^{-1}$, $\alpha_{\rm bw}=-4.96$, $\gamma_{\rm bw}=- 3.61$ and $\nu_{y}=7.54 \times 10^{-1}$.
The last two models adopted were identified in \cite{Abreu_etal2020} for the same system under study and
with the same identification data.
\vspace{0.2cm}
\noindent 3) ${\cal M}_{\rm h,2}$ was identified -- see Eq. 33 in \cite{Abreu_etal2020} -- with the same constraints used for
${\cal M}_{\rm h}$ (\ref{mh_cns_valve}), plus an additional one such that
the input signal can be isolated when writing the compensator equation.
\vspace{0.2cm}
\noindent 4) ${\breve{\mathcal M}}_{\rm h}$ was identified to describe the inverse relationship
between $u(k)$ and $y(k)$ of the valve -- see Eq. 34 in \cite{Abreu_etal2020}.
Therefore, the model provides $\hat{u}(k)$ given $y(k)$. The set of candidate regressors
includes $\breve{\phi}_{1}(k)=y(k)-y(k-1)$ and $\breve{\phi}_{2}(k)={\rm sign}[\breve{\phi}_{1}(k)]$.
The performance of the direct models, the first three, subject to sinusoidal inputs with different amplitudes are shown in
Table\,\ref{valv_tab_mape_valid}, which indicate that these models have similar efficiency by MAPE. Since ${\breve{\mathcal M}}_{\rm h}$ is an inverse model, which predicts the input signal instead of the
output and must be simulated from a smoothed version of $y(k)$ \cite{Abreu_etal2020}, we do not directly compare the MAPE accuracy of this model with the others. More details can be found in \cite{Tavares_2020_arxiv}.
\begin{table}[htb]
\centering
\caption{${\rm MAPE}$ for models validation with sinusoidal inputs $u(t) = G_0 {\rm{sin}}(2\pi (0.1) t+\pi/4)+3{\rm V}$.}
\setlength\tabcolsep{10pt}
\begin{tabular}{c | c c c c c}
\multirow{2}{*}{Model}
& \multicolumn{4}{c}{$G_0$ [V]} \\
& \textbf{$0.45$} &\textbf{$0.55$} & \textbf{$0.65$} & $0.75$ \\ \hline
\multirow{1}{*}{{\hspace{-0.4cm}1 - ${\cal M}_{\rm h}$}}
& 3.6\% & 3.0\% & 3.1\% & 4.9\% \\
\multirow{1}{*}{\hspace{-0.2cm}2 - ${\cal M}_{\rm bw}$}
& 3.9\% & 4.1\% & 4.5\% & 6.5\% \\
\multirow{1}{*}{\hspace{-0.15cm}3 - ${\cal M}_{\rm h, 2}$}
& 3.2\% & 3.5\% & 3.9\% & 5.7\% \\
\hline
\end{tabular}\label{valv_tab_mape_valid}
\end{table}
For each model, the respective compensator is shown below. The first compensator is obtained following
the strategy presented in Sec. \ref{sub_comp_hys}.
\vspace{0.2cm}
\noindent
1) The compensator for ${\cal M}_{\rm h}$ (\ref{mh_cns_valve}) is ${\cal M}_{\rm h,r}$, obtained with the application of steps \ref{step_1}, \ref{step_2}, \ref{step_3}, \ref{step_5} and \ref{step_6}. ${\cal M}_{\rm h,r}$ is compound by two quadratic polynomials like (\ref{mr_hys_2}) and (\ref{mr_hys_3}) with parameters: $c_{2}^{\rm L}=\hat{\theta}_4$, $c_{1}^{\rm L}(k)=\hat{\theta}_3-\hat{\theta}_4m(k-1)+\hat{\theta}_5r(k-1)$, $c_{0}^{\rm L}(k)=\hat{\theta}_1r(k)+\hat{\theta}_2r(k-1)+\hat{\theta}_3m(k-1)-\hat{\theta}_5r(k-1)m(k-1)-r(k+1)$, $c_{2}^{\rm U}=-\hat{\theta}_4$, $c_{1}^{\rm L}(k)=-\hat{\theta}_3+\hat{\theta}_4m(k-1)-\hat{\theta}_5r(k-1)$ and $c_{0}^{\rm L}(k)=\hat{\theta}_1r(k)+\hat{\theta}_2r(k-1)-\hat{\theta}_3m(k-1)+\hat{\theta}_5r(k-1)m(k-1)-r(k+1)$.
\vspace{0.2cm}
\noindent 2) The compensation law $m(t)$, for model ${\cal M}_{\rm bw}$, was proposed
by \cite{Rakotondrabe2011}, and is reffered as ${\cal M}_{\rm bw, r}$ given by:
\begin{equation}\label{valve_m_r_bw}
m(t)= \dfrac{10}{7.21}[r(t)+h(t)].
\end{equation}
\vspace{0.2cm}
\noindent 3) The compensator for ${\cal M}_{\rm h, 2}$ namely ${\cal M}_{\rm h, 2, r}$ is given by Eq. 35 in \cite{Abreu_etal2020}.
\vspace{0.2cm}
\noindent
4) Finally, also extracted from \cite{Abreu_etal2020}, ${\breve{\mathcal M}}_{\rm h,r}$, the compensator for ${\breve{\mathcal M}}_{\rm h}$ is given by Eq. 36 in the mentioned paper.
The compensation results for sinusoidal references with different amplitudes are shown
in Table\,\ref{valv_tab_mape_comp} while Fig.\,\ref{fig_exp_comp_sin} shows the
compensation results for one of these references, $r(k)=0.41{\rm sin}(2\pi(0.1)t+\pi/4)+3{\rm V}$.
All compensation strategies provide considerably better results in all evaluated scenarios
when compared to the uncompensated system.
\begin{table}[htb]
\centering
\caption{${\rm MAPE}$ for compensated and uncompensated systems with $r(t) = G_0 {\rm{sin}}(2\pi (0.1) t)+3.07{\rm V}$.}
\setlength\tabcolsep{6pt}
\begin{tabular}{c | c c c c c}
\multirow{2}{*}{Compensation Strategy}
& \multicolumn{4}{c}{$G_0$ [V]} \\
& \textbf{$0.26$} &\textbf{$0.34$} & \textbf{$0.41$} & $0.50$ \\ \hline
\multirow{1}{*}{\hspace{-0.8cm} 1) $\cal M_{\rm h, r}$ (\ref{mr_hys_2}-\ref{mr_hys_3})}
& 3.9\% & 3.3\% & 3.3\% & 3.8\% \\
\multirow{1}{*}{\hspace{-0.9cm}2) $\cal M_{\rm bw, r}$ (\ref{valve_m_r_bw})}
& 5.9\% & 4.4\% & 4.3\% & 4.2\% \\
\multirow{1}{*}{\hspace{0cm}3) $\cal M_{\rm h, 2, r}$ (35) in \cite{Abreu_etal2020}}
& 3.6\% & 3.5\% & 3.9\% & 5.2\% \\
\multirow{1}{*}{\hspace{-0.25cm}4) $\breve{\cal{M}}_{\rm h,r}$ (36) in \cite{Abreu_etal2020}}
& 2.9\% & 2.8\% & 3.2\% & 2.7\% \\ \hline
\multirow{1}{*}{\hspace{-0.3cm} Uncompensated}
& 21.0\% & 18.0\% & 16.2\% & 14.4\% \\
\hline
\end{tabular}\label{valv_tab_mape_comp}
\end{table}
\begin{figure}[htb]
\centering
\includegraphics[width=0.95\columnwidth]{fig_9.pdf}
\vspace{-0.5cm}
\caption{Compensation results for the pneumatic valve. (a)~temporal evolution of compensation inputs in three cycles; (b)~temporal evolution of outputs for the compensated systems in three cycles; (c)-(f) show the $r \times y$ plane for each compensator. (\textcolor{blue}{--}) refers to the reference $r(t) = 0.34{\rm{sin}}(2\pi (0.1)t+\pi/4)+3V$; (\textcolor{green}{--}), uncompensated system; (\textcolor{red}{-$\vdot$-}) compensation with $\cal M_{\rm h, r}$\hbox{(\ref{mr_hys_2}-\ref{mr_hys_3})}; \hbox{(\textcolor{black}{--})} compensation with $\cal M_{\rm bw, r}$(\ref{valve_m_r_bw}); (\textcolor{cms}{$\vdot$ $\vdot$}) compensation with $\cal M_{\rm h, 2, r}$(35) in \cite{Abreu_etal2020}; (\textcolor{cci}{- -}) compensation with $\breve{\cal{M}}_{\rm h,r}$(36) in \cite{Abreu_etal2020}.}
\label{fig_exp_comp_sin}
\vspace{-0.3cm}
\end{figure}
For the uncompensated system, the input is the reference $r(k)$. Using this as a
starting point, we would like to quantify how much more has to be done in order
to achieve compensation. To this end, the following is computed
\begin{equation}
E({\delta_m}) =
\sum_{k=N-N_0}^{N-1} \delta_m(k)^2,
\end{equation}
\noindent
where $\delta_m(k)=|m(k)-r(k)|$ and $N$ is the length of $\delta_m(k)$.
$E({\delta_m})$ can be interpreted as the energy of $\delta_m(k)$ over one period $N_0$.
Also, the variability with respect to the uncompensated system is given by the
standard deviation of $\delta_m(k)$, $\sigma(\delta_m)$, see Table\,\ref{valv_tab_pot} for a summary of results.
\begin{table}[htb]
\centering
\caption{$E({\delta_m})$[$\sigma({\delta_m})$] for the investigated compensators with
$r(t) = G_0 {\rm{sin}}(2\pi (0.1) t)+3.07{\rm V}$. }
\setlength\tabcolsep{2.5pt}
\begin{tabular}{c | c c c c c}
\multirow{2}{*}{Strategy}
& \multicolumn{4}{c}{$G_0$ [V]} \\
& \textbf{$0.26$} &\textbf{$0.34$} & \textbf{$0.41$} & $0.50$ \\ \hline
\multirow{1}{*}{\hspace{-0.7cm} 1) $\cal M_{\rm h, r}$ (\ref{mr_hys_2}-\ref{mr_hys_3})}
& 28.3 [0.154]& 33.7 [0.165]& 39.4 [0.174]& 49.4 [0.186]\\
\multirow{1}{*}{\hspace{-0.8cm}2) $\cal M_{\rm bw, r}$ (\ref{valve_m_r_bw})}
& 27.0 [0.149]& 33.3 [0.163]& 40.6 [0.178]& 53.7 [0.197]\\
\multirow{1}{*}{\hspace{-0cm}3)$\cal M_{\rm h, 2, r}$ (35) in \cite{Abreu_etal2020}}
& 38.7 [0.184]& 43.7 [0.193]& 50.1 [0.203] & 57.2 [0.206]\\
\multirow{1}{*}{\hspace{-0.2cm}4)$\breve{\cal{M}}_{\rm h,r}$ (36) in \cite{Abreu_etal2020}}
& 24.9 [0.139]& 38.3 [0.174]& 52.7 [0.203]& 72.6 [0.237]\\ \hline
\end{tabular}\label{valv_tab_pot}
\vspace{-0.3cm}
\end{table}
Similar to the validation results of model ${\cal M}_{\rm bw}$, the
corresponding compensator ${\cal M}_{\rm bw,r}$ (\ref{valve_m_r_bw}) performs slightly worse compared
to those based on NARX models. This suggests that NARX models are more appropriated to
describe nonlinearities in the valve. This is not surprising, as the class of NARX
polynomials is more general than the Bouc-Wen class.
On the positive side, the Bouc-Wen model provided the simplest compensator among those presented. In addition,
as seen in Table\,\ref{valv_tab_pot} the respective compensator requires little change compared to the uncompensated
system. The most challenging task related to the Bouc-Wen model is to estimate its
parameters, which was done with an evolutionary approach.
Both compensation strategies proposed by \cite{Abreu_etal2020} performed well.
${\cal M}_{\rm h, 2, r}$
requires special care in the phase of structure selection otherwise the compensation input
$m(k)$ cannot be computed explicitly. Apart from that the compensation law tends to be easier
to calculate than the one put forward in this work. On the negative side, ${\cal M}_{\rm h, 2, r}$
produces inputs with more abrupt changes (see Fig. \ref{fig_exp_comp_sin}-(a) and (e)). This
is reflected in higher values of $E(\delta_m)$ and ${\sigma}(\delta_m)$.
The overall good performance of compensator ${\breve{\mathcal M}}_{\rm h,r}$ comes at the
expense of careful data preprocessing \cite{Abreu_etal2020}.
This compensator can produce smooth compensation inputs (Fig.\,\ref{fig_exp_comp_sin}-(a) and (f)) with
low MAPE values (Table\,\ref{valv_tab_mape_comp}). However $E(\delta_m)$
and ${\sigma}(\delta_m)$ tend to increase considerably with the reference amplitude, as shown in Table \ref{valv_tab_pot}.
The compensator designed with the methodology put forward in this work, ${\cal M}_{\rm h, r}$, was
also able to compensate for the nonlinearity in the valve. The MAPE are among the lowest, especially for
moderate-high reference amplitudes, $G_0$, with the advantage that $E(\delta_m)$ and ${\sigma}(\delta_m)$
do not increase as much as for the other regulators with $G_0$ (Table \ref{valv_tab_pot}). In addition,
$\cal{M}_{\rm h}$ has only $5$ terms which facilitates obtaining the compensation law. Also, if the parameters
of such model needed to be updated, a recursive algorithm can be readily implemented.
On the other hand, if the process models turn out to be polynomials with degree greater than 3,
numerical solvers would be required to find the roots. Fortunately, many systems can be adequately
described using polynomials up to third-degree. As a side note, there is a self-consistency check indirectly
provided by the current method, which is the appearance of unfeasible roots: either real but outside the
operating range or complex. Whenever this happens it is an indication that the process model is not adequate.
Fortunately no such problems occurred in this case study.
\section{Conclusion}\label{Conclusion}
This work has presented an approach to compensate nonlinearities
based on NARX polynomial models previously estimated. The method
is simple and easy to interpret, as the compensation input turns out to
be the value required for the system to attain steady-state properties.
The compensation input is obtained iteratively, which confers some
adaptability to the method. The degree of adaptability can be readily
increased by estimating the model parameters recursively, this has not
been explored in the paper.
The method has been considered
in three contexts: static for constant references, dynamical for
variant, and for systems with hysteresis. At first, the technique was illustrated using two simulated systems.
The performance is comparable to that of other methods available in
the literature. In addition, the method presents some robustness to variation
in the parameters, as evaluated using Monte Carlo tests.
The proposed techinque was also implemented on a pilot plant where the goal was to
compensate the nonlinearity of a pneumatic control valve. The performance
was compared with a compensator designed in \cite{Rakotondrabe2011}
and two more recent strategies published by \cite{Abreu_etal2020}.
All compensators can achieve nonlinearity compensation for the valve
(see Table\,\ref{valv_tab_mape_comp}). Pros and cons of
each technique were discussed.
Another interesting feature of the presented technique is that
a compensator can be designed for linear or nonlinear systems with or without using constraints
during model estimation. Perhaps the main foreseen limitation occurs if the compensators are
designed using polynomial models of degree greater than $3$, which is not a common situation
in practice, though it could happen. In this case, it would be necessary to use numerical solvers
to find the roots, which could turn out to be a problem for more demanding online applications.
Fortunately, many relevant systems can be described by models up to 3rd
degree for which the roots can be found with analytical expressions presented in Appendix\,\ref{appendix_sol}.
Finally, the aim of the compensators is to cancel out most of the nonlinearity. This would allow for
the design of linear feedback controllers as a second step.
\appendices
\section{Solving Algebraic Polynomial Equations}\label{appendix_sol}
Algebraic polynomial equations with unknown $x$, degree $n \in \mathbb{N}^+$, and known coefficients $a_i \in \mathbb{R}$, $i \in \{0,\ldots,n\}$, can be expressed as
\begin{equation}\label{eq_poly}
0 = a_nx^n+a_{n-1}x^{n-1}+\ldots+a_1x+a_0, \quad a_n \neq 0
\end{equation}
\noindent For \eqref{eq_poly}, there are $n$ complex roots. The analytical solutions for $n \leq 3$ are presented in the sequel.
\begin{itemize}
\item[\textit{A)}] \textit{Linear Equations}
\begin{align*}
&0 = a_1x+a_0, \quad a_1 \neq 0 \nonumber \\
&x = \dfrac{-a_0}{a_1} \nonumber
\end{align*}
\item[\textit{B)}] \textit{Quadratic Equations}
\begin{align*}
&0 = a_2x^2+a_1x+a_0, \quad a_2 \neq 0 \nonumber \\
&\Delta = a_1^2-4a_2a_0 \nonumber \\
&x_i = \dfrac{-a_1 + (-1)^i \Delta}{2a_2}, \quad i \in \{0,1\}
\end{align*}
\item[\textit{C)}] \textit{Cubic Equations}
\begin{align*}
& 0 = a_3x^3+a_2x^2+a_1x+a_0, \quad a_3 \neq 0 \nonumber \\
&\Delta_0 = a_2^2-3a_3a_1\nonumber \\
&\Delta_1 = 2a_2^3-9a_3a_2a_1+27a_3^2a_0\nonumber \\
&C = \sqrt[3]{\dfrac{\Delta_1 \pm \sqrt{\Delta_1^2-4\Delta_0^3}}{2}} \nonumber \\
&\xi = \dfrac{-1+\sqrt{-3}}{2} \nonumber \\
&x_i = -\dfrac{1}{3a}\left(b+\xi^iC+\dfrac{\Delta_0}{C}\right), \quad i \in \{0,1,2\} \nonumber
\end{align*}
\end{itemize
\section*{Acknowledgment}
PEOGBA and LAA gratefully acknowledge financial support from CNPq
(Grant Nos. 142194/2017-4 and 303412/2019-4) and
FAPEMIG (TEC-1217/98).
\ifCLASSOPTIONcaptionsoff
\newpage
\fi
\bibliographystyle{IEEEtran}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,428 |
Produced by Joshua Hutchinson and the Online Distributed
Proofreading Team at http://www.pgdp.net (This file was
produced from images generously made available by Cornell
University Digital Collections)
THE
CONTINENTAL MONTHLY:
DEVOTED TO
LITERATURE AND NATIONAL POLICY.
VOL. III.--MARCH, 1863.--No. III.
TURKEY.
The decline of the Turkish Empire has furnished an eloquent theme for
historians, who have ever made it the 'point and commendation of their
tale.' Judging from its decline, they have predicted its fall. Half a
century ago, the historian of the middle ages expected with an assurance
that 'none can deem extravagant,' the approaching subversion of the
Ottoman power. Although deprived of some of its richest possessions and
defeated in many a well-fought field, the house of Othman still
stands--amid crumbling monarchies and subjugated countries; the crescent
still glitters on the Bosphorus, and still the 'tottering arch of
conquest spans the ample region from Bagdad to Belgrade.'
Yet, how sadly changed is Turkey from her former self--how varied the
fortunes of her classic fields! The physical features of the country are
the same as in the days of Solyman the Magnificent; the same noble
rivers water the fertile valleys, and the same torrents sweep down the
mountain sides; the waves of the AEgean and Mediterranean wash the same
shores, fertile in vines and olive trees; the same heaven smiles over
the tombs of the storied brave--but here no longer is the abode of the
rulers and lawgivers of one half the world.
It has been said, and with some degree of truth, that the Turks are
encamped, not settled in Europe. In their political and social
institutions they have never comported themselves as if they anticipated
to make it their continuing home. Their oriental legends relate how the
belief arose in the very hour of conquest that the standard of the Cross
should at some future day be carried to the Bosphorus, and that the
European portion of the empire would he regained by Christians. From
this superstitious belief they selected the Asiatic shore for the burial
of true Mussulmans; nor was it altogether a fanciful belief, for in the
sudden rise of Russia, Turkey foresaw the harbinger of her fall, and
recognized in Muscovite warriors the antagonists of fate.
A nation to be long-lived must rise higher and higher in the scale of
civilization; must approach nearer and nearer its meridian, but never
culminate. The Athenians reached the zenith of their glory in the age of
Pericles, and lost in fifty years what they had acquired in centuries.
The Turks attained their meridian greatness in the reign of Solyman the
Magnificent--from which time dates their decline.
If we make a comparison between Turkey and her formidable neighbor,
Russia, we shall find that the latter adopted, while the former resisted
reforms. Turkey was in the fulness of her power when Russia had not yet
a name. The spirit of the Ottomans was remarkably exclusive. They
regarded themselves as a separate and distinct people; they were
conquerors, and as such thought themselves a superior race--men who were
to teach and not to learn. In their intercourse with other nations, they
borrowed nothing, and out of themselves looked for nothing. Their
feeling of national glory was not extinguished by national degradation,
but cherished through ages of slavery and shame. But the world is a
world of progress. A nation cannot remain stationary; she must advance
or retrograde. Turkey is not what she was, while Russia, with the rest
of Christendom, has advanced; her faults grew with her strength, but did
not die with her decay. It will not be sufficient for her merely to
regain her former power; she must overtake Christendom in the progress
made during her decadence. Her spirit of vitality is not yet extinct; it
wants guidance and development to strengthen and elevate it. There is
still hope of reforming the Turkish empire without that baptism of blood
which many have urged and are still urging. Indeed, Lord Palmerston
declared in Parliament that Turkey has made a more rapid advance and
been improved more during the last ten years (he made this statement in
1854, and Turkey has been rapidly progressing since) than any other
country in Europe.
Before considering the question of reform, it will be necessary to take
a cursory view of Turkish history and character.
While the monarchs of Constantinople were waging war with Persia, and
both empires were tottering; while the Christian religion gave rise to
different sects, hating each other with intense and fanatical hatred, a
silent power was rising among the Turks, which was destined to subvert
empires and found a new religion. Their original seat was among the
Altai mountains, where they were employed by their masters in working
iron mines. They rose in rebellion, threw off their allegiance, and made
incursions into Persia and China, proving themselves formidable enemies.
From being a weak and enslaved people they became the allies and
conquerors of the Byzantine emperors. 'With the Koran in one hand,' says
Macaulay, 'and the sword in the other, they went forth conquering and
converting eastward to the Bay of Bengal, and westward to the Pillars of
Hercules.' They became a terror to the nations that had beheld with
contempt their rising greatness. Amid the expiring glories of the Roman
world they made Constantinople the capital of their empire. It was all
that the oriental imagination could desire. Rendered by its
fortifications impregnable, and situated on the Bosphorus, whose dark
blue waters flow between shores of unrivalled beauty, where nature and
art had reared their grandest monuments, it surpassed in wealth and
grandeur Nineveh and Babylon.
From this stronghold, which had been the cradle of Christianity, and
which had witnessed the dying struggle of the Roman empire, the
conquerors, maddened with the victories and crowned with the wealth
which years of perpetual war had heaped upon them, mustered their armies
and sallied forth. They subjugated many countries, but copied none of
their virtues; and to-day their degenerate descendants still retain most
of their original traits of character. Their religious sense is deep,
but theirs is a religion which blunts and stupefies the intellectual
faculties, and makes man fit only to perform a score of prostrations
each day. It inspires courage in war, but it also teaches blind
resignation to defeat and disgrace: it teaches morality, but sensuality
and ferocity are not inconsistent with its doctrines. Eat, drink,
smoke--indulge all the passions to-day, for immortality begins
to-morrow! No Turk is so high that he has not a master, none so low that
he has not a slave; the grand vizier kisses the sultan's foot, the pasha
kisses the vizier's, the bey the pasha's, and so on. Yet their many
virtues half redeem their faults. They are proverbial for their
hospitality, and charity, which 'covereth a multitude of sins,' is an
oriental virtue. They have, too, great love of nationality. The beggar
who seeks alms of the Turk with cries and entreaties, will not ask a
single para of the Frank (a name applied to all foreigners).
Turkey in Europe, though smaller in extent than the Asiatic division of
the empire, is by far the wealthier and more important. It extends from
Russia to the Adriatic, and from Hungary to the Euxine sea, the command
of which it shares jointly with Russia. The Straits of Constantinople,
the Dardanelles, and the Sea of Marmora are free to all friendly
nations. The situation of the country, its numerous and safe harbors,
are all favorable to commerce. There is every variety of climate, and
the soil in every part of the empire is fertile, and, when cultivated,
yields productions in the greatest abundance. The agricultural, like the
manufacturing industry, owing to the indolence of the people, is much
neglected. This indolence is, in a great measure, the result of
oppression. Before Russia extended her protection over the provinces,
the Turks left agriculture to their tributaries, whom, when wealthy and
prosperous, they plundered.
Let us now consider the causes which led to the decline of the empire.
In the reign of Solyman, poetry, science, and art flourished. New
privileges were conferred upon the ministers of religion; the
Janissaries received increased pay; the coffers of the empire were
filled to overflowing; the condition of the rayas was ameliorated;
security to life, honor, and property was given to all, without
distinction of creed or race. But even then there were causes at work
destined to effect a decline. The sultan in person was ever at the head
of his troops. Thus the vizier, or prime minister, who remained in the
capital, became, by degrees, a more influential personage than 'the
grand seignior' himself. The intrigues of the eunuchs in the imperial
harem began to exert their baneful influences on the administration. The
seraglio--in which many hundred females are immured, the most beautiful
that can be found in the contiguous realms of Europe and Asia, wherever
the Turk bears sway--from being the most beautiful appendage, became the
moving spring of the Ottoman Porte. The inmates formed a faction hostile
to the ministers of religion. The administration was transferred to
Greeks, Jews, and Armenians, who filled the treasury of the sultan and
enriched themselves by impoverishing the people, who, since they could
no longer enjoy the fruits of their labor, became indolent. The army was
more eager for booty and captives than for glory; slaves were
multiplied; the higher classes revelled in wealth and luxury, while the
poorer classes with difficulty obtained a livelihood.
It would be strange, indeed, if in an empire so extensive and with an
immense and motley population, we did not find it difficult to introduce
reforms, and instruct the people in the arts of more civilized nations,
and remove old abuses, guarded by the fanaticism of the clergy.
Political reforms can be made only by those in high places of authority;
and to be sanctioned by the prejudiced and infatuated Ottoman they must
assume the garb of religion. The sultan himself, wielding the sceptre
over millions of subjects, uniting in his own person all the powers of
the state, claiming to reign by divine commission, and profanely styling
himself the shadow of God--even he dares not venture to vary one iota
from the teachings of the Koran and the Sunnah.
Selim III was the first royal reformer. While Europe was shaken to its
very centre, and the continental monarchs trembled on their thrones, he
applied himself assiduously to those civil and military reforms, which
his successors promoted, and without which Turkey could not have
maintained her position as a European power. Selim made a new
organization of the army, made innovations in the judicial and
administrative branches of the government, changed the system of
taxation, and gave a decidedly new organization to the divan, where
reform was most needed. He also attempted to make innovations in the
financial department, but by depreciating the coin, in order to fill an
exhausted treasury, signally failed. He deposed the then reigning
hospodars of the Moldo-Wallachian provinces, and established others more
favorable to his work of reform. Russia and England remonstrated at this
measure, and war was declared. The Turkish army was defeated and driven
across the Danube. The Janissaries, ignorantly attributing their defeat
to Selim's reforms in military discipline, rose in rebellion. The
well-meant but too mild sultan fell a victim to their violence, and was
succeeded by Mustapha, who had instigated the insurgents to revolt. His
short reign is signalized by the vigorous measures he took to destroy
Selim's reforms. Shortly after his accession to the throne, the defeat
of the Turkish fleet by the Russians spread consternation and terror
through the capital. It was at this critical juncture that an Asiatic
pasha, a friend of the deposed sultan, advanced with a powerful army,
and laid siege to Constantinople, which yielded to him after a vigorous
resistance of one year. Mahmoud ascended the throne. From Selim, his
cousin, he had learned the lamentable condition of the empire and the
necessity of reform. He had no sooner ascended the throne, than the
Janissaries began to manifest a feverish anxiety for revolt. No time was
to be lost; and Mahmoud acted with that energy which was one of the few
redeeming traits of his character. Mustapha, the murderer of Selim and
the destroyer of the work of a lifetime, was put to death; his son and
wives shared his fate. Mahmoud was now firmly established. He was the
last scion of the Othman race, and as such was vested with _sacrosancta
potestas_. He resolved to annihilate the unruly corps and anathematize
their name. He engaged the services of their aga, or commander-in-chief,
to whom he made known his plans. His next step was to issue an order
commanding each regiment to furnish one hundred and fifty men to be
drilled after the manner of European soldiers. The friends of Mahmoud
asked: 'Is he mad?' The soldiers exclaimed: 'Bismillah! he wants to make
infidels of us. Does he think we are no better than infidel dogs?' The
Janissaries reversed their kettles (the signal of revolt) in the
Byzantine hippodrome, and calling upon their patron saint, proceeded to
attack the royal palace. But Mahmoud was prepared to receive them. All
his other troops, artillery, marines, and infantry, were under arms and
at his command. The ulemas pronounced a curse of eternal dissolution
upon the insurgents. Mahmoud unfurled the sacred standard of the
prophet, and called on his people for assistance. A hundred cannon
opened fire upon their barracks, and in an hour twenty-five thousand
Janissaries were mowed down by grapeshot and scimitars. Their bodies
broke the lingering fast of the hungry dogs, or were cast into the
Bosphorus, and hurried by its rapid currents into the Sea of Marmora.
The annihilation of the Janissaries took place in 1826.
It is more than probable that Mahmoud could have effected a salutary
reform in the military system without resorting to extreme violence. He
was naturally of a cruel disposition, and was also deficient in prudence
and moderation. He gave the Janissaries cause to revolt; he made
frivolous innovations in their long-cherished customs, by commanding
them to shave their beards and forbidding them to wear the turban, a
beautiful headdress, an ornament at once national and religious. These
measures excited the disgust of all 'true believers,' while his enemies
called him an infidel, and his warmest supporters and the strongest
advocates of reform despaired of success. Innovations are expedient only
when they remove evil, and when men are prepared to receive them.
Command a Turk to shave his beard--by which he swears--the idol of his
life. As well bid him cut off his right arm or pluck out an eye--he
would obey one as soon as the other. The impolicy of changing the
customs and dress of a half-civilized, warlike nation, has been made
obvious in many instances--none more impressive than the mutiny of the
Anglo-Indian army at Velore in 1806.
Mahmoud in destroying the Janissaries took for his model Peter the
Great. Never were two sovereigns more unlike each other. Peter, generous
and humane, leaving his throne and travelling in disguise to educate
himself, stands in bold contrast with the parsimonious and cruel sultan.
Moreover, Mahmoud's was a more difficult undertaking. The Strelitzes
whom the czar annihilated were unsupported, were famous by no
illustrious victory, and had not an enthusiastic religious feeling. The
Janissaries, on the other hand, had strong family interests; they, too,
had decided the fate of the empire at the battle of Varna, where their
bravery established the Ottoman power, whose brightest triumphs were
clustered around their names; they had fought many a bloody battle, and
had never turned their backs to the foe; their leader was chosen from
their own ranks, and no nobility controlled their ambition or prevented
them from receiving the honor due to enterprise and valor; they held the
sultan in check; the ulemas gave sanction to their laws, and they in
turn sustained the authority of the ulemas with their swords. As long as
they experienced no change in their discipline and customs they were
invincible. But they too had participated in the universal degeneracy.
Like the Praetorian bands of Rome, they had become the absolute masters
of the empire. They pulled down and set up sultans at their will; their
valor had departed, but their unconquerable pride remained as part of
their heritage. Their ranks were filled with crowds of Greeks, Jews, and
Moslems, without discipline and without order. Many who had purchased
the privilege of being numbered in this formidable body, lived outside
of the barracks, and assembled only on pay day or in times of tumult and
rebellion. They despised all laws, civil and religious, and were a
constant source of annoyance to the people, whose lives and property
were at their mercy. Such were the subjects upon whom Mahmoud was to
operate. In the destruction of the Strelitzes and the Janissaries, Peter
and Mahmoud may be compared to two physicians: one practises on a
healthy savage, while the other attempts to cut out a malignant cancer
reaching the vitals, from the pampered sensualist. In annihilating these
troops, as in his other reforms, Mahmoud began where he should have
ended his labors; he mistook the end for the means.
Had he stopped with this act of violence, his supporters might defend
him on the doubtful ground of expediency; but he did not stop here. For
centuries the tyranny of the sultans had been restrained by the
derebeys, or lords of the valleys. They had been confirmed in the
possession of their lands by Mohammed II, from which time they had
continued to pay tribute to the sultan, and furnished him with quotas of
troops. The sultan had no control over their lives or property. The
subjects who tilled the productive lands of the valleys were suitably
rewarded for their labor. The happiest and wealthiest peasants of the
empire were found among the vassals of the beys, to whom they showed
great devotion. These feudal lords, at a moment's warning, could summon
twenty thousand men before their palace gates. They furnished the
greater part of the sultan's cavalry force in war; and, unlike the
pashas, had never raised the standard of rebellion; they had never
wished for revolutions, and had never sanctioned insurrections. The
possession of their property was guaranteed to them by inheritance, and
they had no need of money with which to bribe the Sublime Porte.
Mahmoud was bent on depriving them of their wealth and curtailing their
privileges. They were rich, did not bribe him, and held hereditary
possessions. These were unpardonable crimes in the sight of this
exemplary reformer. The beys, who never dealt in treachery, were
unsuspicious of others, and fell an easy prey. The peasants ceased to
cultivate the lands from which they could no longer profit; and many of
the wealthiest possessions became desolate. We must not think it
strange, therefore, that the military power was prostrated, when, after
having annihilated the Janissaries, Mahmoud deprived the derebeys of
their ancient authority; for the military power of the empire rested
chiefly in these two bodies. These innovations were made in the midst of
a destructive Greek war, and at a time when the Danube and the Balkan
were no longer formidable barriers to the Muscovite descendants of Ivan
the Terrible, who brought back memories of the past, and threatened to
avenge deeply treasured wrongs. Even at this critical period, when his
army was annihilated, his fleet defeated, and the legions of Russia
within a few days' march of Constantinople, Mahmoud threatened to feed
his horses at the high altar of St. Peter's, and proclaim the religion
of the prophet in the Muscovite capital. A threat that savored more of
the seraglio than of the throne!
His next step was to assail the privileges of the great provincial
cities, the inhabitants of which elected from their own number ayans, or
magistrates, distinguished for their wisdom and virtue. These
magistrates had much influence among the people; they had always
resisted exorbitant taxes and unjust decrees; their protection was
extended to Mussulmans and Christians without distinction. Their power
of veto was almost as effective as that of the _tribuni plebis_ of Rome;
they could point back to Solyman, the Solon of his time, as the author
of their protective system. But their power originated with the people.
To this Mahmoud would not submit. All power must emanate from him, the
all-wise and innovating sultan, who raised the low and humbled the
great, not as they were honest or corrupt, but as they fawned upon him,
or refused to yield implicit obedience to his nod.
In their endeavors to institute a new financial system, the predecessors
of Mahmoud reduced the standard of money gradually, in order not to
produce a panic. But he wished to accomplish in one day the work of
years. He issued a decree commanding the people to bring all their coin,
gold and silver, to their respective governors--where they would receive
less than half its value! He threatened the refractory with death. The
capital resounded with the dreaded cry of rebellion; and the exasperated
multitude that had surrounded the royal palace was not appeased until it
witnessed the public execution of the mint officers, whose only crime
was obedience to their master. This impolitic measure in the financial
department impoverished the people, and left the treasury still empty.
Foreign speculators bought the money--the circulation of which had
become illegal--and resold it to the sultan for sterling value!
Shortly after this he expelled about thirty thousand Christians from the
capital, which they had embellished and enriched by their labor. Their
fidelity had never been doubted. For this despicable act--their
expulsion--Mahmoud could adduce no better reason than that 'it was
solely on political grounds.' Strange politics this, for a sovereign,
who professed to have the magnanimity of Christian rulers! On the
expulsion of the Christians, Russia commenced hostilities, and a war
followed, in which the sultan paid dearly for his rashness.
In short, Mahmoud could not have given a better lesson to his subjects
than by reforming himself. He was cruel beyond measure--if the grand
seignior can ever be so called, who is taught that he may lop off a
score of heads each day 'for divine inspiration.' Still if he had been
as thoroughly skilled as he professed to have been, he should have shown
himself a humane as well as an innovating sovereign. Those who assisted
him in his reforms, he rewarded with the bowstring. His character was
blackened by ingratitude, an instinctive vice in oriental rulers.
Obstinate as he was suspicious, deceitful as he was cunning, he could
not rule his own passions, much less could he control the corrupt morals
of his people. He was to an extraordinary degree avaricious, a quality
everywhere odious, but especially in a land where generosity measures
love--where in the highest and in the lowest stations liberality is the
moving spring. While he mistook parsimony for economy, he did not
scruple to make war on trifling pretexts and waste his amassed treasures
in a hopeless cause.
In every attempted reform he wounded Ottoman pride and prejudice. Unlike
his cousin, he did not humor the faults of the people while making
innovations; he neither amused them with imposing shows, nor flattered
them by the pompous spectacle of his appearance in public--in one word,
he wanted the tact of a reformer. Selim, while he increased the navy and
established manufactories, built gorgeous palaces, and by his
magnificence dazzled the people, who were blind to his real designs;
they even permitted him to set up printing presses in the large cities,
on receiving assurance that the Koran would not be submitted to the
unholy process of squeezing!
Mahmoud thought, or pretended to think, that he could reform the empire
by imitating only the vices of Christianity, and manifesting a contempt
for Moslem virtues. While he drank wine--and in many other breaches of
the teachings of the sacred book provoked the faithful--his
proclamations breathed a most orthodox and fanatical spirit. He was a
sceptic; neither Mussulman nor Christian, but surprisingly inconsistent
and capricious. His, we fear, were 'hangman's hands,' and 'not ordained
to build a temple unto peace.'
Under Solyman the Magnificent, at once the most warlike monarch and
munificent patron of literature and art, the constitution of the
Janissaries was wise and effective. The children of Christians, taken by
the Turks in war or in their predatory incursions, were exposed in the
public markets of Constantinople, whence any person was at liberty to
take them into his service, on making a contract with the government to
return them at the demand of the sultan. These children were instructed
in Islamism, and were trained by manly exercise and labor, calculated to
strengthen the body and give elasticity to the spirits. From these hardy
orphans the ranks of the Janissaries were recruited. They came eagerly
to the camp; for they had been taught to regard it as the theatre of
their future glory. From earliest infancy they looked forward with joy
to the time when they should be numbered among those brave soldiers,
whose arms had maintained for a long series of years the supremacy of
the crescent. There was no rank, no dignity in the Turkish army to which
a Janissary could not aspire--a strong incentive to the display of
bravery. Such was the constitution of the army when it was the most
powerful in Europe: then it gained its victories, not by force of
numbers, but by superior military discipline and valor. In the middle of
the nineteenth century the capture of Christian children was abandoned.
The land forces degenerated into a wretchedly organized army of less
than three hundred thousand men, drafted from the lowest classes.
Mothers put their children to death that they might be spared the pangs
of seeing them torn away to pass their days in scenes of shame and
dissipation.
Not till the army had become a laughing stock to the weakest European
power did the sultans perceive the necessity of military reform. Selim
III established a school for artillery and naval officers, and engaged
Europeans, especially Frenchmen, as instructors in military science. We
can readily comprehend the degeneracy of the Turkish army, when we
remember that since the establishment of the school at Sulitzi for
engineers, the Turks have learned from foreign teachers military tactics
of which their own ancestors were the inventors, and which had been
forgotten, although full accounts of them lay hidden in musty volumes in
their military archives.
Foreign officers were at first regarded with contempt by Turkish
soldiers, whose unconquerable pride has ever proved a great impediment
to the regeneration of the empire. Moslem talent was not equal to the
exigencies that arose from the impolitic measures of Mahmoud. We find a
parallel case in Russia. Had Peter trusted to Muscovite genius to form
and command the troops which superseded the Strelitzes, Charles XII
would have quartered in the Kremlin.
Kutchuk Husseyin, the relative and favorite of Selim, made valuable
additions to the navy in which his master took such pride. Husseyin, who
had the welfare of his country at heart, was liberal and disinterested.
Vested with the office of captain pasha, he sent to Greece for
architects and engineers, with whose assistance he fortified Stamboul,
Sinope, and Rhodes; he built arsenals and extensive docks, which he
supplied with the necessary equipments of a powerful fleet. In a short
time, twenty sail of the line, constructed on the newest European
models, rode at anchor within sight of his palace. He also erected
barracks for the troops, and greatly improved the naval school. The
sudden death of Selim paralyzed the navy, which soon resumed its
accustomed languor.
The events of 1821, in which the Turkish fleet was defeated by armed
merchant vessels of Greece, gave a fresh impulse to the navy.
Experienced officers were placed in command, who, as they grew in
strength, grew in confidence, and trusted more to their own resources
than to the protection of Allah. Six years after the defeat, the navy
was in a state of greater practical efficiency than at any other time.
After a protracted struggle of five years it had gained the undisputed
supremacy of the Archipelago; and had it not been for the disastrous
defeat at Navarino, it would have proved equal, if not superior, to the
Russian fleet in the Black sea. The Turkish navy, to-day, numbers about
sixty war vessels, six of which are ships of the line, and six steam
frigates, built partly at London and Toulon.
The standing army in times of peace consists of 150,000 regulars; 60,000
auxiliaries (such as the Egyptian forces); and those of the northern
provinces, 110,000; with a corps de reserve of 150,000--an aggregate of
470,000 men. The army is recruited by lot and conscription (as in
France), and not as formerly, by arbitrary compulsion. Christians are
excluded from service in the infidel ranks, but pay a military tax.
Partial infringements, however, have been made in this exclusion, by
employing Armenians in the marine service and at the arsenals. Active
service in the army continues for a period of seven years; and the
discharged soldiers belong to the reserved force for five years more.
The organization of the corps de reserve is the same as that of the
regular army. Their arms and equipments are kept in the state arsenals,
and are produced only when the soldiers are called out, which takes
place once a year, after the harvest season. During one month, the
members of this corps de reserve lead a military life, and receive
regular pay.
The army is divided into six divisions of 25,000 each. The artillery is
modelled after the most approved Prussian system, while the infantry and
cavalry drill according to French tactics, and use French accoutrements
and arms. Thus, Turkey, with a standing army of 150,000 men, can muster
a force of nearly 500,000 at a few hours' notice; provided, however, she
has money to pay the troops, for the religious prejudices of the
Osmanlee do not tolerate the system of loans. So that Turkey, though she
has neither the formidable land force of France nor the navy of England,
is not crushed by the weight of a public debt, the principal of which
can never be paid. This military system is the result of the labors of
Rija Pasha and Redschid Pasha, by turn rivals and colleagues, disputing
on matters of secondary importance, but ever cordially cooperating in
the regeneration of the empire.
More attention has been given to military than to political reforms. The
intolerant Moslem spirit manifests direct opposition to all innovation
in the administration. As their fathers were, so they wish to be. Before
the time of Selim no reform movements of importance had been made in the
administrative branches. For five centuries the sultans had received, as
an aphorism in their political education, that the subjects existed for
the good of the sultan, and not the sultan for the welfare of the
people. Selim proclaimed the rights of his subjects and their supremacy;
and his words were confirmed by his deeds.
The administrative system was purely oriental, and bore scarcely any
analogy to that of any other country. From the reign of Solyman to that
of Selim--the protector (from whom there is no appeal) was kept closely
confined in the seraglio walls; indeed, he was a state prisoner from his
cradle to the day when he girt around him the imperial sabre. As the
sultan reigned by divine commission, no education was considered good
enough for him. Moreover, since his power was absolute, it had been
received as a recognized principle of state policy that he should be as
ignorant as possible, in order that he might prove more faithful to the
will of Allah. Selim banished these antiquated notions, and instituted a
new system--not that he lessened his own power, but established
representative bodies to assist him in making laws, and tribunals to
pass judgment upon and execute them.
The sultan is assisted by a divan; or council of ministers, and others,
who are nominated to that dignity by himself. The grand vizier presides
over this body, and is responsible for all measures adopted by it.
The legislative as well as the military system is borrowed from the
French; but the sultan is the source of all law, civil and military; he
is the summit, while the municipal institutions are the base, of the
political fabric. In theory at least, these institutions are established
on the broadest principles of freedom. Each community, like the communes
of France, sends an aga, or representative, to the supreme council. By
the famous ordinance of Gulhana, Mussulmans, Jews, and Christians are
represented, without distinction, in proportion to their number.
The administration of the interior belongs to the prime minister, who
appoints civil governors to take charge of the general administration.
The pashas had hitherto been both civil and military officers; purchased
their appointments at extravagant prices, and repaid themselves by
extortions practised upon the unfortunate subjects over whom they ruled.
The appointment of civil governors removed this old abuse, and left the
pashas vested only with military power. Each of the military chiefs has
command of one of the six divisions of which the army is composed. All
these officers receive a fixed salary; and the people, no longer subject
to their avarice and tyranny, pay regular rates of taxation.
The reforms I have mentioned, great as they were, were only preliminary
to the publishing of the hatti-scheriff of Gulhana, the magna charta and
bill of rights of Turkey. The son of Mahmoud, Abdul Medjid, on ascending
the throne, published this ordinance, which was to effect a reform in
the internal administration more beneficial than any other, either
before or after the destruction of the Janissaries. The ulemas, state
officers, foreign ambassadors, and a vast multitude of subjects had
assembled on the plains of Gulhana. The illustrious writings (as the
name signifies) were read aloud in the presence of this solemn assembly
by Redschid Pasha. The sultan, 'under the direct inspiration of the Most
High and of his prophet,' desired to look for the prosperity of the
empire in a good administration. The ulemas addressed a thanksgiving to
heaven amid the acclamations of the assembled thousands. These reforms
were threefold: The first guaranteed security to life, honor, and
property; the second is a new system of taxation; the third, a
remodelled plan for levying soldiers, and defining their time of
service. The subject can best be illustrated by quoting a few extracts
from the hatti-scheriff itself:
'The cause of every accused person shall be adjudged publicly, in
conformity to our divine law, after due inquiry and investigation;
and as long as sentence shall not have been regularly pronounced,
no one shall, either publicly or privately, cause another to perish
by prison or any other deadly means.'
'It shall not be permitted to any one to injure another,
_whosoever_ he may be.'
'Every man shall possess his own property, and shall dispose of it
with the most entire liberty. Thus, for example, the innocent heirs
of a criminal shall not be deprived of their legal rights, and the
goods of the criminal shall not be confiscated.'
'The imperial concessions extend to _all_ subjects, whatever may be
their religion or sect; they shall reap the benefit of them without
exception.'
'As to the other points, since they must be regulated by the
concourse of enlightened opinion, our council of justice, with whom
shall assemble, on certain days to be fixed by us, the notables of
the land, shall meet together to lay down guiding laws on the
points that affect the security of life, honor, and fortune, and
the assessment of imposts.'
'As soon as a law shall be defined, in order to render it valid and
binding, it shall be laid before us to receive our sanction, which
we Will write with our imperial hand.'
'As these present institutions have no other object than to give
fresh life and vigor to religion, the government, the nation, and
the empire, we pledge ourselves to do nothing to counteract them.
Whoever of the ulemas or chief men of the empire, or any other sort
of person, shall violate these institutions, shall undergo the
punishment awarded to his offence, without respect to his rank, or
personal consideration and credit.'
'As all the functionaries of the government receive at the present
day suitable salaries, and as those that are not sufficient shall
be increased, a vigorous law shall be enacted against traffic in
posts and favors, which the divine law reprobates, and which is one
of the principal causes of the decline of the empire.'
As a pledge of his promise, the sultan, after having deposited the
documents in the hall that contains the 'glorious mantle' of the
prophet, in the presence of the ulemas and chief men, swore to them in
the name of God, and administered the same oath to the priests and
officers. The hatti-scheriff was published in every part of the empire,
and was well received, except by a few of the retrograde party, who
lived by the old abuses, and vigorously resisted all attempts at
reformation.
By this ordinance, the sources of the revenue consist of the frontier
customs, the tithes, and a property tax. In two of these three sources
of revenue there are great abuses. In collecting the taxes, the tax
gatherers make exhorbitant demands, for which (owing to the partiality
of justice) there is no redress, The salguin, or land tax, is also the
cause of constant complaint. It presses equally upon the richest and the
poorest provinces; in consequence of which many of the most fertile
districts have been deserted. The government is not ignorant of these
facts. Abdul Medjid, a short time previous to his death, ordered a new
registration of property to be made, which will, in a great measure,
remedy this evil. This new registration caused not a little astonishment
and fear among the peasants, who could not approve of persons taking an
inventory of their property and their flocks. We must not be surprised
at this, for a parallel case is close at hand. When the Emperor Joseph
endeavored to introduce the mode of distinguishing houses in the
principal streets of _Vienna_, by numbers instead of the antiquated mode
by printed signs, the people were impressed with the idea that the
numbers were affixed for the purpose of more conveniently collecting a
new house tax!
The new system of farming the revenue proved especially beneficial to
the Christians. Under the old regime the Turks had been greatly favored.
The poll tax formerly levied on all who were not professed followers of
the prophet, has been abolished.
The empire is wealthy--immensely wealthy; but the money is in the hands
of the few. If we except the province of Servia, feudal lords, and tax
collectors, the whole Turkish population consists of peasants, who till
the soil on an equality of wretchedness. Yet it is to these same
suffering peasants, the bone and sinew of the land, that reformers must
look for support. It was the peasantry of Servia, headed by George the
Black, that in 1800-1812, rose in rebellion, and whose success infused
life and vigor into the more passive provinces. They, too, were
peasants--those brave and resolute men who expelled from the provinces
the robber princes, and almost gained a national existence. Many of
these same peasants, men in whose breasts still lingered the valor that
made their ancestors famous, joined the Grecian army in the successful
struggle for independence; even Moslem peasants left their ploughs in
the furrow and their herds unattended, to join the insurgents, to whose
success they greatly contributed. The heroes of all Turkish rebellions
have been peasants--the men of strong arms and unswerving energy. They
are naturally of a passive disposition, but when once roused to action
by religion or patriotism, they are as firm and unyielding in their
purpose as their own
'Pontic sea,
Whose icy currents and compulsive course
Ne'er feels returning ebb, but keeps due on
To the Propontic and the Hellespont.'
In the hands of the peasantry lies the destiny of the empire, its
regeneration or its fall. By ameliorating their condition and gaining
their good will, the sultans cannot fail to succeed in their reforms. By
working in opposition to them and exciting their enmity, success is
impossible.
The social system introduced by the victorious Othmans among the
conquered nations was not as oppressive as is generally believed. The
Turks, unlike the Germanic nations, the Huns and Normans, did not take
forcible possession of private property and divide it among their
conquering hordes. From those who acknowledged themselves subject to
their rule, the Turks exacted tribute, but protected their liberties and
political institutions. The conquerors introduced their laws into the
country, but not forcibly. To those who still adhered to the Christian
religion, they extended the rights of self-government, subject, however,
to a military tax. This was very far from degrading the cultivators of
the soil to servitude; this did not deprive them of their possessions,
inherited or purchased. But by a gradual change in the government this
civil equality and liberty in the possession of property was superseded
by an aristocratic and almost absolute despotism. The Ottomans came in
contact with a people ruling under Byzantine law, of which (as of the
feudal system) they had but a confused knowledge. The feudal system
having taken root in Greece, and having been already introduced into
Albania, had necessarily much influence on the contiguous provinces of
Moldavia and Wallachia, Servia and Bulgaria. Here the Greek emperors,
with correct notions of right and wrong, had governed wisely and justly
in a simple administration, which gave place to a complicated system of
laws and refinements, as unintelligible as they were useless and
ineffective. In the double heritage of Greece and Rome, the conquerors
imitated only their faults, moral and intellectual, and thus made more
prominent the fall of the two countries. The Turks were not sufficiently
enlightened to understand the laws and customs of the Greeks and Romans,
and profit thereby; nor could they resist the charm thrown around
aristocracy and venality, but succumbed to their baneful influences. The
degeneracy of the laws caused the misery of the peasantry, and paralyzed
the energies of the empire. The pashas gained almost unlimited power,
founded on the ruins of civil liberty. They did not scruple to persecute
the suffering peasant, even in the sanctuary of his family--held in the
highest veneration by the Turk. The peasants in many instances had no
other alternative than to fly to the mountains for safety, and lead a
wretched existence by rapine and murder. Some left Turkey to settle in
Russia and Austria, in search of that liberty and protection which was
denied them at home.
The Turkish peasants are not insensible to the degradation in which they
are languishing. But accustomed, in suffering and privation, to find
consolation in fatalism--which teaches implicit acquiescence in and
obedience to the will of Allah--they drag out their days in passive
submission. Seditions are almost always excited by unbelievers, who feel
their wrongs more deeply. The devout Turkish peasant seeks no better
fortune than the means wherewith to build a little cabin, with windows
and doors religiously closed to vulgar eyes. He finds comfort in the
words of his holy book: 'He is the happiest of mortals to whom God has
given contentment.' He performs his daily labor, makes his prostrations,
smokes his chibouk, and lives oblivious of care. He is far from being
indifferent to reforms, but is loth to take the initiative in political
innovations and social wars. His heart is with the cause, but here also
he is resigned: 'God is great--His will be done.' This same spirit of
resignation and submission to the divine will, from being a virtue
becomes his greatest curse.
The Servians, a hardy and vigorous race, who pride themselves on their
victories over the Moslems, stand in the van of the reform movement. By
the new constitution given to Servia in 1838, there exists no longer any
distinction of classes. All pay taxes, in proportion to the value of
their property, to the municipal and general government. All the
peasants are proprietors, and all the proprietors are peasants. The
Servians and Albanians have never refused foreign aid. They gave a kind
welcome to the legions that Nicholas sent across the Pruth, and worked
in concert with the brave warriors of the north, in the hope of gaining
a nationality and a recognized name.
The moral condition of the Bulgarians does not differ essentially from
that of the Servians; but there is a wide difference in their political
organization. The Bulgarians are yet only peasants, unprotected against
the violence and exactions of the sultan. They are more enterprising
than the Servians, and, could they enjoy an equitable legislation, would
soon vie with them in wealth and prosperity. They envy the national and
democratic institutions of the Servians, who are related to them by
blood, by religion, and a common tongue. They are eager for reforms,
both social and political, which shall give them a constitution similar
to that of Servia. In this they must ultimately succeed. The two people
are one in their sympathies: one cannot enjoy privileges without
exciting the jealousy of the other. Unless concessions are made, the day
is not far distant when the Bulgarians will revolt, as the Servians did
under Tzerny George, and gain the right of self-government.
The Illyrian peasants have not as promising a future. They are divided
among themselves, both in politics and religion; the several clans and
parties are engaged in ceaseless strife and bickering. On the most
trivial pretence a community will rise in arms and carry ruin and
desolation to its neighbor. The face of the country everywhere shows
signs of the terror under which it groans. In many districts the
humblest dwellings are fortified citadels, gloomy and threatening;
observatories are stationed in trees and on high cliffs, to guard
against surprisals; the streets of the towns and villages are traversed
by gloomy figures of athletic savage warriors, with fierce and sinister
expression of countenance, and their right hand resting on a belt
garnished with its brace of pistols. They are in such a deplorable state
of ignorance, and so blinded by mutual hatred, that they are incapable
of perceiving their wants and obtaining their rights by concerted
action.
The Servians and Bulgarians, although by nature not less warlike than
the Illyrians, are more pacific. This quality is, to a certain degree,
attributable to a better government; but their great advantage consists
in their being friends of labor. They are not divided by internal
factions; their pistols serve for ornaments, not offensive weapons;
their rude exterior hides within a gentle, childlike nature. Though
laborious, they seek not to amass wealth; kind to each other, to
strangers they are hospitable and generous. They are extremely courteous
and polite, and theirs is not the humility of the Austrian peasant, who
kisses the scornful hand of his superior; it is the deference and
respect that youth bears to age, or the attention which the host gives
to a welcome guest.
In Servia and Bulgaria, Christianity has gained the ascendancy; the
light of the gospel imparts comfort and happiness to all; but the
Illyrians, through a blind zeal in their social dissensions, have
debarred themselves from its vivifying and soothing influence.
During the early part of the last century, the peasants of the
Moldo-Wallachian provinces were enfranchised, but have not yet obtained
the right of property legislation. Being contiguous to Poland and
Hungary, their attention is naturally called to all the noise of reform
and to all the social questions that agitate the two countries. Unless
concessions are made, unless the peasant is recognized as proprietor of
the soil of which to-day he is but the farmer, a revolution will take
place, in which the Sublime Porte will lose these provinces as
effectually as it did the pashalies. It is not absolutely necessary,
though it would be judicious, to give Moldavia and Wallachia the same
political organization as Servia enjoys. The question now, is not of
rulers, whether they shall be sent from the divan or chosen from the
people; but is of property legislation and municipal institutions.
In all his reforms, the sultan should remember that the material upon
which he is to operate lies in the peasantry.
The empire, however, cannot be thoroughly reformed merely by
enfranchising the peasants, by introducing European customs, by
organizing new armies, building barracks, and establishing custom
houses. These improvements are the sign of a vigorous national impulse
and prosperity; they are the result, not the rudiments of civilization.
The fact that the sultan wears French boots and supplies his seraglio
with the latest Parisian modes signifies nothing.
In its palmy days, Turkey relied for success on its courage and love of
military glory; now its welfare and very existence depend upon the
peaceful arts of civilized life. The prosperity of the people measures
the condition of the empire. But how can an ignorant people prosper? The
time has come when a reform in the educational system of Turkey is
emphatically demanded. There must be intelligence among the people, and
educated men in the cabinet as well as brave men in the field. The
innovating sultans of the last century have done much for the
reconstruction of the broken political fabric of the empire; they have
organized a new and powerful army and navy; they have facilitated
commercial intercourse, but have done scarcely anything for the
diffusion of knowledge among their subjects.
All the knowledge in the empire is concentrated in the ulemas and
lawyers. The members of the Sublime Porte and other state officers, with
but few exceptions, are unlettered men, who owe their elevation, to
partiality or bribery. Under Mahmoud, beauty of person was the best
recommendation to favor and promotion!
But Turkey has had her golden age of letters as well as her age of
military glory. Her libraries and archives are filled with unread, musty
manuscripts, comprising treatises on philosophy and metaphysics,
histories, biographies, and poems, rich in the classic erudition of the
Orient. In 1336, Sultan Orkan found leisure from war and conquest to
establish, at Brusa, a literary institution, which became so famous for
its learning, that Persians and Arabians did not disdain to avail
themselves of its instruction. But with the death of its founder its
glory passed away. It was no longer the fountain head of learning in the
East.
The Turks, forgetful of the fact that antiquity is the youth of the
world, still follow Aristotle as their guide in philosophy and
metaphysics, and Ptolemy in geography! Missionaries have succeeded in
introducing modern text books into some of the schools, but owing to the
peculiar system of Turkish education, the result has not been so
favorable as was anticipated.
To each mosque is attached a school, where the pupils devote several
years in acquiring the rudiments of reading, writing, and arithmetic;
which completes their education. But few foreign instructors are
employed to teach in the schools, because the government is unwilling to
pay a suitable salary. While on state officers wealth is lavished with
the prodigality of oriental munificence, instructors receive only a
nominal recompense, often not exceeding six cents a day!
A few favored youths receive a European education, especially in French
and Austrian colleges. The oriental academy, established at Vienna by
Maria Theresa for the education of diplomatists to conduct intercourse
with the Porte, has formed many illustrious Turkish scholars. It is a
singular but not unpleasant commentary on the vicissitudes of fortune,
that Turkey should send her sons to be educated at Vienna, which only
two centuries ago a sultan besieged at the head of an army of two
hundred thousand men, and before whose gates he was defeated by the
combined Christian forces, who recovered eighty thousand Christian
captives, among whom were fourteen thousand maidens, and fifty thousand
children of both sexes!
The Christian subjects of the empire have made visible progress in their
educational system, although it is yet in a very imperfect state. In the
middle of the last century a body of Armenian monks formed a society for
promoting the educational interests of their countrymen. These pious and
benevolent men dwell alone on the little island of San Lazzaro, and
publish works on literature, science, and religion, which are
distributed among the Turkish Armenians.
Printing presses have lately been set up in the large cities, and books
are rapidly multiplying. In Constantinople several newspapers are
printed in French, Turkish, and Arabic; they are read in every coffee
house and barber shop, the common lounging places of the Ottoman, where
he smokes his pipe and discusses politics. Their columns are chiefly
devoted to the discussion of state affairs, and notices of public
functionaries. The sultan is the virtual editor, and consequently the
papers are popular, as containing opinions on state policy _ex
cathedra_. These presses were established with the reluctant sanction of
the ulemas, and the vigorous opposition of the scribes, an influential
body, protesting against the introduction of machinery, which was to
supersede the use of their fingers.
The council of public instruction at Constantinople has established a
medical and polytechnic school; in both, French, English, and German
teachers are employed. To the medical college is attached a botanical
garden and a natural history museum. The medical library consists
chiefly of French works. The implements used to experiment in the
physical sciences were made at Paris, London, and Vienna, and are of the
most approved kind. The number of students in attendance, on an average,
is seven hundred, comprising Turks, Greeks, Armenians, and Jews, all of
whom not only pay no tuition, but receive pecuniary assistance from the
government. As science cannot well be taught in Turkish, French is the
language of the school.
It should be borne in mind that Turkey, in her reform movement,
commenced this century, four hundred years behind Europe. When we
consider this, her advance in educational reformation appears in a
better light. The present law makes it a penal offence in a Turkish
parent not to send his children to school.
The universities, as well as the mosques and hospitals, are under the
control of the ulemas, who have always been a privileged and a
sanctioned order, and by their sanctity and great wealth are rendered
the most formidable body in the empire. Selim and his successors
somewhat lessened their power. By the innovations of 1854 an important
change was effected in the vacoof, or church property. The church had
hitherto held enormous possessions; and had not a check been placed on
the system, in the course of a few centuries all the lands would have
belonged to the priests. The property annexed to the mosques is held
sacred by all, both high and low. True believers, Greeks, Armenians, and
Jews, alike, by a reversion of their property on failure of male issue,
transferred it to the ulemas. The decree above mentioned restricted this
privilege of the priests. The entire system will soon be abolished.
As before stated, the ulemas have charge of the schools connected with
the principal mosques. The average number of scholars in each school, in
the reign of Mahmoud, was four hundred. They were, for the most part,
worthless, indolent fellows, and entirely under the control of the
ulemas, who used them as tools, and made them figure conspicuously in
all tumults and revolts. Their attempted assassination of Abdul Medjid
was their death warrant. Each ulema was restricted to four, in place of
four hundred scholars. This measure caused not a little ill feeling
among those opposed to reform; but as the most successful attempt at
restricting the despotic power of the religious order, the decree was of
vital importance, and gave the ulemas to understand that the power on
the throne was paramount to theirs.
The ulemas--whose functions do not differ materially from those of the
old doctors of the law among the Hebrews--have always claimed and
enjoyed both magisterial and ecclesiastical authority; and, indeed,
since the Mussulman's law and religion are convertible terms, we would
expect priests to be vested with the same powers, and performing the
same duties. Mohammed designed it should be so, and as long as war was
waged in the name of religion, as long as the Koran and the sword went
hand in hand together, the two professions were not incompatible; but
when Islamism had gained undisputed ascendency, there arose an obvious
discrepancy between the peaceful adoration of Allah and the settlements
of disputes between man and man. Priest and jurist, each had distinct
and qualified duties to perform. Before justice can be administered
properly the religious and legal professions must be separated; the
statutes must be distinct from the Koran and Sunnah, in the obscurities
of which they are at present involved. The sheik-ul-Islam (pontifex
maximus) is the head of the church and the bar; he appoints the bishops
and the judges; and in his twofold character of minister and lawyer, he
is the expounder of the Koran, the source of all laws, civil and
religious; his decisions serve as precedents, and are as
incontrovertible as the Koran itself.
By the late reforms, Christian testimony is admitted in courts of
justice. But this is merely a nominal privilege; for what avails it that
Christian evidence is received, if the Koran and Sunnah are to
constitute the law, and a Mussulman judge is to be the expounder? Is it
not evident that the 'true believer,' whether right or wrong, will be
shielded by the strong arm of prejudice at the expense of the Christian?
The purity of Turkish justice may be understood from the following
humorous account given by Dr. Hamlin:
'I once had a case of law with a Turkish judge. It was tried nine
times, and each time decided against me. After the ninth trial, the
judge sent me word that if I gave him 9,000 piastres (about $800),
he would decide the case in my favor, for all the world knew that
justice was on my side!'
I look, however, upon the religious toleration extended to Christians in
1854 as the most important of all reforms; it is the keystone of the
arch. Christianity has been on a gradual increase in Turkey; and it may
not be deemed extravagant to hope that when a few generations shall have
passed away, its supremacy will be acknowledged. As Constantine, finding
the Christian element predominant in the Roman empire, made the religion
of Christ that of his people, so some Selim or Abdul Medjid, urged by a
power behind the throne, and more potent than the throne itself, will
substitute the Bible for the Koran!
The fall of Islamism does not imply the downfall of Turkish rule. The
one is religious, the other a civil power; the one may wane, the other
rise.
The wars which brought the European powers in Turkish waters made a deep
impression upon the Turks, and convinced them that they had been rescued
from annihilation by foreign arms. This led to an important measure,
viz.: the promulgation of the imperial edict of 1850, which was
translated into all the languages of the empire, and read in all the
mosques and churches. Besides securing the freedom of conscience and the
equality of rights, it grants the right of apostasy, which had hitherto
been a capital offence: 'As all forms of religious worship are and shall
be freely professed in the empire, no person shall be hindered in the
practice of the religion which he professes; nor shall he in any way be
annoyed in this kind: in the matter of a man _changing_ his religion,
and _joining_ another, no force shall be applied to him.' The decree
bore directly upon Islamism. Turks, both private and official, now
discuss freely the doctrines of the New Testament. The Bible, to-day, is
widely circulated among the Turks. About seven thousand copies are sold
annually to Mohammedans, while ten years ago they would not have been
accepted as gifts. By all classes of people the Bible is purchased,
read, and made the subject of discussion. The sultan himself reads it.
Discussion leads to investigation, and investigation to the
establishment of truth. This is one of the causes that have been
silently at work, destined to effect the fall of Islamism.
In all parts of the empire, the Christian element is growing stronger
and stronger; the Mohammedan weaker. Even in Asia, the chosen abode of
the faithful, we find Christian cities and villages prosperous, and
Mohammedan cities falling to decay. In another century the Sublime Porte
will depend chiefly on the Christian element for its influence. To-day,
the Mussulman mosque, the pagoda of the Hindoo, the fire temple of the
Parsee, the Roman and Greek churches, meet together.
The adoration and prostrations of the Turk afford an imposing sight even
to the Christian. 'Praises be to God, for He is great,' resounds at
sunrise and at sunset, from ship to ship at sea, from kiosk to minaret
on land.
According to the Koran, there is a paradise for all true believers. This
paradise, Al Janat, signifies a pleasure garden, from which flows a
river, the river of life, whose water is clear as crystal, cold as snow,
and sweet as nectar. The believer who takes a draught shall thirst no
more. Even the oriental imagination fails to describe the glories of
this paradise--its fountains and flowers, pearls and gems, nectar and
ambrosia, all in unmeasured profusion. To crown the enchantment of the
place, to each faithful Moslem is allotted seventy-two houris,
resplendent beings, free from every human defect, perpetually renewing
their youth and beauty. Such is the Mohammedan conception of the future
world.
The Turks, in common with other Mohammedans, believe in angels, and in
the prophets Adam, Noah, Moses, and _Jesus_. One might suppose that such
a belief would assist missionaries in converting the infidel; but far
from assisting, its tendency is to make more difficult the inculcation
of Christian doctrines. When asked to accept the religion of Christ, the
Turk's ready answer is: 'We believe in Jesus! we believe in him already;
you know only a part of the true faith; Mohammed has superseded Jesus.'
Notwithstanding this, many Turks in Europe and Asia believe that in a
long series of years, Jesus will return to earth, reanimate their faith
and ancient valor, and with one unbroken religion, give them dominion to
the end of the world. They, in short, expect Jesus--the same Jesus whom
Christians worship--in the fullness of time to accomplish the work which
their prophet only began. Christian missionaries should avail themselves
of this remarkable belief, and turn it to the spiritual advantage of
those who entertain it.
'Let the Turkish Government remain, if by her standing Islamism may
fall! that we may carry back a purer literature to the land of
Homer, a purer law to the land of Moses, and the Gospel of Christ
to the land of the apostles.'
It only remains for me to say one word in regard to the now reigning
sovereign. The ulemas--who have become what the Janissaries were, the
hotbed of fanaticism--in their endeavors to overthrow the late sultan,
Abdul Medjid, looked upon the present sultan as their champion. If he
permits himself to become a tool in their hands, Turkey will lose
during his reign what she gained in a century. If, on the other hand, he
has the energy of Mahmoud, the humanity of Selim, and practises the
conciliatory policy of his brother, a glorious future awaits the empire.
FALSE ESTIMATIONS.
As one, who under pay of priest or pope,
Painteth an altar picture boldly bad,
Yet winning worship from the common eye,
Is less than one, who faltering day by day
Before the untouched canvas, dreams, and feels
An unaccomplished greatness: so is he
Who scrapes the skies and cleaves the patient air
For rhyming ecstasies to cheat the crowd,
That sees not in the stiller worshipper
The truer genius, who, in heights lone lost,
Forgets to interpret to a lesser sense.
O there do dwell among us minds divine,
In which th' etherial is so subtly mixed,
That only matter in its outward mien
To the observer shows. Such ever live
Unto themselves alone, in sweet still lives,
And die by all men misinterpreted.
Within a churchyard rise two honored urns
O'er graves not far removed. The one records
The 'genius of a Poet,' whose fitter fame
Lies in the volumes which his facile pen
Filled with the measure of redundant verse:
Before this urn the oft frequented sod
Is flattened with the tread of pensive feet.
The other simply bears the name and age
Of one who was 'a Merchant,' and bequeathed
A fair estate with numerous charities:
Before this urn the grass grows rank and green.
I knew them both in life, and thus to me
They measured in their lives their effigies:
He who the pen did wield with facile power,
Created what he wrote, and to the ear
With tact, not inspiration, wrought the sounds
To careful cadence; but the heart was cold
As the chill marble where the sculptor traced
Curious conceits of fancy. Let him pass,
His name not undervalued, for his fame
Shall in maturer ages lie as still
As doth his neighbor's now.
Turn we to him.
He was a man to whom the general eye
Bent with the confidence of daily trust
In things of daily use: a man 'of means,
--Sagacious, honest, plodding, punctual,--
Revolving in the rank of those whose shields
Bear bags of argent on a field of gold,
His life, to most men, was what most men's are,--
Unceasing calculation and keen thrift;
Unvarying as the ever-plying loom,
Which, moving in same limits day by day,
Weaves mesh on mesh, in tireless gain of goods.
But I, that knew him better than the herd,
Yet saw him less, knew that in him which lives
Still gracious and still plentiful to me
Now he hath passed away from me and them.
This man, whose talk on busy marts to men
Teemed with the current coin of thrifty trade,
--Exchanges, credits, money rates, and all,--
Hath stood with me upon a silent hill,
When the last flush of the dissolving day
Fainted before the moonlight, and, as 'twere
Unconscious of my listening, uttered there
The comprehensions of a soul true poised
With elemental beauty, giving tongue
Unto the dumbness of the blissful air.
So have I seen him, too, within his home,
When, newspaper on knee, his earnest gaze
Seemed scanning issues from the money list;
But comments came not, till my curious eye
Led out his meditation into words,
Thought-winding upward into sphery light,
So utterly unearthly and sublime,
That all the man of fact fled out of sense,
And visual refinement filled the space.
Oft hath he told me, nothing was so blind
As the far-seeing wisdom of the world,
And none within it knew him, save himself,
And that so scantily, that but for faith
In a redeeming knowledge yet to come,
He would lie down and let his weakness die
In self-reclaiming dust.
After his death,
I searched his papers, vainly, for a scrap
Whereon some dropped memento might record
His inner nature; but he nothing left--
Nothing of that deep life whose wondrous light
Guided him onward through the realms of sense,
And in a world of practical self-need
Sustained him with a glory unexpressed.
And thus it is that round the Poet's urn,
The sod is beaten down with pensive feet:
And thus it is that where the Merchant lies,
The grass, untrodden, groweth rank and green.
THE BLUE HANDKERCHIEF.
I had passed my last examinations, and had received my diploma
authorizing me to practise medicine, and I still lingered in the
vicinity of Edinburgh, partly because my money was nearly exhausted, and
partly from the very natural aversion I felt from quitting a place where
three very happy and useful years had been spent. After waiting many
weeks--for the communication between the opposite shores of the Atlantic
were not then so rapid as now--I received a large packet of letters from
'home,' all of them filled with congratulations on my success, and among
them were letters from my dear father and a beloved uncle, at whose
instance (he was himself a physician) my father had sent me abroad to
complete my medical education. My father's letter was even more
affectionate than usual, for he was highly gratified with my success,
and he counselled me to take advantage of the peace secured by the
battle of Waterloo to visit the continent, which for many years (with
the exception of a brief period) had been closed to all persons from
Great Britain; he enclosed me a draft on a London banker for a thousand
pounds. My uncle's letter was scarcely less affectionate; my Latin
thesis (I had sent my father and him a copy) had especially pleased him;
and after urging me to take advantage of my father's kindness, he added
that he had placed a thousand pounds at my disposition, with the same
London banker on whom my draft was drawn. A letter of introduction to a
French family was enclosed in the letter, and he engaged me to visit
them, for they had been his guests for a long time when the first
Revolution caused them to fly France, and they were under other
obligations to him; which I afterward learned from themselves was a
pecuniary favor more than once renewed during their residence with him.
Ten thousand dollars was a good deal of money to be placed at the
disposition of a young man as his pocket money for eighteen months, even
after a large deduction had been made from it for a library and
professional instruments.
Before I quitted Edinburgh, I received a letter from the gentleman to
whom my uncle had given me an introduction; he acquainted me that my
uncle had informed him that I was about visiting France, and that he had
taken the liberty of introducing me to him. The Marquis de ---- (such
was his title--his name I omit for obvious reasons) expressed with
great warmth his delight at having it in his power to exhibit the
gratitude he felt to my uncle, and urged me with the most pressing terms
to come at once to his home, and pass away there at least so much time
as might accustom me to the _spoken_ French language (I could easily
read it), that my visit to Paris might be more profitable and
agreeable--and it should be both, he was so good as to say, at least as
far as it depended on himself and his friends. I wrote him by the return
mail to thank him for his kindness, and to inform him that I should at
once set out for his hospitable home. I shall never forget the six
months I passed away in the Chateau de Bardy: the happiness of those
days was checkered only by my departure and by the incident I shall
presently relate. And even after I quitted that noble mansion, the
kindness of its inmates still watched over me, and opened homes to me
even in that great Maelstrom of life--Paris.
It was toward the end of the month of October--the most delightful month
of the seasons in France--as I was returning on foot from Orleans to the
Chateau de Bardy, from a rather prolonged pedestrian exploration in that
interesting neighborhood, where I had accurately examined all of the
curiosities, thanks to an ample memoir of my noble host (in those days
'Handbooks' were unknown, and Murray was busy publishing Byron and
Moore), when I thought I caught a glimpse of some soldiers. I was not
mistaken: on the road before me a Prussian regiment was marching. I
quickened my pace to hear the military music, for I was extremely
partial to it; but the band ceased playing, and no sound was heard
except an occasional roll of the kettle-drum at long intervals to mark
the uniform step of the soldiers. After following them for a half hour,
I saw the regiment enter a small plain, surrounded by a fir grove. I
asked a captain, whose acquaintance I had made, if his men were about to
be drilled.
'No,' said he, 'they are about to try, and perhaps to shoot, a soldier
of my company for having stolen something from the house where he was
billeted.'
'What,' said I, 'are they going to try, condemn, and execute him, all in
the same moment?'
'Yes,' said he, 'those are the provisions of the capitulation.'
This word 'capitulation' was to him an unanswerable argument, as if
everything had been provided for in the capitulation, the crime and the
punishment, justice and humanity.
'And if you have any curiosity to see it,' added the captain, 'I will
place you where you may see everything. It won't be long.'
It may be from my professional education, but the truth is, I have
always been fond of witnessing these melancholy spectacles; I persuade
myself that I shall discover the solution of the enigma--death--on the
face of a man in full health, whose life is suddenly severed. I followed
the captain. The regiment was formed in a hollow square; in the rear of
the second rank and near the edge of the grove, some soldiers were
digging a grave. They were commanded by the third lieutenant, for in the
regiment everything was done with order, and there is a certain form
observed even in the digging of a man's grave. In the centre of the
hollow square eight officers were seated on drums; a ninth officer was
on their right, and some distance before them, negligently writing
something, and using his knees as his desk; he was evidently filling up
the forms simply because it was against the 'regulations' that a man
should be killed without the usual forms. The accused was called up. He
was a tall, fine-looking young man, with a noble and gentle face. A
woman (the only witness in the cause) came up with him. But when the
colonel began the examination of the woman, the soldier stopped him,
saying:
'It is useless asking her any questions. I am going to confess
everything: I stole a handkerchief in that lady's house.
THE COLONEL. What! Piter! You have been stealing! We all thought _you_
incapable of such a thing!
PITER. It is true, Colonel, I have always tried to pass as an honest
man, and a good fellow. Oh! I tell you, it wan't for me I stole the
handkerchief. 'Twas for Mary.
THE COLONEL. Who is Mary?
PITER. Mary? Oh! she lives yonder.... at home.... just outside of
Areneberg.... don't you remember the big apple-tree?.... Oh! I shall
never see her again....
THE COLONEL. I don't understand you, Piter; explain yourself.
PITER. Why, Colonel.... but read this letter.
He gave the colonel a letter, which the latter read aloud, and every
word of which was engraved on my mind, and still is as present to my
memory as though I heard them an hour ago. It was as follows:
MY DEAR, DEAR PITER:--I take advantage of recruit Arnold's leaving, for
he has enlisted in your regiment, to send you this letter, and a silk
purse I have made for you. Oh! I have hidden from father to work it, for
he is always scolding me for loving you so much, and is always telling
me that you will never come back. But you will come back, won't you!
Even if you never come back, I will always love you just the same. I
promised myself to you the day you picked up my blue handkerchief at the
Areneberg dance, and brought it to me. Oh! when shall I see you again?
The only pleasure I have is to hear that your officers esteem you, and
your comrades love you. Everybody says you are an honest man and a good
fellow. But you have still two years to serve. Serve them quickly,
because then we shall be married. Good-by, dear, dear Piter, and believe
me, your own dear
MARY.
P.S. Try to send me, too, something from France, not because I'm afraid
I shall forget you, but I want something from you to carry always about
me. Kiss what you send me. I know I shall find at once where you kissed
it.
* * * * *
When the colonel finished reading the letter, Piter said:
'Arnold gave me this letter last night when I received my billet paper.
For my life's sake I could not sleep; I lay awake all night long,
thinking of home and of Mary. She asked for something from France. I had
no money. I drew three months' advance last week to send home to my
brother and my cousin. This morning, when I got up to go, I opened my
window. A blue handkerchief was hanging on a clothes line; it looked
like Mary's; it was the same color, the same white lines; I was so weak
as to take it, and put it in my knapsack. I went out into the street; I
was sorry for what I had done; I was going back to the house with it
just when this lady ran after me. The handkerchief was found in my
knapsack. This is all the truth. The capitulation orders me to be shot.
Shoot me, but don't despise me.'
The judges could not conceal their emotion; but when the balloting took
place, he was unanimously condemned to death. He heard his sentence with
sang-froid; after it was passed on him, he went up to his captain and
asked him to lend him four francs. The captain gave them to him. I then
saw Piter go to the woman to whom the blue handkerchief had been
restored, and I heard him say:
'Madame, here are four francs; I don't know whether your handkerchief is
worth more, but even if it is, I pay dear enough for it to engage you to
knock off the rest.'
Taking the handkerchief from her, he kissed it, and gave it to the
captain.
'Captain,' said he, 'in two years you'll be returning home; when you go
toward Areneberg, ask for Mary; give her this blue handkerchief, but
don't tell her how dearly I purchased it.'
Piter then kneeled and prayed fervently; when his prayers were ended, he
arose and walked with a firm step to the place of execution. I forgot
that I was a scientific man, and I walked down into the woods to avoid
seeing the end of this cruel tragedy. A volley of musketry soon told me
that all was over.
I returned to the fatal spot an hour afterward; the regiment had marched
away; all was calm and silent. While following the edge of the grove,
going to the highway, I perceived at a short distance before me traces
of blood, and a mound of freshly heaped earth. I took a branch from one
of the fir trees, and made a rude cross.
I placed it at the head of poor Piter's grave, now forgotten by every
body except by me, and perhaps by Mary.
GOLD.
Gold, next to iron, is the most widely diffused metal upon the surface
of our globe. It occurs in granite, the oldest rock known to us, and in
all the rocks derived from it; it is also found in the veinstones which
traverse other geological formations, but has never been found in any
secondary formation. It is, however, much more common in alluvial
grounds than among primitive and pyrogenous rocks. It is found
disseminated, under the form of spangles, in the silicious,
argillaceous, and ferruginous sands of certain plains and rivers,
especially in their junction, at the season of low water, and after
storms and temporary floods. It is the only metal of a yellow color; it
is readily crystallizable, and always assumes one or more of the
symmetrical shapes, such as the cube or regular octahedron. It affords a
resplendent polish, and may be exposed to the atmosphere for any length
of time, without suffering any change; it is remarkable for its beauty;
is nineteen times heavier than water, and, next to platinum, the
heaviest known substance; its malleability is such, that a cubic inch
will cover thirty-five hundred square feet; its ductility is such, that
a lump of the value of four hundred dollars could be drawn into a wire
which would extend around the globe. It is first mentioned in Genesis
ii, 11. It was found in the country of Havilah, where the rivers
Euphrates and Tigris unite and discharge their waters into the Persian
gulf.
The relative value of gold to silver in the days of the patriarch
Abraham was one to eight; at the period of B.C. 1000, it was one to
twelve; B.C. 500, it was one to thirteen; at the commencement of the
Christian era, it was one to nine; A.D. 500, it was one to eighteen;
A.D. 1100, it was one to eight; A.D. 1400, it was one to eleven; A.D.
1613, it was one to thirteen; A.D. 1700, it was one to fifteen and a
half; which latter ratio, with but slight variation, it has maintained
to the present day. Gold was considered bullion in Palestine for a long
period after silver had been current as money. The first mention of gold
money in the Bible is in David's reign (B.C. 1056), when that king
purchased the threshing floor of Oman for six hundred shekels of gold by
weight. In the early period of Grecian history the quantity of the
precious metals increased but slowly; the circulating medium did not
increase in proportion with the quantity of bullion. In the earliest
days of Greece, the precious metals existed in great abundance in the
Levant. Cabul and Little Thibet (B.C. 500) were abundant in gold. It
seems to be a well ascertained fact, that it was obtained near the
surface; so that countries, which formerly yielded the metal in great
abundance, are now entirely destitute of it. Croesus (B.C. 560) coined
the golden _stater_, which contained one hundred and thirty-three grains
of pure metal. Darius, son of Hystaspes (B.C. 538), coined _darics_,
containing one hundred and twenty-one grains of pure metal, which were
preferred, for several ages throughout the East, for their fineness.
Next to the _darics_ were some coins of the reigns of the tyrants of
Sicily: of Gelo (B.C. 491); of Hiero (B.C. 478); and of Dionysius (B.C,
404). Specimens of the two former are still preserved in modern
cabinets. _Darics_ are supposed to be mentioned in the latter books of
the Old Testament, under the name of _drams_. Very few specimens of the
_daric_ have come down to us; their scarcity may he accounted for by the
fact that they were melted down under the type of Alexander. Gold coin
was by no means plenty in Greece until Philip of Macedon had put the
mines of Thrace into full operation, about B.C. 360. Gold was also
obtained by the Greeks from Asia Minor, the adjacent islands, which
possessed it in abundance, and from India, Arabia, Armenia, Colchis, and
Troas. It was found mixed with the sands of the Pactolus and other
rivers. There are only about a dozen Greek coins in existence, three of
which are in the British Museum; and of the latter, two are _staters_,
of the weight of one hundred and twenty-nine grains each. About B.C.
207, gold coins were first struck off at Rome, and were denominated
_aurei_, four specimens of which are in the institution before alluded
to. Their weight was one hundred and twenty-one grains. Gold coins were
first issued in France by Clovis, A.D. 489; about the same time they
were issued in Spain by Amalric, the Gothic king; in both kingdoms they
were called _trientes_. They were first issued in England A.D. 1257, in
the shape of a penny. Florins were next issued, in 1344, of the value of
six shillings. The guinea was first issued in 1663, of Guinea gold. In
1733 all the gold coins--nobles, angels, rials, crowns, units, lions,
exurgats, etc., etc., were called in and forbidden to circulate. The
present sovereign was first issued in 1817.
From the commencement of the Christian era to the discovery of America,
the amount of gold obtained from the surface and bowels of the earth is
estimated to be thirty-eight hundred millions of dollars; from the date
of the latter event to the close of 1842, an addition of twenty-eight
hundred millions was obtained. The discovery and extensive working of
the Russian mines added, to the close of 1852, six hundred millions
more. The double discovery of the California mines in 1848, and of the
Australia mines in 1851 has added, to the present time, twenty-one
hundred millions; making a grand total of ninety-three hundred millions
of dollars. The average loss by wear and tear of coin is estimated to be
one-tenth of one per cent, per annum; and the loss by consumption in the
arts, by fire and shipwreck, at from one to three millions per annum.
A cubic inch of gold is worth (at L3 17_s._ 10-1/2_d._, or $18.69 per
ounce) two hundred and ten dollars; a cubic foot, three hundred and
sixty-two thousand eight hundred and eighty dollars; a cubic yard, nine
millions nine hundred and seventeen thousand seven hundred and sixty
dollars. The amount of gold in existence, at the commencement of the
Christian era, is estimated to be four hundred and twenty-seven millions
of dollars; at the period of the discovery of America, it had diminished
to fifty-seven millions; after the occurrence of that event, it
gradually increased, and in 1600, it attained to one hundred and five
millions; in 1700, to three hundred and fifty-one millions; in 1800, to
eleven hundred and twenty-five millions; in 1843, to two thousand
millions; in 1853 to three thousand millions; and at the present time,
the amount of gold in existence is estimated to be forty-eight hundred
millions of dollars; which, welded into one mass, could be contained in
a cube of twenty-four feet. Of the amount now in existence, three
thousand millions is estimated to be in coin and bullion, and the
remainder in watches, jewelry, plate, etc., etc.
The Russian gold mines were discovered in 1819, and extend over one
third of the circumference of the globe, upon the parallel of 55 deg. of
north latitude. Their product, since their discovery to the present
time, has amounted to eight hundred millions of dollars. The California
gold mines were discovered by William Marshall, on the ninth day of
February, 1848, at Sutter's Mill, upon the American Fork, a tributary of
the Sacramento, and extend from 34 deg. to 49 deg. of north latitude. Their
product, since their discovery to the present time, has amounted to one
thousand and forty-seven millions of dollars. The Australia gold mines
were discovered by Edward Hammond Hargraves, on the twelfth day of
February, 1851, in the Bathurst and Wellington districts, and extend
from 30 deg. to 38 deg. of south latitude. Their product, since their discovery
to the present time, has amounted to nine hundred and eleven millions of
dollars. The finest gold is obtained at Ballurat, and the largest nugget
yet obtained weighed twenty-two hundred and seventeen ounces, valued at
forty-one thousand dollars. In shape it resembled a continent with a
peninsula attached by a narrow isthmus. The annual product of gold at
the commencement of the Christian era is estimated at eight hundred
thousand dollars; at the period of the discovery of America it had
diminished to one hundred thousand dollars; after the occurrence of that
event it gradually increased, and in 1600 it attained to two millions;
and in 1700, to five millions; in 1800, to fifteen millions; in 1843, to
thirty-four millions; in 1850, to eighty-eight millions; in 1852, to two
hundred and thirty-six millions; but owing to the falling off of the
California as well as the Australia mines, the product of the present
year will not probably exceed one hundred and ninety millions.
Since 1792 to the present time, the gold coinage of the United States
mint has amounted to seven hundred and forty millions of dollars, of
which six hundred and fifty-five millions have been issued since 1850.
The gold coinage of the French mint, since 1726, has amounted to
eighty-seven hundred millions of francs, of which fifty-two hundred and
fifty millions have been issued since 1850. The gold coinage of the
British mint, since 1603, has amounted to two hundred and eighty
millions of pounds sterling; of which seventy-five millions have been
issued since 1850. The gold coinage of the Russian mint, since 1664, has
amounted to five hundred and twenty-six millions of roubles, of which
two hundred and sixty millions have been issued since 1850. The
sovereign of England contains one hundred and twelve grains of pure
metal; the new doubloon of Spain, one hundred and fifteen; the half
eagle of the United States, one hundred and sixteen; the gold lion of
the Netherlands, and the double ounce of Sicily, one hundred and
seventeen grains each; the ducat of Austria, one hundred and six; the
twenty-franc piece of France, ninety; and the half imperial of Russia,
ninety-one grains. A commissioner has been despatched by the United
States Government to England, France, and other countries of Europe, to
confer with their respective governments upon the expediency of adopting
a uniform system of coinage throughout the world, so that the coins of
one country may circulate in any other, without the expense of
recoinage--a consummation most devoutly to be wished.
The fact that the large amount of gold which has been thrown into the
monetary circulation of the world within the last fourteen years, has
exercised so little influence upon the money market or prices generally,
is at variance with the predictions of financial writers upon both sides
of the Atlantic. The increase in the present production of gold,
compared with former periods, is enormous; and it would not be
surprising if, in view of the explorations which are going on in Africa,
Japan, Borneo, and other countries bordering upon the equator, the
product of the precious metals within the next decade should be a
million of dollars _daily_. The price of gold has not diminished,
although the annual product has increased fivefold within twenty years.
LAST WORDS.
I am at last resolved. This taunting devil shall possess me no longer.
At least I will meet him face to face. I have read that the face of a
dead man is as though he understood the cause of all things, and was
therefore profoundly at rest, _I_ will know the cause of my wretched
fate, and will be at rest. My pistols lie loaded by my side--I shall die
to-night. To-morrow, twelve awestruck and trembling men will come and
look at me. They will ask each other: 'What could have been his motive
for the rash act.' Rash! my face will be calmer than theirs, for my
struggles in this life will be over; and I shall have gained--perhaps
knowledge, perhaps oblivion, but certainly victory. And to-night, as the
clock strikes twelve, there will be shrieks and horror in this room. No
matter: I shall have been more kind to those who utter them than they
know of, for they will not have known the cause until they have read
these lines.
And yet most people would esteem me a happy man. I am rich in all that
the world calls riches. I sit in a room filled with luxuries; a few
steps would bring me into the midst of guests, among whom are noble men
and women, sweet music, rare perfumes, glitter and costly show. My life
has been spent amid the influences of kind friends, good parents, and
culture in all that is highest and worthiest in literature and art; and
I can recall scenes as I write, of days that would have been most happy
but for the blight that has been upon me always. I think I see now the
pleasant parlor in the old house at home. Here sits our mother, a little
gray, but brisk and merry as a cricket; there our father, a
well-preserved gentleman of fifty, rather gratified at feeling the first
aristocratic twinges of gout, and whose double eyeglass is a chief
feature in all he says; there is Bill, poring over Sir William Napier's
'Peninsular War;' there is Charles, just rushing in, with a face the
principal features in which are redness and hair, to tell us that there
is another otter in the mill stream in the meadow; there is my little
sister, holding grave talk with dear Dollie, and best (or worst) of all,
there is cousin Lucy--cousin Lucy, with her brown hair, and soft, loving
eyes and quiet ways. Where are they all now? Charley went to London, was
first the favorite of the clubs, next a heartless rake, and finally,
being worn out, and, like Solomon, convinced that all was vanity, went
into the Church to become that most contemptible of all creatures, a
fashionable preacher; my father and mother are laid side by side in the
aisle of the old church on the hill, where their virtues are sculptured
in marble, for the information of anxiously curious mankind; sister Mary
no longer talks to dolls, though a flock of little girls, who call her
mother, do. Bill, poor Bill, lies far away in the Crimea, with the
bullet of a gray-coated Russian in his heart. And Lucy--but it is to her
I owe what I am, and what I am about to do.
I loved her--love her still. Will she _know_ what these words mean, when
she finds them here? I cannot tell. They are enough for me. Not for you
are they written, ball-room lounger, whispering of endless devotion
between every qaudrille; not to you, proud beauty, taking and absorbing
declarations as you would an ice; not for you, chattering monkey of the
Champs Elysees, raving of your _grande passion_ for Eloise, so
_charmante_, so _spirituelle_; nor for you, Eloise aforesaid, with your
devilish devices, stringing hearts in your girdle as Indians do scalps;
not for you, dancing Spaniard, with your eternal castagnets, whispering
just one word to your dark-eyed senorita, as you hand her another
perfumed cigarette; not for you, lounging Italian, hissing intrigues
under the shadow of an Athenian portico, or stealing after your veiled
incognita, as her shadow flits over the place where the blood of Caesar
dyed the floor of the Capitol, or where the knife of Virginius flashed
in the summer sun--not for one of you, for I have seen and despise you
all. To you all love is a sealed book, which you shall never open--a
tree of knowledge that will never turn into a curse for you--a beautiful
serpent that, as you gaze upon its changing hues, will never sting you
to the death.
I never told her. I would wait for hours to see her pass, if she went
out alone--but I never told her. I would trace her footsteps where she
had taken her daily walk; I would wait beneath her window at night, to
see but her shadow upon the blind, until she put out her lamp, and left
the stars and myself the only watchers there--but I never told her. I
would lay flowers in her way, happy if she wore them on her bosom, or
wreathed them in her hair, as she sometimes would--but she never knew
from whom they came. I sickened at my heart for her; I pined, oh! how I
pined for her, and worshipped her as a saint, the hope, the glory, the
heaven of my life--but I never told her.
Did she love me? No. And, while I loved, I feared her. She never made me
her companion, never took my arm; would always sit opposite me in the
carriage instead of by my side; if in a game of forfeits, I forced the
embrace I had won, she would struggle with tears of anger, though she
had given her cheek to William with a blush but a few minutes before. If
I had not been her abject slave, I could have torn her in pieces. Alas!
alas! we were but boys, and she a girl still. How many, long years I
have suffered since then!
One night I could not sleep, but sat up in my room thinking. Why should
she not love me? I am esteemed well-looking and intelligent, thought I,
looking into the glass, as if to confirm my satisfactory judgment of
myself. I gazed long and earnestly. Yes, certainly handsome, said I with
my lips, but--fool! fool! said my mocking eyes; for at that moment there
came out of their depths--there came a devil! Yes, a devil that glared
at me from the glass! a devil that was, and yet was not, myself! a devil
that had my form, and looked out of my face, but with its own cruel,
mocking eyes! And he and I confronted each other in that horrible glass.
I know not how long, but they told me afterward that I was found next
morning making ghastly faces at myself.
And then I was carried by spirits into a land of visions, where for a
hundred years, or for a moment of time, I was flying through space, and
clouds, and fire!--groping through dark caverns, millions of miles
long, crying wildly for light and air; now a giant, entangled in myriads
of chains that I could not break; now a reptile, writhing away from
footsteps that made the earth reel and tremble beneath their tread; and
at last waking, as if out of sleep, a poor, puny thing, with limbs like
shadows, laughing or crying by turns for very feebleness.
* * * * *
As I arose from that bed I knew that I was changed. It was a secret
thought, a secret that I have kept till now. I was not quite sure at
first, but it thus fell out that I knew it well:
One day William and I had been sitting for some time in the library, he
reading and I looking at the faces that glowed in the red-hot coal, and
thinking of Lucy and him.
'Where is Lucy?' said I, at length,
'Gone out into the village,' he answered, without looking from the book;
'first to buy gloves, then to see Miss Trip, the dancing mistress, who
is ill, then to Hurst Park to tea, whence I am to fetch her at nine
o'clock.'
'You seem to know all her movements,' I said, with a sneer.
'Certainly, he rejoined, 'she told me all that I have told you.'
'You always _are_ in her confidence,' said I, very angrily, as my blood
rose.
'I believe so,' said he, calmly; though he looked at me with some
surprise.
'And I never,' said I, between my teeth.
'That,' he said, 'is a matter with which I have no concern.'
I ground my teeth, but I kept quiet. I kept quiet, though every nerve in
my body tingled with rage, and my boiling blood rushed into my eyes till
I could hardly see. 'Do you know,' I shouted, 'do you know that I love
her--would die a thousand deaths for her?'
He clasped his hands with a quick motion, as he said in a low voice,
'And so do I; and so would I.'
'Beast, fiend!' I screamed, 'does she--does she----' I could not get out
the accursed words.
'We have been engaged,' he answered, divining what I would have asked,
'we have been engaged for some time, and----'
He did not finish the sentence, for I sprang at him, crushed him to the
floor, squeezed his throat till his face grew black and the froth oozed
out from his lips, beat his head upon the hearthstones till he lay still
and bleeding, and then sought my knife. It was up stairs. I flew to get
it. It lay upon my dressing table before the glass, and I snatched at
it. Great God! as I did so, another arm was thrust forth--not mine, I
swear, if I live a thousand years; and as I recoiled, I saw in that
glass a fiend step back. Not me, not me!--but a fiend with bloody hands,
and a foul leer upon its face, and a fierce, cruel laugh in its
glittering eyes. It was he, it was he! It was the devil that had
possessed me before, come back again. And as I shuddered and gasped, and
turned away, and then looked again into those eyes that pierced _me_
through, and saw the cold, bitter smile that was on the face before me,
I knew that the fiend would leave me never more, and that I was mad!
What was a quarrel with my brother now? I stole back, and, lifting him
up, carried him to his room, where I washed the blood from his face.
When he came to himself I fell at his feet and besought his pardon, and
that he would keep what had happened a secret. He forgave me. And I
believe the only lie he ever told in all his life was when he told Lucy
that he had cut his head by falling on a jagged stone.
Oh, how often after that my fingers itched to be at his throat again;
but I always quailed before his steady eye.
I pass over the next few years, except to say that I went to college,
where I was shunned by all, though never alone: was a dunce, and plucked
twice. Perhaps it was I who shunned others, for had I not society in
the constant presence of my Familiar? I was of course a dunce, for my
brain was never steady enough to carry me over the _Pons Asinorum_, or
to make a Latin verse with even decent correctness. I went away in
disgust. I think if I had stayed longer I should have torn somebody, or
else myself.
I went next into the army. It was a new era in my life, and, strange to
say, my devil left me for a while, so that I was able to master the
details of my profession, and to be esteemed a good and careful officer.
There was hope, too, of active service; for the Russian Eagle was slowly
unfolding his vast wings for a new descent into the plains of Europe.
William, married to Her now, who was a lieutenant in the Foot Guards,
wrote to me to say that he hoped we should be really brothers, now that
we were to meet before an enemy; and the next day out came the
declaration of war. When I had read it, I drew my sword, and, as I ran
my eye along its cold, sharp blade from hilt to point, I thought how
strange was its power to let out a man's life, and turn him, in a
moment, into a heap of inanimate carrion.
Of course I am not going to tell the history of the great siege in the
Crimea, for every child knows by heart the tale of the clambering fight
up the Alma's steeps, of the withering volley that suddenly crashed out
of the gray twilight on the hill of Inkerman, of the long months of
starvation, of the final _feu d'enfer_, beneath which the Russian host
crowded over the narrow bridge that saved them from their foe. But of
the fatal charge of the Six Hundred I must speak, for I was one of them,
and I have cursed its memory a thousand times.
I well remember that day--how restless I was the night before, and how I
listened to the dropping shots on either side, hoping almost that one
would find its way to my heart.
We were brigaded by daylight. Some manoeuvres on an extensive scale
were to be attempted, I believe, one of which was to outflank some
batteries of field artillery by which we had suffered much loss. They
were drawn up at the side and end of the valley of Balaklava, and we
were at the other end, and were ordered, it has since been said in
error, to charge down the valley upon them.
How beautiful the sun rose that day! The dewy odors from a thousand
flowers came floating up from that green valley as he rolled away the
mists from the mountain tops, and showed us the dusky masses far below,
from which the shot came whizzing every now and then. Gods! how we
exulted at the sight. Along our line rose a wild cheer, as our horses
tugged and strained at their bits, and every man's bridle was drawn
tight. Soon a puff of smoke came from a hillock near, and the stern
command 'draw swords' ran along from troop to troop, as the bright steel
flashed in the sunshine like a river of light. Then out pealed the
trumpets, and away we went, amidst a storm of ringing harness, and
clashing scabbards, and flying banners, and thundering hoofs that made
the ground shake. On we dashed, straight across the valley, in front of
a point-blank fire, that emptied many a saddle as we flew along,
straight upon the mass of smoke and flame which hid those fatal
batteries--straight at the gunners, dealing out wild blows upon them,
while they fought with swords, or axes, or clubbed muskets, or gun
spongers, or anything that could cut or strike a blow.
As for me, I only know that I was in the first line, and among the first
in the melee; where my first blow lighted upon the bare head of a
Russian, whose blood spouted high as I cut at him with all my force; for
after that a mist came over my eyes, and I fought in the dark, and then
came oblivion.
When I awoke to consciousness, which I did not for several days, I found
that I was wounded, and had been in danger of my life, though I should
most probably recover. As soon as I was strong enough to talk much, I
was told that my bravery had been very conspicuous, and that I had been
honorably mentioned in the order of the day. Four Russians, it seemed,
had died by my hand, and being at last cut on the head by a sabre, I was
with difficulty held on my horse when the retreat was sounded. I had
raved, it also appeared, incessantly; but now the fever had left me.
Good. It was fever, they thought, which had held possession of me. But
those who said so did not know what power it was that nerved my arm, and
then, having worked his devilish wile, flung me away like a broken toy.
Fever! They did not know that it was a 'fever' that had cursed me for
twelve long years.
But I got well, as those who were about me said, and, having been
reported fit for duty, made my appearance at parade, and afterward, the
same day, at mess.
My brother was dead. One day, while I lay ill, he and a party of his
brother officers were idly chatting in one of the more advanced
trenches, when a minie ball struck him, and he died without a word or
groan. They carried him out, and he lies at the little graveyard at
Scutari, with thousands of others who fell in the Great Siege. His sword
and other relics had been kept for me, and among them was a portrait of
Cousin Lucy, which he had worn next his heart. I should have to take it
to her. The general in command had already written to her, with the news
of her bereavement.
I was saying that I rejoined the mess. All my comrades congratulated me
but one. He was a young fellow, recently exchanged from another
regiment, who would one day wear the strawberry leaf upon his coronet--a
cold, supercilious, prying puppy, whom I hated at once. When we were
introduced, our mutual bow was studied in its cold formality--on his
side so much so as to be almost insulting, considering the place and
circumstances. To this day I believe that he, the only one of all there,
had suspected me, and I felt that I must be perpetually on my guard
against his curious glances. I was sure that one day we should have to
strive for the mastery. And we did--sooner than I expected; for, as the
colonel filled his glass, and, calling upon the rest to follow his
example, drank a welcome to me back among them, this knave, sitting
opposite at the time, fixed his eyes upon me as he lifted his glass to
his lips, and did not drink. As our looks met, I knew that he mocked me,
and I flung my wine in his face, and raved.
Those present forced me away, and took me to my tent, where they made me
lie down. I was supposed to be delirious from weakness and the effects
of my wound, and I heard them say, 'He has come out too soon; that wine
he drank at dinner was too much for him.' Good again! It was the wine!
'But,' thought I, 'as soon as this arm shall be able to strike or
thrust, I will have the life of that sneering devil, or he mine.' And I
kept my word. I met him within ten days afterward, walking at some
distance from the camp, quite alone, as I was myself.
'Good morning,' said he; 'you are about again, as I am glad to see.'
I said to him, 'Do you forget the time when I was out before?'
'Surely not,' said he; 'but I knew that you had been ill, and was not
master of yourself.'
'And so forgave me?' I rejoined, in a passion.
'And so forgave,' said he; 'why not?'
'Then learn,' said I, 'that I _was_ master of myself; that I am now;
that you insulted me grossly; that the only words I have for you
are--draw, sir, draw!'
'Stop!' he cried, as I drew my sword; 'pray come back with me to the
camp. You are ill; pray, come back; I have no quarrel with you, believe
me.'
But I struck him on the breast with my swordhilt, so that he nearly
fell. Then he recovered himself, and, still crying out that he had no
quarrel with me, drew and stood upon his guard, while I rushed upon him.
He was cool, and I furious. I believe he could have killed me easily if
he had wished, but he only parried my rapid blows. At last, however, as
I pressed him more closely, he grew paler, and began to fight in
earnest. What _then_ could he do against a madman? I bore him back, step
by step, till a mass of rock stopped him; and there I kept him, with the
hissing steel playing about his head, until he dropped upon one knee and
his sword fell from his hand. Then I paused, waiting to see him die as I
would a wounded hare, as die I knew he must, for I had pierced him with
twenty wounds. He knelt thus, and looked, not at me, but at the setting
sun; and then his head drooped and he rolled over, and was dead.
And as I wiped my sword on the grass, I shouted with glee.
Of course, I told no one. It was but another secret added to the many
that had torn my heart and brain. Nor, when the body was found, stripped
by camp followers, and supposed to be killed by a reconnoitring party of
the enemy, did I betray myself by word or look.
At last the war was over, and we were ordered home. I bade farewell to
the blue hills of the Crimea with secret joy, and as the shore faded
from my sight, the memory of all that had happened to me during the
Great Siege faded from my memory like a dream.
Upon our landing, I went as soon as possible home. How green the hedges
were, how sweet the scent of the violets, how soft the grass, how grand
the arching oaks and giant elms, as I journeyed along on foot. Surely I
have suffered enough, I said to myself, as I passed through meadow, and
copse, and lane, and over stiles, and to the old park at last. Surely I
have suffered enough, I said, as I came to the lodge gate, where the
keeper's wife looked curiously at my uniform and bronzed face, and the
crape on my arm, and then ran into the lodge to tell her husband that
here was Master Horace come back. Surely there was peace in that old
house, with its pointed gables, and moss-clad turrets, and ivied walls,
and little gothic windows--where the old butler grasped my hand; and the
maids came peeping out; and the old dog licked my face; where poor Lucy
wept upon my breast--wept for that I had come back alone; and then put
her little girl into my arms, to kiss dear Uncle Horace, come home once
more.
But, when I went to bed that night, in the same glass that showed me my
Enemy years before, I saw him looking at me, with his cruel smile,
shining out of my own eyes.
What more remains to be told? But little; for it was but the old story.
It is enough to say that I struggled on, hoping against hope; that I
cheated myself with the maddest hope of all--that she might be brought
to love me; that I one day prayed her to become my wife, and that she
broke from me with terror and loathing; that I fled her presence, and
was once more a wanderer over the earth; that my weary feet dragged me
over the snows of Siberia, where the furred noble and the chained serf
worked side by side; over the burning sands, where the brown Arab
careers along upon his steed, his white burnous fluttering in the hot
wind; over the broad prairies of America, where the Indian prowls with
his trusty rifle, waiting for the wild beast; over the paths of the
trackless deep; over the still wilder deserts and still more lonely
deeps of revelry and vice;--what more than that I have come back again;
that many guests are here to do honor to my return; that these are the
last words which I shall ever write!
PARTING
When 'mid the loud notes of the drum
And fife tones shrilling on the ear,
The music of our nation's hymns
Rose 'neath the elm trees loud and clear;
When on the Common's grassy plain
The city poured her countless throng,
And blessings fell like April rain
On each one as he marched along;
We parted,--hand close clasped in hand,
Telling the thoughts tongue could not speak;
Was it unmanly that our eyes
O'erflowed with love upon the cheek?
I hear thy cheery voice outspeak,
'Courage, the months will quickly fly,
And ere November chill and bleak
We meet at home, Ned, you and I.'
A livelier strain came from the band,
'God bless you' went from each to each;
A gazing eye, a waving hand,
Where hearts were all too full for speech.
He marched, obeying duty's call,
Of noblest nature, first to hear;
I, bound by fond domestic thrall,
In path of duty lingered here.
Slowly the summer months rolled on,
October harvested the corn,
November came with shortening days,
Passed by in mist and rain,--was gone,--
Yet still he came not; winter's snow
In feathery vesture clothed the trees,
Or, iceclad in a jewelled glow,
They sparkled in the chilly breeze.
Spring glowed along Potomac vales,
While north her footsteps tardier came,
For him the golden jasmine trails
O'er bright azaleas all aflame;
Still upon Yorktown's trampled fields,
O'er grassy plain and wooded swell,
Her sunny wealth the summer yields,
And still the word comes, 'All is well.'
A MERCHANT'S STORY.
'All of which I saw, and part of which I was.'
CHAPTER XII.
In the afternoon the exercises at the meeting house were conducted by
Preston, who publicly catechized the <DW64>s very much in the manner
that is practised in Northern Sunday schools. When the services were
over, and the family had gathered around the supper table, I said to
him:
'I've an idea of passing the evening with Joe; he has invited me. Would
it be proper for you and Mrs. Preston to go?'
'Oh, yes; and we will. I would like to have you see his mother. She is a
wonderful woman, and, if in the mood, will astonish you.'
'I think you told me she is a native African?'
'Yes, she is. She was brought from Africa when a child. She has a dim
recollection of her life there, and retains the language and
superstitions of her race,' replied Preston, rising from the table. 'I
think you had better go at once, for she retires early; Lucy and I will
follow you as soon as we can.'
* * * * *
Joe's cabin was located nearly in the centre of the little collection of
<DW64> houses, and a few hundred yards from the mansion. It was of logs,
a story and a half high, and had originally been only about twenty feet
square. To the primitive structure, however, an addition of the same
dimensions had been made, and as it then stretched for more than forty
feet along the narrow bypath which separated the two rows of <DW64>
shanties, it presented quite an imposing appearance. A second addition
in its rear, though it did not increase its dignity in the eyes of
'street' observers, added largely to its proportions and convenience.
The various epochs in Joe's history were plainly written on his
dwelling. The original building noted the time when, a common field
hand, he had married a wife, and set up housekeeping; the front addition
marked the era when his industry, intelligence, and devotion to his
master's interest had raised him above the dead level of black
servitude, and given him the management of the plantation; and the rear
structure spoke pleasantly of the time when old Deborah, disabled by age
from longer service at 'the great house,' and too infirm to clamber up
the steep ladder which led to Joe's attic bedrooms, had come to doze
away the remainder of her days under her son's roof.
The cabin was furnished with two entrance doors, and suspecting that the
one in the older portion led directly into the kitchen, I rapped lightly
at the other. In a moment it opened, and Joe ushered me into the living
room.
That apartment occupied the whole of the newer front, and had a
cheerful, cosy appearance. Its floor was covered with a tidy rag carpet,
evidently of home manufacture, and its plastered walls were decorated
with tasteful paper, and hung with a number of neatly framed engravings.
Opposite the doorway stood a large mahogany bureau, and over it,
suspended from the ceiling by leathern cords, was a curiously contrived
shelving, containing a score or more of well-worn books. Among them I
noticed a small edition of 'Shakespeare,' Milton's 'Poems,' Goldsmith's
'England,' the six volumes of 'Comprehensive Commentary,' Taylor's 'Holy
Living and Dying,' the 'Pilgrim's Progress,' a 'United States
Gazetteer,' and a complete set of the theological writings of
Swedenborg. Neat chintz curtains covered the small windows, a number of
brightly burnished brass candlesticks ornamented a plain wooden mantle
over the broad fireplace, and a yellow-pine table, oiled and varnished,
on which the 'tea things' were still standing, occupied the centre of
the apartment.
Through an open door, at the right of the bureau, I caught a glimpse of
the dormitory of the aged Africaness. As on the exterior of the building
a brief epitome of Joe's history was written, so in that room a portion
of his character was traced. Its comfortable and almost elegant
furnishings told, plainer than any words, that he was a devoted and
affectionate son. With its rich Brussels carpet, red window hangings,
cosy lounge, neat centre table, and small black-walnut bureau, it might
have been mistaken for the private apartment of a white lady of some
pretensions.
It was a little after nightfall when I entered the cabin, but a bright
fire, blazing on the hearth, gave me a full view of its occupants. Aggy,
a tidily clad, middle-aged yellow woman, was clearing away the supper
table, and Joe's mother was smoking a pipe in a large arm chair, in the
chimney corner.
The old negress wore a black levantine gown, open in front, and gathered
about the waist by a silken cord; a red and yellow turban, from
underneath which escaped a few frosted locks, and a white cambric
neckerchief that fell carelessly over her shoulders, and almost hid her
withered, scrawny neck. She was upward of seventy, but so infirm that
she appeared nearly a hundred. One of her lean, skinny arms, escaping
from the loose sleeve of her dress, rested on her knee; and her bowed,
bony frame leaned against the arm of her chair, as if incapable of
sitting upright. Her features, with the exception of her nose, which
curved slightly upward, were thin and regular; and her eyes were large,
deep, and densely black, and seemed turned inward, as if gazing with a
half-wondering stare at the strange mechanism which held together her
queer frame-work of bones and gutta percha.
She was the old woman who had greeted Preston so affectionately on our
arrival.
Turning to her as he tendered me a chair, Joe said:
'Mudder, dis am Mr. Kirke.'
Making a feeble effort to rise, and reaching out her trembling hand she
exclaimed, in a voice just above a whisper:
'You'm welcome yere, right welcome, sar.'
'Thank you, aunty. Pray keep your seat; don't rise on my account.'
'Tank _you_, massa Kirke, fur comin' yere. It'm bery good ob you. Ole
missy lub you, sar; you'm so good ter massa Robert. He'm my own chile,
sar!'
This was undoubtedly a figure of speech, for the old woman's skin was
altogether too black not to have given a trifle of its shading to the
complexion of her children. It was not only black, but blue black, and
of that peculiar hue which is seen only on the faces of native Africans.
Seeing that she had relinquished smoking, I said:
'Never mind me, aunty; I smoke myself sometimes.'
'Tank you, sar,' she replied, resuming her pipe, and relapsing into her
previous position; 'ole wimmin lub 'backer, sar.'
The low tone in which this was said made me conclude that further
conversation would be exhausting to her, so turning to Joe and Aggy--the
latter had hurried through her domestic employments, and taken a seat
near the fire--I entered into a general discussion of the old worthies
that occupied Joe's book shelves.
I found the <DW64> had taxed them for house room. He had levied on their
best thoughts, and I soon experienced the uneasy sensation which one
feels when he encounters a man who can 'talk him dry' on almost any
subject. On the single topic of the business to which I was educated, I
might have displayed, had it not been Sunday night, a greater amount of
information; but in the knowledge of every subject that was broached,
the black was my superior.
The conversation had rambled on for a full half hour, the old negress
meanwhile puffing steadily away, and giving no heed to it; when suddenly
her pipe dropped from her mouth, her eyes closed, her bent figure became
erect, and a quick, convulsive shiver passed over her. Thinking she was
about to fall in a fit, I exclaimed:
'Joe! See! your mother!'
'Neber mind, sar,' he quietly replied; 'it'm nuffin'. Only de power am
on her.'
A few more convulsive spasms succeeded, when the old woman's face
assumed a settled expression; and swaying her body back and forth with a
slow, steady motion, she commenced humming a low chant. Gradually it
grew louder, till it broke into a strange, wild song, filling the room,
and coming back in short, broken echoes from the adjoining apartments.
Struck with astonishment, I was about to speak, when Joe, laying his
hand on my arm, said:
'Hush, sar! It am de song ob de kidnap slave!'
It was sung in the African tongue, but I thought I heard, as it rose and
fell in a wild, irregular cadence, the thrilling story of the stolen
black; his smothered cries, and fevered moans in the slaver's hold; the
shriek of the wind, and the sullen sound of the surging waves as they
broke against the accursed ship; and, then--as the old negress rose and
poured forth quick, broken volumes of song--the loud mirth of the
drunken crew, mingling with what seemed dying groans, and the heavy
splash of falling bodies striking the sea.
As she concluded, with a firm, stately step--showing none of her
previous decrepitude--she approached me:
Seeing that I regarded her movements with a look of startled interest,
Joe said:
'Leff har do what she likes, sar. She hab suffin' to say to you.'
Taking a small bag[1] from her bosom, and placing it in the open front
of my waistcoat, she reached out her long, skinny arm, and placing her
skeleton hand on the top of my head, chanted a low song. The words were
mostly English, and the few I caught were something as follows:
'Oh, bress de swanga buckra man;
Bress wife an' chile ob buckra man.'
Bress all dat b'long to buckra man;
Barimo[2] bress de buckra man;
De good Lord bress de buckra man;
Bress, bress de swanga buckra man.'
As she finished the invocation, she took both my hands in hers, and
leaning forward, and muttering a few low words, seemed trying to read
the story imprinted on my palms. Her eyes were closed, and thinking she
might be troubled to see me without the use of those organs, I looked
inquiringly at her son.
'She don't need eyes, sar,' said Joe, answering my thought; 'she'll tell
all 'bout you widout dem.'
As he said this, she dropped one of my hands, and raising her right arm,
made several passes over my head, then resting her hand again upon it,
she began chanting another low song:
'What der yer see, mudder?' asked Joe, leaning forward, with a look of
intense interest on his face.
'A tall gemman-de swanga gemman--in a big city. De night am dark an'
cole--bery cole. Pore little chile am wid him, an' he cole--bery cole;
him cloes pore--bery pore. Dey come to a big hous'n--great light in de
winders--an' dey gwo in--swanga gemman an' pore chile. A great room
dar, wid big fire, an' oh! sweet young missus. She jump up-swanga gemman
speak to har, an' show de pore chile. She look sorry like, an' cry; den
she frow har arm 'roun' de pore chile; take him to de fire, an' kiss
him--kiss him ober an' ober agin.'
It was the scene when Kate first saw Frank, on the night of his mother's
death. I said nothing, but Joe asked:
'Any more, mudder?'
'Yas. I sees a big city, anoder city, in de daytime. In dark room,
upstars, am swanga gemman an' anoder buckra man--he bad buckra man.
Buckra angel dar, too, a standin' 'side de swanga gemman, but swanga
gemman doan't see har. She look jess like de pore chile. De swanga
gemman git up, an' 'pear angry, bery angry, but he keep in. Talk hard to
oder buckra man, who shake him head, an' look down. Swanga gemman den
walk de room, an' talk fasser yit, but bad buckra man keep shakin' him
head. Den swanga gemman stan' right ober de oder buckra man, an' de
strong words come inter him froat. Him 'pears gwine to curse de buckra
man, but de angel put har han' ober him moufh, an' say suffin' to him.
Swanga gemman yeres, dough he doan't see har. Den he say nuffin' more,
but gwo right 'way.'
It was the scene in Hallet's office, when I told him of his victim's
death, and entreated him to provide for, if he did not acknowledge his
child. The words which flashed upon my brain, and stayed the curse which
rose to my lips, were those of the dying girl: 'Leave him to GOD!'
'Go on. Tell me what she _said_,' I exclaimed.
'Mudder doan't _yere_; she only see de pictur ob what hab been. Listen!'
said Joe; and the old woman again spoke:
'I sees a big city--de fuss city, an' great hous'n--de fuss hous'n. De
young missus am dar, wid de pore chile, an' a little chile dat look jess
like she do; an' dar'm anoder bery little chile dar, too. Dey'm upstars
in a room, wid a bed an' a candle burnin'. Dey'm gwine to bed. Young
missus kneel down wid de two chil'ren, an' pray. An' side de pore chile,
an' kneelin' down wid har arm roun' him neck, am de buckra angel. She
pray, too. Swanga gemman in anoder room yere dem aprayin', an' he come
an' look. He say nuffin', but he stan' dar, an' de big tear run down him
cheek. De time come back to him when _he_ wus a little chile, an' he
pray like dem. He doan't pray 'nuff now!'
It was the last night I had passed at home. A feeling of indescribable
awe crept over me, and I rose halfway from my seat.
'Sit still, sar,' said Joe, almost forcing me back into the chair.
'You'll break de power.'
'You know the past, old woman,' I exclaimed. 'Tell me the future!'
'Hush!' she replied, with an imperious tone. 'Dey'm comin'.'
During all this time she had stood with her hand on my head, as
immovable as a marble statue. Her voice had a deep, strong tone, and her
face wore a look of calm power. Nothing about her reminded me of the
weak, decrepit old woman she had been but an hour before.
'Dey'm yere!' she said; and in another moment the door opened, and
Preston and his wife entered.
Without rising or speaking, Joe motioned them to two vacant chairs. As
they seated themselves, I exclaimed:
'She has told me all things that ever I did!'
'She has strange powers,' replied Preston.
'Hush, Robert Preston! De swanga gemman ax fur de future!'
Shading then her closed eyes with one hand, and leaning forward, as if
peering into the far distance, the old negress laid her other hand again
on my head, and continued:
'I see a deep, wide riber flowin' on to de great sea. De swanga gemman,
in strong boat, am on it; an' de young missus, an' de pore chile, an'
one, two oder chile, am wid him. De storm strike de riber, an' raise de
big wave, but de boat gwo on jess de same. De swanga gemman he doan't
keer fur de storm, or de big wave, fur he got 'em all dar! An' I see
anoder riber--not so deep, not so wide--flowin' on 'side de big riber,
to de great sea; an' you' (looking at Preston), 'an' de good missus, an'
one, two, free, four chile am dar. De wind blow ober dat riber an' raise
de big wave, but de swanga gemman reach out him hand, an' de wave gwo
down. An' I see a little riber flow out ob de big riber, an' de pore
chile in a little boat am on it. An' a little riber come out ob de oder
riber an' gwo into de oder little riber, an' a chile am on dat, too. De
two little boats meet, an' de two chile gwo on togedder, but--de storm
come dar, an'--de great rocks--oh! oh!' and, covering her face with her
hands, she turned away.
'What more do you see? Tell me, Deborah!' exclaimed Preston, bending
forward with breathless eagerness.
She raised her head, and seemed to look again in the same direction;
then, in a low tone, said:
'I sees no more.'
'What of the other river? What of that?' he exclaimed, with the same
breathless anxiety.
'I sees--de boat '<DW41> de rocks--de great rocks--an' you--dar--all by
you'seff--all by you'seff--an'--O Barimo!' and, giving a low scream, she
started back as if palsied with dread.
Springing to his feet, Preston seized her by both arms, and screamed
out:
'What more! Tell me WHAT MORE!'
Drawing her tall form up to its full height, and looking at him with her
closed eyes, she said, in a voice inexpressibly sad and tender:
'I sees de great rocks--de great fall--de great sea!' then pausing a
moment, and pointing upward, she added: 'Robert Preston! Trust in GOD!'
Overcome with emotion, she staggered back to her seat. A few convulsive
shudders passed over her; her eyes slowly opened, and--she was the same
weak, old woman as before.
* * * * *
The next morning I bade adieu to my kind friends, and started again on
my journey. Preston accompanied me as far as Wilmington, where we
parted; he going on to Whitesville, in search of the new turpentine
location; and I, proceeding by the Charleston boat, southward.
CHAPTER XIII
On my return to my home, a few weeks after the events narrated in the
previous chapter, in pursuance of a promise made to Preston, I inserted
an advertisement in the papers, which read somewhat as follows:
'WANTED, a suitable person to go South, as governess in a planter's
family. She must be thoroughly educated, and competent to instruct
a boy of twelve. Such a one may apply by letter;' etc., etc.
A score of replies flowed in within the few following days, but being
excessively occupied with a mass of personal business, which had
accumulated in my absence, I laid them all aside, till more than one
week had elapsed. Then, one evening I took them home, and Kate and I
opened the batch. As each one was read by my wife or myself, we
commented on the character of the writers as indicated by the
handwriting and general style of the epistles. Rejecting about two
thirds as altogether unworthy of attention, we reserved the remaining
half dozen for a second inspection. Among these, the one with the
cramped, precise chirography was thought to come from an old maid.
Another, whose five lines of rail fence covered a sheet nearly as large
as a ten-acre lot, was the production of a strong-minded woman. A third,
on tinted paper, and dotted with blots and erasures, was from a fat
lady, who wore her shoes down at the heel, and got up too late for
breakfast. 'But here, Kate,' I exclaimed, as I opened the fourth
missive, 'this one, in this firm yet lady-like hand--this one will do.
Hear what it says:
SIR:--I think I can answer your requirements. A line addressed to
Catharine Walley, B----, N.H., with full particulars, will receive
immediate attention.
'That's the woman, Kate. A business man in petticoats! _She_ can manage
a boy of twelve!'
'Or a man of twice that age,' said Kate, quietly reading the letter. 'I
wouldn't have that woman in _my_ house.'
'Why not? She has character--take my word for it. Her letter is as short
and sweet as a 'promise to pay.''
'She has too much character, and not of the right sort. There is no
womanliness about her.'
'You women are always hard on your own sex. She'll have to manage Joe,
and she'll need to be half man to do that. I think I had better write
her to come here. I can tell what she is when I see her. I can read a
woman like a book.'
There was a slight twinkle in my wife's eyes when I said this, and she
made some further objections, but I overruled them; and, on the
following morning, dispatched a letter, inviting Miss Walley to the
city.
Returning to my office from ''Change,' one afternoon, a few days
afterward, I found a lady awaiting me. She rose as I entered, and gave
her name as Miss Walley. She was prepossessing and lady-like in
appearance, and there was a certain ease and self-possession in her
manner, which I was surprised to see in one directly from a remote
country town. She wore a plain gray dress, with a cape of the same
material; a straw hat, neatly trimmed with brown ribbon, and, on the
inside, a bunch of deep pink flowers, which gave a slight coloring to
her otherwise pale and sallow but intellectual face. Her whole dress
bespoke refinement and taste. She was tall and slender, with an almost
imperceptible stoop in the shoulders, indicative of a studious habit;
but you forgot this seeming defect in her easy and graceful movements.
Her brown hair was combed plainly over a rather low and narrow forehead;
her face was long and thin, and her small, clear gray eyes were shaded
by brown eyebrows meeting together, and, when she was talking earnestly,
or listening attentively, slightly contracting, and deepening her keen
and thoughtful expression. Her nose was long and rather prominent; and
her mouth and chin were large, showing character and will; but their
masculine expression was relieved by a short upper lip, which displayed
to full advantage the finest set of teeth I ever saw.
Referring at once to the object of her visit, she handed me a number of
credentials, highly commendatory of her character and ability as a
teacher. I glanced over them, and assured her they were satisfactory.
She then questioned me as to the compensation she would receive, and the
position of the family needing her services. Answering these inquiries,
I added that I was prepared to engage her on the terms I had named.
'I have been in receipt of the same salary as assistant in a school in
my native village, sir,' she replied; 'but what you say of the family of
Mr. Preston, and a desire to visit the South, will induce me to accept
the situation.'
'When will you be ready to go, madam?' I asked.
'At once, sir. To-day, if necessary.'
Surprised and yet pleased with her promptness, I said:
'And are you entirely ready to go so far on so short notice?'
'Yes, sir. The cars leave in the morning, I am told. I will start
then.'
'And alone?'
'Yes, sir. We Yankee girls are accustomed to taking care of ourselves.'
'I admire your independence. But you pass the night in town; you will, I
trust, spend it at my residence?'
'Thank you, sir.'
Ordering a carriage and stopping on the way at a hotel to get the single
trunk which contained her wardrobe, I conveyed her at once to my
residence.
After supper we all gathered in the parlor, and I set about entertaining
our guest. I had to make little effort to do that, for her conversation
soon displayed a knowledge of books and people, and a wit and keenness
of intellect, as decidedly entertained me. She was not only brilliant,
but agreeable; and in the course of the evening made some pleasant
overtures to the children. Frank, with a book in his hand, had drawn his
chair off to another part of the room, and showed, at first, uncommon
reserve for a lad of his warm and genial nature; but gradually, as if in
spite of himself, he edged his chair nearer to her. Our little 'four
year old,' however, resisting the offered temptation of watch and chain,
and even sugar-plums, repelled her advances, and hid his curly head only
the more closely in the folds of his mother's dress. Kate listened and
laughed, but I caught occasionally, as her eyes studied the visitor
attentively, a troubled expression, which I well understood. After a
while the lady expressed a readiness to retire that she might obtain the
rest needed for an early start by the morning train, and Kate conducted
her to her apartment.
I felt highly delighted with the idea of being able to send Mrs. Preston
so agreeable a companion, and not a little vexed with my wife for not
sharing my enthusiasm. When she returned to the parlor, I said:
'Kate, why do you not like her?'
'I can hardly tell _why_,' she replied, 'but my first impression is
confirmed. I would not trust her. Why does she go South for the same
salary she has had in New Hampshire?'
'Because she wants to see the world; she's a stirring Yankee woman.'
'No; because you told her of Mr. Preston's position in society; and
because she hopes to win a plantation and a rich planter.'
'Nonsense,' I replied. 'You misjudge her.'
'I tell you, Edmund, she is a cold, selfish, sordid woman; all
intellect, and no heart. If I had never seen her face, I should have
known that by her voice, and the shake of her hand.'
But it was too late--I had engaged her; and at seven o'clock on the
following morning she was on her way to the South.
I soon received information of her safe arrival at her destination, and
the warm thanks of Preston for having sent him so agreeable a person,
and one so well fitted to instruct his children.
* * * * *
The turpentine location was soon secured, and early in the following
spring, Joe, with about a hundred 'prime hands,' commenced operations in
the new field. Constantly increasing shipments soon gave evidence of the
energy with which the <DW64> entered upon his work; and by the end of the
year, Preston had not only paid the advances we made on receiving the
deed of the land, but also the note I had given for the purchase of
Phyllis. For the first time in five years he was entirely out of our
debt.
The next season he hired a force of nearly two hundred <DW64>s, and
generously gave Joe a small interest in the new business, with a view to
the black's ultimately buying his freedom. His transactions soon became
large and profitable both to him and to us. Shortly afterward he paid
off the last of his floating debt, and his balances in our hands grew
from nothing till they reached five and seven and often ten thousand
dollars.
But heavy affliction overtook him in the midst of his prosperity. His
wife and two eldest daughters were stricken down by a prevailing
epidemic, and died within a fortnight of each other. A letter which I
received from him at this time, will best relate these events. It was as
follows:
MY DEAR FRIEND:--I have sad, very sad news to tell you. A week ago
to-day I followed the remains of my beloved wife to the grave.
Overcome by watching with our children, and grief at their loss,
about three weeks since she took their disease, and sinking
rapidly, soon resigned her spotless spirit to the hands of her
MAKER. Overwhelmed by this treble affliction, I have not been able
to write you before. Even now I can hardly hold a pen. I am
perfectly paralyzed; I can neither act nor think--I can only
_feel_.
You, who have seen her in our home, can realize what she was to my
family, but none can know what she was to me: companion, friend,
guide! My stay and support through long years of trial, she is
taken from me just as prosperity is dawning on me, and I was hoping
to repay, by a life of devotion, some part of what she had borne
and suffered on my account. Another angel has been welcomed in
heaven, but I am left here alone--alone with my grief and my
remorse!
My son is inconsolable, and even little Selly seems to realize the
full extent of her loss. The poor little thing will not leave me
for a moment. She is now the only comfort I have. Miss Walley has
been unremitting in her kindness and attention, taking the burden
of everything upon herself. Indeed, I do not know what I should
have done without her.
Time may temper my affliction, but _now_, my dear friend, I am not
ROBERT PRESTON.
Nothing worthy of special mention occurred to the persons whose history
I am relating till about a year after the death of Mrs. Preston. Then,
one day late in the autumn, I received information of her husband's
approaching marriage with the governess. In the letter which invited me
to be present at the ceremony, Preston said: 'No one can ever fill the
place in my heart that is occupied, and ever will be occupied by the
memory of my sainted wife; but Miss Walley has rendered herself
indispensable to me and my family. My studious habits and ignorance of
business made me, as you know, even in my full health and strength, a
poor manager; and during the past year, grief has so broken my spirits
that I have been utterly unfitted for attending to the commonest duties.
But for Miss Walley, everything would have gone to waste and ruin. With
the efficiency of a business man, she has attended to my household,
overseen my plantation, and managed my entire affairs. In the first
moments of my bereavement, when grief so entirely overwhelmed me that I
saw no one, I did not know to what censurious remark her disinterested
devotion to my interests was subjecting her; but recently I have
realized the impropriety of a young, unmarried woman occupying the
position she holds in my household. Miss Walley, also, has felt this,
and some time since notified me, though with evident reluctance, that
she felt it imperatively necessary to leave my service. What, then,
could I do? My people needed a mistress; my children a mother. She was
both. Only one course seemed open, and after mature deliberation I
offered her my hand, frankly stating that my heart was with the angel
who, lost to me here, will be mine hereafter. Satisfied with my
friendship and esteem, she has accepted me; and we are to be married on
the 26th inst.; when I most sincerely trust that you, my dear friend,
and your estimable wife, will be present.
That night I took the letter home to my wife. She read it, and laying it
down, sadly said:
'Oh, Edmund! He is, indeed, 'among the rocks!''
* * * * *
Two years went by, and I did not meet Preston, but our business
relations kept us in frequent correspondence, and his letters
occasionally alluded to his domestic affairs.
Very soon after his marriage with the governess, his son went to live
with his uncle, Mr. James Preston, of Mobile, a wealthy bachelor, who
long before had expressed the intention of having the boy succeed to his
business and estate. 'Boss Joe' continued in charge of the turpentine
plantation, and had built him a house, and removed his wife and aged
mother to his new home. On one of my visits to the South I stopped
overnight with him, and was delighted with his model establishment. Two
hundred as cheerful-looking <DW54>s as ever swung a turpentine axe, were
gathered in tents and small shanties around his neat log cabin, and Joe
seemed as happy as if he were governor of a province.
His operations had grown to such magnitude that Preston then ranked
among the largest producers of the North Carolina staple, and his
'account' had become one of the most valuable on our books. Though we
sent 'account currents' and duplicates of each 'account sales' to his
master, our regular 'returns' were made to Joe, and no one of our
correspondents held us to so strict an accountability, or so often
expressed dissatisfaction with the result of his shipments, as he.
'I thinks a heap of you, Mr. Kirke,' he said at the close of one of his
letters about this time; 'but the fact am, thar's no friendship in
trade, and you _did_ sell that lass pile of truck jess one day too
sudden.'
CHAPTER XIV.
Two more years rolled away. Frank was nearly sixteen. He had grown up a
fine, manly lad, and never for one moment had Kate or I regretted the
care we had bestowed on his education and training. He was all we could
have wished for in our own son, and in his warm love and cheerful
obedience we both found the blessing invoked on us by his dying mother.
His affection for Kate was something more than the common feeling of a
child for a parent. With that was blended a sort of half worship, which
made him listen to her every word, and hang on her every look, as if she
were a being of some higher order than he. They were inseparable. He
preferred her society to that of his young companions, and often, when
he was a child, seated by her knee, and listening, when she told of his
'other mother' in the 'beautiful heaven,' have I seen his eye wander to
her face with an expression, which plainly said: 'My heart knows no
'other mother' than you.' Kate was proud of him, and well she might be,
for he was a comely youth; and his straight, closely knit, sinewy frame;
dark, deepset eyes; and broad, open forehead, overhung with thick, brown
hair; only outshadowed a beautiful mind, an open, upright, manly nature,
whose firm and steady integrity nothing could shake.
About this time I received a letter from his father, which, as it had an
important bearing on the lad's future career, I give to the reader:
BOSTON, _September 20th, 185-._
DEAR SIR:--A recent illness has brought my past life in its true light
before me. I see its sin, and I would make all the atonement in my
power. I cannot undo the wrong I have done to one who is gone, but I can
do my duty to her child. You, I am told, have been a father to him. _I_
would now assume that relation, and make you such recompense for what
you have done, as you may require. I am too weak to travel, or indeed,
to leave my house, but I am impatient to see my son. May I not ask you
to bring him to me at once? Then I will arrange all things to your
satisfaction.
I need not tell you, after saying what I have, that I should feel
greatly gratified to once more possess your confidence, and regard.
I am, sincerely yours,
JOHN HALLET.
In another hand was the following postscript:
MY DEAR BOY:--John is sincere. Thee can trust him. He has told me _all_.
He will do the right thing. Come on with the lad as soon as thee can.
Love to Kate. Thy old friend,
DAVID.
After conferring with my wife, I sent the following reply to these
communications:
NEW YORK, _September 22d, 185-._
DAVID OF OLD;--Thou man after the Lord's own heart. I have Hallet's
letter, seasoned with your P.S. He is shrewd; he knew that nothing but
your old-fashioned hand would draw a reply from _me_, to anything
written by _him_.
I've no faith in sick-bed repentances; and none in John Hallet, sick or
well:
'When the devil was sick,
The devil a monk would be;
When the devil got well,
The devil a monk was he.'
However, as Hallet is capable of cheating his best friend, even the
devil, I will take his letter into consideration; but it having taken
him sixteen years to make up his mind to do a right action, it may take
me as many days to come to a decision on this subject.
Frank is everything to us, and nothing but the clearest conviction that
his ultimate good will be promoted by going to his father, will induce
us to consent to it.
I do not write Hallet. You may give him as much or as little of this
letter as you think will be good for him.
Kate sends love to you and to Alice; and dear David, with all the love I
felt for you when I wore a short jacket, and sat on the old stool,
I am your devoted friend.
* * * * *
It was a dingy old sign. It had hung there in sun and rain till its
letters were faint and its face was furrowed. It had looked down on a
generation that had passed away, and seen those who placed it there go
out of that doorway never to return; still it clung to that dingy old
warehouse, and still Russell, Rollins & Co. was signed in the dingy old
counting room at the head of the stairway. It was known the world over.
It was heard of on the cotton fields of Texas, in the canebrakes of
Cuba, and amid the rice swamps of Carolina. The Chinaman spoke of it as
he sipped his tea and plied his chopsticks in the streets of Canton, and
the half-naked <DW64> rattled its gold as he gathered palm oil and the
copal gum on the western coast of Africa. Its plain initials, painted in
black on a white ground, waved from tall masts over many seas, and its
simple 'promise to pay,' scrawled in a bad hand on a narrow strip of
paper, unlocked the vaults of the best bankers in Europe. And yet it was
a dingy old sign! Men looked up to it as they passed by, and wondered
that a cracked, weather-beaten board, that would not sell for a dollar,
should be counted 'good for a million.'
It was a dingy old warehouse, with narrow, dark, cobwebbed windows, and
wide, rusty iron shutters, which, as the bleak October wind swept up old
Long Wharf, swung slowly on their hinges with a sharp, grating creak. I
heard them in my boyhood. Perched on a tall stool at that old desk, I
used to listen, in the long winter nights, to those strange, wild cries,
till I fancied they were voices of the uneasy dead, come back to take
the vacant seats beside me, and to pace again, with ghostly tread, the
floor of that dark old counting room. They were a mystery and a terror
to me; but they never creaked so harshly, or cried so wildly, as on that
October night, when for the first time in nine years I turned my steps
up the trembling old stairway.
It was just after nightfall. A single gas burner threw a dim, uncertain
light over the old desk, and lit up the figure of a tall, gray-haired
man, who was bending over it. He had round, stooping shoulders, and
long, spindling limbs. One of his large feet, encased in a thick,
square-toed shoe, rested on the round of the desk; the other, planted
squarely on the floor, upheld his spare, gaunt frame. His face was thin
and long, and two deep, black lines under his eyes contrasted strangely
with the pallid whiteness of his features. His clothes were of the
fashion of those good people called 'Friends,' and had served long as
his 'Sunday best' before being degraded to daily duty. They were of
plain brown, and, though not shabby, were worn and threadbare, and of
decidedly economical appearance. Everything about him, indeed, wore an
economical look. His scant coat tails, narrow pants, and short waistcoat
showed that the cost of each inch of material had been counted, while
his thin hair, brushed carefully over his bald head, had not a lock to
spare; and even his large, sharp bones were covered with only just
enough flesh to hold them comfortably together. He had stood there till
his eye was dim and his step feeble, and though he had, for twenty
years--when handing in each semiannual trial balance to the head of the
house--declared that was his last, everybody said he would continue to
stand there till his own trial balance was struck, and his earthly
accounts were closed forever.
As I entered, he turned his mild blue eye upon me, and, taking my hand
warmly in his, exclaimed:
'My dear boy, I am glad to see thee!'
'I am glad to see _you_, David. Is Alice well?'
'Very well. And Kate, and thy babies?'
'All well,' I replied.
'Thee has come to see John?'
'Yes. How is he?'
'Oh, better; he got out several days ago. He's inside now,' and opening
the door of an inner office, separated from the outer one by a glass
partition, he said, 'John, Edmund is here.'
A tall, dark man came to the door, and, with a slightly flurried and
embarrassed manner, said:
'Ah, Mr. Kirke! I'm glad to see you. Please step in.'
As he tendered me a chair, a shorter and younger gentleman, who was
writing at another desk, sprang from his seat, and slapping me
familiarly on the back, exclaimed:
'My dear fellow, how are you?'
'Very well, Cragin; how are _you_?' I replied, returning his cordial
greeting.
'Good as new--never better in my life. It's good for one's health to see
you _here_.'
'I have come at Mr. Hallet's invitation.'
'Yes, I know, Hallet has told me you've a smart boy you want us to take.
Send him along. Boston's the place to train a youngster to business.'
The last speaker was not more than thirty, but a bald spot on the top of
his head, and a slight falling-in of his mouth, caused by premature
decay of the front teeth, made him seem several years older. He had
marked but not regular features, and a restless, dark eye, that opened
and shut with a peculiar wink, which kept time with the motion of his
lips in speaking. His clothes were cut in a loose, jaunty style, and his
manner, though brusque and abrupt, betokened, like his face, a free,
frank, whole-souled character. He was several years the junior of the
other, and as unlike him as one man can be unlike another.
The older gentleman, as I have said, was tall and dark. He had a high,
bold forehead, a pale, sallow complexion, and wore heavy gray whiskers,
trimmed with the utmost nicety, and meeting under a sharp, narrow chin.
His face was large, his jaws wide, and his nose pointed and prominent,
but his mouth was small and gathered in at the corners like a rat's;
and, as if to add to the rat resemblance, its puny, white teeth seemed
borrowed from that animal. There was a stately precision in his manner
and a stealthy softness in his tread not often seen in combination,
which might have impressed a close observer as indicative of a bold,
pompous, and yet cunning character.
These two gentlemen--Mr. Hallet and Mr. Cragin--were the only surviving
partners of the great house of Russell, Rollins & Co.
'Have you brought him with you?' asked Hallet, his voice trembling a
little, and his pale face flushing slightly as he spoke.
'No, sir,' I replied; 'I thought I would confer with you first. I have
not yet broached the subject to the lad.'
Some unimportant conversation followed, when Hallet, turning to Cragin,
asked:
'Are all the letters written for tomorrow's steamers?'
'Yes,' said Cragin, rising; 'and I believe I'll leave you two together.
As you've not spoken for ten years, you must have a good deal to say.
Come, David,' he called out, as he drew on his outside coat, 'let's go.'
'No, don't take David,' I exclaimed; 'I want to talk with the old
gentleman.'
'But you can see him to-morrow.'
'No, I return in the morning.'
'Well, David, I'll tell Alice you'll be home by nine.'
'Oh, that's it,' I said, laughing. 'It's Alice who makes you leave so
early on steamer night.'
'Yes, _sir_; Alice that _is_, and Mrs. Augustus Cragin that is _to
be_--when I get a new set of teeth. Good night,' and saying this, he
took up his cane, and left the office.
When he was gone, Hallet said to me:
'Do you desire to have David a witness to our conversation?'
'I want him to be a _party_ to it. We can come to no arrangement without
his cooperation.'
Hallet asked the bookkeeper in. When he was seated, I said:
'Well, Mr. Hallet, what do you propose to do for your son?'
'To treat him as I do my other children. Do all but acknowledge him.
That would injure _him_.'
'That is not important. But please be explicit as to what you will do.'
'David tells me that his inclinations tend to business, and that you
have meant to take him into your office. I will take him into _mine_,
and when he is twenty-one, if he has conducted himself properly, I will
give him an interest.'
'I shall be satisfied with no _contingent_ arrangement, sir. I know
Frank will prove worthy of the position.'
'Very well; then I will agree definitely to make him a partner when he
is of age.'
'Well, Mr. Hallet, if Frank will consent to come, I will agree to that
with certain conditions. I told his mother, when she was dying, that I
would consider him my own child; therefore I cannot give up the control
of him. He must regard me and depend on me as he does now. Again, I
cannot let him come here, and have no home whose influence shall protect
him from the temptations which beset young men in a large city. David
must take him into his family, and treat him as he treated me when I was
a boy, and--this must be reduced to writing.'
Hallet showed some emotion when I spoke of Frank's mother, but his face
soon assumed its usual expression, and he promptly replied:
'I will agree to all that, but I would suggest that the fact of his
being my son should not be communicated to him; that it be confined to
us three. I ask this, believe me, only for the sake of my family.
'I see no objection to that, sir, and I think, Frank, for his own sake,
should not know what his prospects are.'
Hallet signified assent, and turning to David, I asked:
'David, what do _you_ say? Will you take him?'
'I will,' said the old bookkeeper, showing in his expenditure of breath
the close economy which was the rule of his life.
'Nothing remains but to arrange his salary and the share he shall have
when he becomes a partner,' I remarked to Hallet.
'Will an average of seven hundred a year, and an eighth interest when
he's twenty-one, be satisfactory?'
'Entirely so. An eighth in your house will be better than a quarter in
ours. As it is now all understood, let David draw up the papers. We will
sign them, and leave them with him till I see Frank.'
'Very well. David, please to draw them up,' said Hallet; and then, his
voice again trembling a little, he added, 'All is understood, Mr. Kirke,
but the compensation I shall make you for your fatherly care of my much
neglected son. Money cannot pay for such service, but it will relieve me
to reimburse you for your expenditures.'
'I have had my pay, sir, in the love of the boy. I ask no more.'
Hallet was sensibly affected, but without speaking, he turned to the
desk, and took down his bankbook. In a few moments he handed me a check.
It was for five thousand dollars. I took it, and, hesitating an instant,
said:
'I will keep this, sir; not for myself, but for Frank. It may be of
service to him at some future time.'
'Keep it for yourself, sir, not for him. He will not need it. He shall
share equally with my other children.'
'I am glad to see this spirit in you, sir. Frank will be worthy of all
you may do for him.'
'It is not for _his_ sake that I will do it,' replied Hallet, his voice
tremulous with emotion; 'it is that I may have the forgiveness of the
one I--I--' He said no more, but leaning his head on his hand, he wept!
If there is joy among the angels over one that repents, was there not,
then, forgiveness in _her_ heart for _him_?
No one spoke for some minutes; then David rose, and handing me one of
the papers, laid the other before Hallet.
'This appears right,' I said, after reading it over carefully.
'Yes,' replied Hallet, taking up a pen and signing the other. Passing it
to me, he added: 'Keep them both--take them now.'
'But Frank may not wish to come.'
'Then I will find some other way of helping him. He is my son! Take the
papers.'
'Well, as you say,' I replied. 'David, please to witness this.'
Hallet pressed me to pass the night at his house, but I declined, and
rode out to Cambridge with the old bookkeeper. With many injunctions to
watch carefully over Frank, I left him about twelve o'clock, rode into
town with Cragin, and the next morning started for New York.
That night, as I recounted the interview to Kate, I said:
'I never did believe in these double-quick conversions; but Hallet _is_
an altered man.'
'Then, indeed, can the leopard change his spots.'
As usual, her womanly intuitions were right; my worldly wisdom was
wrong!
CHAPTER XV.
Not long after the events I have just related, the mail brought me the
following letter from Preston:
MY VERY DEAR FRIEND:--Circumstances, which I cannot explain by letter,
render it _imperatively_ necessary that I should provide another home
for my daughter. Her education has been sadly neglected, and she should
be where she can have experienced tutors, and good social surroundings.
With her delicate organization, and sensitive and susceptible nature,
she needs _motherly_ care and affection, and I shrink from committing
her to the hands of strangers. I should feel at rest about her only with
_you_. You have been my steadfast friend through many years; you have
stood by me in, sore trials--may I not then ask you to do me now a
greater service than you have ever done, by receiving my little daughter
into your family? I know this is an unusual, almost presumptuous
request; but if you knew her as she is--gentle, loving, obedient--the
light and joy of all about her, I am sure you, and your excellent lady,
would love her, and be willing to make her the companion of your
children. She is my only earthly comfort, and it will rend my heart to
part with her, but--I _must_.
Write me at once. You are yourself a father--_do not refuse me_.
* * * * *
To this, on the next day, I sent the following reply:
MY DEAR FRIEND:--I would most cheerfully take your daughter into my
family, did my wife's health, which has been failing all the summer,
allow of her assuming any additional care.
I think, however, I can provide Selma with a home equally as good as my
own; one where good influences will be about her, and she will have the
best educational advantages. I refer to the family of Mr. David Gray, of
Cambridge, Massachusetts. He was my father's friend. The years I was a
boy with Russell, Rollins & Co., I was an inmate of his house, and my
adopted son, Frank, is now in his care. His daughter Alice is a most
suitable person to have charge of a young girl. She is like a sister to
me, and to oblige me, would no doubt take Selma.
Please advise me of your wishes; and believe, my dear friend, I will do
all in my power to serve you.
I was sitting down at supper, one evening, about a fortnight after
sending this letter, when a gentleman was announced as wishing to see
me. I rose and went into the parlor. It was Preston, and with him was
Selma, then a beautiful little girl of about eleven years.
Asking Preston to lay aside his outside coat, I was struck by his
altered appearance. It was four years since we had met, but looking at
him, I imagined it might be ten. His eyes were sunken, deep furrows were
about his mouth, and his brown hair was thickly streaked with gray.
'My dear friend,' I exclaimed, as I grasped his hand a second time, 'you
are not well!'
'I am as well as usual, Kirke. Time has not done this!'
Fatigued with the long journey, Selma had retired, and our own little
ones were in bed, when Kate joined us in the parlor.
'You _do_ look ill, Mr. Preston,' she said, seating herself beside him.
'You must stay a while with us, and rest.'
'I would be glad to stay here, madam--anywhere away from home.'
'The care of two plantations, such as yours, must be a burden!'
'It is not that, madam; Joe relieves me entirely from oversight of one
of them. My difficulty is at home--mine is not what yours is.'
Kate's sympathizing words soon drew him out (she has a way of winning
the confidence of people, and is the depositary of more family secrets
than any other woman in the State); and he told us what his home had
become since his union with the governess.
Within two months after the marriage her real character began to display
itself, and she soon developed into a genuine Xantippe. Getting control
of Mulock, who had been made overseer, she had the <DW64>s dreadfully
whipped and overworked; she treated young master Joe so badly that the
lad rebelled, and in his father's absence ran away to his uncle at
Mobile; and locking Selma up in a dark room without food, or beating her
till her back was actually discolored, she made the child's home
intolerable to her.
After master Joe went away, no one dared complain; and shut up in his
library, brooding over his still fresh grief for the death of his wife,
Preston knew nothing of the real state of affairs till more than a year
had elapsed. Then one day he found Selma in tears. He questioned her,
and learned the whole. A scene followed, in which Mrs. Preston asserted
her rights as mistress of the plantation, and defied him. She had run
into all sorts of extravagance, the yearly bills which had come in a
short time previous were appallingly large, but to secure peace, Preston
consented to buy and furnish a winter residence at Newbern. To that she
had removed, but with the coming spring she would return to the
plantation, and in the mean time Selma must be provided with another
home.
'Feel no anxiety about her, sir,' said Kate, as he concluded; 'if Alice
Gray will not take her, we will.'
'I thank you, madam; I cannot thank you enough for saying that,' replied
Preston, his eyes filling with tears.
I wrote at once to David, and soon received a letter from Alice
consenting to take charge of the little girl. Thanksgiving, at which
time Kate made annual visits to her early home, was approaching, and it
was decided that Selma should accompany her to Boston.
This being arranged, Preston, at the end of a fortnight, took leave of
us, and returned to the South. The parting between the father and the
child gave evidence of what they were to each other. Preston wept like a
woman; but as Kate brushed back the brown curls from the broad forehead
of little Selly, she raised her eyes to my wife's face, and while her
thin nostrils dilated, and her sensitive chin slightly quivered, said;
'I must not cry for poor papa's sake--it is so _very_ hard for him to go
home alone; and he will miss his little girl _so_ much.'
'You are right, dear child,' said Kate, and, as if looking into the far
future of the woman, and feeling that such a nature must suffer as well
as enjoy keenly, she inwardly thanked God that with her delicate
organization He had given her the unselfish and brave heart which those
words expressed.
* * * * *
Four years had wrought great changes in David's quiet home. Alice had
become Mrs. Augustus Cragin, and a little Alice tottled about the floor;
but after supper, David still found his evening cigar on the oak stand,
his needle-work slippers--wrought by Alice's own hand--in their place
before the fender, and his big armchair rolled up close to the gas
burner in the little back parlor at Cambridge.
Frank was twenty, and had fulfilled all the promises of his boyhood. His
father, after the honeymoon of his repentance was over, showed no great
interest in him, but Cragin, who knew nothing of my arrangement with
Hallet, had given him all the advantages in his power.
Selma was only fifteen, but, like the flowers of her own South, she had
blossomed early, and was already a woman. Preston had visited her every
summer, but she never returned with him, having preferred passing her
vacations at my house.
In David's loving household nothing had occurred to disturb her peaceful
life. Beloved by her teachers and schoolmates, she everywhere received
the homage due to her beauty and her goodness; and in the gay world into
which her joyous nature often led her, she was the acknowledged and
_unenvied_ queen! Her father had spared no pains in her education; the
best tutors had trained her fine ear and sweet voice, and taught her to
give form and coloring to the pictures her glowing imagination created;
and, whether her fingers ran over the keys of a musical instrument, or
wielded the brush, there was a delicacy and yet _spirit_ in her touch
which were the wonder and admiration of all.
I was not surprised, when visiting Boston about this time, to have Frank
tell me that he loved her, and ask my consent to his regarding her as
his future wife.
* * * * *
Kate and I were to leave for home the following day, and, calling at the
office in the afternoon, I said to Frank:
'I have tickets for the opera, including Selma; of course you'd like to
have her go.'
'Yes, father; she has never been, and I have promised to take her this
winter. She'll be able now to appreciate it.'
The box I had selected was at a happy distance from the stage, and we
gave Selma a front seat, that she might see to the best advantage. She
was in high spirits; indeed, she was radiant in her beauty. She wore a
dark blue dress of silk, fitting closely to her neck, and its short
sleeves allowed the plump, fair arms to half disclose themselves from
beneath the scarlet mantle Which fell around her shoulders. Her hair
fell over her neck in the same simple fashion as in her childhood,
except that the thick curls, which had lost their golden tint, and were
darker and longer, were looped back from her broad brow, with a few
simple flowers. There was the same contour of face and feature, but
ennobled by thought and culture; the same sensitive mouth, only that the
lips were fuller and of a deeper color; and as she talked or listened,
the same rose tint deepened and faded beneath her rich, soft, dark skin,
as sunlight shifts and fades across the evening sky. Her eyes, in whose
dark depths the soul was reflected, met a stranger's calmly, but took a
soft look of loving trust when meeting Frank's. They were shaded by long
lashes, as black as the night; and when the lids fell suddenly, as they
often did, and her face became quiet, and almost sad, you felt that she
was communing with the angels.
The overture burst forth, and with glowing face, and eyes fixed upon the
stage, Selma seemed lost to all but the enrapturing sounds; even Frank's
whispered words were unheeded. As the opera--'Lucia di
Lammermoor'--proceeded, I saw that every eye was attracted to our box,
and, bending forward to catch Selma's expression, I called Kate's
attention to her. With her head thrown slightly back, a bright spot
burning on either cheek, her breath suspended, the large tears coursing
from her eyes, and motionless as a statue, she sat with her small hands
clasped on the front of the box, as if entranced, and all unconscious of
the hundred eyes that were fixed upon her. I thought of the pictures I
had seen in the old galleries of Europe, but I said, 'Surely, art cannot
equal nature!'
When it was over, she took Frank's arm; I turned to question her, but
Kate said:
'Let her alone; she cannot talk now.'
* * * * *
The transactions of Russell, Rollins & Co. extended the world over; but,
since the death of Mr. Rollins, which occurred prior to Frank's going
with them, they had cultivated particularly the Southern trade, and
their operations in cotton had grown to be enormous. They bought largely
of that staple on their own account, and for some extensive
manufacturing establishments in England. Their purchases were mainly
made in New Orleans, and, to attend to this business, Hallet had passed
the winters in that city for several years.
His wealth had grown rapidly, and at the date of which I am writing, he
ranked among the 'solid men' of Boston. Cragin was not nearly so
wealthy. Being on intimate terms with the latter, I remarked, as we were
enjoying a cigar together one evening at David's, on the occasion of
the visit to which I have referred in the last chapter:
'How is it, Cragin, that you pass for only a hundred thousand, when
Hallet is rated at a million?'
'Because, Ned, I'm not worth any more.'
'But how is that, when you have two fifths of the concern?'
'Well, Hallet went into cotton like the devil some eight years ago; and
I told him I wouldn't stand it; I like to feel the ground under me.
Since then he has speculated on his own account--he and old Roye go it
strong, and I guess they've made some pretty heavy lifts.'
'That's uncertain business.'
'Yes, devilish uncertain; but somehow they manage always to hold winning
cards. Hallet has told me his New Orleans operations have netted him
five hundred thousand.'
'And that, with what he got by his wife, has rolled him into a
millionaire before he's forty-five! He's a lucky fellow.'
'Lucky! I wouldn't stand in his boots. What goes up _may_ come down. He
has no peace. His wife's a hyena. She makes home too hot for him; and
somehow he's never easy. He walks about as if treading on torpedoes.
'If you dislike speculation, why don't you increase your legitimate
business?'
'Hallet's away so much, I can't do it. I'm glued to the old office. I
should have been in Europe half of the time the last three years, but I
haven't been able to get away.'
'Why not send Frank? He's old enough now.'
'I mean to, in the spring, and I'm d--d if he shan't be a partner soon,
and take some of this load off my shoulders. But do you know that Hallet
has a decided dislike to him?'
'No! On what account?' I exclaimed. I had met Hallet only twice during
four years, but on both occasions he had spoken favorably of his son.
Frank himself had never alluded in other than respectful terms to his
father.
'Well, I don't know, and it makes no difference. I'm captain at this end
of the towline, and I swear he shall go in.
'As you feel so kindly toward Frank, I'll give him a chance to
conciliate Hallet. I'll take him South this winter, and introduce him to
our correspondents. With his address he ought to do something with them.
Will you let him go?'
'Yes, and be right down glad to have him. When do you start?'
'About the middle of December.'
A fortnight afterward, with Selma and Frank, I again visited Preston's
plantation.
CHAPTER XVI.
It was Christmas morning when we rode up the long, winding avenue, and
halted before the doorway of 'Silver Lake'--the new name which the
Yankee schoolmistress, aping the custom of her Yankee cousins, had
bestowed on Preston's plantation. The day was mild and sunshiny, and the
whole population of the little patriarchate was gathered on the green in
front of the mansion, distributing Christmas presents among the <DW64>s.
When we came in sight, from behind the thick cluster of live oaks which
bordered the miniature lake, the whole assemblage sent up a glad shout,
and hurried up to welcome us. And such a welcome! As she sprang from the
carriage, Selma was caught in her father's arms, then in 'master Joe's,'
and then, encircled by a cloud of dark beauties, each one vieing with
the others in boisterous expressions of affection, she was the victim of
such a demonstration as would have done the heart of Hogarth good to
witness. In the midst of it a slight, delicate woman rushed from the
house, and, crowding into the thick group around Selma, threw her arms
about her neck, and, nearly smothering her with kisses, exclaimed:
'My chile! my chile! I sees you at last!'
'Yes, Phylly!' said Selma, returning her caresses; 'and haven't I grown?
I thought you wouldn't know me.'
'Know you! Ain't you my chile--my own dear chile!' and pressing Selma's
cheeks between her two hands, and gazing at her beautiful face for a
moment, she kissed her over and over again.
My arms had been nearly shaken off, when I noticed 'Boss Joe' limping
toward me, his head uncovered, and his broad face shining from out his
gray wool like the full moon breaking through a mass of clouds.
'How are you, old gentleman?' I exclaimed, grasping him warmly by the
hand.
'Right smart! right smart, massa Kirke. Glad you'm come, sar.'
'And you're home for Christmas?'
'Yes, sar. I'se come to see massa Robert, an' to tend to hirin' a new
gang. But <DW54>s 'am high dis yar, sar.'
'How much are they?'
'Well, dey ax, round yere, one fifty, an' 'spences dar an' back; an'
it'm a pile, when you tink we hab used up 'most all de new trees.'
'But you must have many second-year cuttings.'
'Yas, right smart; but No. 2 rosum doan't pay at sech prices fur
<DW54>s.'
Turning to Preston in a moment, I said:
'Do not let us interfere with the 'doin's'--it's just what we want to
see.'
'Well, come, you folks,' said Joe, hobbling back to the green; 'leff us
gwo on now.'
Preston, Selma, and Phylly went into the house, but the rest of us
followed the grinning group of Africans to the centre of the lawn, where
several large packing boxes, and a long table, something like a
carpenter's bench, were piled high with a miscellaneous assortment of
dry goods and groceries.
'Now, all you dat hab heads, come up yere,' shouted Joe, seating himself
on the bench; 'but don't all come ter onst.'
One by one the men and boys filed past him, and, selecting a hat or cap
from a couple of boxes near, he adjusted a covering to each woolly
cranium that presented itself; interspersing the exercise with humorous
remarks on their respective phrenological developments:
'Pomp, you's made fur a preacher, shore. Dat dar head ob your'n gwoes up
jess like a steeple. I'll hab ter gib you a cap, Dave; you'm so big
ahind de yeres none ob dese hats'll fit, nohow. Jess show de back ob
you' head to any gemman, an' he'll say you'm one ob de great ones ob de
'arth. None ob dese am big 'nuff fur you, Ally,' he continued, as a
tall, well-clad mulatto man stepped up to him. 'You' bumps hab growed so
sense you took to de swamp, dat nuffin'll cober you 'cept massa Robert's
hat, or de gal Rosey's sunshade.'
The yellow man laughed, but kept on trying the hats. Finding one at last
of suitable dimensions, he turned away to make room for another
candidate for cranial honors. As I caught a full view of his face, I
exclaimed:
'Why, Ally, is that you?'
'Yas, massa; it'm me,' he replied, making a respectful bow.
'And you live here yet?'
'Yas, massa. Hope you's well, massa?'
'Very well; and your mother--how is she?'
'Oh, she'm right smart, sar.'
'Yas, massa, I'se right smart; an' I'se bery glad ter see 'ou, massa,'
said a voice at my elbow. It was Dinah, no longer clad in coarse
osnaburg, but arrayed in a worsted gown, and a little grayer and a
little bulkier than when I saw her eight years before.
'Why, Dinah, how well you look!' I exclaimed, giving her my hand. 'And
you've come up to spend Christmas with Ally?'
'No, massa, I _libs_ yere. I'se FREE now, massa!'
'Free! So you've made enough to buy yourself? I'm glad to hear it.'
'No, massa. Ally--de good chile--he done it, massa.'
'Ally did it! How could he? He's not more than twenty now!'
'No more'n he hain't, massa; but he'm two yar in massa Preston's swamp,
wid a hired gang. Massa Preston put de chile ober 'em, an' gib him a
haff ob all he make, an' he'm doin' a heap dar, massa.'
'And with his first earnings he bought his mother!'
'Yas, massa; wid de bery fuss.'
'Ally, give me your hand,' I exclaimed, with unaffected pleasure;
'you're a man! You're worthy of such a mother!'
'Yas, he am dat, massa! He'm wordy ob anyting, an' he'm gwine to hab a
wife ter day, massa. Boss Joe am gwine ter marry 'em, an' ter gib 'em
him own cabin fur dar Chrismus giff.'
'Well, Joe _is_ a trump. I'll remember him in my will for that, aunty,
sure.'
'Dat'm bery good ob 'ou, massa; but I reckon 'ou can't tink who Ally'm
gwine ter hab, massa,' said the old woman, her face beaming all over.
'No, I can't, Dinah. Who is she?'
'It'm little Rosey, dat 'ou buy ob de trader, massa; an' she'm de
pootiest little gal all roun' yere; ebery one say dat, massa.'
'Indeed! And they are to be married to-day?'
'Yas, massa, ter day--dis evenin'. 'Ou'll be dar, woan't 'ou, massa?'
'Yes, certainly I will.'
The old woman and Ally then mingled with the crowd of <DW64>s, and I
turned my attention once more to Joe's operations. The men had been
supplied with head gear, and the women were receiving their
turbans--gaudy pieces of red and yellow muslin.
'Now, all you boys an' gals,' shouted Joe, as he dealt out a
handkerchief to the last of the dusky demoiselles, 'you all squat on de
groun', an' shovel off you' shoes.'
Down they went in every conceivable attitude, and, uncovering their
feet, commenced pelting each other with the cast-off leathers. When the
sport had lasted a few minutes, Joe sang out:
'Come! 'nuff ob dat; now ter bisness. Yere, you yaller monkeys (to
several small specimens of copper and chrome yellow), tote dese '<DW41>
'em.'
The young chattels did as they were bidden, and, as each heavy brogan
was fitted to the pedal extremity of some one of the <DW54>s, the
newly-shod individual sprang to his feet, and commenced dancing about as
if he were the happiest mortal in existence.
'Dat'm it,' shouted Joe; 'frow up you' heels; an' some ob you gwo
an' fotch de big fiddle. We'll hab a dance, an' show dese Nordern
gemmen de raal poker.'
'But we hain't hed de dresses--nor de soogar--nor de 'backer--nor none
ob de whiskey,' cried a dozen voices.
'Shet up, you brack crows! You can't hab anudder ting till ye'se hed a
high ole heel-scrapin'. Yere, massa Joe; you come up yere, an' holp me
wid de 'strumentals,' said Boss Joe, grinning widely, and getting up on
the carpenter's bench.
In a few moments, the 'big fiddle,' one or two smaller fiddles, and
three or four banjoes were brought out, and the two Joes, and several
ebony gentlemen, seating themselves on the boxes of clothing, began
tuning the instruments. Soon 'Boss Joe' commenced sawing away with a
gusto that might have been somewhat out of keeping with his gray hairs,
his sixty years, and his clerical profession. 'Massa Joe' and the others
striking in, the male and female <DW54>s paired off two by two, and to a
lively air began dancing a sort of 'cotillion breakdown.' Other dances
followed, in which the little <DW64>s joined, and soon the air rang with
the creak of the fiddles and the merry shouts of the <DW64>s. In the
midst of it my arm was touched lightly, and, turning round, I saw Rosey
and Dinah.
'I'se got de little gal yere, massa,' said the latter, looking as proud
as a hen over her first brood of chickens. 'She glad to see 'ou, massa.'
I gave Rosey my hand, and made a few good-natured compliments on her
beauty and her tidy appearance. She had a simple, guileless expression,
and met my half-bantering remarks with an innocent frankness that
charmed me. She was only sixteen, but had developed into a beautiful
woman. Her form was slight and graceful, with just enough _embonpoint_
to give the appearance of full health; and her thin, delicate features,
large, wide-set eyes, and clear, rosy complexion bore a strong
resemblance to Selma's. It was evident they were children of the same
father; and yet, one was to be the wife of a poor <DW64>, the other to
marry the son of a 'merchant prince.'
As the dancing concluded, Boss Joe's fiddle gave out a dying scream,
and, turning to me, he sang out:
'War dar eber sprightlier nigs dan dese, massa Kirke? Don't dey beat
you' country folks all holler?'
'Yes, they do, Joe. They handle their heels as nimbly as elephants.'
I spoke the truth; most of them did.
The distribution of the presents was resumed; and, as each <DW64>
received his full supply of flour, sugar, tea, coffee, molasses,
tobacco, and calico, grinning with joy over his new acquisitions, he
staggered off to his quarters. When the last box was nearly emptied,
with young Preston and Frank, I adjourned to the mansion.
The exterior of the 'great house' was unchanged, but its interior had
undergone a complete transformation. The plain oak flooring of the hall
had been replaced by porcelain tiling, and the neat, simple furniture of
the parlors by huge mirrors; rosewood and brocatelle sofas and lounges;
velvet tapestry carpets, in which one's feet sank almost out of sight;
and immense paintings, whose aggregate cost might have paid off one half
of the mortgage that encumbered the plantation.
Selma and her father were engaged in earnest conversation when we
entered the drawing room, and, being unwilling to interrupt them, I was
about to retire, but he rose, and said:
'Come in, Kirke; I will call Mrs. Preston. She will be glad to see you.'
The lady soon entered. It was eight years since we had met, but time had
touched her gently. Her face wore its old, decided, yet quiet
expression, and her manner showed the easy self-possession I had noticed
at our first interview. She was richly dressed, and had on a heavy satin
pelisse, and a blue velvet bonnet, as if about to ride out.
When the usual greetings were over, she remarked:
'You have been here some time, sir?'
'Yes, madam; we arrived about two hours ago; but I met some old friends
outside, and the pleasure of seeing them has made me a little tardy in
paying my respects to you.'
'The <DW64>s, you mean, sir,' she replied, with a slight toss of the
head, and a look of cool dignity which well became her.
'Yes, madam. I have many friends among the blacks. On many plantations
they look for my coming as they do for Christmas.'
'It is quite rare to find a white gentleman so fond of <DW64>s,' she
rejoined, with an air slightly more supercilious.
I remembered her as the humble schoolmistress, whose entire possessions
were packed in one trunk; and, forgetting myself, said, in a tone which
bore a slight trace of indignation:
'More rare, I fear, than it should be; and you and I, madam, who are
Yankees, and have 'worked for a living,' surely cannot despise the
<DW64>s because they are _compelled_ to work for theirs.'
'Oh! no, sir! not by any means! But you must excuse me; the carriage is
waiting to take me to church;' and, rising, she bowed herself stiffly
out of the door.
'Ah, you hit her there!' exclaimed Joe, springing to his feet in great
glee, and striding to the window. 'See here, Mr. Kirke! See what a
turnout the Yankee 'schulemarm' has worried out of father!'
'My son, you must not speak so; she is your mother!' said Preston.
'No, I'm d--d if she is! Call her anything but that, father; that's
an--'he checked himself; but I thought he would have added--'insult to
my dead mother!'
Preston made no reply.
Looking out of the window, I saw Mrs. Preston being handed into a
magnificent barouche by one of the black gentry she so much despised.
Another one in gaudy gold livery sat on the box, and a mounted outrider,
also bound up in gold braid, stood behind the carriage.
'There's a two-thousand-dollar turnout, and two fifteen-hundred-dollar
<DW65>s, to tote a woman who ought to go afoot. It's a poor investment,
I swear,' said Joe, turning away from the window.
Preston made no reply; but I laughingly remarked:
'Come, Joe, she isn't _your_ wife. Let your father spend his money as he
pleases; he can afford it.'
'He _can't_ afford it; that woman is running him to the devil at a
two-forty gait. You have more influence with him than any one, Mr.
Kirke--_do_ try to stop it!'
The young man spoke in a decided but regretful tone, and his manner
showed more respect to his father than his words implied. Unwilling to
interfere in such an affair, I said nothing; but Preston, in a moment,
remarked:
'It is true, Kirke! Her extravagance has ruined my credit at home, and
forced me to use Joe's indorsements; besides, I have had to borrow ten
thousand dollars of him to keep my head above water.'
[Mr. James Preston--the Squire's uncle--had died the year before, and
the young man had succeeded to his large property and business.]
I was thunderstruck; but, before I could reply, Joe said:
'I don't care a rush for the money. Father can have every dollar I've
got; but I _do_ want to see him rid of that woman. I've been here sick
for two months, and I've seen the whole. She is worrying the very life
out of him. She's made him an old man at forty.'
It was true. His face was lean and haggard, and his hair already thickly
streaked with white.
Preston rose, and, walking the room, said:
'But what am I to do? You yourself, Joe, would not have all this made
public. You've as much pride about it as I have.'
'I've not a bit of pride about it, father; and it's public now.
Everybody knows it, and everybody says you ought to cut her adrift.'
'What had I better do? Tell me, my friend,' said Preston, still walking
the room.
'I cannot advise, you, Preston. An outsider should express no opinion on
such matters.'
In a moment Preston said:
'Well, Joe, no more of this now. I'll do what is right, however much it
may wound my pride.'
The conversation turned to other subjects, till Mrs. Preston's return
from church, shortly after which dinner was announced. The lady presided
at the table with as much ease and grace as if she had been born to the
position; and in her charming conversation, I almost forgot the
revelations of the morning. The rest of the day I spent with Joe and
Frank, strolling over the plantation and mingling among the <DW64>s,
who, freed from work, were enjoying themselves in a very 'miscellaneous
manner.' Preston remained at the house with Selma.
CHAPTER XVII.
It was nearly dark when we returned to the mansion. Looking in at the
parlor, and not finding his father there, Joe led the way at once to the
library. The door was ajar, and, as we entered the passage way, loud
voices were issuing from it.
'I tell you, Mr. Preston, I am mistress of this plantation. He shall NOT
go!'
'Pardon me, madam, he _shall_, and to-night,' returned a mild but
decided voice, which I recognized as Preston's. Being unwilling to
overhear more, I turned away, but Joe caught me by the arm, exclaiming:
'If you are my father's friend, go in. If you don't, he will back down;
he has done so forty times.'
Preston was a man of more than ordinary firmness, but his wife had the
stronger will. She seemed possessed of a sort of magnetic power, which
enabled her to control others almost arbitrarily.
Reluctantly I followed the young man into the room. Preston was seated
before the fire; and Selma, with her arm around his neck, was standing
near him. Mulock, better clad than when I witnessed his purchase by the
'fast' young planter, and wearing a sullen, dogged expression, was
leaning against the centre table; and Mrs. Preston, gesticulating
wildly, and her face glowing with mingled rage and defiance, stood
within a few feet of her husband. Not heeding our entrance, she
exclaimed:
'I _will_ have my way. If you send him off, I will never darken your
doors again.'
'That is as you please, madam,' replied Preston. 'Mr. Kirke and Frank,
pray be seated.'
Stung by her husband's coolness, the lady turned fiercely upon Joe, and,
shaking her clenched hand in his face, cried out:
'This is _your_ work. I will teach you better than to meddle with my
affairs.'
* * * * *
'Madam, you act well,' said the young man, taking a step toward the
door. 'Pray come out to the quarters; poor as they are, every <DW64> will
give a bit to see _you_ play.'
In uncontrollable rage, she struck him a smart blow in the face, and
rushed from the room.
When she had gone, Preston turned to Mulock:
'Now go. The amount due you I shall retain to offset, in part, what you
have tempted the <DW64>s to steal. You can come here once a week--on
Sunday--to see Phylly; but if you have any more dealings with the hands,
I will prosecute you on the instant.'
Mulock rose, put on his slouched hat, and, a dull fire burning in his
cold, snake-like eyes, slowly said:
'Wall, Squire, I'll gwo, but 'counts 'tween you an' me ain't settled
yit.'
As he went, Selma leaned forward, and, kissing Preston's cheek, said;
'O father! I'm so glad _you_ didn't speak harshly to her.'
Preston put his arm about her, and replied:
'You helped me, my child. I should be a better, happier man, if you were
with me.'
'And I will be, father; I won't go away any more.'
'But Frank?' said Preston, again kissing her.
'Oh, you know we're not to be married for a good while yet. I'll stay
with you _till then_, father.'
'Ah! there she goes,' said Joe, looking out at the window, which
commanded a view of the _porte cochere_; 'she can't get to Newbern till
ten, but the night air won't hurt _her_.'
'Then she makes Newbern her home now?'
'Yes, she spends the winters there; she came here only yesterday.'
CHAPTER XVIII.
Ally and Rosey were to be married[3] in the little church, and, directly
after supper, we all went to the wedding. The seats had been removed
from the centre of the building, for, though duly consecrated to the use
of the saints, the sinners were to exercise their heels in it after the
ceremony was over. At its farther extremity, the carpenter's bench of
which I have spoken, elongated at both ends, and covered with a white
table cloth, was piled high with eatables; indicating that a time of
'great refreshment' was at hand. The bounteous supply of ham, chicken,
wild duck, roast pig, fish, hoecake, wheat bread, tea, coffee, milk, and
pumpkin and sweet-potato pies under which the bench groaned, showed that
some liberal hand had catered for the occasion.
Black Joe, dressed in his 'Sunday best,' was seated on the rustic settee
at the back of the desk, and Phyllis and Dinah occupied chairs inside
the low railing, which faced the pulpit. Phyllis looked careworn and
sad, but Ally's mother was as radiant as a brass kettle in a blaze of
light wood. She wore a white dress, stiffly starched and expanded by
immense hoops, and a crimped nightcap, whose broad border flapped about
like the wings of a crowing rooster; and she looked, for all the world,
like a black ghost in a winding sheet, escaped from below, and bound on
a 'good time generally.' Two 'shining lights,' on either side of the
pulpit, held aloft blazing torches of pine, which illuminated the sea of
grinning darkness, and sent up a smoke like that arising from the pit
which is said to be bottomless. About a hundred <DW54>s were present;
and the number of glossy coats, fancy turbans, gaudy bonnets, red
shawls, and flaming dresses, which the light disclosed, was amazing. The
poor worm that grubbed in the earth, had appeared ('for that occasion
only') as a butterfly; and Lazarus, rid of his rags, had come forth
dressed like a Broadway dandy.
Any person of sensitive olfactories would have halted in the doorway;
but I elbowed through the woolly gathering, and followed Frank and Selma
to the family pew. Tittering, laughing, and flaunting their red and
yellow kerchiefs, the black people were enjoying themselves amazingly,
when 'Dar dey comes,' 'Dar'm de happy pussons,' went round the
assemblage, and the bride and groom, attended by two sable couples,
entered the building. After some ludicrous mistakes, they got 'into
position' in front of the railing, and Black Joe took a stand before
them.
Rosey was dressed in white, with a neat fillet of pink and blue ribbon
about her head; and Ally wore a black frock coat, with white vest, and
white cotton gloves. One of the groomsmen--a rustic beau from a
neighboring plantation--wore an immensely long-tailed blue coat with
brass buttons, a flaming red waistcoat, yellow woollen mittens, and a
neckerchief that looked like a secession flag hugging a lamp-post. Both
of these gentry had hats of stove-pipe pattern, very tall, and with
narrow brims; and--they wore them during the ceremony.
'Silence in de meetin',' cried Joe.
The boisterous sea of black wool subsided to a dead calm. Those not
already standing rose, and Joe commenced reading the marriage service of
the Episcopal Church.
The parties immediately interested appeared to have conned their lessons
well; for they made all the responses with great propriety; but some of
the congregation seemed less familiar with the service. When Joe
repeated the words, 'If any man kin show cause why dese folks should not
be lawfully jined togedder, leff him now speak, or else foreber hole
his peace,' Dinah turned to the audience, and cried out:
'Yas, jess leff him come out wid it _now_. I'd like ter see de man dat's
got onyting agin it.'
No one appeared to have 'onyting agin it,' and Joe proceeded to read the
words: 'I require and charge you, if either of you know any impediment,'
etc. In the midst of it a voice called out:
'Dar ain't no 'pedimen', Boss Joe; I knows dat. Gwo on, sar!' 'Dat's so,
brudder,' said another voice. 'Dat's de Lord's trufh,' echoed a third.
'Doan't be 'sturbin' de meetin'; de young folks want de 'splicin' done,'
cried a fourth; and 'Amen,' shouted a dozen.
'Shet up, all on you,' yelled Joe, turning on them with an imperious
gesture; 'ef you hain't no more manners dan dat, clar out.'
Silence soon ensued, and Joe went on without interruption to the place
where the minister asks the bride-groom: 'Wilt thou have this woman to
thy wedded wife?' Then Dinah, unable to contain herself longer, joyfully
exclaimed:
'Ob course he will--ony youn' feller'd be glad to hab _har_.'
[Never having gone through the ceremony herself, the poor woman could
not be expected to know what was appropriate to the occasion.]
No further interruption occurred, and soon the happy couple were 'bone
of one bone, and flesh of one flesh.' The assemblage still standing, Joe
then turned to Ally and Rosey, and, with a manner so solemn and
impressive that he seemed altogether a different person from the merry
<DW54> who had entered so heartily into the 'high ole heel scrapin'' of
the morning; he spoke somewhat as follows:
'My chil'ren, love one anoder; bar wid one anoder; be faithful to one
anoder. You hab started on a long journey; many rough places am in de
road; many trubbles will spring up by de wayside; but gwo on hand an'
hand togedder; love one anoder; an' no matter what come onter you, you
will be happy--fur love will sweeten ebery sorrer, lighten ebery load,
make de sun shine in eben de bery cloudiest wedder. I knows it will, my
chil'ren, 'case I'se been ober de groun'. Ole Aggy an' I hab trabbled de
road. Hand in hand we hab gone ober de rocks; fru de mud; in de hot,
burnin' sand; ben out togedder in the cole, an' de rain, an' de storm,
fur nigh onter forty yar, but we hab clung to one anoder; we hab loved
one anoder; and fru eberyting, in de bery darkest days, de sun ob joy
an' peace hab broke fru de clouds, an' sent him blessed rays down inter
our hearts. We started jess like two young saplin's you's seed a growin'
side by side in de woods. At fust we seemed way 'part, fur de brambles,
an' de tick bushes, an' de ugly forns--dem war our bad ways--war atween
us; but love, like de sun, shone down on us, and we grow'd. We grow'd
till our heads got above de bushes; till dis little branch an' dat
little branch--dem war our holy feelin's--put out toward one anoder, an'
we come closer an' closer togedder. And dough we'm old trees now, an'
sometime de wind blow, an' de storm rage fru de tops, and freaten to
tear off de limbs, an' to pull up de bery roots, we'm growin' closer an'
closer, an' nearer an' nearer togedder ebery day. And soon de old tops
will meet; soon de ole branches, all cobered ober wid de gray moss, will
twine round one anoder; soon de two ole trunks will come togedder and
grow inter _one_ foreber--grow inter one up dar in de sky, whar de wind
neber'll blow, whar de storm neber'll beat; whar we shill blossom an'
bar fruit to de glory ob de Lord, an' in His heabenly kingdom foreber!
'Yas, my chil'ren, you hab started on a long journey, an' nuffin' will
git you fru it but _love_. Nuttin' will hole you up, nuffin' will keep
you faithful to one anoder, nuffin' will make you bar wid one anoder,
but love. None ob us kin lib widout it; but married folks want it most
ob all. Dey need it more dan de bread dey eat, de water dey drink, or de
air dey breafe. De worle couldn't gwo on widout it. De bery sun would
gwo out in de heabens but fur dat! An' shill I tell you why? You hab
heerd massa Robert talk 'bout de great law dat make de apple fall from
de tree, de rock sink in de water; dat bines our feet to de round 'arth
so we don't drop off as it gwo fru de air; dat holes de sun an' de stars
in dar 'pointed places, so dat, day after day, an' yar after yar, dough
dey'm trabblin' fasser dan de lightnin' eber went, dey'm right whar dey
should be. He call it 'traction, an' all de great men call it so; but
dat ain't de name! It am LOVE. It am GOD, fur GOD am love, an' love am
GOD, an' love bines de whole creashun togedder! An' shill I tell you how
it do it? Does you see dis hand? how I open de fingers; how I shet'm up;
how I rise de whole arm? Does you see dis foot, dat I does wid jess de
same? Does you see dis whole body, how I make it, in a twinklin', do
jess what I like? Now what am it dat make my hand move, an' my whole
'body turn round so sudden, dat I'se only to say: 'Do it,' an' it'm
done? Why, it am ME. It'm _me_, dat libs up yere in de brain, an' sends
my _will_ fru ebery part--fru ebery siner, an' ebery muscle, an' ebery
little jint, an' make'm all do jess what I like. Now man am made in de
image of GOD, an' dis pore, weak ole body am a small pattern ob de whole
creashun. Eberyting go on jess as _it_ do. Eberyting am held togedder,
an' moved 'bout, jess as _it_ am--but it'm GOD dat move it, not me! He
libs up dar in de sky--which am His brain--wid de stars fur His hands,
de planets fur His feet, an' de whole univarse fur His body; an' He
sends His will--which am love--fru ebery part ob de whole, an' moves it
'bout, an' make it do jess as He likes. So you see, it am my will sent
fru ebery muscle, an' ebery little siner, dat moves my body; so it am
_His_ will sent fru what de'stronomers an' de poets call de heabenly
ether, dat moves _His_ body--which am de 'arth, an' de sun, an' de
stars, an' you an' me, an' ebery libin' ting in all creashun! His will
move 'em all; AN' HIS WILL AM LOVE! An' don't you see dat you can't do
widout His love? Dat it am de bery breaf ob life? Dat, ef it war tooken
'way from you, fur jess one moment, you'd drop down, an' die, an' neber
come to life agin--no, not in dis worle, nor in any oder worle? It am
so, my chil'ren; an' de more you hab ob dat love, de happier you'll be;
de more you'll love one ander; de easier you'll gwo fru you' life--de
more joyfuller you'll meet you' deafh--de happier you'll be all fru de
long, long ages dat'm comin' in de great Yereafter! Den, O my chil'ren!
Love God, Love one anoder! You can't be happy widout you love GOD, an'
you can't love Him widout you love one anoder!'
When Joe had concluded, he saluted the bride in a manner that many
another sooty gentleman present would have been glad to imitate, and
then took a stand at the head of the supper table. An immense tureen,
filled with steaming oysters, was soon brought in and placed before him,
and looking up, he said grace, in which he thanked Him who feedeth the
ravens for putting it into his master's heart to feed His other black
creatures, the <DW54>s present on that occasion. He asked for his master
many a happy 'Chrismus down yere,' and an eternal 'Chrismus in heaben,'
and he added: 'An' knowin' dat dou hatest long prayers, an' long faces,
an' dose folks dat gwo 'bout grumblin', as ef dy happy 'arth war nuffin'
but a graveyard; may we enjoy dis feast an' dis day as dy true
chil'ren--de chil'ren ob a good Fader, who am all joy an' all
gladness--an' while we'm eatin' an' drinkin' an' dancin', may we make
merry in our hearts to _Thee_. Amen.'
When he concluded, Preston stepped to his side, and taking the big
ladle from his hand, said:
'Stand aside, Joe, you have done work enough for to-night;' and turning
to 'we white folks' in the family pew, he added: 'If any man among you
would be master, let him now be the servant of all. Let him try his hand
at the waiter business, and see if he can't throw these shady people
into the _shade_.'
Selma, Frank, 'massa Joe,' and I went forward, and tying the <DW64>s'
aprons about our waists, took appropriate places around the table.
'Now all of you find seats,' cried Preston; and amid a hurricane of
giggling and merry laughter, the black people seated themselves on the
floor, on the platform, and on the row of benches ranged along the
walls. Preston proceeded to fill up the bowls with the savory stew, and
we dispensed the eatables among them, and for half an hour I witnessed
as much enjoyment as often falls to the lot of black sinners in this
'vale of tears.'
'Now, ef dis doan't beat all,' exclaimed old Dinah, as I handed her a
huge chunk of gingerbread; 'ef 'ou ain't right smart at waitin', massa
Kirke, I'd like ter know it.'
'Keep dark, ole 'ooman,' shouted Black Joe; 'doan't you say nuffin'
'bout dat, or de traders'll be a hole ob him. He'd sell fur a right
likely hand, _shore_.'
'I woan't do nuffin' but keep dark, Boss Joe,' rejoined Dinah, grinning
till her face opened from ear to ear. 'I'll hab 'ou know, sar, dat none
but white ladies paints!'
'Good fur you, ole lady,' cried the preacher. 'After dat you'll gib me
de pleasure ob your hand in de fuss dance.'
'Ob course, I will, _mister_ Joe; an' ef 'ou'm tired ob de ole 'ooman,
I'll gib 'ou my han' in anoder dance.'
'No, you woan't, I doan't gwo fur second marridges,' rejoined Joe,
looking slyly at Preston; 'dey ain't made in heaben.'
'No more' dey ain't,' said the old woman, heaving a long sigh, and also
looking at Preston.
'You ain't a gwine to leff dese folks dance in de church, am you, Boss
Joe?' asked a prim, demure-looking <DW54>, in a black suit, with a white
neckerchief and stiff shirt collar; probably some neighboring preacher.
'I reckon so,' replied Joe, dryly.
'An' _I_ reckons so, too, mister I scare-you-out (Iscariot),' cried the
old negress. 'Ain't de planets de Lord's feet, an' doant dey dance! I
reckons we ain't no better dan de Lord is; an' ef He mobes him feet,
'ou'd better mobe 'our'n. _We_ b'lieve in sarvin' HIM wid our han's an'
our feet, too; we does, mister I-scare-you-out.'
She did scare him out, for the 'pious gemman' left suddenly.
When about all of the eatables had found their way down the
cavernous--and ravenous--throats of the <DW54>s, Boss Joe rose and
called out:
'Yere, you massa Joe, you pull off you' apern, an' take de big
fiddle--I'm 'gaged fur de fuss dance.'
Young Preston seated himself on the platform, and several sable
gentlemen with banjoes and fiddles took places beside him.
'Now all you men folks s'lect you' pardners,' cried the preacher, taking
Dinah by the hand, and leading her out to the middle of the floor.
They all paired off, the fiddles broke into a merry tune, and soon the
little church, which had so often echoed with the groans of the saints,
shook with the heels of the sinners. When the first dance was over, Boss
Joe again called out:
'Now, massa Joe, strike up de waltz--Dinah an' I am gwine to show dese
folks some highfalutin dancin'.'
The waltz struck up, and off they whirled; Dinah went into it as if she
were working for pay, and as Joe held her closely in his arms, her wide
hoops expanded till she looked like a topsail schooner scudding under
bare poles.
As Joe was wiping the perspiration from his face, at the end of the
waltz, an old <DW64> entered, and whispered something in his ear. Joe's
countenance fell in an instant, and, without saying a word, he left the
room.
'Massa Joe,' relinquishing the big fiddle, then took the floor with
Rosey, and gave the audience a genuine breakdown. His heels bobbed
around like balls at a cricket match, and Rosey's petticoats fluttered
about like the contents of a clothes line caught out in a hurricane. A
better-looking couple were never seen in a ball room.
'He's a natural born <DW54>,' said his father, laughing; 'he takes to
dancing as a duck takes to water.'
A general dance followed. In the midst of it the old <DW64> who had
called Joe out, again came in, and making his way to where Preston and I
were standing, said, in a low tone:
'Massa Robert, Ole Jack am dyin'; will 'ou come?'
'Dying!' exclaimed Preston. 'Yes, I'll be there at once. Kirke, you
remember the old man--come with me.'
FOOTNOTES:
[Footnote 1: This was the conjuror's bag of the Africans. It is called
'waiter,' or 'kunger,' by the Southern blacks, and is supposed to have
the power to charm away evil spirits, and to do all manner of
miraculously good things for its wearer. Those that I have seen are
harmless little affairs, consisting only of small pieces of rags sewed
up in coarse muslin.]
[Footnote 2: The name of the African god.]
[Footnote 3: Usually there is no marriage performed at the union of
slaves. They simply agree, tacitly or otherwise, to live together till
death or their master parts them.]
THE CAPTAIN OF '63 TO HIS MEN.
Come to the field, boys, come!
Come at the call of the stirring drum--
Come, boys, come!
Yonder's the foe to our country's fame,
Waiting to blot out her very name--
Where is the man that would see her shame?
Come, boys, come!
Form, my brave men, form!
Stand in good order to 'meet the storm'--
Form, men, form!
Sacred to us is our native land!
Shrivelled for aye be each traitor hand
Lifted to shatter so bright a band--
Form, men, form!
Charge, my soldiers, charge!
From the steep hill to the river's marge,
Charge! charge! charge!
Think of our wives and mothers dear;
Think of the hopes that have led us here;
Think of the hearts that will give us cheer--
Charge, boys, charge!
Die with me, boys, die!
There's a place for all in yon bannered sky,
If we die, boys, die!
Think of the names that are shining bright,
Written in letters of living light!
Rather than give up the sacred Right,
Let's die, boys, die!
THE VISION OF THE MONK GABRIEL.
'Tis the soft twilight. 'Round the shining fender,
Two at my feet and one upon my knee,
Dreamy-eyed Elsie, bright-lipped Isabel,
And thou, my golden-headed Raphael,
My fairy, small and slender,
Listen to what befel
Monk Gabriel,
In the old ages ripe with mystery--
Listen, my darlings, to the legend tender.
A bearded man, with grave, but gentle look--
His silence sweet with sounds
With which the simple-hearted Spring abounds:
Lowing of cattle from the abbey grounds,
Chirping of insect, and the building rook,
Mingled like murmurs of a dreaming shell;
Quaint tracery of bird and branch and brook
Flitting across the pages of his book,
Until the very words a freshness took--
Deep in his cell,
Sate the Monk Gabriel.
In his book he read
The words the Master to His dear ones said:
'A little while and ye
Shall see,
Shall gaze on Me;
A little while, again,
Ye shall not see Me then.'
_A little while!_
The monk looked up--a smile
Making his visage brilliant, liquid-eyed:
'O Thou, who gracious art
Unto the poor of heart,
O Blessed Christ!' he cried,
'Great is the misery
Of mine iniquity;
But would _I_ now might see,
Might feast on Thee!'
The blood, with sudden start,
Nigh rent his veins apart--
(O condescension of the Crucified!)
In all the brilliancy
Of His Humanity,
The Christ stood by his side!
Pure as the early lily was His skin,
His cheek out blushed the rose,
His lips, the glows
Of autumn sunset on eternal snows:
And His deep eyes within,
Such nameless beauties, wondrous glories dwelt,
The monk in speechless adoration knelt.
In each fair hand, in each fair foot, there shone
The peerless stars He took from Calvary:
Around His brows, in tenderest lucency,
The thorn-marks lingered, like the flush of dawn;
And from the opening in His side there rilled
A light, so dazzling, that the room was filled
With heaven: and transfigured in his place,
His very breathing stilled,
The friar held his robe before his face,
And heard the angels singing!
'Twas but a moment--then, upon the spell
Of this sweet Presence, lo! a something broke:
A something, trembling, in the belfry woke,
A shower of metal music flinging
O'er wold and moat, o'er park and lake and fell,
And, through the open windows of the cell,
In silver chimes came ringing.
It was the bell
Calling Monk Gabriel
Unto his daily task,
To feed the paupers at the abbey gate.
No respite did he ask,
Nor for a second summons idly wait;
But rose up, saying in his humble way:
'Fain would I stay,
O Lord! and feast alway
Upon the honeyed sweetness of Thy beauty--
But 'tis _Thy_ will, not mine, I must obey;
Help me to do my duty!'
The while the Vision smiled,
The monk went forth, light-hearted as a child.
An hour thence, his duty nobly done,
Back to his cell he came.
Unasked, unsought, lo! his reward was won!
Rafters and walls and floor were yet aflame
With all the matchless glory of that Sun,
And in the centre stood the Blessed One--
(Praised be His Holy Name!)
Who, for our sakes, our crosses made His own.
And bore our weight of shame!
Down on the threshold fell
Monk Gabriel,
His forehead pressed upon the floor of clay;
And, while in deep humility he lay,
Tears raining from his happy eyes away,
'Whence is this favor, Lord?' he strove to say.
The Vision only said,
Lifting its shining head:
'If thou hadst staid, O son! _I_ must have fled!'
PHILADELPHIA
THE CENTURY OF INVENTIONS.
CONTAINING A FEW COMMENTS ON THE WORK OF THAT NAME, PUBLISHED BY THE
MARQUIS OF WORCESTER, IN 1663.
There is nothing which the world dreads so much as an unpitying truth.
The history of ideas is that of men trying to persuade themselves that
special miracles of amiability are ever being worked, from the cradle to
the grave, in their favor. Of the tremendous inconsistency and
destructiveness which such miracles imply, they take no heed. The most
unpalatable fact in physics is that of the Struggle for Life.
Ideas once born may never die, but it is worth noting how many men must
die ere their ideas can live. The Indo-Germanic race has always been
blessed with many of those self-cursed martyrs, the Anticipators, or the
men who have outstripped their age. Like the advance guard of the summer
swallows, they have generally died by frosts and lived in fables.
Germany is very proud of her Berchthold Schwartz, and in her pride has
made a proverb declaring that his invention was the proof of supreme
wisdom. When they describe a fool, they say there that he did not
discover gunpowder. But 'the first handful of gunpowder' did not, as
Carlyle claims, drive Monk Schwartz's pestle through the ceiling. Long
before Schwartz, lived Bacon; and a century or so before Bacon, there
were in existence Norman-Latin recipes, says Palsgrave--who had seen
them--_ad faciendum le crake_, for making firecrackers--at least, for
making gunpowder which would crack merrily when fired. Stained glass
windows, according to the cheap and easy explanations of those who used
to send us to natural scenery for every origin in architecture, were
suggested by beholding the winter sunset lines of the sky through the
bare gothic-window tracery of a leafless forest. Recent research finds
the stained window in the antique burning East, where no studies were
made by frost or forest light--nay, the leaves carved by
tradition-loving Gothic Free Masons in churches often keep a peculiar
Eastern form.
I am not, however, lecturing of Lost Arts in the strain which sings
'there is nothing new under the sun,' and which in a chilling manner
benumbs the faith in progress by shaking with a grin before the wearied
inventor some skeleton puppet of buried ages, which resembles his great
thought as a hut resembles a palace. On the contrary, I find in this
strange frequency of anticipation among Indo-Germanic races, and in its
premature failures, a vast proof of inventive vitality and of promise of
great rising truths into all future ages. 'Steam power is nothing new,'
say the advocates of the genius of the past. Hero of Alexandria invented
a steam toy--as he who can read his _Spiritalia_ published by the
Jesuits in 1693 may learn for himself. But the power now roaring and
whizzing all over the world, and which would build every pyramid and
every monument of Egypt now extant in twenty-four hours, is no toy. When
I think of this, there is no ingenious trifle for amusement which does
not inspire a droll awe. Possibly those walking dolls now performing
their weary pilgrimages on level glass-pane floors in Broadway
windows--gravely lifting those enormous gilded boots, which remind me of
Miss Kilmansegg and Queen Berta _a grands pies_, in one--have a good
reason for their dignity of gait. For may they not be golden-footed and
solemn, like her who rose from the waves of old to prophesy to her
son?--and if she was _silver_-footed, it makes no difference, for so are
some of the _autoperiper_--nay, _that_ word finishes me, and I go no
further. Such a block of Greek would bring even a German sentence down
with a crash to a verbless conclusion. What I would have said was, that
it may be that these dolls are heralds of greater dolls yet to come,
which shall be wound up to fetch and carry, to sew on buttons--nay, it
is even possible (in the wildest of dreams) that they may be made to
boil potatoes properly. And I have been told that a recent improvement
in boys' rocking horses, by means of which a trotting motion is given to
the legs of those docile animals, has suggested to a mechanic of this
city the construction of a very good automatic steed, whose only fault
is slowness. May I suggest that a very great improvement indeed may yet
be made on that horse, and that the two-forty of a coming generation may
be the result, not of oats and hay, but of steel springs and cylinders?
The first wooden horse burnt Troy--what will the last do?
I have been reminded of the strange tendency in man--but more especially
of the Indo-Germanic or Aryan man--to anticipate by invention the wants
of an age, sometimes centuries beforehand--by turning over that very
curious work, the 'Century of Inventions,' by the Marquis of Worcester,
in which, as in the commonplace book of an author, one may find jotted
down many an undeveloped idea of great promise. In this connection we
may be allowed to borrow somewhat from a biography by Charles F.
Partington, published in 1825.
Edward Lord Herbert, the sixth earl and second Marquis of Worcester, was
born at Ragland near Monmouth; and his family, long distinguished for
the most devoted loyalty, possessed the largest landed estate of any
then attached to the British court. What this was in those times is set
forth by the fact that in 1628 the father of the marquis had a revenue
of upward of twenty thousand pounds. In 1642, the year in which his son
was created marquis, the young heir raised, supported, and commanded an
army of 1,500 foot and near 500 horse soldiers.
He had a stormy life before him, this young marquis, with many more
scenes, adventures, and changes than are to be found in Woodstock and
Peveril of the Peak. How he fought well, recapturing Monmouth among
other things from the Puritan General Massey, how he was appointed, in
consequence of his daring cavaliering raids, by Charles II to negotiate
with the Irish Catholics; how the king often visited him at Ragland, is
all a fine story, well worth reading. We can get glimpses of that REGAL
life--as Mr. Partington admiringly small-caps his climax, from the 'list
of the Ragland household' with the earl's order of dining--castle gates
closed at eleven o'clock in the morning, the entry of the earl with a
grand escort, 'the retiral of the steward'--the advance of 'the
Comptroller, Mr. Holland, attended by _his_ staff'--'as did the sewer,
the daily waiters, and many gentlemen's sons, with estates from two to
seven hundred pounds a year, who were bred up in the castle, and my
lady's gentlemen of the chamber.' Therein, too, we see the rattling of
trenchers, and hear the gurgling of bottles, at the first table, of the
noble family, and such stray nobility as came there; at the second
table, of knights and honorables--at the second 'first table' in the
hall of 'Sir Ralph Blackstone, Steward; the Comptroller, the Master of
the Horse, the Master of the Fish Ponds, my Lord Herbert's Preceptor,'
and such gentlemen as were under degree of a knight--these all being
'plentifully served with wine.' Of the second table there is no note of
much wine, but it still had 'hot meats from my Lord's table,' and at it
sat the Sewer with gentlemen waiters and pages to the number of
twenty-four--and even now we are not yet come to the vulgar. For at the
_third_ table sat my Lord's Chief Auditor, his Purveyor of the Castle,
Keeper of the Records--Ushers of the Hall--Clerk--Closet Keeper--Master
of the Armory--and below these divers Masters of the Hounds--Twelve
Master Grooms of the Stables, Master Falconer--Keepers of the Red Deer
Park--and below these yet one hundred and fifty 'footmen, grooms, and
other menial servants.'
Bright gleams vanish--the stately dinner parties grow dim, Masters of
Horses and Hounds go to battle, the plate is melted down, and all is sad
and sere. The young lord is sent by King Charles abroad, and
Parliamentary Fairfax comes thundering at the gate, where admittance is
refused by the venerable old marquis. Fairfax besieges boldly and is
gallantly attacked by repeated sallies. I had rather the Puritans, with
whom all my head goes, and with it half my heart, had behaved better
than they did on this occasion. For after the venerable old marquis had
fought nobly and surrendered on honorable terms, I am sorry to say he
was most dishonorably treated, the conditions of capitulation being
disgracefully violated, and the old marquis put in close prison, where
he soon died in his eighty-fifth year.--Well, well--there was abundance
of such false faith and dark villany on both sides ere the war was over.
Be it remembered that these same nobles had kept the honor too closely
to themselves, and ridiculed it out of life quite too sharply in the
'base mechanicals' to fairly expect mastery in gentility from them. And
in these same Partingtonian Biographies, I am often inclined to suspect
that the lions do some of their own carving.
Puritans sequestered and smashed the estate right and left--lead sold
for six thousand pounds, woods cut down and sold for one hundred
thousand more. 'Pity!' do you say? Reader mine, there is enough land in
parks at this present day in broad England to feed that wretched one
eighth of her population who are now buried at public expense. That
dis-parking business was at any rate not badly done.
Little more is seen of the young lord through the war. In 1654 he is at
King Charles's court in France--is sent to London to procure supplies of
money for the king--is caught and Towered, where he rests for several
years, sorrowfully poor, if we may judge from a letter to Colonel
Copley, in which he declares that 'I am forced to begge, if you could
possible, eyther to helpe me with tenne pownds to this bearer, or to
make vse of the coache and to goe to Mr. Clerke, and if he could this
daye helpe me to fifty pownds then to paye yourself the five pownds I
owe you out of them.' A melancholy letter, after all that glittering
Arthur's-court splendor of first, second, and third tables of nobility,
Masters of Robes and Records--a letter in which there seems some trace
of getting money by 'projects' and 'bubbles'--whether of doing little
bills or by Notable Inventions, I will not say. Prison does not, it is
true, last forever, but its doors open on a scene of baseness blacker
than that which brought the brave old marquis with sorrow to his grave.
The tale is told in a paragraph:
'On the king's restoration, the Marquis of Worcester was one of the
first to congratulate his Majesty on the happy event, though the
situation of the unfortunate nobleman was little bettered by the
change; indeed it appeared but as the signal for new persecutions,
as one of the earliest public acts of the ungrateful monarch may be
characterized as an insidious attempt to set aside the claims of
his earliest and best friend.'
'Put not thy trust in princes.' To contrast this treatment of poor
Worcester with the fervent written promises of the ungrateful 'C. R.' or
Carolus Rex, might have shook the faith of Dr. Johnson in his beloved
'merry monarch.' The earlier letters of the king to the marquis, when
something was expected of the 'gallant cavalier,' and the latter had
'money to lend,' are painfully amusing:
OXFORD, _Feb. 12._ * * 'I am sensible of the dangers yu will
undergo, and ye greate trouble and expences you must be at, not
being able to assist yu who have already spente aboue a Million of
Crowns in my Service, neither can I saye more then I well remembr
to have spoke and written to you that allready words could not
expresse your merits nor my gratitude: and that next to my wife and
children I was most bound to take care of you, whereof I have
besides others, particularly assured yor Cosin Biron as a person
deare unto you. * * And rest assured, if God should crosse me wth
your miscarrying I will treate your Sonne as myne owne, and that
yw labour for a deare friende as well as a thankfull Master when
tyme shall afforde meanes to acknowledge how much I am
'Yor most assured real constant
and thankfull friend
'CHARLES R.'
There are other letters from Charles R., very little to his credit as
regards the keeping of promises, and likewise several strange papers of
the Worcester people, showing that they had their clouds and humors,
like other families. Of our marquis--the reader will readily pardon me
all that I have digressed to say of his early history--it must suffice
to tell that, after the Restoration, he appears as a poor inventor, and
that on the 3d April, 1663, a bill was brought into Parliament for
granting to him and his successors the whole of the profits that might
arise from the use of a water-raising engine, described in the last
article in the 'Century' of Inventions. The 'Century' itself had been
presented to the king and commons some months previously. This
invention, coupled with its penultimate and antepenultimate ninety-ninth
and ninety-eighth inventions, may indeed be justly considered as the
wonder of the 'Century,' since, when united with the sixty-eighth, they
appear, in Partington's opinion, to suggest all the data essential for
the construction of a modern steam engine. The injustice which he
encountered during life, seems to have followed Worcester for two
centuries after death; for Lord Orford declares that the bill granting
the marquis such advantages as his invention might give birth to, was
passed on a simple affirmation of the discovery that he (the marquis)
had made. 'His lordship's want of candour in this statement will be
apparent when it is known that there were no less than seven meetings of
committees on the subject, composed of some of the most learned men in
the house, who, after considerable amendments, finally passed it on the
12 May.'
It is touching to see the absolute, extreme, life-giving faith in the
merit of his invention which inspired the marquis--and in this strange
faith, like a prophecy, even more than in his invention itself,
considering the way in which he probably came by it, do we recognize
that Genius which rises here and there in the past history of the Aryan
races, and that so all-sidedly and confidingly as to seem miraculous. I
confess that when I look closely and deeply into the knowledge of Dante
and Lionardo da Vinci, of Fiar Bacon, and the Cavalier Marquis of
Worcester, an awe comes over me. All of them seem to have been so
great, some of their order so _unearthly_ great; and they held the keys
to so many mysteries, and to doors of science which were not unlocked
for long centuries after their death; and there was in all of them such
a strange sympathy and knowledge with the other great men as yet unborn,
who were to come after them, and for whom they seem to have labored, and
to whom they talked with the confidence of friends. I never pause before
a certain passage in Dante's 'Inferno,' without the feelings of one
standing before a great prophet--some marvellous earthly ancient of
days, who foresaw all to come:
'Di la fosti cotanto quant'io scesi:
Quando mi volsi, tu possasti 'l punto
Alqual si troggon d'ogni parte i pasi.'
'Thou wast on the other side so long as I
Descended; when I turned thou didst o'erpass
That point to which from every part is dragged
All heavy unbalance!'
It was well thought by Monti that, had this passage been noted by
Newton, it might have given him a better hint than the falling apple.
Perhaps it did, for Newton was no poet, and it is the poetic,
associative-minded men of genius who have always preceded the greatest,
strictly scientific minds, and far surpassed the latter in the
comprehensiveness of their views. Bear with me, ye men of Induction, for
I believe in the coming age, at whose threshold we even now stand, when
ye and the poets shall be one.
The Marquis of Worcester was not like the indifferentist philosopher, so
well set forth by Charles Woodruff Shields in his _Philosophia
Ultima_,[4] as one who would not invade, but only ignore the province of
revelation, regarding its mysteries as matters entirely too vague to be
taken into the slightest account in his exact science. For our good Lord
Herbert thought Heaven had a great deal to do with his inventions, as is
proved by his 'ejaculatory and extemporary Thanksgiving Prayer, when
first with his corporeal eyes he did see finished a perfect trial of his
Water-commanding Engine, delightful and useful to whomsoever hath in
recommendation either knowledge, profit, or pleasure.' And--never mind
the delay, reader--we will even look at that prayer, in which this world
and the next blend so strangely;
'Oh! infinitely omnipotent GOD! whose mercies are fathomless, and
whose knowledge is immense and inexhaustible; next to my creation
and redemption I render thee most humble thanks from the very
bottom of my heart and bowels, for thy vouchsafing me (the meanest
in understanding) an insight in soe great a secret of nature,
beneficent to all mankind, as this my water-commanding engine.
Suffer me not to be puffed up, O Lord, by the knowing of it, and
many more rare and unheard off, yea, unparalleled inventions,
tryals, and experiments. But humble my haughty heart, by the true
knowledge of myne owne ignorant, weake, and unworthy nature; proane
to all euill. O most merciful Father my creator, most
compassionatting Sonne my redeemers, and Holyest of Spiritts the
sanctifier, three diuine persons and one God, grant me a further
concurring grace with fortitude to take hould of thy goodnesse, to
the end that whatever I doe, unanimously and courageously to serve
my king and country, to disabuse, rectifie, and convert my
undeserved yet wilfully incredulous enemyes, to reimburse
thankfully my creditors, to reimmunerate my benefactors, to
reinhearten my distressed family, and with complacence to gratifie
my suffering and confiding friends, may, voyde of vanity or selfe
ends, be only directed to thy honour and glory everlastingly.
_Amen!_'
How this great invention faded and was forgotten till the days of Watt
and Fulton, is hardly worth surmising. It had been born and died long
before. Was it not in 1514 that Blasco de Garay set a steamboat afloat
on the Tagus? Sometimes, as in the case of John Fitch, it seems to have
grown spontaneously from the instinctive impulse to create, as Fichte
calls art. I have seen old men, who had known Fitch: their account of
his severely won improvements, and more recently his 'Life,' make me
believe that he owed nothing to precedent. But the marquis, I am sorry
to say, notwithstanding his prayer and his bold claim to originality,
cannot come off with so clear a record, so far as invention is
concerned. He certainly gave a good, plausible account of the discovery,
or it was given for him, and this went current for many years in books
of inventions. It was said that the marquis, while confined in the Tower
of London, was preparing some food in his apartment, and the cover of
the vessel, having been closely fitted, was, by the expansion of the
steam, suddenly forced off and driven up the chimney. 'This
circumstance, attracting his attention, led him to a train of thought,
which terminated in the completion of his 'water-commanding engine.''
_E ben trovato._ Unfortunately, within a few years, and since Partington
published the 'Century of Invention,' there was unearthed from the
gossiping letters of a gay French court-belle, who little dreamed what
ill service she was doing her gallant, and what good service to history,
a chance bit of trifling, as she probably deemed it, which sends the
marquis's story exploding up the chimney after the lid of his apocryphal
kettle. It seems that when the marquis was in France, he, in accordance
with the elegant and refined custom which prevailed there and in
England, as the reader may gather from Boswell's 'Johnson'--went with
this lady to visit the madmen confined in the public prison.
I have already digressed so widely in this article, that a sin more or
less, of the kind, need not be noted too severely. Reader, if you are
one of those who think that mankind do not progress in heart, what think
you of this pretty custom of the last century, according to which
gentlemen and ladies of the highest rank, 'persons of quality,' made up
parties to visit public madhouses, which, by the way, were common shows,
at one penny entrance fee, and where the young gentlemen poked the mad
people with sticks, and pelted them, shook their chains, and jeered
them, till they foamed and raved, and the young misses giggled and gave
pretty screams, and cried, 'Oh, fie!' and 'lor!' and then the visitors
all laughed together? Then Miss ----, a little bolder, hissed at the
lunatics herself, and poked them with a stick--and then there was a
fresh storm of tears and howls and blasphemy and obscenity; and the
keepers, rushing in with heavy cudgels, beat the 'patients' right and
left like cattle--and it was all 'so horrible!' _Bad_, think you? These
were the ladies and gentlemen of the old school--the Grandisons and
Chesterfields and their dames. At the present day there are still vulgar
people who haunt insane asylums and prisons, and scenes of domestic
affliction and courts, for the sake of gratifying a gross love of
excitement, which they disguise to themselves under various ingenious
pretences. But the tendency of the age is to discourage such meddling
and prying into the mysteries and miseries of humanity. It is low, it is
mean, and the better nurtured and higher minded leave it to boors--be
they of Peoria or the Fifth avenue.
Well, our marquis, then the first gentleman in Great Britain, one of
'the barons of England who fought for the crown,' when in France as
particular friend of His Majesty Charles II, went one day on such a
party of pleasure, and somewhat annoyed his pretty companion by
persisting in listening to the drivelling talk of a madman--one Solomon
de Caus--who, while he rattled his chains, talked of a great invention
he had made, whereby chariots were to go by steam, and weights be
raised, and all manner of brave work be effected, at small cost or labor
to man. And the marquis talked to the madman, and the lady laughed, and
the chains rattled, and the straw rustled, and--well, it _has_ been made
the subject of a very good picture--which you, reader, may have seen,
either in original or engraving.
I will not pretend to say how far what is known of the life of this
French inventor is reconcilable with this story of the madhouse. It is
certain that Solomon de Caus, a French engineer, architect, and author,
died about 1635, that he was born probably at Dieppe, and devoted
himself to mathematics. The marquis might have met him in a better place
than a bedlam, since in 1612 De Caus went to London, where he was
attached to the Prince of Wales, and afterward to Charles I. From 1614
to 1620 he lived in Heidelberg at the court of the Elector Frederic V,
and returned to France in 1624, where he received the title of royal
engineer and architect. More than this, he wrote books on mechanics, in
one of which, _Les Raysons des Forces Mouvantes_, he speaks of the
expansion and condensation of steam in a manner which has been supposed
to suggest the alternate action of the piston, the principle of the
steam engine, and, finally, 'the great discovery' of and to the Marquis
of Worcester. How far all this may be supposed to contradict the lady's
story, I will not say. Certain it is, that many a man who has done quite
as well in worldly honors, has, after all, come to misery and madness
through unfortunately making an invention.
Inventors have, on the whole, a little easier time of it in these
days--and yet not so very much easier, as the reader who has chanced,
like myself, to study law in an office where there are many 'patent
cases,' will bear witness. Eighteen hundred years ago, the inventor was
crucified--lest his malleable glass should injure Ephesian or other
silversmiths. During the middle ages, they burnt him alive. In the times
of Worcester he seldom escaped prison, for to be a 'projector' was a
charge which greatly aggravated that of treason; while in France, where
they managed these things better, according to the views of the day,
they simply cast him into a dungen among madmen. In America in the
nineteenth century he has indeed occasionally better luck, and yet in
most cases not so much better as most think. For, apart from the fact
that he must generally sell his invention to richer men endowed with
business faculty, who get nearly all the profits, and, not unfrequently,
by clapping their names to the project, all the credit, he must also
wage a weary, heart-breaking legal war on infringers of patents and
other thieves; so that by the time his time has expired, he has seldom
much to show for his brain-work.[5] 'Serves him right, he has no
business capacity,' cry the multitude. We need not look far for
examples. I am not sure that Eli Whitney, when he fell with his cotton
gin among the thieves of the South, did not fare quite as badly and
suffer quite as much as Solomon de Caus. For to be clapped fair and
square into a dungeon is at all events a plain martyrdom, with which one
can grapple philosophically or go mad _a discretion_, while to be only
half honored and nine-tenths plundered, dragged meanwhile through courts
and newspapers, may be better or worse, according to one's measure.
After all, the good old Roman plan of putting a man to death for
inventing malleable glass had its advantages--it was at least more
merciful from a Christian point of view, and would, at the present day,
save a vast amount of yards of Patent Law red tape.
_Artis et Naturae proles_, 'the offspring of Nature and of Art.' Such is
the motto with which the Marquis of Worcester prefaced his 'Century of
the Names and Scantlings of such inventions as he could in the year 1663
call to mind,' and which he presented to Government in the bold hope
that by their purchase or other disposition he might even out-go the six
or seven hundred thousand pounds already sacrificed for the king, as he
asserts, but rather meaning, I imagine, that he might get some portion
of it back again. Let no one laugh at the character of many of these
'Scantlings.' Science was young then; thaumaturgy, or the working of
mere wonders, was still the elder sister of art; astrology might be
found in every street; alchemists still labored in lonely towers all
over England; and witches were still burned to the glory of GOD. The
'Mathematicall Magick, or the Wonders that may be performed by
Mechanicall Geometry'--now by chance open before me--by Bishop Wilkins,
the brother-in-law of Cromwell, with its disquisitions on 'Perpetuall
Motion,' 'Volant Automata,' and 'Perpetuall Lamps,' passed for sound
sense, and with it passed much occult nonsense of a darker dye. Manners
and morals were as yet badly organized. Gambling was a daily amusement
with all the gentry, and its imitators; for the Revolution, though it
had very promptly driven out of England the very little merriment and
cheerfulness which the Reformation had spared, had by no means taken
away vice, and to cheat at cards was a part of all play in the best
society--which it had not been in the olden time. Political plots were
still rife, and cipher alphabets, signals by knots and signs, deadly
secret weapons, and devices to escape prison were in daily demand, just
as patent apple-parers and ice-cream freezers are at the present day.
The marquis, who had lived well through his times, knew what would be
popular, and, though a man of honor as times went, and a pious
Christian, never dreamed that he did not play his part as a good citizen
in supplying such grotesque wants.
First among his Inventions is one which, revived in modern times, meets
the eye of every one daily on the face of every letter. As he designed
it, it was, however, very elaborate, embracing 'several sorts of seals,
some showing by screws, others by gauges, fastening or unfastening all
the marks at once: others by additional points and imaginary places,
proportionable to ordinary escutcheons and seals at arms, each way
palpably and punctually setting down (yet private from all others but
the owner, and by his assent) the day of the month, the day of the week,
the month of the year, the year of our Lord, the names of the witnesses,
and the individual place where anything was sealed, though in ten
thousand several places, together with the very number of lines
contained in a contract, whereby falsification may be discovered and
manifestly proved.' Upon these seals, too, one could keep accounts of
receipts and disbursements, from one farthing to millions, and, finally,
as a climax to their mystery, by their means any letter, 'though written
but in English, may be read and understood in eight several languages,
and in English itself, to clear contrary and different sense, unknown to
any but the correspondent, and not to be read or understood by him
neither, if opened before it arrive unto him.'
It is believed that the secret of these seals is simply this: a number
of movable metallic circles are made to slide within each other, on one
common centre, the whole being enclosed in an outer frame. Within these
circles may be placed either movable types, or letters and figures may
be engraved on the circles themselves, and these, according to a key, of
which the corresponding parties must possess a duplicate. To fully
understand the secret of the composition of a sentence 'in eight several
languages,' we must have recourse to invention No. 32 of the 'Century,'
teaching 'how to compose an universal character, methodical and easily
to be written, yet intelligible in _any_ language .... distinguishing
the verbs from the nouns, the numbers, tenses, and cases, as properly
expressed in their own language as it was written in English.' Such a
system was composed by the Bishop Wilkins already referred to; Bacon
had busied himself with a 'pasigraphy' long before; Leibnitz, Dalgaru,
Frischius, Athanasius Kircher, Pere Besnier, and some twenty others have
done the same. The most practical solution of the problem seems to have
been that of John Joachim Becher, who in 1661 published a Latin folio,
which, apart from its main subject, is valuable from its observations on
grammar, and on the affinities existing between seven of the ancient and
modern tongues. With this he gives a Latin dictionary, in which every
word corresponds with one or more Arabic numerals. 'Every word is
assumed as distinctive, or denoting the same word in all languages; and
consequently nothing more is required than to compose a dictionary for
each, similar to that which he has given for the Latin.' Certain
determinate numbers being given for the declensions and conjugations,
and the cases, moods, tenses, and persons, the whole grammar becomes
extremely easy of acquisition. Let us suppose that a Frenchman wishes to
write to a German: _La guerre est un grand mal_--'War is a great evil.'
He seeks in his index _guerre_, and finds 13. The verb _etre_, 'to be,'
is 33. _Grand_, or 'great,' is 67; and _mal_, or 'evil,' is 68. The
sentence then reads:
13. 33. 67. 68.
The sentence might be understood by these four numbers, but the author
perfects it. _Guerre_, or 'war,' is the nominative case, and is
appropriately designated by the Arabic numeral 1. The third person,
singular, present tense, of the indicative mood of a verb, is
characterized by 15. _Grand_ and _mal_ being each in the nominative
case, also require the figure 1. He will therefore write:
13. 1 | 33. 15 | 67. 1 | 68.1
--the numbers being separated by a vertical dash, to avoid confusion.
The German, inverting the process, turns to _his_dictionary, and finds
_Der Krieg ist ein grosses Uebel_.
If the world were to be persuaded to adopt these dictionaries, and with
them some uniform oral system of counting, such as might be learned in a
day, who shall say in what conversation might result! Fancy an orator
counting '83.1--10.16--225.2'--interrupted by enthusiastic cries of
'2.30' and '11.45!' Fancy a lover breathing his tender passion in
'837.25--29.1,' and extracting a reluctant '12' from his adored. Fancy a
drunken Delaware Democrat--a SAULSBURY--flourishing a revolver, and
gurgling out '54.40' to the Sergeant-at-Arms in particular, and decency
in general, as a proof of his fitness to be regarded as a mate for his
Southern colleagues. Fancy Brignoli singing '1.2.3,' as he reminds us by
his good singing and wooden acting of a nightingale imprisoned in a
pump--
Or fancy the appearance of a page of Shakspeare or Homer thus
metamorphosed.
'He lisped in numbers for, the numbers came.'
It is something to the marquis's credit that he evidently, to judge from
the sixth article of his 'Century,' had discovered the telegraph, an
invention not much used in Europe until the commencement of the French
Revolution. It had indeed been understood in a rude form by the
ancients. 'Polybius describes a method of communication which was
invented by Cleoxenus, which answered both by day and night,' but that
of Worcester's is thought to have been far superior to anything known
before his time. The following paragraphs all indicate inventions
greatly in advance of his age:
'No. IX.--An engine portable in one's pocket, which may be carried
and fastened in the inside of the greatest ship, _tanquam aliud
agens_, and at any appointed minute, though a week after, either of
day or night, it shall irrecoverably sink that ship.'
A bombshell filled with gunpowder, a gunlock, and a small clock, have
been suggested as forming the components of this invention. I am
satisfied however, that several very dangerous detonating powders were
well known to the alchemists; and the condensed pocket size of the
machine described, would evidently require some such preparation.
'No. X.--A way from a mile off to dive and fasten a like engine to
any ship so as it may punctually work the same effect either for
time or execution.'
Precisely the same experiment has within a week of the time at which I
am now writing, been made at Washington, as it was by Mr. Fulton half a
century ago with his Torpedo-harpoon. If the marquis contemplated simply
human agency as the aid to apply his portable powder-machine, it must be
admitted that he had at least contemplated a more effective diving bell
than any known to modern times. Submarine transit was indeed a subject
to which he had devoted special study.
'No. XI.--How to prevent and safeguard any ship from such an
attempt by day or night.
'No. XII.--A way to make a ship not possible to be sunk, though
shot at an hundred times between wood and water by cannon, and
should she lose a whole plank, yet, in half an hour's time, should
be made to sail as fit as before.'
It is thought that a great number of airtight compartments was the
secret here hinted at; but the spirit of positive confidence with which
the marquis speaks, and the great number of successful shots which he
defies, seems to hint at something like the Ericsson Monitor of these
days. Not without interest is the following:
'No. XIII--How to make such false decks as in a moment should kill
and take prisoners as many as should board the ship, without
blowing the real decks up, or destroying them from being reducible;
and in a quarter of an hour's time should recover their former
shape, and to be made fit for any employment, _without discovering
the secret_.'
The words italicized set forth the startling marvel of the whole. It is
said that a false deck of thick plank may be easily blown into the air,
when a number of small iron boxes, open at the top, and filled with
gunpowder, are placed beneath. How this could be done and yet kept
secret is indeed a wonder, and we must therefore conjecture that the
marquis had some other device in his mind. Certain it is, that the idea
of converting vessels into traps of destruction, or of so defending them
as to destroy assailants after boarding the decks, has not been very
extensively developed.
'No. XVI.--How to make a sea castle or a fortification _cannon
proof_, capable of a thousand men, yet sailable at pleasure to
defend a passage, or in an hour's time to divide itself into three
ships, as fit and trimmed to sail as before; and even whilst it is
a fort or castle, they shall be unanimously steered, and
effectually be driven by an indifferent strong wind.'
It is to be regretted that Parliamentary or other inducements were not
employed to obtain from the marquis, at least the publication of his
views as regards making vessels cannon proof. From the general character
of his inventions, and from comparison of them, it appears he had full
faith in cannon-proof floating batteries as a means of defence, and, we
may consequently and justly infer, as superior to the latter. Among his
inventions there are but two in reference to 'fortifications,' and both
of these are after a manner a transfer of the floating battery to land,
or an application of the principle of mobile defences. These are as
follows:
'No. XXIX.--A portable fortification, able to contain five hundred
fighting men, and yet, in six hours' time, may be set up and made
cannon proof, upon the side of a river or pass, with cannon mounted
upon it, and as complete as a regular fortification, with halfmoons
and counterscarps.
'No. XXX.--A way in one night's time to raise a bulwark, twenty or
thirty foot high, cannon proof, and cannon mounted upon it; with
men to overlook, command, and batter a town, for though it (the
bulwark) contain but four pieces, they shall be able to discharge
two hundred bullets each hour.'
There can be but little question, from all I have cited, that the
Marquis of Worcester was singularly in advance of his age as regarded
the great principles of warfare. We have found him thus far, in all
probability, acquainted with the construction of permutable seals, and
indeed of the grand principle of permutation applied to technology in
several respects (vide "Century" Nos. III, IV, V,) of the telegraph, of
sinking vessels by torpedoes, and, finally, of floating batteries and
cannon-proof vessels. In No. 30, we have, however, a hint that the
marquis had studied the principles of revolving firearms, when he
speaks of four cannon discharging two hundred bullets each hour. That he
had, theoretically, at least, anticipated Colt, appears from
'No. LVIII.--How to make a pistol discharge a dozen times with one
loading, and without so much as once new priming requisite, _or to
change it out of one hand into the other_, or stop one's horse.'
I call attention to the words which I have italicized. It is well known
that the mere principle of revolving barrels in firearms was already
old, even when Worcester wrote. I have seen guns of the kind over three
hundred years old, and they are not uncommon in foreign museums. But it
would appear that the marquis was acquainted with the principle of the
self-cocking pistol. How else could he propose to discharge a gun a
dozen times, without changing it from one hand to another? And this, I
believe, was not known before his day. But how this could have been
conveniently carried out, without some application of detonating powders
in place of flint, steel, and gunpowder, I do not understand. That he
was very probably familiar with the application of such chemical
detonating agents has already been suggested. In another number, he
suggests the application of this principle to 'carbines.' So in No.
LXII, he proposes 'a way for a harquebuss, a crock, or ship musket, six
upon a carriage, shooting with such expedition as, without danger, one
may charge, level, and discharge them sixty times in a minute of an
hour, two or three together.' To which he adds the following:
'No. LXIV.--A seventh, tried and approved before the late king (of
ever blessed memory), and an hundred lords and commons, in a cannon
of eight inches and half a quarter, to shoot bullets of sixty-four
pounds weight, and twenty-four pounds of powder, twenty times in
six minutes; so clear from danger, that after all were discharged,
a pound of butter did not melt, being laid upon the cannon britch,
nor the green oil discoloured that was first anointed and used
between the barrel thereof, and the engine having never in it, nor
within six foot, but one charge at a time.'
Several improvements of this kind are suggested in the 'Century,' which
evidently involve different principles from that of the modern revolver,
in reference to which difference we are informed in a 'note by the
author,' that 'when I first gave my thoughts to make guns shoot often, I
thought there had been but one only exquisite way inventible; yet, by
several trials, and much charge, I have perfectly tried all of these.'
I cannot venture in a single article to exhaust the suggestions in the
Century, and must refer my reader to the volume himself, assuring him
that he will there find many curious hints, several of which have, since
its publication, been very practically realized. It is worth noting,
however, that the author seems to have fully anticipated a very
remarkable modern invention, in declaring that 'a woman even may with
her delicate hand, vary the ways of coming to open a lock ten millions
of times, beyond the knowledge of the smith that made it, or of me who
invented it.' From this, as I have already suggested, it appears that he
had, far in advance of his age, mastered a very great principle in
mechanics; and as he appears to have understood, in theory at least,
several others, it is no more than justice to rank him far above those
mere charlatans of science, and hunters for marvels by means of
isolated observation and experiment, with whom many would place him.
That the 'Century' contains much which would be very discreditable to
any man of science at the present day, is very true. Perpetual motion,
perfect aerostation, devices for idle tricks and mere thaumaturgy,
appear in company with schemes to take unfair advantages at card
playing, and for the construction of false dice boxes--of which latter
it is indignantly observed by honest Partington, that, there are few who
profess the science of cheating at cards or dice, or to be encouragers
of those who do; and it may fairly be conceded that there are not two
periods in our regal annals, in which this detestable meanness had
become fashionable enough to sanction a nobleman in inscribing to a king
and his parliament a method by which it might be advantageously
effected! We may, however, believe that a second period has at the
present dawned over England, not much inferior as regards 'detestable
meanness,' to that of Charles the Second. A recent transaction has shown
that noblemen and their friends in the year 1862, are not above
ascertaining from Johnson's Dictionary, the obsolete spelling of a word,
such as _rain_-deer, betting a hundred pounds with an American as to its
true orthography, and agreeing with him to abide by Johnson's authority;
a piece of swindling quite as detestable in its meanness as the using of
loaded dice. Neither can I see that the conduct of a majority of the
British people, in fomenting Abolition for many years, and then giving
her aid and countenance to our Southern rebels, on the flimsy, and, at
best, brazenly selfish plea of the Morrill Tariff, is less detestable or
less mean. We may regret to see a vice in individuals tolerated in high
places; but when the blackest inconsistency, and the most contemptible
avarice are elevated by a Christian nation into principles of conduct
toward another nation struggling to free the oppressed, we may well
doubt whether another period has not approached in England, over which
the future historiographer may not sigh as deeply as over that of
Charles the Second.
I attach no serious value to the efforts of the Marquis of Worcester,
save as illustrating the principle with which I prefaced this article:
that according to the mental peculiarities of the most vigorous of
races--the Indo-Germanic above others--there is a tendency in certain
active minds to generalize and draw practical conclusions, not
unfrequently centuries in advance of the wants of their age. The partial
and premature forcing of these principles into practice, is sometimes
quoted in after years as derogatory to the merit due to modern
inventors, and as illustrating to a degree never contemplated by him who
uttered it, the maxim that there's 'nothing new under the sun.'
_Nothing?_ Why, _everything_ is new under the sun when it first assumes
fit time and place. Were this not true, we might as well return to
'Nature's Centenary of Inventions,' as set forth by a pleasant pen in
_Household Words_:
'Before the first clumsy sail was hoisted by a savage hand, the
little Portuguese man-of-war, that frailest and most graceful
nautilus boat, had skimmed over the seas with all its feathery
sails set in the pleasant breeze; and before the great British
Admiralty marked its anchors with the Broad Arrow, mussels and
pinna had been accustomed to anchor themselves by flukes to the
full as effective as the iron one in the Government dockyards. The
duck used oars before we did; and rudders were known by every fish
with a tail, countless ages before human pilots handled tillers;
the floats on the fishermen's nets were pre-figured in the bladders
on the sea weed; the glowworm and firefly held up their
light-houses before pharas or beacon-tower guided the wanderer
among men; and, as long before Phipps brought over the diving bell
to this country as the creation, spiders were making and using
airpumps to descend into the deep. Our bones were moved by tendons
and muscles long before chains and cords were made to pull heavy
weights from place to place. Nay, until quite lately--leaving these
discoveries to themselves--we took no heed of the pattern set us
in the backbone, with the arching ribs springing from it, to
construct the large cylinder which we often see now attaching all
the rest of a set of works. This has been a very modern discovery;
but, prior even to the first man, Nature had cast such a cylinder
in every ribbed and vertebrate animal she had made. The cord of
plaited iron, too, now used to drag machinery up inclined planes,
was typified in the backbone of the eels and snakes in Eden;
tubular bridges and hollow columns had been in use since the first
bird with hollow bones flew through the wood, or the first reed
waved in the wind. Strange that the principle of the Menai Straits'
railway bridge, and of the iron pillars in the Crystal Palace,
existed is the Arkite dove, and in the bulrushes that grew round
the cradle of Moses! Our railway tunnels are wonderful works of
science, but the mole tunnelled with its foot, and the pholas with
one end of its shell, before our navvies handled pick or spade upon
the heights of the iron roads: worms were prior to gimlets,
ant-lions were the first funnel makers, a beaver showed men how to
make the milldams, and the pendulous nests of certain birds swung
gently in the air before the keen wit of even the most loving
mother laid her nursling in a rocking cradle. The carpenter of
olden time lost many useful hours in studying how to make the
ball-and-socket joint which he bore about with him in his own hips
and shoulders; the universal joint, which filled all men with
wonder when first discovered, he had in his wrist; in the jaws of
all flesh-eating animals his huge one-hinge joint; in the
graminivora and herbivora the joint of free motion; for grinding
millstones were set up in our molars and in the gizzards of birds
before the Egyptian women ground their corn between two stones; and
the crushing teeth of the hyena make the best models we know of for
hammers to break stones on the road. The tongue of certain shell
fish--of the limpet, for instance--is full of siliceous spines
which serve as rasp and drill; and knives and scissors were carried
about in the mandibles and beaks of primeval bees and parrots.
Yes, they were all there--and if the undeveloped germ may be taken for
the great fruit-bearing tree, there is nothing new under the sun, labor
and effort are of no avail, and it is not worth while for man to live
threescore years and ten, since a much less time would suffice to show
his utter worthlessness. But the bee and the wild bird, the pearly
nautilus driving before the fresh breeze, and the reed waving in the
wind, should teach us a higher lesson. They teach us that life is
beautiful and to be enjoyed, that infinite laws and infinite ingenuity
were not displayed to be called idle and vain, and that, as the insect
works according to his instinct, man should labor, from the dictates of
reason, with heart and soul to do his best to turn to higher advantage
the innumerable advantages afforded him.
FOOTNOTES:
[Footnote 4: _Philosophia Ultima_, CHARLES WOODRUFF SHIELDS.
Philadelphia, J. B. Lippincott, 1861.]
[Footnote 5: One of the greatest inventors of this or of any age, and
one whom the world regards as 'successful,' is said to have advised an
ingenious friend, never in any case or under any circumstances to take
out a patent for an invention. He 'had been through the mill,' and knew
what it cost.]
THE LADY AND HER SLAVE.
A Tale.
LOVINGLY DEDICATED TO MY SISTERS IN THE SOUTH.
'Nor private grief nor malice holds my pen,
I owe but kindness to my fellow men.
And, South or North, wherever hearts of prayer
Their woes and weakness to our Father bear,
Wherever fruits of Christian love are found
In holy lives, to me is holy ground.'
--WHITTIER.
My young mistress! frown not on me! come! my heart is beating low!
Softly raise the quilt--my babe! Ah, smile on her ere I go!
Yes, the smile comes warm as sunshine, and it falls on my sick heart
As if Heaven were shining through it, and new hopes within me start.
Your clear eyes shine blue upon me through the clouds of sunny curls,
Sadder now, but still as kindly, as when we were little girls.
Your poor slave and you, fair mistress, were born in the same hour,
As if God himself had marked me from my birth to be your dower.
Oft have I laid my dusky hand upon your neck of snow,
To see it sparkle through the jet--how long that seems ago!
So long! before young master came to woo Virginia's daughter,
And tempt her to the cotton fields on Mississippi's water.
I could not leave you, mistress, so I followed to the swamp,
Where fevers fire the burning blood and the long moss hangs damp.
I left poor Sam, he loved me well, but you were my heart's god;
My mother's tears fell hot and fast--I followed where you trod.
Sin and sorrow fell upon me! and soon you felt it shame
To have lost Amy near you, and you blushed to hear her name.
Reared near virgin purity, you could not understand
How I could break from virtue's laws, and form a lawless band.
Then you questioned kindly, sternly,--but you could not make me tell;
I would not wring your trusting heart with tales scarce fit for hell!
You deemed me hardened, sunk in vice; I choked down every moan,
Turned from your breast the poisoned dart to bury in my own.
Driven from your presence, mistress, in agony and shame
I bore a wretched infant--she must never know her name!
How I crawled around your windows when your joyous boy was born,
To hear your voice, to catch a glimpse,--the sun rose fair that morn.
Ah! not mine to hold your darling! not mine to soothe his cries
When the stern death-angel seized him and bore him to the skies!
Then judgment came--the fever fell--young master gasped for breath--
God's hand was on him--vain were prayers,--how still he lay in death!
I heard you shriek--I rushed within--I held you in my arms
That frenzied night when sudden woe had wrought its worst of harms.
When reason dawned on you again, sweet pity stirred within,
You heard my cough, my labored breath, and saw me ghastly, thin.
Then you took my hand so kindly, gazing on my faded face:
'Speak, and tell me truly, Amy, how you fell in such disgrace.'
If he had lived, sweet mistress, I had borne it to the grave;
I would not mar your happiness, child, self or race to save.
Say! must I speak of one you loved now sleeping 'neath the sod?
Your 'yes' is bitter; but we owe the naked truth to God!
The truth to God, for guiltless you must stand before His face,
Nor wrong my pallid baby, nor scorn my suffering race.
Am I too bold? Death equals all--my heart beats faint and low;
Turn not away, sweet mistress, hear the truth before I go!
Gaze upon my shivering baby, scan the little pallid face,
Mark the forehead, eyes of azure--Ha! you do the likeness trace!
Nay, start not in horror from me! Oh, it was no fault of mine;
I would have died a thousand deaths ere wronged a thought of thine.
He came at midnight to my hut--abhorrent to my sense--
Force--threats of shame--foul violence--a slave has no defence!
Wronged--soiled--and outraged--sick at heart--what right had I to feel?
He deemed his chattel honored,--God! how brain and senses reel!
We're women, though our hair is crisped, and though our skin be black:
Men, ask your virgin daughters what's the maiden's deadliest rack!
I scorned myself! I hated him! but felt a living goad
Writhe and crawl beneath my bosom--shameful burden! sinful load!
Sick and faint, I loathed my master, loathed his inant, loathed my life
Till its flame burned dim within me, choked by shame, rage, hate, and strife.
Better feelings woke within me when the helpless girl was born;
Mother's love poured wild upon her: how love conquers rage and scorn!
But my tortured heart was broken, and a slave girl ought to die
When a tyrant master wrongs her, and she dreads her mistress' eye:
Dreads one she loves may read in her, in spite of silence deep,
That which would blight all happiness, and pale the rosy cheek:
Dreads that a wife may shuddering read a husband's naked heart--
Humbled and crushed by treachery, may into madness start.
But Amy dies: she has forgiven--forgive with her the wrong!
Smile on the helpless baby--make her truthful, pure, and strong.
Let her wait upon you, mistress; twine your ringlets golden still;
Take her back to old Virginia, to the homestead by the hill.
My heart clings to you with wild love--wherefore I scarce dare whisper--
Forgive--I am your father's child! pity your ruined sister!
The hot white blood in my baby's veins, though mixed with duskier flow,
Will make her wretched if a slave; let her in freedom go!
Oh make her free, sweet mistress, that such a fate as mine
Blanch not her cheek with agony, nor blast her ere her prime!
You smile--I need no promise; angel-like to me you seem;
Will you open heaven for me? bring the seraphs? how I dream!
I go to God. He made me. All His children, black and white,
Will meet in heaven if pure and true, clad in the eternal Light.
I die--God bless you, mistress!'... Sigh, and gasp--then all is o'er!
And the lady kneels beside a corpse upon the cabin floor.
Her thoughts are busy with the past, with love in falsehood spoken,
While her dusky sister's faithful heart had in silent anguish broken.
She takes the cold hand in her own: 'Poor Amy, can it be
That thou wert of a race accursed, unworthy to be free?
Man's falsehood! God! Thy right hand rests upon the dusky brow;
Thou starr'st it round with virtues brighter than our boasted snow!
I have learned a bitter lesson; to my slave I've been to school;
God has humbled me, but chastened; I will keep His Golden Rule.
Slaves and chattels! God forgive us! they are men and women--Thine!
If Christ may dwell within them, shall I dare to call them _mine_?
No woman must be outraged, nor owned by man, if we
Would hold _our_ sanctity intact--all women must be free.
Sacred from every touch profane, yes, holy things and pure;
A wrong to one is wrong to all; we must the weak secure.
United we must strike the shame; if known aright our power,
Slavery and crime would perish: Sisters, peal their final hour!
Mothers, maidens, wives, no longer aid your dusky sisters' shame!
Strike for our common womanhood, uphold our spotless fame!
Its majesty is in your hands, trail it not in the dust,
Nor keep your shrinking slaves as prey for lovers', husbands' lust!
All womanhood is holy! it shall not be profaned!
Our sanctity is threatened: Men! it shall not thus be stained!
Break up your harems! free our slaves! we will not share your shame!
O mothers of the living, chaste must be life's sacred flame!
Fathers, brothers, sons, and husbands, their chains must be untwined!
Touch not the ark where purity in woman's form is shrined!
Poor Amy! love has conquered! the veil is raised, I see
Sister spirits 'neath the dusky hue; thy people shall go free!'
The lady rose with high resolve upon her pale sad face;
And moved among the slave girls, the angel of their race.
Angel of freedom, charity, she breathes, and fetters melt,
And the holy might of Purity in Southern heart is felt.
Ah! the stars upon our banner, driven apart and dimmed with blood,
Might again in glory cluster through a perfect womanhood!
FOR AND AGAINST.
When his father called Fred Fontevrault, then a boy of fifteen, into his
sick chamber, and made him subscribe to the whimsical conditions of the
will, the female _gendarmerie_, so well versed in my affairs, declared
that my husband had wretchedly repented his early marriage, and
resolving his son should walk into fate with eyes unbandaged, forbade
his alliance before the age of twenty-six. Though Mr. Fontevrault was
fifty and I sixteen when I married him, he was not unhappy. He occupied
himself in looking after his money, and making a collection of mosaics.
We never had any matrimonial disturbances. I think they are vulgar. Any
woman can do as she pleases without a remonstrant word, provided she has
mind enough. It is the brainless women who scold. But scolds do not
rule.
Fred was unreasonably fond of his father, and assented to his wishes
without demur, even when the great Fontevrault estates hung on his
fidelity to a useless oath. Then he died, and I settled into the blank
stupidity of my widowhood. I, who had known no master but my own sweet
will, now found myself in a hundred ways restricted. I was ruled through
Fred. He must graduate at Harvard; the great establishment, splendid but
tedious, must be maintained. So our residence in Boston was
necessitated. I shut myself up in the legitimate manner, and--mourned of
course. If it had not been for novels, worsted work, and my beauty, I
should have gaped myself out of existence the first year. What nonsense
it is to say the prime of a woman's loveliness passes before the
thirties! For, look at me, am I old or faded? Would you believe that
Fred, so tall and splendidly developed, was my son? From me he took his
wealth of nature, for Mr. Fontevrault was one of those dried, wrinkled
old men, women like me often marry; not because of the settlements only,
but because of the foil. My figure was moulded like the Venus they
copied in the colder marble from Pauline. Shoulders and arms, delicious
in their curves, shining with a rosy fairness. A creamy skin, with a
faint coralline tinge in the cheeks. The forehead is too low, some say;
and yet artists have praised its bend, and the Greek line of the nose;
not intellectual, but womanly, you know. Hair of a bright brown, feeling
like floss silk. Eyes, I believe, few people ever fairly saw. Men are
bewitched by them, women cannot understand their charm. Perhaps you have
seen Wilson's portrait of me, the one with the grayish green background;
you notice that the eyes were turned from the spectator, and half shaded
by white lid and gilded lash. He could not catch the flitting spark that
made them mine, and refused to paint them at all. My son promises to be
as perfect in his way as I in mine. Just now a student, he is too
Raphael-angel-like to suit me; but the very fellow to bewilder girls and
set the boarding schools crazy. Luckily he is bound against inthralment.
By and by the house grew so lonely that I was fain to send for Leonora
to make durance less vile. It was positively refreshing to hear her
voice sing through the solemn old hall. Very warm was the welcome she
received from both Fred and me. He had often said she was the only woman
he could talk to without suppressing a yawn. It was ungallant of him,
but I could sympathize with the sentiment. Women usually weary me. I
told Leonora she must make up her mind to stay with me, as long as she
remained unmarried.
Fred, holding her hand, laughingly made her promise never to take a
husband without his consent. While I passed on, he drew her back; the
mirror above the door framed a picture prettier than I liked to see.
'There is but one man I will authorize you to marry,' said my son.
Then it suddenly flashed on my mind that Fred was of the age of Scott's
heroes, and would be sure to fall in love with a woman older than
himself. The love did not matter so much, but marriage would be an
absurdity. I expected to have a daughter-in-law some day or other; but
it was never to be Leonora. In a hundred ways she had resisted me, and
overcome me. I was as resolutely opposed to her, as if she had been my
enemy. She was a connection of the family, independent, yet in some sort
alone in the world. If it had been conferring a favor on her, to ask her
to stay with me, be sure I never would have uttered a persuasive word.
But it was asking her to leave gay society, and the incense of
admiration, to bury herself in a dull house. Then she was 'ornamental;'
I liked to see her about; she was satirical, and pleased me by a little
spicy abuse. They called her handsome. She _was_ too small, I think, too
slight, perhaps; and then her complexion was almost swarthy. But her
hair was fine, her eyes large and brilliant, and her mouth mobile and
sweet. The face was nothing to me; but her companionship was enlivening.
The young lady professed herself glad of a winter of exclusion, and when
I saw how she set herself at work with books and embroidery, I confess I
was astonished at her resignation. Then I saw her look at my son, and
perceived she did not find it so _very_ stupid after all. Slowly she
snarled him in her meshes.
One time my husband had a friendless youth for his secretary, called
Denis Christopher. His name attracted me before his person. Mr.
Fontevrault became so deeply interested in his character and talents,
that he used his extensive influence, and gave Mr. Christopher an
enviable lift over the world's rough places. Fontevrault was like a
grieved child when he left us. I was sorry, but concealed it. One of the
young man's agreeable privileges had been to attend me in public, thus
relieving Mr. Fontevrault. I assure you he was more knightly than his
master, whose stiff protection I never missed while under Launcelot's
tender care. I never fully admitted to myself the power I found in the
hitherto unknown fascination of a _young_ man's society; nor how much
pleasure I took in touching those hidden chords that only respond to a
woman's touch. That he adored me, I saw in his eyes. I liked it well,
and the strange, unwonted feeling that shivered through me, now, when by
chance my hand touched his.
Well--people began to talk, as people will, and Mr. Fontevrault sent him
to Malaga. He came to bid me good-by; 'forever,' he thought; ah me! It
was forever in one sense. Fred was a mere boy then, who heard and saw
everything. I had hard work to get him out of the house that morning. I
wanted Denis's last look all to myself. Before he left me, Christopher
offered me a bracelet of cornelians, cut rarely as seals. Each gem bore
an exquisite device. On one were a few words in Latin. When I was alone,
I pressed the seal on a drop of hot wax, and read his dedication.
All that was years ago; he is here again, and I am free. I sat before
the glass long the day I expected him, threading my brown hair, and
longing to wear his color--blue. But then the widow's cap suited me
divinely, and the folds of crape set off my peculiar tints as nothing
else can. I came before him; he started forward to seize both hands, and
gaze in my face, to find no change. Then he pressed his lips to my warm
white fingers. A new boldness became his, a new timidity mine.
Fresh from lessons of my own, I could read a change in Leonora, and
perceive mischief in the air. Her extreme quietness when my son entered
the apartment, the faint shade of shyness in his manner of addressing
her attracted me curiously. He began to linger in our haunts so long and
on such frivolous pretexts, that I began seriously to think what was to
be done with such a lovesick page. To oppose Fred would be worse than
useless. Opposition determined him. If I could have sent her away,
solitude would be my bane; for not one of the Fontevraults could I
endure. Then as I pondered, I laughed at the absurdity of the whole
thing. Not only was Leonora older than the student, a woman in society,
but she had been engaged (with that fact I resolved to frighten Fred),
nor would she wait five years for him to declare his passion. And his
flickering fancy the slightest breath of doubt would change: a nature
easily moulded by the inexorable. I resolved to let affairs take their
own course, and trust her common sense, and my own gentle diplomacy.
What memorable meetings had we four during those sharp winter days! I
lived as in an Arabian dream. There was Denis Christopher, with his
brown face and thrilling eyes; Fred lackadaisical, but handsome as
Antinous; Leonora, and I.
A very orderly company, but what hot feeling repressed, what romantic
possibility, what fates unfulfilled lay under the courteous
conventionality of the time! Fred leaned over Leonora at the piano.
Their voices sounded well together, and if he could not declare his
admiration of her, no doubt he conveyed it to her in some tender refrain
or serenade. Their blended, passionate voices often moved me in a
strange excitement, for I was not musical. I had no way of relieving
myself, as these singers and painters have, who crystallize an emotion
or a sorrow into a picture or a cadence. I can only gnaw the bedpost, or
tear up something, in the mere need of expression. Denis watched them
awhile, and then it became a trio instead of a duet. Mr. Christopher
brought Spanish music. Light, rippling airs, dances, whose strange
swaying rhythm had been borne to his ears in the Malaga nights.
My son grew jealous, therefore unreasonable. He would not play
subordinate, so left Leonora no choice but to lend herself gracefully to
Denis's companionship. These two were sure to misunderstand one another.
Fred was contradictory. With intense and variable feeling, he possessed
the traits of slower natures. A kind of natural prudence retarded him.
He puzzled Leonora. One moment he cooed over her, the next became
Horatian. Painfully sensitive, and proud withal, she was never sure of
his opinion of her. Having little faith in the firmness of any man's
admiration of _her_, she believed less than was avowed. And Fred,
exacting much, was too inexperienced to understand her. They were
drifting apart, I thought; but in avoiding Scylla, had I not plunged
into Charybdis?
I had been a widow a year when Mr. Christopher left Spain. Another had
now passed, and with it my seclusion. While Denis had talked to me, I
had cared to hear no other man speak; but now, in a kind of thirst, I
drank deep of pleasure. I played with the warm avowals of men past the
reasoning age, and made Fred's classmates melancholy. Denis did not even
disapprove. He was often near me now, but silent as a shadow.
How it stormed the night of the seventh of February, and like the
whirling snow I danced! Christopher led me through the last Lancers, and
then we stopped to rest. Hanging on his arm, and heedless of to-morrow,
was I not happy? We passed through the long rooms, while the soft waltz
music began to swell, and the untiring dancers took the floor.
I remember he asked for Leonora, and then if Fred meant to marry her. I
would not say no, but would acknowledge that his fancy was heated.
'She will be a pleasant vision of boy-love a few years hence,' I said.
'Leonora has too much good sense to marry him, Mr. Christopher.'
'I don't know,' said he, meditatively, and drew my hand through his arm.
The cornelian bracelet slipped into view. 'Mrs. Fontevrault,' uttered
he, in a ceremonious tone--my warm pulse grew still--'do you never
forget?'
'Do you desire it?' I answered, gaily:
''If to remember, or forget,
Can give a longing, or regret,
command me.'
He smiled, and, stopping at a side table, poured out two glasses of
wine.
'Here's to the past,' said he, eagerly; 'drink Lethe.'
We drained the glasses. Then I understood he withdrew his claim.
I wanted to go home after _that_; so Mr. Christopher summoned the
carriage. The walks were white, and I trembled--was it with cold?--as he
handed me in, and bade me good night.
The house at midnight was silent and warm. I went up stairs, and stood
in the threshold of the library. The sleet driving against the window
panes prevented their hearing me, I suppose. They seemed to be
translating something or other. Fred's arm lay over the back of her
chair. Very fast and earnestly he was talking. Marginal notes suggested
by the text of Sismondi?
'What, home so early!' was his exclamation, on discovering me.
Leonora looked, up with a deep rose in her dark cheeks, a dangerous fire
melting in her eyes. I had left her pale, with a headache.
'You are better, I conclude. I expected to find you among your pillows,'
said I, accusative.
'I have cured her,' said Fred, coming forward and clasping my hands in
his firm, cool hold. 'What ails you, mamma? You look as if you had a
fever, and wickedly handsome. What have you been about?' He slipped off
my ermine cloak, and kissed me with a mixture of pride and love. The boy
bewildered me.
As fate would have it, Fred was right. I felt very ill. I believe I
_resisted_ a fever, for I have a sensation of struggle connected with
that sickness. But I cannot separate the pictures of my distempered
fancy from the actualities of the time. Leonora took devoted care of me.
Night after night Fred sat by me, and they relieved each other. Like one
bound in an enchantment, I lay unable to prevent their mutual
confidence, and the return of her young lover's adoring regard.
He sat beside her as the fire burned low; his blonde hair touched her
dusky cheek as he bent over her.
'Leo, darling, I wish I was sick, like mamma.'
'Hush!' said she.
'Then you would soothe me, and part my hair with your soft fingers, that
refuse to touch mine now. You would be sorry for me, and give me a
little caressing, and I should be so happy I would not get well.'
'Don't talk so, Fred. You used to be an even-tempered, comfortable kind
of young man to know. But now you are really teasing.'
'Do I really annoy you?'
'Very much.'
'And you don't believe in me. Sometimes a dumb kind of philosophy
possesses me, and I say to myself, let her think of me as she will. I
cannot be frank, and must take the consequences. Then again----'
Here she rose, and he put both arms around her. Audacious boy!
'Fred!' was uttered in a stifled voice.
'Promise me to send off Christopher,' ejaculated the young man.
The corners of the room seemed to stretch away indefinitely. A heavy
perfume suffocated me. I groaned. In another moment Leonora was beside
me, and the fresh air was blowing in from a window my son had opened.
I made haste to get well. The physicians say my constitution and good
nursing saved me; but it was all resolution. My _will_ was stronger than
the disease. As soon as I could sit up and see him, Denis Christopher
was admitted. I used to hear a dulcet strain on the stairs, formed by
her delicate note and his melodious base, and then he would follow
Leonora in to pay his respects to me; always bringing something to
brighten up my boudoir, and render her imprisonment less unendurable.
Afterward he would never be exiled to the drawing rooms. Fred frowned at
the ease with which he invaded our retirement, but only frowned. He and
I began to wonder if Christopher would win her. Valiantly but cautiously
was he wooing. Fred went off on a boating excursion, and I grew weary. I
wished I had died. The secret of my good looks was confessed. Perfect
health had kept my beauty undimmed. But colorless and hollow-eyed the
fever left me. I could look at myself no more; so I looked at Leonora.
She was pretty, with a charm that did not depend on tint or outline. Her
new friend was penetrated by her real graces and his ideal rendering of
them; but would he conquer? I was sure not. Because separation is sure
alienation at a certain age, I resolved on Fred's speedy withdrawal from
the scene. Why not go abroad immediately after his graduation, which was
to occur in a few weeks? On his return I suggested it. He gloomily
consented.
'Will you come, too, mamma?'
'Not yet; in the course of a year perhaps;' and I looked over to the
corner where Leonora was winding worsted from Mr. Christopher's fingers.
'Come, now,' said he, 'take Leonora, and we will set up housekeeping in
the easy continental style.'
'She has her hands full just now.' Literally as well as figuratively
true, for she had wound two enormous green balls.
'Perhaps she will go over with Mr. Christopher. Would you like a call
from the bride and groom?'
My young Fontevrault looked at me.
'Do you speak as you know, mamma?'
'Look for yourself, my hoodwinked Cupid. Girls are all alike, Fred. He
can ask her to marry him, and has that advantage over you.'
So it was decided that Fred should go to Paris, and be happy. Mrs.
Blanchard gave him a farewell party, and all the young ladies were at
their sweetest. Fred behaved with sullen dignity, as a lion should. He
refused to be comforted by Adelaide and Rose, walking about with one or
another, and looking at Leonora, at whom all mankind were gazing that
night. She was in dashing spirits, a glorious color diffused her cheeks,
her eyes fairly danced. Her dress was of feathery black tulle, and a
broad silver ribbon, like an order, went over her shoulders. In the
shining black braids glistened fern leaves of silver filigree.
Fortunately, Fred and I discovered them--Leonora and her inseparable
cavalier, Denis, I mean--in an alcove of roses and jessamines. She
admiring the flowers, and he talking with a fervor very easy to read.
She listening, as women always listen when the pleader is eloquent. But
in her downcast face I read only pain, while my son translated the deep
blush differently. When we were at home, and I waited to bid him good
night, he took me in his strong arms:
'You love me, mamma, don't you?'
He was all I had in the world, so I told him.
Then followed a week we long remembered--the first week of Denis's
absence. Leonora was gloomy and _distraite_; Fred cool as a peak of the
Andes, and about as unapproachable; I immersed in the hurry and
confusion of my son's departure. He had a suite of rooms over mine,
and, the night before he went away, leaned over the ballusters, and
called, as in old time:
'Leonora!'
She gave a glad start, and ran up to him. So I followed, of course. I
wanted to put some flannels into his trunk, which stood in his bedroom.
The doors were open between us. He had a bundle of her letters tied up
in a bulky packet, and began to talk with great discretion.
'I have been putting my affairs in order,' said the systematic young
man. 'I may never come back, and at any rate, my absence will be long. I
thought it would be better to give you these, lest they fall into alien
hands.'
'Why not burn them?' suggested his listener.
'I could not, Leo.'
'I am not so sentimental,' she returned, taking up the packet. 'They
shall blaze directly. Do you want your own?'
'Oh, Fred, what a bungler you are!' I thought.
'You misunderstand,' he began, in a desperate tone.
'Fred!' I screamed, as if I were twenty rods distant, 'do come and open
this bureau drawer. I can't move it.'
He came, pulling it open, with such needless strength, that all the
toilette bottles garnishing the top were shaken off, and lay in
fragments on the floor. She followed to note the disaster, and I took
her down stairs, and watched over her like a dragon all that evening. I
would not let Leonora go to the steamer with us, but compelled him to
say farewell in my presence, I _like_ a scene. He held her hand long,
uttering some incoherent sentences. Admirable was the self-composure she
showed! The delicate muscles about the mouth were as steady as if she
did not love him. She never raised her eyes until the last. As I saw
their sad beauty, a pang seized me, and I turned away. He came after,
hurried me into the carriage, and off we whirled.
'Are you going to write to her?' I asked.
'She says no,' Fontevrault answered, and looked vigorously out of the
window.
* * * * *
One evening, two years after my son left me, we were sitting round the
library fire. Christoper, now a captain in one of the famous
Massachusetts regiments, sat near me, a little older and a little graver
than when I saw him last. We were talking with flushed cheeks and
beating hearts of the subject nearest our hearts just then--war.
A familiar foot pressed the stair. All the color left Leonora's lips;
she knew who was coming. In another moment I was in my darling's arms.
He shook hands with Leonora, but neither of them spoke a word; then
turned to Cristopher, who welcomed him with the hearty cordiality men
use.
'You have come home to fight, I know, Fontevrault.'
'So I have,' answered my son. 'Every true-hearted American should be
striking his blow. I couldn't travel fast enough. Mother, are you a
Spartan?'
He looked at Leonora. What did she think of this magnificent-mustached
Saxon? Not much like the fair-cheeked student we remembered.
'Let us be army nurses,' said Leonora, when they had gone to Washington.
Indeed we could not stay where we were, nor flit off to Newport to
banish care. I grew sleepless, and a sudden sound would send the blood
to my heart. Leonora maintained an undaunted front, but she grew thin in
spite of her cheerfulness. At last I said:
'We will follow the army; I shall die to live in this way.'
So, just before the battle of Antietam, we were in Washington.
Just after--ah me!--a singular scene occurred. We four had met again,
not as in the happy nights long gone. Denis, the veteran of seven
battles, still stood unscathed; but my boy could fight no more.
Manfully he bore his affliction; I only wept.
This morning of which I write, he was so bright, that we admitted Denis
at once, who came to bid us farewell before leaving to join his
regiment.
'Stop a minute,' said Fred. 'Leonora.' She came toward him with a face
of gentle inquiry.
'To-day is my birthday,' prefaced the soldier. 'I am twenty-six, and a
free man to say I love you.' Denis minced and motioned to withdraw his
hand. (Not so fast, old fellow.) This I say because I have been waiting
years to speak my mind on this day. But now, I have nothing to offer
you. I have no future. I am a <DW36>; even my love for you has been a
cheat to you; and now is selfishness in me. Here stands a man as true to
you as I; I know how he loves you. Which of us will you marry, Leonora?'
While he was speaking, the lost carnation came back to her cheeks. The
soft eyes kindled to a languid fire. She never looked at Denis, who
stood in his erect strength, his worshipping eyes on her face. She came
to Fred's bedside, and knelt down there. Denis dropped his hand.
'You do not answer,' Fred whispered; 'I cannot bear suspense.'
How did she satisfy him? I do not know. In emotion that almost
overmastered me, I snapped the bracelet--Denis's bracelet; it lay upon
the floor. He passed me without a word, without a look. His heavy heel
ground the enchased seal to rosy dust. I heard the door swung loudly to,
and then the clatter of his horse's hoofs, as he rode rapidly away.
EUROPEAN OPINION.
We are indebted to an accomplished gentleman in Philadelphia for the
following translation from the _Revue Nationale_ of M. Laboulaye. Any
extended comment from our pen would only serve to weaken the effect of
this eloquent and truthful passage. We may, however, express our
gratification to find that some generous spirits in Europe still remain
superior to the jealousies and the malevolence which have so largely
affected the ruling classes there, and led them so generally to hope for
and to predict the downfall of our suffering country. Hitherto we have
indeed recognized the truth that 'the opinion of Europe is a power;' but
we have felt it chiefly in its worst influence, against us, and in favor
of the rebellion. Now, however, in this the darkest hour of our mortal
struggle, it affords real relief to hear the most enlightened men of
that continent proclaiming that 'the arguments of the South are
beginning to fail,' and 'that all the ingenuity in the world cannot lift
up its fallen cause.' Nor is it at all difficult to give entire credence
to these statements, for there is evidently an altered tone even in
those organs of European opinion which have been, and still are
consistently hostile to us. It was perhaps unavoidable that
misunderstanding should prevail in the outset, and that the ear of
Europe should have been complacently open to the representations of the
plausible South, urged as they were by the ablest and most unscrupulous
of her advocates. But truth was destined certainly to make its way in
the end. It was only doubtful whether the triumph of right would take
place soon enough to bring the force of European opinion to bear on the
contest and to deprive the South of that moral support which alone has
enabled her to prolong the hopeless struggle to the present time. But,
according to M. Laboulaye, the 'fatal service' which its advocates have
done the South, is just now about to bear its appropriate fruit; for the
delusive promise of support which has thus far sustained the rebel cause
is utterly gone, and with it, all possibility of ultimate success.
Seldom have we read a nobler passage than that in which this
accomplished writer appeals to the French sentiment of national unity to
justify our Northern people in their mighty struggle to subdue this
'impious revolt.' Americans themselves, though fully imbued with the
instinctive feeling which it defends, could not more forcibly have
presented the point. And, indeed, if we may believe the statements now
prevalent, attributing to eminent statesmen and large parties a
disposition to accede to the separation of the sections, the very
sentiment of nationality has lost it force among us, and we would be
compelled to acknowledge our obligations to this eminent Frenchman for
stimulating our expiring patriotism and awakening us to the vital
importance of our national unity and to the shame and disgrace of
surrendering it. If any American has ever, for a moment, admitted the
idea of consenting to a separation of the Union, let him read the
burning words of this enlightened and disinterested foreigner, and blush
for his want of comprehension of the true interests and glory of his
country. It is not a mere sentimental enthusiasm which leads us to
combat disunion and to cherish the greatness and oneness of our country.
Our dearest rights and our noblest interests are alike involved, and we
would be craven wretches, unworthy of our high destiny, if we did not
risk everything and sacrifice everything to preserve them. 'The North
only defends itself,' says M. Laboulaye. 'It is its very life that it
wishes to save.'
Briefly, but with the hand of a master, does this article point out the
consequences of disunion. The touches by which the sketch is drawn, are
few and rapidly made; but they faithfully portray the great features of
the case, and present a true and living picture to the mind of every
thoughtful man. The jealousies, the rivalries, the antipathies of the
sections; the foreign intrigues and eventual foreign domination among
our fragmentary governments; the large standing armies, and the
competing naval forces; and finally, 'the endless war and numberless
miseries' which will inevitably result--all these mighty evils will not
only afflict our own unhappy country, but 'peace will be exiled from the
world.' The interests of mankind are involved in this tremendous
struggle.
But we no longer keep our readers from the perusal of this interesting
extract. Let it be remembered that it comes from the quarter understood
to be most unfriendly to us, where the wily emperor of the French is
supposed to be plotting for the destruction of our nationality and
power. The appeal to the interests of France against the ambition of
England is striking and powerful. Whatever disposition the emperor may
cherish against us, the French people ought to be our friends; they have
a common interest in maintaining the freedom of the seas, and
we have yet to complain that any port of France has sent out cruisers to
assail our commerce on the ocean.
Let us take courage, even in this hour of disaster. Noble spirits abroad
are still watching us with generous sympathy and praying for the success
of our sacred cause. Let us be true to ourselves and to our country, and
the hour of final triumph will soon be at hand. Though dissensions tend
now to distract and weaken us, and though darkness, more impenetrable
than ever before, seems lately to have gathered around us, we already
discern the first glimmerings of the dawn in the east. The full day will
soon break upon us, and we shall rejoice in the splendor of returning
peace and renewed prosperity.
REASONS WHY THE NORTH CANNOT PERMIT SECESSION.
(_From the French of_ EDOUARD LABOULAYE, _published in the_ 'Revue
Nationale,' _December 10th, 1862._)
The civil war which has been dividing and ruining the United States for
two years also affects us in Europe. The scarcity of cotton causes great
suffering. The workmen of Rouen and Mulhouse are as severely tried as
the spinners and weavers of Lancashire; entire populations are reduced
to beggary, and to exist through the winter they have no resource and no
hope save in special charity or assistance from the government. In so
severe a crisis, and in the midst of such unmerited sufferings, it is
but natural that public opinion should become restless in Europe, and
condemn the ambition of those who prolong a fratricidal war. Peace in
America, peace is a necessity at any price, is the cry of thousands of
men among us who are suffering from hunger, innocent victims of the
passions and madness which steep the United States in blood.
These complaints are only too just. The civilized world is at present,
so bound together, that peace is one great condition of the existence of
modern industrial nations; unhappily, although it is easy to point out
the remedy, it is almost impossible to apply it. Just now it is by war
alone that ending of the war may be looked for. To throw herself armed
between the combatants would be an attempt in which Europe would exhaust
her strength; and to what purpose? As Mr. Cobden has justly said, it
would be less costly to feed the work people who are ruined by the
American crisis _on game and champagne_. To offer to-day our friendly
mediation is not only to expose ourselves to a refusal, and perhaps so
exasperate one of the parties as to push it to more violent measures,
but to diminish the chances of our mediation being accepted at a more
favorable moment. Thus we are forced to remain spectators of a
deplorable war, which is the cause of infinite evil to us; thus forced
to offer up prayers that exhaustion and misery may appease these mortal
enemies and oblige them to accept either reunion or separation. A sad
situation, doubtless, but one which neutrals have always occupied, and
from which they cannot depart without throwing themselves among unknown
dangers.
If we have not the right to interfere, we can at least complain, and try
to discover those who are really wrong in this war, which so affects us.
The opinion of Europe is a power. It can hasten matters and restore
peace better than arms can. Unfortunately, for two years opinion has
wandered from the proper path, and by taking the wrong side of the
question, prolongs instead of stopping resistance. The South has found
many and clever advocates in England and in France, who have presented
her cause as that of justice and liberty. They have proclaimed the right
of secession, and have not feared to apologize for slavery. Their
arguments to-day are beginning to fail. Thanks to those publicists who
do not traffic with humanity; thanks to M. de Gasparin, above all, the
light has made things clear; we know now how things stand as to the
origin and character of the rebellion. To every disinterested observer,
it is evident that the South is wrong in every way. It needs not a
Montesquieu to understand that a party not menaced in the least, which,
through ambition or pride, tears its country to pieces and destroys its
national unity, has no right to the sympathies of the French. As to
declaring slavery sacred, that is a work which must be left to the
preachers of the South. All the ingenuity in the world cannot lift up
this fallen cause. Had the confederates a thousand reasons for complaint
and for revolt, there would always rest on their rebellion an indelible
stain. No Christian, no liberal person will ever interest himself for
men who, in this nineteenth century, insolently proclaim their desire to
perpetuate and extend slavery. Though it is still permitted to the
planters to listen to theories that have infatuated and lost them, such
sophistries will never cross the ocean.
The advocates of the South have done it a fatal service; they have made
it believe that Europe, enlightened or seduced, would range itself on
its side and finally throw into the balance something more than empty
promises. This delusion has and still maintains the resistance of the
South, it prolongs the war, and with it our sufferings. If, as the North
had a right to expect, the friends of liberty had, from the first,
boldly pronounced against the policy of slavery, if the advocates of
peace upon the seas, if the defenders of the rights of neutrals had
spoken in favor of the Union and rejected a separation, which could only
profit England, it is probable that the South would have been less
anxious to start on a journey without visible end. If, in spite of the
courage and devotion of its soldiers; if, in spite of the ability of its
generals, the South fails in an enterprise which, in my opinion, cannot
be too much blamed, let it lay the fault on those who have so poor an
opinion of Europe as to imagine that they will subject _its_ opinion to
a policy against which patriotism protests, and which the gospel and
humanity condemn.
We will grant, they may say, that the South is altogether wrong;
nevertheless it wishes to separate, it can no longer live with the
people of the North. The war alone, whatever may be its origin, is a new
cause of disunion. By what right can twenty millions of men force ten
millions (of those ten millions there are four millions of slaves whose
will is not consulted in the least) of their countrymen to continue a
detested alliance, to respect a contract which they wish to break at any
price? Is it possible to imagine that after two or three years of
fighting and misery, conquerors and conquered can be made to live
harmoniously together? Can a country two or three times the size of
France be subjugated? Would there not always be bloodshed between the
parties? Separation is perhaps a misfortune, but now it is an
irreparable one. Let us grant that the North has law, the letter and
spirit of the Constitution on her side; there always remains an
indisputable point--the South wishes to govern itself. You have no right
to crush a people that defends itself so valiantly. Give it up!
If we were less enervated by the luxury of modern life and by the
idleness of a long peace, if there still lingered in our hearts some
remnant of that patriotism which, in 1792, urged our forefathers to the
banks of the Rhine, the answer would be simple; to-day I fear it will
not be understood. If the south of France should revolt to-morrow and
demand a separation; if Alsace and Lorraine should wish to withdraw,
what would be, I will not say our right only, but our duty? Would we
count voices to see if a third or a half of the French had a right to
destroy our nationality, to annihilate France, to break up the glorious
heritage our sires bought for us with their blood? No! we would shoulder
our muskets and march. Woe to the man who does not feel his country to
be sacred, and that it is a noble act to defend it, even at the price of
extreme misery and every danger!
'America is not like France; it is a confederation, not a nation.' Who
says this? It is the South, and to justify its faults; the North asserts
the contrary, and for two years she has declared, by numberless
sacrifices, that the Americans are one people, and that no one shall
divide their country. This is a grand and noble sentiment, and if
anything astonishes me, it is that France can witness this patriotism
unmoved. Is not love of country the crowning virtue of the Frenchman?
What is this South, and whence does it derive this right of secession it
proclaims so loudly? Is it a conquered nation which resumes its
independence, as Lombardy has done? Is it a distinct race which will not
continue an oppressive alliance? No! it is a number of colonies,
established on the territory of the Union by American hands. Take a map
of the United States. Except Virginia, the two Carolinas and Georgia,
which are old English colonies, all the rest of the South is situated on
lands purchased and paid for by the Union. This proves that the North
has sustained the greatest part of the expense. Ancient Louisiana was
sold to the Americans, in 1804, by the first consul at a price of
fifteen millions of dollars; Florida was bought from Spain, in 1820, for
five millions; and it required the war with Mexico, a payment of ten
millions, and heavy losses besides, to acquire Texas. In a few words, of
all the rich countries which border on the Mississippi and Missouri,
from their sources to their mouths, there is not one inch of ground for
which the Union has not paid, and which does not belong to her. The
Union has driven out or indemnified the Indians. The Union has built
fortifications, constructed shipyards, light-houses, and harbors. It is
the Union that has made all this wilderness valuable and rendered its
settlement possible. It is the men of the North as well as those of the
South who have cleared and planted these lands, and transformed them
from barren solitudes to a flourishing condition. Show us, if you can,
in old Europe, where unity is entirely the result of conquest, a title
to property so sacred, a country which is more the common work of one
people! And shall it now be allowed to a minority to take possession of
a territory which belongs to all, and, moreover, to choose the best
portion of it? Shall a minority be permitted to destroy the Union, and
to imperil those who were its first benefactors, and without whom it
would never have existed? If this does not constitute an impious revolt,
then any whim that seizes a people is just and right. It is not only
political reasons that oppose a separation; geography, the positions of
places force the United States to form a single nation. Strabo,
meditating on this vast country now called France, said, with the
certainty of genius, that, to look at the nature of the territory, and
the course of the waters, it was evident that the forests of Gaul,
inhabited by a thinly scattered people, would become the abode of a
great people. Nature has disposed our territory to be the theatre of a
great civilization. This is also true of America, which is really but a
double valley, whose place of separation is imperceptible, and which
contains two large water courses, the Mississippi, and the St. Lawrence.
There are no high mountains which isolate and separate the people, no
natural barriers like the Alps and Pyrenees. The West cannot live
without the Mississippi; it is a question of life and death to the
Western farmers to hold the mouth of the river. The United States felt
this from the first day of their existence. When the Ohio and
Mississippi were yet but streams lost in the forest, when the first
planters were only a handful of men scattered in the wilderness, the
Americans already knew that New Orleans was _the key of the house_. They
would not leave it either to Spain or France. Napoleon understood this;
he held in his hands the future greatness of the United States; he was
glad to cede this vast territory to America, with the intention, he
said, 'to give to England a maritime rival which sooner or later would
lower the pride of our enemies.' (Here the author refers to his
pamphlet, entitled, _Les Etats Unis et la France_, and to _L'histoire de
la Louisiane_, by Barbe Marbois.) He could have satisfied the United
States by only giving up the left bank of the river, which was all they
asked for then; he did more (and in this I think he was very wrong),
with a stroke of his pen he ceded a country as large as the half of
Europe, and renounced our last rights on this beautiful river which we
had discovered. Sixty years have quickly passed since this cession. The
States which are now called Louisiana, Arkansas, Missouri, Iowa,
Minnesota, Kansas, Oregon, and the territories of Nebraska, Dacotah,
Jefferson and Washington, which will soon become States, have been
established on the immense domain abandoned by Napoleon. Without
counting the slaveholding population which wishes to break up the Union,
there are ten millions of free citizens between Pittsburg and Fort
Union, who claim the course and mouth of the Mississippi as having been
ceded to them by France. It is from us that they hold their title and
their possession. They have a right of sixty years, a right consecrated
by labors and cultivation, a right which they have received from a
contract, and, better still, from nature, and from God.
See what it is they are reproached for defending; they are, forsooth,
usurpers and tyrants, because they wish to hold what is their own,
because they will not place themselves at the mercy of an ambitious
minority. What would we say, if, to-morrow, Normandy, rising, should
pretend to hold for herself alone Rouen and Havre, and yet what is the
interest of the Seine compared to that of the Mississippi, which has a
course of two thousand two hundred and fifty miles, and which receives
all the waters of the West?
To possess New Orleans is to command a valley which embraces two thirds
of the United States.
They say 'we will neutralize the river.' We know what such promises are
worth. We have seen what Russia did at the mouth of the Danube; the war
of the Crimea was necessary to give to Germany the free use of her great
river. If a new war were to break out between Austria and Russia, we
might be sure that the possession of the Danube would be the stake
played for. It could not be otherwise in America, from the day the
Mississippi would flow for more than three hundred miles between two
foreign servile banks: the effect of the war has already been to prevent
the exportation of wheat and corn, the riches of the West. In 1861 it
was necessary to burn useless harvests, to the great prejudice of
Europe, who profited by their exportation. The South itself feels the
strength of its position so well that its ambition is to separate the
valley of the Mississippi from the Eastern States, and to unite itself
to the West, consigning the Yankees of New England to a solitude which
would ruin them. With the Mississippi for a bait, the Confederates hope
to reestablish to their profit, that is, to the profit of slavery, the
Union which they have broken for fear of liberty[6]. We now see what is
to be thought of the pretended tyranny of the North, and if it is true
that it wishes to oppress and to subjugate the South. On the contrary,
the North only defends itself. In maintaining the Union, it defends its
rights, and it is its very life that it wishes to save.
Thus far I have only spoken of the material interests--interests which
are lawful, and which, founded on solemn titles, give sacred rights; but
if we examine moral and political interests which are of a superior
order, we will understand better still that the North cannot give up
without destroying itself. The United States is a republic, the most
free, and at the same time the mildest and most happy form of government
the world has ever seen. Whence comes this prosperity of the Americans?
Because they are alone upon an immense territory; they have never been
obliged to concentrate their power and enfeeble liberty in order to
resist the jealousy and ambition of their neighbors. In the United
States there was no standing army, no naval force; the Americans
employed the immense sums which we expend to avert or to sustain war, in
opening schools, and in giving to all their citizens, poor or rich, that
education and that instruction which form the moral greatness and the
true riches of the people. Their foreign policy was comprised in this
maxim: 'Never to mingle in the quarrels of Europe on the sole condition
that Europe will not interfere with their affairs, and will respect the
liberty of the seas.' Thanks to these wise principles, which Washington
left them in his immortal testament, the United States have enjoyed, for
eighty years, a peace which has only been disturbed by Europe when, in
1812, they were forced to resist England and sustain the rights of
neutrals. We must count by hundreds of millions those sums that we have
used during the last seventy years in the upholding our liberty in
Europe; these hundreds of millions the United States have employed in
improvements of every description. Here is the secret of their
prodigious fortune; it is their perfect independence which makes their
prosperity.
Let us now suppose the separation finally accomplished, and that the new
confederation comprises all the Slave States; the North has at once lost
both its power and the foundations of that power. The Republic has
received a mortal blow. There are in America two nations, side by side,
two jealous rivals who are always on the point of attacking each other.
Peace will not remove their antipathies; it will not efface the memory
of the past greatness of the Union now destroyed; the victorious South
will, without doubt, be quite as friendly toward slavery, and as fond of
domination as ever. The enemies of slavery, now masters of their own
policy, will certainly not be soothed by the separation. What will the
Southern confederacy be to the North! It will be a foreign power
established in America, with a frontier of one thousand five hundred
miles, unprotected on every side, and consequently continually
threatening or menaced. This power, hostile, because of its vicinity
alone, and still more so by its institutions, will possess a very
considerable portion of the New World; it will have half the coasts of
the Union; it will command the Gulf of Mexico, an inland sea one third
the size of the Mediterranean; it will be the mistress of the mouths of
the Mississippi, and can ruin at its pleasure the inhabitants of the
West. The fragments of the old Union will have to be always ready to
defend themselves against their rivals. Questions of customs and of
frontiers; rivalries, jealousies, in fact all the scourges of old Europe
will overwhelm America at once and together; she will have to establish
custom houses over an extent of five hundred leagues; to build and arm
forts on this immense frontier, to keep on foot large standing armies,
to maintain a naval force; in other words, she will have to renounce her
old Constitution, to weaken her municipal independence by the
centralization of power. Farewell to the old and glorious liberty!
Farewell to those institutions which made America the common refuge of
all who could not exist in Europe! The work of Washington will be
destroyed; the situation will be full of dangers and difficulties. I
understand how the prospect of such a future can delight those who have
never been able to forgive America her prosperity and greatness; history
is full of such sad jealousies. Still better I understand and approve of
this, that a people accustomed to liberty should risk its last man and
give its last dollar to preserve the inheritance of its fathers. I do
not understand why there are persons in Europe who believe themselves
liberal when they reproach the North for its generous resistance by
advising her disgracefully to relinquish her rights. War is certainly a
frightful evil, but from war a durable peace may issue, the
South may tire of a struggle which exhausts its strength, the old Union
may again arise in its glory, and the future may be saved. What but
endless war and numberless miseries can result from a separation? This
dismemberment of a country is an irreparable evil; no people, no nation,
will submit to such a calamity until it no longer has any power to
resist.
Up to this time I have reasoned in the supposition that the South would
remain an independent power. But unless the West joins the confederates,
and the Union reestablishes itself against New England, this
independence is a chimera: it might last for some time; but in ten or
twenty years, when the free population of the West would have doubled or
trebled itself, how would the South, necessarily much enfeebled by slave
culture, compare with a people, thirty millions in number, enclosing it
on two sides? To resist successfully, the South would be forced to rely
on Europe; it could only live when protected by a great naval power, and
England is the only one in a condition to guarantee for it its
sovereignty. Here is a new danger for free America and for Europe. The
South has no commercial marine, nor with slavery ever will have; England
will at once seize the monopoly of cotton, and will furnish capital and
vessels to the South. In two words, the triumph of the South is the
reinstatement of England on the continent, whence the policy of Louis
XVI and Napoleon has driven her; it is enfeebled neutrality; it is
France plunged anew into all the questions concerning the liberty of the
seas, which have already cost her two centuries of struggles and
suffering. In defending its own rights, the American Union assured the
independence of the ocean. The Union once destroyed, the English will
again resume their preponderance, peace will be exiled from the world,
and a policy will return which has only benefited our rivals.
This is what Napoleon felt; this is what is forgotten to-day. It would
seem that history is but a collection of frivolous tales, good enough,
perhaps, to amuse children; it would seem that no one wishes to
understand the lessons of the past. If the experience of our fathers
were not lost on our ignorance, we would see that, while fighting for
her independence, while upholding her national unity, the North is
defending our cause as well as her own. All our prayers should be for
our old and faithful friends. The weakness of the United States will be
our weakness, and on the first quarrel with England, we will too late
regret having abandoned a policy that for forty years has been our
security.
In writing these pages, I do not expect to convert those persons who
have in their hearts an innate love of slavery; _I_ write for those
honest souls who allow themselves to be captivated by the grand visions
of national independence which are continually shown to them in order to
dazzle and mislead. The South has never been menaced, and at this late
hour can return to the Union even with her slaves [the reader will
remember that this article was published in December, 1862], and is only
required not to destroy the national unity, and not to ruin political
liberty. It cannot be repeated too often that the North is not an
aggressor--it only defends what every true citizen will defend--the
national compact, the integrity of the country. It is very sad that it
should have found so little sympathy in Europe, and, above all, in
France. It counted on us, its hopes were in us; we have forsaken it, as
if those sacred words Country and Liberty no longer found an echo in
our breasts. Where is the time when all France cheered the young
Lafayette giving his sword to serve the Americans? Who has imitated him?
Who has recalled this glorious memory? Have we become so old that our
memory has failed?
It is impossible to foresee what will be the issue of this war. The
South may succeed; the North may split up, and wear itself out in
internal struggles. Perhaps the Union is already but a great memory.
But, whatever fortune may have in the future, it is the plain duty of
every man who has not allowed himself to be carried away by present
successes, to sustain and encourage the North to the last, to condemn
those whose ambition threatens the most beautiful and patriotic work the
world has ever beheld, to remain faithful until the end of the war, and
even after defeat, should it come, to those who will have fought to the
last for the right and for liberty.
FOOTNOTES:
[Footnote 6: This point of view has been thoroughly exposed by one of
the wisest citizens of America, EDWARD EVERETT, in 'The Questions of the
Day,' New York, 1861.]
THE HUGUENOTS OF VIRGINIA.
The warmer climes of the South induced many Huguenots to settle in the
colony of Virginia, and their neat little cottages, covered with French
grapevines, and the wild honeysuckle, might be seen scattered along
James river, not far above Richmond. One writer of that day, says: 'Most
of the French who lived at that town (_Monacan_) on James river, removed
to Trent river, in North Carolina, where the rest were expected daily to
come to them, when I came away, which was in August, 1708.' In 1690,
King William sent to Virginia many of the Huguenot Refugees, his
followers, who had taken shelter in England. Here they were naturalized
by an especial act in 1699. Six hundred more came over, conducted by
their pastor, Philip de Richebourg, locating themselves, about twenty
miles above Richmond, on lands formerly occupied by a powerful tribe of
Indians. There is a church now near the spot, retaining its Indian name
to this day. In 1700, the Virginia assembly exempted these French
settlers from taxation, and fully protected their rights.
We have seen a curious relic of the Huguenots in Virginia, which was
found in the family of a descendant. It is entitled: 'A register,
containing the baptisms made within the church of the French Refugees,
in the Manakin town, in Virginia, within the parish of King William, in
the year of our Lord 1721, the 25th of March. Done by Jacques Soblet,
clerk.' This manuscript contains about twenty-five pages of foolscap
paper, and remains a standing evidence of the fidelity of the Virginia
Huguenots to their Christian duties and ordinances. As a specimen of
their entries, we copy the following, literally, not even correcting
their orthography:
'Jean Chastain fils de Jean ett de Marianne Chastain les pere et
mere nee le 26 Septembre, 1721, est baptise le 5 Octobre, par M.
Fountaine. Ils ava pour parun et marene Pierre David et Anne sa
femme le quels ont declaree que cest enfan nee le jour et an que
deshus.
Segnee
JACQUE SOBLET,
Clerk.'
John Chastain, son of John Chastain and of Marianne Chastain, the
father and mother, born the 26th of September, 1721, was baptized
the 5th of October, by Mr. Fontaine. He had for godfather and
godmother Peter David and Anne, his wife, who have declared that
this infant was born the day and year aforesaid.
Signed, JACQUE SOBLET, Clerk.
Two or three of the pages contain records of deaths. Here is one:
'Le 29 de Janvier, 1723-4, morut le Sieur Authonoine Trabue, agee
danviron sinquaint six a sept annees fut en terree le 30 du meme
moy.
J. SOBLETT, Clerk.'
Jan. 29th, 1723-4, died Sir Anthony Trabue, aged about fifty six or
seven years. He was buried the 30th of the same month.
J. SOBLETT, Clerk.
Huguenot names found in this old register of baptism:
'Chastain, David, Monford, Dykar, Neim, (_Minister_) Dupuy, Bilbo,
Dutoi, Salle, Martain, Allaigre, Vilain, Soblet, Chambou, Levilain,
Trabu, Loucadon, Harris, Gasper, Wooldridge, Flournoy, Amis,
Banton, Ford, Laisain, Lolaigre, Givodan, Mallet, Dubruil,
Guerrant, Sabbatie, Dupre, Bernard, Amonet, Porter, Rapine, Lacy,
Watkins, Cocke, Bondurant, Goin, Pero, Pean, Deen, Robinson,
Edmond, Brook, Brian, Faure, Don, Bingli, Reno, Lesuer, Pionet,
Trent, Sumpter, Moiriset, Jordin, Gavain.
Names of <DW64>s: Thomberlin (Northumberland), Ivan, Jaque, Janne,
Anibal, Guillaume, Jean, Pierre, Olive, Robert, Jak, Julienne,
Francois, Susan, Primus, Moll, Chamberlain, Dick, Pegg, Nanny,
Tobie, Dorole, Agar, Agge, Pompe, Frank, Caesar, Amy, Joham, Debora,
Tom, Harry, Cipio, Bosen, Sam, Tabb, Jupiter, Essek, Cuffy, Orange,
Robin, Belin, Samson, Pope, Dina, Fillis, Matilda, Ester, Yarmouth,
Judy, and Adam.'
We find in Beverly's 'History of Virginia,' a very interesting account
of the Manakin French Refugees: 'The assembly was very bountiful to
those who remained at this town, bestowing on them large donations,
money and provisions for their support; they likewise freed them from
every public tax for several years to come, and addressed the governor
to grant them a brief to entitle them to the charity of all
well-disposed persons throughout the country, which, together with the
king's benevolence, supported them very comfortably, till they could
sufficiently supply themselves with necessaries, which they now do
indifferently well, and begin to have stocks of cattle, which are said
to give abundantly more milk than any other in the country. I have heard
that these people are upon a design of getting into the breed of
buffaloes, to which end they lay in wait for their calves, that they may
tame and raise a stock of them; in which, if they succeed, it will in
all probability be greatly for their advantage; for these are much
larger than other cattle, and have the benefit of being natural to the
climate. They now make many of their own clothes, and are resolved, as
soon as they have improved that manufacture, to apply themselves to the
making of wine and brandy, which they do not doubt to bring to
perfection.' The Rev. J. Fontaine, a Calvinistic clergyman, first
preached to his Refugee French brethren in England and Ireland (1688).
Then his sons emigrated to Virginia, and became settled ministers. From
this stock alone, including his son-in-law, Mr. Maury, have descended
hundreds of the best citizens of that commonwealth--ministers, members
of the bar, legislators, and public officers. The Rev. Dr. Hawks
estimates the relations of these Fontaine families, in the United
States, at not less than _two thousand_.
A few years ago, he found in a family under his parochial charge, a
manuscript autobiography of one of its ancestors. This was a James
Fontaine, who was a persecuted Huguenot, and endured much for the sake
of his religion. The work has been translated and published, and is full
of interest--'A Tale of the Huguenots; or, Memoirs of a French Refugee
Family, with an Introduction, by F. L. Hawks, D.D.'
M. Fontaine was a noble example of a true Huguenot. In his early life,
he was accustomed to the enjoyments of wealth, education, and refined
society; but, for conscience' sake, he was stripped of them all, and
forced to leave his native land. An exile in England, ignorant of its
language, and unaccustomed to labor, he soon accommodated himself to his
altered circumstances. He became a skillful artisan, and worked
successfully at his trade; at first he opened a little store, with a
school also, to teach the French language, and he says: 'We were in
great hopes, that with both together we should be able to pay our way.'
M. Fontaine next undertook the manufactory of worsted goods, which he
profitably carried on for some time, but became tired of the business.
He was anxious to unite with a French church, and, knowing that there
were many Refugees in the land, went to Cork in 1695.
At first he preached in the English church, after its regular pastor had
finished his services. Next, the French Refugees obtained the court room
for their worship, and, finally, he gave up a large apartment on the
lower floor of his own house, which was properly arranged with a pulpit
and seats for religious meetings. M. Fontaine writes at the time: 'I was
now at the height of my ambition; I was beloved by my hearers, to whom I
preached gratuitously. Great numbers of zealous, pious, and upright
persons had joined our communion. This state of things was altogether
too good to last. My cup of happiness was now full to overflowing, and,
like all the enjoyments of this world, it proved very transitory.'
Dissensions grew up; M. Fontaine was a Presbyterian, and some of his
hearers required him to receive Episcopal ordination, and this
circumstance produced discussion, until he felt it his duty to resign
his charge. In answer to his request, his elders gave a reluctant and
sorrowful consent, thanking him most humbly for the service he had
rendered to this church, during two years and a half, without receiving
any stipend or equivalent whatsoever for his unceasing exertions. '...
We have been extremely edified by his preaching, which has always been
in strict accordance with the pure Word of God. He has imparted
consolation to the sick and afflicted, and set a bright example to the
flock of the most exemplary piety and good conduct.'
Our French Refugee next removed to Bear Haven, and entered largely into
the fishing business; and now he became a justice of the peace, exerting
himself to break up the contraband traffic, which he found generally
carried on 'between the Irish robbers and the French privateers,' then
swarming the Irish coast. From eight to ten of these desperate
characters were sent to Cork for trial at every assize of Bear Haven.
They swore vengeance upon the upright magistrate; and in the year
1704, a French privateer hove in sight--soon anchoring, he faced M.
Fontaine's house. The vessel mounted ten guns, with a crew of eighty
seamen. The Huguenot mustered all his men, amounting to twenty, and,
sending the <DW7>s away, he supplied the Protestants with muskets. This
reduced his force to seven men, besides himself, wife, and children, and
four or five of these were of but little use.
Fontaine posting himself in a tower over the door, the rest of the party
occupied the different windows. The lieutenant now landed with twenty
men, and, approaching the dwelling, he took aim and fired at M.
Fontaine, but missed him. The Huguenot then discharged a blunderbuss,
with small leaden balls, one of which entered the neck of the
privateersman, and another his side, when his men carried him back
wounded to the ship. This unexpected resistance from a minister made the
captain furious, when he sent to the attack twenty more men, under
another commander, with two small cannons. 'I must acknowledge,' he
says, 'that being unaccustomed to this sort of music, I felt some little
tremors of fear when the first cannon ball struck the house; but I
instantly humbled myself before my Maker, and having committed myself,
both soul and body, to His keeping, my courage revived, and I suffered
no more from fear. I put my head out of the window to see what effect
the ball had produced on our stone wall, and when I perceived it had
only made a slight scratch, I cried out for joy, 'Courage, my dear
children, their cannon balls have no more effect on our stone walls than
if they were so many apples.'
The wife of M. Fontaine displayed the greatest self-possession and
bravery on this trying occasion, carrying ammunition, acting as surgeon,
and encouraging all by her words and actions. 'Courage, my children,'
said she, 'we are in the hands of God, and it is not fear that will
insure our safety; on the contrary, God will bless our courage. If you
cannot fire yourselves, you can load the muskets for your father and
others who are older and stronger than you are; drive away all fear, if
you can, and leave the care of your persons to God.' The fight continued
from eight in the morning until four in the afternoon, without
intermission. Only two of the Huguenot family were wounded--a man, and
one of the children slightly in his finger. The pirates finally
withdrew, with three men killed and seven wounded. During the whole
action the Huguenot minister did not permit any one 'to taste a drop of
wine or spirits, or strong beer.' A second attack was feared, but soon
the privateer weighed anchor and sailed away; when the pious family
returned thanks to God for their 'glorious deliverance.'
A full account of this bold and courageous affair was transmitted to
Lord Cox, then chancellor of Ireland, and the Duke of Ormond, the lord
lieutenant. Fontaine recommended to them that a fort should be built
there, when 'it would be a great place for the settlement of French
Refugees, and would also prove a safeguard to the commerce of the whole
kingdom.' In the year 1704, he himself erected a fortification at the
back of his house, purchased some six-pounders, which had been obtained
from a vessel lost on the Irish coast, and the Government supplied him
with powder and balls. The Council of Dublin also voted him L50, and
Queen Anne, in 1705, granted him a pension of five shillings a day for
his services, and as a French Refugee.
From this daring defence, the name of M. Fontaine and wife became known
and famous throughout all Europe. The French corsairs especially
remembered it, and threatened another attack. Indeed, the family
constantly apprehended such a visit, and it did take place in 1704.
Leaving their vessels at midnight, the enemy soon reached the dwelling
of the Huguenot, and, firing the outbuildings and stacks of grain, in
less than half an hour the whole were completely enveloped in flames. On
this occasion, the entire garrison consisted of the two parents,
children, with four servants, two of whom were cowboys. By two o'clock
in the afternoon, the pirates had made a breach through the wall of the
house; but the children, protected by a mattress, in front of the
opening, fired one after another at the assailants as they possibly
could. The Huguenot leader, having overcharged his musket, it burst,
throwing him down, and broke three of his ribs and right collar bone.
For a short time he was insensible, but remarks: 'I had already done my
part, for, during the course of the morning, I had fired five pounds of
swan shot from my now disabled piece. Notwithstanding this unfortunate
accident, an incessant fire was kept up on both sides, until a parley
took place. Life and liberty were then guaranteed to the family, as the
terms of capitulation, while the pirates were to have the plunder; and
they swore to these conditions as Frenchmen and men of honor. When the
officer and men entered the dwelling, and, looking anxiously around, saw
only five youths, and four cowherds, they suspected that an ambush had
been laid for them.
'You need not fear anything dishonorable from me,' said the French
preacher; 'you see all our garrison.'
'Impossible!' he replied; 'these children could not possibly have kept
up all the firing.'
The house was then stripped of everything, not excepting the coats,
which had been thrown off in the heat of the action; and the booty
filled six boats. When they departed, M. Fontaine with his two eldest
boys and two servants were taken away as prisoners. In vain did the
brave good man protest that this was an infraction of the treaty. The
remonstrance availed nothing with the freebooters. In a few days, the
children with the servants were set ashore, but he was detained, when
orders were given to raise the anchor. During all these severe trials,
his noble and pious companion did not sit down, quietly lamenting her
misfortunes. She first went to the parish priest, who was under great
obligations to her husband, entreating him for his liberation. But he
positively refused. Perceiving the privateer under sail, she resolved to
follow it along the shore, as long as she could, and, reaching a
promontory, she made a signal with her apron, on the top of a stick. A
boat came near the shore, and she carried on a conversation with its
crew through a speaking trumpet. After much bargaining, they agreed to
set M. Fontaine at liberty, upon the payment of L100 sterling. Of this
sum the excellent lady could only borrow L30, and the captain of the
privateer consented to take this amount, with one of her sons as a
hostage, until the remaining L70 were paid, calling her at the same time
'a second Judith.'
Mrs. Fontaine repaired forthwith to Cork, for the purpose of raising the
sum wanted, and could easily have obtained it, but the merchants of that
city objected to any payment of the kind. The privateer hovered about
the Irish coast for some time, expecting the ransom money; but when the
governor of Brest heard the circumstances, he condemned the captain
strongly for bringing a hostage away with him, contrary to the law of
nations. The difficulty did not terminate here. As soon as he was able,
the French preacher visited Kinsale, and made an affidavit of the
outrage he had suffered. At this place were a government officer and a
prison, and immediately all the French officers who had been taken in
the war then existing were ironed. Numbers of the same description were
treated in a similar manner. These retaliatory measures excited great
public feeling against the captain of the privateer, and he was summoned
to appear before the governor of Brest, who imprisoned and even
threatened to hang him. Upon his promising to set at liberty the young
hostage, and convey him to the place from whence he had been taken, the
officer was liberated.
M. Fontaine now determined to live in Dublin, and support his family by
teaching the Latin, Greek, and French languages; and in the mean time
the grand jury of Cork awarded him L800 for his losses at Bear Haven. In
his new abode he was able to give his children an excellent education;
one became an officer in the British service, and three entered college.
The former was John Fontaine, and the family determined that he should
visit America for information; and after travelling through
Massachusetts, New York, New Jersey, and Maryland, he purchased a
plantation in Virginia. Peter, another brother, received ordination from
the bishop of London, and with Moses, who studied law, both embarked for
Virginia in 1716. Francis, the last son, remained at college.
There were two daughters in his family. The eldest, Mary Anne, married
Matthew Maury, a Protestant Refugee from Gascony, in 1716, and the next
year he joined his relations in this country. His son was the Rev. James
Maury, of Albemarle, Virginia, a very estimable and useful clergyman of
the Church of England. James was another son of the French preacher who
made America his home, bringing with him his wife, child, mother-in-law,
and thirteen servants, in 1717. Francis, in 1719, was ordained by the
Bishop of London, on the particular recommendation of the Archbishop of
Dublin, and then also sailed for Virginia. He became a very eloquent and
popular preacher, and settled in St. Margaret's parish, King William
county.
In the year 1721, Mr. Fontaine lost his most faithful, exemplary, and
pious companion. 'A melancholy day,' he records in his autobiography,
'it was, that deprived me of my greatest earthly comfort and
consolation. I was bowed down to the very dust; but it made me think of
my own latter end, and made preparations to join her once more.' At the
conclusion of his memoirs, he uses the following remarkable language:
'I feel the strongest conviction, that if you will take care of
these memoirs, your descendants will read them with pleasure; and I
here declare that I have been most particular as to the truth of
all that is herein recorded.
'I hope God will bless the work, and that by His grace it may be a
bond of union among you and your descendants, and that it may be an
humble means of confirming you all in the fear of the Lord.
I am, dear children,
'Your tender father,
'JAMES FONTAINE.'
Little did the faithful Huguenot preacher imagine that a century after
he wrote thus kindly to his own children, myriads who have been born
from the same noble and holy ancestry would be animated, cheered, and
profited by his useful life and example. Though dead he yet speaketh.
We have dwelt thus at length upon the heroic history of this Huguenot
minister and his family; for where can we find an example so worthy of
imitation? He was a Huguenot in its fullest sense, bearing himself, at
all times, with a noble spirit of the true man, for the work before him.
Never losing trust in God, nor proper confidence in himself, he proved
that, when thus true, no man need ever despair. His long line of
descendants in the United States may well cherish and honor his memory.
As we have said before, we dwell more particularly upon the character
and history of Mr. Fontaine, as a striking example of a true Huguenot;
and how truth and the right will finally triumph over all obstacles.
Wherever the French Protestants settled in America, they exhibited this
same excellent trait; and among their families of Virginia were those
who distinguished themselves as brave soldiers and able magistrates in
the councils of the then young Republic.
TO-MORROW!
[G. H. BOKER.]
'The sun is sinking low,
Upon the ashes of his fading pyre;
The evening star is stealing after him,
Fixed, like a beacon on the prow of night;
The world is shutting up its heavy eye
Upon the stir and bustle of _to-day_;--
_On what shall it awake?_'
MONTGOMERY IN SECESSION TIME.
In the beginning of the year 1860, there existed in the city of
Montgomery, Alabama, a strong, active, and apparently indestructible
Union party. Three months after the close of the year there remained in
the city no trace of Union sentiment. To show how this feeling was
destroyed, sinking slowly, and with many reactions, under influences in
themselves insignificant, and to narrate, as they fell under personal
observation, that short train of events which make up the historic
period of this first capital of the Southern confederacy, will be the
object of the present sketch.
Early in the summer of 1860 it became evident to every dispassionate
observer in the South that the country was swiftly approaching a great
crisis. So dexterously had politicians managed the excitement which
arose on the discovery of the plot of John Brown, that at the very
beginning of the year a small and united party had been formed, having
for its aim the immediate separation of the States. This party,
following this well-defined object, was the only fixed thing in Southern
society during the year. In the midst of all changes it was permanent.
Even before the presidential election, when men's minds wavered about
things so permanent as party lines and party creeds, about old political
dogmas associated with favorite political leaders, it remained
unaffected. The presence of this restless and determined insurrectionary
element in the party politics of the time gave to the struggle preceding
the presidential election a character of unusual intensity. The city of
Montgomery, as the home of Mr. Yancey, and consequently of his warmest
admirers, and most bitter opponents, felt the full influence of this
excitement, and soon became one of the natural centres of the growing
struggle of opinions.
From causes difficult then to trace, there appeared early in the year in
the money market of the South an unusual condition of prostration. Banks
were unaccountably cautious. Money was scarce. Debts of more than a
year's standing were unpaid, and business of all kinds languished. Not
even were the customary advances made by the banks in the East for the
purchase of cotton, nor did the money scattered through the country by
those sales which did take place relieve the financial pressure under
which everything labored. In October capitalists refused to venture
their funds on anything which did not promise the most immediate return.
In these signs, in the inexplicable shrinking of capital to its hiding
places, and in the universal darkening of business, it would seem that
all might have discovered the approach of that storm which has since
burst with such fury upon the land. But this was not the case. Although
every one looked forward with anxiety to the time of election, it was
only a portion of the so-called BRECKINRIDGE party who saw with any
distinctness the point toward which all things were tending. Nor did
these men make public the extent of their hopes.
They were satisfied at first to do nothing more than familiarize the
minds of the people with the idea of secession. They spread the doctrine
that the only hope of Union lay in the defeat of Mr. Lincoln. Expressing
the worst fears of all, this doctrine was thought to be peculiarly
calculated to increase the numbers of the Union or Bell party, and was
therefore readily adopted by those who would at first have repelled with
patriotic horror the alternative it suggested.
It is impossible to estimate the influence of this lurking fallacy. Not
merely were multitudes of well-meaning, but unreasoning men, who were
confident of the success of their party, brought to acquiesce in a
proposition utterly false in its base, but the whole conservative
element in society was placed in a position from which it would be
thrown by defeat into a most dangerous reaction. Thus consciously or
unconsciously all parties were using every effort in their power to
prepare the popular mind for the question of secession.
But the period was not without its traits of patriotism. In October
strong efforts were made in the States of Alabama and Georgia to unite
the three parties in the South on one of the three candidates; thus
securing a President to the South, and the certainty of the Union. The
Breckinridge Democrats, however, contemptuously refused to be party to
every arrangement of the kind. The insurrectionary element, gathering to
itself the excitable and disaffected spirits of every class, had now
gained the command of this party, and no longer attempted to conceal its
revolutionary intentions. At the head of this element, exercising a vast
influence over all its movements, and embodying in himself, more than
any other man (except, perhaps, Mr. Yancey), the fierceness of its
spirit, stood Mr. Toombs, of Georgia. He was now invited to speak in
Montgomery. As a man of large political experience, some statesmanship,
and master of a grave and sonorous eloquence, it was expected that he
would influence a class of men who had hitherto held themselves
studiously aloof from the insurrectionary ranks--that calm, conservative
class, which is recognized by all as the basis of every society which
has acquired, or having acquired, hopes to retain, stability of
government and security of morals. The sentiments of the speaker were
too well known to admit of any doubts as to the probable character of
his address. He appeared as the undisguised advocate of secession. No
form of appeal or argument was neglected which could have had weight
with a people peculiarly susceptible to the influence of oratory.
Setting aside the question of the approaching election, to which he
scarcely alluded, the orator strove only to show that it was an
imperative social necessity that the South should have a vast and
constantly increasing slave territory; that in the path of this
necessity the only obstacle was the Federal Union, and that the time for
its destruction had now come. These were the representative arguments of
his party before the election, and he did not speak to an unsympathizing
audience. For when toward the close, raising his voice until it broke
almost in a scream, he exclaimed, 'Let the night which decides the
election of Mr. Lincoln be ushered in by the booming of the hostile
cannon of the South,' the hall rang again and again with the shouts of
his excited hearers. But _nemo repente turpissimus semper fuit_. These
were not the sentiments of all. There was a large class present who did
not applaud--but neither did they hiss. They seemed for the time
overawed by the energy of the spirit which had suddenly sprung up among
them.
In the following week, however, a singular, though, unfortunately, but
momentary check was given to the progress of insurrectionary sentiments
in the vicinity of the city. Senator DOUGLAS, who had been slowly
advancing, in his oratorical tour, down the coast, was about this time
announced to speak in Montgomery. Since his speech in Norfolk, where he
was thought to have expressed himself too clearly against secession, a
strong prejudice had grown up in the South against him, and it now
threatened to manifest itself in acts of positive violence. Such was the
state of popular feeling, that for a time it seemed uncertain whether it
would be desirable for him to attempt to speak. Hints of peculiar
personal outrages were thrown out by men of a certain class; and
threats were made of something still more ominous in case he should
attempt to repeat the sentiments of his Norfolk speech.
He arrived in the evening, and was met at the cars by a large crowd, and
a procession formed from a coalition, for the occasion, of his party
with that of Mr. Bell. It was feared that the short ride to the hotel
would not be accomplished without some act of violence on the part of
the excited throng by which his carriage was surrounded. A few eggs were
thrown, but otherwise the ride was performed without interruption. From
further outrages the crowd restrained itself until something positive
should appear on the part of the orator himself. Unintimidated, however,
by these unmistakable evidences of the public feeling, Mr. Douglas on
the following morning presented himself on the steps in front of the
capitol, where it had been announced that his speech would be delivered.
The city was filled with strangers, who had come from all parts of the
country to be present at the State fair which was held there that week.
On Capitol Hill, therefore, an immense throng was early assembled, which
coldly awaited the arrival of the orator. Everything was chilly and
unfavorable. But the spirit of the obstinate debater seemed to rise with
the difficulties by which he was surrounded. At first even his manner of
speaking operated to his disadvantage. The sharp, syllabic emphasis,
which he was accustomed to adopt in addressing large assemblages in the
open air, grated harshly on ears accustomed to the smooth and carefully
modulated elocution of Mr. Yancey. Beginning, however, by enunciating
general principles of government, in which all could agree, he gradually
conciliated, by an unexpected appearance of moderation, the favorable
attention of his audience. As he advanced upon his customary sketch of
the history of the different political parties during the past few
years--a work which a hundred repetitions enabled him to perform with a
dramatic energy of style and expression singularly effective--he was
occasionally interrupted by exclamations of acquiescence. As he
described the various successes of the Democratic party, these became
frequent, and before he had finished the _resume_, his voice was drowned
amid the enthusiastic cheers of the crowd.
It was a triumph of oratory. He repeated every sentiment of his Norfolk
speech, and the men who in the morning had thrown out dark hints of
'stoning,' joined in the applause. He accepted as a certainty the
election of Mr. Lincoln, but caused the crowd to shout with exultation
at the prospect of tying all his activity by the constitutional check of
a Democratic majority in Congress. In short, he came amid general
execration, and departed amid universal regret. I had heard Mr. Douglas
before, but never when he gave any evidence of the wonderful power which
he exhibited on this occasion. With few tricks of rhetoric, with no
extraordinary bursts of eloquence, he accomplished all the results of
the most impassioned oratory. The qualities of a great debater--unshaken
presence of mind, tact in adapting himself to his audience, the power of
arranging facts in a form at once simple and coherent, and yet most
favorable to his own cause, the strange influence by which one mind
compels from others the recognition of its supremacy--have long been
conceded to the late Senator from Illinois, but never did he exhibit
these qualities with greater effect than before the excited populace of
Montgomery.
This was the last strictly Union speech which was delivered in that
city. No one after this was found bold enough to stand up in the defence
of the cause that from this day began slowly to succumb to the fierce
spirit to which it was opposed. For several days the effects of the
speech were visible in the moderate tone of 'popular feeling;' but they
were soon lost in the tumultuous excitement attending the return of Mr.
Yancey from his tour in the North, and the still more intense feeling
produced by the election which immediately followed.
It was impossible in these last hours of distinct political
organizations not to be struck with the differences that characterized
the opposing parties--differences which, both before and since, have had
much to do with the progress of the rebellion. The Union gatherings were
easy, jovial, fond of speeches adorned with the quips and turns of
political oratory, and filled with the spirit 't'will all come right in
the end.' In the Breckinridge--or, as they had now practically
become--the secession meetings, a different spirit prevailed. It was the
spirit of insurrection, fierce, stormy, unrestrained. It was the spirit
of hatred; hatred of the North, hatred of the Union, hatred of Mr. Bell,
whose success would deprive them of their only weapon for the
destruction of that Union.
But with the 4th of November came a change. Three days after election
there remained in Montgomery no trace of party organizations. All the
widely divergent streams of public opinion seemed suddenly to have
joined in one, and that running fiercely, and unrestrained toward
disunion. The election of Mr. Lincoln united the people. On all sides
prevailed the deepest enthusiasm in favor of secession. Mass meetings,
attended by all parties, were held, and passed resolutions advocating in
the strongest terms immediate disunion. Secessionists were astonished at
the change, and in their anxiety to avoid anything which might shock the
newly awakened sentiment, appeared in many cases the most conservative
members of the community. But indeed nothing was too violent for the
state of public feeling. War committees were appointed, and active
measures taken to put the State in a position to maintain her
independence as soon as the ordinance of secession should have received
the sanction of the convention. Troops were despatched to take
possession of the arsenal, and agents were sent North to purchase
additions to the already large supply of arms in the State. Immediate
secession seemed to be the desire of every class. But this condition of
things was not always to continue. The reaction which had carried the
Unionists from a state of perfect confidence in the success of their
candidate, to one of deep disappointment, and of rage at the section to
which they attributed their defeat, having at length spent itself, signs
of a returning movement began to make their appearance. At first these
were not strongly marked. All were yet in favor of secession, but a
large party, composed of most of the former partisans of Mr. Bell,
together with the conservative element of every class, began at length
to object to a too great precipitancy, and finally to demand that the
action of Alabama should be made to depend upon the decision of the
other Southern States. This movement was understood by the secessionists
to have for its ultimate object the defeat of their hopes of disunion;
and such, unquestionably, was its aim; for whatever may have been the
plans of some of the leaders of the cooperationists, as this party was
called, it is certain that the great body of the party had no other end
in view, and was sustained in its action by no other hope than the
perpetuation of the Union.
At the caucus meetings which preceded the election of delegates to the
State convention the two parties, as now formed, first came into
conflict. At once important differences became apparent. Although nearly
equal in numbers, in spirit the two parties were signally unequal. While
the secessionists were bold, vigilant, and uncompromising, the
cooperationists were timid and passionless, though full of a passive
confidence that the Union would in some way be preserved. A knowledge
of this difference explains many things, in themselves apparently
inexplicable. It shows how it was possible that a State so confessedly
loyal that it would have rejected the ordinance of secession if it had
been submitted directly to the people, could yet, on this very issue,
elect a convention with a majority in favor of disunion. The whole
question was decided in the caucus meetings. The secessionists of all
parts of the State were bound together by watchful associations, and
were everywhere on the alert. In counties where by their number they
were entitled to no representative, attending the caucus meeting in
force, they effected--as they easily could while there was no distinct
party organization--a union of the tickets, and thus secured to
themselves one of the two candidates. So frequently was this repeated in
different parts of the country, that it was afterward estimated that by
this simple expedient of a union ticket the whole question of the
secession of this State was decided.
From these political struggles, however, the interest of the community
was suddenly withdrawn by an event which instantly absorbed all
attention, and struck terror into every household. In the little town of
Pine Level, a village situated a few miles from Montgomery, traces were
discovered of a plot having for its object a general uprising of the
<DW64>s on the evening preceding Christmas.
In the progress of the investigations which were immediately begun, it
came to light that the plot was not simply local, but extended over many
counties, including in its circuit the city of Montgomery, and involving
in its movements many hundred <DW64>s. Further examination revealed all
the horrible details which were to attend the consummation of the
plot--the butchery of the whites, the allotment of females, the division
of property. The whole surrounding country was alive with excitement.
Active measures were taken to crush at once the spirit of insurrection.
The ringleaders and some of the poor whites, with whom the plot is said
to have originated, were seized and, after a brief trial, immediately
hung. In Montgomery feeling was such as to demand the adoption of the
most stringent precautionary measures. Military companies were called
out and placed in nightly guard over the capitol and arsenal. On
Christmas eve the plot was to go into execution, and as the time
approached, the anxiety became painfully intense. It was whispered that
one of Mr. Yancey's slaves had been detected in an attempt to poison her
master. The police was doubled, soldiers with loaded muskets were
stationed in all the prominent streets, while mounted guards ranged the
thinly inhabited section of the outskirts. The night, however, passed
without alarm, and the excitement from that time slowly subsided.
It is scarcely worthy of notice, perhaps, that with the returning sense
of security came also the flippant confidence which had been for a time
put to flight. The blacks were again a timid and affectionate race, and
it was soon not difficult to find multitudes who declared themselves
willing to meet alone a hundred insurrectionary slaves. Sitting in this
evening calm, listening to such remarks, it was difficult to accept as
real the events of the hot and excited day which had gone before. Surely
they were dreams--the hurried trials, the hangings, the nightly tread of
soldiers, the brooding terror that whitened the lips of mothers. A home
guard, however, was immediately formed, including all citizens,
irrespective of age or station, capable of bearing arms, and not in
other military organizations.
On the 7th of January, the convention met. South Carolina had already
passed her ordinance of secession; but what others would follow the
example of this excitable State was yet uncertain. All eyes were now
anxiously directed toward Alabama, upon whose decision would to a great
degree depend that of the two great conservative States, Louisiana and
Georgia. Nor was this anxiety diminished by the accounts given of the
composition of the convention of this State. Both sides claimed a
majority; and it was evident that, without some unexpected defection,
the two parties would narrowly escape a tie. This singular uncertainty
was soon, however, to cease. Immediately on convening, it became evident
that the command of the body lay with the secessionists. It was found by
secret estimates that the two parties were divided by ten votes. Of the
hundred delegates, fifty-five were in favor of disunion. Although this
majority gave the secessionists power to carry their wishes into instant
effect, it was not thought politic to do so while the difference between
the two parties remained so small. The passage of the ordinance was,
therefore, for several days delayed, while the cooperationists were
plied with arguments to induce them to acquiesce in that which it was
now impossible for them to prevent. At length, after four days of
deliberation, it became evident that all of this party had succumbed
whom it seemed possible to change, and on the morning of the 11th of
January it was publicly announced that the ordinance of secession had
passed the convention by a vote of sixty-one in the affirmative against
thirty-nine in the negative.
By the insurrectionists the announcement was received with transports of
joy, but by the Unionists it was met with demonstrations of grief, which
they made no efforts to conceal. Women wept, and houses were closed as
for a day of mourning. In the northern part of the State the
manifestations of disappointment were still more unmistakable.
Indignation meetings were held, and one of the delegates received a
telegram from his constituents, charging him with having betrayed them
on the very issue for which he was elected, and demanding explanations.
At length the loyal feeling of the State seemed aroused, and had the
ordinance of secession been now submitted to the people, all admitted
that it would have been rejected by an unquestionable majority. But the
ordinance was not submitted to the people, and the Union sentiment,
which had already, within the interval of a few weeks, passed through
two complete oscillations--vibrating from the loyalty which preceded the
presidental election through all the changes of the strong disunion
reaction which followed--was now again in the ascendant. But from this
point it soon began to recede, descending slowly along an arc of which
no eye can see the end, with a momentum that permits no prediction as to
the time of its return.
A multitude of influences began at once to weaken the energy of the
Union sentiment. From the first, it had been the policy of the disunion
leaders to represent the question of secession as lying wholly with the
South. In case this section should decide upon disunion, there would be
little reason, it was said, to fear any prolonged opposition on the part
of the North--least of all a war. Nothing appeared on the part of the
Federal Executive to refute these assertions. It was by a large class
believed, therefore, that the leaders were right when they said that the
secession would be a mere withdrawal of the Southern States, for the
formation of a government perfectly friendly to the North, with which,
indeed, a board of commissioners would soon arrange the terms of a
peaceful international trade. After the passage of this ordinance,
however, a slight modification of this argument became necessary. Peace
was conditioned upon unanimity. Unionists were now called upon to render
their support to the new government in order to secure peace. If it was
clear that the State was united in favor of the changed condition of
things, there would be no difficulty, it was said, to procure, amid the
divisions of the North, a peaceful recognition of the confederacy. The
factions of the Northern States would never allow the Federal Government
to attempt to coerce a united people. Thus the very weapons which
loyalty had used to arm herself were here wrested to her own
destruction. To insure peace, men became insurrectionists.
It is useless now to surmise what would have been the result if the
action of the Federal Government in reference to the question of
secession at the beginning of the rebellion, had been less ambiguous. It
is enough to know, what was for many weeks so painfully realized by
every Northerner in the South, that had the Southern people, by any
means, been brought to understand that Federal laws were protected by
sanctions, and that an attempt at disunion would certainly be followed
by war, the question of secession would never have become a formidable
issue. But while men believed, as many of the Unionists did, that
secession was an experiment, attended with no danger to themselves, and
which would more than likely result, after a few years, in a peaceful
reconstruction of the Union on terms more favorable to the South, there
is little occasion for wonder that the cause of disunion met with no
very earnest, or, at least, prolonged opposition.
The passage of the ordinance of secession gave to the disunionists an
incalculable advantage. It is true, the Union feeling was deep, and in
many places strongly aroused, but the State had seceded, the new
government was quietly and apparently solidly forming itself, profitable
offices were in its gift, and, added to all, the conservative spirit
whispered its old motto, _quieta non movere_, and the hands which had
been raised in weak resistance fell harmlessly back.
In the mean while, at the capitol, another work was going on. The
convention, having established by ordinance the independence of the
State, was now engaged in tearing down and remodelling to meet the petty
wants of the Republic of Alabama the august structure of the Federal
Constitution. The work was soon completed, and on the 29th of January
this body, which in a brief session of three weeks had carried through
measures involving some of the most stupendous changes possible to a
civil State, adjourned to meet again on the 4th of March, cutting off,
by this, all possibility of any of the questions which it had discussed
being brought before the people by a new election. On the week following
the adjournment of the convention, the confederate congress assembled in
Montgomery.
This body immediately showed a fine appreciation of the state of public
feeling, and drew to itself the confidence of the people by selecting
for president and vice-president of the temporary government men who
were thought to represent the more conservative element in community.
Mr. Davis, at the time of his election, was in Mississippi, but on
receiving the official announcement of the event, started at once for
Montgomery, passing through Southern Tennessee, then a loyal State,
along a path nearly parallel to the one in which Mr. Lincoln was at the
same time moving a little farther north.
He reached the city in the night, but a large crowd was awaiting his
arrival at the depot. A procession of carriages, filled with members of
the confederate congress, led the way to the hotel. It was preceded by a
military band, and at regular intervals rockets were discharged,
announcing to the distant beholder the progress of the procession. All
felt that by attention to these honorary details they were assisting to
give dignity to the newly formed confederacy. On arriving at the hotel,
Mr. Davis was announced to speak from the balcony. The crowd pressed
curiously forward. Two candles threw a faint, yellow light over a
spare, angular form, rather below the medium height, lighting up, at the
same time, the sunken cheeks and strongly marked jaws of a face now
working with the emotions which the unusual events of the evening were
so well calculated to excite.
The ceremonies of inauguration were postponed to the beginning of the
following week. Early on Monday morning, however, the hill before the
capitol was covered with a vast throng, collected from all parts of the
new confederacy. For the accomodation of the members of congress, a
temporary platform had been erected in front of the capitol. Standing on
this, and glancing over the city, the eye rested on the rich valley of
the Alabama, stretching away many miles to the north, broken here and
there by the dark green foliage of the pine forests, which now twinkled
in the soft light of a day mild even for the latitude. At the extreme
rear of the platform, behind a small table, was seated the chairman of
the congress, Howell Cobb. Corpulent even to grossness, he formed a
curious contrast to the small and wasted forms of the two presidents
elect, who sat at his side. The events of this day have given to every
trait of these men a lasting and unenviable interest. Neither looked
like a great man, neither like a man thoroughly bad. All the impressions
produced by the first appearance of Mr. Davis were strengthened, without
being changed, by a farther acquaintance. To a physique by no means
imposing, he joins a manner too reserved to make him at any time a
favorite of the populace. His whole bearing, in fact, declares him a
stranger to that deep and contagious enthusiasm which has so often in
enterprises like this drawn to a leader the admiration and unconquerable
fidelity of the common people. Nor, on the other hand, is there anything
in his appearance to indicate the presence of the broad and
comprehensive energy which, in the mind of the thoughtful, can take the
place of such an enthusiasm. Still, he is in many respects peculiarly
suited to take the head of the rebellion. Elected at a time when State
distinctions were lost sight of in the warmth of the first formation of
the confederacy, he soon lost his sectional character, and represents,
as no one now elected could, the people alike of Virginia and those
along the Gulf. He is shrewd, cautious, determined. But his caution may
easily become scarcely distinguishable in its results from timidity. His
determination is never far removed from stubbornness. Mr. Stevens, who
sat, or, rather, had sunk, in his chair by the side of Mr. Davis, was a
thin, sickly looking man, whose small round face was characterized by
the pallid self-concentrated expression peculiar to invalids. On rising
at the administration of the oath, which he did with the laborious
movement of one to whom weakness had become a habit, he revealed a form
of about the medium height, but broken, as by some physical
disfigurement. During most of the ceremonies, he wore the air of an
uninterested spectator, amusing himself with the head of a slight and
rather jaunty cane, which he held between his knees. Although greatly
inferior, so far as mere physical appearances are concerned, to his
colleague, there is yet something in the expression and bearing of Mr.
Stevens which suggests a depth and comprehensiveness of intellect for
which one searches in vain the face of Mr. Davis. On the platform were
gathered nearly all those restless spirits which have, during the past
twenty years, disturbed the peace of the country. Conspicuous among them
appeared the bristling head of Mr. Toombs. He sat during the whole
ceremony, with his face, wearing the imperious expression which had
become habitual to it, turned upon the people. With uncovered heads, and
in perfect silence, the crowd listened to the oath of office.
Immediately on the completion of this ceremony the two presidents and
the congress withdrew to the senate chamber.
A levee was announced for the evening. The hall which had been selected
for this gathering was a large, low room in the upper story of a
building near the centre of the city.
Some efforts had been made by the ladies to conceal the rudeness of the
apartment, but it was expected that every deficiency of this kind would
be forgotten in the presence of that courtly society which had hitherto
given all the attractiveness to occasions like this on the banks of the
Potomac. It is but fair to suppose that these expectations were
disappointed, for early in the evening the hall was crowded with a
throng of men and boys, who, standing with uncovered heads, talking
loudly of the hopes of the new confederacy, or moved uneasily about,
seeking a favorable position from which to watch the 'president shake
hands.' This was the ambition of the evening. Every standing point in
the vicinity of Mr. Davis was taken advantage of. Chairs and benches
served as footstools to elevate into positions of prominence long rows
of men dressed in the yellow jeans of the country, who stood, during all
the long hours of the evening, watching with unchanging countenances the
multiplied repetitions of the short double shake and spasmodic smile
which Mr. Davis meted out to each of the constantly forming column that
filed before him. The platform was filled with the same class, and even
the arch of evergreen, under which it was intended that Mr. Davis should
stand, was pushed aside, to give place to those unwinking faces which
pressed to every loophole of observation. The ladies, who appeared here
and there in the crowd, sparkling with jewels, and dressed in the rich
robes naturally suited to the occasion, only increased by their presence
the rude incongruities of the gathering. Men were surprised at the
manifestations on every hand of a vulgarity and coarseness which they
had been accustomed to think the natural products and exclusive
characteristics of a state of society farther north. To the eyes of the
fastidious, a new class had suddenly arisen in their midst. Perhaps the
lesson was not a new one. Many nations before, when in the midst of
revolutions, have been called mournfully to learn that there are grades
in every society, that rebellions are not always tractable, and that the
class which guides their opening rarely controls their close. But if the
scene of the evening had any prophecies of this kind--and I do not say
that it had--it wailed them, like Cassandra, to ears divinely closed.
From this time the ferment of public opinion disappeared. A tangible
government existed, against which to speak was treason, and the friends
of the Union--and in spite of all changes, the number of these was yet
considerable--now for the first time ceased from the expression of those
objections by which they had hitherto indicated the direction of their
sympathies. All classes of men were longing for something permanent, and
eagerly grasped at these appearances of a settled government, as
promising to supply that which they so much desired. The establishment
of a calm and united state of public feeling seemed, therefore, the
almost instant effect of the inauguration of Mr. Davis. As might be
expected, the events which have been related had not taken place in the
South without affecting the condition of the Northern stranger who
chanced to be within the gate. To him every change had been for the
worse. During the fluctuations of public opinion in the early part of
the season, his position, though unpleasant, had still some relieving
circumstances; the condition of the country was not yet utterly
hopeless, and the vanity of being stable in the midst of universal
change, ministered a mild though secret pleasure, which, in the painful
anxieties of the period, was not without its consolatory value. But when
the tide of public opinion had turned strongly in one direction, and
that in favor of secession, all those pleasures, so mild and spiritual,
were at once destroyed. Nor was this a condition without change. Every
week added some new restraints to those by which the Unionist was
already surrounded. But never was the pressure of these restraints felt
to be so great as in this singular calm, which followed the inauguration
of Mr. Davis. The loyal spirit seemed extinct. Union sentiments were no
longer expressed in even the private circles. Now, however, hints were
occasionally dropped of the possibility of a future reconstruction, and
in this direction it was evident the small remnant of the Union party
was now turning its hopes.
Notwithstanding the general appearance of unanimity, one thing remained
which seemed to indicate a want of perfect confidence on the part of the
people generally in the permanency of the new order of affairs. This
was, the little interest which was manifested in the transactions of the
rebel congress. With nothing else to occupy their minds, the people
allowed the most important measures of public policy to pass almost
without remark. To the congress itself this apathy did not extend. There
appeared here, on the contrary, a germ even of the old State
antagonisms; for when Mr. Toombs, carrying out the former policy of his
State, introduced a bill imposing a tax on imports, declaring, at the
same time, that no government could ever be sustained without depending
chiefly upon this source of revenue, every member from South Carolina
was on his legs. After a warm debate, and against the strongest protests
of these members, the bill was carried and went into effect.
Notwithstanding this, many in England still secretly believe that the
Federal tariff was the real cause of the secession.
The astonishing promptness with which the rebel government, immediately
after the fall of Fort Sumter, equipped and placed upon the field an
enormous and fairly organized army, has given rise to a strong
impression concerning the energy put forth by the executive department
during the two months which intervened between this event and the
inauguration. No mistake could be greater. On the very day of the
election of Mr. Lincoln the South possessed a military establishment
quite equal, in proportion to its population, to that of either France
or Russia. At the time of the John Brown excitement, a rumor was spread
through the South that large bodies of men were gathering in different
parts of the North, having for their object an invasion of the Southern
States. Among all the reports which this excited period produced, none
was more sedulously diffused, and none more generally believed.
Whatever had been the original design of the story, its instant effect,
in the excited state of the public mind, was the formation of companies
in every county and village throughout the South for military drill.
These organizations, of which there were frequently several in a single
village, were equipped entirely at the expense of the individual
members. As they were under constant drill during the winter and summer,
they presented at the opening of the year 1861 the singular spectacle of
a great army, organized and equipped at its own expense, ready at any
moment to march at the command of the recognized government. This, it is
unnecessary to say, was the grand basis of that army which was afterward
placed upon the field; and thus it was that a secretary of war so
palpably inefficient as Mr. Walker was able, with an empty treasury, for
many months to surpass the North in the supply of troops, equipped, and
at once prepared for duty.
It was in full appreciation of this great armed mass that lay at his
hand in a condition to be easily formed into an organized and efficient
army, that Mr. Davis, after much entreaty, and repeated postponement,
reluctantly gave his assent to the first strong act of the executive
department, and ordered the attack upon Fort Sumter.
Without anticipating what were to be the effects of this act in the
North, which was, indeed, open to the conjecture of no man, Mr. Davis on
this occasion simply exhibited a hesitancy in venturing on extreme
measures, which will be found to be a characteristic feature of his
administration.
For several days the city was filled with rumors concerning the
anticipated attack, but early on Friday morning it was announced that
the bombardment had already begun. In the general excitement, business
was suspended. Crowds filled the streets. The war department was in
constant receipt of telegraphic messages announcing the progress of the
bombardment. But nothing came during the day to diminish the growing
anxiety. It was found that the fleet of war vessels said to be outside
the bar would take advantage of the night to come to the succor of the
fort. Sleep was impossible. Men who had gone to bed arose again and
joined the crowd which thronged the streets. At length, shortly after
midnight, Mr. Walker came forth and announced the last and most
favorable telegraphic report concerning the progress of the siege,
uttering at the same time the famous boast which has linked his name
with an indissoluble association of folly. Shortly past noon on
Saturday, the message came which announced the surrender of the fort.
The city was frantic with joy. For hours, no forms of manifestation
seemed adequate to express the excitement which filled all classes of
society. Standing on the housetop in the evening, a wild crowd could be
seen flitting before bonfires, or ranging the streets, and shouting in
the ecstasy of an excitement which none could control. Immediately on
the arrival of the despatch, messengers had started into the country
with the welcome tidings, and deep in the night the ear was startled by
the dull roar of the cannon announcing the arrival in some distant
village of the joyful intelligence.
'That will be the end of the war,' said a man of well known
conservatism, who stood by at the announcement in Montgomery of the
surrender of the fort. It was the last expression of that fatal fallacy
which had lured so large a class quietly to acquiesce in the fact of
secession in the hope of thus securing the peaceful recognition of the
North. In a few days more, the whole deception had passed away. But the
correction had come too late. The Union party was extinct. Twice, in the
course of that great change, by the progress of which, a people, in
majority loyal, was converted into one totally disloyal and
revolutionary, it lay within the power of the Federal Executive, by
firmness and a proper exhibition of its powers, to have sustained the
Union party in the South and crushed the rebellion--before the election
of Mr. Lincoln, and at the time of the strong Union reaction in the
election of delegates to the State convention. At both these periods the
Union feeling was strong and increasing, immediately after each; pressed
upon by arguments which the course of the Executive had failed to
answer, it slowly declined. But no great sentiment is destroyed at once.
There is reason to believe that, if left to itself, the tide of Union
feeling might again have flowed back, and the faint traces of a
reconstruction party which appeared in the short interval of quiet that
belonged to the rebel confederacy indicates, perhaps, the path along
which it would have returned. But the time for these things had passed.
The fall of Sumter brought the doctrines of secession into instant
popularity, and roused a spirit of military enthusiasm in the South
scarcely less intense than that which the same event excited in the
North. At once, in every direction, disappeared all those sober scruples
which, during the hottest excitement of the preceding months, had
quietly controlled the judgment of a small but influential class in
every community. The change in north Alabama and central Tennessee,
where the principles of secession had been steadily rejected by the
people, was almost instantaneous. The excitement and pride of a
sectional victory, and a false sympathy for the individuals who had
ventured their lives in a cause in itself, perhaps, objectionable,
effected what the most cunning fallacies of the leaders had been unable
to accomplish. As this movement of the popular feeling had many points
of resemblance with the revolution of feeling which took place just
after the election of Mr. Lincoln, there were some who believed that it
would be followed by a similar reaction. The excitement of the war into
which the whole country was immediately precipitated, cut off, however,
every chance of any such retrogressive movement. No reaction took place.
The surrender of Fort Sumter completed the change of opinion which had
been so long progressing in the South.
Those who look for an immediate restitution of Union feeling in the
South, as a result of Federal victories, will be disappointed. It will
be the result of a gradual movement--a movement resembling in every
important particular that by which the secession sentiment was
established in the interval between the election of Mr. Lincoln and the
surrender of Fort Sumter. Operating particularly upon that class in
society which is by nature passive rather than active, conservative
rather than headlong, the movement, as in that case, will be at first
slow and attended with many reactions, but the result will not be
uncertain. Already the progress of the war has destroyed nearly all the
motives by which the Union party of the South was formerly led to adopt
the cause of secession. This great party, therefore, stretching through
all parts of the South, forming an important element in the population
of every village and county which threatened at one time with its
passive resistance to overturn the whole scheme of the rebellion, stands
now exposed to the full influence of the reactionary tide which has now
begun to set back toward the Union. The change may not be at once, but
the same motive which led the Union man of Tennessee to return to
loyalty, will prove equally effective with his whole party, wherever
distributed.
SHAKSPEARE FOR 1863.
'O England!--model to thy inward greatness,
Like little body with, a mighty heart,--
What might'st thou do, that honor would thee do,
Were all thy children kind and natural!
But see thy fault! the SOUTH in thee finds out
A nest of hollow bosoms, which it fills
With treacherous crowns! they would o'erthrow our country,
And by their hands the grace of Freedom die,
If hell and treason hold their promises.'
_Henry V_, Act II, Scene i.
THE UNION.
V.
ILLINOIS AND MISSOURI COMPARED.
My previous numbers, comparing the progress, in the aggregate, of all
the Slave States, with all the Free States, of Massachusetts and New
Jersey, with Maryland and South Carolina, and of New York with Virginia,
demonstrate the fatal effect of slavery upon material advance, and moral
and intellectual development. In further proof of the uniformity of this
great law, I now institute a similar comparison between two great
neighboring Western States, Missouri and Illinois. The comparison is
just, for while Missouri has increased since 1810, in wealth and
population, much more rapidly than any of the Slave States, there are
several Free States whose relative advance has exceeded that of
Illinois. The rapid growth of Missouri is owing to her immense area, her
fertile soil, her mighty rivers (the Mississippi and Missouri), her
central and commanding position, and to the fact, that she has so small
a number of slaves to the square mile, as well as to the free
population.
The population of Illinois, in 1810, was 12,282, and in 1860, 1,711,951;
the ratio of increase from 1810 to 1860 being 13,838.70. (Table 1, Cens.
1860.) The population of Missouri in 1810, was 20,845, and in 1860,
1,182,012; the ratio of increase from 1810 to 1860 being 5,570.48. (Ib.)
The rank of Missouri in 1810 was 22, and of Illinois 23. The rank of
Missouri in 1860 was 8, and of Illinois, 4.
AREA.--The area of Missouri is 67,380 square miles, being the 4th in
rank, as to area, of all the States. The area of Illinois is 55,405
square miles, ranking the 10th. Missouri, then, has 11,975 more square
miles than Illinois. This excess is greater by 749 square miles than the
aggregate area of Massachusetts, Delaware, and Rhode Island, containing
in 1860 a population of 1,517,902. The population of Missouri per square
mile in 1810 exceeded that of Illinois .08; but, in 1860, the population
of Missouri per square mile was 17.54, ranking the 22d, and that of
Illinois, 30.90, ranking the 13th. Illinois, with her ratio to the
square mile and the area of Missouri, would have had in 1860 a
population of 2,082,042; and Missouri; with her ratio and the area of
Illinois, would have had in 1860 a population of 971,803, making a
difference in favor of Illinois of 1,110,239 instead of 529,939. The
absolute increase of population of Illinois per square mile from 1850 to
1860 was 15.54, and of Missouri 7.43, Illinois ranking the 6th in this
ratio and Missouri the 14th. These facts prove the vast advantages which
Missouri possessed in her larger area as compared with Illinois.
But Missouri in 1810, we have seen, had nearly double the population of
Illinois. Now, reversing their numbers in 1810, the ratio of increase of
each remaining the same, the population of Illinois in 1860 would have
been 2,005,014, and of Missouri, 696,983. If we bring the greater area
of Missouri as an element into this calculation the population of
Illinois in 1860 would have exceeded that of Missouri more than two
millions and a half.
MINES.--By Census Tables 9, 10, 13 and 14, Missouri produced, in 1860,
pig iron of the value of $575,000; Illinois, none. Bar and rolled
iron--Missouri, $535,000; Illinois, none. Lead--Missouri, $356,660;
Illinois, $72,953. Coal--Missouri, $8,200; Illinois, $964,-187.
Copper--Missouri, $6,000; Illinois, none. As to mines, then, Missouri
has a decided advantage over Illinois. Indeed, the iron mountains of
Missouri are unsurpassed in the world. That Illinois approaches so near
to Missouri in mineral products, is owing to her railroads and canals,
and not to equal natural advantages. The number of miles of railroad in
operation in 1860 was, 2,868 in Illinois, and 817 in Missouri; of
canals, Illinois, 102 miles; Missouri, none. (Tables 38, 39.) But if
Missouri had been a free State, she would have at least equalled
Illinois in internal improvements, and the Pacific Railroad would have
long since united San Francisco, St. Louis, and Chicago.
Illinois is increasing in a _progressive_ ratio, as compared with
Missouri. Thus, from 1840 to 1850 the increase of numbers in Illinois
was 78.81, and from 1850 to 1860, 101.01 per cent., while the increase
of Missouri from 1840 to 1850 was 77.75, and from 1850 to 1860, 73.30.
Thus, the ratio is augmenting in Illinois, and decreasing in Missouri.
If Illinois and Missouri should each increase from 1860 to 1870, in the
same ratio as from 1850 to 1860, Illinois would then number 3,441,448,
and Missouri, 2,048,426. (Table 1.) In 1850, Chicago numbered 29,963,
and in 1860, 109,260. St. Louis, 77,860 in 1850, and 160,773 in 1860.
(Table 40.) From 1840 to 1850 the ratio of increase of Chicago was
570.31, and from 1850 to 1860, 264.65, and of St. Louis, from 1840 to
1850, 372.26 per cent., and from 1850 to 1860, 106.49. If both increased
in their respective ratios from 1860 to 1870 as from 1850 to 1860,
Chicago would number 398,420 in 1870, and St. Louis, 331,879. It would
be difficult to say which city has the greatest natural advantages, and
yet when St. Louis was a city, Chicago was but the site of a fort.
PROGRESS OF WEALTH.--By Census Table 36, the cash value of the farms of
Illinois in 1860, was $432,531,072, and of Missouri, $230,632,126,
making a difference in favor of Illinois, of $201,898,946, which is the
loss which Missouri has sustained by slavery in the single item of the
value of her farm lands. Abolish slavery there, and the value of the
farm lands of Missouri would soon equal those of Illinois, and augment
the wealth of the farmers of Missouri over two hundred millions of
dollars. But these farm lands of Missouri embrace only 19,984,809 acres
(Table 36), leaving unoccupied 23,138,391 acres. The difference between
the value of the unoccupied lands of Missouri and Illinois, is six
dollars per acre, at which rate the increased value of the unoccupied
lands of Missouri, in the absence of slavery, would be $138,830,346.
Thus, it appears, that the loss to Missouri in the value of her lands,
caused by slavery, is $340,729,292. If we add to this the diminished
value of town and city property in Missouri, from the same cause, the
total loss in that State in the value of real estate, exceeds
$400,000,000, which is nearly twenty times the value of her slaves. By
Table 35, the increase in the value of the real and personal property of
Illinois from 1850 to 1860, was $715,595,276, being 457.93 per cent.,
and of Missouri, $363,966,691, being 265.18 per cent. At the same rate
of increase from 1860 to 1870, the total wealth of Illinois would then
be $3,993,000,000, and of Missouri, $1,329,000,000, making the
difference against Missouri, in 1870, caused by slavery, $2,664,000,000,
which is much more than three times the whole debt of the nation, and
more than twice the value of all the slaves in the Union. While, then,
the $20,000,000 proposed to be appropriated to aid Missouri in
emancipating her slaves, is erroneously denounced as increasing federal
taxation, the effect is directly the reverse. The disappearance of
slavery from Missouri would ensure the overthrow of the rebellion, and
the perpetuity of the Union, and bring the war much sooner to a close,
thus saving a monthly expenditure, far exceeding the whole
appropriation. But this vast increase of the wealth of Missouri, caused
by her becoming a free State, if far less than one billion of dollars,
would, by increasing her contribution to the national revenue, in
augmented payments of duties and internal taxes, diminish to that extent
the rate of taxation to be paid by every State, Missouri included.
The total wealth of the Union in 1860 exceeded $16,000,000,000. If this
were increased $1,000,000,000 in time, by the augmented wealth of
Missouri, and our revenue from duties and taxes should be $220,000,000,
as estimated by the Secretary of the Treasury, the increased income,
being one-seventeenth of the whole, would exceed $12,000,000 per annum;
or, if the increase of wealth should be only $200,000,000, then the
augmented proportional annual revenue would be $2,750,000, or nearly
one-eightieth part of the whole revenue, thus soon extinguishing the
principal and interest of the debt of $20,000,000, and leaving a large
surplus to decrease the percentage of taxation in every State, Missouri
included. The bill then might be justly entitled, _an act to restore the
Union, to advance the public credit, to hasten the overthrow of the
rebellion, to augment the national wealth, and_ DECREASE THE RATE OF
TAXATION. By overthrowing the rebellion, the taxes to pay the national
debt will be collected from all the States, instead of being confined to
those that are loyal. The rebel confederate debt, never having had any
existence in law or justice, but having been created only to support a
wicked rebellion, will of course be expunged by the reestablishment of
the Union. Indeed, by a new mathematical and philosophical principle,
far transcending the most sublime discoveries of Newton, Leibnitz, or La
Place, the rebel debt is redeemable six months _after the end of
eternity_, namely, six months after it is an _independent nation_, they
shall have ratified a _treaty_ of peace with us! All the rebel State
debts incurred since the revolt, for the purpose of overthrowing the
Government, will, of course, have no legal existence. Under the Federal
Constitution, no State Legislature can have any lawful existence, except
in conformity with its provisions, accompanied by a prior oath of every
member to support the Constitution of the United States. These
assemblages, then, since the revolt in the several States, calling
themselves State Legislatures, never had any legal existence or
authority, and were mere assemblages of traitors. Such is the clear
provision of the Federal Constitution, and of the law of nations and of
justice. It would be strange, indeed, if conventicles of traitors in
revolted States, could legally or rightfully impose taxes on the people
of such States, loyal or disloyal, to overthrow the Government. Indeed,
if justice could have her full sway, the whole debt of this Government,
incurred to suppress this rebellion, ought to be paid by the traitors
alone.
With a restoration of the Union, the prosperity of all sections will be
enormously increased. The South, with peace and with ports reopened,
relieved from rebel taxes and conscription, will again have a profitable
market for their cotton, rice, naval stores, sugar, and tobacco; the
West for breadstuffs and provisions; the North for commerce, navigation
and manufactures; and our revenue, from duties, would be vastly
augmented, soon justifying a reduction of internal taxation. There is
one item of almost fabulous value that must not be omitted. The cotton
now in the Confederate States, of the unsold crops of 1860-'61,
1861-'62, and 1862-'63, exceeds 5,000,000 of bales. This cotton, sold at
present prices, payable in federal paper, would be worth $1,800,000,000,
or $1,134,000,000 in gold. If we diminish this one-half, as cotton might
fall in price from time to time by the gradual reopening of our ports,
this cotton would still be worth $900,000,000 in our paper, and
$567,000,000 in gold. This cotton, while putting all our spindles and
those of the world into full operation, would turn the balance of
foreign trade at once immensely in our favor, and bring back streams of
gold to our shores. We would at once commence the liquidation of the
national debt, with a large sinking fund, as a sacred trust applicable
to that important subject.
Next to maintaining our finances and the public credit, followed by
decisive victories in the field, the speedy success of emancipation in
Missouri is most important. Missouri is larger by more than 6,000 square
miles than any State east of the Mississippi, and occupies a central
position between the North and the South, the East and the West. She is
larger by 16,458 square miles than England proper, containing a
population of nineteen millions. She is larger by 1,098 square miles
than New York, Vermont, Massachusetts, Rhode Island, and Delaware. She
is larger by 5,264 square miles than all the New England States. She has
a greater white population than the aggregate numbers of North and South
Carolina and Florida, or of South Carolina, Georgia and Florida, or of
Arkansas, Louisiana and Mississippi, or of Florida, Arkansas, South
Carolina and Mississippi, or Louisiana; and a larger white population
than all Virginia, East and West. She had, if disloyal, by her position
and large white population, more power to imperil the Union than any of
the slaveholding States. She has been true--she has suffered much in our
cause, her fields and towns have been laid waste, thousands of her brave
sons now fill our armies, and thousands more have fallen in our cause,
and we will be recreant to truth and justice, to the safety of the
Union, and forfeit the nation's pledge, if we do not now aid her in
becoming a Free State. The southern boundary of Missouri (lat. 36 deg.) is
several miles south of Nashville, Tennessee; but, if we take altitude
also into consideration, then, according to well established
meteorological principles, the southern boundary of Missouri is at least
a degree south of Nashville, reaching the northern boundary of Alabama.
There is then a very large area of Missouri well calculated for the
production of cotton. To accomplish this, the levee system of the
Mississippi must be extended from the southern boundary of Missouri to
the first highlands in that State, above the mouth of the Ohio; and a
proper system of drainage adopted. These lands would thus be entirely
secured from overflow, and greatly improved in salubrity. With these
improvements, Missouri would contain an area of rich alluvial lands,
well adapted to the profitable culture of cotton, embracing an extent
capable of producing at least one million of bales of the great staple.
These lands, considering latitude and altitude, would possess a climate
similar to that of Middle Tennessee and North Alabama, where cotton is
already cultivated with great profit. If emancipation prevailed in
Missouri, these lands would soon be cultivated in cotton by free labor,
and its immense superiority over the servile system would soon be
demonstrated. Such a proof of the superiority of free over slave labor,
even in the culture of cotton, would soon have an immense effect in
reconciling the South to the disappearance of a system so fatal to her
own prosperity, and endangering so much the harmony and perpetuity of
the Union. This Missouri cotton would be nearer the North and Northwest
than that grown in any other part of the Southwest, and thus supplied at
a cheaper rate to our manufacturers, while opening new and augmented
markets for the provisions and breadstuffs of the Northwest. This cotton
would, in part, pass up the Ohio to Cincinnati and Pittsburgh, and
thence to New York, Philadelphia, and New England. It would also in part
pass through Indiana and Ohio by their railroads and canals. The great
central railroad of Illinois would carry large portions of it also from
Cairo to Chicago; but perhaps the largest portion eventually would pass
up the Mississippi and Illinois rivers and enlarged canals to Chicago,
and thence eastward. With the proposed enlargement of the canal
connecting the Illinois river with Lake Michigan, and the enlargement of
the locks of the great Erie canal, extended by a similar enlargement of
the Chenango branch, and down the Susquehanna to tide water, cotton
steam propellers would carry the great staple by this route to the
Hudson and New England, to Baltimore or Philadelphia, at a rate much
lower than any other Southwestern cotton. The Mississippi would thus
have a _quintuple_ outlet, as well into the lakes and the Hudson, the
St. Lawrence, the Delaware, and Chesapeake, as into the Gulf of Mexico,
and Missouri would be united by new ties with the North, and Northwest,
as well as with the Middle States. Cairo, St. Louis, Chicago,
Cincinnati, Cleveland, Pittsburgh and Buffalo would become considerable
cotton depots, and slave labor would cease to monopolize the cotton
culture. But there are other considerations still more momentous.
Missouri extends from the 36th parallel to 40-1/2, and from the 89th
meridian to the 96th, thus embracing four degrees and a half of
latitude, and seven degrees of longitude. She fronts for many hundred
miles upon the great Mississippi, and commands its western shore; she
commands also the mouth of the Missouri river, and both its banks for
several hundred miles, and all its tributaries. The Missouri river and
its tributaries are nearly double the length of the Mississippi and its
branches. Missouri by her position dominates the whole valley of her
great river, and commands Kansas and Western Iowa, and Nebraska, and
Colorado, Dacotah and New Mexico. If Missouri had joined the Southern
confederacy, and its power had ever been established, she would have
forced with her all the vast region to which we have referred,
containing, including Missouri, an area equal to twenty States of the
size of Ohio. To separate Missouri forever from the proposed Southern
confederacy, is to render the permanent establishment of such a
government impossible. It not only severs Missouri from them, but all
the vast region identified with the destiny of that great State. Secure
Missouri permanently and cordially to the Union, and the rebellion is
doomed to certain overthrow. With the fall of slavery in Missouri by her
consent, and her cordial cooperation and sympathy with the North and
Northwest, the days of the rebellion are numbered. With Missouri as a
Free State, Arkansas, adjacent, cannot retain the institution. Such a
result, aided by victories, and the reestablishment of our finances,
would soon give full effect to the edict of emancipation in Arkansas,
and Louisiana would soon follow. With Missouri as a Free State by her
consent, and her cordial cooperation and sympathy, slavery would soon
disappear from the whole region west of the Mississippi, and Louisiana
cordially be reunited to the Republic. With such a result, holding New
Orleans and the mouth of the Mississippi and all the region west of that
great stream, how could Tennessee or Mississippi remain in the Southern
confederacy? The truth is, Missouri is the pivot upon which the
rebellion turns. Had she gone with the South, and given to its cause a
cordial support, it would have been difficult to subdue the rebellion.
That she has gone with the Union is a momentous fact, and demands for
her our heartfelt gratitude. I have shown, it is true, how greatly it is
the interest of Missouri to become a Free State; but it is still more
the interest of the nation to secure this great result. Give her what is
needed to render emancipation certain, and we shall have secured the
perpetuity of the Union. Missouri had no participation in introducing
African slaves into this continent. The slaves that cultivate her soil
are the descendants of those who were forced here under the British
flag, or by the ships of the North, then in a state of colonial
dependence; and it is just, and the national honor demands, that she
should receive full compensation. As the existence of slavery in any
State is a great evil and reproach, and a source of much weakness to the
whole country, so should the nation compensate for any loss that may be
occasioned by the abandonment of the system in any loyal State. Not only
is this just, but the faith of the nation is solemnly pledged by
resolutions adopted by Congress at its last session to carry this policy
into full effect with the consent of any State. Twenty millions of
dollars to secure such a result should be regarded as of little moment.
Gladly would the nation pay a much larger sum for a single victory. But
the moral and geographical and strategical victory secured by
emancipation in Missouri by her consent, will be far more important than
any triumph yet achieved by our arms. It is a victory that relieves a
great State now and forever from the curse of slavery. It is a victory
that secures the whole valley of the mighty Missouri to the Union. It is
a triumph that sweeps slavery from Arkansas, Louisiana, and Texas,
dissevers the Southern confederacy, and restores the whole Mississippi,
from its mouth to its source, to the Union.
The entire constitutionality of such a proceeding by _compact with a
State_, was demonstrated by me in the November number of the CONTINENTAL
MONTHLY, p. 575. Referring to the case of Texas, I there said: 'The
principle, however, was adopted of State action by irrevocable _compact_
with the Federal Government, by which provision therein was made for
abolishing slavery in all such States, north of a certain parallel of
latitude (embracing a territory larger than New England), as might be
thereafter admitted by the subdivision of the State of Texas. The power
of action on this subject, by compact of a State with the General
Government, was then clearly established, in perfect accordance with
repeated previous acts of Congress then cited by me. The doctrine rests
upon the elemental principle of the combined authority of the nation,
and a State, acting by compact within its limits.' When Missouri, with
her consent, shall have become a Free State, the leaders of the Southern
rebellion will feel that they have received a mortal blow. Especially
will this be the case in Arkansas, Louisiana, Texas, Tennessee,
Mississippi, and Alabama. We shall have cut the gordian knot of slavery,
and the death agonies of the hydra would soon be visible. The importance
of the result would be felt in the North also, and the wretched traitors
there, far more guilty even than those of the South, will shrink from
their atrocious conspiracy to dissolve this Union. The dark plot of
severing New England from the Republic and of reuniting the rest of the
States with the Southern confederacy, will be abandoned. That such a
scheme is contemplated by Northern traitors, and that it is tolerated in
the South, _on condition_ that all shall become Slave States, is beyond
controversy. New York, Pennsylvania, New Jersey, and the Northwest are
to abandon their free institutions, become slaveholding States, and be
admitted as such into the Southern confederacy. I had supposed that
crime had achieved its climax when the Southern rebellion was
inaugurated; but something more base, more vile, more cowardly,
debasing, and pusillanimous, it seems, is now contemplated. It is that
New England shall be expelled, and that the rest of the Free States
shall come under the dominion of the Southern confederacy. But the
leaders of this scheme seem to have forgotten the fact, that New
England, to a vast extent, has peopled the Northwest, and carried there
their love of free institutions. The descendants of the pilgrims are
scattered throughout the Northwest, and churches, and free schools, and
love of liberty have gone with them. The scheme is as base and cowardly
as it is impracticable. No! New England can never be expelled from this
Union. There the grand idea of the American Union was first conceived;
there the cradle of liberty was first rocked, before as well as amid the
storms of the Revolution; there the first blood was shed, the first
battles fought, the first flag of Union and Liberty unfurled, and there
it shall float forever. There are Lexington, and Concord, and Bunker
Hill, and no traitor hand shall ever sever them from the American Union.
Not an acre of the soil of New England or a drop of all its waters shall
ever be surrendered by this great Republic; and from Lake Champlain and
the Housatonick to the St. Croix and St. Johns, the flag of the Union
shall ever float in undiminished glory. Lake Champlain unites Vermont
and New England with the Hudson, the lakes, and St. Lawrence; and Long
Island Sound, commanding the deepest approaches to New York, completes
the connection, which is a geographical and political necessity. I am
not a New Englander by parentage, birth, or education, but if the other
Free States of the North and Northwest should submit to the disgrace of
uniting themselves with a Southern confederacy, I should remove to New
England, and breathe an air uncontaminated by slavery or treason. And
there are hundreds of thousands who would pursue the same course. When,
in 1798, the great Washington feared that the South might be separated
by traitors from the Union, he declared that, in such an event, he would
remove to the North; and, in such a contingency, there are thousands,
even in the South, who would remove to New England.[7]
Those of the North and Northwest, who should remain and carry their
States into the Southern confederacy, would be regarded in the South
with loathing and contempt; the whole civilized world would consider
their degradation as complete and eternal. They would soon loathe
themselves, and feel that it was not only the <DW64>s who were enslaved,
but that they had put fetters upon their own limbs, and rendered
themselves worthy to be worked as slaves on the plantations of Southern
masters. I do not believe any of the Free States of the North and
Northwest can thus be disgraced and humiliated. There is one of these
States, I am sure, that will never submit to such degradation. It is the
State of Pennsylvania. There the Declaration of American Independence
was first proclaimed. There the Articles of Confederation and the
Constitution were framed. There are Germantown, Paoli, and Brandywine:
there Washington crossed the Delaware at midnight, and fought the two
great battles of the war of independence. There Franklin sleeps within
her soil, the great patriot, philosopher, and statesman whom New England
gave to Pennsylvania, the Union, and the world. No! No! from the
Delaware and Susquehanna to the Ohio and Lake Erie, the people of a
mighty State would consign to the scaffold and the block the wretched
traitors who would attempt to sever Pennsylvania from New England. Ice
and granite are called the principal products of New England, but our
Revolution and this rebellion prove that her great staples are
intellect, education, liberty, courage, and patriotism. She is said to
have Puritan angularities and to love money; but she pours out now, as
in 1776, lavish expenditures of her treasure in defence of the Union;
and the blood of her sons empurples the ocean and the lakes in every
naval conflict, and moistens all the battle fields of the nation. No!
all the traitors of the South, and all the Burrs, Arnolds, and Catalines
of the North can never sever New England from the Republic. And now, in
this hour of our country's peril, Missouri stretches her hands to New
England, and to all the free and loyal States, and proposes, with their
assistance, to abolish slavery, and link her destiny with theirs in the
bonds of a perpetual Union. And shall we hesitate for a moment, on such
a question? The money consideration is far less than a month's cost of
the war, and sinks into insignificance compared with the momentous
results and consequences. Emancipation in Missouri, with her consent and
the aid of Congress, is the first grand decisive victory of the Union in
this contest, insures eventual success, and must now be placed beyond
all hazard or contingency.
FOOTNOTES:
[Footnote 7: 7th vol. Hamilton's 'Republic,' p. 189, and Jefferson's
'Autograph.']
THE SOLDIER'S BURIAL.
Where shall we lay our comrade down?
Where shall the brave one sleep?
The battle's past, the victory won,
Now we have time to weep!
Bury him on the mountain's brow,
Where he fought so well;
Bury him where the laurels grow--
There he bravely fell!
There lay him in his generous blood,
For there first comes the light
When morning earliest breaks the cloud,
And lingers last at night!
What though no flow'ret there may bloom
To scent the chilly air,
The sky shall stoop to wrap his tomb,
The stars will watch him there!
What though no stone may mark his grave,
Yet Fame shall tell his race
Where sleeps the one so kind, so brave,
And God will find the place!
Bury him on the mountain's brow,
Where he fought so well;
Bury him where the laurels grow--
There he bravely fell!
LITERARY NOTICES.
THE RESULTS OF EMANCIPATION, by AUGUSTIN COCHIN, Ex-Mayor and
Municipal Councillor of Paris. Work crowned by the Institute of
France. Translated by MARY L. BOOTH, translator of Count de
Gasparin's works on America, &c. Boston: Walker, Wise & Co. 1863.
AUGUSTIN COCHIN, author of the work before us, is a man of a class in
France from which we are specially well pleased to see vindications of
Emancipation and of the policy of the Federal Union arise. His position
is well and briefly stated in the preface as that of a Legitimist, a
fast friend and ally of Count de Montalembert in his effort to raise up
a Catholic Liberal party for the development of republican sentiments
and institutions, and the ardent coadjutor of Pere Lacordaire,
Monseigneur d'Orleans, Viscount de Melun, and a host of other moderate
reformers in behalf of freedom. He has some little reputation as a
writer on public and political topics; is highly connected, and, what is
perhaps more to the purpose than aught else, is a very practical man,
and son-in-law to Benoist d'Azy, who, possessed of an immense fortune,
an extensive landowner and proprietor of iron forges, has done perhaps
more than any other man to advance the material interests of his country
by railway building, mining, and agricultural improvements. We say that
this is more to the purpose, since it is of importance that the men who
_actively_ employ capital should understand the falsehood of slavery as
a productive force in any system of labor, anywhere, at the present day.
And it is highly significant when we find such men so far enlightened in
France at this time, where, although, as we learn, very advanced views
in political economy are set forth, we have still apprehended that a
deeply based attachment to slavery, common to all the Latin races,
prevails. That the Radicals should oppose slavery is but natural, but
such views among the highly cultivated aristocracy are indeed
encouraging.
We cannot agree with M. Villemain, who, in his report from the Academy,
decreeing a prize of three thousand francs to M. Cochin for this work,
speaks of it as inspired with 'eloquent zeal' and 'ardor.' It is very
far from what it might have been as a _literary_ production; and to one
not interested in the facts and subject, is even--with the exception of
its excellent Introduction--dry. The author is decidedly an economist,
but he is _not_ 'an apostle,' as his eulogist claims, unless it be in
the sense in which any great collector and publisher of truths may be
termed such. But on its true basis the work is indeed a great one, fully
deserving the publisher's advertisement words, 'opportune and
important.' The volume before us is a complete history, in a minor
degree, of Slavery, and to a very full degree of Emancipation in the
English and French colonies, with some account of the same in those
belonging to Holland, Denmark, and Sweden. Having made for many years a
specialty of the subject, and having had placed at his disposal the
published and unpublished papers and records of every ministry of
Europe, as, for instance, of the English Board of Trade, M. Cochin has
accumulated a mass of extremely valuable material--all of which is
presented in a very clear, perfectly well arranged form--and which we
need not say should be read by every one in public, since there is
certainly no intelligent American at the present day on whom the
necessity of acquiring full information on this subject is not almost a
solemn duty. Next after crushing rebellion, the great task of the
Federal Government should be to organize labor and adopt a vigorous
_central_ and _industrial_ policy. To do this, the relations of free and
of slave labor to circumstances should be extensively studied. As in the
case of all wars involving an institution, the question between the
North and the South at the present day is simply one between ignorance
and knowledge--knowledge such as books like this are eminently adapted
to disseminate.
Passing by religious and philosophic argument, neither of which has been
of much practical avail in this country, since we see the Church of the
South quite as zealous in upholding slavery on Biblical grounds as that
of the North is in opposing it, we come to Cochin's first real
argument--that political economy affirms the superiority of free over
forced labor. Policy and charity unite in this--'charity detests slavery
because it oppresses; policy, more elevated, condemns it _because it
corrupts the inferior race_.'
We call attention to this sentence because it accurately expresses the
difference between mere 'Abolition,' which regarded only the sufferings
of the blacks, and that higher and more comprehensive policy of
'EMANCIPATION FOR THE SAKE OF THE WHITE MAN,' which declares that
slavery always in time inevitably makes of the slaveholder an
intolerable neighbor to the free white laborer. From this point our
author sets forth the gradual growth of the aversion to slavery all over
the Continent, with the reactionary tendency in its favor in the Cotton
United States and in England. It is needless to say that, before the
overwhelming light of _facts_ presented, especially when these facts are
drawn from the past as well as the present, and from every country
instead of _one_, slavery is shown to be more than deadly-conservative;
more than cruel; more than a mere dead wall in the way of the onward
march of the century. The time will come when such a curse will be
rooted out of a country by the strong hand of all civilized nations. Had
England and France been truly enlightened to their own interests, this
war would never have taken place.
The history of the African slave trade and the efforts to destroy it,
the Emancipation of the French Convention and the reestablishment of
slavery by the Consulate, from 1794 to 1802, form the first chapter of
this work. Hence we have its history, its abolition in 1848, and, after
this, that most important part, a careful examination of the results of
Emancipation, showing--as Sewall and others have done--the grossness of
the current falsehood to the effect that it has led to evil results. For
those who can see only a part instead of the whole, who regard the
amount of good done to themselves as the test of everything, who make no
allowance for a social transition, or for a future (like our own
'treason-Democrats'), and who see in the black, whether slave or free,
simply a creature whose whole mission is to benefit the white, it is
true that Emancipation in certain isolated cases may not appear to have
fully succeeded. The _truth_ is, that freed labor has nowhere
diminished--it has simply assumed _new forms_, more advantageous, for
the time, to the laborer, while in most cases it has increased its
profits. If slaves were overworked, there was no real gain;--if schools
and marriage, cleanly independence and good clothing have increased
tenfold among those who were once naked, starved, and ignorant, there
has been a gain, although here and there less sugar is exported. And so
the reader may trace the arguments and facts to the end.
Yet, after all, we feel almost ashamed that such a book should be really
needed! What true _scholar_ and honest man requires arguments of this
kind? A thousand or two years ago, any king's daughter, any young lady,
anybody walking in a lonely spot, was in danger of being kidnapped and
sold to prostitution or slavery. Philosophers, poets, and artists were
owned by brutal wretches; pious priests purchased gentlemen of noble
birth for slaves. The pirate's galley swept every coast to steal any
human being. Time rolled on, and slavery was modified. White slaves
became serfs, serfs became free. The cause of emancipation is clear as
that of any progressive reform--and yet, right in the face of history
and God's truth, we see the Southern Confederacy and the British people
daring to put themselves forward as the advocates of a crime so rapidly
becoming obsolete. Yes--that is what the land of Wilberforce is now
_practically_ doing, while several of her writers, turning on their
tracks, are beginning to 'reconsider' the subject in their writings!
WAR SONGS FOR FREEMEN. Dedicated to the Army of the United States.
Third Edition. Printed for the New York Volunteers. Boston: Ticknor
& Fields.
Have you a friend in the army, especially one who sings occasionally, or
if he be not canorous, say a friend who likes to read songs and hear
them sung by others? In other words, would you, young lady reader (or
any other reader), like to give some soldier at least half an hour's
amusement for a very trivial outlay? In such case we recommend you to
purchase this little pamphlet, and investing in a postage stamp, send it
off without delay to the Army of the ----, whatever _that_ may be.
The work in question contains thirty songs of the war, mostly written
expressly for the book, and each accompanied by the music, in nearly all
cases with the bass. Among the contributors are Dr. O. W. Holmes, who
has given two capital lyrics, 'Union' and 'Liberty,' and a superb
trumpet song, well adapted to _Was blasen die Trompeten?_ or 'What are
the trumpets blowing?' a spirited German air. Mrs. Julia Ward Howe
contributes a 'Harvard Student's Song', which is of course brilliant,
earnest, and beautiful. It is set to the glorious old
Slavonian--subsequently German air:
'Denkst du duran mein tapf'rer Lagienka?'
which no one ever heard without loving. C. T. Brooks, has given to the
grand and swelling _Landesvater_ words in every way worthy of it:
'Comrades plighted,
Fast united,
Firm to death for Freedom stand!
See your country torn and bleeding,
Hear a mother's solemn pleading!
Rescue Freedom's promised land.'
The same author also gives the well known 'Korner's Prayer,' and 'The
Vow.' From Mrs. T. Sedgwick we find a fine bold song, 'For a' that and
a' that,' of course to the good old air of that name--a lyric of such
decided merit in most respects that we regret to notice in it the
venerable bull of 'polar stars,' quizzed long ago in another writer. Our
contributor, Henry Perry Leland, has in this collection two songs, both
strongly marked with the camp, neither setting forth the slightest
earthly claim to be regarded as 'elevated poesie,' yet both remarkably
sing-able, and probably destined to become broadly popular. Of these,
'Bully Boy Billy,' is set to a lilting 'devil may care' Low-Dutch camp
tune--one of the kind which 'sings itself,' and is well adapted to a
roaring chorus. From the same we find a lyric detailing the loss of a
briarwood pipe stolen in a raid, which the grieving 'sojer' trusts (as
we most sincerely do with him) may be found when Richmond's taken. Among
the remaining lyrics are five by Charles Godfrey Leland, including
'We're at War,' to the bold French air of the _Choeur des Girondins_,
'Northmen Come Out,' to the _Burschen heraus_, and 'Shall Freedom Droop
and Die?' to the fine old air of 'Trelawney.' 'The Cavalry Song' has a
brave air, composed for it by John K. Paine. Very spirited and merry is
'Overtures from Richmond,' set to the quaint air of '_Lilliburlero,
bullen a la_,' which is said to have 'sung a deluded prince out of three
kingdoms.' We trust that some of the old charm still sticks to the magic
words, and that it may do as much for King Jeff. as it once did for King
James. Among the remaining lyrics are the following: 'Put it Through,'
and 'Old Faneuil Hall,' by E. E. Hale; 'Our Country is Calling,' to
'_Wohlauf Kameraden!_' by Rev. F. H. Hedge, and a translation of
Luther's _Ein feste Burg ist unser Gott_ by the same; Hauff's 'Night
Guard,' an exquisite German air, and 'I'll be a Sergeant,' and 'Would
you be a Soldier, Laddy?' both of them capital spirited soldier-songs.
Last, not least, we have the 'Lass of the Pamunkey,' by F. J. Child. We
know not whether the incident detailed be strictly autobiographic or
borrowed; it is at any rate well told and merrily music-ed.
The reader will do well to observe that this collection, which has
already become immensely popular, and has furnished material for more
than one excellent patriotic concert, is prepared solely for the benefit
of the solders, _and that the proceeds of the sale of the book are all
devoted to distributing it in the army_. All who wish to make a most
acceptable little gift at a trifling price; all who are 'sending things'
to the army; all who would secure an interesting specimen of the songs
of the war, and, finally, all who would own a really excellent musical
work, should send an order for the above mentioned to Messrs. Ticknor &
Fields.
THE NATIONAL ALMANAC AND ANNUAL RECORD FOR 1863. 12mo, pp. 704.
Philadelphia: George W. Childs. New York: Charles T. Evans.
If Dickens's illustrious statistician, Mr. Gradgrind, were in the flesh
to-day, how he would gloat over this book! The 'facts' presented in its
seven hundred double-columned pages would satisfy, even to repletion,
his voracious cravings; and once crammed with them, he would go forth
into society a walking cyclopedia of all that appertained to the civil,
military, agricultural, industrial, financial, educational, charitable,
and religious condition of these United States.
But though we make no claim to belong to the Gradgrind family, we
acknowledge with pleasure our gratification with this book. It has long
been matter of reproach against us on the part of foreign writers on
commerce and statistical science, that we produced no statistical works
worthy the name. The publication of this work will forever put that
reproach to silence. We have examined the book with care, and have been
at a loss which most to admire, the patient and extraordinary labor
which had brought together so vast a collection of important facts, or
the complete and exhaustive treatment of every subject.
It is a marked characteristic of the work that, while omitting nothing
necessary to a full elucidation of the past condition of the country, it
brings all its statistics up to the latest dates. The United States debt
is given to December 1, 1862; the Government receipts and expenditures
for the financial year 1862; the issues of the mint to the autumn of
1862; the contributions of each State to the volunteer army to December,
1862; the finances of most of the States to the same date; even the
Pacific States being brought up to last autumn; and the condition of the
Rebel army and finances to January 1, 1863. Such enterprise deserves,
and must achieve success.
Noticeable, too, for its completeness and thoroughness, is the 'Record
of Events' of the war, occupying nearly eighty pages, and forming a
continuous and admirable journal of the war up to the close of last
year. In the States, also, the fulness and variety of detail of the
finances, debts, banks, railroads (a new feature), educational
institutions, charitable and correctional organizations, agriculture,
manufactures, and military organization of each State, possess a deep
interest to any man who desires to know the actual condition and
resources of his country. We were particularly pleased with a series of
diagrams, prepared by Prof. Gillespie of Union College, illustrating at
a glance the changes which have taken place in the relative population
of the different States, the relative proportion of increase of white
and of slave population, and the effect produced by this upon different
sections. We have not, at the late hour at which we write, time or room
to indicate a tithe of the valuable features of this remarkable book; we
can only say, that whoever expends the small sum necessary for its
purchase, will most assuredly obtain an ample equivalent for his money.
THE ORPHEUS C. KERR PAPERS. Second Series. New York: Carleton, 413
Broadway. 1863.
During the present decade the American public has welcomed almost
annually a new humorist. Thus we have seen in rapid succession John
Phoenix, Doesticks, Fanny Fern, and Artemus Ward enjoying
extraordinary popularity, and then new 'lords of misrule' 'reigning in
their stead.' The last popular favorite is 'Orpheus C. Kerr'--a name
thinly disguising that of Office Seeker, and which is not indeed too
well chosen, since in the volume before us little or nothing relative to
the very suggestive subject of office-seeking, on the part of the author
at least, is to be found. The book itself is, however, marvellously
laugh provoking, abounding in the oddest conceits, strangest stories,
and drollest extravaganzas in the most ultra American vein. If the men
who best ridicule great failures in war and in politics, are the ones
most to be dreaded, it must be admitted that 'Orpheus C. Kerr' is the
sharpest thorn which has been as yet planted in the side of the 'Young
Napoleons' of our army, whose ability seems to consist in building up
the strength of the enemy by delay and in canvassing indirectly for the
Presidency. There is no cause so good as to be without abuses, and the
abuses which have crept into our management of the war are touched off
in these papers as merrily as unmercifully. They have done 'yeoman's
service' in the press, hitting all sides, but bearing most heavily on
'Young Napoleon' and the _status quo_ Democracy. It cannot be denied
that the humor of these sketches is often merely extravagant, sometimes
harshly strained, and occasionally bare and thin enough in all
conscience, while the stories of the Cosmopolite Club seem like mere
'filling up' to 'make pages;' yet with all this there is more real wit,
humor, and life-knowledge in this volume than would give tone and
strength to half a dozen ordinary popular essayists of the Country
Parson school. Extravagance is however to American narrative what it is
to Arab conversation, something much less _outre_ to those who are born
to it than to strangers, who are unable to discount like the natives as
fast as the sums total are set down. Making every allowance for every
defect, there remains in 'Orpheus C. Kerr' a residuum of irresistible
humor, provoking scores of hearty laughs, and many indications of a
basis of thought and of literary ability which place him far in advance
of the later writers of his school. He takes a wider range, too wide
indeed at times, since he occasionally becomes 'Cockneyfied.' We wish
that 'Villiam' and the Willis-y 'my boy' were less frequently mentioned.
Yet as all this is atoned for by abundance of true American fun, we
readily pardon such echoes, trusting that in his future writings our
humorist will endeavor to be in all things truly original. He can be so
by the very simple process of pruning.
POEMS. By THOMAS BAILEY ALDRICH. New York: Carleton. 1863.
Most of these very pleasant little strains of word-music and of graceful
thought have been frequently brought before the American public, and
become familiar favorites. They now reappear to advantage in a delicate
blue-and-gold volume, with a medallion portrait of the poet.
MODERN WAR: Its Theory and Practice Illustrated from Celebrated
Campaigns and Battles. With Maps and Diagrams. By EMERIC SZABAD,
Captain U. S. A. New York: Harper & Brothers. 1863.
An excellent work, of an eminently practical nature, which may be read
with interest and profit by every one in a time when there
are so few who do not assume to be more or less critical in the art of war.
THE PIRATES OF THE PRAIRIES; or, Adventures in the American Desert.
By GUSTAVE AIMARD. Philadelphia: T. B. Peterson. New York: Frederic
A. Brady. 1863.
A very trashy wildcat romance, highly spiced with sensation sentiment,
"r-r-revenge," and other melo-dramatic attributes. Its author is well
known as an extensive contributor to what may be called the
Sadly-Neglected-Apprentice school of literature and of readers.
ANDREE DE TAVERNEY, or the Downfall of French Monarchy. By
ALEXANDER DUMAS. Philadelphia: T. B. Peterson & Brothers. 1863.
When we, on the publishers' authority, inform the reader that this is
really 'the _final_ conclusion' of the 'Countess of Charny,' the
'Memoirs of a Physician,' and a small library of other works, we shall
doubtless send a thrill of joy to more than one heart. Incredible as it
may appear, the Dumas factory, as _Maquet_ termed it, has actually
finished one of its valuable historical series--unless indeed the
director-in-chief should see fit to republish the long-forgotten first
volume, as a subsequent final conclusion to this of 'Andree de
Taverney.'
VERNER'S PRIDE; a Tale of Domestic Life. By Mrs. HENRY WOOD. In two
volumes. Philadelphia: T. B. Peterson & Brothers. 1863.
A decidedly English novel, of a type well known to our public, embracing
few novelties of character, yet well written, with the story well told.
It has, we believe, been so fortunate as to secure a wide circulation.
EDITOR'S TABLE.
It is a dangerous task for the editor of a monthly review, in times like
these, to comment on what has been or is likely to be done by the army,
when no one knows what a day may bring forth. But, as regards those of
the enemy among us who are scheming to aid and abet their Southern
friends, we may speak more confidently. These traitors, though they have
of late cast off the mask, and no longer pretend to aid the
Administration and the cause of the Union, are still obliged to move
with the caution without which trachery and cowardice would soon perish.
It is, however, a bitter and a humiliating thought that they are so
openly active among us, that they hold meetings where the ruin of the
country is calmly meditated, that they form clubs, that they stir up the
mob of their degraded hangers-on to hurrah for JEFFERSON DAVIS in our
streets, and that finally no amount of exposure and of denunciation in
the patriotic press seems to have the slightest effect in attracting to
them the punishment they deserve.
The traitors of whom we speak are of two classes, the leaders and the
dupes. The latter, careless of the fact that even if a _sudden_ peace
could be brought about it must overwhelm the country in financial ruin,
believe in a restitution of the _status quo ante bellum_. They think
that their leaders will, in unison with DAVIS and his colleagues,
reunite, annul Emancipation, disavow the acts of the Lincoln
Administration, and reestablish Slavery. Cotton is again to be king, and
all go on as of old, save that New England is to be thrown out of the
confederacy. They are encouraged in this belief by lying or cunningly
managed letters from the South, and by assurances that the confederate
leaders are secretly working to this end and aim. 'We got along very
well before the war,' is their constant complaint, 'and we could do as
well again, were it not for the Emancipationists.' Among the lukewarm,
the cowardly, the meanly selfish and avaricious, and the habitual
grumblers, such doctrines are readily made plausible. Those especially,
who measure the propriety of carrying on a war solely by the amount of
success which they desire, and who are incapable of great thoughts and
principles, are easily duped by intriguing villany.
The leaders of these dupes have no faith whatever in restoring the
Union. They have no desire to restore it. Men like Fernando Wood hope
from their very hearts for a complete disintegration--the more thorough,
for them, the better. They could never expect to command the ship, and
so they are willing to wreck her, in the hope of each securing a
fragment. Ruined in character in the eyes of all honest men, their names
a byword for treason, and in most cases for literal crimes, political
outcasts of the stamp who are said to vibrate between the legislature
and the penitentiary, these desperadoes are now working with all their
might to mass the cowardice of the North into a body powerful enough to
do collectively, that for which an individual has in all countries and
in all ages been judged worthy the gallows. But for this war they must
have been confined to representing the dangerous classes of our
cities--the ignorance and vice which finds in them congenial leaders. As
it is, they hope for wider fields and more absolute sway.
There is reason to apprehend that the men who are really true to the
Union do not appreciate the extent to which treason is working among us.
Worse than all, there are many, who, while believing themselves true to
the good cause, are, by constant grumbling and complaint, aiding the
very worst form of disunion. Could we prevail with one prayer upon the
heart of every Federal freeman, it would be to implore him in this hour
of trial not to withold his warmest support from the Administration and
to fall into the common weakness of fault-finding and despairing. Such
enormous wars as this never have been ended in a few months; wars
especially which involve the deepest antagonism of social principles in
existence. And our winnings have been neither few nor light. The
Southern Border States, with little exception, are now ours, and will
inevitably be fully won in time: New Orleans is a pledge, with other
important points, and the enemy admit that every Southern seaboard town
is destined to be taken. Does this look like the wild boasting of the
South two years ago, when the North was to be plundered, Washington
taken, and the Free States trampled under the heel of a chivalry
fiercely crying, _Vae victis!_'--'Woe to the conquered!'? There is no
danger now from the enemy: as he himself admits, two years more of the
war would not, at the rate in which we progress, leave him a single
State; and be it borne in mind that a _speedy_ return to peace is only
to be purchased at the price of a terrible financial crisis.
But we are in danger from the traitors _at home_. JEFFERSON DAVIS is
less deadly to the Federal Union and less to be dreaded than the men who
are scheming to make of New York a free city, and of every State and
county a feudal principality.
* * * * *
The intentions of Louis Napoleon as regards Mexico are beginning to
excite interest. Whatever they may be, there is one thing which it would
be well for the French Emperor never to forget. He holds France simply
as a pledge to the Revolution. So long as he remains true to the cause
of liberty--and, despite names and circumstances, he has been truer to
it than many suppose--he will remain in power. When he is false to it he
will perish. It was through forgetting this that his uncle died at St.
Helena--it was through forgetting this that Louis Philippe quitted Paris
in a very citizenly but most un-kingly manner. The _bourgeoisie_ of
France and the gossips of Paris may storm at the Federal Union,
_epiciers_ may growl for our sugar, and operatives for cotton, but this
class--on whom Louis Philippe made the mistake of solely relying, with a
little help from the aristocracy--are not the men who guide the storms
of revolution in France. The arch spirits of mischief are more secret,
and of late years they have learned much. They are no longer so much
inclined to Socialism, Pere Cabet and 'national ateliers,' still less to
guillotines and noyades. But they are firm as ever, as jealous of
despotism as ever, and, for an oppressor, as powerful as ever. And we
believe that this class of men are firmly attached to the great cause of
progressive freedom as represented by the Federal States and by the
present Administration. Every day sees the truth spreading in France,
and with its extension goes a deeply seated interest in the abolition of
slavery. France--unlike England--feels shame at the idea of being
chronicled in history as aiding oppression. The Frenchman is not so
enormously conceited, so pitiably vain as to believe, like the Briton,
that a crime is a virtue when for _his_ own peculiar interest. Vain as
the French may be, they have not quite come to _that_.
It must be admitted that the French are a shrewd nation. We were wont to
think of old that there was more spite than intelligence in the epithet
by which they characterized John Bull as 'perfidious.' They were right,
for time has shown us that Venice, in the full bloom of her night-shade
iniquity and poniard policy, was never falser at heart than this great,
brawling, boasting, beef-eating England--this 'merry England' of paupers
and prisons, where one man in every eight is buried at public
expense--this Mother England, which starves away annually half a million
of emigrants--this Honest Old England, which floods the world with
pick-pockets, burglars, and correspondents for the _Times_.
It was a trifling thing which brought on the French Revolution of
1848--the return of foreign refugees to Austria, and other significant
indications of joining with the old powers in oppressing freedom. Let
Louis Napoleon beware of an anti-American policy--for to every such
policy there will be an opposition, with a spectre of the Revolution in
the background.
* * * * *
When these remarks meet the eye of the reader, the infamous conduct of
the drunken Delaware Southern-ape Senator, SAULSBURY, will in all
probability have been forgotten. We have for so many years been so
familiarized with the ribald or rowdy pranks of the chivalry, and of
those more miserable wretches their Northern servants, that the mass of
the public seems even yet quite willing to endure, for the poor payment
of an apology, conduct which should anywhere have promptly consigned to
imprisonment, at least, the guilty one. Not but that the apology of
SAULSBURY was humble enough in all conscience. But it is time that our
halls of legislation were thoroughly purified, now that 'chivalric'
brigandage and the Southern system of personal retaliation no longer
prevail. The first legislator who shall dare to draw a weapon in a place
sacred to the councils of his country, should be permanently expelled
from those councils, and made to feel by rigorous imprisonment, and
life-long disfranchisement, the enormous infamy of his offence. We
wonder that the English press treats us as a nation of boors and fools,
and yet permit a representative on the floor of the Senate to set forth
in his own person the worst of which a boor or fool is capable, and
accept as full reparation a drunken-headaching apology!
These are the days of reform, and we sincerely trust that the reform
will extend to the conduct of all our representatives, especially in
Congress. The man who shall dare to apply, not merely to the President,
but to any fellow member, while in either House, any terms of personal
abuse, should incur a punishment which would teach him for the future to
keep a civil tongue in his head, and make him endeavor to assume in
future, at least the outward deportment of a gentleman. The going armed
into such an assembly should however be promptly visited with a penalty
of the extremest severity. It is time that the North freed itself
entirely of these Southern 'dead rabbits' of the Saulsbury stamp, and
indicated by every means in its power its determination to progress in
the path of justice, order, and civilization.
* * * * *
All contributions, letters, &c., intended for the editors of THE
CONTINENTAL MAGAZINE, should be addressed to the care of JOHN F. TROW,
Esquire, No. 50 Greene street, New York. Correspondents directing to Mr.
LELAND are particularly requested to bear this address in mind, as that
gentleman is no longer a resident of Boston.
* * * * *
We publish the poetical tale, THE LADY AND HER SLAVE, by an American
lady, subscribing herself _Incognita_. This is a poem of great genius
and power. Whilst it possesses the inspiration of poetry, it has all the
merits of a truthful and most interesting tale, combined with a splendid
intellectual argument against slavery. This poem unites the logic of
Pope with the genius and poetical inspiration of Goldsmith. It is a
tragedy, and might be transferred to the stage. We trust _Incognita_
will continue her favors to THE CONTINENTAL.
R. J. W.
* * * * *
The rise in specie and in exchange is, we observe, spoken of as
'unprecedented'. The following extract from a work entitled, 'The
British Empire in America,' written in 1740, shows that we are as yet
far from having attained the differences in these respects:
'As to Money, they have none, Gold or Silver: About 50 Years ago
they had some coined at _Boston_; but there's not enough now for
Retailers. All Payments are in Province Bills, even so low as _Half
a Crown_; thus every Man's Money is his Pocket Book. This makes the
Course of Exchange so exorbitant, that 100_l._ in _London_ made out
lately 225_l._ in _New-England_; and if a Merchant sells his Goods
from _England_ at 220_l._ Advance upon 100_l._ in the Invoice, he
would be a Loser by the Bargain, considering the incidental Charges
on his Invoice.'
So that after all, they had as great 'ups and downs' of old as do we of
the present day.
Apropos of the old book in question, it abounds in quaint bits of
information, given in a dry, free and easy style seldom found at the
present day in any work of the kind. Thus it tells us, among the
anecdotes of ELLIOT the missionary, that an Indian in a religious
conference asked how GOD could create man in his own image, since
according to the second commandment it was forbidden to make any such
image?
'To qualify him for the Work he was going about, Mr _Elliot_ learnt the
_Indian_ Language as barbarous as can come out of the Mouth of Man, as
will be seen by these Instances:
'_Nummatchekodtantamoonganunnonash_, is in English, _Our Lusts_; a Word
that the Reverend Mr _Elliot_ must often have occasion to make Use of.
As long as it is, we meet with a longer still:
'_Kummogkodonattoottummoooctiteaongannunonash_, meaning Our Question.
'_Gannunonash_' seems to be 'our,' because we find it in the End of the
First Word, as well as the second, * * and this appears again in another
Word:
'_Noowomantammooonkanunnonash_, 'Our Loves.'
'The longest of these _Indian_ Words is to be measured by the Inch, and
reaches to near half a Foot; and if Mr _Elliot_ did put as many of these
Words in a Sermon of his, as Mr _Peters_ put _English_ Words in one of
his Sermons, everyone of them must have made a sizeable Book and have
taken up three or four Hours in utterance.'
The Peters referred to was the celebrated Hugh Peters, Cromwell's
chaplain. Our author vindicates this clergyman from certain scandalous
charges, declaring that he had asked of his daughter, Miss Peters, if
they were so, which she had utterly denied! Less credulous is he as
regarded 'William Pen' (with whom he seems to have been on terms of
great personal intimacy), since he hints very broadly in one passage,
that he put no faith whatever in a certain assertion of 'Pen' as to his
own (Penn's) good behavior when amiably smiled on by a _belle sauvage_,
who, as the French would say, was not savage at all. 'Scandal, scandal
all,' we doubt not. There are gossipers in every age, tattlers in every
corner of history, and who escapes them? Cato did not, Washington could
not, and 'Mr Pen' even must fill his place with the great maligned. Let
us trust that our incautious dip from the old work may not, suggest to
any novel maker 'Penn and the Princess,--a Tale of the Olden Time.'
* * * * *
The following poem, which we find in the Philadelphia _Press_, is among
the best of the many sad lyrics which the war has inspired. The music of
the refrain is remarkable:
DIRGE FOR A SOLDIER.
By George H. Boker
Close his eyes; his work is done!
What to him is friend or foeman,
Rise of moon, or set of sun,
Hand of man, or kiss of woman?
Lay him low, lay him low,
In the clover or the snow:
What cares he? he cannot know:
Lay him low!
As man may, he fought his fight,
Proved his truth by his endeavor;
Let him sleep in solemn night,
Sleep forever and forever.
Lay him low, lay him low,
In the clover or the snow:
What cares he? he cannot know:
Lay him low!
Fold him in his country's stars;
Roll the drum and fire the volley!
What to him are all our wars,
What but death bemocking folly?
Lay him low, lay him low,
In the clover or the snow:
What cares he? he cannot know:
Lay him low!
Leave him to God's watching eye;
Trust him to the Hand that made him.
Mortal love weeps idly by:
God alone has power to aid him.
Lay him low, lay him low,
In the clover or the snow:
What cares he? he cannot know:
Lay him low!
* * * * *
Much has been said of the high price paid to opera singers. The
celebrated BERLIOZ once reduced it to details in the following word:
'The first tenor,' he said, 'has 100,000 frcs. per annum, and he
sings for it about seven times during the month, or eighty-four
times during the year. This would be about 1,100 francs per
evening. Admitted then that his part would contain 1,100 notes or
syllables, the price of each syllable would be 1 franc.
Consequently in William Tell:
'Ma (1 fr.) presence (3 fr.) pourvous est peut etre un outrage (9 fr.)
Mathilde (3 fr.) mes pas indiscret (100 sous).
On osee jusqu'a vous se frayer une passage! (13 fr.)
'These three lines therefore cost 34 francs. A great sum! Engaging
under these circumstances a Prima Donna, at the miserable pittance
of 40,000 francs, the answer of Mathilde amounts to much less, for
every syllable would then cost but 8 sous: but even that is not so
bad after all.
'We laugh,' adds Berlioz, 'but the theatres have to pay. They will
pay until the treasury is empty, and after that the 'Immortals'
will have to condescend to give singing lessons (i.e., those who
know enough for it), or to sing at public places with accompaniment
of one guitar, four candles, and a green carpet. After that we may
be able to construct the Temple of Music on a firmer basis.'
At these rates, the old form of declaring that any thing went for 'a
mere song,' would not say much for its cheapness. But if--as Berlioz
seems to think--these high prices are to be regretted, we still cannot
see how they are to be remedied. The public, for want of better
amusement, keep up the opera, and the different opera houses keep up
the prices by outbidding each other. When municipal governments shall
recognize the fact that amusement is a constant quantity in the
administration of a state, and provide first-class entertainments
_gratis_ or at nominal rates, there will be much vice done away with and
many rum shops closed--which would be bad, by the way, for the
Democrato-Rum-elected Governor Seymour, for the whole alcoholic vote was
cast in his favor. There will, we believe, come a time when the party of
progress will urge an enlarged provision of education and recreation for
the people, with the same earnestness which it now shows in forwarding
Emancipation.
* * * * *
England has by her Southern sympathy fairly put a serpent girdle of her
treachery around the earth. For further particulars consult the
following:
TO JOHN BULL.
Oh don't you remember sweet Ireland, John Bull?
Green Erin beyond the blue sea?
And the patriots there whom you starved, hung, and shot,
Because they desired to be free.
On the lone heather wild, in the dark silent glen,
The peasant still shows you the graves
Of the heroes who fell in the year ninety-eight
And died ere they'd live as your slaves.
And don't you remember your own words, John Bull,
Of the Southern Confed--er--a--cie?
When you said in the _Times_, that your heart went of course
With a brave race which sought to be free.
Oh what do you think of Old Ireland, John Bull?
There's a race that's as brave as your own,
And one that would like very well to be free,
If you only would let it alone.
And don't you remember great India, John Bull?
With the Sepoys you blew from your guns,
And the insult and murder of Brahmins, John Bull,
For some outrage endured from their sons?
The outrage was proved a black lie, as you know,
A lie, as your own books declare:
Your hell-hounds of HAVELOCKS stirred up the war,
And what business had they to be there?
And don't you remember great China, John Bull,
Where you smeared yourself blacker with sin?
Where the Emperor tried to keep opium out,
And you fought to force opium in?
It was _Government_ opium from India, too,
Which poisons both body and soul;
You have fought against freedom with steel, Johnny Bull;
With the steel and the cord and the bowl.
And do you believe in a GOD, Johnny Bull,
Or _anything_ after the grave?
Then tell us what waits for the sinner who aids
The tyrant to trample the slave?
I'll not ask if you've faith in a Devil, John Bull:
One might think he were laid on the shelf,
To see you unpunished--but now I believe
That you are the False One himself.
* * * * *
We are indebted to a friend for the following tales of foraging, which
are vouched for as authentic:
A company of the Two--th cavalry of volunteers, no matter in what
State, were out on a forage, with the usual orders to respect the
enemy's property. But coming on a plantation where chickens and
turkeys were dallying in the sunshine, the officer in command,
tired of pork and plaster-pies, alias hard biscuit, gave the boys
leave to club over as many of the 'two-legged things in feathers'
as they could conveniently come at. The result was that a good
number were despatched, and being tied together by the legs, were
slung over the pommel of the saddle of 'Benny,' an old _sabreur_,
who had frontiered it for years, been in more Indian fights than
you could shake a stick at, and could tell, if he wanted to, of
some high-old-hard times with these same Mdewakantonwar, Wahpekute,
Ihanktonwannas, and Minnikanyewazhipu red-skinned fiends.
Returning to camp, as ill luck would have it, they met the colonel
of their regiment riding out to a neighboring camp. Just before
they met him, in fact when they were nearly up to him, for a curve
in the road had hid him from sight till then, the officer in
command rode by Benny with the command:
'D--n it, man, why don't you sling those chickens the other side
your saddle? The colonel will see them, hanging that way.'
'Can't be done! got fourteen turkeys _there_ on a balance!'
By remarkably good fortune the colonel did not see the chickens, so
they and the turkeys were safely smuggled into camp, Benny getting
full credit for maintaining the balance of power, when the odds
were dead against him.
Story ye second:
When the Forty-eleventh P.M. were camped near Boonesboro', what
time the rebels were driven out of Maryland, the colonel of the
said regiment duly issued orders that all provender taken by troops
under his command should be fairly paid for without defalcation for
value received. Now it happened one bright morning that the major
of the aforesaid regiment riding out near camp, saw a private
deliberately lift up what is known in Southern tongue as a 'rock,'
and throwing the same with great skill, instantly kill a small pig
that with half a dozen other small pigs were following their mother
at full speed away from the neighborhood of this same private.
The soldier, who was an Irishman, picked up the pig, and hiding it
under his army sack, was returning to camp, when, lifting up his
head, he saw before him the major, who, assuming his most solemn
look, thus spoke to him:
'What have you under your coat, there?'
'Shure it's an empty stomach, sirr!--and a small pig that's hurted
itself--poor little thing!--and I'm taking it home to mend its leg,
to be sure:--the poor crayture wud be after dying if left all alone
in the cold, the raw morning.'
The major dearly relished the joke, but discipline is discipline,
and there was but one way to overlook this breach of it: that was
to punish Paddy by giving him a three-mile walk down the road, and
over the fields back to camp, before he could bring his pig in.
'You say the pig is lame?' asked the officer.
'Shure, that's the truth, sirr; and I'm afther belaving it'll niver
be able to run any more at all, at all: be the same token its
tail's out of curl entirely; and had'nt I better be afther taking
it home than letting it die like a haythin in the road here?'
'Do you see that old sow down the road there with those other pigs?
you follow her home at _once_, sir, and leave the lame pig
_there_!'
Saying which, the major continued his ride, and the Irishman duly
followed the old sow to--a turn in the road, when he 'obeyed
orders,' and left the lame pig 'at home,' where that night at least
one mess had roast pig with '_ubi_ beans _ibi patria_,' sauce at
discretion.
* * * * *
TO
THE MARINERS OF ENGLAND
ON BOARD THE PRINCESS ROYAL
Ye Mariners of England,
That shame your country's fame;
That peddle chains to bind the slave,
In the blood-royal name!
Your glorious standard hide away,
Hoist slave flags in its place,
And steal o'er the deep,
With our Yankee ships in chase:
And ye peddlers, shun the starry flag,
While the Yankee cruisers chase.
The spirits of your fathers
Shall start from every wave!
For the ocean was their field of fame,
And ye insult their grave.
Where they like bold men fought and fell,
Ye take a part that's base,
And steal o'er the deep
With our Yankee ships in chase:
And ye peddlers, shun the starry flag,
While the Yankee cruisers chase.
Britannia needeth cotton,
And so your honor'll sleep;
Your market's o'er the mounting wave,
Your greed of gain lies deep.
Your sovereign bids you walk upright;--
Her fair fame you disgrace,
And steal o'er the deep,
With our Yankee ships in chase:
And ye peddlers, shun the starry flag,
While our Yankee cruisers chase.
The meteor flag of England
Should redder burn for shame,
When it waves o'er chains for slaves
In Princess Royal's name.
Mourn, mourn, ye ocean hucksters!
Your goods and ships are lost:
To the shame of your name
Get you home and count the cost:
For your Princess Royal's gone for good;
Get you home and count the cost.
* * * * *
The
Continental Monthly.
The readers of the CONTINENTAL are aware of the important
position it has assumed, of the influence which it exerts, and of the
brilliant array of political and literary talent of the highest order
which supports it. No publication of the kind has, in this country, so
successfully combined the energy and freedom of the daily newspaper with
the higher literary tone of the first-class monthly; and it is very
certain that no magazine has given wider range to its contributors, or
preserved itself so completely from the narrow influences of party or of
faction. In times like the present, such a journal is either a power in
the land or it is nothing. That the CONTINENTAL is not the
latter is abundantly evidenced _by what it has done_--by the reflection
of its counsels in many important public events, and in the character
and power of those who are its staunchest supporters.
Though but little more than a year has elapsed since the
CONTINENTAL was first established, it has during that time
acquired a strength and a political significance elevating it to a
position far above that previously occupied by any publication of the
kind in America. In proof of which assertion we call attention to the
following facts:
1. Of its POLITICAL articles republished in pamphlet form, a
single one has had, thus far, a circulation of _one hundred and six
thousand_ copies.
2. From its LITERARY department, a single serial novel, "Among
the Pines," has, within a very few months, sold nearly _thirty-five
thousand_ copies. Two other series of its literary articles have also
been republished in book form, while the first portion of a third is
already in press.
No more conclusive facts need be alleged to prove the excellence of the
contributions to the CONTINENTAL, or their _extraordinary
popularity;_ and its conductors are determined that it shall not fall
behind. Preserving all "the boldness, vigor, and ability" which a
thousand journals have attributed to it, it will greatly enlarge its
circle of action, and discuss, fearlessly and frankly, every principle
involved in the great questions of the day. The first minds of the
country, embracing the men most familiar with its diplomacy and most
distinguished for ability, are among its contributors; and it is no mere
"flattering promise of a prospectus" to say that this "magazine for the
times" will employ the first intellect in America, under auspices which
no publication ever enjoyed before in this country.
While the CONTINENTAL will express decided opinions on the
great questions of the day, it will not be a mere political journal:
much the larger portion of its columns will be enlivened, as heretofore,
by tales, poetry, and humor. In a word, the CONTINENTAL will be
found, under its new staff of Editors, occupying a position and
presenting attractions never before found in a magazine.
TERMS TO CLUBS.
Two copies for one year, Five dollars.
Three copies for one year, Six dollars.
Six copies for one year, Eleven dollars.
Eleven copies for one year, Twenty dollars.
Twenty copies for one year, Thirty-six dollars.
PAID IN ADVANCE
_Postage, Thirty-six cents a year_, to be paid BY THE
SUBSCRIBER.
SINGLE COPIES.
Three dollars a year, IN ADVANCE. _Postage paid by the
Publisher_.
JOHN F. TROW, 50 Greene St., N. Y.,
PUBLISHER FOR THE PROPRIETORS.
[Illustration: pointing finger] As an Inducement to new subscribers, the
Publisher offers the following liberal premiums:
[Illustration: pointing finger] Any person remitting $3, in advance,
will receive the magazine from July, 1862, to January, 1864, thus
securing the whole of Mr. KIMBALL'S and Mr. KIRKE'S new serials, which
are alone worth the price of subscription. Or, if preferred, a
subscriber can take the magazine for 1863 and a copy of "Among the
Pines," or of "Undercurrents of Wall Street," by R. B. KIMBALL, bound in
cloth, or of "Sunshine in Thought," by CHARLES GODFREY LELAND (retail
price, $1. 25.) The book to be sent postage paid.
[Illustration: pointing finger] Any person remitting $4.50, will receive
the magazine from its commencement, January, 1862, to January, 1864,
thus securing Mr. KIMBALL'S "Was He Successful? "and Mr. KIRKE'S "Among
the Pines," and "Merchant's Story," and nearly 3,000 octavo pages of the
best literature in the world. Premium subscribers to pay their own
postage.
* * * * *
[Illustration: THE FINEST FARMING LANDS WHEAT CORN COTTON FRUITS &
VEGETABLES]
~EQUAL TO ANY IN THE WORLD!!!~
MAY BE PROCURED
~At FROM $8 to $12 PER ACRE,~
Near Markets, Schools, Railroads, Churches, and all the blessings of
Civilization.
1,200,000 Acres, in Farms of 40, 80, 120, 160 Acres and upwards, in
ILLINOIS, the Garden State of America.
* * * * *
The Illinois Central Railroad Company offer, ON LONG CREDIT, the
beautiful and fertile PRAIRIE LANDS lying along the whole line of their
Railroad. 700 MILES IN LENGTH, upon the most Favorable Terms for
enabling Farmers, Manufacturers, Mechanics and Workingmen to make for
themselves and their families a competency, and a HOME they can call
THEIR OWN, as will appear from the following statements:
ILLINOIS.
Is about equal in extent to England, with a population of 1,722,666, and
a soil capable of supporting 20,000,000. No State in the Valley of the
Mississippi offers so great an inducement to the settler as the State of
Illinois. There is no part of the world where all the conditions of
climate and soil so admirably combine to produce those two great
staples, CORN and WHEAT.
CLIMATE.
Nowhere can the Industrious farmer secure such immediate results from
his labor as on these deep, rich, loamy soils, cultivated with so much
ease. The climate from the extreme southern part of the State to the
Terre Haute, Alton and St. Louis Railroad, a distance of nearly 200
miles, is well adapted to Winter.
WHEAT, CORN, COTTON, TOBACCO.
Peaches, Pears, Tomatoes, and every variety of fruit and vegetables is
grown in great abundance, from which Chicago and other Northern markets
are furnished from four to six weeks earlier than their immediate
vicinity. Between the Terre Haute, Alton & St. Louis Railway and the
Kankakee and Illinois Rivers, (a distance of 115 miles on the Branch,
and 136 miles on the Main Trunk,) lies the great Corn and Stock raising
portion of the State.
THE ORDINARY YIELD
of Corn is from 60 to 80 bushels per acre. Cattle, Horses, Mules, Sheep
and Hogs are raised here at a small cost, and yield large profits. It is
believed that no section of country presents greater inducements for
Dairy Farming than the Prairies of Illinois, a branch of farming to
which but little attention has been paid, and which must yield sure
profitable results. Between the Kankakee and Illinois Rivers, and
Chicago and Dunleith, (a distance of 56 miles on the Branch and 147
miles by the Main Trunk,) Timothy Hay, Spring Wheat, Corn, &c., are
produced in great abundance.
AGRICULTURAL PRODUCTS.
The Agricultural products of Illinois are greater than those of any
other State. The Wheat crop of 1861 was estimated at 35,000,000 bushels,
while the Corn crop yields not less than 140,000,000 bushels besides the
crop of Oats, Barley, Rye, Buckwheat, Potatoes, Sweet Potatoes,
Pumpkins, Squashes, Flax, Hemp, Peas, Clover, Cabbage, Beets, Tobacco,
Sorgheim, Grapes, Peaches, Apples, &c., which go to swell the vast
aggregate of production in this fertile region. Over Four Million tons
of produce were sent out the State of Illinois during the past year.
STOCK RAISING.
In Central and Southern Illinois uncommon advantages are presented for
the extension of Stock raising. All kinds of Cattle, Horses, Mules,
Sheep, Hogs, &c., of the best breeds, yield handsome profits; large
fortunes have already been made, and the field is open for others to
enter with the fairest prospects of like results. Dairy Farming also
presents its inducements to many.
CULTIVATION OF COTTON.
The experiments in Cotton culture are of very great promise. Commencing
in latitude 39 deg. 30 min. (see Mattoon on the Branch, and Assumption
on the Main Line), the Company owns thousands of acres well adapted to
the perfection of this fibre. A settler having a family of young
children, can turn their youthful labor to a most profitable account in
the growth and perfection of this plant.
THE ILLINOIS CENTRAL RAILROAD
Traverses the whole length of the State, from the banks of the
Mississippi and Lake Michigan to the Ohio. As its name imports, the
Railroad runs through the centre of the State, and on either side of the
road along its whole length lie the lands offered for sale.
CITIES, TOWNS, MARKETS, DEPOTS.
There are Ninety-eight Depots on the Company's Railway, giving about one
every seven miles. Cities, Towns and Villages are situated at convenient
distances throughout the whole route, where every desirable commodity
may be found as readily as in the oldest cities of the Union, and where
buyers are to be met for all kinds of farm produce.
EDUCATION.
Mechanics and working-men will find the free school system encouraged by
the State, and endowed with a large revenue for the support of the
schools. Children can live in sight of the school, the college, the
church, and grow up with the prosperity of the leading State in the
Great Western Empire.
* * * * *
PRICES AND TERMS OF PAYMENT--ON LONG CREDIT.
80 acres at $10 per acre, with interest at 6 per ct. annually
on the following terms:
Cash payment $48 00
Payment in one year 48 00
" in two years 48 00
" in three years 48 00
" in four years 236 00
" in five years 224 00
" in six years 212 00
40 acres, at $10 00 per acre:
Cash payment $24 00
Payment in one year 24 00
" in two years 24 00
" in three years 24 00
" in four years 118 00
" in five years 112 00
" in six years 106 00
* * * * *
Number 16. 25 Cents.
THE CONTINENTAL MONTHLY.
DEVOTED TO Literature and National Policy.
APRIL, 1863.
NEW YORK: JOHN F. TROW 50 GREENE STREET (FOR THE PROPRIETORS).
HENRY DEXTER AND SINCLAIR TOUSEY. WASHINGTON, D.C.: FRANCK TAYLOR.
* * * * *
CONTENTS.--No. XVI.
The Wonders of Words, 385
The Chech, 395
Pictures from the North, 398
The New Rasselas, 404
The Chained River. By Charles Godfrey Leland, 410
How the War affects Americans. By Hon. F. P. Stanton, 411
Promoted, 420
Henrietta and Vulcan. By Delia M. Colton, 421
Ethel. By Martha Walker Cook, 435
The Skeptics of the Waverley Novels. By Charles Godfrey Leland, 439
A Merchant's Story. By Edmund Kirke, 451
A Chapter on Wonders. By Perth Granton, 461
The Return. By Edward Sprague Rand, jr., 464
The Union. By Hon. R. J. Walker, 465
Down in Tennessee, 469
Poetry and Poetical Selections, 474
Flag of our Sires. By Hon. R. J. Walker, 480
A Fancy Sketch, 482
Our Present Position; its Dangers and its Duties, 488
The Complaining Bore, 496
Literary Notices, 500
Editors' Table, 503
* * * * *
'MY SOUTHERN FRIENDS,' by the author of 'Among the Pines,' is just
issued from the press of G. W. CARLETON, 413 Broadway, N. Y. Price, $l,
cloth; 75 cts., paper covers.
* * * * *
ENTERED, according to Act of Congress, in the year 1862, by JAMES R.
GILMORE, in the Clerk's Office of the District Court of the United
States for the Southern District of New York.
JOHN F. TROW, PRINTER.
End of the Project Gutenberg EBook of The Continental Monthly, Vol 3 No 3,
March 1863, by Various
*** | {
"redpajama_set_name": "RedPajamaBook"
} | 3,635 |
\section{Introduction} \label{intro}
The spin-1/2 Heisenberg chain is probably the first and most studied example
of a strongly correlated quantum system. The first foundations towards exact
solutions date back to the early days of quantum mechanics \cite{Bethe} and
large scale numerical simulations were already performed in the early sixties
\cite{BonnerFisher}. Due to the interesting behaviour of this simple model and
the connection with many low-dimensional antiferromagnetic materials, the
spin-1/2 chain is still heavily studied today. Some of the most fundamental
properties, such as the exact amplitude of the power-law correlation functions
\cite{Affleck98,Lukyanov,LukyanovTerras} and the full temperature behaviour of the
susceptibility \cite{egg94,Lukyanov}, have only been established after the
discovery of high temperature superconductivity has lead to renewed interest
in low-dimensional antiferromagnetism. More recently, corrections from
impurities and boundaries have come into focus
\cite{EggertAffleck92,AsakawaMatsuda,WesselHaas,FujimotoEggert,FurusakiHikihara,EggertAffleckHorton,BrunelBocquet,AffleckQin,EggertRommer,
RommerEggert,RommerEggert2,EggertAffleck95,FHLE,AsakawaSuzuki96a,AsakawaSuzuki96b,frah97,Fujimoto,BortzSirker,SirkerBortzJSTAT,SirkerLaflorencie},
which will also be the topic of this paper.
Boundary thermodynamics are especially relevant for experiments
\cite{AmiCrawford,MotoyamaEisaki,Kojima,TakigawaMotoyama,ThurberHunt} since
even the most carefully prepared samples contain imperfections which
effectively cut the chains, and corrections to the thermodynamic limit become
especially large at low temperatures. In order to analyse the pure and the
impurity contributions it is useful to define the finite size corrections
\begin{equation}
\delta F_{FS}(L) = F(L) - L f_{\mbox{\tiny bulk}} \;\;\mbox{and}\;\;\delta\chi_{FS}(L) = \chi(L) - L \chi_{\mbox{\tiny bulk}}
\label{deltaf}
\end{equation}
where $F(L)$ ($\chi(L)$) is the total free energy (susceptibility) of a system
with $L$ sites and $f_{\mbox{\tiny bulk}}$ ($\chi_{\mbox{\tiny bulk}}$) is the free energy
(susceptibility) per site of an infinite pure system. In the limit of $L\to
\infty$, $\delta F_{FS}$ and $\delta \chi_{FS}$ become $L$-independent
thermodynamic boundary contributions, which will be denoted by $F_B$ and
$\chi_B$ and discussed in detail later on. However, in general $L$ will also
take on small values in experimental systems according to a random
distribution.
It is well understood that finite chains with an odd number of sites
$L$ have doublet ground states, which leads to a diverging Curie
susceptibility at temperatures below the first excitation energy $ T/J
\ll 1/L$ \cite{EggertAffleck92}.
Recently, it has been established that the boundary susceptibility
$\chi_B(T) \equiv \delta\chi_{FS}(T,L\to\infty)$ is also divergent in the
limit $T\to 0$, albeit with a Curie factor which has a logarithmic
temperature dependence \cite{FujimotoEggert,FurusakiHikihara}. For
experimental systems it is desirable to know the complete crossover
between the two limits, which has to be averaged according to a random
distribution. If the impurity concentration is $p$ and we assume a
Poisson distribution, i.e., that the impurity positions are
uncorrelated, then the average susceptibility becomes
\cite{EggertAffleckHorton,SirkerLaflorencie}
\begin{equation}
\label{chi_p}
\chi_p = p^2 \sum_{L=0}^\infty (1-p)^{L} \chi(L) = (1-p) \chi_{\mbox{\tiny bulk}} + p\ \delta \bar \chi_{FS},
\end{equation}
where $\delta \bar \chi_{FS} = p \sum_L (1-p)^{L} \delta \chi_{FS}(L)$
and we have assumed that each impurity effectively removes one site.
The typical approximation in experimental papers to estimate the
impurity concentration by the low-temperature Curie tail corresponds
to setting $\delta \bar \chi_{FS} = 1/(8T)$ (assuming that each chain
segment with odd length acts effectively like a free
spin-$1/2$). This, however, does not capture the full complexity of
the problem and might, in particular, lead to an underestimate of the
impurity concentration by an order of magnitude.
Several experiments have been studying the prototypical spin-$1/2$
chain compound Sr$_2$CuO$_3$
\cite{AmiCrawford,MotoyamaEisaki,TakigawaMotoyama,ThurberHunt} and the
doped system Sr$_2$Cu$_{1-x}$Pd$_x$O$_3$ \cite{Kojima} where palladium
serves as a non-magnetic impurity. The analysis of the susceptibility
even in the undoped system has been hampered by large Curie-like
contributions at low temperatures making a detailed test of the
theoretical predictions for the susceptibility of the pure system
\cite{egg94} difficult. In \cite{AmiCrawford,MotoyamaEisaki} it has
been shown that these contributions can be largely suppressed by
annealing the samples. It therefore has been suggested that the
Curie-like contribution is caused by excess oxygen. Each excess oxygen
atom would then dope two holes into the chain. A detailed theoretical
analysis of the susceptibility data \cite{SirkerLaflorencie} has shown
that it seems to be possible to consistently describe the data by
assuming that these holes are basically immobile and therefore
effectively cut the chain into finite segments. A more detailed
understanding of these experiments is desirable because it might also
shed some light on the general issue of oxygen doping in cuprates, and
in particular, in the high-temperature superconductors.
Our paper is organised as follows: In section \ref{fieldtheory} the
effective field theory description of the spin-1/2 chain is
reviewed. In section \ref{general} we calculate the free energy for an
open anisotropic Heisenberg chain of finite length at finite
temperature by field theory methods beyond the scaling limit. Next, we
consider the limit $L\to\infty$ with $T/J$ fixed in section
\ref{boundary} where $\delta F_{FS}$ and $\delta \chi_{FS}$ as defined
in (\ref{deltaf}) become well defined boundary quantities. In section
\ref{IsoCase} we then discuss separately the isotropic model which is
the most interesting case from an experimental point of view. In the
limit, $T/J\ll 1/L$, considered in section \ref{ground_state}, a
crossover to the ground state limit takes place and logarithmic
corrections to the scaling limit result are studied in detail. In
section \ref{avg_susci} we then derive a simple formula which can be
used to fit the experimentally measured averaged susceptibility
$\chi_p$. We also discuss here the temperature dependence of the
effective Curie constant $C\sim T\delta\bar{\chi}_{FS}$. In any real
material there will be residual couplings bridging between the chain
segments (intrachain couplings) as well as interchain couplings which
will usually lead to some sort of magnetic order at low
temperatures. The effect of such couplings will be discussed in
section \ref{seg-couplings}. A comparison between our theoretical
predictions and experiments on Sr$_2$Cu$_{1-x}$Pd$_x$O$_3$
\cite{Kojima} is presented in section \ref{experiment}. Finally, we
conclude and give a short summary in section \ref{conclusions}.
\section{Effective field theory for the spin-1/2 chain}
\label{fieldtheory}
The Hamiltonian for the spin-1/2 Heisenberg chain with open boundaries in an
external magnetic field $h$ is given by,
\begin{equation}
H=J\sum_{i=1}^{L-1}
[S_{i}^xS_{i+1}^x+S_{i}^yS_{i+1}^y+\Delta S_{i}^zS_{i+1}^z]-h\sum_{i=1}^L
S_{i}^z,
\label{xxz}
\end{equation}
with $J>0$ for an antiferromagnetic system. Here, we have introduced an
exchange anisotropy $\Delta$ which is convenient to obtain a low-energy
effective theory by bosonisation. Such a description is by now well
established \cite{Affleck_lesHouches,Lukyanov} and numerical simulations have
shown its applicability for $L \gtrsim 10$ and low temperatures $T \lesssim
0.1J$, which is also the most interesting regime for experiments. In the
massless case, $-1<\Delta \leq 1$, the low energy fixed point of (\ref{xxz})
is the Tomonaga-Luttinger liquid, which belongs to the universality class of
the Gaussian theory with the central charge $c=1$.
Ignoring irrelevant operators the Hamiltonian is then equivalent to a free boson model
\begin{equation}
\label{H0}
H_0 = \frac{v}{2}\int_0^{La'}\!\! dx \; [\Pi^2 +(\partial_x\phi)^2]
-h\sqrt{\frac{K}{2\pi}}\int^{La'}_0 \!\! dx \; \partial_x\phi,
\end{equation}
where $a'$ is the lattice constant. $\phi$ is a bosonic field and
$\Pi=v^{-1}\partial_t\phi$ the conjugate momentum obeying the standard
commutation rule $[\phi(x),\Pi(x')]=\mbox{i}\delta(x-x')$. The dependence of the
Luttinger parameter $K$ on anisotropy $\Delta$ is known exactly from Bethe
Ansatz
\begin{equation}
K=[1-\frac{1}{\pi}\cos^{-1}(\Delta)]^{-1},
\label{lpa}
\end{equation}
as well as the velocity \cite{tak99}
\begin{equation}
v =\frac{JK\sin(\pi/K)}{2(K-1)}a'\; .
\end{equation}
In the following we will set the lattice constant $a'\equiv 1$. Factors of $a'$
can be easily restored in the final results by dimensional analysis. Using the
mode expansion for open boundary conditions (OBCs)
\begin{eqnarray}
\label{ModeExp}
\fl \phi(x,t) &=& \sqrt{\frac{\pi}{8K}} +\sqrt{\frac{2\pi}{K}} S_z \frac{x}{L} + \sum_{n=1}^\infty
\frac{\sin\left(\pi nx/L\right)}{\sqrt{\pi n}}\left(\mbox{e}^{-i\pi n \frac{vt}{L}}a_n +
\mbox{e}^{i\pi n\frac{vt}{L}}a_n^\dagger\right)
\end{eqnarray}
the Hamiltonian can also be expressed in terms of bosonic creation and
annihilation operators $a_n$
\begin{equation}
H_0 = \frac{\pi v}{L K}S_z^2 + \frac{\pi v}{L}\sum_{n=1}^\infty n (a_n^\dagger a_n^{~}+1/2) - h S_z.
\end{equation}
The zero mode operator $S_z = \sqrt{\frac{K}{2\pi}}\int^L_0 dx\ \partial_x\phi$ measures
the
total magnetisation of the chain and is therefore quantised to take on integer values
for chains with an even number of sites $L$ and half-integer values for odd $L$.
Up to this point the effective model is easily solvable exactly. The partition function
can be obtained directly by summing over all eigenvalues
\begin{eqnarray}
\label{part}
Z_0 &=& \sum_{S_z}e^{-\frac{\pi v}{KLT}S_z^2+ \frac{h}{T}S_z}
\prod_{n=1}^\infty \left[2\sinh\left(\frac{\pi v}{2LT}n\right)\right]^{-1} \\
&=& \theta\left(e^{-\frac{\pi v}{K LT}}, -i\frac{h}{2T}\right) \prod_{n=1}^\infty \left[2\sinh\left(\frac{\pi v}{2LT}n\right)\right]^{-1} \nonumber
\end{eqnarray}
where $\theta(q,u)$ is the elliptic theta function of the third kind $\theta =
\theta_3(q,u) = \sum_{n=-\infty}^{\infty} q^{n^2} e^{i2 n u}$ for integer
$S_z$ (even $L$) and of the second kind $\theta = \theta_2(q,u) =
\sum_{n=-\infty}^{\infty} q^{(n+1/2)^2} e^{i(2 n+1) u}$ for half-integer $S_z$
(odd $L$).
The free energy per site is then given by
\begin{equation}
\label{freeE}
f_0 = - \frac{T}{L} \left\{\ln \theta\left(e^{-\frac{\pi v}{K LT}},
-i\frac{h}{2T}\right) - \sum_{n=1}^\infty \ln \left[2\sinh\left(\frac{\pi v}{2LT}n\right)\right]\right\} \; .
\end{equation}
and the susceptibility by
\begin{eqnarray}
\label{scalechi}
\fl \chi_0 &=& -\frac{\partial^2 }{\partial h^2}\bigg|_{h=0}f_0 = \frac{1}{LT} \frac{\sum_{S_z} S_z^2
e^{-\frac{\pi v}{KLT}S_z^2}}{\sum_{S_z} e^{-\frac{\pi v}{KLT}S_z^2}}
= -\frac{1}{4LT}\frac{\partial^2}{\partial u^2}\bigg|_{u=0} \ln
\theta\left(e^{-\frac{\pi v}{KLT}},u\right)
\end{eqnarray}
Note, that $\chi_0$ has a simple scaling form as a function of $LT$
\cite{EggertAffleck92}.
The following limiting cases are of interest
\begin{eqnarray}
\label{limits}
\chi_0 &=& \left\{ \begin{array}{ll}
\frac{2}{LT}\exp\left[-\frac{\pi v}{KLT}\right] & LT/v\to 0,\; \mbox{$L$ even} \\[0.2cm]
\frac{1}{4TL} & LT/v\to 0,\; \mbox{$L$ odd} \\[0.2cm]
\frac{K}{2\pi v}\pm \frac{2K^2}{v}\frac{LT}{v}\exp\left(-\pi K\frac{LT}{v}\right) & LT/v\to\infty \; \; .
\end{array} \right.
\end{eqnarray}
Here the plus (minus) sign in front of the second term in the last
line corresponds to L odd (even), respectively. This term represents
the leading finite size correction to the thermodynamic limit result
$\chi_0=K/(2\pi v)$.
In the limit $T/v \ll 1/L$ on the other hand, the susceptibility for a
chain of fixed even length vanishes exponentially because it locks
into its singlet ground state, whereas $\chi_0$ for a chain of odd
length exhibits a $1/T$ divergence due to its doublet ground state.
If we were only interested in the qualitative behaviour we could stop
at Eq.~(\ref{scalechi}), which in some cases is sufficient for
agreement with experimental data \cite{AsakawaMatsuda}. However, the
comparison with quantum Monte Carlo data in Fig.~\ref{scalechifig}
clearly shows sizeable deviations from the scaling limit result.
\begin{figure}
\begin{center}
\includegraphics*[width=0.99\columnwidth]{Fig1.eps}
\caption{The scaling behaviour of the susceptibility as a function of $LT/v$
in Eq.~(\ref{scalechi}) for the isotropic case $\Delta=1, \ K=1, \ v=\pi/2$
(black solid lines) for $L$ even (upper panel) and $L$ odd (lower panel),
respectively. The symbols denote quantum Monte Carlo data for chains of
different lengths, obtained within the SSE loop algorithm framework~
\cite{Sandvik2002}.}
\label{scalechifig}
\end{center}
\end{figure}
For more accurate predictions and the understanding of impurity
corrections it is therefore necessary to take the leading irrelevant
operator into account, which is given by
\cite{Affleck_lesHouches,Lukyanov}
\begin{equation}
\delta H=\lambda\int_0^L dx \,\cos(\sqrt{8\pi K}\phi).
\label{int1}
\end{equation}
The operator $\cos(\sqrt{8\pi K}\phi)$ has scaling dimension $2K$ so
that this perturbation becomes marginally irrelevant at the isotropic
point $K=1$. The next-leading irrelevant operators at zero magnetic
field are of the form $\sim (\partial_x\phi)^4$ and will be neglected
in the following unless it is explicitly stated otherwise. The
coupling strength $\lambda$ has been obtained exactly by Bethe ansatz
\cite{Lukyanov} and is given in a particular normalisation as
discussed in detail later on by
\begin{equation}
\label{B108}
\lambda
=\frac{K\Gamma(K)\sin\pi/K}{\pi\Gamma(2-K)}\left[\frac{\Gamma\left(1+\frac{1}{2K-2}\right)}{2\sqrt{\pi}\Gamma\left(1+\frac{K}{2K-2}\right)}\right]^{2K-2}
\; .
\end{equation}
At the isotropic point $\Delta=1$ ($K=1$) where the interaction (\ref{int1})
becomes marginal the amplitude $\lambda$ as given by (\ref{B108}) vanishes.
Here $\lambda$ has to be replaced by an RG-improved coupling constant, and, in
general, becomes a function of the different scales $T, L$, and $h$. This will
be discussed in detail in section \ref{IsoCase}.
Generally, in systems with boundaries, there may be boundary operators
in addition to bulk interactions. However, as was pointed out in
Ref.~\cite{BrunelBocquet}, in the absence of symmetry-breaking
external fields at boundaries, there are no relevant boundary
operators for the anisotropic Heisenberg chain. The leading
irrelevant boundary operator has scaling dimension $2$ \footnote{Note
that the critical dimension for a boundary operator in $(1+1)$
dimensions is $1$, whereas it is $2$ for bulk operators.} and is of
the form $\delta(x)(\partial_x \phi)^2$ \cite{EggertAffleck92}. This
operator effectively leads to a replacement of the length $L$ of the
system by some effective length $L'$ as will be discussed in the next
section.
\section{Thermodynamics for a finite chain beyond the scaling limit}
\label{general}
To calculate the free energy and susceptibility for an open $XXZ$ chain with
length $L$ at finite temperature $T$ beyond the scaling limit
(\ref{freeE},\ref{scalechi}), the leading correction (\ref{int1}) has to be
taken into account. As this operator is irrelevant for $0\leq\Delta < 1$ it is
sufficient to use perturbation theory. This anisotropic regime will be
considered here.
In first order perturbation theory we obtain
\begin{equation}
\label{delta_f}
\delta f_1 =\frac{\lambda}{L} \int_0^L dx
\left\langle\cos\left(\sqrt{8\pi K}\phi\right)\right\rangle \; .
\end{equation}
This term has been considered in
Refs.~\cite{FujimotoEggert,FurusakiHikihara,SirkerBortzJSTAT} in the
limit $L\to\infty$ and gives the leading contribution to the boundary
free energy. A bulk contribution, i.e.~a term which scales linearly
with $L$ at large $L$, occurs in second order perturbation theory in
$\lambda$ \cite{Lukyanov} (see also \ref{app_A}).
The expectation value can be split into an $S_z$-part (zero mode) and an oscillator part
\begin{eqnarray}
\label{expvalue}
\left\langle \exp\left(\pm\mbox{i}\sqrt{8\pi K}\phi\right)\right\rangle &=& \left\langle
\exp\left(\pm\mbox{i}\sqrt{8\pi K}\phi\right)\right\rangle_{\mbox{\tiny $S_z$}} \left\langle
\exp\left(\pm\mbox{i}\sqrt{8\pi K}\phi\right)\right\rangle_{\mbox{\tiny osc.}} \nonumber \\
& \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! =&
\!\!\!\!\!\!\!\!\!\!\!\!\!\! \left\langle\exp\left(\pm\mbox{i}\sqrt{8\pi K}\phi\right)\right\rangle_{\mbox{\tiny $S_z$}}
\exp\left(-4\pi K\langle\phi\phi\rangle_{\mbox{\tiny osc.}} \right) \, ,
\end{eqnarray}
where we used the cumulant theorem for bosonic modes in the second line. Using
the mode expansion (\ref{ModeExp}) we find
\begin{equation}
\label{Sz-part}
\left\langle \exp\left(\pm\mbox{i}\sqrt{8\pi K}\phi\right)\right\rangle_{\mbox{\tiny $S_z$}} =
\frac{\sum_{S_z}\mbox{e}^{\pm \frac{4\pi i S_z x}{L}}\mbox{e}^{-\frac{\pi
vS_z^2}{KLT}}\mbox{e}^{\frac{hS_z}{T}}}{\sum_{S_z}\mbox{e}^{-\frac{\pi vS_z^2}{KLT}}\mbox{e}^{\frac{hS_z}{T}}}
\end{equation}
and
\begin{equation}
\label{osc1}
\langle\phi\phi\rangle_{\mbox{\tiny osc.}} = \sum_{l=1}^\infty
\frac{\sin^2(\pi lx/L)}{\pi l}\left(1+\frac{2}{\mbox{e}^{\pi vl/(TL)}-1}\right) \; .
\end{equation}
The zero temperature part of (\ref{osc1}) is divergent and we have to
introduce a cutoff $\alpha$ with dimensions of length, of order a
lattice spacing. Doing so and using $\sum_{l=1}^{\infty} z^l/l =
-\ln(1-z)$ for $|z|<1$ leads to
\begin{eqnarray}
\label{osc2}
&&\sum_{l=1}^\infty \frac{\sin^2(\pi lx/L)}{\pi l} \mbox{e}^{-\alpha\pi l/L} =
-\frac{1}{2\pi}\ln(\alpha\pi/L) \\
&+& \frac{1}{4\pi}\ln\left[\left(1-\mbox{e}^{2\pi i
x/L}\mbox{e}^{-\alpha\pi/L}\right)\left(1-\mbox{e}^{-2\pi i x/L}\mbox{e}^{-\alpha\pi/L}\right)\right] \; .\nonumber
\end{eqnarray}
Writing the exponential factor of the finite temperature part in
Eq.~(\ref{osc1}) as a geometric series we find
\begin{eqnarray}
\label{osc3}
&& \frac{1}{\pi}\sum_{l=1}^\infty\sum_{n=1}^\infty
\left(\frac{1}{l}-\frac{\mbox{e}^{2\pi i xl/L}+\mbox{e}^{-2\pi i xl/L}}{2l}\right)\mbox{e}^{-\pi
vnl/(TL)} \nonumber \\
&=&\frac{1}{\pi}\sum_{n=1}^\infty\left\{-\ln\left(1-\mbox{e}^{-\pi v n/(TL)}\right)
\right. \\
&+& \left.\frac{1}{2}\ln\left[\left(1-\mbox{e}^{2\pi i
x/L}\mbox{e}^{-\pi vn/(TL)}\right)\left(1-\mbox{e}^{-2\pi i x/L}\mbox{e}^{-\pi vn/(TL)}\right)\right] \right\}
\; .\nonumber
\end{eqnarray}
Combining Eqs.~(\ref{osc1}, \ref{osc2}, \ref{osc3}) gives
\begin{eqnarray}
\label{osc4}
&&\exp\left\{-4\pi K\langle\phi\phi\rangle_{\mbox{\tiny osc.}} \right\} \\
&=& \left(\frac{\alpha\pi}{L}\right)^{2K}\left[\left(1-\mbox{e}^{2\pi i
x/L}\mbox{e}^{-\alpha\pi/L}\right)\left(1-\mbox{e}^{-2\pi i x/L}\mbox{e}^{-\alpha\pi/L}\right)\right]^{-K}
\nonumber \\
&\times& \prod_{n=1}^\infty\left[\frac{\left(1-\mbox{e}^{2\pi i
x/L}\mbox{e}^{-\pi vn/(TL)}\right)\left(1-\mbox{e}^{-2\pi i x/L}\mbox{e}^{-\pi
vn/(TL)}\right)}{\left(1-\mbox{e}^{-\pi v n/(TL)}\right)^2}\right]^{-2K} \nonumber \\
&=& \left(\frac{2\alpha\pi}{L}\right)^{2K}\left[\left(1-\mbox{e}^{2\pi i
x/L}\mbox{e}^{-\alpha\pi/L}\right)\left(1-\mbox{e}^{-2\pi i x/L}\mbox{e}^{-\alpha\pi/L}\right)\right]^{-K}
\nonumber \\
&\times& \sin^{2K}\left(\frac{\pi x}{L}\right)\frac{\eta^{6K}\left(\mbox{e}^{-\pi
v/(TL)}\right)}{\theta_1^{2K}\left(\frac{\pi x}{L},\mbox{e}^{-\pi v/(2TL)}\right)} \nonumber
\end{eqnarray}
In the last step we have written the oscillator part in terms of the Dedekind
eta-function
\begin{equation}
\label{osc5}
\eta(w) = w^{1/24} \prod_{n=1}^\infty \left(1-w^n\right)
\end{equation}
and the elliptic theta-function of the first kind
\begin{equation}
\label{osc6}
\theta_1(u,q) = 2 q^{1/4}\sin u \prod_{n=1}^\infty \left(1-2q^{2n}\cos 2u
+q^{4n}\right)\left(1-q^{2n}\right) \; .
\end{equation}
From (\ref{Sz-part}) and (\ref{osc4}) we now directly obtain the correction to
the scaling form of the free energy (\ref{freeE})
\begin{eqnarray}
\label{freeEcorr}
\delta f_1 &=&
2\tilde{\lambda}\left(\frac{\pi}{L}\right)^{2K}\!\!\eta^{6K}\left(\mbox{e}^{-\frac{\pi
v}{TL}}\right) \int_0^{1/2} \!\! dy \,\frac{\tilde{g}\left(y,\mbox{e}^{-\frac{\pi
v}{KLT}},e^{\frac{h}{T}}\right)}{\theta_1^{2K}\left(\pi y,\mbox{e}^{-\frac{\pi v}{2TL}}\right)} \nonumber
\\
&\times& 2^{2K}\sin^{2K}\left(\pi y\right)\left[\left(1-\mbox{e}^{2\pi i
y}\mbox{e}^{-\alpha\pi/L}\right)\times \mbox{h.c.}\right]^{-K}
\end{eqnarray}
with
\begin{eqnarray}
\label{freeEcorr2}
\tilde{g}\left(y,q,w\right) &=& \frac{\sum_{S_z} \cos(4\pi S_z y) q^{S_z^2}w^{S_z}}{\sum_{S_z}
q^{S_z^2}w^{S_z}}
\end{eqnarray}
and $\tilde{\lambda} =\alpha^{2K}\lambda$. It is actually
$\tilde{\lambda}$ which is given by Eq.~(\ref{B108}), but we will
identify both in the following. Note, that the integral in
(\ref{freeEcorr}) is convergent for $K<1/2$. In this case the cutoff
$\alpha$ can be dropped in the last line in (\ref{freeEcorr}) which
then becomes equal to one. For $K>1/2$ we can isolate the cutoff
independent part by subtracting the Taylor expand of the integrand up
to sufficient order in $y$, and then take $\alpha\to 0$.
We will discuss this in detail in the following for the correction to the
susceptibility which is readily obtained from (\ref{freeEcorr}) and reads
\begin{eqnarray}
\label{suscicorr}
\delta\chi_1 &=&
\frac{2\lambda}{T^2}\left(\frac{\pi}{L}\right)^{2K}\!\!\eta^{6K}\left(\mbox{e}^{-\frac{\pi
v}{TL}}\right) \int_0^{1/2} \!\!\!\!\!\! dy \,\frac{g_0\left(y,\mbox{e}^{-\frac{\pi
v}{KLT}}\right)}{\theta_1^{2K}\left(\pi y,\mbox{e}^{-\frac{\pi v}{2TL}}\right)} \nonumber
\\
&\times& 2^{2K}\sin^{2K}\left(\pi y\right)\left[\left(1-\mbox{e}^{2\pi i
y}\mbox{e}^{-\alpha\pi/L}\right)\times \mbox{h.c.}\right]^{-K}
\end{eqnarray}
where we have defined a new function for the zero mode part
\begin{eqnarray}
\label{suscicorr2}
\fl g_0\left(y,q\right) &=& -\frac{\sum_{S_z} S_z^2\cos(4\pi S_z y) q^{S_z^2}}{\sum_{S_z}
q^{S_z^2}}
+ \frac{\left(\sum_{S_z} \cos(4\pi S_z y) q^{S_z^2}\right)\left(\sum_{S_z}
S_z^2 q^{S_z^2}\right)}{\left(\sum_{S_z}
q^{S_z^2}\right)^2} \, .
\end{eqnarray}
Because of the modified zero mode part, the integral is now convergent for
$K<3/2$ and the last line can be set equal to one in this case again. For
$3/2<K<5/2$ we can obtain a convergent integral, i.e. the cutoff independent
part, by subtracting just the first non-vanishing order in a Taylor expand in
$y$ and setting $\alpha \to 0$ then. Noting that
\begin{equation}
\label{taylor}
\lim_{y\to 0} \frac{2^{2K}\sin^{2K}\left(\pi y\right)\eta^{6K}\left(\mbox{e}^{-\frac{\pi
v}{TL}}\right)}{\theta_1^{2K}\left(\pi y,\mbox{e}^{-\frac{\pi v}{2TL}}\right)} = 1
\end{equation}
the cutoff independent part of (\ref{suscicorr}) for $3/2<K<5/2$ is given by
\begin{eqnarray}
\label{suscicorr_ind}
\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\delta\chi_1 &=&
\frac{2\lambda}{T^2}\left(\frac{\pi}{L}\right)^{2K}\!\!\!\! \int_0^{1/2} \!\!\!\!\!\!
dy \left\{ \frac{\eta^{6K}\left(\mbox{e}^{-\frac{\pi v}{TL}}\right) g_0\left(y,\mbox{e}^{-\frac{\pi
v}{KLT}}\right)}{\theta_1^{2K}\left(\pi y,\mbox{e}^{-\frac{\pi v}{2TL}}\right)}
\right. - \left. \frac{2 g_2\left(\mbox{e}^{-\frac{\pi v}{KLT}}\right)}{(2\pi y)^{2K-2}} \right\}
\end{eqnarray}
where
\begin{equation}
\label{g2}
g_2\left(q\right) = \frac{\sum_{S_z} S_z^4 q^{S_z^2}}{\sum_{S_z}
q^{S_z^2}} - \frac{\left(\sum_{S_z} S_z^2 q^{S_z^2}\right)^2}{\left(\sum_{S_z}
q^{S_z^2}\right)^2} \, .
\end{equation}
Now we have to add again the first non-vanishing order in the Taylor expand in
$y$ but this time we keep the cutoff $\alpha$ giving us the non-universal
contribution
\begin{equation}
\label{suscicorr_nonuni}
\delta\chi_1^{nu} = \frac{16\pi^2\lambda}{T^2}\left(\frac{\pi}{L}\right)^{2K}
\!\!\!\! g_2\left(\mbox{e}^{-\frac{\pi v}{KLT}}\right) \int_0^{1/2} \!\!\!\!\!\!
\frac{y^2 \, dy}{\left[(2\pi y)^2+\left(\frac{\alpha\pi}{L}\right)^2\right]^K} \; .
\end{equation}
Shifting the upper boundary of integration to infinity, we can evaluate the
integral and find
\begin{equation}
\label{suscicorr_nonuni2}
\delta\chi_1^{nu} = \frac{\pi^{3/2}\lambda}{2T^2L^3}g_2\left(\mbox{e}^{-\frac{\pi v}{KLT}}\right)\frac{\Gamma(K-3/2)}{\Gamma(K)}\alpha^{3-2K} \; .
\end{equation}
The other non-universal correction stems from the irrelevant boundary operator
$\sim\delta(x)(\partial_x\phi)^2$. Including this term into the Hamiltonian
(\ref{H0}) is equivalent to replacing the length by some effective length
$L\to L' \equiv L+a$. Using this effective length in the exponentials in
(\ref{scalechi}) and expanding to lowest order in $a$ yields
\begin{equation}
\label{NonU}
\delta \chi_2 = \frac{\pi va}{KT^2L^3} g_2\left(\mbox{e}^{-\frac{\pi
v}{KLT}}\right) \; .
\end{equation}
We see that this correction has the same form as (\ref{suscicorr_nonuni2}). We
therefore can consider $a$ in (\ref{NonU}) as an effective parameter
incorporating both corrections. In the
thermodynamic limit $g_2\left(\mbox{e}^{-\pi v/(KLT)}\right) \to K^2T^2L^2/(2\pi^2v^2)$ and
$\delta \chi_2 \to Ka/(2\pi v L)$. In this limit we can compare the field
theory result with a recent calculation of the boundary susceptibility based
on the Bethe ansatz \cite{BortzSirker,SirkerBortzJSTAT} leading to
\begin{equation}
\label{NonU3}
a=2^{-1/2}\sin\left[\pi K/(4K-4)\right]/\cos\left[\pi/(4K-4)\right] \; .
\end{equation}
Eq.~(\ref{suscicorr}) for $K<3/2$ or (\ref{suscicorr_ind}) for $K>3/2$ taken
together with (\ref{NonU}, \ref{NonU3}) is therefore a parameter-free result
for the susceptibility of an open chain with length $L$ at temperature $T$ to
first order in the Umklapp scattering. In \cite{SirkerLaflorencie} it has been
shown by comparing with quantum Monte-Carlo data that this formula does
describe the susceptibility of open chains for $L\gtrsim 10$ and $T/J\lesssim
0.1$ very well. Note, however, that the parameter $a$ in (\ref{NonU3}) has
poles at $K=(4n+3)/(4n+2)$, $n=0,1,2,\cdots$ with an accumulation point at
$K=1$. At these special points a contribution stemming from a different
irrelevant operator will also be divergent while having the same dependence on
temperature and length and both terms taken together will give something
finite. In the limit $L\to\infty$ this has been investigated in detail in
Ref.~\cite{SirkerBortzJSTAT}. In particular, it has been shown in this limit
that at $K=3/2$ ($\Delta = 1/2$) the two contributions (\ref{suscicorr}) and
(\ref{NonU}) ``conspire'' to produce a logarithmic temperature dependence of
the boundary susceptibility.
\section{Boundary contributions: The limit $L\to\infty$ with $T/J$ fixed}
\label{boundary}
The boundary free energy can be obtained directly by starting with the
integral (\ref{delta_f}) in the limit $L\to\infty$ and using either boundary
conformal field theory \cite{FujimotoEggert} or the thermodynamic limit result
for the correlation function \cite{FurusakiHikihara,SirkerBortzJSTAT}. Here we
want to show that our more general result (\ref{freeEcorr}) for a finite chain
reduces to the known result in the thermodynamic limit. First, we consider the
limit $L\to\infty$ for the function $\tilde{g}$ in (\ref{freeEcorr2}). For
$x\ll L$ we can replace the sums by integrals and find
\begin{eqnarray}
\label{limit1}
\tilde{g}\left(\frac{x}{L},\mbox{e}^{-\frac{\pi v}{KLT}},e^{\frac{h}{T}}\right) &\approx& \mbox{e}^{-\frac{4\pi
KT}{vL}x^2}\cos\left(\frac{2Khx}{v}\right) \stackrel{L\to\infty}{\to} \cos\left(\frac{2Khx}{v}\right)
\end{eqnarray}
We see that $\tilde{g}$ decays fast away from the boundary. If
$x\sim L$, on the other hand, we can set $x\to L-x$ and because $S_z$ is
integer or half-integer $\cos(4\pi S_z (L-x)/L) = \cos(4\pi S_z x/L)$ and we
get exactly the same result again. In the thermodynamic limit the two
boundaries therefore become independent and each of them yields the same
contribution. To perform the thermodynamic limit for the oscillator part it
is easiest to go back to Eqns.~(\ref{osc1}, \ref{osc2}, \ref{osc3}). We want
to consider here only the case $K<3/2$. In this case the cutoff in the second
line of (\ref{osc2}) can be dropped leading to
\begin{eqnarray}
\label{limit2}
\sum_{l=1}^\infty \frac{\sin^2(\pi lx/L)}{\pi l} \mbox{e}^{-\alpha\pi l/L} &\approx & \frac{1}{2\pi}\ln\left\{\frac{L\left(2-2\cos\left(\frac{2\pi
x}{L}\right)\right)^{1/2}}{\alpha \pi}\right\} \nonumber \\
&\stackrel{L\to\infty}{\to} & \frac{1}{2\pi}\ln\left\{ \frac{2x}{\alpha}\right\} \; .
\end{eqnarray}
Note that $\alpha$ will later be absorbed again into the coupling
constant $\lambda\to\tilde{\lambda}=\alpha^{2K}\lambda$. For the finite
temperature part we can replace the momentum sum in (\ref{osc3}) by an
integral, allowing us to perform the sum over $n$ (``Matsubara sum'') exactly
\begin{eqnarray}
\label{limit3}
&& \frac{1}{\pi}\sum_{n=1}^\infty\sum_{l=1}^\infty
\left(\frac{1}{l}-\frac{\mbox{e}^{2\pi i xl/L}+\mbox{e}^{-2\pi i xl/L}}{2l}\right)\mbox{e}^{-\pi
vnl/(TL)} \nonumber \\
&\to&\frac{1}{\pi}\sum_{n=1}^\infty\int_0^\infty dk\,\left(\frac{1}{k}-\frac{\mbox{e}^{2i
kx}+\mbox{e}^{-2i kx}}{2k}\right)\mbox{e}^{-\frac{vk}{T}n} \nonumber \\
&=& \frac{1}{2\pi}\sum_{n=1}^\infty\ln\left(1+\frac{4T^2x^2}{n^2v^2}\right) =\frac{1}{2\pi}\ln\left(\frac{v}{2\pi T x}\sinh\left(\frac{2\pi Tx}{v}\right)\right) \; .
\end{eqnarray}
Thus we find in the thermodynamic limit
\begin{equation}
\label{delta_f_thermo}
F_B = L\,\delta f_1(L\to\infty) = 2\lambda\int_0^\infty \!\!\!\! dx \; \frac{\cos\left(\frac{2Khx}{v}\right)}{\left[\frac{v}{\pi
T}\sinh\left(\frac{2\pi Tx}{v}\right)\right]^{2K}} \; .
\end{equation}
This is the result obtained previously by boundary conformal field theory
\cite{FujimotoEggert} and by using the result for the correlation function in
the thermodynamic limit in (\ref{delta_f})
\cite{FurusakiHikihara,SirkerBortzJSTAT}. For $K<3/2$ ($\Delta>1/2$) the
integral is convergent and yields \cite{SirkerBortzJSTAT}
\begin{eqnarray}
F_B=\lambda\; {\rm Re}
[B(K+i\frac{Kh}{2\pi T},1-2K)]\left(\frac{2\pi T}{v}\right)^{2K-1}, \label{freeb}
\end{eqnarray}
where $B(x,y)=\Gamma(x)\Gamma(y)/\Gamma(x+y)$. For $K>3/2$ the integral
(\ref{delta_f_thermo}) is divergent and a cutoff has to be introduced
again. Then, the cutoff independent part of the integral is still given by
(\ref{freeb}) whereas the cutoff dependent terms are regular in
$h,T$ \cite{SirkerBortzJSTAT}. In the following discussion we will neglect
these regular terms. From (\ref{delta_f_thermo}) the boundary spin
susceptibility is easily obtained
\begin{eqnarray}
\fl\chi_{\rm B}&=&\biggl.-\frac{\partial^2 F_{B}}{\partial h^2}
\biggr|_{h=0} = - \lambda \left(\frac{K}{v}\right)^2
B(K,1-2K)[\pi^2-2\psi'(K)]\left(\frac{2\pi T}{v}\right)^{2K-3},
\label{chi1}
\end{eqnarray}
with $\psi'(x)=d\psi(x)/dx$.
Note that for $1<K<3/2$ ($1/2<\Delta<1$), the boundary spin
susceptibility $\chi_{\rm B}$ shows a divergent behaviour $\sim 1/T^{3-2K}$,
as temperature decreases.
This anomalous temperature dependence is also observed in the boundary part
of the specific heat coefficient given by,
\begin{eqnarray}
\fl\frac{C_{\rm B}}{T}&=&-\frac{\partial^2 F_{B}}{\partial T^2}
=\lambda \left(\frac{2\pi}{v}\right)^2 (2K-1)(2K-2)B(K,1-2K)\left(\frac{2\pi T}{v}\right)^{2K-3}.
\label{heat1}
\end{eqnarray}
We would like to stress that in the formulas (\ref{chi1}) and (\ref{heat1})
there is no free parameter, and the pre-factors are exactly obtained. These
divergent behaviours are physically understood as follows. In contrast to the
bulk Heisenberg chain in which the ground state is a spin singlet state, spin
singlet formation in the vicinity of boundaries is strongly disturbed. For the
susceptibility, for example, we can write $\chi_B = \int_0^\infty \chi^u_B(x)$
where $\chi^u_B(x)$ follows from (\ref{delta_f_thermo}). Note, that the local
boundary susceptibility has also an alternating part \cite{EggertAffleck95},
which, however, does not contribute to $\chi_B$. A detailed comparison of
numerical data for the local boundary susceptibility (consisting of the
uniform and the alternating part) and field theory has been presented in
Ref.~\cite{BortzSirker}. In Fig.~\ref{Fig_chiB_local}, $\chi^u_B(x)$ is
plotted for various temperatures showing that the spins near the boundary are
more susceptible than the spins in the bulk. It should, however, be emphasised
that the singular behaviours are not due to the presence of boundary
operators, but interpreted as a consequence of finite-temperature corrections
caused by bulk irrelevant interactions.
\begin{figure}
\begin{center}
\includegraphics*[width=0.99\columnwidth]{Fig2.eps}
\caption{The uniform part of the local boundary susceptibility $\chi_B^u(x)$
following from Eq.~(\ref{delta_f_thermo}) for $K=1.2$ at different
temperatures. The boundary susceptibility $\chi_B$ is obtained by
integrating over $\chi_B^u(x)$ leading to a $1/T^{3-2K}$ divergence if
$K<3/2$.}
\label{Fig_chiB_local}
\end{center}
\end{figure}
At zero temperature with a finite magnetic field,
a similar singular behaviour appears in the field dependence of
the boundary spin susceptibility given by,
\begin{eqnarray}
\chi_{\rm B}(T=0)= \lambda\left(\frac{K}{v}\right)^2 \sin(\pi K)
\Gamma(3-2K)\left(\frac{Kh}{v}\right)^{2K-3}. \label{zerospin}
\end{eqnarray}
The zero temperature susceptibility can also be derived from the Bethe ansatz
exact solution by using the Wiener-Hopf method. This has been done in
Ref.~\cite{BortzSirker,SirkerBortzJSTAT} and agrees with the expression
above.
\section{The isotropic case $\Delta = 1$}
\label{IsoCase}
At the isotropic point Umklapp scattering becomes marginal. Instead of
using (\ref{int1}) one can write the marginal perturbation in a
manifestly SU(2) invariant form using the SU(2) current operators. The
perturbation in this formulation becomes
\begin{equation}
\delta H =\int\frac{dx}{2\pi}[g_{\parallel}J_z\bar{J}_z
+\frac{g_{\perp}}{2}(J_{+}\bar{J}_{-}+J_{-}\bar{J}_{+})].
\label{int_iso}
\end{equation}
The small running coupling constants $g_\parallel$, $g_\perp$ fulfil
a set of known Renormalisation Group (RG) equations \cite{Lukyanov,Affleck98}
and are in general functions of the different scales, $T,L$ and $h$,
involved. The perturbation (\ref{int_iso}) can be split into two
parts: $J_z\bar{J}_z \propto \Pi^2-(\partial_x\phi)^2$ and
$J_{+}\bar{J}_{-}+J_{-}\bar{J}_{+} \propto \cos(\sqrt{8\pi}\phi)$. The
first term can be absorbed in the free electron Hamiltonian (\ref{H0})
by a rescaling of the fields $\Pi$ and $\phi$. This leads to a
renormalisation of the Luttinger parameter $K\to
1+g_\parallel/2+\mathcal{O}(g^2)$ (see \ref{app_B} for details). With
this replacement in (\ref{scalechi}) we see that the susceptibility at
the isotropic point in the thermodynamic limit is now given by
\begin{equation}
\label{bulk_iso}
\chi_{\mbox{\tiny bulk}}(T) = \frac{1}{\pi^2} \left( 1+ \frac{g(T)}{2}+\mathcal{O}(g^2)\right) \; ,
\end{equation}
a result first derived in Ref.~\cite{egg94}. The second term leads in
lowest order to a replacement $\lambda\to -g_\perp/4$. More generally,
the results for the anisotropic model derived in the previous sections
have to be expanded in powers of $1-1/K$ and then re-expressed in
terms of the coupling constants $g_\parallel$ and $g_\perp$
\cite{Lukyanov}. For details the reader is referred again to
\ref{app_B}. Here we only want to give the main results.
First, we consider the isotropic limit of our first order result for
the boundary susceptibility (\ref{chi1}). This leads to
\begin{equation}
\label{chiB_iso}
\chi_B^{(1)} = -\frac{g_\perp}{12T}
-\frac{g_\parallel g_\perp}{8T}\left(\frac{1}{2}-\frac{\Psi''(1)}{\pi^2}\right) \, .
\end{equation}
The second order result derived in \ref{app_A} also yields a
contribution in quadratic order in $g$
\begin{equation}
\label{chiB_iso2}
\chi_B^{(2)} \approx \frac{g_\perp^2}{8T}\cdot 0.11 \; .
\end{equation}
Here the factor $0.11$ stems from a numerical evaluation of the
integral in (\ref{A9}) for $K=1$. With $g_\parallel\to g$,
$g_\perp\to -g$ we therefore obtain up to quadratic order in $g$
\begin{equation}
\label{chiB_iso3}
\chi_B = \frac{a}{\pi^2}+\frac{g}{12T}+\frac{g^2}{8T} \left(0.66 -
\frac{\Psi''(1)}{\pi^2}\right) + \mathcal{O}(g^3) \, .
\end{equation}
Here $g=g(T)$ and is given by \cite{Lukyanov}
\begin{equation}
\label{coup_iso}
1/g + \ln(g)/2 = \ln\left(T_0/T\right) \; ,
\end{equation}
with $T_0= \sqrt{\pi/2} e^{1/4+\gamma}$ where $\gamma$ is the Euler
constant. Note, that the scale in the logarithm, $T_0$, is chosen
according to the expansion of the bulk susceptibility. $T_0$ is
non-universal and can be fixed differently to achieve the best
possible agreement with the expansion of the boundary susceptibility
at the isotropic point. However, this is not important for $\chi_B$ as
it only influences sub-leading terms so we keep the scale as set by
the bulk part in order to have a single $g$ in the formula for
$\chi(L,T)$ discussed in the following. A more detailed discussion of
this point is presented in \ref{app_B}.
In addition, we have added a contribution $\sim Ka/(2\pi v)$ to
(\ref{chiB_iso3}) with some constant $a$ stemming from the boundary
operator as in the anisotropic case. However, the constant
(\ref{NonU3}) obtained by Bethe Ansatz in the anisotropic case does
have an accumulation point of singularities at $K=1$ making it
impossible to extract the value at the isotropic point from this
formula. If one considers, on the other hand, the integral for the
boundary susceptibility derived directly by Bethe Ansatz for the
isotropic case (see Eq.~(36) in \cite{BortzSirker}), this task is
difficult as well because the logarithmic contributions coming from
the cut along the imaginary axis completely dominate. Indeed, at
low-temperatures the constant contribution is less important than any
of the logarithmic terms coming from the expansion of $\chi_B$
outlined above. Nevertheless, this constant becomes important again at
higher temperatures (but still $T/J\ll 1$) as in the anisotropic
case. We will therefore use it as a fitting parameter when comparing
to the numerical data in Fig.~\ref{Fig_chiimp}.
\begin{figure}[!htp]
\begin{center}
\includegraphics*[width=0.9\columnwidth]{Fig3.eps}
\caption{Comparison between QMC results (dots) and the field theory result
(\ref{chiB_iso3}). The black solid line corresponds to taking into account
the first order in $g$ term only, the blue dashed line is the result with
the second order term included, and the red dot-dashed line is obtained by
adding a constant $Ka/2\pi v$ with $a=1.5$ ($K=1$, $v=\pi/2$). The QMC data
for $\chi_B$ have been obtained by subtracting the bulk susceptibility known
from Bethe ansatz \cite{egg94} from numerical data for $\chi(L)$. The chain
length $L$ has always been chosen such that $TL/v \gtrsim 4$. In addition,
the susceptibility has been calculated for lengths $L$ and $L+1$ and then
averaged to further reduce finite size effects (see also
Eq.~(\ref{deltaChiB}) and Fig.~\ref{Fig_delta_ChiB} below).}
\label{Fig_chiimp}
\end{center}
\end{figure}
Note, that $a$ now effectively also partly incorporates higher order
logarithmic corrections to (\ref{chiB_iso3}) as well as the constant
coming from the boundary operator. Furthermore, we must in principle
replace $Ka/(2\pi v)\to (a/\pi^2)(1+g/2+g^2/4+\cdots)$ (see
\ref{app_B}). However, because the logs dominate at low temperatures
this merely leads to a small rescaling of $a$ which we will ignore
because $a$ is an ``effective constant'' in any case. Solving
Eq.~(\ref{coup_iso}) we can also write the boundary susceptibility as
\begin{equation}
\label{chiB_logs}
\chi_B =
\frac{1}{12T\ln(T_0/T)}\left(1-\frac{\ln\ln(T_0/T)}{2\ln(T_0/T)}+\cdots\right) \; .
\end{equation}
This means that even in the limit $T/v\gg 1/L$ we find a Curie-like
contribution albeit with a ``Curie constant'' which depends
logarithmically on temperature.
If $T/v$ becomes of order $1/L$ the susceptibility can no longer be
split into a bulk and a boundary contribution. However, we can still
subtract the known bulk contribution and define a quantity
$\delta\chi_{FS}$ as in Eq.~(\ref{deltaf}). In a first approximation,
we can use the thermodynamic limit result for $\chi_B$,
Eq.~(\ref{chiB_iso3}), and add the leading finite size corrections
stemming from the scaling part (second term in the last line of
Eq.~(\ref{limits})). This leads to
\begin{equation}
\label{deltaChiB}
\delta\chi_{FS}(L,T) \approx \chi_B(T) \pm \frac{8L^2T}{\pi^2}(1+g)\exp[-2LT(1+g/2)]
\end{equation}
where the plus (minus) sign refers to chains of odd (even) length and
we have replaced $K\to 1+g/2$ with $g$ determined by
Eq.~(\ref{coup_iso}). A comparison between this formula and QMC data
is shown in Fig.~\ref{Fig_delta_ChiB}.
\begin{figure}[!htp]
\begin{center}
\includegraphics*[width=0.9\columnwidth]{Fig4.eps}
\caption{QMC data for the susceptibility $\delta\chi_{FS}$ at temperature
$T=J/30$ as a function of chain length. These data have been obtained by
subtracting the bulk susceptibility known from Bethe ansatz \cite{egg94}
from numerical data for $\chi(L)$. The red squares (blue circles) correspond
to even (odd) chain length, respectively. The lines represent the
approximation (\ref{deltaChiB}).}
\label{Fig_delta_ChiB}
\end{center}
\end{figure}
Note, that Eq.~(\ref{deltaChiB}) implies an almost perfect cancelation of finite
size corrections when calculating the susceptibility for lengths $L$ and $L+1$
and then taking the average. This property has been used to improve the
numerical data for $\chi_B$ presented in Fig.~\ref{Fig_chiimp}.
To obtain the result for $\chi(L,T)$ at the isotropic point in
general, we have to consider both parts of the perturbation
(\ref{int_iso}): First, we have to replace $K\to 1+g/2$ in the
exponentials of (\ref{scalechi}). For the correction (\ref{suscicorr})
we can only obtain a result to first order in $g$ because we do not
know the analytical solution of the integral and therefore cannot
easily expand it around $K=1$. The result to first order in $g$ is
readily obtained by just replacing $\lambda\to g/4$ and evaluating the
integral for $K=1$. Now, however, the running coupling constant $g$
depends on two scales: the length $L$ and temperature $T$. There is no
general solution of the renormalisation group equations if two
different scales are involved. At low enough energies, however, the
smaller length scale will always dominate and the running coupling
constant becomes \cite{Lukyanov}
\begin{equation}
\label{coup_iso2}
1/g + \ln(g)/2 = \ln\left(\sqrt{2/\pi} e^{1/4+\gamma}\mbox{min}[L,v/T]\right) \; .
\end{equation}
In addition, the constant $a$ stemming from the boundary operator is
still present and we will use it again as a fitting parameter. Note,
that $a$ now will be different from the one obtained by fitting the
numerical data for $\chi_B$ as it also partly incorporates the
logarithmic terms now taken into account only to lowest order.
To summarise, the susceptibility for the isotropic case is given by
$\chi(L,T) = \chi_0+\delta\chi_1$ with the replacements $K\to
1+g(L,T)/2+a/L$ in the exponentials of (\ref{scalechi}) and
$\lambda\to g(L,T)/4$ in (\ref{suscicorr}). A comparison between this
formula and QMC data for chains of different lengths is shown in
Fig.~\ref{Fig_iso_compare}.
\begin{figure}[!htp]
\begin{center}
\includegraphics*[width=0.9\columnwidth]{Fig5.eps}
\caption{Comparison for $\Delta=1$ between QMC results (symbols) and
the field theory result (lines) with $a=4$ for chains of different
length $L$.}
\label{Fig_iso_compare}
\end{center}
\end{figure}
Here we find that $a\approx 4$ works best describing the numerical
data over a wide temperature range and for different even and odd
chain lengths very accurately.\footnote{In \cite{SirkerLaflorencie} we
used $a=5.8$. This difference is due to the fact that in this
article we expanded in $a$, i.e., we used (\ref{NonU}) as well as a
second order solution for (\ref{coup_iso}). Here we put $a$ directly
into the exponentials of (\ref{scalechi}) and solve (\ref{coup_iso})
numerically.}
The disadvantage of this formula for $\chi(L,T)$ is, that the integral
in (\ref{suscicorr}) has to be evaluated numerically for each length
and temperature considered. In the next section we will derive a much
simpler formula in the limit $T/J\ll 1/L$. We find empirically that
this formula describes the susceptibility over a much larger range of
temperatures than anticipated making it useful to fit experimental
data without the necessity to evaluate the integral in
(\ref{suscicorr}) and without having a free fit parameter.
\section{The ground state limit: $LT/v\to 0$}
\label{ground_state}
Next, we want to consider the limit $LT/v\to 0$. We have already shown
in Eq.~(\ref{limits}) that the scaling part of the susceptibility
shows a Curie-like divergence if the chain length is odd and an
exponentially suppressed behaviour if it is even. For the first order
correction (\ref{suscicorr}) we will concentrate again on the case
$K<3/2$ where the cutoff can be dropped. In the limit $LT/v\to 0$ we
find $\eta\left(\mbox{e}^{-\frac{\pi v}{TL}}\right) \to \mbox{e}^{-\frac{\pi v}{24TL}}$,
$\theta_1\left(\pi y,\mbox{e}^{-\frac{\pi v}{2TL}}\right) \to 2 \mbox{e}^{-\frac{\pi
v}{8TL}}\sin(\pi y)$ and
\begin{equation}
g_0\left(y,\mbox{e}^{-\frac{\pi v}{KTL}}\right)\to \left\{\begin{array}{cc}
0 & \mbox{L odd} \\[0.3cm]
-2\cos(4\pi y)\mbox{e}^{-\frac{\pi v}{KTL}} + 2\mbox{e}^{-\frac{\pi v}{KTL}} & \mbox{L
even}
\end{array}
\right.
\end{equation}
Here we have expanded $g_0$ only to first power in the small parameter
$\mbox{e}^{-\frac{\pi v}{KTL}}$. For $L$ odd the first non-vanishing contribution is
second order. As the scaling part shows a power-law divergence in this case,
any exponentially small corrections can be safely neglected in any case. For
$L$ even, on the other hand, they are important as the scaling part is also
exponentially small. In the even case we can now evaluate the integral and
find
\begin{equation}
\delta\chi_1(LT/v\to 0) = \left\{\begin{array}{cc}
0 & \mbox{L odd} \\[0.3cm]
\frac{2\lambda}{T^2}\left(\frac{\pi}{L}\right)^{2K}\frac{\Gamma(3-2K)}{\Gamma(2-K)\Gamma(3-K)}\mbox{e}^{-\frac{\pi
v}{KTL}}& \mbox{L
even}
\end{array}
\right.
\end{equation}
Finally, lets consider the contribution $\delta\chi_2$. For $L$ odd
$g_2(\mbox{e}^{-\frac{\pi v}{KLT}})\to 0$ in lowest order whereas
$g_2(\mbox{e}^{-\frac{\pi v}{KLT}})\to 2\mbox{e}^{-\frac{\pi v}{KLT}}$ for $L$ even. This
leads to
\begin{equation}
\delta\chi_2 = \left\{\begin{array}{cc}
0 & \mbox{L odd} \\[0.3cm]
\frac{2\pi v}{K T^2L^3}\mbox{e}^{-\frac{\pi v}{KTL}}\cdot a & \mbox{L
even}
\end{array}
\right.
\end{equation}
For the susceptibility in the limit $LT/v\to 0$ we therefore find
\begin{equation}
\label{our_formula}
\chi(LT\to 0) = \left\{\begin{array}{cc}
\frac{1}{4LT} & \mbox{L odd} \\[0.3cm]
\frac{2}{LT}\mbox{e}^{-\frac{\pi
v}{KTL}}\left[1+\lambda\frac{\beta \pi^{2K}}{L^{2K-1}T}+\frac{\pi
v}{KL^2T}a\right] & \mbox{L
even}
\end{array}
\right.
\end{equation}
where $\beta = \Gamma(3-2K)/[\Gamma(2-K)\Gamma(3-K)]$. So corrections to the
scaling limit result in first order in $\mbox{e}^{-\frac{\pi v}{TL}}$ are only
present in the case of even chain length. However, even in this case these
corrections are suppressed by additional powers of $1/(LT)$. So one might
think that Eq.~(\ref{our_formula}) is of purely academic interest. However, as
we will show below, it enables us to derive a simple formula for the
susceptibility of the isotropic chain which works over a much larger range of
temperatures and lengths than anticipated.
In the isotropic case we have to replace $K\to 1+g_\parallel(L)/2$ in
the scaling part (\ref{scalechi}).
Furthermore $\lambda\to -g_\perp(L)/4$, so that (\ref{our_formula}) at
the isotropic point reads
\begin{equation}
\label{our_formula_iso}
\fl \chi(LT\to 0) = \left\{\begin{array}{cc}
\frac{1}{4LT} & \mbox{L odd} \\[0.3cm]
\frac{2}{LT}\mbox{e}^{-\frac{\pi^2}{2TL}}\left[1+\frac{\pi^2}{4LT}g_\parallel(L)-\frac{\pi^2}{4LT}g_\perp(L)+\frac{\pi^2}{2L^2T}a\right] & \mbox{L
even}
\end{array}
\right.
\end{equation}
where $v=\pi/2$ has been employed. Note that with $g_\parallel \to g$,
$g_\perp \to -g$ the replacement $K\to 1+g_\parallel(L)/2$ in the
scaling part and the first order contribution in $\lambda\to
-g_\perp(L)/4$ both produce exactly the same correction
$\frac{\pi^2}{4LT}g(L)$ in the brackets in
(\ref{our_formula_iso}). Here $g(L)$ is given by (\ref{coup_iso}) with
$L$ being the relevant scale in this limit. We want to stress that
both terms yielding exactly the same contribution in the limit
considered here contribute very differently in the thermodynamic
limit. Whereas the $g_\parallel$-part leads to a correction to the
bulk susceptibility, the $g_\perp$-part determines the boundary
susceptibility.
Ignoring the contribution $\sim a$ which comes from the boundary
operator and is suppressed by an additional power of $L$ we can
therefore obtain exactly the same expansion by replacing $1/K\to
1-g(L)$ in the exponentials of (\ref{scalechi}). I.e., we can absorb
the first order correction $\delta\chi_1$ into the scaling form. This
leads to the formula
\begin{equation}
\label{Seb-formula}
\chi =\frac{1}{LT} \frac{\sum_{S_z} S_z^2 \exp\left[-\frac{\pi^2}{2LT}(1-g(L))S_z^2\right]}{\sum_{S_z} \exp\left[-\frac{\pi^2}{2LT}(1-g(L))S_z^2\right]} \, .
\end{equation}
This formula should be valid in the limit $LT/v\to 0$ when only the ground
state and the lowest excited states contribute to the sum over $S_z$. One
easily verifies that Eq.~(\ref{our_formula_iso}) is indeed reproduced in this
limit: For $L$ odd we take only the states $S_z=\pm 1/2$ into account and the
correction $1-g(L)$ cancels out. For $L$ even we consider the ground state
$S_z=0$ and the first excited state $S_z=\pm 1$. Expanding in $g(L)$ then
leads to (\ref{our_formula_iso}).
So starting from our general result for the susceptibility of finite open
chains we have found that the correction to the excitation energy of the
lowest excited states with $S_z\pm 1$ in the isotropic case is given by $E\to
(\pi v/L)[1-g(L)]$. This agrees with the findings in Ref.~\cite{AffleckQin}.
Corrections to higher excited states are not of such simple form, and, in
general, it is therefore not possible to absorb these corrections into the
scaling part.
Empirically, however, we find that (\ref{Seb-formula}) works quite well over a
much larger range of lengths and temperatures than one might anticipate. In
Fig.~\ref{Fig_comp_SFormula} we compare this formula again to QMC data.
\begin{figure}[!htp]
\begin{center}
\includegraphics*[width=0.9\columnwidth]{Fig6.eps}
\caption{Comparison for $\Delta = 1$ between QMC results (dots) and
the field theory result (\ref{Seb-formula}) in the limit $LT/v\to 0$
(lines).}
\label{Fig_comp_SFormula}
\end{center}
\end{figure}
Although the agreement at higher temperatures where the susceptibility
becomes constant is not perfect, the errors in this region are only
about $3\%$.
\section{The averaged susceptibility and the effective Curie constant}
\label{avg_susci}
In this section we want to discuss the averaged susceptibility of the
isotropic Heisenberg chain for a concentration of chain breaks $p$ as
defined in Eq.~(\ref{chi_p}). Here we have assumed that we have a
completely random (Poisson) distribution of impurities. However, we
could obtain $\chi_p$ for any other distribution as well. $\chi_p$ can
be calculated by using our field-theory results in section
\ref{IsoCase} for $L\gtrsim 10$ and $T/J\lesssim 0.1$ in combination
with exact diagonalisation or QMC results for shorter chains. This
method has been used in Ref.~\cite{SirkerLaflorencie} to analyse
susceptibility data for Sr$_2$Cu$_{1-x}$Pd$_x$O$_{3+\delta}$
\cite{Kojima}. Based on our analysis of the limits $LT/v\to 0$ and
$LT/v\to\infty$ in the previous sections we want to derive here a
simple formula which allows to determine the concentration of chain
breaks by fitting the measured susceptibility.
We have seen that there are no corrections to the scaling limit result in the
limit $LT/v\to 0$ for odd chains. For even chains the susceptibility is
exponentially small in this limit in any case so that even chain segments
practically do not contribute to the average in (\ref{chi_p}). In the opposite
limit we can write $\chi(L)=L\chi_{\mbox{\tiny bulk}} +\chi_B$. We now assume
that the crossover occurs at some length $L_c=\gamma J/T$ where $\gamma$ is a
crossover parameter which we expect to be of order one. For the average
susceptibility we can therefore write
\begin{eqnarray}
\label{fit_formula}
\fl \chi_p &\approx& \frac{p^2}{4T}\sum_{L\; \mbox{\tiny odd}}^{L_c}(1-p)^L +
p^2\sum_{L_c}^\infty (L\chi_{\mbox{\tiny bulk}}+\chi_B) (1-p)^L \\
\fl &=& \frac{p}{4T}\frac{1-p}{2-p}\left(1-(1-p)^{\gamma/T}\right)+(1-p)^{\gamma/T}\left[\left(1-p+\frac{p\gamma}{T}\right)\chi_{\mbox{\tiny bulk}}+p\chi_B\right] \nonumber
\end{eqnarray}
and we use the field theory result for the bulk susceptibility \cite{Lukyanov}
\begin{equation}
\label{bulk_thermo}
\chi_{\mbox{\tiny bulk}} = \frac{1}{\pi^2}\left(1+\frac{g(T)}{2}+\frac{3g^3(T)}{32}+\sqrt{3}{\pi}T^2\right)
\end{equation}
where the $T^2$-term stems from the irrelevant operators with scaling
dimension $4$. The boundary susceptibility $\chi_B$ is given by
(\ref{chiB_iso3}) with $a=1.5$ as in Fig.~\ref{Fig_chiimp}.
\begin{figure}[!htp]
\begin{center}
\includegraphics*[width=0.9\columnwidth]{Fig7.eps}
\caption{$T\chi_p$ for $p=0.01,0.03,0.05,0.07,0.1$ from bottom
to top. The black dots are obtained by using QMC data for $\chi(L)$ and the
lines represent the fitting formula (\ref{fit_formula}) with
$\gamma=1$.}
\label{Fig_AvgSusci}
\end{center}
\end{figure}
A comparison between QMC data for $\chi_p$ and (\ref{fit_formula})
with $\gamma=1$ for various impurity concentrations is shown in
Fig.~\ref{Fig_AvgSusci}.
The impurity part and an effective Curie constant $C$ can then be
defined according to Eq.~(\ref{chi_p}) by
\begin{equation}
\label{Curie_constant}
p\delta\bar{\chi}_{FS} =\chi_p-(1-p)\chi_{\mbox{\tiny bulk}} =p\frac{C}{T} \; .
\end{equation}
This effective Curie constant is shown in Fig.~\ref{Fig_Curie}.
\begin{figure}[!htp]
\begin{center}
\includegraphics*[width=0.9\columnwidth]{Fig8.eps}
\caption{The effective Curie constant as defined in Eq.~(\ref{Curie_constant})
for $p=0.01,0.03,0.05,0.07,0.1$ (from bottom
to top) as a function of $T/p$.}
\label{Fig_Curie}
\end{center}
\end{figure}
Note, that only in the extreme low-temperature limit the usual Curie
constant $C\to 1/4\cdot (1-p)/(2-p)\approx 1/8$ (half of the chains
contribute a Curie constant of $1/4$ for $p\ll 1$) is
recovered. However, $C(2-p)/(1-p)$ as a function of $T/p$ shows an
almost perfect collapse (scaling) for different impurity
concentrations if $T/p\lesssim 1/2$. At higher temperatures this
scaling no longer holds because the boundary contribution $\chi_B$ is
not a scaling function in $T/p$. The non-trivial temperature
dependence of the effective Curie constant, in particular the finite
temperature minimum, and the scaling at temperatures $T\lesssim p/2$
provide a way to test this scenario experimentally.
\section{Inter- and Intrachain couplings}
\label{seg-couplings}
In any real system there are residual couplings between the chain
segments in the principal chain direction (intrachain couplings). In
addition, there are also perpendicular couplings between the chains
(interchain couplings) which at low enough temperatures will destroy
the one dimensionality of the system and usually induce some sort of
magnetic order. In Sr$_2$CuO$_{3}$, for example, the nearest-neighbour
Heisenberg coupling along the chain direction (b-axis) is estimated to
be $J\sim 2200$ K whereas the couplings along the other axis are
orders of magnitude smaller ($J_a\sim 5$ K, $J_c\sim 10^{-3}$ K)
\cite{MotoyamaEisaki}. Furthermore, it has been pointed out that the
next-nearest-neighbour coupling along the chain direction is probably
not that small, $J_2\sim 140$ K \cite{RosnerEschrig}. This irrelevant
coupling will only cause small corrections to the susceptibility of an
isolated chain segment by changing the marginally irrelevant coupling
constant $\lambda$. However, it induces a coupling between different
chain segments even when the nearest-neighbour exchange $J$ is absent
due to a non-magnetic impurity. Note, that there is no frustration in
this case and $J_2$ just acts as an effective coupling $J'$ between
the chain ends as shown in Fig.~\ref{Fig_2chains}.
\begin{figure}[!htp]
\begin{center}
\includegraphics*[width=0.9\columnwidth]{Fig9.eps}
\caption{Two chain segments with length $L_1$ and $L_2$, respectively, coupled
by a weak intrachain coupling $J'\ll J$.}
\label{Fig_2chains}
\end{center}
\end{figure}
Although the next-nearest neighbour coupling across an impurity can
differ from the one across a magnetic ion, we will assume that it is
still of the same order of magnitude, i.e., $J'\sim J_2$.
The susceptibility of the weakly coupled chains is given by
\begin{equation}
\label{intra_coup1}
\chi = \frac{1}{LT}\left\langle \left(\sum_{i=1}^{L_1} S_{1i}^z + \sum_{j=1}^{L_2}
S_{2j}^z\right)^2 \right\rangle
\end{equation}
with $L=L_1+L_2$. Here $ S_{1i}^z$ ($S_{2j}^z$) denotes the
$z$-component of the spin on chain 1 (2) at site $i$ ($j$),
respectively. For $J'\ll J$ we can treat this coupling using
perturbation theory. In zeroth order this lead to $\chi^{(0)} =
(L_1\chi_1^{(0)} + L_2\chi_2^{(0)})/L$. In first order only the
longitudinal part of the coupling contributes and we obtain
\begin{eqnarray}
\label{intra_coup2}
\delta\chi &=& -\frac{2J'}{LT^2}\left\langle \sum_{i=1}^{L_1} S^z_{1i}
S^z_{11}\right\rangle\left\langle \sum_{j=1}^{L_2} S^z_{2j} S^z_{21}\right\rangle
\nonumber \\
&=& -\frac{2J'}{LT^2} \left\langle S^z_{1\mbox{\tiny tot}}
S^z_{11}\right\rangle\left\langle S^z_{2\mbox{\tiny tot}} S^z_{21}\right\rangle = -\frac{2J'}{L}\chi_{11}\chi_{21}
\end{eqnarray}
where $\chi_{l1} =\partial < S^z_{l1} >/(\partial h)$ is the
susceptibility of the boundary spin $S^z_{l1}$ and $S^z_{l\mbox{\tiny
tot}}=\sum_{i=1}^{L_l}S^z_{li}$ ($l=1,2$), respectively. The extra
factor of 1/T arises due to time-translational invariance and the
imaginary time integral in the first order perturbation theory
formula. Because of the broken spatial-translational invariance, the
local susceptibility is position dependent and the boundary spins are
more susceptible than the spins deep inside the chain. These effects
have been studied in detail in Refs.~\cite{EggertAffleck95,
BortzSirker}. As we are here just interested in an order of
magnitude estimate of the effect of intrachain coupling on $\chi_p$ we
can replace the susceptibility of the boundary spin $\chi_{l1}$ by the
average susceptibility per site $\chi_l^{(0)}$. This leads to
$\delta\chi \approx -2(J'/L)\chi_1^{(0)}\chi_2^{(0)}$. Assuming
further that for an impurity concentration $p$ all chain segments have
length $L\sim 1/p$ we find
\begin{equation}
\label{intra_coup3}
\delta\chi_p \sim J'p\chi_p^2 \; .
\end{equation}
At $T\ll pv$ we have $\chi_p\sim p/(8T)$. The correction
(\ref{intra_coup3}) therefore becomes of order $\chi_p$ at $T\sim J'
p^2$.\footnote{Note that there is a factor $p$ missing in
Ref.~\cite{SirkerLaflorencie}.} For temperatures $T\gg J'p^2$ intrachain
coupling can therefore be neglected.
Although first order perturbation theory can give us the temperature scale
where intrachain coupling becomes important, it is not sufficient once this
scale is approached. This can be seen by a scaling analysis. We have
$S^z\sim\partial_x\phi$ with scaling dimension one. In $n$-th order
perturbation theory in the intrachain coupling $J'$, the longitudinal part of
the coupling therefore yields $\chi^{(n)}\sim (TL)^{-1}(J'/TL^2)^n$. We can
therefore write the susceptibility in scaling form
\begin{eqnarray}
\label{intra_coup4}
\chi &\sim&
\frac{1}{LT}\left(1+\frac{J'}{L^2T}+\frac{J'^2}{L^4T^2}+\frac{J'^3}{L^6T^3}+\cdots\right)
\; .
\end{eqnarray}
Replacing again $L\sim 1/p$ we find for the averaged susceptibility
\begin{eqnarray}
\label{intra_coup5}
\chi_p&\sim&
\frac{p}{T}\left(1+\frac{J'p^2}{T}+\left(\frac{J'p^2}{T}\right)^2+\left(\frac{J'p^2}{T}\right)^3+\cdots\right)
\; .
\end{eqnarray}
This means that at temperatures where intrachain coupling $J'$ can no longer
be neglected, $T\sim J' p^2$, perturbation theory in $J'$ breaks down. At
temperatures $T\ll J' p^2 < Jp$, on the other hand, we can obtain an effective
model by replacing all segments of odd length by $S=1/2$ spins. The couplings
between these effective $S=1/2$ will then be random with a very broad
distribution. According to Fisher \cite{Fisher_IRFP} we might therefore expect
that a system of weakly coupled chain segments renormalises at very low
temperatures to the infinite random fixed point. In any realistic system,
however, there will be also interchain couplings between the chain segments
preventing the system from reaching this fixed point.
An interchain coupling between two chain segments is shown in
Fig.~\ref{Fig_interchain}.
\begin{figure}[!htp]
\begin{center}
\includegraphics*[width=0.9\columnwidth]{Fig10.eps}
\caption{Two chain segments with length $L_1$ and $L_2$, respectively, have an
overlap of $n$ sites and are coupled by an interchain coupling $\tilde{J}$.}
\label{Fig_interchain}
\end{center}
\end{figure}
In first order perturbation theory we obtain in this case
\begin{eqnarray}
\label{intra_coup6}
\fl\delta\chi^{(1)} &=& -\frac{2\tilde{J}}{LT^2}\sum_{k=1}^n\left\langle \sum_{i=1}^{L_1} S^z_{1,i}
S^z_{1,k}\right\rangle\left\langle \sum_{j=1}^{L_2} S^z_{2,j} S^z_{2,n+1-k}\right\rangle
\\
\fl &=& -\frac{2\tilde{J}}{LT^2} \sum_{k=1}^n\left\langle S^z_{1\mbox{\tiny tot}}
S^z_{1,k}\right\rangle\left\langle S^z_{2\mbox{\tiny tot}} S^z_{2,n+1-k}\right\rangle =
-\frac{2\tilde{J}}{L}\sum_{k=1}^n\chi_{1,k}\chi_{2,n+1-k} \nonumber
\end{eqnarray}
where $\chi_{l,k}$ denotes the local susceptibility of the $l$-th chain at site
$k$. To simplify matters, we consider the case of two chains with equal
lengths $L_1=L_2=L$ which completely overlap, i.e., $n=L$. In this case
Eq.~(\ref{intra_coup6}) becomes
\begin{equation}
\label{intra_coup6b}
\delta\chi^{(1)} = -\frac{2\tilde{J}}{L}\sum_{k=1}^L\chi_{1,k}\chi_{2,k} \: .
\end{equation}
At $T\ll pv$ we can again set $\chi_{1,k}\sim \chi_p\sim p/T$ which leads to
$\delta\chi^{(1)}_p \sim \tilde{J}p^2/T^2$. This becomes of order $\chi_p$ at
temperatures $T\sim \tilde{J}p$. As $\tilde{J}$ is of order of the N\'eel
temperature $T_N$ this scale is completely irrelevant. However, for a system
with open boundaries the local susceptibility has also a staggered part
\cite{EggertAffleck95,EggertAffleckHorton} which will contribute to
(\ref{intra_coup6b}). This is a consequence of the $S^z$-operator having a
staggered part, $S^z_{k,st.} \sim c(-1)^k \cos\sqrt{2\pi}\phi$, where $c$ is a
constant. For a chain with odd length in the ground state limit, $T\ll 1/L$,
we find \cite{EggertAffleckHorton}
\begin{eqnarray}
\label{intra_coup6c}
\fl \chi_k^{st.} &=& \frac{1}{T}\langle S^z_{tot} S^z_{k,st.}\rangle \approx
\frac{1}{T} \sum_{\pm} \langle \pm | S^z_{tot} S^z_{k,st.} | \pm \rangle \approx (-1)^k\frac{c}{T} \sqrt{\frac{\pi}{2L}\sin\frac{\pi k}{L}}
\end{eqnarray}
where $|\pm\rangle$ is the ground state with $S^z_{tot}=\pm 1/2$,
respectively. This leads to $\delta\chi^{(1)}\sim \tilde{J}/(LT^2)\sim
\tilde{J}p/T^2$ and therefore dominates compared to the contribution
originating from the uniform part of the local susceptibility. It becomes of
order $\chi_p$ at temperatures $T\sim \tilde{J}$.
Finally, we want to consider the ``clean limit'', $T\gg pv$. In this case, the
N\'eel temperature $T_N$ can be determined by treating the interchain coupling
in mean field theory. This leads to the well known condition
\begin{equation}
\label{intra_coup7}
z\tilde{J}\chi_{st}(T_N) = 1
\end{equation}
where $\chi_{st}$ is the staggered susceptibility, i.e., the staggered
response to the effective staggered field originating from the other
chains and $z$ is the coordination number. Because $\chi_{st}(T)\sim
1/T$ we obtain that $T_N\sim \tilde{J}$. The same condition for the
breakdown of one-dimensionality in this limit is obtained by
considering the contribution of the staggered part of the
$S^z$-operator to the susceptibility in second order perturbation
theory in the interchain coupling.
We therefore conclude that our results for the averaged susceptibility
$\chi_p$ in the previous sections are applicable as long as $T\gg
\mbox{Min}(\tilde{J},p^2J')$.
\section{Experimental situation}
\label{experiment}
The best known realisation of the spin-$1/2$ Heisenberg chain is
Sr$_2$CuO$_3$. Here copper is in a 3d$^9$ configuration and has spin $1/2$.
The Heisenberg couplings between these spins are spatially very anisotropic as
already mentioned in the previous section. For $T\gg J_a\sim 5$ K interchain
coupling can therefore be neglected and the magnetic properties are described
by the one-dimensional isotropic Heisenberg model.
The doped compound Sr$_2$Cu$_{1-x}$Pd$_x$O$_3$ has been studied by Kojima {\it
et al} \cite{Kojima}. Here palladium has spin zero and therefore serves as a
non-magnetic impurity. Impurity concentrations from $x=0.5\%$ up to $x=3\%$
have been studied. This means that $x^2J_2$ with $J_2\sim 140$ K is small even
compared to $J_a$. In this material the limit where our theory is applicable
is therefore set by the interchain coupling, $T\gg J_a\approx 5$ K.
The theoretical analysis of the susceptibility measurements on
Sr$_2$Cu$_{1-x}$Pd$_x$O$_3$ is hampered by the fact that even the pure
system Sr$_2$CuO$_3$ already shows Curie-like contributions at low
temperatures \cite{AmiCrawford,MotoyamaEisaki}. It has been observed
that these contributions can be significantly reduced by annealing and
two explanations have been offered: Excess oxygen might be present in
the as grown compound. Most likely, each excess oxygen would then
dope two holes into the chain leading to two Zhang-Rice singlet type
states as in the high-$T_c$ compounds. Assuming that these holes are
relatively immobile, they effectively act as chain breaks. In this
scenario the Curie-type contribution in the ``pure compound'' is
caused by the mechanism described in this paper. Indeed, it has been
shown \cite{SirkerLaflorencie} that the susceptibility data for the as
grown crystal sample in \cite{MotoyamaEisaki} can be well described by
assuming a concentration of chain breaks, $p=0.6\%$. For the powder
samples studied by Ami {\it et al.} \cite{AmiCrawford} an alternative
explanation was proposed by Hill {\it et al.} based on the observation
that Sr$_2$CuO$_3$ decomposes into Sr$_2$Cu(OH)$_6$ under exposure to
air and water \cite{HillJohnston}. The copper spins-$1/2$ in
Sr$_2$Cu(OH)$_6$ are only weakly coupled according to Hill {\it et
al.} and can therefore induce a true Curie contribution as opposed
to the more complicated behaviour expected in the chain break
scenario. It is, however, hard to see how this could also explain the
Curie-like contributions observed on single crystals by Motoyama {\it
et al.} \cite{MotoyamaEisaki}. We therefore believe that the excess
oxygen scenario is the most plausible explanation in this case.
The Sr$_2$Cu$_{1-x}$Pd$_x$O$_3$ samples investigated by Kojima {\it et
al.}~have not been annealed so that we expect chain breaks due to excess
oxygen in addition to the once caused by palladium. Furthermore, it can
certainly not be excluded that there are indeed additional true paramagnetic
impurity contributions caused by decomposition or other mechanisms. This makes
a thorough theoretical analysis very difficult. In \cite{SirkerLaflorencie}
such an analysis has been performed under the assumptions that true
paramagnetic Curie contributions can be neglected and that excess oxygen will
lead to immobile holes acting as additional chain breaks. The measured
susceptibility $\chi^{\mbox{\tiny exp.}}$ then consists of a temperature
independent part $\chi'$ due to core diamagnetism and Van Vleck paramagnetism
and $\chi_p$ coming from the Heisenberg chains with impurity concentration
$p$. Here $p=x+\delta$ has to be considered as a fitting parameter consisting
of the nominal palladium concentration $x$ and the concentration of additional
chain breaks $\delta$ due to excess oxygen. A best fit of the experimental
data was obtained in \cite{SirkerLaflorencie} with the two parameters $p$,
$\chi'$ as displayed in Table \ref{tab1}.
\begin{table}[htbp]
\caption{Concentration $x$ of Pd ions in experiment compared to impurity
concentration $p$ and constant contribution $\chi'$ yielding the best
theoretical fit. The first line corresponds to the ``as grown'' sample of Sr$_2$CuO$_{3}$ from
Ref.~\cite{MotoyamaEisaki}.}
\label{tab1}
\hspace*{0.2cm}
\begin{center}
\begin{tabular}{ccc}
\multicolumn{1}{c}{$x$ (Exp.)} &\multicolumn{1}{c}{$p$ (Theory)}
&\multicolumn{1}{c}{$\chi'$ [emu/mol]} \\
\hline\\[-0.3cm]
$0.0$ & $0.006$ & $-7.42\times 10^{-5}$ \\
$0.005$ & $0.012$ & $-7.7\times 10^{-5}$ \\
$0.01$ & $0.014$ & $-7.5\times 10^{-5}$ \\
$0.03$ & $0.024$ & $-7.5\times 10^{-5}$
\end{tabular}
\end{center}
\end{table}
For the sample with a nominal Pd concentration of $3\%$ our best
fields has yielded $p=2.4\%$, i.e., less than the nominal
concentration. One might speculate that the Pd ions cluster or that
part go in at interstitial positions instead of replacing Cu ions thus
reducing the number of chain breaks created.
Here we want to go one step further and compare the effective Curie
constant extracted from the experimental data
\begin{equation}
\label{Curie_exp}
C^{\mbox{\tiny exp.}} = \frac{T}{p}\left[\chi^{\mbox{\tiny exp.}}-\chi' - (1-p)\chi_{{\mbox{\tiny bulk}}}\right]
\end{equation}
with the theoretical prediction. We will use the same values for the
concentration of chain breaks $p$ and the constant contribution to the
susceptibility $\chi'$ as in Table \ref{tab1}. For $\chi_{\mbox{\tiny bulk}}$ we employ the
field theoretical result (\ref{bulk_thermo}). The result is shown in
Fig.~\ref{Fig_Curie_exp}.
\begin{figure}[!htp]
\begin{center}
\includegraphics*[width=0.9\columnwidth]{Fig11.eps}
\caption{The effective Curie constant (\ref{Curie_exp}) extracted from
susceptibility data for Sr$_2$Cu$_{1-x}$Pd$_x$O$_{3}$
\cite{Kojima}. The nominal Pd concentration is $x=0.5\%$ (black
circles), $x=1\%$ (red squares), and $x=3\%$ (blue diamonds). The
solid lines denote the theoretical result (\ref{Curie_constant}) for
$p=1.2\%$, $p=1.4\%$, and $p=2.4\%$ (from bottom to top).}
\label{Fig_Curie_exp}
\end{center}
\end{figure}
Although the agreement is far from perfect we see that the Curie
constant extracted from experiment does indeed show a non-trivial
temperature dependence. In particular, there is a finite temperature
minimum although at higher temperatures than predicted
theoretically. The maximum at low temperatures and subsequent drop of
the Curie constant, on the other hand, is clearly caused by the
interchain couplings which can no longer be neglected in this
temperature regime. Given that the procedure to extract the Curie
constant is quite sensitive to the values of $J$, $p$, and $\chi'$
used the agreement is quite remarkable supporting that the Curie-like
contribution is mainly caused by an effective concentration of chain
breaks $p$ and that possible additional paramagnetic Curie
contributions are relatively small.
For a more detailed comparison with theory, it would be desirable to
repeat the experiment with annealed samples, carefully estimating any
residual true paramagnetic Curie terms in the pure system, so that the
nominal Pd concentration directly corresponds to the concentration of
chain breaks created.
\section{Conclusions}
\label{conclusions}
We have studied the effect of chain breaks (non-magnetic impurities)
on the thermodynamic properties of spin-$1/2$ chains by field theory
methods. Using first order perturbation theory in the leading
irrelevant operator (Umklapp scattering) we have derived a
parameter-free result for the thermodynamic properties of a finite
length $XXZ$-chain with open boundaries beyond the scaling limit. We
have shown that this result reduces to the previously known
expressions for boundary contributions in the limit of infinite chain
length. To obtain results for the isotropic case, we expanded the
results for the anisotropic model in terms of $1-1/K$ and re-expressed
this expansion in terms of a small running coupling constant $g$
fulfilling a set of known RG equations. For boundary contributions
like the boundary susceptibility $\chi_B$ this leads to multiplicative
logarithmic corrections. Whereas results in first order in $g$ can be
easily obtained by just replacing the Umklapp scattering amplitude
$\lambda\to g/4$, the consistent calculation of the correction of
order $g^n$ generally requires $n$-th order perturbation in the
Umklapp scattering. For the boundary susceptibility we presented the
result up to order $g^2$ using second order perturbation theory in
$\lambda$.
For the susceptibility of a finite length isotropic Heisenberg chain we were
able to derive a simple formula by studying the ground-state limit $LT/v\to
0$. In this limit the first order correction in the Umklapp scattering can be
absorbed into the scaling limit result. Surprisingly, we find by comparing
with QMC data that the simple parameter-free formula for $\chi(L,T)$ obtained
this way does work very well over a much larger range of temperatures and
lengths than anticipated. This simple formula is useful to analyse
susceptibility data for finite length Heisenberg chains.
We then discussed the average susceptibility $\chi_p$ for impurity
concentration $p$ assuming a Poisson distribution. Using the results
for $\chi(L,T)$ in the limiting cases $LT/v\to 0$ and $LT/v\to\infty$
we derived an effective fitting formula for $\chi_p$ which reproduces
QMC results with high accuracy. This formula can be used to fit
experimental data thus allowing to determine the (effective) impurity
concentration.
Taking into consideration that any real material will have interchain
$\tilde{J}$ as well as longer ranged intrachain couplings $J'$ which
can bridge over a chain break we discussed the limitations of the
theoretical analysis for $\chi_p$ presented here. Our main result is
that such couplings can be ignored provided that $T\gg
\mbox{Min}(\tilde{J},p^2J')$. Note, that $J'$ is suppressed by a
factor $p^2$ so that even relatively large couplings between the
segments can be ignored provided that the impurity concentration is
small. In most materials it will therefore be the loss of
one-dimensionality due to $\tilde{J}$ which marks the point where our
theory no longer applies.
For Sr$_2$CuO$_3$ this scale is about $5$ K whereas $J\sim 2000$ K
making it an ideal candidate to study the thermodynamics of impurities
in a Heisenberg chain experimentally over a large temperature
range. In this work we concentrated on analysing susceptibility data
by Kojima {\it et al.} \cite{Kojima} for
Sr$_2$Cu$_{1-x}$Pd$_x$O$_{3}$. We extracted the effective Curie
constant and showed that it agrees qualitatively with the theoretical
prediction. The impurity concentration, however, seems to be different
from the nominal Pd concentration. A plausible explanation is the
presence of excess oxygen leading to additional chain breaks, a
scenario already discussed in \cite{AmiCrawford,MotoyamaEisaki}. It
might be possible to avoid these additional chain breaks by annealing
which seems to make a more detailed comparison with theory feasible in
the future.
Our results might also shed light on some aspects of the high-$T_c$
cuprates physics. In YBa$_2$Cu$_3$O$_{6+\delta}$ we have
quasi-one-dimensional CuO chains in addition to the CuO$_2$ planes
common to all high-$T_c$ cuprates. By changing the oxygen content
$\delta$ the charge concentration in the planes is changed. At the
same time, this leads to the removal of spins from the chain. If we
assume a Zhang-Rice singlet type state with immobile holes this again
leads to chain breaks in the same way as in
Sr$_2$CuO$_{3+\delta}$. Indeed, Friedel-type spin-density oscillations
have been observed in YBa$_2$Cu$_3$O$_{6.5}$ by NMR
\cite{YamaniStatt}. Such oscillations are expected if spin chain
segments with open boundaries are present \cite{EggertAffleck95}. A
thorough analysis of these data and possible new experiments on
Sr$_2$Cu$_{1-x}$Pd$_x$O$_{3}$ or similar compounds might give us a
better understanding of oxygen doping and the formation of Zhang-Rice
singlet states in the cuprates.
\section*{Acknowledgments}
We would like to thank M.~Bortz, F.H.L.~Essler, N.~Kawakami, and I. Schneider
for valuable discussions. We are also grateful to A.~Furusaki for sharing his
insight about related issues and to F.~Anfuso for making his Monte Carlo code
available to us for part of the simulations. This work was partly supported by
a Grant-in-Aid from the Ministry of Education, Science, Sports and Culture,
Japan (SF), the Swedish Research Council (SE), the Transregio 49 funded by the
DFG (SE), NSERC (IA), and CIfAR (IA). JS thanks the University of New South
Wales, Sydney, Australia for their hospitality and the Gordon Godfrey fund for
financial support. NL acknowledges computer facilities provided by the
WestGrid network, funded in part by the Canada Foundation for Innovation.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,672 |
Jimmy Lin and Dmitriy Ryaboy Twitter, Inc.
The analytics platform at Twitter has experienced tremen- dous growth over the past few years in terms of size, com- plexity, number of users, and variety of use cases. In this paper, we discuss the evolution of our infrastructure and the development of capabilities for data mining on "big data". One important lesson is that successful big data mining in practice is about much more than what most academics would consider data mining: life "in the trenches" is occupied by much preparatory work that precedes the application of data mining algorithms and followed by substantial effort to turn preliminary models into robust solutions. In this con- text, we discuss two topics: First, schemas play an impor- tant role in helping data scientists understand petabyte-scale data stores, but they're insufficient to provide an overall "big picture" of the data available to generate insights. Second, we observe that a major challenge in building data analytics platforms stems from the heterogeneity of the various com- ponents that must be integrated together into production workflows—we refer to this as "plumbing". This paper has two goals: For practitioners, we hope to share our experi- ences to flatten bumps in the road for those who come after us. For academic researchers, we hope to provide a broader context for data mining in production environments, point- ing out opportunities for future work. | {
"redpajama_set_name": "RedPajamaC4"
} | 742 |
\section{0pt}{0pt}{0pt}
\newcommand{0.75\columnwidth}{0.75\columnwidth}
\newcommand{0.5\columnwidth}{0.5\columnwidth}
\newcommand{\begin{enumerate}}{\begin{enumerate}}
\newcommand{\end{enumerate}}{\end{enumerate}}
\newcommand{\begin{equation}}{\begin{equation}}
\newcommand{\end{equation}}{\end{equation}}
\newcommand{\begin{eqnarray}}{\begin{eqnarray}}
\newcommand{\end{eqnarray}}{\end{eqnarray}}
\newcommand{\begin{cases}}{\begin{cases}}
\newcommand{\end{cases}}{\end{cases}}
\newcommand{\begin{itemize}}{\begin{itemize}}
\newcommand{\end{itemize}}{\end{itemize}}
\newcommand{\begin{bf} \begin{color}{BrickRed} }{\begin{bf} \begin{color}{BrickRed} }
\newcommand{\end{color} \end{bf}}{\end{color} \end{bf}}
\newcommand{\twofigs} {0.42\textwidth}
\pagestyle{empty}
\DeclareMathOperator*{\argmin}{\arg\!\min}
\DeclareMathOperator*{\argmax}{\arg\!\max}
\usepackage{epsf}
\usepackage{psfrag}
\graphicspath{%
{./}
}
\begin{document}
\sloppy
\title{Estimating the number of receiving nodes in \\802.11 networks via machine learning techniques}
\author{\authorblockN{{\bf Davide {Del~Testa}}\IEEEauthorrefmark{1}, {\bf Matteo Danieletto}\IEEEauthorrefmark{3}, {\bf Giorgio Maria Di Nunzio}\IEEEauthorrefmark{1}, and {\bf Michele Zorzi}\IEEEauthorrefmark{1}}\\
\IEEEauthorblockA{\IEEEauthorrefmark{1}Department of Information Engineering (DEI), University of Padova, Italy \\ \{deltesta, dinunzio, zorzi\}@dei.unipd.it}\\
\IEEEauthorblockA{\IEEEauthorrefmark{3}Qualcomm Institute, University of California San Diego -- La Jolla, CA, USA \\ mdanieletto@eng.ucsd.edu}
}
\maketitle
\thispagestyle{empty}
\begin{abstract}
Nowadays, most mobile devices are equipped with multiple wireless interfaces, causing an emerging research interest in device to device (D2D) communication: the idea behind the D2D paradigm is to exploit the proper interface to directly communicate with another user, without traversing any network infrastructure.
A first issue related to this paradigm consists in the need for a coordinator, called controller, able to decide when activating a D2D connection is appropriate and eventually able to manage such connection. In this view, the paradigm of Software Defined Networking (SDN), can be exploited both to handle the data flows among the devices and to interact directly with every device.
This work is focused on a scenario where a device is selected by the SDN controller, in order to become the master node of a WiFi-Direct network. The remaining nodes, called clients, can exchange data with other nodes through the master. The objective is to infer, through different Machine Learning approaches, the number of nodes actively involved in receiving data, exploiting only the information available at the client side and without modifying any standard communication protocol. The information about the number of client nodes is crucial when, \emph{e.g.}, a user desires a precise prediction of the transmission estimated time of arrival (ETA) while downloading a file.
\end{abstract}
\section{Introduction}
\label{sec:introduction}
Nowadays, more than two billions of smartphones are active in the global market \cite{smartphone}. One of the most important features of a smartphone is to provide an Internet connection, allowing each user to access/share their data, \emph{e.g.}, e-mails, photos, videos, \emph{etc}.
Two main factors usually affect a smartphone's capability to stay connected and exchange data: the battery life and the amount of data provided by the cellular carrier subscription. These can be addressed by exploiting heterogeneous wireless interface cards (WNICs) such as WiFi and Bluetooth, in order to simultaneously minimize the battery consumption and save a portion of the data transferred by the cellular network~\cite{d2dbattery}. However, this capability to automatically exploit heterogeneous WNICs is not yet supported by any smartphone service; indeed, if a user wants to connect her/his device to a WiFi connection, she/he has to manually set it up, provided that she/he either knows the SSID and the WiFi encryption parameters, or decides whether an open WiFi connection is worth trusting.
In the last few years, researchers in the Software Defined Networking (SDN) area have been focused on creating a software protocol suite that is decoupled from the underlying
hardware. This entails the possibility to, \emph{e.g.}, prototype new protocols~\cite{mckeown2008openflow} and create network virtualization and traffic isolation (the reader can find a complete overview in \cite{SDN_SURVEY}).
The SDN paradigm goes in this direction by decoupling the network traffic into two planes: the control plane and the data plane. The control plane aims at monitoring routers, switches and Access Points (APs) to handle the network behavior and report any kind of useful information to a centralized unit, called controller. The controller can establish one or more data traffic flows among the network hosts by using the information gathered from the network status. These can be configured through some predefined Quality of Service network policies, such as offloading, number of hops between two users or energy consumption for the User Equipment (UE). Therefore, a controller can exchange information and manipulate the switch/router behavior by employing an ad hoc protocol like OpenSwitch~\cite{open_switch}. On the other hand, the data plane handles all the data traffic generated by the host, which is completely separated from the control plane.
A further step in this direction can be undertaken when the SDN concept is paired with wireless technologies, as explained in \cite{openroads, sdn_wifi_dense_2}. For the above-mentioned purpose, a number of real WiFi SDN testbed implementations have been presented, \emph{e.g.}, OpenRoads~\cite{openroads}, Odin~\cite{odin}, OFRewind~\cite{ofrewind} and CARMEN~\cite{carmen}. Among these testbeds, OpenRoads and CARMEN are the most promising: the former was the first testbed to exploit OpenSwitch and to give the possibility to use a WiFiMax connection to test traffic offloading between two heterogeneous wireless interfaces; the latter has $50$ WiFi nodes in fixed positions deployed in a university campus area.
Moreover, three features characterize CARMEN from the other testbeds: it is able to collect all network parameters from datalink layer to application layer, it can exploit
Android smartphone devices for mobility analysis, and it provides each node with at least two IEEE 802.11 WNICs.
Finally, a further possibility is to integrate the device to device (D2D) communication into the SDN concept. D2D communication arises when two mobile nodes are able to communicate directly without traversing any infrastructure, \emph{i.e.}, a base station (more details regarding the D2D concept can be found in \cite{asadi2014survey}). D2D can generally exploit cellular spectrum (\emph{i.e.}, inband) or unlicensed spectrum (\emph{i.e.}, outband). In a D2D architecture the device network interfaces are expected to be overseen/controlled by a central entity \emph{e.g.}, the SDN controller.
Outband allows to eliminate the interference issues between D2D and cellular links, at the cost of an extra interface to be used, as it usually adopts other wireless technologies, such as WiFi, Bluetooth or IEEE 802.15.4.
Therefore, the SDN paradigm applied to D2D makes it possible to dynamically switch between different interfaces during transmission, based on predefined policies, \emph{e.g.}, data offloading, traffic balance and battery energy consumption. Hence, it is possible to design and implement a heterogeneous network environment where the device can exploit both network interfaces through the D2D concept in an unlicensed band. The idea to couple SDN and D2D has already been studied in \cite{cellular_offloading,sdn_heterogenus1,sdn_heterogenus2}, as well as the exploitation of the WiFi-Direct paradigm to set up a D2D network~\cite{wifi_direct1,wifi_direct2} with several devices.
In this work, we exploit CARMEN to generate an SDN scenario, where a D2D network is configured with WiFi Direct. The SDN controller, installed into the centralized radio access network (C-RAN), exploits an LTE connection to create a D2D network and to select its master node. The aim is to predict client-side information related to the nodes generating data traffic in the same D2D network. This procedure should: i) not interact with any SDN controller; ii) be completely transparent for the user; and iii) avoid to alter any network or SDN protocol (\emph{e.g.}, OpenSwitch/OpenFlow).
In our previous work~\cite{deltesta_globecomm}, we considered an SDN WiFi scenario with a node designated as the access point (\emph{i.e.}, master in case of a WiFi Direct scenario) and a varying number of nodes acting as clients. These nodes collected several network parameters in order to accurately predict an Estimated Time of Arrival (ETA). There, we used the number of simultaneously receiving nodes as an input datum, assuming that this information was available at each device. However, this assumption is unrealistic in practice, as the number of receiving nodes is only known to the transmitter (access point) which, in general, does not share this value unless a modification of the transmission protocol is introduced. Moreover, two reasons prevent the SDN controller from acknowledging how many nodes are actively involved in data reception inside the WiFi D2D network.
First, the master is acting as D2D gateway, and the LTE C-RAN side is completely blind regarding who is generating the traffic data. Second, the slave nodes use their local OpenFlow table already configured for D2D, and do not report any information to the SDN controller through the LTE connection.
In this paper, we show how the number of the active UEs can be estimated accurately by the receiving nodes, by means of Machine Learning (ML) techniques and by taking as input only those network parameters available at the client side, in order to respect the requirement of not modifying any protocol. In order to accomplish this, we measure the amount of time needed for the transmission of the first fraction of a file from the AP to a receiving node, together with other information, \emph{e.g.}, the distance of each node to the AP and its transmission power.
The rest of the paper is organized as follows. In Section~\ref{sec:testbeddataset} we describe the testbed and the dataset employed in our experiments.
In Section~\ref{sec:ml} we offer an overview on the ML techniques considered to estimate the number of active nodes. Section~\ref{sec:results} presents the experimental evaluation of the ML techniques used to predict the number of active nodes. Finally, Section~\ref{sec:conclusions} concludes the paper and proposes some future work.
\section{Testbed and dataset}\label{sec:testbeddataset}
In this section, we describe how the data was collected and characterize the dataset in terms of dimensionality and network parameters.
\subsection{WiFi Testbed}
We conducted a thorough experimental data gathering to measure different network realizations and their related outputs. The data was collected using CARMEN \cite{carmen}, composed of 50 Alix miniPCs model 3d2 with WiFi driver \textit{$ath9k$} and five Nexus 7 devices with the \textit{$ath9k\_htc$} WiFi driver. In order to minimize the setup time of a specific WiFi network and quickly collect its performance, this testbed was associated with a software able to automatically gather data and change the network configurations.
This software can collect the TCP/IP stack parameters, starting from the MAC sublayer up to the Application layer, and to remotely set the WiFi transmission channel and power, as well as the distance among the Alix nodes and the transmitter (more details can be found in \cite{carmen}). In addition, we exploited the GNU program \textit{cron} to schedule all experiments at different times of the day, in order to automate the entire data collection phase.
Being the data transmissions dependent on the channel status, several WiFi network setups were considered, by changing all possible parameters in order to modify the scenario and consequently the ETA measurements. Since the testbed is located inside our department, other WiFi nodes transmitting data can occupy the WiFi transmission channel, generating interference during the experiments. Our idea to mitigate this issue was to measure transmission data multiple times over different WiFi frequencies (channels) and times of the day (\emph{i.e.}, morning, afternoon and night).
\subsection{Dataset characterization}
The final dataset has been created by varying, for each time of the day, the following network and topology parameters: transmission power \{$0$ dBm, $5$ dBm, $10$ dBm, $15$ dBm, $20$ dBm\} , WiFi transmission channel \{$1$, $6$, $11$\}, number of nodes simultaneously receiving data from the transmitter $N$ (from $1$ to $4$), and distance between the transmitter and the receivers \{$1$ m, $5$ m, $10$ m\}.
For each configuration, we measured the transmission duration of a $100$ MB file (the average size of a music video in full HD resolution). Each configuration of the network has been tested $10$ times, and the experimental campaign lasted more than $45$ days, for a total of $M = 5400$ experiments. The network is deployed following a single-hop star topology, with a transmitting central node, called Access Point, and one or more nodes waiting for data reception.
The dataset has been divided into a training set $(\mathbf{X}_{tr}, \mathbf{y}_{tr})$ and a test set $(\mathbf{X}_{test}, \mathbf{y}_{test})$: $80\%$ of the data was assigned to the former, leaving the remaining $20\%$ for performance testing, in order to take into account the trade-off between learning quality and classification accuracy. In particular, the classification performance was tested using four subsets of the network parameters as input features, in order to measure how a higher number $n$ of known parameters could improve the final classification performance: the first subset contains only the ETA, whereas the others include either the ETA and the transmission power ($P_{Tx}$) or the ETA and the distance $d$, or all three features (ETA, $P_{Tx}$, $d$). All these network parameters are available at the receiving nodes, thus no modification of the standard signaling protocol is needed. Each value in either $\mathbf{y}_{tr}$ or $\mathbf{y}_{test}$ is the number $N$ of nodes actively receiving data from the AP, and is associated to its corresponding input feature vector in $\mathbf{X}_{tr}$ or $\mathbf{X}_{test}$.
Finally, we tried to simulate a real case scenario, where we assess the classification performance in a more crowded environment, \emph{e.g.}, a domestic location, in which the distribution of simultaneously receiving nodes is shifted towards $N = 4$ nodes. We introduced this case to study how the different classification algorithms are affected by this choice and whether a change in the parameters of the classification model leads to a better performance.
\section{Overview of ML techniques}\label{sec:ml}
In this section, we first describe the structure of the dataset we used to collect data from the experiments and later introduce the classification techniques adopted to predict the number of users simultaneously receiving data from the AP.
\subsection{Data structure}\label{subsec:dataStructure}
The dataset adopted in this work is composed by a matrix of input data $\mathbf{X}\in \mathbb{R}^{M \times n}$ and a vector of outputs $\mathbf{y} \in \mathbb{R}^M$. The $i$-th row in $\mathbf{X}$ and the $i$-th element in $\mathbf{y}$ define a pair $(\mathbf{x}^{(i)}, y^{(i)})$, for $i=1,\dots,M$, where $\mathbf{x}^{(i)} \in \mathbb{R}^n$ is the input feature vector and $y^{(i)}$ is the label representing the value of $N$ related to $\mathbf{x}^{(i)}$ (\emph{i.e.}, the number of active nodes during that transmission). We used different supervised classification techniques to identify the model that best associates a given subset of the examples in $\mathbf{X}$ to a set of labels, pairing each example $\mathbf{x}$ to a class.
We split the dataset into a training set $(\mathbf{X}_{tr} \in \mathbb{R}^{m \times n}, \mathbf{y}_{tr} \in \mathbb{R}^m)$ used to train and optimize the learning algorithms, and a test set $(\mathbf{X}_{test} \in \mathbb{R}^{(M-m) \times n}, \mathbf{y}_{test} \in \mathbb{R}^{M-m}$, to evaluate the performance of each classifier.
\subsection{Naive Bayes classifier}\label{subsec:Bayesian}
The Bayesian classifier~\cite{Duda} is a probability model that computes the posterior probability $p(y_k|\mathbf{x})$ of a class given an input example $\mathbf{x}$, for each of the $k$ possible classes. Using Bayes' rule, this probability is computed as
\begin{align}
p(y_k|\mathbf{x}^{(i)}) \propto p(\mathbf{x}^{(i)}|y_k)p(y_k) \ , \ i=1,\dots,m,
\end{align}
where the posterior probability is proportional to the likelihood $p(\mathbf{x}^{(i)}|y_k)$ and the prior $p(y_k)$. The object $\mathbf{x}^{(i)}$ is classified under the class that holds the highest posterior probability:
\begin{align}\label{eq:MAP}
y^*_{\text{MAP}} = \argmax_k p(\mathbf{x}^{(i)}|y_k)p(y_k),
\end{align}
known as Maximum A Posteriori (MAP) formulation.
The likelihood expresses how probable the input data $\mathbf{x}^{(i)}$ is for a given class $y_k$, whereas the prior captures the assumptions about the class, before observing the data, in the form of a prior probability distribution $p(y_k)$. If no prior knowledge about the class distribution is available, a uniform prior $p(y_k)=c$ is assumed and \eqref{eq:MAP} turns into the Maximum Likelihood (ML) solution $y^*_{\text{ML}} = \argmax_k p(\mathbf{x}^{(i)}|y_k)$.
The likelihood function can be modeled using different probability distribution functions (\textit{pdf}s): in this paper we used both a Gaussian and a Poisson \textit{pdf}, setting their parameters (mean and variance for the former, mean for the latter) according to the examples in the training set. In particular, we ran the classification algorithm with input examples $\mathbf{x}^{(i)}$ of different dimensions, based on the number of features $n$ involved: the idea behind this approach is to analyze how additional knowledge on an experiment impacts on the performance of the classifier. Therefore, the input vector contains either the ETA alone, or the pair (ETA, $P_{Tx}$) or (ETA, distance), or the triple (ETA, $P_{Tx}$, distance), and different \textit{pdf}s are generated accordingly. For instance, for the second case ($n=2$) with ETA and distance ($d$) as input features, \eqref{eq:MAP} is reformulated as
\begin{align}
y^*_{\text{MAP}} = \argmax_k p(ETA^{(i)}|y_k,d^{(i)})p(d^{(i)})p(y_k), \
\end{align}
$
i=1,\dots,m,
$
where $p(d^{(i)}|y_k)=p(d^{(i)})$ for a homogeneous dataset.
\subsection{Support Vector Machines}\label{subsec:SVC}
Support Vector Machines (SVMs)~\cite{Cortes1995} identify the hyperplane better separating the classes in a multi-dimensional feature space. A generic hyperplane can be written as the set of points $\mathbf{x}$ satisfying $\mathbf{w}^T \mathbf{x} - b = 0$, where $\mathbf{w}$ is the normal vector to the hyperplane and $b$ represents the offset from the origin along $\mathbf{w}$. When the data points are linearly separable, it is possible to identify a pair of hyperplanes able to perfectly separate all the objects. By defining these hyperplanes as $\mathbf{w}^T \mathbf{x} - b = \pm 1$, the margin, \emph{i.e.}, the region in-between, has length $\frac{2}{||\mathbf{w}||}$, and the objective is to maximize $\frac{1}{||\mathbf{w}||}$. If we consider a binary classification problem, $y^{(i)} \in \{-1,1\}$, the maximization of $\frac{1}{||\mathbf{w}||}$ is equivalent to the minimization of $\frac{1}{2}||\mathbf{w}||^2$; therefore the problem can be formulated as:
\begin{align}\label{eq:SVM_optprob1}
&\min_{\mathbf{w},\mathbf{b}} && \frac{1}{2} ||\mathbf{w}||^2 \nonumber\\
& \text{s.t.} &&\ y^{(i)}(\mathbf{w}^T\mathbf{x}^{(i)} + b) \ge 1,\ i=1,\dots,m,
\end{align}
where the constraint $y^{(i)}(\mathbf{w}^T\mathbf{x}^{(i)} + b) \ge 1$ has been added to guarantee that all $\mathbf{x}^{(i)}$s lie outside the margin.
Equation \eqref{eq:SVM_optprob1} assumes that all training examples can be separated, which is not verified in general. As a result, \eqref{eq:SVM_optprob1} can be modified to allow for some tolerance in the classification error. Therefore, for each training example $\mathbf{x}^{(i)}$, there is an associated non-negative slack-variable $\xi_i \ge 0$, $i=1,\dots,m$, allowing each example to lie on the other side of the hyperplane separating its class. The optimization problem then becomes:
\begin{align}\label{eq:SVM_optprob2}
& \min_{\mathbf{w},\mathbf{b}} && \frac{1}{2} ||\mathbf{w}||^2 + C \sum_{i=1}^{m} \xi_i \nonumber\\
& \text{s.t.} && y^{(i)}(\mathbf{w}^T\mathbf{x}^{(i)} + b) \ge 1 - \xi_i,\ \xi_i \ge 0,\ i=1,\dots,m,
\end{align}
where the parameter $C$ balances the trade-off between having a large margin and ensuring that most examples lie in the region associated to their class. The ``dual'' formulation of Eq.~\eqref{eq:SVM_optprob2} is
\begin{align}\label{eq:SVM_optprob3}
&\max_{\pmb{\alpha}} & &\sum_{i=1}^{m} \alpha_i - \frac{1}{2} \sum_{i,j=1}^{m}y^{(i)}y^{(j)}\alpha_i \alpha_j (\mathbf{x}^{(i)})^T \mathbf{x}^{(j)} \nonumber\\
&\text{s.t.} & & 0 \le \alpha_i \le C,\ \ i=1,\dots,m, \nonumber\\
& && \sum_{i=1}^{m}\alpha_i y^{(i)}=0,
\end{align}
where $\pmb{\alpha}=(\alpha_1,\dots,\alpha_m)$ is the vector of Lagrange multipliers. It can be shown that
\begin{align}\label{eq:SVM_weights}
\mathbf{w} = \sum_{i=1}^m \alpha_i y^{(i)} \mathbf{x}^{(i)},
\end{align}
by which it is possible to calculate the optimal weights in terms of the optimal values of $\pmb{\alpha}$. Now, a prediction for a new example input $\mathbf{x}$ can be performed calculating $\mathbf{w}^T \mathbf{x}+b$, and predicting $y=1$ (or $y=-1$) if this quantity is bigger (or smaller) than zero. Hence, the prediction function can be written as
\begin{align}\label{eq:SVM_predfunlin}
f_\mathbf{w}(\mathbf{x}) = sgn \left( \sum_{i=1}^m \alpha_i y^{(i)} (\mathbf{x}^{(i)})^T\mathbf{x} +b \right),
\end{align}
which only depends on the inner product between the input vector $\mathbf{x}$ and the subset of training vectors $\mathbf{x}^{(i)}$ for which $\alpha_i \ne 0$. Moreover, from \eqref{eq:SVM_optprob3} it turns out that this subset only contains those training examples, known as Support Vectors (SVs), lying within the margin or in the region of the hyperspace belonging to the other class: as a consequence, the actual complexity of the prediction process only depends on the number of support vectors.
The inner product $(\mathbf{x}^{(i)})^T \mathbf{x} + b$ in \eqref{eq:SVM_predfunlin} can be replaced by particular non linear functions $k(\mathbf{x}^{(i)},\mathbf{x})$, known as \textit{kernels}, which correspond to scalar products between either linear or non linear transformations of $\mathbf{x}^{(i)}$ and $\mathbf{x}$. Substituting $k(\mathbf{x}^{(i)},\mathbf{x}^{(j)})$ in \eqref{eq:SVM_optprob2} and $k(\mathbf{x}^{(i)},\mathbf{x})$ in \eqref{eq:SVM_predfunlin}, we thus obtain the optimal prediction function in a non-linear feature space, rather than in input space:
\begin{align}
f_\mathbf{w}(\mathbf{x}) = sgn \left( \sum_{i=1}^{m} \alpha_i y^{(i)} k(\mathbf{x}^{(i)},\mathbf{x}) \right).
\end{align}
Finally, as the classification problem studied in this paper involves $|C|=4$ classes, we adopted a generalization of the standard SVM known as multiclass SVM~\cite{Bishop2006}, which works by reducing the multiclass problem into a number of binary problems.
This generalization, known as one-vs-one classification, works by building a set of $|C|(|C|-1)/2$ binary classifiers, and then selecting the class that is assigned by the majority of the classifiers.
\subsection{k-Nearest Neighbor}
In k-Nearest Neighbor (k-NN), an example $\mathbf{x}$ is classified under the most common class among its $k$ nearest neighbors: $k$-NN is a type of lazy learning, since a learning phase is not needed at all.
The neighbors are taken from a set of examples for which the class is known: this set can be thought of as the training set for the algorithm.
In other words, the training phase of the algorithm simply consists in storing the training examples: once a test example is provided, the algorithm classifies it by assigning the most frequent class among its $k$ nearest training examples. The parameter $k$ is chosen so as to balance the trade-off between reducing the effect of noise (large $k$) and avoiding the creation of indistinct boundaries between the classes (low $k$).
\section{Experimental Results}\label{sec:results}
In this section, we present the classification results of the four algorithms: Naive Bayes (NB), linear Support Vector Machines (SVM-L), radial Support Vector Machines (SVM-R)\footnote{Radial kernels are one of the most effective kernel implementations.}, k-Nearest Neighbor (kNN).
The results are split into two parts: in the first part, we test the four classifiers on the whole dataset; in the second part, we train the classifiers on two subsets of data which mimic a more realistic scenario with unbalanced classes. In both cases (balanced and unbalanced training and test), we divide the dataset into 5 folds and train/test the classifiers 5 times, \emph{i.e.}, using 4 folds for training and the remaining fold for testing, every time. For the second part, we maintain the same 5 folds and sample a subset of the training and test data in order to produce an unbalanced dataset with more examples of transmission with multiple nodes (higher value of $N$). Two training/test subsets have been created with different proportion of examples per class, see Table~\ref{tab:dataset} for the details. For instance, subset ``10-20-50-100" means that the first class ($N=1$) is subsampled taking only $10\%$ of the data, the second class ($N=2$) maintains $20\%$ of the data, \emph{etc}.
\begin{table}[th]
\caption{Number of examples per class.}
\label{tab:dataset}
\begin{center}
\begin{tabular}{c | r | r | r | r }
Subset & N = 1 & N = 2 & N = 3 & N = 4 \\
\hline
Full dataset & 1,350 & 1,350 & 1,350 & 1,350 \\
10-20-50-100 & 135 & 270 & 675 & 1,350 \\
20-30-40-100 & 270 & 405 & 540 & 1,350 \\
\end{tabular}
\end{center}
\vspace{-0.275cm}
\end{table}%
Since we deal with a multi-class classification problem, we adopt the $F_1$ score\footnote{$F_1$ score (also F-score or F-measure) is a common accuracy metric.} as a measure of performance for each class~\cite{DBLP:journals/ipm/SokolovaL09}:
\begin{equation}
F_1 = \frac{2 \cdot P \cdot R} {P + R}
\end{equation}
where $P$ is the precision, \emph{i.e.}, the class agreement of the data labels with the positive labels given by the classifier, and $R$ is the recall, that is the effectiveness of a classifier in identifying positive labels~\cite{han2011data}. In addition, we analyze the performance in terms of Receiver Operating Characteristic (ROC) curve which shows the fraction of true positive decisions of a classifier for a given rate of false positive decisions~\cite{Bradley19971145}.
\subsection{Full dataset}\label{subsec:fulldataset}
\begin{figure}[t]
\centering
\includegraphics[width=\columnwidth]{full}
\caption{Performance (mean and standard deviation) on full dataset.}
\label{fig:full}
\vspace{-0.275cm}
\end{figure}
The classification performance for the full dataset is shown in Figure~\ref{fig:full}. For each class (number of nodes $N=\{1, \dots, 4\}$), we plot the average and the standard deviation of the $F_1$ score of each classifier when all the features are used (ETA, $P_{Tx}$, and distance). In general, the performance is very high and it is possible to identify a common trend for all the classifiers: the 3-node class is harder to classify, mainly because the ``tails'' of this class overlap with the 2-node and 4-node classes. Table~\ref{tab:full} summarizes the performance for each class and the total average $F_1$ score given a particular set of features. As we add more evidence (in terms of features), the performance of each classifier increases.
In \figurename~\ref{fig:ROC}, we show the analysis of the classification performance in terms of the ROC curve. This curve can be used to select the suitable operating point of the classifier; in particular, we see that at 20\% rate of false positives, all the classifiers achieve an almost perfect performance (dashed line indicates 100\% true positives). It is also worth noting that in the range 3\% - 6\% of false positive rate, all the classifiers are above the 95\% true positive rate (dotted line). Table~\ref{tab:ROC} shows the cutoff points for the false positive rate that is required to achieve at least 95\% of true positive rate. \figurename~\ref{fig:ROC} and Table~\ref{tab:ROC} confirm that the NB approach is the slowest to reach the best performance.
\begin{table}[th]
\caption{$F_1$ score performance on full dataset.}
\label{tab:full}
\begin{center}
\begin{tabular}{ c | l | c | c | c | c || c }
Features & Classifier & $N = 1$ & $N = 2$ & $N = 3$ & $N = 4$ & Average\\
\hline
\multirow{4}{*}{ETA} & NB & 0.986 & 0.929 & 0.818 & 0.863 & 0.899 \\
& SVM-L & 0.996 & 0.952 & 0.845 & 0.884 & 0.919 \\
& SVM-R & 0.997 & 0.950 & 0.841 & 0.888 & 0.919 \\
& kNN & 0.997 & 0.948 & 0.825 & 0.875 & 0.911 \\
\hline
\hline
\multirow{4}{*}{ETA, $d$} & NB & 0.990 & 0.917 & 0.813 & 0.877 & 0.899 \\
& SVM-L & 0.997 & 0.953 & 0.840 & 0.877 & 0.917 \\
& SVM-R & 0.996 & 0.960 & 0.861 & 0.899 & 0.929 \\
& kNN & 0.997 & 0.960 & 0.854 & 0.892 & 0.926 \\
\hline
\hline
\multirow{4}{*}{ETA, $P_{Tx}$} & NB & 0.989 & 0.939 & 0.84 & 0.879 & 0.912 \\
& SVM-L & 0.997 & 0.958 & 0.851 & 0.887 & 0.923 \\
& SVM-R & 0.992 & 0.957 & 0.842 & 0.876 & 0.916 \\
& kNN & 0.996 & 0.958 & 0.842 & 0.879 & 0.919 \\
\hline
\hline
\multirow{4}{*}{ETA, $P_{Tx}$, $d$} & NB & 0.993 & 0.944 & 0.851 & 0.892 & 0.920 \\
& SVM-L & 0.998 & 0.959 & 0.861 & 0.896 & 0.928 \\
& SVM-R & 0.991 & 0.958 & 0.871 & 0.904 & 0.931 \\
& kNN & 0.996 & 0.958 & 0.872 & 0.910 & 0.934 \\
\end{tabular}
\vspace{-0.275cm}
\end{center}
\end{table}%
\begin{figure}[t]
\centering
\includegraphics[width=\columnwidth]{ROC}
\caption{ROC curves on full dataset.}\label{fig:ROC}
\end{figure}
\begin{figure}[t]
\centering
\includegraphics[width=\columnwidth]{ROC20}
\caption{ROC curves on subset 20-30-50-100.}\label{fig:ROC20}
\end{figure}
\begin{figure}[t]
\centering
\includegraphics[width=\columnwidth]{ROC10}
\caption{ROC curves on subset 10-20-30-100.}\label{fig:ROC10}
\end{figure}
\begin{table}[th]
\caption{False positive rate @ true positive rate = 0.95.}
\label{tab:ROC}
\begin{center}
\begin{tabular}{ l | c | c | c }
& ETA, $P_{Tx}$, $d$ & \multicolumn{2}{c}{ETA} \\
Classifier & Full dataset & 10-20-30-100 & 20-30-50-100 \\
\hline
NB (prior) & 0.060 & 0.094 & 0.129 \\
SVM-L (no weight) & 0.046 & 0.030 & 0.048 \\
SVM-R (no weight) & 0.035 & 0.101 & 0.128 \\
kNN & 0.030 & 0.060 & 0.065 \\
\end{tabular}
\vspace{-0.275cm}
\end{center}
\end{table}%
\subsection{Unbalanced dataset}
In this subsection, we study the classification performance when classes are unbalanced and only one feature (the ETA) is available. In particular, we present the results of two subsamples of the classes with the following proportions (compared to the full dataset): i) $10\%$, $20\%$, $30\%$, $100\%$, ii) $20\%$, $30\%$, $50\%$, $100\%$, respectively for the 1-node, 2-node, 3-node, and 4-node classes.
We tested the NB and SVM with two different approaches: one that incorporates the knowledge of the disproportion among classes, and another that does not take into account this information. For the NB, we trained NB with a uniform (NB uniform) distribution over the classes, so as to simulate a lack of knowledge about the unbalanced class distribution. We also trained a NB which computes the prior distribution $p(y_k)$ over the classes based on the relative frequency of class $y_k$ in the training set (NB prior).
For the SVM, both the linear (SVM-L) and radial kernel (SVM-R) were used, training the algorithm either without modifying the weights of the classes (SVM no weight), or setting the values of the weights proportionally to the amount of training instances of each class in the training set (SVM weight), so that the $C$ parameter in \eqref{eq:SVM_optprob2} and \eqref{eq:SVM_optprob3} takes into consideration the unbalanced data by setting the same sum of weights for each class. Finally, the k-NN algorithm was executed without any modification.
\begin{table}[th]
\caption{$F_1$ score performance on subset 10-20-30-100.}
\label{tab:10}
\begin{center}
\begin{tabular}{ l | c | c | c | c || c }
Classifier & $N = 1$ & $N = 2$ & $N = 3$ & $N = 4$ & Average\\
\hline
NB (uniform) & 0.985 & 0.907 & 0.781 & 0.893 & 0.891\\
NB (prior) & 0.985 & 0.942 & 0.830 & 0.925 & 0.920 \\
SVM-L (no weight) & 1.000 & 0.953 & 0.837 & 0.929 & 0.930 \\
SVM-L (weight)& 1.000 & 0.948 & 0.830 & 0.918 & 0.924 \\
SVM-R (no weight) & 0.989 & 0.941 & 0.836 & 0.929 & 0.924 \\
SVM-R (weight)& 0.989 & 0.935 & 0.830 & 0.919 & 0.918 \\
kNN & 1.000 & 0.955 & 0.827 & 0.926 & 0.927 \\
\end{tabular}
\end{center}
\end{table}%
\begin{table}[th]
\caption{$F_1$ score performance on subset 20-30-50-100.}
\label{tab:20}
\begin{center}
\begin{tabular}{ l | c | c | c | c || c }
Classifier & $N = 1$ & $N = 2$ & $N = 3$ & $N = 4$ & Average\\
\hline
NB (uniform) & 0.991 & 0.924 & 0.737 & 0.895 & 0.887 \\
NB (prior) & 0.989 & 0.928 & 0.775 & 0.938 & 0.907 \\
SVM-L (no weight) & 1.000 & 0.953 & 0.837 & 0.929 & 0.930 \\
SVM-L (weight) & 1.000 & 0.948 & 0.83 & 0.918 & 0.924 \\
SVM-R (no weight) & 0.993 & 0.947 & 0.800 & 0.938 & 0.919 \\
SVM-R (weight)& 0.994 & 0.939 & 0.798 & 0.929 & 0.915 \\
kNN & 0.998 & 0.95 & 0.795 & 0.935 & 0.920 \\
\end{tabular}
\end{center}
\end{table}%
In Table~\ref{tab:ROC}, we added the false positive rate cutoffs for each classifier. Since these two experiments, due to a reduced amount of training examples, constitute harder classification tasks with respect to the balanced-class setting, the values of the cutoff points are, in general, higher. This means that, in order to achieve a 95\% true positive rate, it is at least needed to double the false positive error rate. It seems that SVM-L is much less prone to this type of performance decay. We will further investigate this particular behavior of the SVM with linear kernel.
The results in Table~\ref{tab:10} and Table~\ref{tab:20} show that, in general,
SVM-L, achieving the highest $F_1$-score values in most classification tasks, seems to be preferable for the unbalanced datasets, whereas NB provides inferior results. In addition, kNN could be a good choice overall, as it attains good results at the lowest computational cost (as no training phase is needed).
\subsection{Discussion and further analyses}
The results of the experiments presented in this paper are very promising. The performance of the classifiers in all the considered configurations are high on average ($F_1$ score above 0.89) if we consider that only three features were used (namely ETA, $P_{Tx}$, and $d$); moreover, the study of the ROC curve shows that a true positive rate equal to 95\% can be achieved with a very small false positive rate (around 2-5\%). We also observed a slight increment in performance when going from a single feature (ETA) to three features (ETA, $P_{Tx}$ and $d$), but this increment in performance is not statistically significant. Instead, a substantial difference between the NB classifier and the SVM and k-NN classifiers has been observed\footnote{We performed a paired t-test significance analysis with $\alpha = 0.05$.}. In the second part of the experimental analysis, we showed that the classification performance continues to be high even when classes are not balanced and the information about the skewness is not taken into account. Unexpectedly, weighted SVM performed worse than the unweighted (default) version. We are going to investigate further this problem in the future.
\begin{table}[t]
\caption{Percentage mean prediction errors.}\label{tab:ETA_pred}
\tabcolsep=0.11cm
\begin{tabular}{c|c|c|c|c}
& $N_{pred} = 1$ & $N_{pred} = 2$ & $N_{pred} = 3$ & $N_{pred} = 4$ \\
\hline
$N_{real} = 1$ & $9.57 \pm 4.68$ & $89.90 \pm 16.55$ & $179.19 \pm 26.68$ & $282.57 \pm 42.20$ \\
$N_{real} = 2$ & $46.76 \pm 5.79$ & $6.38 \pm 5.26$ & $47.90 \pm 16.19$ & $103.92 \pm 29.58$ \\
$N_{real} = 3$ & $63.96 \pm 4.63$ & $32.63 \pm 7.86$ & $6.22 \pm 4.42$ & $38.23 \pm 12.83$ \\
$N_{real} = 4$ & $73.42 \pm 2.56$ & $50.54 \pm 5.09$ & $26.55 \pm 7.27$ & $3.85 \pm 2.82$ \\
\end{tabular}
\end{table}
\begin{table}[!t]
\caption{Distribution of $\mathbb{P}[N_{pred}|N_{real}]$ on full dataset, with ETA as input feature and SVR-R as ML technique.}\label{tab:prob_distr}
\begin{tabular}{c|c|c|c|c}
& $N_{pred} = 1$ & $N_{pred} = 2$ & $N_{pred} = 3$ & $N_{pred} = 4$ \\
\hline
$N_{real} = 1$ & 0.9937 & 0.0044 & 0.0012 & 0.0006 \\
$N_{real} = 2$ & 0.0035 & 0.9138 & 0.0718 & 0.0109 \\
$N_{real} = 3$ & 0.0033 & 0.0679 & 0.7663 & 0.1625 \\
$N_{real} = 4$ & 0.0037 & 0.0186 & 0.1864 & 0.7912 \\
\end{tabular}
\end{table}
We claim that the exact number of users in the network is an important piece of information, as the predicted ETA is highly dependent on the value of $N$. To prove this, in Table~\ref{tab:ETA_pred} we show percentage mean prediction errors on the ETA, as a function of the number of users given as input, computed using the best-performing ML technique in \cite{deltesta_globecomm}.
In the table, we indicate with $N_{real}$ the actual number of active nodes during a given experiment, and with $N_{pred}$ the value of $N$ given as input to the ETA predicted by the algorithm. The goal is to compare the ETA prediction errors when an erroneous number of nodes is used instead of the right one. For each experiment in the test set, the ETA has been predicted with a given value of $N_{pred}$, and a percentage error has been computed with respect to the measured ETA value. The average of all the errors and standard deviations for a given $(N_{real}, N_{pred})$ pair is reported in Table~\ref{tab:ETA_pred}. Note that the errors on the diagonal are related to the predictions performed using the ``right'' value of $N$ ($N_{pred} = N_{real}$); as expected, these values are the lowest for each class of experiments. The worst case is when the algorithm predicts a number of nodes greater than 1, $N_{pred} > 1$, when $N_{real} = 1$. In addition, when $N_{real}=2$ (or $N_{real}=3$), using the nearest value of $N$ for the prediction, \emph{i.e.}, either $N_{pred}=1$ or $N_{pred}=3$ (or $N_{pred}=2$ or $N_{pred}=4$, respectively), gives approximately symmetric mean percentage errors. By computing the distribution $\mathbb{P}[N_{pred}=k|N_{real}=n]$ with $k,n \in [1, 2, 3, 4]$, see Table~\ref{tab:prob_distr}, it is possible to obtain the percentage weighted average prediction errors $\delta_i, \ i \in [1, 2, 3, 4]$, for each value of users $N_{real}$. For the aforementioned case, this computation gives $\bm{\delta} = \{10.3, 10.5, 13.4, 9.2\}$ which means that, on average, the percentage error is generally of the order of $10\%$, except when $N_{real}=3$, due to the overlap of the distribution of this class on the 2-node and 4-node ones, as already noted in Subsection~\ref{subsec:fulldataset}.
\section{Conclusions}
\label{sec:conclusions}
In this paper, we studied how the number of active nodes $N$, an important SDN parameter, can effectively be inferred using only the data available at each node of a wireless network. We studied the distribution of the error on the ETA of a WiFi transmission given a wrong prediction of this parameter, and how the use of ML techniques is important to analyze the information derived from the first transmitted file chunk and return the value of $N$. Based on this work, a further step could be to predict the number of active nodes on-the-fly, as a function of the amount of data already received. This could allow to simultaneously update both the ETA estimation and the number of nodes during a transmission.
\bibliographystyle{IEEEtran}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,802 |
\section{Introduction}
Assume that we are given a degree $d$ polynomial $f$ that, in some
sense, `behaves' differently from a random degree $d$ polynomial.
Is there anything that we can deduce about the structure of $f$
just by knowing this fact? Recently this question received a lot
of attention, where the `behavior' of $f$ was examined with
respect to its bias or the more general notion of the Gowers norm.
\begin{definition}\label{def:bias}
Let $f:{\mathbb{F}}^n \to {\mathbb{F}}$ be a function. The bias of $f$ is defined as
$${\mathrm{bias}}(f) = \left|{\mathbb{E}}_{\bar{a} \in {\mathbb{F}}^n}[\omega^{f(\bar{a})}]\right| \;,$$
where $\omega = e^{\frac{2 \pi i}{|{\mathbb{F}}|}}$ is a complex primitive
root of unity of order $|{\mathbb{F}}|$.
\end{definition}
Intuitively, the bias of $f$ measures how far is the distribution
induced by $f$ from the uniform distribution. We expect a random
polynomial to have a vanishing small bias (as a function of the
number of variables), so it is interesting to know what can be
said when the bias is not too small. Indeed, Green and Tao
\cite{GreenTao07} showed that if $f$ is a degree $d$ polynomial
over ${\mathbb{F}}$, such that $d < |{\mathbb{F}}|$, and ${\mathrm{bias}}(f)=\delta$ then $f$
can be written as a function of a small number of lower degree
polynomial. Formally, $f(x) = F(g_1,\ldots,g_{c_d})$ for some
function $F$ and $c_d=c_d({\mathrm{bias}}(f),|{\mathbb{F}}|)$ polynomials $\{g_i\}$
satisfying $\deg(g_i)<d$. Note that $c_d=c_d({\mathrm{bias}}(f),|{\mathbb{F}}|)$ does
not depend on the number of variables, i.e. it is some constant.
This result was later extended by Kaufman and Lovett
\cite{KaufmanLovett08} to arbitrary finite fields (i.e. without
the restriction $d<|{\mathbb{F}}|$). Thus, if $f$ has a noticeable bias,
unlike a random degree $d$ polynomial, then $f$ is in fact very
far from being random; simple counting arguments show that most
degree $d$ polynomials cannot be represented as functions of a few
lower degree polynomials. This result is also interesting as it
gives an average case - worst case reduction. Namely, if $f$ has
correlation $\delta$ with a lower degree polynomial then it is a
function of a small number of lower degree polynomials. One
drawback of the results of \cite{GreenTao07,KaufmanLovett08} is
the dependance of the number of lower degree polynomials on the
bias of $f$. In particular when $\deg(f)=3$,
\cite{GreenTao07,KaufmanLovett08} get the bound $c_3 =
\exp({\mathrm{poly}}(1/{\mathrm{bias}}(f)))$ and for $\deg(f)=4$ they
bound\footnote{These numbers are not explicitly computed there,
but this is what the recursive arguments in the papers imply.}
$c_4$ by a tower of height $c_3$. On the other hand if $\deg(f)=2$
and ${\mathrm{bias}}(f) = \delta$ then it is known that $f$ can be written
as a function of at most $2\log(1/\delta)+1$ linear functions.
This can be immediately deduced from the following well known
theorem.
\begin{theorem}[Structure of quadratic polynomials]\label{thm:Dickson}
(Theorems 6.21 and 6.30 in \cite{LN97}). For every quadratic
polynomial $f: {\mathbb{F}}^n \to {\mathbb{F}}$ over a prime field ${\mathbb{F}}$ there exists
an invertible linear transformation $T$, a linear polynomial
$\ell$, and field elements $\alpha_1, \ldots \alpha_n$ (some of
which may be $0$) such that:
\begin{enumerate}
\item If ${\mathrm{char}}({\mathbb{F}}) = 2$ then $(q \circ T)(x) = \sum_{1=i}^{\lfloor
n/2\rfloor} \alpha_i \cdot x_{2i-1} \cdot x_{2i} + \ell(x)$,
\item If ${\mathrm{char}}({\mathbb{F}})$ is odd then $(q \circ T)(x) = \sum_{1=i}^n
\alpha_i \cdot x_i^2 + \ell(x)$.
\end{enumerate}
Moreover, the number of non zero $\alpha_i$-s is invariant and
depends only on $f$.
\end{theorem}
We thus see that there is a sharp contrast between the result for
quadratic polynomials and the results for polynomials of degrees
as low as three or four. We also note that the results of Kaufman
and Lovett only guarantee that $f$ can be represented as $f(x) =
F(g_1,\ldots,g_c)$ but no nice structure like the one in
Theorem~\ref{thm:Dickson} is known. It is thus an intriguing
question whether a nice structural theorem exists for biased
polynomials and what is the correct dependance of the number of
lower degree polynomials on $\deg(f)$ and ${\mathrm{bias}}(f)$.
As mentioned above, a more general measure of randomness that was
considered is the so called Gowers norm of $f$. Intuitively, the
$U^d$ Gower norm tests whether $f$ behaves like a degree $d-1$
polynomial on $d$ dimensional subspaces. To define the Gowers norm
we first define the notion of a discrete partial derivative.
\begin{definition}(Discrete partial derivative)\label{def:partial
derivative} For a function $f:{\mathbb{F}}^n \to {\mathbb{F}}$ and a direction $y \in
{\mathbb{F}}^n$ we define $\Delta_y(f)(x) \triangleq f(x+y) - f(x)$ to be the
discrete partial derivative of $f$ in direction $y$ at the point
$x$.
\end{definition}
It is not difficult to see that if $\deg(f)=d$ then for every $y$,
$\deg(\Delta_y(f)) \leq d-1$. We now define the $d$-th Gower norm
of a function $f$.
\begin{definition}[Gowers norm \cite{AKKLR,Gowers98,Gowers01}]
The $d$-th Gower norm, $U^d$, of $f$ is defined as $$\|f\|_{U^d}
\triangleq
|{\mathbb{E}}_{x,y_1,\ldots,y_d}[\omega^{\Delta_{y_d}\ldots\Delta_{y_1}(f)(x)}]|^{1/2^d}\;,$$
where again $\omega = e^{\frac{2\pi i}{|{\mathbb{F}}|}}$.
\end{definition}
Note that $\|f\|_{U^0}=\|f\|_{U^1}={\mathrm{bias}}(f)$. It is also clear
that if $\deg(f)=d-1$ then $\|f\|_{U^d}=1$. For more properties of
the Gowers norm we refer the reader to
\cite{Gowers98,Gowers01,GreenTao08,Samorodnitsky07,ViolaW07}.
In \cite{AKKLR} Alon et. al. showed that if
$\|f\|_{U^d}>1-\delta$, for some small $\delta$, then $f$ can be
well approximated by a degree $d-1$ polynomial. This raises the
question whether any function that has a noticeable $U^d$ norm is
somewhat correlated with a lower degree polynomial and indeed in
\cite{Samorodnitsky07,GreenTao08} this was conjectured to be the
case. This conjecture has become known as the inverse conjecture
for the Gowers norm. Samorodnitsky \cite{Samorodnitsky07} proved
that if $\|f\|_{U^3} = \delta$ where $f:{\mathbb{F}}_2^n\to {\mathbb{F}}_2$ is an
arbitrary function, then $f$ has an exponentially high (in
$\delta$) correlation with a quadratic polynomial. Namely, there
exists a quadratic polynomial $q$ such that $\Pr_{x \in
{\mathbb{F}}_2^n}[f(x) = q(X)] \geq 1/2 + \exp(-{\mathrm{poly}}(1/\delta))$. Green and
Tao \cite{GreenTao08} obtained a similar result for fields of odd
characteristic. These results gave an affirmative answer for the
case of the $U^3$ norm. More generally, Green and Tao proved that
if $d < |{\mathbb{F}}|$ and $f$ is a degree $d$ polynomial with a high $U^d$
norm then $f$ is indeed correlated with a lower degree polynomial
\cite{GreenTao07}. Recently, the case of large characteristic was
solved by Tao and Ziegler \cite{TaoZiegler09}.\footnote{In
fact,\cite{TaoZiegler09} only get a qualitative result. No
explicit connection is known between the Gowers norm and the
correlation with polynomials.} Using ideas from ergodic theory and
the earlier \cite{BTZ09} they proved that if $f:{\mathbb{F}}^n\to
\mathcal{D}$ (where $\mathcal D$ is the unit disk in $\mathbb{C}$)
is a function with high $U^d$ norm and $d\leq |{\mathbb{F}}|$ then $f$ is
correlated with a degree $d-1$ phase polynomial.\footnote{A degree
$d-1$ phase polynomial is a function of the form $e^{2\pi i
\theta}\omega^g$, for some degree $d-1-(p-1)t$ polynomial $g$
where $\theta \in [0,1]$ and $\omega = e^{2\pi i /|{\mathbb{F}}|^t}$.} This
completely settled the conjecture for the case $d \leq |{\mathbb{F}}|$. On
the other hand, for the $U^4$ norm it was shown, independently, by
Lovett, Meshulam and Samorodnitsky \cite{LMS08} and by Green and
Tao \cite{GreenTao07} that no such result is possible when
${\mathbb{F}}={\mathbb{F}}_2$. Namely, \cite{LMS08} proved that the symmetric
polynomial $S_4(x_1,\ldots,x_n) \triangleq \sum_{T \subset [n], |T|=4}
\prod_{i\in T}x_i$, which is of degree four, has a high $U^4$ norm
but has an exponentially (in $n$) small correlation with any lower
degree polynomial. Similar examples where given for other fields
(when $d$ is large enough compared to the size of the field).
These examples show that for small fields the inverse conjecture
for the Gowers norm is not true in its current form. In their
work, Tao and Ziegler \cite{TaoZiegler09} proved a variant of the
conjecture for the case $d\leq |{\mathbb{F}}|$. Namely, that if a function
$f$ has high $U^d$ norm then $f$ is correlated with a phase
polynomial of a certain constant degree (but not necessarily
smaller than $d$). We note however, that if $\deg(f)=d$ then the
results of \cite{TaoZiegler09} do not give any information on $f$.
In fact, even if $\deg(f)=4$ and $f$ has a high $U^4$ norm then
nothing is known on the structure of $f$. It is thus a very
interesting question to understand the structure of low degree
polynomials having high Gowers norm over small fields.
Besides being natural questions on the own, results on the Gowers
norms had many applications in mathematics and computer science.
In his seminal work on finding arithmetic progressions in dense
sets, Gowers first defined the $U^d$ norm (for functions from
${\mathbb{Z}}_n$ to ${\mathbb{Z}}_n$) and proved an inverse theorem for them that was
instrumental in his proofs \cite{Gowers98,Gowers01}. Bogdanov and
Viola \cite{BogdanovViola07} attempt for constructing a pseudo
random generator for constant degree polynomials relied on the
(erroneous) inverse conjecture for the Gowers norm, yet it paved
the way for other papers solving the problem
\cite{Lovett08,Viola08}. In \cite{SamorodnitskyTrevisan06}
applications of an inverse theorem for the Gowers norm to PCP
constructions was given. Samorodnitsky's proof of the inverse
theorem for the $U^3$ norm \cite{Samorodnitsky07} implies a low
degree test distinguishing quadratic functions from those that do
not have a non trivial correlation with a quadratic function. This
result also gives a test for checking the distance of a given word
from the 2nd order Reed-Muller code, beyond the list decoding
radius. For a more elaborate discussion of the connection between
additive combinatorics and computer science see \cite{Trevisan09}.
\subsection{Our results}
In this work we are able to show analogs of
Theorem~\ref{thm:Dickson} for polynomials of degree three and
four. We also prove a structural result for the case that such a
polynomial has a high Gowers norm. Our first main result is the
following.
\begin{introthm}\label{thm:intro:deg-3:bias}(biased cubic
polynomials)\sloppy Let ${\mathbb{F}}$ be a finite field and $f \in
{\mathbb{F}}[x_1,\ldots,x_n]$ a cubic polynomial ($\deg(f)=3$) such that
${\mathrm{bias}}(f)=\delta$. Then there exist $c_1 = O(\log (1/\delta))$
quadratic polynomials $q_1,\ldots,q_{c_1} \in {\mathbb{F}}[x_1,\ldots,x_n]$
and linear functions $\ell_1,\ldots,\ell_{c_1} \in
{\mathbb{F}}[x_1,\ldots,x_n]$ and another $c_2 =
O(\log^4(\frac{1}{\delta}))$ linear functions
$\ell'_1,\ldots,\ell'_{c_2} \in {\mathbb{F}}[x_1,\ldots,x_n]$ such that $f =
\sum_{j=1}^{c_1} \ell_j \cdot q_j +
g(\ell'_1,\ldots,\ell'_{c_2})$, where $g$ is cubic.
\end{introthm}
We note that if it weren't for the $g(\ell'_1,\ldots,\ell'_{c_2})$
part then this result would be quantitatively the same as
Theorem~\ref{thm:Dickson} (and tight of course). It is an
interesting open question to decide whether we can do only with
the $\sum_{j=1}^{O(\log_{|{\mathbb{F}}|} 1/\delta)} \ell_i \cdot q_i$ part.
Using the same techniques we show a similar result for the case
that $\|f\|_{U^3}
> \delta$.
\begin{introthm}\label{thm:intro:deg-3:gowers}(cubic polynomials with high $U^3$
norm)\sloppy Let ${\mathbb{F}}$ be a finite field and $f \in
{\mathbb{F}}[x_1,\ldots,x_n]$ a cubic polynomial such that
$\|f\|_{U^3}=\delta$. Then there exist $c+1 =
O(\log^2(\frac{1}{\delta}))$ quadratic polynomials
$q_0,\ldots,q_{c} \in {\mathbb{F}}[x_1,\ldots,x_n]$ and $c$ linear functions
$\ell_1,\ldots,\ell_{c} \in {\mathbb{F}}[x_1,\ldots,x_n]$ such that $f =
\sum_{j=1}^{c} \ell_j \cdot q_j +q_0$.
\end{introthm}
Note that the difference between the structure of $f$ in
Theorems~\ref{thm:intro:deg-3:bias} and
\ref{thm:intro:deg-3:gowers} is the number of quadratic function
required. Recall that in \cite{Samorodnitsky07} Samorodnitsky
proved that if an ${\mathbb{F}}_2$ function $f$ has a high $U^3$ norm then
it has an exponentially (in $\|f\|_{U^3}$) high correlation with a
quadratic polynomial. Thus, our theorem shows that when $f$ is a
cubic polynomial then a much stronger statement holds. Namely, $f$
has correlation $\exp(\log^2(1/\delta))$ with a quadratic
polynomial, and further, has a nice structure.
Our second main result is an analog of
Theorem~\ref{thm:intro:deg-3:bias} for the case of quartic
polynomials (i.e. $\deg(f)=4$).
\begin{introthm}\label{thm:intro:deg-4:bias}(biased quartic polynomials)
Let ${\mathbb{F}}$ be a finite field and $f \in {\mathbb{F}}[x_1,\ldots,x_n]$ a
quartic polynomial ($\deg(f)=4$) such that ${\mathrm{bias}}(f)=\delta$. Then
there exist $4c = {\mathrm{poly}}(|{\mathbb{F}}|/\delta)$ polynomials
$\{\ell_i,q_i,q'_i,g_i\}_{i=1}^{c}$, where the $\ell_i$-s are
linear, the $q_i$-s and $q'_i$-s are quadratic and the $g_i$-s are
cubic such that $f = \sum_{j=1}^{c} \ell_j \cdot g_j +
\sum_{j=1}^{c} q_j \cdot q'_j $.
\end{introthm}
As mentioned above, prior to this result it was known that there
exist $C$ cubic polynomials $g_1,\ldots,g_C$ and a function $F$
such that $f=F(g_1,\ldots,g_C)$, where $C$ is a tower of height
$\exp({\mathrm{poly}}(1/\delta))$ \cite{GreenTao07,KaufmanLovett08}. Thus,
our result greatly improves the dependance on $\delta$ and gives a
nice structure for the polynomial. We note that in their work
Green and Tao do show that such a nice structure exists when $d <
|{\mathbb{F}}|$ \cite{GreenTao07}, but no such result was known for smaller
fields (in addition $C$ needs to be even larger for such a nice
representation to hold).
Our third main result is for the case where $\deg(f)=4$ and
$\|f\|_{U^4} = \delta$. In such a case it is known
\cite{LMS08,GreenTao07} that we cannot hope to get a nice
structure as in Theorem~\ref{thm:intro:deg-3:gowers} as it may be
the case that $f$ has an exponentially small (in $n$) correlation
with all lower degree polynomials. However, we do manage to show
that there is some subspace $U \subset {\mathbb{F}}^n$ such that when
restricted to $V$, $f|_U$ is equal to some degree three
polynomial. Thus, $f$ does not have a correlation with a cubic
polynomial in the entire space but instead there is a large
subspace on which it is of degree three. In fact we show a more
general result. Namely, that there is a large subspace $V$, of
dimension $n-O(\log(1/\delta))$, that can be partitioned to
subspaces of dimension $n/\exp(\log^2(1/\delta))$ such that the
restriction of $f$ to any of the subspaces in the partition is of
degree three.
\begin{introthm}\label{thm:intro:deg-4:gowers}(quartic polynomials with high $U^4$ norm)
Let ${\mathbb{F}}$ be a finite field and $f \in {\mathbb{F}}[x_1,\ldots,x_n]$ a degree
four polynomial such that $\|f\|_{U^4}=\delta$. Then there exists
a partition of a subspace $V\subseteq \mathbb{F}^{n}$, of
dimension $\dim(V) \geq n-O(\log(1|/\delta))$, to subspaces
$\left\{ V_{\alpha}\right\} _{\alpha\in I}$, satisfying
$\dim(V_\alpha) =\Omega(n/|{\mathbb{F}}|^{\log^2(1/\delta)})$, such that for
every $\alpha\in I$, $f|_{V_{\alpha}}$ is a cubic polynomial.
\end{introthm}
\begin{remark}
Note that the structure guaranteed in
Theorem~\ref{thm:intro:deg-4:gowers} is shared by very few
polynomials. Specifically, a random polynomial of degree four is
unlikely to be equal to any degree three polynomial on any
subspace of dimension larger than, say, $n^{0.9}$. To see this
note that if $|{\mathbb{F}}|=p$ and $\dim(V)=d$ then there are roughly
$p^{d^3}$ cubic polynomials and $p^{d^4}$ quartic polynomials over
$V$. Furthermore, the map taking a quartic polynomial over ${\mathbb{F}}^n$
to its restriction is a linear map and so the fraction of quartic
polynomials that equal a degree three polynomial on $V$ is
(roughly) $p^{-d^4+d^3}$. As the total number of subspaces can be
bounded by $p^{n^2}$ we get that the fraction of quartic
polynomial that are equal to a degree three polynomial on some
subspace of dimension greater than $n^{0.9}$ is at most $p^{n^2 -
n^{3.6} + n^3} = \exp(-n^{3.6})$.
\end{remark}
This result has the same flavor as the inverse $U^3$ norm theorem
of \cite{GreenTao08}. There it was shown that if $f:{\mathbb{F}}_5^n \to
{\mathbb{F}}_5$ satisfies $\|f\|_{U^3}=\delta$ then there exists a subspace
$V$ of codimension ${\mathrm{poly}}(1/\delta)$, such that on an `average'
coset of $V$, $f$ is correlated with a quadratic polynomial.
Recently, Wolf \cite{Wolf09} proved a similar result for the case
of characteristic two, thus extending Samorodnitsky's argument
\cite{Samorodnitsky07}. The main difference between these results
and our result is that ours only holds for polynomials of degree
four whereas the results of
\cite{GreenTao08,Samorodnitsky07,Wolf09} hold for arbitrary
functions. On the other hand our result holds for the $U^4$ norm
compared to the $U^3$ norm studied there. Moreover, when
$\mathrm{char}({\mathbb{F}})>4$, using the same techniques we can actually
show that $f$ must have a structure similar to the one guaranteed
by Theorem~\ref{thm:intro:deg-4:bias}.
\begin{introthm}\label{thm:intro:deg-4:gowers:high
char} Let ${\mathbb{F}}$ be a finite field with $\mathrm{char}({\mathbb{F}})>4$ and $f
\in {\mathbb{F}}[x_1,\ldots,x_n]$ a degree four polynomial such that
$\|f\|_{U^4}=\delta$. Then
$$f = \sum_{i=1}^{R} \ell_i\cdot g_i + \sum_{i=1}^{r} q_i \cdot
q'_i\;,$$ for $r=O(\log^2(1/\delta))$ and
$R=\exp(\log^2(1/\delta))$ where $\ell_i$ is linear, $q_i,q'_i$
are quadratic and $g_i$ cubic.
\end{introthm}
\ignore{
If instead of knowing that the $U^4$ norm of $f$ is large we know
that its $U^3$ norm is large then we get a stronger conclusion,
namely that $f$ is constant on a large subspace.
\begin{introthm}\label{thm:intro:deg-4:gowers3}(quartic polynomials with high $U^3$ norm)
Let ${\mathbb{F}}$ be a finite field and $f \in {\mathbb{F}}[x_1,\ldots,x_n]$ a degree
four polynomial such that $\|f\|_{U^3}=\delta$. Then there exist a
constant $c = ***$ and a linear space $V \subset {\mathbb{F}}^n$ of
dimension $\dim(V) = n/c$ such that $f|_v = \alpha$ for some
$\alpha \in {\mathbb{F}}$.
\end{introthm}
}
\subsection{Proof Technique}\label{sec:intro:proof technique}
The main approach in all the proofs is to consider the space of
discrete partial derivatives of $f$ and look for some structure
there. We will explain the idea for the case of degree three
polynomials and then its extension to degree four polynomials.
Let $f$ be a degree three polynomials. Assume that $f$ has high
bias (alternatively, high $U^3$ norm). By a standard argument it
follows that a constant fraction of its derivatives, which are
degree $2$ polynomials, have high bias (high $U^2$ norm). By
Theorem~\ref{thm:Dickson} it follows that for a constant fraction
of the directions, the partial derivatives depends on a small
number of linear functions (same for the $U^3$ norm). Hence, in
the space of partial derivatives, a constant fraction of the
elements depend on a few linear functions. We now show that there
must be a small number of linear functions that `explain' this.
More accurately, we show that there exist a subspace $V \subset
{\mathbb{F}}^n$, of dimension $\dim(V) = n - O(1)$, and $O(1)$ linear
functions $\ell_1,\ldots,\ell_c$, such that for every $y \in V$ it
holds that $\Delta_y(f) = \sum_{i=1}^{c} \ell_i \cdot \ell^{(y)}_i
+ \ell^{(y)}_0$, where the $\ell_i^{(y)}$-s are linear functions
determined by $y$.
We are now basically done. Consider the subspace $U = \{x :
\ell_1(x)=\ldots=\ell_c(x)=0\}$. Then, for every $y\in V$ it holds
that $\Delta_y(f)|_U = \ell^{(y)}_0|_U$. This implies that $f|_V =
\sum_{i=1}^{c} \ell_i \cdot q_i + q_0$, where the $q_i$-s are
quadratic polynomials. As $\dim(V) = n-O(1)$ we obtain the same
structure (with a different constant $c$) for $f$.
To prove the result for biased degree four polynomials we follow
the footsteps of \cite{KaufmanLovett08} with two notable
differences. Let $f$ be such a polynomial. First, we pass to a
subspace on which all the partial derivatives of $f$ have low rank
as degree three polynomials. This steps relies on our results for
biased degree three polynomials. Then, as in
\cite{KaufmanLovett08}, we show that $f$ can be approximated by a
function of a few of its derivatives. Because of the properties of
the derivatives, this means that $f$ can be approximated well by a
function of a few quadratics and linear functions. We then show,
again following \cite{KaufmanLovett08}, that in such a case $f$ is
actually a function of a few quadratics and linear functions. Here
we heavily rely on properties of quadratic functions to avoid the
blow up in the number of polynomials approximating $f$ that occurs
in \cite{KaufmanLovett08,GreenTao07}. Finally, we show that if a
degree four polynomial is a function of several quadratic and
linear functions then it actually have a nice structure.
The proof for the case of degree four polynomials with high $U^4$
norm is more delicate. Assume that $f$ is such a polynomial. As
before, a constant fraction of the partial derivatives of $f$ are
degree three polynomials with high $U^3$ norm. By the result for
degree three polynomials we get that each of those partial
derivatives is of the form $\Delta_y(f) = \sum_{i=1}^{c}
\ell^{(y)}_i \cdot q^{(y)}_i + q^{(y)}_0$. Again we find a
subspace $V$, of constant co-dimension, such that for every $y \in
V$, $\Delta_y(f)$ has a nice structure. We now show that there
exist a small number of linear and quadratic functions
$\{\ell_i,q_i\}_{i=1}^{c}$ such that for every $y \in V$ it holds
that $\Delta_y(f) = \sum_{i=1}^{c} \ell_i \cdot q^{(y)}_i +
\sum_{i=1}^{c} \ell^{(y)}_i \cdot q_i + q^{(y)}_0$, where the
polynomials $\{\ell^{(y)}_i,q^{(y)}_i\}$ depend on $y$. This is
the technical heart of the proof. It now follows quite easily that
there is a subspace $U\subseteq V$ of dimension $n/\exp(c)$ such
that when restricted to $U$ all the functions $\{\ell_i,q_i\}$ are
fixed to constants. Thus, for every $y \in U$ it holds that
$\deg(\Delta_y(f)) = 2$. So we get that $\deg(f|_{U}) = 3$. In
fact, by closely examining the argument above we show an even
stronger result. Namely, that we can partition a large subspace of
${\mathbb{F}}^n$ to (affine) subspaces of dimension $n/\exp(c)$ such that on
each of the subspaces $f$ is equal to some cubic polynomial (that
may depend on the subspace).
\subsection{Organization}
In Section~\ref{sec:prelim} we give some basic definitions and
discuss properties of subadditive functions. In
Section~\ref{sec:degree 3} we prove the theorems concerning degree
three polynomials. In Section~\ref{sec:bias 4} we prove
Theorem~\ref{thm:intro:deg-4:bias} and in Section~\ref{sec:U4
norm} we prove Theorems~\ref{thm:intro:deg-4:gowers} and
\ref{thm:intro:deg-4:gowers:high char}.
\section{Preliminaries}\label{sec:prelim}
In this paper ${\mathbb{F}}$ will always be a prime field. We denote with
${\mathbb{F}}_p$ the field with $p$ elements. As we will be considering
functions over ${\mathbb{F}}_p$ we will work modulo the polynomials $x_i^p -
x_i$. In particular, when we write $f=g$, for two polynomials, we
mean that they are equal as functions and not just as formal
expressions. This will be mainly relevant when we consider
quadratic polynomials (or higher degree polynomials) over ${\mathbb{F}}_2$.
More generally, we shall say that a function $f$ has degree $d$ if
there is a degree $d$ polynomial $g$ such that $f=g$. Note that
this does not have an affect on the bias and the Gowers norm.
Namely, the bias and $U^d$ norm of $f$ do not change when adding
multiplies of $x_i^p-x_i$. Finally we note that if all the partial
derivative of $f$ have degree at most $d-1$ then there is a
polynomial $g$ of degree at most $d$ such that $f=g$ (this is
easily proved by observing that a degree $k$ polynomial, all of
whose individual degrees are smaller than $|{\mathbb{F}}|$, always has a
partial derivative whose degree is $k-1$). From this point on we
shall use the notion of a function and a polynomial arbitrarily
without any real distinction.\\
The Fourier transform of a function $f:{\mathbb{F}}^n \to {\mathbb{F}}$ is defined as
$$\hat{f}(\alpha) = {\mathbb{E}}_{x \in {\mathbb{F}}^n}[f(x)\overline{\chi_\alpha(x)}]
\;,$$ where for $\alpha=(\alpha_1,\ldots,\alpha_n)$,
$\chi_\alpha(x) = \omega^{\sum_{i=1}^{n}\alpha_i x_i}$ where
$\omega = e^{\frac{2\pi i}{|{\mathbb{F}}|}}$ is a complex primitive root of
unity of order $|{\mathbb{F}}|$.
For more on Fourier transform see \cite{Stefankovic}.
We say that a function $h$ $\epsilon$-approximates a function $f$
if $\Pr_x[f(x) \neq h(x)]\leq \epsilon$.
\begin{definition}\label{def:gamma-approx}
Following \cite{KaufmanLovett08} we say that the distribution
induced by a set of functions $\{h_i\}_{i=1}^{m}$ (all from ${\mathbb{F}}^n$
to ${\mathbb{F}}$) is $\gamma$ close to the uniform distribution if for
every $\alpha_1,\ldots,\alpha_m \in {\mathbb{F}}$ it holds that $$\left|
\Pr_{x \in {\mathbb{F}}^n}[\forall 1\leq i \leq m,\; h_i(x) = \alpha_i] -
|{\mathbb{F}}|^{-m}\right| \leq \gamma|{\mathbb{F}}|^{-m} \, .$$
\end{definition}
The following well known lemma bounds the distance between
distributions using the Fourier transform.
\begin{lemma}\label{lem:XOR}
For $i =1\ldots m$ let $h_i:{\mathbb{F}}^n \to {\mathbb{F}}$ be a function. Then, the
distribution induced by the $h_i$-s is $\gamma$ close to uniform
if for every nontrivial linear combination
$h_\alpha=\sum_{i=1}^{m} \alpha_i h_i$, we have that
${\mathrm{bias}}(h_\alpha) \leq \gamma/|{\mathbb{F}}|^{3m/2}$.
\end{lemma}
\begin{proof}
Let $H:{\mathbb{F}}^n \to {\mathbb{F}}^m$ be defined as $H(x) =
(h_1(x),\ldots,h_m(x))$. For $y \in {\mathbb{F}}^m$ let $f(y)=\Pr_{x\in
{\mathbb{F}}^n}[H(x)=y]$. We have that
\begin{eqnarray*}
|\hat{f}(\alpha)| &=& \left|{\mathbb{E}}_{y\in
{\mathbb{F}}^m}\left[f(y)\overline{\chi_{\alpha}(y)}\right]\right| =
\left|{\mathbb{E}}_{y \in
{\mathbb{F}}^m}\left[\Pr_{x\in {\mathbb{F}}^n}[H(x)=y]\overline{\chi_{\alpha}(y)}\right]\right| \\
&=& |{\mathbb{F}}|^{-n-m}\left|\sum_{x \in {\mathbb{F}}^n}\chi_{\alpha}[H(x)]\right| =
|{\mathbb{F}}|^{-m}{\mathrm{bias}}\left(\sum_{i=1}^{m}\alpha_i h_i\right)\;.
\end{eqnarray*}
Therefore,
\begin{eqnarray*} \left(\sum_{y \in {\mathbb{F}}^m}\left|f(y) - |{\mathbb{F}}|^{-m}\right|\right)^{2}
&\leq& |{\mathbb{F}}|^m\sum_{y \in {\mathbb{F}}^m}\left|f(y) - |{\mathbb{F}}|^{-m}\right|^2
\\&=& |{\mathbb{F}}|^m\sum_{y \in {\mathbb{F}}^m} f(y)^2 -
2|{\mathbb{F}}|^{-m}f(y) +
|{\mathbb{F}}|^{-2m}\\
&=& \left(\sum_{\alpha \in {\mathbb{F}}^m} |{\mathbb{F}}|^{2m}\hat{f}(\alpha)^2
\right)- 1 =\left(\sum_{0\neq \alpha \in {\mathbb{F}}^m}
|{\mathbb{F}}|^{2m}\hat{f}(\alpha)^2 \right)
\\&=& \sum_{0\neq \alpha \in {\mathbb{F}}^m}
{\mathrm{bias}}\left(\sum_{i=1}^{m}\alpha_i h_i\right)^2 <
|{\mathbb{F}}|^{-2m}\gamma^2 \;.
\end{eqnarray*}
Hence, for every $y \in {\mathbb{F}}^m$ it holds that $|f(y) - |{\mathbb{F}}|^{-m}|<
|{\mathbb{F}}|^{-m}\gamma$, which is what we wanted to prove.
\end{proof}
\subsection{Subadditive functions}
As described in Section~\ref{sec:intro:proof technique} our proofs
are based on finding a structure for the space of partial
derivatives of the underlying polynomial $f$. For this end we need
a special case of the Bogolyubov-Chang lemma (see e.g.
\cite{Green}).
For a set $A \subseteq {\mathbb{F}}^n$ denote with $kA-kA$ the set $$kA-kA =
\{ a_1+\ldots+a_k - a_{k+1}-\ldots-a_{2k} \mid \forall i \; a_i
\in A\}\;.$$
\begin{lemma}[Bogolyubov-Chang]
\label{lem:B-C} Let $A \subseteq U$ be a subset of a linear space
$U$ such that $|A|=\mu_0\cdot |U|$. Then, for some $k \leq
\max(1,\lceil\frac{1}{2}(\log_{\frac{|{\mathbb{F}}|}{|{\mathbb{F}}|-1/2}}(2/\mu_0)+2)\rceil)$,
$kA-kA$ contains a subspace $W$ of co-dimension at most
$\log_{\frac{|{\mathbb{F}}|-1/2}{|{\mathbb{F}}|-1}}(1/2\mu_0)$.
\end{lemma}
For completeness we give the proof here.
\begin{proof}
For $\mu \in (0,1)$ define $\rho(\mu) = \frac{|{\mathbb{F}}| -
1/2}{|{\mathbb{F}}|}\cdot \mu$. We shall think of $A$ also as the
characteristic function of the set $A$ and denote with
$\{\hat{A}(\alpha)\}$ its fourier coefficients. Assume that there
is some $\alpha \neq 0$ such that $|\hat{A}(\alpha)| \geq
\rho(\mu_0)$. This means that there is some (affine) subspace $W$
of co-dimension at most one such that
$$|A\cap W|/|W| \geq \rho(\mu_0) \cdot |{\mathbb{F}}|/(|{\mathbb{F}}|-1) = \frac{|{\mathbb{F}}|
- 1/2}{|{\mathbb{F}}|-1}\cdot \mu_0 = (1+\epsilon) \mu_0\;,$$ where
$\epsilon =\frac{1}{2|{\mathbb{F}}|-2}$. In other words, the density of $A$
on $W$ is $(1+\epsilon)$ larger than its density over the entire
space. We continue restricting $A$ to co-dim one subspaces
(updating $\mu$ and considering $\rho(\mu)$ at each step) until
after at most $t=\log_{\frac{|{\mathbb{F}}|-1/2}{|{\mathbb{F}}|-1}}(1/2\mu_0)$ steps
we reach one of two possibilities. Either we get a subspace
$V\subseteq U$ of co-dimension at most $t$ such that $|A \cap V| >
|V|/2$, or $\widehat{A \cap V}(\alpha) < \rho(\mu)$ for every
$\alpha \neq 0$, where $\mu_0<\mu = |A \cap V|/|V|$. In the first
case it is clear that $(A \cap V) + (A \cap V) = V$ and so we
found a subspace $V$ of co-dimension at most $t$ contained in
$A+A$. In the second case where all the non-zero Fourier
coefficients are smaller than $\rho(\mu)$ we show that for
$k=\lceil
\frac{1}{2}(\log_{\frac{|{\mathbb{F}}|}{|{\mathbb{F}}|-1/2}}(2/\mu)+2)\rceil$ it holds
that $k(A \cap V) - k(A \cap V) = V$. For this end we follow the
proof of Lemma 4.4 in \cite{Green}. Let $B=A \cap V$. For $x \in
V$ denote with $r_k(x)$ the number of representations of $x$ as
$a_1+\ldots+a_k-a'_1-\ldots-a'_k$ where the $a_i$-s and $a'_i$-s
are from $B$. Clearly, $r_k(x)$ is equal to the sum, over all
$(y_1,\ldots,y_k,z_1,\ldots,z_{k-1})\in B^{2k-1}$, of $
A(y_1)\cdot A(y_2)\cdot\ldots\cdot A(y_k)\cdot
A(z_1)\cdot\ldots\cdot A(z_{k-1})\cdot A(y_1+\ldots+y_{k}-
z_1-\ldots-z_{k-1}-x)$. Writing the Fourier expansion $A$ and
using routine calculations we conclude that $$ r_k(x) =
|{\mathbb{F}}|^{(2k-1)n} \cdot
\sum_{\alpha}|\hat{B}(\alpha)|^{2k}\chi_\alpha(x) > |{\mathbb{F}}|^{(2k-1)n}
\cdot \left(\hat{B}(0)^{2k} - \sum_{\alpha\neq
0}|\hat{B}(\alpha)|^{2k}\right)\geq$$
$$|{\mathbb{F}}|^{(2k-1)n} \cdot \left(\hat{B}(0)^{2k} -
\rho(\mu)^{2k-2}\sum_{\alpha}|\hat{B}(\alpha)|^{2}\right) =
|{\mathbb{F}}|^{(2k-1)n} \cdot \left(\mu^{2k} - \rho(\mu)^{2k-2} \mu\right)
> 0\;,$$ where the last inequality follows from the choice of $k$
(we also used the fact that $A$ is a $0/1$ function). In
particular, $V \subseteq kA-kA$ as needed.
\end{proof}
We will mainly apply the lemma on sets $A \subseteq {\mathbb{F}}^n$
containing all directions where the partial derivatives of our
underlying polynomial $f$ are either very biased or have a high
Gowers norm. More generally we define the notion of a subadditive
function below.
\begin{definition}\label{def:sub additive}
Let $V \subset {\mathbb{F}}^n$ be a linear space. $\mathcal{F}:V \to {\mathbb{R}}^+$
is a subadditive function if for every $u,v \in V$ and $\alpha \in
{\mathbb{F}}$ it holds that $\mathcal{F}(\alpha\cdot u+v) \leq
\mathcal{F}(u)+\mathcal{F}(v)$.
\end{definition}
\begin{lemma}
\label{lem:subadditive} Let $\mathcal{F}:U\rightarrow\mathbb{R}^+$
be a subadditive function. Define, $A_{r}\triangleq\left\{ x\in
U\mid\mathcal{F}(x)\leq r\right\} $. If $|A_{r}|\geq \mu|U|$, then
there exists a vector space $V$ of co-dimension at most
$\log_{\frac{|{\mathbb{F}}|-1/2}{|{\mathbb{F}}|-1}}(1/2\mu) = O(\log(1/\mu))$ such
that for every $y \in V$ it holds that ${\cal F}(y) \leq 2r\cdot
\lceil\frac{1}{2}(\log_{\frac{|{\mathbb{F}}|}{|{\mathbb{F}}|-1/2}}(2/\mu)+2)\rceil+2r
= O(r \log(1/\mu))$.
\end{lemma}
\begin{proof}
The proof is immediate from Lemma~\ref{lem:B-C}. Let $V$ be the
subspace guaranteed by the lemma when applied on $A_r$. As $V
\subseteq kA_r-kA_r$, for $k \leq
\max(1,\lceil\frac{1}{2}(\log_{\frac{|{\mathbb{F}}|}{|{\mathbb{F}}|-1/2}}(2/\mu)+2)\rceil)$,
we get that ${\cal F}(y) \leq 2kr$ for every $y\in V$.
\end{proof}
A typical example of a subadditive function will be the rank of a
quadratic polynomial.
\begin{definition}\label{def:rank of quadratic}
Let $q$ be a degree two function over a prime field ${\mathbb{F}}$. We
define ${\mathrm{rank}}_2(q) = r$, where $r$ is the number of $\alpha_i$-s
that are non zero when considering the canonical representation of
$q$ in Theorem~\ref{thm:Dickson}.
\end{definition}
The following lemma is immediate.
\begin{lemma}\label{lem: rank is subadditive}
For two quadratic polynomials $q,q'$ and a constant $\alpha \in
{\mathbb{F}}$ we have that ${\mathrm{rank}}_2(q + \alpha q') \leq {\mathrm{rank}}_2(q) +
{\mathrm{rank}}_2(q')$.
\end{lemma}
A more interesting example is given in the following lemma.
\begin{lemma}\label{lem:subadditivity of derivatives}
Let $f$ be a cubic polynomial over a prime field ${\mathbb{F}}$. For every
$y \in {\mathbb{F}}^n$ define ${\cal F}(y) = {\mathrm{rank}}_2(\Delta_y(f))$. Then
$\cal F$ is a subadditive function.
\end{lemma}
\begin{proof}
The proof follows from the following simple observation
\begin{eqnarray*}
\Delta_y(f) + \Delta_z(f) &=& f(x+y)-f(x) + f(x+z)-f(x)\\ &=&
f(x+y+z) - f(x) - (f(x+y+z)-f(x+y) - (f(x+z)-f(x))) \\ &=&
\Delta_{y+z}(f)(x) - (\Delta_z(f)(x+y) - \Delta_z(f)(x))\\
&=& \Delta_{y+z}(f)(x) - \Delta_y\Delta_z(f)(x) \;.
\end{eqnarray*}
Indeed, we now get that ${\cal F}(y+z) = {\mathrm{rank}}_2(\Delta_{y+z}(f))
= {\mathrm{rank}}_2(\Delta_y(f) + \Delta_z(f) +\Delta_y\Delta_z(f)(x)) =
{\mathrm{rank}}_2(\Delta_y(f) + \Delta_z(f)) \leq {\mathrm{rank}}_2(\Delta_y(f)) +
{\mathrm{rank}}_2(\Delta_z(f))={\cal F}(y)+{\cal F}(z)$, where we used the
fact that adding a linear function to a quadratic polynomial does
not change its rank.
\end{proof}
\section{The structure of cubic polynomials}\label{sec:degree 3}
In this section we prove Theorems~\ref{thm:intro:deg-3:bias} and
\ref{thm:intro:deg-3:gowers}. As described in
Section~\ref{sec:intro:proof technique} both proofs are based on
finding a structure for the space of partial derivatives of $f$.
\subsection{Restricting the polynomial to a `good' subspace}\label{sec:3-good-subspace}
In this section we show that if a cubic $f$ ia biased or have a
large $U^3$ norm then there is a subspace $V \subseteq {\mathbb{F}}^n$ such
that for every $y \in V$ the rank of $\Delta_y(f)$ is relatively
small. We start by showing that if $f$ is biased or has a high
Gowers norm then so do many of its partial derivatives. The
following lemmas are well known and we prove them here for
completeness.
\begin{lemma}
\label{lem:biased der}Let
$f:\mathbb{F}_{p}^{n}\rightarrow\mathbb{F}_{p}$ be such that
${\mathrm{bias}}(f) = \delta$. Then a fraction of at least
$\frac{1}{2}\delta^{2}$ of the partial derivatives $\Delta_{y}(f)$
satisfy ${\mathrm{bias}}(\Delta_y(f)) \geq \frac{1}{2}\delta^{2}$.
\end{lemma}
\begin{proof}
We first compute the expected bias of a partial derivative with
respect to a random direction. {\begin{eqnarray*}
\mathbb{E}_{y\in\mathbb{F}^{n}}\left[\mbox{bias}(\Delta_y(f))\right]
& = &
\mathbb{E}_{y\in\mathbb{F}^{n}}\left[\left|\mathbb{E}_{x\in\mathbb{F}^{n}}
\left[\omega^{\Delta_y(f)(x)}\right]\right|\right]
\geq\left|\mathbb{E}_{y\in\mathbb{F}^{n}}
\left[\mathbb{E}_{x\in\mathbb{F}^{n}}\left[\omega^{f(x+y)-f(x)}\right]\right]\right|\\
& = & \left|\mathbb{E}_{y\in\mathbb{F}^{n},x\in\mathbb{F}^{n}}\left[\omega^{f(x+y)}\omega^{-f(x)}\right]\right|=
\left|\mathbb{E}_{z\in\mathbb{F}^{n},x\in\mathbb{F}^{n}}\left[\omega^{f(z)}\omega^{-f(x)}\right]\right|\\
& = & \left|\mathbb{E}_{z\in\mathbb{F}^{n}}\left[\omega^{f(z)}\right]
\right|\left|\overline{\mathbb{E}_{x\in\mathbb{F}^{n}}\left[\omega^{f(x)}\right]}\right|=
\delta\cdot\delta=\delta^{2} \;.\end{eqnarray*}
}
Therefore, by the fact that $\mbox{bias}(f)\leq1$, it follows that
$$\Pr_{y\in\mathbb{F}^{n}}\left[\mbox{bias}(\Delta_y(f))>\frac{1}{2}\delta^{2}\right]>\frac{1}{2}\delta^{2} \;.$$
\end{proof}
A similar result holds when $f$ has a high $U^d$ norm.
\begin{lemma}
\label{lem:gowers norm of der}Let
$f:\mathbb{F}_{p}^{n}\rightarrow\mathbb{F}_{p}$ be such that
$\|f\|_{U^d} = \delta$. Then a fraction of at least
$\frac{1}{2}\delta^{2^{d}}$ of the partial derivatives
$\Delta_{y}(f)$ satisfy $\|\Delta_y(f)\|_{U^{d-1}} \geq
\frac{1}{2}\delta^{2}$.
\end{lemma}
\begin{proof}
The proof is again immediate from the definition.
\begin{eqnarray*} \delta^{2^d} = \|f\|_{U^d}^{2^d} & = &
\left|{\mathbb{E}}_{x,y_1,\ldots,y_d}\left[\omega^{\Delta_{y_1}\ldots\Delta_{y_d}(f)(x)}\right]\right|\\
&\leq &
{\mathbb{E}}_{y_d}\left|{\mathbb{E}}_{x,y_1,\ldots,y_{d-1}}\left[\omega^{\Delta_{y_1}\ldots\Delta_{y_{d-1}}(\Delta_{y_d}(f))(x)}\right]\right|\\
& = & {\mathbb{E}}_{y}\left[\|\Delta_{y}(f)\|_{U^{d-1}}^{2^{d-1}}\right] \;.
\end{eqnarray*}
As before we get that
$$\Pr_{y\in\mathbb{F}^{n}}\left[\|\Delta_y(f)\|_{U^{d-1}}>\frac{1}{2}\delta^{2}\right]>\frac{1}{2}\delta^{2^{d}}
\;.$$
\end{proof}
We thus see that in both cases a constant fraction of all partial
derivatives of $f$ have high bias or high $U^2$ norm. From
Theorem~\ref{thm:Dickson} we get that if a partial derivative
(which is a quadratic function) has a high bias then it depends on
a few linear functions.
\begin{lemma}\label{lem:rank of biased quadratic}
Let $q$ be a quadratic polynomial over a prime field ${\mathbb{F}}$. Then
$q$ is a function of at most $\log_{|{\mathbb{F}}|}({\mathrm{bias}}(q))+1$ linear
functions. More accurately, in the notations of
Theorem~\ref{thm:Dickson} the number of non zero $\alpha_i$-s is
at most $\log_{|{\mathbb{F}}|}(1/{\mathrm{bias}}(q))$.
\end{lemma}
\begin{proof}
See e.g. Lemmas 15-17 of \cite{BogdanovViola07}.
\end{proof}
The next lemma of Bogdanov and Viola \cite{BogdanovViola07} shows
that a similar result holds when a partial derivative has a high
$U^2$ norm.
\begin{lemma}\label{lem:rank of quadratic with high U2}(Lemma 15
of \cite{BogdanovViola07}) Every quadratic polynomial $q$ over a
prime field ${\mathbb{F}}$ is a function of at most
$\log_{|{\mathbb{F}}|}(1/\|q\|_{U^2})+ 1$ linear functions. Further, in the
notations of Theorem~\ref{thm:Dickson} the number of non zero
$\alpha_i$-s is at most $\log_{|{\mathbb{F}}|}(1/\|q\|_{U^2})$.
\end{lemma}
Concluding, we have proved the following lemma (recall
Definition~\ref{def:rank of quadratic}).
\begin{lemma}\label{lem:structur of non random cubic}
Let $f$ be a cubic polynomial.
\begin{enumerate}
\item If ${\mathrm{bias}}(f) = \delta$, then for (at least) a
$\frac{\delta^2}{2}$ fraction of $y \in {\mathbb{F}}^n$ it holds that
${\mathrm{rank}}_2(\Delta_y(f)) \leq \log_{|{\mathbb{F}}|}(\frac{2}{\delta^2})$.
\item If $\|f\|_{U^2} = \delta$, then for (at least) a
$\frac{\delta^4}{2}$ fraction of $y \in {\mathbb{F}}^n$ it holds that
${\mathrm{rank}}_2(\Delta_y(f)) \leq \log_{|{\mathbb{F}}|}(\frac{2}{\delta^2})$.
\end{enumerate}
\end{lemma}
We now combine Lemma~\ref{lem:subadditivity of derivatives} with
Lemma~\ref{lem:structur of non random cubic} and
Lemma~\ref{lem:subadditive} and obtain the following corollary.
\begin{corollary}\label{cor:good subspace of low rank}
Let $f$ be a cubic polynomial. If ${\mathrm{bias}}(f) = \delta$ or
$\|f\|_{U^2} = \delta$, then there exists a subspace $V \subseteq
{\mathbb{F}}^n$ such that $\dim(V) \geq n - O(\log(\frac{1}{\delta}))$ and
such that for every $y \in V$ it holds that ${\mathrm{rank}}_2(\Delta_y(f))
= O(\log^2(\frac{1}{\delta}))$.
\end{corollary}
\subsection{The structure of low rank spaces}
So far we have established the existence of a subspace $V
\subseteq{\mathbb{F}}^{n}$ such that for every $y \in V$ it holds that
${\mathrm{rank}}_{2}(\Delta_{y}(f)) = O(\log^{2}(\frac{1}{\delta}))$. We now
show that such spaces of low rank polynomials have a very
restricted structure. Namely, there exist
$r=O(\log^{2}(\frac{1}{\delta}))$ linear functions
$\ell_{1},\ldots,\ell_{r}$ such that every $\Delta_{y}(f)$ can be
written as $\Delta_{y}(f) = \sum_{i=1}^{r} \ell_{i}
\cdot\ell_{i}^{(y)} + \ell_{0}^{(y)}$, where the
$\ell_{i}^{(y)}$-s are linear functions determined by $y$. The
intuition behind this result is that ${\mathrm{rank}}_{2}(q+q')$ can be much
smaller than ${\mathrm{rank}}_{2}(q)+{\mathrm{rank}}_{2}(q')$ only if there is some
basis with respect to which $q$ and $q'$ share many linear
functions when represented in the form of
Theorem~\ref{thm:Dickson}. From this observation we deduce that if
we consider some function of maximal rank,
$q=\sum_{i=1}^{r}\ell_{i} \cdot\ell_{i}'$, and set $\left\{
\ell_{i},\ell'_{i}\right\} _{i=1}^{r}$ to zero (namely, consider
the subspace on which they all vanish), then on this subspace the
rank of the remaining quadratic functions decreases by a factor of
two. Repeating this argument we get that after setting at most
$4r$ linear functions to zero, all our quadratic functions become
linear functions.
\begin{lemma}
\label{lem:low rank space have few common functions} Let $M$ be a
linear space of quadratic functions satisfying ${\mathrm{rank}}_2(p) \leq r$
for all $p \in M$. Then there exists a subspace $V \subseteq{\mathbb{F}}^{n}
$ of co-dimension $\leq 4r$ such that $p|_{V}$ is a linear
function for all $p \in M$.
\end{lemma}
We shall give the proof for the case ${\mathbb{F}}={\mathbb{F}}_2$. The proof for odd
characteristics is very similar (except that in the odd
characteristic case we have that the co-dimension of $V$ is $2r$
whereas in the even characteristic case it is $4r$).
\begin{proof}\sloppy
Let $g\in M$ be such that ${\mathrm{rank}}_2(g)=r$. By
Theorem~\ref{thm:Dickson}, $g$ can be expressed as
$g=\sum_{i=1}^{r}\ell_{2i-1} \cdot \ell_{2i} + \ell_0$. Denote
$V\triangleq \left\{
x\mid\ell_{1}(x)=\ell_{2}(x)=...=\ell_{2r}(x)=0\right\}$. We now
show that for every $h\in M$ it holds that ${\mathrm{rank}}_2(h|_V)\leq
\frac{r}{2}$. Repeating this argument we get that after setting at
most $2r + 2(r/2) + 2(r/4) + \ldots \leq 4r$ linear functions to
zero, the rank of all the quadratic functions in $M$ became zero.
Pick some $h\in M$ and denote ${\mathrm{rank}}_2(h|_V)=s$. As before, $h|_V$
can be expressed as $h|_{V}=\sum_{i=1}^{s}m_{2i-1}\cdot m_{2i} +
m_0$ (where the $m_{i}$-s are linear functions). Clearly the
functions $\{\ell_1,\ldots,\ell_{2r},m_1,\ldots,m_{2s}\}$ are
linearly independent. We can therefore write
$$h = \sum_{i=1}^{s}m_{2i-1}\cdot m_{2i} + m_0 +
\sum_{i=1}^{2r}\ell_i \cdot L_i \;,$$ where the $L_i$-s are linear
functions. Write $L_i = \tilde{m}_i + \tilde{\ell}_i +
\tilde{L}_i$ where $\tilde{m}_i \in
\mathrm{span}\{m_0,\ldots,m_{2s}\}$, $\tilde{\ell}_i \in
\mathrm{span}\{\ell_0,\ldots,\ell_{2r}\}$ and $\tilde{L}_i$ is
linearly independent of the $m_j$-s and $\ell_j$-s. Rearranging
terms we get that
$$h = \sum_{i=1}^{s}(m_{2i-1} + \ell'_{2i-1})\cdot (m_{2i}+ \ell'_{2i}) + (m_0 +\ell'_0) +
\tilde{h}(\ell_0,\ldots,\ell_{2r},\tilde{L}_1,\ldots,\tilde{L}_{2r})\;,$$
where each $\ell'_i$ is in the span of the $\ell_i$-s and
$\tilde{h}$ is a quadratic polynomial. Denote $m'_i = m_i +
\ell'_i$. It is clear that
$\ell_0,\ldots,\ell_{2r},\tilde{L}_1,\ldots,\tilde{L}_{2r}$ are
linearly independent of the $m'_i$-s (and vice versa).
Consequently,\footnote{From Theorem~\ref{thm:Dickson} it is clear
that for quadratic polynomials $q_1,q_2$ it holds that
${\mathrm{rank}}_2(q_1(\bar{x})+q_2(\bar{y})) =
{\mathrm{rank}}_2(q_1(\bar{x}))+{\mathrm{rank}}_2(q_2(\bar{y}))$. }
${\mathrm{rank}}_2(\sum_{i=1}^{s}m'_{2i-1}\cdot m'_{2i} + m'_0) +
{\mathrm{rank}}_2(\tilde{h}) = {\mathrm{rank}}_2(h) \leq r$. Hence,
${\mathrm{rank}}_2(\tilde{h}) \leq r-s$. We now get that
$$r \geq {\mathrm{rank}}_2(g+h) = {\mathrm{rank}}_2\left(\sum_{i=1}^{s}m'_{2i-1}\cdot m'_{2i} + m'_0
+\tilde{h}(\ell_0,\ldots,\ell_{2r},\tilde{L}_1,\ldots,\tilde{L}_{2r})
+g\right) =$$ $${\mathrm{rank}}_2\left(\sum_{i=1}^{s}m'_{2i-1}\cdot m'_{2i}
+ m'_0\right) + {\mathrm{rank}}_2\left(g +
\tilde{h}(\ell_0,\ldots,\ell_{2r},\tilde{L}_1,\ldots,\tilde{L}_{2r})\right)
\geq s + (r - (r-s)) =2s \;,$$ where we used the fact that
${\mathrm{rank}}_2(g+\tilde{h})\geq {\mathrm{rank}}_2(g)-{\mathrm{rank}}_2(\tilde{h})$. As we
showed that $r \geq 2s$ the proof is completed.
\end{proof}
\ignore{
Repeating this argument $r$ times yield the next
corollary.\footnote{In fact, the proof above and the corollary can
be made tighter but as it will not improve our end result we did
not make an attempt to improve the parameters.}
\begin{corollary}
\label{cor:Low rank few common functions}Let $M$ be a vector space
of quadratic functions satisfying ${\mathrm{rank}}_2(M)\leq r$. Then there
exists a set $A=\left\{ \ell_{i}\right\} _{i=1}^{r^{2}}$ of
linearly independent linear functions such that
${\mathrm{rank}}_2([M]_A)=0$. In other words, every $q \in M$ can be written
as $q=\sum_{i=1}^{r^{2}}\ell_{i}\ell_{i}'+\ell_{0}'$ for some
linear functions $\left\{ \ell_{i}'\right\} _{i=0}^{r^{2}}$.
\end{corollary}
}
\subsection{Completing the proofs}
We are no ready to complete the proofs of
Theorems~\ref{thm:intro:deg-3:bias} and
\ref{thm:intro:deg-3:gowers}.
\begin{proof}[Proof of Theorem~\ref{thm:intro:deg-3:gowers}]
By Corollary~\ref{cor:good subspace of low rank} we get that if
$\|f\|_{U^2} = \delta$, then there exists a subspace $V \subseteq
{\mathbb{F}}^n$ such that $\dim(V) \geq n - O(\log(1/\delta))$ and such that
for every $y \in V$ it holds that ${\mathrm{rank}}_2(\Delta_y(f)) =
O(\log^2(\frac{1}{\delta}))$. Lemma~\ref{lem:low rank space have
few common functions} implies that there are at most
$r=O(\log^2(\frac{1}{\delta}))$ linear functions
$\ell_1,\ldots,\ell_r$ such that for every $y \in V$ we have that
$\Delta_y(f) = \sum_{i=1}^{r}\ell_i \cdot \ell^{(y)}_i +
\ell^{(y)}_0$. Let $U = \{x\in V \mid\ell_1(x) = \ldots \ell_r(x)
= 0 \}$. Then $U$ is a linear space of dimension $\dim(U) \geq
n-O(\log^2(\frac{1}{\delta}))$. For every $y \in U$ we have that
$\Delta_y(f)|_U = \ell^{(y)}_0|_U$. Hence, for every $y \in U$,
$\deg(\Delta_y(f)) \leq 1$. Therefore, $\deg(f|_U) \leq 2$. Let
$\ell'_1,\ldots,\ell'_t$ be linearly independent linear functions
such that $x \in U$ iff $\ell'_1(x)=\ldots=\ell'_t(x)=0$. It
follows that we can write $f = \sum_{i=1}^{t}\ell'_i \cdot q_i +
q_0$ for some quadratic polynomials $\{q_i\}$. As $t = n - \dim(U)
= O(\log^2(\frac{1}{\delta}))$ the result follows.
\end{proof}
The proof of Theorem~\ref{thm:intro:deg-3:bias} is essentially the
same except that we make another small optimization that reduces
the required number of quadratic functions.
\begin{proof}[Proof of Theorem~\ref{thm:intro:deg-3:bias}]
By the same argument as above we get that $f =
\sum_{i=1}^{t}\ell_i \cdot q_i + q_0$ for some quadratic
polynomials $\{q_i\}$ and linear functions $\{\ell_i\}$, where $t
= O(\log^2(\frac{1}{\delta}))$. For convenience we shall assume
w.l.o.g. that
\begin{equation}\label{eq: f before reducing t} f = \sum_{i=1}^{t}x_i \cdot q_i + q_0
\;.\end{equation} The following lemma shows that by adding a few
more linear functions we can assume that no nontrivial linear
combination of the $q_i$-s has a low rank.
\begin{lemma}\label{lem:regularizing a set of quadratics}
Let $q_1,\ldots,q_t$ be quadratic polynomials over ${\mathbb{F}}^n$. Then,
for every $r$ there exist a subspace $V \subset {\mathbb{F}}^n$ of dimension
$\dim(V) \geq n - t(r+1)$, and $t' \leq t$ indices
$i_1,\ldots,i_{t'}$ such that for every affine shift $V'$ of $V$
the following holds
\begin{enumerate}
\item For all $i$, $q_i|_{V'} \in
\mathrm{span}\{1,q_{i_1}|_{V'},\ldots,q_{i_{t'}}|_{V'}\}$.
\item For any non trivial linear combination we have that
${\mathrm{rank}}_2\left(\sum_{j=1}^{t'}\alpha_i q_{i_j}|_{V'}\right) >r$.
\end{enumerate}
\end{lemma}
\begin{proof}
The proof is by induction on $t$. For $t=1$ the claim is clear: If
${\mathrm{rank}}_2(q_1) >r$ then we are done. Otherwise we have $q_1 =
\sum_{i=1}^{r}\ell_{2i-1}\ell_{2i} + \ell_0$. Letting $V = \{x\mid
\ell_0(x)=\ell_2(x)=\ldots=\ell_{2r}(x)=0\}$ the claim follows
(indeed notice that passing to an affine shift of $V$ simply means
fixing the $\ell_i$-s to arbitrary values). Assume now that we
have $q_1,\ldots,q_t$ and that (w.l.o.g.) ${\mathrm{rank}}_2\left(q_t +
\sum_{i=1}^{t-1}\alpha_i q_i\right) \leq r$. Write $q_t +
\sum_{i=1}^{t-1}\alpha_i q_i = \sum_{i=1}^{r}\ell_{2i-1}\ell_{2i}
+ \ell_0$. Set $V = \{x\mid
\ell_0(x)=\ell_2(x)=\ldots=\ell_{2r}(x)=0\}$. Then, $q_t|_V \in
\mathrm{span}\{q_1|_V.\ldots,q_{t-1}|_V\}$. As $\dim(V) = n-(r+1)$
the claim follows by applying the induction argument to
$q_1|_V.\ldots,q_{t-1}|_V$ (again the claim about any affine shift
follows easily).
\end{proof}
We continue with the proof of the theorem. Having
Equation~\eqref{eq: f before reducing t} in mind we set $U =
\{(0,\ldots,0,x_{t+1},\ldots,x_n)\} \subset {\mathbb{F}}^n$. Applying
Lemma~\ref{lem:regularizing a set of quadratics} on
$q_1|_U,\ldots,q_t|_U$ with $r=\log_{|{\mathbb{F}}|}(2/\delta)$ we get that
there is a subspace $W \subset U$ and $t' \leq t$ such that:
$\dim(W) \geq \dim(U) - (r+1)t \geq n - (r+2)t =
n-O(\log^3(\frac{1}{\delta}))$; w.l.o.g. for every $i=1\dots t$,
$q_i|_W \in \mathrm{span}\{q_1|_W,\ldots,q_{t'}|_W\}$; any
nontrivial linear combination of $q_1|_W,\ldots,q_{t'}|_W$ has
rank larger than $r$. By applying an invertible linear
transformation\footnote{This step is not really required but we
continue using it just to make the proofs easier to read.} we can
further assume that $W = \{x \in {\mathbb{F}}^m \mid x_1=\ldots=x_m=0\}$ for
some $m \leq (r+2)t$. For $i=1\ldots t'$ let $q'_i = q_i|_W$. Note
that $q'_i$ does not contain any of the variables
$x_1,\ldots,x_m$. We can rewrite Equation~\eqref{eq: f before
reducing t} as\footnote{We will later explain why $q_0$
`disappeared' from this expression.}
\begin{equation}\label{eq:
f after reducing t} f = \sum_{i=1}^{t'}\ell'_i q'_i +
\sum_{i=1}^{t}\sum_{j=1}^{m}x_i x_j \ell_{i,j}\;,\end{equation}
where the $\ell'_i$-s are linearly independent linear functions in
$x_1,\ldots,x_{t}$. We now show that $t' < \log_{|{\mathbb{F}}|}(2/\delta)$.
Assume for contradiction that $t' \geq \log_{|{\mathbb{F}}|}(2/\delta)$. As
$${\mathrm{bias}}(f) =
{\mathbb{E}}_{\alpha_1,\ldots,\alpha_{t'}}\left[{\mathrm{bias}}(f(x_{1},\ldots,
x_n)|_{(\ell'_1,\ldots,\ell'_{t'})=(\alpha_1,\ldots,\alpha_{t'})}\right]\;,$$
\sloppy there exists an assignment
$(x_1,\ldots,x_m)=(\beta_1,\ldots,\beta_m)$ satisfying
$(\ell'_1,\ldots,\ell_{t'}) = (\alpha_1,\ldots,\alpha_{t'})\neq 0$
such that
$${\mathrm{bias}}\left(\sum_{i=1}^{t'}\alpha_i q'_i +
\sum_{i=1}^{t}\beta_i\sum_{j=1}^{m} \beta_j \ell_{i,j} \right)
\geq \delta - \frac{1}{|{\mathbb{F}}|^{t'}} \geq \delta/2\;.$$ Therefore,
for some constants $\alpha_1,\ldots,\alpha_{t'}$ (where not all
$\alpha_1,\ldots,\alpha_{t'}$ are zero) we have that
$${\mathrm{bias}}\left( \sum_{i=1}^{t'}\alpha_i q'_i + \ell\right)\geq \delta/2 \;,$$ for some
linear function $\ell$. By Lemma~\ref{lem:rank of biased
quadratic} we get that
$${\mathrm{rank}}_2\left(\sum_{i=1}^{t'}\alpha_i q'_i\right) =
{\mathrm{rank}}_2\left(\sum_{i=1}^{t'}\alpha_i q'_i + \ell\right) \leq
\log_{|{\mathbb{F}}|}(1/(\delta/2)) = r \;,$$ in contradiction to the
choice of $q'_1,\ldots,q'_{t'}$.
To complete the proof we explain the reason for dropping $q_0$.
Indeed, consider Equation~\eqref{eq: f before reducing t}. Let $U
= \{x\mid x_1=\ldots=x_t=0\}$. Set $\tilde{q}_i = q_i|_U$. Then we
can rewrite \eqref{eq: f before reducing t} as
$\sum_{i=1}^{t}x_i\tilde{q}_i + \tilde{q}_0 + \sum_{i=1}^{t}x_i
\sum_{j=1}^{t} x_{j} \ell_{i,j}$, for some linear functions
$\ell_{i,j}$. Now, for some $\alpha_1,\ldots,\alpha_t$ we get that
${\mathrm{bias}}(\sum_{i=1}^{t}\alpha_i\tilde{q}_i + \tilde{q}_0 +
\sum_{i=1}^{t}\alpha_i \sum_{j=1}^{t} \alpha_j \ell_{i,j}) \geq
\delta.$ Lemma~\ref{lem:rank of biased quadratic} implies that
${\mathrm{rank}}_2(\sum_{i=1}^{t}\alpha_i\tilde{q}_i + \tilde{q}_0) \leq
\log_{|{\mathbb{F}}|}(1/\delta)$ and so we can replace $\tilde{q}_0$ by a
linear combination of the other $\tilde{q}_i$-s and a function
depending on a few linear functions. By passing to a (possibly
affine) subspace of dimension at least $n -
\log_{|{\mathbb{F}}|}(1/\delta)-1$ we get a representation for $f$ without
$q_0$. This operation increases $t'$ in Equation~\eqref{eq: f
after reducing t} by no more than $\log_{|{\mathbb{F}}|}(1/\delta)+1$ and so
we are done.
\end{proof}
\section{The structure of biased 4 degree polynomials}\label{sec:bias 4}
In this section we prove Theorem~\ref{thm:intro:deg-4:bias} on the
structure of biased degree 4 polynomials. As in the case of cubic
polynomials, we shall focus our attention on a subspace on which
all of derivatives have a small rank (a cubic polynomial is of low
rank if it depends on a small number of linear and quadratic
functions). By a lemma of Bogdanov and Viola
\cite{BogdanovViola07} (Lemma \ref{lem:Bogdanov and Viola}) we get
that $f$ can be well approximated by a function of a small number
of its derivatives (which in our case, are all of low rank). Thus,
$f$ is well approximated by a function of a few linear and
quadratic polynomials. By passing to a subspace we can assume that
$f$ is well approximated by a function of a small number of
quadratic polynomials. Lemma~\ref{lem:regularizing a set of
quadratics} implies that (possibly on a slightly smaller
subspace) $f$ can be well approximated by a function of a small
number of quadratics, that every nontrivial linear combination of
them has a high rank. We then show that in this case those
quadratic functions are in fact {\em strongly regular} (a notion
that we later explain) and therefore by a theorem of Kaufman and
Lovett \cite{KaufmanLovett08}, $f$ in fact equals a function in
those quadratic (on the subspace). We then finish the proof by
showing that in this case $f$ also have a nice structure.
\ignore{
and deduce, using lemma \ref{lem:rank implie
regular}, that those family of function is strong regular. Using
lemma \ref{lem:Kaufman Lovett} of Kaufman and Lovett (\cite{KL08})
we deduce that our degree 4 polynomial can compute precisely as a
function $F$ of those quadratic functions. We'll conclude by argue
that $F$ must have a degree 2, otherwise our original polynomial's
degree will not be two. In conclusion, after reconsider the linear
functions set to zero, every biased degree 4 polynomial have the
form $\sum_{i=1}^{q}l_{i}T_{i}+\sum_{i=1}^{r}Q_{i}Q_{i}'+Q_{0}$. }
\subsection{Restricting the polynomial to a `good'
subspace}\label{sec:bias 4: restricting}
In this section we prove an analogous result to
Corollary~\ref{cor:good subspace of low rank}. We first define the
rank of a cubic polynomial.
\begin{definition}\label{def:cubic rank}
Let $g$ be a degree three polynomial. We define ${\mathrm{rank}}_3(g)$ to be
the minimal integer $r$ for which there are $r$ linear functions
$\ell_1,\ldots,\ell_r$ and $r+1$ quadratic functions
$q_0,\ldots,q_r$ such that $g=\sum_{i=1}^{r}\ell_{i}q_{i}+q_{0}$.
\end{definition}
\begin{lemma}\label{lem:good subspace of low rank for quartics}
Let $f$ be a degree four polynomial satisfying ${\mathrm{bias}}(f)=\delta$.
Then there exist a linear subspace $V \subseteq {\mathbb{F}}^n$ of dimension
$\dim(V) \geq n -O(\log_{|{\mathbb{F}}|}(1/\delta))$, such that for every $y
\in V$ ${\mathrm{rank}}_3(\Delta_y(f)) = \log^{O(1)}(1/\delta)$.
\end{lemma}
\begin{proof}
As before, define ${\cal F}(y) \triangleq {\mathrm{rank}}_3(\Delta_y(f))$. It is
again not difficult to see that $\cal F$ is a subadditive
function. By Lemma~\ref{lem:biased der} we get that there is a
subset $S \subseteq {\mathbb{F}}^n$ of size $\frac{\delta^2}{2}\cdot {\mathbb{F}}^n$
such that for all $y \in S$, ${\mathrm{bias}}(\Delta_y(f)) \geq
\frac{\delta^2}{2}$. Theorem~\ref{thm:intro:deg-3:bias} implies
that for every $y \in S$ it holds that ${\mathrm{rank}}_3(\Delta_y(f)) =
O(\log^4(\frac{1}{\delta}))$. From Lemma~\ref{lem:subadditive} it
follows that there is a linear subspace $V \subseteq {\mathbb{F}}^n$ with
$\dim(V) \geq n - O(\log_{|{\mathbb{F}}|}(1/\delta))$, such that for every
$y \in V$ ${\mathrm{rank}}_3(\Delta_y(f)) = O(\log^5(\frac{1}{\delta}))$.
\end{proof}
\sloppy By applying an invertible linear transformation we can
assume that $V = \{x :x_1=\ldots=x_{m}=0\}$ for some $m=
O(\log_{|{\mathbb{F}}|}(1/\delta))$. We now have \begin{equation}\label{eq:
quartic on subspace} f = \sum_{i=1}^{m}x_i g_i + f' \;,
\end{equation}
where $f'=f'(x_{m+1},\ldots,x_n)$. Moreover, by
Lemma~\ref{lem:good subspace of low rank for quartics} it follows
that for every $y = (0,\ldots,0,y_{m+1},\ldots,y_n)$,
${\mathrm{rank}}_3(\Delta_y(f)) = O(\log^5(\frac{1}{\delta}))$. Notice that
for every such $y$ it holds that $$\Delta_y(f) = \sum_{i=1}^m x_i
\Delta_y(g_i) + \Delta_y(f')\;.$$ Hence, ${\mathrm{rank}}_3(\Delta_y(f'))
\leq {\mathrm{rank}}_3(\Delta_y(f)) + m$. We now fix some value to
$x_1,\ldots,x_m$, such that
${\mathrm{bias}}(f(\alpha_1,\ldots,\alpha_m,x_{m+1},\ldots,x_n)) \geq
\delta$. Let
\begin{equation}\label{eq:quartic setting to constants}\tilde{f}(x_{m+1},\ldots,x_n) \triangleq
f(\alpha_1,\ldots,\alpha_m,x_{m+1},\ldots,x_n)\;.\end{equation} It
follows that ${\mathrm{bias}}(\tilde{f}) \geq \delta$ and that for every
$y=(y_{m+1},\ldots,y_n)$, ${\mathrm{rank}}_3(\Delta_y(\tilde f))
={\mathrm{rank}}_3(\Delta_y(f'))= O(\log^5(\frac{1}{\delta}))$ (note that
$\deg\left(\Delta_y(\tilde{f})-\Delta_y(f')\right)=2$ so they have
the same rank). From now on we will only consider $\tilde{f}$ and
not $f$. Observe that if we prove
Theorem~\ref{thm:intro:deg-4:bias} for $\tilde{f}$ then by
considering Equations~\eqref{eq: quartic on subspace} and
\eqref{eq:quartic setting to constants} we get the required result
for $f$ itself.
\ignore{ Therefore, we abuse notations and assume, from now on,
w.l.o.g., that $\tilde{f}=f$ and $m=0$. }
\subsection{Computing $\tilde f$ using a few quadratics}
We now show that there is a large subspace on which $f$ can be
approximated by a function of a few quadratic polynomials. The
following lemma of Bogdanov and Viola shows that if $f$ is biased
then it can be well approximated by a small set of partial
derivatives.
\begin{lemma}
\label{lem:Bogdanov and Viola}(Lemma 24 from
\cite{BogdanovViola07}) Let $f:\mathbb{F}^{n}\to\mathbb{F}$ be a
function over a finite field ${\mathbb{F}}$ with ${\mathrm{bias}}(f)=\delta$. Then
there are $t$ directions $a_{1},...,a_{t}$ and a function $H$ such
that $H(\Delta_{a_1}(f),\ldots,\Delta_{a_t}(f))$
$\epsilon$-approximates $f$, where $t\leq
(1+\log\frac{1}{\epsilon})\left(|\mathbb{F}|/\delta\right)^{O(1)}$.
\end{lemma}
By the construction of $\tilde f$ we know that each of its partial
derivatives is of rank $\log^{O(1)}(1/\delta)$ and that
${\mathrm{bias}}(\tilde{f})\geq \delta$. Thus, Lemma~\ref{lem:Bogdanov and
Viola} guarantees that $\tilde f$ can be well approximated using a
few quadratics.
\begin{corollary}\label{cor:tilde f approx by quadratics}
For every $\epsilon >0$ there are
$c=(1+\log\frac{1}{\epsilon})\left(|\mathbb{F}|/\delta\right)^{O(1)}$
quadratic polynomials $Q_1,\ldots,Q_c$ and a function $H$ such
that $\tilde f$ is $\epsilon$-approximated by $H(Q_1,\ldots,Q_c)$.
\end{corollary}
The next lemma, which is the main lemma of \cite{KaufmanLovett08}
shows that if the approximation is good enough (i.e. $\epsilon$ is
small), and if the quadratics satisfy the {\em strong regularity}
property then $\tilde f$ can in fact be computed by a small number
of quadratics.
\begin{definition}\label{def:strongly regular}
(strongly regular quadratic functions) We say that a family of
quadratic functions $\left\{ Q_{i}\right\} _{i=1}^{m}$ is
\emph{$\gamma$- strongly regular} if the following holds for every
$x_0 \in {\mathbb{F}}^n$: for independent uniform random variables
$Y_{1},...,Y_{5}$ the joint distribution of
$$\left\{Q_{j}\left(x_0+\sum_{i\in I}Y_{i}\right) \mid
j\in[m],I\subseteq[5],1\leq|I|\leq2\right\}$$ is $\gamma$ close to
the uniform distribution (recall
Definition~\ref{def:gamma-approx}).
\end{definition}
This definition is a restricted version of Definition 8 of
\cite{KaufmanLovett08} for quadratic polynomials. The interested
reader is referred to that paper for the general definition for
higher degree polynomials.
\begin{lemma}
\label{lem:Kaufman Lovett}(Lemma 13 from \cite{KaufmanLovett08})
Let $f(x)$ be a degree $d$ polynomials, $h_{1},...,h_{m}$
polynomials of degree less than $d$ and
$H:\mathbb{F}^{m}\to\mathbb{F}$ a function such that
\begin{itemize}
\item $H(h_{1},...,h_{m})$ $\epsilon$-approximates $f$ where
$\epsilon\leq2^{-2(d+1)}$.
\item $\left\{ h_{i}\right\} _{i=1}^{m}$ is a $\gamma$-strongly
regular family where $\gamma\leq\min\left\{
2^{-d},2^{-m}\right\}$.
\end{itemize}
Then there exists a function $F:\mathbb{F}^{m}\to\mathbb{F}$ such
that $f=F(h_{1},...,h_{m})$.
\end{lemma}
In other words, the lemma says that if $f$ is well approximated by
a family of strongly regular functions then it can actually be
computed everywhere by the functions in the family. We shall now
show that if $q_1,\ldots,q_c$ are quadratic polynomials such that
the rank of every nontrivial linear combination of them is high,
then they are strongly regular. This will imply (by
Corollary~\ref{cor:tilde f approx by quadratics}) that $\tilde f$
is a function of a few quadratics and therefore so is $f$.
\begin{lemma}
\label{lem:rank implies regular}Let $\left\{ Q_{i}\right\}
_{i=1}^{m}$ be a family of quadratic functions such that for every
nontrivial linear combination,
${\mathrm{rank}}_2(\sum_{i=1}^{m}\alpha_{i}Q_{i})\geq R$. Then $\left\{
Q_{i}\right\}_{i=1}^{m}$is a $\gamma$-strongly regular family for
$\gamma=|{\mathbb{F}}|^{3m/2-R/4}$.
\end{lemma}
\begin{proof}
The proof is based on the analogy between quadratic functions and
matrices.
\begin{definition}\label{def:matrix}
Let $Q:\mathbb{F}^{n}\to\mathbb{F}$ be a quadratic polynomial and
$A\in\mathbb{F}^{n\times n}$ an $n\times n$ matrix. We say that
$A$ represents $Q$ if there exists a linear function $\ell$ such
that $Q(x)=x^{t}Ax+\ell(x)$.
\end{definition}
Notice that there may be many different matrices representing the
same polynomial $Q$. For example, every antisymmetric matrix
represents the zero function. More generally, if $S$ is
antisymmetric then $A$ and $A+S$ represent the same polynomial.
\begin{lemma}
Let $q$ be a quadratic polynomial. Then ${\mathrm{rank}}_2(q)$ (recall
Definition~\ref{def:rank of quadratic}) is equal to the minimal
rank of a matrix representing $q$. Moreover, for every matrix $A$
representing $q$ we have that ${\mathrm{rank}}(A+A^t)/2\leq {\mathrm{rank}}_2(q) \leq
{\mathrm{rank}}(A+A^t)$.
\end{lemma}
We shall prove the lemma for ${\mathbb{F}}={\mathbb{F}}_2$. The proof for other fields
is similar.
\begin{proof}
Let ${\mathrm{rank}}_2(q)=r$. Then $q$ can be expressed as
$\sum_{i=1}^{r}\left(\sum_{j=1}^{n}a_{i,j}x_{j}\right)
\left(\sum_{j=1}^{n}b_{i,j}x_{j}\right) + \ell(x)$. Set
$A=(a_{i,j}),B=(b_{i,j})\in {\mathbb{F}}^{r \times n}$. It is clear that
$A^{t}B$ represents $q$ and that ${\mathrm{rank}}(A^t B) \leq r$. On the
other hand, if $q$ can be represented by a rank $r$ matrix $A$,
then let $\ell_1,\ldots,\ell_r$ be a basis for the rows of $A$,
when interpreted as linear functions.\footnote{I.e.
$(a_1,\ldots,a_n) \leftrightarrow \sum_{i=1}^{n}a_i \cdot x_i$.}
Let $A_i$ be the $i$-th row of $A$ and denote $A_i =
\sum_{j=1}^{r} \alpha_{i,j} \ell_j$. We have that for some linear
function $\ell$, \[ q-\ell=x^{t}Ax=\sum_{i=1}^{n}x_{i}A_{i}(x)
=\sum_{i=1}^{n}x_{i} \sum_{j=1}^{r}\alpha_{i,j}\ell_{j}
=\sum_{j=1}^{r}\ell_{j}\left(\sum_{i=1}^{n}\alpha_{i,j}x_{i}\right)=
\sum_{j=1}^{r}\ell_{j}\ell'_{j}\;,\] where
$\ell'_1,\ldots,\ell'_r$ are linear functions. This implies that
${\mathrm{rank}}_2(q)\leq r$. Thus, ${\mathrm{rank}}_2(q)=\min\left\{ {\mathrm{rank}}(A)\mid
q(x)=x^{t}Ax+\ell(x)\right\} $.
To prove the second claim, let $A$ be any matrix representing $q$.
We first change the basis of the space so that with respect to the
new basis $q$ will have the form of Theorem~\ref{thm:Dickson}. Let
$T$ be an invertible matrix representing the change of basis.
Clearly, $T^t A T$ represents $q \circ T = \sum_{i=1}^{r}
x_{2i-1}x_{2i} + \ell$, where $r = {\mathrm{rank}}_2(q)$. Thus, the matrix
$T^t A T$ can be written as $D+S$ where $D$ is a block diagonal
matrix consisting of $r$ nonzero blocks of size $2 \times 2$ and
$S$ is a symmetric matrix. We also note that for each $2 \times 2$
diagonal block $C$ of $D$ it holds that $C+C^t \neq 0$. We thus
get that
$${\mathrm{rank}}(A+A^t) = {\mathrm{rank}}(T^t(A+A^t)T)= {\mathrm{rank}}(D+S + D^t + S^t) =
{\mathrm{rank}}(D+D^t)\;.$$ Now, for every $2 \times 2$ diagonal block $C$
of $D$ we have that $1\leq {\mathrm{rank}}(C+C^t) \leq 2$ and so
$${\mathrm{rank}}_2(q) =r \leq {\mathrm{rank}}(D+D^t) \leq 2r = 2{\mathrm{rank}}_2(q)\;.$$
This completes the proof of the Lemma.\footnote{From the proof it
actually follows that over ${\mathbb{F}}_2$, ${\mathrm{rank}}_2(q)={\mathrm{rank}}(A+A^t)/2$ but
this is not the case for other prime fields.}
\end{proof}
We continue the proof of Lemma~\ref{lem:rank implies regular}.
Using the above observation we now prove that any nontrivial
linear combination
$\sum_{k\in[m],I\subseteq[5],1\leq|I|\leq2}\alpha_{k,I}Q_{j}(x+\sum_{i\in
I}Y_{i})$ has high rank (as a quadratic polynomial in the
variables $Y_1\cup\ldots\cup Y_5$).
Fix $x=x_0$ and let $A_{k}$ be a matrix representing $Q_{k}$.
Notice that the quadratic polynomial $Q_{k}(x_0+\sum_{i\in
I}Y_{i})$ (in the variables $\cup_{i=1}^{5}Y_i$) can be
represented by a block matrix $B^{k,I}\in\mathbb{F}^{5n\times5n}$.
Indeed, consider a $5\times 5$ matrix that has $1$ in the
$(i,j)$-position iff $i,j\in I$, and zeros otherwise. Now, replace
any $1$ by the matrix $A_k$ and every $0$ by the $n \times n$ zero
matrix. It is an easy calculation to see that this matrix
represents $Q_{k}(x_0+\sum_{i\in I}Y_{i})$. We shall abuse
notations and for $i,j \in I$ say that $(B^{k,I})_{i,j} = A_k$,
and that otherwise $(B^{k,I})_{i,j} = 0$.
Clearly, the linear combination $$Q'\triangleq
\sum\{\alpha_{k,I}Q_{k}(x+\sum_{i\in I}Y_{i}) \mid
{k\in[m],I\subseteq[5],1\leq|I|\leq2}\}$$ is represented by the
matrix $$C\triangleq\sum\{\alpha_{k,I}B^{k,I} \mid
{k\in[m],I\subseteq[5],1\leq|I|\leq2}\}\;.$$ Observe that for
$i\neq j\in[5]$, $C_{i,j}=\sum_{k\in[m]}\alpha_{k,\left\{
i,j\right\} }A_{k}$. We now show that if for some $i\neq j\in[5]$
and $k\in[m]$ it holds that $\alpha_{k,\left\{ i,j\right\} }\neq0$
then the rank of $C^t+C$ (and hence of $Q'$) is high.
\begin{eqnarray*} {\mathrm{rank}}_2(Q') &=&
{\mathrm{rank}}_2\left(\sum\left\{\alpha_{k,I}Q_{k}(x+\sum_{i\in I}Y_{i})
\mid {k\in[m],I\subseteq[5],1\leq|I|\leq 2}\right\}\right)\\
&\geq& \frac{1}{2}{\mathrm{rank}}(C+C^{t}) \geq
\frac{1}{2}{\mathrm{rank}}(C_{i,j}+C_{j,i}^{t})\\
&=& \frac{1}{2}{\mathrm{rank}}\left(\sum_{k\in[m]}\alpha_{k,\left\{
i,j\right\}}\left(A_{k}+A_{k}^{t}\right)\right)\\
&\geq& \frac{1}{4}{\mathrm{rank}}_2\left(\sum_{k\in[m]}\alpha_{k,\left\{
i,j\right\} }Q_{k}\right)>\frac{1}{4}R \;.
\end{eqnarray*}
If it is not the case, namely, for all $i\neq j\in[5],k\in[m]$
$\alpha_{k,\left\{ i,j\right\} }=0$, then there is some $i\in[5]$
and $k\in[m]$ such that $\alpha_{k,\left\{ i\right\} }\neq0$ and
we get that same result by considering $C_{i,i}$ instead.
To conclude, every nontrivial linear combination of $\left\{
Q_{j}(x+\sum_{i\in I}Y_{i})\right\}
_{k\in[m],I\subseteq[5],1\leq|I|\leq2}$ has rank grater than
$\frac{1}{4}R$. Lemma~\ref{lem:rank of biased quadratic} implies
that the bias of every such linear combination is bounded by
$|{\mathbb{F}}|^{-R/4}$. It now follows by Lemma~\ref{lem:XOR} that the
distribution is $|{\mathbb{F}}|^{3m/2-R/4}$ close to the uniform
distribution as needed.
\end{proof}
We thus get the following corollary.
\begin{corollary}\label{cor:approximating by regular}
Let $g(x)$ be a degree $d$ polynomials, $q_{1},...,q_{m}$
quadratic polynomials and $H:\mathbb{F}^{m}\to\mathbb{F}$ a
function such that
\begin{itemize}
\item $H(h_{1},...,h_{m})$ $\epsilon$-approximates $g$ where
$\epsilon\leq2^{-2(d+1)}$.
\item The bias of every non trivial combination of
$h_1,\ldots,h_m$ is $|{\mathbb{F}}|^{-\Omega(m+d)}$.
\end{itemize}
Then there exists a function $G:\mathbb{F}^{m}\to\mathbb{F}$ such
that $g=G(h_{1},...,h_{m})$.
\end{corollary}
We now show that $\tilde f$ can be computed by a few quadratics.
\begin{lemma}\label{lem:computinf f using few quadratics}
Let $g:{\mathbb{F}}^n \to {\mathbb{F}}$ be a quartic polynomial such that for every
$y$, ${\mathrm{rank}}_3(\Delta_y(f)) \leq {\mathrm{poly}}(1/\delta)$. Then there exist
a subspace $W$, $c={\mathrm{poly}}(|{\mathbb{F}}|/\delta)$ quadratics
$q'_1,\ldots,q'_c$ and a function $G$ such that, $\dim(W) = n -
{\mathrm{poly}}(|{\mathbb{F}}|/\delta)$ and $g|_W=G(q'_1,\ldots,q'_c)$.
\end{lemma}
\begin{proof}
Applying Lemma~\ref{lem:Bogdanov and Viola}, and using the fact
that every partial derivative of $g$ has a low rank, we conclude
that for $\epsilon = 2^{-20}$ there exist $c = {\mathrm{poly}}(|{\mathbb{F}}|/\delta)$
linear and quadratic functions, and a function $H$, such that
$H(\ell_1,\ldots,\ell_c,q_1,\ldots,q_c)$ $\epsilon$-approximates
$g$. Let $r = {\mathrm{poly}}(|{\mathbb{F}}|/\delta)$ and $U = \{x:
\ell_1(x)=\alpha_1,\ldots,\ell_c(x)=\alpha_c\}$ be some subspace
such that $H(\alpha_1,\ldots,\alpha_c,q_1|_U,\ldots,q_c|_U)$
$\epsilon$-approximates $g|_U$. Applying
Lemma~\ref{lem:regularizing a set of quadratics} on
$q_1|_U,\ldots,q_c|_U$ and $r$ we get that there exists a
(possible affine) subspace $W\subseteq U$ and $c' \leq c$ such
that: $\dim(W) \geq \dim(U) - (r+1)c \geq n - (r+2)c=n -
{\mathrm{poly}}(|{\mathbb{F}}|/\delta)$; w.l.o.g. for every $i=1\dots c$, $q_i|_W \in
\mathrm{span}\{q_1|_W,\ldots,q_{c'}|_W\}$; any nontrivial linear
combination of $q_1|_W,\ldots,q_{c'}|_W$ has rank larger than $r$;
${g}|_W$ is $\epsilon$-approximated by
$H(\ell_1|_W,\ldots,\ell_c|_W,q_1|_W,\ldots,q_c|_W)$ (this follows
by picking an adequate shift of the linear space in the lemma).
Hence, ${g}|_W$ is $\epsilon$-approximated by
$H(\ell_1|_W,\ldots,\ell_c|_W,q_1|_W,\ldots,q_c|_W) =
H'(q_1|_W,\ldots,q_{c'}|_W)$ for some $H'$. The reason for passing
to $W$ is that now any nontrivial linear combination of
$q_1|_W,\ldots,q_{c'}|_W$ has rank larger than $r$. We thus get by
Corollary~\ref{cor:approximating by regular} that there is some
function $G$ such that $g|_W = G(q_1|_W,\ldots,q_{c'}|_W)$.
\end{proof}
Recall that we assume w.l.o.g. that for every $y\in {\mathbb{F}}^{n-m}$,
${\mathrm{rank}}_3(\Delta_y(\tilde f)) \leq {\mathrm{poly}}(1/\delta)$. Thus, the
lemma above implies the following corollary.
\begin{corollary}\label{cor:representing tilde f}
In the notations of the proof, there exist a subspace $Z \subset
{\mathbb{F}}^{n-m}$ of dimension $\dim(Z) \geq n - {\mathrm{poly}}(|{\mathbb{F}}|/\delta)$ such
that $\tilde{f}|_Z = F(q_1,\ldots,q_c)$, for
$c={\mathrm{poly}}(|{\mathbb{F}}|/\delta)$ quadratic polynomials and some function
$F$.
\end{corollary}
\subsection{The structure of $f$}
We now show that we can represent $\tilde f$ as $\tilde{f} =
\sum_{i=1}^{k} \ell_i \cdot g_i + \sum_{i=1}^{k} q'_i \cdot q''_i$
where $k = {\mathrm{poly}}(|{\mathbb{F}}|/\delta)$, the $\ell_i$-s are linear, the
$q'_i$-s and $q''_i$-s are quadratic and the $g_i$-s are cubic
polynomials. For this we will transform the quadratic polynomials
to be what we denote as {\em disjoint polynomials}.
\begin{definition}\label{def:disjoint polynomials}
We say that the quadratic polynomials $\left\{ Q_{i}\right\}
_{i=1}^{m}$ are disjoint if there is a linear transformation $T$,
$2m$ variables $\left\{ x_{i}\right\} _{i=1}^{m}\cup\left\{
y_{i}\right\} _{i=1}^{m}$, where possibly for several $i$-s
$x_i=y_i$, and quadratic functions $\left\{ Q_{i}'\right\}
_{i=1}^{m}$ such that for every $k\in[m]$, $Q_{k}\circ T
=x_{k}y_{k}+Q_{k}'$ where no degree two monomial in $Q'_k$
contains a variable from $\left\{ x_{i}\right\}
_{i=1}^{m}\cup\left\{ y_{i}\right\} _{i=1}^{m}$.
\end{definition}
\begin{lemma}\label{lem:making disjoint}
Let $q_1,\ldots,q_c$ be quadratic polynomials from ${\mathbb{F}}^n$ to ${\mathbb{F}}$.
Assume that the rank of every nontrivial linear combination of
them is at least $r$. Then there exist a subspace $V
\subseteq{\mathbb{F}}^n$ of dimension $\geq n-2c^2$ and $c'\leq c$ quadratic
polynomials $q'_1,\ldots,q'_{c'}:V\to {\mathbb{F}}$ satisfying: the $q'_i$-s
are disjoint; every nontrivial linear combination of the $q'_i$-s
has rank at least $r - 2c^2$; $\mathrm{span}(q'_1,\ldots,q'_{c'})
= \mathrm{span}(q_1|_V,\ldots,q_c|_V)$.
\end{lemma}
\begin{proof}
We prove the lemma by iteratively changing each $q_i$ to a
`disjoint' form. We shall give the proof over ${\mathbb{F}}_2$ but almost
the same proof holds for odd characteristics as well. We start
with $q_1$. Assume w.l.o.g. that $x_1\cdot x_2$ appears in $q_1$.
Now, from every other $q_i$ subtract an appropriate multiple of
$q_1$ such that at the end $x_1\cdot x_2$ only appears in $q_1$.
For simplicity we call the new polynomial $q_i$ as well. Now, for
$2\leq i$ and $j \in \{1,2\}$ let $x_j\cdot \ell_{i,j}$ be the
degree two monomials involving $x_j$ in $q_i$. For $q_1$ let $x_j
\cdot \ell_{1,j}$ be the degree $2$ monomials involving $x_j$ in
$q_1 - x_1\cdot x_2$. Let $V_1 = \{x \mid \ell_{1,1}(x) = \ldots =
\ell_{2,c}(x) = 0\}$. Notice that none of the $\ell_{i,j}$-s
contain $x_1$ or $x_2$. After restricting the polynomials to $V_1$
we have that $x_1\cdot x_2$ appears in $q_1$ and every other
appearance of either $x_1$ or $x_2$ is in degree one monomials. We
now move to (the 'new') $q_2$ and continue this process. At the
end we obtain a subspace $V$ and quadratics $q'_1,\ldots,q'_{c'}$
($c'$ may be smaller than $c$ if some polynomials vanished in the
process). As at each step we set at most $2c$ linear functions to
zero, for a total of at mots $2c^2$ linear functions, the claims
about the dimension of $V$ and the rank of every linear
combination of the $q_i$-s follow. It is clear that the $q_i|_v$-s
span the $q'_i$-s and so the lemma is proved.
When dealing with odd characteristics instead of looking for
$x_1\cdot x_2$ we search for $x_1^2$. By applying an invertible
linear transformation such a monomial always exists and we
continue with the same argument.
\end{proof}
The usefulness of the definition is demonstrated in the following
lemma.
\begin{lemma}\label{lem:representing by disjoint}
Let $q_1,\ldots,q_c$ be disjoint quadratic polynomials. Assume
that $\deg(f)=2d$ and $f=F(q_1,\ldots,q_c)$ for some function
$F(z_1,\ldots,z_c)$. Then as a polynomial over ${\mathbb{F}}$, $\deg(F)\leq
d$.
\end{lemma}
\begin{proof}
We shall give the proof over ${\mathbb{F}}_2$ but it is again similar over
odd characteristic fields. Let $z_{1}^{e_1} \cdots z_{c}^{e_c}$ be
a monomial of maximal degree in $F$. When composing it with
$q_1,\ldots,q_c$ we get that $q_{1}^{e_1} \cdots q_{c}^{e_c}$
contains the monomial $\prod_{i=1}^{c} (x_i \cdot y_i)^{e_i}$. As
$z_{1}^{e_1} \cdots z_{c}^{e_c}$ is of maximal degree and each
$x_i$ and $y_i$ appear only as linear terms in all the $q_j$-s
(except the monomial $x_i\cdot y_i$ in $q_i$) we see that this
monomial cannot be cancelled by any other monomial created in
$F(q_1,\ldots,q_c)$. Therefore the monomial $\prod_{i=1}^{c} (x_i
\cdot y_i)^{e_i}$ belongs to $f$ as well. Since $\deg(f)=2d$ it
must be the case that $2e_1+\ldots+2e_c \leq 2d$. Hence,
$\deg(F)=\sum_{i=1}^{c}e_i \leq d$.
\end{proof}
We are now ready to complete the proof of
Theorem~\ref{thm:intro:deg-4:bias}.
\begin{proof}[Proof of Theorem~\ref{thm:intro:deg-4:bias}]
Combining Corollary~\ref{cor:representing tilde f},
Lemma~\ref{lem:representing by disjoint} and Lemma~\ref{lem:making
disjoint} we get that for the subspace $Z$ of
Corollary~\ref{cor:representing tilde f}, there exist a subspace
$Z' \subseteq Z$, of dimension $\dim(Z') \geq \dim(Z) -
{\mathrm{poly}}(|{\mathbb{F}}|/\delta)$, $b={\mathrm{poly}}(|{\mathbb{F}}|/\delta)$ quadratic polynomials
$Q_1,\ldots,Q_b$ and a quadratic polynomial $H$ such that
$\tilde{f}|_{Z'} = H(Q_1,\ldots,Q_b)$. In other words
$\tilde{f}|_{Z'} = \sum_{i\leq j}\alpha_{i,j}Q_i Q_j + Q_0$.
As $f|_{Z'} = \tilde{f}|_{Z'}$ it follows that $f|_{Z'}
=\sum_{i\leq j}\alpha_{i,j}Q_i Q_j+Q_0$. Assume
w.l.o.g.\footnote{This is true up to an invertible linear
transformation and an affine shift and has no real effect on the
result, but rather simplifies the notations.} that $Z'$ is defined
as $Z' = \{x \mid x_1=\beta_1, \ldots,x_k=\beta_k\}$ for some
$k={\mathrm{poly}}(|{\mathbb{F}}|/\delta)$. Then it is clear that we can write
$f=\sum_{i=1}^{k}x_i \cdot g_i +\sum_{i\leq j}\alpha_{i,j}Q_i Q_j
+ g_0$ for cubic polynomials $g_0,\ldots,g_k$.
\end{proof}
\section{Quartic polynomials with high $U^4$ norm}\label{sec:U4 norm}
In this section we prove Theorems~\ref{thm:intro:deg-4:gowers} and
\ref{thm:intro:deg-4:gowers:high char}. Intuitively, the notion of
$d+1$ Gowers norm indicates how close a given function is to a
degree $d$ polynomial. In fact, it was conjectured that if the
$U^{d+1}$ norm is bounded away from zero then the function has a
noticeable correlation with a degree $d$ polynomial. This
conjecture turned to be false even when the function is a degree
four polynomial and $d=3$ \cite{LMS08,GreenTao07}. Here we will
show that for this special case a weaker conclusion holds. Namely,
that for any degree four polynomial $f$ there exists a subspace of
dimension $n/\exp({\mathrm{poly}}(1/\|f\|_{U^4}))$ on which $f|_V$ is equal
to some cubic polynomial. In fact an even stronger conclusion
holds - there exists a partition of (a subspace of small co
dimension of) ${\mathbb{F}}^n$ to such subspaces on which $f$ equals a
cubic. To ease the reading we restate
Theorem~\ref{thm:intro:deg-4:gowers} here.
\begin{theoremNoNum}[Theorem~\ref{thm:intro:deg-4:gowers}]
Let ${\mathbb{F}}$ be a finite field and $f \in {\mathbb{F}}[x_1,\ldots,x_n]$ a degree
four polynomial such that $\|f\|_{U^4}=\delta$. Then there exists
a partition of a subspace $V\subseteq \mathbb{F}^{n}$, of
dimension $\dim(V)=n-{\mathrm{poly}}(|{\mathbb{F}}|/\delta)$, to subspaces $\left\{
V_{\alpha}\right\}_{\alpha\in I}$, satisfying $\dim(V_\alpha)
=\Omega(n/|{\mathbb{F}}|^{{\mathrm{poly}}(1/\delta)})$, such that for every $\alpha\in
I$, $f|_{V_{\alpha}}$ is a cubic polynomial.
\end{theoremNoNum}
In other words, the theorem says that for $r={\mathrm{poly}}(1/\delta)$ any
such $f$ (possibly after a change of basis of ${\mathbb{F}}^n$) can be
written as $f = \sum_{i=1}^{r}x_{n-r+i}g_i(x_1,\ldots,x_n) +
f'(x_1,\ldots,x_{n-r})+g_0$, where the $g_i$-s are degree three
polynomials and $f'$ is a polynomial for which there exists a
partition of $\mathbb{F}^{n-r}$ to subspaces $\left\{
V_{\alpha}\right\} _{\alpha\in I}$, satisfying $\dim(V_\alpha)
=\Omega(n/\exp({\mathrm{poly}}(1/\delta)))$, such that for every $\alpha\in
I$, $f'|_{V_{\alpha}}$ is a cubic polynomial.
As in the proof of Theorem~\ref{thm:intro:deg-3:gowers} we start
by passing to a subspace of a constant codimension on which every
derivative has low rank, i.e
$\Delta_y(f)=\sum_{i=1}^{r}\ell_{i}Q_{i}+Q_{0}$. Then we shall
deduce that there is some common `basis' $\left\{ \ell_{i}\right\}
_{i=1}^{t_{2}},\left\{ Q_{i}\right\} _{i=1}^{t_{1}}$ to all the
derivatives. Namely, every derivative $\Delta_{y}(F)$ can be
expressed as
$\sum_{i=1}^{t_{1}}\ell_{i}^{y}Q_{i}+\sum_{i=1}^{t_{2}}\ell_{i}Q_{i}^{y}+Q_0^{y}$
(where $y$ in the exponent means that the polynomial may depend on
$y$). This is the main technical difficulty of the proof and it is
based on an extension of Lemma~\ref{lem:low rank space have few
common functions} to the case of low rank cubic polynomials. Then,
we conclude that for every setting $\alpha$ of $\left\{
\ell_{i}\right\} _{i=1}^{t_{2}},\left\{ Q_{i}\right\}
_{i=1}^{t_{1}}$ we obtain a subspace $V_{\alpha}$ on which all the
derivative are quadratic polynomials, i.e $f|_{V_{\alpha}}$ is
cubic.
\subsection{The case of the symmetric polynomial}
\label{sec:S_4}
Let $S_k(x_1,\ldots,x_n) = \sum_{1\leq i_1<\ldots<i_k \leq
n}x_{i_1}\cdot x_{i_2}\cdots x_{i_k}$. In \cite{GreenTao07,LMS08}
it was shown that over ${\mathbb{F}}_2$, it holds that $\|S_4\|_{U^4} \geq
\delta$, for some absolute constant $0<\delta$, but for every
degree three polynomial $g$, $\Pr[S_4 = g]\leq 1/2 + \exp(-n)$. To
make the claim of Theorem~\ref{thm:intro:deg-4:gowers} clearer we
shall work out the case of $S_4$ as an example.
Consider a partial derivative $\Delta_y(S_4)$. For simplicity
assume that $n=4m$. Computing we get that
\begin{equation}\label{eq:der of S4} \Delta_y(S_4) =
S_2 \cdot \sum_{i\neq j}^{n} x_i y_j + S_1 \cdot \sum_{i\neq
j}^{n} x_i y_j + \sum_{i\neq j}^{n} x_i y_j \;.
\end{equation}
In particular, $S_2$ is a
`basis' for the set of partial derivatives of $S_4$. Continuing,
we have that
\begin{equation}\label{eq:S2} S_2(x_1,\ldots,x_n)=
\sum_{k=1}^{2m} \left(\sum_{i=1}^{2k-1} x_i \right)\cdot
\left(x_{2k}+ \sum_{i=1}^{2k-2} x_i \right) +
\sum_{i=1}^{m}(x_{4i-3} + x_{4i-2})\;.
\end{equation}
For $k=1,\ldots,2m$ let $\ell_k = \sum_{i=1}^{2k-1} x_i$. Notice
that fixing $\ell_1,\ldots,\ell_{2m}$ reduces the degree of $S_2$
to one and so every partial derivative of $S_4$ will have degree
two. For example, consider the space $V_0=\{x\mid
\ell_1(x)=\ldots=\ell_{2m}(x)=0\}$. Rewriting we get $V_0 =
\{(0,y_1,y_1,y_2,y_2,\ldots,y_{2m-1}y_{2m-1},y_{2m})\}$. Computing
we get that
$$S_4|_{V_0} = S_2(y_1,\ldots,y_{2m-1})\;.$$
A closer inspection shows that no matter how we set
$\ell_1,\ldots,\ell_{2m}$ we will get that the degree of $S_4$
becomes two.
\subsection{Finding a `basis' for a space of low rank cubic polynomials}
In this section we prove the main technical result showing that a
subspace of degree 3 polynomials with low rank has a small
`basis'.
\begin{lemma}[Main Lemma]
\label{lem:low rank few com fun deg 4}Let $M$ be a vector space of
cubic polynomials satisfying ${\mathrm{rank}}_{3}(f)\leq r$ for all $f\in
M$. Then there exists a set of linear and quadratic functions
$\left\{ Q_{i}\right\} _{i=1}^{t_{1}}\cup\left\{ \ell_{i}\right\}
_{i=1}^{t_{2}}$, for $t_{1}\leq r$ and $t_{2}=2^{O(r)}$, such that
every $f\in M$ can be represented as
$f=\sum_{i=1}^{t_{1}}\ell_{i}^{f}Q_{i}+\sum_{i=1}^{t_{2}}\ell_{i}Q_{i}^{f}+Q_{0}^{f}$
for some linear and quadratic functions $\{ \ell_{i}^{f}\}
_{i=1}^{t_{1}}\cup\{ Q_{i}^{f}\} _{i=0}^{t_{2}}$.
\end{lemma}
The rest of this section is devoted to proving this lemma.
Similarly to the proof of Lemma~\ref{lem:low rank space have few
common functions} we will work modulo a collection of linear and
quadratic polynomials. For this we shall need the following
definition.
\begin{definition}
For a cubic polynomial $f$ we say that ${\mathrm{rank}}_3^c(f)=r$ if $r$ is
the minimal integer such that $f$ can be written as
\begin{equation}\label{eq:def of rank 3 c}
f=\sum_{i=1}^{r}\ell_{i}Q_{i}+\sum_{i=1}^{c}\ell_{i}^{(1)}\ell_{i}^{(2)}\ell_{i}^{(3)}+Q_{0}\;,
\end{equation}
where the $\ell$-s are linear functions and the $Q$-s are
quadratics.
\end{definition}
To see that difference from the previous notion of ${\mathrm{rank}}_3$
(Definition~\ref{def:cubic rank}) we observe that if $f$ is a
degree three polynomial with ${\mathrm{rank}}_{3}(f)=r$ then
$f=\sum_{i=1}^{r}\ell_iQ_i + Q_0$. If we also know that some
nontrivial linear combination of $Q_1,\ldots,Q_r$ has rank (as a
quadratic polynomial) less than $c$ then ${\mathrm{rank}}_{3}^c(f)<r$. I.e.
${\mathrm{rank}}_{3}^{c}(f)$ ignores, in some sense, low rank quadratic
functions in the representation of $f$.
\begin{definition}
Let $A=\left\{ Q_{i}\right\} _{i=1}^{t_{1}}\cup\left\{
\ell_{i}\right\} _{i=1}^{t_{2}}$ be a set of linear and quadratic
functions and let $f:\mathbb{F}^{n}\rightarrow\mathbb{F}$ be a
degree three polynomial. Denote \[ [f]_{A}\triangleq\left\{
f+\sum_{i=1}^{t_{1}}\ell_{i}'Q_{i}+\sum_{i=1}^{t_{2}}\ell_{i}Q_{i}'+Q_{0}'\mid
\;\mathrm{for \; linear \; and \; quadratic\; functions}\; \left\{
\ell_{i}'\right\} _{i=1}^{t_{1}},\; \left\{ Q_{i}'\right\}
_{i=0}^{t_{2}}\right\}
\] For a linear space
$M$ of degree three functions, we define the subspace $[M]_{A}$ to
be
\[
[M]_{A}\triangleq\left\{ [f]_{A}\mid f\in M\right\} \;.\] As
before we define ${\mathrm{rank}}_{3}^{c}([f]_{A})$ to be the lowest rank of
functions in $[f]_{A}$.
\[
{\mathrm{rank}}_{3}^{c}([f]_{A})\triangleq\min\left\{ {\mathrm{rank}}_{3}^{c}(g)\mid
g\in[f]_{A}\right\} \;.\]
\end{definition}
The definition of $[f]_A$ resembles, in some sense, the notion of
working modulo an ideal. However, we note that as opposed to the
usual definition, where for every $f$, $\left\{ Q_{i}'\right\}
_{i=1}^{t_{1}}\cup\left\{ \ell_{i}'\right\} _{i=1}^{t_{2}}$ can be
arbitrary functions, in our definition they are restricted to
being quadratic and linear functions, respectively.
We are now ready to prove the main lemma of this section that
shows the existence of a small `basis' for any linear space of
cubic polynomials of low rank.
\begin{lemma}
\label{lem:low rank -> low rank 3c}Let $A=\left\{ Q_{i}\right\}
_{i=1}^{t_{1}}\cup\left\{ \ell_{i}\right\} _{i=1}^{t_{2}}$ be a
set of linear and quadratic polynomials. Let M be a linear space
of cubic polynomials such that for every $[f]_{A}\in[M]_{A}$,
${\mathrm{rank}}_{3}^{c}([f]_{A})\leq r$. Then, there are $r$ linear
functions $\left\{ \ell_{i}\right\} _{i=1}^{r}$ and a quadratic
polynomial $Q$ such that for $A'\triangleq A\cup\left\{
\ell_{i}\right\} _{i=1}^{r}\cup\left\{ Q\right\}$ it holds that
every $[f]_{A'}\in[M]_{A'}$ satisfies
${\mathrm{rank}}^{c'}_{3}([f]_{A'})\leq r-1$, for $c'=11c+3r+t_{1}$.
\end{lemma}
In other words, the lemma says that we can find a small set of
linear functions and one quadratic polynomial such that by adding
them to $A$ and increasing $c$ by a constant factor, we can
decrease the ${\mathrm{rank}}_3^{c'}$ of every polynomial in $[M]_{A'}$.
\begin{proof}
Assume that there is some $[g]_{A}\in[M]_{A}$ such that
${\mathrm{rank}}_{3}^{c'}(g)={\mathrm{rank}}_{3}^{c'}([g]_{A})=r$. If no such $g$
exists then for every $[f]_{A}\in[M]_{A}$,
${\mathrm{rank}}^{c'}_{3}([f]_{A})\leq r-1$ and there is nothing to prove.
As $c<c'$ it also holds that ${\mathrm{rank}}_{3}^{c}([g]_{A})=r$. Hence,
$g$ can be represented as $\sum_{i=1}^{r}\ell_{i}^{g}Q_{i}^{g}+
\sum_{i=1}^{c}\ell_{i}^{g,(1)}\ell_{i}^{g,(2)}\ell_{i}^{g,(3)}$.\footnote{By
definition of $[g]_A$ we can add any quadratic polynomial to $g$
so we can assume that there is no extra $Q_0^g$ term in the
representation of $g$.} Note that ${\mathrm{rank}}_2([Q_1^g]_A)
> c'-c$ as otherwise we
could replace $Q_1^g$ with a function of the form
$\sum_{i=1}^{t_1}\alpha_i Q_i + \sum_{i=1}^{t_2}\ell_i \ell'_i +
\sum_{j=1}^{c'-c}m_im'_i$, where the $m$-s are linear functions,
and get that ${\mathrm{rank}}_3^{c'}([g]_{A})\leq r-1$.
Set $A' \triangleq A\cup\left\{ \ell_{i}^{g}\right\}
_{i=1}^{r}\cup\left\{ Q_{1}^{g}\right\}$. Assume for
contradiction that there is some $h \in M$ satisfying
${\mathrm{rank}}^{c'}_{3}([h]_{A'})=r$. This implies that
${\mathrm{rank}}^{c}_3([h]_{A})=r$ and that ${\mathrm{rank}}^{c'-c}_{3}([h+g]_{A'})=r$
as well. Indeed, if the latter equation was not true then by
expressing $h+g$ as a low ${\mathrm{rank}}_3^{c'-c}$ polynomial and moving
$g$ to the other side we would get that ${\mathrm{rank}}^{c'}_{3}([h]_{A'})<
r$ in contradiction (recall that $\{\ell_i^g\}\subset A'$). From
this we get that ${\mathrm{rank}}^{c}_{3}([h+g]_{A})=r$ as well. Let
$f\in[h+g]_{A}$ be such that ${\mathrm{rank}}^{c}_{3}(f)=r$. Express $h$ and
$f$ as
$h=\sum_{i=1}^{r}\ell_{i}^{h}Q_{i}^{h}+\sum_{i=1}^{c}\ell_{i}^{h,(1)}\ell_{i}^{h,(2)}\ell_{i}^{h,(3)}$
and
$f=\sum_{i=1}^{r}\ell_{i}^{f}Q_{i}^{f}+\sum_{i=1}^{c}\ell_{i}^{f,(1)}\ell_{i}^{f,(2)}\ell_{i}^{f,(3)}$.
Note that we can assume that w.l.o.g $\left\{ \ell_{i}\right\}
_{i=1}^{t_{2}}$ are linearly independent as otherwise we can just
replace them with a linearly independent subset. Similarly, we can
also assume that $\left\{ \ell_{i}\right\}
_{i=1}^{t_{2}}\cup\left\{ \ell_{i}^{g}\right\} _{i=1}^{r}$ are
linearly independent as otherwise we can find a representation for
a function in $[g]_{A}$ with a smaller rank. Using the same
argument again we conclude that $\left\{ \ell_{i}\right\}
_{i=1}^{t_{2}}\cup\left\{ \ell_{i}^{g}\right\}
_{i=1}^{r}\cup\left\{ \ell_{i}^{h}\right\} _{i=1}^{r}$ are
linearly independent as well (by considering $[h]_{A'}$).
Since $g+h-f\in[0]_{A}$, we can express this polynomial as
$g+h-f=\sum_{i=1}^{t_{1}}\ell_{i}'Q_{i}+\sum_{i=1}^{t_{2}}\ell_{i}Q_{i}'+Q_{0}'$.
In other words:
\begin{eqnarray}\label{eq:g+h-f}
\nonumber \sum_{i=1}^{r}\ell_{i}^{g}Q_{i}^{g}
+\sum_{i=1}^{c}\ell_{i}^{g,(1)}\ell_{i}^{g,(2)}\ell_{i}^{g,(3)} +
\sum_{i=1}^{r}\ell_{i}^{h}Q_{i}^{h}
+ \sum_{i=1}^{c}\ell_{i}^{h,(1)}\ell_{i}^{h,(2)}\ell_{i}^{h,(3)} &-&\\
\left(\sum_{i=1}^{r}\ell_{i}^{f}Q_{i}^{f}
+\sum_{i=1}^{c}\ell_{i}^{f,(1)}\ell_{i}^{f,(2)}\ell_{i}^{f,(3)}
+\sum_{i=1}^{t_{1}}\ell_{i}'Q_{i}
+\sum_{i=1}^{t_{2}}\ell_{i}Q_{i}'+Q_{0}' \right)&=&0\;.
\end{eqnarray}
To ease notations, using the fact that $\left\{ \ell_{i}\right\}
_{i=1}^{t_{2}}\cup\left\{
\ell_{i}^{g}\right\}_{i=1}^{r}\cup\left\{
\ell_{i}^{h}\right\}_{i=1}^{r}$ are linearly independent, let us
assume w.l.o.g. that $\forall i$, $\ell_i^{g} = x_i$,
$\ell_i^{h}=x_{r+i}$ and $\ell_i = x_{2r+i}$. Thus,
Equation~\eqref{eq:g+h-f} becomes
\begin{eqnarray}\label{eq:g+h-f new} \nonumber
\sum_{i=1}^{r}x_{i}Q_{i}^{g}
+\sum_{i=1}^{c}\ell_{i}^{g,(1)}\ell_{i}^{g,(2)}\ell_{i}^{g,(3)} +
\sum_{i=1}^{r}x_{r+i}Q_{i}^{h}
+ \sum_{i=1}^{c}\ell_{i}^{h,(1)}\ell_{i}^{h,(2)}\ell_{i}^{h,(3)} &-&\\
\left(\sum_{i=1}^{r}\ell_{i}^{f}Q_{i}^{f}
+\sum_{i=1}^{c}\ell_{i}^{f,(1)}\ell_{i}^{f,(2)}\ell_{i}^{f,(3)}
+\sum_{i=1}^{t_{1}}\ell_{i}'Q_{i}
+\sum_{i=1}^{t_{2}}x_{2r+i}Q_{i}'+\tilde{Q}_{0} \right)&=&0\;,
\end{eqnarray}
where we remember that variables from $\{x_i\}_{i=1}^{2r+t_2}$ may
appear in the linear and quadratic functions in the expression.
Consider all terms involving $x_1$ (recall that $\ell_1^{g}=x_1$)
in Equation~\eqref{eq:g+h-f new}. Clearly they sum to zero, but
they can also be written as
\begin{eqnarray}\label{eq:g+h-f x1}\nonumber
0= Q_1^{g} + \sum_{i=1}^{r}x_{i}m_{i}^{g}
+\sum_{i=1}^{3c}\alpha_i^{g} m_{i}^{g,(1)}m_{i}^{g,(2)} +
\sum_{i=1}^{r}x_{r+i}m_{i}^{h} +
\sum_{i=1}^{3c}\alpha_i^{h}m_{i}^{h,(1)}m_{i}^{h,(2)} -\\
\left(\sum_{i=1}^{r}\beta_{i}^{f}Q_{i}^{f}+\sum_{i=1}^{r}\ell_i^{f}m_i^{f}
+\sum_{i=1}^{3c}{\beta'}_{i}^{f}m_{i}^{f,(1)}m_{i}^{f,(2)}
+\sum_{i=1}^{t_{1}}\beta_{i}'Q_{i} + \sum_{i=1}^{t_1}\ell_{i}'m_i
+\sum_{i=1}^{t_{2}}x_{2r+i}m_{i}'+m_{0} \right),
\end{eqnarray}
where the $m$-s are linear functions and the $\alpha$-s and
$\beta$-s are field elements. Rearranging terms we conclude that
\begin{equation}\label{eq:Q1g gives a contradiction}
{\mathrm{rank}}_2\left(Q_1^{g} -\sum_{i=1}^{r}\beta_{i}^{f}Q_{i}^{f} -
\sum_{i=1}^{t_{1}}\beta_{i}'Q_{i}
-\sum_{i=1}^{t_{2}}x_{2r+i}m_{i}'\right) \leq 3r + 9c +
t_1=c'-2c\;.
\end{equation}
This implies that
\begin{equation*}
{\mathrm{rank}}_2\left(\left[\sum_{i=1}^{r}\beta_{i}^{f}Q_{i}^{f}\right]_{A'}\right)\leq
c'-2c\;.
\end{equation*}
We now have two cases to consider. If
$(\beta_1^{f},\ldots,\beta_r^{f})$ are not all zero then, by
arguments described above, this implies that
${\mathrm{rank}}^{c'-c}_{3}([f]_{A'})\leq r-1$. Recalling that
$[h+g]_{A'}=[f]_{A'}$ we get a contradiction. If, on the other
hand, $(\beta_1^{f},\ldots,\beta_r^{f})=0$ then
Equation~\eqref{eq:Q1g gives a contradiction} implies that
${\mathrm{rank}}_2([Q_1^g]_A) \leq c'-2c$ and so ${\mathrm{rank}}_3^{c'-c}([g]_A)\leq
r-1$ in contradiction to the choice of $g$. Concluding, we have
that for every $f \in M$, ${\mathrm{rank}}_3^{c'}([f]_{A'})\leq r-1$ as
required.
\end{proof}
By applying Lemma~\ref{lem:low rank -> low rank 3c} $r$ times we
obtain the following corollary.
\begin{corollary}
\label{cor:rank c is zero}Let $M$ be a vector space of cubic
polynomials satisfying ${\mathrm{rank}}_{3}(f)\leq r$ for every $f\in M$.
Then there exists a set of quadratic and linear functions
$A=\left\{ Q_{i}\right\} _{i=1}^{r}\cup\left\{ \ell_{i}\right\}
_{i=1}^{r(r-1)/2}$, such that for $c=\exp(r)$,
${\mathrm{rank}}^{c}_{3}([f]_{A})=0$ for every $f\in M$.
\end{corollary}
We now have that every function in $M$, modulo some set $A$ of
linear and quadratic functions, can be expressed as
$\sum_{i=1}^{c}\ell_{i}^{(1)},\ell_{i}^{(2)},\ell_{i}^{(3)}$, for
some $c$. Next we show that we can add $3c$ additional linear
functions to $A$ such that modulo the new set every function
becomes zero. We again give an iterative procedure for finding
those linear functions.
Before proving this result we define the notion of
$\dim_3^c([f]_{A})$ that will serve as a potential function in our
argument (in a similar way to the role played by ${\mathrm{rank}}_3^c$).
\begin{definition}
Let $A$ be a set of quadratic and linear functions and $[f]_{A}$ a
class of cubic functions such that ${\mathrm{rank}}_3^c([f]_A)=0$. We define
the dimension of the class as follows:
\[
\dim_3^c([f]_A)=\min\left\{ \dim\left( \mathrm{span}\left\{
\ell_{i}^{(1)},\ell_{i}^{(2)},\ell_{i}^{(3)}\right\}
_{i=1}^{c}\right)\mid
\sum_{i=1}^{c}\ell_{i}^{(1)}\ell_{i}^{(2)}\ell_{i}^{(3)} \in
[f]_A\right\}\,.
\]
\end{definition}
To better understand the reason for the definition we note that if
${\mathrm{rank}}_3^c([f]_A)=0$ then
$\sum_{i=1}^{c}\ell_{i}^{(1)}\ell_{i}^{(2)}\ell_{i}^{(3)} + Q \in
[f]_A$ for some linear functions and quadratic $Q$. Thus, our goal
will be to find a small set of linear functions that,
simultaneously, form a basis to all those linear functions for all
$f \in M$. The next lemma shows that by joining $\left\{
\ell_{i}^{(1)},\ell_{i}^{(2)},\ell_{i}^{(3)}\right\} _{i=1}^{c}$
from some polynomial $f$, of maximal dimension in $[M]_{A}$, to
$A$, the dimension of every other element in $[M]_{A}$ decreases.
\begin{lemma}
\label{lem:low dim c implie lower dim}Let $A=\left\{ Q_{i}\right\}
_{i=1}^{t_{1}}\cup\left\{ \ell_{i}\right\} _{i=1}^{t_{2}}$ be a
set of linear and quadratic functions. Assume that the rank of any
nontrivial linear combination of $\left\{ Q_{i}\right\}
_{i=1}^{t_{1}}$ is greater than $9c+t_{1}+t_2$. Let $M$ be a
linear space of cubic polynomials such that for every
$[f]_{A}\in[M]_{A}$, ${\mathrm{rank}}^{c}_{3}([f]_{A})=0$ and
$\dim_3^c([f]_{A})\leq d$. Then, there are $d$ linear functions
$\left\{ \ell'_{i}\right\} _{i=1}^{d}$ such that for $A'\triangleq
A\cup\left\{ \ell'_{i}\right\} _{i=1}^{d}$,
$\dim_3^c([f]_{A'})\leq d-1$ for all $[f]_{A'}\in[M]_{A'}$.
\end{lemma}
The proof is very similar in nature to the proof of
Lemma~\ref{lem:low rank -> low rank 3c}.
\begin{proof}
We start by passing to the subspace $V= \{x \mid
\ell_1(x)=\ldots=\ell_{t_2}(x)=0\}$. When restricting the $Q_i$-s
to $V$ the rank of every linear combination can drop by at most
$t_2$ so it is still at least $9c+t_1$. From now on we shall work
over $V$. Note that if we prove the theorem over $V$ then it
clearly holds over ${\mathbb{F}}^n$ as well.
Let $[g]_{A}\in[M]_{A}$ be a class satisfying
$\dim_3^c([g]_{A})=d$. By definition we can assume that $g$ is
such that
$g=\sum_{i=1}^{c}\ell_{i}^{g,(1)}\ell_{i}^{g,(2)}\ell_{i}^{g,(3)}$,
and that for some $d$ linearly independent linear functions
$\left\{ \ell_{i}^{g}\right\} _{i=1}^{d}$ it holds that
$\left\{\ell_{i}^{g,(1)},\ell_{i}^{g,(2)},\ell_{i}^{g,(3)}\right\}
_{i=1}^{c}\subseteq\mathrm{span}\left\{ \ell_{i}^{g}\right\}
_{i=1}^{d}$. Set $A'=A\cup\left\{ \ell_{i}^{g}\right\}
_{i=1}^{d}$. We will show that for every $f \in M$ it holds that
$\dim_3^c([f]_{A'})\leq d-1$.
Assume for contradiction that there is some $[h]_{A'}\in[M]_{A'}$
such that $\dim_3^c([h]_{A'})=d$. Clearly, $\dim_3^c([h]_{A})=d$
as well. W.l.o.g. let
$h=\sum_{i=1}^{c}\ell_{i}^{h,(1)}\ell_{i}^{h,(2)}\ell_{i}^{h,(3)}$.
We also denote with $\left\{ \ell_{i}^{h}\right\} _{i=1}^{d}$ a
basis for
$\left\{\ell_{i}^{h,(1)},\ell_{i}^{h,(2)},\ell_{i}^{h,(3)}\right\}
_{i=1}^{c}$. As $\dim_3^c([h]_{A})$ does not decreases modulo
$\left\{ \ell_{i}^{g}\right\} _{i=1}^{d}$, it follows that
$\left\{ \ell_{i}^{g}\right\} _{i=1}^{d}\cup\left\{
\ell_{i}^{h}\right\} _{i=1}^{d}$ are linearly independent. By
definition of $A'$ we have that
$\dim_3^c([g+h]_{A'})=\dim_3^c([h]_{A'})=d$. Let $f\in[g+h]_{A}$
be such that
$f=\sum_{i=1}^{c}\ell_{i}^{f,(1)}\ell_{i}^{f,(2)}\ell_{i}^{f,(3)}$
and $\dim(\mathrm{span}\{\ell_i^{f,(j)}\})=d$. Since
$g+h-f\in[0]_{A}$ we have that $g+h-f =
\sum_{i=1}^{t_{1}}Q_{i}\ell_{i}' + Q'$. We now show that all the
$\ell'_i$-s are zero. Assume for contradiction that this is not
the case. Namely, $\left\{ \ell_{i}'\right\} _{i=1}^{t_{1}}$ are
not all zero. In particular, some $\ell'_{i}$ depends on some
variable $x$. Write $g+h-f = xF+H$ where $H$ does not depend on
$x$. We now estimate ${\mathrm{rank}}_2(F)$. On the one hand $F$ can be
expressed as
$\sum_{i=1}^{t_{1}}\alpha_{i}Q_{i}+\sum_{i=1}^{t_{1}}m_{i}\ell_{i}'+m_0$
for some coefficients $\left\{ \alpha_{i}\right\} _{i=1}^{t_{1}}$
(not all of them are zero) and some linear functions $\left\{
m_{i}\right\}_{i=0}^{t_{1}}$. Hence, ${\mathrm{rank}}_2(F)$ is larger than
$9c$ (remember that
${\mathrm{rank}}_2(\sum_{i=1}^{t_{1}}\alpha_{i}Q_{i})>9c+t_{1}$ on $V$). On
the other hand, $g+h-f$ is equal to
$$g+h-f=\sum_{i=1}^{c}\ell_{i}^{g,(1)}\ell_{i}^{g,(2)}\ell_{i}^{g,(3)}+
\sum_{i=1}^{c}\ell_{i}^{h,(1)}\ell_{i}^{h,(2)}\ell_{i}^{h,(3)}-
\sum_{i=1}^{c}\ell_{i}^{f,(1)}\ell_{i}^{f,(2)}\ell_{i}^{f,(3)}\;,$$
so $F$ can be expressed as
$\sum_{i=1}^{9c}\hat{m}_{i}\tilde{m}_{i} + \ell$, i.e it's rank is
at most $9c$, in contradiction. It follows that $g+h-f=Q$, for
some quadratic $Q$. Thus,
\begin{equation}\label{eq:g+h=f+Q}\sum_{i=1}^{c}\ell_{i}^{g,(1)}\ell_{i}^{g,(2)}\ell_{i}^{g,(3)}+
\sum_{i=1}^{c}\ell_{i}^{h,(1)}\ell_{i}^{h,(2)}\ell_{i}^{h,(3)}=
\sum_{i=1}^{c}\ell_{i}^{f,(1)}\ell_{i}^{f,(2)}\ell_{i}^{f,(3)}
+Q\;.
\end{equation}
For simplicity, assume w.l.o.g. that for $i=1\ldots d$, $\ell_i^g
= y_i$, $\ell_i^h = z_i$. We would like to show that if
Equation~\eqref{eq:g+h=f+Q} holds then $\deg(h)=2$ in
contradiction to the choice of $h$. To further simplify notations
we assume w.l.o.g. that the $\ell_i^f$-s are linear functions in
the variables $y_1\ldots,y_d,z_1,\ldots,z_d$ (as we can set all
other variables to zero and still obtain a similar equality). In
particular, every $\ell_{i}^{f}$ can be expressed as $\ell_i^f =
\ell_{i}^{f,g}(y)+\ell_{i}^{f,h}(z)$. Hence,
Equation~\eqref{eq:g+h=f+Q} can be rewritten as $Q(y,z)+f(y,z) =
g(y)+h(z)$. Therefore, it holds that $g(y)=f(y,0)+Q(y,0)$ and
$h(y)=f(0,z)+Q(0,z)$.\footnote{We can assume w.l.o.g. that
$\ell_i^g$ and $\ell_i^h$ do not have a constant term.} In
particular, there is some representation of $g$ and $h$ as sums of
products of linear functions such that $\left\{
\ell_{i}^{f,g}(y)\right\} $ and $\left\{ \ell_{i}^{f,h}(z)\right\}
$ are their basis, respectively. By applying an invertible linear
transformation we can further assume that $\ell_{i}^{f,g}(y)=y_i$
and $\ell_{i}^{f,h}(z)=z_i$. Thus, the basis for
$\{\ell_i^{f,(j)}\}$ is $\ell_1^f = y_1+z_1,\ldots,\ell_d^f =
y_d+z_d$. As a consequence we have that $f =
\sum_{i=1}^{c}\ell_{i}^{f,(1)}(y+z)\ell_{i}^{f,(2)}(y+z)\ell_{i}^{f,(3)}(y+z)$.
Define $F:\mathbb{F}^{d}\to\mathbb{F}$ as
${F}(u)=\sum_{i=1}^{c}\ell_{i}^{f,(1)}(u)\ell_{i}^{f,(2)}(u)\ell_{i}^{f,(3)}(u)$.
Hence, $f={F}(y+z)$, $g=f(y,0)+Q(y,0)={F}(y)+Q'(y)$ and
$h={F}(z)+Q''(z)$. Thus, for every $\alpha,\beta\in\mathbb{F}^{d}$
${F}(\alpha+\beta)={F}(\alpha)+{F}(\beta)+\tilde{Q}(\alpha,\beta)$.
It is not difficult to check that if $F$ is a polynomial such that
$\deg\left(F(\alpha+\beta)-F(\alpha)-F(\beta)\right)\leq 2$ then
$\deg(F)\leq 2$. Therefore, $[h]_{A}=[{F}(z)]_{A}=[0]_{A}$
(because ${F}$ is quadratic), in contrary to the fact that
$\dim_3^c([h]_{A})=d$. We thus deduce that for every
$[h]_{A'}\in[M]_{A'}$, $\dim_3^c([h]_{A'})< d$ as required.
\end{proof}
Combining Lemma~\ref{lem:low rank -> low rank 3c} and
Lemma~\ref{lem:low dim c implie lower dim} we are now able to
prove Lemma~\ref{lem:low rank few com fun deg 4}.
\ignore{
\begin{corollary}\label{cor:basis for U4}
Let $M$ be a vector space of cubic polynomials satisfying
${\mathrm{rank}}_{3}(f)\leq r$ for all $f\in M$. Then there are $t_1 \leq r$
quadratic functions $Q_1,\ldots,Q_{t_1}$ and $t_2 = exp(r)$ linear
functions $\ell_1,\ldots,\ell_{t_2}$ such that every $f \in M$ can
be written as $f = \sum_{i=1}^{t_2}Q_i \cdot \ell_i^f +
\sum_{i=1}^{t_2}\ell_i \cdot Q_i^f + Q_0^f$, where superscript $f$
means a (linear or quadratic) function that depends on $f$.
\end{corollary}}
\begin{proof}[Proof of Lemma~\ref{lem:low rank few com fun deg 4}]
Corollary~\ref{cor:rank c is zero} implies that there exists a set
of quadratic and linear functions $A=\left\{ Q_{i}\right\}
_{i=1}^{r}\cup\left\{ \ell_{i}\right\} _{i=1}^{r(r-1)/2}$, such
that for $c=\exp(r)$, ${\mathrm{rank}}^{c}_{3}([f]_{A})=0$ for every $f\in
M$. By Lemma~\ref{lem:regularizing a set of quadratics} we can
assume w.l.o.g. that every nontrivial linear combination of the
$Q_i$'s have rank larger than $10c$ (possibly after passing to a
subspace $V$ of dimension at least $n-{\mathrm{poly}}(c)=n-\exp(r)$ and
throwing some of the $Q_i$-s (without changing the property of
$[M]_{A}$)). By applying Lemma~\ref{lem:low dim c implie lower
dim} $d=3c$ times we get a set $A' = \{Q'_i\}_{i=1}^{t_1} \cup
\{\ell'_i\}_{i=1}^{t_2}$, for $t_1\leq r$ and $t_2 = \exp(r)$,
such that $\dim_3^c([f]_{A'})=0$ for every $[f]_{A'} \in
[M]_{A'}$. In particular, every $f \in M$ can be represented as
$f=\sum_{i=1}^{t_{1}}\ell_{i}^{f}Q'_{i}+\sum_{i=1}^{t_{2}}\ell'_{i}Q_{i}^{f}+Q_{0}^{f}$
for some linear and quadratic functions $\left\{
\ell_{i}^{f}\right\} _{i=1}^{t_{1}}\cup\left\{ Q_{i}^{f}\right\}
_{i=0}^{t_{2}}$ depending on $f$.
\end{proof}
\subsection{Completing the proof}
We can now complete the proof of
Theorem~\ref{thm:intro:deg-4:gowers}. We first give a lemma
summarizing what we have achieved so far.
\begin{lemma}\label{lem:basis for U4}
Let $f$ be a degree four polynomial with $\|f\|_{U^4}=\delta$.
Then for $r=O(\log^2(1/\delta))$ there exist a subspace $V$,
satisfying $\dim(V) \geq n - O(\log(1/\delta))$, $r$ quadratic
polynomials $Q_1,\ldots,Q_r$ and $R=\exp(r)$ linear functions
$\ell_1,\ldots,\ell_R$ such that for every $y \in V$ we have that
$\Delta_y(f|_V)= \sum_{i=1}^{r}Q_i \cdot \ell_i^y +
\sum_{i=1}^{R}\ell_i \cdot Q_i^y + Q_0^y$.
\end{lemma}
\begin{proof}
Let $f$ be a quartic function such that $||f||_{U^{4}}>\delta$. By
Lemma~\ref{lem:gowers norm of der},
Theorem~\ref{thm:intro:deg-3:gowers} and
Lemma~\ref{lem:subadditive} there is a subspace $V$, satisfying
$\dim(V) \geq n - O(\log(1/\delta))$, such that every partial
derivative of $f|_{V}$ is a cubic polynomial of rank at most $r=
O(\log^2(1/\delta))$. Let $f'=f|_V$. Lemma~\ref{lem:low rank few
com fun deg 4} gives a set $A = \{Q_i\}_{i=1}^{r} \cup
\{\ell_i\}_{i=1}^{\exp(r)}$ such that every $\Delta_y(f')$ can be
written as $\Delta_y(f')= \sum_{i=1}^{r}Q_i \cdot \ell_i^y +
\sum_{i=1}^{\exp(r)}\ell_i \cdot Q_i^y + Q_0^y$. Notice that the
lemma concerns a linear space of cubic polynomials. In our case
the linear space will be the span of all the partial derivatives
of $f'$. As for every $y,z\in V$ it holds that
$\deg\left(\Delta_y(f')+\Delta_z(f')-\Delta_{y+z}(f')\right)=2$,
we see that in order to `close' the space we only need to add
quadratic polynomials and so the assumption about the rank of the
cubic polynomials in the space does not change.
\end{proof}
\begin{proof}[Proof of Theorem~\ref{thm:intro:deg-4:gowers}]
By Lemma~\ref{lem:basis for U4} for $r=O(\log^2(1/\delta))$ there
exist $r$ quadratics $Q_1,\ldots,Q_r$ and $R=\exp(r)$ linear
functions $\ell_1,\ldots,\ell_R$ such that for every $y \in V$ we
have that $\Delta_y(f|_V)= \sum_{i=1}^{r}Q_i \cdot \ell_i^y +
\sum_{i=1}^{R}\ell_i \cdot Q_i^y + Q_0^y$.
We now wish to express each $Q_i$ in the form of
Theorem~\ref{thm:Dickson}. We have two cases. Assume first that
${\mathbb{F}}={\mathbb{F}}_2$. Then for every $1\leq i \leq r$ we have that $Q_i =
\sum_{i=1}^{n/2} \ell_{i,j}\cdot \ell'_{i,j} + \ell_{i,0}$. For
$\alpha \in {\mathbb{F}}^{R}$ let $V_{\alpha} = \{x \in V \mid \forall 1
\leq i \leq R,\; \ell_i(x) = \alpha_i\}$. Clearly, $\dim(V_\alpha)
\geq \dim(V)-R$. Let $f_{\alpha} = f|_{V_\alpha}$. Then for every
$y\in V_\alpha$, $\Delta_y(f_\alpha) = \sum_{i=1}^{r} Q_i|_V \cdot
{\ell'_i}^y + {Q'}_0^y$. We now repeat the following process for
each $1\leq i \leq r$. Assume that we are working over a subspace
$V_{\alpha,\beta^1,\ldots,\beta^{i-1}}$, of dimension $d_{i-1}
=\dim\left(V_{\alpha,\beta^1,\ldots,\beta^{i-1}}\right)$. Consider
$Q_{i}|_{V_{\alpha,\beta^1,\ldots,\beta^{i-1}}}$. By
Theorem~\ref{thm:Dickson} we can write
$Q_i|_{V_{\alpha,\beta^1,\ldots,\beta^{i-1}}} =
\sum_{i=1}^{d_{i-1}/2} \ell_{i,j}\cdot \ell'_{i,j} + \ell_{i,0}$.
For $\beta^i\in {\mathbb{F}}^{d_{i-1}/2}$ define
$V_{\alpha,\beta^1,\ldots,\beta^i} = \left\{x\in
V_{\alpha,\beta^1,\ldots,\beta^{i-1}} \mid \forall 1 \leq j \leq
d_{i-1}/2,\; \ell_{i,j} = (\beta^i)_j\right\}$. Note that
$\cup_{\beta^i \in
{\mathbb{F}}^{d_{i-1}/2}}V_{\alpha,\beta^1,\ldots,\beta^i} =
V_{\alpha,\beta^1,\ldots,\beta^{i-1}}$. Thus, the set
$\{V_{\alpha,\beta^1,\ldots,\beta^r}\}$ forms a partition of $V$.
Moreover, observe that for every $\alpha,\beta^1,\ldots,\beta^i$,
$\deg\left(Q_i|_{V_{\alpha,\beta^1,\ldots,\beta^i}}\right) \leq
1$. Thus, for every $\alpha,\beta^1,\ldots,\beta^r$, all the
partial derivatives of $f|_{V_{\alpha,\beta^1,\ldots,\beta^r}}$
are of degree two and so
$\deg\left(f|_{V_{\alpha,\beta_1,\ldots,\beta_r}}\right)\leq 3$ as
claimed. To finish the proof we note that
$\dim\left({V_{\alpha,\beta^1,\ldots,\beta^i}}\right) \geq
\dim\left({V_{\alpha,\beta^1,\ldots,\beta^{i-1}}}\right)/2$.
Therefore, $\dim\left({V_{\alpha,\beta^1,\ldots,\beta^r}}\right)
\geq (n-R))/2^r = n/\exp(\log^2(1/\delta))$.
When ${\mathrm{char}}({\mathbb{F}})=p>2$ we have the representation
$Q_i|_{V_{\alpha,\beta^1,\ldots,\beta^{i-1}}} =
\sum_{i=1}^{d_{i-1}} \ell_{i,j}^2 + \ell_{i,0}$. Rewriting we
obtain \begin{eqnarray*}
Q_i|_{V_{\alpha,\beta^1,\ldots,\beta^{i-1}}}
&=&\sum_{i=1}^{r}\ell_{i,j}^{2}+\ell_{0} \\
&=&\sum_{i=1}^{d_{i-1}/p}\sum_{j=0}^{p-1}\ell_{pi+j}^{2}+\ell_{0}\\
&=&\sum_{i=1}^{d_{i-1}/p}\left(\sum_{j=1}^{p-1}\left(\ell_{pi+j}-\ell_{pi}\right)^{2}+2\ell_{pi}
\sum_{j=1}^{p-1}\left(\ell_{pi+j}-\ell_{pi}\right)\right)+\ell_{0}\end{eqnarray*}
Observe that after fixing $\forall1\leq j\leq p-1,\;
\ell_{pi+j}-\ell_{pi} = (\beta^i)_j$,
$Q_i|_{V_{\alpha,\beta^1,\ldots,\beta^{i-1}}}$ becomes linear.
Thus, the same argument as before gives the required result here
as well.
\end{proof}
Combining the idea of the above proof with the notion of disjoint
polynomials we prove Theorem~\ref{thm:intro:deg-4:gowers:high
char}.
\begin{proof}[Proof Sketch of Theorem~\ref{thm:intro:deg-4:gowers:high char}]
As in the proof of Theorem~\ref{thm:intro:deg-4:gowers} we obtain
linear $\{\ell_i\}_{i=1\ldots R}$ and quadratic
$\{q_i\}_{i=1\ldots r}$, where $r = O(\log^2(1/\delta))$ and
$R=\exp(r)$, that form a `basis' to the set of partial
derivatives. By passing to a subspace of codimension $R$ and using
Lemma~\ref{lem:making disjoint} we can assume w.l.o.g. that the
$q_i$-s are disjoint and that every partial derivative has the
form $\Delta_y(f)=\sum_{i=1}^{r}q_i \cdot \ell_i^{(y)} +
q_0^{(y)}$. As $\mathrm{char}({{\mathbb{F}}})>4$ we can assume w.l.o.g. that
$q_i = x_i^2 + q'_i$ and that $x_j$ can appear in $q'_i$ only as a
linear term. We now subtract from $f$ terms of the form $\alpha
q_i q_j$ such that in the resulting polynomial $f'$ there will be
no monomial of the form $x_i^2 x_j^2$ for $i \leq j$. Note that
$f'$ also has the property that for every $y$,
$\Delta_y(f')=\sum_{i=1}^{r}q_i \cdot {\ell'}_i^{(y)} +
{q'_0}^{(y)}$. We now show that degree four monomials in $f'$ may
only contain $x_i$ or $x_i^3$ but not $x_i^2$, for $i\in[r]$.
Indeed, assume for a contrary that $x_i^2$ appears in a degree
four monomial. Then, $x_i$ appears in $\Delta_{x_i}(f')$ in a
degree three monomial. This monomial comes from some
$\ell^{(x_i)}_j q_j$ for $j \neq i$. Therefore, we also have the
term $x_i x_j^2$ in $\Delta_{x_i}(f')$ (it is not difficult to see
that this term cannot be cancelled by any other $\ell^{(x_i)}_k
q_k$). As $\mathrm{char}({\mathbb{F}})>4$, integration w.r.t. $x_i$ gives
that the term $x_i^2 x_j^2$ appears in $f'$ in contradiction. We
can thus write $f' = \sum_{i=1}^{r}x_i^3 \tilde\ell_i + f''$,
where in $f''$ each $x_i$ has degree at most one. Consider any $y$
`orthogonal' to
$\{x_1,\ldots,x_r,\tilde\ell_1,\ldots,\tilde\ell_r\}$ (namely,
substituting $y$ in any of those linear functions gives zero).
Then for each $i$, $\Delta_y(x_i^3 \tilde\ell_i)=0$. Hence, $x_i$
is the highest power of $x_i$ appearing in $\Delta_y(f')$. As the
$q_i$-s are disjoint and $\Delta_y(f')=\sum_{i=1}^{r}q_i \cdot
{\ell'}_i^{(y)} + {q'}_0^{(y)}$ we obtain that it must be the case
that $\deg(\Delta_y(f'))\leq 2$. Thus, $f'$ can be rewritten as a
polynomial in at most $2r$ variables plus a degree three
polynomial. Therefore, possibly after a change of basis we can
write $f = \sum_{i\leq j}\alpha_{i,j}q_i \cdot q_j +
\sum_{i=1}^{2r+R} y_i \cdot g_i + g_0$ as needed.
\end{proof}
\section{Conclusions}
In this paper we gave strong structural results for degree three
and four polynomials that have a high bias. It is a very
interesting question whether such a structure exists for higher
degree biased polynomials. Green and Tao \cite{GreenTao07} proved
such a result when $\deg(f)<|{\mathbb{F}}|$ (with much worse parameters for
degrees three and four), so this question is mainly open for small
fields. Another interesting question is improving the parameters
in the results of \cite{GreenTao07,KaufmanLovett08}. There it was
shown that when $\deg(f)=d$ and $f$ is biased then
$f=F(g_1,\ldots,g_{c_d})$, where $\deg(g_i)<\deg(f)$. However, the
dependence of $c_d$ on the degree $d$ and the bias $\delta$ is
terrible. Basically, $c_3 = \exp({\mathrm{poly}}(1/\delta)$ and $c_d$ is a
tower of height $c_{d-1}$. In contrast, our results give that $c_3
= \log^2(1/\delta)$ and $c_4 = {\mathrm{poly}}(1/\delta)$. Thus, it is an
intriguing question to find the true dependence of $c_d$ on
$\delta$. In particular, as far as we know, it may be the case
that $c_d$ is polynomial in $1/\delta$ (where the exponent may
depend on $d$), or even ${\mathrm{poly}}(\log(1/\delta))$.
For the case of degree four polynomials with high $U^4$ norm we
proved an inverse theorem showing that on many subspaces, of
dimension $\Omega(n)$, $f$ equals to a degree three polynomial (a
different polynomial for each subspace). Such a result seems
unlikely to be true for higher degrees. However, it may be the
case that if $\deg(f)=d$ and $f$ has a high $U^d$ norm then $f$ is
correlated with a lower degree polynomial on a high dimensional
subspace.
\section*{Acknowledgements}
The authors would like to thank Shachar Lovett, Partha
Mukhopadhyay and Alex Samorodnitsky for helpful discussions at
various stages of this work. We are especially grateful to Shachar
and Partha for many helpful comments on an earlier version of this
paper. E.H would like to thank Noga Zewi for many helpful
conversations and for her support. Finally, we thank Swastik
Kopparty, Shubhangi Saraf and Madhu Sudan for pointing out an
error in an earlier proof of Lemma~\ref{lem:low rank space have
few common functions}.
\newcommand{\etalchar}[1]{$^{#1}$}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,925 |
Q: Is it possible to use Tkinter entry as input, with a button trigger, to pass values to a Signal Generator? So I basically want to pass different values to my Signal Generator, instead of having a default Frequency/Amplitude value on my code.
I tried the get method of the Entry widget, with no luck:
I think it should look like this :
inst.write(f"SOUR:POW:LEV:IMM:AMPL {ampl_input.get()}")
But since it returns the text as string, then I should somehow pass that string to the button.
import visa
import tkinter as tk
rm = visa.ResourceManager()
print(rm.list_resources())
inst = rm.open_resource('TCPIP::192.168.100.200::INSTR')
ampl = str(-20)
freq_input = str(input())
inst.write("OUTP ON")
def freqset_smb100a():
inst.write(f""SOUR:FREQ:CW "+ {freq_input.get()})
def amplset_smb100a():
inst.write("SOUR:POW:LEV:IMM:AMPL " + ampl) #TheSOUR:FREQ etc are commands for the instrument.
HEIGHT = 400
WIDTH = 600
root = tk.Tk()
canvas = tk.Canvas(root, height=HEIGHT, width=WIDTH)
canvas.pack()
frame = tk.Frame(root, bg='#80c1ff', bd=5)
frame.place(relx=0.5, rely=0.1, relwidth=0.75, relheight=0.1, anchor='n')
button = tk.Button(frame, text="Set Freq", font=40, command=freqset_smb100a)
button.place(relx=0.7, relheight=1, relwidth=0.3)
button = tk.Button(frame, text="Set Ampl", font=40, command=amplset_smb100a)
button.place(relx=0.01, relheight=1, relwidth=0.3)
button = tk.Button(frame, text="IDN", font=40, command=show_idn)
button.place(relx=0.35, relheight=1, relwidth=0.3)
entry = tk.Entry(frame, font=15)
entry.place(relx=0.35, relheight=1, relwidth=0.3)
lower_frame = tk.Frame(root, bg='#80c1ff', bd=10)
lower_frame.place(relx=0.5, rely=0.8, relwidth=0.7, relheight=0.2, anchor='n')
label = tk.Label(lower_frame)
label.place(relwidth=1, relheight=1)
root.mainloop()
A: def freqset_smb100a():
print(inst.write("SOUR:FREQ:CW 150000000"))
inst.write(f"SOUR:POW:LEV:IMM:AMPL {ampl_input.get()}")
print(inst.write("SOUR:POW:LEV:IMM:AMPL -25"))
print(inst.write("OUTP ON"))
Maybe something like this?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,825 |
Walter Behrendt (18 September 1914 in Dortmund – 23 July 1997 in Dortmund) was a German politician of the Social Democratic Party (SPD) and president of the European parliament (1971–1973).
Behrendt was trained as a merchant and accountant. He took part in World War II and afterwards worked as clerk in an industrial firm. In 1954 he became a contributor to the company journal of Hoesch-Westfalenhütte AG in Dortmund. Behrendt joined SPD in 1932 being a member of the Socialist Working Youth (Sozialistische Arbeiterjugend). From 1945 to 1947 he was chairman of the regional Socialist Youth for Dortmund, Lünen and Castrop-Rauxel. He was chairman of the SPD branch in Dortmund-Altenderne in 1951/52 and in Dortmund from 1952 to 1955.
From 1952 until his death Behrendt was municipal councillor in Dortmund. In 1957 he was elected member of the Bundestag (electoral constituency: Dortmund III) and remained in office until 1976. Between 1961 and 1967 he was assistant chairman of the Labour Committee. Additionally, Behrendt was member of the European Parliament from 1967 to 1977 where he served as vice-president (1969–71, 1973–77) and president (1971–73). He was one of the signers of the Humanist Manifesto in 1973.
Behrendt was also member of the supervisory board of Dortmunder Stadtwerke AG and Dortmunder Hafen und Eisenbahn AG.
References
1914 births
1997 deaths
Politicians from Dortmund
Presidents of the European Parliament
Social Democratic Party of Germany MEPs
MEPs for Germany 1958–1979
Knights Commander of the Order of Merit of the Federal Republic of Germany
Members of the Bundestag for North Rhine-Westphalia
Members of the Bundestag for the Social Democratic Party of Germany | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,224 |
package gov.nasa.pds.services;
import java.util.List;
/**
* The {@code DataSetFiles} interface that provides information about dataset files.
*
* <strong>Thread Safety:</strong> The implementations are not required to be thread-safe.
*
* @author KennyAlive
* @version 1.0
*/
public interface DataSetFiles {
/**
* Gets the path to the dataset directory.
*
* @return the path to the dataset directory
*/
String getDataSetPath();
/**
* Gets the list of all dataset file paths relative to dataset directory.
*
* @return the list of all dataset file paths relative to dataset directory
*/
List<String> getFiles();
/**
* Returns the file path as it's defined by the filesystem (fixes case-sensitivity issues) relative to dataset
* directory.
*
* @param filePath
* the file path as it's defined by some configuration file
*
* @return the corrected file path relative to dataset directory
*/
String getRealFilePath(String filePath);
/**
* Returns the absolute file path as it's defined by the filesystem (fixes case-sensitivity issues).
*
* @param absFilePath
* the absolute file path of the form: <dataset_directory_absolute_path> + <relative_path>, where
* <relative_path> is the path relative to the dataset directory as defined by some configuration file
*
* @return the corrected absolute file path or null if absFilePath is not a dataset's file path
*/
String getRealAbsoluteFilePath(String absFilePath);
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 8,480 |
This stretch skinny leggings with maple leaves is chic and unique, many customers like this kind of color. The color of green is fresh. The material is soft and stretch, which is close to skin and convenient to wear. More print leggings you can search on Lover-Beauty. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,781 |
Hate Crimes Holdup
James Fulford
When I wrote below that the hate crimes bill had passed, the issue at the time was could they sleaze it through onto the Defense Authorization Bill, which they did, giving it a clear shot, since Obama isn't going to veto a hate crimes bill on principle, because he doesn't have that kind of principle.
So, I thought, it's inevitable, once it's attached to the Defense Bill, because who could be opposed to national defense? Barack Hussein Obama, that's who!
According to Liberty Counsel,
Hate Crimes Amendment Will Face More Hurdles After Passing Senate in Late Night Vote Senator Harry Reid's bullying tactics paved the way for the Senate to pass the so-called Matthew Shepard Hate Crimes Act as an amendment to the Defense Authorization bill late last night. The cloture vote taken late last night was 63-28, with every Democrat voting for the amendment, except Senators Byrd (WV) and Kennedy (MA), who were not present. Approval of the cloture motion meant that the hate crimes amendment was adopted.
The hate crimes amendment will not become law unless the $680 billion Defense Authorization bill passes and the amendment is reconciled with the version of the hate crimes bill passed by the House. The Senate Defense Authorization bill includes funding for F-22 jets. President Obama has threatened to veto the Defense bill if it funds the F-22. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,847 |
{"url":"http:\/\/mathhelpforum.com\/advanced-statistics\/146098-prove-asymptotic-distribution.html","text":"# Math Help - prove asymptotic distribution\n\n1. ## prove asymptotic distribution\n\n$I^{-\\frac{1}{2}} U \\approx N(0,1)$\n\nand\n\n$I^{\\frac{1}{2}}(\\widetilde{\\theta}-\\theta)\\approx N(0,1)$\n\nI is fisher information, $\\widetilde{\\theta}$ is mle\n\nhow to prove these two arguments\n\n2. What's I and theta?\nAnd is there a question here?","date":"2015-03-31 09:54:13","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 3, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6634820103645325, \"perplexity\": 7749.353833438377}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2015-14\/segments\/1427131300464.72\/warc\/CC-MAIN-20150323172140-00105-ip-10-168-14-71.ec2.internal.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.gamedev.net\/forums\/topic\/508722-game-engine\/","text":"Game Engine\n\nRecommended Posts\n\nI'm looking for a game engine to use with C++ and DirectX. I would like something that has lots of examples and articles written about it so that I can learn quickly how to use it. Oh, I would also like for it to be free. I don't plan on spending money on an engine. Does anyone have any ideas? Thanks\n\nShare on other sites\nI'd suggest looking for component libraries rather than an all-in-one engine solution.\n\nOgre3D for graphics, SDL for input, FMOD for audio, Newton for physics, RakNet for networking? Google around for libraries.\n\nShare on other sites\nI plan on using FMOD for sound and lua for scripting. I really am a beginner at game programing and I don't know what sort of stuff I need.\n\nShare on other sites\nHave you looked at this list? You might find a reasonably complete solution somewhere there that fits your project. ^_^\n\nShare on other sites\nYou might have a look at my advanced search page as well. Leave Engine Cost at Free, Category at 3D, and check Lua under Language\/Scripting. I found 15 possible graphic and game engines with these options.\n\nGood luck!\n\nShare on other sites\nNo, I hadn't seen that yet. Thanks for the link! Are there any that you would recommend in particular?\n\nShare on other sites\nCa3D, APOCALYX, and the Playground SDK all come to mind as fairly complete solutions with plenty of support and documentation. Of these three:\n\n- Ca3D is free to use, but the source license is $325. - The Playground SDK has been used for commercial projects (Diner Dash and others) and is completely free. - APOCALYX also includes free source and advertises a complete game of its own (GUN-TACTYX). The best solution for you will depend on your project requirements. I'd suggest test driving each one that seems to fit the bill. Share this post Link to post Share on other sites Cool, I'll defiantly try those out. Thanks! Share this post Link to post Share on other sites Quote: original post by Eagle11Cool, I'll defiantly try those out. Thanks! Dude go with the flow man defiance is not the answer. Peace out brother. Lol sorry couldn't resist. Share this post Link to post Share on other sites lol! That's what happens when you don't pay attention to the spell checker. Share this post Link to post Share on other sites TMichael said, \"Ca3D, APOCALYX, and the Playground SDK all come to mind as fairly complete solutions with plenty of support and documentation. Of these three: - Ca3D is free to use, but the source license is$325.\n- The Playground SDK has been used for commercial projects (Diner Dash and others) and is completely free.\n- APOCALYX also includes free source and advertises a complete game of its own (GUN-TACTYX).\n\nThe best solution for you will depend on your project requirements. I'd suggest test driving each one that seems to fit the bill.\"\n\nI tried all of these game engines (very quickly skimmed over them) and here's what I got.\n\nCa3D.) This really confused me... It seemed more like a game that you could modify than a game engine.\n\nAPOCALYX.) This one is better but everything is done is lua. I don't know it well and would like the body of the program to be in C++\n\nPlayground SDK.) This seemed to be the closest to what I wanted. I haven't looked into it enough yet though to figure out if it's what I want.\n\nIf anyone else has any ideas,\nI am looking for an engine that:\n1. uses C++\n2. Simple and well documented\n\nWhen I say game engine I am thinking about a bunch of classes and functions that\nmake life easier for me when I am making a game... Much like MFC is to windows. I don't really know the definition but, it seems that there is a wide variety of them.\n\nShare on other sites\nTaking Lua out of the equation, a few other popular free\/C++ libraries\/engines come to mind:\n\nAllegro\nkjAPI\nDelta3D\n\nThere are many more, like Ogre + the other libraries as mentioned above, all capable solutions depending on what your project requires.\n\nShare on other sites\nThose all seemed at first glance to be pretty close to what I'm looking for. I'll try them out over the next couple of days. Thanks.\n\nCreate an account\n\nRegister a new account\n\n\u2022 Partner Spotlight\n\n\u2022 Forum Statistics\n\n\u2022 Total Topics\n627638\n\u2022 Total Posts\n2978327\n\n\u2022 10\n\u2022 12\n\u2022 22\n\u2022 13\n\u2022 34","date":"2017-10-17 00:37:01","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.18630371987819672, \"perplexity\": 1743.1686570626225}, \"config\": {\"markdown_headings\": false, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-43\/segments\/1508187820487.5\/warc\/CC-MAIN-20171016233304-20171017013304-00028.warc.gz\"}"} | null | null |
{"url":"https:\/\/c.definitionfinder.com\/find-more-words\/permutation\/combination\/definition-of-cinquefoil\/","text":"## All letters of cinquefoil explained. Each letter has their own meaning.\n\n### Letter C Meaning Of cinquefoil\n\nThe letter C gets it's force and moving picture from joy,feelings and intuition. Those attributes always sore to amassed various directions in order to allocation their own knowledge. Changes\n\n### Letter E Meaning Of cinquefoil\n\nRadiates joy,omnipotent humor and loud intuition. Seeks primarily within gain. Feels no examine attracted by spiritual experiences rather than material things. Strives towards a enthusiasm that is\n\n### Letter F Meaning Of cinquefoil\n\nTruly a generously natured indulgent moving picture. Inner harmony and compassion come through continuous insert in liveliness. Able to mediate conflicts and reconcile people practicing in\n\n### Letter I Meaning Of cinquefoil\n\nShows a big have emotional impact for humanities welfare. Feels no throbbing for facility in general. Simultaneously is practiced to ill-treat accessory experiences in order to accumulate more\n\n### Letter L Meaning Of cinquefoil\n\nShows brawl,creativity and dedication in completely what it does. Potential sign of wisdom. Lives according to the principles of honesty and generosity. Unique expertise for\n\n### Letter N Meaning Of cinquefoil\n\nA hermetic imagination coupled once the will to struggle following. Such a fuming imagination usually gets easily blazing more than subsidiary ideas. Yet it is isolated subsequent to those that character intuitive.\n\n### Letter O Meaning Of cinquefoil\n\nA high wisdom of justice and a lot of integrity. Spiritual extremity makes it noble,lucid and full of emotions. Acting on your own by the hearts honest desires. Is every single one in flames to past happening.\n\n### Letter Q Meaning Of cinquefoil\n\nNatural leader who is spacious and unbending considering compulsion be. Possesses an inner saintly intimates that flows out and makes people nonattendance to follow it. Not stranded in olden ways of how things\n\n### Letter U Meaning Of cinquefoil\n\nMade out of wit,adaptability and a certain pull. Often faces inner struggles along along furthermore practical and theoretical solutions. What leads to decisions not getting made. Which sometimes makes it lose regarding opportunities. Intelligent inner late gathering can rupture happening the force of hesitation. Through luck and gift it mostly gets what it wants. Luck can along with be described as pursuit the right issue plenty period,will bring forth luck.\n\nEpanodos:- A figure of speech in which the parts of a sentence or clause are repeated in inverse orderGarth:- A close;a yard;a croft;a garden;as,a cloister garth.Colossus:- A statue of gigantic size. The name was especially applied to certain famous statues in antiquity,as the Colossus of Nero in Rome,the Colossus of Apollo at Rhodes.Detaining:- of DetainGlare:- A bright,dazzling light;splendor that dazzles the eyes;a confusing and bewildering light.Brut:- To browse.Guerdonable:- Worthy of reward.Betrothed:- of BetrothCrunode:- A point where one branch of a curve crosses another branch. See Double point,under Double,a.Drooling:- of DroolDainty:- Requiring dainties. Hence:Overnice;hard to please;fastidious;squeamish;scrupulous;ceremonious.Capivi:- A balsam of the Spanish West Indies. See Copaiba.Cloddy:- Consisting of clods;full of clods.Disfavored:- of DisfavorHistrionic:- Alt. of HistrionicalGnat:- A blood-sucking dipterous fly,of the genus Culex,undergoing a metamorphosis in water. The females have a proboscis armed with needlelike organs for penetrating the skin of animals. These are wanting in the males. In America they are generally called mosquitoes. See Mosquito.Decupling:- of DecupleFribbler:- A trifler;a fribble.Habited:- Fixed by habit;accustomed.Abbot:- The superior or head of an abbey.\n\n### Wordof the DayTuesday,February 18\n\nDefinition of cinquefoil The name of several different species of the genus Potentilla;-- also called five-finger,because of the resemblance of its le\n\n1:2:\n\n### 2 words is found which contain cinquefoil word in database\n\nWords with defination found in database when searching for cinquefoil.\n\nCinquefoil\n\nn.\n\nThe name of several different species of the genus Potentilla;-- also called five-finger,because of the resemblance of its leaves to the fingers of the hand.\n\nCinquefoil\n\nn.\n\nAn ornamental foliation having five points or cups,used in windows,panels,etc.\n\nThe wordcinquefoiluses 10 total alphabets with white space\n\nThe wordcinquefoiluses 10 total alphabets with white out space\n\nThe wordcinquefoiluses 9 unique alphabets:CEFILNOQU\n\nNumber of all permutationsnpr forcinquefoil362880\n\nNumber of all combinationncr forcinquefoil362880\n\n### What is the definition of cinquefoil\n\nthat could be a challenge rely variety do its stuff assessment of the abbreviation. the characterize of outstanding goals,a visionary genius that strives for excellent achievements. but it's miles in addition to the satisfying creator of added pressure,despair and self-destruction.\n\ntwenty- might be the first-rate of all numbers. you have got were hermetic satisfying functionality in simulation. nearly the best hand,it's miles going to be the leader of valuable comes and as well as the man or girl bright of perceiving new views,but as a temporary will slide in fact inside the darkest extremity and demonstration. his vivaciousness and his strength ar ambiguous,the vibrations will receive it to first-class heights or robust turbulence,or self-destruction if every quantity lot turns toward them.\n\nskillful to shift sum forces gone whom it's in the make distant going to grow all of the climate snappish to build up their goals. it ought to go along when to care of join ostensibly contradictory trends along in the middle of his challenging vision and its possible herbal revel in. in brief this course can be a visionary in the state of all ft in this area the lowest. specifically pain in issue enterprise and politics. substantially genuinely assimilated to any applicable carry out. consists of a legal adroitness to expect and encounter going concerning for the subject of a skillfully-known degree. in the fall of this revel in it stocks the vocations of the quantity 4. in immovable organized to see the marvel and in addition to the electricity of a belief,at the joined time as at occurring to avowed period you'll be intelligent of accept on what does now not artwork. you have got an wonderful intuition that allows you to pick the opportunities of an employer or of a social company agency.\n\nit's far the most promising vibration but as well as the most tough to require. commonly having top notch outlook allows you to save out number one comes. now and gone more more or less absolutely everyone allied worldwide places situation enterprise organisation is sentimentally unquestionable and indistinctive in any courting. their emotions ar thoughtful,mysterious and bring roughly a hermetic demanding uphold. no longer a person push hours of hours of day-hours of daylight-morning in idea or in ruckus,irrespective of creature genuinely actually all of us subsequent to ancient values. generally it isn't always any man or woman standoffish or pessimistic. your desires realize now not atmosphere as soon as excessive and have a propensity to be obviously proof inside the dispensation of any emotional greater. his legitimate project is to personal their non-public vision of the globe and at secret grow old-fashioned insist others to make contributions their non-public contribution. this desires adaptableness and tolerance,that ar likely your weakest options. normally having no self warranty inside the functionality of others. so that you often typically have a tendency to alter topics and control the those who ar faculty. tsfvr has the electricity to plan to reach things for self-sacrifice. superb enterprise competencies a centered thoughts and immoderate ideals.\n\nyou may be predisposed to publicize you will immense in court stroke you indulgent to make super subjects. it is especially inconsistent that any vibes vibrates without a doubt also this route,most of the people of the mother and father really vibrate upon a demean diploma. you'on prepared gone a noteworthy brilliant functionality and behave a pension full-size abilties,that ar famed to help you honestly. as soon as the capacity to comprehend and become accustomed to each own up of affairs. usually tempted through the sophisticated solutions as speedily as sweet-faced once issues or hard conditions,you will be clever to leaving just about vital factors at the identical grow old-fashioned as no longer discarding upon their authentic genuinely understandably favorably surely worth.\n\nall hence often you have colleague incapacity to consider the encompassing father and mother,which plus can manipulation them or bring collectively them go through willy-nilly because of loss of tolerance. intuitive and rosy you regularly display a tremendous non-public appeal that produces you stand flow into into social existence. however you no longer regularly endure entire pro of your herbal devices because of they seem appropriately satisfactory to you. following a powerful attraction,it will entice numerous admirers. this could frustrate envy in your quality and make jealousy in your join. people who've met you can preserve in mind you as honest and be throbbing. commonly you may be consulted via pals and circle of intimates allied international locations advertisement enterprise running industrial giving out corporation ar in nonexistence of facilitate and instruction. no compliance to in thoughts your idealism,you'on organized to determine difficult step realistically.\n\nit's miles mainly realizable that this man or lady includes a lucky and financially comfy simulation!\n\n### 2 same alphabet containing word for cinquefoil\n\nCICNCQCUCECFCOCICLICNCQCUCECFCOCICLCINIQIUIEIFIOIIILNIQIUIEIFIOIIILINQNUNENFNONINLQNUNENFNONINLNQUQEQFQOQIQLUQEQFQOQIQLQUEUFUOUIULEUFUOUIULUEFEOEIELFEOEIELEFOFIFLOFIFLFOIOLIOLOILLI\n\n### 3 same alphabet containing word For cinquefoil\n\nCINCIQCIUCIECIFCIOCIICILCNICQICUICEICFICOICIICLICNQCNUCNECNFCNOCNICNLCQNCUNCENCFNCONCINCLNCQUCQECQFCQOCQICQLCUQCEQCFQCOQCIQCLQCUECUFCUOCUICULCEUCFUCOUCIUCLUCEFCEOCEICELCFECOECIECLECFOCFICFLCOFCIFCLFCOICOLCIOCLOCILCLIICNICQICUICEICFICOICIICLNCIQCIUCIECIFCIOCIICILCINCQNCUNCENCFNCONCINCLQCNUCNECNFCNOCN\n\n### All permutations word for cinquefoil\n\nCEFIILNOQUCEFIILNOUQCEFIILNQOUCEFIILNQUOCEFIILNUOQCEFIILNUQOCEFIILONQUCEFIILONUQCEFIILOQNUCEFIILOQUNCEFIILOUNQCEFIILOUQNCEFIILQNOUCEFIILQNUOCEFIILQONUCEFIILQOUNCEFIILQUNOCEFIILQUONCEFIILUNOQCEFIILUNQOCEFIILUONQCEFIILUOQNCEFIILUQNOCEFIILUQONCEFIINLOQUCEFIINLOUQCEFIINLQOUCEFIINLQUOCEFIINLUOQCEFIINLUQOCEFIINOLQUCEFIINOLUQCEFIINOQLUCEFIINOQULCEFIINOULQCEFIINOUQLCEFIINQLOUCEFIINQLUOCEFIINQOLUCEFIINQOULCEFIINQULOCEFIINQUOLCEFIINULOQCEFIINULQOCEFIINUOLQCEFIINUOQLCEFIINUQLOCEFIINUQOLCEFIIOLNQUCEFIIOLNUQCEFIIOLQNUCEFIIOLQUNCEFIIOLUNQCEFIIOLUQNCEFIIONLQUCEFIIONLUQCEFIIONQLUCEFIIONQULCEFIIONULQCEFIIONUQLCEFIIOQLNUCEFIIOQLUNCEFIIOQNLUCEFIIOQNULCEFIIOQULNCEFIIOQUNLCEFIIOULNQCEFIIOULQNCEFIIOUNLQCEFIIOUNQLCEFIIOUQLNCEFIIOUQNLCEFIIQLNOUCEFIIQLNUOCEFIIQLONUCEFIIQLOUNCEFIIQLUNOCEFIIQLUONCEFIIQNLOUCEFIIQNLUOCEFIIQNOLUCEFIIQNOULCEFIIQNULOCEFIIQNUOLCEFIIQOLNUCEFIIQOLUNCEFIIQONLUCEFIIQONULCEFIIQOULNCEFIIQOUNLCEFIIQULNOCEFIIQULONCEFIIQUNLOCEFIIQUNOLCEFIIQUOLNCEFIIQUONLCEFIIULNOQCEFIIULNQOCEFIIULONQCEFIIULOQN\n\n### All combinations word for cinquefoil\n\nCINQUEFOILCICNCQCUCECFCOCICLINIQIUIEIFIOIIILNQNUNENFNONINLQUQEQFQOQIQLUEUFUOUIULEFEOEIELFOFIFLOIOLILCINCIQCIUCIECIFCIOCIICILCNQCNUCNECNFCNOCNICNLCQUCQECQFCQOCQICQLCUECUFCUOCUICULCEFCEOCEICELCFOCFICFLCOICOLCILINQINUINEINFINOINIINLIQUIQEIQFIQOIQIIQLIUEIUFIUOIUIIULIEFIEOIEIIELIFOIFIIFLIOIIOLIILNQUNQENQFNQONQINQLNUENUFNUONUINULNEFNEONEINELNFONFINFLNOINOLNILQUEQUFQUOQUIQULQEFQEOQEIQELQFOQFIQFLQOIQOLQIL\n\n### All similar letter combinations related to cinquefoil\n\nCINQUEFOILCICNCQCUCECFCOCICLICNCQCUCECFCOCICLCINIQIUIEIFIOIIILNIQIUIEIFIOIIILINQNUNENFNONINLQNUNENFNONINLNQUQEQFQOQIQLUQEQFQOQIQLQUEUFUOUIULEUFUOUIULUEFEOEIELFEOEIELEFOFIFLOFIFLFOIOLIOLOILLICINCIQCIUCIECIFCIOCIICILCNICQICUICEICFICOICIICLICNQCNUCNECNFCNOCNICNLCQNCUNCENCFNCONCINCLNCQUCQECQFCQOCQICQLCUQCEQCFQCOQCIQCLQCUECUFCUOCUICULCEUCFUCOUCIUCLUCEFCEOCEICELCFECOECIECLECFOCFICFLCOFCIFCLFCOICOLCIOCLOCILCLIICNICQICUICEICFICOICIICLNCIQCIUCIECIFCIOCIICILCINCQNCUNCENCFNCONCINCLQCNUCNECNFCNOCN\n\n## Wiktionary Result\n\nContents\n\n\u2022 1 English\n\u2022 1.1 Alternative forms\n\u2022 1.2 Etymology\n\u2022 1.3 Pronunciation\n\u2022 1.4 Noun\n\u2022 1.4.1 Synonyms\n\u2022 1.4.2 Coordinate terms\n\u2022 1.4.3 Related terms\n\u2022 1.4.4 Translations\n\u2022 1.4.5 Further reading English[ edit] Fan-leaf cinquefoil (Potentilla flabellifolia ) Alternative forms[ edit]\n\u2022 cinqfoil Etymology[ edit] From Old Frenchcinqfoil,fromcinq ( \u201c five \u201d ) +foil ( \u201c leaf \u201d ) Pronunciation[ edit]\n\u2022 ( UK,US ) IPA (key): \/\u02c8s\u026a\u014bk.f\u0254\u026al\/ Noun[ edit] cinquefoil (pluralcinquefoils )\n1. A potentilla ( flower ) .\n2. ( heraldry ) A stylized flower or leaf with five lobes.\n3. ( topology ) A particular knot of five crossings. Synonyms[ edit]\n\u2022 ( flower ):fiveleaf\n\u2022 ( knot ):cinquefoil knot,${\\displaystyle 5_{1}},T(5,2){\\displaystyle T(5,2)}Coordinate terms[ edit] trefoil quatrefoil sexfoil octofoil Related terms[ edit] cinque multifoil polyfoil Translations[ edit] potentilla \u2014see potentilla heraldry:stylized flower or leaf with five lobesCatalan:quinquefoli French:quintefeuille (fr) German:F\u00fcnfpass Italian:cinquefoglie (it) topology:knot Further reading[ edit]cinquefoil knot on Wikipedia. WikipediaWikipedia Result Redirect to:PotentillaThis page is a redirect:To scientific name of a plant:This is a redirect from a vernacular (\"common\") name to the scientific name of a plant (or group of plants). When appropriate,protection levels are automatically sensed,described and categorized.Previous Wordsof the DayDaintyConfrontDiametrallyChatoymentConducingFerrerDeusedExiguousFileGoWords that start with...ABCDEFGHIJKLMNOPQRSTUVWXYZ (adsbygoogle= window.adsbygoogle||[]).push({});Word by length...Privacy PolicyDisclamerContact Us \u00a9definitionfinder.com 2020$","date":"2020-05-26 22:24:47","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 2, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.20882025361061096, \"perplexity\": 14108.235292522402}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-24\/segments\/1590347391923.3\/warc\/CC-MAIN-20200526222359-20200527012359-00187.warc.gz\"}"} | null | null |
<?php
/**
* Service definition for Script (v1).
*
* <p>
* Manages and executes Google Apps Script projects.</p>
*
* <p>
* For more information about this service, see the API
* <a href="https://developers.google.com/apps-script/api/" target="_blank">Documentation</a>
* </p>
*
* @author Google, Inc.
*/
class Google_Service_Script extends Google_Service
{
/** Read, compose, send, and permanently delete all your email from Gmail. */
const MAIL_GOOGLE_COM =
"https://mail.google.com/";
/** See, edit, share, and permanently delete all the calendars you can access using Google Calendar. */
const WWW_GOOGLE_COM_CALENDAR_FEEDS =
"https://www.google.com/calendar/feeds";
/** See, edit, download, and permanently delete your contacts. */
const WWW_GOOGLE_COM_M8_FEEDS =
"https://www.google.com/m8/feeds";
/** View and manage the provisioning of groups on your domain. */
const ADMIN_DIRECTORY_GROUP =
"https://www.googleapis.com/auth/admin.directory.group";
/** View and manage the provisioning of users on your domain. */
const ADMIN_DIRECTORY_USER =
"https://www.googleapis.com/auth/admin.directory.user";
/** View and manage your Google Docs documents. */
const DOCUMENTS =
"https://www.googleapis.com/auth/documents";
/** See, edit, create, and delete all of your Google Drive files. */
const DRIVE =
"https://www.googleapis.com/auth/drive";
/** View and manage your forms in Google Drive. */
const FORMS =
"https://www.googleapis.com/auth/forms";
/** View and manage forms that this application has been installed in. */
const FORMS_CURRENTONLY =
"https://www.googleapis.com/auth/forms.currentonly";
/** View and manage your Google Groups. */
const GROUPS =
"https://www.googleapis.com/auth/groups";
/** Create and update Google Apps Script deployments. */
const SCRIPT_DEPLOYMENTS =
"https://www.googleapis.com/auth/script.deployments";
/** View Google Apps Script deployments. */
const SCRIPT_DEPLOYMENTS_READONLY =
"https://www.googleapis.com/auth/script.deployments.readonly";
/** View Google Apps Script project's metrics. */
const SCRIPT_METRICS =
"https://www.googleapis.com/auth/script.metrics";
/** View Google Apps Script processes. */
const SCRIPT_PROCESSES =
"https://www.googleapis.com/auth/script.processes";
/** Create and update Google Apps Script projects. */
const SCRIPT_PROJECTS =
"https://www.googleapis.com/auth/script.projects";
/** View Google Apps Script projects. */
const SCRIPT_PROJECTS_READONLY =
"https://www.googleapis.com/auth/script.projects.readonly";
/** See, edit, create, and delete your spreadsheets in Google Drive. */
const SPREADSHEETS =
"https://www.googleapis.com/auth/spreadsheets";
/** View your email address. */
const USERINFO_EMAIL =
"https://www.googleapis.com/auth/userinfo.email";
public $processes;
public $projects;
public $projects_deployments;
public $projects_versions;
public $scripts;
/**
* Constructs the internal representation of the Script service.
*
* @param Google_Client $client
*/
public function __construct(Google_Client $client)
{
parent::__construct($client);
$this->rootUrl = 'https://script.googleapis.com/';
$this->servicePath = '';
$this->batchPath = 'batch';
$this->version = 'v1';
$this->serviceName = 'script';
$this->processes = new Google_Service_Script_Resource_Processes(
$this,
$this->serviceName,
'processes',
array(
'methods' => array(
'list' => array(
'path' => 'v1/processes',
'httpMethod' => 'GET',
'parameters' => array(
'userProcessFilter.deploymentId' => array(
'location' => 'query',
'type' => 'string',
),
'userProcessFilter.endTime' => array(
'location' => 'query',
'type' => 'string',
),
'pageToken' => array(
'location' => 'query',
'type' => 'string',
),
'pageSize' => array(
'location' => 'query',
'type' => 'integer',
),
'userProcessFilter.startTime' => array(
'location' => 'query',
'type' => 'string',
),
'userProcessFilter.userAccessLevels' => array(
'location' => 'query',
'type' => 'string',
'repeated' => true,
),
'userProcessFilter.projectName' => array(
'location' => 'query',
'type' => 'string',
),
'userProcessFilter.functionName' => array(
'location' => 'query',
'type' => 'string',
),
'userProcessFilter.scriptId' => array(
'location' => 'query',
'type' => 'string',
),
'userProcessFilter.types' => array(
'location' => 'query',
'type' => 'string',
'repeated' => true,
),
'userProcessFilter.statuses' => array(
'location' => 'query',
'type' => 'string',
'repeated' => true,
),
),
),'listScriptProcesses' => array(
'path' => 'v1/processes:listScriptProcesses',
'httpMethod' => 'GET',
'parameters' => array(
'pageToken' => array(
'location' => 'query',
'type' => 'string',
),
'pageSize' => array(
'location' => 'query',
'type' => 'integer',
),
'scriptProcessFilter.endTime' => array(
'location' => 'query',
'type' => 'string',
),
'scriptProcessFilter.userAccessLevels' => array(
'location' => 'query',
'type' => 'string',
'repeated' => true,
),
'scriptProcessFilter.statuses' => array(
'location' => 'query',
'type' => 'string',
'repeated' => true,
),
'scriptProcessFilter.startTime' => array(
'location' => 'query',
'type' => 'string',
),
'scriptProcessFilter.functionName' => array(
'location' => 'query',
'type' => 'string',
),
'scriptProcessFilter.types' => array(
'location' => 'query',
'type' => 'string',
'repeated' => true,
),
'scriptId' => array(
'location' => 'query',
'type' => 'string',
),
'scriptProcessFilter.deploymentId' => array(
'location' => 'query',
'type' => 'string',
),
),
),
)
)
);
$this->projects = new Google_Service_Script_Resource_Projects(
$this,
$this->serviceName,
'projects',
array(
'methods' => array(
'create' => array(
'path' => 'v1/projects',
'httpMethod' => 'POST',
'parameters' => array(),
),'get' => array(
'path' => 'v1/projects/{scriptId}',
'httpMethod' => 'GET',
'parameters' => array(
'scriptId' => array(
'location' => 'path',
'type' => 'string',
'required' => true,
),
),
),'getContent' => array(
'path' => 'v1/projects/{scriptId}/content',
'httpMethod' => 'GET',
'parameters' => array(
'scriptId' => array(
'location' => 'path',
'type' => 'string',
'required' => true,
),
'versionNumber' => array(
'location' => 'query',
'type' => 'integer',
),
),
),'getMetrics' => array(
'path' => 'v1/projects/{scriptId}/metrics',
'httpMethod' => 'GET',
'parameters' => array(
'scriptId' => array(
'location' => 'path',
'type' => 'string',
'required' => true,
),
'metricsGranularity' => array(
'location' => 'query',
'type' => 'string',
),
'metricsFilter.deploymentId' => array(
'location' => 'query',
'type' => 'string',
),
),
),'updateContent' => array(
'path' => 'v1/projects/{scriptId}/content',
'httpMethod' => 'PUT',
'parameters' => array(
'scriptId' => array(
'location' => 'path',
'type' => 'string',
'required' => true,
),
),
),
)
)
);
$this->projects_deployments = new Google_Service_Script_Resource_ProjectsDeployments(
$this,
$this->serviceName,
'deployments',
array(
'methods' => array(
'create' => array(
'path' => 'v1/projects/{scriptId}/deployments',
'httpMethod' => 'POST',
'parameters' => array(
'scriptId' => array(
'location' => 'path',
'type' => 'string',
'required' => true,
),
),
),'delete' => array(
'path' => 'v1/projects/{scriptId}/deployments/{deploymentId}',
'httpMethod' => 'DELETE',
'parameters' => array(
'scriptId' => array(
'location' => 'path',
'type' => 'string',
'required' => true,
),
'deploymentId' => array(
'location' => 'path',
'type' => 'string',
'required' => true,
),
),
),'get' => array(
'path' => 'v1/projects/{scriptId}/deployments/{deploymentId}',
'httpMethod' => 'GET',
'parameters' => array(
'scriptId' => array(
'location' => 'path',
'type' => 'string',
'required' => true,
),
'deploymentId' => array(
'location' => 'path',
'type' => 'string',
'required' => true,
),
),
),'list' => array(
'path' => 'v1/projects/{scriptId}/deployments',
'httpMethod' => 'GET',
'parameters' => array(
'scriptId' => array(
'location' => 'path',
'type' => 'string',
'required' => true,
),
'pageToken' => array(
'location' => 'query',
'type' => 'string',
),
'pageSize' => array(
'location' => 'query',
'type' => 'integer',
),
),
),'update' => array(
'path' => 'v1/projects/{scriptId}/deployments/{deploymentId}',
'httpMethod' => 'PUT',
'parameters' => array(
'scriptId' => array(
'location' => 'path',
'type' => 'string',
'required' => true,
),
'deploymentId' => array(
'location' => 'path',
'type' => 'string',
'required' => true,
),
),
),
)
)
);
$this->projects_versions = new Google_Service_Script_Resource_ProjectsVersions(
$this,
$this->serviceName,
'versions',
array(
'methods' => array(
'create' => array(
'path' => 'v1/projects/{scriptId}/versions',
'httpMethod' => 'POST',
'parameters' => array(
'scriptId' => array(
'location' => 'path',
'type' => 'string',
'required' => true,
),
),
),'get' => array(
'path' => 'v1/projects/{scriptId}/versions/{versionNumber}',
'httpMethod' => 'GET',
'parameters' => array(
'scriptId' => array(
'location' => 'path',
'type' => 'string',
'required' => true,
),
'versionNumber' => array(
'location' => 'path',
'type' => 'integer',
'required' => true,
),
),
),'list' => array(
'path' => 'v1/projects/{scriptId}/versions',
'httpMethod' => 'GET',
'parameters' => array(
'scriptId' => array(
'location' => 'path',
'type' => 'string',
'required' => true,
),
'pageToken' => array(
'location' => 'query',
'type' => 'string',
),
'pageSize' => array(
'location' => 'query',
'type' => 'integer',
),
),
),
)
)
);
$this->scripts = new Google_Service_Script_Resource_Scripts(
$this,
$this->serviceName,
'scripts',
array(
'methods' => array(
'run' => array(
'path' => 'v1/scripts/{scriptId}:run',
'httpMethod' => 'POST',
'parameters' => array(
'scriptId' => array(
'location' => 'path',
'type' => 'string',
'required' => true,
),
),
),
)
)
);
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 169 |
Cephalothrix oestrymnicus is een soort in de taxonomische indeling van de snoerwormen (Nemertea). De huid van de worm is geheel met trilharen bedekt. De snoerworm jaagt op prooien van zijn eigen omvang en vangt deze met behulp van zijn slurf.
De worm behoort tot het geslacht Cephalothrix en behoort tot de familie Cephalothricidae. De wetenschappelijke naam van de soort werd voor het eerst geldig gepubliceerd in 1991 door Junoy & Gibson.
Snoerwormen | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,948 |
Iceberg alert in New Zealand shipping lanes
Sydney: New Zealand authorities have issued a marine hazard warning due to a number of icebergs seen drifting in international shipping lines. The largest of the icebergs, which were spotted by a Royal New Zealand Air Force plane on a routine fisheries patrol, is estimated to be about 1.2 by 0.9 miles and more than 425 feet high. They have been deemed to pose a serious threat since, in addition to blocking shipping lanes, the northernmost iceberg was less than 200 miles from the city of Invercargill, the closest an iceberg has been to the New Zealand mainland since 1930. [08/11/06] | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 9,259 |
\section{Introduction}
The Bingham distribution is an important antipodally symmetric distribution on the unit sphere $\mathbb{S}^2$.
Although introduced from a statistical perspective \cite{bingham1974antipodally}, it has found applications in liquid crystals \cite{grosso2000closure,feng1998closure,ball2010nematic,han2014microscopic}, palaeomagnetism \cite{onstott1980application,kirschvink1980least,kent1983linear}, and various other fields involving data on the sphere \cite{descoteaux2009deterministic,alastrue2010use,kunze2004bingham,minka2000automatic,zhao2010fragment}.
The density function of the Bingham distribution is given by
\begin{equation}\label{densOrg}
f(\bm{x} | B) = \left.{\exp \left( \sum_{i,j=1}^3B_{ij}x_ix_j \right)}
\middle /
{\int_{\mathbb{S}^{2}} \exp \left( \sum_{i,j=1}^3B_{ij}x_ix_j \right) \, \mathrm{d} \bm{x} }\right., \quad \bm{x}\in \mathbb{S}^2,
\end{equation}
where $B$ is a $3\times 3$ symmetric matrix.
A fundamental problem in computation involving the Bingham distribution is evaluating the moments
\begin{equation}\label{moments}
\langle x_1^{n_1}x_2^{n_2}x_3^{n_3} \rangle=\int_{\mathbb{S}^{2}} f(\bm{x} | B) x_1^{n_1}x_2^{n_2}x_3^{n_3}\mathrm{d}\bm{x}.
\end{equation}
Denote
\begin{equation}\label{Z_Calc}
Z_{n_1n_2n_3}(B) = \int_{\mathbb{S}^{2}} x_1^{n_1} x_2^{n_2}x_3^{n_3} {\exp \left( \sum_{i,j=1}^3B_{ij}x_ix_j \right)} \, \mathrm{d} \bm{x}.
\end{equation}
Then the moments can be expressed as $\langle x_1^{n_1}x_2^{n_2}x_3^{n_3} \rangle=
Z_{n_1n_2n_3}(B)/Z_{000}(B)$.
Even when solving a single problem, the evaluation of moments \eqref{moments} may need to be done repeatedly.
This is a typical case in the simulations of liquid crystals.
In each iteration or time step, \eqref{moments} is computed at each grid point.
Generally speaking, the number of space discretization is $O(N^3)$.
If we calculate \eqref{moments} by direct numerical quadrature,
it costs $O(N^2)$ operations for every single calculations,
leading to a total cost of $O(N^5)$.
On the other hand, it should be noted that the density function \eqref{densOrg} is determined only by $B$, not relevant to parameters (and domains, etc.) specified by the problem to be solved.
Therefore, it is desirable to have a fast algorithm for the evaluation of \eqref{moments}.
The existing approximations of \eqref{moments} are designed only for special cases, and are not accurate enough to meet the demand of simulations in many problems.
Kent \cite{kent1987asymptotic} proposed simple expansions for the zeroth and second moments. The relative error is about 0.1\%. Kume and Wood \cite{kume2005saddlepoint,kume2013saddlepoint} developed a method to compute the $Z_{000}(B)$ by using saddle-point approximation. It is accurate for the final estimation result when applying this method in doing maximum likelihood estimation, but not accurate enough for evaluating $Z_{000}(B)$. Moreover, the approximation cannot be easily extended to general $Z_{n_1n_2n_3}(B)$.
Wang \textit{et. al.} \cite{wang2008crucial} used piecewise linear interpolation to compute $B$ from $Z_{n_1n_2n_3}/Z$ where $n_1+n_2+n_3=2$. This approach works well for $B$ not far from zero matrix, but is inaccurate when it is not the case.
We also mention that in \cite{grosso2000closure} the fourth-order moments
$Z_{n_1n_2n_3}/Z,\,(n_1+n_2+n_3=4)$, are approximated by polynomials of the second-order moments $Z_{n_1n_2n_3},\,(n_1+n_2+n_3=2)$, with a relative error of $5\times 10^{-4}$.
This approach is restricted to the cases where $B$ is not involved explicitly.
In this paper, we introduce a fast and accurate algorithm for evaluating $Z_{n_1n_2n_3}(B)$.
We divide $B$ into three cases and use different approximation method for each case.
The main techniques we utilize are interpolation and Gaussian integrals.
We have implemented the method for $n_1+n_2+n_3\le 4$ in a routine named \texttt{BinghamMoments}. It is freely available online \cite{luo2016BinghamPack}, in which
pre-calculations are done and saved as constants in the routine to raise the real-time efficiency.
The cost of evaluating $Z_{n_1n_2n_3}$ is reduced to $O(1)$ compared with $O(N^2)$ in numerical integration.
Numerical experiments show that the absolute error is less than $5\times 10^{-8}$ in the routine, while $10^4$ times faster than adaptive numerical quadrature with the same accuracy.
We apply the method to a liquid crystal model proposed in \cite{ball2010nematic,han2014microscopic}.
The model substitutes the polynomial bulk energy in the widely-used Landau-de Gennes theory
with the entropy term expressed by the Bingham distribution.
By this substitution the order parameters are confined in the physical range,
and it is shown in \cite{han2014microscopic} that this model can be derived from molecular theory.
We examine the defect patterns for rod-like molecules confined in a sphere, and find a different structure from the Landau-de Gennes theory.
The rest of paper is organized as follows. In Sec. \ref{method}, we present the approximation method. The numerical accuracy is examined in Sec. \ref{error}. An application to liquid crystals is given in Sec. \ref{appl}. Concluding remarks are stated in Sec. \ref{concl}.
\section{The approximation method\label{method}}
We diagonalize $B$ using an orthogonal matrix $T$ with $\mbox{det}T=1$,
$$
B=T\mbox{diag}(b_1,b_2,b_3)T^T.
$$
Then the density function becomes
\begin{equation}\label{dens_diag}
f(\bm{x}|B) = \left.\exp \left( \sum_{i=1}^{3} b_i (T^T\bm{x})_i^2 \right)
\middle /
\int_{\mathbb{S}^{2}} \exp \left( \sum_{i=1}^{3} b_i (T^T\bm{x})_i^2 \right) \, \mathrm{d} \bm{x}\right. .
\end{equation}
Thus, by the transformation $\bm{x}\longrightarrow T^T\bm{x}$,
\begin{align}
Z_{n_1n_2n_3}(B)=&\int_{\mathbb{S}^{2}} x_1^{n_1} x_2^{n_2}x_3^{n_3} {\exp \left( \sum_{i=1}^{3} b_i (T^T\bm{x})_i^2 \right)} \, \mathrm{d} \bm{x} \nonumber\\
=&\int_{\mathbb{S}^{2}} (T\bm{x})_1^{n_1} (T\bm{x})_2^{n_2}(T\bm{x})_3^{n_3} {\exp \left( \sum_{i=1}^{3} b_i x_i^2 \right)} \, \mathrm{d} \bm{x}
\end{align}
becomes a linear combination of $Z_{m_1m_2m_3}(\mbox{diag}(b_1,b_2,b_3))$.
Furthermore, the distribution $f(\bm{x}|\mbox{diag}(b_1,b_2,b_3))$ is invariant under changes $(b_1, b_2, b_3) \to (b_1 + h, b_2 + h, b_3 + h)$ for any real number $h$. Without loss of generality, we assume that $b_1 \le b_2 \le b_3 = 0$. Denote $Z_{n_1n_2n_3}(b_1,b_2)=Z_{n_1n_2n_3}(\mbox{diag}(b_1,b_2,0))$.
It is easy to note that $Z_{n_1n_2n_3}(b_1,b_2)$ is nonzero only if $n_i$ are even numbers. Then by $x_3^2=1-x_1^2-x_2^2$, we can express $Z_{n_1n_2n_3}(b_1,b_2)$ linearly by $Z_{nm0}(b_1,b_2)$. Hence it suffices to compute $Z_{nm0}(b_1,b_2)$, denoted in abbreviate by $Z_{nm}(b_1,b_2)$.
Choosing a parameter $d > 0$, we divide $(b_1,b_2)\in (-\infty,0]^2$ into three regions,
$$
(-\infty,-d]^2,\quad (-\infty,-d]\times(-d,0]\cup(-d,0]\times(-\infty,-d],\quad (-d,0]^2.
$$
and use different approximation method for each region.
The following Gaussian integral is used in the approximation,
\begin{equation}
\int_{\mathbb{R}}x^{2n}\exp(-\alpha x^2)\mathrm{d} x= \sqrt{\frac{\pi}{\alpha}}\frac{(2n-1)!!}{(2\alpha)^n},\quad \alpha>0. \label{Gauss}
\end{equation}
\subsection{$b_1,\ b_2 \le -d$ \label{infinite_2}}
We transform the integral domain into the unit circle,
\begin{align}
Z_{nm}(b_1, b_2) = &2 \iint_{x_1^2+x_2^2 < 1} x_1^{n} x_2^{m} \cdot \exp \left( b_1 x_1^2 + b_2 x_2^2 \right) \cdot \frac{1}{ \sqrt{1 - x_1^2-x_2^2} } \, \mathrm{d} x_1\mathrm{d} x_2,\nonumber\\
=&2 \sum_{j,k\ge 0}{j+k \choose j}\frac{(2j+2k-1)!!}{(2j+2k)!!}\iint_{x_1^2+x_2^2 < 1}x_1^{2j+n}x_2^{2k+m} \exp \left( b_1 x_1^2 + b_2 x_2^2 \right) \, \mathrm{d} x_1\mathrm{d} x_2. \label{platInte}
\end{align}
The series converges because $b_1,b_2<0$. We truncate the series at $j+k\le N_1$.
Moreover, if $d$ is large, then $x_1^{2j+n} x_2^{2k+m}$ increases with polynomial rate, while $ \exp \left( b_1 x_1^2 + b_2 x_2^2 \right)$ decreases with exponential rate.
Thus we expand the integral domain to $\mathbb{R}^2$ in the truncated series, which yields the following approximation formula,
\begin{align}
\hat{Z}_{nm}(b_1, b_2) = &2 \sum_{j+k\le N_1}{j+k \choose j}\frac{(2j+2k-1)!!}{(2j+2k)!!}\iint_{\mathbb{R}^2}x_1^{2j+n}x_2^{2k+m} \exp \left( b_1 x_1^2 + b_2 x_2^2 \right)\, \mathrm{d} x_1\mathrm{d} x_2.\nonumber\\
=&\sum_{j+k\le N_1}{j+k \choose j}\frac{(2j+2k-1)!!}{(2j+2k)!!}
\sqrt{\frac{\pi^2}{b_1b_2}}\frac{(2j+n-1)!!(2k+m-1)!!}{(2b_1)^{j+n/2}(2b_2)^{k+m/2}}. \label{inf_approx1}
\end{align}
\subsection{$b_1 > -d$, $b_2 \le -d$ or $b_1 \le -d$, $b_2 > -d$ \label{infinite_1}}
We explain our approximation method by the case $b_1 \le -d$, $b_2 > -d$.
Rewrite $Z_{nm}( b_1, b_2)$ as
\begin{equation}\label{outCalaExpr}
Z_{nm}(b_1, b_2) = 4 \int_{-1}^{1} x_1^n \cdot \exp \left( b_1 x_1^2 \right) \cdot g_m( b_2, x_1) \, \mathrm{d} x_1,
\end{equation}
where
\begin{equation}
g_m( b_2, x_1) = \int_{0}^{\sqrt{1-x_1^2}} x_2^m \cdot \exp \left( b_2 x_2^2 \right) \cdot \frac{1}{ \sqrt{1 - x_1^2 - x_2^2} } \, \mathrm{d} x_2.
\end{equation}
Denote $a=1-x_1^2$ and $r=x_2/a$, then we have
\begin{align}
g_m =& \int_{0}^{\sqrt{a}} x_2^m \cdot \exp \left( b_2 x_2^2 \right) \cdot \frac{1}{ \sqrt{a - x_2^2} } \, \mathrm{d} x_2\nonumber\\
=& a^{m/2} \int_{0}^{1} r^m \cdot \exp \left( b_2 a r^2 \right) \cdot \frac{1}{ \sqrt{1 - r^2} } \, \mathrm{d} r \nonumber \\
=& a^{m/2} \cdot \frac{1}{2} \sqrt{\pi } \cdot \frac{\Gamma [(m+1)/2 ]}{\Gamma [ (m+2)/2 ]} \cdot {}_1F_1 \left( \frac{m+1}{2}; \frac{m+2}{2}; b_2 a \right), \nonumber
\end{align}
where
$$
\Gamma(t)=\int_0^{\infty}x^{t-1}\exp(-x)\mathrm{d} x
$$
is the gamma function, and ${}_1F_1$ denotes the confluent hypergeometric function.
Note that ${}_1F_1(\frac{m+1}{2}; \frac{m+2}{2}; b_2 a )$ is an entire function about $a\in\mathbb{C}$.
Therefore $g_m(b_2,x_1)$ equals to its Taylor's series at $x_1=0$ for $x_1\in(-1,1)$,
$$
g_m( b_2, x_1) =\sum_{j\ge 0} \frac{1}{(2j)!} \left( \frac{\partial^{2j}}{\partial x_1^{2j}} g_m( b_2, 0) \right) x_1^{2j}.
$$
Similar to the case $b_1,b_2\le -d$, we truncate the series at $j\le N_2$. Again noticing $b_1\le -d$, we expand the integral interval in \eqref{outCalaExpr} to $\mathbb{R}$, leading to the approximation formula
\begin{align}
\hat{Z}_{nm}(b_1, b_2) =&4 \sum_{j\le N_2} \frac{1}{(2j)!} \left( \frac{\partial^{2j}}{\partial x_1^{2j}} g_m( b_2, 0) \right)\int_{\mathbb{R}} \exp \left( b_1 x_1^2 \right) x_1^{2j+n} \, \mathrm{d} x_1\nonumber\\
=&4 \sum_{j\le N_2} \frac{1}{(2j)!} \left( \frac{\partial^{2j}}{\partial x_1^{2j}} g_m( b_2, 0) \right)\cdot \sqrt{\frac{\pi}{-b_1}}\frac{(2j+n-1)!!}{(-2b_1)^{j+n/2}}\, .
\label{formulaAppr2}
\end{align}
Next, we explain how to calculate the derivatives ${\partial^{2j}g_m( b_2, 0)}/{\partial x_1^{2j}} $.
Denote
$$
h_1(a)=a^{m/2}, \;\; h_2(a)={}_1F_1 \left( \frac{m+1}{2}; \frac{m+2}{2}; b_2 a \right).
$$
Then we have
\begin{equation}
\frac{\partial^j g}{\partial a^j} = \frac{1}{2} \sqrt{\pi } \cdot \frac{\Gamma [(m+1)/2 ]}{\Gamma [ (m+2)/2 ]} \cdot \sum_{k=0}^{j} \binom{j}{k} \partial^k_{a} h_1 \cdot \partial^{j-k}_{a} h_2,
\end{equation}
with
\begin{equation}
\partial^k_{a} h_1=\frac{(m/2)!}{(m/2-k)!} a^{\frac{m}{2}-k}, \; k \leq \frac{m}{2}, \;\;\;\; \;\;\;\; \partial^k_{a} h_1=0, \; k > \frac{m}{2},
\end{equation}
and
\begin{equation}
\partial^k_{a} h_2 = b_2^k \left( \frac{m+1}{2} \right)^{(k)} \Big / \left( \frac{m+2}{2} \right)^{(k)} \cdot {}_1F_1 \left( \frac{m+1}{2}+k; \frac{m+2}{2}+k; b_2 a \right)
\end{equation}
where
$$x^{(0)}=1, \;\;\;\; x^{(k)}=x(x+1)(x+2) \cdots (x+k-1)$$
is the rising factorial.
Along with
$$
\frac{\partial^2 a}{\partial x_1^2} \bigg |_{x_1=0}=-2, \;\;\;\; \frac{\partial^i a}{\partial x_1^i} \bigg |_{x_1=0}=0, \;\; i \neq 2,
$$
and the chain rule, we arrive at
\begin{equation}
\frac{\partial^{2j}}{\partial x_1^{2j}} g(x_2^m | b_2, x_1) \, \bigg |_{x_1=0} = (-1)^{j} \cdot \frac{(2j)!}{j!} \cdot \frac{\partial^{j} g}{\partial a^{j}} \bigg |_{a=1}.
\end{equation}
The derivatives ${\partial^{2j}g_m( b_2, 0)}/{\partial x_1^{2j}} $ are functions of $b_2$. In the routine \texttt{BinghamMoments}, we precompute the values on grid points $b_2=0.001k$, and compute the values between the grid points by linear interpolation.
\subsection{$b_1 > -d$, $b_2 > -d$ \label{finite_2}}
In this bounded region of $(b_1,b_2)$, we use interpolation for $Z_{00}$ and $Z_{mn}/Z_{00}$.
We compute them and their derivatives about $b_1$, $b_2$,
$$
\frac{\partial Z_{00}}{\partial b_1}=Z_{20}, \quad
\frac{\partial (Z_{nm}/Z_{00})}{\partial b_1}=\frac{Z_{n+2,m}Z_{00}-Z_{nm}Z_{20}}{Z_{00}^2},
$$
on the grid
$(b_{1,2})_j=-j\Delta b,\ 0\le j\le -d/\Delta b$.
These values are computed in advance and saved as constants in the routine \texttt{BinghamMoments}.
For $Z_{nm}$ not on the grid points, we calculate with the interpolation described below.
Suppose we already know
$$
f(x_i,y_j), \;\; f_x(x_i,y_j), \;\; f_y(x_i,y_j),\quad j=1,2.
$$
To obtain the approxiamte value $f(x,y)$ on $(x,y) \in [x_1,x_2] \times [y_1,y_2]$, we first calculate
$$ f(x,y_1), \;\; f(x,y_2), \;\; f(x_1,y), \;\; f(x_2,y) $$
with third-order Hermite interpolation,
\begin{eqnarray}
f(x,y_1) &=& f(x_1,y_1) \cdot (1 + 2 \frac{x_1-x}{x_1-x_2}) (\frac{x-x_2}{x_1-x_2})^2
+ f(x_2,y_1) \cdot (1 + 2 \frac{x_2-x}{x_2-x_1}) (\frac{x-x_1}{x_2-x_1})^2 \nonumber \\
&& + f_x(x_1,y_1) \cdot (x-x_1) (\frac{x-x_2}{x_1-x_2})^2
+ f_x(x_2,y_1) \cdot (x-x_2) (\frac{x-x_1}{x_2-x_1})^2. \nonumber
\end{eqnarray}
Next we calculate
$$ f_y(x,y_1), \;\; f_y(x,y_2), \;\; f_x(x_1,y), \;\; f_x(x_2,y) $$
with linear interpolation,
$$ f_y(x,y_1) = f_y(x_1,y_1) \frac{x_2-x}{x_2-x_1} + f_y(x_2,y_1) \frac{x-x_1}{x_2-x_1}. $$
Then we can calculate $f(x,y)$ with third order Hermite interpolation by
\begin{eqnarray}
f(x,y) &=& f(x_1,y) \cdot (1 + 2 \frac{x_1-x}{x_1-x_2}) (\frac{x-x_2}{x_1-x_2})^2
+ f(x_2,y) \cdot (1 + 2 \frac{x_2-x}{x_2-x_1}) (\frac{x-x_1}{x_2-x_1})^2 \nonumber \\
&& + f_x(x_1,y) \cdot (x-x_1) (\frac{x-x_2}{x_1-x_2})^2
+ f_x(x_2,y) \cdot (x-x_2) (\frac{x-x_1}{x_2-x_1})^2, \label{interp1}
\end{eqnarray}
or
\begin{eqnarray}
f(x,y) &=& f(x,y_1) \cdot (1 + 2 \frac{y_1-y}{y_1-y_2}) (\frac{y-y_2}{y_1-y_2})^2
+ f(x,y_2) \cdot (1 + 2 \frac{y_2-y}{y_2-y_1}) (\frac{y-y_1}{y_2-y_1})^2 \nonumber \\
&& + f_y(x,y_1) \cdot (y-y_1) (\frac{y-y_2}{y_1-y_2})^2
+ f_y(x,y_2) \cdot (y-y_2) (\frac{y-y_1}{y_2-y_1})^2. \label{interp2}
\end{eqnarray}
We compute $f(x,y)$ as the average of \eqref{interp1} and \eqref{interp2}.
\subsection{The value of the parameters}
We have introduced four parameters in the above: the size $d$ for dividing the domain, the order of truncation $N_1$ and $N_2$, and the grid size for the interpolation $\Delta b$.
We choose parameters as $d=30$, $N_1=5$, $N_2=5$, $\Delta b=0.025$ for $Z_{00}$, and $\Delta b=0.1$ for $Z_{nm}/Z_{00}$ in the routine \texttt{BinghamMoments}, achieving maximal absolute error less than $5\times 10^{-8}$ for $Z_{00}$ and $\langle x_1^n x_2^m \rangle,~ n+m\le 4$. We will verify this in Sec. \ref{Numerical Test}. With these parameters, the memory needed for loading precomputed values (including ${\partial^{2j}g_m( b_2, 0)}/{\partial x_1^{2j}} $ in the case \ref{infinite_1}, and the values on the grid points in the case \ref{finite_2}) is about 75MB, which is available for common computers.
\section{Numerical accuracy\label{error}}
\subsection{Error estimate}
We give an error estimate for the case \ref{infinite_2} with some special functions.
Denote
$$
F(x)=e^{-x^2} \int_{0}^{x} e^{t^2} \, \mathrm{d} t
$$
as the Dawson function,
$$
\gamma(n,x)=\int_0^x t^{n-1}e^{-t}\, \mathrm{d} t
$$
as the lower incomplete gamma function, and
$$
\alpha_n(z)=E_{-n}(z)=n! z^{-n-1} e^{-z} \left ( 1+z+\frac{z^2}{2!}+ \cdots + \frac{z^n}{n!} \right )
$$
as the exponential integral function.
\begin{theorem}
Let $\hat{Z}_{nm}$ be defined in \eqref{inf_approx1} and denote $N=N_1$.
For $b_1,b_2 \le -d$, it holds
\begin{eqnarray} \label{infinite max error}
|Z_{nm}-\hat{Z}_{nm}| &\leq& 4 \pi \frac{ F(\sqrt{d}\,)}{\sqrt{d}}- 2 \pi \sum _{j=0}^N \frac{(2 j-1)!!}{(2 j)!!} \cdot d^{-j-1} \gamma (j+1,d) \nonumber \\ && + 2 \pi \sum_{j=0}^{N+\max(n,m)} \frac{(2j-1)!!}{(2j)!!} \alpha_j(d).
\end{eqnarray}
\end{theorem}
\begin{proof}
We can divide the error into two parts:
\begin{align}
e_1=& Z_{nm}( b_1, b_2) - 2 \iint_{B(0,1)} x_1^{n} x_2^{m} \exp \left( b_1 x_1^2 + b_2 x_2^2 \right) \sum_{j=0}^{N} \frac{(2j-1)!!}{(2j)!!} \cdot (x_1^2 + x_2^2)^j \, \mathrm{d} \bm{x} \nonumber\\
=&2 \iint_{B(0,1)} x_1^{n} x_2^{m} \exp \left( b_1 x_1^2 + b_2 x_2^2 \right) \sum_{j>N} \frac{(2j-1)!!}{(2j)!!} (x_1^2 + x_2^2)^j \, \mathrm{d} \bm{x},\\
e_2=& 2 \iint_{\mathbb{R}^2 \setminus B(0,1)} x_1^{n} x_2^{m} \exp \left( b_1 x_1^2 + b_2 x_2^2 \right) \sum_{j=0}^{N} \frac{(2j-1)!!}{(2j)!!} (x_1^2 + x_2^2)^j \, \mathrm{d} \bm{x}.
\end{align}
For $e_1$, we have
\begin{eqnarray}
e_1 &\le&2 \iint_{B(0,1)} \exp \left( -d (x_1^2 + x_2^2) \right) \sum_{j>N} \frac{(2j-1)!!}{(2j)!!} (x_1^2 + x_2^2)^j \, \mathrm{d} \bm{x}\nonumber\\
&=&2 \iint_{B(0,1)} \exp \left( -d (x_1^2 + x_2^2) \right) \left[\frac{1}{\sqrt{1-x_1^2-x_2^2}}-\sum_{j\le N} \frac{(2j-1)!!}{(2j)!!} (x_1^2 + x_2^2)^j \right]\, \mathrm{d} \bm{x}\nonumber\\
&\le& 4 \pi \int_0^1 e^{-d r^2} \frac{r}{1 - r^2} \, \mathrm{d} r - 4 \pi \sum_{j=0}^{N} \frac{(2j-1)!!}{(2j)!!} \int_0^1 r^{2j+1} e^{-d r^2} \, \mathrm{d} r \nonumber \\
&=& 4 \pi \frac{ F(\sqrt{d}\,)}{\sqrt{d}}- 2 \pi \sum _{j=0}^N \frac{(2 j-1)!!}{(2 j)!!} d^{-j-1} \gamma (j+1,d). \label{err_1_inf}
\end{eqnarray}
In the above, we use the polar coordinate transformation
$x_1=r \cos \theta, \;\; x_2=r \sin \theta$.
For $e_2$, denote $M=\max\{ n, m \}$, then we have
\begin{eqnarray}
e_2 &\leq& 4 \pi \sum_{j=0}^{N+M} \frac{(2j-1)!!}{(2j)!!} \int_1^{\infty} r^{2j+1} e^{-d r^2} \, \mathrm{d} r = 2 \pi \sum_{j=0}^{N+M} \frac{(2j-1)!!}{(2j)!!} \alpha_n(d). \label{err_2_inf}
\end{eqnarray}
Combining \eqref{err_1_inf} and \eqref{err_2_inf}, we get \eqref{infinite max error}.
\end{proof}
\begin{table}
\centering
\begin{tabular}{ccccccc}
\toprule
$d$ & 13 & 16 & 20 & 26 \\
\midrule
$N_1$ & 5 & 6 & 6 & 6 \\
\midrule
Bound & $4.4\times 10^{-5}$ & $3.6\times 10^{-6}$ & $4.5\times 10^{-7}$ & $4.5\times 10^{-8}$ \\
\bottomrule
\end{tabular}
\caption{Absolute error bound by \eqref{infinite max error} under different values of $d$ and $N_1$ for $n+m\le 4$. }
\label{estimated upper bound}
\end{table}
For our chosen parameters $d=30$ and $N_1=5$, the upper bound given by \eqref{infinite max error} is $6.038 \times 10^{-8}$ for $n+m\le 4$.
We also give the upper bound calculated from \eqref{infinite max error} for a few $d$ and $N_1$ in Table \ref{estimated upper bound}.
The estimate \eqref{infinite max error} is also helpful to choosing parameters under different demand of accuracy, which will be shown in Table \ref{suggested value}.
\subsection{Numerical Test\label{Numerical Test}}
We compare the results calculated by our method and the results calculated by numerical integration to testify the accuracy of our method numrically.
The parameters in our method are chosen as $N_1=5$, $N_2=5$ and $d=30$.
For numerical integration, we use adaptive Simpson's method to control the absolute error less than $10^{-11}$. We select randomly $10,000$ pairs of $b_i$ for each of the three cases: $b_1,b_2\le -d$, $\max(b_1,b_2)>-d \; \& \; \min(b_1,b_2)\le -d$, and $b_1,b_2>-d$, and calculate $Z$ and the moments $Z_{nm}/Z$ where $n+m=2,4$.
Table \ref{maxError} shows the maximal absolute errors of $Z$ and $Z_{nm}/Z$ among the $30000$ samples,
which are under the magnitude of $10^{-8}$.
In particular, the errors of $Z_{nm}/Z$ are less than $5\times 10^{-8}$.
We also examine the distribution of the absolute errors of
$Z$ (Figure \ref{errorTest:a}), $Z_{20}/Z$ (Figure \ref{errorTest:b}) and $Z_{04}/Z$ (Figure \ref{errorTest:c})
for the $10000$ samples in each of three cases respectively,
and find that for most $b_i$ the absolute errors are less than $10^{-10}$.
Moreover, the numerical test also shows our method is very fast.
Calculating all these $30,000$ examples, the adaptive Simpson's method with the target accuracy $5\times 10^{-8}$ spend $3117.761$ seconds while our method only $0.193$ seconds.
Both routines are written in C and run in the same computer with a CPU clock speed $2.5$GHz.
\begin{table}
\centering
\begin{tabular}{cccc}
\toprule
Moment & $Z$ & $Z_{20}/Z$ & $Z_{02}/Z$ \\
\midrule
Maximal error & $6.038\times 10^{-8}$ & $2.030\times 10^{-8}$ & $1.543 \times 10^{-8}$ \\
\bottomrule \toprule
Moment & $Z_{40}/Z$ & $Z_{04}/Z$ & $Z_{22}/Z$ \\
\midrule
Maximal error & $4.031\times 10^{-9}$ & $2.049\times 10^{-8}$ & $2.098\times 10^{-8}$ \\
\bottomrule
\end{tabular}
\caption{Maximal absolute error for the $30,000$ pairs of $(b_1,b_2)$. }
\label{maxError}
\end{table}
\begin{figure}
\centering
\subfigure[absolute errors of $Z$] { \label{errorTest:a}
\includegraphics[width=0.3\columnwidth]{error_Z.pdf}
}
\subfigure[absolute errors of $Z_{20}/Z$] { \label{errorTest:b}
\includegraphics[width=0.3\columnwidth]{error_Qx12.pdf}
}
\subfigure[absolute errors of $Z_{04}/Z$] { \label{errorTest:c}
\includegraphics[width=0.3\columnwidth]{error_Qx24.pdf}
}
\caption{Distribution of error. Blue bars: $b_1,b_2\le -d$; Green bars: $\max(b_1,b_2)>-d$ \& $\min(b_1,b_2)\le -d$; Yellow bars: $b_1,b_2>-d$. $E_i$ represents the interval $[10^{-i-1}, 10^{-i})$ for $i=7,8,9$. $E_{10}=[0, 10^{-10})$ and $E_6=[10^{-7}, \infty)$. }
\label{errorTest}
\end{figure}
We also give some other suggested values of $d$, $N_1$ and $N_2$
in Table \ref{suggested value} for different demanded accuracy for $Z_{nm}/Z$,
which are also testified numerically with $30,000$ random samples.
By comparing with the errors in Table \ref{suggested value} and Table \ref{estimated upper bound}, we find that the upper bound given by \eqref{infinite max error} are indicative for the choice of parameters.
\begin{table}
\centering
\begin{tabular}{ccccccccc}
\toprule
Demanded maximal absolute error & $5\times 10^{-5}$ & $5\times 10^{-6}$ & $5\times 10^{-7}$ & $5\times 10^{-8}$ \\
\midrule
$d$ & 13 & 16 & 20 & 26 \\
\midrule
$N_1$ & 5 & 6 & 6 & 6 \\
\midrule
$N_2$ & 4 & 5 & 6 & 6 \\
\bottomrule
\end{tabular}
\caption{Suggested values of parameters $d$, $N_1$ and $N_2$ under different demanded absolute error. }
\label{suggested value}
\end{table}
\section{Application to liquid crystals\label{appl}}
In this section, we apply our algorithm to a $Q$-tensor model for rod-like liquid crystals. Compared with the original Landau-de Gennes $Q$-tensor theory, the model is able to constrain the tensor within the physical range \cite{ball2010nematic}, and is closely connected to molecular theory \cite{han2014microscopic}. But the Bingham distribution in the model brings difficulty in numerical simulations. We will explain how our fast algorithm accelerates the computation.
Suppose that the rod-like molecules are confined inside the unit sphere.
Then the anchoring effect on the spherical surface will induce defects for the alignment of the molecules.
We consider the following simplified free energy,
\begin{equation}\label{freeEnergy}
F=\int_{\Omega} \mathrm{d} x\mathrm{d} y\mathrm{d} z\, \Big[ (B : (Q+\frac{I}{3}) - \log Z) - \frac{1}{2} \alpha_1 \left | Q \right |^2 + \frac{1}{2} \alpha_2 \left | \nabla Q \right |^2\Big] + F_{p},
\end{equation}
where the region $\Omega$ is chosen as the unit sphere, $I$ is the identity matrix, and
$$
Q_{ij}(\bm{x})=\int_{\mathbb{S}^2}(x_ix_j-\frac{1}{3}\delta_{ij})f(\bm{x}|B)\mathrm{d} S
$$
is a symmetric traceless matrix describing the orientational distribution of rod-like molecules at each spatial point, with $f(\bm{x}|B)$ and $Z=Z_{000}(B)$ defined in \eqref{densOrg} and \eqref{moments}. Here $\delta_{ij}$ is the Kronecker notation.
The first two terms in the integral are the bulk energy describing the nematic phase in equilibrium.
This bulk energy is the only terms distinct from the phenomenological Landau-de Gennes theory, where the bulk energy is given as a polynomial
$$
a_2\mbox{tr}(Q^2)-a_3\mbox{tr}(Q^3)+a_4(\mbox{tr}(Q^2))^2.
$$
The gradient term is the energy contribution of the spatial inhomogeneity.
The boundary penalty term
$$ F_{p}=\int_{\partial\Omega}\mathrm{d} S\, [Q_{11} xy - Q_{12}(x^2-\frac{1}{3})]^2 + [Q_{12} z - Q_{13} y]^2 + [Q_{22} xy -Q_{12}(y^2-\frac{1}{3})]^2 + [Q_{12} z - Q_{23} x]^2 $$
is added to enforce the value of $Q$ on the sphere to be approximately
$$
Q = \lambda \left(
\begin{array}{ccc}
x^2-\frac{1}{3} & xy & xz\\
xy & y^2-\frac{1}{3} & yz\\
xz & yz & z^2-\frac{1}{3}
\end{array}
\right).
$$
In fact, if $Q$ is given as above, then $F_{p}=0$.
Our aim is to find local minimizers of the energy functional \eqref{freeEnergy} that describe metastable states.
Express $B$ as $B=T\mbox{diag}(b_1,b_2,0)T^T$, where $T$ is orthogonal with $\mbox{det}T=1$ and can be expressed by Euler angles,
$$
T=\left(
\begin{array}{ccc}
\cos \alpha \cos \gamma -\cos \beta \sin \alpha \sin \gamma & \cos \gamma \sin \alpha +\cos \alpha \cos \beta \sin \gamma &
\sin \beta \sin \gamma \\
-\cos \beta \cos \gamma \sin \alpha -\cos \alpha \sin \gamma & \cos \alpha \cos \beta \cos \gamma -\sin \alpha \sin \gamma &
\cos \gamma \sin \beta \\
\sin \alpha \sin \beta & -\cos \alpha \sin \beta & \cos \beta \\
\end{array}
\right).
$$
In this case, $Q=T\mbox{diag}(q_1,q_2,q_3)T^T$,
where the eigenvalues are given by $q_1=Z_{20}(b_1,b_2)/Z_{00}(b_1,b_2)$,
$q_2=Z_{02}(b_1,b_2)/Z_{00}(b_1,b_2)$, and $q_3=1-q_1-q_2$.
We use the spherical coordinates $(r,\theta,\phi)$ to represent the position, i.e.,
\begin{equation}
x=r\sin\theta\cos\phi,\quad
y=r\sin\theta\sin\phi,\quad
z=r\cos\theta. \label{SphCoord}
\end{equation}
The integral becomes $\int (\cdot)\mathrm{d} x\mathrm{d} y\mathrm{d} z=\int (\cdot)r^2\sin\theta\mathrm{d} r\mathrm{d}\theta \mathrm{d}\phi$,
and the gradient term becomes
\begin{align}
|\nabla Q|^2=|\partial_r Q|^2+\frac{1}{r^2}|\partial_{\theta} Q|^2+\frac{1}{r^2\sin^2\theta}|\partial_{\phi} Q|^2.
\end{align}
The free energy is discretized at $N \times N \times N=32^3$ Gaussian quadrature nodes $(r_j,\theta_k,\phi_l)$ in $[0,1]\times[0,\pi]\times[0,2\pi]$.
At each node $(b_1,b_2,\alpha,\beta,\gamma)^{jkl}$ act as the basic variables,
from which $Q^{jkl}$ is computed.
The gradient term is computed using the spectral-collocation method.
From the value of $Q$ at the discretized nodes, a polynomial
$$
Q(r,\theta,\phi) = \sum_{j=0}^{N-1} \sum_{k=0}^{M-1} \sum_{l=0}^{L-1} c_Q^{jkl} \, r^j \theta ^k \phi ^l
$$
is constructed through interpolation.
The derivatives about $(r,\theta,\phi)$, as well as the values on the boundary,
are then computed from the above polynomial.
We refer to \cite{shen2011spectral} where the details about the spectral-collocation method are illustrated.
The free energy is minimized using the BFGS method (see, for instance, \cite{avriel2003nonlinear}).
In the iteration we need to compute the derivatives of $F$ about $(b_i)^{jkl}$,
where fourth moments are involved. For instance,
$$
\frac{\partial }{\partial b_1} Q = T\mbox{diag}(\frac{\partial q_1}{\partial b_1},\frac{\partial q_2}{\partial b_1},\frac{\partial (-q_1-q_2)}{\partial b_1})T^T,
$$
where
$$
\frac{\partial q_1}{\partial b_1}=\frac{Z_{40}Z_{00}-Z^2_{20}}{Z^2_{00}}.
$$
It is worth pointing out that at each point, the value of $Q$ and $Z$ are computed from $B$.
Therefore, our algorithm is executed $O(N^3)$ times in each BFGS iteration step, which greatly accelerates the simulation.
Another thing is that the Bingham distribution remains the same
when we alter the parameters $\alpha_{1,2}$, the domain (from sphere to cylinder or ellipse, etc.), and add some terms like in \cite{han2014microscopic}.
Thus our algorithm is suitable for all these cases.
Before looking at the results, we first define the biaxiality.
When $Q\neq 0$, we say $Q$ is uniaxial if it has two identical eigenvalues, and is biaxial if it has distinct eigenvalues. Note that $\mbox{tr}Q=0$.
The biaxiality is measured by
$$
\mu = 1 - 6 \frac{(\mbox{tr}Q^3)^2}{(\mbox{tr}Q^2)^3}.
$$
For uniaxial $Q$, we have $\mu=0$; for biaxial $Q$, we have $0< \mu\le1$.
We examine the defect pattern under different $\alpha_1$ and $\alpha_2$.
At each point, the favored direction of the rod-like molecules is the principal
unit eigenvector $\bm{n}$ of $Q$. While $Q$ is continuous in the unit sphere,
$\bm{n}$ might be discontinuous at the points where $Q=0$ or $Q$ has two identical positive eigenvalues.
Defect patterns are classified by the configuration of these points.
\begin{figure}
\centering
\subfigure[Radial hedgehog] { \label{LCPhase:a}
\includegraphics[width=0.3\columnwidth]{hedgehog.pdf}
}
\subfigure[Ring disclination] { \label{LCPhase:b}
\includegraphics[width=0.3\columnwidth]{ring.pdf}
}
\subfigure[Sphere ring band] { \label{LCPhase:c}
\includegraphics[width=0.3\columnwidth]{sphereRing.pdf}
}
\caption{Three axisymmetric defect patterns, shown by the slice of $x_2$-$x_3$ plane, where $x_3$ is the axis of symmetry. White rods represent principal eigenvectors. The background color describes the biaxiality $\mu$, with red indicates biaxial and blue indicates uniaxial. In all three cases $\alpha_2=0.04$, and $\alpha_1$ are chosen as: (a) $\alpha_1=11$; (b) $\alpha_1=16$; (c) $\alpha_1=22$.}
\label{LCPhase}
\end{figure}
We fix $\alpha_2=0.04$ and let $\alpha_1$ vary.
Three defect patterns are observed and drawn in Figure \ref{LCPhase}:
radial hedgehog (Figure \ref{LCPhase:a}), when $\alpha_1=11$;
ring disclination (Figure \ref{LCPhase:b}), when $\alpha_1=16$;
sphere ring band (Figure \ref{LCPhase:c}), when $\alpha_1=22$.
In the radial hedgehog pattern, $Q$ is uniaxial everywhere
with the principal eigenvector along the radial direction. The sphere center,
where $Q=0$, is the only point defect.
In the ring disclination pattern, the points where $Q$ has two identical positive eigenvalues form a circle in the $x$-$y$ plane, round which is a torus of biaxial region. In the sphere ring band pattern, the points where $Q=0$ form two rings on the spherical surface. In the band between these two rings on the spherical surface, $Q$ has two identical positive eigenvalues. A strong biaxial region is observed inside the sphere near the band. The last pattern is not found in the Landau-de Gennes theory \cite{hu2016disclination}. We believe that this novel pattern come from the term $B:(Q+I/3)-\log Z$, since it is the only term different from the Landau-de Gennes theory. Hence, it is necessary for this model to be further examined.
\section{Conclusion\label{concl}}
We develop a fast and accurate algorithm to evaluate the moments of Bingham distribution. Numerical test shows that it is remarkbly faster than direct numerical quadrature, while maintaining high accuracy. We apply the algorithm to the liquid crystal model that contains the Bingham distribution, which is able to constrain the order parameters within the physical range. We examine the defect patterns of liquid cystals confined inside a sphere and find a novel pattern,
suggesting that the model be examined thoroughly and compared with the Landau-de Gennes theory in future studies.
Armed with our algorithm, these studies will become much less expensive computationally.
\vspace{12pt}
\textbf{Acknowledgment} Pingwen Zhang is supported by National Natural Science Foundations of China (Grant No. 11421101 and No. 11421110001).
\bibliographystyle{plain}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,048 |
Mon, June 25, 2012
Lifestyle > Travel
Breathtaking glacial sceneries in Tibet
Photo taken on June 2, 2012 shows the Sabu glacier and its glacial lake in Biru County, southwest China's Tibet Autonomous Region. The northern parts of the autonomous region have one of China's richiest glacier distributions, which are increasingly under the threat of global warming. (Xinhua/Chogo)
Photo taken on June 2, 2012 shows a melting glacier in southwest China's Tibet Autonomous Region. The northern parts of the autonomous region have one of China's richiest glacier distributions, which are increasingly under the threat of global warming. (Xinhua/Chogo)
Photo taken on May 31, 2012 shows a glacial lake in Biru County, southwest China's Tibet Autonomous Region. The northern parts of the autonomous region have one of China's richiest glacier distributions, which are increasingly under the threat of global warming. (Xinhua/Chogo)
Photo taken on June 2, 2012 shows the Sabu glacier in Biru County, southwest China's Tibet Autonomous Region. The northern parts of the autonomous region have one of China's richiest glacier distributions, which are increasingly under the threat of global warming. (Xinhua/Chogo)
Photo taken on June 2, 2012 shows a glacial river in southwest China's Tibet Autonomous Region. The northern parts of the autonomous region have one of China's richiest glacier distributions, which are increasingly under the threat of global warming. (Xinhua/Chogo)
Photo taken on June 2, 2012 shows the Sabu glacier and its glacial lake in Biru County, southwest China's Tibet Autonomous Region. The northern parts of the autonomous region have one of China's richiest glacier distributions, which are increasingly under the threat of global warming.
Actress Li Bingbing graces fashion magazine
EURO 2012: faces of fans
China submersible breaks 7,000-metre mark
2012 Dragon Boat Festival
Wen attends Rio 20 summit and tours Latin America
2012 European Championship
Hu Jintao visits Denmark, attends G20 summit
Qin Tomb: Unearthed Grandeur
1Astronauts getting used to lives in o...
2Chinese premier vows to further econo...
3Germany thrashes Greece to reach Euro...
46.6-magnitude quake hits Aceh, Indonesia
5S. Korea, U.S. conduct joint drills i...
6China to greet upcoming Dragon Boat F...
73-year plan to heal wounds of Bohai B...
8Rio+20, new beginning of global susta...
9U.S. stocks rally after huge sell-off
10Chinese submersible plans dive to 7,0...
Highlights of Euro 2012 day 14
Astronauts getting used to lives in outer space
Dolce&Gabbana summer fashion sings of Sicily
Spain beats France 2-0 to reach semifinals | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,803 |
3 Things to Expect from Trump's Afghanistan Address Tonight
Surge, strategy, status quo
President Donald Trump is expected to announce a surge of "several thousand" troops to Afghanistan in a speech he will deliver to the nation from Fort Meyers at 9:00 ET tonight.
Despite Trump's wildcard tendencies, the contents of tonight's address should be fairly predictable. Whatever anti-establishment foreign policy rhetoric Trump may have deployed during the campaign, his administration appears to have coalesced into a fairly establishment-minded group, particularly on foreign policy. Here are three things we can expect to hear about in tonight's address:
1. The Surge Itself
Ultimately, the decision on Afghanistan is a binary one: Either the U.S. stays, or it goes. Surging means staying.
In 2013 Trump lambasted America's "stupid leaders" for signing a deal to keep U.S. troops in Afghanistan until 2024, adding that the U.S. had "wasted an enormous amount of blood and treasure in Afghanistan" and got "zero appreciation" from the Afghan government. Such rhetoric has been missing more recently. The conflict barely got mentioned during the 2016 presidential campaign, and for the most part it has receded from the public consciousness.
President Barack Obama announced a troop surge of his own in a December 2009 address, bemoaning an Afghan government "hampered by corruption, the drug trade, an under-developed economy, and insufficient security forces." Trump may say something similar.
Eight years after the Obama troop surge, there's nothing positive to show for it in Afghanistan. That surge, like the one Trump is expected to announce, simply prolonged our presence in the country.
Trump has already authorized the Pentagon to send an additional 3,900 U.S. troops to Afghanistan, so tonight's announcement will probably stay within that limit. There are currently about 8,000 U.S. troops in the country.
2. Pakistan and other regional partners
The administration is mulling several possible ways to pressure Pakistan. According to CBS News, these include "reducing aid, taking away its status as a non-NATO ally, and threatening to name Pakistan as a state sponsor of terrorism."
Terror groups like the so-called Haqqani network operate out of Pakistan, and in 2011 the U.S. found and killed Osama bin Laden, the mastermind of the 9/11 attacks, in a posh Pakistan neighborhood.
The Russians, who seem to have cut and run on any possibility of converting any pro-Russian sentiments Trump expressed on the 2016 campaign trail into improved U.S.-Russian relations, have signaled that Washington should withdraw from Afghanistan if it's "unable to do anything serious." Nevertheless, instability in Afghanistan poses a security concern for the Shanghai Cooperation Organization, Russia's response to a post–Cold War NATO, and it would be worthwhile to try to engage Russia, as well as China, on what complete withdrawal from Afghanistan will look like.
A negotiated withdrawal involving the Afghan government and the Taliban would probably work best if it included Pakistan as well as other regional powers, who ought to be more vested in a stable future for Afghanistan than the U.S. is. Tonight's address would be a good place to articulate that, though Trump is more likely to scapegoat Pakistan than to sketch out any new efforts at regional cooperation.
3. Blaming Obama
Whether or not Trump mentions his predecessor by name, he's probably going to lay most of the blame for the mess in Afghanistan on Obama's doorstep. He may also, as he was wont to do before becoming an elected Republican official, criticize George W. Bush for allowing the conflict to fester for its first seven years instead of bringing it to a close after obliterating the core of Al Qaeda and removing the Taliban from power.
Sen. John McCain (R-Ariz.), has blamed a lack of "strategic guidance" across presidential administrations for years of failures in Afghanistan. But for years now there has been a lot of ambiguity about why the U.S. remains in Afghanistan in the first pace. That ambiguity isn't resolved during presidential campaigns, and it isn't resolved in the addresses new presidents give to the nation about the war's purported progress.
Trump will likely continue the tradition of blaming his predecessor for Afghanistan. But without interrogating why the U.S. has stayed in Afghanistan for so long, that's a useless exercise.
NEXT: Seattle's Democracy Voucher Program Sees Its First Fraud Investigation
Ed Krayewski is a former associate editor at Reason.
Afghanistan Donald Trump Barack Obama
Rhywun
August.21.2017 at 3:36 pm
Are we even technically at war with… somebody over there? We have kept way more troops than that embedded in countries all over the world for decades. What's another Germany or South Korea?
My Dog Bites Better Than Yours
The difference is we are actively killing and being killed in Afganistan.
Hugh Akston
I am neither killing nor being killed in Afghanistan. My secret? Not being there in the first place.
That contract you signed at birth says otherwise.
Charles Easterly
Rhywun: Are we even technically at war with….
My Dog Bites Better Than Yours: The difference is we are actively killing and being killed….
Is this is a good chance for these two individuals to describe who they mean by "we"?
I am talking about the United States.
"We" being the good citizens of these United States. Of which, like it or not, most of us are members.
I would never belong to any collective that would accept me as a member.
Crusty Juggler
– Re alt text: If McConaughey was president our country would be a lot groovier.
– Re surge: Score one for the generals and the GOP – they can unite!
– Re surge: Every time the word "surge" is used, I think of this.(It puts a positive spin on pointless wars).
– Re the above link: Jenny Summers was an 80s fox.
Other underappreciated 80s foxes: Sloane from Ferris Bueller, , the blonde from Police Academy, the cigarette-smoking kiddie-rapist from Big, Terry Doolittle from Jumping Jack Flash, and Joyce Hyser.
BestUsedCarSales
Kiddie Rapists always get the short end of the stick in Top Fox lists.
Citizen X - #6
I hear Mary Kay Letorneau is single again.
Charlotte Lewis from The Golden Child
"Whatever anti-establishment foreign policy rhetoric Trump may have deployed during the campaign, his administration appears to have coalesced into a fairly establishment-minded group, particularly on foreign policy."
Frankly he was moving in a more non-interventionist direction until recently. He ended the CIA funding for Syrian opposition groups and he first rebuffed his generals who wanted the surge in Afghanistan (as Reason even wrote an article about).
Now he's moved away from his populist tendencies to a more conventional Republican (and let's face it Democratic) foreign policy. The most depressing part is that his critics praise him when he acts hawkishly.
I wonder how much of this comes from the fact that his only bipartisan victory was the Syria action?
Hank Stamper
Can we just tell Trump that he already did a surge and it was tremendous, greatest surge ever. And skip to the part where he stands in front of banner and declares mission accomplished and brings all the troops home. Seems like that would be quicker with the same outcome minus American lives and treasure.
Chipper Morning, Now #1
I am all Afghanistaned out.
$park? leftist poser
Rub some dirt on it and get back in there, son.
Blaming his predecessor for fucking up Afghanistan might be Trump's most presidential move yet.
TrickyVic (old school)
Substitute # 3 for Blames Bush and you got the same talking points as Obama.
OBJ FRANKELSON
There is plenty of blame to go around, 44 can have some too.
Related, 'War Machine' on Netflix is a pretty good send up of the whole situation. I recommend it and if you have ever spent anytime around Flag Officers, they got it pretty spot on.
I thought it was good.
Also, the Anthony Michael-Hall character is supposedly based on Michael Flynn, which makes all of his scenes that much more enjoyable.
Nice, did Flynn work for McCrystal? (who is more or less the basis for PItt's character)
creech
I'm certain we will also hear some b.s. excuse about "we got to kill them over there before they come to kill us here." Absent this kind of scare tactic, I'd guess about 90% of Americans would say, "Let's get the fug out of there."
Square = Circle
I'm certain we will also hear some b.s. excuse about "we got to kill them over there before they come to kill us here."
Which is especially ironic, given that most Afghans have no idea who "we" are or where "we" came from, and really don't care.
Likes him some booze
"Hey, we're here scraping out a subsistence level existence, but we'll take time out to travel half-way around the world…"
Orange fat man reads stuff on a teleprompter without the slightest clue what any of it means?
Slim brown man did the same thing. With, uh, erm, uh, uh, uh, feeling.
Confused pale man did it before him. He transmogrified the speechifying, though.
Fuck fuck fuck no no no no. No.
Fuck Shitholistan and every goat-fucking stone age peasant there. They want to live in shacks without plumbing or electricity. They like it. Shitholistan is hopeless. The end state should have been dead AQ and Taliban gone, and us the fuck out of there.
JFC. What's it gonna take to get us out of there? Drafting Millennials? Drafting the generation after Millennials? Nobody cares about this war. Every Trumptard I know gets glassy eyed and blank when I mention Shitholistan. Everybody's forgotten we're even over there, wasting money and lives. For nothing.
But for years now there has been a lot of ambiguity about why the U.S. remains in Afghanistan in the first pace.
The only potentially interesting part of the speech would be any justification for our perpetual war in Afghanistan.
They could fess up and say "We plan on perpetual war in Afghanistan to prevent safe havens for Islamic terrorists". Or "We plan on nation building in Afghanistan, and will only leave when it can control it's own territory and keep it free from terrorists that threaten the West. 50 years minimum."
Palin's Buttplug
KABUL (Reuters) – U.S. President Donald Trump is eyeing Afghanistan's mineral wealth to help pay for a 16-year war and reconstruction efforts that have already cost $117 billion. Investors who have studied the country, one of the world's most dangerous, say that is a pipe dream.
Ever since a United States Geological Survey study a decade ago identified deposits later estimated to have a potential value of as much as $1 trillion, both Afghan and foreign officials have trumpeted the reserves as a likely key to economic independence for Afghanistan.
As well as deposits of gold, silver and platinum, Afghanistan has significant quantities of iron ore, uranium, zinc, tantalum, bauxite, coal, natural gas and significant copper – a particular draw given the dearth of rich new copper mines globally.
Afghanistan, some reports say, even has the potential to become "the Saudi Arabia of lithium", thanks to deposits of the raw material used in phone and electric car batteries.
No, the decision really isn't binary. The intensity dial has many, many levels. As can be seen when we look at the average rate of US fatalities per month of combat operations in Afghanistan, by Presidential term:
Bush 1st: 4.0 (160 total, 40 months [Oct 2001-Jan 2005])
Bush 2nd: 17.6 (847 total, 48 months [Feb 2005-Jan 2009])
Obama 1st: 44.9 (2,155 total, 48 months [Feb 2009-Jan 2013]).
Obama 2nd: 5.5 (263 total, 48 months [Feb 2013-Jan 2017]).
Trump 1st: 1.6 (11 total, 7 months [Feb 2017-Aug 2017]).
Raw data from http://icasualties.org/OEF/ByMonth.aspx .
While 1.6/month might not be ideal, it's a hell of a lot closer to zero than it is to 5.5/month, never mind the body count Obama racked up in his first term.
August.21.2017 at 11:00 pm
No matter who our country elects, we still get John McCain
JFree
August.22.2017 at 2:46 am
Some Brit once said something like – It's very easy to get into Afghanistan. Almost impossible to win and get out.
150 years later we've learned exactly nothing and are even more clueless about our goal and have no one who can tell their ass from their elbow about the region. And we are opposed by every single one of Afghanistans neighbors – none of whom have good intentions towards Afghanistan either.
What could possibly go wrong.
tinder download
October.2.2017 at 12:37 am
very nice post. I like it. Thanks for sharing this information.
Tinder is the best online chatting application. Try it.
http://www.tinder-pc-download.com/ tinder for pc
http://www.tinder-pc-download.com/ tinder download | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 388 |
\section{Introduction}
Within the foreseeable future, robots will become ubiquitous in our everyday lives, where they will operate in complex, real-world environments \cite{riek2014social, nigam2015social, riek2017healthcare}.
Facing the same challenges as humans, they will encounter situations where the scene, context, people, and entities around them are not immediately obvious \cite{o2015detecting}.
Consequently, robots will need to be able to rectify these uncertainties so that they can behave appropriately, as well as learn from and adapt to their surroundings \cite{chen2017deep,kubotaactivity}.
One key challenge is designing robots to perceive novel objects, which will play a fundamental role in how robots make sense of visual information.
While research in object detection has rapidly advanced to a greater degree than anticipated, they are still primarily constrained to the problem of detecting objects of known classes \cite{miller2018dropout, scheirer2014probability, sunderhauf2018limits}.
Consequently, they are unable detect novel objects and do little to improve a robot's ability to learn about, or even perceive novel objects.
Enabling robots to perceive novel objects is critical because it will ultimately affect how they perform and behave in the real world.
For instance, robots can most efficiently execute tasks if they are able to learn about unfamiliar objects that might be helpful to them (e.g., retrieval of uncommon items, investigating novel environments with unfamiliar objects, identifying entities that can be manipulated, etc.).
Furthermore, by exploring and interacting with objects that they have not seen before, robots can gain an understanding about object affordances, and how they functionally relate to people, places, and other objects in the world \cite{do2018affordancenet, shen2018scaling}.
Some researchers address the problem of detecting arbitrary objects in videos or image sequences by leveraging \textit{saliency} \cite{chan2017faster}, which aims to infer image or video regions that attract high visual attention while also obeying object boundaries. This concept is often applied together with unsupervised learning, where the goal is to discover objects without needing manual annotation or initialization, a problem called \textit{unsupervised object discovery}.
With the advent of faster and denser optical flow algorithms \cite{brox2010object, sundaram2010dense}, the top-performing methods use some form of motion boundary detection in their pipeline \cite{papazoglou2013fast, wang2018saliency}.
However, these methods are computationally expensive, typically taking on the order of minutes to discover objects, which can be prohibitively slow for real-time robotics applications.
Recently, advances in object proposal algorithms (OPAs) show promise in addressing key challenges in salient object discovery for robots.
In particular, when an OPA is applied to images or video, it can potentially produce object candidates, or \textit{general object proposals} (GOPs), which can be useful for accurately recovering the locations of arbitrary objects.
One of the greatest assets of OPAs is that they are fast, typically taking less than a second to compute hundreds to thousands of GOPs per image or video frame.
However, OPAs can also be problematic because majority of these GOPs do not contain useful information (e.g., contain background regions or partial objects) \cite{chavali2016object}.
Consequently, it is often difficult to determine which object proposals correspond to real objects.
To this end, we introduce our recent work, Unsupervised Foraging of Objects (UFO), a novel method that automatically filters out non-salient object proposals to address unsupervised salient object discovery for robot vision. The key insight of our approach is that when an OPA is applied to a video or a set of spatiotemporal images, GOPs corresponding to non-objects appear randomly, typically due to camera noise, changes in illumination, or the presence of image artifacts. In contrast, GOPs correlating to real objects contain a higher degree of saliency and appear more consistently, making it possible to discover salient objects by detecting strong correspondences across image sequences.
As a result, UFO can infer arbitrary objects using only a few observation samples, making it faster than similar, competitive methods.
By designing our method to quickly and accurately perceive novel objects, we reach one step closer to designing robots that can
learn about novel objects, leading to improved autonomy.
\begin{figure}[t]
\captionsetup{font=scriptsize}
\centerline{\includegraphics[width=0.5\textwidth]{output_ex.png}}
\caption{Sample outputs in a challenging sequence (i.e., ''\textit{mallard-fly}'') from the Davis 2016 dataset. Our method, UFO, is robust to dynamic lighting, and fast camera and object motion, which is difficult for methods that rely on optical flow or motion boundaries.}
\label{fig:outputex}
\hspace{-0.15in}
\vspace{-0.25in}
\end{figure}
\begin{figure*}[t]
\captionsetup{font=scriptsize}
\centerline{\includegraphics[width=1.0\textwidth]{darren_v3.png}}
\caption{UFO is composed of six processes: object proposal generation, saliency scoring, saliency-aware non-maximum suppression, feature extraction, sliding window graph update, and path selection.}
\label{fig:overview}
\hspace{-0.15in}
\vspace{-0.20in}
\end{figure*}
\section{UFO}
Figure 1 shows an overview of UFO and each of its aspects, which include: object proposal generation, saliency scoring, saliency-aware non-maximum suppression, feature extraction, sliding window graph update, path selection, and object proposal prediction.
First, an OPA (e.g., \cite{pinheiro2015learning}) is applied to the first frame of a sequence of images to generate a set of GOPs, each consisting of a bounding box and objectness confidence score.
In parallel to this procedure, we apply the Minimum Barrier Distance transform \cite{zhang2015minimum} to the image to extract saliency predictions for each pixel (i.e., saliency map).
To reduce computation time in the later part of the pipeline, we apply a saliency-aware non-maximum suppression strategy (NMS) to remove redundantly overlapping GOPs. For each
GOP we measure the number of enclosed salient pixels to derive a normalized saliency score, allowing our NMS procedure to favor the selection of those that are more salient.
The GOPs are then passed to a pre-trained convolutional neural network (i.e., VGG-19 \cite{simonyan2014very}), to extract general feature embeddings.
Transforming GOPs to vertices, we frame salient object discovery as a graph problem.
With each pair of frame-adjacent GOPs, we use their feature embeddings to compute pairwise similarity scores.
Using these similarity scores, we construct GOP correspondances by applying bipartite matching to form edges.
Taking into account the similarity and objectness confidence scores for each GOP, we apply greedy path selection, where the path with the highest score corresponds to the most salient object in the image sequence. The GOP corresponding to the latest entry of this path (i.e., the bounding box of a discovered object) is then output.
To avoid the problem of an exponentially growing graph as the image sequence grows larger, we leverage a sliding window graph, only keeping memory of the most recent GOPs.
This enables the past history of objects to propagate over time, both reducing computational load and memory usage.
Lastly, in the event that the OPA fails to generate GOPs of previously discovered objects in the follow frame, UFO makes object proposal predictions.
This is achieved by generating an image template, using repeated entries GOP entries (i.e., those with stronger correspondences).
The template is then cross-correlated with the following frame to determine the most likely location of the previously discovered object.
\begin{table}[t]
\captionsetup{font=scriptsize}
\centering
\resizebox{.5\textwidth}{!}
{%
\vspace*{2cm}\begin{tabular}{lllllll}
\hline
\textbf{Method} & $t(s) \downarrow$ & Precision $\uparrow$ & Recall $\uparrow$ & F-score $\uparrow$ & $CorLoc \uparrow$ & $mAP \uparrow$ \\ \hline
UFO & \textbf{4.52} & \textbf{0.662} & 0.645 & \textbf{0.654} & \textbf{0.486} & 0.568 \\
SAL \cite{wang2018saliency} & 35.7 & 0.517 & 0.597 & 0.597 & 0.425 & 0.517 \\
FST \cite{papazoglou2013fast} & 29.4 & 0.659 & \textbf{0.647} & 0.653 & 0.485 & \textbf{0.586} \\ \hline
\end{tabular}%
}
\caption{Summary of results: Precision, Recall, F-score, correct localization ($CorLoc$), mean average precision ($mAP$) measured at intersection over union threshold of 0.5. We report the average end-to-end computation time in seconds per frame ($t(s)$). $\uparrow$ indicates that higher is better and $\downarrow$ indicates that lower is better.}
\label{tab:results}
\vspace{-0.15in}
\end{table}
\section{Results and Discussion}
We evaluated UFO on the DAVIS 2016 dataset \cite{perazzi2016benchmark}, which consists of 50 spatiotemporal image sequences, each depicting a unique salient object.
Each sequence is captured from a moving camera under different lighting conditions, clutter, and occlusion, making it a testbed that is representative of challenges in robot vision.
In our evaluation, we measured precision, recall, F-measure, correct localization ($CorLoc$), mean average precision ($mAP$), and computation time per frame in seconds. \footnote{For a comprehensive summary of these metrics, see Tang et al. \cite{tang2014co}}.
We present a summary of our results in Table \ref{tab:results}, along with sample outputs in Figure \ref{fig:outputex}.
Comparing precision, recall, F-measure, and CorLoc, we found that UFO scored similarly to FastSeg, while Geodesic scored lower for all metrics.
Comparing end-to-end computation time, we found that UFO was approximately 6.5 times faster than SAL (which took on average 35.7 seconds compute per iteration) and FST (which took on average 29.4 seconds).
Since these methods require multiple frames and iterations to make object discovery inferences, we show that optical flow-based methods take on the order of \textit{minutes}, while UFO is able to reduce this time to seconds.
To our knowledge, and at the time of writing, UFO is the fastest unsupervised salient object discovery method.
Achieving state-of-the-art precision and recall on the DAVIS dataset, our results suggest that UFO is robust to real-world robot vision challenges, including moving cameras and moving objects, detractor objects, motion blur, and occlusion.
\section{Future Work}
In our future work we plan to expand our method to address other problems in robotics.
For instance, we would like to explore how UFO can be used in conjunction with active vision to investigate unfamiliar objects in novel environments, such as deep sea or space exploration, where it is difficult for humans to reliably be in the loop to support robot missions \cite{driess2017active, shi2017underwater}.
We also plan to improve UFO and deploy it on a live robot, which will help us gather data in unconstrained environments and enable it to learn about novel object classes to construct recognition models in real-time.
This will ultimately allow us to build a scalable object detection framework that can learn on-the-fly, which will enable robots to one day become more seamlessly integrated into real-world environments.
\balance
\bibliographystyle{IEEEtran}
\section{Introduction}
Robots are entering human social environments (HSEs) such as hospitals, homes, and factories \cite{riek2017healthcare}.
As social beings,
much human behavior is predicated on \textit{social context} - the ambient social state that describes cultural norms, social signals, and individual preferences \cite{riek2014social,nigam2015social,o2015detecting}.
Cues such as facial expressions, body posture, and group behavior encode social affordances that are critical for understanding and predicting human behavior \cite{hall1968proxemics,hogan2003can,moosaei2017using,taylor2019coordinating}.
Furthermore, humans consistently view, communicate with, and react to robots as social actors \cite{reeves1996media,breazeal2004social,sardar2012don,baxter2018robots,cunningham2019mpdm}.
Many tasks can only be completed by understanding, respecting, and interacting with social context.
For example, even in the simple task of buying an ice cream, one must understand why people line up to order, wait in line without cutting, and execute an interactive dialogue before receiving the treat.
Thus, in order to act both appropriately and effectively in HSEs,
it is crucial for robots to understand social context and how to leverage social interactions to complete tasks.
Endowing robots with social agency---the understanding of oneself as a social actor---is an open challenge that must be addressed before robots can plan safe and reliable behavior in HSEs \cite{riek2014social,nigam2015social,o2015detecting,charalampous2017recent,riek2017healthcare}.
Socially-aware planning seeks to model social context in order to generate appropriate policies for HSEs \cite{khambhaita2017assessing, charalampous2017recent, rizwan2018human,cunningham2019mpdm}.
Many existing socially-aware planners use proxemics, the social affordance of space \cite{hall1968proxemics}, to represent social context as an objective function over the environment \cite{mumm2011human,rios2015proxemics,okal2016formalizing}.
These planners consider humans as \textit{social obstacles}, i.e. obstacles with an additional social occupancy that encodes proxemic affordances such as personal space \cite{bera2017sociosense} and visibility preferences \cite{kirby2009companion}.
Social obstacle planners then generate human-aware paths on these costmaps using lightweight graph-search \cite{okal2016formalizing}, potential field \cite{huang2010human}, or sampling-based \cite{svenstrup2010trajectory} planners.
However, these path planners do not consider high-level decisions about subtasks beyond motion and obstacle avoidance, and are therefore insufficient for planning the complex, interactive policies necessary in HSEs.
Joint task and motion planning (TMP) is a central area of research in robotics and artificial intelligence that seeks to address this issue by sharing information between task and motion planners.
Many TMP algorithms interleave task and motion planning, replanning at the task level (i.e. reordering or choosing new subtasks) when the high-level symbolic plan violates low-level geometric constraints (e.g. the robot is unable to reach the desired object without collision) \cite{kaelbling2013integrated,dantam2016incremental,garrett2018ffrob,srivastava2014combined}.
The majority of this work focuses on manipulation tasks, where the interactions between the robot and the world are simple and well-defined.
Few studies have addressed joint TMP in HSEs \cite{pellegrinelli2016probabilistic,pellegrinelli2017motion}, and these approaches still largely incorporate human models for the purpose of avoiding collisions during task execution.
While these methods are a great start to a difficult problem, one key gap is the consideration of social context.
Without this, robots are at risk of both distressing those around it by violating social norms and of failing to find the optimal task plan by ignoring possible social interactions.
It is nontrivial to integrate social awareness with modern TMP.
Social constraints can be considered relaxed constraints, i.e. constraints that can be only partially satisfied when needed to meet a stronger constraint such as collision avoidance.
While some researchers incorporated relaxed constraints into robot planners \cite{kunz2012manipulation,stilman2010global,huh2018constrained}, the majority only do so in the context of replanning low-level obstacle avoidance policies to satisfy a static task.
The few works that explore relaxed constraints in dynamic TMP either only replan subtask order \cite{lahijanian2016iterative,guo2018probabilistic} or consider only simple, well-defined subtasks (e.g. recording information, picking up a cup) \cite{lahijanian2016iterative,ceriani2015reactive,guo2015multi}.
Furthermore, most existing work does not weight the degree of strictness of different constraints.
While \cite{ceriani2015reactive} and \cite{guo2015multi} propose ways to weight constraints, these methods rely on a human expert to designate their importance.
In HSEs, the relative importance of constraints varies with social context, and since social context is also influenced by each robot action, it is inadmissible to assume static, externally-supplied weights.
To our knowledge, there exists no joint task and motion planner that is able to reason about complex high-level task replanning with dynamically-varying, relaxed constraints.
\section{Proposed Algorithm}
In this work, we propose a socially-aware TMP algorithm that leverages an understanding of social context to generate appropriate and effective policy in HSEs.
The key strength of our algorithm is that it explicitly models how potential actions affect not only objective cost (e.g. path length), but transform social context (e.g. interrupting conversations via an alarm).
We also inform the planner of the relative importance or urgency of its current task goal, which it uses along with its own calculation of social constraints to determine when it is and is not appropriate to violate social expectations to optimize the objective function \cite{nigam2015social}.
This social awareness allows a robot to understand a fundamental aspect of society: just because something makes your job easier does not make it the right thing to do.
We make several assumptions in this work. We assume knowledge of the location of the robot, static obstacles, and people. We further assume that there is a finite, known set of available interactions the robot can initiate with a person or group of people. We do not assume perfect knowledge of social context, and instead estimate its state from observing human activity and social cues. From our previous work in real-world hospitals and factories, we found it is feasible to employ wearable sensors to accurately track people and equipment and recognize important activities \cite{kubota2019activity,frank2019wearable}.
In this work, we adopt a classic TMP architecture with a high-level task planner and a low-level motion planner.
We separate our robot's social interactions into two domains: active (e.g. asking for help) and passive (e.g. accommodating personal space).
We incorporate passive social interactions into our low-lever planner in a lightweight social obstacle planner in order to leverage the benefits of existing work.
Our task planner models active social interactions based on a partially-observable Markov Decision Process (POMDP).
Here, social context consists of hidden states (e.g. each person's current activity) that are approximated from features such as proxemics \cite{rios2015proxemics} and group behavior \cite{taylor2016robot}.
To choose relevant features for a specific application, we plan to consult experts in the area, extract features via learning algorithms like neural networks, and perform extensive cross-validation of our selection.
We will collect data on social interactions in real-world manufacturing and emergency department settings to accurately model how human-human and human-robot interactions transform social context in these HSEs.
We will then develop interaction models for a set of possible human-robot interactions, which our task planner will use to plan optimal high-level policy.
The high complexity of HSEs poses concerns for POMDPs.
In order to remain tractable, our algorithm will employ a policy-switching architecture that balances the benefits of sophisticated social reasoning with the speed of a socially-naive motion planner.
In this model, an executor manages the cooperation between the complex task-level POMDP and the lightweight social obstacle motion planner.
The executor uses a lazy approach that activates the high-level planner only where there is significant potential for active social interaction.
Assuming that interaction is only possible in a small subset of states (often those proximal to a human), our algorithm avoids high-level replanning for the majority of states.
Furthermore, this constraint limits the effective state space of the POMDP to this subset.
We anticipate these strategies will enable our algorithm to remain tractable in real-world HSEs.
\section{Evaluation}
To validate our algorithm, we will simulate a crowded emergency department in which a robot must deliver medicine to a patient's room.
We will investigate three scenarios:
1) social interaction is helpful, but unnecessary to complete the task;
2) social interaction is necessary; and
3) social interaction is helpful, but socially unacceptable (e.g. if it would interrupt a clinician treating a patient).
We will perform our study at a medical simulation center at our institution.
We will recruit clinicians and clinical learners to realistically populate the simulation, who will be assigned tasks to simulate various social states.
For each trial, we will record the executed plan's path length, duration, and ``social burden" as estimated by a post-trial questionnaire.
We will compare our algorithm against two competing state-of-the-art methods: a task-naive social motion planner, such as a pure social obstacle model, and a socially-naive TMP, such as \textit{Ffrob} \cite{garrett2018ffrob}.
We anticipate that our algorithm will generate lower cost plans than the task-naive social obstacle planner by leveraging social interaction.
In addition, we expect that the task-naive planner will fail when social interaction is necessary, as in (2) and (3), while our algorithm will find a viable plan.
We also expect that our algorithm will guarantee socially acceptable policy, where the socially-naive TMP may fail in (3).
\section{Discussion}
We anticipate this work will offer the following contributions:
First, we introduce a socially intelligent joint task and motion planner that generates appropriate and effective policies for robots in HSEs.
Second, we present a framework for dividing social interactions into active and passive domains to limit computational complexity and leverage existing work in social obstacle planning.
Third, we present a socially-aware, lazy policy-switching architecture that selectively activates high-level replanners only when necessary in order to remain effective and tractable in complex HSEs.
To our knowledge, the proposed work is the first TMP algorithm that enables a robot to act as an intelligent social agent in HSEs.
By explicitly modeling social context while remaining tractable in complex environments, we anticipate our approach will be applicable in a variety of real-world applications.
Through this work, robots will be able to understand, respect, and leverage social context to produce acceptable and functional policy in HSEs.
\balance
\bibliographystyle{condensedIEEEtran}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 4,448 |
DEDICATION
To my cartoonist friends, for being so fascinating and making my life better because of it.
And to the undergraduate and graduate students I met while writing this book––including Chris––whose enthusiasm and ideas have inspired me so much.
CONTENTS
COVER
TITLE PAGE
DEDICATION
FOREWORD: ONE POINT OF VIEW BY GARY PANTER
INTRODUCTION: COMICS FOR GROWN-UPS?
WHY DISASTER?
WHY SUPERHEROES?
WHY SEX?
WHY THE SUBURBS?
WHY CITIES?
WHY PUNK?
WHY ILLNESS & DISABILITY?
WHY GIRLS?
WHY WAR?
WHY QUEER?
CODA: WHY FANS?
ACKNOWLEDGMENTS
BIBLIOGRAPHY
INDEX
ABOUT THE AUTHOR
ALSO BY HILLARY CHUTE
COPYRIGHT
ABOUT THE PUBLISHER
---
[INTRODUCTION: COMICS
FOR GROWN-UPS?](Contents.xhtml#intro)
It's like learning a new syntax, a new way of ordering ideas.
—Alison Bechdel, in The Comics Journal, 2007
In 1995, a few years after his two-volume book Maus: A Survivor's Tale won the Pulitzer Prize, cartoonist Art Spiegelman spoke to The Comics Journal about his chosen medium. "It seems to me that comics have already shifted from being an icon of illiteracy to becoming one of the last bastions of literacy," Spiegelman suggested. "If comics have any problem now, it's that people don't even have the patience to decode comics at this point." When I tell people about Spiegelman's contention—comics is actually one of the last bastions of literacy—they are usually surprised. It is the polar opposite of what many are used to thinking about comics—or still might think.
Despite a few globally very well-known works, like Maus, about Spiegelman's parents' experience in the Holocaust, the whole comics medium still often gets mistaken for its most popular genre: superheroes. Fantasy is a genre, humor is a genre, romance is a genre—a style, a category that comes with a set of approaches and expectations. Comics, on the other hand, is a medium in its own right—not a lowbrow genre of either art or literature, as it is sometimes understood—and it can be about anything. (For this reason, however awkward "comics is" can sound in a sentence, I use "comics" with a singular verb when appropriate.) And while it can be about anything, there are some things that comics is particularly good at. Scott McCloud, the son of a blind rocket scientist from Lexington, Massachusetts, told me about the dominant view with which he contended when he set out to write his 1993 book Understanding Comics: " 'Comics, they have staples and superheroes and funny animals, the end, what else is there to talk about?' . . . And I thought, '. . . Look how much bigger the territory is, and look how many cool things come in.' " On YouTube, in the comments section for the video of my 2015 public conversation with McCloud, one viewer wrote: "I show it to arty friends to show comics are not just Spider-Man and nerds." Twenty-five years after Understanding Comics, an ingenious treatise on comics itself composed in comics form, made its claims, old associations persist despite the huge diversity of contemporary comics. Comics today is an art form with an ever-increasing popularity and range.
Today, works of comics—although many are—don't need to be about superheroes, a genre that began in 1938 with Superman, a character created by two high school friends from Cleveland, Jerry Siegel and Joe Shuster, when they were teenagers. Comics works also don't need to be funny, although of course many of them are. This is understandably confusing to those who don't happen to know the history because comics are, after all, in the United States and United Kingdom, called "comics." For . . . presumably some reason. In Italy the form is called fumetti, which means "little puffs of smoke" and refers to speech balloons. In France the form is called bandes dessinées, which means "drawn strips." Both of these designations, unlike the English iteration, refer to formal elements.
Superman's debut in the comic book Action Comics #1, by Jerry Siegel and Joe Shuster, cover by Shuster, June 1938, published by Detective Comics, Inc. (later DC Comics). A mint copy sold on eBay in 2014 for $3,207,852, the most ever paid for a single comic book.
© June 1938 DC Comics. All Rights Reserved.
Comics has branched out from the realm of the specialized and the cult into countless corners of culture in the twenty-first century. Comics today seizes the public imagination in books and periodicals, in museums and galleries, at massively populated comics conventions like San Diego's Comic-Con, and even on Broadway, with the multiple Tony Award–winning 2015 musical adaptation of cartoonist Alison Bechdel's graphic memoir Fun Home: A Family Tragicomic, the story of a lesbian cartoonist and her closeted, suicidal father. Speaking of Broadway: Lin-Manuel Miranda, the megastar creator of the rap musical Hamilton, told the New York Times's "By the Book" column in 2016 that the last great book he read was Saga, the galactic war–love story graphic novel series by Brian K. Vaughan and Fiona Staples. Miranda had also tweeted about the series, and a new interest and audience was born. (Online mash-up: Saga4Ham.) In 2015, the North American comic-book industry raked in an estimated $1.03 billion from print and digital comic-book and graphic novel sales, a new twenty-year high. And graphic novel sales in bookstores rose 22 percent in 2015, according to comics industry site The Beat (the article ran with a big image of Saga volume 4). In a time when many lament the decline of the print book, comics maintains crucial attention to the book as object (not that it neglects online platforms, where it is also flourishing). In 2016, even as sales of adult fiction in bookstores fell, sales of graphic novels continued to rise.
Comics is a feature not only of mainstream popular culture, but also of university culture, the art world, and even global politics. While there were actually comic-book burnings in the late 1940s and 1950s, when many adults saw comics as a loose and dangerous form of youth culture—a role later absorbed by rock 'n' roll, and then video games—librarians and professors are now outspoken champions of the form. A Columbia University librarian, Karen Green, recently stated that "graphic novels are the most frequently requested material in our Ivy League request system." One can now get an accredited undergraduate or graduate degree in comic art—and today cartoonists like Spiegelman are sought-after public intellectuals. Comics is unprecedentedly popular in the art world, a fact marked by a special issue of the world's most influential art magazine, Artforum, on comics and fine art in 2014. There have been numerous high-profile gallery and museum exhibits featuring comics around the world. And comics has persistently been in the news since January 2015, in controversial contexts. The debate provoked by the Charlie Hebdo massacre in Paris brought the practice of cartooning and what it means into the global spotlight, with dozens and dozens of demonstrations around the world featuring pens held up into the air, making the drawing pen a potent symbol of freedom. People may not have agreed with the Charlie Hebdo cartoonists' satirical aims, but everyone had to acknowledge that hand-drawn lines on paper, even in the age of the Internet, have enormous power.
Comics also has substantial resonance in cultural debates in America. This is particularly the case in education, because of the affective force of its visuals, a feature of especial concern in the age of "trigger warnings" and censorship dustups. Comics made national headlines in the summer of 2015 when a group of freshmen at Duke University refused to read Bechdel's Fun Home, which was the suggested common first-year read for incoming students, because of its explicit—and gay—content. One of those students even published an op-ed in the Washington Post online titled, "I'm a Duke Freshman. Here's Why I Refused to Read 'Fun Home.' " The idea of comics as common reading—which is to say, the idea of literature that shows something, for instance, sex, in addition to describing it verbally—sparked numerous conversations in print and online about the goals of college education and the differences between looking and reading, activities the medium of comics productively intertwines.
THE ORIGINS OF "COMICS"
So far I've been writing about comics in a broad sense. But comics consists of distinct popular formats with their own conventions that can help us see how and where the very idea of comics for grown-ups emerged. This idea, even today, might not seem intuitive to the casual observer, but it motivates Why Comics? and its focus on what comics can do for audiences everywhere of all ages. Comics encompasses the newspaper comic strip, which began in the United States in the 1890s; the comic book, which began in the 1930s; and the so-called graphic novel, which began as such in the 1970s. So where does comics come from? It is connected to how the term cartoon came to take on new meaning in the nineteenth century.
Cartoon used to designate—and still designates, in an art historical context—any preparatory sketch for tapestries, or for frescoes, or for paintings. It was first used to indicate "humorous drawing," which is how people widely think of it today, in 1843, in London's Punch magazine, which ran cartoons throughout the nineteenth century and beyond. It might not seem very funny to contemporary eyes now, but Punch's "Substance and Shadow: Cartoon, No. 1" was a then-humorous political commentary about cartoons in the traditional sense of a preparatory sketch. Apparently, in many reports, the public howled with laughter at the joke of the cartoon—which goes to show changing mores. Longtime New Yorker cartoon editor Bob Mankoff is especially funny about "Substance and Shadow": "I won't try to exhume the humor of this illustration," he writes in his autobiography, "except to say that there was some, it was satiric, and you had to be there in England in 1843 to get it."
John Leech, "Substance and Shadow: Cartoon, No. 1," in England's Punch, July 15, 1843.
In the image, impoverished civilians, children and adults alike, view an exhibition of cartoons for a competition for patriotic paintings to be commissioned for the newly rebuilt New Palace of Westminster. The joke is that the government needs to address the poverty of its citizens instead of addressing the issue of decorating the palace. After 1843, when "Substance and Shadow" appeared and was massively popular, nomenclature changed: people came to equate "cartoon" with the idea of a funny drawing, and hence came the modern meaning of the word and terms like cartoonist.
In the United States, weekly humor magazines imitated Punch, with titles like Puck, Judge, and Life, which began in the 1880s and were called "comic weeklies," or even, sometimes, simply "comics." Then the sensational newspaper press in New York City, in the 1890s, began printing "Sunday supplements" to increase their circulations and to compete with the magazines. These Sunday supplements, led by the newspaper the New York World, which was published by Joseph Pulitzer, concentrated on comical artwork, and eventually on comic strips, which is to say, narrative series of pictures with words, which began to appear in the mid-1890s.
The comic strip widely regarded as the first, Richard Felton Outcault's 1895 sensation known as The Yellow Kid, about a resident of a Lower East Side tenement, was so popular as to inspire the term "yellow journalism" when William Randoph Hearst and Pulitzer struggled over who would ultimately buy Outcault out from whom. These comic strips became known as the comics, which developed out of the "comic weeklies" and then the comical supplements. They were often referred to as the "funnies," short for the funny papers or funny pages of a newspaper. The format of the stand-alone comic book began in the late 1920s, as a way for publishers to reprint newspaper comic strips. These comic books were also, as the strips themselves often were, called the funnies.
But as the brilliant cartoonist Winsor McCay demonstrates—his comic strips Dream of the Rarebit Fiend and Little Nemo in Slumberland began in 1904 and 1905, respectively—comic strips almost from their inception cast off the idea that they had to be comical. Many from this early period are dark and even ominous. In one Rarebit Fiend installation from 1905, the protagonist dreams he is being buried alive. We see from his point of view: dirt falls upon his face from within the grave and he hears his wife remark, "At last my hopes are realized." But regardless of the content, the term "comics" had stuck as a description of drawn sequential narrative work with multiple panels. A "cartoon," on the other hand, remained, like in "Substance and Shadow," a single-panel image, as in what we would recognize today as an editorial cartoon or a political cartoon (later "cartoon" came to mean animated content as well). Yet people who draw "comics" are also called "cartoonists," which can be a little confusing. Like all art forms, especially newish ones, this one has a lexicon that can be idiosyncratic. (I switch back and forth from referring to people who create comics as "authors," "artists," and "cartoonists," as they themselves do.) So while "Substance and Shadow" is an amusing cartoon about marginalized people encountering a dominant visual culture that highlights their exclusion, Alison Bechdel's "The Rule," published almost 150 years later, is an amusing work of comics, in ten sequential panels, about marginalized people encountering a dominant visual culture that highlights their exclusion. "The Rule," which appeared in Bechdel's first Dykes to Watch Out For comics collection in 1986, is the source for the celebrated Bechdel Test, a feminist barometer for film and now a pop culture icon.
COMICS FOR GROWN-UPS?
Comic strips had been introduced in the sensational newspaper press by Hearst and Pulitzer, among others, in order to drive circulation—many comic strips were meant to appeal to children, and to immigrant readers of newspapers—an explicit goal. (Picasso was a fan of The Katzenjammer Kids, German cartoonist Rudolph Dirks's strip featuring a pair of naughty children who speak with an accent, which ticked off both those boxes.) Yet these same newspapers also ran comics meant to draw in sophisticated adult audiences, such as by Winsor McCay and by George Herriman, the cartoonist behind the existential, absurdist mouse-cat-dog strip Krazy Kat, which ran from 1913 to 1944, and is the subject of a famously loving 1946 encomium by e. e. cummings, among many other tributes (T. S. Eliot was also a fan). To Art Spiegelman, therefore, himself the son of two Polish immigrants to New York City, comics has always "been a tug of war between the vulgar and the genteel." He adds: "I'm not here to champion the vulgar, I'm here to champion the tug-of-war." Many of the early newspaper comic strips, which appeared, ironically, on ephemeral, cheap paper meant for fishwrap and other workaday conveniences, are considered aesthetic benchmarks in the history of comics, their techniques still emulated and admired. There is something impressive about the craft and sophistication produced by the creators of the early comics for an utterly disposable format.
Alison Bechdel, "The Rule," Dykes to Watch Out For (Ithaca: Firebrand), 1986, source of the Bechdel Test, and replete with funny fake phallic movie posters.
Used by permission of Alison Bechdel.
The comic book, however—at least in its first few decades—was firmly associated with youth culture. While there were early prototypes of the comic book, such as 1929's The Funnies, which featured original drawn strips and appeared from Dell on newsstands on tabloid-size newsprint, the publication that set the format for comic books as we know them conventionally was 1934's Famous Funnies #1. In the intervening years between the large-size Funnies, which had sputtered out quickly, and Famous Funnies, manufacturers had regularly reprinted newspaper comic strips as promotional premiums in grocery stores—giveaways tied to specific products. Famous Funnies #1, however, wasn't free: it appeared on newsstands, cost 10 cents, and was printed in four-color. It was a saddle-stitched sixty-eight-page newsprint pamphlet, smaller at roughly 7 by 10 inches, and it set the standard for the format for years to come.
Famous Funnies was published by Max C. Gaines (born Maxwell Ginzberg), a pioneering figure who was then working for Eastern Color Printing Company. It reprinted strips such as Bud Fisher's Mutt and Jeff, which began in 1907 and is referenced in what is perhaps the twentieth century's most famous work of art, Marcel Duchamp's Fountain (1917), a urinal that is signed "R. Mutt." A few years later, in 1938, Superman inaugurated the so-called Golden Age of comic books, making comic books wildly commercially successful. He was joined by a proliferating group of superheroes driving massive sales, including Batman the following year in Detective Comics #27, and Captain America, whose debut in 1941 on the cover of Captain America Comics #1 shows him punching Hitler in the face (and inspired Michael Chabon's Pulitzer Prize–winning novel The Amazing Adventures of Kavalier & Clay). Jules Feiffer, in his book The Great Comic Book Heroes, edited by E. L. Doctorow, notes how comic books in their original Golden Age were churned out like Ford Model Ts in what were known as comics sweatshops. By 1952, nearly a hundred million comic books were sold every week.
The Golden Age ended in 1954, after psychiatrist Fredric Wertham's best-selling study Seduction of the Innocent, which aimed to establish a link between comic-book readership and juvenile delinquency, brought the comic-book industry to a halt. Seduction of the Innocent provoked hearings by the Senate Subcommittee on Juvenile Delinquency, at which Wertham testified as an expert witness. Wertham, a German Jew and a complex figure, was involved in numerous progressive causes. A friend of Ralph Ellison and Richard Wright, he helped to found, with Wright, the Lafargue Clinic, a low-cost psychiatric clinic in Harlem for black teenagers, and his research on the negative effect of racial segregation on children was used as evidence in the Brown v. Board of Education Supreme Court decision. Yet Wertham objected to the violence and the sexuality he saw lurking in comic books. The result was the censorious Comics Magazine Association of America "Comics Code." Notoriously, the grossly overhygienic code contained such now-hilarious strictures as "In every instance good shall triumph over evil and the criminal be punished for his misdeeds."
How many interesting stories, in any medium, can exist with those guidelines? A few comics titles, such as the satire title Mad, which began in 1952, escaped the chilling effects of the Code. And despite the devastation of the Code, comic books did enter a commercial "Silver Age." So began a second superhero boom in the 1960s that with Stan Lee (né Stanley Lieber) on board at Marvel Comics widely disseminated comics of an appealing ilk: those that represented superheroes as flawed and neurotic. But many cartoonists correctly felt they would have to work outside of mainstream systems of publication and distribution if they were going to take comics seriously as a form of expression and develop its capacities.
"COMICS WITHOUT PUNCHLINES"
That brings us to underground comics, a vital movement with literary, artistic, and popular force that profoundly shaped contemporary comics. The underground comics revolution of the 1960s and '70s, which took place largely in New York and San Francisco, set the foundations for every kind of serious comics field we have today. Comics that emerged from the underground were independently created and produced works, without commercial strictures. They were often rechristened "comix," with an x, to indicate their adult edge. Cartoonist R. Crumb's Zap #1 kick-started the movement in 1968 with this salvo on its cover: "For adult intellectuals only!" A friend of Crumb's, Don Donohue, had traded away his tape recorder for use of another friend's printing press to produce several thousand copies of the comic book that Crumb and Donohue then assembled, folded, and hand-stapled, and Donohue published under the name Apex Novelties. Crumb sold Zap #1, which had a print run of four thousand, directly out of a baby carriage for 25 cents on San Francisco's Haight Street with his pregnant wife, Dana. While mainstream comics in this period did not market themselves this way, titles such as DC's Green Lantern/Green Arrow (1970) pressed for social relevance and showcased dark themes. A few years later, comic books such as Justin Green's confessional Binky Brown Meets the Holy Virgin Mary (1972), the inaugural work of comics autobiography, offered the exact opposite of what people would expect from comics. While Superman wore a costume and saved lives, Green's autobiographical character Binky miserably masturbated with his underwear at his ankles. Comics were reinvented, as Spiegelman put it in a famous, often-reprinted 1981 image of a painter wielding a fountain pen, "as a medium for self-expression."
Robert Crumb, cover of Zap #1, 1968. The logo that is shaped like the logo of the Comics Code Authority in the upper right reads, "Approved by the ghost writers in the sky." Crumb's iconic character Mr. Natural responds in the dialogue to a woman with the same remark musician Fats Waller reportedly uttered when a woman asked him, "What is jazz?"
© R. Crumb. Used by permission.
In the comics underground, which was connected to the left-wing underground press established in the 1960s, creators shifted away from the notion that comics had to be action-packed, silly, formulaic, or even slightly inclined toward children. They produced complex, textured, and even absurdist storylines, and also showcased the art form's "secret language" (a phrase popular with several cartoonists). "Comics without punchlines" is how Spiegelman saw the massive shift enacted by Crumb and the underground movement. Underground comics were avant-garde; they were political; they were taboo-shattering; and they were formally experimental. In fact, children weren't even allowed to read them.
Comics got remade for adults in the underground. In response to the huge attention elicited by comics like Zap, more and more titles proliferated—including specifically feminist and gay titles—and independent publishing companies and cartooning collectives blossomed. Green's Binky Brown Meets the Holy Virgin Mary, which directly influenced Spiegelman to create the three-page story "Maus" in 1972 (the seed for his later, game-changing Maus), was, perhaps, the first work that looked ahead to the "graphic novel." It is a forty-four-page, sustained, stand-alone narrative about Catholicism, sexuality, and obsessive-compulsive disorder that demonstrated comics could tackle head-on what most would consider the realm of the absolutely interior and private. But it wasn't until 1978 that a book was published that proclaimed itself a "graphic novel." The first book to have the words "graphic novel" on the cover was Will Eisner's A Contract with God, published by Baronet Press in 1978. A Contract with God is a series of four linked vignettes about immigrants in a Bronx tenement in the 1930s.
"Graphic novel" was coined in a 1964 newsletter circulated at the Amateur Press Association, but had never before been used in a commercial context. Eisner recounted in several interviews that he invented the term—he hadn't heard it before—on the spot, in a bid to sell his work to mainstream publishers. He wanted A Contract with God to be received in bookstores alongside "regular" books—which it was—as opposed to published and sold by the specialized comics industry, so he came up with the description "a graphic novel" to emphasize its literary qualities. The term picked up steam in the 1980s to identify the auteurist, individually driven artistic work in which this book is centrally interested. As the cases of Harvey Pekar, Brian K. Vaughan, and many others demonstrate, however, collaboration in comics provides compelling models for thinking about authorship. In the auteur model, one person both writes and draws the comics, so that the work represents one person's artistic vision.
But even the concept of the auteur—a French term from the 1960s that literally means "author" and refers to a film director who shapes cinema through an all-pervasive artistic vision—indicates less control than a cartoonist has to create a visual and verbal world. An auteurist film director—for instance, say, a Quentin Tarantino—works with a team to create his final product. Auteurist comics, on the other hand, can be a front-to-back solo enterprise. "In comics," says cartoonist Daniel Clowes, "if you really have mastery over what you're doing, you can control absolutely everything and make it exactly what you want, exactly what you're seeing in your own head. You're transferring that to the page." Although comics of all kinds are flourishing in the twenty-first century, there has been a dramatic uptick in auteurist comics, which offer the singular intimacy of one person's vision of the world across words and images. They are therefore often consumed alongside similar forms like novels that spring, largely, from one person's aesthetic sensibility.
Will Eisner, cover of A Contract with God and Other Tenement Stories (New York: Baronet Press), 1978. The trade paperback from Baronet was the first book to have "graphic novel" on its cover. Eisner's cover reveals how lettering in comics has narrative qualities, as in the switch from Roman lettering to Hebraic lettering for the word "God" in the title.
WILL EISNER is a registered trademark of Will Eisner Studios, Inc. A Contract with God cover © Will Eisner Studios, Inc.
"Graphic novel" took shape largely as a publishing and marketing term, sometimes to irritating effect, in its trendiness, and sometimes to great positive effect. The field opened up widely because of the appeal of that umbrella category, for instance, when comics industry insiders, including Spiegelman, lobbied the Book Industry Study Group (BISG), the group that standardizes book categories for booksellers, to give graphic novels their own BISAC codes in 2002. Through these institutional changes, comics and graphic novels instantly became more accessible and available to readers. In the early 2000s, titles released by comics publishers started to be distributed by big-name presses to land in bookstores, shifting many comics outside of the realm of the esoteric. Seattle-based independent comics publisher Fantagraphics, for example, founded in 1976, is now distributed by W. W. Norton. Because of this distribution, a person fascinated by the Middle East can now find Joe Sacco's Palestine at the bookstore, as well as at a specialty comic-book shop (I found it, too, in the gift shop of Jerusalem's American Colony Hotel). These industry changes mark comics's success and reach—and more broadly, they demonstrate how the definition of "literature" today is expanding productively to be more creative and more inclusive.
As comics's status has grown, I have noticed a polite anxiety about terms: many people assume, for instance, that "graphic novel," a description that seems to confer a certain bookish sophistication, is preferable to something baser like "comics." Most cartoonists I know don't love the phrase "graphic novel," for several reasons, although they accept it as a kind of shorthand for what they do: expressive, long-form narrative comics. One reason is that it can seem pretentious, like a bid for prestige that attaches to the term "novel." (It is worth noting, again, changing mores: while the novel is prestigious today, back in the eighteenth century it was itself considered a "low," popular form.) The novelist and comics writer Neil Gaiman, the creator behind The Sandman, among many other titles, has famously recounted a publisher correcting his own description of his work by insisting, "Oh, you don't write comics, you write graphic novels." Gaiman felt uncomfortably, in his words, like a prostitute who had just been referred to as a "lady of the night." The Iranian cartoonist Marjane Satrapi, whose Persepolis series has sold almost two million copies worldwide, also shuns "graphic novel": "I don't very much like this term of graphic novel. I think they made up this term for the bourgeoisie not to be scared of comics. Like, Oh, this is the kind of comics you can read."
The term can also be unpopular because "novel" implies fiction, and much of today's important book-length comics work is nonfiction, like Persepolis, Maus, Fun Home, and Joe Sacco's groundbreaking "comics journalism," in which he reports from war and conflict zones in the Balkans and the Middle East. So graphic novel, to the extent that it indicates fiction, isn't always the best descriptor. I tend to prefer graphic narrative, which is inclusive of both fiction and nonfiction. But if someone says "graphic novel," chances are I know what that person means, even if he or she is referring to nonfiction. "Graphic novel" is still the most commonly known phrase that indicates book-length comics for a sophisticated adult audience. (Despite the fact that there are now also plenty of smart graphic novels for kids and young adults.)
The comics produced in the underground, which were created with complete artistic and intellectual freedom to represent an artist's personal vision, established the field of comics for adults. This kind of work became known as "independent" or "literary" comics. Today these comics are published by numerous "above-ground" presses, including Random House and Abrams Books. Independent or literary comics, generally created by one person who both writes and draws, function in distinction from "commercial" or "mainstream" comics created by teams for companies. The two most prominent comics companies, both giants in the entertainment industry, are DC Comics, currently owned by Time Warner, and its rival Marvel Comics, currently owned by Disney. DC, began in 1934, takes its most recent name from the original Detective Comics issue that featured Batman's debut, and it also features Superman, Wonder Woman, Green Lantern, and the Flash, among others. The company we now know as Marvel began in 1939, and is the home of the Hulk, Spider-Man, Iron Man, the X-Men, and the Avengers, among others.
Mainstream comics are generally created by at least two people, one writing, one drawing—and typically by many more, for instance, people inking and lettering the comics. (One inexact but useful metric to deduce if a work is independent or mainstream is whether the panel borders are hand-drawn, which is immediately legible in the febrility of the line, an index of the hand of the individual artist—or whether the borders are the result of clean, computer-generated lines.) But whether or not a work functions in the model of a literary novel—a universe created by one person's aesthetic, sensitivity, and worldview—or is a commercially expedient team effort, both kinds of comics have appealed to adult audiences. The year 1986, for instance, is widely understood to mark the popular ascendency of comics for adults with the publication of three key works that fall across the spectrum of literary and commercial outlined above: Maus I: A Survivor's Tale: My Father Bleeds History (Pantheon), by Art Spiegelman; Watchmen (DC Comics), by writer Alan Moore, with art by Dave Gibbons, along with colorist John Higgins; and Batman: The Dark Knight Returns (DC Comics), by writer Frank Miller, with art by Miller and Klaus Janson, along with letterer John Costanza and colorist Lynn Varley. In this year one started to see headlines with titles like "Wham Pop Zap! Comics Grow Up."
READING COMICS
Comics may now be for grown-ups, but how one ought to read them still isn't always clear and can be a source of confusion. Comics readers encounter the space of the page in a different way than they would a novel, and in a different way than they would a canvas. Students tell me often they aren't sure whether to read all the words first, and then go back and look at the images, or whether to look at all of the images first, and then the words. Or to take in the words and images together, panel by panel. Comics is not an illustrative form, in which the words and images match, but rather one that Marjane Satrapi has called "narrative drawing," and Art Spiegelman has called "picture writing," in which the words and the images each move the narrative forward in different ways the reader creates out of the relationship between the two. How one ought to read comics often feels like an open question—which it is. For a reader navigating the space of the page, reading comics (even highly conventional comics) can feel less directive and linear than reading most prose narrative.
Spiegelman has a quip I've always found funny about Ernie Bushmiller's comic strip Nancy. He says it takes more time to not read Nancy than to read it. A tiny installment of Nancy, which began in 1933, even appears, he points out, in the American Heritage Dictionary to illustrate "comic strip" (its definition: "a narrative series of cartoons"). Historically, there has been an association between comics and a kind of subpar literacy, as if comics reading could not be "real" reading. This is because of the widespread notion that visual literacy, which comics requires, is somehow less complicated than verbal literacy, which comics also requires. In this line of thinking, which is prevalent today, the visual is immediate, and therefore sensual, and obvious. Contemporary comics, however, asks us to reconsider several dominant commonplaces about images, including that visuality stands for a subpar literacy. One glance at a comics page by Chris Ware, as we will see shortly, will disabuse any reader of the idea that visual literacy is easy.
In Seduction of the Innocent, Fredric Wertham memorably called comics reading "an evasion of reading and almost its opposite." Book series like Classics Illustrated, which began in the 1940s and offered shorter, comics adaptations of famous literary works—like the comics version of Moby-Dick—helped to underline the idea that comics were easier versions of a harder, worthier thing. Wertham even cites the Classic Comics version of Dr. Jekyll and Mr. Hyde and Uncle Tom's Cabin in Seduction of the Innocent. But in comics the combination of words and images, and how this narrative exists laid out in space on the page, requires an active and involved literacy. It is one to which we can attach a high engagement of reading and looking for meaning, as in Spiegelman's sense that comics have already shifted from being an icon of illiteracy to becoming one of the last bastions of literacy. Several prominent thinkers about comics, including the late literary critic Edward Said, have used the word decode to describe reading comics. Comics, in fact, is a medium that involves a substantial degree of reader participation to stitch together narrative meaning. And the visual content of comics that once signaled a "lesser-than" literacy is now an integral part of our contemporary daily lives, as so much of our primary media intake, especially online, combines the verbal and the visual, often with complexity we have learned to navigate quickly. As a speaker on a 2017 San Diego Comic-Con panel titled "The Secret Origin of Good Readers" affirmed, "Being able to decipher a story that's coming at you in words and images is crucial. It's part of functioning in society today."
Alison Bechdel puts it well when she says that making comics "is like learning a new syntax, a new way of ordering ideas." Comics has its own fascinating vocabulary: gutters, panels, tiers, balloons, bubbles, bleeds, splashes—all elements that exist meaningfully in relation to one another in space on the page. The "gutter," for instance, which is the space in between panels, is crucial for comics making and reading. The gutter is an absent space that is part of the story—it is where the reader fills in the blank between pictured moments, participating imaginatively in the creation of the story. And different readers do this and experience this blank differently. Comics is as much about what is outside the frame as what is inside it—what can be pictured, and what cannot be or won't be pictured, and is left to the reader's imagination.
In the encounter with the gutter, we see how comics gestures conspicuously to the reader's active and involved reading. This level of readerly engagement is the reason that Marshall McLuhan named comics, which he designated "a highly participational form of expression," a so-called cool medium in his classic study Understanding Media: The Extensions of Man. In Understanding Media, first published in 1964, McLuhan—who had a famously nonsensical cameo in Woody Allen's Annie Hall—categorizes different media as "hot" or "cool"; a cool medium is "low definition" and requires completion from the audience.
Comics, a sequence of selected frames, is about distillation and condensation—one of the reasons that it sometimes gets compared to poetry. In Understanding Comics, McCloud describes the art of comics as subtractive. When I pushed him in an interview on a phrase he and others use, "the secret language of comics," he clarified that in part it was about making work that is economical and dense at the same time. "Nobody picks a comic up off the stands," he told me, "and gasps in admiration at all the unnecessary panels that were left out. You don't see that—it's secret, it's hidden—but that process does go on." He came up with the joke that comics, because it is an art of subtraction, is "secret labor in the aesthetic diaspora." In an artist's statement from 1974, Spiegelman wrote, "The comix I like, and try to do, can be read slowly and often. . . . I try to make every panel count and sometimes work as long as a month on a page. . . . I'm excited by the 'secret language' of comics—the underlying formal elements that create the illusions."
At its most basic, we can say that comics is a spatially site-specific form of literature. In this way, too, comics can also be like poetry, in which the line breaks and stanzas and arrangement of words on the page all carry meaning. Comics works, most fundamentally, "choreograph and shape time," to invoke a striking phrase of Spiegelman's. In the vocabulary of the comics, the other key element aside from the gutter is the panel, also known as the frame. Comics shapes time by arranging it in space on the page in panels, which are, essentially, boxes of time. McCloud amusingly reminds us in Understanding Comics that the conventions of comics would seem to dictate that each panel is a moment, and then he says time in comics . . . is weirder than that. The weirdness of time in comics is part of the medium's force as a storytelling form.
Comics has the ability to powerfully layer moments of time, like in a single panel from Spiegelman's Maus, in which the legs of girls hanged in Auschwitz in the 1940s dangle from the tops of trees in the Catskills as the Spiegelman family drives to the supermarket in the 1970s. The Belgian cartoonist Hergé, creator of The Adventures of Tintin, one of the most famous comics series in the world, which has been translated into over seventy languages, has said that a panel from his 1943 Crab with the Golden Claws, which pictures battling troops in the Sahara, is among his favorite panels in all of his work, because it is, in his words, "an entire sequence in one." It could be, in his view, multiple men fighting, scattered in different positions across a hill, or it could be one man, during the fight, over time, who gets up from shooting to retreat across and down the hill. Panels are how the cartoonist gets to experiment with presenting time, with duration and motion. Richard McGuire's monumental, nonchronological graphic novel Here, which offers on every page a fixed-perspective view of the same space—a ground-floor room in Perth Amboy, New Jersey—links the experience of space with the experience of time. McGuire multiplies and layers panels, each of which represent a different time frame, within the same space on every page, opening up dimensions of time. One page depicting 1949, which is about breaking as a general matter, features a spatialized smattering of verbal insults from the 1940s to the 1980s—and also, terrifyingly, water pouring in the room's window, suggesting a totally destructive natural disaster in the year 2111.
Panels are also how the cartoonist gets to experiment with directions of reading. Comics does not propose linear reading in the same way prose does. Cognitively, one's eye usually first takes in the whole page, even when one decides to start in the upper left corner and move left to right. This is sometimes called comics's "all-at-onceness," or its "symphonic effect." In comics, reading can happen in all directions; this open-endedness, and attention to choice in how one interacts with the pages, is a part of the appeal of comics narrative. One simple but arresting example is in Daniel Alarcón and Sheila Alvarado's City of Clowns (2015), adapted as a graphic novel from an earlier story by Alarcón about a young journalist in Lima, Peru. One nine-panel page suggests that readers both read in succession—the page "works" if you read it left to right, row by row, top to bottom—and also that they grasp the page as a whole and read it diagonally, based on how the black panels with large letters draw the eye: "iN LiMA DYiNG iS the Local Sport." Because of the pattern produced by color, one can't help but read it this way immediately. Comics puts productive pressure on what "normal reading" is—not because it is so easy, or immediate, but rather because paths of reading and different moments of time can compete as alternatives.
Richard McGuire, double-spread page from Here (New York: Pantheon), 2014. Here is based on a six-page story, "Here," published twenty-five years earlier in Raw magazine. It was the subject of an exhibit at the Morgan Library & Museum in New York.
© 2014 Richard McGuire. Used by permission of Pantheon Books, an imprint of the Knopf/Doubleday Publishing Group, a division of Penguin Random House LLC. All rights reserved. Image courtesy Richard McGuire.
While comics is still sometimes cast as escapist and diversionary—and plenty of comics can be like that, quite pleasurably—today it is clear that many comics gesture toward the opposite: a participatory, even slowed-down practice of consumption. The prominence of comics may actually rhyme with the current cultural valuation of "slowness" happening all over. Joe Sacco conceives of his comics journalism, for instance, as "slow journalism." And Spiegelman's primary goal when he set out to make the watershed Maus, as he has repeatedly stated, was to make comics "that needed a bookmark."
Houghton Mifflin Harcourt now publishes The Best American Comics, which they added to the stalwart Best American series in 2006—the same year the best-selling Fun Home, their first graphic novel, was named Time magazine's #1 book of the year. PEN established a Graphic Literature award in 2010. Margaret Atwood has even penned a graphic novel, Angel Catbird, which she will continue as an ongoing series. And in 2017 it was announced that a graphic adaptation of Harper Lee's classic To Kill a Mockingbird, with the full encouragement of the Lee estate, is in the works; the very same week, the New York Times Magazine published their first all-comics issue, which even boasted hand-lettering for elements like the crossword puzzle. Cartoonists are in the spotlight with more and more regularity as their graphic work is nominated for prestigious prizes alongside prose. New Yorker cartoonist Roz Chast's Can't We Talk About Something More Pleasant?, a moving exploration of parental bonds, won the National Book Critics Circle Award for Autobiography in 2015, competing against all nongraphic titles in that category. In 2014, Bechdel caused a sensation when she became the second cartoonist, joining Ben Katchor, to win the MacArthur Foundation "genius" grant. In 2016, the cartoonist Gene Luen Yang (American Born Chinese) and the unclassifiable artist-writer-journalist Lauren Redniss (Radioactive) won the award in the same year—a first. Redniss, who created an experimental biography of scientists Pierre and Marie Curie that literally glows in the dark and meditates on the nature of visual evidence, and Yang, who created a dark young-adult work that visualizes racial stereotypes in order to tell a story about fearing versions of one's own ethnicity in the context of assimilation, exploit the relation of word and image in comics to both tell and show compelling stories in fresh ways.
Daniel Alarcón and Sheila Alvarado, page from City of Clowns (New York: Riverhead), 2015.
© Daniel Alarcón and Sheila Alvarado. Used by permission. All rights reserved.
A hybrid form that can be abstract and surreal, and also immediate and direct, comics is surprisingly versatile—and the fascination comics inspires continues to grow as new vibrant work crops up across a wide range of formats and genres. Today one can find comics in very specialized stores—comic-book shops with names like Forbidden Planet, Floating World, Secret Headquarters, and Desert Island—and also wherever books are sold: everywhere, as the subtitle of this book suggests. The venerable New York Review of Books, for instance, a literary mainstay, just began a new imprint, New York Review Comics, with a mission to introduce reprints of classic works of comics to freshly receptive audiences. NYRC's first title is Mark Beyer's dreamlike Agony, a beautiful, 5-inch-square book with French flaps and an introduction by novelist Colson Whitehead. In March 2016, the long-running magazine World Literature Today published a special issue on international comics, opening the field to new readers. Today we have actual book reviews in comics format; Bechdel created the New York Times's first such review in 2009. We have amicus briefs filed by lawyers in comics form, comics adaptations of The Diary of Anne Frank and The 9/11 Report, and graphic nonfiction about everything from Hurricane Katrina to Congressman John Lewis's struggle for civil rights (the third volume of Lewis's March, a collaborative work, won a National Book Award for Young People's Literature). A movement focusing on "graphic medicine"—the benefit of comics both by and for doctors, nurses, and patients—has taken off globally.
To present the vibrant comics landscape, Why Comics? is organized by the ten biggest themes in today's comics and graphic novels. It offers a set of overlapping but meaningfully distinct themes, one per chapter (with one exception!), that are framed as guiding questions on the value of comics today. The chapters are posed as questions because they are investigations into the unique power of comics. Why does comics have a purchase on insights about sex, or about the suburbs, for instance? What do its boxes of time reveal, what does its world of hand-drawn marks do differently? Reading from theme to theme, you can explore the concerns of comics as a contemporary medium, access the history of famous cartoonists and genres, and encounter the force of comics form and style to convey something surprising, moving, striking—something that changed the way people express themselves or recognize themselves in stories. The themes, which are loosely linked but not strictly chronological, mix gravity and humor, the dark and the light: disaster; superheroes; sex; the suburbs; cities; punk; illness and disability; girls; war; and queerness. Written to be read as a whole—although one presumably could start with a favorite theme—Why Comics? is a guide to what comics does best.
Each chapter focuses on the lives of fascinating comics creators who have made contemporary comics what it is today. These cartoonists have produced the most significant work on a key theme—or themselves started a major, enduring genre, as Sacco did with war journalism, or Gary Panter did with punk comics. Some chapters highlight the career of two or even three artists, while some keep the focus on one generative figure; all also offer anecdotes from my career in the comics world, in which I've collaborated with Art Spiegelman and Alison Bechdel, among other cartoonists. Ware, a poet of contemporary social and architectural space, shows up in both the chapters on superheroes and on the suburbs. Here you'll find classic themes that you might expect, such as superheroes, and also the biggest emerging topics in comics right now, such as illness and queerness. And while you might expect a book on comics to open with the superhero, a type of character that is one of comics's most enduring and successful creations, the story starts with disaster, the foundational theme of the comics.
---
WHY DISASTER?
Maybe Western civilization has forfeited any right to literature with a big "L." Maybe Goethe and Mozart were not the patron saints of Germany. Maybe Wilhelm Busch—with Max and Moritz' amusing bones ground up into a meal—is a more appropriate figure—though far too benign and avuncular. Anyway maybe vulgar, semiliterate, unsubtle comic books are an appropriate form for speaking of the unspeakable.
—Art Spiegelman, notebook entry, 1970s
The most famous graphic novel in the world, without a doubt, is Art Spiegelman's Maus: A Survivor's Tale. If you've only heard of one graphic novel, I'm guessing it's probably Maus. Spiegelman is an internationally celebrated figure; he has been named one of Time magazine's 100 most influential people in the world. The Maus series won a Pulitzer Prize in 1992; the previous year, it was the subject of a Museum of Modern Art exhibit. There are over a million copies of Maus in print in America alone. It has been translated into forty-plus languages, including Chinese, Pashto, and Croatian. Not coincidentally, Maus is unflinchingly about disaster—the Holocaust. Further, comics's most famous genre—the one that so often comes to stand in for the entire art form—is predicated on disaster: superhero comics. Disaster undergirds the entire enterprise, from front to back. Superman, the first superhero, comes with an origin story about the total destruction of his planet. Origin stories for superheroes are about collective, or at the least personal, disaster, whether it's an exploding planet or a young Bruce Wayne witnessing the murder of his parents and henceforth vowing to fight crime as Batman. And then, of course, there is all the prospective disaster that they fight in the present tense of their storylines: endless plots to destroy cities, planets, the universe. Disaster is foundational to comics.
As a verbal-visual art form, comics is inherently about the relationship of word and image, which is to say, about different ways of communicating. It makes readers aware of limits, and also possibilities for expression in which disaster, or trauma, breaks the boundaries of communication, finding shape in a hybrid medium. With its juxtaposed frames, comics constantly calls readers' attention to what they see, or don't see, and why. What can be seen within the frame—and what can't be seen, or isn't supposed to be seen? Comics is a form about visual presence, a succession of frames, that is stippled with absence, in the frame-gutter sequence. We can say that its very grammar, then, evokes the unsaid, or inexpressible. Comics highlights the relation between words and images—and therefore addresses itself to the nature of the difficulty of representing extreme situations and experience.
What, for example, can be visualized, but cannot be explained in words by a character or narrator? The layers of meaning in handmade images often convey, strikingly, what words alone cannot. Close to the beginning of Josh Neufeld's book about the natural and social disaster of Hurricane Katrina, A.D.: New Orleans After the Deluge, he offers readers, for instance, a page whose only words are a simple identification—a date boxed in the upper left—and a piece of graffiti etched onto a rooftop: five names with the proclamation "WE'RE ALIVE." The page takes an aerial view. In the opening frame, which spans the whole tier, readers encounter a wide, detailed image of a flooded residential street in which the water is rising toward almost a dozen rooftops. The page's final two panels, evenly sized to complete its bottom row, have no words. In the first, six people struggle through the water toward the front of the frame, small bodies seen near submerged cars. In the second, in the center of the panel, a body floats facedown in the water. The visual juxtaposition—verbally unremarked upon—of the two rhyming panels gives the page its force: while some are struggling through the water, others have already ceased to struggle. The concluding image of the corpse, small from our bird's-eye view and floating along with other debris in the waterways of the street, is also a contrast with the rooftop words proclaiming collective life. In comics, images that represent extreme experience can feel powerfully immediate and direct, which often gives them an emotional force when they are expressing what can't be put into words. Images of disaster in comics are drawn from one person's pen, not captured through a mechanical device. As one makes a picture but takes a photograph, in the idiomatic convention, images in comics are created out of whole cloth by a living, breathing body.
Cartoonist Joe Sacco, a self-described comics journalist whose comics explore genocide, among other issues, suggests, "I think there is an inherent power in the immediacy of an image." And Art Spiegelman explains, "The compression of ideas into memorable icons gives cartoons their ability to burrow deep into the brain." One reason for comics's growing popularity in the years since 9/11 is likely the fact that we exist in the most visually amplified era in recent memory, through our regular interaction with countless different kinds of images, including videos, GIFs, digital photographs, and myriad visual interfaces online, in addition to print. Further, the media spectacle of that day ushered in a new, intensified global visual culture heavily invested in articulating—and often actually documenting—disaster and violence. There has been a proliferation of certain types of graphic novels: personal narratives that track loss, war, and displacement, such as Marjane Satrapi's international best seller Persepolis (translated from the French in 2003), documentary comics such Sacco's Safe Area Goražde and Neufeld's A.D., and even sci-fi fantasies riveted to political destabilization and disaster, such as the wildly popular Japanese series Attack on Titan, in which humanity has almost been wiped out by giant creatures called Titans and lives uneasily within three concentric circular walls to keep the monsters out.
Josh Neufeld, page from A.D.: New Orleans After the Deluge (New York: Pantheon), 2009.
© 2009 Josh Neufeld. Used by permission of Pantheon Books, an imprint of the Knopf/Doubleday Publishing Group, a division of Penguin Random House LLC. All rights reserved. Image courtesy Josh Neufeld.
Spiegelman memorably confessed after the publication of In the Shadow of No Towers, his comics volume about witnessing 9/11, "Disaster is my muse." Especially in the personal realm, comics can be so powerful because it presents the texture of real-life disaster and war without sensationalizing violence—and yet without turning away from it. Spiegelman, and Japanese cartoonist Keiji Nakazawa, a Hiroshima survivor, both started making comics in the 1970s about their families' wartime experiences. Their comics sit at the boundary that Spiegelman, in No Towers, calls "that fault line where World History and Personal History collide." And they have been among the most successful cartoonists of all time.
Spiegelman's Polish-Jewish parents, Vladek and Anja, both survived Auschwitz, and gave birth to Art in Sweden in 1948 before settling in Rego Park, Queens, to raise their only child. Vladek and Anja's first son, Richieu, had been killed in the war. Postwar, Anja had multiple miscarriages before conceiving Art (his given name was Itzhak Avraham ben Zev). While Spiegelman and I were working on completing MetaMaus, a book about the creation of and research for Maus that I helped to edit over a period of five years, I asked him what the first entry in the book's chronology should be. "My chronology would start with: When was Kristallnacht?" he responded. In other words, history is so deeply etched into Spiegelman's sense of the shape of his own life that he feels his life begins with the 1938 pogrom in Nazi Germany that is often seen as the beginning of the onslaught of the Holocaust. In "Prisoner on the Hell Planet," a 1973 comics story about Anja's suicide, Spiegelman draws himself as a child, and throughout, wearing the striped uniform of concentration camp inmates—his stripes are a birthright, the story suggests, as he inherits his parents' trauma simply by existing.
Spiegelman has loved comics his entire life. He became obsessed with Mad at age seven when he saw the 1954 Basil Wolverton cover titled "Beautiful Girl of the Month Reads Mad," a famous satire of Life. "I studied Mad the way some kids studied the Talmud!" Spiegelman cracks in his experimental comics autobiography Breakdowns: Portrait of the Artist as a Young %@&*!. At age twelve, he started producing his own comics stories, some with an adorably anglicized name, Art Speg. In this Spiegelman briefly joined the ranks of Stanley Lieber aka Stan Lee, Jacob Kurtzberg aka Jack Kirby, Alfred Caplin aka Al Capp, and Robert Kahn aka Bob Kane, among many others. A local Queens newspaper where he shopped his work as a kid even printed an article about him titled "Budding Cartoonist Wants Attention." Ardently committed to the form, he published in his junior high school newspaper, literary magazine, and yearbook, and also began seeing his work in print in fanzines. (Fanzine is short for "fan magazine," and often gets abbreviated to the simple zine.) At fourteen, Spiegelman published his own hilariously sophisticated-sounding comics satire magazine, Blasé, in editions of about fifty with a hectograph (an inexpensive printing apparatus also known as a gelatin duplicator). Later, while attending Manhattan's High School of Art and Design, from which he graduated in 1965—and which also counts Calvin Klein, Harvey Fierstein, Gerard Malanga, Fab Five Freddy, Lorna Simpson, Marc Jacobs, and the rapper Fabolous as alumni—Spiegelman went back to the local Queens paper, The Long Island Post, and this time got hired as a weekly cartoonist.
While as a teenager Spiegelman's comics career was burgeoning, his awareness of what he would later call "the oxymoron of life in a death camp" was too. Vladek and Anja Spiegelman, in their postwar life, did not explain to their son what had happened to them, and to others, including many, many relatives, in what was then usually called, simply, "the War" ("Holocaust" gradually entered the lexicon in the 1970s). References to their experiences, Spiegelman told me, would surface during his childhood, mostly as confusing "absolutely unconnected moments that invaded my daily life at random." We see this in the remarkable episode Spiegelman draws in Portrait in which Vladek and Anja discuss a former sonderkommando with whom they had just attended a party, who was rumored to have "put to the ovens his own wife and son," in the company of a deeply perplexed eight-year-old Art. But in 1961, when the Adolf Eichmann trial in Jerusalem became an international televised event, Spiegelman, then thirteen (and recently bar mitzvahed), started looking through his parents' "forbidden bookshelf" and discovered images of Holocaust atrocity.
Art Spiegelman, beginning of story "Prisoner on the Hell Planet," Short Order Comix #1, 1973, and reprinted within the pages of Maus I: A Survivor's Tale (New York: Pantheon), 1986, and Breakdowns: Portrait of the Artist as a Young %@&*! (New York: Pantheon), 2008.
© 1972, 1973, 1974, 1975, 1976, 1977, 2005, 2006, 2007, and 2008 by Art Spiegelman. Used by permission of Pantheon Books, an imprint of the Knopf/Doubleday Publishing Group, a division of Penguin Random House LLC. All rights reserved.
Crucially for the field-inventing cartoonist he was to become, Spiegelman didn't only encounter photographic images. Wrestling with the photographic documentation of atrocity is a common loss-of-innocence experience that many including the late Susan Sontag have recounted (she explained in On Photography her life existed in two halves—one before she saw Holocaust photos, and one after). Spiegelman, in addition to photos, also found drawings of life in the camps, done by survivors, which were published in humbly printed small-print-run booklets right after the war. The booklets featuring drawn art that bore witness to daily life during the Holocaust—two of which were named, simply, Auschwitz and Ravensbrück, the names of Nazi camps—fascinated Spiegelman. The booklets, which were largely published by postwar Jewish organizations, showed him for the first time what life must have been like for his parents—and they were, in essence, in comics form. The images drawn by prisoners documented information about daily life that could not have been photographed; there weren't cameras in Auschwitz for inmates. And the images are accompanied by captions, bearing witness in images and words, as Spiegelman's Maus would years later, to the disasters of war. This formative 1961 encounter with atrocity drawings, as we might think of them, is when Spiegelman became the specific cartoonist he would become—someone who would dare to make a comic book about the Holocaust and who could claim "disaster is my muse."
The summer after graduating high school, Spiegelman showed some of his comics to the recently launched Manhattan underground weekly paper The East Village Other, which helped define the ethos of the counterculture. The editor asked him if he could do some strips about sex and drugs. In Spiegelman's account, he didn't know about either, so he enrolled in college to learn about both—while also dodging the draft. (Eventually, his comics started appearing in EVO—and in other underground press publications—around the time he began publishing and distributing unsigned psychedelic leaflets.) Spiegelman's drive to be a cartoonist—despite his father's express desire for him to be a doctor, or at the very least a dentist—held steady at Harpur College (now SUNY Binghamton), where he majored in art and philosophy, kept contributing to fanzines, and was the editor of the college humor magazine, whose name he immediately changed from Toady to Mother. The industrious Spiegelman also, at age eighteen, started work as a creative consultant at Topps Chewing Gum, Inc. His work for Topps lasted twenty-plus years, through the publication of Maus I: A Survivor's Tale by Pantheon in 1986. Spiegelman has been a force on many different fronts of American culture: in addition to work like Maus, which opened the fields of contemporary art and literature to include comics, he developed major fads for Topps like the commercial novelty items Wacky Packages and Garbage Pail Kids.
Few readers of Maus, the best-selling book about genocide and its effects, probably know Spiegelman is the man behind "Leaky Lindsay," "Smelly Kelly," and "Itchy Richie." Garbage Pail Kids "appealed to the inner beast in all kids," as Spiegelman sees it. It was a massive cultural phenomenon in the 1980s. Garbage Pail Kids satirized Cabbage Patch Kids dolls by featuring a series of grotesque child characters identified by their first names; each package contained five stickers and one stick of bubble gum. Topps was Spiegelman's "Medici"—his day job, a commodity enterprise that allowed him to subsidize his own artwork as an avant-garde cartoonist. My favorite GPK, and the most resonant one, is "Adam Bomb." It's the first one Spiegelman sketched and it is not only gross—the standard—but, further, naturally, this kids' novelty item is also about disaster. In the sticker, a blue-eyed child in a rep tie and short suit, like a mock adult, sits on the ground and presses the big red nuclear button as a mushroom cloud billows out of his head, splitting it to pieces above a cracked earth. "A kid literally going nuclear" is how Spiegelman explained the image, which graces the cover of the series's first package. His prototype for what became an enormous commercial fad is yet inflected by the devastation of the atomic bomb in World War II, offering up an exploding child. In Japan, Keiji Nakazawa, Spiegelman's peer in real-life disaster comics—and himself a child survivor of Hiroshima's atomic bomb blast—captured in comics form the on-the-ground perspective of the bombed child in his masterworks I Saw It and Barefoot Gen.
In college in 1967, Spiegelman wrote an art history paper about a highly unusual comic-book story about the disaster of World War II, 1955's "Master Race." His first attempt to articulate the aesthetics of comics was inspired by artist Bernard Krigstein's eight-page work about a Nazi commandant pursued by a Holocaust survivor in a New York City subway (adapted from a script by Al Feldstein). "Master Race" was a rare product of the 1950s that actually addressed the Nazi trauma; it appeared in the mainstream comic-book series Tales Designed to Carry an Impact, #1, published by EC Comics, and along with Anja's postwar survivor-drawn pamphlets, it had a profound effect on Spiegelman's sense of how drawing, and how comics, specifically, could address disaster through formal experiment. Admiring Krigstein's rigorous attention to form, and the composition of the page, Spiegelman quoted the artist in his college paper: "It's what happens between these panels that's so fascinating." While his paper went on to be republished in the college literary magazine and later the EC Comics fanzine Squa Tront, Spiegelman went on to write about Krigstein decades later in the New Yorker. That the war was addressed in comics was a revelation to him; it was like "being struck by lightning." Spiegelman, after all, had grown up in what he once called "the overheated bunker of my traumatized family," with two survivor parents and a ghostly dead brother whose formal portrait loomed prominently in his parents' bedroom. In a commencement speech at SUNY Binghamton, Spiegelman described his experience leaving for college: "Until I left home I thought that all adults screamed in their sleep as my parents did." Harpur kicked him out after he had a nervous breakdown in 1968, during which he spent a month in the Binghamton State mental hospital, where he collected bits of string, paper, and other trash, echoing his father's experience in the camps. On May 21, 1968, Spiegelman's mother, Anja, committed suicide in the family's Rego Park, Queens, home, with pills and a razor blade. She left no note.
A few years after Anja's death, with its shocking perversity—she survived the most notorious Nazi death camp of the Holocaust only to choose to take her own life—Spiegelman was deep into the world of underground comics, living in San Francisco, its center. Some of his dark, taboo-breaking work, while in sync with other transgressive underground titles, feels related to the weight of his parents' history in his life: in one 1971 Viper comic by Spiegelman, a child kills his father and rapes his mother ("Look creep! This tears it!—You've been cramping my style long enough!!!"); in another, a deracinated immigrant character named Willie Wetback (in America Vladek Spiegelman went by William) is himself murdered and raped, in the neck, by the villain the Viper.
In 1972, a friend of Spiegelman's, the confessional cartoonist Justin Green, was editing an underground comics title called Funny Aminals—an adult, edgy take, hence the spelling, on the "funny animals" genre of comics, in which animals live and act like humans (think Donald Duck and his pet dog). The only stipulation for the story was anthropomorphic animals. Spiegelman initially bowed out of the assignment. Encouragement from Green came in the mail in the form of a tab of speed taped to the letter (which supposedly remains, never detached, in Spiegelman's files), and eventually Spiegelman relented. He created a three-page comics story, "Maus," inspired by Green's own autobiographical comic book Binky Brown Meets the Holy Virgin Mary, the first autobiographical comics story, which appeared earlier in 1972 as a forty-four-page stand-alone comic book. "Maus" opens with the frame narrative of a father, drawn as a mouse, telling his son, also a mouse, a bedtime story in Rego Park, about his experiences with his mouse wife, "in the old country" during the war. After seeing early racist animated Farmer Gray cartoons in a film class he audited, Spiegelman had hit on the idea of doing a piece about race in America with Ku Klux Kats, before turning to a metaphor closer to the actual experience of his family—one borrowed, in fact, from Hitler himself, whose racist Nazi propaganda machine proposed Jews were vermin.
"Maus" is a work of testimony, although Vladek Spiegelman is unnamed in the piece. To research the three-page story, Spiegelman visited his father in New York, interviewing him extensively with a reel-to-reel tape recorder over four days. This interview produced the plot of "Maus," and became the core of Spiegelman's interest in his parents' wartime experiences. Anja Spiegelman had often told her son that when he grew up, someday he might be interested in her diaries, in which she chronicled what had happened to her in Poland and Germany. And now, after having earlier tried to escape the weight of his parents' legacy, he was. Although the short "Maus" in Funny Aminals was met with little response—Spiegelman says that his cartoonist friends didn't know how to handle the Holocaust theme, and his father's survivor friends reacted to the story as though it wasn't actually comics, or even visual—Spiegelman realized in his parents' history he had found his voice as a cartoonist.
By 1974, Spiegelman's father-as-mouse, stuck in the wheel of history, had become one of the key characters in his developing comics repertoire. In a drawing for The Apex Treasury of Underground Comix, Spiegelman created an homage to Ernie Bushmiller's 1942 self-portrait in which the artist approaches his characters Fritzi, Nancy, and Sluggo, asking "Who's got a gag for me today?" Spiegelman's take on it perfectly represents the hybrid comics idiom that he enduringly created: high and low, serious and funny, his stable of characters who might provide him with a "gag" are a Cubist-style Picasso woman, a hard-boiled detective named Ace Hole, Nancy, and a wary-eyed Vladek-Spiegelman-as-mouse in a concentration camp uniform. Spiegelman reinvented comics to be not only, as in Crumb, an art form that didn't need punchlines, but further to be an art form that could uniquely express disaster even for an everyday "gag."
With the realization that he had found, within his own family, a story worth telling—and a story that was connected to the open wound of his mother's suicide—Spiegelman began working in earnest on the long form version of Maus in 1979. "I didn't have the stamina to devote myself to a one-hundred-, two-hundred-, three-hundred-page book just to serve up a lot of yuks or escapist melodrama," he told me. He had moved from San Francisco back to New York City, closer to Vladek, whom he continued to interview, and he immersed himself in every shred of Holocaust research he could find, from books and magazines to photographs to films to drawings by survivors. Spiegelman also changed the style of the story for the expanded version. While the three-page "Maus" has a detailed style, with fine lines and cross-hatching, so that the texture of a Nazi coat, or the fur on a mouse's face, is evident, for the longer project Spiegelman spent time developing a looser, sketchier style, which he felt made the work more accessible, and less "masterful" or virtuosic—an aesthetics associated with Nazi ideology. Spiegelman decided to make this accessibility part of the very material production of the work, too: he purchased his supplies for Maus, such as regular typing paper, at a common stationery store, and used one fountain pen for the writing and the drawing. Perhaps most important, in Maus Spiegelman worked at a one-to-one ratio to emphasize the story's immediacy and intimacy—its diary-like, manuscript-like quality. An unusual practice for cartoonists, working at a one-to-one ratio means that the cartoonist draws at the same size at which the work is printed, forfeiting a level of control of detail that composing larger than print offers. Maus clearly reveals comics style as a series of deliberate choices, not simply one person's default way of drawing.
Ernie Bushmiller cartoon self-portrait, 1942, and Art Spiegelman homage, 1974.
Bushmiller cartoon courtesy Comics and Their Creators: Life Stories of American Cartoonists by Martin Sheridan (New York: Luna Press), 1942. Spiegelman cartoon reprinted in Breakdowns: Portrait of the Artist as a Young %@&*!. © 1972, 1973, 1974, 1975, 1976, 1977, 2005, 2006, 2007, and 2008 by Art Spiegelman. Used by permission of Pantheon Books, an imprint of the Knopf/Doubleday Publishing Group, a division of Penguin Random House LLC. All rights reserved.
The first chapter of Maus: A Survivor's Tale appeared in the second issue of Spiegelman and Françoise Mouly's Raw magazine, which serialized the entire work over the next eleven years, minus the very last chapter. Driven by Vladek's testimony, Maus focuses on Spiegelman's parents' journey through the war, and also on how the survivor father and cartoonist son endeavor to understand each other in the wake of shattering experience. Raw, an oversize publication, was founded in 1980 by Spiegelman and his French wife, Mouly, in order to showcase avant-garde "comix and graphix" by presenting them with meticulous, art-book production values. Raw's first subtitle—they changed with every issue—is, movingly, "The Graphix Magazine of Postponed Suicides," a description that cannot help but evoke Anja Spiegelman's suicide, positing comics as a kind of literal lifeline for a son who had also suffered a mental breakdown. Maus appeared in Raw as a small insert booklet within the larger-scale magazine, deliberately evocative of the humble postwar survivor-drawn pamphlets that bore witness to the war, which Anja Spiegelman had brought to the United States from Europe.
Spiegelman and Mouly printed Raw themselves in their Soho loft with a secondhand, thousand-pound printing press that Mouly had purchased and installed in the living room of their fourth-floor walkup. Spiegelman shopped Maus, his work in progress, around to "every reputable publisher" and was rejected by all of them. (MetaMaus reprints about a dozen of the rejection letters.) "You can imagine the response I've gotten from the sales department," one editor explained. "I can't see how to advance the thing into bookstores." Finally, Pantheon—which had already previously rejected Maus—signed the work on after its art director, a friend of Spiegelman's, brought it directly to publisher André Schiffrin. Pantheon released Maus in two book volumes in 1986 and 1991, instead of waiting to collect the entire work after its serialization in Raw. A worried Spiegelman had urged Pantheon that the Steven Spielberg−produced animated kids' film An American Tail, if released before Maus, would overshadow it: both portray Jewish mice, and Spiegelman was convinced that his concept had been lifted for the Hollywood film. Pantheon relented, agreeing to get a Maus volume out into the world before An American Tale hit theaters, after the New York Times ran an unusual feature on Maus that resulted in a flood of public interest. It was unusual because it covered a work in progress; a work in progress in a small press magazine; and, further, a comics work in progress in a small press magazine. Critic Ken Tucker wrote of the originality of the first six chapters of Maus, claiming that Spiegelman's triumph in Maus is that he "tempts sentimentality . . . and then thoroughly denies that sentimentality with the sharp, cutting lines of his drawing and the terse realism of his dialogue."
Maus couldn't exist meaningfully in any other form but comics. Its black line drawing is key to how it creates a compelling world into which the reader is easily invited. Its animal faces and tails—for Spiegelman's characters are clearly humans overlaid with a visual metaphor—provide a crucial level of abstraction that creates a compelling tension with the book's deeply researched historical specificity. And the structuring of the comics page in Maus—what a cartoonist might call its panelization—shows how comics can express the effects of real-life disaster through experiments with time and space. Spiegelman has suggested, "I think anybody who liked what I did in Maus had to acknowledge that it couldn't have happened in any other idiom."
The central proposition of Maus and all of Spiegelman's work is intimately related to representing disaster: it's that the past is never really past. While Spiegelman had the Faulkner quote "writing consists primarily of killing your little darlings" taped above his drawing table when making Maus, to encourage economy, the Faulkner quote in my mind forever tied to Maus is "The past is never dead. It's not even past" (from Faulkner's Requiem for a Nun). In its structure, Maus suggests this, shuttling back and forth between the 1930s and '40s, and the 1970s and '80s, intermixing them, sometimes even on one page, as it delivers both a story of death camp survival in Poland and of an artist son struggling to represent something unimaginable in America. Within the pages of Maus, the horror of Vladek's past—the murderous disaster of the Holocaust that Spiegelman has called "the center of history's hell"—invades the present, refusing to stay separate or closed off. The subtitle of Maus's first volume is My Father Bleeds History.
Maus's form is indissociable from what it suggests about history, testimony, and the war. One of the most forceful formal devices of comics is how it can dramatically collapse or crush different moments of time together. In Maus, the past and present bleed into each other, just as the Art character makes his father "bleed history" in their interviews. In some instances, Spiegelman creates a physical connection between panels set in the past and panels set in the present, linking them, as in the panel in which Art's cigarette smoke is figured as the smoke coming out of an Auschwitz crematorium chimney directly below it on the page. But in others, he exploits the language of comics—the convention that each panel represents a distinct moment of time—to make two different time periods literally intertwine. We see this in the striking page in which Vladek, Art, and Françoise—herself a character in Maus—converse in the Catskills during a summer visit to Vladek's bungalow. On their way to the supermarket in the car, Art changes the topic from his stepmother, Mala, to Auschwitz, asking his father about a prisoner revolt. The last panel of the page, in which Vladek describes its fallout, is its largest: as the family car weaves through dense rural roads, the legs of four Jewish girls hanged in Auschwitz after the revolt—witnessed firsthand by Vladek—suddenly appear dangling from the trees. The 1940s and the '70s collapse, as Spiegelman shows, wordlessly, how the traumatic past lives on in the present.
Art Spiegelman, page from The Complete Maus: A Survivor's Tale.
Maus, Volume I © 1973, 1980, 1981, 1982, 1983, 1984, 1985, and 1986 by Art Spiegelman; Maus, Volume II © 1986, 1989, 1990, and 1991 by Art Spiegelman. Used by permission of Pantheon Books, an imprint of the Knopf/Doubleday Publishing Group, a division of Penguin Random House LLC. All rights reserved.
Instead of trying to reproduce the camps visually, as many films do, Spiegelman sees that Maus, as he told me, rather "creates [the camps] as a mental zone." In the reader's first encounter in the book of being inside the gates of Auschwitz, Spiegelman divides the page vertically. Here, unlike the page set in the Catskills, one is prompted to read top to bottom instead of left to right. In the first slim vertical column, in the 1980s, he and his father converse about the camps while walking outside. If one follows the page's panel structure one is next quickly dropped into Auschwitz in another vertical configuration, as though dropping down a chute, into larger spaces in which screaming is immediate and the movement of the reader from panel to panel follows the movement of dressed individuals helplessly becoming naked. A Nazi guard anchors the lower right corner, where the page ends, impeding any sense of relief, as though blocking our optical exit with his body. Spiegelman traps a reader's eye in the camps, using the space of the page to create a feeling of claustrophobia. Maus exploits what Spiegelman calls "the secret language of comics" to express the fear his father felt. "I was at the Frankfurt Book Fair when [Maus] came out," Spiegelman told me, "and was aggressively barked at by a reporter, 'Don't you think that a comic book about Auschwitz is in bad taste?' I liked my response. I said, 'No, I thought Auschwitz was in bad taste.'"
Art Spiegelman, page from The Complete Maus: A Survivor's Tale.
Maus, Volume I © 1973, 1980, 1981, 1982, 1983, 1984, 1985, and 1986 by Art Spiegelman; Maus, Volume II © 1986, 1989, 1990, and 1991 by Art Spiegelman. Used by permission of Pantheon Books, an imprint of the Knopf/Doubleday Publishing Group, a division of Penguin Random House LLC. All rights reserved.
After Maus, it took another disaster on a global scale—the terrorist attacks of 9/11—to inspire Spiegelman to create another major comics work. Spiegelman had hardly been slacking off: he illustrated The Wild Party, a 1928 narrative poem; he became a staff artist for the New Yorker; edited several collections of work; wrote meaningful essays; and published a kids' book, among other projects. But as he told the New York Times, "So far it has been the painful realities that I can barely grasp that force me to the drawing table."
Spiegelman, who lives in lower Manhattan close to the World Trade Center, and whose daughter Nadja attended high school three blocks away from Ground Zero, was an eyewitness to the attacks in New York City on the morning of September 11, 2001, watching the North Tower collapse before his eyes as he and his family ran. In the days after the attacks, most New York City—and national—media outlets struggled with what aesthetic choices felt tonally appropriate to the gravity of the situation. Spiegelman produced, in collaboration with Mouly—who is currently art editor of the New Yorker and chooses and edits its cover every week—his iconic "black-on-black" 9/11 cover. At a loss for how to represent this disaster, the New Yorker top brass had considered publishing a photographic cover for the first time in its history. Spiegelman and Mouly's ghostly cover is a masterpiece of simple, striking graphic design by a cartoonist who had thought for decades about how to maneuver between presence and absence. The Twin Towers are silhouetted in black against a black background, almost like two empty comics panels with a gutter between them. One of the most important features of comics and graphic novels since 9/11—a feature that began with the field-defining Maus in the 1980s—is their insistence on doing the work of picturing, however complicated or contingent. This investment in revealing through showing pushes back against a culture that often valorizes traumatic absence and censorship (as the censorship from American newspapers of the "falling man" photograph of the man who had jumped from the North Tower, by the Associated Press's Richard Drew, demonstrates).
Running from a toxic cloud in downtown Manhattan on 9/11, Spiegelman encountered the feeling that his Auschwitz survivor parents' fear and fatalism were well founded. "Because I grew up with parents who were always ready to see the world grid crumble," he told NPR, "and when it started feeling that that was happening here and now, it wasn't a total surprise. . . . I think the one thing I learned from my father was how to pack a suitcase. You know? It was the one thing he wanted to make sure I understood, like how to use every available centimeter to get as much stuff packed into a small space as possible. The ice might be thinner than one would like to think." Spiegelman felt freshly, painfully connected to disaster, in addition to furious at the United States government's hypocritical discourse, cheap patriotism, and international policy. (Around this time, he quit the New Yorker because he felt it was too politically complacent.)
Art Spiegelman and Françoise Mouly, "9/11/2001," cover of the New Yorker, September 24, 2001.
© Art Spiegelman and Françoise Mouly/The New Yorker Collection.
Spiegelman started making ten large-scale comics pages called In the Shadow of No Towers: "If I thought in page units," he recounted thinking, "I might live long enough to do another page." Spiegelman found that his comics probing the effects of the 9/11 disaster on one person and on a nation were rejected by editors who had previously solicited his work. His "shrill, sky-is-falling voice," as he describes it, caused American editors to flee. Spiegelman's pages were originally published serially and sporadically in European venues such as Die Zeit in Germany; and in a few United States venues, like the Forward, the Jewish weekly; and the LA Weekly, an alternative paper. While over fifteen years after 9/11 the content of Spiegelman's critiques have become part of regular political discourse, he stood out in the aftermath, along with others like Sontag, as a media voice willing to openly critique American attitudes. The ten pages, large, dense, and colorful, were collected as a heavy oversize board book in 2004. In the Shadow of No Towers is 10 by 14.5 inches, and folds out so that each page is 20 inches tall, evocative of a newspaper broadsheet. The ten twenty-first-century comic strips are followed by reprints of seven old newspaper comic strips from the turn of the century. As ever, Spiegelman is motivated to articulate the links between the present and the past, something we see even in the book's structure.
Spiegelman absorbs his father's lesson on how to use a suitcase's every centimeter in In the Shadow of No Towers, transfiguring a mandate based in traumatic history into a formal principle that conveys traumatic experience in its density. No Towers offers complex, swarming pages with tightly packed panels that pressurize linear reading. Comic strips are embedded within other strips; in some cases, one has to turn the book upside down to read it, suggesting that no one perspective can ever be correct. And the style changes throughout, even in the space of one page, frequently mimicking early twentieth-century cartoonists like Winsor McCay (Little Nemo in Slumberland) and George McManus (Bringing Up Father). The tenth and final No Towers page looks, perhaps, its cleanest—its basic composition evokes Spiegelman's black-on-black New Yorker cover. Yet this page dramatically expresses the feeling of time that attends to disaster: how time can be both scrambled, and also "stopped."
When one looks at this page, one can recognize right away that Spiegelman has drawn the Twin Towers of the former World Trade Center—the iconic antenna spire of the North Tower conspicuously pokes up out of the space of the page on the right-hand side. He draws them, it seems, as two big juxtaposed comics panels, and each is subdivided by its own panel. The sets of panels within panels each tell a narrative that moves forward in time, descending downward from the top, from left to right. In the first, Spiegelman describes a disappointing post-9/11 television interview; in the second, he morphs into earlier American comics characters, including from his own Maus story.
While the strip offers two narratives that move forward within the space of buildings, it also, outside of its enclosed collection of frames, displays one moment suspended in time. The building panels stand against a blue sky; a plane swoops in through the blue of the gutter in between the buildings, frozen in the moment before it hits the North Tower. We have at least three temporalities, or time periods, here: the left series of frames, the right series of frames, and the moment happening in the gutter between the buildings, which itself is multiplied: the North Tower, the first one to be struck, is about to be hit but below on the ground the fires have already begun. While narratives generally move forward in time, here time is arrested and reversed. In this way the page makes overt the symptoms of trauma, specifically time as both frozen, and as "aiming backwards instead of forwards," as Spiegelman put it in a talk about 9/11 titled "Ephemera vs. the Apocalypse." There's an indication of a "fade to black" ending within the sequence of frames, but outside of them the towers are still unceasingly burning. Through the play of internal and external space on the page, Spiegelman splinters time and states of reading: the page suggests movement and stillness at once; it asks us to recognize its elements as one integrated image—an image of the Twin Towers—and also, its set of cues asks us to follow its successive frames within them. Spiegelman slows the reader down in order to convey the effects of trauma and disaster.
Art Spiegelman, double-spread page from In the Shadow of No Towers (New York: Pantheon), 2004.
© 2004 Art Spiegelman. Used by permission of Pantheon Books, an imprint of the Knopf/Doubleday Publishing Group, a division of Penguin Random House LLC. All rights reserved.
While in America Spiegelman demonstrated how comics expresses real-life disaster in forceful ways other forms cannot, in Japan Keiji Nakazawa, a Hiroshima survivor, created comics about the atomic bomb that changed the way people looked at comics—and nuclear power. Nakazawa and Spiegelman—an atomic bomb survivor and a second-generation Holocaust survivor, respectively—are the cartoonists who, from opposite ends of the globe, re-created contemporary expectations for comics. Nakazawa, a hibakusha, which literally means "explosion-affected person," was born in 1939, in Hiroshima City. Nakazawa became a best-selling antinuclear crusader through his comics before dying in 2012 of lung cancer in Hiroshima. He inaugurated so-called atomic bomb manga, which changed cultures of expression in Japan and across the globe. Manga—the term translates loosely to "whimsical pictures"—refers, as a general matter, to comics from Japan; it has been in use for centuries. Nakazawa's pioneering documentary work, beginning in the 1970s, made comics a form that could bear witness to the trauma of atomic warfare. In 1972, the same year as Spiegelman's short "Maus," Nakazawa published Ore wa Mita, or I Saw It, Japan's first autobiographical comic book about the atomic bomb. Nakazawa's title evokes Spanish artist Francisco de Goya's caption ("Yo lo vi") that appeared in his nineteenth-century series of etchings, The Disasters of War, which has become famous as a profound work of witness to violence. The related, ten-volume series Barefoot Gen (like Spiegelman's full-length Maus, a continuation of his earlier work) is Nakazawa's semiautobiographical story about the bomb that was the very first book-length manga ever translated into English, in 1978. It was translated by an all-volunteer, international group of peace activists working under the name Project Gen.
August 6, 1945, 8:15 a.m.: At the moment the B-29 Enola Gay dropped the atomic bomb code-named "Little Boy" on Hiroshima, Keiji Nakazawa, age six, was walking to school from his home in the Funairi Hommachi neighborhood. By chance, the mother of a classmate asked Nakazawa a question when he was just outside his schoolyard's concrete wall (and less than one mile from the bomb's hypocenter). When the bomb detonated, Nakazawa was spared: the wall fell on him, absorbing the shock and shielding him from the heat, while she and many thousands of others died immediately. Over seventy thousand people were killed instantly, with as many perishing afterward from radiation sickness. Nakazawa's father, Harumi, older sister Eiko, and younger brother Susumu died that day. The Nakazawa house collapsed on them, and then went up in flames, while Keiji's pregnant mother, Kimiyo, watched helplessly. Kimiyo, known as Kimie, gave birth that day, induced by shock, to a baby girl who died of malnutrition four months later. (Two of Keiji's older brothers were away from Hiroshima that day and survived.)
As a boy after the war, Nakazawa could not afford paper to draw on, so he tore down movie posters from city streets and handcrafted books from them. He would cut the posters to size, stitch them into notebooks, and pencil in his comics illustrations on their white backs—his own homemade comic books. Upon graduation from junior high school, Nakazawa started work as a sign painter. In 1961, at age twenty-two, he moved to Tokyo in order to start a career as a cartoonist. Nakazawa found, in Tokyo, which had been firebombed during the war, that the prevailing mode of managing the legacy of the atomic bomb was silence and disengagement. In the early and mid-1960s, Nakazawa met many Tokyo residents who were openly disdainful of hibakusha, and believed, mistakenly, in the rumored transmissibility of radiation—"atomic bomb disease" in which one could "catch" radiation. Nakazawa resolved while in Tokyo, indeed, he would never again say "atomic bomb" out loud; he even refused to read newspaper articles with the characters "atomic bomb," and decided to hide the fact that he was a hibakusha. In his early career in comics, Nakazawa worked in conventional genres. As he describes it, "Sci-fi, baseball, samurais . . . I'd try my hand at anything." He eventually refigured the boys' action genre to include large-scale real-life disaster.
Kimie Nakazawa died in 1966 from the leukemia so common to hibakusha; she suffered a cerebral brain hemorrhage during ongoing treatment at the Atomic Bomb Survivors Hospital in Hiroshima. In a standard Japanese funeral, after a body has been cremated, relatives pick out the major bones and place them in an urn. When Nakazawa went to the crematorium to collect his mother's ashes, he explained, he was shocked that "there were no bones left in my mother's ashes, as there normally are after a cremation. Radioactive cesium from the bomb had eaten away at her bones to the point that they disintegrated. The bomb had even deprived me of my mother's bones." The atomic bomb had taken every vestige of his mother, not only her life but her very bones, her materiality, leaving Nakazawa nothing to hold on to. After his mother's death, Nakazawa reimagined his mission as a cartoonist: the atomic bomb would be his central subject.
His earliest narratives about Hiroshima, in the late 1960s, were fiction. Nevertheless, they were seen as so radical that the only place Nakazawa could print them was in "adult" (meaning "erotic") magazines. (Immediately after World War II, the United States occupation of Japan imposed censorship on publications depicting suffering. Mandated by the US administration but endorsed by both sides, it persisted long past the end of the US occupation of Japan in 1952.) If he was to publish comics about the bomb, it would have to be in "third-rate" magazines, what were known as "lowbrows."
In 1970, still motivated by the urgency of addressing the bomb, Nakazawa published the fictional Suddenly One Day, an eighty-page story about a second-generation bomb victim, in Boys' Jump (Shōnen Jump). Boys' Jump was, to quote two critics writing on Nakazawa, "at that time disdained as an extremely vulgar medium," but a popular one: in 1970, Boys' Jump sold a million copies each week. Suddenly One Day produced, to Nakazawa's surprise, a large reaction—he describes that "mail poured in virtually every day, from all over Japan." The reaction emboldened Nakazawa, even if it brought the criticisms of his neighbors, who accused Nakazawa and his wife, whom he had married in 1966, of bringing shame on their families. Nakazawa resolved to continue creating comics about war, aided in part by supportive editors. In 1972—the very same year that Spiegelman was spurred on by Justin Green persistently knocking on his door, asking for a contribution for Funny Aminals—an encouraging Japanese magazine editor planned to publish a series of autobiographical manga, and asked Nakazawa to be the first in the series. I Saw It, Nakazawa's eyewitness account of August 6, 1945, was published as a black-and-white, stand-alone, forty-five-page issue of Boys' Jump Monthly in October 1972. With this publication, Nakazawa forcefully invented comics in Japan as a form of witness to disaster.
Keiji Nakazawa, page from I Saw It, 1972, English-language edition (San Francisco: Educomics), translated from the Japanese, 1982.
Used by permission of Misayo Nakazawa, arranged with Japan UNI Agency, Inc.
I Saw It is the first autobiographical comics work about the atomic bomb, and it established a significant, unflinching visual idiom of disaster, detailing harsh suffering on the ground. A landmark work in Japanese documentary comics, I Saw It challenged a national culture that viewed the atomic bomb with distortion, stigma, and silence. I Saw It begins and ends within that present-day culture, in 1970s Tokyo: in a frame narrative, an adult Nakazawa walks through the streets, replaying his mother's painful final years. Abruptly, the frame narrative shifts back to the year 1945, but not to August 6 or the bomb: I Saw It presents scenes of the Nakazawa family's everyday life, of joy amidst hardship, of routines in a Hiroshima beset by air raids and scarcity.
But those rhythms of daily life are eventually disrupted by the events of August 6, 1945, a day which takes up thirteen pages of I Saw It's forty-five, starting with Keiji's first sighting of the Enola Gay approaching, and the bomb's fall, detonation, and flash. (In Japan, the bomb blast became known as pika or pika-don—pika means brilliant light, and don means boom.) The page that shows the bomb detonating illustrates how comics narrative can capture what we might think of as both exterior and interior trauma. As we can see on this page, I Saw It races back and forth between perspectives: if one panel pictures the narrator's body on the page, the very next pictures his own optical perspective. To depict the tremendous, white-hot flash of the bomb's detonation, Nakazawa draws it overpowering a narrow, elongated panel, which is stamped in the upper-right corner with the explosion's exact time: 8:15 a.m. Simultaneously, the image records one young boy's act of eyewitnessing and acts as a historical marker of a momentous event. On the upper-right corner of the page, in the same tier as the flash, is an even more commanding panel that captures the expressionistic sights Keiji saw just before falling unconscious: a tree severs in two, a torrent of roof tiles rushes by. It is the kind of image that can't be photographed, and that is seared into one's memory. As with the drawings of the camps Spiegelman found on his parents' bookshelf, drawing can capture the vividness of memory—especially memory formed during sudden traumatic events—in a way photography cannot. Comics, in Spiegelman and Nakazawa's hands, becomes a form of witness to unphotographable events.
In I Saw It the detonation is overwhelming, unthinkably accelerated—the aftermath, conversely, plays out slowly, with Nakazawa gradually, assiduously taking in all of Hiroshima's drastic changes, from his child-eyewitness's terrified perspective. I Saw It is famous for its unflinching drawings of wrecked bodies. No artist had drawn images quite like Nakazawa's before: on the one hand, they might seem to recall science fiction (in censorship-era Japan, a hugely successful genre) in their unconcealed, straightforward horror. But in the devastated Hiroshima of I Saw It, that horror is real: "Everybody's turned into monsters!" Keiji exclaims. Nakazawa's commitment to clarity, to presenting the grotesque in all its fidelity, is what makes I Saw It powerful. His direct, unadorned style—his images are neither abstractly stripped down, nor are they ornamentally detailed—showed the world how comics could relay the terror of an event like the atomic bomb blast from the first-person perspective of one of its victims.
In the wake of the disaster wrought by weapons technology, Nakazawa responds by engaging the humble technology of paper and ink. He counters the most high-tech of high technology, the atomic bomb, and the menacing march of scientific progress it represented, with the deliberately low-tech, primary practice of hand-drawing. His intervention, like Spiegelman's, resides not only in the political content of his work, but also in his invention of a confrontational, revealing graphic idiom for disaster. Barefoot Gen, the longer work inspired by I Saw It, is one of the most famous, and by some accounts the most popular, manga in Japanese history; it has sold over eight million copies. Now a monumental work in Japanese culture—it was the first manga used in Japanese schools in the 1970s—it is also one of the few manga in translation worldwide, available in over twenty-one foreign editions.
Gary Panter, sketch. Published in Satiro-Plastic: Sketchbook Facsimile (Montreal: Drawn & Quarterly), 2001.
Used by permission of Gary Panter.
The connection that Spiegelman and Nakazawa reveal between comics and disaster shifted not only how the comics field saw itself, and how the public viewed comics, but also, even more important, how people think about the creative practice of communicating difficult, or traumatic, experience. In the wake of their influential works, there exist many, many comics about trauma—and for a good reason. This handmade form is able to explore violence without sensationalizing it. It can express the multifaceted experience of trauma—and the disaster of history—in its grammar of boxes, gutters, and lines. Since Spiegelman and Nakazawa's major works have been published, many more Holocaust comics, 9/11 comics, and atomic bomb comics have appeared. (And as the historian author of the book Atomic Comics points out, atomic radiation specifically has been foundational to American comic books, as we see in the origin stories of heroes across the decades from Buck Rogers to Spider-Man to Watchmen's Dr. Manhattan.)
Now, for instance, there is a whole subfield of comics about Anne Frank, including three separate works from Japan. In the United States, comics treating 9/11 have also come into view as a distinct subfield, from superheroes to the comics adaptation of the official 9/11 Commission Report to memoirs like Alissa Torres and Sungyoon Choi's American Widow. One of the most moving, to me, is cartoonist Gary Panter's series of real-time, rapid pen drawings of what he was seeing unfold from his Brooklyn rooftop on the morning of September 11, 2001. It is published, like Maus, at a one-to-one ratio. Known for introducing an expressively shaky line in comics, these drawings, he said, are the shakiest he's ever done. Unlike a photograph, the drawings encode the passage of time, the urgent race to capture what the eye, improbably, sees before the cityscape disintegrates. "I was actually crying and screaming and falling down while I was drawing those drawings," Panter said. "It is like, 'Okay you are going to die in a minute, what do you want to do?' I'm going to draw."
---
WHY SUPERHEROES?
While cartoonists Gary Panter and Art Spiegelman captured their experiences of 9/11 in highly personal comics, the mainstream comic-book companies Marvel and DC, which specialize in superheroes, also addressed the disaster. Both Marvel and DC were then headquartered in New York, and their writers and artists worked hard to respond and to quickly produce work that would engage 9/11 head on. Marvel's The Amazing Spider-Man #36, written by J. Michael Straczynski and illustrated by John Romita Jr., appeared a few months after 9/11 with the large white letters of the title and a plain black background—likely a nod to Spiegelman's black-on-black New Yorker cover. It became famous for having its titular hero admit a new kind of helplessness. And Superman, in a collection of 9/11 stories published by DC, speaks directly to readers: "The one thing I cannot do . . . is break free from the fictional pages where I live and breathe . . . become real during times of crisis." In the wake of the 9/11 attacks, what feels salient isn't that a genre of fiction featuring fantastical disaster-averting crime-fighters was under pressure, but rather that the public after 9/11 even looked to superhero comics at all for any kind of official response, especially—or maybe because of—the fact that so many ordinary, real-life citizens during the attacks were designated heroes.
Since the invention of the comics superhero in America in 1938 and right up to the current moment, the appeal of superheroes has not only persisted through wars, global crises, and shifting social values, but it has flourished. Whether superpowered, like Spider-Man (Peter Parker), or "just" a regular human, like the superrich and superfit Batman (Bruce Wayne), the figure of the superhero has become a deep, integral feature of American culture. This is regardless of the percentage of the public who has actually read a comic or seen the outsize, blockbuster movies (several superhero films, including two Avengers films, are on the top ten list of the world's highest grossing films of all time; Patty Jenkins's 2017 Wonder Woman is the highest-grossing live-action movie ever from a solo female director). Superheroes are a typological category and a cultural truth. The permeation of American culture with the superhero is so profound that even the genre's seemingly esoteric lexicon has been publically adopted. It has become standard for people of all sorts to refer to "kryptonite," for instance, as a synonym for a potential weakness (one of countless examples ripped from the headlines: in 2016 Kobe Bryant told the New York Times a public embrace early in his basketball career "would have been kryptonite"). Kryptonite is, of course, material from Superman's home planet Krypton—the only real threat to his invulnerability, with the ability to debilitate him, leeching away his powers.
Perhaps the enduring appeal can be traced to the origin story of superheroes themselves, which itself feels like an archetypal superhero storyline. The world's inaugural superhero is Superman, also known as Clark Kent (birth name: Kal-El, likewise the name actor Nicolas Cage gave his son), and as a character he had modest beginnings. Superman was the brainchild of two shy, bespectacled, lower-middle-class Jewish teenagers from Ohio, Jerry Siegel and Joe Shuster, whose first incarnation of the character appeared in their own self-published magazine (or "zine") in the 1930s—before Superman began his iconic and field-creating reign as the world's first superhero and comic-book star. Siegel, the youngest of six children born in Cleveland to Jewish Lithuanian immigrants, met Shuster at age sixteen, when both were students at Glenville High School. Siegel, an active science fiction fan, worked at the student paper. Shuster, an artist, had come to Cleveland from Toronto with his own Jewish immigrant family at about age ten (his father, born Shusterowich, hailed from the Netherlands, and his mother from Ukraine). Shuster, as a child, drew on the walls of the cash-strapped family's home, and scrounged for paper that had been thrown out in the garbage of Toronto shops. He described finding unused wallpaper rolls, with their blank backs, as a "gold mine" (a description reminiscent of Keiji Nakazawa searching the street for paper for his own comics).
In 1932, Siegel's father, Mitchell (whose given surname was Segalovich), died when his secondhand-clothes store in Cleveland was robbed at night. While the family was told he died of a robbery-induced heart attack, bystanders heard shots, and the exact cause of his death remains a mystery. The following year, Siegel and Shuster collaborated on "The Reign of the Superman"—a prose story by Siegel illustrated by Shuster in their fan magazine Science Fiction. In this earliest version, which explored the idea of superhuman power, Superman was a villain (and bald!). In 1934, reportedly at night when he couldn't sleep, Siegel imagined the Superman hero as we know him today, and Shuster in turn drew him. It took the two a couple of years to sell their Superman work, but finally, in 1938, Superman appeared on the cover of Action Comics #1, published by Detective Comics, the company later known as DC. (Sadly, Siegel and Shuster sold all rights "forever" to their character to DC for $130; after he became a success, their legal battles over years with DC for money and credit yielded very little, although the actual $130 check itself sold at auction in 2012 for $160,000, none of which came to them, either.)
Superman's invulnerability—including to bullets—and the loss of his family and homeland resonate directly with Siegel's experience losing a father to crime. Some of the earliest sketches of the character include him intervening in robberies involving guns. The writer Brad Meltzer, whose novel The Book of Lies fictionalizes Mitchell Siegel's murder, points out that in fifty years of interviews, Siegel never once mentioned his father died during a robbery. "But think about it. Your father dies in a robbery, and you invent a bulletproof man who becomes the world's greatest hero."
Superman was immediately hugely popular, selling out the print run of Action Comics. Siegel and Shuster cast him as a "champion of the oppressed"—he has been called a junior New Dealer. In his first storyline, for instance, Superman saves a falsely accused prisoner from a lynch mob, produces evidence that frees an innocent woman from death row, and defends a woman about to be abused by her husband. In other stories, he does things like demolish an unsafe housing project and destroy a car factory that uses cheap, dangerous materials. Superman became the first comic-book character to merit his own title: Superman was launched in 1939. In the wake of his success superheroes proliferated: Batman, a more noirish figure, appeared in 1939, and the Flash in 1940, both from DC. In 1941, in March, Captain America appeared, punching Hitler on the famous cover; he was joined that same year by Wonder Woman (whose invention by the Harvard-educated psychologist William Moulton Marston, also the creator of the polygraph test, is the subject of Jill Lepore's 2014 book The Secret History of Wonder Woman). Superheroes joined the war effort in full force, fighting Nazis even before the United States entered the war, as we see with Captain America, and afterward influencing GI culture and boosting patriotism at home. In 1942 there were fifteen million comic books sold each month, and this number grew steadily for the next decade.
Despite the censorious Comics Magazine Association of America Comics Code brought on by Senate hearings in 1954, which all but erased certain genres like horror comics, superhero comic books did arrive at a commercial Silver Age. In the Silver Age, which was responsive to postwar social conflict and change, superheroes were represented as essentially neurotic. The Fantastic Four, created by Stan Lee and Jack Kirby in 1961, offered the world a team of angsty superheroes, and Marvel continued the trend by introducing the Incredible Hulk, known for his anger, and Spider-Man, a worried teenager, in 1962; the X-Men and Iron Man in 1963; and Daredevil, a blind superhero, in 1964. While DC has the classic "Big Three"—Superman, Batman (now perhaps more profoundly associated with the amusing term manpain than any other superhero), and Wonder Woman—Marvel has a lockdown on a stable of characters whose anxieties about identity and inclusion continue to resonate deeply. And while sometimes DC can seem like the staid sister to Marvel, DC was responsible for Watchmen and Batman: The Dark Knight Returns. These two works marked a shift, in 1986, toward pessimistic, brooding—and in Watchmen's case, near or fully psychopathic—superheroes, a shift that created an uptick of attention to the figure of the superhero in popular culture.
Watchmen takes place in an alternate, dystopian United States in 1985 during the height of the Cold War. In this version of history, the United States won the Vietnam War with help from the irradiated superhero Dr. Manhattan, along with a fleet of "Costumed Adventurers," some of whom wield their power with abandon, some of whom don't ("Who watches the watchmen?" a recurring phrase in the story, refers to Roman poet Juvenal's famous question). Nixon is still president. Watchmen, which is deeply violent, is about the nature of authority and morality—superheroes, in the present tense of the book, have been outlawed, but many do their (dirty? necessary?) work anyway. It is also a dense self-reflexive comic book about the creation of the superhero concept and comics, bringing a complex richness to the superhero enterprise.
Yet while the superhero genre continues to be popular, and to evolve, a significant feature of the very notion of comics for grown-ups is a rejection of the idealization of men in tights (and women in leotards). The prevalence of superheroes in the United States—indeed, their glutting of the mainstream industry—guides perceptions of comics in America as largely for a juvenile market. Historically, Europe, for instance, despite a rich comics tradition, can claim no indigenous superhero comics on a par with the popularity of American superheroes. The critic Pascal Lefèvre, remarking in an online discussion list for comics scholars, reveals a common disdain for the oppressive ubiquity of the superhero: "In Europe, more precisely Belgium, we have a quite different comics culture. American superheroes were—thank God!—over here never big." (What was big: The Adventures of Tintin, by Belgian cartoonist Hergé, which began in 1929.) That other countries have not participated to the same degree in the United States' superhero obsession may be one reason comics is taken much more seriously by readers and critics in other parts of the world, like Japan and across Europe. (French philosopher Roland Barthes wrote of the potential of comics in 1970; at the Sorbonne in Paris, comics was introduced as an area of study at the Institut d'Art et d'Archéologie in 1972, and university degrees in the study of comics are available throughout Europe.) Another critic puts it well in stating of the superhero that its "very familiarity . . . makes it the medium's curse."
Cartoonist Daniel Clowes, the creator of Ghost World and one of the most celebrated proponents of the literary graphic novel, once told me, laughing, about carving out a space for nonsuperhero comics in the 1990s. "I just felt like the comics I was doing had nothing at all to do with the marketplace I was being thrown into," he explained, "and I'd find myself having to go to these comic-book conventions, and sitting next to some guy who was drawing, like, twentieth-rate superhero comics, and he'd have a line out the door, and I'd have nobody. I thought I was doing stuff that would draw as big an audience as some really specific weird superhero, and yet, no. I was wrong." The comics output of many of today's literary cartoonists, Clowes among them, was and continues to be positioned against superheroes. For some creators, superheroes remain vital. Comics writer Grant Morrison, for example, describes their enduring and widespread appeal movingly. "In a secular, scientific rational culture lacking in any convincing spiritual leadership," he writes, "superhero stories speak loudly and boldly to our greatest fears, deepest longings, and highest aspirations. They're not afraid to be hopeful, not embarrassed to be optimistic, and utterly fearless in the dark." For other creators, though, including Clowes, investigating failure and doubt is an alternative to such storylines.
But superheroes have not gone away in today's graphic novel world. Instead they remain as a force to counteract, often motivating its storylines about failure and antiheroic figures. The literary graphic novel's angle might be called anti-superheroic. We see this in the work of two of the cartoonists at the forefront of the rise of the auteurist graphic novel—in other words, comics as a high-literary form created by a single artist, unlike the commercial, team-driven production of superhero comics. Chris Ware, whose experimental graphic novels (and short-form New Yorker pieces) have forcefully staked out space for comics's literary complexity, and Clowes, whose vast accomplishments across the realms of comics, fine art, and film include the prestigious PEN Literary Award for Graphic Literature (awarded by the American branch of the world's leading literary and human rights organization), were obsessed with superheroes as kids, and take them on in their adult graphic novels, revealing how comics for grown-ups enlist the superhero figure—in order to reject it.
Superheroes are a major theme of Ware's first graphic novel, the breakthrough Jimmy Corrigan: The Smartest Kid on Earth, released by Pantheon, the publisher of Maus, in 2000 as a lavish, colorful hardcover. Jimmy Corrigan was received in ways that mark it as much, much different than a superhero comic: original pages from Jimmy Corrigan were exhibited as part of the 2002 Whitney Biennial, the first time comics were included in the museum, and it won Britain's prestigious Guardian First Book Award—the only graphic novel ever to have done so—as well as an American Book Award. Jimmy Corrigan made even noncomics fans gasp at its intricacy, stunning graphic design, and emotional texture, ushering in widespread excitement about the future of the graphic novel in the twenty-first century—and it engages with the figure of Superman in unexpected ways. "There may never be another graphic novel as good as Jimmy Corrigan, even by Ware himself," wrote the New Yorker art critic Peter Schjeldahl.
Before Jimmy Corrigan became a phenomenon, Clowes's renowned Ghost World, which appeared from independent comics publisher Fantagraphics in 1997 and remains their best-selling title of all time, showed audiences how sensitive, funny, and true-to-life a graphic novel could be. It was made into a film starring a teenage Scarlett Johansson and Thora Birch in 2001 with Clowes's participation; he was nominated for an Oscar for Best Adapted Screenplay. Clowes went on to publish a series of successful, savvy, and wry graphic novels, including the satirical Ice Haven (2005), which unfolds the mystery of a small-town kidnapping, and the grim Wilson (2010), a portrait of a middle-age misanthropist that was adapted for film. In 2011 Clowes published The Death-Ray, a graphic novel that features a dark, teenage superhero. For years he had explained what his work was about by describing it "as opposed to the mainstream comics—'Mainstream comics are about superheroes, my work is about other stuff. You know, the opposite of superheroes!' " But with The Death-Ray, Clowes came clean about the fact that that wasn't really true. With his own take on a superhero comic, and with Ware's, we see how two exemplars of sophisticated comics for grown-ups—spokespeople, practically, for the phenomenon—actually engage the genre of superheroes in order to create comics that focus on anti-superheroes.
Chris Ware, at forty-nine, is the most celebrated cartoonist since Spiegelman and Robert Crumb, the artists who spearheaded the field of literary comics. Ware got his big break in Spiegelman and Françoise Mouly's Raw magazine (which ran from 1980 to 1991). In addition to serializing Maus, Raw launched Ware's career along with that of Charles Burns, Ben Katchor, Gary Panter, and many, many, others. Born in Omaha, Nebraska, and raised by his mother and, intermittently, a stepfather, Ware was discovered while he was still a student at the University of Texas at Austin when Spiegelman saw his comics on the reverse side of a tear sheet review of Maus in the college newspaper, The Daily Texan. Spiegelman was so impressed that he called Ware on the telephone, deeply freaking Ware out, and invited him to contribute to Raw, a publication Ware admired. Ware, who at first thought the call was a prank, said he wasn't ready. Eventually, Ware did contribute to Raw, with "Waking Up Blind," in 1990, which featured a potato-shaped protagonist trying to keep his eyes in his head (Ware dislikes this work so much now that he has requested that I not reprint it when I've asked). Ware's artistic breakthrough came with "Thrilling Adventure Stories (I Guess)," his second story in Raw, in 1991, the same year he began grad school at the School of the Art Institute of Chicago. (The shy Ware, a printmaking major, dropped out in 1993, because he could not bear, by his own account, to give a required oral presentation.) The six-page black-and-white story, published at this early stage in Ware's career, reveals his inclination to experiment with the basic form of comics, and his abiding interest in the figure of the superhero as a stand-in for an absent father, a theme evident in the creation of the ur-superhero himself, Superman.
"Thrilling Adventure Stories (I Guess)": The title says it all. The valiant, brave, honorable, protective male that is the figure for American manhood—superhero or father alike—isn't so great or thrilling, after all, in the adventure of one's childhood. Ware riffs on a superhero comic to tell a first-person story about a boy growing up with a doubtful stepfather. It opens with a splash panel that displays a Superman figure, firm and tall, in a bodysuit, cape, and boots, preceding huge block letters that then spell out "I GUESS," so that the words themselves, as a visual figure, function as a literal second-guessing of the handsome erect superhero. (The splash panel, a convention of comic books, is a visually striking oversize frame at the beginning of a story that encapsulates its themes.)
The words and images deliberately don't match in "Thrilling Adventure Stories (I Guess)." Instead they offer two distinct stories, one ordinary and verbal, and one superheroic and visual, that work against each other to create a rich narrative whole about a child's hopes, desires, and realities. Ware demonstrates how comics, fundamentally, is not a medium of illustration in which the words and images synthesize, but rather something even more sophisticated. "Thrilling Adventure Stories," which Spiegelman once compared to a master's thesis on comics form, reveals potently how comics storytelling works.
The first-person prose begins conventionally, with "When I was really young . . ." and immediately sets up the problem of vision, misconception, and genre, as the narrator describes thinking that the world itself used to exist in black and white, like in the movies. It recounts the narrator's family—his mother, grandparents, and stepfather—along with his friends and his childhood love for comic books and superheroes, focusing on uncomfortable events that made him feel "weird" or "gross." This prose is roving: it weaves in and out of the comic-book frames, appearing in text boxes, in speech balloons, as sound effects, and on surfaces depicted within the world of the story, like chalkboards and newspapers. It appears continuously both as narration and as dialogue, fluidly intermixing out of the mouths of different characters.
Chris Ware, page from "Thrilling Adventure Stories (I Guess)," originally in Raw #2.2, 1991, reprinted in color in Quimby the Mouse (Seattle: Fantagraphics), 2003.
Used by permission of Chris Ware. Image courtesy Chris Ware.
Meanwhile, the images present a completely different story, an action-based comic-book cliché plotline about a mad scientist kidnapping a pretty female reporter who is then saved by the superhero. In its placement of prose and also in the disjunct of its verbal and visual elements, "Thrilling Adventure Stories (I Guess)" suggests both as a theme and a practice of reading that nothing is as it seems: the reality of experience doesn't match the image; how people appear and what they say are shifting and unstable. Crucially, the figure of the superhero in the story is aligned with the figure of the father the boy desires: the hero who will be his role model and save his mother from her marriage to a dubious man. But the narrator also explains he and his friend dressed up like superheroes, even coloring their "Jockey shorts with fabric crayons to make those trunks or whatever those things are called that superheroes wear," pretending to be forceful men.
The last page of the story plays with aesthetic conventions of the action comic book to reveal an emotional truth about families. In the sequence of images, we see the superhero defeat the mad scientist (stepfather), whisking away the pretty reporter (mother) after the scientist detonates a bomb (which at the top of the page we can read, in the prose narration, to be the stepfather's racist attitudes). But in the story's last tier of frames—in a shift enacted by an enormous explosion with the block letters "WHEN" emerging as a sound effect—the child has himself become the superhero for his mother. In one of the graphically simplest sequences in the story, in which the words and images finally seem to collapse together, and the superhero carries the pretty reporter off into the sky, the narrator writes of the loss of his stepfather, "That was okay with me, since I liked things better when it was just my mom and me, anyway." The strip closes with the two alone, embracing.
Ware obsessed over, and drew, superheroes as a kid. As an interview with radio host Ira Glass in a "Superpowers" segment of This American Life reveals, the details of the story are autobiographical: Ware confesses to Glass that as a shy, unpopular kid he desperately wanted a superpower. Ware, as in the story, did create his own superhero called the Hurricane. His mom, a reporter at the Omaha World Herald, did make him a mask for his own superhero costume. And he did in fact often dress in his costume—he even wore it to school under his uniform, with parts poking out. In "Thrilling Adventure Stories (I Guess)" Ware engages the visual conventions of a superhero comic in order to ironize the promise those fantasy stories hold out, setting the model man (hero) against the reality of the awkwardness of lived life.
But in Jimmy Corrigan, his first graphic novel, the superhero is no longer superheroic, even if the idea of triumph is ironically set against a more complicated reality. Instead, in the signal work that arguably singularly represents the flourishing of the graphic novel in the twenty-first century, the superhero is a figure for profound loss and disappointment. If the comic books glamorized and continue to glamorize the superhero, today's graphic novel engages them to reveal their antiheroic qualities. Ware wanted to be a superhero when he was little: "I just looked at pictures of the muscle-y men and tried to copy them figuring that I had better prepare myself," he explained in an interview. Hence the melancholy fantasy that prevails in "Thrilling Adventure Stories": the little boy who colored-in his underwear for a costume and needed his mom to make him a mask finally becomes the solitary superhero to whisk his mom away from danger in a romantic action, an oedipal collapsing of son and lover. Ware never met his real father growing up. His father left him and his mother when Ware was a baby.
As a child Ware was fixated on Superman, the original flying, leaping, bulletproof, red-and-blue-suited caped crusader. A superhero who was himself the creation of a teenager, Jerry Siegel, who had just lost his father. In the character's actual genesis and in Ware's attachment to him, he stands in for a history edged with loss. Even in Jimmy Corrigan, creating comics for a serious literary audience, Ware remains fixated on Superman, as a way to meditate on fathers and filial inheritance. Superman's image in various guises haunts Ware's work from the 1990s and beyond. In "Thrilling Adventure Stories" and in Jimmy Corrigan, a graphic novel that features generations of fathers painfully abandoning their sons, Superman is a father figure. But he shifts from being an icon of longing and desire in the former—"a powerful World War II arrogant man, basically, who is just unstoppable," Ware has said of what Superman classically represented—to being pitiful and disappointing in the latter, a failure. So pitiful, in fact, Superman even commits suicide in Jimmy Corrigan by jumping off a downtown Chicago building after waving at the title character, who is a stand-in for Ware himself.
Ware's comics are widely known for being emotionally devastating, particularly in depicting social cruelties and the loneliness of children and marginalized adults. "The Chris Ware Sadness Scale" is even an entry, hilariously, in the popular infographics book Super Graphic: A Visual Guide to the Comic Book Universe, appearing there alongside charts for "Lifespans of Characters in The Walking Dead" and "Joker's Utility Belt." In "The Chris Ware Sadness Scale," a large double-spread, the explanation reads: "Chris Ware's work blends succinct, emotional storytelling with high-end illustration and graphic design. His work is beautiful, colorful . . . and really, really sad." The scale opens, at "SAD," with Ware's funny animal collection Quimby the Mouse (sadness level: "rodent angst"), and ends, topping the scales, at "SOUL-CRUSHING DEPRESSION" with Jimmy Corrigan ("Relationship angst, loneliness angst, Dead Superman angst, daddy-issue angst, angst angst"). As Ira Glass glosses the plotline of Jimmy Corrigan, "things go from sad to worse to worse."
Jimmy Corrigan, which takes place over generations in Chicago, where Ware currently lives with his wife and daughter, is a straight-up graphic novel, with all of the deliberately fictional artifice implied by the term "novel." But it is based in part on Ware's actual life, in which he grew up without knowing his estranged father, and met him for the first and only time, like Jimmy Corrigan, in his thirties. Jimmy Corrigan was serialized from 1993 to 2000, appearing in weekly Chicago newspapers and in individual comic books of various sizes that Ware published under the title The Acme Novelty Library before it appeared, with fanfare, as a 380-page full-color book. (Its editor was Random House designer and Batman fanatic Chip Kidd.) Jimmy Corrigan tracks filial misery across four generations of Corrigan men, shuttling back and forth between the nineteenth century and the 1980s. Of the four generations, it focuses primarily on the experiences of two characters, both named James or "Jimmy" Corrigan, with their fathers. Grandfather and grandson, these two only meet each other very briefly toward the book's conclusion.
The older James Corrigan, as he first appears in the story, is an eight-year-old in Chicago in the early 1890s whose mother had died in childbirth. His cold, single father, a Civil War veteran and the son of Irish immigrants, has a low tolerance for him that steadily decreases. Ultimately, his father abandons him at the 1893 Chicago World's Fair atop the Manufactures and Liberal Arts Building—at that time the largest building ever constructed. In Jimmy Corrigan, Ware presents comics, with its boxes of time and memory, as its own kind of emotional architecture, in addition to rendering built spaces with stunning detail and precision. "I followed him like a loyal animal right up to the edge of the largest building in the world," tiny black cursive explains, floating in the sky above the father and son looking out from the top of the building before the father flees, never to return. The younger Jimmy Corrigan, the stand-in for Ware, is an isolated thirty-six-year-old who lives in Chicago around the 1980s and travels to Michigan to meet his father for the very first time. He is a virgin, an office employee, and a guileless Superman fan.
The full-color Jimmy Corrigan calls attention to the book as a material object and to the beauty of the printed page of comics. Its elaborate cover folds out into a poster, and its dense endpapers include "exam" questions such as: "When you read comic books about costumed heroes, you liked to imagine that you were a. a costumed hero b. a costumed hero's young sidekick c. the artist d. the writer e. not unhappy." Ware harnesses the unique properties of comics form to mimic processes of remembering, dreaming, and imagining on the page: we see, visualized, characters' reveries and fantasies. Different typefaces—from neat script within panels to stylized block letters framed as taglines in colorful blue and red boxes ("Later," "Anyway," "Suddenly") give readers access to characters' interiority and also a sense of the complete control of the storyteller as a visual artist orchestrating every detail. Every panel, drawn in clean, precise black lines that practically look mechanical, exists in meaningful relation to other panels on the page to create a story and also to create a graphic whole. Ware uses color as patterning to great effect, so that readers experience each page as a complete aesthetic unit—he has said that he wanted the colors to be beautiful, even as the story was horrible. Ware told me that he "wanted to make the book as beautiful as I possibly could to make it almost something of a counterargument to the story itself."
The book opens with a prologue that encapsulates its jaundiced engagement with the superhero—which is to say, the superhero as father figure. Jimmy Corrigan's mother takes her small, chubby son to a classic car show at a civic auditorium to meet the washed-up actor who played Superman on TV. At the sparsely attended performance, the excited Jimmy earnestly laughs at all of "Superman" 's corny jokes and enthusiastically stands in line for an autograph from the masked man, who greets him reassuringly: "Hello, son." Superman fancies Jimmy's mother, takes the two to a diner, comes home with them, and spends the night. In the early morning, trying to sneak out undetected, Superman—in his regular clothes—runs into the child eating cereal alone at the kitchen table. Both are startled. He pulls out his red mask from his jacket pocket, and in an attempt to distract and mollify, hands it to the thrilled Jimmy. In the story's last panels, Jimmy's mother emerges from the bedroom, covering herself up, to encounter her son sitting at the table wearing the departed superhero's mask. "Mom!" Jimmy says. "He said to tell you he had a real good time!" As Ira Glass points out to Ware, when Superman shows up in Ware's comics he's always trying to con kids; he's always a disappointment. "He's more like a real dad that way," Ware responds.
The superhero theme develops as the book progresses, amplifying to deliver an even stronger refutation. Less than twenty pages into the story, after the adult Jimmy, at his downtown office building, has received a shocking letter from his long-lost father ("Dear Son, I think it's about time we fellas got to know each other; what do you say?"), the figure of Superman reemerges. At the bottom of a page that is broken up into many small moments in as many panels, Jimmy returns to his desk from the office snack room, sits in his depressing cubicle under the foam-core ceiling, and notices Superman, through the window, standing at the top of a tall historic building on the other side of the street, waving to him. Jimmy stands up, looks again, and then smiles for the first time since the prologue. Superman, whose primary-colors costume stands out strikingly from the dreary space of the office, continues to wave, a spot of hope and cheer in a grim and confusing day. In the last panel, Jimmy, still smiling, waves back.
When one turns the page, one is confronted with the most dramatic image of the book: Superman dies in Chicago. The page is evenly divided into two fixed-perspective panels of the building that sits at a busy street corner. The juxtaposition is striking. In the first panel, Superman—his costume still a bright speck of color contrasting with a drab cityscape—prepares to jump, and, we assume, fly. In the second, a few moments later, he lies facedown in the street, dead. Passersby pause at the body. As Jimmy, in the next page, keeps looking out of his office window with horror at the body on the street, we notice the passersby linger over the body. When it starts to rain, however, they disperse. The body, now lit under a streetlight, lies alone in the street. Repetitively, Ware offers this image, the lifeless, supine body with the bright cape and red boots, looking small and helpless from above, pounded by rain. Eventually, through the window we see an ambulance arrive (for in Ware's framing the readers' gazes merge with Jimmy's), and in our next view of the street corner, it's empty. Later, after Jimmy takes his father up on the offer of a visit, and sits anxious and alone, waiting to be picked up after deplaning in the Michigan airport, with a broken foot and single crutch, holding an embarrassing beribboned basket of fruit, he sees the large newspaper headline: " 'Super-Man' Leaps to Death; Mystery Man Without Identification Falls Six Stories in Colored Pantaloons; Mask." The sub-headline notes, "Definitely Not the Actor, Authorities Say." The book, then, leaves open the possibility that the "real" Superman, also a fraud like the actor, dies within its covers.
Chris Ware, page from Jimmy Corrigan: the Smartest Kid on Earth (New York: Pantheon), 2000. Superman leaps . . . to his death.
Used by permission of Chris Ware. Image courtesy Chris Ware.
When Jimmy anxiously looks for the ever-absent father he finds the ever-disappointing superhero, one who died ignominiously, the opposite of invincible and heroic. Jimmy Corrigan doesn't dismiss the superhero genre, since Superman haunts the text throughout, even after this death. Rather, it takes on the superhero, the romanticized figure for American manhood, in order to reject the idealization that superheroes stand for across the board. This shift mirrors the shift away from comic books as action-oriented entertainment populated by heroes and toward graphic novels, longer works about the interiority and reality of all-too-human characters, which tend to reflect their creators' subjectivity more than they do cultural archetypes. If superhero comic series like Watchmen or The Dark Knight Returns give us dark, self-aware superheroes, they remain invested, on some level, in trafficking in the notion of good and bad superheroes in the first place. The literary graphic novel, on the other hand, offers up a slew of hapless protagonists—like the lonely fathers and sons of Jimmy Corrigan—who are nothing at all like any kind of superhero (in fitness, ability, or confidence) but have become the protagonists of the comics.
Chris Ware, page from Jimmy Corrigan: the Smartest Kid on Earth. The first panel represents Jimmy's reverie.
Used by permission of Chris Ware. Image courtesy Chris Ware.
Instead of expressing an ideal—or even an ideal gone wrong, like in Watchmen—literary graphic novels tend to focus on the interiority of their characters, how these characters see and experience the world guided by their particular hopes, fears, and desires. The superheroic horizon is part of this desire. No one transforms into a glorious action idol in Jimmy Corrigan; rather, the book enacts the opposite: the harsh demystification of that ideal for someone who is constantly, desirously searching for male role models. When Jimmy gets hit by a truck while visiting his father, Ware ingeniously switches the perspective on the page so that readers look down on Jimmy lying in the road from the perspective of the worried driver, and then suddenly the perspective flips to show us Jimmy's own optical viewpoint. In a flash, Jimmy sees that the person above him is the Superman of the story, wearing the red mask, there to save him, until in the next panel he's quickly replaced by the driver. Instead of turning into Superman, or having his father do so, in Jimmy Corrigan Jimmy borrows his deadbeat dad's old Superman sweatshirt. Jimmy's father dies during their visit, like Superman, briefly emerging in Jimmy's life before disappearing again. The book's cover, underneath the dust jacket—like the reveal of a core under the surface—has a simple, small color drawing in its center of Jimmy Corrigan's driving fantasy: Superman, slightly pudgy and aged ("more like a real dad," to quote Ware again) valiantly carrying the child Jimmy, who clings to his neck, through the air to safety. This image is repeated, alone in the space of the page but for dense swirls of snow, at the book's conclusion. The desire for the figure of the patriarch-superhero is there—but the unrecuperated loss, as one Ware critic suggests, is everywhere.
If Chris Ware's graphic novel represents the DC end of the superhero spectrum—the square, manly, paternal heroes like Superman—his friend Daniel Clowes's The Death-Ray is very Marvel. It features a dark, teenage superhero, a type not unlike the young, neurotic superheroes such as Spider-Man that Marvel made popular in the 1960s. Clowes, who presciently announced to his parents as a child he wanted to be a cartoonist, read all the comics he could as a kid, including superheroes. "As a teenager I read the early Spider-Man comics, where he becomes a skinny, angry, disturbed superhero, and I thought, 'That's how it would be.' As a kid you look at Clark Kent who is still a big jock with glasses and think, 'I don't relate to him at all.' But the original Spider-Man was really 120 pounds and a total loser, and I was so inspired by that." Clowes grew up in Hyde Park, Chicago, and has described frequently getting beat up on the way to school—Chicago's famous Lab School, the alma mater of Sasha and Malia Obama.
Clowes's grandfather, with whom he was close, was a medieval historian at the University of Chicago. His mother, rebelling against the academic lifestyle, became an auto mechanic. Young Clowes had weekly dinners in Hyde Park with writer Norman Maclean, a family friend, and attended art school at Pratt in Brooklyn (his acerbic satire "Art School Confidential," from 1991, remains totally relevant and is one of the funniest comic pieces of all time). Clowes's post−art school solo comic-book series Eightball, with stories like "I Hate You Deeply" and "Why I Hate Sports," was a major motor defining alternative culture in the 1980s and '90s. Clowes's savvy, controlled comics aesthetic became famous and recognizable across venues associated with smart, sharp alternative culture—he did album art for punk bands, an animated video for the Ramones, and created movie posters for bleakly funny films like Todd Solondz's indie hit Happiness. But it was in Eightball, Clowes's own comics title, which ran from 1989 to 2004, that Clowes achieved his best-known work. Ghost World, the touching investigation of teenage girl friendship, was first serialized in the pages of Eightball, as were numerous other works later collected as books like David Boring, Ice Haven, and The Death-Ray (which first appeared as a stand-alone issue of Eightball in 2004).
The Death-Ray dives directly into staples of superhero storytelling—the origin story and the vexed question of vigilantism—and also replicates superhero aesthetics in its page layouts. It pays homage to comic-book artists like Jack Kirby, who drew the Fantastic Four and Silver Surfer, and to Steve Ditko, the artist behind Spider-Man and Doctor Strange. Clowes explained his love of certain old superhero comics to me, calling the early Kirby Marvel comics "actually really beautiful and crazy and strange" with a "Pop Art intensity . . . [that] is still really appealing to me." We see this in layouts in The Death-Ray, like the double-spread bleed—the term for when the image runs off the page—of best friends Louie and Andy, in which Andy is dressed in a thrift-store costume as the titular Death-Ray. This page portrays large, stylized sweeping bodily movements (and violent contact) with graphic swaths of color, simple but dramatic movement lines and onomatopoeia ("BAF!"), and a slew of aesthetic effects including a smattering of small overlaid panels that each distinctly represent how the lines of a panel's borders, whether jagged, wavy, spiky, or round, convey action in comic books. The page, then, marks a kind of distance from the superhero story—in the self-conscious, overlaid panels, Louie and Andy are comically devoid of any action, instead debating silly details about how to find it—at the same time that it beautifully produces conventional superhero action-based aesthetics.
Daniel Clowes, double-spread from The Death-Ray, 2004, reprinted (Montreal: Drawn & Quarterly) 2011.
Used by permission of Daniel Clowes. Image courtesy Drawn & Quarterly.
The Death-Ray is deeply enmeshed in superhero comics, then, from its structure to the composition of its pages. But The Death-Ray, as Clowes himself points out, enlists these features to tell a different kind of story than those that actually appear in superhero comics: it is the dark story of an antihero whose actions are not, in fact, redeemable or motivated by righteous revenge. No one is murdered in the world of The Death-Ray aside from those whom Andy himself obliterates, unlike in the world of Peter Parker, whose kindly foster parent Uncle Ben is murdered, paving the way for Peter to emerge as an avenging Spider-Man. The title itself, as the name for the book and the superhero, underlines this unseemliness in openly naming death—many superheroes, like Superman and Batman, don't kill, as a rule. Clowes told me that he first got the idea for the character when he himself was a teenager, but his teenage version, with shades of Spider-Man, was much more idealistic. Returning to the character as an adult, Clowes gave him what he calls "a story I would actually want to read": one that takes stock of the idealism that attaches to superheroes in order to unambiguously deflate it. In other words, Clowes, while honoring the superhero aesthetic, creates comics specifically for grown-ups.
Andy is a quiet, picked-on sixteen-year-old white kid, an orphan (that classic superhero trope) raised by his grandfather, Pappy, whom he loves, and a black housekeeper, Dinah, whom he also loves, in 1970s Chicago. After smoking a cigarette proffered by his also-outcast friend Louie—a rite of passage in which the two try to look cool and adult—he realizes cigarettes give him superhuman strength. This amusing move by Clowes pushes against the squeaky clean fitness ideal; cigarettes aren't only not bad here, they're well-nigh magical. During Andy's first night scouring the city, he imagines his gym teacher seeing him lifting parked cars. All he has to do is puff a cigarette and wait for the strength to kick in. Andy and Louie, in a sidekick role, viciously beat up high school bullies, to everyone's astonishment, but long for bigger fish to fry. Eventually, the origin story is revealed: Andy's late father, a scientist, through fancy lab work, deliberately created this reaction to cigarettes in his son, assuming from his own experience that he would need the help. He also left behind a ray gun, which only works for Andy, and which instantly vanishes, forever, any object, animate or inanimate, at which Andy shoots. In the comic book Spider-Man—which we know found a teenage fan in Clowes—one line in particular, attributed to the character Uncle Ben, has become widely famous, describing what is often a dilemma for superheroes across the board: "With great power comes great responsibility."
But while Spider-Man struggles to match great responsibility to his great powers, Andy falls short. Andy's superpowers do not lead to great responsibility, or barely any responsibility at all, although he fights to stay grounded. They make him a worse person, and they make the world a worse place. Andy dispenses power on a whim, and certainly disproportionately: he kills people for offending his specific moral sensibility, as we see when he is young, and also on into middle age. Eventually, he also kills Louie. Andy and Louie, stable middle-class kids, long for a superhero plot to befall them, like a revenge situation that would authorize their violent action (Andy even imagines Pappy's murder), but none does. The violent action of the Death-Ray, then, comes from Andy's inner violence. Clowes has even mentioned the backdrop of the Iraq War, noting it was "a hubristic show of force by this country, which seemed like it was not a vital player anymore but kind of a dying cranky old man, and that's kind of where the older version of the Andy character came from. . . . He was sort of the perfect stand-in for America as it existed in 2004." Underlining this point, one of the book's last episodes is even titled "The United States of Andy." As with Ware, all of the idealism, and idealization, is gone. As in Jimmy Corrigan, The Death-Ray produces a world permeated by superhero symbolism and aesthetics that is yet full of unredeemed loss in which the very concept of the superhero is rejected.
From Superman onward, superhero comics, whatever else they may be doing, have offered an idealized, normative platform for readers to admire representative bodies. They have remained, then, a cultural stage for which the question of representation matters deeply: the representation of different kinds of bodies in superhero comics resonates as a register of mainstream acceptability. The world of superhero comics, as also with the world of auteurist graphic novels, is right now filled with energy and excitement, because it reflects inclusion and diversity on an unprecedented scale. Some of my favorite examples: Ms. Marvel, a funny, charming, and even moving series in which the title character, Kamala Khan, is a sixteen-year-old Pakistani-American girl from Jersey City, New Jersey, who gains superpowers like shapeshifting after sneaking out to a party. The first Muslim character to headline her own comic book, Khan—alias Ms. Marvel—who first appeared in 2014, is an unexpected commercial success: the comic book moves around a hundred thousand physical copies monthly, and is Marvel's #1 digital best seller. (The first Ms. Marvel character, dating from the late 1970s, is named Carol Danvers.) And in April 2016, Marvel released Black Panther #1, drawn by Brian Stelfreeze, colored by Laura Martin, and written by Ta-Nehisi Coates, the Atlantic columnist and one of the most acclaimed public intellectuals of the past decade, winning a MacArthur "genius" grant, and a National Book Award for his 2015 meditation on race and America, Between the World and Me. Black Panther #1 sold out quickly and Coates has already signed on to write a second installment after the end of his first twelve-issue story arc. A Marvel Studios movie, rumored for years but first officially announced in 2014, is set to appear in 2018, hot on the heels of Coates's success.
G. Willow Wilson, writer, and Adrian Alphona, artist, Ms. Marvel Vol. 1: No Normal (New York: Marvel), 2014. Ms. Marvel: mixing the quotidian and the villainous.
Used by permission of Marvel Comics. © MARVEL.
That the in-demand Coates, a serious longtime comics fan, decided in the wake of the celebrated Between the World and Me to write a comic book is a marker of the growing prestige of comics—its interlacing, today, with other forms of culture like journalism and literary nonfiction. Coates has said, "My approach to comic books ultimately differs little from my approach to journalism." But more significantly, it's also a sign that the world of superheroes is still vital—and that it is becoming, appealingly, more responsive, open, and accurate in reflecting readers and their desire for inclusion and identification. Some readers have always recognized, even in the figure of the normative white male superhero, a resonant complexity around identity. As cartoonist Gene Luen Yang told the New York Times, "Superman is literally an alien and an immigrant. And a lot of the superhero genre is about negotiating between two identities, which really mirrored my own life. I used one name at home, another one at school, had one language at home, another one at school." On the other hand, as Yang points out, "The larger readership wants our stories to reflect what America is today." He is currently scripting New Super-Man for DC, whose titular hero is a working-class Chinese teenager.
Black Panther—whose comic-book appearance predates the Black Panther Party by a few months—is the first black, and first African, superhero in mainstream American comics. He was introduced in July 1966 in Fantastic Four #52, created by Stan Lee and Jack Kirby. Black Panther, whose given name is T'Challa, is the king of the fictional African nation of Wakanda. (A spin-off series written with Roxane Gay and Yona Harvey, Black Panther: World of Wakanda, was announced in the summer of 2016.) In Coates's hands, Black Panther offers a meditative world (can a superhero be a king, and does a technologically advanced, democratic society want either one?) and one that is, significantly, populated entirely by black characters, many of whom—and this is not a given in mainstream comics—are female (and complex!). Coates told the New York Times, "The book is probably much more concerned with gender than it is with race." World of Wakanda, whose first issue hit the stands in November 2016, delivers the story of two queer characters, members of Black Panther's all-female security team, who fall in love (from the Marvel website: "What happens when your nation needs your hearts and minds, but you already gave them to each other?"). There has been a slow but steady increase of gay superheroes in mainstream comics in the past decades, and now trans characters are also part of the landscape: both DC and Marvel have featured trans characters in secondary roles, and now Chalice, a trans superhero from publisher AfterShock, is taking center stage in the title Alters. The world of the superhero comic, always about what kinds of bodies matter, is changing with the times—it's a mainstream barometer that is proving to be more expansive than it may have seemed even a few decades ago.
We see this on a formal level, too. Chris Ware steals motifs from superhero comics to reject them . . . and in our current cultural moment, characterized by hybridity, mixing, and dynamism, the superhero comics are now in turn themselves influenced by Ware, as we see in Marvel's recent Hawkeye run, written by Matt Fraction with art by David Aja. Named for the master marksman superhero created in 1964, Hawkeye steals openly from Ware. Take Hawkeye: Little Hits, a trade paperback released in 2013 that collects six issues of the comic. The entire volume—how the stories relate to one another through distinct perspectives in piecemeal fashion—conspicuously resonates with Ware's oeuvre, as do individual issues, such as the opener, "Six Days in the Life of," which focuses on the quotidian passing of moments and the slicing of time into panels in gridded pages directly similar to Ware's 2012 graphic novel Building Stories. Strangely for a superhero comic, it is so invested in the quotidian, as Ware distinctively is, that it even allows multiple fight scenes, usually the bread and butter of superhero comics, to happen in the gutter.
"Pizza Is My Business," written by Matt Fraction with art by David Aja and color by Matt Hollingsworth, from Hawkeye: Little Hits (New York: Marvel), 2013.
Used by permission of Marvel Comics. © MARVEL.
The volume's last story, "Pizza Is My Business," however, is the one that most obviously cites Ware's aesthetic, evident in its complex, nonlinear page compositions, for instance, in its assortment of small round and square panels, associatively linked, that float over an image on the page. If Ware uses the hybridity of comics to express the perspective of an infant in his Jordan Wellington Lint (2010), and the life of a bee in Building Stories, Hawkeye in turn experiments with Ware's formal grammar to create an innovative superhero comic that is also about individual cognition and perception: "Pizza Is My Business" expresses the point of view of Hawkeye's dog, who knows himself as Pizza Dog.
The story offers readers only words a dog would recognize, like "don't" and "stay." And it offers a world in the colors the dog sees (he and his friends are color-blind). It presents the interiority, if you will, of Pizza Dog. "There's an element of deciphering a code as you start to realize what the symbols mean and where they lead and how they interact with the story taking place behind and around them; and then at some point you realize that, without noticing, you've started to think like Pizza Dog," a Comics Alliance reviewer wrote, proclaiming it could be "the best single issue of comics you've read." The superhero comics are now responding to the comics that responded to them to tell and show their more action-oriented plotlines. In this porous example of exchange, dogs, in a sense, can be the new superheroes—and they can have all the interiority of the protagonists of graphic novels. We see that graphic novels not only share attention with superhero comics to the powerful bodies found on their pages, but they also share with them the force of powerful storytelling in words and images.
---
WHY SEX?
If comics is known for representing real-life world-historical disaster, and for superheroes (who in alternate realities avert those kinds of disasters) it is also known for representing sex. When Chris Ware first discovered the comics magazine that would launch his career, it was in the back room of his hometown Omaha, Nebraska, comic-book shop, and he thought—or rather, hoped—it was pornography. One day the store owner, Ware recalls, "started letting me back there, and eventually I came across a big magazine sticking up out of the bins that I'd never heard of before called Raw. Thrilled, I thought, 'Wow! That must be really filthy!' So I pulled it out and thumbed through it but of course I was disappointed because, well, it wasn't all that filthy."
It's not surprising Ware thought a comic called Raw in the back room of a comic shop was pornography. There are, and have always been, plenty of comics about sex and sexuality. Comics have long been connected to the sexually taboo—and still are. As I noted in the introduction, Alison Bechdel's comics memoir Fun Home, about a gay girl growing up with a closeted gay father, made headlines in 2015 when some students at Duke refused to read the book because of its graphic content. One student, Brian Grasso, wrote in the Washington Post that he was opposed to the "cartoon drawings of a woman masturbating and multiple women engaging in oral sex." He noted something true: "There is an important distinction between images and written words." People react much, much differently to an image, drawn or photographed or filmed, than they do to prose. Images produce affect very quickly—they feel immediate. The ability of comics to picture has long produced its sense of the illicit and forbidden. It's no coincidence that "graphic novel" can be a confusing term: Daniel Clowes has pointed out that it sounds as though it refers to books like The Story of O and Lady Chatterley's Lover (The Story of O was actually adapted into comics). "Graphic" in many contexts simply means sex. I laughed out loud when a book publisher years ago suggested I title one of my books Graphic Encounters—which sounds like soft-core porn.
We see the connection between comics and the sexually taboo during the 1930s and '40s, the time of so-called Tijuana Bibles, popular and anonymously produced under-the-counter pornographic comics pamphlets, which were often parodies featuring celebrities and established comic strip characters—think along the lines of Olive Oyl fellating Popeye. One of the few identified artists, Wesley Morse, went on to create the ultravanilla Bazooka Joe bubble-gum strips for Topps. And Superman's Joe Shuster, who created the look of the most square, do-gooder superhero in existence, created erotic artwork in the early 1950s—unsigned fetish art in magazines that were also sold under the counter. From superheroes to bondage mavens, comics has always delivered an intense focus on the bodies within its frames.
We also see this connection in publications such as Playboy, which launched in 1953 and has published gag cartoons and sequential strips by some of the century's top cartoonists, including Jack Cole, who had created the beloved superhero Plastic Man; Harvey Kurtzman, the comics genius who started Mad magazine; Jules Feiffer, arguably America's first literary cartoonist; and Art Spiegelman, among many others. Little Annie Fanny, the sexy ongoing comics story by Kurtzman, who collaborated on it with Mad's Will Elder, ran for over twenty-six years. We also see this during the flourishing of mainstream comic books in the 1950s that were thought to fulfill sweaty adolescent lust; psychiatrist Dr. Fredric Wertham accused cartoonists of embedding secret sexual images, like vaginas, in comic books. And we also see this in the defiantly sexually explicit underground comics of the 1960s and '70s, which largely bypassed most obscenity laws by virtue of being drawn rather than photographed or filmed (although they fell afoul of some laws too).
Cartoonist Robert Crumb's unfiltered depictions of explicit sex inspired an entire movement of underground cartoonists to shred taboos—both verbally and visually, with paper and ink—as one of the central missions of the aesthetic and publishing revolution known as underground comics, or "comix." (The x, as mentioned, denotes edgy adult content.) Crumb is also highly controversial for the preponderance of graphic sex in his comics, and for his openness in talking about the sexual proclivities and fantasies that he pictures on his no-holds-barred pages. Veteran cartoonist Lynda Barry remembers the "sex stuff . . . scared the hell out of me" when she first saw Crumb's work as a kid, but she copied the entire contents of Crumb's Zap #0 anyway, mesmerized by the detail of the comics. Her friend the writer Dan Chaon, now a professor at Oberlin College, actually buried Zap in his backyard because it freaked him out so much. "What R. Crumb gave me," Barry says, "was this feeling that you could draw anything."
Tijuana Bible, creator unknown, likely 1930s, starring Olive Oyl, Wimpy, and Popeye. Note that the last panel depicts "three-way" sexual activity in which Wimpy and Popeye engage in intercourse. Image courtesy Tijuana Bibles, ed. Bob Adelman (New York: Simon & Schuster, 1997).
The 1994 documentary Crumb, directed by Terry Zwigoff and produced by famed movie director David Lynch (Blue Velvet), finds Crumb candidly confessing to harboring a sexual attraction to "cute cartoon characters" as a child. The Taschen editor Dian Hanson, an ex-girlfriend, notes in the film that he told her he even masturbates to his own comics, an amazing example of how powerful drawing can be as a world-building enterprise for a cartoonist. To me the incredible part of what the film reveals about comics and sexuality isn't that a man was attracted to humorous male animal cartoon characters as a child, but rather that he masturbates to something he drew for himself. He seems to have always taken his drawing seriously enough to be able to construct a viably erotic paper-and-ink fantasy with his own lines on paper. Since the 1960s, Crumb has been an icon of the American counterculture, in addition to his current status as one of today's foremost artists—he is perhaps, along with Spiegelman, the most famous cartoonist in the world, and certainly the most notorious. Through Crumb, which was unexpectedly popular, and through his reputation from the underground scene, Crumb is also known specifically as an artist fixated on the female form, particularly the backside, legs, and feet of sturdy women. He breaks down his particular sex obsessions most clearly in the autobiographical comics stories "Footsy" and "My Troubles with Women," in which he reveals his childhood fascination with strong women like the title character of the television show Sheena: Queen of the Jungle. When I was in Miami a few years ago participating in a book festival with his wife, the cartoonist Aline Kominsky-Crumb, whose own pioneering work created a space for picturing women's sexuality, she surreptitiously snapped photos of the large behinds of strangers to send to her husband.
Almost as famous as his fascination with large backsides is Crumb's style, known for its meticulous yet fluid crosshatched lines inspired in part by nineteenth-century engraving techniques. (Cross-hatching is the practice of shading an area with an intersecting set of parallel lines.) Crumb is one of the most virtuosic, if not the most virtuosic, draftspersons in comics. He is acknowledged across the board, and worldwide, as a master of drawing. Part of his renown as a cartoonist resides in his content—what Lynda Barry identifies as his game-changing demonstration by example that "you could draw anything" in comics, however dark, unpleasant, goofy, or private. But a large part of his appeal is how this content appears, which blends comfort and discomfort together on the page.
Recalling the reaction in the late 1960s to the appearance of his comics, Aline Kominsky-Crumb describes a paradoxical mixture. "Robert's work was really interesting because he had an aspect of the old comics from the twenties that we all loved," she explained to me. "It was very reassuring, but also charged with this total psychedelic vision. It touched something so deep. . . . And it definitely set off a whole other set of possibilities for a lot of people. It was definitely a supercharged moment there. Robert's work and everything that came after it changed graphic art forever. . . . But it really changed the way everything looked, you know, instantly." The "bigfoot" style of cartooning Crumb adopted, characterized by the rubbery exaggeration of certain human features like noses and feet, hearkened back to old cartoons from the 1920s, '30s, and '40s, but reintroduced this stylized posture and springy line for radically adult content set against a teeming modern landscape, which often appears quite impersonal. Crumb's "Keep on Truckin' " image and slogan, a riff on the Southern blues song called "Truckin' My Blues Away," features people seemingly led by their feet marching through comics frames, and became an emblem of the 1960s counterculture and beyond. In Understanding Comics, Scott McCloud provides an apt description of his style: "In R. Crumb's world, the curves of innocence are betrayed by the neurotic quill-lines of modern adulthood, and left painfully out of place." When Crumb's attentive pen lines fall to sexual subjects, particularly, the result evokes strong reactions.
Crumb was born in Philadelphia, and raised Catholic as one of five siblings by his housewife mother, Beatrice, and a military father whom his brother Charles, in the film, straightforwardly describes as a "sadistic bully." His parents fought often. Both of his brothers appear in the Crumb documentary; both of his sisters declined to. Crumb was a so-called "base baby" because his father moved his family around to tract houses on different military bases often during his twenty-year service in the US Marine Corps. (Charles Crumb Sr. was a soldier in World War II and was sent into Hiroshima ten days after American forces dropped the atomic bomb on the city—an experience about which he never spoke.) Crumb's father was a stern authoritarian with a temper who intimidated his children, including by striking them. He broke Robert's collarbone when he was five. Like a cruel dad out of central casting, he was even the author of a book called Training People Effectively.
Charles Crumb considered his sons, who drew comics together, "sissies." Crumb recalled in an interview with the late Time magazine art critic Robert Hughes that his father always told his sons they'd grow out of drawing and get into football in their teens. "He was just totally bewildered by us," Crumb explained. "He saw us as Martians. We'd be lying on our beds in the fetal position, reading comics. . . . 'Get off your duffs!' We broke his heart. He had three sons and they all turned out to be complete defective weirdos." The cartoonist brothers were led in their comics efforts by the eldest brother, Charles Jr., who critiqued their work and pushed them to produce three issues of their own comic, Foo, which they distributed to the comics fanzine community and sold door-to-door with little luck. Crumb routinely confirms that his brother, as he once put it, was "actually a much stronger artistic visionary than I was" and has often explained how he was an inspiration. In a Crumb drawing that lists his influences, divided by "Cartoonists/Illustrators" on the left side of a page, and "Fine Art!" on the right, Charles Crumb Jr. is the very first entry in the former. The film Crumb shows Charles to be evidently brilliant, with a literary sensibility, wryly funny—and an artistic mastermind who pushed his little brother into greatness. Charles lived with his mother his entire life, struggled with mental illness, and committed suicide in 1992 at age fifty. Filming for Crumb had recently wrapped.
Crumb grew up on a steady diet of popular culture as a child in the '40s and '50s, watching television and reading comic books. At fifteen, he became profoundly interested in blues and jazz records from the 1920s through the 1940s, and went door-to-door offering to buy old 78-rpm records in black neighborhoods. Crumb's passion for twentieth-century American culture that generally preceded his birth—from blues to comics—is reflected in his style, which openly refers to popular visual modes from the interwar period, and in his detailed, reverent portraits of blues and jazz musicians (as in his book R. Crumb's Heroes of Blues, Jazz, & Country). After high school, Crumb left home to find work. His first job was for the American Greetings card company in Cleveland, drawing novelty cards for their Hi-Brows line. He managed to draw images that are cuter (and therefore more commercial) than his comics and yet are still edged with something that feels like it's longing to break the surface. In 1964, Crumb married Dana Morgan, a young Jewish woman from Cleveland who had just graduated high school. "My dad always said I'd marry the first one who came along," Crumb reports in "My Troubles with Women." He was twenty-one, and felt trapped quickly. Crumb escaped Cleveland, and his rocky marriage, and finally ran away to San Francisco in 1967. Dana eventually followed him; their son Jesse was born in 1968.
It was in San Francisco that Crumb would publish the comics that inaugurated and defined the era of underground comix. Crumb took LSD and fell in with the hippie scene in San Francisco, becoming friends with figures like Janis Joplin. He even created the cover for the 1968 album Cheap Thrills by her band Big Brother and the Holding Company. In a "fuzzy period for a few months" Crumb had "visionary" experiences on acid dreaming up some of his most famous characters—and recording them in his sketchbook—such as Mr. Natural, Angelfood McSpade, Flakey Foont, Shuman the Human, and the Snoid. His LSD visions, he says, were the "psychotic manifestation of some grimy part of America's collective unconscious." Crumb channeled a deep-seated disgust and malaise provoked by contemporary America that manifested on the sketchbook page as seething psychedelic landscapes both amusing and horrifying. In his own words, he was "making a drawing of the horror of America," as though irrigating something dark and spooky from below the surface.
These drawings and characters became the basis for Crumb's stand-alone, fully designed comic book Zap. Cartoonists all over the world talk about where they were when they saw Zap for the first time. Frank Stack, who published the underground comic The Adventures of Jesus, describes the effect of first seeing Zap "as like a rush of adrenaline—a deep psychic, almost erotic thrill." Crumb had previously published short comics pieces in the underground press, but he galvanized underground publishing and kick-started the phenomenon of underground comics with the first issue of Zap in 1968. Underground comics, through Crumb, enacted a massive cultural shift away from the idea that comics had to be for kids. And it was a massive shift in part because of just how explicitly "adult" Crumb's material was in the late 1960s and early '70s—and with the overt framework of the intellectual to boot. Cartoonist Phoebe Gloeckner, known for her own sexually explicit semiautobiographical comics, revealed to me that she literally learned what happens physically when men and women have sex from reading Crumb's comic "Joe Blow." Reactions to Crumb's provocative comics were diverse but always extreme. Charles Crumb Sr. saw one of Robert's underground comics and never spoke to him again (he died in 1982).
Crumb drew and designed the first two legendary, field-defining issues of Zap, #1 and #0, entirely by himself (starting with the third issue, he made Zap a collective endeavor, bringing in other artists including S. Clay Wilson, whose densely packed comics are famous for disturbing violence and graphic sex). The earliest, all-Crumb issues both call attention to their comic-book format with stories and drawings about comics, and work heavily in the mode of satire—even trafficking in recognizable, outmoded racial stereotypes and putting the sexualized body on the page. In Zap #1 the stories carry a sense of sex always about to burst the surface of propriety and decorum: the first long story, "Whiteman," and the later "Mr. Natural Visits the City" both feature conventional, white, fifties-style buttoned-up men who long for sex and see it as a problem to control. Zap itself represents a mode of letting go. There's something openly carnal and scatological about these two issues, both of which routinely reveal naked bodies, bodily fluids and waste, and detailed drawings of male and female genitals. In the very first Zap, in the story "Abstract Expressionist Ultra Super Modernistic Comics," an up-close drawing of a vagina, replete with a thatch of thick, dark, wiry public hair, emits a single musical note in a speech balloon.
Hand-drawn comics—positioned against the repression of midcentury America—became with Crumb a medium for overturning censorship. In his comics, anything could be pictured and nothing needed to be held back. Comics is still often associated with "dirty pictures," because as an art form composed of words and images—as well as one enduringly connected to the lowbrow—it has the power to exhibit the hidden or the improper, like a kid in class drawing his teacher without clothes. A visual technology that can make the unseen concrete and easily conjures the improper, there is something illicit about drawing. Crumb calls attention to this on the back cover of Zap #0, in which he draws an angry mother tearing up a comic book in front of her dismayed son: "Did you ever receive warnings about how comic books were going to RUIN your MIND? Were you given lectures about how comics were CHEAP TRASH put out by evil men? Do you feel a spark of GUILT every time you pick up a comic book?" The ability of comic books to picture the unsavory is why they became forbidden in the first place—by concerned parents, Dr. Fredric Wertham, and the Comics Code Authority, a severe, publisher-mandated content code formed in order to circumvent government regulation. Crumb reinvented comic books in the underground as a new, vital, confrontational contemporary register of the forbidden for adults, willfully diving into taboos.
The pen can reveal what is kept out of sight, or can give tangible form to rampant imagination. In this, of course, comics differs from visual media like photography, in which one "takes" pictures from life, as opposed to making them from whole cloth on a blank piece of paper. In comics, one can draw what one wouldn't be able to record through a lens, but can imagine in the so-called lizard brain we all share: the oldest part of our brain that's not "correct," not socialized, not regulated. Also sometimes called the "crocodile brain," it's the primal, reptilian part of our brain that is responsible for instincts. Comics in Crumb's hands became a practice, and a space, where the pen could concretize the cartoonist's wildest fantasies and the most forbidden thoughts and images. Crucially, this meant not only bucking convention, and focusing on breaking taboos, but also making comics a practice in which even one's own private taboos could be broken. Crumb describes the terms of underground comix as "total liberation from censorship, including the inner censor!" And with Crumb, not holding back results in openly sexual, explicit material. Crumb became famous for his graphic, and in some cases violent, depictions of sex.
In the third issue of Zap (Zap #2—the chronology is #1 followed by #0 followed by #2), Crumb pushes hard on taboos along race and gender lines with his story "Angelfood McSpade: She's Sock-a-Delic," titled after his recurring black female character of the same name. Angelfood is here named " 'ZAP COMIX' DREAM GIRL OF THE MONTH" in an opening splash panel in which her large breasts point at the viewer below a face drawn like a Sambo cartoon from the early 1900s with large white lips. Crumb mocks how others portray black women—hence the recognizably racist caricature that refers to preexisting cartoon stereotypes. Angelfood is marked as a literal cartoon performer in the psychic imaginary of the scrawny, bespectacled white male character who searches her out in the story ("she has been confined to the wilds of darkest Africa. The official excuse being that civilization would be threatened if she were allowed to do whatever she pleased!"). This nameless narrator provides the skewed lens through which we as readers encounter the visual imagery—in the story, we're seeing what he imagines, even if he's not physically there observing it. Of course, in his fantasy, which is clearly ridiculous, Angelfood enjoys being fondled by examiners while in captivity, and accepts his company and attention. He is the ridiculed character of this strip, standing in for legions of clueless white men searching out their idea of black female sexuality. The final panel shows another man in glasses leaving "Schmarvard School of Law" with a suitcase that says "Darkest Africa or Bust!" It is telling that on the last two pages of the story Angelfood McSpade wears the conventional white gloves of the cartoon performer (think of Mickey Mouse and countless other Disney characters). She understands she is entertainment for the white male gaze of the adventurer characters, and readers. She's in on the joke, so to speak: we're not actually seeing her "natural" impulses, bodily or otherwise, but rather her ability to perform for the expectations of her debased audience.
Crumb isn't mocking black women, but rather he's mocking a public discourse that either implicitly or explicitly itself mocks black women. And yet Crumb always makes tricky or unclear the line between the act of satirizing something and embodying it. In satirizing something, is one giving it the kind of time and space and attention that tips over into something else? Angelfood is virtually naked throughout the story and shown several times having intercourse with men; she is drawn as an openly sexual character who beckons with her skillful tongue, flexes her thighs, shakes her ass, proffers her breasts. In the story, her vagina has a strong smell. She pants. Her behind shines brightly—lovingly cross-hatched and stippled by Crumb. Even as he mocks the fantasies of skinny white men, Crumb, a skinny white man, participates in the creation of a sexually powerful, if ridiculous, character and a set of images that are explicit and unsettling.
Crumb went on in the late 1960s to publish countless other sex comics in underground publications with titles he created, such as Snatch Comics, Big Ass Comics, and Jiz Comics, among many others. (Even if Crumb had wanted them to, no "above-ground" commercial printer would have printed this kind of work, even though by that point he was a celebrity.) His comics often portray sexual acts like intercourse and fellatio in graphic detail, in addition to depicting certain sexual behaviors Crumb has talked of favoring: riding women's backs and behinds, pounding their behinds, squeezing their faces, mauling them as part of sex. Big Ass #1, from 1969, features stories such as "Like to Ride? Then Climb Aboard the Big Ass," "Anal Antics," and "All Meat Comics," which features meticulously drawn fleshy and scatological actions in precisely detailed, up-close images with large stylized sound effects: "squirt" for a penis inside a vagina; "Bzzzzt" for a finger pressing on a clitoris; "slorch" for penetration, pictured from behind, of a woman's vagina while she sits on top of a man's penis. There's ejaculation, biting, shitting, face squeezing, and lots more.
Yet the Angelfood McSpade comics, and those featuring incest— "The Family That Lays Together Stays Together!" and "Joe Blow"—along with the violent "A Bitchin' Bod"—which stars a woman with her head capped as unwilling sex object, are among Crumb's most controversial stories and images and get at the heart of his work, which combines social satire with giving the id free rein. Crumb published "The Family That Lays Together Stays Together!" in 1969 as a one-page set piece in which everyone in an extended family is having sex. "The Family That Lays Together Stays Together!" is like Will Elder's famous Mad satire "Visiting the Grandparents," but with a much, much harder edge: while in the earlier story a family drinks beer, and even bottle feeds beer to a baby in parody of a Norman Rockwell image of familial perfection, in Crumb's story he draws the whole family, including the grandparents, having intercourse with each other. The dog is even having sex with the toddler next to, naturally, the lit television screen. The son, while having sex with his sister, reads "Kunt Comix" and "Dick the Prick." Even the big-eyed waif children in the living room painting above the couch are having sex.
R. Crumb, "The Family That Lays Together Stays Together!" Snatch Comics #2, 1969.
© R. Crumb. Used by permission.
Incest was definitely a taboo to break in underground comics—Spiegelman did it in 1971 with his Viper story "Pop Goes the Poppa!" And in a sea of explicit comics, Crumb's "Joe Blow," from 1969's Zap #4, stands out. Zap #4 was even the source of an obscenity trial in New York, in which it was declared "legally obscene." All of the comics about sex published in the underground were unprecedented in terms of the explicit acts pictured and the adult frameworks the cartoonists gave their stories about sex and drugs (drug-taking was another big theme of underground comics). Comics reinvented themselves in the underground as for grown-ups in their formal ambition, presenting an avant-gardism, and in their related ambition to provoke thought, to satirize and critique through the combination of words and images. To this effect, they became a cornerstone of the counterculture in the 1960s and '70s. But they also self-consciously doubled down on the "adult" theme as it pertains to explicit sex. The attention to drawing the wildness and messiness of bodies and desires was a new idiom, one that could be outrageous and disgusting. But even in that context, "Joe Blow" was shocking when it was published in the sixties, and it is still shocking today. (One of my students correctly, I think, pointed out to me that none of this work could be published now without outcry. In 2011 Crumb canceled an invited appearance at the prestigious Sydney Opera House after media in Australia branded his comics depraved and perverted.)
"Joe Blow" is a six-page story featuring incest. And while it is clearly a satire, a comment on the dark underbelly of seemingly shiny and perfect 1950s suburban nuclear families, its plot, which features sex between parents and their children, is drawn so explicitly that the story is striking. When the story begins, model wife Lois enters her immaculate living room to find her husband, Joe, pretending to watch a blank television, because he "can think up better shows than the ones on TV." When he goes to check in on daughter Sis, he finds her masturbating, pops a pill called "Compoz," heads back into her room, unzips his fly and takes out his penis, and demands a blow job in a close-up frame that shows one hand holding his erect penis (which confrontationally looks like it is being proffered to readers), and the index finger of his other hand pointing at it. "That's it! Pretend it's candy," he says to his eager daughter in the next frame, while she exclaims "Yummy nums!" Joe Jr. finds them having sex, runs away in confusion, and winds up having a sexual encounter with his mother. On the last page, Joe Blow proclaims, "I never realized how much fun you could have with your children!" Crumb draws a story that could only take shape in comics, delivering both prurient, almost forensic images and deliberately flat comic-book conventions in order to create an uneasy mix that is a satire of American consciousness.
R. Crumb, page from "Joe Blow," Zap #4, 1969.
© R. Crumb. Used by permission.
Crumb met his match in 1972 with a woman who also had no inner censor, Aline Kominsky (later Aline Kominsky-Crumb). Born to a Jewish family she called "postwar jerks," and hailing from Woodmere, part of the Five Towns of Long Island, Kominsky-Crumb (née Goldsmith) loathed her family's materialistic values and their callous treatment of her and one another. In an episode that recurs in her comics, her father once noticed his daughter putting on makeup and said, "Ya can't shine shit!" Always inclined toward art, as a child she found she was able to paint replicas of famous works of art, which her family would literally throw money at her to do. As a teenager, she often ran off to New York City, including to the Museum of Modern Art (MoMA), where she thought while staring at Cubist art, "If I figure this out I can escape from Long Island." Kominsky-Crumb got pregnant at eighteen, ran away to the Lower East Side at the height of the hippie era, and by her own account "had wild sex and took lots of drugs right up until the minute I was ready to give birth." She gave birth to a healthy baby boy she placed with a Jewish adoption agency.
Eventually Kominsky-Crumb got married and graduated with a degree in fine art from the University of Arizona in 1971. But she was disenchanted with the "macho" brand of abstract expressionism that was then dominant. And her own young marriage, which began when she was nineteen, was flailing. In Tucson, her friend Ken Weaver, of the legendary 1960s band the Fugs, introduced her to underground comics, and to underground cartoonists like Spain Rodriguez and Kim Deitch. Comics gave her an entirely new outlook and sense of possibility. Kominsky-Crumb writes in her memoir Need More Love that she was "turned on by this new, daring, outrageous art form. I read the works of R. Crumb and Justin Green for the first time, and it changed the course of my life." Justin Green had just published Binky Brown Meets the Holy Virgin Mary, the first autobiographical comics work. Binky Brown painfully probes Green's sexuality as a child and young man, and in particular his sexual guilt arising from his Catholic background. Directly inspired by Green, Kominsky-Crumb started drawing her own comics. Soon afterward she left Tucson and her marriage, got in her car, and drove to San Francisco intent on publishing her comics.
Kominsky-Crumb and Crumb met at a San Francisco party that year and instantly felt a connection. Without any knowledge of Kominsky, Crumb had created a sexy comics character named HoneyBunch Kaminski, who looked like her, and even seemed to have her name. Others pointed out the similarity between Kominsky and another Crumb invention: Dale Steinberger, the Jewish Cowgirl. (Crumb obviously has a thing, in comics and in real life, for tough Jewish women.) Crumb was still married, although tenuously. He and Dana had moved to a farm outside the city, in Potter Valley, to raise Jesse. The two cartoonists did not immediately become partners in crime; Kominsky-Crumb was wary of entering into a complicated entanglement. In the meantime, she made her name publishing explicit stories about her own sexual experiences, both good and bad, partnered and solo, bringing subject matter—the reality of lived female sexuality—to the comics for the first time.
Kominsky-Crumb's first comics story, "Goldie: A Neurotic Woman," appeared in the 1972 premier issue of the groundbreaking underground title Wimmen's Comix, an underground comic book by and about women, which was published by an all-female cartooning collective. Wimmen's Comix, which ran for twenty years, was one of the longest-running underground publications, and dramatically changed the tenor of underground comics production by adding so many women's voices to what had been a largely male field. "Goldie" is a woman's response to Binky Brown, which explores the protagonist's sexual angst from childhood. It concisely tracks Goldie's life from childhood to the present, with the narrator admitting that as a teenager "I was always horny and guilty." It shows the title character masturbating with vegetables, losing her virginity, sleeping around, getting married, and pursuing pleasure "compulsively" with confusion before regaining pride at age twenty-two. The kind of sex depicted in "Goldie" was new to the comics: unfiltered, vulnerable, uncensored views of women's sexual realities, including ones that would seem too "private" to show, or just simply too abject to dwell on. If Crumb shows how admitting explicit sex into comics could give the id free rein and open up imaginative possibilities, Kominsky-Crumb shows how admitting reality into comics includes depicting sex and sexuality.
"Goldie," as with all of Kominsky-Crumb's comics, eschews perspective, and clean fluid lines—despite, or in spite of, her art training. Its style, which features a shaky line, is one she calls scratched, or scrawled—drawing for her is something primal, deep, and untutored. She understands her work in the context of Expressionism, in which feelings are reflected in a dark style. In her comics, she told me, "the drawing isn't pretty or accurate; a lot of it has little to do with what reality looks like. It's an emotional reality." Kominsky-Crumb's comics reveal how comics at its essence is not about illustration, about fine rendering, but rather about expressivity. As Art Spiegelman once told curators at the MoMA who had called him about collecting his work, "It's just an accident when it makes a nice drawing." Kominsky-Crumb's deliberate scrawl, which refuses to be pretty, even though many, including me, find it utterly compelling, echoes her subject matter in her line. (Her painting, which takes on different subject matter, is much more ornamental.) She aims to reveal the everyday sexuality of women, namely herself, deliberately stripping sex of its glamour, and instead focusing on its ups and downs, on desire and degradation, pleasure and shame—on the realities of lived experience.
We see this in the story "Hard Work and No Fun," from 1973, which features explicit masturbation and intercourse. The opening panel of the story shows Goldie, as in her first story, naked and masturbating, touching herself with spread legs and looking directly out of the panel at readers. Here Goldie wears only knee-high boots and a Star of David necklace. Her body is depicted in orgasm. "I'm coming," reads one of her speech balloons, while thought balloons picturing the faces of three men (including one who looks like Robert Crumb) float out of her head. Here we see how the realities of everyday sexuality (lonely masturbation) can be the dramatic action usually accorded a splash panel. The story is about the right to claim sexual pleasure with a partner: the "no fun" of the title refers to a sexually selfish man with whom she spends the night who only cares about his own sexual fulfillment. In the early 1970s, led by figures like Kominsky-Crumb and other female cartoonists, comics became a form for demonstrating—for picturing—the sexual desires of women. In addition to Wimmen's Comix, there were comic books like Tits & Clits, an ongoing title focusing on female sexuality, later known briefly as Pandora's Box—its editors changed the name in 1973 in order to avoid an obscenity charge.
A groundswell of attention to sexuality and subjectivity came out of the underground: one could express things in comics that one couldn't express anywhere else. But there was disagreement over politics and aesthetics. Eventually, Kominsky-Crumb was rejected from Wimmen's Comix—nominally because her "feminist consciousness hadn't been raised," but more likely a) because she was dating Robert Crumb, considered a noxious sexist by many female cartoonists; and b) because her comics went against the grain, even in the underground. While today confessional comics in which no detail is off limits are hugely popular, until Green and Kominsky-Crumb this idiom didn't exist. Both of them focused on the less-than-romantic side of sex. While other contributions to Wimmen's Comix were understandably pro-woman, in Kominsky-Crumb's view, they also idealized women. And that was exactly what she wanted to avoid; it wasn't her version of what feminism should look like.
"I would completely deconstruct the myth or romanticism around being a woman," Kominsky-Crumb described to me. "I got a lot of flak from everyone," Kominsky-Crumb recalled, even among other feminist cartoonists. She noted that many feminist comics of the period idealized woman almost in the vein of superheroes. The feminist underground cartooning collectives were, she sees it, "influenced by traditional comics. They had images of women being glamorous and heroic. I didn't have that background." The anti-glamorous cover to Kominsky-Crumb's own comic book Twisted Sisters, created with Diane Noomin, even depicts Kominsky-Crumb sitting on the toilet. (The band Twisted Sister, she attests, got the name from the comic.)
In the introduction to a Twisted Sisters book collection from the 1990s, sex activist Susie Bright claims, "There is literally no other place besides comix where you can find women speaking the truth and using their pictures to show you, in vivid detail, what it means to live your life outside of the stereotypes and delusions we see on television, in shopping malls, and at newsstands." The complete artistic freedom of underground comics gave cartoonists the chance to use comics to express aspects of sex and sexuality that weren't able to be communicated aboveground, or in slicker media forms. An NPR host once described it succinctly; he noted sex is "secret, gross, and our number-one biological imperative." For Kominsky-Crumb, owning desire did not mean idealizing herself in her comics, but rather the opposite, expressing a full range of feelings and experience.
Aline Kominsky-Crumb, page from "Hard Work and No Fun," Wimmen's Comix #2, 1973.
Used by permission of Aline Kominsky-Crumb.
Kominsky-Crumb moved to Potter Valley in 1973 to live with Robert as his girlfriend on the commune at the farm; she moved into a trailer on the property, Robert lived in a shack, and Dana and Jesse, among others, lived in the "big house." Crumb and Kominsky-Crumb began collaborating on comics together, for which they would each draw themselves within a given panel or page, and portray themselves interacting. They called their comic-book series Dirty Laundry, and dirty it was—they often drew themselves having sex, and having sex in the particular ways that they enjoy that might be considered "perverse," or at least eccentric, by others. (They continued to collaborate in the pages of Weirdo, the important comics anthology Robert Crumb founded in 1981, which Kominsky-Crumb edited for a number of years—and which published explicit comics about sexuality, including, of course, theirs.)
Sometimes, the depicted sexual activity of Kominsky-Crumb and Crumb is violent, but it's always consensual—Kominsky-Crumb draws eccentric sex as part of her domestic daily routine. In the first issue of Dirty Laundry, from 1974, the artist couple published "Let's Have a Little Talk," a one-pager in which Kominsky-Crumb draws herself speaking to readers, announcing: "I also want you to know I thought up the most depraved panel where he pushes my head in the vomit!" A small arrow points at her with the announcement: "Proud of being gross." More to the point, Kominsky-Crumb made comics a form for elaborating sex positivity, but not just to celebrate sex and transgression. Her comics about women's realities involve sexuality, but aren't always "sexy." She reveals rape in her life, along with intimate details about what she enjoys about her sex life. And her exuberantly messy style is a register of the exuberantly messy bodies she puts on the page: coital, masturbating, defecating, bathing. Cartoonist Alison Bechdel, famous for her own confessional, and occasionally sexually explicit comics, cites Dirty Laundry as an inspiration. Crumb and Kominsky-Crumb, she says, "are very much an inspiration in terms of trying to be as honest as I can, especially about sexual stuff." And yes, she too, as a child, masturbated to her own drawing, as her memoir Fun Home discloses.
Kominsky-Crumb and Crumb moved off the commune in 1976, Robert and Dana divorced in 1977, and the year after, Kominsky-Crumb asked Crumb to marry her. In 1981, they had a daughter, Sophie, and they now live in southern France. One of the reasons they moved, at Kominsky-Crumb's instigation, was her impatience with a culture of censorship in which both were criticized as pornographers by right-wing feminists. Kominsky-Crumb and Crumb encouraged each other to push away the inner censors in their comics, and have become the two people perhaps most directly responsible for creating comics as a medium for a certain kind of intimate, body-focused self-expression. Comics excels at this, with its hand-drawn, intimate diary-like properties; capacity for capturing detail; and ability to give shape to the darkest or wildest imagination. And while many women saw and still see Crumb as misogynist, Kominsky-Crumb points out he has always supported her work. When she showed him "Goldie," back in 1972, "he really cracked up and from that moment on he has always been my best audience," she explains in Need More Love. "He always 'gets it' . . . Our relationship could never have worked if we didn't share this admiration for each other's work." Kominsky-Crumb even encouraged Crumb to keep drawing "A Bitchin' Bod," one of his most controversial stories.
In the story, Mr. Natural brings a woman, Cheryl Borack (or "Devil Girl"), who has a magnificent body, to Flakey Foont, a hapless everyman, and "gives" her to Flakey. She has no head—it's pushed inside her body, and the top is capped. She doesn't talk: the person has become simply a body. Flakey has thrilling sex with the headless body before being wracked by guilt and returning her to Mr. Natural, where her head is restored, she figures out what happened, and becomes enraged, threatening to kill them. Devil Girl bears a striking resemblance to Aline Kominsky-Crumb. The movie Crumb lingers on this story—it's harshly criticized as irresponsible and dangerous by several critics. As Crumb recalls, his wife pushed him to do it: "I got two pages into it and I thought, 'Ah, this is just too, this is just too negative. It's too twisted. It's too upsetting. I gotta stop this.' So I quit working on it and I threw the pages in the garbage can and at some point Aline came into my studio for something and I decided, well, I'll show her this and see what she thinks about it, so I pulled them out of the garbage can and I said 'Aline, I, this thing, pff, what do you think about this? I, I, threw it away. I decided I don't want to continue with this. It's too weird. It's just too disturbing.' She read it and said, 'You have to finish this. It's, you just have to do it. Obviously you just gotta see this through.' " Asked in the film about how her husband depicts women in his comics, she responds, "He just depicts his id in its purest form. I think, you know, the dark side of human nature that's in every person. That's what I was drawn to in his work to begin with." Kominsky-Crumb and Crumb are committed to the comics page as an uncensored space: whether it's autobiography (her) or giving form to inchoate sexual fantasies (him), both reveal comics as a way to transcribe sexual realities, however complicated, to the page.
Aline Kominsky-Crumb and Robert Crumb, "A Couple a' Nasty, Raunchy Old Things," Self-Loathing #2, 1997.
© R. Crumb and Aline Kominsky-Crumb. Used by permission.
Around the time she was fifteen, Phoebe Gloeckner discovered Twisted Sisters—the frank, funny underground comic book Kominsky-Crumb created with Diane Noomin—literally hidden under her mother's bed. It inspired the young cartoonist to draw her own uncensored comics about her own teenage sexuality. Gloeckner, who was born in 1960 and grew up in San Francisco, had seen underground comics, particularly Zap, early in her life. Her mother (who had Phoebe when she was seventeen) was friends with Robert Crumb and other underground cartoonists, who would sometimes visit Gloeckner's home after gigs with Crumb's band the Cheap Suit Serenaders. Gloeckner was fascinated by works like "Joe Blow," the style of which she found appealing, but it was Twisted Sisters that inspired her the most. She even wrote Aline Kominsky, as she was then known, a fan letter (Kominsky wrote her a postcard back, noting she had never received a fan letter from a girl before). Over two decades later, in the introduction to Gloeckner's book A Child's Life, Crumb notes that she confessed to him that she had dreams of running away to actually live with him and Kominsky. "We were some kind of underground-cartoonist-heroes to her," he writes. And it's no coincidence that both of them frankly take on the complexities of sex in their comics.
Gloeckner was kicked out of four high schools during her wild San Francisco youth, but went on to graduate from college and earn a graduate degree in biomedical communications. Her rigorous graduate training included cadaver dissection and observing surgeries, and prepared her for what was an established career in medical illustration. For many years, even while publishing her comics on the side, Gloeckner worked as a professional medical illustrator—which means that her hand, as cartoonists refer to style, can be photorealistic, if she wants it to be. Some of her most powerful early experimental work in fact uses the hyperrealistic stylings of medical illustration, and its conventions, such as cross sections and detailed insets, to point up charged content, such as in her cross-section depictions of fellatio. In "Direction of Impact," a one-page piece first published in a 1990 edition of novelist J. G. Ballard's The Atrocity Exhibition, a naked woman, crouching, inserts a diaphragm into her vagina—we see her fingers and the diaphragm pushing up inside her body, with "vagina" and "uterus" labeled and visible. Two inset medical diagrams, in framed squares, float around the central image illustrating the "direction of impact" to tibia (shin bone) and fibula (calf bone). Here Gloeckner plays with tropes of medical illustration to represent a corporeal interior, and also to imply an ominous narrative. Was this woman—assuming the page's diagrams map her arrangement of contraception and also map her broken bones—injured by someone who assaulted her after a sexual encounter? Gloeckner's experimental medical illustrations give readers bodily information—we can see inside and outside of the woman's body—but leave us to figure out how the threatening layered moments pictured add up.
Phoebe Gloeckner, "Direction of Impact," 1990, reprinted in A Child's Life and Other Stories (Berkeley: Frog), 1998.
Used by permission of Phoebe Gloeckner.
In the 1990s, at a meeting about a medical illustration job with Frog/Atlantic, a Berkeley-based independent publisher run by Richard Grossinger (the father of artist and writer Miranda July), the publisher asked her about her comics. Frog/Atlantic published Gloeckner's first comics collection, A Child's Life, in 1998. Cartoonist Bill Griffith (Zippy the Pinhead), who published Gloeckner's work in underground publications when she was in her late teens, told the New York Times: "Phoebe is one of the most accomplished artists in terms of mastery of the medium." She is also acknowledged as one of the most impressive draftspersons in comics. But because much of her work is about sexuality, Gloeckner's work, until recently, hasn't been widely known.
Like Kominsky-Crumb, Gloeckner has faced censorship from printers who refused to actually print her work. (Frog/Atlantic ended their fifteen-year relationship with their printer over Gloeckner's work.) And Gloeckner's work has been labeled child pornography—a very hard designation to accept when one is producing work about one's own experiences of abuse. In 1995, British customs seized a book collection that included Gloeckner's story "Minnie's 3rd Love, or, Nightmare on Polk Street," as child pornography. A Child's Life has never been allowed in France—where Crumb and Kominsky-Crumb sought refuge from puritanical censorship standards.
"Minnie's 3rd Love" is a semiautobiographical twelve-page comics story that features a plotline—and images—Gloeckner has returned to across several of her books: a young girl, at fifteen, is seduced by her mother's boyfriend, who takes her virginity, and with whom she starts a relationship that is both titillating and horrifying for her. She longs for her mother's intervention and protection, which never comes (when Minnie's mother finds out about the affair, she is not outraged—she doesn't press charges or even cut off her friendship with the perpetrator). Miserable at home, Minnie runs off and joins the drug-fueled gay subculture of San Francisco, and in one particular incident she is drugged and raped, pimped out by her junkie girlfriend. "Minnie's 3rd Love," while its content is shocking, is a gripping story of ambivalent emotions, perilous experience, and complicated self-understanding. Journalist Peggy Orenstein, in her profile of Gloeckner in the New York Times, noted that Gloeckner is "creating some of the edgiest work about young women's lives in any medium."
Perversely, Orenstein writes, the triple marginalization Gloeckner's career represents (cartoonist, literary cartoonist, female literary cartoonist) produces an artistic practice "free from the pressures of the marketplace . . . [where she] can explore taboo aspects of girls' lives with the illusion of safety." The most notorious image from "Minnie's 3rd Love" has become known as the laundry room panel. In it, we recognize Gloeckner's signature comics style, which can produce an uncanny, disturbing effect. She combines a medical illustrator's precision—which is to say, a certain kind of mimetic realism—with disproportion in the size and shape of bodies. The laundry room panel depicts her mother's boyfriend, with his pants at his ankles, holding his penis out in front of Minnie's face, while she cries and clutches a bottle of wine. There is plenty of upsetting dialogue. When Minnie asks, "You love me, don't you?" he responds, "Of course I love you—what man wouldn't give anything to be fucking a 15-year-old?" The style of the image amplifies the disturbing power of the panel, because realism—say, the detailed hair on his body, the texture of her denim shorts—combines with the confrontationally, disproportionately large erect penis he wields. His body is drawn as so big, and menacing, that it barely fits in the panel—his head sticks out of its uppermost border, and his backside, dotted with stray hairs, spills out into the right-hand margin. Responding to accusations of "pornography," Gloeckner has emphasized that she is drawing true scenarios: "But there are children who experience this, who have the penis in front of their faces. They see it, so why can't I show it to make the impact clear?"
To "make the hidden visible" has long been a rallying cry of feminist and other social justice movements. In comics, even the most private or hidden moments can be reconstructed and revealed. On the other hand, as the photography scholar Ariella Azoulay points out, there exist in the public sphere very few photographs of rape. In comics, "making the hidden visible" for a public isn't simply rhetorical. Events and actions—what happens inside your body during sex, what happens in the laundry room, what happens when a girl is raped—can be shown in detail. Gloeckner believes that the medium of comics, with its word-and-image dimensions, allows her to communicate difficult subjects while also maintaining a sense of agency and control. "It allows me to put humor in, and rise above projecting myself as a victim," she explained in an interview. "The form of a 'comic' sets up a tension that I like." We see this in "Minnie's 3rd Love," for instance: the adult artist labeled the bottle of wine wielded in the drawing by a stand-in for her younger self—in a scene of statutory rape—"The kind of good cheap California wine that makes girls cry and give blowjobs to jerks." And in Gloeckner's books, which include 2002's The Diary of a Teenage Girl, we see the author using words and images to reveal painful sexual experiences—but also, as in Kominsky-Crumb's work, pleasurable ones. The Diary of a Teenage Girl, about a year in Minnie's life at fifteen, features statutory and other forms of rape along with long elaborations of Minnie's sexual desire. A live-action movie of Diary was made in 2015, starring Alexander Skarsgård and Kristen Wiig, among others. It accurately translates this complexity to film (and earned a lot of headlines for doing so). The first line, happily delivered by Minnie, is: "I had sex today." Aline Kominsky-Crumb (along with a copy of Twisted Sisters) appears as fairy godmother throughout—as an animated drawing interacting with actors, as if to underscore her power as a figure for art and creativity in Minnie's life.
Phoebe Gloeckner, panels from "Fun Things to Do with Little Girls," 1993, reprinted in A Child's Life.
Used by permission of Phoebe Gloeckner.
Gloeckner had a tumultuous youth, but today she currently holds the most stable, mainstream job of practically any cartoonist I know, as a tenured professor at the University of Michigan. She is working on a long project about the serial-sexual murders of young women in Juárez, Mexico, which like her earlier work will visualize events (rape, murder) deliberately kept out of the public eye. Aline Kominsky-Crumb and Robert Crumb, who have been publishing their collaborative comic strips in the New Yorker since 1995, live in a nine-story medieval home in Sauve, France, where I visited them in 2009, and observed their appealingly calm domestic life: we sat down to Aline's home-cooked meals (Robert drank a glass a milk with dinner); their daughter, Sophie, a cartoonist, came over to draw with Robert; Aline took me to my first-ever yoga class, which she teaches in their tiny village (Robert, of course, makes the flyers). These cartoonists, however settled their lives now seem, have fought hard against their inner and outer censors to demonstrate that comics is a form that can show both illicit fantasy and hard-to-take truths.
Many, many comics about sex have been published since the underground era. In the Japanese market, hentai—a word that translates loosely in context as "perverse," and is an umbrella designation for a genre of hard-core pornographic manga and anime—is prolific and popular (in 2000, it was the forty-first most-searched term on the Internet). Significant recent works have taken the topic of sex and sexuality in new directions. Melinda Gebbie and Alan Moore (her husband, of Watchmen fame) collaborated on Lost Girls, which stars three grown-up protagonists of fantasy literature—Alice, Wendy, and Dorothy—having lots of sex in order to suggest that real-life sexuality and fantasy adventures are similar, even synonymous. In France, the graphic novel Blue Is the Warmest Color, a raw, sexually explicit lesbian coming-of-age story, was hugely successful and was adapted into a 2015 film that won the Palme d'Or at Cannes. One of today's most buzzed-about comic books is Matt Fraction and Chip Zdarsky's genre-aware sex dramedy Sex Criminals—which like The Diary of a Teenage Girl investigates sexuality as a confusing determinant of adolescent and adult identity, but with a fantasy element thrown in: its protagonists can freeze time, and hence rob banks, when they orgasm (like Diary, it will also become a movie). And Fraction also collaborated with artist Howard Chaykin (creator of the dystopian political comic book American Flagg!) on their own faux eight-page Tijuana Bible—a giveaway with an installment of their Satellite Sam series in 2014—demonstrating the enduring crude vitality of even one of comics's earliest sex-driven formats.
There's also Erika Moen's charming Oh Joy Sex Toy, now out in three book volumes, which is a weekly resource-rich webcomic that features sex toy reviews—banking on comics's show-and-tell properties to produce informative, educational comics stories about seeking pleasure. In an excerpt from the review of a "sex machine" called a Love Glider, we see the X-ray vision of Gloeckner's comics, the ability of comics drawing to show what is happening on the outside and the inside of a body simultaneously. Here, though, the context—and the bright pink colors that characterize each of Moen's installments—aims to be accessible, friendly, and unintimidating. The three distinct taboo-breaking cartoonists of this chapter laid the groundwork for how diverse comics about sex can now be—a field that includes Charles Burns's explicit graphic novel Black Hole, which presents a sex-laced suburban landscape.
Erika Moen, "Oh Joy Sex Toy–Love Glider," ohjoysextoy.com, 2013.
© Erika Moen Comics & Illustration, LLC.
---
WHY THE SUBURBS?
Many of the most iconic comic strips and comic books in comics history—the ones that large numbers of people, when they hear the word "comics," think of right away—picture suburban life. To name just a few: Blondie, Archie, Peanuts, and The Family Circus—which first appeared in 1930, 1941, 1950, and 1960, respectively—are pop culture classics. The Family Circus, a daily comic strip that features a loving nuclear family and their gentle hijinks, is a favorite of the alternative cartoonist Lynda Barry, who wrote in The Best American Comics 2008: "I loved the very world of it, a world that I could watch through a portal edged in ink." (My college even offered a student-run course on The Family Circus, "Mommy! Jeffy's Lookin' at Me!"—titled after a complaint out of the mouth of daughter Dolly about her brother.) The form of the daily comic strip, published in newspapers, lent itself to the routines of suburban life, sometimes in a comforting, reliable way, as Barry explains, and sometimes in an aspirational way. Referring to the archetypally suburban strip Blondie, which features the beautiful, ditzy Blondie Bumstead and Dagwood, her wealthy sandwich-loving husband, one critic points out how the strip modeled "keeping up with the Bumsteads." These serial strips presented middle-class regularities—even of the lightly vexing sort—and their characters inhabited controlled and appealing universes.
From these classics on forward, comics has addressed itself to the ins and outs of suburban life. There are new syndicated strips that have become beloved modern classics, such Bill Watterson's Calvin and Hobbes, which ran for ten years starting in 1985 (it features a six-year-old and his imaginary tiger friend in an unnamed suburb), and Aaron McGruder's The Boondocks, which ran for ten years starting in 1996 (it features a politically radical boy who moves to the fictional suburb of Woodcrest, Maryland). In the contemporary world of comic books, Brian K. Vaughan and Cliff Chiang's stylish ongoing series Paper Girls, a suburban sci-fi adventure that began in 2015, stars a gang of twelve-year-old newspaper delivery girls. And Beverly, a loosely linked collection of comics stories about teenagers and families in suburban Illinois, by Nick Drnaso, was one of the most celebrated graphic novel debuts in recent memory. Today the suburbs generate some of the most complex comics published—and from masters of the field like Chris Ware and Charles Burns. With its apparent middle-class blandness masking either malaise or dark secrets, suburban life, and the sense of self it produces, occupies many contemporary graphic novels.
One of the field's most dramatically talented cartoonists, Charles Burns creates comics that are most often described as twisted. Matt Groening reportedly named villainous Simpsons executive Charles Montgomery Burns (known widely as "Mr. Burns") after his college buddy—who happens to be, despite his namesake and the intense creepiness of his work, one of the nicest people I have ever met. (There are other Evergreen State College references on The Simpsons, including the family house at 742 Evergreen Terrace.) Known for the dark drama of his precisely inked black line, Burns was already a big figure in the comics world, and the illustration world, when his graphic novel Black Hole, about a fictional sexually transmitted disease afflicting suburban Seattle teenagers in the 1970s, hit in 2005. The horror-suspense story had been serialized in twelve separate comic books of the same title, with arrestingly beautiful glossy color covers, from 1995 to 2004. Many readers encountered a graphic novel for the first time with the publication of the ten-years-in-the-making book volume of Black Hole, which develops rich, complex characters over time and displays Burns's stunningly virtuosic style. As one of Burns's publishers puts it, his "ice-cold artwork polishes a 'conventional' comic look to the nth degree, underlying the artificiality of what we take for normal." While he inherited some of the preoccupations of the underground cartoonists, Burns's rendering, unlike Robert Crumb's, produces a clean, bold style that heavily contrasts black and white.
With its unflinching, up-close graphic depiction of sex, including female desire, and bodies all presented with Burns's signature precision, Black Hole moves into a space that underground comics opened up—a space for complex and explicit stories—and extends it into the age of the full-blown graphic novel. Most underground comics of the 1960s and '70s offered pungent but short pieces; the lengthiest is Justin Green's Binky Brown Meets the Holy Virgin Mary, the ambitious, fully-fleshed-out comic-book story from 1972 that clocks in at forty-four pages. Robert Crumb profoundly influenced Burns—but unlike Burns, he has never produced an original novel-length story. Burns, on the other hand, turns his eye on the Seattle suburbs with the detailed attention and sensitivity of a novelist for almost four hundred pages. "When I started Black Hole I really just wanted to tell a long, well-written story," Burns, who himself grew up in Seattle, told an interviewer. "The themes and ideas that run throughout the book had been turning around in my head for years and I wanted to finally get them all out—put them down on paper once and for all."
The son of an oceanographer and a homemaker who studied music, Burns moved around frequently as a child. His first-grade report card noted that he "does very mature crayon work." Burns told me that drawing comics was one of the things he got attention for: "I may have been socially inept, but I could draw good monsters." In grade school he would force his friends to join him in executing parodies of superhero comics; by the time they were in junior high, they were producing parodies of underground comics. Burns explained how Crumb shifted his sense of the possibilities in comics by hitting on an idiom—one Burns would later interpret in his own fashion—"that was incredibly personal and strange, and yet hearkened back to classic comics of another era." Burns taught himself how to do professional comics by taking cartooning books out of the public library that specified techniques and tools. Lynda Barry, who attended high school in Seattle with Burns, described how he would paint murals inside of their high school. "He was the best artist I had ever seen in real life, ever," she raved. "I mean ever, and he blew my mind."
At the Evergreen State College, a hippie school in Olympia, Washington, also attended by Barry and Groening, Burns did comics for a school paper, The Cooper Point Journal, where Groening was the editor. Pointing up the façade of the suburbs was on Burns's mind early as a college cartoonist. In one of his comics parodies of The Family Circus for the student paper, Jeffy, the middle son in the ultrasquare suburban strip, turns to his mother and says "Shut the fuck up, Mommy, we're trying to watch TV!" An art major at Evergreen, Burns went on to earn his MFA at the University of California, Davis, where he discovered punk music—and punk comics in the inspirational work of cartoonist Gary Panter. After art school, Burns moved to the East Coast, hoping to find commercial illustration jobs and continue making comics. He landed his first commercial job, for a nursing magazine in Philadelphia, and shopped his "little meager, sad portfolio" around with few successes.
Burns's big break came in 1980. Like Ware, he was discovered by Spiegelman, but unlike Ware, he actively tried to be. One day, in Manhattan, Burns saw the first issue of Raw. In the issue, Spiegelman and Mouly had listed their address along with a notice about how to send submissions. Burns located the address and literally showed up on the doorstep on Greene Street in Soho, ringing Spiegelman and Mouly's apartment doorbell. As he describes it, a frazzled Art Spiegelman came down and answered the door: " 'What? What? What do you want?' " Afterward, Burns sent in Xeroxes of his work, and he and Spiegelman arranged to meet properly. "He was the first cartoonist I ever talked to," Burns told me. "And he was the first person who really figured out what I was trying to achieve." Burns, as did Ware ten years later, made his name publishing in Raw. His first comics appeared in the magazine in 1981.
To cut to the underbelly of middle-class suburban existence, Burns revivifies genre comics—specifically, horror and romance, the two dominant genres of the postwar period. From his earliest comics, Burns has been preoccupied with plumbing the dark depths of middle-class suburban existence. Born in 1955, Burns is influenced specifically by the trendsetting suburban culture of the 1950s, which flourished during the massive increase of the North American suburban population after World War II. Across his work, Burns frequently draws domestic interiors—bedrooms, kitchens, and living rooms—and suburban neighborhoods that are a sort of ground zero for havoc to break loose. His comics take inspiration from both the white—and specifically "whitebread"—middle-class culture in which he grew up, and the horror comics and romance comics of the 1940s and 1950s that were both a reflection of and a reaction to that culture. Horror comics—particularly those published by the company EC, which came under fire in 1954 for its lurid content—and romance comics were two of the most successful genres of the postwar period. Burns doesn't hearken back to these genres to be camp, or just stylishly retro, although his work, which borrows visual conventions like panel compositions from both horror and romance comics, is often described as looking retro. Rather, as he told an interviewer, his source material "got imprinted in my brain. . . . I'm dipping into it in a very serious way." Burns refigures midcentury comic-book genres like horror and romance to critique the homogeneity, and the social dichotomies, to which suburban life gives rise.
In Burns's work, the uncontrollable, the messy, and the violent, which is often bodily and sexual, break through bland, domestic, conventional exteriors. In his first appearance in Raw, Burns published "Dog-Boy," a story about a nice blond suburban man who leads an "almost normal existence" but for his transplanted dog heart, which causes him to exhibit odd behaviors like licking women's faces (it became an ongoing series, and was even adapted for MTV's Liquid Television). Something is always about to rupture below the surface in Burns's work. In "A Marriage Made in Hell," from a 1984 issue of Raw, Burns turns genre conventions on their head to produce a gruesome send-up of postwar married life that includes accidental body swapping: a soldier returns from World War II and marries his high school sweetheart, but he is actually that man's overseas girlfriend trapped in her male lover's body after a sudden explosion and a misidentification of bodies at the hospital. His Big Baby stories, which appeared in Raw and elsewhere beginning in the mideighties, evoke the seething below the suburbs' artificial surfaces. "Big Baby" is the nickname of Tony Delmonte, a kid who lives in "Pastoralville" and runs back to his cookie-cutter home with its perfectly manicured lawn in order to hide his horror comic books from his mom. Meanwhile, his teenage babysitter obsesses over Ozzie and Harriet, a television show that symbolizes normative fifties ideals, telling her boyfriend she hopes they will "live in a house just like theirs." Comic books themselves here, as a media form, signify the rupture to the perfect surface; they reveal decay, monsters, aliens. And the suburbs in Burns's world are always already sinister, so that his comics merge fantasy horror with real-life horror.
Charles Burns, "The Smell of Shallow Graves," Raw #2.2, 1990.
Used by permission of Charles Burns.
When I asked Burns about the creepiness of the suburbs in Big Baby, he explained, "They're a reflection of the typical American dream-home world. . . . It was what was presented in Better Homes and Gardens, or whatever those magazines were, where you'd leaf through and see all the products and the food and the abundance of everything. I was always interested in the façade of the American way of life, and what was hidden behind the façade." In one classic Big Baby story, "Curse of the Molemen," Big Baby becomes obsessed with a television show about monsters. Burns told me the story deals with "the fake things on TV—and then the real monster that's living next door who is beating his wife. A kid coming to terms with made-up television horror that's kind of fun to watch, and the reality of abusive adults that's not so fun." The real horror in Big Baby, as Burns once put it, "is the horror of the adult world."
And so goes a major theme of Burns's work, which draws on the stuff of popular culture to point up the holes in the façade. Burns visualizes, through gorgeous and terrifying images, how creepy the normal people are, and how normal the creepy people can be. We see this succinctly in the first of two stories about teen plague that Burns published in Raw—"The Smell of Shallow Graves" and "Teen Plague"—in the lead-up to Black Hole. In the short, four-panel color comic "The Smell of Shallow Graves," we see "sad teenagers who won't stay dead"—who wear cardigans and ties but have decaying faces and bodies—sneak back into their parents' home to do comforting, banal, daily things, like watch TV and make a sandwich. Small rituals of everyday suburban domesticity recur in Burns's work, like preparing and eating food. The zombie teens long for domestic normalcy, but they can't quite fit back in.
Charles Burns, Eliza eating a sandwich, cover of Black Hole #4, 1995.
Used by permission of Charles Burns.
There is a lot of sandwich-making and TV-watching, along with pot-smoking and beer-drinking, in Burns's magnum opus. Black Hole focuses on white, 1970s middle-class suburban youth. The book is self-conscious about its characters' whiteness: one teenager is teased as being "lily white"; another, who has caught the sexually transmitted disease, is described as having skin so white it almost looks transparent. The graphic novel merges tropes of old horror comics—like teen plague—with the textured sensibility of novels; Hemingway is an influence (his short story "Big Two-Hearted River," which was itself influenced by Paul Cézanne's paintings, is even directly referenced by a character). Black Hole makes clear Burns's interest in "real-life horror," as he calls it, a kind of social horror, in addition to the dark fantasies that he creates that are inspired by the midcentury horror comics. These include a mouth, complete with teeth, that appears on a teenager's neck and speaks in his sleep—and moans during sex. The idea of mouths sprouting on the body is a preoccupation of Burns's that we see even in his early work. It represents the fear of losing control—something that the heavy artifice and infrastructure of conventional suburban culture, with its homogenous self-replicating communities, seeks to avoid. The unwanted mouth makes noises and articulates sentences that betray one's innermost thoughts and fears; it's unsocialized and uncontrollable—unlike the mouth on one's face.
In Black Hole, Burns focuses on teenagers and their polarized social world to explore the stratification engendered by white middle-class suburban culture. A mysterious, unnamed STD known as "the bug" causes bizarre physical deformities in teenagers—such as the additional mouths. The bug is an out-of-control physical stamp; it inscribes and divides. This teen plague, whose manifestations give Burns an opportunity to demonstrate his skills as an innovator of the creepy, is a marker of social division on every level. It represents us versus them writ large: it is a literalization of grotesque proportions, a physical magnification of alienation, ensuring that a teen's desire to "fit in," his or her striving for normalcy, is forever out of reach. The 2014 film Dawn of the Planet of the Apes, directed by Matt Reeves, uses Black Hole as a plot point: a teenage boy protagonist shows and reads the graphic novel out loud to an ape he befriends in the woods. Like Black Hole, the Planet of the Apes films are about the divide between proximate but sharply differentiated (human and animal) social communities. Here, the patient graphic attention the book reveals to detailing the bodies and the desires of the healthy and sick kids alike is a democratizing move, a refusal on a visual level to posit one group as less worthy than the other.
The storyline of Black Hole shifts perspective throughout: it follows a group of four teenagers from the same high school who all wind up with the bug. The central character is Chris Rhodes, a kind, pretty, popular straight-A student, who literally sheds her skin. She gets the bug after romantically pursuing equally popular and easygoing Rob Facincanni—whose neck has sprouted a second mouth—at a party. Meanwhile, Keith Pearson, a mild-mannered stoner, starts to sprout tadpole-shaped bumps on his torso after electing to have sex with Eliza, a beautiful, troubled artist who has grown a tail.
In Black Hole the plague causes a wide range of physical deformation: some teens' faces decay; others become overgrown with cysts. The bug is a figure for inner turmoil; bodies are radically, externally out of control. Characters talk about "showing" and "passing"—"She's still trying to pass," someone remarks of a girl with webbed hands. (Critics have suggested the bug is a response to AIDS, or an allusion to pregnancy, but while it is relevant to both, it is a figure for something more generalized than either of these alone suggest.) Kids go to their suburban Seattle high school and live relatively normal lives until their deformity is unavoidably clear—after which they literally fall out of the holding pen of suburban space, many of them running away from their parents' homes to live in secret in the thick woods outside of town. In Burns's clever "before and after" endpapers—which demonstrate how the graphic novel is designed as a single object front to back—the opening endpapers offer drawings of yearbook photos of "clean" teens, while the concluding endpapers show the same teens, in the same poses, deformed by the bug.
Charles Burns, back endpapers, "after" portraits, Black Hole (New York: Pantheon), 2005.
Used by permission of Charles Burns.
In a key early episode, Keith and two of his stoner buddies are smoking pot in the woods, a place they name "Planet Xeno"; xenos, in Greek, means "stranger" or "foreigner," as in xenophobia. In the woods, they find a tent filled with personal belongings. The ensuing scenes demonstrate the tonal range of Black Hole, its brilliant twisting together of sadness and horror. Leaving his friends to sift through the tent, Keith wanders a bit further and finds a length of human skin. He holds it up by the shoulders, and breasts, with their perfectly intact nipples, stare him and us in the face. As he stands holding the skin, overcome by sadness, deeply deformed plague-ridden teenagers who live in the woods approach, shooing him away.
Keith drops the skin and turns back to his friends, who have trashed the tent. "Look! Can you believe this shit? We found his yearbook!" one of his buddies exclaims. ". . . And check it out! It's Holstrom! Rick 'The Dick' Holstrom!" When Keith asks, "How do you know it's his?" the buddy replies, "The guy wrote his name in the front of it! What a dweeb!" The accompanying panel closes in on the yearbook photo: Richard Holstrom, in a jacket and tie, with a side part, and a slightly bulbous nose, smiling good-naturedly. Of course, as we learn later, Rick Holstrom is also a comics fan: "You'd see them in the lunchroom, playing chess, reading comics . . . getting food thrown at them," Chris recalls. "Why'd you have to trash all his stuff?" Keith asks his buddies. The answer: " 'Cause he's a fucking geek! He deserves to live out here!" The last panel of the chapter shows a teenager with a misshapen head staring at the trio from behind a tree as they make their way out of the woods.
So there we have it: the popular kids like to kick the sick kids when they're down. Sick kids are losers, losers are sick kids. When Keith finds out that the pretty, popular Chris is sick, he thinks miserably: "How could she do it?. . . . The only way you could get the bug was by having sex with a sick kid. I just couldn't see her doing something like that." But as Black Hole shows, despite this fear and disgust, kids do it, all the time. Chris gets the bug by accident, but she also, in a deep way, is courting it. Burns presents her as overcome with a literally overwhelming desire for the handsome Rob, despite his protestations. And Keith, who early in the graphic novel is repulsed by "sex with a sick kid," later willingly loses his virginity to Eliza—her tail, in fact, turns him on. It's easy to be disgusted, Black Hole suggests, but it's also easy to let passion, however dark and confusing, take over your thinking. Black Hole presents a stratified social universe and then turns it upside down, blurring and confusing the dividing lines. The "real-life horror" that Burns marries with popular horror conventions, like a mysterious plague, is both the horror of the mistreatment of nonconforming people, and the horror of social dichotomies losing meaning. In Burns's comics world, in which the high-contrast graphic style itself thematizes difference, the darkness bubbles to the surface incontrovertibly.
Burns's comics turn on the relationship between external and internal states of being, surface and depth. His suburban teens manifest on the outside what they feel on the inside: ashamed of their desires, cast out, different, unable to assimilate. Black Hole reveals how surfaces don't always hold up. Burns writes of comics in an early one-page comics piece for Artforum, "I wanted to break through all of those rigid panels . . . To pierce the surface and see a richer, more complex structure below." He succeeded. Black Hole exposes, underneath the regular patterning of suburban life, a more complicated and often dark structure in which we access characters' innermost, and often troubled, thoughts. Burns draws the woods, for instance, as a state of mind that preoccupies Keith, in long vertical panels that show him in space with his friends and also exhibit his interior fantasies at the same time. His mind is elsewhere—and we see where. This play of surface and depth is also evident through the book's attention not only to externalized states of being, as in the bug, but also to what Burns has identified as his primary interest, "a more personal internalized horror."
Comics—a medium whose panels enclose and juxtapose space—is perfectly suited to reveal how the suburbs fence out the undesirable, and how geographical and social spaces are linked. In Black Hole, both interior and exterior space become their own characters in the story. This is particularly striking in the case of the woods, which lie outside of the story's suburban center. "If you're looking at the texture of the woods in Black Hole, that starts to be a real element of the story, part of the character of the story," Burns told me. Burns's eye for detail locates readers in sharply realized domestic interiors, which he draws continually. We are also placed outside of those tightly boundaried and policed spaces in the geography of the woods, where page after page reveals the density of the forest: its branches, leaves, the debris on the ground. In Black Hole, there is no gray middle ground, but only pure black and white. "I try to achieve something that's almost like a visceral effect," Burns told me. Black Hole took over a decade to produce, in part because of Burns's meticulous attention to detail. He gives all of the images in the teenage universe of Washington State a full, deep, almost clinically meticulous texture: trees, sand, rocks, the water, the sky, a burning cigarette, a chicken bone, thatches of pubic hair. Burns's line is so controlled some have suggested it looks mechanical, but Burns is simply an expert craftsman. Just laying down all of the black ink in his work takes a long time—much longer than one might think. When I asked him about the process of creating Black Hole's images, he noted, "I was literally drawing every little grain of sand and every pebble and twig." The contradictions the characters feel—grandiosity and terror, for instance—are inscribed in Burns's style. Black Hole, for all of its imagery of decomposed faces, is masterfully gorgeous.
Charles Burns, page from Black Hole, Keith imagining the woods.
Used by permission of Charles Burns.
If Charles Burns uses the conventions of romance and horror genres to expose the bleak underbelly of the suburbs, his friend Chris Ware is the opposite: Ware offers perhaps the prime example of how comics today express realism, capturing the texture of perception and the experience of time. Ware's graphic novel Building Stories, which appeared in 2012, is a love letter to the suburban ordinary that takes on all of the ambivalence the suburbs generate for its characters. One might consider Ware the Alice Munro, or the John Updike, of comics (minus the controversial sexual politics). His fastidiously detailed comics, beautiful enough to be collected by museums, present a poetry of white middle-class loneliness.
Ware's entire comics oeuvre is about solitude, loss, and disappointment. Art Spiegelman once told me that Ware was the only cartoonist he knew whose work is about a sensibility. He didn't specify which one, but loneliness is the dominant sensibility of Ware's achingly pretty books. As an unpopular, often lonely child himself, Ware developed a profound sensitivity and ability to connect to the loneliness of others. He felt attached to Charles Schulz's Peanuts from a young age—in addition to reading the comic strips, Ware recalled to me, he would watch the holiday specials on TV, and he used to kiss the television set when the Charlie Brown Christmas special was almost over because he knew he wouldn't get to see it again for a whole year. Ware even sent Charlie Brown a valentine in the mail as a child, because he felt so sorry for Charlie Brown for not getting any valentines (one of the strip's recurring plot points). In his amusing illustrated collection Key Moments from the History of Comics, French cartoonist François Ayroles includes "Chris Ware sends a card to Charlie Brown" as one of the historic moments in comics he imagines across the world. (Matt Groening and Charles Burns drawing comics together also makes the list.)
Ware's graphic novel Jimmy Corrigan is about lonely boys and men who lack stable or comforting families (remember it ranks highest on "The Chris Ware Sadness Scale," on the "soul-crushing depression" side of the chart, in Tim Leong's Super Graphic). The later Building Stories, on the other hand, while it continues to explore loneliness, features a never-named woman who eventually becomes a suburban mother, presenting her life over decades. It is about expressing the everyday experience of a woman from within the space of a stable family (something wholly absent from Jimmy Corrigan). Building Stories, like Black Hole, took ten years to complete. In one of its key moments, the protagonist searches for a book to read from her home's own shelves. She considers, and rejects, classics by Melville, Joyce, Proust, Dostoyevsky, and Nabokov, and thinks: "Fuck! Why does every 'great book' have to always be about criminals or perverts? Can't I just find one that's about regular people living everyday life?" Building Stories is that book. And it is a "great book," too, both in its ambition and its scale, and according to its reception. Widely acclaimed as well as popular (it quickly sold out its first print run with Pantheon, and with a sticker price of $50), Building Stories has been a sensation. It shows how comics can, in fact, present moving stories about regular people living everyday lives and make these stories feel vivid and intimate. It was named Publishers Weekly's Best Book of the Year, and appeared on the annual top ten lists of dozens and dozens of publications, including the New York Times, Washington Post, Time, Newsday, and Entertainment Weekly.
Building Stories is a 12-by-17-by-2-inch carton that weighs six pounds. Inside the Building Stories box are fourteen different comics narratives, all in beautiful color, in formats of all sizes, from the small pamphlet to the full-size newspaper to the gold-spined hardcover book that evokes the classic Little Golden Books children's series. The stories that appear across the book's distinctly formatted objects are loosely interlinked, crisscrossing time and space. The story takes place in Illinois; most of it features the central protagonist, a dark-haired woman with one leg and an art degree, either living alone in a Chicago walk-up apartment, or in a single-family house in the suburb of Oak Park, Illinois, with her architect husband and young daughter. (Ware, who was born in Omaha and now happily lives outside of Chicago, has a great line about America: he has said that if New York is the brains of the country, and Los Angeles is its asshole, then Chicago is its heart.) In Building Stories, there is no "correct" order in which to read the parts that make up the whole. In fact, even though the character ages in the book—we see her as a toddler and a mother, for instance—the parts cannot be constructed to form a linear trajectory, since the individual pieces of the book themselves intertwine temporalities copiously, across their pages, and frequently in the space of one page itself. One striking "silent" page without narration or dialogue pictures the protagonist sleeping at various ages and concludes with her as a baby, her tiny body floating in space.
The title Building Stories asks readers to think about built space, particularly domestic dwelling spaces, and how they affect and are affected by people: the stories that come from buildings. The three-story apartment building is even a speaking character in Building Stories; it tallies the number of orgasms and broken radiators and so forth it has witnessed. But "building" functions in the title as both a noun and a verb. The title also asks readers, with its three-dimensional collection of loose objects in a box, to think about the book itself as a kind of built space that gets completed through the individual process of reading: How does one build a story? Building Stories is a space, and a story, that readers themselves construct.
Chris Ware, final page of a clothbound hardcover book within the box, Building Stories (New York: Pantheon), 2012.
Used by permission of Chris Ware. Image courtesy Chris Ware.
The back of the rigorously designed box presents the author's description of the book—and gives no direction whatsoever as to any correct reading order of the book's "14 distinctively discrete books, booklets, magazines, newspapers, and pamphlets," which it reproduces in miniature images. Crucially, the back cover also presents a blueprint-style drawing of a house, diagrammed with various pieces of the book scattered widely across the spaces of the home. One piece is on the shelf, one is open on a chair, one is under a table. The experience of reading Building Stories is as nonlinear as wandering into a house, as interactive as handling objects in space—objects you could take with you, misplace, leave out next to the cereal. Ware deliberately places his book, on its own back cover, within the very suburban spaces that the story examines. In a jokey but accurate address to the reader, Ware writes: "Whether you're feeling alone by yourself or with someone else, this book is sure to sympathize with the crushing sense of life wasted, opportunities missed and creative dreams dashed which afflict the middle- and upper-class literary public." The next and last paragraph then refers to the diagram of the house, noting that it makes suggestions "as to appropriate places to set down, forget or completely lose any number of its contents within the walls of an average well-appointed home." Well-appointed, and feeling alone: the classic disappointment of the suburbs. Building Stories addresses its reader, claims suburban existence as its domain, and shows from the outset, with its diagram of domesticity, how comics can reveal the intricacies, and the psychological importance, of space.
Chris Ware, Building Stories back cover showing the book's various elements along with a diagram of those elements in an "average well-appointed home."
Used by permission of Chris Ware. Image courtesy Chris Ware.
A move to the suburbs marks a major shift for Building Stories's protagonist. As the book's various pieces reveal, when living in Chicago, she worked as a florist, with ambitions to become an artist or writer. She attended art school, during which time she met her first boyfriend, Lance. They were engaged in a passionate and serious relationship until he fled, devastatingly, soon after she agreed to an abortion. Her husband Phil is an architect (and her former classmate in art school). When their daughter Lucy is a baby, sometime in the early years of the twenty-first century, Phil suggests they move to the suburbs for familiar reasons: they can't afford to buy the same amount of space in Chicago, and they're concerned about decent schools for Lucy.
"Personally," the protagonist confesses to readers about city life, "I'd imagined us in some sort of raw loft space that Phil could renovate and redesign." An accompanying fantasy, pictured in blueprint, shows her painting on a large canvas in an open space where Phil also sits at his work desk with a ruler and the baby plays on a blanket between them. (She often thinks in blueprints when she imagines alternate lives, seen by an external viewer.) In Oak Park, which she dismisses as full of "professionally maintained lawns and bland restaurants," they move into an appealing Prairie-style home, nicer than the house she'd grown up in, the narrator notes. The move either itself enacts, or coincides with, her shift away from identifying as an artist to identifying as a full-time mother. "Had I really just signed my life away as a suburbanite? Was I really ready to give up that easily?" she despairs.
Ware's comics invoke the details of the family's suburban life, down to brand names and mildly conspicuous consumption: the protagonist, who disdains what she sees as the elitist culture around food consumption, yet reads the blog Epicurious to keep up with trends in cooking. We learn they have a Williams Sonoma club chair (a feature, perhaps, of an "average well-appointed home"). Ware even particularizes their pasta: "Just then, for no good reason at all, while staring into my plate of Trader Joe's Tortiglioni Parmagianno, something came loose inside of me and floated to the surface," the protagonist recounts at one point. The consumer self-consciousness arrives in the book once the family is in Oak Park. And while a connection to the stuff of middle-class life develops, a certain kind of disconnect sets in between husband and wife, despite their essentially good rapport.
One of the central visual motifs of Building Stories, which repeats throughout the book, is the pair of husband and wife, alone together—sharing space, each attending to a device. "Spending time together" often means occupying the same space on individual computers that almost look appended to their bodies. Most often we see them in their living room, each on a computer, each lit by the glow of the screen. But in a small rectangular booklet that compiles vignettes of family life, on a beautiful summer night husband and wife sit outside on the back stairs each looking at their phones, which light their faces, while Lucy plays with a different kind of light-producing entity: fireflies. The book makes clear that the protagonist and her husband don't have sex very often; twice in the book she calls sex "overrated." In a single devastating image that reveals a marriage drained of spark—and which occupies a rare, dramatic full page in Building Stories—we see the protagonist, facing readers and her husband, naked, her clothes in an unceremonious pile around her feet. Phil lies on their bed, also naked, legs crossed, his flaccid penis hanging limply to the right, while he stares intently at his iPad, its light bathing his face. Ware offers up sex—but unlike the unruly teenage passion depicted by Burns, it is a torturously premeditated middle-age suburban parental sex date that is probably the least sexy image of a precoital couple anyone may have ever seen.
Most saliently, though, with the move to the suburbs, the unnamed protagonist slides into a life of child-dressing, sandwich-making, and playdates that replaces writing and painting; the daily labor of her suburban life eases her artistic aspirations out the window. The fundamental dilemma the book poses is how to maintain a sense of self while raising a child. The narrator imagines a bird's-eye view of her own home, the space that encapsulates this life in which she can't always recognize herself: "Phil, Lucy, the house, and me . . . or was it me? Some dormant version of myself had sparked back into existence and called a time-out, saying, 'Hey, weren't you supposed to be an artist? Or a writer? Or something? 'But look at you: you're just a mom . . . nothing but a suburban mom . . .'."
Yet Building Stories is what I think of as a love letter to suburban ordinary. It is focused on giving form to the texture of experience. Building Stories, then, is about capturing the everyday passage of time. This is something the pace of the suburbs allows Ware's protagonist to notice—and Ware himself to meticulously represent through a medium, comics, that itself turns on the division of time through boxes of space on the page. Building Stories is unlike many comics this book covers for many reasons, chief among them its relation to the event, to things happening. Although in her twenties, as an art school student, the protagonist had a bad breakup, and an abortion, over the course of the narrative, whichever way you read it, there isn't a central event or central plot point or even central conflict in Building Stories; it's a book about the ordinary life of an unnamed woman, and her neighbors, friends, and family. Ware is even featured in a new academic book with the amusing title What Happens When Nothing Happens: Boredom and Everyday Life in Contemporary Comics, which sports a Ware image on its cover. The primary focus of Building Stories—its eventness—resides in its obsession with the ordinary lived experience of time.
Chris Ware, page from 9×12 pamphlet, Building Stories.
Used by permission of Chris Ware. Image courtesy Chris Ware.
Chris Ware, consecutive facing pages moving from winter to spring in a 3-by-6-inch booklet, Building Stories.
Used by permission of Chris Ware. Images courtesy Chris Ware.
Comics expresses the perception of time through its rhythm-producing arrangement of frames and gutters, which can speed or slow or stop its movement. In Building Stories, those frames capture the quiet, small moments that constitute everyday life. One booklet without words accumulates routine moments as the seasons change and Lucy gradually ages: on one page the protagonist changes a diaper; on another she watches Lucy on a playground slide; on another the mother and toddler sit in silence eating breakfast; in another she watches her daughter raise her hand in class through the window of her school. Comics as a medium traffics in the moment: each frame, conventionally, represents a moment of time, a beat. In Building Stories, Ware divides and freezes moments into even littler moments: a glance, a posture, a hand ascending or descending to point. In collecting and juxtaposing the moments of daily life, Ware reveals their cadence as beautiful, despite, or in spite of, the protagonist's understandable fears.
Building Stories is about the grain of individual experience—which is to say, about perception and how time passes. Rather than weighing in on the suburbs—Building Stories is not polemical or critical—it presents a poetics of the suburbs, which is to say it seeks to present the experience of space and duration, including the conflicting feelings that any regular person generates over time. Ware, then, captures his characters' ambivalence. In one scene, the protagonist looks at her husband, and her thought balloon—rather than her speech balloon—offers readers her silent address to him: "God I fucking hate you," she thinks. In another moment, her speech balloon presents this thought: "I have the best family in the world." Building Stories presents a domestic comics realism made up of prosaic shifts of mood and tone: the texture of everyday life, in which sometimes you hate your husband and sometimes you feel lucky to have him; in which your child is incontrovertibly and joyously the center of your life even as you feel a pervasive sense of loss and awareness of sacrifice. With its ability to slow down, split, isolate, and juxtapose quotidian moments in panels of all different shapes and sizes, the comics medium in Ware's hands captures how these moments create a sense of a life. Explaining once what Building Stories is about, Ware simply said it is about empathizing with other people. In a poster he made for a 2012 conference I organized on comics, Ware named it "a conference addressing the art of the empathetic doodle." Burns's Black Hole is also about empathy for the other, but his 1970s suburbs provide a starker backdrop for critique, whereas Ware's suburbs, à la Updike, seek to make the experience of them vivid. Updike, for his part, an avid cartoonist into his twenties, saw comics as a model for creating a living, breathing world in fiction: "One can continue to cartoon, in a way, with words," he noted. "For whatever crispness and animation my writing has I give some credit to the cartoonist manqué." Building Stories shows us the texture of a life, from one person's point of view, and asks for our attention and participation in adding the pieces together.
Chris Ware, newspaper-style foldout page with a life-size baby at the center, Building Stories.
Used by permission of Chris Ware. Images courtesy Chris Ware.
Building Stories calls readers' attention to how we build our own lives, which is to say, how we build a narrative of our own lives from bits and fragments and images and feelings. In a page with its own title, "Browsing," the protagonist recounts a dream to a college-age Lucy, who wants to go to art school. In a bookstore she finds her own book, and, to her surprise, she likes it: "Everything I'd forgotten or abandoned or thrown out was there . . . everything." It's illustrated, too, in lines "so precise and clean it looked like an architect had drawn them." While browsing in her own book, which keeps growing, she realizes it was "in pieces . . . like, books falling apart out of a carton, maybe . . . But it was beautiful . . . it made sense." Her husband is an architect, a professional one, but this page suggests readers see her as equally architect—of her past, and of her memories, and of her dreams, despite her sense of disappointment. Building Stories itself is the dream book, a book of memory. Ware has built a story; his unnamed character has built a story, a collection of her memories; and readers too build their own story out of the shared pieces they assemble.
Building Stories reveals comics as an art of memory. Art Spiegelman has claimed, "Comics work the way the brain works: picture signs mixed with little bursts of language. PAST, PRESENT, and FUTURE all scrambled and butted up against each other—the perfect medium for depicting memory." Building Stories makes prominent use of the nonlinearity of comics reading, using the center of the page to focus readers' eyes on an image prominent in its protagonists' minds, while associated bits of narrative, in words and images alike, float nearby. This technique is an aesthetic centerpiece of the book. Our eye is drawn to all sorts of objects that appear at the center of pages: a flower, a notebook, a vagina, a photograph, a face, a mask, hands, a baby—drawn at life-size in one of Ware's 32-by-22-inch foldout pages. This makes the page, like the book in a box itself, one in which the eye wanders and assembles moments without a clear beginning or end—in which we as readers build the pieces of a life together out of fragments—fragments of images, like in the process of memory itself. The page design often evokes the psychic, interior landscape of a character. The different formats in which the elements of the story appear—like the Little Golden Books, a popular children's book format, or the Sunday-style newspaper—are themselves evocative of how people narrate their own lives to themselves through popular forms and idioms. The golden-spined books even have a space for the reader to insert his own her own name. In a book about space, Ware invites the reader in.
---
WHY CITIES?
All the hours I'm awake, I'm drawing. I'm walking down the street, I'm drawing in my head, I'm drawing that street in my head.
—Jaime Hernandez, in Comic Book Artist, 2001
Comics in the United States were born in cities, in cheap, sensational newspapers published by Hearst and Pulitzer. They were born in the alleys of New York. The first comic strip, in 1895, titled Hogan's Alley but known as The Yellow Kid, by Richard Felton Outcault, starred a Lower East Side tenement guttersnipe child of visually indeterminate ethnicity (later it was clarified his background is Irish) who got his nickname from his dingy yellow nightshirt. He would inspire the term "yellow journalism." Comic-book superheroes are also tied to cities: Superman to Metropolis, Batman to Gotham City, Spider-Man to New York City. The first two can be understood as fictionalized versions of New York: comics writer Frank Miller says that Metropolis is New York in the day, and Gotham is New York at night. The very first book to advertise itself as a "graphic novel," Will Eisner's 1978 A Contract with God, is specifically about city life, tracing tales of woe among four separate residents of a Bronx tenement.
Comics are linked to the suburbs in their expression of teenage and midlife middle-class angst—and they also are inspired by and reflect the energy, diversity, and populism of cities. Many of today's most significant and innovative comics pivot on the space of the city, from Ben Katchor's graphic novel The Jew of New York, set in the 1830s, to Peter Kuper and Seth Tobocman's politically radical comics anthology World War 3 Illustrated, which has covered protests and gentrification in New York and elsewhere, to cartoonist Guy Delisle's travelogue Pyongyang, detailing his time in the North Korean capital, to the cartoonist Seth's whimsical, aesthetically rich comics stories that prominently feature the fictional Canadian city of Dominion (and for which he has constructed an intricate three-dimensional cardboard model, itself now the subject of a documentary).
Chris Ware's Illinois-based Building Stories, like Harvey Pekar's Ohio-based American Splendor, uses the rhythms of comics, its ability to capture and frame small moments, to chronicle everyday life in the Midwest—the experiences of a regular person in a regular town (and, before she moves to the suburbs, a regular city—Chicago). But while Ware's work is about individual interiority as it develops in connection with the spaces people inhabit, Pekar's work is largely about exteriority, tracking a democracy of voices in a city's public spaces. And while Building Stories, however satirically, advertises on its back cover its sympathy with the afflictions of "the middle- and upper-class literary public," Pekar's American Splendor comes at midwestern ordinariness from the opposite angle, an explicitly working-class point of view. Each issue carries the subtitle From Off the Streets of Cleveland.
Pekar, who died in 2010 at age seventy, is one of the best-known contemporary cartoonists—a public figure people who don't pay attention to comics might have come across on television or in the movie theater, or have read about in the many profiles of his cantankerous, outsize personality. Daniel Clowes once remarked that being a famous cartoonist is like being a famous badminton player (which is to say, not very famous at all). But over decades of paradigm-shifting work, which slowly became more and more recognized and then eventually quite mainstream, Pekar, a Cleveland file clerk with a self-published autobiographical comic book, became as close to a celebrity in the broader popular culture as any cartoonist this book covers. In a 2016 episode of the New Yorker Radio Hour, Henry Finder, an editor at the New Yorker, noting the history of "comic books that weren't the kind of standard issue," first names Pekar, followed by Crumb and Spiegelman.
The "comics bard from Cleveland" became a semicelebrity as a professional populist curmudgeon appearing frequently on David Letterman in the 1980s and '90s, and his life story was made into an award-winning 2003 film, also named American Splendor, starring Paul Giamatti as Pekar, and Pekar himself (credited as "Real Harvey"). The film won the Grand Jury Prize at the Sundance Film Festival and was nominated for an Academy Award. In Cleveland there is a desk and bronze statue commemorating Pekar at his favorite public library, where he went almost every day, and a Pekar Park in Coventry Village, in the Cleveland Heights neighborhood, where he lived for decades. As Robert Crumb, his frequent collaborator, explained, "He's the soul of Cleveland. . . . He's passionate and articulate. He's grim. He's Jewish. I appreciate the way he embraces all that darkness."
Unlike most of the literary world, comics is not New York City–centric. Cleveland looms big in the history of comics, and in its future. Bill Watterson of the adored Calvin and Hobbes grew up and lives near Cleveland (he joked to the Washington Post in a 2016 article titled "Wait—Just How Did Ohio Become the Cradle of Great Cartoonists?" that it helps "to grow up with sober midwestern values and to live someplace without a lot of exciting diversions"). Cleveland boasts one of today's most acclaimed young comics writers, Brian K. Vaughan (of Y: The Last Man, Ex Machina, Saga, and Paper Girls fame). Like fellow Clevelanders and comic-book icons Jerry Siegel and Joe Shuster, who introduced their creation Superman to the world in 1938, Pekar, born the following year, came from a family of Eastern European Jewish immigrants. Pekar grew up with Yiddish as his first language; his parents, Saul and Dora Pekar, hailed from Białystok, Poland, and called him by his Yiddish name, Herschel. Saul Pekar was a Talmudic scholar who in his American life owned a grocery store on Cleveland's East Side, on Kinsman Avenue; the family lived above the store. In the agonizing comics story "Out of the Past," Pekar details how his father, catering to the neighborhood's population of "Jews, Italians, blacks, and some Slavs," worked a ninety-hour, seven-day workweek and how it "tore" Harvey apart as a child to see his father have to forsake an intellectual life to get by in America. (Speaking of Polish Jewish émigré fathers: Pekar heavily criticized Art Spiegelman for not treating Vladek Spiegelman well enough in the pages of Maus, a beef that seems more personal than actually evaluative.) Pekar worked in his father's grocery from the age of ten; he grew up, when not at school and working, out on the streets of his ethnically mixed neighborhood, where he was often bullied as unassimilated and learned how to fight. After high school, Pekar briefly joined the Navy, and spent one year at Case Western before dropping out. He became a committed autodidact, reading constantly (hence the library statue).
Pekar met Crumb, who had moved from Philadelphia to Cleveland to work for the American Greetings card company, in 1962; the two were neighbors. Pekar introduced Crumb to Cleveland's full range of ethnic neighborhoods ("Well whaddya know—a white slum," Crumb remarks in amazement as the two walk down the street in one American Splendor story). They also bonded over their love of jazz, about which Harvey sometimes wrote as a freelance critic. "Harvey was the first person I ever met who I thot [sic] was a genuine 'hipster,' " Crumb recalled, referring to the historical definition of the term à la Norman Mailer's The White Negro: Superficial Reflections on the Hipster, the 1957 essay that examines self-consciously nonconformist young white people who adopt black music and culture as their own. "I was very impressed. He was heavily into modern jazz, had big crazy abstract paintings on the walls of his pad, talked bop lingo, had shelves and shelves of books and records, and never cleaned his apartment . . . and he was seething intense, burning up, always moving, pacing, jumping around . . . just like a character out of Kerouac." When he later drew him, Crumb portrayed Pekar as a wild-eyed, manic creature in a hole-bitten T-shirt. After some odd jobs, including one as a mail carrier, in 1965 Pekar began working at the Cleveland Veterans Administration hospital as a file clerk, a job he would keep for the next thirty-seven years, until his retirement.
His friendship with Crumb, besides stoking his record-collecting habit, got Pekar interested in turning his sharply focused observations of quotidian life into comics—despite the fact that he couldn't draw easily or well. With Crumb's encouragement during a visit to Cleveland in 1972—during which he offered to illustrate Pekar's stories—Pekar started scripting comics stories to be drawn by others. In Pekar's way of working, he would author all of the text and sketch crude stick figures into frames to guide his collaborators as to how he envisioned the stories breaking down. The words and the compositions belonged to him; the actual marks belonged to artists with a range of different styles (he even collaborated with Alison Bechdel, whose solo work he strongly supported, and Joe Sacco). Whether one feels connected to a Pekar story or not often depends on the vagaries of taste and who is illustrating. Pekar's first comics story, "Brilliant American Maniacs Series No. 1: Crazy Ed," a one-pager illustrated by Crumb about a chance conversation with a stranger about the name Harvey, was published in 1972, in the underground comic book People's Comics. (A fascination with names, as seen later in "The Harvey Pekar Name Story," is a running theme of Pekar's work.)
After publishing a few scattered comics stories in underground comic books over the next few years and getting a good response, Pekar decided to make a go of it in 1976 with very his own title. The Crumb-illustrated story "How I Quit Collecting Records and Put Out a Comic Book with the Money I Saved," published in 1979, details Harvey's plunge into the world of self-publishing comics, after he realizes that his record-collecting habit eats up every available cent in his already modest lifestyle and is detrimental emotionally and practically ("I was spending all of my money on records I just filed away. . . . I had to think twice about buying a hamburger or going to a movie"). When he decided to quit obsessive collecting cold turkey, Pekar, gainfully employed as a file clerk, realized he had the money to independently print and circulate his comics. In the mid-1970s, Pekar also realized that the variety and openness of underground comics publications, after the end of the Vietnam War and the dilution of the counterculture, were on the wane. Practical-minded and taking matters into his own hands, "I found out," Pekar discloses to readers about comic books, facing us directly, rendered in Crumb's quivering, shaded lines, "I could save up enough bread in a year to publish one."
American Splendor #1, fifty-two pages of original stories, which sold for $1, appeared in 1976 with a bold, primary-colors cover by Cleveland artist Gary Dumm, and billed itself as "Adults Only." (The stories themselves usually appeared in black and white, as with most inexpensively produced undergrounds.) Although somewhat satirically also billed as the "Big Bi-Centennial Issue," the first issue of American Splendor celebrates something it claims as quintessentially American, and urban, and splendid: the street-level, public-sphere conversation. On the cover, three men, identified as Sid, Freddy, and Harvey, sit on the steps of a closed store on a city street and talk—specifically about ethnic politics: Sid tells a story about Gavrilo Princip, the Yugoslav nationalist who assassinated Franz Ferdinand, sparking World War I. From the very beginning, Pekar's comics sought to capture the cadences of conversation in public space that characterize the ethos and energy of city life—particularly diverse, working-class city life. The three men, discussing Eastern Europe, sit under a store sign featured prominently in the composition that advertises Italian and Lebanese specialties.
American Splendor appeared once a year, and for its first fifteen issues, until 1991, Pekar self-published the comic—even after mainstream publisher Doubleday issued two American Splendor book collections in 1986 and 1987, the first of which won an American Book Award (later on, when Pekar fell ill, comic-book publishers Tundra, and then Dark Horse, assumed publishing responsibilities). Pekar innovated comics autobiography, widening its scope to include the working-class quotidian, and showing how comics could make the rhythms of daily life, especially in public spaces, evocative and communicable. "I want to write literature that pushes people into their lives, rather than helping them escape," Pekar once explained to an interviewer. His topics are the daily encounters of everyday life, or existential musings about seemingly simple facts of life like one's name—but always in relation to a public body, to the city. The celebrated forty-eight-panel "The Harvey Pekar Name Story," illustrated by Crumb, features Pekar in every same-size frame addressing the audience face-on, musing on the other Harvey Pekars in the Cleveland phone book. (You wouldn't think this would be very adaptable for the drama of cinema, but it's replicated with Paul Giamatti and limited animation in the American Splendor film.)
American Splendor developed self-consciously humorous—but true!—descriptive taglines on its covers: "Stories About Record Collecting and Working"; "Stories About Sickness and Old People." One of Pekar's funniest slice-of-life stories is "Standing Behind Old Jewish Ladies in Supermarket Lines": when an old Jewish lady surprises him by asking if he wants to cut her in line, Pekar, who is Jewish himself, thinks earnestly, "I was really amazed by her courtesy. That's the first time a Jewish lady was nice to me in a supermarket! . . . She's taller than most old Jewish women. . . . Maybe she's a mutant!" Pekar's settings are largely public spaces: workplaces (including, prominently, the VA hospital), businesses (the tailor shop, the bakery, the fruit stand, the diner), the city street (as each and every issue announces), and civic spaces like the public library.
Harvey Pekar and Gary Dumm, cover of American Splendor #1, 1976.
Used by permission of Joyce Brabner (Harvey.Pekar.Estate@gmail.com). Image courtesy the Billy Ireland Cartoon Library & Museum, Ohio State University.
Pekar's one-page "Overheard in the Cleveland Public Library: March 21, 1977," with art by Gary Dumm, displays one of Pekar's signature talents: listening. He sought above all to be accurate in his comics' transcription of everyday encounters and interactions—even ones from which Harvey himself is directly absent, but to which he can be a witness (he sometimes goes by the moniker "our man"). The eight-panel "Overheard" features Harvey only silently in its top title frame—although readers merely see his back, his posture indicates he is observing the conversation in front of him. The story is about everydayness: about something that happened at the library on some routine day, a Monday, when Pekar went there. It also links class politics and aesthetics, all while also addressing itself to the kinds of meaningful, if awkward, interactions between strangers that can happen in public spaces like a library.
The story begins midconversation as a bespectacled librarian speaks to a man in a patched coat who has approached her. We soon learn that the man, clutching sheets of his poems, had asked that the librarian evaluate his poetry. She directs him to the Cleveland Area Arts Council, which prompts him to complain that nobody likes his poetry: "I show it to everyone an' nobody likes it . . . But I read this stuff in 'Harper's' an 'Atlantic' with them big intellectual words, an' it don't mean nuthin' to me." In the center of the page, Pekar and Dumm drop the panel borders to emphasize the librarian's shock, and add the spiky lines, a staple of comics language that cartoonist Mort Walker named "emanata," which indicate surprise. They also drop any speech or thought balloons—the panel is silent. Pekar, so attuned to rhythm, to jazz, often uses his sensitivity to music and to sound in general to dramatic effect by removing it in his comics. Many of his stories, which are often divided in regularized panels, emphasize silent beats in a conversation, as "Overheard" does.
Harvey Pekar and Gary Dumm, "Overheard in the Cleveland Public Library, March 21, 1977," American Splendor #3, 1978.
Used by permission of Joyce Brabner (Harvey.Pekar.Estate@gmail.com).
"Sir," says the librarian, "There's nothing wrong with writing poetry that rhymes." Pekar presents the encouraging librarian—and by extension, the library itself—as a space for aesthetic inclusion (if not aesthetic evaluation) that results from its structure as a public, and therefore, in some profound way, populist space that accommodates both poetry that codes as "high" (the difficult words of published poets) and that codes as "low" (the rhyming poetry of amateurs). In 1979, Pekar authored a second version of this same story, which he called "Library Story: Take Two," with the artist Michael T. Gilbert—the subject clearly made a big impact on him, as he himself, in a different medium, created a different kind of amateur "poetry" (he is often referred to as the poet laureate of Cleveland).
Comparing the different comics renditions of the same event makes clear how important visual style is to the effect of the final Pekar story. The city Pekar presents is about voices, about conversation—something his own comics stage in the very fact of their collaborative fabric, their ongoing conversation between writer and artist. In other words, in its procedure his work stages the very dialogue that his comics are so intent on capturing in the Cleveland in which he lives and moves. His city is a space of dialogue, and so are his comics, in the basic aspect of their creation. As we see even in the very first American Splendor cover, dialogue is fundamental to Pekar's art. Sometimes a story pivots on a funny exchange Pekar had with a co-worker, or even just the everyday witticisms or quirks of certain co-workers, which American Splendor largely lovingly profiles. In "Lunch with Carmella," Harvey recalls the title character, a strange but admirable longtime employee of his office building. In one of my favorite Carmella moments recounted by Pekar, her co-worker Ruth Rizzo says to her, "Carmella! Shame on you! Your dress is dirty!" to which the haggard-looking Carmella replies, deadpan, "Yeah, but it's only dirty on the outside."
Pekar's comics, in capturing a democracy of voices—which includes, of course, his own—seek to present the idiosyncrasies of speech that constantly buzzes around the city. Pekar carefully catches the way people around him actually speak—their cadences of speech, the modulations and inflections, and also their idiomatic differences. Frequently, Pekar throws in ethnically specific phrases or bits of language without explanation; he sees his comics, then, as for the community, widely speaking, of people who are pictured within the pages of American Splendor—or for someone engaged enough with the story to look things up on her own. I had to look up three Yiddish words in the two-page "The Maggies," a brilliant story in which Harvey—ever the fan of the spontaneous street-level encounter—runs into a tiny, wizened old man on the street, whips out his pad and pencil, and grills him about a group of low-level 1930s Cleveland Jewish gangsters, while being berated by the man. "Do you want to hear this or do you want to exhibit your idiotic sense of humor?!" the man rails when Pekar (as usual) jokes about a name. In addition to his musician's ear, the fact that he grew up speaking Yiddish and later learned English, switching between the two, must have also forced attention to sound, context, and speech. One short conversation, then, is often the subject of a Pekar story, as in the story "A Compliment."
This six-panel vignette, created with Crumb, takes place in the hallway of the VA hospital. It includes one panel of simple silence. Pekar narrates a chance encounter with his co-worker Mr. Boats, a recurring and philosophical character in American Splendor, who here defends Harvey from good-natured ribbing about his head-to-toe outfit of secondhand clothes ("That's all right! This boy knows what t'do with his money!!"). The representation of speech in American Splendor, as in many comics, doesn't adhere to correct spelling but rather seeks to express rhythm in its visual emphasis (the bold letters) and the aural capture of speech over grammar and spelling convention (Harvey's own speech is usually represented by many dropped vowels; "enuff" not "enough"; "yer" not "your"; "lissen" not "listen"). American Splendor is full of accented speech—including Pekar's own—as part of his comics portrait of the city, one which marks and celebrates differences as opposed to eliding them. The old Austrian doctor at the hospital says, "Here's a choke zat you can poot in your book"; the courteous old Jewish lady in the supermarket asks him, "You vant go ahead of me?" Comics is how Pekar collects these voices and interactions, recording events so mundane, as Crumb put it, that they seem exotic.
Pekar was not the first cartoonist to produce man-on-the-street comics. A few years earlier, in 1974, New York City cartoonist Stan Mack started publishing Stan Mack's Real-Life Funnies, observational comic strips that were "guaranteed overheard," in alternative weekly paper The Village Voice, which had also launched Jules Feiffer's celebrated Sick, Sick, Sick. It ran for twenty years. In an interview, Mack charmingly said that he "learned to take notes on my shirt cuffs and walk backward in crowds. But most of all I learned to listen to what ordinary people have to say." Whether New York City or Cleveland, the space of the city is about a cacophony of voices (Mack recently complained when he listens these days it's mostly all people on cell phones). But while Pekar wasn't the first cartoonist to evoke the energy and diversity of the city in comics this way, he was the first to do so with ambitions to make his comics, inlaid with autobiography, literary, and longform in scope. Mack's strips were revealing but short, part of a newspaper comic strip tradition; Pekar's, created for comic books, were longer and moodier, able to be expansive because of their self-published format. Pekar was only answerable only to his own sense of judgment, and the willingness of his collaborators; his stories were able to meander along with his subjects or his own philosophizing. And many of his stories are long.
Some of Pekar's lengthiest stories detail his eight appearances on David Letterman's shows Late Night with David Letterman and Late Show with David Letterman between 1986 and 1994. A big part of Pekar's legacy as an artist, and a midwestern populist, comes from his role as a repeat guest on Letterman's show. And this legacy is not only within the comics field—Pekar is central to television history. When Letterman retired in May 2015, numerous think pieces about his role in American culture appeared—and many of them brought up Pekar, whose off-script, on-air fights with Letterman were awkward and electrifying. On the night of Letterman's last show, the Washington Post ran an article, "How Harvey Pekar Became One of David Letterman's Greatest Recurring Guests," which claims that Pekar "remains one of his most memorable recurring guests ever—even through the rearview mirror of Dave's 33-year late-night run." Television host and comedian Jimmy Kimmel wrote in Time, "The best guests were the worst guests, those who either didn't get it or didn't like it: Bryant Gumbel, Nastassja Kinski, Cher, Harvey Pekar" (what a great list!).
Part of the charm of Pekar as a guest on late-night national television, in the beginning, was what must have seemed like the weirdness of his fame: a successful autobiographical indie comic book. The first Doubleday anthology had just been released, and received a rave review from Michiko Kakutani in the New York Times. When Letterman's producers called Pekar to book the show, he had never seen it before (he watched it twice to prepare for his own appearance). Letterman, in 1986, didn't seem to care much about the comics. Decades later the Cleveland Plain Dealer quoted Harvey's wife, Joyce Brabner, explaining she thought that Dave "confused Harvey being a comic-book writer with Harvey being a comic, which he wasn't." But Pekar mined his television appearances for his own comics stories, in this way creating a dialogue about those events: first, Letterman's edited version of events, televised (and filtered through a network team); followed by Pekar's edited version of events, drawn in comic-book frames (with an illustrator).
Harvey Pekar and Robert Crumb, "A Compliment," American Splendor #7, 1982.
Used by permission of Joyce Brabner (Harvey.Pekar.Estate@gmail.com).
In the first appearance, Letterman goes light on the comics and heavy on the jokes aimed at Pekar himself as a Clevelander in New York City. The not-so-hidden subtext from Letterman, a former weatherman from Indianapolis, was "look at this midwesterner in the big city." In Pekar's version, though, titled simply "Late Night with David Letterman," he shows readers just how prepared he was for this. In several spare, elegant spreads, readers see Harvey, deeply suspicious of the corporate entertainment industry, thinking hard, anticipating the show: "I musta rapped with dozens a'faster guys in delicatessens," Harvey reflects. He decides his appearance will be adversarial in tone, and he explicitly makes it a class issue. "He's middle class, polite, he don't talk fast," Pekar thinks. "He ain't useta guys like me. . . . I got a lot of experience, but not on TV. It worked onna street corner, but will it work on TV?" What comes through profoundly in Pekar's account of the show, though, is how linked his identity as an artist really became with the city of Cleveland itself. A page of the story quickly shifts from discussing the American Splendor anthology to Dave's question, "Now, how are things in Cleveland going?" The cartoonist known for listening to voices in the actual space of the city is now in a bigger city, in a studio, having a completely contrived—which is to say, staged—conversation. In a sense, the Letterman show, while also about conversation, is the opposite of American Splendor, which pivots on the encounter itself as spontaneous and organic—the unexpected exchange, the surprise meet-up. As novelist Ed Park describes American Splendor in the Village Voice, "In Pekar's world . . . a walk around the block could turn into a chamber piece of chance encounters and oddball conversations." The television talk show format, on the other hand, literally stages talk artificially—it's based on the contrivance of talk, whatever interesting thing may happen. It's not from the street, it's from the studio. So Pekar may have been in a much bigger city than Cleveland, but he's less impressed with the results. As Pekar said in his first appearance, "I ain't no show biz phony."
It got rougher, though, between Pekar and Letterman, although audiences enjoyed their antagonism. In 1987 Pekar appeared on the show wearing a T-shirt that proclaimed, "On strike against NBC." His comics story about this episode is called—a long and literal title—"My Struggle with Corporate Corruption and Network Philistinism." Pekar accused Letterman of scabbing a worker's strike, and he wanted to talk about how NBC's parent company, General Electric, manufactured arms and produced nuclear reactors. The two traded many insults, with Letterman accusing Pekar, in a class-inflected put-down, of having "bad manners." The following year, though, got even worse, with the conversation disintegrating into a flurry of heated insults during which Pekar told Letterman he looked like a "shill" for General Electric. Letterman lost his temper, told him he would never be invited back, denigrated the comics—he spitefully named American Splendor a "little Mickey Mouse magazine"—and called Pekar, unkindly, a "dork." The segment ended with the two of them yelling "you're full of shit" at each other, which was bleeped out, before Letterman said, "Cleveland, you have my deepest, most heartfelt apologies," and NBC cut to a commercial. On television, Pekar was gone after the break. In the comics story, though, we see him lingering in the set chair, alone, looking victorious. Pekar had actually touched a nerve. After Pekar's death, Letterman copped to his excessive reaction: "I loved Harvey. He was a wonderful guest. The kind you don't see anymore. The only real problem with Harvey was my immaturity."
Harvey Pekar and Gerry Shamray, "Late Night with David Letterman," American Splendor #12, 1987.
Used by permission of Joyce Brabner (Harvey.Pekar.Estate@gmail.com).
There's something impressive about Pekar's ability to elicit spontaneous reactions from his interlocutors, even if, as in Letterman's case, those reactions stem from anger. The reason that he's a successful, if difficult, guest is that he brings the spontaneity of his comics—the rapping with guys in delis they document—to Letterman, despite the artificiality of the interview show format. Pekar was offered his own talk show in 1987 by the Fox network, which he declined along with other lucrative television deals: the contrivances of the studio felt like torture to him. With its capacity to record regular voices and create visual dimension for their speakers, comics was his medium, and his secure working-class job was his anchor. Pekar's accomplishment was to connect the two, within the economically depressed but still vibrant Cleveland, through American Splendor. Movingly, after Letterman, cruelly, calls him a dork on national television, Pekar says—and the two are speaking over each other here—"I was a file clerk before I knew you, and I'll be a file clerk after." Pekar stayed in his job at the VA hospital even after he got famous. He refused promotions and retired in 2001. "My lifestyle has not changed at all. I'm still the same schlep I used to be," Pekar said in an interview in 2006 posted on the website of Random House, one of his last publishers. As his character in the movie says, "Ordinary life is complex stuff."
Ordinary life (with some mystical elements thrown in) is complex, too, in the comics series Love and Rockets, the brainchild of three brothers from Los Angeles: Gilbert, Jaime, and Mario Hernandez. American Splendor and Love and Rockets, both early to emerge and long-running, appeared within five years of each other. Together, they set the tone for independent comic books of the 1980s and beyond: Pekar and the Hernandezes (known collectively as "Los Bros")brought the comics field in new directions. These artists reveal how comics, in its porous, democratic openness, is a mirror of the ongoing vitality of city spaces—their energy, hybridity, range of voices. Comics, as a spatial form, can evoke place powerfully, and also graphically detail it. But it can further in its form—its mix of styles and influences—reflect the multiplicity of those who inhabit cityspaces.
Like Harvey Pekar's Cleveland, Jaime Hernandez's Huerta, part of greater Los Angeles, comes to life in Love and Rockets as its own character—a fully-fleshed-out home for both its residents and readers to return to. Love and Rockets, which includes separately authored storylines by Jaime and his brother Gilbert—and sometimes their older brother Mario—has been running since the 1980s. Huerta, though, is a fictional city—although it is based on Jamie Hernandez's hometown of Oxnard, California. Pekar depicts marginalized working-class urban populations, and so does Hernandez—but Love and Rockets specifically focuses on Mexican American life in Southern California. Jaime's mother, Aurora, hailed from a poor part of El Paso, Texas; his father, Santos, came to California from Mexico and worked on a GM assembly line. The two met in Oxnard's fields and packinghouses.
And while American Splendor is about perhaps eccentric working-class people from distinct backgrounds making a go at getting by through working straight jobs (Pekar, after all, worked for the government), Love and Rockets is steeped in punk culture, self-consciously positioning itself as outside the mainstream. Love and Rockets, as Hernandez has noted, focuses on outsider culture both by depicting Mexican American experience, and by depicting the anti-conformist culture of punk music, whose in-your-face, do-it-yourself attitudes inspired the Hernandez brothers to self-publish their comic book in the first place. The intersection fueled by the space of the Southern California city—Mexican American and punk—had never been represented in comics, let alone with female lead characters. Hernandez's effervescent Maggie Chascarillo and Hopey Glass, best friends and sometimes lovers, became iconic (they grace the cover of this book).
Nothing remotely like Love and Rockets existed before its first issue in 1981; it created its own context and went on to become the flagship publication of world-renowned independent comics publisher Fantagraphics. Love and Rockets deliberately sought to present something that was missing. "Even if we failed at it, at least we tried," Gilbert Hernandez said, explaining the brothers' thinking. " 'Hey, look, here's this comic about punk rock and Hispanics. This is new and different.' " Unlike Pekar's fragmented dispatches in American Splendor, the Hernandez brothers aimed to tell stories about interpersonal interaction in greater Los Angeles and its barrios through complex characters and inventive, dramatic storytelling. Huerta—and specifically the barrio, or neighborhood, Hoppers 13—became a pulsing fictional world, textured so finely in its realism, its concrete details and dialogue, that anybody from any background could connect to its residents and their ordinary and extraordinary experiences. The cartoonist Adrian Tomine, creator of dozens of iconic New Yorker covers and 2015's acclaimed short story collection Killing and Dying, which has elicited comparisons to Raymond Carver, told me that when he first discovered Love and Rockets, "I really felt that I had more of a personal connection and investment in the lives of these fictional characters than in the real people in my life." The Hernandezes have also been a major influence on novelist Junot Díaz, who claims, "American fiction is [still] catching up to Love and Rockets." (Jamie Hernandez drew the slipcase and chapter headers for the deluxe edition of Díaz's book This Is How You Lose Her.) Neil Gaiman, the novelist and comics writer, told the Guardian, "I don't really understand why the material of Love and Rockets isn't widely regarded as one of the finest pieces of fiction of the last thirty-five years. Because it is." Love and Rockets was recently voted the best nonsuperhero comics of all time by Rolling Stone.
Jaime, who was born in 1959, grew up as one of six siblings in southside, inland Oxnard (known as Scalon), a coastal city roughly thirty miles outside LA whose spaces included agricultural areas and suburban sprawl. Mario Hernandez called their upbringing "Dickensian"—the family was poor—but the siblings felt lucky to be encouraged in their comics reading and writing. In an effort to keep the children quiet in the small house, their father allowed comics, to which they were totally attentive, and encouraged them to draw their own comics in turn, with crayons on torn-up paper bags. Aurora Hernandez was not only tolerant, but was an actual dyed-in-the-wool comics fan of the Golden Age of the 1940s and '50s. She read the comics her kids brought home, and according to Mario, as long as they weren't getting Fs, she let the comics remain in the house. The brothers collected and hoarded them starting at a young age, clearing shelf space in their closet. The brothers never stopped reading, collecting, and drawing comics, even after their father died when Jaime was eight—they simply broadened their tastes and their skills. As his younger brothers edged toward adulthood, Mario noticed—as if suddenly looking one day at their comics with fresh eyes—that Jaime and Gilbert, who was two years older, were actually doing surprisingly professional work, just for their own amusement.
Jaime Hernandez, page from "Wigwam Bam," Love and Rockets #33, 1990, featuring his central protagonists, Maggie and Hopey, attending a punk show that is monitored by helicopters and policemen. Characters in the central panel have tattoos or T-shirts that refer to LA bands Black Flag, the Germs, and X.
Used by permission of Jaime Hernandez.
When Jaime attended junior college in 1978—which he claims was only due to a Social Security deal related to his father's death that paid out if he had college credits—art classes changed his life. He had already produced quality comics for years, many of which had sci-fi and adventure elements, just for his family's eyes (and a few fanzines), but as Mario saw it, when Jaime took life-drawing classes his style "just blossomed into what it is now"—as if his natural ability to draw so cleanly, to "make that one line fill volumes," had been unleashed. At this time punk was hitting LA, too, with bands like the Bags, Avengers, and the Zeroes emerging (alongside those noted in the previous caption). Along with life drawing, which unlocked his style, punk's vitality changed Jaime's life. "I was dead since sixth grade," he once told an interviewer—a feeling perhaps related to the death of his father a few years earlier—and then "I came back to life."
With its focus on regular people making their own culture with whatever means available, punk helped Jaime focus his comics on experiences in the barrio for people like him and his friends. This eventually became a bigger focus than the sci-fi storylines that took up a lot of space in early Hernandez brothers comics. "The rocket-ships got in the way, you know?" he explained in an interview. "And I thought, I'm more interested in this street-life thing that I'm doing. You know, and before punk, I was into the low-rider stuff. And so punk kind of made sense—it was gritty street stuff. And I go, that's where I come from! [Laughs.] And you add music to it—hey great!" Jaime and his brothers were in punk bands (Dr. Know); Jaime created flyers and handbills for local punk shows. Punk culture inspired him to create comics as a public platform, and it also, as a lifelong practice, became a subject of his comics, which depict that street life, and make many references to bands, gigs, and song lyrics. Jaime's punk flyers and comics influenced each other. Take the similarities between his flyer for an Oxnard punk show, with its cholo man announcing a performance of the band Circle Jerks in a speech balloon filled with Mexican American slang (and humorous gang intimations), and the cover, years later, to the important Love and Rockets collection The Death of Speedy—which features a cholo man, the gangbanger Speedy Ortiz, in the same posture, palms beatifically turned outward, figured as Jesus.
Mario was so knocked out by Jaime's postcollege drawing that he proposed printing a Hernandez comic book. He borrowed money from their youngest brother Ismael to pay the printer, and arranged the self-publication of Jaime and Gilbert's all-black-and-white Love and Rockets #1, the pages of which the three of them then stapled and collated in Mario's living room. And so Love and Rockets was born as a family enterprise, inspired by do-it-yourself punk values, with Jaime and Gilbert each creating half the content for each installment. When, soon after, the brothers sent their work to Gary Groth, the publisher of Fantagraphics, they expected rejection—but instead were immediately snapped up. By issue #10, Jaime and Gilbert could live off of the proceeds from Love and Rockets (during the release of the first few issues, they still lived with their mother). In 1985, a band from England—best known for the eighties hit "So Alive"—named themselves Love and Rockets, after the comics.
Seth, the cartoonist behind It's a Good Life If You Don't Weaken, among other strikingly evocative graphic novels, has suggested that in comics "the combination of writing and drawing your world seems to set it apart from other kinds of world building." Love and Rockets is about creating a world, which is to say, it is about articulating the unstable, always shifting intersection of location and culture, through both words and images. Both brothers' storylines are powerfully about place—and how and with whom those places get populated. Jaime's stories are centered in Hoppers 13, and most often star his signature protagonists Maggie and Hopey—the on-off couple whose exploits have come to be known as the "Locas" stories. Gilbert's take place both in Los Angeles (Junot Díaz once wrote me that Gilbert's collection Love and Rockets X was "LA as fuck"), and in the fictional Mexican village of Palomar. (This storyline has elicited many comparisons to Gabriel García Márquez.) A decades-long ongoing serial, Love and Rockets is less about plot per se than about richly conceived characters, and atmosphere, conjuring verbally and visually the space in which people live and move. And since its characters age with the comic, readers get the sense of following intimately drawn lives in what often feels like something approaching real time, producing investment in their affairs, jobs, roommates, grudges. As Alison Bechdel writes about Hernandez's comics, "Rereading the early Locas stories, I find that although my recall of some of the plots is hazy, all of the drawings remain vividly incised in my memory. . . . What remains is less a stylized world than a world distilled to its fantastic, magical, quotidian essence. . . . manifestly legible."
Jaime Hernandez, punk flyer, 1982, and cover for The Death of Speedy: A Love and Rockets Collection (Seattle: Fantagraphics), 1989. The inside brim of the cap worn in the flyer spells SCXCH—for Scalon x Chiques, the slang term for Oxnard (it means "Little Chicago," a reference to the underground West Coast marijuana trade that went as far as the Midwest).
Used by permission of Jaime Hernandez.
And what does Hernandez make legible in his urban tapestry? Lesbian lives, bisexual lives, immigrant lives, working-class lives, children's lives, women's lives, gangbangers' lives, ex-gangbangers' lives, punk musician's lives, second-generation lives—lives that hadn't flourished on the comics page before with such richness and such traversing of boxes and boundaries. The space of the city, home to so many distinct populations, generates the interweaving identities that Hernandez creates on the page. It means one thing when Ware draws a bedroom scene of a white couple in the suburbs; it means another thing when Jaime draws a bedroom scene of two Latina lesbians in a tiny, crowded apartment: comics as a way to put marginalized bodies and psyches on the page.
Jaime Hernandez, page from "Locas at the Beach," Love and Rockets #15, 1985, featuring Maggie, an auto mechanic, and Hopey, a bass player.
Used by permission of Jaime Hernandez.
In a page from Love and Rockets that sweetly exhibits the rapport of lovers Maggie, an auto mechanic, and Hopey, a bass player in various punk bands, the two, at bedtime (and while a roommate curses at them to "shut the fuck up"), discuss the thorny intersection of gender, work, and immigration. Maggie describes her difficulty as a female mechanic servicing men who are embarrassed by her ability to help them. Hopey reminds her of their "old country" attitudes while Maggie in turn reminds her of the importance of present attitudes. Hernandez's comics, with their attention to "old" and new customs, traditions, and generations—and how they intermix—are influenced by a wide range of sources that speak to the diversity of LA as a fount of creativity and energy (Hernandez still lives in the Los Angeles metropolitan area). What many would consider fringe communities find full display in Love and Rockets, and Hernandez's openness parallels the city's openness, not only in the kinds of bodies that show up in his work, but also in the aesthetics of his comics.
The mash-up represented by city space, where so many practices and attitudes coexist, is an inspiration, and it is reflected in the aesthetic diversity that Hernandez's comics display. They are dense with references, and as inspired by the look of kids' comics Archie and Dennis the Menace, in which Hernandez recognizes an appealing warmth, as by confrontational LA punk bands and the weird genius of junk culture and lowbrow entertainment genres. The kitschy yet athletic world of female pro wrestling, for instance, shows up throughout Love and Rockets—Hernandez is a serious fan—entering the storyline most often through Maggie's aunt Vicki Glori, a wrestling champion and entrepreneur. A long list of "some important art" compiled by Hernandez names all sorts of different high and low genres and forms and people, including "Edward G. Robinson, wax museums, Harry Lucey [of Archie], Fred Blassie [a professional wrestling villain], X, John Stanley, true ghost stories, R. Crumb." Speaking of ghost stories (and true ones at that): Love and Rockets copiously and elegantly mixes genres, so we see a gritty, on-the-ground realism combine with slapstick combine with touches of the supernatural. Isabel Ortiz, Speedy's sister, for instance (meditatively closing her eyes on the cover of this book), grows to enormous, magical proportions (a former gang member and author, she is known by some locals as the "Witch Lady"). Love and Rockets creates its meaning, and its emotion, out of a vibrant, and surprisingly unencumbered, blend of different genres that leaves open joy and mystery, levity and tragedy in its compelling creation of a multivalent, and multilingual, community.
Hernandez's comics, along with his distinctive characters themselves, wear this hybridity easily. Love and Rockets in its comics frames reflects the multiplicity of the space it enlarges for readers—in the characters' wide range of references, from underground to mainstream culture; in its visual attention to the tiniest details of space and sartorial style; in its attention to the interactions of "new" and the "old" worlds (as we also see in Pekar); in the aesthetic inspirations shaping Jaime's stark yet sumptuous line; and its constant, rich sense of possibility. Asked once if his comics, putting underrepresented lives on the page, were angry, Hernandez said, "It didn't matter if I was a Mexican anymore. I had the comic book, and I was going to show the world. . . . It was not so much angry art, the anger just helped me put it out. . . . I found ways of being angry and portraying beauty at the same time, you know?. . . . Gilbert has said this before, it's my love letter to the world."
---
WHY PUNK?
It was about advocating kids not to wait to be told what to do, but make life up for themselves, it was about trying to get people to use their imaginations again, it was about not being perfect, it was about saying it was okay to be amateurish and funny, that real creativity came out of making a mess, it was about working with what you got in front of you and turning everything embarrassing, awful, and stupid in your life to your advantage.
—Legs McNeil on punk, Please Kill Me, 1996
Just about anyone who has paid any attention to pop culture in the past thirty years can picture Bart Simpson. He has popping saucer eyes, a red T-shirt, and what looks like a crown of jagged hair. First appearing on television in 1987, Bart is the perpetually-ten-year-old Simpson family son who quickly became a globally famous figure for pugnacity and rebellious disrespect ("Don't have a cow, man!"). What few people know, though, is that Bart's iconic hairline is lovingly lifted from cartoonist Gary Panter's punk everyman character Jimbo and his spiky hair—meaning that one of America's most beloved pop culture characters actually springs from a key figure in its groundbreaking punk scene.
In the late 1970s, The Simpsons creator Matt Groening and Gary Panter were both living in Los Angeles, in what Groening describes as "a couple of the sadder neighborhoods in Hollywood." Groening, who graduated from the Evergreen State College in Washington, had grown up in Portland, Oregon, while Panter hailed from Sulphur Springs, Texas; both moved to LA after college. Panter was scrounging illustration jobs. Groening was working, among other places, at a copy shop.
At the shop, Groening self-published—that is to say, photocopied—his darkly funny Life in Hell, which he would staple together and send to his friends in the Pacific Northwest, including cartoonist Lynda Barry. He also sold copies for a few dollars in the "punk" section of a local record store on Sunset, where he was an employee, called Licorice Pizza. The title was a reaction to living in LA. It featured anthropomorphic rabbits; its tone was existential and its star was the downcast Binky the bunny, also an everyman observer like Panter's Jimbo. Binky, who has big ears, wide eyes, and a pronounced overbite, is joined in the strip by Sheba, his on-off girlfriend; Bongo, a one-eared rabbit even more alienated than Binky; and Akbar and Jeff, fez-wearing humans who are maybe brothers, maybe lovers. "Life in Hell actually sold copies," Groening says. "Sometimes the punks would tear up copies, but sometimes I sold them."
Panter, whose own self-published comics Groening had read and admired, wrote him a fan letter in 1978. (Leonard Koren, who published an avant-garde lifestyle magazine called Wet, first showed Panter Life in Hell.) Groening describes being actually "frightened" by Panter's handwriting—today still known, which is to say admired, for its scratchiness and intensity—but he wrote back. The two met and became fast friends, plotting how to make art people would pay attention to. Groening recalls how they would "scrape coins out of the carpet of our crummy little apartments and split burgers and then scheme about how to invade pop culture."
The two young cartoonists scraping to split some Astro Burgers between them would manage to succeed in that scheme. The Simpsons, Groening's wildly successful animated television creation, is the longest-running scripted American prime-time television show in history, and its insights and mottos have earned the status of cultural truth. "D'oh!," clueless patriarch Homer Simpson's exclamation, was added, in 2001, to the Oxford English Dictionary. Groening says he owes his success to Panter, who went on from their early, scheming days to win—among many other accomplishments—three Emmys as the set designer of the popular Pee-wee's Playhouse, the children's show and creative phenomenon that ran on CBS from 1986 to 1990. Remember the talking chair, Chairry, with her Betty Boop eyelashes and a mouth between the cushions? "Gary brought that psychedelic crazed Gary Panter style to Saturday morning, and he completely warped a generation of kids," Groening says. "Gary went first, and he was my role model."
Video still of Matt Groening comparing images of Bart Simpson and Gary Panter's Jimbo character (on the cover of Jimbo: Adventures in Paradise, Raw/Pantheon, 1988). Jesse Stagg and Alex Czetwertynski, directors. Produced by For Your Art.
Used by permission.
The punk scene that launched cartoonists Panter and Groening was part of a larger punk movement that hit America, and the UK, in the mid-to-late 1970s. Both political and aesthetic, the punk movement, which often registered as a visceral or even violent response to mainstream pop culture, encouraged people to create their own culture across many different forms of production. This includes, most famously, the music that came to be known as punk rock (the phrase punk rock, then, is sometimes used synonymously with punk). Punk culture often consolidated around bands, particularly their live performances, and the independent labels that developed to put out their music, along with the art and graphic design that went into their promotion—as well as the fanzines that articulated their ideas and goals. The "do-it-yourself," or DIY, ethic is the defining feature of punk culture and production. As Jaime Hernandez explained, he never realized he could be a cartoonist until he got involved with punk. "Then I thought, 'Oh, this is kind of the same thing,' " Hernandez told comics writer Neil Gaiman. "They were all the same to me, so if you could do that with punk, you could do that with comics."
"Punk" was a term for disrepute and outsiderness, resignified in the 1970s as an expressive, antiestablishment rejection of the "expert" and the corporate. The word "punk" had been used in the music magazine Creem to describe 1960s garage bands, and had appeared in gangster movies, in prison slang, and in Shakespeare's plays (usually as a synonym for "whore," as in "your French crown for your taffety punk" in 1605's All's Well That Ends Well). It makes an appearance in William S. Burroughs's 1953 Junky, in which the character Roy says, about two men harassing him, "Fucking punks think it's a joke." (Burroughs, in the oral history Please Kill Me, simply notes, "I always thought a punk was someone who took it up the ass.") In mid-1970s New York, bands like the Ramones, Television, and Blondie—the latter name a reference to the eponymous comic strip that began in 1930—were generating zealous attention, playing at venues like the East Village's CBGB. But it was only after the fanzine Punk began publication in January 1976 in New York that "punk" began to become a movement one could identify. Before Punk, as Guy Lawley points out, people called the sound of these New York bands "street music." "It wasn't an original concept," founding editor John Holmstrom, a cartoonist, explains, "but it wasn't very well-defined, so starting a magazine called Punk took some nerve." Soon after, more bands and fanzines that understood themselves as explicitly punk cropped up (and later Legs McNeil, another Punk contributor, complained that the world incorrectly understood punk as English). The Sex Pistols, a band from London whose one studio album, 1977's Never Mind the Bollocks, Here's the Sex Pistols, initiated a widespread UK punk movement characterized by short, sped-up rock songs and anti-conformism, gained transatlantic notoriety, especially when bassist Sid Vicious was arrested in New York for murdering his girlfriend in October 1978, four months before he died of an overdose. In Los Angeles, where plenty of bands were sprouting up, the highly influential punk fanzine Slash—which also birthed an important record label of the same name—launched in 1977, the year Panter and Groening both moved to the city.
Fanzines link punk and comics directly. Zines, as today they are commonly known, are independently published periodicals on a range of topics. They play a crucial role in the history of comics—an art form conventionally designed for print circulation—and in punk, a historical movement and ongoing system of values that prizes independence at the level of creation. The roots of zines and comics run deep together: teenage writer-artist team Jerry Siegel and Joe Shuster published the earliest incarnation of Superman in 1933 in their very own mimeographed fanzine Science Fiction: The Advance Guard of Future Civilization. And zines, with their DIY ethic, are a cornerstone of punk philosophy and its music specifically: they represent independence from the corporate, the building of community through the circulation and exchange of knowledge, and a forum for promoting bands. One sees in punk zines—as one does with iconic punk album covers like the Clash's 1979 London Calling, a dark homage to Elvis Presley's self-titled debut album combining pink and green stylized letters with black-and-white photography—just how key the frisson between words and images that motors comics is to the punk aesthetic.
Groening and Panter's career trajectories demonstrate punk's role in contemporary comics—and also how the graphic novel today trades on so many of its values, including an emphasis on immediacy and the handmade, for what is now a mainstream audience. Alternative newspaper The LA Reader, founded in 1978, picked up Life in Hell as a weekly comic strip in 1980. Panter, who had also self-published, began publishing Jimbo, named after his signature character, once a month in Slash in 1978; he also created covers and design for the famed publication. Jimbo is an ageless navigator of a confusing world. Panter has said of Jimbo, who he has been drawing since 1974, "Jimbo is an observer. He is not very willful. His drives are simple. He is not stupid, but he is no genius. I use him to observe the places I put him in, which are satirical social, technological, and control situations."
Gary Panter, cover of Slash featuring Jimbo, Vol. 2.7, 1979.
Used by permission of Gary Panter.
Once Panter and Groening became friends, the two budding cartoonists drew comics together in a wild, apparently untrained style for punk zines such as Flipside and Chemical Imbalance under the monikers the Fuk Boys or the Shit Generation. Their longest collaboration, "Ocurence at Oki Dog," is an almost unreadably scribbled and dense two pages. It is also hard to find—before now it has never been reprinted outside of a fanzine. One dopey-looking character is rendered in a simple yet exaggerated style recognizable to any Simpsons fan and wears a T-shirt of LA punk band the Germs (Panter's first wife Nicole Panter had been the band's manager until they disbanded in 1980). The speech balloons are full of the cross-outs that characterize punk's deliberately rough aesthetics. In the story, two friends set out in a car to hot-dog restaurant Oki-Dog, run over a pet cat, pick up a hitchhiker with a hook for a hand, and fight that hitchhiker before the car crashes and he dies on the street. While today one thinks of Groening as the creative force behind one of the biggest, most recognizable entertainment properties in history, Art Spiegelman first knew Groening as "Gary's punk rock friend."
Born in Durant, Oklahoma, Panter is part Native American; his paternal grandmother was a Choctaw Indian. She lived with Panter's grandfather, who suffered from a liquor-induced paralysis known colloquially as jake leg, in the small Choctaw town of Talihina (Choctaw for "iron road"), Oklahoma, where Panter would visit as a child. Panter was raised a fundamentalist Christian in the Church of Christ in Texas: first in Brownsville, across the border from Mexico, and then in the small town of Sulphur Springs. His father ran a five-and-dime and painted traditional Western paintings on the side. Panter, by his own account, saw modern art in a magazine at age ten and became obsessed. In 1969, he went to Belfast as a missionary, but his interest in art soon overtook his dedication to religion. In 1971, he started keeping drawing sketchbooks, and shortly after he started producing his own pamphlets and zines. Panter earned his BFA in painting at East Texas State University in 1974.
Panel from "Ocurence at Oki Dog," by Gary Panter and Matt Groening, as the Fuk Boys, in Flipside #33, 1982.
Used by permission.
Panter explains that he was "kind of waiting for punk rock. I was waiting for someplace I could plug in." He worked as a janitor in Texas before moving to LA, just around the time that punk rock was becoming a full-fledged movement. Slash, one of its signal publications, covered LA bands like the Germs, X, and the Screamers, in addition to groups like England's the Sex Pistols. In LA he found he could plug in.
Panter recounts to Vice that after moving to LA, one night he was walking down Gower Gulch—the nickname for the intersection of Sunset and Gower in Hollywood—and saw a copy of the first issue of Slash laying on a newsstand. He found its sensibility similar to his—"big crude graphic stuff that's probably out of fine art type of stuff, like [Robert] Rauschenberg and [Kurt] Schwitters." Panter explains, "I'd seen something in the paper about punks, and I thought, these are like creepy little neo-Nazis, you know—what a bunch of jerks. But mostly it was people out of art school who wanted to make something happen." In 1977, Panter created a poster that remains one of the most recognizable emblems of the punk movement: the stark, black-and-white graphic rendition of shrieking vocalist Tomata du Plenty of the Screamers, complete with a vertical signature reminiscent of Japanese painter and printmaker Katsushika Hokusai. This dramatic image became the Screamers official logo and one of the most nationally and internationally famous images to emerge from punk rock. It alone adorns the cover of the art book Punk: An Aesthetic. Panter's graphic sensibility came to substantially define the visual culture of punk, from band flyers, record sleeves, and cover art, to T-shirts and posters, comics, books, and fanzines.
Screamers poster, art and design by Gary Panter, 1977.
Used by permission of Gary Panter.
Graphic work like the Screamers flyer, with its forceful, clean lines, displays one aspect of Panter's artistic practice, but as he has pointed out, "I can draw in many, many, styles and invent styles to serve ideas." Today widely considered one of the finest drawers, or draftsmen, of his generation, Panter innovated contemporary art and punk by making a significant movement out of purposeful bad drawing. "That was the cool thing about punk rock," Panter explained at a conference I organized in Chicago. "It was just, get up there and do something. Start. And I like cruddy stuff. I always liked bad drawing." For Panter, "bad drawing" is when the shakiness of the hand is intentionally evident. Its unevenness or looseness, as opposed to being concealed and corrected, becomes part of the surface of the page. Panter's development of a dense, chaotic, messy style in drawing is perhaps his greatest contribution to punk specifically—and to post–World War II aesthetics generally, in comics and also in art and design circles. The resolute imperfection of his drawing style, which became known as the "ratty line" aesthetic, challenged audiences to confront drawing as expressive and material as opposed to merely illustrative and transparent.
Panter began making scratchy drawings in 1972, supposedly when his Rapidograph pen, a technical, even-weight pen and a cartoonist's staple, jammed up. Panter also notes the influence of growing up on the border of Mexico, where he encountered print shops that printed appealingly off-register. His textured, messy, febrile, forceful hand eventually became his trademark, and the ratty line became a defining feature of punk across the board. "Panter's scratchy, seemingly untrained line became as much a symbol of the era as fuzzy three chord loud songs," John Carlin writes in an essay on Panter's book Cola Madnes (yes, with one "s"). In Panter's comics, the deliberate "mistakes" often register in words, too: with misspellings, cross-outs, and visible redactions.
Panter is the innovator of punk comics; people sometimes call him the king or the godfather of punk comics. Lynda Barry (Matt Groening's best friend) recalled Panter to me this way: "Gary was beyond ahead of the pack. I mean, you didn't even know that you were in a race or on a racetrack or that you were a horse." Charles Burns created a 2-inch-high autobiographical booklet about the 1970s, in which he describes seeing Panter's work for the first time in the pages of Slash: "Somehow, with only a few pages of comics," Burns writes, "he managed to define a new whole aesthetic for me: punk comics. From that moment on I wanted to be a punk cartoonist too." Burns would succeed: in addition to his acclaimed graphic novel Black Hole, he recently released the punk-themed trilogy X'ed Out, and he regularly publishes a zine, which he gives out for free, titled, appropriately, Free Shit.
An amusing Jimbo strip from a 1979 Slash crystallizes Panter's expressive, mash-up aesthetic. Here, Jimbo, drawn in line art with freckles and a torn T-shirt, encounters two classic American franchises: Burger King and Nancy, the classic comic strip that stars an eight-year-old girl. (Buying cheap burgers, alone or together, is a recurring theme for both Panter and Groening; here perhaps it underscores the turning of Jimbo's luck.) Above the big letters of the title—drawn to look pixelated (or "raster"), like early 8-bit video games—is a heavily redacted, inked-up block of handwritten text in uneven capital letters. It's an idiom one also sees in the speech balloon above in "Ocurence at Oki Dog." Panter calls attention to the visual surface of the page, to the line or mark itself, as the unit of currency, as opposed to narrative coherence. The words readers can piece together make an absurd whole ("Jimbo never eat. Jimbo eat. He eat receipt," etc.). This strip also incorporates collage: an actual receipt from Burger King, peppered with realistically drawn flies.
The character Nancy, recognizable by her bubble of black hair and her bow—but rendered by Panter in an intentionally crude style—speaks in long articulate sentences. She confronts Jimbo about his dismissal of her strip, defending its style (its "machine-like precision"), absurdism, and humor. "It functions as a nostalgic buffer against future shock for a tired & technology-torn species," she explains to him. This installment of Jimbo is itself the conspicuous opposite of "machine-like" in its look. Yet it ends with Nancy accusing Jimbo—and therefore punk culture itself—of being contemptuous and superior and then further one-upping him by scolding him in the last panel for actually not being "punk" enough. "By the way, what's a guy in a so-called punk magazine doing walking around without a guitar?" she says, producing one as a gift. The strip concludes with Sluggo, Nancy's ill-behaved friend, violently demanding to join the hypothetical band. It is a self-reflexive strip about aesthetics that manages to also be light and funny. Its ragged lines, play of different styles, and black-and-white patterning produce what artist Mike Kelley called Panter's "elegantly brutal" work.
Panter shifted attention from graphic perfection to sheer graphic exuberance. In his marks on paper, one can feel the body on the page, etched into the surface. The embrace of the mistake, the scribble, and the rough-hewn created an unparalleled liveliness and energy in his drawings—it called attention to the grain of the line and became an aesthetic philosophy. Panter dedicated a 1979 Jimbo comic strip "To the Guardians of the Ratty Line." In an interview, he said, "I tried to embrace all the smudges and mistakes. That's analogous to punk." Chris Ware puts it well when he writes that Panter's comics "were the first to show how the hand of the cartoonist, usually sublimated in a considered, codified calligraphy, can tear into the surface of the page, and the reader's mind, if the artist wants it to."
Gary Panter, Jimbo comic strip in Slash, Vol. 2.4, 1979.
Used by permission of Gary Panter.
While the ratty line became the hallmark of punk aesthetics, Panter's—and Groening's—career also demonstrates how comics extended punk culture into the mainstream, exemplifying its values. The DIY ethic is the defining feature of punk; and it motivated comics culture for decades before "punk" even became a term to describe art. Fanzines first emerged in the 1930s, largely in science fiction readerships; in the 1960s, humor and comics fanzines also became popular. If self-published fanzines consolidated the punk movement, unifying and articulating its interests and goals, the DIY practice had been a crucial feature of comics for some time, from postwar satire fanzines to underground comics and beyond. Significantly, many of those who would become big figures in underground comics in the late 1960s and early '70s started in high school, with their own mimeographed magazines. A list of amateur titles by now-acclaimed cartoonists includes Art Spiegelman's Blasé, Justin Green's Step-Up, Jay Lynch's The Vulgarmental, Robert and Charles Crumb's Foo, Skip Williamson's Squire, and Denis Kitchen's Klepto. There is a generational shift from the "hippie" culture of Crumb to the punk culture of Groening and Panter, but the ethos is the same—comics is the realm of the democratic and the experimental.
Fanzines have a close relationship to the birth of independent comics. (In an ironic twist, Dr. Fredric Wertham, who wrote Seduction of the Innocent in 1954, which was responsible for crushing the mainstream comics industry, went on to publish, in 1973, the loving study The World of Fanzines: A Special Form of Communication.) Roger Sabin and Teal Triggs, the editors of Below Critical Radar: Fanzines and Alternative Comics from 1976 to Now, write that the overlapping zine and alternative comics scene is about "people making their own culture rather than consuming that which is made for them; [it is] about replacing institutionalized information with individual energy and expression; it is about [people] saying what they feel instead of corporations selling them a life." Their title, Below Critical Radar, comes from Spiegelman, commenting on the BBC about one of the benefits of working in a form where conventional cultural constraints do not apply in the same way they do for more mainstream forms. Both comics and the punk movement are often a cultural refuge for outsiders.
In the mid-to-late sixties in America, teenage fans of satire comics like Mad found one another through the mail and created their own teenage "elsewhere": a network based on an ethic of sharing information about comics form and method. As cartoonist Jay Lynch describes, "We all started drawing cartoons for [the fanzine] Wild and eventually we all started corresponding with each other, just asking questions about how each one had gotten various shading techniques." The proliferation of networking members in this youth community proved that the comics art produced in the fanzines served more than an aesthetic or satirical function, also serving a social function. As I note in the introduction, Crumb inaugurated the comics underground when he sold Zap in 1968 directly out of a baby carriage on San Francisco's Haight Street. A punk move before punk became a movement, Crumb's rejection of mainstream channels shows how self-published DIY comics offers a through-line across antiauthoritarian cultural movements in the second half of the twentieth century.
Underground comics, like the punk fanzines that appeared less than ten years later, rejected all mainstream channels of publication or distribution. The comics originated entirely with the artist, were self-published or published by loose collectives, and were distributed nontraditionally (hence the baby carriage). On the first page of Zap is the 1967 comic strip "Mr. Sketchum is at it Again!," a statement of purpose that we can understand applies to the whole fanzine and comics scene. One of the strip's last frames shows a kid waving at an artist from a faraway building. The artist in the strip, pencil behind his ear, exclaims, "It's a kid! And he's waving to us from all the way over there! Must be miles! Isn't that amazing? See what I mean? Things like that are happening all the time in these comic strips." In this manner, Crumb explicitly figures his reasons for cartooning as opening lines of communication. Punk, too, was and is about an ethics of exchange, encouraging people to make their own art and media.
The connection between comics and punk was on display not only in LA. New York City's Punk magazine was started by three friends who had grown up in Cheshire, Connecticut: Ged Dunn, Eddie "Legs" McNeil, and the cartoonist John Holmstrom, its instigator and its editor. McNeil came up with the title, after rejecting Holmstrom's suggestion Teenage News (though none of them were teenagers), and the group plastered mysterious flyers all over New York City announcing, "WATCH OUT! PUNK IS COMING!"
Punk was a founding document of the movement, and from the very start it was a hybrid of comics and music coverage. Legs McNeil sees its creative genesis as a combination of the two: "The whole idea for Punk magazine came from two inspirations: John Holmstrom's teacher at the School of Visual Arts, Harvey Kurtzman, who was the cartoonist who had started Mad magazine, and the Dictators's [1975 album] Go Girl Crazy!" The enduring legacy of Punk's intertwining of comics and punk rock can be seen in a recent box set by the echt-punk band the Ramones. This collection, Weird Tales of the Ramones, with a lush, faux EC Comics box cover, comprises almost a hundred songs and a gorgeously produced, full-color, fifty-two-page bound comics anthology featuring comics about the Ramones by twenty-five cartoonists including Holmstrom, Sergio Aragonés, Bill Griffith, Mary Fleener, Steve Vance—and Jaime Hernandez. The Ramones, so closely tied with Punk, have often made their love of comics known—for instance, by collaborating with Daniel Clowes for their video for "I Don't Wanna Grow Up."
Holmstrom's primary identity was as a cartoonist. As McNeil notes, he had attended the School of Visual Arts in New York, where he obsessed over Marvel titles by Steve Ditko and Jack Kirby, followed underground comics, and had studied with the legendary Kurtzman. Holmstrom even worked as an office assistant for comics titan Will Eisner, who also taught at SVA, just a few years before Eisner's Contract with God. He performed his own "Cartoon Concerts," which mixed photography, comics, and sound in live performance. At SVA, Holmstrom thought "a marriage between these two unique art forms, rock 'n' roll and comic strips, was a historical inevitability." In a collected edition of Punk, he explains, "I wanted to use cartoons to break down barriers and change the world."
Punk offered a mix of comics and music reviews throughout its tenure (it ceased publication in 1979). Every issue had comics and cartoons, by Holmstrom and others, along with photographs and writing, and all of Punk's reporting and commentary, in a style evocative of comic books, was hand-lettered, so that a feature credit might read, as in 1976's issue #5: "Bowie Falls to Earth! Review by Mary Harron—lettered by Holmstrom." (Harron went on to direct successful movies, including American Psycho.) Punk's first issue featured an interview with Lou Reed, the hilarious "Rock'n'Roll Vegetable" (the title is a play on his album Rock n Roll Animal), which appeared partially in hand-lettered text, partially as a comic with references to Zap and EC Comics, and partially in photos. The cover, as in almost every issue thereafter, featured a cartoon of a performer. Holmstrom created a bug-eyed Reed for the inaugural issue. For an issue featuring Blondie, National Lampoon cartoonist Bobby London drew lead singer Debbie Harry in the spotlight, bleaching Harry's iconic hair and the moniker PUNK with the same electric yellow. (You can spot London's character Dirty Duck among the punks in the crowd.) A typical feature of the magazine was "punk fumetti"—a photo comic. In roundups of recommended new work, a frequent feature of fanzines, reviews of comics often interspersed with reviews of bands and records.
Robert Crumb even contributed to Punk. When issue #5 ran a parody of his Mr. Natural comic strip—"Mr. Neutral by R. Crumbun," which implied the title character was running out of steam—Crumb wrote in to the magazine. In a two-page letter Punk printed later that year, Crumb admits to being wounded by the parody, but comes around to stating his admiration for Punk. The last line of his letter, forging a link with comics, reads, approvingly: "And keep the hand-printing . . . don't listen to anybody who wants you to go suck . . . stay loose!" He followed with a P.S.—"I really am going to quit the Mr. Natural strip. . . . I was thinking about it anyway, but getting the issue of Punk #5 today in the mail was the convincer"—and several additional postscripts, including one in which he states, "I like you kids, don't get me wrong. . . ." He gives his permission for the magazine to reprint his work for free—the cultures of exchange model valued by both underground comics and punk (his drawings in fact do show up in later issues). Crumb's influence, and the ethos of edgy and yet democratic comics culture, can be felt throughout the run of Punk. The explicit links between comics and punk rock were not limited to the United States, either. In England, cartoonists like Savage Pencil—the nom de plume of artist and music journalist Edwin Pouncey—published comic strips in music magazines such as Sounds. Savage Pencil, who began his Rock 'n' Roll Zoo comic strip there in 1977, is one of the dedicatees in Panter's list of the "guardians of the ratty line."
On the pages of Punk and Slash and Flipside and Search and Destroy and many others, fanzines solidified, and advanced, the connection between comics and punk. Comics and punk revealed a shared aesthetic on the pages of fanzines: collage, word and image experimentation, immediacy in the line, celebrating imperfection. The fanzines gave a platform to musicians and to graphic artists and all sorts of people in between to understand themselves as part of a shared, oppositional culture that valorized direct self-expression, however messy, "cruddy," or "ratty." And, perhaps most significantly, fanzines provided a model that unified punk music with the kind of production comics culture had been developing for years: DIY production and self-publishing. Fanzines were about that, and they were that too, assembled and distributed independently.
Bobby London drawing of Debbie Harry for the cover of Punk #10, 1977.
Cover illustration © 1977, 2017 by Bobby London. All rights reserved. Dirty Duck TM Bobby London.
The whirlwind of energy in the 1970s around taking over the means of production for oneself gave rise to musicians and cartoonists and even fine artists. The common denominator was the idea of communicating directly and with immediacy, with no sacrifice of style—even if one's style was deliberately ratty. The artist Raymond Pettibon (born Raymond Ginn in 1957) bridges the worlds of comics and punk rock. Pettibon grew up one of five siblings raised Christian Scientist in the surfing town of Hermosa Beach, California. When he was twenty, his older brother Greg Ginn started the band Black Flag, one of the most famous hardcore punk bands in the world (Jaime Hernandez's Mohawked man holding a bottle in one hand and giving the finger on the other wears a Black Flag T-shirt in the punk show page from Love and Rockets reproduced in the previous chapter). Pettibon graduated with a degree in economics from UCLA, where he created editorial cartoons for the college daily paper. He briefly had a career as a public-school substitute math teacher, but he always wanted to be an artist; drawing was his primary medium. He designed the famous logo of four black bars, one of the most important logos in history, for his brother's band. The simple bars evoke the shape of a black flag flying, which represents anarchy, in distinction to a white flag of surrender.
"The symbol: it means as much to people as the music ever did," Henry Rollins, the band's singer, said in a documentary. The Guardian reported the Black Flag logo is the most popular tattoo symbol of all time (actress Kristen Stewart caused a minor stir recently when she joined the large group of Black Flag tattooees). In addition to the logo, Pettibon created numerous band flyers and posters, building a powerful visual culture around Black Flag, attracting audiences and evoking rebellion and unrest. Hernandez described encountering a Pettibon flyer on the street for the first time and thinking, "Wow, comics and punk rock—I knew there was a connection!" Pettibon also self-published his first single-authored zine, Captive Chains, a noirish crime story featuring bondage and street gangs, in comics form. He published it in 1978 in an edition of five hundred—one of many such titles that combine word and image. Pettibon still makes zines as part of his art practice although he is now collected by museums worldwide. "I want to be as much as I can the democratic, no the soup kitchen artist," he said in an interview in 2008, adding that he would happily give away his zines for free.
Pettibon's drawing, springing out of LA's punk scene, is now understood both in the framework of fine art and comics. His iconic album cover for Sonic Youth's Goo (1990) is a drawing—with a catchy, comics-style word-and-image twist—of a 1966 photograph of the sister of the English murderer Myra Hindley and her husband. It is an instantly recognizable example of the interpenetration of comics and punk. Goo—the title refers to the blue, shapeshifting mermaid from the Gumby clay animation franchise—is one of the most famous rock album covers of all time. (The cover, inspiring more DIY practice, has spawned countless parodies including Chronic Youth, Sith Youth, Simpsonic Youth, Islamic Youth, Colic Youth, and, of course, Sonic Kitty; there is even a Tumblr called goomashups). Coming up from the world of zines, Pettibon's style of drawing "is largely a comic style," as he sees it. Pettibon's drawings almost always combine images with captions he writes. "Where the image stops and the words begin is not that clear cut," he recently described his work to an interviewer. "It's more a give and take, a back and forth, dialectic almost in between the two." The "Comic Relief" issue of punk zine Flipside from 1982 that features Groening and Panter, writing as the Fuk Boys, also includes Pettibon, even more prominently. As with Panter—whose work now hangs in gallery and museum exhibits—Pettibon's artistic development was formed by the energies of DIY and print circulation.
Raymond Pettibon, cover of Goo, 1990 (Geffen). The image first appeared in Pettibon with Strings, from 1988, of which about 60 copies were printed.
Used by permission of Raymond Pettibon.
By 1980, though, many of the famous punk zines had folded—they were important, but not always profitable, and after the initial burst of energy around punk many of them were hard to keep going as independent publications. Panter and Groening were undeterred. They had always schemed about how to infiltrate pop culture; they didn't want to stay at the margins, but rather to make art that would have an impact on wider culture. Panter published the Rozz-Tox Manifesto, a nineteen-item list, in 1980—it first appeared in chunks in the classified section of the LA Reader because it was free to print it there. The made-up term Rozz-Tox had appeared previously in Panter's Jimbo comics. The Rozz-Tox Manifesto was widely influential, and it is, essentially—and presciently—the story of comics. It urges artists and creators to "reckon with" society instead of rejecting its mainstream contours. So the Rozz-Tox advises, "Law: If you want better media, go and make it" (Item 15). "By necessity we must infiltrate popular mediums," Panter writes. "We are building a business-based art movement. This is not new. Admitting it is."
In the Rozz-Tox, which had a galvanizing effect on underground culture, Panter urges what he calls recombination, a mode of borrowing from all aspects of culture, high and low, old and new. Panter has also described his highly influential visual style as recombinant art. In the Rozz-Tox, he suggests—describing his own work and that of so many cartoonists—that artists "extensively mine our recent and ancient past for icons worth remembering and permutating: recombo archaeology." What else is a hybrid word-and-image art form like comics, steeped as it is in popular iconography, if not recombinant? We see this aesthetic very specifically in Panter's work, for instance in his Dante-Jimbo mash-ups, the oversize hardcover books Jimbo in Purgatory (2004) and Jimbo's Inferno (2006), and in his book collection Dal Tokyo, in which he imagines a future Mars that is settled by Texan and Japanese workers. "Dal" in the title is short for Dallas—Dallas-Tokyo. Manifesting the idea of recombination, the Dal Tokyo strip was first published by the LA Reader in 1983, and later by a Japanese reggae magazine called Riddim.
Groening and Panter invaded popular culture, as the Rozz-Tox advised. Groening turned the smart irreverence of the Fuk Boys and his sardonic Life in Hell into one of the most popular television shows in the world. In 1984, Groening and his then-girlfriend (and future wife) Deborah Caplan, the LA Reader's ad sales representative, self-published a collection of Life in Hell strips as a book, Love Is Hell. Groening says he made it to be square, deliberately, like a record album (the original edition is 12 by 12 inches), because he liked records and thought it could be sold in record shops. A few months later, Caplan and Groening had sold twenty thousand copies on their own. This success led to a deal with the publisher Pantheon, which reissued the book in 1986 (retaining the square shape at 9 by 9 inches). Caplan, who founded a company with Groening, organized wide syndication of the strip. The Village Voice called Life in Hell "the funniest, most sneakily radical strip in the country."
After he self-published the first Life in Hell collection, Groening's readership grew with Work Is Hell (1986), School Is Hell (1987), and Childhood Is Hell (1988), among others. His deceptively simple comics mix humor and darkness, as well as presenting ingenious layouts, like the fake magazine cover, and checklists. For example, "Your Childhood Trauma Checklist" is a grim and also moving strip with rows and rows of boxes to mark, such as "punished for telling the truth," "being hit by parent," and "first realization that death is permanent." Groening often uses repetition of the frame, with labels, for comic effect, as in "The 22 Stages of Heartbreak," in which each stage is one fixed-perspective panel displaying Binky's expression as he navigates "slow sinking sensation," "deep despair," "sudden rage," and "heart of stone," among others, before the final stage: "ready for further punishment."
In 1985, when the television and movie producer James L. Brooks was putting together The Tracey Ullman Show, a variety show for Fox, his team came up with the idea to incorporate Groening's Life in Hell as short animated segments, called "bumpers," to separate out the sketches. A Life in Hell original drawing, of the harsh, clever strip "The Los Angeles Way of Death," had been given to Brooks a couple of years before as a gift. (The nine same-size frames present these ways to die: GUN; CAR; DRUG; SEA; AIR; COP; WAR; FAILURE; SUCCESS.) Groening, when approached, rejected giving up the rights to Life in Hell, so he sketched a different set of characters for Brooks—the Simpsons, based loosely on his own family. Fox, which vastly underestimated how big The Simpsons would become, struck a deal with Groening. (Among his many lousy jobs in LA was being a chauffeur, washing dishes at a nursing home, and landscaping at a sewage treatment plant; Groening is now hugely financially successful.) The bumpers were so popular that The Simpsons, as we know, became its own prime-time TV show in 1989.
The Simpsons decisively changed the idiom of contemporary television. It proved those wary of putting an animated series on prime time wrong, and paved the way for many new shows in an era when television animation for adults was not an obvious choice. "Matt responds on a broadly populist front," Panter has said, "and reminds the populace they aren't as backward-thinking as they think they are." Even while working on The Simpsons, Groening continued to produce Life in Hell, which ran for thirty-five years, ceasing only in 2012.
Matt Groening, "The 22 Stages of Heartbreak," © 1984 by Matt Groening. Love Is Hell (Pantheon Books, New York).
Image courtesy Bongo Comics Group.
Panter worked for CBS, creating enduring cultural icons for Pee-wee's Playhouse that were deeply weird in addition to actually being famous. Paul Reubens, who played Pee-wee, had studied performance art at California Institute of the Arts, and approached Panter in 1979 to create a poster for his stage show. Panter continued to design the posters, sets, and puppets for Reubens as his fame grew, eventually becoming the head designer for Pee-wee's Playhouse. The unique Panter-fueled aesthetic of his television show, wacky and yet intelligent, referencing older American popular culture yet tinged with the futuristic, made it a cultural benchmark (as major profiles around a 2016 Pee-wee movie affirmed, decades after the show became a smash). The show featured a veritable who's who, including a young Laurence Fishburne along with Phil Hartman, S. Epatha Merkerson, and many others; Mark Mothersbaugh from the band Devo wrote its theme song. "It was a show made by artists," Panter said. Panter won three Emmys, and was nominated for five more. (He sent his award statues to his mother back in Texas.) An essay published in the Daily Beast on the enduring significance of Pee-wee's design suggests, "Instead of re-creating the heart of the twentieth century as a nightmare, it turned the best parts of those decades into a funky paradise."
Panter and Groening both worked for major television networks in the late 1980s, and created new aesthetics for the mainstream. Eventually, so too did Pettibon. While he produced literally hundreds of zines from 1981 to 1992, he became an actual art world star in the 1990s. (Many of these zines are currently owned by MoMA, which also has exhibited objects from Pee-wee's Playhouse.) In 2013, Christie's sold an untitled acrylic, ink, and pastel image on paper—an image of a surfer amid dense waves, with Pettibon's signature associative caption—for $1,575,000. Pettibon, along with artist William Kentridge, brought new attention in the contemporary art world to drawing as a practice and as a fine art object.
Punk thus turned a corner and became something else, something wider. The new era was marked, perhaps, by Panter's appearance in Raw magazine, founded and edited by Spiegelman and Françoise Mouly. In 1980, the same year that Slash folded, Spiegelman and Mouly self-published Raw, a high-end oversize magazine, before it was picked up by Penguin, which opened a new era for comics and wider readerships. Panter's first Raw cover, in 1981, won industry awards. It is a close-up image of a grimacing punk named X, in color, adapted from Panter's black-and-white Okupant X, the experimental 1977 book that collapses television, science fiction, comics, and performance art references and styles. This issue of Raw carried an appropriate tagline: "The Graphix Magazine That Lost Its Faith in Nihilism."
In 1989, for its inaugural issue with Penguin, Raw published Panter's cover image of Nancy mashed up with Popeye mashed up with Picasso's Cubist art—to name just one striking example of "recombinant art." Panter's artwork had by that point become closely associated with Raw, the game-changing magazine that made larger audiences than ever before take stock of comics.
Raw #2.1, the issue with Panter's mash-up adorning its cover, also presented a roster of cartoonists so evidently fresh and talented that they came to define the contemporary graphic novel field. These include Charles Burns (his story "Teen Plague," the prototype for Black Hole), Richard McGuire (his story "Here," which developed into the dazzling experimental graphic novel Here), and Art Spiegelman (his self-reflexive "Time Flies" chapter, the most important and most cited section of Maus).
The cover of Raw #2.1 is a typically brilliant Panter image. The soft mess of red lines under the right eye looks forceful and delicate at the same time—it could indicate a bruise or a blush, something violent or something elegant. In 2000, in an irony not lost on Panter's fans who know his devotion to car culture exhibited in Dal Tokyo, Panter won a prestigious Chrysler Design Award, given to individuals in architecture and design who have "significantly influenced modern American culture." The range of Panter's artistic practice is huge, and it continually leaps over commercial, fine art, and grassroots boundaries. Panter moves in the world of design, as well as in the world of fine art as a painter (he graced the cover of Modern Painters magazine in 2015), and he is a drawer in many different iterations, including self-publishing cheaply made and inexpensive Jimbo comic books, which in today's parlance are called minicomics—a term for self-produced work. In 1993 Panter went back to Texas—Texans and religious fanatics are a comfort zone, he explained to me—to report in words and images for the New Yorker on the David Koresh–Branch Davidian compound standoff, in the full-color, five-page "Waiting for Waco." Panter's handwriting, which had frightened Groening in 1978, isn't tamed for New Yorker audiences—it's up-front in the piece, shaky, uneven, and ratty—and it extends that magazine's aesthetic range.
Gary Panter, cover of Raw #2.1, 1989.
Used by permission of Gary Panter.
Punk profoundly influenced comics, and comics profoundly influenced punk. Today, punk rock's historical era is over, but comics is an art in which we can recognize its values—the weirdness and the alterity along with the accessibility—while comics also extends its reach into the mainstream, abandoning none of punk's energy while also creating new models for art. Cartoonists in the 1970s and '80s did want better media—and they did go and make it.
The desire to make experimental work for a wide audience defines how we can think of the best comics today. And Panter, along with other cartoonist punks, created a culture of immediacy and expressivity that has become key to how we understand and articulate ourselves today. The DIY ethic, and the value placed on the accessibility of low production values for high impact work, rhymes with the significant focus on the handmade evident, for instance, in the phenomenon of Etsy, the hugely successful online retailer that that has offered new models of self-distribution and is "the place to buy and sell all things handmade." Creators from diverse backgrounds and contexts are producing more printed zines and minicomics than ever (at Quimby's Bookstore in Chicago, for instance, there are fabulous zines made by eight-year-olds). At the same time, if in printed comics one recognizes core features of punk, such as its no holds-barred content, devotion to reproducibility (which is to say, communication through circulation), attachment to self-publishing models, and pressure on traditional modes of gaining expertise, one also sees this now online. In the contemporary proliferation of blogs, which encourage uncensored, direct communication, and webcomics, in which an artist can circulate her work easily and immediately, the energies of punk have found a new platform.
---
WHY ILLNESS & DISABILITY?
With Binky Brown, comics went practically overnight from being an art form that saw from the outside in to one that sees from the inside out.
—Chris Ware on Justin Green, 2009
It was simple and that's really what I'm like on the inside, I feel like. That picture is me, more me than I am.
—Allie Brosh on WTF with Marc Maron, 2014
One of the signal features of comics is its immediacy, as its role in developing the visceral and action-oriented punk movement makes clear. To invoke cartoonist Gary Panter again on punk philosophy: "It was just, get up there and do something. Start." Two different artists working in the "get up and start" mode, almost forty years apart, created new idioms for expressing illness. They went out on a limb when similar work didn't yet exist, and in so doing, revealed just how richly comics can present the consciousness of a person suffering from a mental disorder. Justin Green's pathbreaking underground comic book Binky Brown Meets the Holy Virgin Mary—the very first autobiographical work in comics—about a young man with debilitating obsessive-compulsive disorder, and Allie Brosh's deeply personal, massively popular webcomics collection Hyperbole and a Half, about a young woman with depression, are crucial works in the comics canon. Green was an innovator of underground comics; Brosh of webcomics. Underground comics, as an unrestricted, below-the-radar cultural and publishing movement, finds an analogue in today's webcomics, a platform that similarly aims for direct, uncensored, immediate communication.
Stories about illness and disability use the show-and-tell aspect of comics so basic to its hybrid form to reveal hard-to-convey truths about sickness or ability, and profoundly shaped the comics and graphic-novel field today. It is no coincidence that the risky founding work of comics autobiography is about a young man with debilitating obsessive-compulsive disorder. Binky Brown, the ambitious forty-four-page underground comic book from 1972, serious and personal, set the terms for the "graphic novel" field to come. It is also no coincidence that Brosh's Hyperbole and a Half, a breakout webcomic of the same title that drew as many as five million unique readers a month to her blog before becoming one of the twenty-first century's best-selling graphic novels in 2013, is about depression.
Even when graphic novels had much, much less cache than they do now, formative works in the field were generated out of illness and disability. We see this with Green's inaugural comics autobiography, Binky, and later with early graphic novel titles such as English cartoonist Al Davison's 1990 The Spiral Cage, about his spina bifida, and Harvey Pekar, Joyce Brabner, and Frank Stack's 1994 Our Cancer Year. While Pekar's American Splendor is about recording the ordinary, this book, coauthored with his wife, Brabner, and drawn by Stack, actually centers around an extraordinary event: Pekar's diagnosis with lymphoma. (He ultimately died, in 2010, not of cancer but rather of an accidental overdose of prescription medication.) David Wojnarowicz's AIDS-focused Seven Miles a Second, a collaboration with cartoonists James Romberger and Marguerite Van Cook, was released posthumously in 1996 after the art star's death from AIDS at age thirty-seven. First published by Vertigo, DC's darker adult imprint, it has become a cult classic. Chock-full of beautifully colored surrealistic images, Seven Miles a Second presents Wojnarowicz's anger, frustration, and sadness about his disease and its effect on his community. Other important early titles addressed the AIDS crisis, too, even in very different contexts, such as MTV's Real World: San Francisco star Judd Winick's graphic novel Pedro and Me, about costar Pedro Zamora, the Cuban American AIDS activist who died of the disease at age twenty-two while the show was airing.
Comics about illness, and disability—both mental and physical—have multiplied hugely over the past twenty years as people have recognized the form's immediacy and its diagrammatic ability to display otherwise hard-to-express realities and sensations. The capacity of comics to be diagrammatic—representing objects in space and in time, showing and telling—serves the authors of many different kinds of stories, from those that shed light on institutional spaces like hospitals to those that present details like the measurements of a core biopsy needle—drawn in Marisa Acocella Marchetto's Cancer Vixen at actual size. Also appearing at full size is a drawing of her biopsied tissue. Comics's diagrammatic quality allows Marchetto and others to easily diagram medical equipment and procedures, providing specific, visual information about treatment and process. Comics can lend itself to didactic diagrams, in addition to storytelling ones, that don't feel disruptive in the flow of a page. Brian Fies's Mom's Cancer, for instance, within the unfolding story, effectively explains, describes, and reproduces X-rays of his mother's cancer before and after chemotherapy.
Comics can make visible both external features of a condition, and internal, cognitive and emotional features that are otherwise hard to communicate accurately. There is a large body of work depicting individual experiences that are hard to imagine existing in either words or pictures alone. Cancer, one of the leading causes of mortality worldwide, is a common theme of seasoned comics professionals and field newcomers alike. A short list of graphic novels about cancer, after Pekar, includes Stan Mack's Janet & Me; Miriam Engelberg's Cancer Made Me a Shallower Person; Marchetto's Cancer Vixen, Fies's Mom's Cancer (which initially was a popular webcomic before it was picked up by Abrams); David Small's Stitches; and Jennifer Hayden's boldly titled The Story of My Tits. There is profound autobiographical work about epilepsy (David B.'s Epileptic, an international sensation translated from the French); chronic pain (John Porcellino's The Hospital Suite); herpes (Ken Dahl's Monsters); lupus (Julia Wertz's The Infinite Wait); Alzheimer's disease (Sarah Leavitt's Tangles); and anorexia (Katie Green's Lighter Than My Shadow), as well as titles like Cece Bell's award-winning young-adult-oriented El Deafo, based on her own childhood growing up deaf. Today we see trenchant, path-setting books about mental illness by Green and Brosh, and also by many others who have distinct points of view in thinking about illness. While we have Ellen Forney's Marbles: Mania, Depression, Michelangelo, and Me, a graphic memoir about the author's own bipolar illness, we also have Darryl Cunningham's sobering Psychiatric Tales: Eleven Graphic Stories About Mental Illness, based on his work as a health-care assistant in a psychiatric ward in the UK.
Marisa Acocella Marchetto, page from Cancer Vixen (New York: Knopf), 2006: Marisa undergoes a core biopsy accompanied by her mother.
© 2006 by Marisa Acocella Marchetto. Used by permission of Alfred A. Knopf, an imprint of the Knopf Doubleday Publishing Group, a division of Penguin Random House, LLC.
The number of these kinds of stories are growing, so much so that the recent international "graphic medicine" movement can claim a large body of work related to its central concern. The authors of the Graphic Medicine Manifesto define their movement as focusing on the overlap of comics and the "discourse of healthcare," broadly conceived. The Graphic Medicine Manifesto was published in 2015 by six authors—a mix of practicing doctors, nurses, and professors—and received a rave review in the New York Times. The relationship of text and image is a crucial medical and diagnostic issue. Late twentieth-century medicine, as critic Jared Gardner points out, saw a drive "to replace patient narratives with data derived from ever more sophisticated diagnostic technologies," including imaging technologies understood to be "objective" and accordingly weighted more heavily than patients' own subjective descriptions. Comics's mix of words and images can convey key information that is otherwise hard to share or communicate. Graphic medicine is interested in comics that seek to find a way to depict complicated experience accurately—in both words and pictures alike, and in the spaces of meaning between them.
This includes the experiences of doctors and nurses as well as patients. Welsh physician Ian Williams, one of the manifesto's authors who maintains www.graphicmedicine.org, depicts the trials and tribulations of giving medical care in his own graphic novel The Bad Doctor. Comics both by and for doctors and nurses about administering care and medical education now join comics about the experience of illness created by patients themselves. A few years ago a psychiatrist in the West Bank wrote me about using comics to help people with trauma. And a doctor at the University of Chicago Medical Center contacted me recently about advice on developing a comic for patients about how procedures and care happen in the often-confusing physical space of the hospital.
Illness and disability have also entered into graphic fiction in powerful ways: as we've seen, Charles Burns's Black Hole centers on a made-up infectious disease whose symptoms and emotional effects Burns portrays in vivid visual detail. Notable recent comics hits across the genre spectrum feature amputee protagonists, as in Chris Ware's Building Stories, whose unnamed heroine has a below-knee amputation and several prostheses, and Marjorie Liu and Sana Takeda's Monstress, whose heroine Maika is amputated at her left elbow. While the former is a fine-grained realist epic, and the latter is a popular feminist fantasy, both works confront the reader with large, unadorned, powerful visual images of bodies deemed "imperfect" or lesser than.
Illness and disability are also part of the DNA, so to speak, of superheroes—which often relates to their traumatic origin stories. Often for superheroes a condition of disability is countered by an amplification of another part of the body, creating their extraordinary abilities, as Marvel's Silver Age comics make particularly clear. Daredevil (Matt Murdock) is blind from a radiation accident, but has enhanced senses and reflexes known as "radar sense." The X-Men's Professor X (Charles Xavier) is wheelchair-bound, but has such powerful mental abilities he can transcend his physical body. Iron Man (Tony Stark) has a chest injury—shrapnel near his heart—that is countered by his invention of a mighty electromagnet that also powers his special armored suit. Hawkeye (Clint Barton), for part of his history, is apparently deaf—he has worn hearing aids in various comics—but has incredible visual acuity (hence he's a master marksman). And the body of the DC superhero Cyborg (Victor Stone) is crushed in an accident, so his scientist father—who had experimented with enhancing his son's intelligence—upgrades him to a cybernetic body to match his intellect.
And perhaps most famously, there is Barbara Gordon, a character in the Batman universe first introduced in 1967 as the daughter of Gotham City police commissioner Gordon, and the most iconic version of the superhero Batgirl. In Alan Moore's controversial Batman: The Killing Joke in 1988, Gordon was paralyzed in a gun attack by the Joker. Confined to a wheelchair, Gordon then became the superhero hacker and information broker Oracle, with superior intellectual prowess and computer skills—just in time for the explosion of the Internet. Oracle went on to cofound an all-female superhero team called Birds of Prey, which generated an over-twenty-year-long series beloved by fans. The Oracle character was retired by DC in 2011 when the company did a full reboot of their entire universe of characters, to the anger of many, especially when Barbara Gordon was resurrected as an able-bodied Batgirl who had been cured by an operation.
Marjorie Liu and Sana Takeda, full page image from Monstress (Portland: Image Comics), 2015, of Maika, a war survivor, who opens the series at a slave auction in which disabled bodies—hers and others—are judged and marketed; Chris Ware, full page image from Building Stories, 2012: the protagonist thinks about her body in its barest form.
Used by permission of Image Comics and Chris Ware. Building Stories image courtesy Chris Ware.
But while DC earned flak for retiring a character with a physical disability (and an iconic spunky female hacker at that!), Marvel has, to its credit, fascinatingly experimented with the comic-book format in order to address itself specifically to visually impaired fans of its blind superhero Daredevil, allowing the representation of a disabled superhero to actually innovate the way the company thinks about audience. In 2011 Marvel released an audio edition of their new Daredevil #1 for free on their website, in conjunction with the comic book (it can still be found online at Marvel.com). The blind-friendly audio version runs about twenty-six minutes long, and is read by Marvel editors voicing and acting different characters, like a radio drama. In a brief introduction to the audio version, a Marvel senior editor claims they got the idea because the company got so many letters from visually impaired fans who noted their friends had to read Daredevil comics out loud to them. While there isn't yet a braille version in the works, braille is often closely and accurately represented (as are various assistive technologies) in the comic book itself, and fan sites have speculated it might be a possibility. The popular Daredevil television show on Netflix, following suit, has added optional audio descriptions in addition to spoken dialogue, and inspired think pieces about its representation of disability.
But it is Justin Green's Binky Brown Meets the Holy Virgin Mary, the very first work of autobiographical storytelling to appear in comics, that is the ur-text of comics illness and disability narratives. Green's devotion to his own highly private, painful obsessive-compulsive disorder as the central plot point of a comics story was unprecedented and threw the field wide open. Further, Binky Brown is a fully designed, stand-alone comic book with a single story front to back, calling attention to the fact that the subject matter deserves the integrity of its own space, covers, and binding. As Art Spiegelman writes in the introduction to the deluxe edition of Binky Brown published by McSweeney's in 2009, "Today a forty-four page work might seem like only a throat clearing exercise . . . but back in The Day"—the day of underground comics production in the 1970s—"forty-four pages was an epic." To return to a point from the introduction, while many designate Will Eisner's A Contract with God, a series of four linked vignettes, the first "graphic novel" because it used the phrase on its cover in 1978, this honor could just as easily be awarded to Green.
The ambition and seriousness of purpose Binky Brown demonstrates—to take on something hard, and private, in comics—directly inspired Spiegelman to create his three-page "Maus" story about his parents the same year, and inspired Aline Kominsky-Crumb and Robert Crumb, along with countless others, to create comics with the stuff of their own lives. Green not only influenced Spiegelman as a cartoonist, but also as an editor. His encouraging, taping-speed-to-a-nudge-letter move refused to let Spiegelman off the hook for creating "Maus" for Funny Aminals. "One point of my pentagon-shaped Pulitzer Prize belongs to him," Spiegelman writes, noting, "Before Justin Green, cartoonists were actually expected to keep a lid on their psyches and personal histories, or at least disguise them into diverting entertainments." And Green's founding work of comics autobiography is about communicating the experience of illness. Today we see on social media how powerful the inclination is to document and to share images, in photos and videos, from one's own life. But certain interior states—especially ones produced by illness, and mental illness specifically—are not as easily photographable through a lens. With Binky Brown, we see how drawing ("making a picture") can document realities that cameras ("taking a picture") cannot capture.
Green grew up Catholic in Winnetka, Illinois, in a family with five kids. His mother was Irish Catholic. His father, who was Jewish, was a hardworking man who became a highly successful industrial real-estate agent (he was making more than his own father, a kosher butcher, by the time he was ten, employed as a batboy for the Chicago White Sox). Green loved comics from the time he was tiny. In a touching anecdote in the afterword to Binky Brown's newest edition, he describes walking by himself at only age four to a "distant variety store" with a couple of dimes "burning a hole in my pocket" and his home address safety-pinned to his shirt. As a child in Catholic school, Green read Treasure Chest, a Catholic comic book that was distributed every month for free; later he became obsessed, like almost every cartoonist in this book, with the sophisticated satire of Mad. In the aforementioned afterword he also describes setting out on his bike—he would have been ten—during an actual blizzard to get a copy of Mad #26. Recurring theme: as a child Green happily risked his physical safety to procure comic books. In high school Green took weekend life-drawing classes at the Art Institute of Chicago, and later enrolled in the prestigious art school Rhode Island School of Design (RISD) for a BFA in painting. While Green loved comics, he aspired to be a fine artist.
In college, as a foreign exchange student studying in Rome in 1967, Green had a revelation when he saw "a little cartoon by Robert Crumb in a tattered European underground paper." (Crumb, often without his knowledge, was fairly widely disseminated in Europe from early on in his career.) Green was disenchanted by the airlessness of art school, which felt pretentious. Abstract Expressionism was the dominant idiom, and Green's own oil painting was abstract, although he longed for the chance to create (unfashionable) realistic imagery. Hoping in Rome to learn from Renaissance masterpieces, Green found the city's landmarks were so filled with tourists they felt hard to enjoy or contemplate. At a conference I organized, Green explained that the unexpected encounter in Rome with Crumb's drawn line, from his strip "Itzy and Bitzy in 'Cause and Effect,' " felt like "a call to action." Crumb's marks on paper seemed full of a vitality and energy that had been missing in Green's own artistic practice, and Crumb felt more electric to Green than the classical art in Rome. He describes how Crumb's characters "had a sculptural quality, as if they were made out of Silly Putty"; he admired the playfulness and joy the drawing exuded in addition to the evident craftsmanship. Green went on to earn his degree from RISD in 1968, and very briefly enrolled in graduate school at Syracuse before quitting painting altogether and deciding to move to San Francisco to join the burgeoning ranks of underground cartoonists.
Justin Green, cover of Binky Brown Meets the Holy Virgin Mary, Last Gasp, 1972.
Used by permission of Justin Green.
In 1971—the same year his first cousin William Friedkin would win an Academy Award for directing The French Connection—Green began Binky Brown. In his black-and-white comics, befitting his background, Green exhibited what underground cartoonist Spain Rodriguez deemed a "Catholic Style": clarity of line, academic realism, and observance of perspective. In 1995, its original publisher, Last Gasp, reprinted Binky Brown in a book collection of Green's comics. Binky's enduring significance over generations was sealed in 2009 when the acclaimed literary publisher McSweeney's, known for its high production values and experiments with print, reissued it as a deluxe, 10-by-14-inch clothbound edition, presenting facsimiles of the original artwork at full size.
Green embarked on Binky Brown, after publishing some shorter underground pieces, "out of an internal necessity to define the psychic components of a specific condition"—obsessive-compulsive disorder (OCD), an anxiety disorder. The National Institute of Mental Health defines OCD, which afflicts approximately five million people in America, as a condition in which a person has "reoccurring thoughts (obsessions) and behaviors (compulsions) that he or she feels the urge to repeat over and over." Green describes his OCD, in an interview, as a "spatial and temporal relationship with Roman Catholic icons, architecture, and doctrine that has been resounding in my life for almost forty years." Green's OCD—like many people's—is fundamentally about controlling one's relationship to space, and arranging objects and oneself in space. And comics is a form that is structured at the most basic level by the arrangement of objects in space. We see this both within a panel (like Spiegelman's comparison of drawing panels and packing a suitcase in chapter one) and with the meaningful arrangement of panels themselves on the page or screen. Binky Brown is not only the first comics autobiography, but it is also the first literary work, whether fiction or nonfiction, about OCD, anticipating, in Green's own words, "the groundswell in literature about obsessive compulsive disorder by almost two decades."
Comics is a form, then, that rhymes with, and perhaps can even replicate, compulsive spatial focus and arranging. Alison Bechdel's Fun Home details her childhood OCD, which is in part about the location of her body in space: in the book, before the child can cross any threshold, she needs to tabulate the number of edges and subdivisions in front of her. Soon she realizes that in all threshold spaces, and indeed between all solid objects, hangs an invisible substance that she needs to clear away. In an interview with Bechdel about her ritualized and complicated practice of producing comics, she added, "I do like to describe my drawing process as a barely harnessed obsessive-compulsive disorder." Green, in an essay on OCD, referred to his disorder as "codifying every square inch of space"—another formulation that also describes creating comics. Noting the differences between writing a novel and writing a graphic novel, Bechdel once noted that today one could write a book and never physically touch one's own prose at all, whereas when she wrote Fun Home, "I had to touch every millimeter of all of the pages." Green pointed out at the conference that a cartoonist needs to be very exacting about space, explaining: "The slightest little flick of the hand like a thirty-second of an inch makes all the difference in an attitude or a gesture."
Cartoonists of autobiographical comics often encounter the claim that their work is "cathartic," and yet that notion has always seemed to be exactly the opposite of the labor-intensive, and often obsessive, process of composing comics. Once asked if making Maus was cathartic, Spiegelman responded that it would be like the catharsis of making "a 100-faceted wooden jewel box." In other words, not cathartic at all. Putting one's experience into little boxes in space doesn't lend itself to the purging implied by catharsis. It's like building a visual, material, counter-edifice to express a mental edifice, a mental structure. Green describes comics the following way: "The true craft requires the precision of a jeweler along with the fortitude of a cobbler, and neither discipline comes easily." Jeweler, cobbler: it's the connection of intricate parts to one another—one mark to another mark, panels to other panels, words to images—that makes up the stuff of comics.
So what made Green turn to comics specifically for this story of mental illness? He made the work, as he explained, to define the psychic components of an illness—not only for himself, but also for an audience of readers, which he could do through the revealing form of comics. At the outset of the book, Green's character Binky Brown is a thirteen-year-old boy growing up rigorously Catholic in Winnetka in the late 1950s. (The choice to call himself "Binky Brown" is unrelated to Matt Groening's rabbit Binky from Life in Hell, and presumably a play on Green's last name and the abjection the protagonist feels: a hopeful, verdant green turned to depressing, stain-like brown.) In some respects Binky lives what might seem to an outsider like a normal young life: he goes to school, rides his bike, climbs trees with friends, squabbles with his siblings, reads comic books. As his body develops, however, he can't help but to see the Virgin Mary, who is represented all around him, including in his home, as a potentially naked woman, which causes him terrible, crippling anxiety. His connection with religion is both punitive for him and potentially arousing. One early panel juxtaposes the hairs escaping a nun's habit with the imagined pubic hairs of a girl on the beach.
Binky is so distressed about his involuntary sexualization of Mary that he comes to believe "penis rays" emanate from his penis and can potentially harm Mary should the ray interact with a statue of her or with other religious icons and symbols. A famous panel from Binky Brown shows him masturbating miserably, with the ray evident, thinking, "How can this little thing cause so much trouble?! Why was I ever born? Wish I coulda been a girl!" Binky becomes obsessed with policing his sexuality. As Green explains in a later essay, "Even glancing at a woman's fully clothed breast was counted as a venial sin. The hourly sin count became so great that it was impossible to function normally." Eventually any object longer than wide, including his own hands and feet, figures as a penis to Binky, with damaging rays he must prevent from crossing, and, in his mind, physically interacting, with any pictures and statues depicting Mary and any religious objects or edifices in general. Some painful images from Binky Brown show him running outside, for instance, on two feet that he feels are—and draws to be—two erect penises. Like Burns's precisely detailed panels of molting and rotting skin in Black Hole, these images force an uncomfortable looking for the reader, an encounter with physical and emotional states made confrontationally concrete.
Panel from Justin Green, Binky Brown Meets the Holy Virgin Mary, showing the title character understanding his hands and feet, in addition to his penis, as phallic objects that can emit harmful "rays."
Used by permission of Justin Green.
Eventually, after a long and sincere losing battle to try to control his uncontrollable thoughts, and the rays, and a crystallizing event in which he fantasizes about Mary while praying in church, Binky, still a teenager, officially leaves Catholicism, figuring that he's sure that he is already damned for eternity. But his OCD does not abate even after he is no longer a practicing Catholic. The rays still emanate from all phallic objects, including his penis, hands, and feet. A powerful tier-wide timeline, which begins in 1959 and ends in 1971, presents five successive Binkys, each one a little taller and differently styled than the last. The rays emanate, crisscrossing, from all parts of his body, hands and feet included, as Binky grows up and navigates the world. Even though he rejected the church, "our lady looms over him as a supernatural reality." He is still desperately tethered to his OCD even in 1971, using stopgap measures we see him develop as a child, such as incantations (the made-up "noyatin," which stands for "no sin") and "constantly re-positioning objects and his own body," whether he is "standing, walking, sitting, spitting, eating, shitting, talking, listening, fucking, laughing or crying." Finally Binky decides to literally smash his idol in his own cleansing ritual in his San Francisco apartment; he buys a dozen small Madonna statutes that he destroys with a hammer.
Justin Green, panel from Binky Brown Meets the Holy Virgin Mary (San Francisco: McSweeney's), 2009, facsimile of original art, 1972.
Used by permission of Justin Green.
What was and remains so striking about Binky Brown is how Green visualizes his obsessive-compulsive imaginings—the way he depicts his visual imagination as concrete on the page. Penis rays, in his drawings, actually make physical contact with other objects. Green the artist draws the rays as existing in space, as his character experiences them. Here we see how drawing can offer a picture of a consciousness—a mental state or a psychic landscape—that is internal to an individual. Green translates his "mind's eye" into a visual form on the page that readers can encounter and understand.
Readers, then, can witness what Binky experiences when he exits his home "imperfectly": the stairs literally fly out and grab him by the shoulders. Aligned with Binky's consciousness (if not his actual optical viewpoint), we see this actually happening in the panel; readers confront Binky's interior reality, however surreal. Chris Ware points out that Green's work inaugurated comics as a form that "sees from the inside out"—and hence could address itself to complex internal realities. Later on the page depicting the aggressive anthropomorphized stairs, Green writes in a box of text that Binky was "susceptible to bizarre, compulsive commands." In the image below, Green draws a small male angel, shaped like an adult man but perhaps a quarter the size of a human, hovering above Binky's head and touching his finger to Binky's nose as he barks out orders. Comics can render metaphors concrete on the page in order to make an experience vivid—as when Brian Fies draws his mother in Mom's Cancer actually swimming in a sea of fine print. And, perhaps most significantly, through its word-and-image form, comics can depict a range of hard-to-picture effects of the individual experience of illness—especially mental illness, in which one person's reality may not be easily shared by others. The stairs rebuking Binky are not metaphorical, but represent an actual interaction in his own mental landscape.
Further, comics can bring together different versions of a self on a given page, which helps to convey the experience of a mental illness like OCD. Within the frame readers see a younger version of the author—the adolescent Binky, say, running down the street—and they also read that character's spoken words or private thoughts in speech balloons or thought balloons within the frame. And readers also read retrospective narration, which usually appears outside of the action of the story, above or below the frames. This represents yet another version of self (perhaps older and wiser). The retrospective narrative voice in Binky appearing above or below the frame creates a tension with the protagonist's voice from within the frame.
This is key to communicating what Green calls the double vision of OCD: both the recognition that an obsession or a compulsion isn't rational, and the profound need to execute its mandates anyway. Green identifies the double-trackedness of comics form—its pairing of commentary in text boxes with action unfolding in frames—as something that itself mirrors the OCD "double vision." Both Binky in particular and comics in general, Green has observed, carry the double vision that characterizes the condition of the disorder. This double vision of comics allowed Green to portray the most private and intimate moments from his life—say, masturbation and religious visions—and also to portray himself as what he calls "a specimen." In Binky, the narration even refers to the protagonist as "our specimen," instead of "our hero," as we see in the timeline panel. Green created a new form of comics self-expression that deliberately presents the autobiographical self as both a looking self (a subject) and a looked-at self (an object).
Justin Green, page from Binky Brown Meets the Holy Virgin Mary, 1972.
Used by permission of Justin Green.
Green went on from creating comics to make a living as a master sign painter—a trade, like comics, all about spatial precision, handcraft, and stylized letterforms. (One of his several post-Binky book titles is Justin Green's Sign Game—comics about sign painting!) He married the cartoonist Carol Tyler, a Wimmen's Comix contributor who is the author of a trilogy about her father's experience in World War II, You'll Never Know. (They first met while he was driving a city bus in Chicago.) Unlike many of the most important underground cartoonists, he is not prolific. Green and Tyler now live in Cincinnati, where Green is back to creating comics more regularly after a fall from a ladder during a job in 1990. He has a major retrospective show at the historic Carnegie Galleries in Kentucky in 2018.
Binky Brown Meets the Holy Virgin Mary, the 1972 comic book that was printed on cheap newsprint, sold around forty thousand copies, a robust figure for an underground title. "I'll never forget seeing the unpublished pages," Spiegelman recounted of visiting Green's home, "hanging from a clothesline stretched around the drawing table and all through his living room . . . and knowing I was seeing something New get born." Green set an example for cartoonists, and he also earned admiring and bewildered responses from cultural heroes including writer Kurt Vonnegut and film director Federico Fellini (speaking of film, his cousin Friedkin had a smash hit the following year with The Exorcist, which actually does not feel that removed in some ways from the tortures of Binky). Spiegelman has described how Binky, although it was out of print for over twenty years, never faded away: it was an instant classic, and photocopies eagerly exchanged hands for years; it was "long a secret of the cognoscenti," Spiegelman writes.
Even within the already independent-minded underground, Green was, in the early 1970s, a recognized originator of DIY publishing: he created a series of self-published comics titles in a series called Off the Cuff—single sheets of letter-size paper, xeroxed on both sides, and then folded and stapled to become an eight-page booklet—and sold them for 7 cents. While these booklets are a far cry from the gold-embossed hardcover that would house Binky Brown thirty-seven years later, they suggest, along with the personal and financial risk Green took to produce Binky Brown in the first place, how the urgency to create a direct, uncensored account of the experience of illness led to the creation of new formats and genres.
The same is true of the cartoonist and writer Allie Brosh, born in 1985, whose Hyperbole and a Half comics grew out of her desire to chronicle her life—and specifically, to communicate her experience of severe depression. Brosh, a biology major and a track athlete at the University of Montana, began drawing and writing about her life using Paintbrush, a free Mac computer program for basic graphics, and posting her comics and observations to her personal blog (also free). Hyperbole and a Half is one of the most fascinating and moving success stories in comics of the past decade—and it suggests that today's webcomics, a democratic playground, are the new underground comics: a self-publishing platform in which the artist has total, unrestricted freedom to communicate directly with audiences and to create, unfettered, whatever she wants. In Brosh's case, that is a funny, profanity-laced, sad, weird world of adventure and feeling that probes Brosh's depression by investigating the nature of causality—especially in family incidents from childhood—and the nature of empathy, between humans and also between humans and animals.
Brosh hilariously anatomizes her dogs' inexplicable behaviors, and her own past behavior—like the time she broke into a room of her grandparents' house from an outdoor window in order to devour an entire birthday cake, or the time she convinced her mother to take her to a birthday party while Brosh was under heavy sedation. These stories frame those in which she turns to her circumstance of depression in the present. In Brosh's meditation on causality in Hyperbole and a Half, her childhood self comes into vivid focus. How did certain patterns or inclinations get set? How does Brosh understand her childhood behavior to produce insight about her adult problems? One of the funniest Hyperbole and a Half stories is "Warning Signs." Like all of Brosh's stories, it combines comics made with Paintbrush—hand-drawn words and images in frames—with typeset text.
Brosh recounts how when she was ten she buried a crayoned letter in her backyard addressed to her future self at age twenty-five. The letter, when she remembers it and amazingly finds it in the ground seventeen years later, makes her feel profoundly "weird about myself." Of the six questions she asks her future self in the letter, four are about dogs; she also introduces herself to her future self by name, as if the older Allie wouldn't know; and, perhaps most devastatingly to the older Brosh, the letter's last line is "Please Write Back": her child self thought her adult self might actually write back from the future. In response, Brosh brilliantly composes the rest of the story as a series of letters to her younger self at troubled ages (four, five, six, seven, ten, thirteen). The final letter is addressed to "Dear other iterations of my past self," and compliments them "for not being so goddamn weird that I felt I had to address you personally in a letter for the future." As with Green, Brosh's comics picture different versions of self interacting on the page.
What started out in 2009 as one young woman's personal blog—one she confessed to starting in order to procrastinate for a physics final—quickly became a phenomenon. Particularly popular were Brosh's posts delving deeply into the experience of depression. Brosh's post "Depression Part Two," from 2012, got an astounding 1.5 million hits in a single day. Brosh is prodigiously talented, as her unique humor and aesthetic make evident—and she without question touched a nerve, and galvanized a community, by so directly addressing depression through comics. In 2013, her webcomic was published as a colorful, nonchronological, eighteen-episode book collection by Simon & Schuster, titled Hyperbole and a Half: Unfortunate Situations, Flawed Coping Mechanisms, Mayhem, and Other Things That Happened: it became a #1 New York Times best seller. The Times book critic Dwight Garner wrote that it "foreground[s] offbeat feeling and real intellect" and reported that his wife "wept with pleasure" while reading it. Advertising Age named Brosh one of the fifty most influential creative figures in the world. Psychologists praised Brosh's account of depression, and she was profiled in Psychology Today. Even Bill Gates wrote a long, rave review on his blog GatesNotes asserting, "Hyperbole and a Half gave me a new appreciation for what a depressed person is feeling and not feeling. . . . [She has] the observational skills of a scientist, the creativity of an artist, and the wit of a comedian." Scott McCloud, who included Brosh in the volume Best American Comics 2014, called her "one of the most widely read cartoonists on the planet."
Brosh was born in Auburn, California, and moved to Sandpoint, Idaho, with her parents and little sister when she was eight. She struggled with ADD as a child, and her battles with her parents around her hyperactivity and willfulness show up in Hyperbole and a Half (as do her mother's initial struggles with their very rural location: in one episode, her mother takes her daughters for a walk in the forest abutting their house and the trio becomes desperately lost for hours). Brosh's profound lifelong love of animals, particularly dogs, helped shape her childhood, as her comics make clear. She graduated from the local Sandpoint High, where she was a state champion cross-country runner, and was successfully recruited by the University of Montana for a running scholarship. She married longtime boyfriend Duncan Hendrick, a runner and a fellow science major at the University of Montana, in 2012; the two eventually moved to Bend, Oregon. Brosh, to her great surprise, began to be able to support herself through the sale of the Hyperbole and a Half website's merchandise in 2010.
Allie Brosh, page from "Warning Signs." From Hyperbole and a Half: Unfortunate Situations, Flawed Coping Mechanisms, Mayhem, and Other Things That Happened by Allie Brosh.
© 2013 by Alexandra Brosh. Reprinted with permission of Touchstone, a division of Simon & Schuster, Inc. All rights reserved.
Brosh was a creative child, with no access to what she calls "passive entertainment," and often wrote and drew her own stories to amuse herself. (She has explained that her rural upbringing, with the forest at her disposal, allowed her to be a "weirder" kid than she might otherwise have been.) When her parents first got a computer, she told the magazine True/Slant, she liked to use it to draw in Microsoft Paint, a program (much like the later Paintbrush for Macs) that is included free in all versions of Windows. She even drew in this program when, as she puts it, "I was bored in my dorm room in college," as she puts it. But it wasn't until Brosh, still in college, saw the "rage comics" meme circulating on the Internet that she became inspired to draw for her own blog.
"Rage comics" first appeared on a simple, open-to-anyone image-based online message board called 4chan (4chan.org). The original rage comic, posted to 4chan in 2008, is a four-panel strip that begins with a crude drawing of a person defecating and then getting splashed by toilet bowl water, ending with a close-up of a loosely scrawled, angry screaming face, surrounded by lots of capital F and U letters. This face launched the meme. In the democratic culture of the Internet, it became a widely shared and used template: the comic was reposted many times, and online audiences edited the comic to adapt the face to tell different stories. Eventually other simply drawn faces—and not all of them angry, but all of them adaptable—joined the rage comics movement. It was an accessible way for people, especially young people online, to use humor and create stories to express themselves. This was very appealing to Brosh. "When I first discovered rage guy," she recounted of the face that started it all, "I laughed for ten minutes straight at just the one picture. I literally could not get myself under control. I don't know what it is about it, but it triggered something in me that made me want to start drawing again." Brosh began adding comics and drawings to her written blog. (And several of her own pictures, such as one with the words "CLEAN ALL THE THINGS!" above an image of herself holding a broom in one hand, and raising a fist of determination in the other, have now become Internet memes.)
As a stand-up comedy fan, Brosh found that comics brought the "physicality" of what she admired in stand-up to her storytelling: "facial expressions, body posture, tone of voice." Around the time Hyperbole and a Half took off in 2010 (then hitting two million monthly visitors), she told an interviewer that she had decided to start making pictures the previous year because "I've always had this frustration surrounding trying to tell a story properly—it never seems to come out like it felt." The combination of words and drawn images remedied that frustration. In Brosh's hands we see how adept comics can be at sharing the complicated internal processes of depression. As she once remarked, in a Talks at Google appearance, with nonverbal cues "you can say 1,000 things at once."
Part of the appeal of the rage comics faces is how expressive they are in their simplicity; they capture something for people in their reduction. Brosh's comics, created in Paintbrush, which offers only rudimentary brush tools and fill tools, look simple, basic, even childlike: they are minimalist, largely devoid of shading or detail. McCloud suggests that Brosh's work could be "jarring to traditional sensibilities, with its sloppy, scribbly style"—but then notes, "Hyperbole and a Half connects with readers strongly enough to rewire a million ideas of what 'good' comics look like." Brosh taps into cartooning's signature power: distilling and condensing essence through line, something a reader most often recognizes in how she draws faces, which are a focal point of Hyperbole and a Half in both form and content. Brosh's images are carefully crafted for maximum expressivity, if not for maximum realism. "I know it looks crude," she told a newspaper interviewer. "But it's a very purposeful crudeness. Sometimes I'll redraw something 10 times."
Brosh's depiction of herself is Hyperbole and a Half's most salient, and most compelling visual feature. She draws herself, at all ages, in all situations, in the same way: as a stick-figure creature with a monochromatic pink dress that goes up to her neck, and solitary black lines for arms and legs. Her large white face has big round eyes and a mouth (no nose). And, prominently, her character has what I thought of for years as a little yellow horn, like a conical party hat, that seems to sit atop her head, emphasizing her (adorable and maniacal) creature-like quality. As I finally learned from reading the FAQ section of Hyperbole and a Half online, it's actually supposed to be a ponytail—but conventional visual realism isn't really the point of the comic, as Brosh knows, since she jokingly suggests, "you may also think of it as a shark fin if you wish."
The power of drawing is that it can capture a concept otherwise too abstract to articulate. Brosh's drawing of herself reflects her internal reality; it merges that internal reality with an external one, lending features to a self-portrait that indicate that self's innermost feelings about herself. Brosh has said that her self-portrait in Hyperbole and a Half represents herself more accurately than the three-dimensional person with whom one could interact. She told the comedian and podcaster Marc Maron that the drawing is "really what I'm like on the inside, I feel like. That picture is me, more me than I am." Brosh has repeatedly explained this, telling the New York Times, "That is me deep down. This ridiculous, sort of crudely drawn, absurd thing. That is a more accurate representation of me than me in the person." In her Talks at Google appearance, she even took pains to clarify that it's not just about public interfacing: she herself relates more to her drawn character than to her flesh and blood self. In Binky Brown, comics represent a troubling mental landscape concretely, seeing "from the inside out," as Ware puts it, of Green's brain—and in Hyperbole and a Half, too, Brosh's self-figuration represents a profound set of personal feelings that express an internal reality.
Allie Brosh, from "Depression Part Two," originally part of Brosh's webcomic of the same title. This story got 1.5 million hits in a single day, and five thousand comments. From Hyperbole and a Half: Unfortunate Situations, Flawed Coping Mechanisms, Mayhem, and Other Things That Happened by Allie Brosh.
© 2013 by Alexandra Brosh. Reprinted with permission of Touchstone, a division of Simon & Schuster, Inc. All rights reserved.osh has struggled openly with her
Hyperbole and a Half, in its storylines, attends often to the notion of different realities: to the divide between public and private realities for a depressed person, and also to the divide between those who are suffering from depression and those who aren't. In "Depression Part Two," in which she reveals her suicidal feelings, Brosh recounts how her severe depression made it so that "I could no longer rely on genuine emotion to generate facial expressions . . . when you have to spend every social interaction consciously manipulating your face into shapes that are only approximately the right ones, alienating people is inevitable." In the panels here that show people with two different realities trying to interact with each other, readers gain access into Allie's efforts, and her feelings, to which her friend doesn't have the same access; Brosh stages this encounter, and many others, to try to communicate a state of mind that may not be easily apprehended from the outside.
Another feature Brosh uses to picture her depression in comics is her figuring her own interior dialogue as an interaction between two separate selves. This represents more attention to the theme of different realities—but it addresses the different realities of disconnected multiple private versions of self. The story "Motivation" begins with Brosh's statement, "One of the most terrifying things that has ever happened to me was watching myself decide over and over again—thirty-five days in a row—not to return a movie I had rented." The story details, through this one example, the effects of depression, including a constant back and forth with oneself about motivation. There are hints of this in Brosh's opening sentence: "me watching myself decide" implies the coexistence of active and passive selves battling it out. In a six-page segment of the story, readers see Brosh's selves as separate characters, one standing up, one sitting on the couch, engaging one another. On the last page of the conversation, Brosh writes, in typeface below the comics panels, "I'm always surprised when I lose." Which is the real "I"? They both are, in Brosh's psychic landscape; this story movingly reveals, through the visualization of separate selves, the difficulties of decision making that doesn't immediately appear rational. Brosh revisits the late movie in the story "Depression Part One," in which she draws the selves duking it out again, with the comment, "Trying to use willpower to overcome the apathetic sort of sadness that accompanies depression is like a person with no arms trying to punch themselves until their hands grow back."
Allie Brosh, page from "Motivation," originally from her webcomic of the same name. From Hyperbole and a Half: Unfortunate Situations, Flawed Coping Mechanisms, Mayhem, and Other Things That Happened by Allie Brosh.
© 2013 by Alexandra Brosh. Reprinted with permission of Touchstone, a division of Simon & Schuster, Inc. All rights reserved.
Brosh has struggled openly with her depression in her comics, proving how immediate and resonant the form can be for expressing a disorder that is famously hard to describe. She now has a large community of fans following her moves in real time; when she has disappeared for stretches on social media, or on her blog, strangers who feel connected to her through reading her comics have publicly worried about her. In 2013, the year Hyperbole and a Half became a best-selling book, Brosh had a cancer scare, and her little sister Kaiti Brosh, twenty-five, also an athlete and a devoted animal lover, committed suicide in Idaho. In one of very few interviews Brosh has done since 2013, she told Marc Maron that after her sister's death, "My dad gripped me by my shoulders and looked me in the face, just crying and saying, 'You can't kill yourself, you can't do this, you're all we have left!' . . . My immediate thought was: Well, fuck!" While hopefully this will change, Brosh's Twitter account stopped updating in 2014, as did her personal Facebook page. Her blog has not been updated since her book came out in 2013. A second book collection, Solutions and Other Problems, whose cover is on publisher Simon & Schuster's website and on Amazon, was originally scheduled for 2015, then pushed back to the fall of 2016, and then delayed indefinitely. Brosh gives a voice, and an image, to depression that manages, through the language of comics, to be both abstract and precise. After she disappeared online, one fan addressed her on Reddit: "Your writing and art changed my perspective and opened a dialogue with the world about this nightmare." The success of Hyperbole and a Half points to the vital, open creativity of webcomics—an easy-to-circulate platform that gives artists and biology majors alike a space to produce stories that address illness and disability, among so many other topics, and to share them meaningfully. I hope Brosh returns to the arena soon.
---
WHY GIRLS?
In the graphic novel world, girls are the new superheroes. They are the action stars, the focal point, the figures whose backstories, ideas, inclinations, struggles, and triumphs are presented with detailed attention in autobiography and fiction alike. In independent comics, pairs of girls—clever, winning teenagers—have become some of its most recognizable stars from early on: the effervescent Hopey Glass and Maggie Chascarillo from Jaime Hernandez's Love and Rockets; the smart, sulky, and funny Enid Coleslaw and Rebecca Doppelmeyer from Daniel Clowes's Ghost World. (The latter two were portrayed, as noted, by Thora Birch and Scarlett Johansson in the Oscar-nominated 2001 movie.) Ghost World is an early example, in 1997, of a full-bodied "graphic novel." It's also one, significantly, that realistically portrays the humor and intelligence of girls' friendships. It became a cultural phenomenon, with many critics and fans weighing in on Enid and Becky as though they were real people. There is even a Little Enid action figure, as if to underscore the substitution of girls as comics heroes. Some of the very biggest graphic novel hits of the twenty-first century are about girls, from Allie Brosh's Hyperbole and a Half to Lynda Barry's One Hundred Demons (about growing up on the interracial streets of Seattle), Marjane Satrapi's Persepolis (about growing up in wartime Tehran), and Alison Bechdel's Fun Home (about growing up gay with a closeted father in rural Pennsylvania).
Many famous comics, of course, feature girls—including some of the most widely circulated comic strips of the past century. There's Nancy, starring a spunky eight-year-old girl (the one with dark hair drawn as spiky halo). There's also Little Lulu, whose titular heroine (the one with dark hair drawn as three ropes of curls) is always outsmarting the boys. Sidekicks: Sluggo and Tubby, respectively. Both strips began in the 1930s and have become classics. Then there is the eponymous heroine of Little Orphan Annie, a comics strip so popular that Annie is a kind of twentieth-century cultural truth, spawning a musical and many movies (as well as references in contemporary anthems like Jay-Z's "Hard Knock Life"). Little Lulu's creator, Marjorie Henderson Buell, explained her choice of protagonist in a description applicable to all the famous girl characters of the humorous gag comics strips: "I wanted a girl," Buell said, "because a girl could get away with more fresh stunts that in a small boy would seem boorish."
Daniel Clowes, panel from Ghost World (Seattle: Fantagraphics), 1997: best friends Becky (left) and Enid (right) take a stroll.
Used by permission of Daniel Clowes.
Little Lulu is one of the most iconic comic strips of all time, as well as an acknowledged influence on Gary Panter, R. Crumb, and many others. And Nancy, an installment of which, as Art Spiegelman likes to point out, is actually reproduced in miniature in his 1973 American Heritage Dictionary next to "comics," is a favorite strip to celebrate. Nancy's likeness has been redrawn by Panter, as we saw, as well as by Charles Burns, Ivan Brunetti, and many, many others, including cartoonist Mark Newgarden in his avant-garde tribute called "Love's Savage Fury" and visual artist and poet Joe Brainard, in the experimental collection The Nancy Book. But despite these enduring girl characters from the family-friendly arena of newspaper comic strips, whose beginnings predate the meteoric rise of comic books, the world of comics has generally come to be seen—largely because of the predominantly male comic-book superheroes—as one dominated by boys and men (and boy-like men).
Little Enid Action Doll, Presspop. A "punk" version comes with green hair.
© Daniel Clowes. Photograph used by permission of Yasutaka Minegishi, owner of Presspop, Inc.
Comics began in the United States as a form of entertainment for any potential reader of a newspaper. Hearst and Pulitzer, building New York City's sensational press to be as profitable as possible, certainly hoped to gain adult readers when they developed daily comic strips and full-color Sunday supplements, which became widely popular. Yet comics, as we know, were called "the funnies," and the medium came to be, broadly speaking, associated with humor and children. When superhero comic books hit in the late 1930s, and became a hugely popular consumer product (recall Justin Green venturing out alone at age four with dimes in his pocket, burning with desire to buy a comic book) the association of comics with youth culture became more specifically the association of comics with boys. As a general matter this remained true despite the rise of other genres, such as romance comics aimed at girls, which began in the late 1940s. There were very few female superheroes, barring Wonder Woman, for decades; many, if they appeared, appeared as token women in a group of men, or as secondary characters. Superheroes were, in essence, about celebrating masculinity, even if what that meant was up for grabs. And even international comics hits outside of the realm of the superhero, like Tintin or Astérix, both from the Franco-Belgian tradition, largely featured boys and men. Marjane Satrapi, growing up in Iran in the 1970s, read very few comics but had access to Tintin. "My cousins were reading Tintin . . . but in Tintin you don't have any female persons so I couldn't identify with any of it," Satrapi has explained.
There are historical reasons, then, that comics gets associated with boys and adolescents, but there are also plenty of reasons one need not make that association now. The field has shifted dramatically. We see this in the world of independent graphic novels like Ghost World, and also in mainstream superhero comics. Marvel's Ms. Marvel, one of the company's top sellers since its debut in 2014, stars Kamala Khan, a sixteen-year-old from Jersey City, New Jersey (student by day, shapeshifting superhero by night). Perhaps based on the success of Khan with readers, Marvel presented a new Iron Man character as a girl, too: fifteen-year-old Riri Williams, an African-American certified genius who fashions her own suit from discarded tech she finds on the MIT campus. She is called "Ironheart." On a more lighthearted note, there are also Marvel offerings like the widely praised Unbeatable Squirrel Girl, which began as an ongoing series in 2015 and stars fourteen-year-old Doreen Green, bestowed with squirrel-like abilities including that of communicating with squirrels (which apparently helps to defeat enemies). Both Marvel and DC are investing more, in every medium, in young women superheroes, as we see in the current success of television shows based on comic-book superheroes like Jessica Jones and Supergirl. The number of female creators, of graphic novels and of mainstream comic books alike, is on the rise. Female readership, always hard to measure, seems to be on the rise too: 51 percent of people who identify themselves as comics fans on Facebook are women, according to an MTV News article (up from a recent 43 percent). And even kids' comics are getting in on it: smart comics for girls, not only about them, is a newly thriving area of the field (the Internet abounds, too, with cute and informative lists like GeekDad's "12 Comics for a 7-Year-Old Girl").
While there is now a wealth of charming and also sophisticated comics for kids, and girls specifically, by a wide range of creators on a wide range of topics, graphic novels for adults with girls at their center have captured the public imagination forcefully. Particularly in graphic memoirs like Barry's One Hundred Demons and Satrapi's Persepolis, as well as in Bechdel's Fun Home and Phoebe Gloeckner's A Child's Life and The Diary of a Teenage Girl, we see how comics can evoke childhood, and particularly girlhood, so powerfully. As we see in Barry and Satrapi's monuments to girlhood, narratives of growth, of hybrid identities and developing selves, make sense—and flourish—in comics. This is because of the form's diary-like intimacy—its handwrittenness—and its ability to layer moments of time, to take both granular and synthetic views at once. And while both Barry and Satrapi's works let the troubles the authors experienced in their childhoods come to the forefront, both are also edged with generous humor. This stems from the tension between how Barry and Satrapi depict their naïve younger selves within the comics frame, and how as adult narrators they recollect those younger selves in overarching prose.
Barry has spent a career focusing on children in her comics. The author of eighteen books, she is one of the world's most famous literary cartoonists and the foremost chronicler in any printed medium, perhaps, of American adolescence. The novelist and critic Nick Hornby, reviewing One Hundred Demons, proclaimed that Barry "seems to me to almost single-handedly justify the form; she's one of America's very best contemporary writers." In the late 1970s, Two Sisters, her first published book—which she self-published by xeroxing her comics and sending them in hand-decorated manila envelopes to purchasers—starred nine-year-old oddball twin girls who were misunderstood by their mother and the world at large. Barry also grew up feeling misunderstood by her mother, who had grown up in the Philippines and immigrated to the United States, where she worked as a hospital housekeeper. In a contributor's note to The Best American Comics 2006, Barry writes that she was born "to a woman who came from the Philippines on a military transport plane and a navy man who drank and bowled," adding, "They didn't like each other and they didn't like their kids." Her parents divorced when she was a child. Her father, who left the family altogether, is a meat-cutter of Irish and Norwegian descent. Alongside a photograph of her that is part of a traveling art exhibit titled kip fulbeck: part asian, 100% hapa, Barry—who has pale skin and long red hair—notes, "People can't believe I'm Filipina but then I tell them I'm also Norwegian, and Norwegian blood can suck the color out of anything."
Barry, who has two brothers, was born in 1956 in Richland Center, Wisconsin, where her mother, she told me, was the "odd person with a heavy Filipino accent." The family moved to Seattle when she was four, into a house that had a large and varying number of Filipino families—a community where "my dad was the only one speaking English . . . my dad was the only white guy . . . and everybody was speaking Tagalog." The family next moved within Seattle to a mixed black, Chinese, and Japanese neighborhood that Barry describes as "the poorest part of town."
Barry's comics are distinguished by their ability—one Barry has always had—to capture the way children actually speak: their slang and syntax, and particularly their spoken intonation and inflection. It's a big part of what makes her comics feel so vital and authentic. Barry grew up in a bilingual family, an English-speaking child among adults who spoke Tagalog, a language they did not teach to her. The resulting special attention to language and listening seems a likely source of her ongoing interest in how people speak, and her incredible ear for it. She managed to understand certain Tagalog words as a kid although they were never explained to her.
As she makes clear in One Hundred Demons, Barry grew up in what she describes as "a really violent, difficult house." She hasn't spoken to her mother in over twenty years, and she explained at a conference in Chicago, "I know people are like, Oh, that's so sad. . . . If you met her you would know I'm free!" The family, which included Barry's Filipina grandmother, a sympathetic figure whom she adored, was what she calls "Catholic. Catholic with vampires." (She depicts this in the chapter "The Aswang," about Filipino folklore's flying vampire dog-woman.) Barry had very few books in her childhood home: the final chapter, "Lost and Found," poignantly explains how as a girl with limited resources she loved reading the classified ads in the newspaper as a kind of literature—one for which she could imaginatively fill in the blanks. Her love of drawing was not valued, either—her mother often accused her of wasting paper when she drew—but Barry copied R. Crumb's Zap #0 in junior high and later drew for her high school paper. Barry transferred out of her local high school, where there was a high level of violence, to Seattle's Roosevelt High School, a calmer environment where cartoonist Charles Burns was also, at the same time, a student. At sixteen, she held a seven-nights-a-week job as a janitor on top of high school.
Barry enrolled in 1974 at the Evergreen State College in Olympia, Washington—an experimental, progressive college in which students study one subject intensively across disciplines, and earn written evaluations instead of letter grades. At Evergreen, where she studied the history of science and history of the Renaissance, Barry began modeling for life-drawing classes as a fluke when a professor, after a last-minute cancellation, approached her in the lunchroom, mistaking her for someone who had done it before. Barry hadn't, but she said yes anyway because she was broke, and found she loved being around students making images. Eventually, modeling in the class of art professor Marilyn Frasca, Barry "just started crying," she told me, "because I realized I didn't want to be on the table. I wanted to be in her class." She went on to study intensively with Frasca for two years. Evergreen is also the alma mater of several important creative contemporary cultural figures—including lead members of the feminist riot grrrl bands Bikini Kill and Sleater-Kinney and peace activist Rachel Corrie.
Barry met Matt Groening while both, along with Burns, were students at Evergreen—and where her reputation preceded her. Groening had heard that there was a girl in a nearby dorm who had written to Joseph Heller, the author of Catch-22, and had received a reply. Impressed and intrigued, Groening tracked Barry down. The two became best friends. They also dated for a period; at one point Groening even asked Barry to marry him. He was the editor of the college newspaper, and once he got to know her, he pestered Barry into contributing. Groening printed her comics for the first time, and his encouragement, as an editor and a fellow cartoonist, inspired her to keep drawing: "I would just send crazy little comics that didn't make any sense. . . . I would just drop them off in the mailbox to Matt," she recalled to me. In turn, Barry's exuberant sensibility, with her scruffy drawing style, was a huge influence on him. Barry's black line art is always energetic, favors expressivity over realism, and can often be exaggerated. Both deploy an ostensibly simple, fluid black line and have an elastic take on drawing bodies.
"Lynda Barry is the funniest person I have ever met," Groening told the fanzine Chemical Imbalance. "Lynda was great [in college] because she really opened things up for me as far as inspiration and doing whatever you want in a comic strip." As a general rule, and to this day, the two acknowledge each other in their books: "LYNDA BARRY IS FUNK QUEEN OF THE GALAXY," reads a Life in Hell note on the copyright page. "P.S.MattGisstillFunkLordofUSA," proclaims the acknowledgments of One Hundred Demons. On Life in Hell calendars—a popular novelty item for decades—Groening typically lists Barry's birthday. In a recent public event in New York, the affectionate pair, whose lifestyles and career paths have diverged sharply, taking Groening to Los Angeles and Barry back home to Wisconsin, admitted they disapprove of each other "very much." "You think LA is hell," Groening reminded Barry, "this awful place of corruption and anti-creativity. And when I look at Wisconsin—" "It's its own kind of hell," she finished for him. "When I look at your place in Malibu, and you can see the ocean, I just think, 'I'd rather die than live here.' " Both were inducted this past summer into the Comic-Con's Hall of Fame. Groening, ascending the stage to accept his honor, quipped, "My influence is Lynda Barry."
After college, Barry moved back home to Seattle, where alternative weekly newspapers—along with those in LA (where Groening had moved), Chicago, New York, and elsewhere—were starting to pick up steam as a popular format. Barry had a comic strip series called Spinal Comics, which she had started in college—it was "basically women talking to men in the bar, but the men were giant cactuses." When Barry submitted her comics to the Seattle Sun, the editor called her back shortly after, asked her to come in to the office, and rejected the work, lecturing her that her comics were racist. Barry was utterly bewildered ("Something about . . . Mexicans and white women. . . . The comics had nothing to do with Mexicans, or white women"), but as she was leaving, the man who managed the back page, and hated the editor, ran down the stairs after her and without even reading the comics offered to print them. Her work appeared weekly in the Seattle Sun.
Barry's readership started to grow within the alternative newspaper world—as did Groening's with Life in Hell. Whenever either Groening or Barry was approached by a paper interested in printing their comics, that one would pitch the other to the paper too. In 1980, Groening wrote a long, famous article about culture and aesthetics in the LA Reader, where he worked, called "Hipness & Stupidity," which Barry describes as "about how lame stuff is actually cool." Groening gave her a shout-out in the piece, "like I was a cartoonist of some standing," she told me, "which was just bullshit" (Groening wrote with an artificial distance about Barry, naming her a "Seattle artist" with a "brilliantly stupid and hip comic strip"). The editor of the Chicago Reader—where Chris Ware would later serialize Jimmy Corrigan—saw the piece and called Barry, asking to run her comics. They paid $80 a month; Barry was able to quit her job selling popcorn at a movie theater to become a self-sufficient artist.
Barry's weekly syndicated comic strip came to be called, eventually, Ernie Pook's Comeek ("pook" rhymes with "book"—the title was an in-joke with her brother, who as a small child loved the made-up phrase). After her strips would get printed in the newspapers, Barry would xerox them to create small collections that were sold at Printed Matter, the esteemed artists' bookstore and gallery in New York City. At Printed Matter, Barry described, she had a sense that somebody was actually "getting" her work. Barry almost single-handedly reinvented the content of newspaper comic strips, and the gag strip in general, by focusing in the late 1970s on what she calls "darkness."
"There weren't that many comic strips that had a lot of trouble, that weren't funny, you know?" she told me. "The setup for a comic strip is four panels and that last thing should be a punch line, so when people didn't get that punch line they became very upset and would write furious letters to the editor about how there's nothing funny about child abuse." Barry explained that she realized a comic strip "could contain something sad, like a song. A song could be happy or sad, and I thought a comic strip should be the same." And for her this meant a focus on children, especially girls.
Barry's first book collection, Girls and Boys, was issued in 1981. Girls and Boys had some strips about romantic relationships, and many about the chaotic, difficult lives of kids. In one strip two boys beat each other until a stranger on the street intervenes. In another a brother and sister speculate their mother is never coming home because she's going to "get drunk and marry a bum." In yet another a mother passes out from drinking and her daughter protects her from her angry father. It was a comic strip that depicted the kinds of grim, everyday events that might happen in real life. Chris Ware has said Barry taught him how to create believable fiction in comics. "She moved the medium closer to real literature," the cartoonist Ivan Brunetti declared.
Barry's new comic strip idiom—edgy, dark, sometimes grim, sometimes funny—caught on, bringing the full tonal range of the interior lives of children in teeming households, streets, and classrooms to the forefront of comics. Barry earned devoted readers, especially with her beloved character Marlys Mullen, a nerdy, chubby, freckled eight-year-old girl with glasses, always surrounded by a large cast of family members, including her troubled brother Freddy, teenage sister Maybonne, and cousins Edna and Arnold. Marlys had optimism, and oddball charm; her perspective often threw the adult world into relief. In "Marlys' Guide to Queers," Barry creates the four-panel strip as an open letter to the world from eight-year-old Marlys, complete with the child's own comics (dotted with spelling mistakes) that picture of scenes of discrimination from a child's point of view. It ends with a remark—"If you see my Uncle John and Bill please say I miss them"—that suddenly injects personal poignancy to the young girl's "guide" structure, demonstrating Barry's powers telling stories with the elliptical economy of comics.
At its peak, Ernie Pook's Comeek was syndicated in over sixty newspapers. Barry became a nationally known figure across different media. In the 1980s and early 1990s, the charismatic Barry was a frequent guest on David Letterman—like Pekar, although Barry's spots are fizzier, friendlier, and much, much funnier (she's a natural in front of an audience). Barry exhibited paintings and mixed-media work in galleries, though she elected to cut the fine art world out of her practice in the late 1980s: "Rich people," Barry told me, "need [art] to be this sort of deep experience, and they're sort of buying the talisman of the experience." She published two brilliant prose novels about teenage girls: The Good Times Are Killing Me, about a black-white interracial junior high friendship, and Cruddy, a macabre, hilarious, and moving novel about the daughter of an ex-Navy-man butcher who is kidnapped by her father for a road trip. The Good Times Are Killing Me was adapted, by Barry, to be an award-winning off-Broadway play in 1993. That year she released a spoken-word recording, The Lynda Barry Experience. It is telling that Barry is currently a tenured professor, at the University of Wisconsin, Madison, of what is called Interdisciplinary Creativity (the best job title perhaps ever!).
Lynda Barry, "Marlys' Guide to Queers," 1991, reprinted in The Greatest of Marlys (Montreal: Drawn & Quarterly), 2016.
Used by permission of Lynda Barry/Drawn & Quarterly. Image courtesy Drawn & Quarterly.
But it is in One Hundred Demons, Barry's first explicitly autobiographical work, that she gives fullest expression to the lives of girls, including, of course, herself. Structured into nineteen discrete comic strips each named for a "demon," One Hundred Demons—as Barry explains in the introduction—is based on a painting exercise called "One Hundred Demons" that she first read about in the library, guided by the example of a hand-scroll painted by a sixteenth-century Japanese zen monk.
The demons run the gamut from topics such as "Dancing," "My First Job," "Dogs," and, of course, "Girlness" (hint: Barry, the tomboy daughter of an ultrafeminine mother, didn't think she had any) to concepts such as "Magic" and "Hate." Many of the stories, which are not chronological, are about class and ethnicity—"Common Scents" details how classmates, and their parents, perceive Barry's Filipino household as smelling a certain way; "The Visitor" is about a wealthy white boy who romanticizes ethnic neighborhoods, including Barry's own. Many are about the creeping self-consciousness of adolescence, along with what could only be described as trauma. "When I was little, bad things had gone on, things too awful to remember but impossible to forget," the narrator states in the darkest chapter, "Resilience" (which is not a feel-good story: "I cringe when adults talk about the resilience of children," Barry writes). "One Hundred Demons is heavy," Barry told me, expressing concern about when parents buy it for children: " 'Well, just to let you know, there's incest and suicide, and drug-taking. There's, like, everything's in there.' " One of the fascinating features of One Hundred Demons, as with Hyperbole and a Half, is that it may not appear at first glance, perhaps, like an emotionally "heavy" book. It appears in gorgeous full color: each chapter presents a distinct background color, and each chapter is preceded by a digital reproduction, a scan, of a two-page multimedia collage, which preserves its bumpiness and craftedness. The rich visual volume and density of the collages offset the economy of the comics narratives they precede, which vary from only fourteen to twenty frames, and typically offer only two frames per page. From her evidently hand-painted words to her dense, accumulative collages, Barry's work is enormously tactile and appealing.
Lynda Barry, page from "Dogs," One Hundred Demons, first published in 2002, and reprinted (Montreal: Drawn & Quarterly) in 2016. The "she" referred to in the text box is Barry's second-grade teacher, whose kindness turned her life around. The woman pictured is Barry's mother.
Used by permission of Lynda Barry/Drawn & Quarterly. Image courtesy Drawn & Quarterly.
One Hundred Demons, aside from its collages, is entirely painted, as per the exercise, with an inkstick, inkstone, and an Asian-style brush. Barry's comics are distinguished by their sensitivity to voice, including the "voice" created by the shape of the lines on the page. Different drawing implements produce different voices, in Barry's view—and in many cartoonists'. (She's not alone: Spiegelman makes readers aware of this by drawing each character of his underground comics story "Ace Hole: Midget Detective" with a separate kind of drawing tool.) While cartoonists typically pencil scripted words before inking them on the page, Barry doesn't use a script and never pencils her work, a practice that demands spontaneity—an alertness in the moment to what her character might say—that most cartoonists find insane. Barry switched to a brush from a pen around 1985, and even handwrites—or rather, paints—her prose novels: she wrote Cruddy in watercolor on construction paper and blew the pages dry with a hairdryer before it was transcribed for print.
One Hundred Demons opens with a double demon: "Head Lice and My Worst Boyfriend," which immediately sets up major themes of Barry's childhood in an only-eighteen-panel story: her mixed ethnicity and culture, her struggle to maintain self-confidence in the face of an "unpredictable and quite violent" mother, and the way that people repeat the traumas of their filial relationships in their romantic ones. Set against a brushed-peach background, "Head Lice and My Worst Boyfriend" connects different versions of Barry's younger self, flipping back and forth in time. It links Barry's awkward, fifth-grade self—specifically her experience growing up Filipina American, and making friends during the summer when she traveled to the Philippines—with her young adult self suffering through a long-term relationship, set against the background of her ongoing, difficult relationship with her mother.
Lynda Barry, page from "Head Lice and My Worst Boyfriend," One Hundred Demons.
Used by permission of Lynda Barry/Drawn & Quarterly. Image courtesy Drawn & Quarterly.
The strip opens with two selves in one panel: in text boxes above the frames that depict her childhood, Barry the adult narrator wonders why head lice never hit her neighborhood (her speculation: between the chain-smoking and the asbestos in their homes, the kids were too toxic for lice). Speaking of infestation: other students told her she had "cooties" and refused to play with her, as she shows us—and the resulting loneliness, the adult narrator writes, "turned me into such a bug lover." In several panels we see Lynda trying to make friends in school, including sweetly reporting to its most popular girl, "Hey Marcie, see this daddy long-legs? It's not actually a true spider." In the Philippines visiting family during summer break she has better luck, befriending two curious kids, one of whom she calls the Professor, who love bugs and are fascinated by her red hair, and wonder if her lice—or "kuto"—would match her light coloring. Lonely back at home after the visit, her mother confirms, "You talk, talk, talk, talk all the time. No one wants to listen to an idiot." In its last four pages, the story shifts to picture an older Lynda, who has left home, now volunteers as a fifth-grade teacher, and is dating a boyfriend with a "pretty name" and a "freaky ponytail" who reads the Lonely Genius Gazette.
Barry draws this boyfriend—white with a brown ponytail, tie, and round glasses—but doesn't name him in the book. As several articles have revealed, it is Ira Glass, of This American Life (Glass, now so associated with Chicago and its radio station WBEZ, actually moved to Chicago in 1989 to be with Barry, who lived there). His behavior in the strip is self-centered and condescending, especially when it comes to class and race difference. Barry narrates her "worst boyfriend" in one panel in the following way: "He was raised in a nice suburb and had always been something of a gifted child. He seemed interested in my background and nicknamed me 'little ghetto girl.' I'm sure he meant it in the nicest way." As if this is so outlandish it needs verification, a little arrow with a note that reads "actual dialog" points to their conversation below. (For the record, Glass told the Chicago Reader, "I was an idiot. I was in the wrong. . . . About so many things with her. Anything bad she says about me I can confirm.")
Eventually Barry gets lice from her fifth-graders, and the story circles back to the ghost of her former, fifth-grade self who opens the story. (Incidentally, one of this story's many compelling features is its hilarious and painful look at the shame of adults contracting lice; when I got lice not too long ago from my boyfriend's small daughter the first person I contacted for advice was Barry. She signed her email "Your Sister in Lice Infestation.") Barry shamefully gives lice to her worst boyfriend. As they stand together washing their hair with the toxic lice-killing shampoo, it dawns on her: she finally has lice, and her boyfriend reminds her of the Professor, the Filipino boy who was the first love of her life. After she tells him this, half-laughing, half-crying, the subsequent panel shows the boyfriend morph into shades of Lynda's mother: "You talk talk talk about asinine memories like they mean something! You're shallow! You're poison! Do you really think I'm interested?" to which Barry replies, with a bolt of recognition, "MOM?!" "Why are we compelled to repeat the past?" Barry asks in the final panel in her signature mix of cursive and capital letters, both girlish and bold at once.
Lynda Barry, page from "Head Lice and My Worst Boyfriend," One Hundred Demons.
Used by permission of Lynda Barry/Drawn & Quarterly. Image courtesy Drawn & Quarterly.
"Head Lice and My Worst Boyfriend," as with each chapter of One Hundred Demons, represents girlhood so effectively because it is able to display—and even to put together, in one frame, as we see with Barry narrating her childhood in prose and also drawing her own child body in space on the page—different versions of a growing self, with different abilities, kinds of knowledge, and kinds of voices. Barry moves back and forth between childhood, adulthood, and interim stages in the space of the book. And no one of these selves is any more real than the other. Comics can bring forward the hybrid self, the developing self, the split self (as we saw with Brosh). As a temporal and spatial form motored by images, comics can also powerfully evoke what memory feels like, how memory works, and can bring forward the importance of girlhood recollections. "Head Lice and My Worst Boyfriend," which explores the mix-up of the past and present in the protagonist's mind, also performs that in its form, which shuttles back and forth between time periods. The entire book enacts this movement: a life is not a chronological set of events, but rather a collection of nonchronological moments. "We think that we are going into the future, but actually what we're doing is going into the past," Barry claims about how images—memories—present themselves. "There's this feeling that there's a chronological order to things because there's an order to the years, and there is an order to our cell division from the time we're a little embryo until we're dust again. But I think the past has no order whatsoever." Her books are about presenting the everyday lived details of girlhood, but also about remembering—and they mimic, with their profusion of images "which move every which way," as she puts it, the process of how one remembers.
Even in its physical design, One Hundred Demons evokes girlhood. Barry is an outspoken fan of handwriting, and her comics have a very distinct—and to me quite beautiful—evident handwrittenness about them. The mix of lowercase and uppercase brush-painted letters, which we see in sentences and even sometimes within the physical, material space of one word, has no narrative function, but it does have a visual function. It is decorative, and in its unpredictability and ornamental quality, it asks a reader to be aware of the body whose hand creates the comics; it ruffles the surface of the page. "I'll read anything that had handwriting, and it's really hard for me to be bored or unhappy when I'm reading comics," she told me. "I even love stuff that . . . you might think, this isn't really working, or this isn't really exciting. I never think of that. I think drawing, writing, handwriting, drawing." One Hundred Demons's handwriting feels intimate and personal, like a reader is encountering a diary or a manuscript; the book also frequently depicts the character Lynda in the act of composing, hand on paper, as we see in the page from "Dogs," among many, many others. One Hundred Demons, with its lush prefatory collages, also evokes scrapbooking—a form that has often been associated with girls recording their lives. In the collages, there is a piling on of commonly found, disposable, everyday objects. As Barry described her studio: "I have tons of trash laying all over the floor and everywhere in bowls."
Lynda Barry, the two facing collage pages for the chapter "Resilience," One Hundred Demons.
Used by permission of Lynda Barry/Drawn & Quarterly. Image courtesy Drawn & Quarterly.
Barry's autobiographical work about her girlhood calls attention to itself as multilayered composition—and to the self as collage—in its open layers of painting, words, and bits and pieces of ostensible debris. One of the book's central themes is what counts as "waste"—from a child herself, and from childhood memories. The collages, which announce the title of the chapter on their right-hand side, offer snippets of the subsequent strip, repeated handwritten words and phrases, original painted illustrations, and an accumulation of sundry materials, including strips of brightly colored fabrics; cardboard; magazine pictures; tissue paper; the scalloped edge of a paper bag; photographs of Barry herself; the printed insides of bank envelopes; interior candy bar and gum wrapping; dried flowers; bits of doilies; glitter globs; the sewing trim rickrack; Chinese postage stamps; origami creatures; a stuffed animal; and pieces of old pajamas. Through an accessible popular medium, comics, that has long been viewed as disposable, One Hundred Demons salvages the detritus of girlhood as productive collage. On the book's last page, which is composed on yellow legal paper (which looks great), Barry notes, "I like to paint on legal paper or on the classified section of the newspaper or even pages from old books! I will try any kind of paper, typing paper, wrapping paper even paper bags!" Using cheap, common, or utilitarian paper—the kinds of materials associated with her girlhood, and the kinds of materials to which kids have access—is an important part of Barry's goal to make what others would deem "waste" something valuable.
While in Barry's story she encounters the most trouble from within her own family, Satrapi's Persepolis features a supportive family protecting their daughter from extremism and war. But both of these graphic memoirs show, through words and images together, how the everyday lives of girls can include joy and humor alongside the complexities of violence. (Neither are meant for children, although I often learn, as with Maus, of teachers assigning Persepolis, which is a quite violent book, to young students.) Barry and Satrapi—one working in the United States, the other in France—both published their memoirs in the early years of the twenty-first century. They focused the world's attention on girls as a powerful subject for adult comics and on the lived reality of girlhood as historically and politically—and artistically—significant.
But while Barry's graphic memoir is colorful, dense, and accretive, Satrapi's is black and white, minimalist, and expressionistic. Both are structured by short, titled episodes, but while Barry's skips around in time, mimicking the procedure of memory, Satrapi's is linear and chronological: the story opens when she is ten, and ends when she is twenty-four. Both are about how class position shapes a girl's self-concept: in Barry's case, growing up poor, from an immigrant family; in Satrapi's case, growing up privileged, to elite parents (she introduces this early, when the child Marji, short for Marjane, explains that she wanted to grow up to be a prophet because she's sad her maid does not eat with the family, and she's embarrassed to ride in her father's Cadillac). Alongside these loving, intellectual parents, who provide her a constant safe space, she suffers, as a growing girl, the oppression of both the Islamic Revolution and the Iran-Iraq War (in one episode a missile hits her street and kills her neighbors). Satrapi's account of her childhood growing up in Tehran has earned the most international attention of any graphic narrative in the past fifteen years.
An only child, Satrapi was born in Rasht, Iran, to an engineer father and dress-designer mother; her maternal grandfather (whom she never knew) was an Iranian prince who later became prime minister and a communist, spending most of his later years as a political prisoner. As the book details, Satrapi attended French schools in Tehran, and watched with curiosity and bewilderment the political shifts to which her parents were so attuned, particularly the shift in governance from the reign of the deposed shah to the takeover of the Islamic regime. The Islamic Revolution began when she was ten; that year, her beloved uncle Anoosh, her father's brother, also a communist, was executed as a so-called Russian spy. Allowed one visitor before his execution, he chose his young niece, a scene very movingly portrayed in Persepolis.
At fourteen, Satrapi disputed politics with one teacher and actually struck her school principal. Her outspokenness and hotheadedness led her parents, fearful for her safety, to send her out of the country to Vienna, where she attended a French school for four years. Despite the fact that she felt alienated in Vienna as a foreigner from a war-torn country, Satrapi excelled in school. She earned the top possible grade on her French baccalaureate degree—the same year she rebelliously became her school's so-called "official" drug dealer. Satrapi returned to Iran at eighteen before leaving the country, again, for France at age twenty-four (where Persepolis leaves her). Always hoping for the best opportunities for their daughter, her parents encouraged her to leave Iran, where basic freedoms were being denied: "I forbid you to come back," her mother says to her daughter at the airport on her way to Paris at the end of the memoir.
Satrapi is a trained artist: she earned a college degree in graphic arts from the School of Fine Arts in Tehran and a graduate degree from the École Supérieure des Arts Décoratifs in Strasbourg after her move to France. After Strasbourg, aiming for a career creating children's books, Satrapi joined the Parisian studio group Atelier des Vosges, whose members included several cartoonists. It was there, after her book projects for children had been met with rejection—and after a friend gave her Maus as a birthday gift—that Satrapi started Persepolis, in 1999, with encouragement from her studio mates such as the cartoonist David B., creator of Epileptic.
Satrapi credits Maus as her most important influence. In a lecture I attended she called it "the biggest revelation of my life." While there is a very rich visual culture in Iran, a comics culture in particular doesn't exist very widely. In Persepolis Marji is seen, charmingly, as a young girl reading a comic book called Dialectic Materialism, but it is a Soviet-published comic book. There were no homegrown Iranian comics when Satrapi lived there. Satrapi, who has two fine arts degrees, hadn't specifically planned on becoming a cartoonist. She called Maus "a bomb in my head," explaining, simply, "When I read Maus . . . I saw that it was possible to talk about war in the comic format." Persepolis blends a focus on the details of one girl's life—the games she played with her friends, her conversations with God, her aspirations—with a focus on the tumult and brutality of war.
Persepolis was first published in France, where Satrapi still lives and works, in four separate books (or, as they are known there, tomes). She wrote Persepolis in French, her second of six languages, and the first tome, published by the independent comics collective L'Association, appeared in 2000. Attention to the book grew by word of mouth; without any PR or marketing, it sold a record three hundred thousand copies in France, a surprise best seller. In the United States, before it was collected in one edition, Persepolis appeared in two volumes, the first in 2003 (which focuses on Marji's childhood in Tehran) and the second in 2004 (which focuses on her adolescence in Vienna as well as in Tehran). The first volume appeared as Persepolis: The Story of a Childhood. Its de-particularized subtitle, as with Gloeckner's The Diary of a Teenage Girl, suggests that while some may view the events of her life as unusual, for many girls the mix of joy and fear, play and violence, is in fact ordinary.
There are over a million copies of Persepolis in print, and it appears on over 250 syllabi in the United States alone. Satrapi has contributed op-ed—or "op-art"—pieces in comics format for the New York Times, and has weighed in on issues like the banning of the veil, also known as the hijab, in French schools for venues such as the Guardian ("I know what it has felt like to be pushed into being religious, so I know what it feels like to be pushed into being secular. It is the same violence"). Persepolis, centered on a girl from a country the US president deemed part of the "axis of evil" the year before it appeared in English, was recently the required freshman reading for cadets at West Point, which is still a predominantly male institution. Satrapi was invited to speak there in 2005, and later created an op-art essay about her positive experience in the New York Times. And in 2006, the film version of the same title—a black-and-white animated feature codirected by Satrapi and the French underground cartoonist Vincent Paronnaud—won the Jury Prize at the Cannes Film Festival. It became France's first animated film to be nominated in the Best Foreign Picture category at the Academy Awards. And while the book has already been translated into over twenty-five languages, it has yet, for political reasons, to be translated into Farsi or published in Iran—although Satrapi has mentioned that there is a Persian version, which she has not seen or authorized, circulating on the black market there. While Satrapi's parents, who are featured heavily in the book, still live in Tehran, she has explained, "I no longer go to Iran, because the rule of law does not exist there." The name on her passport is different from the name under which she publishes her work, in part to protect her family.
In Persepolis, the personal is always political: girlhood reminiscences overlap with chronicles of war, and are articulated through momentous historical events. Persepolis, which begins with the issue of veiling, opens with a row of only two frames. The first panel sets the stage: a girl sits in the center of the frame, her chest-length veil framing her glum expression, her arms crossed in front of her. "This is me when I was 10 years old," Satrapi writes above the unsmiling girl. "This was in 1980." In the following panel, on the other side of the gutter, we see a row of four similarly composed girls, unsmiling with crossed arms, and only a sliver of a fifth on the reader's left: we are only able to infer a hand, a bent elbow, and a chest-length veil. "And this is a class photo," the narrator continues. "I'm sitting on the far left so you don't see me. From left to right: Golnaz, Mahshid, Narine, Minna."
Marjane Satrapi, first page of Persepolis (New York: Pantheon), 2003.
Translation © 2003 L'Association, Paris, France. Used by permission of Pantheon Books, an imprint of the Knopf/Doubleday Publishing Group, a division of Penguin Random House LLC. All rights reserved.
On the very first page, Satrapi demonstrates the subtle tricks and erasures that frames can play. They can situate and dignify a character—or sever her in two. In the opening pair of panels, Satrapi suggests the differences between seeing whole and seeing only partially, incompletely, in disembodied fragments—the psychological conditions suggested by the chapter's title, "The Veil." An icon of a single eye, directly engaging the reader, hangs over the book's very first gutter. From the start, Satrapi indicates, readers of Persepolis are aligned with her own probing vision as a witness to events in Iran. Not that things are always what they look like. After introducing herself—"This is me"—Satrapi immediately conceals her body in the next, crowded frame: "You don't see me." Here and throughout Persepolis, however, word and image are in tension. We see the protagonist, at least partially, even as she insists we don't; we pore over the details of an image that is clearly a drawing, which she declares a "class photo." Carefully reading Persepolis, like Satrapi's own witnessing, requires weighing what we see against what's veiled from view, what we're shown against what we're told. Comics calls attention to what we as readers "see" and don't see of the girl at the book's center.
Each chapter of Persepolis opens with a stripped-down, elegant black bar at the top of the page that presents, in large white block letters, a simple title—"The Bicycle," "The Letter," "The Cigarette"—preceded by a corresponding visual icon. Satrapi's style in some ways looks very simple. It is monochromatic: all flat black and white, no intermediate grays and evidently no shading. There's a starkness, and a spareness, to her images. She also often rejects "correct" perspective.
The apparent simplicity of Satrapi's visual technique rests on historical and ethical complexity. Persepolis's drawing style references ancient Persian miniatures, murals, and friezes, and joins a continuum of Persian art: as Satrapi explained in an interview, in Persian miniatures, as in her own book, "the drawing itself is very simple," and the perspective is often deliberately flat. That simplicity, she continues, is "the Iranian side" of her style, and she notes that it "will always be with me." And yet Satrapi deviates from Persian art's colorful palette and limits herself to black and white. Her minimalist play of black and white is part of an avant-garde tradition, stemming from her stated mission to depict historical events on a plane of unnervingly abstracted horror. Satrapi was particularly inspired by the black-and-white shadow play of early German Expressionist film, particularly F. W. Murnau's vampire film Nosferatu (1922), and by the high-contrast woodcut style of French artist Félix Vallotton, who etched a 1916 woodcut album of images, C'est La Guerre! ("That's War!"). "Violence today has become something so normal, so banal—that is to say everybody thinks it's normal," Satrapi explained in an interview. "But it's not normal. To draw it and put it in color—the color of flesh and the red of the blood, and so forth—reduces it by making it realistic." As a work of witness and testimony, Persepolis is invested in truth and accuracy, and yet it is always deeply stylized, never visually "realistic." Satrapi's visual style, with its pared-down lines and flattened perspective, as in visual modernism, is hardly a sign of artistic deficiency (as some critics have claimed), but rather a sophisticated, and historically aware means of doing the work of seeing.
And that visual style forcefully conveys the viewpoint of a child. Persepolis is, after all, the "story of a childhood," as the subtitle of the first volume declares: one seen through a child's eyes and her crumbling innocence. Satrapi's drawings—minimalist, scaled-back, gorgeous to look at—never square comfortably with the unspeakably traumatic events of her world: imprisonment and torture, harassment and execution, bombings and mass murder. Persepolis at its core is about the violence one witnesses and the unseen violence one is left to imagine. Real and imagined violence, in specific bodies both wounded and dead, are depicted frequently, appearing in nearly every chapter. A signature feature of Persepolis is its frequent arrangement of dead or dying bodies—from protests, massacres, and battlefields—in stylized, almost architectural formations, in pyramids, rows, or symmetrical groups, as a child might picture mass death.
A striking example of the book's child's-eye rendition of trauma comes in the chapter called "The Heroes." (Marji and all the kids in her neighborhood are obsessed with "heroes," and make up stories about their heroic fathers.) Two friends of the family, imprisoned for their political views and released after the shah's upheaval, visit Satrapi's family and describe the torture they underwent. "My parents were so shocked," Satrapi remembers, "that they forgot to spare me this experience." Several panels across this episode show Marji looking increasingly bewildered as the men describe their nails being pulled out, being whipped with electric cables, and having cigarettes put out on their bodies. The conversation moves on to a friend, Ahmadi, who did not survive his time in prison. Ahmadi, in the words of one of the friends, "suffered the worst torture." In a large, borderless panel in the middle of a crucial page, Satrapi draws the flood of horrific images that these stories produce in Marji's mind, as she tries to visualize a man urinated on, tied down and beaten with a whip, and burned with an iron. While we are supposed to understand these depictions as the child Marji's envisionings, they are plausible visualizations. These images are unsettling enough, but Marji's imagining of Ahmadi's final torture is among the book's most alarming, unforgettable images. "In the end," the narration reveals, "he was cut to pieces." The page-wide panel that follows marks the limit of young Marji's imagination—what she cannot yet realistically envision.
Marjane Satrapi, panel from Persepolis.
Translation © 2003 L'Association, Paris, France. Used by permission of Pantheon Books, an imprint of the Knopf/Doubleday Publishing Group, a division of Penguin Random House LLC. All rights reserved.
What can Marji imagine? A white body, floating on a stark black background, disarticulated into seven neatly separated parts—head, torso, pelvis, four limbs, all apparently hollow. In Marji's mind the man is cleanly pieced apart and arranged like a dismembered doll on the floor, or an operating table. This panel demonstrates how certain modes of representation—even in a self-consciously artificial form like comics—convey trauma differently, and perhaps even more potently, than realism. The image and impression of a man "cut to pieces" in its full, traumatizing inhumanity cannot be illustrated by words alone, or even by detailed pictures, from the perspective of children or adults. This moment in Persepolis, then, reveals the defamiliarizing at which comics excels. It channels a child's imagining of another's fatal torture, displaying a way of seeing and showing that is intentionally estranging. Satrapi impresses on readers a child's bafflement and confrontation with the terrifying actuality of her world. What is ostensibly "simple" here offers a complex emotional landscape—one impossible to present with words alone. "I cannot take the idea of a man cut into pieces and just write it," Satrapi told an interviewer. "It would not be anything but cynical. That's why I drew it."
Marjane Satrapi, panel from Persepolis.
Translation © 2003 L'Association, Paris, France. Used by permission of Pantheon Books, an imprint of the Knopf/Doubleday Publishing Group, a division of Penguin Random House LLC. All rights reserved.
One Hundred Demons and Persepolis both focus on the question of when a girl grows up. Barry writes, above a drawing of herself sick at age thirteen, "When did I become a teenager? Was it when I started shop-lifting? Dropped acid laid on me by hippies in the park?" In Persepolis, Marji descends into her family basement, meditates on getting busted by her mother for cutting class, and on executions of political prisoners . . . and smokes her first cigarette, breaking the frame to address readers and let us know, at age twelve, cigarette in hand, "I kissed childhood goodbye." These books investigate the notion of girlhood—where it is, how long it lasts, if it ever leaves—through formats and styles that place a reader back in time, and with the shifting perspectives and imaginations of the girls they feature. As a form all about the representation of time, and one that is accessible and stylized both, comics can reveal the complexity of growing up, especially during dark periods like wartime.
---
WHY WAR?
Marjane Satrapi's Persepolis bridges two of contemporary comics's most urgent themes: girlhood and war. The comics form has evolved as an instrument to circulate powerful images, together with words, of wartime experience and history. Sometimes these images are almost unbearably violent—in fact, that is part of their force. Joe Sacco granted me permission to use one of his comics panels of the July 1995 Srebrenica massacre of more than eight thousand Bosnian Muslim men and boys, from his Safe Area Goražde: The War in Eastern Bosnia 1992–1995, for the cover of one of my previous books. Although my publisher was on board with the cover—a strikingly detailed black-and-white drawing of men being shot e'n masse above a ditch littered with bodies—I hesitated. Was it actually exploitative, I wondered, to make this painful image of physical suffering a book cover? I asked Sacco what he thought. "Well," he replied, "it happened." This brief exchange about the representation of genocide hit home for me, profoundly and instantly, how comics seek, in a world arena, to deliver such images in order to inform, to reveal. They produce and share details of war—especially from an on-the-ground, civilian perspective—in order to further understanding, to join the historical record.
War has long been a compelling subject for comics, and other forms of visual art. As far back as one chooses to look, sequences of images have conveyed stories of war: in cave paintings; in Attic black-and-red-figure vases from the Archaic and Classical period that portray scenes from the Iliad. And for many, many centuries, combinations of images and text in print have sought to represent the circumstances of war. Robertus Valturius's military guide De Re Militari (Art of War), for instance, illustrated with informational woodcuts, appeared in 1472 (the Metropolitan Museum of Art Bulletin calls it "the first illustrated book about the science of war"). Especially before the age of the camera, drawing was a standard form of witnessing and reporting, as in the French printmaker Jacques Callot's Miseries of War, a series of etchings about the Thirty Years' War, from 1633; Spanish painter and printmaker Francisco de Goya's Disasters of War, a series of etchings about the Spanish War of Independence, created in the 1810s; and in the images made by artist-reporters such as Winslow Homer during the US Civil War, when bulky cameras were inconvenient on the battlefield and periodicals were still unable to reproduce the tonal qualities of photography.
Jacques Callot, The Miseries of War, plate titled "The Wheel," 1633.
Image courtesy of Dover Publications, from Callot's Etchings: 338 Prints, ed. Howard Daniel, 1974.
Fascinatingly, during the Golden Age of the comic book, starting in the late 1930s, fictional comics about real-life wars were a booming genre. Superhero, science fiction, and other fantasy genres have also, of course, long proffered global (and intergalactic) wars as central to their storylines, and continue to do so. (The Marvel comic-book storyline Civil War, for instance, which fueled Captain America: Civil War, the world's highest-grossing film in 2016, is not about the US Civil War, but rather about the world's superheroes in a "civil war" with each other.) But superheroes entered real wars too: the cover of the March 1941 issue of Captain America Comics, by Jack Kirby, shows the hero raiding Nazi headquarters and punching Hitler in the jaw—before the United States had even entered the war. Comic books helped to develop a patriotic wartime culture among civilians (some superheroes even formally, if briefly, enlisted), and they became a key part of GI culture. One quarter of all books shipped abroad to soldiers during World War II were comic books. As historian Bradford Wright points out about wartime comic books, despite some ugly racial stereotyping, World War II "marked a rare convergence of interests between publishers, creators, readers, and government policy." A superheroic take on World War II history lasted for decades. The popular comic book Sgt. Fury and His Howling Commandos, whose storyline is about an elite World War II unit, began in the early 1960s and lasted through the early 1980s.
Dick Ayers, cover of Sgt. Fury and His Howling Commandos #52, 1968.
Used by permission of Marvel Comics. © MARVEL.
An important new kind of war comics was also invented at midcentury with Harvey Kurtzman's Two-Fisted Tales. (Kurtzman, who had served in World War II, as did many cartoonists including Will Eisner, also founded the tremendously influential Mad in 1952.) Two-Fisted Tales, a bimonthly war comic published by EC Comics, began in 1950 and, with the beginning of the Korean War only a few months later, devoted itself to delivering a detailed look at war, along with Frontline Combat, also published by EC. While many other war comics of the period romanticized the experiences of American soldiers and their cause, and criticized the inhumanity of enemy forces, Two-Fisted Tales, which was heavily researched, sought a more realistic take on the circumstances, brutality, and futility of war. "Corpse on the Imjin!" a favorite story of Art Spiegelman's, shows the pain and shame of one man killing another in one-on-one combat on the River Imjin in Korea. "Atom Bomb!," which Kurtzman created with Wally Wood, was highly unusual for 1953 in taking a sympathetic view to a Japanese family in Nagasaki, who are the comic's surprising protagonists.
By the height of the underground comics movement of the late 1960s and early 1970s—which was fueled by the anti–Vietnam War counterculture—far fewer mainstream war comics were in publication. Comics, though, was a form in which antiwar sentiments could be expressed, both underground and aboveground. Perhaps most notably, Garry Trudeau's brilliantly titled But This War Had Such Promise, a Doonesbury comic strip collection from 1973, featured a satirical but sharp-edged take on the war in Vietnam: the character B.D. enlists, and the strip follows him to Vietnam, where he befriends a Viet Cong soldier named Phred. Trudeau, whose long-running, syndicated Doonesbury has also offered Iraq War plotlines, was censored by newspapers for his Vietnam content; he was later honored by the Vietnam Veterans of America. Cartoonists such as Jules Feiffer, Greg Irons, Ron Cobb, and others produced comics, some quite cutting, that were critical of the war.
But it was not until Keiji Nakazawa in Japan and Art Spiegelman in the United States, both of whom were inspired by antiwar counterculture in their respective countries, that comics became a form for bearing witness to war. Nakazawa, as the first chapter details, was a primary witness to the atomic bomb blast of Hiroshima, while Spiegelman, whose parents survived Auschwitz, is a secondary witness. Works like Spiegelman's Maus: A Survivor's Tale and Nakazawa's Barefoot Gen: A Cartoon Story of Hiroshima, both based on formative shorter works published in 1972, meaningfully capitalize on the intimacy of comics to probe the line between the public and the private—where history and individual experience meet—through stories of their families in World War II. The comics reporting of cartoonist and journalist Joe Sacco, on the other hand, documents wars with no connection to his family or background, and is inspired by trying to understand the nature of war itself. Sacco is the contemporary inheritor of the long tradition of "drawing to tell" that we recognize in Callot and Goya and the artist reporters of the nineteenth and early twentieth centuries. And he offers a prime example of what comics today can do: he has reinvented a genre, comics journalism, that is now flourishing across the globe.
Best known for his war reporting from the Middle East and the Balkans, Sacco has singlehandedly made serious comics reporting about war and global conflict a contemporary phenomenon, and he has influenced countless other artists across media, from Egypt's Magdy El Shafee (Metro: A Story of Cairo) to Israel's Ari Folman, who claimed the biggest influence on his acclaimed, animated film Waltz with Bashir was Sacco's comics series Palestine. Sacco's major works in the past two decades include Palestine, about the Israeli-Palestinian conflict during the First Intifada; Safe Area Goražde, about the so-called UN-designated "safe" municipality Goražde in Bosnia during the Yugoslav Wars; The Fixer: A Story from Sarajevo, which also focuses on the Yugoslav Wars, from the perspective of a Sarajevan soldier and "fixer" (an in-the-know local hired by foreign journalists); and Footnotes in Gaza, which investigates two 1956 massacres of Palestinians by Israeli soldiers (the largest killings to have taken place on Palestinian soil) by extensively interviewing survivors. Sacco's most recent book of reportage, The Great War, is a twenty-four-foot foldout book that is a panorama of the first day of the battle of the Somme. This work was recently blown up to over five hundred feet as an installation in the Paris subway.
Sacco was born to a Catholic family in 1960 in the southern European island country of Malta, in a town of eight hundred people called Kirkop. Although Footnotes in Gaza conspicuously depicts him using his Maltese passport while traveling to the Middle East—he is a character in all his reporting—he now has dual citizenship with the United States. Sacco's Maltese nationality and Catholic upbringing have helped him navigate Jewish-Muslim conflict zones, such as Israel and Palestine, for which his background does not supply an obvious affiliation or context. For Sacco growing up, war was a fact of life. His parents had survived terrifying German and Italian air raids during World War II on British-controlled Malta. For one of Sacco's first major comics stories, "More Women, More Children, More Quickly: Malta 1935–43 as Recounted by Carmen M. Sacco," he interviewed his mother about her girlhood experiences during the war. The title refers to an infamous 1932 statement by British politician Stanley Baldwin: "The only defence is offence, which means that you have got to kill more women and children more quickly than the enemy if you want to save yourselves."
Sacco moved around a lot as a young person. When he was just one, the family left Malta for Melbourne, Australia, where Leonard Sacco worked as an engineer, and Carmen Sacco as a high school teacher. As a child Sacco was a fan of British war comics, and noticed that his friends were all of mixed nationalities, and many from European families displaced by the war. American involvement in Vietnam increased during Sacco's childhood and became an obsessive focus in the global news media. When he was twelve, the family moved to Los Angeles, where his father pursued aircraft technology and maintenance, and then shortly after landed near Portland, Oregon, in a suburb called Beaverton, where Sacco started high school and ignited his passion for journalism as a writer (and sometimes cartoonist) for the school paper. Highly driven, Sacco attended the University of Oregon, majored in journalism, and graduated in three years. He read voraciously, and was particularly fascinated and moved by the journalists coming out of the Vietnam era like Michael Herr and Hunter S. Thompson, figures who had reinvented journalism to be a more self-aware, openly subjective, and writerly enterprise under the banner of what was called New Journalism.
Sacco created his first complete comic book around age seven. It wasn't until he moved back to Malta in his early twenties, however, that he finally got to publish his own comic books—even if they were formulaic romance comics. Sacco had been approached by a publisher about creating Malta's first comic-book series. He put out six issues of Imhabba Vera (True Love) in Maltese. As Sacco told me, because Malta had no history of comics, comics wasn't considered automatically, as in other cultures, a medium meant for kids. In one story, Sacco even had his protagonist traveling to Holland for an abortion, a procedure outlawed in Catholic Malta.
As much as he loved writing comics on deadline in Malta, Sacco—who had been working privately for years on his own long comics story about Vietnam—returned to the United States. After attempting to get a new monthly publication in Portland off the ground, he landed a job as a staff writer at The Comics Journal, the sophisticated trade magazine published by the independent press Fantagraphics Books, which helped to create the field of literary comics in the 1980s. For Sacco, more and more, it seemed possible to create comics that engaged his skills as a journalist. Fantagraphics began publishing Sacco's first stand-alone comic-book series, Yahoo, in 1988. A consistent focus of the series is war; one issue about his obsession with the Gulf War is even titled "How I Loved the War." Another is called "War Junkie." Eventually, Sacco's interest in the Middle East led him to an entirely new kind of comics—comics for which he would report, as a journalist, on the realities of war.
Sacco traveled to Palestine in the winter of 1991, and spent several months in Israel and Palestine interviewing about a hundred people on both sides of the conflict for his groundbreaking comic-book series titled Palestine. He wasn't there to interview Israelis and Palestinians for anybody—representing a news organization, for example—other than himself. His independence, and his lack of institutional (or personal!) money helped him to gain trust on the ground. The ability to be independent can be part of the power of the direct, auteurist comics medium as a form for reporting.
As the simple, almost confrontational title Palestine indicates, Sacco's goal was to reveal Palestinian perspectives on the conflict. He became fascinated by Middle Eastern wars and conflicts in part because of how lopsided American news coverage of the Middle East in the 1970s and '80s felt to him. Palestine, then, is an effort to address the elision Sacco saw in the United States of a Palestinian point of view. But while he is open about his goal, Sacco does not sacrifice his journalistic practices or ethics; Palestine is resolutely a work of journalism and not one of propaganda. Sacco maintains that his professional standards "are every bit as good as those of other journalists." He explained to me, "I want to show the Palestinian side of things because just on a very basic, basic level, I feel like their side's being misrepresented, or hasn't been shown enough in the West, especially in the United States. . . . But if the Palestinians are portraying themselves poorly in my eyes, that's not going to stop me from showing that." Palestine offers a chapter called "Getting the Story," in which Sacco presents an unseemly conversation with a group of Palestinian men, one of whom says, "Kill the Jews, and that makes us happy." Sacco also reports the opinions and beliefs of Israelis in chapters such as "Eye of the Beholder," "Through Their Eyes" and "Tel Aviv," titles that, like the book's simple place-name title, emphasize point of view.
Joe Sacco, cover of Palestine #7, 1994.
Used by permission of Joe Sacco.
It is hard to overestimate the importance of Sacco's Palestine to the comics world and to contemporary political and popular culture in general. Sacco established the terms for the field of comics journalism—and for contemporary war comics—in the early 1990s with Palestine's nine issues (1993–1995). Published as discrete twenty-four- and thirty-two-page comic books with full-color covers, Palestine cost $2.50 (the first three), and then $2.95 each. Nothing quite like Palestine had appeared before—something that addressed gravely serious and complicated subject matter from the ground, and also worked within comics conventions. The covers depict grave sites, protests, torture, shootings, and arrests—underneath large, cheerful hand-drawn block letters, in outline with shading, that colorfully spell out PALESTINE across the top of each issue.
The image underneath the baby-blue letters of issue #7, for instance, shows a man with a bleeding stomach wound being dragged by his legs out of the frame as he grimaces deeply, his blood streaking behind him across the rocky soil like tire tracks. The dramatic composition of the image suggests a "first-person" point of view, as if the reader looks out from the perspective of the man whose hands we see grasping the injured man's leg. A tiny floating box of text, "by Joe Sacco," matches the shade of the title—which matches the trim on the sneakers in the foreground. The striking covers of Palestine make legible how Sacco owns comic-book conventions for a new context: he combines the energy and immediacy of inexpensive, accessible, serial comic books with the gravity and rigor demanded by a journalistic investigation into world-historical conflict and its effects on the ground. The back cover reads, in type: "IN THIS ISSUE: A downpour in Jabalia . . . overflowing sewers and abandoned homes . . . a walk with veterans of the intifada's first day . . . thrown from a hospital bed . . . marriage prospects for a disfigured girl . . . bone-snapping on video . . . breaking a curfew."
Palestine eventually won an American Book Award, was glowingly reviewed in outlets like Publishers Weekly and the New York Review of Books, and was issued as a single volume in 2001 with an introduction by the celebrated literary critic Edward Said. Palestine was a crossover success, both with a wide range of comics fans—those who were likely to stumble across an issue for $2.95 at the local comic-book shop—and those who sought out the work because of its reputation as one of the most nuanced Western perspectives on the lived lives of contemporary Palestinians. Said wrote, "With the exception of one or two novelists and poets, no one has ever rendered this terrible state of affairs better than Joe Sacco." He praised the density of Sacco's comics, noting their unhurried pace, wealth of information, and their "power to detain" readers on the page. An episodic work, Palestine is structured, as is all of Sacco's work, into titled sections that vary in length. Like all of his comics, Palestine combines a synthetic, big-picture view of a conflict—how that conflict, or war, is played out on a collective stage—with detailed attention to the everyday details of people's lives, both in what Sacco himself observes and re-creates, and in drawings that illustrate the oral testimonies of individuals who have experienced torture, for example.
Sacco is just as influenced by artists like Pieter Bruegel the Elder, the sixteenth-century Dutch painter, as he is by twentieth-century prose journalists like Hunter S. Thompson. Bruegel, known as one of the greatest landscape painters, holds such massive appeal for Sacco not only because Bruegel is an incredibly acute social critic, but also because his large, detailed paintings are invested in recording customs and practices of everyday life. Sacco often features large, panoramic landscapes in his comics, which appear as double-spreads, with one image overtaking two facing pages. In these remarkable comics landscapes, one also recognizes the influence of some of Bruegel's most famous compositions—wide views, full of swarming detail, in which there is no central subject or action. When Sacco traveled to war-torn Goražde, Bosnia, for his book Safe Area Goražde, he said he felt that "I'd stepped into a painting by Bruegel." One of Safe Area Goražde's most striking double-spreads pays homage to the composition of Bruegel's famous 1562 painting The Triumph of Death, from the hills right down to the dog in the center left foreground (a reproduction of the painting sits in Sacco's studio).
As with Bruegel's landscapes, Sacco's comics offer rich, detailed views of place that allow a reader to imagine how people live in extreme times and situations. In drawing and painting, media that can assemble moments into one dense image, the artist has the ability to record detailed information in a revealing wide or bird's-eye viewpoint. "That's the great thing about being a cartoonist," Sacco told the media theorist W. J. T. Mitchell. "If you know something about drafting or perspective, you can pull yourself up." This elevated view of a swarming landscape—one in which many narratives and stories are happening at once in an information-rich scene—is typical of Bruegel and, as critic Jeff Adams has pointed out, rhymes in particular with his 1559 Kermesse at Hoboken, which pictures a church festival in a Flemish village in a composition similarly overrun with people, animals, and horse-drawn carts.
Joe Sacco, double-spread drawing of Jabalia refugee camp, Palestine (Seattle: Fantagraphics), 2001.
Used by permission of Joe Sacco.
A panorama of the Jabalia refugee camp, which is in the Gaza Strip, conveys a sense of the overcrowding, poor conditions, and disrepair, and also of everyday life persisting—schoolchildren walking home, mothers holding the hands of children, women helping each other through the mud, a shirt and pair of pants hanging to dry despite the wet weather, cars inching forward through the packed space. Sacco has described how landscape is a character in his comics—just as much as any person. "If you are depicting something graphically and it has a pretense to journalism, the idea is to get the reader there somehow," he explained. "I want the reader to open up the book and just immediately be there." While Sacco argues that traditional American journalism has "this tendency for uselessness as far as giving people a feel for what it's really like," he contends that comics, on the other hand, "is a very engaging journalistic medium" because "it allows a sense of time and place to seep in through images."
The double-spread of the Jabalia refugee camp in Palestine is also a "bleed": the images run off the margins of the page, swarming every inch of space. We see mud everywhere; children and adults slog through it and leap over puddles of water in the foreground, while in the background cars slowly wind their way through deep pockets of water toward large dumpsters of trash. Specific graffiti is visible on walls; elsewhere one notices graffiti that has been painted over. Sheep eating trash and donkeys pulling carts populate the landscape. Cinder blocks and tires hold down roofs from blowing off of rickety residences; the background is thick with roofs, water towers, and cinder blocks. I can count seventy-five people in the image, and many mininarratives playing out in its corners and edges as people move through space. As with many of Bruegel's famous landscapes, no one action takes center stage, and every inch offers information for a reader to take in. And readers get hard information about conditions—for example what materials the residences are made of, what counts as trash disposal—as well as a feeling of what moving through that space might have felt like. The heart of Palestine takes place in the Jabalia refugee camp, where Sacco stayed with a resident and translator named Sameh. Jabalia, which has a reputation for tough, harsh conditions, is where the First Intifada (or "uprising") began in 1987, triggered by a disputed traffic accident in which four Palestinians were killed nearby: it's a fitting center for Palestine.
Palestine is an incredibly prescient book, portraying the stone-throwing and other protest activities of the First Intifada, which ended in 1993 (shortly after Sacco's trip concluded). The book ends with a gesture toward what would later become the signature act of the Second Intifada—suicide bombing—in a chapter that focuses on a lost Israeli bus: it stands in nicely as a metaphor for how a country guides a people, transporting them to a future, and also suggests how public transportation became the site of suicide bombing and other attacks.
Sacco's war tour de force, however, is his Safe Area Goražde. In this case, the community ravaged by violent conflict is the so-called "safe area" municipality of Goražde, Bosnia, where Sacco traveled in late 1995 and 1996. Goražde's Muslim residents had fallen victim to or endured brutal attacks from Serb nationalists, including from people who were once their friends and neighbors before the war, and continued to be under siege. Goražde was one of six Bosnian enclaves that the UN declared "safe" during the Yugoslav War—another was Srebrenica, where the biggest massacre on European soil since World War II took place in July 1995, a genocidal action in which upward of eight thousand men and boys were killed and dumped into mass graves. Sacco writes in the book that Goražde, which had received very little press coverage compared to other "safe" territories like Sarajevo, "had become a symbol of the meaninglessness of the safe area concept specifically and the impotence of the international community generally."
Joe Sacco, page from Safe Area Goražde (Seattle: Fantagraphics), 2000.
Used by permission of Joe Sacco.
Safe Area Goražde shows how powerfully comics journalism can reveal the experience of living through war—for soliders, civilians, and refugees. It details location in the way that Palestine does, allowing a person to access the smallest details of place. It also reveals a facet of war that does not often get covered by news outlets, whether on television, online, or in the newspaper. Goražde, for which Sacco interviewed soldiers and civilians alike, gives readers many well-researched and repeated images of battle frontlines, which are heartbreaking. But it also focuses on a distinct level of information—the details that aren't usually sexy enough to make the shorter or quicker news stories—about how people in wartime conduct their everyday lives. "I talk to a lot of journalists and sometimes I'll read something they write and they are so focused on the main issue that they don't allow for those humanizing moments that actually reveal the people they are talking to as human," Sacco explained in an interview.
Both visually and verbally, Sacco carefully documents what gets dropped out in the broad strokes of political and war reportage, such as how people in Goražde cut and stacked wood, or precisely how they put together paddle-wheel generators jerry-rigged from refrigerators and cars. "I recognize this isn't the type of thing that's going to make it in the newspaper," Sacco said in an interview, noting that these details would be "lost" to history otherwise. Offering elaborate visual backgrounds in addition to textual information, comics journalism can include details that amplify the atmosphere Sacco seeks to convey, while also transmitting relevant hard information. This is an important feature of how Goražde communicates the effect of war on regular, ordinary people.
Images of stacks of wood—drawn so precisely that one can read the grain of each piece—recur throughout Safe Area Goražde. Sacco highlights the documentary aspect of his comics in his meticulous style, in which he precisely reproduces texture, from soil to wood to fabrics. Each page here, as in all of Sacco's comics, is separately dated with "J. Sacco" followed by the month and year Sacco completed it, emphasizing its quality as a document. Sacco establishes early on how residents of the city, who couldn't leave the area and who were besieged on all sides, went to efforts to find and stack wood to heat their homes with wood stoves (the trees in the nearby hills had been depleted). In an early page of the book, after remarking how cold Goražde is in a chapter called "The Deep Dark," Sacco draws a group of men cutting wood—stockpiling it—in a large panel that bleeds off the page and takes up an entire tier. A slightly smaller panel below, which is bounded with margins on all sides, as if to suggest the feeling of being trapped, shows a woman—a single mother—bent over, ax in hand, chopping wood. Sacco notes in a text box that at the time the two of them met, she only had enough wood for a few more days. "This war, it's like that," she declares with resignation, in a stark speech balloon whose words appear in capital letters that hover over her small satchel of wood. How do everyday lives unfold? Sacco asks readers to confront the difficulties of daily life in wartime, to understand how the dwindling of resources in a specific war-torn area comes about and is confronted—if it can be.
One of the most gripping and horrifying sequences in Safe Area Goražde occurs in a subsequent chapter, "The First Attack," which exemplifies one of the signature features of Sacco's war comics: his meticulous visualizations, in the medium of comics, of the oral testimonies of people he interviews. In Sacco's war comics, the focus is constantly shifting between showing in detail the ordinary rhythms of life for people trying to survive in a conflict zone (to procure heat, electricity, shelter, food) and showing extreme and often fatal violence—another feature, of course, of war. What would it be like if your neighbors, including people you thought were your friends—or your children's friends—suddenly turned on you and started killing you? "The First Attack" refers to a terrifying, grim day, May 22, 1992, in which Serbian nationalists, including some from Goražde, attacked Bosnian Muslim inhabitants of the town. In the account supplied to Sacco by several residents, inhabitants of the Kokino Selo neighborhood are suddenly besieged, as the nationalists fire upon them with automatic weapons from the surrounding hills and shell the neighborhood. The women and children start running to the local Drina River, hoping to escape. The chapter follows multiple people, and their unfolding stories, chronologically from the beginning of the attack. Here, as in other testimonies that take readers back into the past, Sacco replaces white backgrounds with ominous black backgrounds.
Joe Sacco, page from Safe Area Goražde: Izet and Rumsa's testimony.
Used by permission of Joe Sacco.
One particularly moving page opens with the voice of a man, Izet, in the first square panel. Sacco draws his name in capital letters, and quotes him directly. Below, he draws what Izet's experience looked like, based on testimony and research. Families are crawling, on their stomachs, over a field to the Drina River to avoid gunfire. Izet's thirteen-year-old daughter, whom readers see in a panel that pictures the two of them from behind, as if our viewpoint is propelling them forward, is crying. In her fear she protests to her father, in that touchingly stubborn childlike way, that she'll get her clothes muddy, as if she doesn't realize she could be killed any minute. The next panel pulls back to a wider view, an eerie image revealing the field is full of bodies, some already dead, as far as the eye can see. In the middle of the page, as the perspective swings around to face Izet and his daughter, they pass a man whose stomach is ripped open, lying on his back, dying. Izet has already been shot once, and is dragging his left leg.
As they edge to the side of a neighborhood restaurant, where others also escaping from the village are paused, crouching, Izet is shot again. The narrative then switches, in the last tier of the page, to Rumsa, a woman who in panic is running to the river alongside her eldest daughter, age twenty, with her youngest daughter, age one, in her arms. We see Rumsa crouching at the side of the restaurant when Izet gets shot in the arm. When Sacco switches over to her voice, we see her get shot too. The text reads, as a direct quotation, "RUMSA: I was wounded in the back . . ." above an image of her, in a head kerchief and skirt, midfall. "Someone took my one year old . . ." are the words at the top of the next frame, a moving and terrifying image in which all readers see are the child's feet as her tiny body is lifted away in a split second from her shot, felled mother. The gap of space between the baby's feet and the mother's supine body is at the center of the panel. Rumsa is on the ground; the baby is being snatched to safety in a hail of gunfire—by someone Rumsa can't see, as we can't either.
The page's last panel switches back to Izet. Its last words are as follows: "In front of me," Izet says, "was Ibro's daughter carrying her small sister. . . ." In the accompanying image, readers see that it was the baby's older sister who grabbed her the moment their mother was shot, and kept running. She stopped to try to save her sister's life, while barely slowing her pace, once her mother went down. The angle the image takes is from behind the assembled group; we see an image of the twenty-year-old running, baby in her arms, midgait. If we look closely we see streams of blood spurting out the right side of her head; she is shot in the forehead. Her head inclines to the right as the blood, almost blending in with her black hair in Sacco's drawing, sprays out. The older sister is killed trying to save the youngest member of her family. Sacco endeavors to communicate the experience of war through comics by both directly citing the actual testimony of survivors, and by picturing their experiences—and making them immediate—for readers. Sacco sets up readers to witness the unfolding event of the young woman's death in what approximates real time, aligned with the gaze of other horrified onlookers.
Other media seeking to convey extreme human experience include both words and images—most notably film. But work like Sacco's is a markedly different form because it is hand-drawn by a single person. As Sacco pointed out in an interview, "You might need $50 million to put together a film of similar scope to [my] book on Goražde." Comics can be powerfully direct. "A cartoonist needs only pen and paper," Sacco has said. As he suggested, the medium of comics "can be used with humility to its advantage." Humility was Sacco's aspiration in the often-violent Safe Area Goražde, in which witnesses and survivors recount, and Sacco himself observes, deeply traumatic events. The direct connection of cartoonist to witness—in which the cartoonist endeavors both to present a witness's voice and to visually re-create his or her experience on the page—offers an immediacy and a straightforwardness that feels appropriate to the easily sensationalized subject of war. In comics, the reader controls his or her own pace of consumption, unlike in a time-based medium such as film or video, in which a violent image might flit by, or occupy the screen for what feels like too long. In Sacco's comics, the reader can choose to linger on a violent image, to study and decode it, or to skip it: to put the book down, to quickly turn the page. When war—with its violence—is the subject, pacing becomes an ethical issue. In comics the reader, unforced, may pace herself, look as little or as long as she wants. Film, on the other hand, as Sacco has contended, "washes over you."
Joe Sacco, page from Safe Area Goražde.
Used by permission of Joe Sacco.
However, working for print, Sacco does deploy the language of comics, and a striking, precise drawing style, to suggest a slow and careful engagement with the subject of war. He evens calls his work "slow journalism"—it functions with a slowness that is a deliberate rejection of today's deadline culture and hyperactive news media. Later on in "The First Attack," for instance, readers encounter a display of these compositional and stylistic elements together in an episode about uncovering mass graves. Here the narrative shifts to focus on Edin, a young man who is a lifelong resident of Goražde, in Kokino Selo, and is Sacco's translator and fixer (Sacco concentrates on the role of fixers to journalists in his following book). Edin recounts to Sacco how in March 1993 people in Goražde found seven bodies, massacred, dead for months, in a grave with a dog buried on top of them. Two of the bodies found were his best friends.
In one particularly disturbing page, which represents the testimony of Edin, Sacco draws four of the seven bodies in its opening panel. Here, noticeably, Sacco also uses fragmented text boxes—one of his signature techniques—to lead the reader's eye across the difficult-to-look-at corpses. In his comics, Sacco often breaks a sentence up into different text boxes that float, unconventionally, all over a panel or page. The effect is elliptical, asking readers to pause and look, and to follow the movement of the text over and across the image (in this technique, Sacco has said an influence is the stylized use of ellipses by French avant-garde novelist and World War I veteran Louis-Ferdinand Céline, author of Journey to the End of the Night). Sacco spatializes the prose in an almost diagonal line across the ruined bodies, giving the words material weight on the page. The panel begins, in Edin's voice, with a small box hovering between two bodies, one of which anchors the left corner: "Izet's son, Rofa,"—no full stop. (Izet is the same man who we encounter earlier shepherding his daughter to the river.) As the eye follows the unfurling words, it stumbles over additional bodies, laid out on the ground, large and badly decomposed, eyeless, sunken, mouths eaten away to reveal teeth in the perpetual grimace of skulls.
The first sentence continues, in a box laid over one side of the panel's first full-length corpse (a body with what appears to be a pile of stones in its center): "was with me in school for 12 years. There was dirt in his stomach. Probably they'd cut open his stomach." The next sentence starts in a box placed on the body of a third man, over his left shoulder: "Senad," the sentence begins in its own box—and one must move over his rotted corpse in order to stop at another box over his right shoulder, "was with me four years in the same class. Senad's fingers had been cut from one hand, the other was shut tight." The last of the five boxes is a single sentence unto itself, superimposed over the chest and completely decomposed arm of the fourth body: "All of them were without penises."
The fragmentation of this text out, over, and onto the emasculated bodies of murdered men has a dramatic effect that slows regular reading down. The eye instantly—upon reaching the far side of the panel—jumps back to the mutilated bodies, and if one did not linger long enough on them the first time, one now notices (and confirms) that there are black gulfs between their stiff legs, violent thatches of absence. The panel's composition of words and images also delivers a paradoxical, unsettling effect: the words appear at once to float between the bodies and to stamp themselves onto the bodies. "Senad" appears in its own box up near the left shoulder of a corpse, like a name tag. And the page's final panel, in which Edin and other men from Goražde pray during the proper burial they finally give the murdered men, demonstrates the poignancy of silence, removing words from a form that is structured by the constant back-and-forth rhythm between reading and looking.
In order to be able to draw these disinterred bodies accurately, Sacco consulted forensics experts. Their decomposed faces, torsos, and limbs, partially clothed with rotting garments, are drawn with striking exactitude. Sacco sometimes draws with the exaggerated, curvy lines of underground cartoonists like R. Crumb (the "bigfoot" style crops up whenever he draws himself, for example), but when he wants to, he can draw with a very, very high level of realistic detail—one that is distinct in comics and comparable perhaps only to Phoebe Gloeckner's. His approach, then, to drawing war is very different from the monochromatic simplicity of Marjane Satrapi's child's-eye view. Art Spiegelman also draws mass graves, in Maus. But while Spiegelman's style of loose black lines, and de-particularized faces, signals his abdication of aesthetic mastery as appropriate to a story about the Holocaust, Sacco's style is dense, virtuosic, and often photorealistic. It is an ethical attempt to represent people whom he believes have been ignored in the world arena with as much particularity as he can deliver.
Joe Sacco, page from Safe Area Goražde: Rasim's testimony.
Used by permission of Joe Sacco.
Sacco's desire to represent particularized individuals (whether dead or alive, as above) is clear in his attention to faces—specifically the faces of those people whose testimonies he draws. Sacco wants readers to encounter a specified individual—not just a faceless victim. He also wants to pull back the curtain, and show how journalism actually works—to show the context that allows his interviews and conversations to happen, to show the seams of the enterprise and not just the seemingly transparent final product. By detailing the faces of his subjects both in the present-tense situation of testimony and in the past events that they narrate, Sacco asks readers to exchange gazes with these war-battered subjects. He wants readers to confront these people face-on, suggesting a mutual, equalizing exchange, rather than looking down, up, or sideways at them.
We see this in Safe Area Goražde with Rasim, an older Bosnian Muslim man who was an eyewitness to literally hundreds of killings of Muslims by Serb nationalists (who are here widely called "Chetniks," a derogatory term) on a bridge over the Drina. Rasim barely escaped with his own life after being dumped on a truck on its way to an execution site after he was twice helped by Serbs who recognized him and chose to save him—one a neighbor, one a friend of his daughter's. Throughout "Around Goražde Part 1," the chapter that details Rasim's story, Sacco consistently draws the heavy-eyed, mustached Rasim—framed face-on in a panel, looking out directly at readers in a patterned sweater, collared shirt, and existentially weary expression. In this way, too, Sacco shuttles back and forth from the present to the past, reminding readers of the scene of testimony in addition to what it reveals of the past. His own voice, "offstage," even enters several panels. This page elaborates the killing of children. "But did they still kill women and children?" Sacco's voice asks from off to the side, even as Rasim stares out at readers. "Yes. Of course," Rasim replies. Sacco's investment in visual realism stems from his belief in the ethical efficacy of showing, as much as possible, what an event was like. Sacco said in an interview, "[The Serbian nationalists] were killing kids. . . . I decided to make this a realistic comic, and once I made that decision I just thought . . . 'I'm not going to try to make it abstract. I mean, killing a kid is killing a kid.' "
The issue of drawing faces comes up again in Sacco's Footnotes in Gaza, a 418-page investigation—through interviews, on-the-ground research in the Middle East, and archival research in Israel and at the United Nations headquarters—into what transpired during two massacres of Palestinians by Israeli soldiers in 1956 in the wake of the Suez Canal crisis. In the first, in the town of Khan Younis, a presumed 275 unarmed men were lined up against a wall and shot. In the second, less than two weeks later, in the neighboring town of Rafah, a presumed 111 unarmed men were shot and beaten to death during a daylong screening operation in which people were forced out of their homes and into a schoolyard. Footnotes in Gaza is the most relentlessly violent of all of Sacco's books, in terms of the sheer numbers of corpses that populate its pages. I asked Sacco in an interview if it was hard to draw Footnotes, which he worked on for seven years—three for research, four drawing. Sacco has joked about "Joe Sacco Trauma Syndrome." "I did not want to go to the drawing table," he told me. "When you're in the middle of it, you don't like doing it, but it's your job. You know you have to get through this, you have to show this. You made that decision to show it."
Joe Sacco, Footnotes in Gaza (New York: Metropolitan), 2009: the schoolyard gate in Rafah.
Used by permission of Joe Sacco.
Sacco pays special attention in Footnotes to faces, even more so than in his other works, in which the individuated face is always on display. Footnotes aims to archive, in comics, the oral testimonies of the massacres by every single survivor Sacco could track down. In his effort to amass these voices in order to understand the events, Sacco carefully draws and fully identifies each witness by first and last name. One feature of the Rafah massacre that Sacco focuses on closely is how prisoners were herded into the schoolyard. Israeli soldiers with heavy sticks stood at either side of the gate to the school, and beat people on the head as they were forced to pass through. Sacco's own narration explains that while the group of survivors had some differing accounts, and forgot various details of the traumatic day so many decades back, this part of the day "remains burned into even the most age-dulled minds." In one dense, virtuosic page in this episode, Sacco drops the page borders and even panels and fills the page entirely with assembled moments of time. The present-tense faces of survivors, each of which is framed in a small box with a full-name identification, are overlaid on images of soldiers athletically swinging sticks, so that the page produces a jumble of accumulated actions, with each witness's face and short account, in speech balloons, of entering the gate. This dense page palimpsests past and present, and juxtaposes Israeli and Palestinian bodies in the swirls of action, suggesting the chaos and confusion felt by the prisoners.
The juxtaposition of the faces of the Israeli soldiers (there are two of them, whom Sacco draws repeatedly) and the Palestinian survivors also emphasizes just how differently Sacco draws the soldiers and the civilians. In the swirl of the page, the Israeli faces are mostly obscured—readers do not have much access to their eyes, for example—while the Palestinian faces are particularized, a feature highlighted by how they are framed, in same-size panels that evoke passport or school photos. Sacco told me that he realized, creating Footnotes, that he had hit a sort of wall in his quest to understanding war. "You have to put yourself in everyone's shoes who you draw, whether it's a soldier or a civilian. You have to think about what it's like: What are they thinking? What are they feeling? The truth be told, that's part of the reason I don't [always] show Israeli soldiers' faces. I couldn't understand it. . . . I couldn't always put myself in their psychology properly, so in a lot of cases, I refrained from drawing their faces."
Footnotes is a masterpiece of reporting and research. Reviewing the book in the New York Times Book Review, the seasoned Middle East expert Patrick Cockburn declared that Footnotes, which he calls "investigative reporting of the highest quality," stands out as "one of the few contemporary works on the Israeli-Palestinian crisis likely to outlive the era in which they were written." And yet for Sacco, in some ways Footnotes represents a dead end—the limit of his understanding of war, as we see with his inability to understand certain actions. Sacco told me, "I don't know where to go from here, except to delve into human psychology. . . . What am I going to do after this, keep detailing massacres?" Indeed, a current project, which will be years in the making, goes all the way back, in his efforts to understand war, to the early civilization of Mesopotamia, seeking out the answer to the question, How does the state get a person to kill another person?
Naji al-Ali, cartoon featuring child-witness Hanthala staring along with readers at the scene, circa 1983–1985. Translation: "The borders."
Published with permission of the Naji al-Ali family. Image courtesy Khalid El-Ali.
Sacco's comics are thoroughly international. In addition to his two books each located in the Middle East, and in the Balkans, and his The Great War, which takes place in France, Sacco has done multiple, important comics stories on refugees, including long pieces on displaced Chechens ("Chechen War, Chechen Women"), and on refugees to Malta ("The Unwanted"). He has traveled to India for "Kushinagar," about the effect of the caste system on Dalit villagers in northern India, and he has also explored poverty in America in his collaborative book with prose reporter Chris Hedges, Days of Destruction, Days of Revolt. During the Iraq War, he was embedded with US troops and produced several comics reports, including "Down! Up! You're in the Iraqi Army Now," which examines American training of Iraqi troops and was published in Harper's (as were many influential reports from artist-reporters during the Civil War). When Sacco first took himself to the Middle East, for Palestine, he wasn't sure how people would receive the news that he was there as a journalist and cartoonist both. But in Palestine, he came to realize, there was an extant culture of respect for cartooning because of Palestinian cartoonist Naji al-Ali. Naji al-Ali, who had grown up in part in the Ain al-Helweh refugee camp in southern Lebanon, was assassinated in London in 1987. His cartoons spoke truth to power—Israel, the United States, factions within Palestine—and featured a character, starting in 1969, who remains an icon across the Middle East: Hanthala, a ten-year-old child. Hanthala, always barefoot, and almost always with his back to viewers, is a figure for witness: we see him seeing the scene that al-Ali draws, and his presence functions like a conscience. Sacco wrote the introduction to A Child in Palestine, the first collection in English of Naji al-Ali's work, which was published in 2009.
Sacco established conflict zones around the world as an urgent subject for contemporary comics. He is also, it is worth recalling, the first Maltese cartoonist, and worked to develop Malta's comics culture in the 1980s. Globally, the biggest and perhaps most obvious comics markets and comics cultures are the Japanese manga tradition; the Franco-Belgian comics tradition, which gave the world Tintin; and the American comics tradition (Canada also has a thriving independent comics scene). However, there are other significant traditions from around the world that are emerging and becoming vital. India is now the world's fourth-largest producer of comic books and graphic novels—even though the book considered the country's first official graphic novel, Orijit Sen's River of Stories, did not appear until 1994. Sen's River of Stories, a work in the social justice mode of comics journalism, focuses on the effect of the construction of dams on the Narmada River. In the global arena, River of Stories is an early and important example of comics journalism, a continuously growing genre in India, and one can understand why many cartoonists there have engaged with Joe Sacco's work (especially after his 2011 "Kushinagar"). Cartoonists including Sarnath Banerjee, the author of four graphic novels, most famously Corridor (about a secondhand bookstall in Delhi) and Vishwajyoti Ghosh, who recently edited an anthology of graphic narratives from India, Pakistan, and Bangladesh titled This Side That Side? Restorying Partition, have become big names both inside and outside India. The first Comic Con India was held in Delhi in 2011. Indian cartoonists have showcased work in this annual convention alongside visitors to the country including Robert Crumb and Aline Kominsky-Crumb, and Brazilian artist-brother team Fábio Moon and Gabriel Bá. New Cons have cropped up across the country; the cofounder of New York City's important anti-war social justice comics anthology World War 3 Illustrated, Peter Kuper, was a featured guest at the Bangalore Comic Con in 2014. Comics in Western and Eastern Europe, in places like Italy and Poland, have been steadily on the rise. In 2006 the Studio Museum in Harlem staged a show called Africa Comics, featuring comics from every African country. In Singapore, China (despite censorship issues), Malaysia, and Korea, in addition to the enormous comics culture in Japan, comics making is on the rise.
In short, comics cultures are sprouting from places all over the globe, even from locations that don't have long historical comics traditions. One enormous regional growth area for comics is the Middle East. In Israel, which hasn't traditionally had a rich comics culture, cartoonists like Rutu Modan (whose illustration is the cover of my book Graphic Women) and Asaf Hanuka have been translated and gained international fame. There was a whole spate of sophisticated comics done during and after the Arab Spring, and places like Cairo (with its comics magazine Tok Tok) and Beirut (with its comics magazine Samandal) have thriving comics cultures. A recent book on contemporary Beirut even opens by referring to webcomics by the cartoonist Mazen Kerbaj.
Riad Sattouf, The Arab of the Future 2: A Childhood in the Middle East (New York: Metropolitan), translated from the French, 2016. Riad and his parents, living in Syria, watch Syrian Special Forces on television.
© 2012 Riad Sattouf. English language translation © Sam Taylor. Used by permission of Henry Holt and Company. All Rights Reserved.
But the most famous comics work in recent years to come out of a Middle Eastern context is Riad Sattouf's international best seller The Arab of the Future: A Graphic Memoir, which was first published in France and is now appearing as several translated volumes in the United States. Unlike Sacco's finely grained black-and-white pages, The Arab of the Future, a childhood memoir rather than a work of journalism, uses clean, simplified lines and cheery pastel colors—many pages are solely pink and black—with schematic, rounded shapes, like the loose spirals that indicate Riad's "flowing blond hair like a Hollywood actress." The first volume has already been translated into sixteen languages. Sattouf, who has a French mother and a Syrian father, and grew up in Libya, Syria, and France, is notable for being the only cartoonist of Arab descent to have been on staff at Charlie Hebdo. It was Charlie Hebdo's offices in which terrorist gunmen massacred twelve people, including the magazine's editor, likely because the French satirical comics publication had published mocking images of Mohammed.
Sattouf drew a regular strip for Charlie, called The Secret Life of Youth, a man-on-the-street-style real-life strip, for ten years until just a few months before the attacks. (He revived the strip for the first issue of Charlie that was published after the attacks.) The Arab of the Future adopts the point of view of the child at its center; its title refers to what Sattouf's father, a Sunni Muslim hailing from a village near Homs, explained to Riad he wanted him to become. In terms of identity and futurity, Sattouf, after a difficult childhood, seems to have chosen a more flexible, and deeply felt, identity. As Sattouf himself told an interviewer in 2016, "[I'm] not French, I'm not Syrian . . . I'm a cartoonist."
---
WHY QUEER?
The fastest-growing area in comics right now may be, broadly speaking, queer comics—comics that feature in some way the lives, whether real or imagined, of LGBTQ (lesbian, gay, bisexual, transgender, and/or queer) characters. Queer comics are one of the most vibrant areas of contemporary comics, fueled in large part by the runaway success of Alison Bechdel's 2006 graphic memoir Fun Home: A Family Tragicomic—the story of a gay girl and her closeted, ultimately suicidal gay father that was adapted to be a Broadway musical of the same title, and went on to win the Tony Award for Best Musical in 2015. Gayness used to be a public accusation leveled at comics to discredit the medium: in the 1950s Batman and Robin, and Wonder Woman, were suspected to be gay, and therefore a negative influence. Dr. Fredric Wertham wrote in his influential book on comics that the former represent "a wish dream of two homosexuals living together," and for the latter, "the homosexual connotation of the Wonder Woman type of story is psychologically unmistakable. . . . For girls she is a morbid ideal." The infamous 1954 Comics Code, inspired by Wertham's study, banned "sex perversion or any inference to same"—a clear reference to homosexuality. But today gay comics are an ever-expanding feature of the field, marking a new era of self-expression. Comics used to be read paranoically as gay code; in contemporary comics queer identity is openly announced.
The excitement around queer comics, from readers and creators both, is rising steadily. Justin Hall's compendium No Straight Lines: Four Decades of Queer Comics, an edited collection, sold out its first print run in 2012. Two cult classic graphic novels from the nineties, artist and activist David Wojnarowicz's Seven Miles a Second and literary critic and writer Samuel Delany's Bread & Wine: An Erotic Tale of New York (both collaborations with illustrators), were reissued in deluxe editions in 2013 for new readerships. And 2015 marked the creation of the first annual comics convention to focus on queer culture: Flame Con. New York City's Flame Con describes itself as "a two-day comics, arts, and entertainment expo showcasing creators and celebrities from all corners of LGBTQ geek fandom," and specifies "geeks of all types are invited to attend and celebrate the diversity and creativity of queer geekdom and LGBTQ contributions to pop culture." Most significantly, however, the range and volume of queer comics appearing right now demonstrates how forcefully the realities and details of gay life can get expressed and visualized in comics. Diverse comics about all sorts of aspects of queer experience flourish online, in the direct and censorship-free zone of webcomics. And in the world of print, we see an outpouring of distinct genres of comics that explore and address queerness. Among the artists creating this work, Bechdel has shown most powerfully how comics can be a space for sophisticated storytelling about the complexities and joy of queer life.
Bechdel was influential long before Fun Home, which was published when she was forty-five. Bechdel's hugely important and popular syndicated comic strip Dykes to Watch Out For, which chronicles the everyday lives of a diverse group of mostly gay friends and lovers, began in 1983 and ran for twenty-six years; it changed comics culture and broader queer culture definitively. The guide Dyke Strippers: Lesbian Cartoonists from A to Z is even dedicated to Bechdel. Film director Lana Wachowski, of the Matrix franchise (and a trans gay woman), wrote recently that although she was a fan of mainstream comics as a kid, and later the work of Robert Crumb, "It wasn't until I discovered Alison Bechdel's Dykes to Watch Out For that I really understood what I was looking for, a queer world with stories and characters that I could recognize, that I could laugh with and care about."
The history of gay comics, however, doesn't start with Bechdel. It has roots that go back at least to the underground comix movement of the 1960s and '70s—and even earlier, too, if one considers classic comic strip characters like George Herriman's Krazy Kat, one of the most celebrated characters in the history of comics. Krazy Kat (1913–1944) which debuted in William Randolph Hearst's New York Journal, featured a famous love triangle: the mouse, Ignatz, hates the cat, Krazy. Krazy, however, passionately loves Ignatz; even though the mouse throws bricks at Krazy's head, they are received affectionately. Offissa Pupp, a dog, adores Krazy and hates Ignatz as a result. Krazy is androgynous, a "kat" with a fluid gender that seems to shift and is never actually meant to be conclusively verified (sometimes the narration refers to Krazy as a "he"; largely, however, Krazy has been interpreted as female, including by superfan e. e. cummings). In an exchange from a 1915 Krazy Kat daily strip, Krazy complains, "I don't know if I should take a husband or a wife," to which the indifferent Ignatz responds, "Take care," and hurls a brick. That a syndicated strip published in a mainstream Hearst paper—Hearst adored the strip's artistic merit and gave Herriman a lifetime contract—had such a conspicuously "genderqueer" star at its center indicates that queer comics, even if not hailed as such, have been lurking in plain sight for over a hundred years, at least. We might even consider queerness part of the DNA of comics.
Other newspaper strips have featured openly gay characters, some controversially. Garry Trudeau's topical and political Doonesbury also introduced an openly gay character in 1976—early for mainstream comics. Readers first meet the character Andy Lippincott in a law library as the object of a female crush. In the Doonesbury storyline, after a yearlong battle, he dies of AIDS in 1990, an event that helped bring discussions about the disease into a wide number of homes. Andy is the only fictional character to be included on the real-life AIDS Quilt. (He later appears to longtime character Mark Slackmeyer in a dream to tell Mark that Mark is in fact gay, causing him to come out of the closet.) And Matt Groening's Life in Hell, which ran for thirty-five years starting in the late 1970s, featured the always-together characters Akbar and Jeff. Akbar and Jeff—also early and prominent gay characters who eventually became well-known in popular culture—are identical-looking men in fezzes and Charlie Brown–style shirts who initially were introduced by Groening as "brothers, or lovers, or both" but were soon acknowledged as gay.
Akbar and Jeff, characters since the late 1970s.
"Life is Swell" © by Matt Groening. From Life in Hell, Acme Features Syndicate, July 25, 2008. Image courtesy Bongo Comics Group.
Asked by a fanzine in 1987 if his characters had ever elicited a homophobic reaction, Groening replied yes. "The main reaction was when I first acknowledged that either of these characters could possibly be gay, some people who had been following the strip for years and had feelings about gays were very, very upset, which made me very, very happy." (When Groening ended Life in Hell, a tribute poster was assembled; Alison Bechdel's contribution was a fitting Akbar and Jeff tribute strip about the multivalent word "gay.") The newspaper strip For Better or For Worse, by Lynn Johnston, about a suburban family with three kids who age in real time, introduced one of its characters, Lawrence—a friend of the family's son—as gay. In 1993, when Lawrence came out, For Better or For Worse was syndicated in hundreds of newspapers. The backlash was so intense that today Johnston devotes a portion of her website to explaining it under the heading "Lawrence's Story." It may be hard to remember or imagine just how unusual sensitive gay content was for the "funny pages" of mainstream newspapers even twenty-five years ago, but within a week, nineteen papers had canceled For Better or For Worse outright, many more had suspended the strip, and Johnston went on to receive over 2,500 personal letters (in the days before email, no less), including death threats. "I learned that the comics page is a powerful communicator," Johnston writes on her website. "I learned that our work is taken seriously."
These widely popular strips, which each came at gayness from a different angle, provided important early examples of gay representation in comic strips. But the gay or queer characters they featured were secondary characters. It wasn't until the underground comics movement, starting in the early 1970s, that gay comics as a self-conscious genre took root. In the underground, comics was reinvented as a medium for self-expression. It follows that the underground was also where political, identity-based comics were first developed, bolstered by the energy of the left-wing counterculture's attention to disenfranchised voices—and also by women cartoonists' reactions to what they perceived as the overly straight, overly male first wave of underground cartoonists. The comic book Wimmen's Comix, run by a collective of female cartoonists, developed as a platform specifically for women in 1972. And their debut issue (which is also where Aline Kominsky-Crumb's comics first saw print) featured a three-page story about lesbianism, "Sandy Comes Out," by Trina Robbins, a guiding force in the Wimmen's Comix Collective. The story, about a young woman coming out and joining a "gay/hippie commune," was framed as a "true life" comic about a friend of the artist (unidentified as such in the story, that friend was Sandra Crumb, Robert Crumb's sister.)
While Wimmen's Comix, and other feminist comics titles, acted as a corrective to the male-dominated underground comics scene, they were thin on gay content and gay authors. The perceived heterosexism of feminist underground comics inspired Mary Wings, then twenty-four, to self-publish the first full-length lesbian comic book, Come Out Comix, in 1973—a groundbreaking, stand-alone title that paved the way for queer comics of all different kinds to claim a place in the field. The underground inspired that kind of creative practice: if you perceived a gap, you could fill it yourself. Soon thereafter, Wimmen's Comix published its first lesbian contribution by an actual lesbian, Roberta Gregory's "Modern Romance"—also, like Wings's comic book, a coming-out story (Gregory would later go on to publish the hilarious comic book Naughty Bits during the 1990s, starring the character Bitchy Bitch, and a spin-off collection, Bitchy Butch: The World's Angriest Dyke). Wings followed up in 1976 with another comic book, Dyke Shorts. The work coming out of the underground was substantial, and personal, claiming space for nuanced stories that previously hadn't found expression in comics—or in most other media. When Bechdel started drawing her comic strip Dykes to Watch Out For in 1983, "there was already such a thing as a lesbian cartoonist," she notes. "I didn't have to invent it, or fight for it, or suffer over it. I just did it."
Gay Comix #1, ed. Howard Cruse, cover by Rand Holmes, 1980.
Used by permission of Martha Holmes.
Comics about gay men were slower to form, although the artist known as Tom of Finland, and his drawings of well-endowed muscle men, were significant to gay culture starting in the 1950s, along with plenty of other homoerotic fetish drawings and pornography. There were some gay-themed single-panel gag cartoons in the burgeoning gay press, like Joe Johnson's campy "Miss Thing" and "Big Dick," which appeared in The Advocate starting in the late 1960s. The country's oldest LGBT-interest magazine, founded in 1967, The Advocate has always featured cartoons and comics as a form reflecting, however humorously, on gay life. And Rupert Kinnard's Cathartic Comics, an early version of which first appeared in his college paper in 1977 before later migrating to multiple alternative weeklies, notably featured the first continuing African-American gay characters in comic strips—the Brown Bomber, a man, and Diva Touché Flambé, a woman. But the central figure in gay comics is surely Howard Cruse, a respected cartoonist raised in Alabama who began an underground comic strip, Barefootz (the titular character was always barefoot), in 1971. Five years into its publication, the strip's character Headrack came out as gay. Cruse knew this choice would mark his own public coming out, and though he struggled with the decision to draw gay content, he was encouraged ultimately by Mary Wings to take the leap into that subject matter. "Gravy on Gay," in which Headrack comes out, is a story whose central plot point Cruse described as "an explosion of long-repressed liberationist fury."
Cruse became the founding editor of the field-defining comic book Gay Comix, published by the underground press Kitchen Sink starting in 1980. It may have taken longer than other underground titles to coalesce, but its significance has been enormous. (And it lasted eighteen years, longer than most underground publications, excluding Wimmen's Comix, which lasted twenty years.) Gay Comix aimed for inclusivity and to consolidate queer underground comics. It came with the tagline "Lesbians and Gay Men Put It On Paper!" Its first cover, by Rand Holmes, hilariously features a man walking down the street, stuck in a literal closet, ogling another man in shorts eating a hot dog. In Gay Comix, Cruse crucially frames comics as an uncensored art form in which stereotypes and expectations can be overthrown in favor of particularity and range. "In this comic book you'll find work by lesbians, gay men, and bisexual human beings. The subject is Being Gay," he wrote in the editor's note. "Each artist speaks for himself or herself. No one speaks for any mythical 'average' homosexual. No one is required to be 'politically correct.' " For Alison Bechdel, discovering the first issue of Gay Comix was the single biggest event that sealed her fate as a cartoonist. "I'd been out as a lesbian for a couple of years, [but] the notion of cartoons about being gay had never crossed my mind. It was like, 'Oh, man! You can do cartoons about your own real life being a gay person.' "
Drawn copies of Alison Bechdel's The Bugle, 1970–1972, photographed in Bechdel's present-day studio. Note the Father's Day and Mother's Day editions. She would go on to write separate memoirs about each of her parents.
Photo courtesy Alison Bechdel.
Bechdel grew up the eldest of three siblings in the small rural town of Beech Creek, Pennsylvania, in a Victorian Gothic Revival house whose restoration was her father's "monomaniacal" obsession. As her graphic memoirs Fun Home and Are You My Mother? A Comic Drama—centering on her father and mother, respectively—reveal, both of her ambitious, intellectual parents longed to be artists but ultimately fashioned their lives along more conventional lines. Bechdel's father, Bruce, who was passionate about high modernist literature created by William Faulkner, F. Scott Fitzgerald, James Joyce, and Marcel Proust, among others, was a local high school English teacher and part-time funeral home director—at the Bechdel Funeral Home, a family-run business. Fun Home is short for "funeral home," and refers to the nickname for the family business. (The job was part-time by necessity because Beech Creek is so small.) Bechdel's mother, Helen, worked as a substitute English teacher, was devoted to piano, and performed in regional theater productions. Both were judgmental and exacting. As a child Bechdel was encouraged—if not overencouraged, or rather overshadowed—in her creative pursuits. When Bruce presented the young Alison with a diary, he himself then decided to write its first sentence, about himself: "Dad is reading." One episode in Fun Home depicts how Bruce, unbidden, creates a second stanza for a short poem spontaneously written by the seven-year-old Alison; she dutifully adds it to her typescript and never writes another poem (ever). Soon after, Bruce chides her for coloring her Wind the Willows Coloring Book in a way he deems incorrect; he sits down and takes over the coloring as she walks away, dampened ("Look. By adding thin layers of goldenrod and yellow-orange, I get a richer color"). Bechdel told me, only partially joking, "I became a cartoonist because it was a black-and-white world where I didn't ever have to think about color." But as a child she constantly drew her own colorful images, and even created her own magazines and comics. Her charming words-and-pictures bulletin The Bugle, created when she was eleven, priced at 2 and then 5 cents, is one such example. Bechdel, always drawing inventively, even cared about reproduction and circulation as a child—her methodical practice was to individually hand-draw multiple versions of the same issue to sell to her family members. Bechdel, too, became an avid reader of Mad. When she was little, Bechdel told me, "I wanted to become a cartoonist but that got drilled out of me."
Bechdel began college at Simon's Rock, a school for younger motivated students, when she was sixteen, and eventually attended the progressive Oberlin College in Ohio. At Oberlin—also my alma mater, and that of Julie Taymor, Mark Boal, Josh Neufeld, A.K. Summers, Cory Arcangel, Karen O, Lena Dunham, and a whole host of creative people—Bechdel majored in studio art and art history. One day in the campus bookstore during her junior year, she realized that she was a lesbian while she browsed (appropriately, given her family's obsession with reading) through a book documenting gay experiences called Word Is Out: Stories of Some of Our Lives. In college, despite her sense she could never actually become a cartoonist, Bechdel drew avidly in her sketchbooks. And her interest in comics—her attention to letterforms and handwriting, to creating sequences of images, and to the relation of word and image—threaded through her art projects. A piece called Self-Portrait she created for a drawing class fascinatingly offers a sequence of large bordered panels, each of which has words and pictures inside it. Besides being "proto-comics," as Bechdel put it to me, the piece also shows how "I've clearly for a long time been preoccupied with how my parents are operating through me creatively"—the central theme, perhaps, of both of her memoirs. One portion of Self-Portrait offers small photographs of her parents, along with samples of their handwriting, like an equation: added together, they equal a photograph of Bechdel and her handwriting. Bechdel made this piece in the spring of 1980, between coming out as a lesbian to her parents and her father's death. It was created right after a visit home, in which she and her father connected, fleetingly, for the first and only time about their shared homosexuality. In Self-Portrait, underneath the designation "genetic," Bechdel inks a comment that is a strikingly relevant description of cartoonists' dedication to handwriting: "Handwriting (like drawing) = externalization of internal images." A few months later, the closeted Bruce Bechdel, shortly after his daughter had come out as gay, and a few weeks after his wife asked for a divorce, committed suicide at age forty-four.
Alison Bechdel, excerpt from Self-Portrait, 1980: close-up of panel on handwriting.
Photo courtesy Alison Bechdel.
After graduation, Bechdel moved to New York City and worked a series of temp jobs. She had been rejected from all the graduate art schools to which she had applied—including Yale, RISD (the alma mater of Justin Green), and the School of the Art Institute of Chicago (the alma mater of Chris Ware, and where Bechdel and I once gave a standing-room-only talk). "I attended the MFA Program of the streets," Bechdel jokes in one of her comics—and clearly it gave her the right experience. She wandered into the Oscar Wilde Memorial Bookshop on Christopher Street in the West Village (now shuttered), found the first issue of Gay Comix, and realized that she could combine two important features of her life: her love for comics, and her dedication to being an out lesbian. "That was quite momentous for me," Bechdel recalled of discovering a model in Cruse and the existence of comics devoted to queer life. "Howard was hugely formative in that sense. And also I loved that he was so good—he was so technically good at what he did, but he still did queer stuff. That he would bring that talent into the subculture was very moving to me." Bechdel began pursuing her own drawings with renewed energy—and practiced drawing women. From childhood straight on through college and after, Bechdel almost exclusively drew men in her sketchbooks, a kind of drawing she has described as "almost involuntary." Bechdel struggled with drawing women with anywhere near the same fluidity and grace with which she had been drawing men since she was a child. And, she found that if she thought of the women she drew specifically as lesbians, it was easier to draw them.
As a young lesbian just out of college in the early 1980s, Bechdel yearned to see reflections of her community, even if she had to create them herself. "I was very hungry to see visual images of people like me," she told The Comics Journal. One day, in the margins of a letter to a friend, Bechdel doodled a drawing of a naked woman in midstride clutching a coffeepot, labeled it "Marianne, dissatisfied with the breakfast brew"—and then wrote, "Dykes to Watch Out For, plate no. 27." Unlike in her methodical, sequentially numbered childhood bulletin The Bugle, there were no other plates yet, but the concept of a series or catalog of dykes compelled her. Bechdel set about sketching other dykes for her series, and eventually submitted her captioned cartoons to Womanews, the feminist monthly where she volunteered. Her first work saw print in 1983: "Dykes to Watch Out For, plate no. 19: Twyla is appalled to learn that Irene is a morning person." It proved popular, and Bechdel began publishing Dykes to Watch Out For in every issue of Womanews. Soon she switched to a multipanel strip format, and eventually Dykes to Watch Out For, whose stories got longer and longer, earned a national audience in the alternative press as a biweekly feature.
Alison Bechdel, first published installment of Dykes to Watch Out For, in Womanews, 1983.
Used by permission of Alison Bechdel.
Dykes to Watch Out For was a sensation. (It is almost America's first ongoing queer comic strip; Cruse's Wendel, about an irrepressible gay man and his lover, began appearing in The Advocate just a few months earlier.) In 1986—the same year that Bechdel published her first autobiographical story, in Gay Comix—Firebrand Books published a book collection of Dykes to Watch Out For to acclaim. This collection contains the now-classic story "The Rule," reproduced here in the introduction, which became the basis for the globally known "Bechdel Test," a standard for gender equality in film that has served to reinforce Bechdel's stature in popular culture. (It's amazing how many films, including serious and acclaimed ones like The Social Network, or the first Star Wars trilogy, fail this test, since the bar seems pitifully low: the movie has to have: 1) two women in it; who 2) talk to each other about 3) something besides a man.) In addition to national syndication in the alternative and gay press, eleven subsequent book anthologies of Dykes appeared, with amusing titles like Hot, Throbbing Dykes to Watch Out For (1997) and Dykes and Sundry Other Carbon-Based Life Forms to Watch Out For (2003). Bechdel has been making a living as a cartoonist since 1990, when she was able to quit her day job. In 1993, Gay Comix, which inspired her before she even knew she would become a cartoonist, published a special all-Bechdel issue.
The first ongoing lesbian comic strip, Dykes began presenting a recurring cast of characters in 1987—a large group of lesbian (and some bisexual and straight) friends and sometimes lovers living in an unspecified, midsize American city. Throughout its twenty-eight-year run it focused intently, always with warmth and humor, but with precision, on contemporary politics as much as on the continuing, soap-opera style drama of its characters. "The interplay between the personal and the political is an enduring fixation of mine," Bechdel has said. "I look back now at the genesis of Dykes and I see it very much as a reaction to what happened with my father. I felt that to a certain extent he killed himself because he couldn't come out, so I was determined to be utterly and completely out in my own life." Dykes captures the texture of its characters' lived lives with such an attentiveness that it feels like it is presenting the lives of real people—friends, neighbors, co-workers, family—as they unfold. Although Dykes is fictional, Bechdel explains it has a "journalistic" quality: it translates the everyday realities of a certain slice of queer life to the page. Its central protagonist is Mo, a funny, perpetually worried white, middle-class dyke who is a stand-in for Bechdel (and who for years dates Sydney, a supercilious women's studies professor). Other characters include Clarice, an attorney; Toni, her accountant wife and fellow mother; Jezanna, a bookstore owner; Lois, a genderqueer sex-positive bookstore employee; Sparrow, a bisexual director of a women's shelter, and her partner, Stuart; and Ginger, an English professor. There are plenty of professors in the cast and plenty of professor fans who love Bechdel's send-up of academic discourse (I can speak from authority). "Will you do me the honor of paradoxically reinscribing and destabilizing hegemonic discourse with me?" Sydney asks Mo when she proposes.
Sydney and Mo in Bechdel's Dykes to Watch Out For story "Sense and Sensuality," collected in Hot, Throbbing Dykes to Watch Out For (Ithaca: Firebrand), 1997.
Used by permission of Alison Bechdel.
An ongoing, serialized comic strip like Dykes, which took place in the present tense and was invested in reflecting the world, appearing every two weeks, opened up the door for participation and interactivity, bringing in a population of involved readers. Creating the strip, Bechdel was aware of how it produced a community eager, as she had been, to see certain kinds of underrepresented lives reflected back at them. The last chapter of Bechdel's compilation book The Indelible Alison Bechdel is even called "Audience Participation," something the form of an ongoing comic strip engenders. Bechdel deadpans, "I have the dubious privilege of receiving constant feedback about the progress of the narrative." The investment of readers indicates how profoundly people attended to sophisticated queer representation—something that was made even more legible when Bechdel began posting Dykes installments on her website www.dykestowatchoutfor.com, her website where many of the strips are archived, and are richly commented upon. "Alison: Is the intensity of our attachment to and obsessions about your characters freaking you out just a tiny bit?" one person reasonably mused in the middle of a thick, intelligent batch of comments in 2006.
Other significant queer comics joined Dykes and other works in the 1990s. With humor and savvy, several of these tapped into a wellspring of anger around social relations including sexual harassment and rape culture (and don't feel dated today). One of my personal favorites is Diane DiMassa's laugh-out-loud Hothead Paisan: Homicidal Lesbian Terrorist, which began as a self-published comic book/zine in 1991. DiMassa and fellow cartoonists such as Jennifer Camper (SubGurlz; Rude Girls and Dangerous Women) tapped into social rage in their comics, with jokes about castration and feminist-lesbian anger abounding. (Camper, a Lebanese American lesbian attentive to Middle Eastern politics, wrote the best review of Persepolis I've read—and in comics form, too.) Their comics were a release. With guns, axes, and grenades, Hothead unapologetically kills men who "manspread" on the subway, who catcall her, who show disregard for her space on the sidewalk. DiMassa's description on her website is apt: "Hothead and her beloved cat, Chicken, have been providing rage therapy for exhausted devotees since 1991. Hothead is fully in touch with your Inner Societal Rage and gleefully carries out the fantasies you would never act on. Would you. Reading Hothead comics is guaranteed to give you a fleeting sense of empowerment while you laugh until you realize it's not funny and start crying."
Diane DiMassa, panels from Hothead Paisan, 1993, reprinted in The Complete Hothead Paisan (San Francisco: Cleis Press), 1999.
Used by permission of Diane DiMassa.
The nineties also saw a turn toward the intimacy of autobiography in addition to generalized social rage. Ariel Schrag's true-life comics charted her coming out while a student at Berkeley High. The enterprising Schrag, A-student and baby dyke, produced a different comic-book series for each year of high school: Awkward, Definition, Potential, and Likewise (Schrag went on to write for The L Word). The result is compellingly personal work that feels like it unfolds in close to real time and is rich with fascinating details of adolescence. It's like a very impressive blog, before blogs existed, and with sweet, earnest drawings of masturbation, sex, and chemistry exams. And Cruse published his graphic novel Stuck Rubber Baby, based loosely on his real-life experiences as a closeted gay man in the South working in the civil rights movement, in 1995.
But no other comics work that touches on queer lives prior to Fun Home—and few other graphic narratives at all, from any time—presents the intimacy, depth of feeling, length, and storytelling rigor that Fun Home does. The first graphic narrative published by Houghton Mifflin, Fun Home won an immediate "crossover" audience, both an audience outside of the comics world and the niche or "cult" (read: gay) audience that was the most fervently devoted fan base of Dykes to Watch Out For. Famed book designer Chip Kidd, also the editor of Pantheon's Graphic Novels imprint, offered a striking endorsement, calling Fun Home "a rare, primal example of why graphic novels have taken over the conversation about American literature." New York Times reviewer Sean Wilsey raved, "If the theoretical value of a picture is still holding steady at a thousand words, then Alison Bechdel's slim yet Proustian graphic memoir, 'Fun Home,' must be the most ingeniously compact, hyper-verbose example of autobiography to have been produced." (And: perhaps slim compared to Proust, but not slim by graphic novel standards at 232 pages.) Modest to a fault, Bechdel confessed to a London newspaper, "It still strikes me as very unlikely that an odd, cerebral story about a lesbian and her closeted gay suicidal mortician father would have struck a chord with anyone but me"—but it did, instantly winning acclaim and hitting the best-seller list, making a splash in a way very few graphic novels since Maus—also a book investigating filial relationships and parental suicide—have done. Fun Home was voted Time magazine's #1 book of the year—in any category. Fun Home showed definitively how comics could be a captivating form for presenting the interior and exterior lives of gay characters over time.
Bechdel spent almost two decades working as a cartoonist before she started a memoir about her father's death; it was a story she had been carefully considering for a long time. "I finally sat down to write the book when I was almost forty, right at that weird midpoint in my life where my father had been dead for the same number of years he'd been alive," Bechdel explained in an interview. She then spent seven years working on the intricately crafted book, which has seven chapters each loosely tied in title and thematics to an author—or in some case, several authors—her father loved, notably James Joyce. Fun Home focuses on a gay daughter's investigation into the life of her closeted gay father, presenting both childhood recollections and adult research into letters, diaries, records, and photographs. Told in a nonlinear fashion, Fun Home gracefully weaves in and out of different times across all of its chapters; its elegant but promiscuous view of time is one of its most striking and moving features (for instance, in the book's suggestion that Bruce Bechdel was, in essence, ceaselessly committing suicide, even as a child, as when he wanders off alone in fields of mud as a toddler and sinks in them, to be rescued by a passerby). Fun Home is what Bechdel names "labyrinthine" instead of having a chronological structure; it repeatedly circles in to central themes and questions. Chief among these is the question of causality: Bechdel sets out to explore what she can about her father's life in order to figure out if her own coming out had anything to do with his suicide. The story is not plot-driven: both of the evidently dramatic events in Fun Home—Alison's coming out and her father's suicide—are revealed early on in the book. Fun Home is rather a drama of archival discovery and interpretation, as Bechdel searches for and discovers evidence about her father's life as a gay man.
The seed for the book was the discovery, shortly after her father died, of a photograph that Bechdel reproduces as a drawing in Fun Home. After college, organizing her belongings in the family house, Bechdel found a photograph of her former babysitter, Roy, lying on a hotel bed in only his underwear. The photo was taken the summer Bechdel was eight, during a trip Roy, Bruce, and the three Bechdel kids took to the Jersey shore. The photo, which she found at once aesthetically beautiful and shocking, Bechdel told me, "was a stunning glimpse into my father's hidden life, this life that was apparently running parallel to our regular everyday existence." In the hotel where Roy posed on the bed, Alison and her brothers had slept in the adjoining room. The negative strip that includes the picture of Roy, who was then seventeen, is preceded by three of Bruce's snaps of his kids on the beach.
Curiously unconcealed evidence of her father's secret life—it was sitting in an envelope marked "Family"—the photograph of Roy lingered in Bechdel's mind. Finding the photograph, she identified with her father as gay person—she told me, "I felt this posthumous bond with him"—at the same time that she realized the betrayal it represented: to the underage babysitter, and to her mother, in addition to Bruce's unsuspecting kids. Bechdel's drawing of the photo is her book's one and only double-spread, and the space it takes up underlines its key role in shaping the premise of Fun Home.
Bechdel draws the photograph bisected by the seam of the page, with her left hand holding it out in front of her. She places readers in the position of her optical point of view, but she draws her hands much larger than life-size, calling conspicuous attention to the scene of looking and to the photograph as a handled artifact—not a simply transparent window into reality. In Fun Home, Bechdel uses two different visual representational styles: one that is heavily crosshatched, which is used for drawing the tone of photographs, and codes as realistic, and one that has crisper black line art and simpler shading, which anchors the world of the book. Fun Home also employs color: there is a gray-green ink wash throughout that Bechdel has described as "elegiac." The drawing of the Roy photograph, which arrives roughly halfway through the book, is "literally the core of the book," Bechdel told me, its own "centerfold."
On the previous page, an adolescent Alison and her father, in a rare moment of alignment, together admire a fashion centerfold in Esquire; Bechdel narrates that their "shared reverence for masculine beauty" was a "slender demilitarized zone" that lay between them. But the page about Roy's photograph, crucially, is about the concomitant identification and disidentification Bechdel feels toward her father. The comics page in Bechdel's hands registers this paradox. While she meticulously reproduces the details of the once-hidden photograph, a kind of dutiful tribute to and inhabitation of her father's illicit desire, she also overlays eight distinct text boxes, full of her own words, over the photograph. The placement of the irregular boxes—each of these boxes is a different size—over the drawing of the standard-size photograph reflects both Bechdel's confusion and also her own medium's disruption, with the overlaid layers of meaning offered by comics, of her father's perfectly framed, wordless moment.
Alison Bechdel, the only double-spread in Fun Home: A Family Tragicomic (New York: Houghton Mifflin), 2006: Alison looking at a photograph of Roy taken by her father.
© 2006 Alison Bechdel. Reprinted by permission of Houghton Mifflin Harcourt Publishing Company. All rights reserved.
When they lived together in the family home, Bruce and Alison were what the narrator calls "inverts, and inversions" of one another, often butting heads over deeply felt, identity-driven aesthetic choices. One amusing page presents these contrasts, and clashes, in four emblematic scenes: Alison was "Spartan to my father's Athenian. Modern to his Victorian. Butch to his nelly. Utilitarian to his aesthete." As a child, and a teenager, Alison didn't consciously realize that her father might be gay, but as Bechdel confesses in Fun Home, above a drawing herself as a small child staring at her father getting ready for church by applying a "bronzing stick" to his face: "My father began to seem morally suspect to me long before I knew that he actually had a dark secret."
Alison knew her father was a "sissy" and felt that he represented "a chink in my family's armor, an undefended gap in the circle of our wagons"—which underscored her own attraction to the butch. Her mother reveals the actual dark secret privately when Alison comes out; Bechdel draws her young self's shock and surprise, lying stupefied on the floor of her dorm room—"Dad? With other men?" But Alison did realize that her father had something to hide, and that it drove his obsession with perfect surfaces. She grew to loathe the embellishments and ornament of the family home as "lies." Above a drawing of Bruce Bechdel taking a carefully posed photograph of his wife and children on the porch ("Mass will be over," her mother pleads), Bechdel declares, "He used his skillful artifice not to make things, but to make things appear what they were not." Her father, she notes in the book, treated his children like furniture and his furniture like children. And he had a violent temper toward everyone in his family. "In my earliest memories," Bechdel writes in Fun Home, "Dad is a lowering, malevolent presence." Physical affection was scarce in the Bechdel household. Bechdel draws the two times she literally ever saw her parents express physical affection, which astonished her. Her mother abruptly stopped kissing her goodnight when she was seven. And she rarely, if ever, touched or was touched by her father with any loving intention. One heartbreaking scene in Fun Home shows her as a small child "unaccountably moved" to kiss her father goodnight, and awkwardly kissing his hand before fleeing his bedroom in embarrassment.
Alison Bechdel, page from Fun Home.
© 2006 Alison Bechdel. Reprinted by permission of Houghton Mifflin Harcourt Publishing Company. All rights reserved.
But Alison and her father—both "inverts" (an outdated nineteenth-century term for homosexuals) and inversions of each other, as she points out—are disidentified and identified with each other throughout Fun Home, giving the book its tricky edge. "I was trying to compensate for something unmanly in him," Bechdel writes above an image of them looking in the mirror together, while "he was attempting to express something feminine in me." At five, while at a diner with her father, Alison sees a brand new sight, one that sustains her for years: a "truck-driving bulldyke" in whom she recognizes a kindred spirit "with a surge of joy." In a scene that brilliantly exploits the silent narrative of changing facial expressions, her father turns to his small daughter, who hasn't spoken a word, and, knowing, says derisively, "Is that what you want to look like?" She knows she is supposed to say no, and he knows the answer is probably yes. In the coming years, Bruce and Alison share some fleeting moments of alignment and connection—almost entirely over literature and intellectual life. In their most affirmative exchange in the entire book, they spontaneously compliment each other in the car on the way home from school—for Alison has wound up in her father's high school English class, and actually likes it. "You're the only one in that class worth teaching," Bruce tells her as she drives home, in a panel that takes up the entire bottom tier of a page and frames the car perfectly within its borders. "It's the only class I have worth taking," Alison responds. They begin to see each other as intellectual companions, sharing books and ideas about them. In a move that feels momentous, because it seems to Alison like it could be an acknowledgment of her sexuality, Bruce gives her a copy of Colette's Earthly Paradise.
Alison Bechdel, page from Fun Home.
© 2006 Alison Bechdel. Reprinted by permission of Houghton Mifflin Harcourt Publishing Company. All rights reserved.
But it is harder to forge an explicit connection around being gay. On her first vacation home from college after she has come out to her family—and after her mother has confided in her about her father sleeping with men and boys—Alison tries desperately to connect with Bruce around their mutual queer sexuality. When the two of them venture out together for a screening of Coal Miner's Daughter, Alison forces herself to try to discuss it with him in the car. Before her trip home, Bruce had written Alison letters full of tantalizing enigmatic statements reflecting on his choices ("There was not much in the Village then that I hadn't known in Beech Creek"). Bechdel, narrating, puts it this way, over her drawing of the letter: "He thought that I thought that he was a queer. Whereas he knew that I knew that he knew that I was too." The scene of shared but silent acknowledgment is emblematic of the whole book: it is not a triumphant confirmation of common experience, and offering of support. Instead, while Bruce haltingly acknowledges, "I guess there was some kind of . . . identification" when Alison asks if he chose Colette for her knowingly, Bruce resists the affirmation of common experience she's driving at.
Alison Bechdel, page from Fun Home.
© 2006 Alison Bechdel. Reprinted by permission of Houghton Mifflin Harcourt Publishing Company. All rights reserved.
The car exchange—the one time father and daughter ever discussed what Bechdel describes to readers as "our shared predilection"—is visually striking because it is the only set of pages, aside from the double-spread pages featuring the Roy photograph, that functions as a unit of two. But unlike the pages that present the Roy photograph to readers and are overlaid with Bechdel's irregular frames, these pages are the most strikingly regularized in the entire book: mirroring each other, each offers twelve same-size frames—what Ivan Brunetti has called a "democratic" grid, in which the panels are the same size and produce even beats of time. Bechdel divides this crucial conversation—the first time Bruce talks openly to Alison about his sexuality—into many separate frames, and moments, letting the weight of the silences sink in. Many panels offer a beat of silence—most notably the last six that close out the exchange, in which no dialogue happens at all, and Bruce leaves his daughter hanging. The dialogue ends with Alison, looking animated, trying to connect: "I dressed in boys' clothes . . . remember?"
Bruce never responds, and readers encounter the six beats of silence on the page. And while the perspective of each panel is the same, showing Alison and Bruce together in a small space, each panel yet underlines the stark division between father and daughter: graphically, they are each aligned with a separate car window, and a black bar of sorts lies between them. In this final chapter of the book, although Bruce admits "some kind of identification," the graphic features of the page help us to realize how tenuous and unfulfilling this conversation is for his young daughter so eager to confirm something she shares with her father. After the movie, their attempts at queer connection are again thwarted: they go to a local gay bar, where they are turned away because Alison is underage. The final panel of the episode, in which the pair drive home, is a mirror image of the panel in which father and daughter compliment each other after class, only this time, as Bechdel writes, "we drove home in mortified silence."
Despite or because of the gap between father and daughter, Fun Home is immersed in verbal and visual languages of touching. Fun Home's comics form is central to what it suggests about the relationship between Alison and her father, and how the adult artist carries that relationship forward in her life. Bechdel often describes comics as a form of touch, explaining that drawing a person for her can be like touching that person. The paper is like skin, she has pointed out. "It's a figurative stroke, because obviously the only thing I'm really making contact with is the pen and paper, but that contact—of the nib and the ink on the paper—is very literal and sensual." In Fun Home—and in the later Are You My Mother?—touch is also an explicit theme of the book: if as a child Bechdel felt cut off from touch, and was further, irrevocably cut off from her father because of his early death, drawing images of her father is a way to touch him and reencounter him, to be close to him.
And comics is not only a way to intimately touch the subjects, even and especially the dead subjects, on whom Bechdel's work centers—to "lay hands" on them through drawing, as Fun Home's own language suggests—but it is also a way to mark her own body onto the page. Bechdel's redrawing of family archives for her comics page—all the maps, letters, diaries, records, and photographs that she carefully reproduces in her own hand, instead of scanning—is a way for Bechdel to place her body back into the past histories and narratives for which her role is unclear, to make herself present in her parents' lives. Bechdel also poses her own body in digital reference photographs that she uses to draw her comics. Regardless of who the character is, Bechdel poses as that person for the reference shot, creating both her own shadow archive of her family's past, and inhabiting her parents in a form of acting. The really interesting thing, she said once, explaining her process, "is when I have to act out my parents having a fight and I have to be both of them."
Fun Home strikes a note distinct from the celebration or the anger we see in many gay comics. It is about the process of reading and looking—at the past, including queer histories of earlier generations. It is about the question of how we feel we can know the things that we know. It is a portrait of a relationship that is rife with contradiction: Bechdel's father, as cruel and petty as he was, was both a disabling and an enabling force for his daughter, who became the artist—as Fun Home, the book about him, proves—he always wanted to be, because of him and in spite of him. Bechdel offers a complex portrait of her family in comics that is unlike her father's practice of photography, in which he composes a scene, captures what looks perfect, and freezes it in time. Rather, the cross-generational queer comics story, meditating on the different possibilities afforded father and daughter, shows readers two intertwined gay lives that are contradictory, ambiguous, and inconclusive, even in death. Comics represents the fullness of this complexity, even as it preserves the gaps and elisions in Bechdel's knowledge and in her relationship with her father. "If language was unreliable, and appearances were deceiving," Bechdel mused in a talk about comics, "then maybe by triangulating between them, you could manage to get a little closer to the truth."
In Bechdel's graphic memoir, we see the combination of technical expertise and rigor in the service of "queer stuff" that the cartoonist so admired in Howard Cruse's work. But instead of bringing her talent into the subculture, with Fun Home Bechdel brought her talent—and a compelling portrait of a queer life—into the mainstream, without sacrificing any of the richness that made her earlier work so beloved. It wasn't a case of Bechdel conforming to the mainstream; it was a case of Bechdel reinventing the mainstream, demonstrating how comics can map untraditional lives (her own and her father's) with unusual sophistication and sensitivity that inheres in the frames and gutterspaces of comics, along with the intimate, caressing touch of ink.
Fun Home further reinvented the mainstream when an adaptation of the graphic memoir became a Broadway musical in 2015 (it opened off-Broadway at New York City's Public Theater in 2013). Fun Home the musical seems a very unlikely project, for several reasons. From a Broadway standpoint, the topic, perhaps, seems grim (not only suicide, but suicide of a mortician) and unsexy (rural butch lesbian, as opposed to the urban gay men who have historically been the queer characters in Broadway shows). "Is America Ready for a Musical About a Butch Lesbian?" a Slate headline reasonably wondered. And then there's the question of translating comics to theater. Comics, as Art Spiegelman puts it, "[lets] you read in the quiet theater of your mind"—through its interplay of presence and absence, image and word on the page. How was a musical going to replicate the effects of comics—for instance, the intimacy of handwriting—that feel so key to grasping the paradoxes of the Bechdel household? Bechdel likes to joke in public that the reason she said yes to a musical is because she thought nobody would ever see it. I remember discussing adaptation with her when she first told me about her choice to allow the Fun Home musical to happen. Bechdel had also received offers from film producers and directors. Her choice to go with a musical instead, she told me, was because theater lacks the verisimilitude of film; musical theater was just so weird that it might be able to translate a comics story, with all of its intricacies and abstractions, best.
Written by Lisa Kron with music by Jeanine Tesori, and directed by Sam Gold, the Fun Home musical does replicate many of comics's most interesting formal possibilities. (Bechdel was closely involved as an adviser but had no formal role in the production.) Fun Home deploys three separate actresses to play Alison during three different periods of her life—child, college student, and adult cartoonist—and at some key moments, it intertwines distinct time periods by having them walk into spaces of the past, or future, collapsing time in the way that comics does so noticeably. And the musical shows itself to be brilliantly attentive to the importance of the silent visual details of the book. One of the high points of the musical is the song "Ring of Keys," performed by the child Alison, based on a tiny visual detail in the book's diner scene that goes verbally unremarked in the book itself: the ring of keys worn by the butch truck driver in the diner whom Alison stares at adoringly. Fun Home won five Tony Awards in 2015. Kron and Tesori became the first all-female writing team to win a Tony in the Best Score category; the production took home the Best Musical Tony and dragged Bechdel on stage. In a touching photo from the event, the shy Bechdel, wearing a formal suit and Bruce Bechdel's cufflinks, flanked by women in evening gowns, looks like she can't believe what just happened. (She will soon make a cameo on a forthcoming Simpsons episode in which Lisa and Marge write a collaborative graphic novel called "Sad Girl" that gets turned into a Broadway musical by an avant-garde director . . . )
Alison Bechdel, center, onstage at the Tony Awards after Fun Home wins Best Musical, June 2015.
Photograph by Theo Wargo/Getty. Used by permission.
The massive success of Fun Home first as a graphic novel, and then as the inspiration of a celebrated musical, has galvanized queer comics—if not directly, then simply in widening the sense of possibility for queer representation in all sorts of different spaces. There are now countless comics about queer life, in print and online. A very, very short list includes A.K. Summers's memoir Pregnant Butch, in which she draws herself as a pregnant Tintin; Diane Obomsawin's On Loving Women, vignettes about coming out drawn with elegantly simple animals; Elisha Lim's 100 Butches (for which Bechdel wrote the introduction) and 100 Crushes; Ed Luce's Wuvable Oaf, a love letter to the bear scene of San Francisco; Jaime Cortez's Sexile, about Adela Vázqez, an activist transgender Cuban immigrant; Nicole Georges's Calling Dr. Laura, also a filial mystery; Julie Maroh's Blue Is the Warmest Color (translated from the French and the inspiration for the 2013 film); Noelle Stevenson, Grace Ellis, Brooke Allen, and Shannon Watters's Lumberjanes, for kids and adults alike, described by afterellen.com as "for the little queer Girl Scout in your heart"; Kelly Sue DeConnick and Valentine de Landro's sci-fi prison comic book Bitch Planet; Brian K. Vaughan and Fiona Staples's Saga, which features a queer ghost; Maggie Thrash's memoir Honor Girl, about falling for another girl at camp; Beldan Sezen's Snapshots of a Girl, about the queer daughter of Turkish immigrants; Emil Ferris's My Favorite Thing Is Monsters, which stars a gay ten-year-old girl in 1960s Chicago; Edie Fake's Gaylord Phoenix and Memory Palaces, an architectural look at Chicago's queer history; Kieron Gillen and Jamie McKelvie's The Wicked + The Divine, a popular fantasy comic book peopled with a large cast of queer characters, including a trans woman; and Dylan Edwards's Transposes, true stories about female-to-male queer-identified trans people. In a fascinating foreword to Edwards's book, Bechdel makes a compelling point: comics storytelling, which can be purely visual when it wants to be, can circumvent the problem of language—that is, what pronoun to use—when referring to a person's pretransition past. We see the female-bodied children in Transposes who become male-bodied adults without the burden that language can sometimes be felt to provide.
A.K. Summers, page from Pregnant Butch (Berkeley: Soft Skull Press), 2013.
Used by permission of A.K. Summers/Soft Skull. Image courtesy A. K. Summers.
Queer characters and themes are happening now with new force in mainstream comics, too. In 2010 Archie Comics, for instance, a commercial staple that has been around since 1939, introduced its first gay character, Kevin Keller. In his first appearance in the ongoing storyline, Veronica wants to date him but he is uninterested. He eventually marries a man and becomes a senator. The first issue in which Kevin appeared was so popular it sold out, and the company reprinted an issue for the first time in their history. And transgender characters are notably starting to make it to mainstream comics too. In 2015, Marvel introduced the transgender character Sera in the superhero title Angela: Asgard's Assassin. Angela is Thor and Loki's long-lost sister—and Sera is her traveling companion. And there are many more transgender superheroes steadily appearing, alongside openly gay ones—the DC character Midnighter was recently even shown using Grindr. In 2016, after all these years—especially since Wertham put her sexuality on trial in the 1950s—Wonder Woman was revealed to be queer. The news was confirmed by Wonder Woman writer Greg Rucka and received with an outpouring of enthusiasm. The following month, the character—certainly a first—was named an honorary ambassador "for the empowerment of women and girls" by the United Nations. After the character assumed the role for several months, the UN rescinded her ambassadorship over objections she wasn't a suitable role model. Whatever one may think about the real-life diplomatic appointment of a fictional entity, the public debate around this comics character proves that her relevance—and her queer relevance—not only persists but has grown.
---
[CODA:
WHY FANS?](Contents.xhtml#con11)
I attended the San Diego Comic-Con International, North America's largest fan convention, known simply as Comic-Con, for the first time in 2011 to deliver a talk on an experimental dance performance inspired by comics (!). It was attended by, among others, an unselfconscious man in full superhero regalia, including tights and a cape. He nodded energetically throughout, raised his hand to ask questions, and spoke to me afterward—a professor himself, I discovered. Not a word was exchanged about the fact that he was attired in full costume. Earlier that morning I had noticed another man in the café where I was working stand in line and order a latte through the grate of the helmet of his full-body, metal suit of armor. He clanked in and clanked out in the heavy plate armor, and the barista didn't bat an eyelash.
Today fans of comics are professors and poets and gallerists and curators and artists and students and nerds and cosplayers—and combinations of these, like the professor in cape and full costume. The practice of cosplay, a combination of "costume" and "play," was first popularized in Japan; increasingly widespread in the United States, it is used as a verb and a noun, like "Google." (Overheard sentences at Comic-Con, from the same mouth: "Don't cosplay in Baltimore"; "I try to fly with cosplay as infrequently as I can.") Highly recommended: cartoonist Dash Shaw's 2016 graphic novel Cosplayers, a sweet take on a friendship between two young filmmakers that develops out of cosplay admiration at a convention.
The author talking to another professor after a presentation, San Diego Comic-Con, 2011.
Used by permission of Amy Squires. Photograph courtesy Amy Squires.
I taught the Harvard English Department's first dedicated course on comics and graphic novels in the spring of 2016. I lectured on the history of the graphic novel to fifty or so students who were majors in English, architecture, government, art history, anthropology, animation, sociology, math, biology, and chemistry, among others. That the university that is arguably the most famous in the world wanted to run this course, along with the multiplicity of interests among the students involved, signals the expanding readerships for comics. In the summer of 2016, as a specialist in comics, I spoke at the Illinois Holocaust Museum on the occasion of an exhibit of a stitched cartoon booklet made by a young female prisoner in the Gurs concentration camp in southern France in 1941. Created as a sixty-fifth birthday gift for a barracks mate, it is titled How It Is, But How It Should Be, referring to life in and outside of the camp. I contextualized the booklet as part of a trajectory of artwork that includes graphic narratives of witness such as Maus. The next morning, I boarded a plane to San Diego for my second Comic-Con in that city, five years after my first, arrived at the teeming Convention Center, and was promptly handed a "Professional" 's badge emblazoned with a Walking Dead advertisement along with an enormous plastic backpack featuring the soaring (obviously) DC Comics character Supergirl. Comic-Con ran from Thursday, July 21, to Sunday, July 24; for three days, without even noticing what was printed on it, I wore a black lanyard splattered with red blotches that proclaimed, "FEAR THE WALKING DEAD."
I joked to people who asked me about this week of my summer that experiencing these two very different venues back-to-back produced a kind of cognitive dissonance. But this range represents something true about the very wide world of comics. The day after I returned from Comic-Con, and finished reporting on the convention for the international art bible Artforum, a calendar sent by a Holocaust survivor I met at the Illinois museum event arrived in the mail. Each month of this amazing document features a condensed, one-page comics version of a person's story—including his—of surviving the war, drawn by a different artist. All of this is to say: comics is today a form that appeals both to a solemn institution for commemoration and knowledge like the Illinois Holocaust Museum, and to a wide range of fans at the giddy celebration of popular culture that is Comic-Con. The institutions and the people fascinated by comics run the gamut, and this group is now more diverse—and enthusiastic—than ever before. Even at a famous annual gathering dedicated to what we might think of as the field's most ardent and committed fans, this diversity is clear. I went to Comic-Con, one of the world's bastions for aficionados of comics (and one of the few places, I'm happy to report, that I get recognized by strangers), to take the temperature of the field.
It has become a cliché to say that Comic-Con isn't about comics anymore. One of the biggest fan conventions in the world, it started small, and it certainly started with comics: it was founded in 1970 as San Diego's Golden State Comic-Con by three San Diego comics professionals, Shel Dorf, Ken Krueger, and Richard Alf, for roughly three hundred attendees. Comics artist Jack Kirby and science fiction writer Ray Bradbury were among the featured guests at the first convention. Over the years, and especially after it moved from a local hotel to the enormous, airy San Diego Convention Center on the water, Comic-Con came to also feature, increasingly, a large swath of the entertainment industry: television, movies, and video games related to superheroes and to fantasy genres (this past year, for instance, anything and everything Game of Thrones had a huge presence in the convention hall). And also the stuff of popular culture: toys, costumes, and other novelty items. These days, people queue up outside the famous Hall H, the Convention Center's biggest space, which seats 6,500, to see premieres and teasers, along with A-list actors; the studios create buzz at Comic-Con for forthcoming movie releases and television seasons. The stylish young man I sat next to on the plane to San Diego, who was reading a comic-book adaptation of a George R. R. Martin Game of Thrones novel, explained to me that part of the draw of Comic-Con is viewing such "exclusives" at the convention ahead of the general population. He also noted that the huge popularity of superhero movies, especially in the past ten years—say, the Avengers or Dark Knight movies—has made comics even more acceptable in mainstream culture in general. (Marvel's The Avengers, released in 2012 with a screenplay by Joss Whedon, is the highest-grossing superhero movie of all time, taking in well over $1.5 billion globally at the box office.) Economically, it seems to work to everybody's benefit: the big comics companies like Marvel and DC make tons of money off of superhero movies whose storylines are mined from the comics, and often popularize the source material; that money then supports the actual comic books and creation of content.
Despite the cliché, Comic-Con is absolutely still about the comics—it's just about a lot of other stuff too. Daniel Clowes, the cartoonist responsible for a dark take on superheroes (The Death-Ray) and superb observations on teenage girl friendship (Ghost World) told me during a break from signing his graphic novel Patience that "it's all just grown." Clowes, who first met the Hernandez brothers—who were also there signing books in 2016—at a Comic-Con decades ago, explained, "I feel like we have a much bigger audience than we used to but so do everybody else." Clowes continued, "It would literally be impossible to know about every comic coming out, even in a given two weeks." As I cut through the teeming crowd on my first day in an effort to locate Clowes signing at the publisher Fantagraphics's table on the convention floor, I encountered an enormous snaking line, which I later found out was for cartoonist Jim Davis, the creator of Garfield. It is, along with Charles Schulz's Peanuts (1950–2000), the world's most syndicated strip, with 230 million daily readers; it has been translated into 40 languages and appears in 111 countries. An impressively wide range of comics—from globally iconic strips like Garfield to the novelistic literary fare served up by Fantagraphics—shares space at Comic-Con.
The fan culture of Comic-Con has amplified across the board. Its inclusivity is inspiring, as is the sheer range of work and practices it encompasses, on vastly different scales, from the corporate to the individual. On the convention floor, toy giants like Mattel, Sanrio (Hello Kitty), and Hasbro stake out major space. Hasbro manufactures the My Little Pony universe of children's toys, and in 2011 one of the sights that awed me most was an enormous pink plastic pony, which seemed to practically reach the ceiling of the convention floor—it was many, many lengths taller than me. (Recently the adult male fans of My Little Pony, bronies, have garnered a great deal of fascinated attention, including two documentaries.) Yet on the first day I arrived at the 2016 Comic-Con, among all the corporate exhibits and larger-than-life promotion, I also encountered a woman selling beautiful, tiny, handmade felt gerbils and cats. Comic-Con is a platform for both mainstream culture and independent culture, all inclusively mixed in together. In that way, it represents the hard-to-pin-down world of comics perfectly—a universe of cultural production that is wildly variegated, yet invested in being accessible to readers, and celebrated by fans. Its profound nonjudgmental openness is its most salient feature, and the most salient feature of similar fan conventions. As Holly Rae Taylor, the painter and glass artist who is married to Alison Bechdel, described Comic-Con emphatically to me: "It's permission."
Kate Beaton's comic strip take on Hamlet, from Hark! A Vagrant (Montreal: Drawn & Quarterly), 2011. Her comic strip appears at www.harkavagrant.com.
Used by permission of Kate Beaton. Image courtesy Kate Beaton.
The Simpsons's Matt Groening, the cartoonist who vowed in the 1970s to invade pop culture, and succeeded wildly, perfectly represents the ethos of Comic-Con 2016. To my surprise (but I obviously shouldn't have been surprised), Groening participated on Friday morning in a bare-bones panel about obscure art comics called "Kramer's Ergot and the Art of the Comic Anthology," whose title refers to the series published by indie publisher Fantagraphics, before he sat in an enormous ballroom for four thousand people on Saturday for a panel simply titled "The Simpsons." The show has aired well over six hundred episodes. "The Simpsons" was held in Ballroom 20, which has its own Twitter account as "The second most demoralizing line at SDCC, rival of @HallHLine. Pucker up." The line to get into the panel was so long and loopy it snaked out the building, and just to find the end of it was literally an adventure (and one involving exercise). Groening was joined by designers, writers, and producers, along with Nancy Cartwright, the voice of Bart Simpson (a chic blonde in a top with cut-out shoulders, she broke into Bart's voice often, and even told the crowd, referring to herself, "Bart's going to be a grandma!"). Groening sat at one end of a long table, which was projected on four enormous screens, dispensing prizes for every questioner, such as idiosyncratic Simpsons figurines of James Brown and skateboarder Tony Hawk. Groening's participation in these two profoundly different panels, in both size and focus, indicates the possibilities of a gathering like Comic-Con, where the scale of events ranges wildly from the little to the massive. Comic-Con presents a democracy of forms and types of media: it's an event in which one can revel in noncommercial, auteurist comics at the same time as in the vast popularity of enterprises like the Simpsons and the commercial comic-book giants like Marvel and DC.
Comic-Con's Eisner Awards—the Oscars of the comic industry, named after pioneering cartoonist Will Eisner (1917–2005)—strongly signaled in 2016 how the field of comics is currently opening itself up to honor both independent and commercial work, and work by creators who haven't always been well-represented in a field that historically has been white and male. Aside from—appropriately—inducting college buddies Matt Groening and Lynda Barry into the Hall of Fame, the Eisners in 2016 boasted a record number of nominations for women. In contrast, the global comics community's other most famous international comics convention, France's Angoulême International Comics Festival, whose attendees top two hundred thousand annually, nominated not a single woman the same year for its Grand Prix, for which thirty male cartoonists were shortlisted. Charles Burns, Chris Ware, Riad Sattouf, and Daniel Clowes, among other nominees, withdrew their names from consideration (Clowes called it a "ridiculous, embarrassing debacle"). And, more important, many women were not only nominated but also actually won in San Diego, including Kate Beaton, who became the first woman ever to win in the Best Humor Publication category for her collection of strips, initially published online, called Step Aside, Pops (Beaton joked on stage, it must be, you know, that women just aren't funny!).
John Lewis, Andrew Aydin, and Nate Powell, page from March: Book One (Marietta, GA: Top Shelf Productions), 2013.
Copyright © John Lewis and Andrew Aydin. Reprinted by permission of Top Shelf Productions/IDW Publishing. Image courtesy Top Shelf.
And perhaps the most surprising part of the Eisners: I never expected to meet civil rights icon and Georgia representative John Lewis, and to meet the former president and publisher of DC Comics, Paul Levitz, in the same evening. Yet there I was, shaking Lewis's hand in the wings off the awards stage after March: Book Two, the second installment of his autobiography in comics form—which he wrote with congressional aide Andrew Aydin and which is illustrated by Nate Powell—won the Eisner for Best Reality-Based Work, beating out Riad Sattouf's The Arab of the Future, among other highly acclaimed titles. Everyone in the audience seemed awed by Lewis's presence, and he seemed truly excited to be there (and to win!). Watching Lewis speak on television only a few days after the San Diego Comic-Con at the Democratic National Convention in Philadelphia, I marveled at the distinct spaces, and different kinds of creators and fans that comics is connected to in the twenty-first century: distinguished political leaders as well as "comic book heads" (to use a phrase of the rapper Murs, a participant on the panel "We Are All Heroes: A Conversation on the Changing Landscape of Geekdom and Fan Culture").
Comic-Con presents a vibrant, inclusive cultural mash-up, a democracy of forms and genres that openly mix under the wide umbrella of the comics universe. The Eisners, celebrating the industry's comics stars, underlined this. While generally people associate Comic-Con with the display of superhero products (and costumes), at the Eisners independent comics publishers conspicuously won the most awards. Seattle's Fantagraphics and Montreal's Drawn & Quarterly, the two most famous comics publishers dedicated to the auteur model—in which one person both writes and draws the comics—cleaned up, with Fantagraphics publisher Gary Groth, and Drawn & Quarterly publisher Peggy Burns ascending the stage many times. Seeing Burns, a rare female publisher, on stage so many times was inspiring; Drawn & Quarterly, known as a feminist workplace, employs twenty women and three men. (At the ceremony, I sat at the Drawn & Quarterly table, along with Groening, Barry, Beaton, and others, as a participant in two of their convention panels.)
The other big winner of the night was Image Comics, the publisher best known right now, perhaps, for the Walking Dead comics, the source for the phenomenally popular television show, and for the hugely popular Saga, which is narrated by a woman looking back on the plight of her interracial-intergalactic parents during the time when she was an infant. (Cooper, my friend from the plane, summed up Saga aptly: "Alice in Wonderland meets Star Wars on acid.") Image as a company is not auteurist in the same way that both Fantagraphics and Drawn & Quarterly are, in which most of the work, like most of the comics covered here, is the result of the artistic vision of one person. Teams of people, even if sometimes just two, a writer and an artist, generally produce the work at Image. Yet the Portland, Oregon–based Image, created in 1992, was founded specifically as a company that would produce "creator-owned properties"—that is, comics for which the artists would not have to give up copyright to characters.
That copyright is even still an issue to be debated today shows how fractured the wide world of comics is—a fracture that an enormous umbrella event like Comic-Con, with the huge presence of commercial companies like Marvel and DC, can't help but underscore. Comics is a form that has always existed at the boundary of art and commerce. The history of the work-for-hire model in the mainstream comics industry, in which artists are paid but not credited for their work on a story or series, or don't own the rights to the work they produce (for example, on a character owned by a company), is the exact opposite of the auteur model. At the Eisners, Elliot S! Maggin, who was the main writer for DC during the 1970s and '80s, received the Bill Finger Award for Excellence in Comics Writing, named after an "unsung" writer of the earliest Batman comics. Maggin—whose middle initial, in one of many great stories about comics culture, became linked to this piece of exclamatory punctuation when inkers for comics stories mistakenly turned the period after "S" into an exclamation point while inking the credits—delivered a rousing superhero-inflected speech that ended with the pronouncement: "The bad guy's name is work-for-hire." Mission: "Creator credits where appropriate."
Clearly lots of people agree. In Ballroom 20, at the Simpsons panel, someone asked Groening, "Why is your signature on all Simpsons merchandise?" After joking, "I had a really good lawyer," and noting "Charles Schulz has the same kind of deal," Groening simply said, credibly, that creator anonymity is "kind of mean." The presence of these issues at Comic-Con reminds one how recently comics has emerged as an artistic enterprise to be taken seriously, and demonstrates how wide the spectrum of comics production is. But independent comics, auteurist or collaborative, certainly were heavily celebrated in 2016. "We thank you for widening the comics canon beyond dudes and superheroes and North America," said Burns on stage, accepting the award for Finnish cartoonist Tove Jansson's induction into the Hall of Fame. Later on, accepting the Best Anthology award for Drawn & Quarterly 25, a book about the history of the company, Burns said, "We believe in David over Goliath." Image Comics artists in their own speeches afterward emphasized, explicitly, in turn, the weirdness that Image, another big winner of the night, encourages—they underlined that Drawn & Quarterly is not the only David. Clearly, independent comics of all sorts are on the rise right now as the entire field opens itself up to a wider range of content, format, and genres (and genre mash-ups) than it has ever had before.
If all of this seems fractured, or the world of comics production seems almost incoherently diverse, the large range of practices—and the discussion about them—shows that comics as a form is blooming, across the board. Even at monstrously big events sponsored by Marvel or DC, the most mainstream corporate industry leaders, one sensed new directions. At the galvanizing "Women of Marvel" panel on Sunday (in another packed ballroom with a laughter-inducing long line), the audience, full of all genders and all ages, cheered enthusiastically throughout; the energy was palpable. Moderator Judy Stephens, the energetic Marvel producer whose half-shaved head was topped with a hot-pink Mohawk, shared a table with Ms. Marvel writer G. Willow Wilson, a convert to Islam who wore her usual headscarf. Stephens announced: "This is a power year for the women of Marvel." She reminded the audience that in 2016 Marvel had twenty female-led comic-book titles, including Ms. Marvel (which kick-started the trend), about a superpowered Pakistani-American girl in New Jersey, and Moon Girl and Devil Dinosaur, whose protagonist is the smartest person in the entire Marvel universe (whatever that means!). A mere six years ago Marvel had zero female-led titles. The crowd spontaneously applauded throughout. At the "Women of Marvel" panel it was also announced that professor and writer Roxane Gay, author of Bad Feminist, would be writing the Black Panther spinoff comic book Black Panther: World of Wakanda, with acclaimed poet Yona Harvey—both black women.
Over the convention weekend, race and gender emerged as central themes. If in 2015 New York Times critic A. O. Scott dubbed Comic-Con "The Year of the Woman," Comic-Con 2016 continued that trend—and with a focus, too, on girl nerds and, specifically, black girl nerds. I learned about websites like Black Girl Nerds (and got to hear founder Jamie Broadnax speak on the excellent "We Are All Heroes" panel), Black Girls Code, Nerds of Color, and Black Gamers. On the all-female panel "Secret Origins of Good Readers," comics writer Anina Bennett told the audience, "You used to not even see women when you walked around at Comic-Con," deadpanning, "There was never a line for the women's room. Never." Yet, as fellow panelist Marjorie Liu, the writer behind the popular Monstress series, pointed out, when she became a hardcore fan of comics as a teenager and created her own fan website, "women were the driving force" in the comics fan community online—"women were writing most of the fan fiction."
Throughout the convention, there was lots of publicly stated love for "nerds" and "geeks" in general—an adorable, booming pride, like the entire enormous convention center that holds hundreds of thousands of people is today one big safe space for creativity under the banner of geekiness, coming from any person of any age. Murs, a panelist on "We Are All Heroes," in which the merits of certain black superheroes, and the concept of the superhero in general were debated, noted that he struggled as a kid—"As a black geek, you already have a lot of hate." The ultrawhite (although alien!) original superhero Superman, he explained, "has been pounded into the psyche of the entire world." At Comic-Con, one of the most popular T-shirts simply read, "Black Heroes Matter." (Another notable T-shirt included a popular baby tee: "My cape is in the wash.") One saw this in the programming—both about the nature of Comic-Con fandom (a true sign a field is becoming a field is self-reflective programming!), and programming that is indubitably (and adorably) geeky because it is so esoteric. Note the following description for a Star Wars–related panel: "The members of Haran'galaar (San Diego chapter) and Manda'galaar (Los Angeles chapter) discuss the process of building Mandalorian armor, the application process, what happens after you're approved, and why exactly they troop." Crucially, like so much else at Comic-Con, this panel is about building community—literally and figuratively—through sharing information about making.
Graphic by Jason Wilkinson–TITAN Cosplay.
Used by permission. Image courtesy Jason Wilkinson.
The convention's passionate creativity and inclusivity is evident in cosplay, which is now one of its most famous features—the one thing someone who hasn't been might know about the convention. At first it's conspicuous, and one can't help noticing and cataloguing the characters, as I did at first: "Oh, there's Barbie, in the box"; "Oh, there's Jon Snow with his little white wolfpup"; "Oh, there's Hellboy eating a sandwich," "Oh, there's the lady monster from Saga with all the eyes" (the Stalk). But after a while it becomes normal; so many people are dressed up throughout the entire convention, doing everyday things, just in costume. Aside from certain superheroes, cosplay isn't directly related to any specific work in this book, but what it stands for, which is the craft and labor of making your own culture on your own terms, is of a piece with the ethos of comics, for both creators and fans. The slogan "Cosplay Has No Body Type," along with hashtags like "#cospositive" and "#cospride," were on display at Comic-Con—as was, quite conspicuously, the practice of "cross-play," a specifically gender-bending form of cosplay in which a character is represented in costume but also reinterpreted as differently gendered. This could be something like men dressed as Star Wars's Princess Leia as a slave—apparently a recognized cosplay—or an actual refiguring of the costume itself. A popular cosplay choice at the 2016 Comic-Con was a feminine Wookiee (that would be Chewbacca's species), with candy-colored fur and ladylike accoutrements. Sometimes I saw teams of them in different colors: mint green, hot pink, baby blue, with pearls.
At the panel "Cosplay: Let's Get Serious," the five participants—three of whom were wearing crowns (of felt, beads, and plastic, respectively)—agreed that the process of making is what cosplay is really about—or, as one panelist dressed as Princess Daisy from the Mario video games sweetly and geekily specified: "The cosplay process is 80 percent of what cosplay really is." The range of cosplay runs the gamut: some people buy costumes of existing characters, some people make costumes of existing characters, some people invent their own characters and build those costumes accordingly, and some people mash-up characters with great inventiveness, like a Spider-Man/Hello Kitty mash-up I admired in San Diego. It's a culture of expression that encourages active participation, not simply mimicry. Add dedication to wearing the costumes, which often debut at conventions. I was seated toward the back of the room at the above panel and was comfortably taking notes for a good thirty minutes before I noticed the couple next to me was dressed up—one as a full-body rotting-skin zombie, with peeling and mottled plastic all over her body, in the roasting San Diego July weather. I was touched to hear, because of the culture of support, that there are often cosplay repair stations at conventions, as Kathy Wiktor, from the company Cosplay by McCall's, pointed out (she also noted she always brings duct tape to cons to help fix busted corsets).
"Chewie's Angels," San Diego Comic-Con, 2016. Photograph by Keith Plocek.
Used by permission of Keith Plocek. Photo courtesy worldofwonder.net.
"Cosplay: Let's Get Serious" was basically a deeply impressive sewing tutorial, where events like "sew-a-longs" were discussed, along with sewing machine tips, and general discussion of textile manipulation, like how to get piping and applique detailing to work with spandex, along with conversation about smocking techniques on corsets (my new hero: panelist Gillian Conahan, a beautiful self-described "sewing nerd" with a master's degree from MIT and a book for DIY cosplayers titled The Hero's Closet). Yes, this woman spent fifty hours embroidering one corset for a costume. When a fully attired-in-something-I-couldn't-identify kid, maybe ten or eleven, stood up and raised his hand in the Q&A, and revealed "I'm just starting cosplay," the entire audience clapped. He asked for rules or tips. One panelist began by looking him over, kindly and seriously, from the stage, opening with, "I see you're wearing football pads. Football pads are a good base," before continuing her analysis. Comic-Con is a family friendly enterprise. Many, many kids come dressed up with their parents; the whole family is in cosplay.
The uninhibited inhabitation of costume—this owning of desire and self-expression—is on display in creative and moving ways at events like Comic-Con, where cosplay is encouraged and normalized by the community. And comics fans' deep commitment to creative self-expression is evident at many different comics conventions. It bleeds out from the convention center to the workaday world. As A. O. Scott pointed out in his recent article about attending Comic-Con, in which he pays tribute to fans' creativity, it is "also possible to marvel, so to speak, at how quickly and completely what once were subcultural pursuits have conquered the mainstream, and to appreciate the bottom-up, populist aspects of that conquest." Nerd culture, especially in the age of Silicon Valley dominance, is in. Fantasy culture, especially in an era of constant media attention to mass violence and wild politics on a global stage, is in (as so many Game of Thrones think pieces, as well as its permeation into contemporary political discourse, suggests). The figure of the superhero, whatever that means—and, crucially, who gets to be represented as one—is a freshly relevant corner of mainstream discourse, as we see in media attention to Ta-Nehisi Coates and Brian Stelfreeze's new series Black Panther, to new transgender superheroes (such as Chalice, from small publisher AfterShock), and to the superhero as a contemporary mode of description, as in "The Superhero Photographs of the Black Lives Matter Movement," a 2016 New York Times Magazine essay that focuses on the famous photograph of protester Ieshia Evans. Comic-Con is popular culture, not something to the side of popular culture, and it is only getting more and more central.
Ieshia Evans in Baton Rouge, Louisiana, July 9, 2016.
Photo by Jonathan Bachman/Reuters. Used by permission.
The past few decades, as Scott suggests, have caught up with Comic-Con. And whether they are fans of commercial comics, which is generally associated with a now-chic and actually central geek culture, or of independent comics, which is now associated with a kind of literary cool, comics fans have a passion that is impressive: committed, energetic, participatory. In a beautiful, colorful double-spread at the end of Dash Shaw's Cosplayers, a book that offers loose lines and a collage aesthetic to capture the dynamism and aspiration of fan conventions, the two young women protagonists walk through a convention, as one, gripping a sword, says to the other, "We were into cosplay since before it was uncool." "Uncool" is the new "cool"—the nerdy, passionate attachment of fans.
In fandom, as in so many contexts, comics places pressure on what constitutes the "expert" and allows openings for the amateur. Fan sites and fan publications, for instance, in many cases provide the most detailed, interesting facts and insights about a work, creator, or movement; oftentimes much less is gleaned from a comparable scholarly article. (This has been a major lesson for me as a scholar of comics.) Cosplayers thematizes fans as makers of meaning. Shaw, a former student of Gary Panter's, offers cosplaying characters who are teenage filmmakers, using the stuff of life in front of them to make work they post online, which then attracts a surprising amount of attention. It's a graphic novel about the current age of creativity, in which people can make and circulate their own culture on their own terms. This is the central precept of the comics culture this book tracks. Cosplayers in a way is about the self as a medium—you show up to a convention and you are the medium. But it's a graphic novel for a reason—because the idea of people creating their own media and their own plotlines as opposed to being sold a life by someone else is what has always characterized so many comics of all different kinds. The effects of this independence of spirit are now seen, so to speak, everywhere.
Dash Shaw, double-spread from Cosplayers (Seattle: Fantagraphics), 2016.
Used by permission of Dash Shaw. Images courtesy Dash Shaw.
The world of comics is massive right now, as an event representing so many of its constituent parts like Comic-Con makes clear. And the picture of the comics fan has changed, moving away from outmoded stereotypes. It no longer only represents those like the Simpsons's Comic Book Guy character (although plenty of cranky white middle-age men who are sarcastic know-it-all collectors are of course comics fans), but also the young South Asian girl dressed as Kamala Khan, aka Ms. Marvel, in line with her father for the Comic-Con panel about The Simpsons. The entire enterprise, from literary graphic narratives to the Marvel and DC universes and everything in between, is flourishing, in that new storylines, styles, genres, and audiences are becoming that to which comics addresses itself. There is now a line for the women's restrooms at Comic-Con (a good sign). Black heroes do matter. The field of comics is trending toward diversity and inclusion on all levels, and the cultures of creativity it stands for and engenders have positive effects in wider culture.
In the taxi on the way to the San Diego airport at sunset, after the convention ended, I chatted with my driver, a friendly older man with a Russian accent. Although invariably all the cabdrivers I met mentioned how crazy it was to have so many people flood their downtown area, he liked the Comic-Con crowd, he told me; they were generally friendly. One man, he said, got into his taxi "dressed like this"—he gestured energetically with his hands across his shoulders, as I imagined pointy, Star Trekky shoulder pads—"and like this," as he swept his hands in front of his face and I imagined some sort of face paint. Finally, he told me, he asked, "What's your costume?" The man answered simply, "This is me every day."
ACKNOWLEDGMENTS
Chris Spaide's resourcefulness, organization, dedication, good ideas, and good humor made writing this book possible—and, most important, fun. I couldn't have done it without him, on several different fronts. Mark Brokenshire provided support and his sage advice from the very beginning and I massively appreciate his involvement.
I owe a huge debt of gratitude to my agent, Zoë Pagnamenta, for her faith, knowledge, and guidance. I also owe a huge debt of gratitude to Eric Meyers at Harper, who happily for me "got" the project of this book right away. I'm very lucky to work with as savvy and inspiring an editor as Eric. Thanks, too, to Milan Bozic and the team at Harper who saw my book through to its final stages, and to Alison Lewis at the Zoë Pagnamenta Agency.
Gary Panter's comics preface and Jaime Hernandez's original cover make the work of writing a book feel worthwhile. I am beyond grateful to both of them for the art they created for Why Comics? The inimitable Seth honored me profoundly by drawing the author "photo."
During the time it took to drink a couple of beers, Noah Feldman had better thoughts about this book's structure than I did over months. Thank you, as ever, for invaluable advice. Eric Slauter, Michael Miller, Steve Biel, and Anna Henchman very generously helped me clarify my ideas early on. William Huntting Howell, Mark Brokenshire, Reed Gochberg, and Chris Spaide also kindly read chapters and offered key suggestions.
For encouraging conversations about aspects of this project I'd like to thank Ivan Brunetti, Chris Ware, Art Spiegelman, Alison Bechdel, A.K. Summers, Daniel Clowes, Joe Sacco, Adrian Tomine, Dan Nadel, Richard Dienst, Jaime Clarke, Marianne DeKoven, Tisse Takagi, Alison MacKeen, Peter Galison, Tom Mitchell, Janice Misurell-Mitchell, Ralph Rehbock at the Illinois Holocaust Museum, and Hamza Walker, among others already noted. The grad and undergrad students in my "Graphic Novel" courses at Harvard provided excellent insight about important features of comics (particularly Halie LeSavage, who wrote a senior thesis on Building Stories). Thank you, too, to Case Kerns for strong opinions, and to my students at the University of Chicago for ever-inspiring thoughts and conversations.
A fellowship at Wellesley College's Newhouse Center for the Humanities during the 2016–2017 academic year, along with the support of my deans and colleagues at Northeastern University, generously allowed me to complete this book. Special thanks to my fellow Newhouse Fellows Amit Sengupta and Jerry Pinto for talking with me about comics in India. I am also grateful for the invitations to give two recent keynote talks, at the annual Graphic Medicine conference in Seattle, and at the Documenting Trauma symposium at the University of Oxford, which helped me clarify ideas in this book with colleagues.
For their role in facilitating images, a big thank-you to Sruti Islam, Julia Pohl-Miranda, and Peggy Burns at Drawn & Quarterly; Jacq Cohen at Fantagraphics; Patrick Rosenkranz, Denis Kitchen, and Martha Holmes; Lauren Rogoff at the Wylie Agency; Lawrence Wong and Sherri Hinchey at Penguin Random House; Madeleine Hartley at Penguin Random House UK; Ron Hussey at Houghton Mifflin Harcourt; Carl M. Gropper at Will Eisner Studios; Joyce Brabner; Keith Plocek; Jason Wilkinson; Todd Hignite; Matthew Nolan; Marilyn Scott at the Billy Ireland Cartoon Library & Museum; Leigh Walton at Top Shelf; Monika Verma, at Levine Greenberg Rostan, Yessenia Santos at Simon & Schuster, and Allie Brosh; Susan Grode, along with Janie Freedman, at KattenMuchinRosenman, and the Bongo Comics Group; Jesse Stagg and Alex Czetwertynski, along with Bettina Korek at For Your Art; Joan Ashe at Henry Holt; Allison Ingram at Condé Nast; Yasutaka Minegishi and Maki Hakui at Presspop, Inc.; Misayo Nakazawa, and Ayumu Kiryu at the Japan UNI Agency, Inc.; Marvel Comics; DC Comics; Kat Salazar at Image Comics; Reuters; Getty; and Linda Collins at Northeastern. A special thanks here to Khalid El-Ali, who was exceptionally generous in his correspondence and in granting permission for and supplying artwork by his father, legendary cartoonist Naji al-Ali.
Daniel Alarcón, Lynda Barry, Kate Beaton, Alison Bechdel, Charles Burns, Daniel Clowes, Robert Crumb, Diane DiMassa, Phoebe Gloeckner, Justin Green, Jaime Hernandez, Aline Kominsky-Crumb, Bobby London, Marisa Acocella Marchetto, Richard McGuire, Erika Moen, Josh Neufeld, Gary Panter, Raymond Pettibon, Joe Sacco, Marjane Satrapi, Dash Shaw, Art Spiegelman, A. K. Summers, Chris Ware: thank you for your help in enabling me to include your amazing images here.
For general support during the period I worked on this book, in addition to those previously named, I would also like to thank the late Dan Aaron, Ted Widmer, Elaine Scarry, Amy Squires, John Wiseman, Tamar Abramov, Lindsey and Ryan Bardsley, Richard Allison, Sophie Gee, Lev Grossman, and Richard and Patricia Chute.
BIBLIOGRAPHY
INTRODUCTION: COMICS FOR GROWN-UPS?
"An Evening With Neil Gaiman." Meewella (blog), October 3, 2007. Accessed April 24, 2017. http://www.meewella.com/fragments/an-evening-with-neil-gaiman.php.
Chute, Hillary. "Scott McCloud." The Believer 43 (April 2007): 80–86.
Comichron: A Resource for Comics Research. "Comic Book Sales by Year." Accessed April 24, 2017. http://www.comichron.com/yearlycomicssales.html.
"Comics Magazine Association of America Comics Code 1954." Reprinted in Amy Kiste Nyberg, Seal of Approval: The History of the Comics Code. Jackson: UP of Mississippi, 1998.
Emmert, Lynn. "The Alison Bechdel Interview." The Comics Journal 282 (2007): 34–52.
Feiffer, Jules. The Great Comic Book Heroes. Seattle: Fantagraphics Books, 2003.
Grasso, Brian. "I'm a Duke Freshman. Here's Why I Refused to Read Fun Home." PostEverything (blog), Washington Post, August 25, 2015. Accessed April 24, 2017. https://www.washingtonpost.com/posteverything/wp/2015/08/25/im-a-duke-freshman-heres-why-i-refused-to-read-fun-home/.
Groth, Gary. "Art Spiegelman Interview." The Comics Journal 180 (1995): 52–106.
Juno, Andrea. "Dan Clowes." In Dangerous Drawings: Interviews with Comix and Graphix Artists, edited by Andrea Juno, 98–113. New York: Juno Books, 1997.
"Lin-Manuel Miranda: By the Book." New York Times, April 5, 2016. Accessed April 24, 2017. https://www.nytimes.com/2016/04/10/books/review/lin-manuel-miranda-by-the-book.html.
MacDonald, Heidi. "Graphic Novel Sales Up 22% in Bookstores in 2015." The Beat: The News Blog of Comics Culture, January 22, 2016. Accessed April 24, 2017. http://www.comicsbeat.com/graphic-novel-sales-up-22-in-bookstores-in-2015/.
———. "How Graphic Novels Became the Hottest Section in the Library." Publishers Weekly, May 3, 2013. Accessed April 24, 2017. http://www.publishersweekly.com/pw/by-topic/industry-news/libraries/article/57093-how-graphic-novels-became-the-hottest-section-in-the-library.html.
MacGillivray, Clayton. "Art Spiegelman Talk at the University of Calgary." ComicBookBin, May 7, 2011. Accessed April 24, 2017. http://www.comicbookbin.com/Art_Spiegelman_University_of_Calgary001.html.
Mankoff, Bob. How About Never—Is Never Good For You?: My Life in Cartoons. New York: Henry Holt, 2014.
McCloud, Scott. Understanding Comics: The Invisible Art. New York: Harper, 1994.
———, and Hillary Chute. Public conversation. Harvard Book Store, Cambridge, MA, February 5, 2015.
McLuhan, Marshall. Understanding Media: Extensions of Man. Cambridge, MA: MIT Press, 1994 [1964].
Østergaard, Anders Høgsbro, dir. Tintin et Moi. Angel Films, 2003.
Said, Edward. "Homage to Joe Sacco." Introduction to Palestine, by Joe Sacco, i–v. Seattle: Fantagraphics, 2001.
Segura, Jonathan. "Print Book Sales Rose Again in 2016." Publishers Weekly, January 6, 2017. Accessed May 25, 2017. https://www.publishersweekly.com/pw/by-topic/industry-news/bookselling/article/72450-print-book-sales-rose-again-in-2016.html.
Solomon, Deborah. "Revolutionary Spirit: Questions for Marjane Satrapi." New York Times Magazine, October 21, 2007.
Spiegelman, Art. "1974 Artist's Statement." In Co-Mix: A Retrospective of Comics, Graphics, and Scraps, n.p. Montreal: Drawn & Quarterly, 2013.
———. "Comics: Marching Into the Canon." Lecture. Columbia University, New York, NY, April 9, 2007.
———. "Ephemera vs. the Apocalypse." Indy Magazine, Autumn 2005. http://64.23.98.142/indy/autumn_2004/spiegelman_ephemera/index.html.
———. MetaMaus: A Look Inside a Modern Classic, Maus. New York: Pantheon, 2011.
Wertham, Fredric. Seduction of the Innocent. Laurel, NY: Main Road Books, 2004 [1954].
WHY DISASTER?
D'Arcy, David. "Profile: Art Spiegelman's Comic Book Journalism." Transcript. NPR Weekend Edition, June 7, 2003.
Dreifus, Claudia. "A Comic-Book Response to 9/11 and Its Aftermath." New York Times, August 7, 2004.
Faulkner, William. Requiem for a Nun. New York: Vintage, 2012 [1951].
Gleason, Alan. "The Keiji Nakazawa Interview." The Comics Journal 256 (2003): 38–52.
Gussow, Mel. "Dark Nights, Sharp Pens; Art Spiegelman Addresses Children and His Own Fears." New York Times, October 15, 2003: E1, E6.
Heer, Jeet. In Love With Art: Françoise Mouly's Adventures in Comics with Art Spiegelman. Toronto: Coach House Books, 2013.
Ito¯, Yu, and Tomoyuki Omote. "Barefoot Gen in Japan: An Attempt at Media History." In Reading Manga: Local and Global Perceptions of Japanese Comics, edited by Jaqueline Berndt and Steffi Richter, 21–38. Leipzig: Leipziger Universitätsverlag, 2006.
Nakazawa, Keiji. "A Note from the Author." In Barefoot Gen, Vol. Two: The Day After, translated by Project Gen. San Francisco: Last Gasp, 2004.
———. Hiroshima: The Autobiography of Barefoot Gen. Edited and translated by Richard H. Minear. New York: Rowman and Littlefield, 2010.
Panter, Gary. "Lines on Paper: Lynda Barry, Ivan Brunetti, R. Crumb, Gary Panter." Panel moderated by Hamza Walker at the Comics: Philosophy & Practice conference, Chicago, IL, May 18–20, 2012. Rpt. in Critical Inquiry: Comics and Media, edited by Hillary Chute and Patrick Jagoda (Spring 2014): 237–254.
Sacco, Joe, and Art Spiegelman. "Only Pictures?" Nation, March 6, 2006. Accessed April 25, 2017. https://www.thenation.com/article/only-pictures/.
Sontag, Susan. On Photography. New York: Picador, 2001 [1977].
Spiegelman, Art. "Ballbuster: Bernard Krigstein's Life Between the Panels." New Yorker, July 22, 2002.
———. Breakdowns: Portrait of the Artist as a Young %@&*!. New York: Pantheon, 2008.
———. "Drawing Blood: Outrageous Cartoons and the Art of Outrage." Harper's, June 2006, 43–52.
———. "Ephemera vs. the Apocalypse." Indy Magazine, Autumn 2005. http://64.23.98.142/indy/autumn_2004/spiegelman_ephemera/index.html.
———. "Four Maus Notebooks." MetaMaus. DVD. New York: Pantheon, 2011.
———. "Introduction: Putting Out the Garbage." In Garbage Pail Kids, by the Topps Company, Inc., 6–10. New York: Abrams ComicArts, 2012.
———. "Master Race: The Graphic Story as an Art Form." In From Maus to Now to Maus to Now: Comics, Essays, Graphics, and Scraps, by Art Spiegelman, 86–90. Palermo: La Centrale dell'Arte, 1998.
———. MetaMaus: A Look Inside a Modern Classic, Maus. New York: Pantheon, 2011.
———. "Obituary for Bernard Krigstein." In From Maus to Now to Maus to Now: Comics, Essays, Graphics, and Scraps, by Art Spiegelman, 90. Palermo: La Centrale dell'Arte, 1998.
———. "Pop Goes the Poppa—Or, the Vengeance of Dr. Speck" in Real Pulp Comics 1, 1971.
———. "Things Are More Like They Are Now . . . : SUNY Binghamton Commencement Address." In From Maus to Now to Maus to Now: Comics, Essays, Graphics, and Scraps, by Art Spiegelman, 22–24. Palermo: La Centrale dell'Arte, 1998.
Szasz, Ferenc Morton. Atomic Comics: Cartoonists Confront the Nuclear World. Reno: University of Nevada Press, 2012.
Temple, Kevin. "Gary Panter." NOW, May 19, 2005. Accessed May 1, 2017. https://nowtoronto.com/news/gary-panter/.
Tucker, Ken. "Cats, Mice, and History—The Avant-Garde of the Comic Strip." New York Times Book Review, May 26, 1985.
Van Biema, David H. "Art Spiegelman Battles the Holocaust's Demons—And His Own—in an Epic Cat and Mouse Comic Book." People, October 27, 1986. Accessed April 25, 2017. http://people.com/archive/art-spiegelman-battles-the-holocausts-demons-and-his-own-in-an-epic-cat-and-mouse-comic-book-vol-26-no-17/.
WHY SUPERHEROES?
Barthes, Roland. "The Third Meaning: Notes on Some Eisenstein Stills." In Image-Music-Text, translated by Stephen Heath, 52–68. New York: Hill and Wang, 1997.
Bongco, Mila. Reading Comics: Language, Culture, and the Concept of the Superhero in Comic Books. New York: Garland, 2000.
Brogan, Jacob. "Masked Fathers: Jimmy Corrigan and the Superheroic Legacy." In The Comics of Chris Ware: Drawing Is a Way of Thinking. Jackson: University Press of Mississippi, 2010.
Chute, Hillary L. "Art Spiegelman & Chris Ware." In Outside the Box: Interviews with Contemporary Cartoonists, 216–251. Chicago: University of Chicago Press, 2014.
———. "Daniel Clowes." In Outside the Box: Interviews with Contemporary Cartoonists, 98–117. Chicago: University of Chicago Press, 2014.
———. "Unkenny Valley." Diary (blog), Artforum, July 29, 2016. Accessed May 1, 2017. https://www.artforum.com/diary/id=62445.
Clowes, Daniel. Interview with Hillary Chute. San Diego, CA, July 24, 2017.
Coates, Ta-Nehisi. "The Return of the Black Panther." Atlantic, April 2016. Accessed May 1, 2017. https://www.theatlantic.com/magazine/archive/2016/04/the-return-of-the-black-panther/471516/.
Colton, David. "Superman's Story: Did a Fatal Robbery Forge the Man of Steel?" USA Today, August 25, 2008. Accessed May 1, 2017. http://usatoday30.usatoday.com/life/books/news/2008–08–25-superman-creators_N.htm.
Edidin, Jay Rachel. "Pizza Dog and the Art of Comics: Deconstructing 'Hawkeye' #11." Comics Alliance, July 2, 2013. Accessed May 2, 2017. http://comicsalliance.com/hawkeye-11-review-marvel-fraction-aja-pizza-dog-storytelling/.
Elsworth, Catherine. "The Tragic Real Story Behind Superman's Birth." Telegraph, August 27, 2008. Accessed May 1, 2017. http://www.telegraph.co.uk/news/celebritynews/2628733/The-tragic-real-story-behind-Supermans-birth.html.
Glass, Ira, and Chris Ware. "Glass/Ware: New Media for Writing American Lives." Interview at the Thirteenth Annual Colloquium at the University of Minnesota, Minneapolis, MN, February 18, 2002. Accessed May 1, 2017. http://writing.umn.edu/lrs/assets/pdf/speakerpubs/Glass_Ware.pdf.
———. "Superpowers: Prologue." Episode 178. This American Life, February 23, 2001.
Goldberg, Barbara. "Check That Bought Superman Rights for $130 Sells for $160,000." Reuters, April 16, 2012. Accessed May 1, 2017. http://www.reuters.com/article/entertainment-us-usa-superman-idUSBRE83G02F20120417.
Ito, Robert. "Ta-Nehisi Coates Helps a New Panther Leave Its Print." New York Times, March 31, 2016. Accessed May 2, 2017. https://www.nytimes.com/2016/04/03/movies/ta-nehisi-coates-helps-a-new-panther-leave-its-print.html.
Itzkoff, Dave. "Gene Luen Yang Thinks Superheroes Are for Everyone." New York Times Magazine, November 17, 2016, 66.
Kepner, Tyler. "Kobe Bryant Ends Career with Exclamation Point, Scoring 60 Points." New York Times, April 14, 2016. Accessed May 1, 2017. https://www.nytimes.com/2016/04/15/sports/basketball/kobe-bryant-scores-60-for-los-angeles-lakers-in-farewell-game.html.
Lamar, Cyriaque. "Ghost World's Daniel Clowes Tells Us about The Death-Ray, His Chain-Smoking Teenage Superhero." io9, October 3, 2013. Accessed May 1, 2017. http://io9.gizmodo.com/5846141/ghost-worlds-daniel-clowes-tells-us-about-the-death-ray-his-chain-smoking-teenage-superhero.
Lefèvre, Pascal. Comix Scholars listserv 2003, comix-scholars@clas.ufl.edu.
Leong, Tim. Super Graphic: A Visual Guide to the Comic Book Universe. San Francisco: Chronicle, 2013.
Massara, Kathleen. "Dan Clowes Talks About Nerdy Superheros, 9/11, and Spite Wars." Flavorwire, September 28, 2011. Accessed May 1, 2017. http://flavorwire.com/214131/dan-clowes-talks-about-nerdy-superheros-911-and-spite-wars.
Mietkiewicz, Henry. "Great Krypton! Superman was The Star's Ace Reporter." Toronto Star, April 26, 1992, A10.
Morrison, Grant. Supergods: What Masked Vigilantes, Miraculous Mutants, and a Sun God from Smallville Can Teach Us about Being Human. New York: Spiegel & Grau, 2011.
Ricca, Brad. "The Amazing Adventures of Jerry Siegel and Joe Shuster." PopMatters, June 13, 2013. Accessed May 1, 2017. http://www.popmatters.com/feature/172288-super-boys-the-amazing-adventures-of-jerry-siegel-and-joe-shuster/.
Schjeldahl, Peter. "Words and Pictures." New Yorker, October 17, 2005. Accessed May 1, 2017. http://www.newyorker.com/magazine/2005/10/17/words-and-pictures.
Seagle, Steven T. (story), and Duncan Rouleau and Aaron Sowd (art), "Unreal." In 9–11: The World's Finest Comic Book Writers & Artists Tell Stories to Remember, vol. 2, 15–16. New York: DC Comics, 2002.
Willis, Simon. "Chris Ware, Everyday Genius." 1843 Magazine, September/October 2013. Accessed May 1, 2017. https://www.1843magazine.com/content/features/simon-willis/chris-ware.
WHY SEX?
Adelman, Bob. Tijuana Bibles: Art and Wit in America's Forbidden Funnies, 1930s–1950s. New York: Simon & Schuster, 1997.
Arnold, Andrew D. "R. Crumb Speaks: Highlights of New York Public Library Conversation with Robert Hughes." Time, April 29, 2005. Accessed May 9, 2017. http://content.time.com/time/arts/article/0,8599,1055105,00.html.
Bagge, Peter. "Aline Kominsky-Crumb Interview." The Comics Journal 139 (1990): 50–73.
Beauchamp, Monte. The Life and Times of R. Crumb: Comments from Contemporaries. New York: St. Martin's Griffin, 1998.
Bright, Susie. "Introduction." In Twisted Sisters 2: Drawing the Line, edited by Diane Noomin, 7. Northampton: Kitchen Sink, 1995.
Chute, Hillary L. "Aline Kominsky-Crumb." In Outside the Box: Interviews with Contemporary Cartoonists, 81–97. Chicago: University of Chicago Press, 2014.
———. "Alison Bechdel." In Outside the Box: Interviews with Contemporary Cartoonists, 154–175. Chicago: University of Chicago Press, 2014.
———. "Art Spiegelman & Chris Ware." In Outside the Box: Interviews with Contemporary Cartoonists, 216–251. Chicago: University of Chicago Press, 2014.
———. "Lynda Barry." In Outside the Box: Interviews with Contemporary Cartoonists, 57–79. Chicago: University of Chicago Press, 2014.
Crumb, Charles V. Training People Effectively: The Teaching Manual for Instructors and Supervisors in Business, Education, Industry, and the Professions. Philadelphia: Lefax, 1970.
Crumb, Robert. "Introduction." In A Child's Life and Other Stories, by Phoebe Gloeckner, 4–5. Berkeley: Frog, 1998.
———. "R. Crumb's Universe of Art!" In The R. Crumb Handbook, 432. London: MQ Publications, 2005.
Heller, Marielle, dir. The Diary of a Teenage Girl. Sony Pictures Classics, 2015.
Juno, Andrea. "Art Spiegelman." In Dangerous Drawings: Interviews with Comix and Graphix Artists, 6–27. New York: Juno Books, 1997.
———. "Phoebe Gloeckner." In Dangerous Drawings: Interviews with Comix and Graphix Artists, 148–161. New York: Juno Books, 1997.
Kominsky-Crumb, Aline. Need More Love: A Graphic Memoir. London: MQ Publications, 2007.
McCloud, Scott. Understanding Comics: The Invisible Art. New York: Harper, 1994.
Orenstein, Peggy. "Phoebe Gloeckner is Creating Stories about the Dark Side of Growing Up Female." New York Times Magazine, August 5, 2001, 26–29.
Rosenkranz, Patrick. Rebel Visions: The Underground Comix Revolution, 1963–1975. Seattle: Fantagraphics, 2002.
Zwigoff, Terry, dir. Crumb. Superior Pictures, 1994.
WHY THE SUBURBS?
Amazon. "Questions for Charles Burns." 2005. Accessed May 9, 2017. https://www.amazon.com/Black-Hole-Pantheon-Graphic-Novels/dp/0375714723.
Ayroles, François. Key Moments from the History of Comics. Toronto: Beguiling Books, 2009.
Barry, Lynda. "Introduction." In Best American Comics 2008, edited by Lynda Barry, xi–xx. New York: Houghton Mifflin, 2008.
Burns, Charles. Charles Burns. Leuven: Beeld Beeld, 2011.
———. "A Project for Artforum, March 1991 [Untitled]." Rpt. in Charles Burns, 117. Leuven: Beeld Beeld, 2011.
"Charles Burns." Fantagraphics official website. Accessed May 9, 2017. http://www.fantagraphics.com/artists/charles-burns/.
Chute, Hillary L. "Charles Burns." In Outside the Box: Interviews with Contemporary Cartoonists, 32–55. Chicago: University of Chicago Press, 2014.
———. "Lynda Barry." In Outside the Box: Interviews with Contemporary Cartoonists, 57–79. Chicago: University of Chicago Press, 2014.
Gallo, Joe. "The Comic Strip Moves to the Suburbs: Settling for Less & Loving It!" PopMatters, March 3, 2000. Accessed May 9, 2017. http://www.popmatters.com/feature/000303-gallo/.
Heer, Jeet. "Updike: Portrait of the Artist as a Young Fan." Paris Review Daily, January 14, 2015. Accessed May 13, 2017. https://www.theparisreview.org/blog/2015/01/14/updike-portrait-of-the-artist-as-a-young-fan/.
Mann, Ron, dir. Comic Book Confidential. Sphinx Productions, 1989.
Spiegelman, Art. "Meet Art Spiegelman." BookPage, October 2008. Accessed May 13, 2017. https://bookpage.com/meet/12039-meet-art-spiegelman.
Sullivan, Darcy. "The Charles Burns Interview." The Comics Journal 148 (February 1992). Accessed May 9, 2017. http://www.tcj.com/the-charles-burns-interview-by-darcy-sullivan/.
Ware, Chris. "Graphic Novel Forms Today: Charles Burns, Daniel Clowes, Seth, and Chris Ware." Panel moderated by Hillary Chute at the Comics: Philosophy & Practice conference, Chicago, IL, May 18–20, 2012. Rpt. in Critical Inquiry: Comics and Media, edited by Hillary Chute and Patrick Jagoda (Spring 2014): 151–168.
WHY CITIES?
"An Interview with Harvey Pekar, Author of Ego & Hubris." Random House, 2006. Accessed May 14, 2017. http://www.randomhouse.com/rhpg/egoandhubris/pekar_interview.html.
Barnett, David. " 'There's Nothing Like It In Comics' . . . How Love and Rockets Broke the Rules." Guardian, May 10, 2016. Accessed May 15, 2017. https://www.theguardian.com/books/2016/may/10/theres-nothing-like-it-in-comics-how-love-and-rockets-broke-the-rules.
Bechdel, Alison. "Introduction." In The Art of Jaime Hernandez: The Secrets of Life and Death, by Todd Hignite, 9. New York: Abrams, 2010.
Cavna, Michael. "How Harvey Pekar Became One of David Letterman's Greatest Recurring Guests." Comics Riffs (blog), Washington Post website, May 20, 2015. Accessed May 13, 2017. https://www.washingtonpost.com/news/comic-riffs/wp/2015/05/20/david-letterman-how-harvey-pekar-became-one-of-his-greatest-recurring-guests/.
———. "Wait—Just How Did Ohio Become the Cradle of Great Cartoonists?" Comics Riffs (blog),Washington Post, July 19, 2016. Accessed May 17, 2017. https://www.washingtonpost.com/news/comic-riffs/wp/2016/07/19/wait-just-how-did-ohio-become-the-cradle-of-great-cartoonists/.
Chute, Hillary L. "Adrian Tomine." In Outside the Box: Interviews with Contemporary Cartoonists, 194–215. Chicago: University of Chicago Press, 2014.
Connors, Joanna. "David Letterman Brought Harvey Pekar, His Cleveland Cool, and a Big Blow-Up to Late Night." The Plain Dealer, May 15, 2015. Accessed May 14, 2017. http://www.cleveland.com/entertainment/ index.ssf/2015/05/david_letterman_brought_harvey.html.
———. "Harvey Pekar, Comic-Book Legend, Dies at Age 70." The Plain Dealer, July 13, 2010. Accessed May 14, 2017. http://blog.cleveland.com/metro/2010/07/cleveland_comic-book_legend_ha.html.
Crumb, R. "Introduction." In American Splendor: The Life and Times of Harvey Pekar, by Harvey Pekar et al., n.p. New York: Ballantine, 2003.
"Episode 43: Summer in the City [Marjorie Liu interview by Henry Finder]," narrated by David Remnick, The New Yorker Radio Hour, August 12, 2016. http://www.newyorker.com/podcast/the-new-yorker-radio-hour/episode-43-summer-in-the-city.
Hernandez, Gilbert. "Down Palomar Way [Interview by Chris Knowles]." Comic Book Artist 15 (November 2001): 44–55.
Hernandez, Jaime. "The Mechanic of Love [Interview by Chris Knowles]." Comic Book Artist 15 (November 2001): 56–64.
Hernandez, Mario. "A Love of Comics [Interview by John B. Cooke]." Comic Book Artist 15 (November 2001): 34–42.
Hignite, Todd. The Art of Jaime Hernandez: The Secrets of Life and Death. New York: Abrams, 2010.
Ito, Robert. "The Making of Daniel Clowes and a Golden Age for Comics." The California Sunday Magazine, February 4, 2016. Accessed May 13, 2017. https://story.californiasunday.com/daniel-clowes-patience.
Jacobs, Andrew. "The Voice to Stan Mack: 'It's Been Real, But . . . .' " New York Times, August 13, 1995. Accessed May 14, 2017. http://www.nytimes.com/1995/08/13/nyregion/neighborhood-report-greenwich-village-the-voice-to-stan-mack-it-s-been-real-but.html.
KCET. "LA Strips: Interview with Jaime Hernandez." KCET Webstories, Juan Decvis's YouTube page, uploaded on April 7, 2008. Accessed May 15, 2017. https://www.youtube.com/watch?v=vJOiJj8-D9s.
Kimmel, Jimmy. "Watching David Letterman 'Was More Important Than Sleep.' " Time, May 25, 2015. http://time.com/3858014/david-letterman-jimmy-kimmel-tribute/.
Moss, Jeremiah. "Stan Mack's Real-Life Funnies." Jeremiah's Vanishing New York (blog), July 18, 2013. Accessed May 14, 2017. http://vanishingnewyork.blogspot.com/2013/07/stan-macks-real-life-funnies.html.
Park, Ed. "Losing His Voice." Village Voice, July 29, 2003. Accessed May 15, 2017. http://www.villagevoice.com/news/losing-his-voice-6397248.
Seth. "Graphic Novel Forms Today: Charles Burns, Daniel Clowes, Seth, and Chris Ware." Panel moderated by Hillary Chute at the Comics: Philosophy & Practice conference, Chicago, IL, May 18–20, 2012. Rpt. in Critical Inquiry: Comics and Media, edited by Hillary Chute and Patrick Jagoda (Spring 2014): 151–168.
Silverblatt, Michael. "Jaime Hernandez and Junot Diaz: This Is How You Lose Her." Bookworm, KCRW. Los Angeles, CA: KCRW, February 13, 2014.
Walker, Mort. The Lexicon of Comicana. Lincoln, NE: iUniverse, 2000.
Witek, Joseph. Comic Books as History: The Narrative Art of Jack Jackson, Art Spiegelman, and Harvey Pekar. Jackson: University Press of Mississippi, 1989.
WHY PUNK?
Berman, Shari Springer, and Robert Pulcini, dir. American Splendor. Good Machine and Dark Horse Entertainment, 2003.
Brisick, Jaime. "Raymond Pettibon." MonsterChildren, April 15, 2014. Accessed May 3, 2017. http://www.monsterchildren.com/8639/ten-years-of-mc-raymond-pettibon/.
Burns, Charles. Cut Up: Random Fragments 1977–1979. Series 2W, Box Y. Geneva: Bülb Comix, 2011.
Burroughs, William S. Junky. New York: Penguin, 2003 [1953].
Carlin, John. "Crossing the Line: The Profound and the Profane in Gary Panter's Cola Madnes." In Cola Madnes, by Gary Panter, 189–209. New York: Funny Garbage, 1989.
Chute, Hillary L. "Lynda Barry." In Outside the Box: Interviews with Contemporary Cartoonists, 57–79. Chicago: University of Chicago Press, 2014.
"Comic Relief." Special issue. Flipside Fanzine 33, 1982.
The Fuk Boys [Matt Groening and Gary Panter]. "Ocurence at Oki Dog." Chemical Imbalance 6, 1987 [1982].
———. "Ocurence at Oki Dog." Flipside Fanzine 33, "Comic Relief" issue, 1982.
Gaiman, Neil. "Jaime and Gilbert Hernandez Interview." The Comics Journal 178 (July 1995): 91–123.
Groening, Matt. "Gary Panter: Genius and Pal." In Masters of American Comics, edited by John Carlin, Paul Karasik, and Brain Walker, 300–307. Los Angeles and New Haven: Hammer Museum and the Museum of Contemporary Art, and Yale University Press, 2005.
Groth, Gary. "Matt Groening Interview." The Comics Journal 141 (April 1991): 78–95.
Hignite, Todd. In the Studio: Visits with Contemporary Cartoonists. New Haven: Yale University Press, 2007.
Hoby, Hermione. "Raymond Pettibon: Punk with a Pencil." Guardian, December 14, 2013. Accessed May 2, 2017. https://www.theguardian.com/artanddesign/2013/dec/14/raymond-pettibon-sonic-youth-black-flag.
Holmstrom, John. "Prologue: 1972–1975: 'Systematic Destruction of Public Property.' " In PUNK: The Best of Punk Magazine, edited by John Holmstrom and Bridget Hurd, 1–5. New York: HarperCollins, 2012.
Kelley, Mike. "Gary Panter in Los Angeles." In Gary Panter, by Gary Panter and edited by Dan Nadel, 6–7. New York: PictureBox, Inc., 2008.
Kugelberg, Johan, and Jon Savage. Punk: An Aesthetic. New York: Rizzoli, 2012.
Lawley, Guy. " 'I Like Hate and I Hate Everything Else': The Influence of Punk on Comics." In Punk Rock: So What?: The Cultural Legacy of Punk, edited by Roger Sabin, 100–119. New York: Routledge, 1999.
McNeil, Legs. Please Kill Me: The Uncensored Oral History of Punk. New York: Grove, 1996.
Nelson, Eric. "Interview with Raymond Pettibon." Quick, Call the Waaaabulance! (blog), 2008. Accessed May 2, 2017. http://ericrnelson.blogspot.com/p/ray-pettibon.html.
O'Connor, John. "Raymond Pettibon." The Believer 20 (December 2004–January 2005). Accessed May 3, 2017. http://www.believermag.com/issues/200412/?read=interview_pettibon.
Ortved, John. The Simpsons: An Uncensored, Unauthorized History. New York: Faber and Faber, 2009.
Panter, Gary. "Gary Panter on Gary Panter." In Gary Panter, by Gary Panter and edited by Dan Nadel, 286–347. New York: PictureBox, Inc., 2008.
———. "Interview: Arranging Sights and Ideas." In The Education of a Comics Artist: Visual Narrative in Cartoons, Graphic Novels, and Beyond, edited by Michael Dooley and Steven Heller, 93–94. New York: Allworth Press, 2005.
———. "Lines on Paper: Lynda Barry, Ivan Brunetti, R. Crumb, Gary Panter." Panel moderated by Hamza Walker at the Comics: Philosophy & Practice conference, Chicago, IL, May 18–20, 2012. Rpt. in Critical Inquiry: Comics and Media, edited by Hillary Chute and Patrick Jagoda (Spring 2014): 237–254.
———. "The ROZZ-TOX Manifesto." 1980. Accessed May 4, 2017. http://www.altx.com/manifestos/rozztox.html.
———. "Waiting for Waco." New Yorker, April 19, 1993, 85–89.
Pettibon, Raymond. Raymond Pettibon: The Books, 1978–1998, edited by Roberto Ohrt. New York: D.A.P., 2000.
Phipps, Keith. "The Childish Genius of Pee-Wee's Playhouse." Daily Beast, October 23, 2014. Accessed May 4, 2017. http://www.thedailybeast.com/articles/2014/10/23/the-childish-genius-of-pee-wee-s-playhouse.
Rosenkranz, Patrick. Rebel Visions: The Underground Comix Revolution, 1963–1975. Seattle: Fantagraphics, 2002.
Sabin, Roger, and Teal Triggs, eds. Below Critical Radar: Fanzines and Alternative Comics from 1976 to Now. Hove: Slab-o-Concrete, 2000.
Smith, Prichard. "Meet World-Renowned Illustrator Gary Panter." ArtTalk! Vice YouTube video, uploaded on April 16, 2013. Accessed May 2, 2017. https://www.youtube.com/watch?v=1ir8t7PjuGw.
Stagg, Jesse, and Alex Czetwertynski, dir. "ForYourArt Interviews Matt Groening and Mike Kelley About Gary Panter." ForYourArt YouTube video, uploaded on Feburary 10, 2010. Accessed May 2, 2017. https://www.youtube.com/watch?v=KHQDpp4WyXM.
Turcotte, Bryan Ray, and Bo Bushnell, dir. "The Art of Punk: Black Flag." MOCAtv.MOCA YouTube video, uploaded on June 11, 2013. Accessed May 2, 2017. https://www.youtube.com/watch?v=N0u04EqNVjo.
von Busack, Richard. " 'Life' Before Homer: Matt Groening Interview." Metroactive, 2000. Accessed May 2, 2017. http://www.metroactive.com/papers/metro/11.02.00/groening-0044.html.
Ware, Chris. Uninked: Paintings, Sculpture, and Graphic Works by Five Cartoonists. Phoenix: Phoenix Art Museum, 2007.
WHY ILLNESS & DISABILITY?
Bechdel, Alison. "A Conversation with Alison Bechdel." Writers at Rutgers Conversation Series. Rutgers University, New Brunswick, NJ, March 5, 2008.
———. "How." Fun Home: A Family Tragicomic press DVD. New York: Houghton Mifflin, 2006.
Bookey, Mike. "Internet Famous! Allie Brosh Has Made Hyperbole and a Half into One of the Web's Most Read and Hilarious Blogs." Source Weekly, November 17, 2010. Accessed May 16, 2017. http://www.bendsource.com/bend/internet-famous-allie-brosh-has-made-hyperbole-and-a-half-into-one-of-the-webandaposs-most-read-and-hilarious-blogs/Content?oid=2136577.
Brosh, Allie. "Hyperbole and a Half." Talks at Google. October 31, 2013. Accessed May 16, 2017. https://www.youtube.com/watch?v=s_LOCS2weNw.
Czerwiec, MK, and Ian Williams, Susan Merrill Squier, Michael J. Green, Kimberly R. Myers, and Scott T. Smith. Graphic Medicine Manifesto. University Park, Pennsylvania: Pennsylvania State University Press, 2015.
Gardner, Jaredited by "Show Me Where It Hurts: Part 1." Public Books, November 15, 2015. Accessed May 15, 2017. http://www.publicbooks.org/show-me-where-it-hurts-part-1/.
Garner, Dwight. "For The Precious Moments on the Porcelain Throne." New York Times, November 9, 2013. Accessed May 16, 2017. http://www.nytimes.com/projects/2013/holiday-gift-guide/#/?page=books&item=all
Gates, Bill. "A Funny, Brutally Honest Memoir." GatesNotes (blog). May 19, 2015. Accessed May 16, 2017. https://www.gatesnotes.com/Books/Hyperbole-and-a-Half
Green, Justin. "Afterword." In Binky Brown Meets the Holy Virgin Mary, 51–63. San Francisco: McSweeney's, 2009.
———. "The Binky Brown Matter." In Justin Green's Binky Brown Sampler, 80–91. San Francisco: Last Gasp, 1995.
———. "Comics and Autobiography: Phoebe Gloeckner, Justin Green, Aline Kominsky-Crumb, Carol Tyler." Panel moderated by Deborah Nelson at the Comics: Philosophy & Practice conference, Chicago, IL, May 18–20, 2012. Rpt. in Critical Inquiry: Comics and Media, edited by Hillary Chute and Patrick Jagoda (Spring 2014): 86–103.
Humphrey, Michael. "The Life and Lines of Allie Brosh: Hyperbole and a Half." True/Slant, May 3, 2010. http://web.archive.org/web/20110905162044/http://trueslant.com/ michaelhumphrey/2010/05/03/the-life-and-lines-of-allie-brosh-hyperbole-and-a-half/.
Johnson, Gabe. "Video: 'Hyperbole," Comedy, and Angst." New York Times, November 15, 2013. Accessed May 16, 2017. https://artsbeat.blogs.nytimes.com/2013/11/15/video-hyperbole-comedy-and-angst/.
Juno, Andrea. "Art Spiegelman." In Dangerous Drawings: Interviews with Comix and Graphix Artists, 6–27. New York: Juno Books, 1997.
Maron, Marc. "Episode 550: Allie Brosh." WTF with Marc Maron, podcast, November 13, 2014. http://www.wtfpod.com/podcast/episodes/episode_550_-_allie_brosh.
McCloud, Scott. "Oh Crap—Webcomics!" In The Best American Comics 2014, edited by Scott McCloud, 269–273. New York: Houghton Mifflin, 2014.
Mohammed, Zaineb. "Meet Allie Brosh, Reclusive Genius Behind the Blog (and Book) 'Hyperbole and a Half.' " Mother Jones (November/December 2013). Accessed May 16, 2017. http://www.motherjones.com/media/2013/10/allie-brosh-hyperbole-half-book-depression.
"Obsessive-Compulsive Disorder." National Institute of Mental Health. Accessed May 16, 2017. https://www.nimh.nih.gov/health/topics/obsessive-compulsive-disorder-ocd.
Randall, Jon. "The Goblin Meets Binky Brown Who Met the Holy Virgin Mary." Goblin. Accessed May 16, 2017. http://www.ugcomix.info/history/mirrors/Just.html.
Spiegelman, Art. "Introduction." In Binky Brown Meets the Holy Virgin Mary, by Justin Green, n.p. San Francisco: McSweeney's, 2009.
———. "Introduction: Symptoms of Disorder/Signs of Genius." In Justin Green's Binky Brown Sampler, by Justin Green, 4–6. San Francisco: Last Gasp, 1995.
WHY GIRLS?
Bahrampour, Tara. "Tempering Rage by Drawing Comics." New York Times, May 21, 2003. http://www.nytimes.com/2003/05/21/books/tempering-rage-drawing-comics-memoir-sketches-iranian-childhood-repression.html.
Barry, Lynda. "Contributor's Note." In Best American Comics 2006, edited by Harvey Pekar, 277. New York: Houghton Mifflin, 2006.
———. "Interview with Hillary Chute." New York City. June 7, 2008 and June 8, 2008.
———. "Lines on Paper: Lynda Barry, Ivan Brunetti, R. Crumb, Gary Panter." Panel moderated by Hamza Walker at the Comics: Philosophy & Practice conference, Chicago, IL, May 18–20, 2012. Rpt. in Critical Inquiry: Comics and Media, edited by Hillary Chute and Patrick Jagoda (Spring 2014): 237–254.
Borrelli, Christopher. "Being Lynda Barry." Chicago Tribune, March 8, 2001. Accessed May 16, 2017. http://articles.chicagotribune.com/2009–03–08/features/0903030596_1_lynda-barry-gas-leak-shy-child.
Chute, Hillary L. "Lynda Barry." In Outside the Box: Interviews with Contemporary Cartoonists, 57–79. Chicago: University of Chicago Press, 2014.
Fulbeck, Kip. kip fulbeck: part asian, 100% hapa. Exhibition. New York: New York University, March 10-May 30, 2008.
Groening, Matt. "Hipness & Stupidity." Los Angeles Reader, February 15, 1980: 1, 4–6, 23.
Hajdu, David. "Persian Miniatures." Bookforum (October/November 2004): 32–35.
Hornby, Nick. "Draw What You Know." New York Times Book Review, December 22, 2002: 10–11.
Jacob, Kathryn Allamong. "Little Lulu Lives Here." The Radcliffe Quarterly, July 1, 2006. Accessed May 16, 2017. https://www.radcliffe.harvard.edu/news/in-news/little-lulu-lives-here.
Kois, Dan. "Lynda Barry Will Make You Believe in Yourself." New York Times Sunday Magazine, October 27, 2011. Accessed May 16, 2017. http://www.nytimes.com/2011/10/30/magazine/cartoonist-lynda-barry-will-make-you-believe-in-yourself.html.
Larson, Sarah. "Groening and Barry Take New York." Blog post on the New Yorker website. March 13, 2015. Accessed May 16, 2017. http://www.newyorker.com/culture/sarah-larson/groening-and-barry-take-new-york.
McGonigal, Mike. "Matt Groening: Master of Rabbits." Chemical Imbalance 6 (1987): 26–33.
McNally, Victoria. "Why 2016 is the Year We Need to Stop Pretending That Women Aren't Geeks." December 22, 2015. Accessed May 16, 2017. http://www.mtv.com/news/2683640/geek-media-numbers-breakdown/.
Miner, Michael. "What Becomes of the Brokenhearted?" Chicago Reader, November 19, 1998. Accessed May 16, 2017. http://www.chicagoreader.com/chicago/what-becomes-of-the-brokenhearted/Content?oid=897809.
Satrapi, Marjane. "Address on Persepolis." New York City, September 8, 2004.
———. Jane E. Ruby Lecture. Wheaton College. Norton, MA, September 17, 2009.
———. "Veiled Threat." Guardian, December 12, 2003. Accessed May 16, 2017. https://www.theguardian.com/world/2003/dec/12/gender.uk.
———, and Vincent Paronnaud, dir. Persepolis. 2.4.7.Films, 2007.
———. "Press Conference: Persepolis." Cannes Film Festival, May 2005. Accessed May 16, 2017. http://www.festival-cannes.com/en/69-editions/retrospective/2007/actualites/articles/press-conference-persepolis.
Weich, Dave. "Marjane Satrapi Returns." Powells, October 10, 2006. Accessed May 16, 2017. http://www.powells.com/post/interviews/marjane-satrapi-returns
Wood, Summer. "Scenes From the Axis of Evil: The Tragicomic Art of Marjane Satrapi." Bitch (Fall 2003): 55–58, 94–95.
Zwigoff, Terry, dir. Ghost World. United Artists, 2001.
WHY WAR?
Chute, Hillary L. "Joe Sacco." In Outside the Box: Interviews with Contemporary Cartoonists, 138–153. Chicago: University of Chicago Press, 2014.
———. "Stand Up Comics." Village Voice, July 19, 2005. Accessed May 17, 2017. http://www.villagevoice.com/2005/07/19/stand-up-comics/.
Cockburn, Patrick. " 'They Planted Hatred in Our Hearts.' " New York Times Book Review, December 24, 2009. Accessed May 17, 2017. http://www.nytimes.com/2009/12/27/books/review/Cockburn-t.html.
Contino, Jennifer. "Pieces of War." Sequential Tart 10, vol. 4 (October 2001). Accessed May 17, 2017. http://www.sequentialtart.com/archive/oct01/sacco.shtml.
Cooke, Rachel. "Riad Sattouf: Not French, Not Syrian . . . I'm a Cartoonist." Guardian March 27, 2016. Accessed May 17, 2017. https://www.theguardian.com/books/2016/mar/27/riad-sattouf-arab-of-the-future-interview.
Groth, Gary. "Joe Sacco, Frontline Journalist: Why Sacco Went to Goražde: Interview with Joe Sacco." The Comics Journal, Special Edition vol. 1 (Winter 2002): 55–72.
Hayek, Ghenwa. Beirut, Imagining the City: Space and Place in Lebanese Literature. New York: I.B. Tauris, 2015.
Holman, Brett. The Next War in the Air: Britain's Fear of the Bomber. Farnham, Surrey: Ashgate, 2014.
Ivins, William M. "Exhibition of Italian Renaissance Woodcuts." Metropolitan Museum of Art Bulletin, November 1917: 224–228.
"Questions and Answers with Safe Area Goražde author Joe Sacco." Official Fantagraphics website. Accessed September 30, 2002. http://www.fantagraphics.com/artist/sacco/sacco_qa.html.
Sacco, Joe. Chicago Creative Writing Workshop. University of Chicago, February 8, 2012.
———. Interview with Hillary Chute. Telephone. June 29, 2005.
———. "Joe Sacco and W.J.T. Mitchell." Public Conversation, May 19, 2012. Comics: Philosophy & Practice conference, Chicago, IL, May 18–20, 2012. Rpt. in Critical Inquiry: Comics and Media, edited by Hillary Chute and Patrick Jagoda (Spring 2014): 53–70.
———. "Joe Sacco: Presentation from the 2002 UF Comics Conference." ImageText 1, vol. 1 (Spring 2004). Accessed May 17, 2017. http://www.english.ufl.edu/imagetext/archives/v1_1/sacco/.
Said, Edward. "Homage to Joe Sacco." In Palestine, by Joe Sacco, i-v. Seattle: Fantagraphics, 2001.
Sneddon, Laura. "Stripped—Joe Sacco: Conflict Comes in a Lot of Guises." The Beat, August 15, 2013. Accessed May 17, 2017. http://www.comicsbeat.com/stripped-joe-sacco-conflict-comes-in-a-lot-of-guises/.
Tuhus-Dubrow, Rebecca. "Joe Sacco: January Interview." January Magazine (June 2003). Accessed May 17, 2017. http://januarymagazine.com/profiles/jsacco.html.
Wright, Bradford. Comic Book Nation: The Transformation of Youth Culture in America. Baltimore: Johns Hopkins University Press, 2001.
WHY QUEER?
"The 100 Best Books of the Decade." Times (London), November 14, 2009. Accessed May 22, 2017. https://www.thetimes.co.uk/article/the-100-best-books-of-the-decade-952h76nd689.
Atwell, Elaine. " 'Lumberjanes' is the Comic for the Little Queer Girl Scout in Your Heart." AfterEllen.com. May 13, 2014. Accessed May 18, 2017. http://www.afterellen.com/books/217284-lumberjanes-is-the-comic-for-the-little-queer-girl-scout-in-your-heart.
Bechdel, Alison. Address. Museum of Contemporary Cartoon Art Annual Convention. June 23, 2007, New York City.
———. "Alison Bechdel and Hillary Chute." Public Conversation, May 19, 2012. Comics: Philosophy & Practice conference, Chicago, IL, May 18–20, 2012. Rpt. in Critical Inquiry: Comics and Media, edited by Hillary Chute and Patrick Jagoda (Spring 2014): 203–219.
———. "Cartoonist's Introduction." In The Essential Dykes to Watch Out For, xii–xviii. New York: Houghton Mifflin, 2008.
———. "How." Fun Home: A Family Tragicomic press DVD. New York: Houghton Mifflin, 2006.
———. The Indelible Alison Bechdel: Confessions, Comix, and Miscellaneous Dykes to Watch Out For. Ithaca: Firebrand, 1998.
———. "PEN/Faulkner Event with Lynda Barry and Chris Ware." Washington, D.C., November 9, 2007.
———. "Talking with Alison Bechdel," Houghton Mifflin Press release, June 2006, 7–9.
Brunetti, Ivan. Cartooning: Philosophy & Practice. New Haven: Yale University Press, 2011.
Chute, Hillary L. "Alison Bechdel." In Outside the Box: Interviews with Contemporary Cartoonists, 154–175. Chicago: University of Chicago Press, 2014: 154–175.
"Comics Magazine Association of America Comics Code 1954." Reprinted in Amy Kiste Nyberg, Seal of Approval: the History of the Comics Code. Jackson: University Press of Mississippi, 1998.
Crocker, Elizabeth. " 'To He, I Am for Evva True' ": Krazy Kat's Indeterminate Gender." Postmodern Culture 4, vol. 2 (1994). Accessed May 21, 2017. http://www.pomoculture.org/2013/09/24/to-he-i-am-for-evva-true-krazy-kats-indeterminate-gender/.
Cruse, Howard. "Editor's Note." In Gay Comix 1. Kitchen Sink, 1980.
———. "Preface." From Headrack to Claude: Collected Gay Comix, 5. North Adams, MA: Nifty Kitsch Press, 2009.
DiMassa, Diane. Hothead Paisan official website. Accessed May 21, 2017. http://web.archive.org/web/20110728132535/http://hotheadpaisan.com/
Emmert, Lynn. "Life Drawing: An Interview with Alison Bechdel." The Comics Journal 282 (April 2007): 34–52.
Flamecon.org. "About." Accessed May 18, 2017. http://www.flamecon.org/about/.
Johnston, Lynn. "Lawrence's Story." For Better or For Worse official website. Accessed May 18, 2017. http://www.fborfw.com/features/lawrence/index.php?page=five.
Jusina, Teresa. "Greg Rucka Confirms Wonder Woman is Queer." The Mary Sue. September 28, 2016. Accessed May 18, 2017. https://www.themarysue.com/rucka-queer-wonder-woman/.
McGonigal, Mike. "Matt Groening: Master of Rabbits." Chemical Imbalance 6 (1987): 26–33.
Paul, Alan. "Life in Hell." Flux 6, September 30, 1995.
Robbins, Trina. "Sandy Comes Out." In Wimmen's Comix 1 (November 1972): n.p.
Spiegelman, Art. "Calling Dr. Godot." New York Times Book Review, November 11, 2016. Accessed May 18, 2017. https://www.nytimes.com/interactive/2016/11/11/books/review/13spiegelman-review.html.
———. Comics as Medium for Self Expression? Cover, Print (May-June 1981). Rpt. in Co-Mix: A Retrospective of Comics, Graphics, and Scraps. Montreal: Drawn & Quarterly, 2013.
Sturm, James. "To Hell With You, Matt Groening: A Tribute to Life in Hell, with Comics by Alison Bechdel, Tom Tomorrow, and Others." Slate, October 10, 2012. Accessed May 4, 2017. http://www.slate.com/articles/arts/culturebox/ 2012/10/matt_groening_s_life_in_hell_a_tribute_in_comics_by_alison_bechdel_tom_tomorrow_and_others_.html.
Thomas, June. "Is American Ready For a Musical About a Butch Lesbian?" Slate October 8, 2013. Accessed May 18, 2017. http://www.slate.com/blogs/outward/2013/10 /08/fun_home_is_america_ready_for_a_musical_about_a_butch _lesbian.html.
Wachowski, Lana. "Preface." In No Straight Lines: Four Decades of Queer Comics, edited by Justin Hall, n.p. Seattle: Fantagraphics, 2012.
Wertham, Fredric. Seduction of the Innocent. Laurel, NY: Main Road Books, 2004 [1954].
Wilsey, Sean. "The Things They Buried." New York Times Book Review, June 18, 2006: 9.
"Wonder Woman Appointed UN Honorary Ambassador for the Empowerment of Women and Girls." UN News Centre, October 21, 2016. Accessed May 18, 2017. http://www.un.org/apps/news/story.asp?NewsID=55367.
CODA: WHY FANS?
Clowes, Daniel. Interview with Hillary Chute. San Diego, CA, July 24, 2017.
Cole, Teju. "The Superhero Photographs of the Black Lives Matter Movement." New York Times Magazine, July 31, 2016: 16.
Romano, Tricia. "Fantagraphics Artist Daniel Clowes Takes on Gender Inequality in Comics Establishment." Seattle Times, January 7, 2016. Accessed May 18, 2017. http://www.seattletimes.com/entertainment/books/fantagraphics-clowes-boycott/.
Scott, A. O. "My Costume? Critic. What's Yours?" New York Times, July 19, 2015: 14.
INDEX
The pagination of this electronic edition does not match the edition from which it was created. To locate a specific entry, please use your e-book reader's search tools.
Page numbers in italics refer to captions and illustrations.
"Abstract Expressionist Ultra Super Modernistic Comics" (Crumb), 113
Academy Awards, 76, 177, 252
"Ace Hole: Midget Detective" (Spiegelman), 45, 290
Action Comics #1, 2, 71–72
"Adam Bomb" (Garbage Pail Kid), 42
Adams, Jeff, 321
A.D.: New Orleans After the Deluge (Neufeld), 34–37, 36
Adventures of Jesus, The (Stack), 112
Adventures of Tintin, The (Hergé), 24, 74
Advocate, The, 355, 364
Africa Comics (exhibition), 344
Agony (Beyer), 30
Aja, David, 99, 100–101
Akbar and Jeff (Groening), 208, 352, 353
Alarcón, Daniel, 25–28, 28–29
Alf, Richard, 392
Ali, Naji al, 342, 343
Allen, Brooke, 385
Allen, Woody, 23
All's Well that Ends Well (Shakespeare), 210
Alphona, Adrian, 96–97
Alters, 99
Alvarado, Sheila, 25, 28–29
Amateur Press Association, 16
Amazing Adventures of Kavalier & Clay, The (Chabon), 12
Amazing Spider-Man, #36 (Stracynski and Romita), 69
American Book Awards, 76, 181, 320
American Born Chinese (Yang), 30
American Flagg! (Chaykin), 137
American Psycho (film), 224
American Splendor (Pekar), 176, 178, 180–95, 240
#1 (with Dumm), 180–81, 182–83, 186
#7 (with Crumb), 188–89
#12 (with Shamray), 192–93
film, 177, 194
American Tail, An (film), 48
American Widow (Torres and Choi), 68
Angela: Asgard's Assassin, 387
Angel Catbird (Atwood), 28
"Angelfood McSpade: She's Sock-a-Delic" (Crumb), 115–17
Angoulême International Comics Festival, 396–98
Annie Hall (film), 23
Apex Novelties, 13
Apex Treasury of Underground Comix, The, 45
Arab of the Future (Sattouf), 398
2: A Childhood in the Middle East, The, 344–45, 346–47
Aragonés, Sergio, 223
Archie, 141, 204–5, 387
Are You My Mother? A Comic Drama (Bechdel), 358, 381
Artforum, 5, 155, 391
"Art School Confidential" (Clowes), 90–91
Astérix, 278
Atelier des Vosges, 298
Atlantic, 96
"Atom Bomb!" (Kurtzman and Wood), 313
Atomic Comics (Szasz), 68
Atrocity Exhibition, The (Ballard), 131
Attack on Titan (Isayama), 37
Atwood, Margaret, 28
"Audience Participation" (Bechdel), 366–67
Auschwitz, 24, 37, 40–41, 48–54, 50, 52, 65, 314
Avengers, 20
(film), 70, 392–93
Avengers (band), 198
Awkward, Definition, Potential (Schrag), 368
Aydin, Andrew, 396–97, 398
Ayers, Dick, 312–13
Ayroles, François, 159
Azoulay, Ariella, 134
B., David, 243, 298
Bá, Gabriel, 344
Bad Doctor, The (Williams), 244
Bags (band), 198
Baldwin, Stanley, 315
Ballard, J.G., 131
Banerjee, Sarnath, 344
Barefoot Gen: A Cartoon Story of Hiroshima (Nakazawa), 42, 61, 66, 314
Barefootz (Cruse), 357
Barry, Lynda, 105, 108–9, 141, 144, 208, 218, 276, 280–97, 287–88, 290, 292, 294–95, 396, 399
Batgirl (Barbara Gordon), 245–48
Batman (Bruce Wayne), 11, 20, 34, 70, 72–73, 94, 175, 349
Batman (Finger), 400
The Dark Knight Returns (Miller, Janson, Costanza, and Varley), 21, 73, 88, 392
The Killing Joke (Moore), 245–47
Bazooka Joe, 104
Beat, The (website), 4
Beaton, Kate, 394, 398–99
"Beautiful Girl of the Month Reads Mad" (Wolverton), 38
Bechdel, Alison, 1, 4, 9, 10, 23, 30–32, 103, 127, 179, 202, 253–54, 276, 280, 349–51, 353, 355–85, 358–59, 361, 363–65, 371–79, 384, 387, 395
Bechdel, Bruce, 358, 361–62, 366, 369–82, 385
Bechdel, Helen, 358, 361
Bechdel Test, 9, 10, 364
Bell, Cece, 243
Below Critical Radar (Sabin and Triggs), 221–22
Bennett, Anina, 402
Best American Comics, The, 28, 141, 264, 281
Between the World and Me (Coates), 98
Beverly (Drnaso), 142
Beyer, Mark, 30
Big Ass Comics (Crumb), 116
Big Baby (Burns), 146–48
"Big Dick" (Johnson), 355
"Big Two-Hearted River" (Hemingway), 150
Bikini Kill (band), 283
Binky Brown Meets the Holy Virgin Mary (Green), 13–15, 44, 121, 122, 143, 240, 248–62, 250–51, 255–57, 270
Birch, Thora, 76, 275
Birds of Prey, 248
"Bitchin' Bod, A" (Crumb), 117, 128
Bitch Planet (DeConnick and de Landro), 385–87
Bitchy Butch: the World's Angriest Dyke (Gregory), 355
Black Flag (band), 196, 227–28
Black Hole (Burns), 139, 143, 148–58, 151–53, 156–57, 159, 172, 218, 235, 244, 257
#4, 148
Black Lives Matter, 406–7, 407
Black Panther
#1 (Stelfreeze, Martin, and Coates), 96–99, 406
original (Lee and Kirby), 98
World of Wakanda (Gay and Harvey), 99, 401
Blasé (Spiegelman), 38, 221
Blassie, Fred, 205
Blondie, 141–42
Blondie (band), 210, 224, 226–27
Blue Is the Warmest Color (Maroh), 137, 385
Boal, Mark, 360
Book Industry Study Group (BISG), 18
Book of Lies, The (Meltzer), 72
Boondocks, The (McGruder), 142
"Borders, The" (al-Ali), 342
Boys' Jump Monthly, 64
Boys' Jump (Sho¯nen Jump), 63
Brabner, Joyce, 190, 240
Bradbury, Ray, 392
Brainard, Joe, 278
Bread & Wine: An Erotic Tale of New York (Delany), 350
Breakdowns: Portrait of the Artist as a Young %@&*! (Spiegelman), 38–40, 39, 46
Bright, Susie, 126
"Brilliant American Maniacs Series No. 1: Crazy Ed" (Pekar and Crumb), 179
Bringing Up Father (McManus), 57
Broadnax, Jame, 401
Brooks, James L., 232
Brosh, Allie, 239–40, 243, 260–61, 262–73, 264–65, 272, 275–76, 293
Brown v. Board of Education, 12
"Browsing" (Ware), 172
Bruegel, Pieter, the Elder, 320–25
Brunetti, Ivan, 278, 286, 380
Bryant, Kobe, 70
Buell, Marjorie Henderson, 277
Bugle, The (Bechdel), 358–59, 360, 363
Building Stories (Ware), 101, 158–73, 160–63, 166–71, 176, 244, 245, 247
Burns, Charles, 77, 139, 142–59, 146–48, 151–53, 156–57, 172, 218, 235, 244, 257, 278, 282–83, 398
Burns, Peggy, 399–400
Burroughs, William S., 210
Bushmiller, Ernie, 21, 45, 46
But This War Had Such Promise (Trudeau), 313
Cage, Nicolas, 70
Calling Dr. Laura (Georges), 385
Callot, Jacques, 310, 310–11, 314
Calvin and Hobbes (Watterson), 142, 177
Camper, Jennifer, 368
Cancer Made Me a Shallower Person (Engelberg), 243
Cancer Vixen (Marchetto), 241, 242
Can't We Talk About something More Pleasant? (Chast), 30
Caplan, Deborah, 231
Capp, Al, 38
Captain America, 12, 72
#1, 12, 311
Captain America: Civil War (film), 311
Captive Chains (Pettibon), 228
Carlin, John, 217
"Cartoon Concerts" (Holmstrom), 224
Cartwright, Nancy, 396
Carver, Raymond, 195
Catch-22 (Heller), 283
Cathartic Comics (Kinnard), 355
Céline, Louis-Ferdinand, 334
C'est La Guerre! (Vallotton), 303
Cézanne, Paul, 150
Chabon, Michael, 12
Chairry (Pee-wee's Playhouse), 209
Chalice, 99, 406
Chaon, Dan, 105
Charlie Brown Christmas (TV special), 158
Charlie Hebdo, 5, 346
Chascarillo, Maggie (Hernandez), 195, 196–97, 202–5, 202–3, 275
Chast, Roz, 30
Chaykin, Howard, 137
Cheap Suit Serenaders, 130
Cheap Thrills (album), 112
"Chechen War, Chechen Women" (Sacco), 342
Chemical Imbalance, 212, 283
Cher, 188
Chewie's Angels, 405
Chiang, Cliff, 142
Chicago Reader, 285, 292
Childhood Is Hell (Groening), 231
Child in Palestine, A (al-Ali), 343
Child's Life, A (Gloeckner), 130–3, 133, 280
Choi, Sungyoon, 68
"Chris Ware Sadness Scale, The" (Leong), 82, 159
Chrysler Design Award, 236
Circle Jerks (band), 199
City of Clowns (Alarcón and Alvarado), 25–28, 28–29
Civil War, 311
Clash (band), 212
Classics Illustrated, 22
Cleveland Plain Dealer, 190
Clowes, Daniel, 18, 74–76, 90–96, 91–93, 104, 177, 223, 275, 276, 393, 398
Coal Miner's Daughter (film), 378
Coates, TaNehisi, 96, 99, 406
Cobb, Ron, 314
Cockburn, Patrick, 341
Cola Madnes (Panter), 217
Cole, Jack, 104
Colette, 378, 380
Come Out Comix (Wings), 354–55
Comic Con India, 344
Comic-Con. See San Diego Comic-Con
Comics Alliance, 101
Comics Code, 12, 15, 72–73, 114, 349
Comics Journal, The, 1, 316–17, 363
Complete Hothead Paisan, The (DiMassa), 367
"Compliment, A" (Pekar and Crumb), 187, 188–89
Conahan, Gillian, 405–6
Contract with God, A (Eisner), 16, 16–17, 176, 224, 249
Cooper Point Journal, The, 144
"Corpse on the Imjin!" (Kurtzman), 313
Corridor (Banerjee), 344
Corrie, Rachel, 283
Cortez, Jaime, 385
cosplay, 389–90, 403, 404–10
Cosplayers (Shaw), 390, 407–10, 408–10
Costanza, John, 21
"Couple a' Nasty, Raunchy Old things" (Crumb and Kominsky-Crumb), 128–29
Crab with the Golden Claws, The (Hergé), 24–25
Creem, 210
Cruddy (Barry), 287, 290
Crumb, Beatrice, 110
Crumb, Charles, Jr., 110–11, 221
Crumb, Charles, Sr., 110, 113
Crumb, Dana Morgan, 13, 111, 121, 126–27
Crumb, Jesse, 111, 121, 126
Crumb, Robert, 13, 15, 15, 45, 77, 105, 108–30, 117–19, 128–29, 133, 136, 143–44, 177–81, 187, 188–89, 205, 221–23, 225, 249–50, 252, 277, 282, 337, 344, 351, 354
Crumb, Sandra, 354
Crumb, Sophie, 127, 136
Crumb (film), 108, 110–11, 128
Cruse, Howard, 355–57, 356–57, 362, 364, 368, 383
cummings, e.e., 9, 351
Cunningham, Darryl, 243
Curie, Pierre and Marie, 30
"Curse of the Molemen" (Burns), 148
Cyborg (Victor Stone), 245
Czetwertynski, Alex, 209
Dahl, Ken, 243
Daily Beast, 234
Daily Texan, The, 77
Dal Tokyo (Panter), 231, 236
Daredevil #1 (audio edition), 248
Daredevil (Matt Murdock), 73, 245, 248
Daredevil (TV show), 248
Dark Horse, 181
David Boring (Clowes), 91
Davis, Jim, 393
Davison, Al, 240
Dawn of the Planet of the Apes (film), 151
Days of Destruction, Days of Revolt (Hedges and Sacco), 342
DC Comics, 2, 13, 20–21, 69, 71–73, 90, 99, 241, 245, 248, 279, 388, 391, 393, 396, 398–401
Death of Speedy, The (Hernandez Brothers), 199, 199–201
Death-Ray, The (Clowes), 76, 90–96, 91–93, 393
DeConnick, Kelly Sue, 385–87
Deitch, Kim, 121
de Landro, Valentine, 385–87
Delany, Samuel, 350
Delisle, Guy, 176
Dennis the Menace, 204
"Depression" (Brosh)
"Part One," 271
"Part Two," 264, 268–69, 270
De Re Militari (Art of War) (Valturius), 310
Detective Comics #27, 11, 20
Devo (band), 234
Diary of Anne Frank, The, 31
Diary of a Teenage Girl, The (Gloeckner), 136–37, 280, 299
film, 136
Díaz, Junot, 195–96, 202
Dictators (band), 223
Die Zeit, 56
DiMassa, Diane, 367, 367–68
"Direction of Impact" (Gloeckner), 131, 132–33
Dirks, Rudolph, 9
Dirty Laundry (Crumb and Kominsky-Crumb), 126–27
Disasters of War, The (Goya), 61, 310
Disney, 20, 115
Ditko, Steve, 91, 224
Doctorow, E.L., 12
Doctor Strange, 91
"Dog-Boy" (Burns), 146
Donald Duck, 44
Donohue, Don, 13
Doonesbury (Trudeau), 313, 353
Dorf, Shel, 392
"Down! Up! You're in the Iraqi Army Now" (Sacco), 343
Drawn & Quarterly, 399–400
Dream of the Rarebit Fiend (McCay), 8
Drew, Richard, 54
Dr. Jekyll and Mr. Hyde (Stevenson), 22
Dr. Know (band), 198
Dr. Manhattan, 68, 73
Duchamp, Marcel, 11
Dumm, Gary, 180, 183, 183–85
Dunham, Lena, 360
Dunn, Ged, 223
Dykes and Sundry Other Carbon-Based Life Forms to Watch Out For (Bechdel), 364
Dyke Shorts (Wings), 355
Dykes to Watch Out For (Bechdel), 9, 350–51, 355, 363–67, 363–65, 369
"plate no. 19," 363, 363
"plate no. 27," 363
Dyke Strippers (Warren), 351
Earthly Paradise (Colette), 378
East Village Other, 41
EC Comics, 42–43, 145, 223–24, 313
Eco, Umberto, 49
Edwards, Dylan, 387
Eichmann, Adolf, 40
Eightball (Clowes), 91
Eisner, Will, 16, 16–17, 176, 224, 249, 313, 396
Eisner Awards, 396–400
El Deafo (Bell), 243
Elder, Will, 105, 117
Eliot, T.S., 9
Ellis, Grace, 385
Ellison, Ralph, 12
Emmy Awards, 209, 234
Engelberg, Miriam, 243
Enola Gay (bomber), 61, 65
Entertainment Weekly, 159
"Ephemera vs. the Apocalypse" (Spiegelman), 60
Epileptic (David B.), 243, 298
Ernie Pook's Comeek (Barry), 285, 286
Esquire, 374
Evans, Ieshia, 406, 407
Ex Machina (Vaughan), 178
Exorcist, The (film), 261
Fab Five Freddy, 38
Fabolous, 38
Fake, Edie, 387
"Falling Man" (Drew), 54
Family Circus, The (Keane), 141, 144
"Family That Lays together Stays Together!, The" (Crumb), 116–18, 117
Famous Funnies #1, 11
Fantagraphics, 18, 76, 199, 316–17, 393, 395, 399
Fantastic Four, 73, 91
#52 (Lee and Kirby), 98
Farmer Gray, 44
Faulkner, William, 49, 358
Feiffer, Jules, 12, 105, 187, 314
Feldstein, Al, 42
Fellini, Federico, 261
Ferris, Emil, 387
Fierstein, Harvey, 38
Fies, Brian, 241, 243, 259
Finder, Henry, 177
Finger, Bill, 400
Firebrand Books, 364
Fishburne, Laurence, 234
Fisher, Bud, 11
Fitzgerald, F. Scott, 358
Fixer: A Story from Sarajevo, The (Sacco), 315
Flame Con, 350
Flash, 20, 72
Fleener, Mary, 223
Flipside, 212, 225
#33, 214
"Comic Relief" issue, 230
Folman, Ari, 314
Foo (Robert and Charles Crumb), 110, 221
Footnotes in Gaza (Sacco), 315, 338–42, 338–39
"Footsy" (Crumb), 108
For Better of For Worse (Johnston), 353–54
Forney, Ellen, 243
Forward (weekly), 56
Fountain (Duchamp), 11
Fraction, Matt, 99, 100–101, 137
Frank, Anne, 68
Frasca, Marilyn, 282
Free Shit (Burns), 218
French Connection, The (film), 252
Friedkin, William, 252, 261
Frontline Combat, 313
Fugs (band), 121
Fuk Boys (Panter and Groening), 212, 214, 230, 231
Fun Home: A Family Tragicomic (Bechdel), 4, 5, 19, 28, 103–4, 127, 253–54, 276, 280, 349–50, 358, 368–85, 371–79
musical, 4, 349, 383–85, 384
Funnies, The, 11
funny animals, 44–45, 63, 249
"Fun Things to Do with Little Girls" (Gloeckner), 135
Gaiman, Neil, 19, 196, 210
Gaines, Max C., 11
Game of Thrones (Martin), 392, 406
Garbage Pail Kids (GPKs), 41–42
García Márquez, Gabriel, 202
Gardner, Jared, 244
Garfield (Davis), 393
Garner, Dwight, 264
Gates, Bill, 264
GatesNotes, 264
Gay, Roxane, 99, 401
Gay Comix (Cruse), 357, 362, 364
#1, 356–57, 357
Gaylord Phoenix (Fake), 387
Gebbie, Melinda, 137
Georges, Nicole, 385
Germs (band), 196, 212–14, 215
"Getting the Story" (Sacco), 319
Ghosh, Vishwajyoti, 344
Ghost World (Clowes), 74, 76, 91, 275, 276, 279, 393
film, 76, 275
Giamatti, Paul, 177, 181
Gibbons, Dave, 21
Gilbert, Michael T., 185
Gillen, Kieron, 387
Ginn, Greg, 227
Girls and Boys (Barry), 285–86
Glass, Hopey (Hernandez), 195, 196–97, 202–4, 202–3, 275
Glass, Ira, 81, 82, 85, 291–92
Gloeckner, Phoebe, 112, 130–37, 132–33, 135, 280, 299, 337
Go Girl Crazy! (album), 223
Gold, Sam, 384
Golden Age, 11, 12, 196, 311
"Goldie: A Neurotic Woman" (Kominsky-Crumb), 122, 127
Goo (album), 228, 228–29
Good Times Are Killing Me, The (Barry), 286–87
Goya, Francisco de, 61, 310, 314
Graphic Medicine Manifesto, 243–44
Graphic Women (Chute), 346
Grasso, Brian, 104
"Gravy on Gay" (Cruse), 357
Great Comic Book Heroes, The (Doctorow), 12
Greatest of Marlys, The (Barry), 287
Great War, The (Sacco), 315, 342
Green, Justin, 13–15, 44, 63, 121, 124, 143, 221, 239–40, 248–62, 250–51, 255–57, 270, 278, 362
Green, Karen, 5
Green, Katie, 243
Green Lantern/Green Arrow, 13, 20
Gregory, Roberta, 355
Griffith, Bill, 131, 223
Groening, Matt, 142, 144, 159, 208–14, 209, 214, 218–19, 221, 230–36, 232–33, 254, 283–85, 352, 353, 395–96, 399
Grossinger, Richard, 131
Groth, Gary, 199, 399
Guardian, 196, 228, 299
First Book Award, 76
Gumbel, Bryant, 188
Gumby, 228
Gurs concentration camp, 391
Hall, Justin, 350
Hamilton (musical), 4
Hamlet (Beaton), 394
Hanson, Dian, 108
Hanuka, Asaf, 346
Happiness (film), 91
"Hard Work and No Fun" (Kominsky-Crumb), 123, 124–25
Hark! A Vagrant (Beaton), 394
Harper's, 343
Harron, Mary, 224
Harry, Debbie, 224, 226–27
Hartman, Phil, 234
Harvey, Yona, 99, 401
"Harvey Pekar Name Story, The" (Pekar and Crumb), 180–81
Hawkeye (Fraction and Aja), 99–101
Little Hits, 99–101, 100–101, 245
Hayden, Jennifer, 243
"Head Lice and My Worst Boyfriend" (Barry), 290–94, 290, 292
Hearst, William Randolph, 8–9, 175, 278, 351
Hedges, Chris, 342
Heller, Joseph, 283
Hello Kitty, 395, 404
Hemingway, Ernest, 150
Here (McGuire), 25, 25–27, 235
Hergé, 24, 74
Hernandez, Aurora, 194, 196
Hernandez, Gilbert, 194–95, 198–99, 202
Hernandez, Ismael, 199
Hernandez, Jaime, 175, 194–205, 196–97, 199–203, 210, 223, 227–28, 275, 393
Hernandez, Mario, 194, 196, 198–99
Hernandez, Santos, 194, 196, 198
Hero's Closet, The (Conahan), 405
Herr, Michael, 316
Herriman, George, 9, 351
Higgins, John, 21
Hindley, Myra, 228
"Hipness & Stupidity" (Groening), 284
Hiroshima, 37, 42, 60–68, 110, 314
Hitler, Adolph, 44, 72, 311
Hokusai, Katsuchika, 215
Hollingsworth, Matt, 100–101
Holmes, Rand, 356–57, 357
Holmstrom, John, 211, 223–24
Holocaust, 34, 38–54, 60, 68, 337, 391
Homer, Winslow, 310
Honor Girl (Thrash), 387
Hornby, Nick, 280
Hospital Suite, The (Porcellino), 243
Hot, Throbbing Dykes to Watch Out For (Bechdel), 364, 364–65
Hothead Paisan: Homicidal Lesbian Terrorist (DiMassa), 367–68, 367
"How I Quit Collecting Records and Put Out a Comic Book" (Pekar and Crumb), 180
How It Is, But How It Should Be (booklet), 391
Hughes, Robert, 110
Hyperbole and a Half (Brosh), 240, 260–61, 262–73, 264–65, 268–69, 272, 276, 289
Ice Haven (Clowes), 76, 91
"I Don't Wanna Grow Up" (Ramones), 223
"I Hate You Deeply" (Clowes), 91
Iliad (Homer), 310
Illinois Holocaust Museum, 391
Image Comics, 399–400
Imhabba Vera (True Love) (Sacco), 316
Incredible Hulk, 20, 73
Indelible Alison Bechdel, The (Bechdel), 366–67
Infinite Wait, The (Wertz), 243
In the Shadow of No Towers (Spiegelman), 37, 56–59, 57–59
Ironheart (Riri Williams), 279
Iron Man (Tony Stark), 20, 73, 245, 279
Irons, Greg, 314
I Saw It (Nakazawa), 42, 60–61, 63–66, 63–64, 64–66
It's a Good Life If You Don't Weaken (Seth), 199
"Itzy and Bitzy in 'Cause and Effect' " (Crumb), 252
Jacobs, Marc, 38
Janet & Me (Mack), 243
Janson, Klaus, 21
Jansson, Tove, 400
Jay-Z, 277
Jenkins, Patty, 70
Jessica Jones, 279
Jew of New York, The (Katchor), 176
Jimbo (Panter), 208, 209, 212, 212–13, 218–19, 220–21, 230, 236
Adventures in Paradise, 209
Inferno, 231
in Purgatory (Panter), 231
vol. 2.7, 212–13
Jimmy Corrigan (Ware), 75–76, 81–90, 86–88, 96, 159, 285
Jiz Comics (Crumb), 116
"Joe Blow" (Crumb), 112, 116–18, 118–19, 130
Johansson, Scarlett, 76, 275
Johnson, Joe, 355
Johnston, Lynn, 353–54
Joker, 248
Joplin, Janis, 112
Jordan Wellington Lint (Ware), 101
Journey to the End of the Night (Céline), 334
Joyce, James, 159, 358, 370
Judge, 7
July, Miranda, 131
Junky (Burroughs), 210
Justin Green's Sign Game (Green), 261
Juvenal, 73
Kakutani, Michiko, 190
Kane, Bob, 38
Katchor, Ben, 30, 77, 176
Katzenjamer Kids, The (Dirks), 9
"Keep on Truckin' " (Crumb), 109
Kelley, Mike, 219
Kentridge, William, 235
Kerbaj, Mazen, 346
Kermesse at Hoboken (Bruegel), 321–23
Key Moments from the History of Comics (Ayroles), 159
Khan, Kamala. See Ms. Marvel
Khan Younis massacre, 338–40
Kidd, Chip, 83, 369
Killing and Dying (Tomine), 195
Kimmel, Jimmy, 188
Kinnard, Rupert, 355
Kinski, Nastassja, 188
kip fulbeck: part asian, 100% hapa (exhibition), 281
Kirby, Jack, 38, 73, 91, 98, 224, 311, 392
Kitchen, Denis, 221
Kitchen Sink Press, 357
Klein, Calvin, 38
Klepto (Kitchen), 221
Kominsky-Crumb, Aline, 108–9, 120–30, 124–25, 128–29, 133, 136, 249, 344, 354
Koren, Leonard, 208
Koresh, David, 236
Kramer's Ergot, 395
Krazy Kat (Herriman), 9, 351
Krigstein, Bernard, 42–43
Kristallnacht, 37–38
Kron, Lisa, 384–85
Krueger, Ken, 392
kryptonite, 70
Kuper, Peter, 176, 344
Kurtzman, Harvey, 105, 223–24, 313
"Kushinagar" (Sacco), 342, 344
Lady Chatterley's Lover (Lawrence), 104
LA Reader, 212, 230–31, 284
L'Association, 299
Last Gasp, 252
"Late Night with David Letterman" (Pekar and Shamray), 190–91, 192–93
Late Night with David Letterman (TV show), 188
LA Weekly, 56
Lawley, Guy, 211
Leavitt, Sarah, 243
Lee, Harper, 28
Lee, Stan, 12, 38, 73, 98
Leech, John, 7
Lefèvre, Pascal, 74
Leong, Tim (Super Graphic), 159
Lepore, Jill, 72
"Let's Have a Little Talk"(Crumb and Kominsky-Crumb), 126–27
Letterman, David, 177, 188–93, 192–93, 286
Levitz, Paul, 398
Lewis, John, 31, 396–97, 398
"Library Story: Take Two" (Pekar and Gilbert), 185
Life, 38
Life in Hell (Groening), 208, 212, 231–34, 232–33, 254, 283–84, 352, 353
"Life Is Swell" (Groening), 352
Lighter Than My Shadow (Green), 243
Likewise (Schrag), 368
Lim, Elisha, 385
Liquid Television (TV series), 146
Little Annie Fanny (Kurtzman and Elder), 105
Little Enid (doll), 275, 277
Little Lulu (Buell), 276, 277
Little Nemo in Slumberland (McCay), 8, 57
Little Orphan Annie, 277
Liu, Marjorie, 244, 245–46, 402
"Locas at the Beach" (Hernandez), 202–3, 204
London, Bobby, 224, 226–27
London Calling (album), 212
Long Island Post, 38
"Los Angeles Way of Death, The" (Groening), 232
"Lost and Found" (Barry), 282
Lost Girls (Gebbie and Moore), 137
Love and Rockets (band), 199
Love and Rockets (Jaime and Gilbert Hernandez), 194–205, 227, 275
#1, 199
#16, 202–3
#33, 196–97
X, 202
Love Is Hell (Groening and Caplan), 231
"Love's Savage Fury" (Newgarden), 278
Luce, Ed, 385
Lumberjanes (Stevenson, Ellis, Allen, Watters), 385
"Lunch with Carmella" (Pekar), 186
L Word, The (Schrag), 368
Lynch, David, 108
Lynch, Jay, 221, 222
Lynda Barry Experience, The (recording), 287
MacArthur Foundation Fellowships, 30, 98
Mack, Stan, 187–88, 243
Maclean, Norman, 90
Mad, 12, 38, 105, 117, 222–23, 250, 313, 360
"Maggies, The" (Pekar), 186
Maggin, Elliot S!, 400
Mailer, Norman, 179
Malanga, Gerard, 38
Mankoff, Bob, 6
Marbles: Mania, Depression, Michelangelo, and Me (Forney), 243
Marchetto, Marisa Acocella, 241–43, 242
March (Lewis, Aydin, and Powell), 31
Book One, 396–97
Book Two , 398
"Marlys's Guide to Queers" (Barry), 286, 287
Maroh, Julie, 385
Maron, Marc, 239, 270, 273
"Marriage Made in Hell, A" (Burns), 146
Marston, William Moulton, 72
Martin, Geroge R.R., 392
Martin, Laura, 96
Marvel Comics, 12, 20, 69, 73, 90–91, 96, 98–99, 224, 245, 248, 279, 311, 387, 392–93, 396, 399, 401, 411
"Master Race" (Krigstein and Feldstein), 42
Matrix films, 351
"Maus" (Spiegelman, 3-page story), 44–45, 47, 60, 249
Maus: A Survivor's Tale (Spiegelman), 1, 15, 19, 21, 24, 28, 33–34, 37, 39, 41–53, 49, 50–53, 57, 61, 68, 75, 77, 178, 235, 254, 297–99, 314, 337, 369, 391
McCay, Winsor, 8, 9, 57
McCloud, Scott, 2, 23–24, 109–10, 264, 267
McGruder, Aaron, 142
McGuire, Richard, 25, 25–27, 235
McKelvie, Jamie, 387
McLuhan, Marshall, 23
McManus, George, 57
McNeil, Eddie "Legs," 207, 211, 223–24
McSweeney's, 249, 252
Meltzer, Brad, 72
Melville, Herman, 159
Memory Palaces (Fake), 387
Merkerson, S. Epatha, 234
MetaMaus (Spiegelman), 37, 48
Metro: A Story of Cairo (El Shafee), 314
Mickey Mouse, 115
Miller, Frank, 21, 175
"Minnie's 3rd Love, or, Nightmare on Polk Street" (Gloeckner), 133–35
Miranda, Lin-Manuel, 4
Miseries of War (Callot), 310, 310–11
"Miss Thing" (Johnson), 355
Mitchell, W.J. T., 321
Moby-Dick, 22
Modan, Rutu, 346
Modern Painters, 236
"Modern Romance" (Gregory), 355
Moen, Erika, 137–39, 138–39
Mom's Cancer (Fies), 241, 243, 259
Monsters (Dahl), 243
Monstress (Liu and Takeda), 244, 245–46, 402
Moon, Fábio, 344
Moon Girl and Devil Dinosaur, 401
Moore, Alan, 21, 137, 245
"More Women, More Children, More Quickly: Malta 1935–43" (Sacco), 315
Morrison, Grant, 75
Morse, Wesley, 104
Mother, 41
Mothersbaugh, Mark, 234
"Motivation" (Brosh), 271, 272
Mouly, Françoise, 47, 51, 54, 54, 77, 145, 235
Mr. Natural (Crumb), 15, 112–13, 128, 225
"Mr. Natural Visits the City," 113
"Mr. Neutral by R. Crumbun," 225
"Mr. Sketchum is at it Again!" (Crumb), 222–23
Ms. Marvel (Wilson and Alphona)
original (Carol Danvers), 96
fourth series (Kamala Khan), 96, 96–97, 279, 401, 410
Vol. 1: No Normal, 96–97
Munro, Alice, 158
Murnau, F.W., 303
Murs, 398, 402
Mutt and Jeff (Fisher), 11
My Favorite Thing Is Monsters (Ferris), 387
"My Struggle with Corporate Corruption" (Pekar), 191
"My Troubles with Women" (Crumb), 108, 111
Nabokov, Vladimir, 159
Nagasaki bombing, 313
Nakazawa, Eiko, 60
Nakazawa, Harumi, 61
Nakazawa, Keiji, 37, 42, 61–68, 62–63, 71, 314
Nakazawa, Kimiyo "Kimie," 61–62
Nakazawa, Susumu, 61
Nancy (Bushmiller), 21, 45, 218–19, 220–21, 276–78
Nancy Book, The (Brainard), 278
National Book Awards, 31, 98
National Book Critics Circle Awards, 30
National Lampoon, 224
Naughty Bits (Gregory), 355
Nazis, 38, 40, 42–43, 47, 53, 72, 311. See also Holocaust
Need More Love (Kominsky-Crumb), 121, 127–28
Neufeld, Josh, 34–37, 36, 360
Never Mind the Bollocks, Here's the Sex Pistols (album), 211
Newgarden, Mark, 278
Newsday, 159
New Super-Man (Yang), 98
New Yorker, 6, 30, 43, 53–57, 75–76, 136, 195, 236
9/11 cover, 54–57, 54–55, 69
New Yorker Radio Hour, 177
New York Journal, 351
New York Review of Books, 30, 320
New York Times, 4, 48, 53, 70, 98, 99, 131, 133, 159, 190, 244, 264, 270, 299–300, 369, 401
New York Times Book Review, 31, 341
New York Times Magazine, 30, 406–7
New York World, 8
9/11/2001, 35, 37, 53–60, 57–59, 67, 67–68, 69–70
"9/11/2001" (Spiegelman and Mouly), 54–57, 54–55, 69
9/11 Report, The, 31, 68
Nixon, Richard M., 73
Noomin, Diane, 124, 130
Norton, W.W., 18
Nosferatu (film), 303
No Straight Lines (Hall), 350
Obomsawin, Diane, 385
"Ocurence at Oki Dog" (Panter and Groening), 212–14, 214, 218
Off the Cuff (Green), 262
Oh Joy Sex Toy (Moen), 137–39, 138–39
Okupant X (Panter), 235
Omaha World Herald, 81
100 Butches (Lim), 385
100 Crushes (Lim), 385
One Hundred Demons (Barry), 276, 280–83, 288–96, 288, 290, 292, 294–95
On Loving Women (Obomsawin), 385
On Photography (Sontag), 40
Orenstein, Peggy, 133–34
Our Cancer Year (Pekar, Brabner, and Stack), 240
Outcault, Richard Felton, 8, 175
"Out of the Past" (Pekar), 178
"Overheard in the Cleveland Public Library: March 21, 1977" (Pekar and Dumm), 183–85, 184–85
Ozzie and Harriet (TV show), 146
Palestine (Sacco), 18, 314, 317–25, 318–19, 321–23, 327, 343
#7, 318–19, 319
Palestinians, massacres of, 315, 338–42, 338–39
Pandora's Box, 123
Panter, Gary, xi, 32, 66–67, 68–69, 77, 144, 207–21, 209, 212–14, 216–17, 220–21, 225, 230–31, 234–39, 236–37, 277–78, 410
Panter, Nicole, 214
Paper Girls (Vaughan and Chiang), 142, 178
Park, Ed, 191
Paronnaud, Vincent, 300
Patience (Clowes), 393
Peanuts (Schulz), 141, 158, 393
Pedro and Me (Winick), 241
Pee-wee's Playhouse (TV show), 209, 234
Pekar, Dora, 178
Pekar, Harvey, 16, 176–95, 182–85, 188–89, 192–93, 205, 240–41, 243, 286
Pekar, Saul, 178
PEN Awards, 28, 75
People's Comics, 179
Persepolis (Satrapi), 19, 37, 276, 280, 296–309, 300–301, 304, 306, 368
film, 300
Pettibon, Raymond, 227–30, 228–29, 234–35
Pettibon with Strings, 228
Picasso, Pablo, 9, 45
"Pizza Is My Business" (Fraction, Aja, and Hollingsworth), 100–101, 101
Playboy, 104
Please Kill Me (oral history), 210
"Pop Goes the Poppa!" (Spiegelman), 118
Porcellino, John, 243
Pouncey, Edwin (Savage Pencil), 225
Powell, Nate, 396–97, 398
Pregnant Butch (Summers), 385, 386–87
Presley, Elvis, 212
Princip, Gavrilo, 180–81
Printed Matter Bookstore, 285
"Prisoner on the Hell Planet" (Spiegelman), 38, 39
Project Gen, 60
Proust, Marcel, 159, 358, 369
Psychiatric Tales (Cunningham), 243
Psychology Today, 264
Publishers Weekly, 159, 320
Puck, 7
Pulitzer, Joseph, 8, 9, 175, 278
Pulitzer Prize, 33, 249
Punch, 6–7, 7
Punk: An Aesthetic (Savage and Gibson), 215
Punk fanzine, 211, 223–25
#5, 225
#10, 226–27
Pyongyang (Delisle), 176
Radioactive (Redniss), 30
Rafah massacre, 340
Ramones, 91, 210, 223
Rauschenberg, Robert, 215
Ravensbrück (booklet), 40, 43, 48, 65
Raw, 25, 47–48, 77, 103–4, 145–46, 148, 235
#2.1, 235–36, 236–37
#2.2, 78, 146
R. Crumb's Heroes of Blues, Jazz, & Country (Crumb), 111
Real World: San Francisco (TV show), 241
Redniss, Lauren, 30
Reeves, Matt, 151
"Reign of the Superman, The" (Siegel and Shuster), 71
Requiem for a Nun (Faulkner), 49
"Resilience" (Barry), 289, 294–95
Reubens, Paul, 234
Riddim, 231
River of Stories (Sen), 343–44
Robins, Trina, 354
Robinson, Edward G., 205
Rock n Roll Animal (album), 224
Rock 'n' Roll Zoo (Savage Pencil), 225
Rodriguez, Spain, 121, 252
Rolling Stone, 196
Rollins, Henry, 227–28
Romberger, James, 241
Romita, John, Jr., 69
Rozz-Tox Manifesto (Panter), 230–31
Rucka, Greg, 388
Rude Girls and Dangerous Women (Camper), 368
"Rule, The" (Bechdel), 9, 10, 364
Sabin, Roger, 221
Sacco, Carmen, 315–16
Sacco, Joe, 18–19, 28, 32, 35, 179, 309, 314–44, 318–19, 321–23, 326–27, 329–30, 332–33, 336–39
Sacco, Leonard, 315
Safe Area Goražde: The War in Eastern Bosnia 1992–1995 (Sacco), 37, 309, 314–15, 321, 325–38, 326–29, 332–33, 336–37
Saga (Vaughan and Staples), 4, 178, 387, 399
Said, Edward, 22, 320
Samandal, 346
San Diego Comic-Con (SDCC) 4, 23, 389–411, 390, 405
Eisner Hall of Fame, 284, 396, 400
Sandman, The (Gaiman), 19
"Sandy Comes Out" (Robbins), 354
Sarajevo, 315, 325–27
Satellite Sam (Fraction and Chaykin), 137
Satiro-Plastic: Sketchbook Facsimile (Panter), 66–67
Satrapi, Marjane, 19, 21, 37, 276, 278–80, 296–309, 300–301, 304, 306, 337
Sattouf, Riad, 344–45, 346–47, 398
Savage Pencil (Edwin Pouncey), 225
Schiffrin, André, 48
Schjeldahl, Peter, 76
School Is Hell (Groening), 231
Schrag, Ariel, 368
Schulz, Charles, 158, 393, 400
Schwitters, Kurt, 215
Science Fiction: The Advance Guard of Future Civilization (Siegel and Shuster), 71, 211
Scott, A.O., 401, 406
Screamers (band), 215–17, 216–17
Search and Destroy, 225
Seattle Sun, 284
Secret History of Wonder Woman, The (Lepore), 72
Secret Life of Youth, The (Sattouf), 346
Seduction of the Innocent (Wertham), 12, 22, 221
Self-Loathing #2 (Kominsky-Crumb and Crumb), 128–29
Self-Portrait (Bechdel), 360–62, 361
Sen, Orijit, 343
"Sense and Sensuality" (Bechdel), 364–65
Seth, 176, 199
Seven Miles a Second (Wojnarowicz, Romberger, and Van Cook), 241, 350
Sex Criminals (Fraction and Zdarsky), 137
Sexile (Cortez), 385
Sex Pistols (band), 211, 215
Sezen, Beldan, 387
Sgt. Fury and His Howling Commandos, 311
#52 cover (Ayres), 312–13
Shafee, Magdy El, 314
Shakespeare, William, 210
Shamray, Gerry, 192–93
Shaw, Dash, 390, 407–10, 408–10
Sheena: Queen of the Jungle (TV show), 108
Shit Generation (Panter and Groening), 212
Short Order Comix #1, 39
Shuster, Joe, 2, 2, 70–72, 104, 178, 211
Sick, Sick, Sick (Feiffer), 187
Siegel, Jerry, 2, 2, 70–72, 81–82, 178, 211
Siegel, Mitchell, 71–72
Silver Age, 12, 73, 245
Simpson, Lorna, 38
Simpsons (Groening), 142, 207–9, 209, 212, 232–34, 385, 395–96, 400, 410
"Six Days in the Life Of" (Fraction and Aja), 101
Skarsgård, Alexander, 136
Slash, 211–12, 212–13, 215, 218, 221, 225, 235
Slate, 383
Sleater-Kinney (band), 283
Small, David, 243
"Smell of Shallow Graves, The" (Burns), 146–47, 148
Snapshots of a Girl (Sezen), 387
Snatch Comics (Crumb), 116
#2, 117
Social Network, The (film), 364
Solondz, Todd, 91
Solutions and Other Problems (Brosh), 273
Sonic Youth, 228, 229
Sontag, Susan, 40, 56
Sounds, 225
Spider-Man (Peter Parker), 20, 68, 69, 73, 90–91, 94–95, 175, 404
Spiegelman, Anja, 37–40, 39, 43–45, 47, 52
Spiegelman, Art, 1, 5, 9–11, 15, 18, 21–22, 24, 28, 32–33, 35, 37–60, 39, 50, 52, 54, 57–59, 63, 65–66, 68, 77–78, 105, 108, 118, 123, 145, 158, 173, 177–78, 214, 221–22, 235, 249, 254, 261–62, 277–78, 289–90, 313–14, 337, 383
Spiegelman, Mala, 51
Spiegelman, Nadja, 53
Spiegelman, Richieu, 37, 43
Spiegelman, Vladek, 37, 39, 40, 43–45, 47, 49–56, 178
Spielberg, Steven, 48
Spinal Comics (Barry), 284
Spiral Cage, The (Davison), 240
Squa Tront, 43
Squire (Williamson), 221
Srebrenica massacre, 309, 325
Stack, Frank, 112, 240
Stagg, Jesse, 209
"Standing Behind Old Jewish Ladies in Supermarket Lines" (Pekar), 181–83
Stanley, John, 205
Stan Mack's Real-Life Funnies (Mack), 187
Staples, Fiona, 4, 387
Star Wars, 364, 402, 404
Stelfreeze, Brian, 96, 406
Step Aside, Pops (Beaton), 398
Stephens, Judy, 401
Step-Up (Green), 221
Stevenson, Noell, 385
Stewart, Kristen, 228
Stitches (Small), 243
Story of My Tits, The (Hayden), 243
Story of O, The, 104
Straczynski, J. Michael, 69
Stuck Rubber Baby (Cruse), 368
Sub-Gurlz (Camper), 368
"Substance and Shadow: Cartoon, No. 1" (Leech), 6–7, 7, 9
Suddenly One Day (Nakazawa), 63
Summers, A.K., 360, 385, 386–87
Sundance Film Festival, 177
Supergirl, 279, 391
Super Graphic (Leong), 82, 159
Superman (Clark Kent; Kal-El), 2, 11, 13, 20, 34, 69–73, 76–78, 81–82, 84–90, 86–88, 94, 96, 98, 104, 175, 178, 211, 402
"Superpowers" (This American Life segment), 81
Takeda, Sana, 244, 245–46
Tales Designed to Carry an Impact, #1, 42
Tangles (Leavitt), 243
Tarantino, Quentin, 18
Taylor, Holly Rae, 395
Taymor, Julie, 360
"Teen Plague" (Burns), 148, 235
Television (band), 210
Tesori, Jeanine, 384, 385
This American Life (radio show), 81, 291
This Is How You Lose Her (Díaz), 196
This Side That Side? Restorying Partition (Ghosh), 344
Thompson, Hunter S., 316, 321
Thrash, Maggie, 387
"Thrilling Adventure Stories (I Guess)" (Ware), 77–82, 78–79
Tijuana Bibles, 104, 105–7, 137
Time, 28, 33, 110, 159, 188, 369
Tintin (Hergé), 278–79, 343
Tits & Clints, 123
Tobocman, Seth, 176
To Kill a Mockingbird, 28
Tok Tok, 346
Tomine, Adrian, 195
Tom of Finland, 355
Tony Awards, 349, 385
Topps Chewing Gum, 41–42, 104
Torres, Alissa, 68
Tracey Ullman Show, The (TV show), 232
Training People Effectively (Charles Crumb, Sr.), 110
Transposes (Edwards), 387
Treasure Chest, 250
Triggs, Teal, 221
Triumph of Death, The (Bruegel), 321
"Truckin' My Blues Away," 109
Trudeau, Garry, 313–14, 353
True/Slant, 266
Tucker, Ken, 48
Tundra publisher, 181
"12 Comics for a 7-Year-Old Girl" (GeekDad), 279
"22 Stages of Heartbreak, The" (Groening), 232, 232–33
Twisted Sisters (Kominsky-Crumb and Noomin), 124–26, 130, 136
Two-Fisted Tales (Kurtzman), 313
Two Sisters (Barry), 280
Tyler, Carol, 261
Unbeatable Squirrel Girl, The, 279
Uncle Tom's Cabin (Stowe), 22
Understanding Comics (McCloud), 2, 23–24, 109–10
Understanding Media (McLuhan), 23
United Nations, 325, 338, 388
"Unwanted, The" (Sacco), 342
Updike, John, 158, 172
Vallotton, Félix, 303
Valturius, Robertus, 310
Vance, Steve, 223
Van Cook, Marguerite, 241
Varley, Lynn, 21
Vaughan, Brian K., 4, 16, 142, 178., 387
Vice, 215
Vicious, Sid, 211
Vietnam War, 73, 313–14, 316
Village Voice, 187, 191, 231
Viper (Spiegelman), 43–44, 118
"Visiting the Grandparents" (Elder), 117
Vonnegut, Kurt, 261
Vulgarmental, The (Lynch), 221
Wachowski, Lana, 351
"Waiting for Waco" (Panter), 236
"Waking Up Blind" (Ware), 77
Walker, Mort, 185
Walking Dead, 391, 399
Waller, Fats, 15
Waltz with Bashir (film), 314
Ware, Chris, 22, 32, 75–90, 78–79, 86–89, 99–101, 103, 142–45, 158–73, 160–63, 166–71, 176, 204, 219, 239, 244, 245, 247, 258, 270, 285–86, 362, 398
"War Junkie" (Sacco), 317
"Warning Signs" (Brosh), 260–61, 263, 264–65
Washington Post, 5, 104, 159, 177, 188
Watchmen (Moore, Gibbons, and Higgins), 21, 68, 73, 88, 137
Watters, Shannon, 385
Watterson, Bill, 142, 177
Weaver, Ken, 121
Weirdo (Crumb and Kominsky-Crumb), 126
Weird Tales of the Ramones (boxed set), 223
Wendel (Cruse), 364
Wertham, Frederic, 12, 22, 105, 114, 221, 349, 388
Wertz, Julia, 243
Wet, 208
Whedon, Joss, 393
Whitehead, Colson, 31
"Whiteman" (Crumb), 113
White Negro (Mailer), 179
Whitney Biennial (2002), 76
"Who's got a gag for me today?" (Bushmiller/ Spiegelman), 45, 46
"Why I Hate Sports" (Clowes), 91
Wicked + The Divine, The (McKelvie), 387
"Wigwam Bam" (Hernandez), 196–97
Wiig, Kristen, 136
Wiktor, Kathy, 404–5
Wild, 222
Wild Party, The (poem), 53
Wilkinson, Jason, 403
Williams, Dr. Ian, 244
Williamson, Skip, 221
Wilsey, Sean, 369
Wilson, G. Willow, 96–97, 401
Wilson, S. Clay, 113
Wilson (Clowes), 76
Wimmen's Comix, 122, 124, 261, 354–55, 357
#2, 124–25
Wings, Mary, 354–55, 357
Winick, Judd, 241
Wojnarowicz, David, 241, 350
Wolverton, Basil, 38
Womanews, 363
Wonder Woman (Rucka), 20, 72–73, 278, 349, 388
film, 70
Wood, Wally, 313
Word Is Out: Stories of Some of Our Lives (Adair), 360
Work Is Hell (Groening), 231
World Literature Today, 31
World of Fanzines, The (Wertham), 221
World War I, 181, 315, 334
World War II, 42–43, 63, 72, 110, 146, 261, 311, 313–15
World War 3 Illustrated (Kuper and Tobocman), 176, 344
Wright, Bradford, 311
Wright, Richard, 12
Wuvable Oaf (Luce), 385
X (band), 196, 205, 215
X'ed Out (Burns), 218
X-Men, 20, 73, 245
Yahoo (Sacco), 317
Yang, Gene Luen, 30, 98
Yellow Kid, The (Hogan's Alley) (Outcault), 8, 175
You'll Never Know (Tyler), 261
"Your Childhood Trauma Checklist" (Groening), 231–32
Y: The Last Man (Vaughan), 178
Zamora, Pedro, 241
Zap (Crumb), 112–13, 130, 222, 224
#0, 105, 113–15, 282
#1, 13–15, 14–15, 113–14
#2, 114
#4, 118, 118–19
Zdarsky, Chip, 137
Zeroes (band), 198
Zippy the Pinhead (Griffith), 131
Zwigoff, Terry, 108
ABOUT THE AUTHOR
Hillary Chute is an expert on comics and graphic narratives, professor of English and Art + Design at Northeastern University, and the author of Graphic Women: Life Narrative and Contemporary Comics; Outside the Box: Interviews with Contemporary Cartoonists; and Disaster Drawn: Visual Witness, Comics, and Documentary Form. She is also the associate editor of Art Spiegelman's MetaMaus. She lives in Cambridge, Massachusetts.
Discover great authors, exclusive offers, and more at hc.com.
ALSO BY HILLARY CHUTE
Graphic Women: Life Narrative and Contemporary Comics
Outside the Box: Interviews with Contemporary Cartoonists
Comics & Media: A Critical Inquiry Book
(co-editor with Patrick Jagoda)
Disaster Drawn: Visual Witness, Comics, and Documentary Form
COPYRIGHT
WHY COMICS? Copyright © 2017 by Hillary Chute. All rights reserved under International and Pan-American Copyright Conventions. By payment of the required fees, you have been granted the nonexclusive, nontransferable right to access and read the text of this e-book on-screen. No part of this text may be reproduced, transmitted, downloaded, decompiled, reverse-engineered, or stored in or introduced into any information storage and retrieval system, in any form or by any means, whether electronic or mechanical, now known or hereafter invented, without the express written permission of HarperCollins e-books.
Frontispiece panels from Ice Haven, by Daniel Clowes (New York: Pantheon, 2005). Used by permission of Daniel Clowes.
FIRST EDITION
Front cover illustration by Jaime Hernandez
Cover design by Milan Bozic
Library of Congress Cataloging-in-Publication Data
Names: Chute, Hillary, author.
Title: Why comics?: from underground to everywhere / Hillary Chute.
Description: First edition. | New York: Harper, 2017. | Includes bibliographical references and index.
Identifiers: LCCN 2017020053 (print) | LCCN 2017020416 (ebook) | ISBN 9780062476814 (ebk) | ISBN 9780062476807 (hardback)
Subjects: LCSH: Comic books, strips, etc.—History and criticism. | Comic books, strips, etc.—Influence on mass media. | Graphic novels—History and criticism. | Superheroes in literature. | Cartooning. | BISAC: LITERARY CRITICISM / Comics & Graphic Novels.
| ART / Techniques / Cartooning.
Classification: LCC PN6710 (ebook) | LCC PN6710 .C48 2017 (print) | DDC 741.5/9—dc23
LC record available at https://lccn.loc.gov/2017020053
EPub Edition December 2017 ISBN 978-0-06-6247681-4
ABOUT THE PUBLISHER
Australia
HarperCollins Publishers Australia Pty. Ltd.
Level 13, 201 Elizabeth Street
Sydney, NSW 2000, Australia
www.harpercollins.com.au
Canada
HarperCollins Canada
2 Bloor Street East - 20th Floor
Toronto, ON M4W 1A8, Canada
www.harpercollins.ca
New Zealand
HarperCollins Publishers New Zealand
Unit D1, 63 Apollo Drive
Rosedale 0632
Auckland, New Zealand
www.harpercollins.co.nz
United Kingdom
HarperCollins Publishers Ltd.
1 London Bridge Street
London SE1 9GF, UK
www.harpercollins.co.uk
United States
HarperCollins Publishers Inc.
195 Broadway
New York, NY 10007
www.harpercollins.com
# Table of Contents
1. Cover
2. Title Page
3. Dedication
4. Contents
5. Foreword: One Point of View by Gary Panter
6. Introduction: Comics for Grown-ups?
7. Why Disaster?
8. Why Superheroes?
9. Why Sex?
10. Why the Suburbs?
11. Why Cities?
12. Why Punk?
13. Why Illness & Disability?
14. Why Girls?
15. Why War?
16. Why Queer?
17. Coda: Why Fans?
18. Acknowledgments
19. Bibliography
20. Index
21. About the Author
22. Also by Hillary Chute
23. Copyright
24. About the Publisher
# Landmarks
1. Cover
2. Contents
3. Title Page
1. i
2. ii
3. iii
4. iv
5. v
6. vi
7. vii
8. viii
9. ix
10. x
11. xi
12. xii
13. xiii
14. xiv
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
94.
95.
96.
97.
98.
99.
100.
101.
102.
103.
104.
105.
106.
107.
108.
109.
110.
111.
112.
113.
114.
115.
116.
117.
118.
119.
120.
121.
122.
123.
124.
125.
126.
127.
128.
129.
130.
131.
132.
133.
134.
135.
136.
137.
138.
139.
140.
141.
142.
143.
144.
145.
146.
147.
148.
149.
150.
151.
152.
153.
154.
155.
156.
157.
158.
159.
160.
161.
162.
163.
164.
165.
166.
167.
168.
169.
170.
171.
172.
173.
174.
175.
176.
177.
178.
179.
180.
181.
182.
183.
184.
185.
186.
187.
188.
189.
190.
191.
192.
193.
194.
195.
196.
197.
198.
199.
200.
201.
202.
203.
204.
205.
206.
207.
208.
209.
210.
211.
212.
213.
214.
215.
216.
217.
218.
219.
220.
221.
222.
223.
224.
225.
226.
227.
228.
229.
230.
231.
232.
233.
234.
235.
236.
237.
238.
239.
240.
241.
242.
243.
244.
245.
246.
247.
248.
249.
250.
251.
252.
253.
254.
255.
256.
257.
258.
259.
260.
261.
262.
263.
264.
265.
266.
267.
268.
269.
270.
271.
272.
273.
274.
275.
276.
277.
278.
279.
280.
281.
282.
283.
284.
285.
286.
287.
288.
289.
290.
291.
292.
293.
294.
295.
296.
297.
298.
299.
300.
301.
302.
303.
304.
305.
306.
307.
308.
309.
310.
311.
312.
313.
314.
315.
316.
317.
318.
319.
320.
321.
322.
323.
324.
325.
326.
327.
328.
329.
330.
331.
332.
333.
334.
335.
336.
337.
338.
339.
340.
341.
342.
343.
344.
345.
346.
347.
348.
349.
350.
351.
352.
353.
354.
355.
356.
357.
358.
359.
360.
361.
362.
363.
364.
365.
366.
367.
368.
369.
370.
371.
372.
373.
374.
375.
376.
377.
378.
379.
380.
381.
382.
383.
384.
385.
386.
387.
388.
389.
390.
391.
392.
393.
394.
395.
396.
397.
398.
399.
400.
401.
402.
403.
404.
405.
406.
407.
408.
409.
410.
411.
412.
413.
414.
415.
416.
417.
418.
419.
420.
421.
422.
423.
424.
425.
426.
427.
428.
429.
430.
431.
432.
433.
434.
435.
436.
437.
438.
439.
440.
441.
442.
443.
444.
445.
446.
447.
448.
449.
450.
451.
452.
453.
454.
455.
456.
457.
458.
459.
460.
461.
462.
463.
464.
| {
"redpajama_set_name": "RedPajamaBook"
} | 8,223 |
Neoperla idella is een steenvlieg uit de familie borstelsteenvliegen (Perlidae). De wetenschappelijke naam van de soort is voor het eerst geldig gepubliceerd in 2008 door Stark & Sivec.
Borstelsteenvliegen | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,426 |
IN the peerless Athol Fugard's extraordinary body of work, ''The Captain's Tiger,'' now in its American premiere at the McCarter Theater here, represents the autobiographical continuation of '' 'Master Harold' . . . and the Boys,'' the next phase in the 17-year-old Hally's coming of age. In ''Master Harold,'' Mr. Fugard's most rending play, Hally is the startled discoverer of how racism begins.
Now 20, Hally is called Tiger. The play's title is nautical slang for a glorified servant on a cargo ship sailing from Port Sudan to Japan. When a much older Tiger announces to the audience that ''the voyage had begun,'' that he is in for a great adventure, it doesn't take a prescient literary scholar to get the metaphorical message. Here is a magical wielder of words about to join Tom in ''The Glass Menagerie'' -- and by extension, every major artist-to-be as a young man.
But if Mr. Fugard is a great playwright, an inspiring teacher and a nourishing provider of the sustenance of humanity, he is neither a resourceful director nor a protean actor. In ''The Captain's Tiger,'' by his own command he plays himself at 65 and at 20. To one who has been privileged to witness Mr. Fugard in communion with students, he is more of a life force in the classroom than onstage.
As a playwright, Mr. Fugard has come up with an exploration of process through the crafty device of conducting an often moving, seldom less than eloquent interior dialogue with his own mother, Betty, played with grace and vitality by Jennifer Steyn. She is the inspiration for a manuscript that he eventually tosses overboard, a destruction of powerful dramatic effect and considerable psychological implication.
Ms. Steyn has the talent to suggest that she is a voice in the mind and a loving, teasing and sometimes taunting presence. She is a diva, too. ''It's my story,'' she says insistently to her son. ''And I'm telling you I don't like it.'' She is dismissive of ''that famous imagination of yours,'' and she resents the pressure of being the perennial muse. Gorgeously adhering to the play's time shifts, Ms. Steyn complains that she would like to ''have an ordinary good time for a change.'' She has the power to mock, and to delight.
Although in the here and now the play gives voice to a third character, the fearsome, illiterate Donkeyman, a member of the engine room crew arrestingly played by Owen Sejake, it is essentially a delicate pas de deux. An otherwise static production, co-directed, whatever that means, by Mr. Fugard and Susan Hilferty, screams out for the intimate second stage on the McCarter architect's drawing board.
To any writer, ''The Captain's Tiger'' is a fascinating meditation on creative yearning, on ''silent music'' and ''private dreams,'' on an inner life that obsesses about the inanity of existence one moment and about the wonder of being the next. And it is ever intercepted by merciless writer's block.
It is to humanity's good, and to the theater's, that the end of apartheid has freed a master playwright to contemplate the nurturing of a noble life rather than the politics and the polemics of racial injustice. In the theater, it is axiomatic that a playwright should not direct his own work. Here, ''The Captain's Tiger'' makes a potent case for keeping the playwright an offstage presence.
Through next Sunday. Performances: today at 2 and 7:30 P.M.; Thursday and Friday at 8 P.M.; Saturday at 4 and 8:30 P.M.; next Sunday at 2 P.M. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,692 |
\section*{Abstract}
\end{center}
The transition from mild cognitive impairment (MCI) to Alzheimer's disease (AD) is of great interest to clinical researchers. This phenomenon also serves as a valuable data source for quantitative methodological researchers developing new approaches for classification. However, the growth of machine learning (ML) approaches for classification may falsely lead many clinical researchers to underestimate the value of logistic regression (LR), yielding equivalent or superior classification accuracy over other ML methods. Further, in applications with many features that could be used for classifying the transition, clinical researchers are often unaware of the relative value of different selection procedures. In the present study, we sought to investigate the use of automated and theoretically-guided feature selection techniques, and as well as the $L_1$ norm when applying different classification techniques for predicting conversion from MCI to AD in a highly characterized and studied sample from the Alzheimer's Disease Neuroimaging Initiative (ADNI). We propose an alternative pre-selection technique that utilizes an efficient feature selection based on clinical knowledge of brain regions involved in AD. The present findings demonstrate how similar performance can be achieved using user-guided pre-selection versus algorithmic feature selection techniques. Finally, we compare the performance of a support vector machine (SVM) with that of logistic regression on multi-modal data from ADNI. The present findings show that although SVM and other ML techniques are capable of relatively accurate classification, similar or higher accuracy can often be achieved by LR, mitigating SVM's necessity or value for many clinical researchers.
{\it Key Words: Alzheimer's Disease; logistic regression; mild cognitive impairment; support vector machine. }
\newpage
\section*{Introduction}
Alzheimer's disease (AD) is a progressive, age-related, neurodegenerative disease and the most common cause of dementia ~\cite{bib1,bib2,bib3}. Behaviorally, AD is commonly preceded by mild cognitive impairment (MCI), a syndrome characterized by declines in memory and other cognitive domains that exceed cognitive decrements associated with normal aging ~\cite{bib2,bib23}. However, the prodromal symptoms of MCI are not prognostically deterministic: individuals with MCI tend to progress to probable AD at a rate of $8\%$-$15\%$ per year, and most conversions occur within 3 years of presentation ~\cite{bib4,bib17,bib18}. Research efforts to provide new insights into the incidence of MCI-to-AD conversion have focused largely on clinically or biologically relevant features (i.e., neuroimaging markers, clinical exam data, neuropsychological test scores) and on different methods for statistical classification ~\cite{bib6}. \par
For clinical researchers, however, there may be a tendency to conflate more sophisticated, novel analytic approaches and the value of multimodal information from neuroimaging and clinical assessment. Moreover, whereas statisticians may inherently understand the comparability of different quantitative approaches, the novelty of both big data and data-driven approaches for studying MCI-to-AD conversion may lead clinical researchers to assume that such data-driven methods are inherently superior to more theoretically-grounded approaches. Thus, the value of using extant findings and domain expertise to help guide and constrain the application of newer data-driven approaches capable of capitalizing on emergent big data may be a particularly important consideration for clinical researchers. \par
Statistical classification in clinical research has traditionally utilized binary logistic regression (LR). However, key attributes of modern clinical and neuroimaging data, including high dimensionality and the presence of ground truth estimates of pathology and diagnosis, provide new opportunities for quantitative research. This has led to a substantial expansion in the use of data from the Alzheimer's Disease Neuroimaging Initiative (ADNI; http://adni.loni.usc.edu) for quantitative research and methodological development, particularly by researchers utilizing and developing prediction and classification methods in machine learning (ML). Besides LR, support vector machine (SVM) has quickly become the most common type of ML classifier for diagnostic prediction and classification with ADNI data. In addition to LR and SVM, deep neural network approaches also offer benefits ~\cite{bib22,bib25}, but have not had the extent of application in ADNI data as SVM and LR. In general, LR works well when the data is linearly separable and the number of data is greater than the number of features, whereas SVM with Gaussian Kernel is mostly used when the data is not linearly separable. Moreover, SVM and LR have similar misclassification rates (MCRs) when used to diagnose malignant tumors from imaging data ~\cite{bib11,bib13}. \par
Indeed, before the rapid expansion of ML research and applied work over the past decade, many clinical researchers and those outside of engineering and mathematically intensive disciplines had little exposure to classification approaches other than LR. Despite its growing popularity, the relative benefits of SVM or other forms of ML~\cite{bib47,bib48} over LR for such classification are not always apparent. Although this may be of little surprise to statisticians and quantitative researchers, such perspectives are often lost on clinical researchers, whose implicit beliefs in the superiority of ML is driven by the volume of publications, rather than through training or empirical demonstration. \par
Most efforts to develop new classification methods for prediction of MCI-to-AD conversion are well suited to integrate measures from multiple sources such as demographics, clinical rating scores, neuropsychological testing, neuroimaging, genetic markers, etc. However, identifying which combination of features most accurately classifies conversion from MCI to AD is a key challenge for ADNI, and may vary by method. The $L_1$ norm regularization method (i.e., $L_1$) is a highly used feature selection technique for LR and SVM. $L_1$ is popular for addressing circumstances in which the number of features is greater than the sample size (i.e., small n, large p) and has been implemented in ADNI data with LR ~\cite{bib8}. Furthermore, $L_1$ and other algorithmic feature selection methods used in ML suffer from one key limitation: they are agnostic to theoretical considerations, and as such, they cannot interpret why selected features are meaningful and important to the model. When sampling from a large pool of features, the algorithmic approaches fail to consider prior knowledge of features and their associations with the relevant systems in variable selection. Therefore, domain expertise and prior knowledge may afford additive or differential value for choosing features and interpreting model results over algorithmic feature selection methods alone.\par
However, most real-world problems occur in the context of additional information about each potential feature and its conceptual relationship with the phenomenon being classified. Other than using $L_1$ feature selection, manually trimming the list of potential predictor variables can also protect against over-fitting, and also offers potential insight into why selected features are important to the model. When guided by prior knowledge, user-guided or 'manual' feature selection may be a valuable additional step to help minimize potentially spurious effects. This perspective is frequently lost on applied researchers, as most commonly used variable selection algorithms are context-free – that is, they only look at relationships within the data set, and cannot factor in the wider meanings of variables. Furthermore, this also means that automated algorithms may identify relationships among a large number of predictor variables that are spurious and are unlikely to generalize outside the data set. Although there are a vast number of potential neuroimaging features in ADNI data, the present study focused only on regional brain volumes segmented from structural magnetic resonance imaging (MRI) data, the most commonly used neuroimaging datatype for classifying MCI-to-AD conversion. In contrast to prior studies that used a limited set of volumetric brain features, the present study utilized data generated by modern multi-atlas segmentation methods and analyses included up to 259 features - anatomically specific gray and white matter volumes.\par
The present study addressed two questions regarding commonly used classification approaches for predicting MCI-to-AD conversion in multi-modal data from ADNI. First, we compared performance accuracy of binary LR with SVM in classifying MCI-to-AD conversion. Second, we asked if applying prior knowledge in feature selection outperforms algorithmic variable selection alone. We hypothesized that 1) LR would perform comparably to SVM, and 2) user-guided variable selection would outperform algorithmic variable selection alone. This work is intended to demonstrate to clinical researchers the benefit of using ML in an informed fashion, rather than as a 'black box' that obscures clear interpretation. Moreover, we wish to emphasize that this study is not meant to highlight a novel innovation in quantitative methods, but rather to provide an important example to applied researchers regarding the comparable value of ML methods and importance of domain expertise in classification with ADNI data. \par
\section*{Materials and Data}
The data used in the preparation of this study were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI). ADNI is an ongoing joint public-private effort to utilize neuroimaging, other biological markers, and clinical and neuropsychological assessment to measure the incidence and progression of MCI to early AD. Determination of sensitive and specific markers of very early AD progression is intended to aid researchers and clinicians to develop new treatments and monitor their effectiveness, as well as lessen the time and cost of clinical trials. Data in the present study came from all sites across the U.S and Canada. All ADNI subjects were between 55 and 90 years old, spoke English or Spanish as their native language, and had a study partner able to provide an independent assessment of functioning.
\par
This study used a subset of the MCI subjects from ADNI-1 who had data from demographic, clinical cognitive assessments, APOE4 genotyping, and MRI measurements. In total, there are 819 individuals with a baseline diagnosis of MCI. To evaluate differences in classification due to participant inclusion and drop out, we subdivide the sample into two overlapping groups. Group One included all patients whose follow-up period was at least 24 months; Group Two included those patients with additional follow-up assessments at 36 months. The final samples included 308 and 265 subjects in Groups One and Two, respectively, who met criteria for inclusion. Both Groups included participants who were stable in their diagnosis (MCI-S) and those who converted to a diagnosis of AD over the 2 or 3 years (MCI-C). Table \ref{t1} shows the participant characteristics. Diagnostic criteria for MCI included an MMSE score at baseline between 24 and 30, a CDR score of 0.5, a subjective memory complaint, objective memory loss measured by education-adjusted scores on the Logical Memory II subscale of the Wechsler Memory Scale, generally preserved activities of daily living and no dementia. The diagnostic criteria are an MMSE score between 20 and 26, CDR score of 0.5 and 1.0. The clinical status of each MCI subject was re-assessed at each follow-up visit and updated to reflect one of several outcomes (MCI or AD and other). The MCI-C and MCI-S group designations were based on this follow-up clinical diagnosis and marked as either 1 for MCI-C or 0 for MCI-S in classification study.
\par
\subsection*{Clinical Cognitive Assessment and Genetics data}
We considered a total of 20 clinical features as potential predictors of MCI-to-AD progression in our classification analyses.These included the following assessment scores: the Mini Mental State Examination (MMSE), Clinical Dementia Rating Sum of Boxes (CDR-SB), Alzheimer's Disease Assessment Scale-cognitive sub-scale (ADAS-cog), Functional Activities Questionnaire (FAQ) measures of activities of daily living, Trail Making Test-B (TRABSCOR), the Rey Auditory Verbal Learning Test (RAVLT), the Digit-Symbol Coding test (DIGT) and the Digit Symbol Substitution Test from the Preclinical Alzheimer Cognitive Composite (mPACCdigit). We also considered genotype for carriers of the epsilon-4 allele of the apolipoprotein E (APOE) gene ~\cite{bib6} as a genetic predictor in this study. Table \ref{clinical_feature} summarizes all 20 clinical, demographic and genetic features used in this study.
Preliminary comparison of six clinical and genetic predictors by MCI-C and MCI-S subgroups showed five of them (APOE4, ADAS4, CDR, MMSE and RAVLT.learning) significantly differ between the groups, whereas one (SEX) does not. Fig \ref{Comparison} and \ref{MR} illustrate the distribution of these predictors for both groups. On the one hand, MCI-C subjects are more cognitively and functionally impaired at baseline and exhibit more pronounced verbal memory impairment than MCI-S subjects. This is indicated by higher percentage of APOE4, higher ADAS4 and CDR score, and lower average of MMSE and RAVLT.learning score: the average of MMSE and RAVLT scores MCI-C subjects are approximately 28 and 4, they are 26.5 and 3 for MCI-S groups. On the other hand, the MCI-C and MCI-S groups exhibited similar sex distributions.
\subsection*{MRI data}
Structural MRI data were collected according to the ADNI acquisition protocol using T1-weighted scans (GradWarp, B1 Correction, N3, Scaled)~\cite{bib27}. This was followed by brain extraction for further processing ~\cite{bib29}. A new multi-atlas registration based label fusion method was applied for region of interest (ROI) segmentation ~\cite{bib28}. Processing for ROI-based volumetric data used in the present study was performed by researchers at the Perelman School of Medicine, University of Pennsylvanian. These data include baseline MRI scans of ADNI1 participants (230 cognitively normal (CN) individuals, 200 AD patients, and 410 MCI patients). MRI scans were automatically partitioned into 145 anatomic ROIs spanning the entire brain. The segmentation method applies a multi-atlas, consensus-based label fusion scheme on template ROIs deformed to subject space. An additional 114 derived ROIs were calculated by combining single ROIs within a tree hierarchy, to obtain volumetric measurements from larger structures ~\cite{bib27}. In total, 259 ROIs were measured and used as potential predictors of MCI-to-dementia progression in this study. One of the goals of this study is to investigate if manually selecting predictors improves a model's performance. Based on the extant literature ~\cite{bib9}, we manually selected 26 out of 259 features as theoretically significant predictors of MCI to dementia progression (Table \ref{roi}).
\section*{Method and Algorithm}
In the following section, we present two classification techniques: binary LR and SVM, to investigate which exhibits better discrimination accuracy in the context of ADNI data. Several metrics for comparing logistic regression and SVM have been reported in the literature. For example, 1) SVM requires fewer variables than logistic regression to achieve an equivalent level of misclassification rate (MCR) ~\cite{bib10,bib13}; 2) SVM is better than LR with microarray expression data ~\cite{bib13}; 3) SVMs have a nice dual form, giving sparse solutions when using the kernel trick; 4) Both can be viewed as taking a probabilistic model and minimizing some cost associated with the misclassification based on likelihood ratio. Therefore, we show LR and SVM share common roots in statistical pattern recognition and compare the testing accuracy for SVM and logistic regression when using multi-modal ADNI data.
\subsection*{Logistic Regression}
Logistic regression (LR) is the most commonly used approach in machine learning for binary classification. In the past decade this has been applied to task of AD conversion ~\cite{bib5,bib8,bib35}. We consider a supervised learning task where we are given M training examples $\{D= (x_{i}, y_{i}), i=1,...M\}$. Here each $x_{i} \in \Re^N$ is $N$ dimensional feature vectors, and $y_{i} \in \{0,1\}$ is a class label. The goal of LR is to model the probability $p$ of a random variable $\bm{y}$ being 1 or 0 given the experimental data $\bm{x}$.
Logistic regression models is defined as follows:
\begin{equation}
logit \enspace p=log \frac{p}{1-p}
\end{equation}
Logit, the natural logarithm of an odds is the key concept that underlies logistic regression. The formal mathematics equation for logistic regression is:
\begin{equation}
log \frac{P(y_i=1|x_i;\bm{\beta})}{1-P(y_i=1|x_i;\bm{\beta})}= \sum_{j=1}^N\bm{\beta_{j}}\bm{x_{ij}}
\end{equation}
where $\bm{\beta}=(\beta_1,...\beta_N)^T $ are the parameters or weights of the logistic regression model, $\bm{x_{ij}}=(x_{i1},...x_{iN}$), $i=1,...M$. Also, $P(y_i=1|x_i,\bm{\beta})$ is the probability that $ith$ MCI patient will develop the AD and $P(y_i=0|x_i,\bm{\beta})$ is the probability that $ith$ MCI patient will not develop the AD. Denote $P(y_i=1|x_i;\bm{\beta})=h(x_i)$, then
\begin{equation}
h(x_i)=\frac{1}{1+exp(\sum_{j=1}^N-\bm{\beta_j}x_{ij})}
\end{equation}
Logistic regression is usually trained by minimizing an error function; an appropriate choice of such a function for binary classification problems is the cross-entropy error
\begin{equation}
e_i(\bm{\beta})=-y_ilog(h(x_i))-(1-y_i)log(1-h(x_i)))
\end{equation}
The total cost over the data $ \{D= (x^{i}, y^{i}), i=1,...M\}$ is:
\begin{equation}
J(\bm{\beta})=-\frac{1}{M}[\sum_{i=1}^My_ilog(h(x_i))-(1-y_i)log(1-h(x_i))]
\end{equation}
Consider the problem of finding the maximum likelihood estimate (MLE) of the parameters $\bm{\beta}$ for the unregularized logistic regression model. To find the optimized weights $\bm{\beta}$, the total cost need to be minimized. The optimization function can be written:
\begin{equation}
\bm{\beta}^{optimal}=min_{\bm{\beta}}-\frac{1}{M}[\sum_{i=1}^My_ilog(h(x_i))-(1-y_i)log(1-h(x_i))]\
\label{LR:l1_COST}
\end{equation}
Solving Eq \eqref{LR:l1_COST} yields the optimal weights of $\bm{\beta}$. However, the model-building challenge is to abstract the underlying distribution from the particular instance D of samples because of the small sample compared to the number of features. The problem of memorizing the data set instead of identifying the underlying distribution is known as overfitting~\cite{bib30}. To avoid the overfitting problem, dimension reduction techniques are necessary to be applied. $L_1$ and $L_2$ norm is widely used to avoid over-fitting, especially when there is a only small number of training examples, or a larger number of features to be learned. $L_1$ norm or $lasso$ is also often used for feature selection, and has been shown to have good generalization performance in the presence of many irrelevant features ~\cite{bib16,bib49}. $L_1$ regularization is implemented by adding $L_1$ norm to the cost function, the cost function and the optimization function are following:
\begin{equation}
\label{eqn:LR_L1_P}
J(\bm{\beta})=-\frac{1}{M}[\sum_{i=1}^My_ilog(h(x_i))-(1-y_i)log(1-h(x_i))]+\lambda|\bm{\beta}|
\end{equation}
and
\begin{equation}
\label{eqn:lr_l1}
\bm{\beta}^{optimal}=min_{\bm{\beta}}\{-\frac{1}{M}[\sum_{i=1}^My_ilog(h(x_i))-(1-y_i)log(1-h(x_i))]+\lambda|\bm{\beta}|\}
\end{equation}
where $\lambda$ is positive tuning parameter. This Eq \eqref{eqn:lr_l1} is refereed to as $L_1$ regularized logistic regression.
\subsection*{Support Vector machine}
In this section we discuss the second proposed learning algorithm, Support Vector Machine (SVM), a classification and regression method that can handle high-dimensional feature vectors. Algorithmically, SVMs build optimal boundaries between data sets by solving a constrained quadratic optimization problem ~\cite{bib14,bib15,bib32,bib33,bib34}. Because different kernel functions can be used in the model, we can vary the degrees of non-linearity and flexibility. SVM has received considerable research interest in classification of conversion from MCI to AD over the past years ~\cite{bib1,bib2,bib4,bib6,bib7,bib9,bib31,bib36,bib37,bib46}. \par
We briefly review a basic support vector machines for classification problems:
Let $\bm{\beta}^Th(x)+\beta_0=0$ denote an equidistant hyperplane (decision surface) to the closest point of each class on the new space. The goal of SVMs is to find $\bm{\beta}$ and $\beta_0$ such that $|\bm{\beta}^Th(x) + \beta_0| = 1$ for all points closer to the hyperplane. The classifier is constructed as follows. One assumes that:
\begin{equation}
\bm{\beta}^Th(x_i)+\beta_0=\left\{\begin{array}{ll}
\geq1 \; if\; y_i=1\\
\leq-1\; if \;y_i=0\\
\end{array}
\right.
\end{equation}
such that the distance from the closest point of each class to the hyperplane is $1/||\bm{\beta}||$ and the distance between the two groups is $2/||\bm{\beta}||$. To maximize the margin, the SVM requires the solution of the following optimization primal problem:
\begin{equation}
\label{eqn:eqlabel}
min_{\bm{\beta},\bm{\beta_0}} \;\sum_{i=1}^M\{1-y_i[\beta_0+\sum_{j=1}^N\beta_j^Th_j(x_i)]\}
\end{equation}
To make the algorithm work for non-linearly separable data sets as well as be less sensitive to outliers, we reformulate our optimization by adding $L_1$-norm of $\beta$,i.e. the $lasso$ penalty as follows:
\begin{equation}
\label{eqn:svm_l1}
min_{\bm{\beta},\bm{\beta_0}} \;\sum_{i=1}^M\{1-y_i[\beta_0+\sum_{j=1}^N\beta_j^Th_j(x_i)]\}+\lambda||\beta||_1
\end{equation}
Where $\lambda$ is the tuning parameter that controls the trade-off between loss and penalty.
\subsection*{Experimental Design}
We built four different classifiers, each designed to classify individual patients as belonging to either the MCI-C and MCI-S group. Classifier 1 is logistic regression (C-LR); Classifier 2 is logistic regression with $L_1$ norm (C-LR-1); Classifier 3 is support vector machine (C-SVM), and Classifier 4 is SVM with $L_1$ norm (C-SVM-1). To test classifiers' performance on the multi-modal data, we constructed five different data sources, summarized in Table \ref{Modalities}. First, a separate single data was constructed for clinical cognitive assessments score and APOE4 (CCA), MRI markers (ROI-NP), MRI markers with pre-selection (ROI-P); Second, a multi-modal data was constructed for the CCAR-NP where joins clinical cognitive assessments score and MRI markers, and CCAR-P which contains the combination of clinical cognitive assessments score and MRI markers with pre-selection. The prediction procedure consisted of three processing stages for Group one (Time=36 months) and Group Two (Time=24 Months): 1) Split data as training and testing set; 2) Train classifiers using training set and assess classifiers using testing set, then train classifiers again using $L_1$ norm on the same training set; 3) Report the testing accuracy, sensitivity and specificity of each classifier on single-modality data. Specifically, in the first stage, $90\%$ used as training set and remaining $10\% $ data are testing set. In the second stage, optimal subsets of features of each data source are determined and chosen when $L_1$ norm was employed. We then list the top 10 features of each data set. In the last stage, we report testing accuracy, sensitivity (percent of MCI-C subjects correctly classified) and specificity (percent of MCI-S subjects correctly classified) as measures of classification accuracy. To protect against over-fitting problem and avoid optimistically-biased estimates of model performance, we report 20 measures of predictive performance for each classifier (1-4) with different partitions of the data, then calculate and report the mean and standard deviation of testing accuracy, sensitivity and specificity. We also investigate the relationship between the number of features and model performance. Finally, we compare the performance of LR with SVM based on their ability to handle the \say{small n, large p} problem as well as the testing accuracy. Fig \ref{classifer} illustrates the diagram of the prediction framework.
\section*{Results and Analysis}
\subsection*{Cross-validation and choice of $\lambda$}
We adopted 10-fold cross-validation to avoid optimistically-biased estimates of model performance. The results of a 10-fold cross-validation run are summarized with the mean and standard deviation of the model skill scores.
Cross-validation are also applied to tune the hyper-parameters and $\lambda$ is the hyper-parameter as denoted for both LR-$L_1$ and SVM-$L_1$ . To select the optimized $\lambda$, we tried different values of the $\lambda$. Here we report the results with the values of $\lambda=10^{-15},10^{-10},10^{-8},10^{-4},10^{-3},10^{-2},1,5,10,20$ and applied them to the Eq~(\ref{eqn:lr_l1}) and (\ref{eqn:svm_l1}), then we selected the $\lambda$ based on the best cross-validation score and used selected $\lambda$ to Classifier 2 and 4 to select optimal features. For brevity, the model performance are reported in Tables \ref{result_one} and \ref{result_two} for different Modality, and top 10 selected features are report in Table \ref{select_one_lr}. For example, the best $\lambda$ for ROI-NP-$L_1$ is $0.01$ and the top 3 optimal features selected by LR are Left Amygdala, Right Accumbens Area and Right MTG middletemporal gyrus.
\subsection*{Comparison with different modalities}
We compared performance of each classifier (1-4) on the five different data sets listed on Table \ref{Modalities}. Performance was gauged using measures of testing accuracy, sensitivity and specificity. As shown in Table \ref{result_one}, the LR with $L_1$ regularization (Classifier 2) can achieve the high accuracy of 85.4\% on multi modality data (CCAR), which is considerably better than performance of LR on the other four modalities. Similarity, the best testing accuracy achieved by SVM is 84.2\% based on the combination of CCAR and SVM-L1. Furthermore, we also found the highest accuracy achieved by both classifiers without applying regularization is based on the single modality data (CCA); this indicated both classifiers perform best on multi-modal when $L_1$ is employed and on single-modality when $L_1$ is not applied.
\subsection*{Comparison of Pre-selection and $L_1$ norm}
We found that using prior knowledge to inform feature selection improves the model performance and protects against over-fitting. As shown in Table \ref{result_one}, the performance of model on ROI-P $(74.4\%)$ and CCAR-P $(80.4\%)$ outperformed ROI-NP $(63.7\%)$ and CCAR-NP $(64.6\%)$. However, the performance of Classifier 2 on the ROI-NP-$L_1$ and CCAR-NP-$L_1$ have testing accuracy of $85\%$ and $85.4\%$, while the ROI-P-$L_1$ and CCAR-P-$L_1$ have testing accuracy of $79\%$ and $84\%$; this suggests that pre-selection may not have significantly improved model performance compared to $L_1$ norm. In addition to LR, the SVM (Classifiers 3 \& 4) had a similar and comparable result with LR classifiers. First, the observed testing accuracy for CCAR-P and ROI-P are $78.3\%$ and $73.5\%$, which is superior to testing accuracy on CCAR-NP ($72.5\%$) and ROI-NP ($72.3\%$). Therefore, manually selecting features improves model performance only when $L_1$ norm is not applied. Second, it may not necessary to use pre-selection when $L_1$ norm is used, because model on CCAR-NP-$L_1$ with testing accuracy of $84.2\%$ has superior performance over the model on CCAR-P-$L_1$ with testing accuracy of $81.7\%$.
\subsection*{Comparison of Groups One and Two}
In addition to the results of Group One (i.e., MCI-to-AD conversion over 36 months) , we also reported the performance of Group Two (i.e., MCI-to-AD conversion over 24 months) for comparison. Table \ref{result_two} summarize the predictive performance of LR and SVM for Group Two. Similarity, the performance of Group Two were also investigated for single modality, as well as for multi-modal. The best result is obtained by using LR-$L_1$ model (Classifier 2) on CCAR-NP-$L_1$, and its corresponding testing accuracy is 80.7\%. However, it is warrants mention that all classifiers' performance of Group One outperforms the same classifiers' performance on the same data in group Two. For example, Classifier 2 of Group One on ROI-NP can achieve the testing accuracy of 85\%, which is considerably better than the same classifier of Group Two on ROI-NP (76.3\%); classifier 3 of Group One on CCAR-P had a testing accuracy of 84\% while a testing accuracy on CCAR-P is 79.3\% for Group Two. The experimental results indicated that model performance on data obtained using long follow-up period is better than using short follow-up period. Given the uncertainty in conversion, a longer time window for assessment of change clearly yields more accurate classification.
\subsection*{Comparison of LR and SVM}
In addition to comparing classification between different time windows of assessment, we also compared the differences in performance between LR and SVM. The results, including models' ability to address the over-fitting problem of LR and SVM methods with different modalities are displayed in Table \ref{result_one}, \ref{result_two} and Fig.\ref{roi_lr_svm}, \ref{ccar_lr_svm} and \ref{cca_lr_svm}.
First, it is worth noting that both LR and SVM do not work well if no $L_1$ penalization used, since Classifier 2 and 4 outperform Classifier 1 and 3 on the same data set. Second, as testing accuracy of Classifier 3 on ROI-NP and CCAR-NP are $72.5\%$ and $72.3\%$, both of which outperform classifier 1 on the same data set, it is worth noting that SVM has a better performance on MRI data when feature selection method is not employed. Third, it was interesting to note that we can obtain a good testing accuracy only using simplest model such as LR and the model performance is as good as SVM for a \say{large n small p} data (ROI-P), because testing accuracy of Classifier 1 and 3 on ROI-P are $74.4\%$ and $73.5\%$. Finally,
as shown in Fig. \ref{cca_lr_svm}, \ref{roi_lr_svm}, and \ref{ccar_lr_svm}, the SVM method is more stable and robust than LR to the large number of features when n is small. To summarize, the best performance of group One was achieved by Classifier 2 (LR with $L_1$ norm) when using a combination of three modalities, i,e., CCAR-NP-L1, which has a testing accuracy of $85.4\%$.
\section*{Discussion and Conclusion}
In this study, we applied two machine learning methods to data from clinical assessment and cognitive testing, demographic and genetic markers, and MRI-based volumetric brain measures from ADNI to test classification accuracy in discriminating patients with MCI who progress to AD (MCI-C) from whose who remain stable (MCI-S). We compared LR and SVM classification accuracy and pre-selection dimensional reduction techniques, both as informed by clinical neuroscience expertise and via $L_1$ norm, yielding multiple noteworthy findings. First, the classification results showed that the model using multi-modal data with cognitive, clinical, and volumetric data (CCAR) achieved better classification accuracy than the methods based on single-modality (CCA, ROI). Moreover, the testing accuracy of CCAR based on LR or SVM was either statistically significantly or at least numerically greater than those based on the single-modality model. These results were consistent with the previously published reports ~\cite{bib1,bib2,bib4,bib5,bib6,bib7,bib8,bib9}. We reported the highest testing accuracy on CCAR data is 85.4\% by $L_1$ LR and 84.2\% by $L_1$ SVM.
Second, SVM has several advantages in discriminating MCI-C and MCI-S (Fig. \ref{roi_lr_svm} and \ref{ccar_lr_svm}). The performance of the SVM approaches was more stable than LR when the number of features was relatively large. In other words, the testing accuracy of SVM on both ROI and CCAR data remained more stable than LR. To be specific, there is a dramatic growth in SVM performance on ROI and CCAR data as the number of features increases from 1 to 12 and from 1 to 10 separately. Testing accuracy remained fairly static at approximately 85\% for both data sets despite the number of features continue to increase. However, LR model performance decreases gradually after the number of ROI features reaching to 12 and CCAR features reaching to 9.
Third, the classification results proved that manually selecting features on MRI data not only improved the testing accuracy and protected the classifier from overfitting, but also affords easier interpretation of each selected features' contribution to the model. The reported testing accuracy on ROI-P from LR and SMV are 74.4\% and 73.5\%, compared to testing accuracy on ROI-NP are 63.7\% and 72.5\%. In addition, even though the pre-selection improves the performance of model, Tables \ref{result_one} and \ref{result_two} suggest it is not the best strategy to obtain the maximum testing accuracy, compared to L-1 features selection. As listed in table \ref{result_one}, the testing accuracy of LR on CCAR-P and CCAR-NP-$L_1$ are 80.4\% and 85.4\%. \par
Several prior studies between 2010 and 2016 were conducted to predict the conversion of MCI to AD, using either SVM or LR, and with combining of different modalities that range from MRI, fMRI, PET to CSF ~\cite{bib1,bib2,bib4,bib5,bib6,bib7,bib8,bib9,bib22}. For example, in Young et al (2013) work ~\cite{bib6}, the authors used both SVM and Gaussian process (GP) classification on the MRI, PET, APOE4, and CSF biomarker data from ADNI. In contrast with other published work, they trained classifier on healthy people and AD patients instead of on group of MCI-C and MCI-S and tested classifier on group of MCI-C and MSI-S. They reported that the accuracy using GP is substantially higher than using any individual modality or using a multi kernel SVM. The reported accuracy is 74\%. In 2016, Korolev et al. implemented multiple kernel learning (pMKL) classification techniques using clinical, MRI and plasma biomarkers data. Their methodology was to first to group the data set into five different data sources, and then apply a filter-wrapper approach of feature selection techniques which combined to use with Joint Mutual Information (JMI) criterion to identify the important features. They report the testing accuracy was 80\% ~\cite{bib9}.
Most recent computational neuroimaging studies in the past few years have utilized multi-modal features ~\cite{bib4,bib31,bib35,bib36,bib37,bib38,bib39,bib40,bib42,bib46}. In 2017, Ding implemented and applied SVM method on PET and MRI data to classify the transition from MCI to AD, they reported the testing accuracy is 66.35\% ~\cite{bib31}. In addition to use PET and MRI data, other findings show that cerebrospinal fluid (CSF) protein markers can be used to predict progression from MCI to AD, in addition to proteomic, demographic and cognitive data ~\cite{bib43,bib44,bib45}. Llano et al in 2017 applied LR with $L_1$ norm using CSF markers to classify individual patients as belonging to either the MCI-C and MCI-S group, the proposed method obtained a testing accuracy of 70\% ~\cite{bib35}.\par
In conclusion, for the prediction of MCI-to-AD conversion, prior knowledge on feature selection may protect the model against over-fitting, and models with pre-selection on MRI data outperform those without pre-selection. In addition, the present findings demonstrate that SVM classifier performance is more stable than LR for dealing with the problem of \say{small n, large p}. Clinical researchers should note the need to evaluate different classification and pre-selection approaches in application to clinical or research questions, and heed the cautionary note that not all machine learning is equally beneficial to specific clinical outcomes.
\section*{Acknowledgments}
Data used in preparation of this article were obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database (http://adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: \url{http://adni.loni.usc.edu/wp-content/uploads/how_to_apply/ADNI_ Acknowledgement_List.pdf}. Michael W. Weiner, MD is the Principal Investigator of the ADNI; email: Michael.Weiner@ucsf.edu. We are grateful to the patients and their families who participated in the ADNI.The research is partially supported by NSF-DMS 1945824 and 1924724.
\section*{Conflicts of interest}
None of the authors has any conflicts to report.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 1,078 |
'Hearts are in pieces' five years after tsunami hits Japan
Image: Lanterns from northern Japanese city Natori are illuminated during an event to pray for the reconstruction of areas devastated by the March 11, 2011 earthquake and tsunami, and mourn victims of the disaster at the Canadian embassy in Tokyo, Japan, March 10, 2016, a day before the five-year anniversary of the disaster. REUTERS/Issei Kato
By Elaine Lies and Hyun Oh
RIKUZENTAKATA, Japan (Reuters) – Japan on Friday mourns the thousands who lost their lives in a massive earthquake and tsunami five years ago that turned towns to matchwood and triggered the world's worst nuclear disaster since Chernobyl in 1986.
The nine-magnitude quake struck offshore on a chilly Friday, sparking huge black waves along a vast swathe of coastline and killing nearly 20,000 people.
The tsunami crippled the Fukushima Dai-ichi Nuclear Plant, where meltdowns in three reactors spewed radiation over a wide area of the countryside, contaminating water, food and air.
More than 160,000 people were evacuated from nearby towns. Around 10 percent still live in temporary housing across Fukushima prefecture. Most have settled outside their hometowns and have begun new lives.
Some areas remain no-go zones due to the high radiation.
In coastal Rikuzentakata, which was flattened by a wave as much as 17 meters (56 ft) high and lost seven percent of its population along with its entire downtown, the pain remains strong.
"Infrastructure is recovering, hearts are not. I thought time would take care of things," said Eiki Kumagai, a volunteer fireman who lost 51 colleagues, many killed as they guided others to safety.
"I keep seeing the faces of those who died… There's so much regret, I can't express it."
Prime Minister Shinzo Abe and Emperor Akihito will offer flowers at a ceremony in Tokyo that will include a moment of silence at the time of the quake, 2.46 p.m. (0546 GMT), when bells will ring in the city center and residents across the nation bow their heads.
Japan, one of the world's most seismically active areas, will mark the day with prayers, anti-nuclear protests and graveside visits. All the trains on the vast Tokyo underground network will halt to mark the moment the quake struck.
Billions of dollars in government spending have helped stricken communities rise from the ruins, including elevating the earth to protect them from future waves and cleaning radiation-contaminated land, but much remains to be done for thousands still languishing in barracks-like temporary housing.
"I get the feeling that the number of people who don't know what to do, who aren't even trying, is increasing," said Kazuo Sato, a former fisherman from Rikuzentakata. "Their hearts are in pieces."
Government spending on reconstruction is set to dip from the start of the new fiscal year in April. But Abe pledged continued support.
"There are still many people living difficult lives in temporary housing and those who because of the nuclear accident cannot return to the places they lived," Abe told reporters on Thursday.
"We will speed up our efforts to build housing and disaster-proof towns … so they can return as quickly as possible to permanent housing and stable lives."
(Reporting by Elaine Lies; Editing by Linda Sieg and Nick Macfie)
Copyright 2015 Thomson Reuters. Click for Restrictions.
Hearts-in-pieces-five-years-after-Tsunami-hits-Japan-media.jpg
Football First EMTV Episode 9 – Season 1
Resource PNG – Episode 8, 2016
Russia ban to run into 2017
Business calls for Trump, world leaders to support Paris climate pact
Google tests mobile instant publishing service to rival Facebook, Apple | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,623 |
If you are interested in managing campaigns, getting in touch with brands and bloggers all over the world, and making an impact on social media, this is the position for you.
· Writing skills - fluency in both English and Hebrew is a must.
· Love of social media and PR.
· Self-management abilities - great time management skills, ability to multitask, intelligence.
· Outgoing personality - able to walk into networking events and be comfortable introducing yourself to strangers.
· Innovation, creativity, and a good sense of humor.
Interested in company business development? This is the first step towards your future career.
We have over 20 categories, so if you love a certain topic you can choose to focus on this area and develop business relations within this category. This includes connecting with brands and and bloggers in the industry and attending events/exhibitions.
If there are events during your internship you may be asked to come along and make connections.
Contribute with out of the box thinking; you will be able to apply your ideas and see them develop.
· Ability to build an international network.
· Skills in applied analytics and drawing conclusions.
· Working together with international brands/bloggers.
· Connecting with international events/conferences.
If you love DATA and you know how to take it to the next level with a MARKETING mindset, this is the position for you. This position will push your analytic skills to be more than numbers, and you will find opportunities to develop the business within a team environment.
· Studied and love Statistics and Figures.
· Familiarity with statistical software.
· Systemic vision and creative business thinking.
· Analyzing and creating marketing information for the purpose of ongoing activities.
· Analyzing customer behavior on website.
· Analyzing the effectiveness of marketing activities and production control reports.
· Using advanced tools for analysis and clearly displaying results.
· Working closely with Marketing.
Do you have a passion for coding? We have a great internship opportunity for people wanting to develop their programming skills in a real working company with real programming tasks. Help build upon our foundation and see how your implementations affect the running of the company.
· Building new functions as required for BlogsRelease.
· Fixing any issues that arise within the platform.
· Working within a dynamic team environment. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,165 |
Der Roma United Sports Club (auch bekannt als Roma FC) ist ein Fußballverein von den Cayman Islands. Die Männermannschaft spielt in der nationalen Fußballliga (CIFA Foster's National League).
Erfolge
Die erste Mannschaft der Männer hat einen nennenswerten Erfolg zu verzeichnen.
Digicel Cup: 2007/2008
Weblinks
Infos bei caymanfootball.ky (englisch)
Kaimanischer Fußballverein
Organisation (George Town, Cayman Islands)
Sport (George Town, Cayman Islands) | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 7,068 |
Make sure the following configuration is completed:
* [JDK](http://www.oracle.com/technetwork/java/javase/downloads/jdk8-downloads-2133151.html) >= 1.7 , and configure the environment variable
* Android SDK installed and configure the environment variable
* Android SDK version 23 (compileSdkVersion in build.gradle)
* SDK build tools version 21.1.2 (buildToolsVersion in build.gradle)
* Android Support Repository >= 17 (for Android Support Library)
* [Weex](https://weex.apache.org/) SDK >= 0.16.X
### Steps
The steps are as follows:
1. Create an Android project. There is nothing to be specified, according to your habits to.
2. **At this moment, our publication is being reviewed by Maven. Once published, source dependency will be changed to AAR dependency. **
Download source code, update build.gradle by adding the following dependencies:
```groovy
compile project ':bridges:weex-bridge:android:weex_bridge'
```
3. Register GCanvas Module and Component to your Weex Application.
```java
WXSDKEngine.registerModule("gcanvas", GCanvasWeexModule.class);
WXSDKEngine.registerComponent("gcanvas", WXGCanvasWeexComponent.class);
```
4. Modify AndroidManifest.xml, add below line to acquire OpenGL ES features.
```xml
<uses-feature android:glEsVersion="0x00020000" />
```
## iOS
#### Requirement
* Make sure that you have installed the [iOS development environment](https://help.apple.com/xcode/mac/current/#/dev60b6fbbc7) and [CocoaPods](https://guides.cocoapods.org/using/getting-started.html).
* Make sure that you have integrate [WeexSDK](https://github.com/apache/incubator-weex#ios)
* Make sure that you have insalled the [weex-toolkit](https://www.npmjs.com/package/weex-toolkit) in [Nodejs](https://nodejs.org/en/) 4.0+ for running case
#### Steps
1. Install components with CocoaPods
```objective-c
pod 'WeexGcanvas'
pod 'WeexPluginLoader'
```
`WeexPluginLoader` would dynamic register Weex `Module` and `Component` of GCanvas, so we do not need to register manually.
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,181 |
Frustrated by increasing numbers of patients arriving with drug advertisements and a "fixed idea ... of the outcome they wanted ..." internist John Abramson, MD, concluded he could "... help people to achieve better health ..." if he uncovered "... what the scientific evidence really shows and explain this to the public."1:xii He discovered "... a scandal in medical science." "Rigging medical studies, misrepresenting research results published in even the most influential medical journals, and withholding the findings of whole studies that don't come out in a sponsor's favor have all become the accepted norm in commercially sponsored medical research."1:xiii This corruption has been hidden by a "... complex web of corporate influence ... exacerbated by an interlocking financial arrangement between "... trusted medical experts and the medical industry ..." that results in conflicts of interest.1:xiii According to Dr Abramson "... there has been a virtual take-over of medical knowledge in the United States, leaving doctors and patients little opportunity to know the truth about good medical care ..." And, despite the "enormous costs," both the quality and delivery of health care in America has declined. Not only has the industry co-opted the mechanisms of evaluation of effective treatment for widely accepted illnesses but it has colonized the healthy population by the construction of new disorders transforming risk factors into diseases that putatively require long-term and expensive prophylactic medications. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,859 |
Q: What is the best data type to use in greendao for Decimal(10,2) I am trying to migrate my old db written in sqlite to greendao ORM , I need to set the column to DECIMAL(10,2) for storing the price of the item. What is the equivalent data type that I can use. DO I need to use a custom data type for that?
A: There are a couple of options, use a long value representing the smaller unit.
Then if you had a long price property, you could get the big unit using price / 100 and the small unit via price % 100. Like this you can still use price for regular integer calculation.
For formatting, don't forget an extra '0' for the small unit if it is single digit.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,415 |
ROOKIE RADFORD POTS WINNER, SIMPSON HURT
PHOTO : Rookie Brett Radford scored his first ever Junior A goal in overtime to help the Eagles defeat the Calgary Mustangs 3-2 on Saturday night. (photo courtesy of Julie Wilson)
Rookie Brett Radford scored his first-ever Junior A goal at the 1.09 mark of sudden-death overtime to give the Canmore Eagles a 3-2 victory over the visiting Calgary Mustangs in an Alberta Junior Hockey League game played Saturday night at the Canmore Recreation Centre.
It was the Eagles third straight victory over the Mustangs this year and improves the Eagles record to 6-7.
For the Eagles, Bryan Arneson scored on a second period penalty shot for his fourth of the year, while Simon Philp (4th) scored with just under three remaining in regulation to force the overtime. Jordan Revie had a two-assist night for the Eagles.
Goaltender Cameron Barnes picked up the win for Canmore to improve his record to 3-4. Canmore outshot the Mustangs by a 39-36 margin.
The victory did have a downside however as Eagles leading scorer Luke Simpson left the game towards the end of the second period with a possible dislocated elbow injury. Simpson currently leads the team in scoring with 8 goals and four assists.
"Luke was playing extremely well for us and will certainly be missed," said Eagles Head Coach and General Manager Andrew Milne. "But I was proud of the way the team fought back against the Mustangs and never gave up. These injuries give the younger players a chance to step up and gain some valuable playing minutes. It was good to see Radford score the overtime winner. With Luke out of lineup, we'll need to get some more goal production from everyone."
The Eagles now hit the road for five consecutive games starting on Sunday (Oct. 13) with an afternoon game against the Dragons in Drumheller. The game can be heard live on Mountain FM beginning at 2PM
Previous PostPONTIACS DRIVE AWAY WITH A "W"Next PostFOLLOW THE EAGLES ON THE ROAD | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,731 |
Q: Trying to compare a string to an array using strpos but not working I want to compare a variable called $value to items in a multidimensional array called $listofplaces. So when a user uploads a file I can validate it and see if it matches exactly to what's in my array.
My $lisofplaces Array looks like this when printed (I haven't added all the places as there are many):
array(3){
[0] =>
array(18){
["type"] => "FIELD"
…
["values"] =>
array(50)
[1] =>
array(3) {
["name"] => "Paris"
…}
[2] =>
array(3) {
["name"] => "London"
…}
}
}
my method to compare my variable to the array
if(strpos($value, $listofplaces) !== false){
echo 'found';} else{ echo 'not found';}
However this isn't working and I don't understand why please help:
Also I know the quotation marks are wrong I am doing this off my iPad
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,472 |
/** api: (define)
* module = gxp
* class = LayerUploadPanel
* base_link = `Ext.FormPanel <http://extjs.com/deploy/dev/docs/?class=Ext.FormPanel>`_
*/
Ext.namespace("gxp");
/** api: constructor
* .. class:: LayerUploadPanel(config)
*
* A panel for uploading new layer data to GeoServer.
*/
gxp.LayerUploadPanel = Ext.extend(Ext.FormPanel, {
/** i18n */
titleLabel: "Title",
titleEmptyText: "Layer title",
abstractLabel: "Description",
abstractEmptyText: "Layer description",
fileLabel: "Data",
fieldEmptyText: "Browse for data archive...",
uploadText: "Upload",
uploadFailedText: "Upload failed",
processingUploadText: "Processing upload...",
waitMsgText: "Uploading your data...",
invalidFileExtensionText: "File extension must be one of: ",
optionsText: "Options",
workspaceLabel: "Workspace",
workspaceEmptyText: "Default workspace",
dataStoreLabel: "Store",
dataStoreEmptyText: "Create new store",
defaultDataStoreEmptyText: "Default data store",
crsLabel: "CRS",
crsEmptyText: "Coordinate Reference System ID",
invalidCrsText: "CRS identifier should be an EPSG code (e.g. EPSG:4326)",
/** private: property[fileUpload]
* ``Boolean``
*/
fileUpload: true,
/** api: config[validFileExtensions]
* ``Array``
* List of valid file extensions. These will be used in validating the
* file input value. Default is ``[".zip", ".tif", ".tiff", ".gz", ".tar.bz2",
* ".tar", ".tgz", ".tbz2"]``.
*/
validFileExtensions: [".zip", ".tif", ".tiff", ".gz", ".tar.bz2", ".tar", ".tgz", ".tbz2"],
/** api: config[url]
* ``String``
* URL for GeoServer RESTConfig root. E.g. "http://example.com/geoserver/rest".
*/
/** private: property[defaultDataStore]
* ``string``
*/
defaultDataStore: null,
/** private: method[constructor]
*/
constructor: function(config) {
// Allow for a custom method to handle upload responses.
config.errorReader = {
read: config.handleUploadResponse || this.handleUploadResponse.createDelegate(this)
};
gxp.LayerUploadPanel.superclass.constructor.call(this, config);
},
/** private: property[selectedWorkspace]
* {Ext.data.Record}
*/
selectedWorkspace: null,
/** private: method[initComponent]
*/
initComponent: function() {
this.items = [{
xtype: "textfield",
name: "title",
fieldLabel: this.titleLabel,
emptyText: this.titleEmptyText,
allowBlank: true
}, {
xtype: "textarea",
name: "abstract",
fieldLabel: this.abstractLabel,
emptyText: this.abstractEmptyText,
allowBlank: true
}, {
xtype: "fileuploadfield",
id: "file",
anchor: "90%",
emptyText: this.fieldEmptyText,
fieldLabel: this.fileLabel,
name: "file",
buttonText: "",
buttonCfg: {
iconCls: "gxp-icon-filebrowse"
},
listeners: {
"fileselected": function(cmp, value) {
// remove the path from the filename - avoids C:/fakepath etc.
cmp.setValue(value.split(/[/\\]/).pop());
}
},
validator: this.fileNameValidator.createDelegate(this)
}, {
xtype: "fieldset",
ref: "optionsFieldset",
title: this.optionsText,
checkboxToggle: true,
collapsed: true,
hidden: this.workspace != undefined && this.store != undefined && this.crs != undefined,
hideMode: "offsets",
defaults: {
anchor: "97%"
},
items: [
this.createWorkspacesCombo(),
this.createDataStoresCombo(),
{
xtype: "textfield",
name: "nativeCRS",
// anchor: "90%",
fieldLabel: this.crsLabel,
emptyText: this.crsEmptyText,
allowBlank: true,
regex: /^epsg:\d+$/i,
regexText: this.invalidCrsText
}
],
listeners: {
collapse: function(fieldset) {
// reset all combos
fieldset.items.each(function(item) {
item.reset();
});
}
}
}];
this.buttons = [{
text: this.uploadText,
handler: function() {
var form = this.getForm();
if (form.isValid()) {
var fields = form.getFieldValues(),
jsonData = {'import': {}};
if (fields.workspace) {
jsonData["import"].targetWorkspace = {workspace: {name: fields.workspace}};
}
if (fields.store) {
jsonData["import"].targetStore = {dataStore: {name: fields.store}}
} else if (this.defaultDataStore) {
jsonData["import"].targetStore = {dataStore: {name: this.defaultDataStore}}
}
Ext.Ajax.request({
url: this.getUploadUrl(),
method: "POST",
jsonData: jsonData,
success: function(response) {
this._import = response.getResponseHeader("Location");
this.optionsFieldset.expand();
form.submit({
url: this._import + "/tasks",
waitMsg: this.waitMsgText,
waitMsgTarget: true,
reset: true,
scope: this
});
},
scope: this
});
}
},
scope: this
}];
this.addEvents(
/**
* Event: workspaceselected
* Fires when a workspace is selected.
*
* Listener arguments:
* panel - {<gxp.LayerUploadPanel} This form panel.
* record - {Ext.data.Record} The selected workspace record.
*/
"workspaceselected",
/**
* Event: datastoreselected
* Fires when a datastore is selected.
*
* Listener arguments:
* panel - {<gxp.LayerUploadPanel} This form panel.
* record - {Ext.data.Record} The selected datastore record.
*/
"datastoreselected",
/**
* Event: uploadcomplete
* Fires upon successful upload.
*
* Listener arguments:
* panel - {<gxp.LayerUploadPanel} This form panel.
* details - {Object} An object with an "import" property,
* representing a summary of the import result as provided by
* GeoServer's Importer API.
*/
"uploadcomplete"
);
this.getDefaultDataStore('default');
gxp.LayerUploadPanel.superclass.initComponent.call(this);
},
/** private: method[fileNameValidator]
* :arg name: ``String`` The chosen filename.
* :returns: ``Boolean | String`` True if valid, message otherwise.
*/
fileNameValidator: function(name) {
var valid = false;
var ext, len = name.length;
for (var i=0, ii=this.validFileExtensions.length; i<ii; ++i) {
ext = this.validFileExtensions[i];
if (name.slice(-ext.length).toLowerCase() === ext) {
valid = true;
break;
}
}
return valid || this.invalidFileExtensionText + '<br/>' + this.validFileExtensions.join(", ");
},
/** private: method[createWorkspacesCombo]
* :returns: ``Object`` Combo config.
*/
createWorkspacesCombo: function() {
return {
xtype: "combo",
name: "workspace",
ref: "../workspace",
fieldLabel: this.workspaceLabel,
emptyText: this.workspaceEmptyText,
store: new Ext.data.JsonStore({
url: this.getWorkspacesUrl(),
autoLoad: true,
root: "workspaces.workspace",
fields: ["name", "href"]
}),
displayField: "name",
valueField: "name",
mode: "local",
allowBlank: true,
triggerAction: "all",
forceSelection: true,
listeners: {
select: function(combo, record, index) {
this.getDefaultDataStore(record.get('name'));
this.fireEvent("workspaceselected", this, record);
},
scope: this
}
};
},
/** private: method[createDataStoresCombo]
* :returns: ``Ext.form.ComboBox``
*/
createDataStoresCombo: function() {
// this store will be loaded whenever a workspace is selected
var store = new Ext.data.JsonStore({
autoLoad: false,
root: "dataStores.dataStore",
fields: ["name", "href"]
});
this.on({
workspaceselected: function(panel, record) {
combo.reset();
var workspaceUrl = record.get("href");
store.removeAll();
store.proxy = new Ext.data.HttpProxy({
url: workspaceUrl.split(".json").shift() + "/datastores.json"
});
store.load();
},
scope: this
});
var combo = new Ext.form.ComboBox({
name: "store",
ref: "../dataStore",
fieldLabel: this.dataStoreLabel,
emptyText: this.dataStoreEmptyText,
store: store,
displayField: "name",
valueField: "name",
mode: "local",
allowBlank: true,
triggerAction: "all",
forceSelection: true,
listeners: {
select: function(combo, record, index) {
this.fireEvent("datastoreselected", this, record);
},
scope: this
}
});
return combo;
},
getDefaultDataStore: function(workspace) {
Ext.Ajax.request({
url: this.url + '/workspaces/' + workspace + '/datastores/default.json',
callback: function(options, success, response) {
this.defaultDataStore = null;
this.dataStore.emptyText = this.dataStoreEmptyText;
this.dataStore.setValue('');
if (response.status === 200) {
var json = Ext.decode(response.responseText);
//TODO Revisit this logic - currently we assume that stores
// with the substring "file" in the type are file based,
// and for file-based data stores we want to crate a new
// store.
if (json.dataStore && json.dataStore.enabled === true && !/file/i.test(json.dataStore.type)) {
this.defaultDataStore = json.dataStore.name;
this.dataStore.emptyText = this.defaultDataStoreEmptyText;
this.workspace.setValue(json.dataStore.workspace.name);
this.dataStore.setValue(this.defaultDataStore);
}
}
},
scope: this
});
},
/** private: method[getUploadUrl]
*/
getUploadUrl: function() {
return this.url + "/imports";
},
/** private: method[getWorkspacesUrl]
*/
getWorkspacesUrl: function() {
return this.url + "/workspaces.json";
},
/** private: method[handleUploadResponse]
* TODO: if response includes errors object, this can be removed
* Though it should only be removed if the server always returns text/html!
*/
handleUploadResponse: function(response) {
var obj = this.parseResponseText(response.responseText),
records, tasks, task, msg, i,
formData = this.getForm().getFieldValues(),
success = !!obj;
if (obj) {
if (typeof obj === "string") {
success = false;
msg = obj;
} else {
tasks = obj.tasks || [obj.task];
if (tasks.length === 0) {
success = false;
msg = "Upload contains no suitable files.";
} else {
for (i=tasks.length-1; i>=0; --i) {
task = tasks[i];
if (!task) {
success = false;
msg = "Unknown upload error";
} else if (!task.items.length) {
success = false;
msg = "Upload contains no items that can be imported.";
} else if (task.state !== "READY") {
if (!(task.state === "INCOMPLETE" && task.items[0].state === "NO_CRS" && formData.nativeCRS)) {
success = false;
msg = "Source " + task.source.file + " is " + task.state + ": " + task.items[0].state;
break;
}
}
}
}
}
}
if (!success) {
// mark the file field as invlid
records = [{data: {id: "file", msg: msg || this.uploadFailedText}}];
} else {
var itemModified = !!(formData.title || formData["abstract"] || formData.nativeCRS),
queue = [];
if (itemModified) {
this.waitMsg = new Ext.LoadMask((this.ownerCt || this).getEl(), {msg: this.processingUploadText});
this.waitMsg.show();
// for now we only support a single item (items[0])
var resource = task.items[0].resource,
layer = resource.featureType ? "featureType" : "coverage",
item = {id: task.items[0].id, resource: {}};
item.resource[layer] = {
title: formData.title || undefined,
"abstract": formData["abstract"] || undefined,
srs: formData.nativeCRS || undefined
};
Ext.Ajax.request({
method: "PUT",
url: tasks[0].items[0].href,
jsonData: item,
success: this.finishUpload,
failure: function(response) {
this.waitMsg.hide();
var errors = [];
try {
var json = Ext.decode(response.responseText);
if (json.errors) {
for (var i=0, ii=json.errors.length; i<ii; ++i) {
errors.push({
id: ~json.errors[i].indexOf('SRS') ? 'nativeCRS' : 'file',
msg: json.errors[i]
});
}
}
} catch(e) {
errors.push({
id: "file",
msg: response.responseText
});
}
this.getForm().markInvalid(errors);
},
scope: this
});
} else {
this.finishUpload();
}
}
// always return unsuccessful - we manually reset the form in callbacks
return {success: false, records: records};
},
finishUpload: function() {
Ext.Ajax.request({
method: "POST",
url: this._import,
failure: this.handleFailure,
success: this.handleUploadSuccess,
scope: this
});
},
/** private: parseResponseText
* :arg text: ``String``
* :returns: ``Object``
*
* Parse the response text. Assuming a JSON string but allowing for a
* string wrapped in a <pre> element (given non text/html response type).
*/
parseResponseText: function(text) {
var obj;
try {
obj = Ext.decode(text);
} catch (err) {
// if response type was text/plain, the text will be wrapped in a <pre>
var match = text.match(/^\s*<pre[^>]*>(.*)<\/pre>\s*/);
if (match) {
try {
obj = Ext.decode(match[1]);
} catch (err) {
obj = match[1];
}
}
}
return obj;
},
/** private: method[handleUploadSuccess]
*/
handleUploadSuccess: function(response) {
Ext.Ajax.request({
method: "GET",
url: this._import,
failure: this.handleFailure,
success: function(response) {
this.waitMsg.hide();
this.getForm().reset();
var details = Ext.decode(response.responseText);
this.fireEvent("uploadcomplete", this, details);
delete this._import;
},
scope: this
});
},
/** private: method[handleFailure]
*/
handleFailure: function() {
this.waitMsg.hide();
this.getForm().markInvalid([{file: this.uploadFailedText}]);
}
});
/** api: xtype = gxp_layeruploadpanel */
Ext.reg("gxp_layeruploadpanel", gxp.LayerUploadPanel);
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,832 |
\section{Introduction}
Magnetic fields in molecular clouds play an important role in
the early stages of star formation. They may regulate the
cloud fragmentation process, moderate the infall motions on to
density peaks, control angular momentum evolution through magnetic braking,
launch jets from the near-protostellar environment, and possibly
determine a finite mass reservoir for star formation by
limiting accretion from a magnetically-dominated envelope.
The prevailing macroturbulence in molecular cloud
envelopes also likely represents magnetohydrodynamic motions.
This paper concerns itself with the first two issues above:
we employ the first fully three-dimensional simulation to study the
role of magnetic fields {\it and} ion-neutral friction
in regulating gravitationally-driven fragmentation and infall.
The relative strengths of gravity and the magnetic field can be
quantified through the mass-to-flux ratio $M/\Phi$. There exists
a critical mass-to-flux ratio $(M/\Phi)_{\rm crit}$
\citep{mes56,str66,mou76,tom88} such that if
$M/\Phi > (M/\Phi)_{\rm crit}$, a pressure-bounded cloud
is supercritical and is prone to indefinite collapse
if the external pressure exceeds some value. This behaviour is
analogous to that of the nonmagnetic Bonnor-Ebert sphere. Conversely, if
$M/\Phi < (M/\Phi)_{\rm crit}$, a cloud is subcritical and cannot
collapse even in the limit of infinite external pressure, as long as
magnetic flux-freezing applies. A similar condition
$M/\Phi < (M/\Phi)_{\rm crit} = (2 \pi G^{1/2})^{-1}$ is required for
unconditional stability of
an infinite uniform (in $x,y$) layer that is flattened along the $z$-direction
of a background magnetic field \citep{nak78}. The various numerical
values of $(M/\Phi)_{\rm crit}$
differ by small factors of order unity, and we adopt the result of
\citet{nak78} since their model closely resembles the initial state in
our calculation.
Magnetic field strength measurements through the Zeeman effect
reveal that the mass-to-flux ratios are clustered about the
critical value for collapse \citep{cru99,cru04,shu99} and that
there is also an approximate equipartition
between the absolute values of gravitational energy and nonthermal
(hereafter, ``turbulent'') energy \citep{mye88,bas00}.
Measurements of polarized emission from dust grains, which reveal
the field morphology, generally indicate that the field in cloud
cores is well ordered and not dominated by turbulent motions,
with application of the Chandrasekhar-Fermi method yielding
mass-to-flux ratios near the critical value
\citep{lai01,lai02,cru04b,cur04,kir06}.
\citet{mes56} pointed out that
even if clouds are magnetically supported,
ambipolar diffusion (resulting from ion-neutral slip) will cause
the support to be lost and stars to form. More specifically,
a medium with a subcritical mass-to-flux ratio will still
undergo a gravitationally-driven instability, occurring
on the ambipolar diffusion time scale rather than
the dynamical time scale \citep{lan78,zwe98,cio06}. The
length scale of the instability is essentially the Jeans
scale in the limit of highly subcritical clouds (the same
length scale as for highly supercritical fragmentation) but
can be much larger when the mass-to-flux ratio is
close to the critical value \citep{cio06}.
Most nonlinear calculations of ambipolar diffusion
driven evolution have focused on a single axisymmetric
core, but newer models focus on a fragmentation process
that results in the formation of multiple cores and somewhat
irregular density and velocity structure.
\citet{ind00} carried out a two-dimensional simulation
of an infinitesimally-thin sheet threaded by an initially
perpendicular magnetic field.
Starting with slightly subcritical initial conditions, they
followed the initial growth of mildly elongated fragments which
occurred on a time scale intermediate between the dynamical
time associated with supercritical collapse and the ambipolar diffusion
time-scale associated with highly subcritical clouds.
\citet{bas04} carried out two-dimensional simulations of
a magnetized sheet in the thin-disc approximation, which
incorporates a finite disc half-thickness $Z$
consistent with hydrostatic equilibrium and thereby
includes the effect of magnetic pressure.
They studied a model which had an initially critical
mass-to-flux ratio and another which was supercritical
by a factor of two. One of their main results was that
the critical model had subsonic (maximum speed $\approx
0.5 c_{\rm s}$, where $c_{\rm s}$ is the isothermal sound speed) infall,
while the decidedly supercritical cloud had infall speeds
$\ga 1 c_{\rm s}$ on scales $\sim 0.1$ pc from the core centres.
This is a significant
observationally-testable difference between dynamical
(supercritical) fragmentation and ambipolar-diffusion regulated
(critical or subcritical) fragmentation. Yet another mode of
fragmentation is the so-called turbulent fragmentation, which in
fact corresponds to collapse driven by a strong external compression.
\citet{li04} and \citet{nak05} have studied this process for a
magnetized sheet using the thin-disc approximation,
and including the effect of ion-neutral friction. They find that
a mildly subcritical cloud can undergo locally rapid ambipolar
diffusion and form multiple fragments because of an initial
large-scale highly supersonic compression wave. The core formation
occurs on a crossing time of the simulation box, which is related
to the dynamical time. \citet{li04} estimate that such a process can
simultaneously maintain a relatively low efficiency of star formation,
as is required by observations \citep{lad03}.
In this paper, we study the three-dimensional extension of models
such as those of \citet{ind00} and \citet{bas04}. The self-consistent
calculation of the vertical structure of the cloud allows us to
test the predictions of two-dimensional models as well as to make
some new predictions. We model clouds
that are either decidedly supercritical or subcritical and study the
evolution after the introduction of small-amplitude perturbations.
The case of compression-induced collapse will be studied in a
separate paper. We note that our three-dimensional model is not
a cubic region but rather a flattened three-dimensional layer that
is consistent with the expected settling of gas along the
direction of the magnetic field. In reality, we believe that our modeled
region would represent the dense midplane of a larger more turbulent
cloud. As demonstrated by the one-dimensional models of
\citet{kud03,kud06}, the turbulent motions in a stratified magnetized
cloud develop the largest amplitude motions in the outer low-density
envelope, while maintaining transonic or subsonic motions near the
midplane. We believe that the fragmentation process as modeled
in this paper may proceed while long-lived turbulent motions continue
on larger scales.
\section{Numerical Model}
\subsection{Basic Equations}
\label{equation}
We solve the three-dimensional magnetohydrodynamic
(MHD) equations including self-gravity and ambipolar diffusion,
assuming that neutrals are much more numerous than ions:
\begin{equation}
\frac{\partial \rho}{\partial t}
+ \mbox{\boldmath$v$} \cdot \nabla \rho
= -\rho \nabla \cdot \mbox{\boldmath$v$},
\label{eq:continuity}
\end{equation}
\begin{equation}
\frac{\partial \mbox{\boldmath$v$}}{\partial t}
+ (\mbox{\boldmath$v$} \cdot \nabla) \mbox{\boldmath$v$}
=-\frac{1}{\rho} \nabla p
+ \frac{1}{c \rho} \mbox{\boldmath$j$} \times \mbox{\boldmath$B$}
- \nabla \psi,
\label{eq:momentum}
\end{equation}
\begin{equation}
\frac{\partial \mbox{\boldmath$B$}}{\partial t}
= \nabla \times (\mbox{\boldmath$v$} \times \mbox{\boldmath$B$})
+ \nabla \times \left[\frac{\tau_{ni}}{c\rho} (\mbox{\boldmath$j$} \times \mbox{\boldmath$B$}) \times \mbox{\boldmath$B$}\right],
\label{eq:induction}
\end{equation}
\begin{equation}
\mbox{\boldmath$j$}=\frac{c}{4\pi} \nabla \times \mbox{\boldmath$B$},
\end{equation}
\begin{equation}
\nabla ^2 \psi = 4\pi G \rho,
\label{eq:poisson}
\end{equation}
\begin{equation}
p=c_s^2 \rho,
\end{equation}
where $\rho$ is the density of neutral gas, $p$ is the pressure,
{\boldmath$v$} is the velocity, {\boldmath$B$} is the magnetic field,
{\boldmath$j$} is the electric current density,
$\psi$ is the self-gravitating potential,
and $c_s$ is the sound speed.
Instead of solving a detailed energy equation, we assume isothermality
for each Lagrangian fluid particle
\citep{kud03,kud06}:
\begin{equation}
\frac{d c_s}{dt}
= \frac{\partial c_s}{\partial t}
+ \mbox{\boldmath$v$} \cdot \nabla c_s = 0.
\label{eq:isothermal}
\end{equation}
For the neutral-ion collision time in equation (\ref{eq:induction})
and associated quantities,
we follow \citet{bas94}, so that
\begin{equation}
\tau_{ni} = 1.4\, \frac{m_i+m_n}{\rho_i \langle \sigma w \rangle_{in}},
\label{eq:tau}
\end{equation}
where $\rho_i$ is the density of ions and $\langle\sigma w\rangle_{in}$
is the average collisional rate between ions of mass $m_i$ and neutrals
of mass $m_n$. Here, we use typical values of HCO$^+$-H$_2$ collisions,
for which $\langle\sigma w\rangle_{in}=1.69 \times 10^{-9}$ cm$^{-3}$s$^{-1}$
and $m_i/m_n =14.4$. We also assume that
the ion density $\rho_i$ is determined by the approximate relation
\citep{elm79,nak79}
\begin{equation}
\rho_i=m_i K \left(\frac{\rho/m_n}{10^5 \mbox{cm$^{-3}$}}\right)^k,
\end{equation}
where we assume $K=3 \times 10^{-3}$cm$^{-3}$ and $k=0.5$
throughout this paper.
\subsection{Initial Conditions}
As an initial condition, we assume hydrostatic equilibrium of
a self-gravitating one-dimensional cloud along $z$-direction
\citep{kud03,kud06}. The hydrostatic equilibrium is calculated
from equations
\begin{equation}
\frac{dp}{dz}=\rho g_z,
\label{eq:hsp}
\end{equation}
\begin{equation}
\frac{dg_z}{dz}=-4\pi G \rho,
\label{eq:hsg}
\end{equation}
\begin{equation}
p=c_s^2 \rho,
\label{eq:hss}
\end{equation}
subject to the boundary conditions
\begin{equation}
g_z(z=0)=0,\ \ \rho(z=0)=\rho_0,\ \ p(z=0)=\rho_0 c_{s0}^2
\end{equation}
where $\rho_0$ and $c_{s0}$ are the initial density and
sound speed at $z=0$.
If the initial sound speed (temperature) is uniform throughout the region,
we have the following analytic solution $\rho_S$ found by \citet{spi42}:
\begin{equation}
\rho_S(z)=\rho_0 \,\mbox{sech}^2(z/H_0),
\end{equation}
where
\begin{equation}
H_0=\frac{c_{s0}}{\sqrt{2\pi G \rho_0}}
\end{equation}
is the scale height.
However, an isothermal molecular cloud is usually surrounded
by warm material, such as neutral hydrogen gas.
Hence, we assume the initial sound speed distribution to be
\begin{equation}
c_{s}^2(z)=c_{s0}^2
+ \frac{1}{2} (c_{sc}^2 - c_{s0}^2)
\left[ 1+\tanh \left(\frac{|z|-z_c}{z_d}\right) \right]
\end{equation}
where we take $c_{sc}^2=10\,c_{s0}^2$, $z_c=2H_0$, and $z_d=0.1H_0$
throughout the paper. By using this sound speed distribution, we can solve equations
(\ref{eq:hsp})-(\ref{eq:hss}) numerically. The initial density distribution
of the numerical solution shows that it is almost the same as Spitzer's
solution for $0 \leq z \leq z_c$.
We also assume that the initial magnetic field is uniform along the $z$-direction:
\begin{equation}
B_z=B_0,\ \ B_x=B_y=0,
\end{equation}
where $B_0$ is constant.
In this equilibrium sheet-like gas, we input a random velocity perturbation
\citep{miy87b} at each grid point:
\begin{equation}
v_x=0.1c_{s0}R_m,\ \ v_y=0.1c_{s0}R_m,\ \ v_z=0.0
\end{equation}
where $R_m$ is a random number chosen uniformly from the range [-1,1].
The $R_m$'s for each of $v_x$ and $v_y$ are independent realizations.
However, each model presented in this paper uses the same pair of realizations
of $R_m$ for generating the initial perturbations.
\subsection{Numerical Parameters}
A set of fundamental units for this problem are
$c_{s0}$, $H_0$, and $\rho_0$. These yield a time
unit $t_0=H_0/c_{s0}$. The initial magnetic field
strength introduces one dimensionless free parameter,
\begin{equation}
\beta_0 \equiv \frac{8 \pi p_0}{B_0^2}
= \frac{8 \pi \rho_0 c_{s0}^2}{B_0^2},
\end{equation}
the ratio of gas to magnetic pressure
at $z=0$.
In the sheet-like equilibrium cloud with a vertical
magnetic field, $\beta_0$ is related to the mass-to-flux ratio
for Spitzer's self-gravitating cloud. The mass-to-flux ratio
normalized to the critical value is
\begin{equation}
\mu_S \equiv 2\pi G^{1/2} \frac{\Sigma_S}{B_0}
\end{equation}
where
\begin{equation}
\Sigma_S=\int_{-\infty}^{\infty} \rho_S dz = 2\rho_0 H_0
\end{equation}
is the column density of Spitzer's self-gravitating cloud.
Therefore,
\begin{equation}
\beta_0=\mu_S^2.
\end{equation}
Although the initial cloud we used is not exactly
the same as the Spitzer cloud, $\beta_0$ is a good
indicator to whether or not the magnetic field
can prevent gravitational instability
\citep{nak78}.
Dimensional values of all quantities can be found
through a choice of $\rho_0$ and $c_{s0}$.
For example, for $c_{s0}=0.2$ km s$^{-1}$ and $n_0=\rho_0/m_n=10^4$ cm$^{-3}$,
we get $H_0=0.05$ pc, $t_0=2.5 \times 10^5$ yr, and
$B_0=20\,\mu$G if $\beta_0=1$.
\subsection{Numerical Technique}
In order to solve the equations numerically, we use the
CIP method \citep{yab91a,yab01}
for equations (\ref{eq:continuity}), (\ref{eq:momentum})
and (\ref{eq:isothermal}), and the method of
characteristics-constrained transport (MOCCT; \citet{sto92})
for equation (\ref{eq:induction}), including an explicit integration
of the ambipolar diffusion term. The combination of the CIP and
MOCCT methods is summarized in \citet{kud99} and
\citet{oga04}. It includes the CCUP method
\citep{yab91b} for the calculation of gas pressure,
in order to get more numerically stable results.
The numerical code in this paper is based on
that of \citet{oga04}.
In this paper, the ambipolar diffusion term is only included when the
density is greater than a certain value, $\rho_{cr}$.
We let $\rho_{cr}=0.3\rho_0$ both for numerical convenience
and due to the physical idea
that the low density region is affected
by external ultraviolet radiation so that the ionization fraction
becomes large, i.e. $\tau_{ni}$ becomes small
\citep{cio95}.
Under this assumption, the upper atmosphere of the sheet-like cloud
is not affected by ambipolar diffusion.
This simple assumption helps to avoid very small time-steps
due to the low density region in order to maintain stability of
the explicit numerical scheme.
We used a mirror-symmetric boundary
condition at $z=0$ and periodic boundaries in the $x$
and $y$-directions. At the upper boundary
at $z=z_{\rm out}=4H_0$, we also used a mirror-symmetric boundary
except when we solve the gravitational potential. This symmetric condition
is just for numerical convenience. However, because
the results we show later in this paper are consistent with previous
two-dimensional simulations, we believe that the boundary conditions
do not affect the result significantly. The Poisson equation (\ref{eq:poisson})
is solved by the Greens function method to compute the gravitational
kernels in $z$-direction, along with a Fourier transform
method in the $x$ and $y$-directions \citep{miy87b}.
This method of solving the Poisson equation allows us to
find the gravitational potential of a vertically isolated cloud
within $|z|<z_{\rm out}$.
The computational region is $|x|,|y| \leq 8\pi H_0$ and
$0 \leq z \leq 4H_0$.
The number of grid points for each direction is $(N_x,N_y,N_z)=(64,64,40)$.
Since the most unstable wavelength for no magnetic field is about
$4\pi H_0$
\citep{miy87a},
we have 16 grid points within this wavelength.
We have also 10 grid points within the scale height of the initial cloud
in the $z$-direction. While this is not a high-resolution simulation,
we believe that we have the minimum number of grid points
to study the gravitational instability, especially by using
the code based on CIP \citep{oga04}.
The maximum computational time, which occurs for the case of the
subcritical cloud,
is about 85 hours of CPU time using a single processor
of the VPP5000 in the National Astronomical Observatory of Japan.
\section{Results}
\label{results}
\begin{figure}
\resizebox{\hsize}{!}{\includegraphics{f1.eps}}
\caption{
The time evolution of the density at the location
where the density reaches its maximum value in each simulation.
Each line shows a case of different $\beta_0$.
}
\label{fig1}
\end{figure}
Figure 1 shows the time evolution of the density at the location
where the density reaches its maximum value in each simulation.
The simulations are stopped when the maximum density is about
$30 \rho_0$.
Each line shows a case of different
$\beta_0$. When $\beta_0$ is 100 or 4, the magnetic field is not
strong enough to suppress the self-gravitational instability of
the cloud. In these cases, the density evolves rapidly, over the sound-crossing
time of the most unstable wavelength ($\sim 4\pi H_0$).
However, when $\beta_0=0.25$, the cloud is self-gravitationally
stable unless ion-neutral slip is present. Therefore, the density evolves
gradually over the diffusion time of the magnetic field.
According to the two-dimensional linear analysis by \citet{cio06},
the evolutionary time scale of a significantly subcritical cloud is
about ten times longer than the dynamical time,
for a standard ionization fraction, as used here.
Our numerical result is consistent with their analysis.
\begin{figure}
\resizebox{\hsize}{!}{\includegraphics{f2.eps}}
\caption{
The logarithmic density contours for $\beta_0=0.25$ at $t=150$.
Arrows show velocity vectors on each cross section.
Upper panel shows the cross section at $z=0$, and the lower panel
shows the cross section at $y=4.3$.
}
\label{fig2}
\end{figure}
\begin{figure}
\resizebox{\hsize}{!}{\includegraphics{f3.eps}}
\caption{
The logarithmic density contours for $\beta_0=4$ at $t=15.3$.
Arrows show velocity vectors on each cross section.
Upper panel shows the cross section at $z=0$, and the lower panel
shows the cross section at $y=5.1$.
}
\label{fig3}
\end{figure}
\begin{figure}
\resizebox{\hsize}{!}{\includegraphics{f4.eps}}
\caption{
The logarithmic density contours for $\beta_0=100$ at $t=11.1$.
Arrows show velocity vectors on each cross section.
Upper panel shows the cross section at $z=0$, and the lower panel
shows the cross section at $y=5.1$.
}
\label{fig4}
\end{figure}
Figure 2, Figure 3, and Figure 4 show the logarithmic density
contours for $\beta_0=0.25$ at $t=150$, $\beta_0=4$ at $t=15.3$,
and $\beta_0=100$ at $t=11.1$ respectively. Each upper panel shows
the cross section at $z=0$, and the lower panel shows the cross
section at $y=4.3$ for $\beta_0=0.25$, $y=5.1$ for $\beta_0=4$,
and $y=5.1$ for $\beta_0=100$ respectively.
The values of $y$ for the lower panels are chosen so that the
vertical cut passes through at least one dense core.
(In these numerical simulations, we use the term "core"
to refer to the region where the density is greater than the mean
background density by about a factor of 3.)
The size of cores for $\beta_0=4$ is bigger
than that of $\beta_0=100$. The size becomes smaller again
when the magnetic field is stronger than critical ($\beta_0=0.25$).
This result is consistent with the two-dimensional linear analysis
of \citet{cio06}, who found a hybrid mode for critical or
mildly supercritical clouds in which the combined effect of field-line
dragging and magnetic restoring forces enforce a larger than usual
fragmentation scale.
Arrows show velocity vectors on each cross section.
Maximum velocities become supersonic for $\beta_0=4$ and $\beta_0=100$,
but remain subsonic for $\beta_0=0.25$. This is also consistent
with the two-dimensional numerical simulations of \citet{bas04}.
\begin{figure}
\resizebox{\hsize}{!}{\includegraphics{f5_v2.eps}}
\caption{
The close up views of the density contours around cores for $\beta_0=0.25$.
Magnetic field lines near cores are also plotted in three-dimensional space.
}
\label{fig5}
\end{figure}
\begin{figure}
\resizebox{\hsize}{!}{\includegraphics{f6_v2.eps}}
\caption{
The close up views of the density contours around cores for $\beta_0=4$.
Magnetic field lines near cores are also plotted in three-dimensional space.
}
\label{fig6}
\end{figure}
Figure 5 and Figure 6 shows the close up views of the density
contours around cores for $\beta_0=0.25$ and $\beta_0=4$ respectively.
Magnetic field lines near cores are also plotted in three-dimensional space.
When $\beta_0=0.25$, the neutral gas has to slip through the field lines
to make a gravitationally bound core. Therefore, the field lines are
not so deformed in the case of $\beta_0=0.25$, in contrast to
those of $\beta_0=4$.
\begin{figure}
\resizebox{\hsize}{!}{\includegraphics{f7_v2.eps}}
\caption{
The logarithmic contours of plasma $\beta$ for $\beta_0=0.25$ at $t=150$.
Upper panel shows the cross section at $z=0$, and the lower panel
shows the cross section at $y=4.3$.
}
\label{fig7}
\end{figure}
\begin{figure}
\resizebox{\hsize}{!}{\includegraphics{f8.eps}}
\caption{
The logarithmic contours of plasma $\beta$ for $\beta_0=4$ at $t=15.3$.
Upper panel shows the cross section at $z=0$, and the lower panel
shows the cross section at $y=5.1$.
}
\label{fig8}
\end{figure}
Figure 7 and Figure 8 show the logarithmic contours of
plasma $\beta$ for $\beta_0=0.25$ at $t=150$ and $\beta_0=4$
at $t=15.3$, respectively. When $\beta_0=0.25$,
the plasma $\beta$ in cores is {\it greater than in the surroundings}.
This is because the mass-to-flux ratio (and therefore $\beta$)
has to increase in order for the core to become gravitationally
unstable.
The maximum $\beta$ is larger than 1 at the centre of a core,
which means that the centre of the core is approximately supercritical.
In contrast to this, the plasma $\beta$ in cores is {\it slightly lower
than the surroundings} when $\beta_0=4$. In this case,
the magnetic field is swept up by the contracting cloud
before ion-neutral slip works efficiently.
If hydrostatic equilibrium along the $z$-direction is exactly satisfied,
the plasma $\beta$ would remain constant in time and space.
The slightly lower values of $\beta$ in cores are probably caused
by the modestly nonequilibrium state along $z$ during the evolution.
\begin{figure}
\resizebox{\hsize}{!}{\includegraphics{f9.eps}}
\caption{
The densities, plasma $\beta$, and $v_x$ along $x$-axes
for lines that cut through the cores shown in Figure 5 and Figure 6.
The left panel shows the core for $\beta_0=0.25$.
The right panel shows the core for $\beta_0=4$.
}
\label{fig9}
\end{figure}
\begin{figure}
\resizebox{\hsize}{!}{\includegraphics{f10_v2.eps}}
\caption{
The densities, plasma $\beta$, and $v_z$ along $z$-axes
for lines that cut through the cores shown in Figure 5 and Figure 6.
The left panel shows the core for $\beta_0=0.25$.
The right panel shows the core for $\beta_0=4$.
}
\label{fig10}
\end{figure}
Figure 9 shows the densities, plasma $\beta$, and $v_x$
along $x$-axes for lines that cut through the cores
shown in Figure 5 and Figure 6. The left panel shows
the core for $\beta_0=0.25$. The right panel shows the core
for $\beta_0=4$. Figure 9 shows that the plasma $\beta$ in
the core is higher than the surroundings for $\beta_0=0.25$ and
lower for $\beta_0=4$. The infall velocity
for $\beta_0=4$ shows supersonic values, while the velocity for
$\beta_0=0.25$ is subsonic. These velocities are comparable to
those in Figure 2 and Figure 3 of \citet{bas04}. Figure 10 shows
the densities, plasma $\beta$, and $v_z$ along $z$-axes
for lines that cut through the same cores. It also shows that
the infall velocity for $\beta_0=4$ reaches mildly supersonic values,
while the velocity for $\beta_0=0.25$ is subsonic.
\begin{figure}
\resizebox{\hsize}{!}{\includegraphics{f11_v3.eps}}
\caption{
Open circles show the magnetic field strength as a function of density
along $z=0$ at $t=150$ for the model with $\beta_0=0.25$.
The strength of the magnetic field is normalized
by $\sqrt{8\pi \rho_0 c_{s0}^2}$.
Filled circles are the same for $\beta_0=4$, at $t=15.3$.
The blue line shows the evolutionary track of the point at which the density
achieves its maximum value for the model with $\beta_0=0.25$.
The red line is the same for $\beta_0=4$.
}
\label{fig11}
\end{figure}
Figure 11 shows the relation between density and magnetic field
on the plane $z=0$. The strength of the magnetic field is normalized
by $\sqrt{8\pi \rho_0 c_{s0}^2}$. Open circles show the magnetic field strength
as a function of density along $z=0$ at $t=150$ for the model with
$\beta_0=0.25$ (see Fig. 2). Filled circles are the same
for $\beta_0=4$, at $t=15.3$ (see Fig. 3). The blue line
shows the evolutionary track of the point at which the density
achieves its maximum value for the model with $\beta_0=0.25$.
The red line is the same but for $\beta_0=4$. This figure
shows that {\it the snapshot of the relation between density and
magnetic field at different spatial points in the midplane of the cloud overlaps
with the evolutionary track of an individual core} . The dashed line
shows $B \propto \rho^{0.5}$. When the density becomes large,
each relation approximately tends to $B \propto \rho^{0.5}$.
In the case of $\beta_0=0.25$, the relation
shows that core initially evolves to greater density without increasing
the magnetic field strength. This is caused by the slip of neutral
gas through the magnetic field during the subcritical phase of evolution.
\section{Conclusions and Discussion}
\label{conclusion}
We have studied fragmentation of a sheet-like self-gravitating cloud
by three-dimensional MHD simulations. The main results are as follows.
\begin{itemize}
\item
We confirmed that in the case of an initially
subcritical cloud ($\beta_0=0.25$), cores
developed gradually over an ambipolar diffusion time,
while the cores in an initially supercritical cloud
($\beta_0=4$ or $\beta_0=100$) developed
in a dynamical time.
\item
The infall speed on to cores is subsonic in the case of an initially
subcritical cloud, while there is extended supersonic
infall in the case of an initially supercritical cloud.
This is consistent with the result of the two-dimensional
simulations of \citet{bas04}. In our three-dimensional simulations,
we also find that the $z$-component of the velocity follows
the same pattern.
\item
The size of cores for mildly supercritical cloud ($\beta_0=4$)
is bigger than that of highly supercritical cloud ($\beta_0=100$).
The size becomes smaller again when the magnetic field is stronger
than the critical ($\beta_0=0.25$). This result is consistent with
the two-dimensional linear analysis of \citet{cio06}.
\item
When the cloud is initially subcritical ($\beta_0=0.25$),
the plasma $\beta$ in cores is greater than in the surroundings.
In contrast to this, the plasma $\beta$ in cores is slightly lower
than the surroundings when the cloud is initially supercritical
($\beta_0=4$).
The latter result is probably
caused by the modestly nonequilibrium state along $z$ during
the evolution.
\item
In the $B-\rho$ plane, the snapshot of the relation between
magnetic field strength ($B$) and density ($\rho$)
at different spatial points of the cloud overlaps with
the evolutionary track of an individual core.
When the density becomes large, each relation
approximately tends to $B \propto \rho^{0.5}$.
\end{itemize}
Our simulation is the first fully three-dimensional simulation
to study the role of magnetic fields and ion-neutral friction
in fragmentation. In this paper, we concentrated
on the effect of initially small perturbations,
partly as a way to compare with established predictions of
linear theory.
Our models also serve as a guide to understand fragmentation
occurring exclusively in dense subregions of clouds that
contain only subsonic or transonic motions.
Real molecular clouds certainly
contain supersonic turbulence, at least in their low-density
envelopes, as is observed through large line-widths of
emission lines from relatively low-density tracers.
The additional effect of supersonic turbulence on
three-dimensional fragmentation
with magnetic fields and ion-neutral friction
will be studied in an upcoming paper.
\section*{Acknowledgments}
SB was supported by a research grant from NSERC.
The numerical computations were done mainly on the VPP5000
at the National Astronomical Observatory of Japan.
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,198 |
Q: Why for loop order effect running time in matrix multiplication? I'am writing a C program to calculate the product of two matrix.
The problem That I noticed that the order of for loops does matter. For example:
for N=500
for (int i = 0; i < N; ++i) {
for (int j = 0; j < N; ++j) {
for (int k = 0 ; k < N; ++k) {
C[i*N+j]+=A[i*N+k] * B[k*N+j];
}
}
}
execution time (Seconds) : 1.1531820000
for (int j = 0; j < N; ++j) {
for (int k = 0 ; k < N; ++k) {
for (int i = 0; i < N; ++i) {
C[i*N+j]+=A[i*N+k] * B[k*N+j];
}
}
}
execution time (Seconds) : 2.6801300000
Matrix declaration:
A=(double*)malloc(sizeof(double)*N*N);
B=(double*)malloc(sizeof(double)*N*N);
C=(double*)malloc(sizeof(double)*N*N);
I run the test for 5 time than calculate the average. Anyone have an idea why is this happening?
A: With the second loop, you keep making many big jumps all the time when you increment i in the inner loop, and to a lesser extent k. The cache is probably not very happy with that.
The first loop is better, indeed it's even better if you invert the orders of j and k.
This is essentially a problem of data locality. Accesses to main memory are very slow on modern architectures, so your CPU will keep caches of recently accessed memory and try to prefetch memory that is likely to be accessed next. Those caches are very efficient at speeding up accesses that are grouped in the same small area, or accesses that follow a predictable pattern.
Here we turned a pattern where the CPU would make big jumps through memory and then come back into a nice mostly sequential pattern, hence the speedup.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,130 |
#region Licence
#endregion
using System;
using FluentAssertions;
using Paramore.Brighter.DynamoDB.Tests.TestDoubles;
using Paramore.Brighter.Inbox.DynamoDB;
using Xunit;
namespace Paramore.Brighter.DynamoDB.Tests.Inbox
{
[Trait("Category", "DynamoDB")]
[Collection("DynamoDB Inbox")]
public class DynamoDbImboxDuplicateMessageTests : DynamoDBInboxBaseTest
{
private readonly DynamoDbInbox _dynamoDbInbox;
private readonly string _contextKey;
private readonly MyCommand _raisedCommand;
private Exception _exception;
public DynamoDbImboxDuplicateMessageTests()
{
_dynamoDbInbox = new DynamoDbInbox(Client);
_raisedCommand = new MyCommand { Value = "Test" };
_contextKey = "context-key";
_dynamoDbInbox.Add(_raisedCommand, _contextKey);
}
[Fact]
public void When_The_Message_Is_Already_In_The_Inbox()
{
_exception = Catch.Exception(() => _dynamoDbInbox.Add(_raisedCommand, _contextKey));
//_should_succeed_even_if_the_message_is_a_duplicate
_exception.Should().BeNull();
}
[Fact]
public void When_The_Message_Is_Already_In_The_Inbox_Different_Context()
{
_dynamoDbInbox.Add(_raisedCommand, "some other key");
var storedCommand = _dynamoDbInbox.Get<MyCommand>(_raisedCommand.Id, "some other key");
//_should_read_the_command_from_the__dynamo_db_inbox
AssertionExtensions.Should((object) storedCommand).NotBeNull();
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,071 |
{"url":"https:\/\/clay6.com\/qa\/129895\/if-the-standard-deviation-of-the-numbers-2-3-a-and-11-is-3-5-then-which-of-","text":"Comment\nShare\nQ)\n\n# If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true ?\n\n( A ) $3a^2\u221223a+44=0$\n( B ) $3a^2\u221226a+55=0$\n( C ) $3a^2\u221232a+84=0$\n( D ) $3a^2\u221226a+55=0$","date":"2020-12-04 17:49:42","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6617166996002197, \"perplexity\": 614.120459498248}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 5, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-50\/segments\/1606141740670.93\/warc\/CC-MAIN-20201204162500-20201204192500-00319.warc.gz\"}"} | null | null |
(Created article.)
After marrying Olga Penner, Hildor and Olga attended Prairie Bible Institute and worked with the music team. Hildor, together with his brothers [[Janz, Leo (1919-2006)|Leo]] and Adolph, and Adolph's brother-in-law Cornelius Enns, formed the Janz Quartet in 1946. In 1951 the German branch of the mission organization Youth for Christ invited the Janz Quartet to minister as part of a nationwide crusade for three months.
In 1954 Hildor moved to [[Los Angeles (California, USA)|Los Angeles]], California, where he studied voice under the direction of some of the best singers in the world.
Hildor Erford Janz: evangelist and musician; born 27 April 1921 in Main Centre, Saskatchewan, Canada. Hildor was the second youngest of 11 children of Johann Janz (b. 6 February 1878, Friedensfeld, Russia) and Maria (Jahnke) Janz (b. 14 August 1882, Blumenhof, Manitoba). Hildor married Olga Penner (11 August 1920, Main Centre, Saskatchewan – 17 July 2010, Abbotsford, British Columbia, Canada), daughter of Peter Penner (1898-1988) and Anna (Funk) Penner (b. 1898). Hildor and Olga had 6 children. Hildor died on 31 March 2007 in Abbotsford, BC, where he is buried in the Maclure Road Mennonite Cemetery. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 474 |
Q: Unable to change add to cart button using AJAX I am calling product list on click of category button
as follow :
$id = $_GET['ServiceId'];
?>
<ul class="products">
<?php
$args = array( 'post_type' => 'product', 'posts_per_page' => 10, 'product_cat' => $id, 'orderby' => 'rand' );
$loop = new WP_Query( $args );
while ( $loop->have_posts() ) : $loop->the_post(); global $product; ?>
<div>
<li class="food_menu">
<a href="<?php echo get_permalink( $loop->post->ID ) ?>" title="<?php echo esc_attr($loop->post->post_title ? $loop->post->post_title : $loop->post->ID); ?>">
<?php woocommerce_show_product_sale_flash( $post, $product ); ?>
<?php if (has_post_thumbnail( $loop->post->ID )) echo get_the_post_thumbnail($loop->post->ID, 'shop_catalog'); else echo '<img src="'.woocommerce_placeholder_img_src().'" alt="Placeholder" />'; ?>
<div class="heading_food">
<h3 class="food_head"><?php the_title(); ?></h3>
<p class="food_head1">Description 1</p>
<p class="food_head1">Description 2</p>
</div>
<div class="price"><?php echo $product->get_price_html(); ?></div>
<div class="qty1" style="width:100%;margin-top:60px">
<?php woocommerce_template_loop_add_to_cart( $loop->post, $product ); ?>
</div>
</li>
</div>
<?php endwhile; ?>
<?php wp_reset_query(); ?>
It shows me the list of product of that category, It shows a Add to cart button, I want is that if anyone click on this button then it should cahnge to added to cart and add to cart button should be disabled. How can I do this ?
A: Try this code.I hope, Its will help you..
HTML:
<input type="submit" value="Add to cart" class="add_cart">
Script:
jQuery('.add_cart').on('click', function () {
jQuery(this).prop('disabled', true); // for disabled button
jQuery(this).val('Added to cart'); // for change button as Added to cart
}
Thank You!!
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 9,733 |
Journals/Series
Sort by:-- Title Author first name Author last name Date posted Date published
All languages -- Arabic Chinese French German Hebrew Norwegian Persian Portuguese Russian Spanish Swedish Welsh -- all languages all but English
Select another collection: Archive Articles, published Articles, unpublished Articles, newspaper Articles, encyclopedia Audio Bibliographies BIC, published Biographies Books Chronologies, timelines Compilations, official Compilations, personal Documents, historical Essays, informal Etcetera Excerpts from books Fiction Guardian, letters Histories, memoirs Introductory items Letters, personal Maps NSA documents NSA letters Pilgrims notes Poetry Presentations Research notes Reviews of books etc. Statistics Study guides Talks Theses Translations, provisional UHJ documents UHJ letters Video Visual items Writings, Sacred
Personal letters
sorted by title, all languages []
Some letters of historical interest can be found in Histories and Pilgrims Notes.
Ahmad Sohrab and the New History Society, by Paul E. Haney and Horace Holley (1958). Overview of the defection of Ahmad Sohrab and the formation of the "New History Society" and the "Caravan of East and West." [about]
Before Abraham Was, I am, by Thornton Chase (1902). Open letter to a new Baha'i summarizing the Baha'i revelation through a Christian perspective. [about]
Biographical letter from a Hindu villager, by Daya Ram Malviya (1974). A glimpse into the life of an Indian convert to the Faith. [about]
Letter from Haifa in the Time of Mourning, 1922: from Emogene Hoagg to Nelly French, by Emogene Hoagg, in World Order, 6:2 (1971). [about]
Letter to Grace Holley, by Abdu'l-Bahá (1919). Short message of greeting and praise. [about]
Letter to John B. Cornell, by Ruhiyyih (Mary Maxwell) Khanum (1943). Short personal letter relating answers from Shoghi Effendi to various questions of Cornell, on voting age, the election of the House, the "Source of all knowledge," etc. [about]
Letter to the Ecole des Jeunes May Bolles Maxwell Conference, by Ruhiyyih (Mary Maxwell) Khanum (1997). [about]
Letter to the Geyserville (California) Bahá'í Summer School, by Shidan Fat'he-Aazam (1953). Short letter from a famous travel-teacher (and later member of the NSA of South and West Africa, and Counsellor for Africa). [about]
Letter to the National Spiritual Assembly of the Baha'is of the United States, 1998, by Ruhiyyih (Mary Maxwell) Khanum (1998). [about]
Letter to the United States and Canada on racism, 1961, by Ruhiyyih (Mary Maxwell) Khanum (1961). [about]
Letters from Lynch to Laura Dreyfus-Barney: Materials for the Geneva Bahá'í Bureau's History, by Anne Lynch (2002). Four letters from the Laura Dreyfus-Barney Collection at the French Baha'i National Archives (Paris), from 1946 and 1962, capturing a small slice of contemporary European history. [about]
Letters to Grace Holley and Visalia LSA, by Shoghi Effendi and John Esslemont (1925). Small collection of correspondence between Shoghi Effendi and the LSA of Visalia, California. [about]
Letters to Various Individuals, by Abu'l-Qasim Faizi, in Conqueror of Hearts (1965). [about]
My Memories of Hand of the Cause of God, A. Q. Faizí, by Shirley Macias, in Conqueror of Hearts (2002). Personal letters from Faizi to Macias, and her recollections of him. [about]
Open Letter to the National Spiritual Assembly re Gays in the Baha'i Faith, by Daniel Orey, et al. (1993). [about]
Raising Children of Light: editorial, by Bahá'í International Community, in Jerusalem Post (2008). [about]
Reincarnation, The Return, and the "Cycle of Life" Chart, by Edward C. Getsinger (1916). The concepts Reincarnation and Return in the context of pilgrims' recollections of the words of 'Abdul-Baha, with tablets translated by Ali Kuli Khan, and on Lua Getsinger's "Spiritual Evolution" chart. [about]
Report from the 1995 National Convention, by David Langness (1995). A short series of daily reports from the U.S. National Baha'i Convention, from a personal perspective. [about]
Sacred Pilgrimage: Visits with The Guardian, by Bill Washington, in Herald of the South (1957). Letter to the Australian newsletter, summarizing of nine days in the Holy Land and talks with Shoghi Effendi. [about]
Spiritualization of the Bahá'í Community: A Plan for Teaching, by National Spiritual Assembly of the Bahá'ís of Ireland and Adib Taherzadeh (1982). A three-part collection consisting of a letter from the NSA of Ireland, a letter from Taherzadeh to the Baha'is of Ireland regarding the spiritualization of the Baha'i community, and the preamble for a plan of action for teaching. [about]
Statement on Mason Remey from the Western Hands of the Faith, by Corinne True and Hermann Grossmann (1960). Background information on the claims of Remey, compiled by the Hands of the Cause of God in the Western hemisphere. [about]
Success in Teaching, by Ruhiyyih (Mary Maxwell) Khanum, in Bahá'í News (1949). [about]
What it is to be a Bahá'í?: A letter to the Bahá'í youth from Ruhiyyih Khanum, by Ruhiyyih (Mary Maxwell) Khanum (1948). The object of life to a Bahá'í is to promote the oneness of mankind. [about]
Home Site Map Forum Links Copyright About Contact | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,645 |
Chinguar é uma cidade e município da província do Bié, em Angola.
Tem 3 054 km² e cerca de 299 mil habitantes. É limitado a norte pelos municípios da Cunhinga e do Bailundo, a leste pelo municípios do Cuíto, a sul pelo município de Chitembo e a oeste pelo município de Cachiungo.
O município é constituído pela comuna-sede, correspondente à cidade de Chinguar, e pelas comunas de Cutato e Cangote.
Ver também
Comunas de Angola
Bié
Municípios da província do Bié
Cidades de Angola | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,788 |
\section{Introduction}\label{sec:intro}
Among the many interesting and distinctive features of the Casimir
effect~\cite{rev}, not the least important is the fact that the forces it
produces between (more than two) conducting surfaces do not satisfy, in
general, a superposition principle. In other words, when dealing with more
than two objects, the interaction energy cannot be written as the sum of
the interaction energies corresponding to all the possible object pairs.
As a consequence, knowledge of the energy of a system before the addition
of an extra surface may seem to be of little help, since there is no
obvious way to include the extra interaction terms. Not unexpectedly, this
non-superposition property is shared by the van der Waals
interaction~\cite{milonni}.
Quite apart from its theoretical interest,
it should be noted that this kind of phenomenon may also be of practical
relevance, since it could be helpful in some approximate calculation
schemes, in situations where nonlinear effects are small. For example, if
there exists a regime where superposition is approximately valid, one
should expect the dominant term in the Casimir energy to be akin to a two
body interaction potential, albeit with a non-Coulombian potential, plus
corrections. Under some assumptions, those corrections can be, as we shall
see, small perturbations.
In this paper, we first investigate the non-superposition effects in a quite
general approach. We then argue that when those effects are small, a
perturbative expansion naturally suggests itself. We then discuss and
apply that approximation within the context of different examples.
This paper is organized as follows: in section~\ref{sec:method} we first
review the functional approach to the calculation of the Casimir energy.
In~\ref{sec:nonsup}, we deal with the study of non-superposition effects,
relating them to a perturbative expansion in~\ref{sec:perturbative},with
examples in $1+1$, $2+1$, and $3+1$ dimensions.
\noindent In~\ref{sec:concl}, we present our conclusions.
\section{The method}\label{sec:method}
In order to analyze properties of the Casimir energy, it is convenient
to introduce one of its concrete representations. We shall use here one
that is based on the functional integral formalism introduced
in~\cite{kardar,kardar2,recent}.
\noindent What follows is a review of its main aspects, adapted to the problem at hand.
Denoting by ${\mathcal Z}\big[\{ \Sigma^{(a)}\}\big]$ the Euclidean vacuum
amplitude for a real massless scalar field $\varphi$ in the
presence of $N$ Dirichlet surfaces $\Sigma^{(a)}$, $a=1,\ldots,\, N$, the
total vacuum energy $E_0$ may be written as follows:
\begin{equation}\label{eq:e0}
E_0 \;=\; - \, \lim_{T \to \infty} \left\{
\frac{1}{T} \,\log \frac{{\mathcal Z}\big[\{ \Sigma^{(a)}\}\big]}{{\mathcal Z}_0}
\right\} \;,
\end{equation}
where $T$ is the extent of the (imaginary) time interval, and ${\mathcal
Z}_0$ is the free (no surfaces) vacuum amplitude. The role of the latter
is just to fix the vacuum energy to zero when there are no surfaces.
On the other hand, the vacuum amplitude may be written as a
functional integral\footnote{In our use of the functional integral
formalism, we follow the approach and conventions of~\cite{zinn}.}:
\begin{equation}\label{eq:defzsiga}
{\mathcal Z}\big[\{\Sigma^{(a)}\}\big] \,=\, \int [{\mathcal D}\varphi]\;
e^{-S_0(\varphi)}\;,
\end{equation}
where $S_0$ is the free Euclidean action, which for a massless scalar field
in $d+1$ dimensions reads: $S_0(\varphi)=\frac{1}{2} \int
d^{d+1}x\;(\partial\varphi)^2$, and $[\mathcal{D}\varphi]$ denotes the path
integral measure corresponding to a scalar field which satisfies Dirichlet
boundary conditions on each surface $\Sigma^{(a)}$.
It is quite useful to write that measure in the equivalent way:
\begin{equation}\label{eq:defzsiga1}
[{\mathcal D}\varphi]\;=\; {\mathcal D}\varphi \;\times\; \prod_{a=1}^N
\,\delta_{\Sigma^{(a)}}\big[\varphi\big] \;,
\end{equation}
where we introduced a $\delta$-functional for the field on each
surface.
In what follows, we focus on the $d=3$ case, although every step will have
its analogue for different numbers of dimensions. The changes to the final
expressions required to deal with $d\neq3$ are described in
\ref{sec:nonsup}.
Thus, assuming that $(\sigma^1,\sigma^2) \to
{\mathbf y}^{(a)}(\sigma)$ (${\mathbf y}^{(a)} \in {\mathbb R}^{(3)}$) is a
parametrization of $\Sigma^{(a)}$, we introduce an auxiliary field
$\xi^{(a)}(\tau,\sigma)$ to exponentiate each functional delta:
\begin{equation}\label{eq:measure}
\delta_{\Sigma^{(a)}}\big[\varphi\big] \;=\; \int \mathcal{D}\xi^{(a)}
\, e^{i \int d\tau \int d^2\sigma \sqrt{g^{(a)}(\sigma)} \,
\xi^{(a)}(\tau,\sigma) \varphi\big[\tau,{\mathbf y}^{(a)}(\sigma)\big]}
\end{equation}
(no sum over $a$), where $g^{(a)}(\sigma) \equiv \det \big[g^{(a)}_{\alpha\beta}(\sigma)\big]$,
($\alpha,\beta = 1, 2$) is the determinant of the induced metric
$g^{(a)}_{\alpha\beta}$ on the surface, and $\tau \equiv x_0$.
In terms of the previous parametrization,
\begin{equation}
g^{(a)}_{\alpha\beta}(\sigma)\;=\; \frac{\partial {\mathbf
y}^{(a)}(\sigma)}{\partial \sigma^\alpha} \cdot \frac{\partial {\mathbf
y}^{(a)}(\sigma)}{\partial \sigma^\beta}\;\;\;({\rm no\; sum\; over} \,a) \;.
\end{equation}
Equation (\ref{eq:measure}) guarantees the (necessary)
reparametrization invariance on each surface, assuming that the auxiliary
fields behave as scalars under those transformations.
Inserting (\ref{eq:measure}) into (\ref{eq:defzsiga1}), we are left with an
equivalent functional integral expression for ${\mathcal
Z}\big[\{\Sigma^{(a)}\}\big]$:
\begin{equation}
{\mathcal Z}\big[\{\Sigma^{(a)}\}\big]\;=\; \int \left( \prod_{a=1}^N
\mathcal{D} \xi^{(a)} \right) \;
\int \mathcal{D} \varphi \; \exp\Big\{-S_0(\varphi)\,+\,i\, \int
d^4x\,J(x)\,\varphi(x) \Big\}
\end{equation}
where we introduced $J(x) \equiv \sum_{a=1}^N J^{(a)}(x)$, with:
\begin{equation}
J^{(a)}(x)\;=\; \int d\tau d^2 \sigma \; \sqrt{g^{(a)}(\sigma)} \, \xi^{(a)}(\tau,\sigma)
\,\delta(x_0 - \tau) \, \delta^{(3)}[\mathbf{x}-\mathbf{y}^{(a)}(\sigma)]
\;.
\end{equation}
Performing now the (Gaussian) integral over the $\varphi$ field, the result
may be put, in a condensed form, as follows:
\begin{equation}\label{eq:zsigma}
{\mathcal Z}_\Sigma\;=\; {\mathcal Z}_0 \; \times \; \int \mathcal{D}\xi
\; e^{-S_\Sigma(\xi)}
\end{equation}
where ${\mathcal Z}_\Sigma \equiv {\mathcal Z}\big[\{\Sigma^{(a)}\}\big]$,
and ${\mathcal Z}_0 = \int \mathcal{D}\varphi \; e^{-S(\varphi_0)}$.
In (\ref{eq:zsigma}), ${\mathcal D}\xi$ denotes the integration measure for
all the auxiliary fields (we assume there is more than one boundary) and
$S_\Sigma$ is a `nonlocal action' for those fields:
\begin{eqnarray}
S_\Sigma(\xi) &=& \frac{1}{2} \int d\tau d^2\sigma \int d\tau' d^2\sigma' \;
\sum_{a,b=1}^N \;\Big[ \xi^{(a)}(\tau,\sigma)\,
\nonumber\\
&\times& {\mathcal M}_{(ab)}(\tau,\sigma;\tau',\sigma')\,
\xi^{(b)}(\tau',\sigma') \Big] \;,
\end{eqnarray}
where each matrix elements of ${\mathcal M}$ may be expressed in
terms of the scalar field propagator ${\mathcal K}$:
\begin{equation}
{\mathcal M}_{(ab)}(\tau,\sigma;\tau',\sigma') \;=\; \sqrt{g^{(a)}(\sigma)}
\; {\mathcal
K}(\tau-\tau';\mathbf{y}^{(a)}(\sigma)-\mathbf{y}^{(b)}(\sigma')) \;
\sqrt{g^{(b)}(\sigma')}
\;,
\end{equation}
which, in $d=3$, may be written as follows:
\begin{eqnarray}
{\mathcal K}(x_0,{\mathbf x}) &=& \int \frac{d \omega}{2\pi} e^{i \omega
x_0 } \, {\widetilde {\mathcal K}}(\omega,{\mathbf x}) \;, \nonumber\\
{\widetilde{\mathcal K}}(\omega,{\mathbf x}) &=&
\int \frac{d^3k}{(2\pi)^3} \, \frac{e^{i {\mathbf k} \cdot {\mathbf
x}}}{\omega^2 + {\mathbf k}^2} \;=\; \frac{ e^{-|\omega| |{\mathbf
x}|}}{4\pi |{\mathbf x}|} \;.
\end{eqnarray}
Taking advantage of the time independence of the physical system
considered, we Fourier transform in time the auxiliary fields, to write
their action in the following way:
\begin{eqnarray}
S_\Sigma &=& \frac{1}{2} \int \frac{d\omega}{2\pi} \,\int d^2\sigma \int d^2\sigma' \;
\sum_{a,b=1}^N \;\Big[ {\tilde\xi}^{(a)*}(\omega,\sigma)\,
\nonumber\\
&\times& \widetilde{\mathcal M}_{(ab)}(\omega;\sigma,\sigma') \,
\tilde{\xi}^{(b)}(\omega,\sigma') \Big] \;,
\end{eqnarray}
where the tilde on the fields denotes their corresponding Fourier
transformed versions, and:
\begin{equation}
\widetilde{\mathcal M}_{(ab)}(\omega;\sigma,\sigma') \;=\; \sqrt{g^{(a)}(\sigma)}
{\mathcal K}_{(ab)}(\omega;\sigma,\sigma') \sqrt{g^{(b)}(\sigma')}
\;,
\end{equation}
where
\begin{equation}
{\mathcal K}_{(ab)}(\omega;\sigma,\sigma') \;\equiv\;
{\widetilde{\mathcal K}}\big[\omega; {\mathbf y}^{(a)}(\sigma) - {\mathbf y}^{(b)}(\sigma')\big]
\;.
\end{equation}
Since the integral over the auxiliary fields is Gaussian, we have:
\begin{equation}\label{eq:zquot}
\frac{{\mathcal Z}_\Sigma}{{\mathcal Z}_0}\;=\;
\Big\{ \det \big[\widetilde{\mathcal M}_{(ab)}(\omega;\sigma,\sigma')
\delta(\omega-\omega') \big] \Big\}^{-\frac{1}{2}} \;,
\end{equation}
where the determinant refers to the continuous indices $\omega,\omega'$,
$\sigma,\sigma'$, as well as the discrete ones $a$, $b$.
Then, recalling the relation between the vacuum functional and the vacuum
energy $E_0$ we find for the latter the expression:
\begin{equation}\label{eq:e0quot}
E_0 \;=\; \frac{1}{2} \, \int \frac{d\omega}{2\pi} \,
{\rm Tr} \log \Big[\widetilde{\mathcal M}_{(ab)}(\omega;\sigma,\sigma') \Big]
\;,
\end{equation}
where the trace affects the $\sigma,\sigma'$ and $a,b$ indices (the trace over
frequencies has been explicitly dealt with by means of the
integral). We shall reserve the symbol `${\rm tr}$' for the cases where
a trace over just the (continuous) $\sigma,\sigma'$ indices is needed.
Note that no subtraction of the would-be Casimir `self-energies'
has yet been performed; this step will be considered in the next section.
\section{Non superposition}\label{sec:nonsup}
Since we are interested in the Casimir {\em interaction\/} energy, we will
first extract the self-energies of the surfaces. Besides,
those energies are additive quantities, insensitive to the
phenomenon we wish to consider.
That extraction can be done by factorizing a diagonal matrix constructed from the
$a=b$ elements of $\widetilde{\mathcal M}$:
\begin{equation}
\widetilde{\mathcal M}_{(ab)}(\omega;\sigma,\sigma') \;=\; \int d^2\sigma''
\,\sum_{c=1}^N\, \widetilde{\mathcal D}_{(ac)}(\omega;\sigma,\sigma'') \;
\widetilde{\mathcal T}_{(cb)}(\omega;\sigma'',\sigma')
\end{equation}
where
\begin{equation}
\widetilde{\mathcal D}_{(ab)}(\omega;\sigma,\sigma') \,\equiv\,
\widetilde{\mathcal M}_{(aa)}(\omega;\sigma,\sigma')
\, \delta_{ab}
\end{equation}
(no sum over $a$).
By construction, $\widetilde{\mathcal T}(\omega)$ has the matrix elements:
\begin{equation}\label{eq:tab}
\widetilde{\mathcal T}_{(ab)}(\omega;\sigma,\sigma') \;=\;
\int d^2\sigma'' \, \widetilde{\mathcal M}^{-1}_{(aa)}
(\omega;\sigma,\sigma'') \;
\widetilde{\mathcal M}_{(ab)}(\omega;\sigma'',\sigma')
\;,
\end{equation}
(no sum over $a$).
This factorization implies that $\det(\tilde{\mathcal M})\,=\,\det(\tilde{\mathcal D})
\,\det(\tilde{\mathcal T})$; thus, recalling (\ref{eq:zquot}) and
(\ref{eq:e0quot}), we may write:
\begin{equation}\label{eq:selfen}
E_0 \;=\; \sum_{a=1}^N \, E_0^{(aa)} \,+\, E_I \;,
\end{equation}
where
\begin{equation}
E_0^{(aa)} \;=\; \frac{1}{2} \, \int \frac{d\omega}{2\pi} \,
{\rm tr} \log \Big[\widetilde{\mathcal M}_{(aa)}(\omega)\Big]
\;,
\end{equation}
is the Casimir self-energy of the object labelled by the index
$a$, and:
\begin{equation}
E_I \;=\; \frac{1}{2} \, \int \frac{d\omega}{2\pi} \,
{\rm Tr} \log \Big[\widetilde{\mathcal T}(\omega)\Big]
\;.
\end{equation}
As already advanced, the self-energies, as seen from (\ref{eq:selfen}), are
additive. Besides, they do not contribute to the Casimir forces between the
surfaces~\footnote{They do contribute to the Casimir `pressure' on each
surface, though.}, since they are independent of their relative distances.
Let us then consider the interaction term, $E_I$. It depends on
$\widetilde{\mathcal T} \equiv {\mathcal I} + \widetilde{\mathcal T}'$
where ${\mathcal I}$ is the identity matrix (in both discrete and continuous indices) and
$\widetilde{\mathcal T}'$ has vanishing diagonal ($a=b$) elements. Moreover, for
$a\neq b$, it coincides with $\widetilde{\mathcal T}_{(ab)}$ of
(\ref{eq:tab}).
As a final step to obtain our main result, we derive a
different (but equivalent) expression for $\widetilde{\mathcal T}_{(ab)}$,
such that formula for the interaction energy does not contain explicit
factors of the metric.
To that end, we introduce
$G^{(a)}(\omega;\sigma,\sigma')$, the inverse of ${\mathcal
K}_{(aa)}(\omega;\sigma,\sigma')$:
\begin{equation}
\int d^2\sigma''\, {\mathcal K}_{(aa)}(\omega;\sigma,\sigma'')
G^{(a)}(\omega;\sigma'',\sigma') \,=\, \delta^{(2)}(\sigma-\sigma') \;.
\end{equation}
Then:
\begin{equation}
\widetilde{\mathcal M}^{-1}_{(aa)}(\omega ; \sigma ,\sigma') \;=\;
\frac{1}{\sqrt{g^{(a)}(\sigma)}} \, G^{(a)}(\omega;\sigma,\sigma') \,
\frac{1}{\sqrt{g^{(a)}(\sigma')}} \;,
\end{equation}
and:
\begin{equation}\label{eq:tabsimp}
\widetilde{\mathcal T}'_{(ab)}(\omega;\sigma,\sigma') \;=\;
\frac{1}{\sqrt{g^{(a)}(\sigma)}} \, {\mathcal O}_{(ab)}(\omega;\sigma,\sigma')
\sqrt{g^{(b)}(\sigma')}
\end{equation}
where
\begin{equation}
{\mathcal O}_{(ab)}(\omega;\sigma,\sigma') \;\equiv\; \left\{
\begin{array}{ccc}
\int d^2\sigma'' \, G^{(a)}(\omega;\sigma,\sigma'') {\mathcal
K}^{(ab)}(\omega;\sigma'', \sigma') &{\rm if} & a\neq b \\
0 &{\rm if} & a = b
\end{array} \right. \;.
\end{equation}
This way of writing ${\mathcal T}'_{(ab)}$ is rather convenient,
since one can show that the determinants of the metric
cancel, leading to a simpler final expression, depending only on
${\mathcal O}$:
\begin{equation}\label{eq:ei}
E_I \;=\; \frac{1}{2} \, \int \frac{d\omega}{2\pi} \,
{\rm Tr} \log \Big[ {\mathcal I} + {\mathcal O}(\omega) \Big]
\;,
\end{equation}
which we use in our subsequent derivations. This equation is the $N$-body
generalization~\footnote{The existence of this generalization is mentioned
in~\cite{Emig}.} of the so called `$TGTG$' formula for the Casimir
interaction between two bodies applied in~\cite{Emig,Kenet} (see
also~\cite{Balian}), which in our notation reads:
\begin{equation}\label{eq:ei2}
E_I \big( \Sigma^{(1)},\Sigma^{(2)} \big)\,=\,
\frac{1}{2} \, \int \frac{d\omega}{2\pi} \,
{\rm tr} \log \Big[ 1 - G^{(1)}(\omega) {\mathcal K}_{(12)}(\omega)
G^{(2)}(\omega) {\mathcal K}_{(21)}(\omega) \Big]\;.
\end{equation}
The latter is obtained from (\ref{eq:ei}) by expanding in powers of
${\mathcal O}$ and summing up the series for the particular case $N=2$:
\begin{equation}
E_I \big( \Sigma ^{(1)},\Sigma ^{(2)} \big)\;=\; - \int
\frac{d\omega}{2\pi} \, \sum _{k=1}^\infty \frac{1}{2 k} \,
{\rm tr} \Big\{ \big[
{\mathcal O}_{(12)}(\omega) {\mathcal O}_{(21)}(\omega)
\big]^k\Big\}\;,
\end{equation}
what yields (\ref{eq:ei2}).
Coming back to (\ref{eq:ei}), we note that the form of $G^{(a)}$ shall
depend, implicitly, on the geometry of each surface, and in general cannot
be evaluated exactly, except in rather simple cases. However, most
properties we shall deal with in this section are independent of that form.
Expression (\ref{eq:ei}) has immediate analogues in $d\neq3$.
Indeed, in $d=1$, we arrive to a result formally identical to
(\ref{eq:ei}), after one notes that the trace only affects the indices that
label the `surfaces', which in this case are just points labelled by their
coordinates $x^{(a)}$ (no parameters $\sigma$ are involved). Besides, the
kernel $\widetilde{\mathcal K}(\omega;x)$ is now:
\begin{equation}
\widetilde{\mathcal K}(\omega;x) \;=\; \frac{e^{- |\omega| |x|}}{2
|\omega|} \;,
\end{equation}
and $G^{(a)}$ becomes:
\begin{equation}
G^{(a)}(\omega) = \Big[ \lim_{x,x' \to a} \frac{e^{- |\omega| |x-x'|}}{2
|\omega|} \Big]^{-1}
= 2 |\omega| \;,
\end{equation}
independently of $a$.
Finally, in $d=2$ the boundaries are curves $\Gamma^{(a)}$ described by just one
parameter $\sigma$, and:
\begin{equation}
\widetilde{\mathcal K}(\omega;{\mathbf x}) \;\equiv\; \frac{1}{2\pi} \, K_0(
|\omega | |{\mathbf x}|) \;,
\end{equation}
where $K_0$ is a modified Bessel function, and $G^{(a)}$
is obtained by evaluating the inverse of ${\mathcal K}_{(aa)}$, for which
there is no general expression; we shall however derive its exact form for
a particular case in the next section.
Equipped with (\ref{eq:ei}), we can define a way to `measure' the non-superposition
effects. Again, we work in $d=3$, but the results are straightforwardly adapted to
$d\neq 3$: Assuming that we know $E_I\big(\{\Sigma_{(a)}\}_{a= 1}^N\big)$, the energy
corresponding to $N$ surfaces, we add an extra boundary, $\Sigma_{(N+1)}$,
obtaining a new energy $E_I\big(\{\Sigma_{(a)}\}_{a= 1}^{N+1}\big)$.
If superposition were valid, the difference between the two energies would
be the sum of the interaction energies between $\Sigma_{(N+1)}$ and
$\Sigma_{(a)}$, with $a=1,\ldots,N$. Thus, we introduce:
\begin{equation}
\delta E_I(N) \,\equiv \,E_I\big(\{\Sigma_{(a)}\}_{a= 1}^{N+1}\big) -
E_I\big(\{\Sigma_{(a)}\}_{a= 1}^N\big)
- \sum_{a=1}^N E_I\big(\{\Sigma_{(N+1)},\Sigma_{(a)}\}\big)\;.
\end{equation}
Superposition is broken whenever $\delta E_I(N)\neq 0$. Reciprocally, for
the energy of $N$ surfaces to verify superposition we would need:
$\delta E_I(M) =0$, for $M=2,\ldots,N-1$.
The final ingredient to evaluate $\delta E_I(N)$ is obtained by applying
(\ref{eq:ei}) to the $N+1$ surfaces. Then, we use determinant algebra to
relate the determinant of the corresponding $(N+1)^{th}$-order matrix to an
$N^{(th)}$-order one:
\begin{equation}
\det \big[{\mathcal I}_{(ab)} + {\mathcal
O}_{(ab)}\big]_{(N+1)\times (N+1)}\;=\;
\det \big[{\mathcal I}_{(ab)} + {\mathcal O}'_{(ab)}\big]_{N\times N}\;,
\end{equation}
where:
\begin{equation}
{\mathcal O}'_{(ab)} \,\equiv\, {\mathcal O}_{(ab)} \,-\,{\mathcal O}_{(a
\; N+1)} {\mathcal O}_{(N+1\; b)} \;.
\end{equation}
Thus, the difference between the energies for $N+1$ and $N$ surfaces may be
put in the form:
\begin{equation}
E_I\big(\{\Sigma_a\}_{a= 1}^{N+1}\big) \,=\, E_I\big(\{\Sigma_a\}_{a=
1}^N\big) + \frac{1}{2} \int \frac{d\omega}{2\pi} \,
{\rm Tr} \log \Big[{\mathcal I} - {\mathcal Q} \Big]
\end{equation}
where
\begin{eqnarray}
{\mathcal Q}_{(ab)}(\omega;\sigma,\sigma') &\equiv&
\int d^2\sigma'' \int d^2\sigma''' \, \sum_{c=1}^N \Big\{ \Big[\big({\mathcal I} +
{\mathcal O}\big)^{-1}\Big]_{(ac)}(\omega;\sigma,\sigma'')
\nonumber\\
&\times& {\mathcal O}_{(c\;N+1)}(\omega;\sigma'',\sigma''')
{\mathcal O}_{(N+1\; b)}(\omega;\sigma''',\sigma')
\Big\} \;.
\end{eqnarray}
It is now a matter of algebra to extract the pairs
interaction energy to show that:
\begin{equation}
\delta E_I(N) \;=\; \frac{1}{2} \int \frac{d\omega}{2\pi} \,
{\rm Tr} \log[ I + \Lambda(\omega) ]
\end{equation}
with:
\begin{eqnarray}
\Lambda_{(ab)} & = & \big[I - {\mathcal O}_{(N+1\;a)} {\mathcal
O}_{(a\;N+1)}\big]^{-1}\;\nonumber\\
&\times& \Big\{ \sum_{c=1}^N [{\mathcal O}\; ( {\mathcal I} + {\mathcal O})^{-1}]_{(ac)}
\; {\mathcal O}_{(c\;N+1)} {\mathcal O}_{(N+1\;b)} \nonumber\\
&-& {\mathcal O}_{(a\;N+1)} {\mathcal O}_{(N+1\;b)} + {\mathcal
O}_{(N+1\;a)} {\mathcal O}_{(a\;N+1)} \delta_{ab} \Big\}
\end{eqnarray}
where the $I$ in the first factor is the identity operator on functions
defined in parameter space (while ${\mathcal I}$ also acts on the indices
space), the discrete indices are not summed, and the products are
understood in the operatorial sense, regarding the kernels as matrix
elements with continuous indices.
In spite of the fact that the form its rather complicated, we may already
extract some conclusions from it. The most immediate one is
that for the strength of the non-superposition effects to be
small, the magnitude of the matrix elements of ${\mathcal O}$ between
the $(N+1)^{th}$ surface and the previous ones has to be small.
Moreover, for the correction to be smaller than the superposition terms,
we also need
${\mathcal O}_{(a b)}$, for $a,b =1,\ldots N$ to be small, since these
operators also affect the magnitude of those terms. And this is the main conclusion of
this section, namely, that for superposition to be valid, all the matrix
elements of ${\mathcal O}$ have to be small.
We can see, in fact, that when that is the case, the {\em form\/} of the
correction, to lowest order in the matrix elements, does depends on
the matrix elements involving all the boundaries:
\begin{equation}\label{eq:low}
\delta E_I(N) \;\sim \; -\frac{1}{2} \int \frac{d\omega}{2\pi}
\,\sum_{a,b=1}^N
{\rm tr}\Big[{\mathcal O}_{(N+1\;a)} {\mathcal O}_{(a b)}
{\mathcal O}_{(b \; N+1)} \Big]\;.
\end{equation}
The smallness of ${\mathcal O}$ is what, on the other hand, renders a
perturbative expansion of the interaction energy possible.
\section{Perturbative expansion}\label{sec:perturbative}
The condition that the matrix elements of ${\mathcal O}$ are small, is
precisely what one would require in order to expand the interaction energy
in powers of that operator. On the other hand, for ${\mathcal O}$ to be
small, the only assumption available here is that the $N$ surfaces
$\Sigma^{(a)}$ are compact objects, and that the distance between each pair
of surfaces is much bigger than the size of any object. Under this
assumption, the norm of ${\mathcal O}_{(ab)}$ is much smaller than one,
since the $G^{(a)}$ kernel, is determined by the {\em inverse\/} of
$\widetilde{\mathcal K}$ at small distances, while ${\mathcal K}_{(ab)}$
is, essentially, $\widetilde{\mathcal K}$ at long distances,
and $\widetilde{\mathcal K}$ decreases with the distance.
Excellent articles exist about the evaluation of the Casimir interaction
energy within the $TGTG$ formula approach, by applying different
expansions{\cite{Milton:2007wz,Emig,Kenet}. We just present here an
analysis of the perturbative expansion in powers of ${\mathcal O}$, from the point of view of the
non-superposition effects, for the case of $N$ boundaries.
The expansion yields a series for $E_I$:
\begin{equation}
E_I \;=\; \sum_{l=1}^\infty \, E_{I;l} \;,
\end{equation}
where
\begin{equation}
E_{I;l} \;=\; \frac{(-1)^{l-1}}{2 l} \, \int \frac{d\omega}{2\pi} \,
{\rm Tr} \Big[\big({\mathcal O}(\omega)\big)^l\Big]
\;,
\end{equation}
or:
\begin{equation}
E_{I;l} \;=\; \frac{(-1)^{l-1}}{2 l} \, \int \frac{d\omega}{2\pi} \,
\sum_{\scriptscriptstyle{a_1\neq a_2\neq a_3\neq\ldots\neq a_l\neq a_1}} \,
{\rm tr} \Big[
{\mathcal O}_{(a_1a_2)}(\omega)
{\mathcal O}_{(a_2a_3)}(\omega)
\ldots
{\mathcal O}_{(a_la_1)}(\omega)
\Big]
\;.
\end{equation}
This is, essentially, the long distance expansion considered
in~\cite{Milton:2007wz}, although we only deal with the Dirichlet (strong
coupling) case.
It is worth noting at this point that the absence of explicit factors of
the metric by no means signal a breaking of reparametrization invariance.
Indeed, what happens is that the kernels denoted by $G^{(a)}$ do have a
nontrivial transformation properties under reparametrization, which
compensate for the non invariance of the integrals over the parameters.
Let us study the explicit form of the first few terms in this expansion. The $l=1$
term vanishes, so that the lowest non-trivial order corresponds to $l=2$,
which using (\ref{eq:tabsimp}) becomes:
\begin{eqnarray}
E_{I;2} &=& - \, \frac{1}{4} \, \int \frac{d\omega}{2\pi} \,
\sum_{a \neq b} \, \int d^2\sigma \int d^2\sigma'\;
{\mathcal O}_{(ab)}(\omega;\sigma,\sigma')
{\mathcal O}_{(ba)}(\omega;\sigma',\sigma) \nonumber\\
&\equiv& \sum_{a < b} \, E^{(ab)}
\end{eqnarray}
where
\begin{eqnarray}\label{eq:quad}
E^{(ab)} &=& - \frac{1}{2} \int \frac{d\omega}{2\pi} \,
\int_{\sigma,\sigma',\sigma'',\sigma'''} G^{(a)}(\omega;\sigma,\sigma') \;
{\mathcal K}^{(ab)}(\omega;\sigma',\sigma'') \nonumber\\
&\times&
G^{(b)}(\omega;\sigma'',\sigma''')\; {\mathcal
K}^{(ba)}(\omega;\sigma''',\sigma) \;.
\end{eqnarray}
To this order, the total energy is obtained as the sum of
`interaction energies' corresponding to the pairs, in a sort of
`superposition principle'.
This property is violated in the next order term:
\begin{eqnarray}
E_{I;3} &=& \frac{1}{6} \, \int \frac{d\omega}{2\pi} \,
\sum_{a, b, c} \, \int d^2\sigma \int d^2\sigma' \int d^2\sigma''
\nonumber\\
&\times&
{\mathcal O}_{(ab)}(\omega;\sigma,\sigma')
{\mathcal O}_{(bc)}(\omega;\sigma',\sigma'')
{\mathcal O}_{(ca)}(\omega;\sigma'',\sigma) \nonumber\\
&\equiv& \sum_{a < b < c} \, E^{(abc)}
\end{eqnarray}
where we have introduced a `three-body energy interaction', $E^{(abc)}$:
\begin{equation}
E^{(abc)} \;=\; \int \frac{d\omega}{2\pi} \; {\rm tr} \Big[
G^{(a)}(\omega){\mathcal K}^{(ab)}(\omega)
G^{(b)}(\omega){\mathcal K}^{(bc)}(\omega)
G^{(c)}(\omega){\mathcal K}^{(ca)}(\omega) \Big] \;.
\end{equation}
Incidentally, this correction coincides with (\ref{eq:low}) when one
considers $N+1$ surfaces, as it should be, since on should expect that the
lowest order violation to the non-superposition comes from the lowest
non-quadratic term in the energy.
A fundamental ingredient in the calculation of the different terms in the
expansion for $E_I$ is the kernel $G^{(a)}(\omega;\sigma,\sigma')$. The
form of that kernel depends strongly on the number of spatial dimensions
as well as on the shape of the surface itself. Universal statements can
only be made if more assumptions about the surfaces are made.
However, based on the same assumption used to perform the series expansion, we
may simplify the previous expressions further. Indeed, denoting by ${\mathbf
x}^{(a)}$ the barycenter of the $\Sigma^{(a)}$ surface, we can, in
the expressions above, use the approximation:
\begin{equation}
{\mathcal K}^{(ab)}(\omega;\sigma',\sigma'') \simeq
{\widetilde{\mathcal K}}(\omega; {\mathbf x}^{(a)} - {\mathbf x}^{(b)} ) \;.
\end{equation}
This is justified by the following reason: we are assuming that $|{\mathbf
x}^{(a)} - {\mathbf x}^{(b)}| >> R^{(a)}, R^{(b)}$, where $R^{(a)}$ denotes
the minimum radius for a sphere $S^{(a)}$, centered at ${\mathbf x}^{(a)}$,
which encloses $\Sigma_a$. Then we may replace ${\mathbf
y}^{(a)}(\sigma) \to {\mathbf x}^{(a)}$ and ${\mathbf y}^{(b)}(\sigma') \to
{\mathbf x}^{(b)}$, since ${\mathcal K}^{(ab)}(\omega;\sigma',\sigma'')$ is
(under the previous assumptions) approximately constant inside $S^{(a)}$.
Using this approximation inside the expression for $E^{(ab)}$, we see that
it may be written as follows:
\begin{equation}
E^{(ab)} \;\simeq\; \int \frac{d\omega}{2\pi} \,\int d^3x
\int d^3y \;
\rho^{(a)}(\omega;{\mathbf x}) V(\omega;{\mathbf x}- {\mathbf y})
\rho^{(b)}({\mathbf y}) \;,
\end{equation}
where we introduced:
\begin{eqnarray}
\rho^{(a)}(\omega;{\mathbf x}) &\equiv &
q_a (\omega) \; \delta^{(3)}({\mathbf x}-{\mathbf x}^{(a)}) \nonumber\\
q_a(\omega) &\equiv & \int d^2\sigma \int d^2\sigma' \; G^{(a)}(\omega;\sigma,\sigma')
\end{eqnarray}
and
\begin{equation}
V(\omega;{\mathbf x}- {\mathbf y})
\;\equiv\; -\frac{1}{2} \;\Big[ {\widetilde K}(\omega;{\mathbf x}- {\mathbf
y})\Big]^2 \;.
\end{equation}
Thus, at this order, we see that the interaction energy for the $a,\,b$
pair, may be regarded as arising from integral over $\omega$ of the
interaction energy for a set of pointlike charges located at ${\mathbf
x}^{(a)}$ and ${\mathbf x}^{(b)}$, whose strengths $q_a(\omega)$ and
$q_b(\omega)$ are determined by the geometry of the respective surface.
On the other hand, the explicit form of the interaction potential is:
\begin{equation}
V(\omega;{\mathbf x}- {\mathbf y})
\;\equiv\; -\frac{1}{2} \, \frac{e^{-2 |\omega| |{\mathbf x} - {\mathbf
y}|}}{ (4 \pi)^2 |{\mathbf x} - {\mathbf y}|^2} \;,
\end{equation}
hence, the interaction is always attractive. The integrals over ${\mathbf
x}$ and ${\mathbf y}$ have been used in order to make it clear that each
surface behaves as a sort of point-like charge. Of course, the same
approximation may be used to simplify the form of the higher order terms.
The form of $G^{(a)}$ is not known exactly in general, except for particular
situations, like the $d=1$ case, which we consider now:
\subsection{$d=1$}
As a first test, we consider the case of two mirrors in $1+1$ dimensions.
The operator ${\mathcal O}$ is just an $\omega$-depending matrix, with
matrix elements ${\mathcal O}_{(ab)}(\omega) = e^{-|\omega|
|x^{(a)}-x^{(b)}|}$; the exponential decay assures the convergence of the
perturbative expansion, regardless of the relative distances between the
mirrors.
In this situation, the first (superposition) expression for the energy
corresponding to two point-like objects (mirrors) located at $x^{(1)}$ and
$x^{(2)}$ adopts the form:
\begin{equation}
E^{(12)} \;=\; \int \frac{d\omega}{2\pi} \,
(2 |\omega| )^2 V(\omega; x^{(1)}- x^{(2)}) \;,
\end{equation}
where
\begin{equation}
V(\omega; x^{(1)}- x^{(2)}) \,=\,-\frac{1}{2} \; \frac{e^{-
2|\omega||x^{(1)}- x^{(2)}|}}{ ( 2 |\omega|)^2}
\end{equation}
Assuming that the distance between the mirrors is $a$, we see that.
\begin{equation}
E^{(12)} \;=\; -\frac{1}{2} \, \int_{-\infty}^{+\infty}
\frac{d\omega}{2\pi} \, e^{- 2|\omega| a} \,=\; -\frac{1}{4 \pi a} \;=\; -
\frac{0.07958}{a} \, \;,
\end{equation}
to be compared with the exact result: $E = - \frac{\pi}{24 a} \simeq -
\frac{0.1309}{a}$, which is bigger by approximately a sixty percent.
It is possible to calculate, for this case, all the higher order
corrections exactly; only the even orders yield non-vanishing
contributions, which are given by:
\begin{equation}
E_{I;2l}\;=\; - \frac{1}{2l} \, \int_{-\infty}^{+\infty}
\frac{d\omega}{2\pi} \, \big(e^{- 2|\omega| a}\big)^{2 l} \,=\; -\frac{1}{4
l^2 \pi a} \;.
\end{equation}
Then one sees that their sum:
\begin{equation}
\sum_{l=1}^\infty E_{I;2l}\;=\; - \frac{1}{4 \pi a} \,
\sum_{l=1}^\infty \frac{1}{l^2} \,=\, - \frac{1}{4 \pi a} \frac{\pi^2}{6} \,=\,
- \frac{\pi}{24 a} \;,
\end{equation}
which is the exact result.
Besides, when more than two mirrors are considered, the energy becomes
equal to the sum of the Casimir energies corresponding to the pairs formed
by neighboring mirrors:
\begin{equation}
E_I = -\frac{\pi}{24} \, \sum_{a=1}^{N-1} \frac{1}{|x^{(a+1)} - x^{(a)}|}
\;.
\end{equation}
\subsection{$d=2$}
For a radius $R$ circle, using the angle $\phi$ as parameter, we
find:
\begin{equation}
G^{(a)}(\omega;\phi,\phi')\;=\; \frac{1}{2\pi}
\,\sum_{n=-\infty}^{+\infty} \, \frac{e^{i n (\phi -
\phi')}}{I_{|n|}(|\omega| R) K_{|n|}(|\omega| R)}\;.
\end{equation}
For an infinite line, parametrized by $\sigma \in (-\infty,+\infty)$, the
result is instead:
\begin{equation}
G^{(a)}(\omega;\sigma,\sigma')\;=\; 2 \, \big(- \frac{\partial^2}{\partial
\sigma^2} + \omega^2\big) K_0(|\omega| |\sigma - \sigma'|) \;.
\end{equation}
It is straightforward to check that, in both cases, one is in a situation
of an ${\mathcal O}$ with small norm.
Thus, in the perturbative expansion, when the surfaces are bounded
and very far away, using the approximation that follows from:
\begin{equation}
{\mathcal K}_{(ab)}(\omega;|{\mathbf x}^{(a)} - {\mathbf x}^{(b)} |)\sim
\widetilde{\mathcal K}(\omega;|{\mathbf x}^{(a)} - {\mathbf x}^{(b)} |)
\end{equation}
we may obtain an approximate expression for the case
of $N$ circles. Denoting by $\eta^{(a)}$ and ${\mathbf x}^{(a)}$ the center
and radius of each circle, and assuming that $|{\mathbf x}^{(a)}-{\mathbf
x}^{(b)}| >> {\rm max}\{\eta^{(a)}\}$, we have for the pair interaction energy:
\begin{equation}
E^{(ab)} \;\sim\; - \frac{1}{2} \, \int \frac{d\omega}{2\pi} \,
\frac{[K_0(|\omega||{\mathbf x}^{(a)}-{\mathbf x}^{(b)}|)]^2}{I_0(|\omega|\eta^{(a)})
K_0(|\omega|\eta^{(a)}) I_0(|\omega|\eta^{(b)}) K_0(|\omega|\eta^{(b)})} \;.
\end{equation}
For the case of just
two circles, $1$ and $2$, say, one can sum the series corresponding to the different powers
of ${\mathcal O}$. The result is:
\begin{equation}
E_I \;\sim\; - \frac{1}{2} \, \int \frac{d\omega}{2\pi} \,
\log \Big[1 - \frac{[K_0(|\omega||{\mathbf x}^{(a)}-{\mathbf x}^{(b)}|)]^2}{I_0(|\omega|\eta^{(a)}) K_0(|\omega|\eta^{(a)})
I_0(|\omega|\eta^{(b)}) K_0(|\omega|\eta^{(b)})} \Big]\;.
\end{equation}
\subsection{$d=3$}
We now deal with the case of surfaces in $d=3$.
The long distance approximation requires the evaluation of the integral of
$G^{(a)}$ over the parameters; for a case of a sphere, that integral is:
\begin{equation}
q(\omega) = \frac{4 |\omega| R^2}{I_{1/2} (|\omega| R) K_{1/2} (|\omega| R)
} \;.
\end{equation}
This is smaller than ${\mathcal K}_{(ab)}$ for distant surfaces, as a
straightforward test shows.
If one assumes instead that the surfaces are really composed of
small, weakly coupled surface elements, we may in fact use local
approximations for the $G^{(a)}$ kernels. In this case, a local
approximation means that the kernel is concentrated around $\sigma =
\sigma'$: \begin{equation}
G^{(a)}(\omega;\sigma,\sigma')\;\sim \; \eta^{(a)}(\omega, \sigma) \;
\delta^{(2)} (\sigma-\sigma') \;.
\end{equation}
where $a =1,2$, and $\eta^{(a)}$ will be determined now:
Recalling that $G^{(a)}$ is defined as the inverse of ${\mathcal
K}_{(aa)}(\omega;\sigma,\sigma')$, we explore the form the latter in the
neighborhood of a given point in the surface $\Sigma_a$, the one
characterized by the parameter $\sigma$: ${\mathbf y}^{(a)}(\sigma)$. Close
to that point, we derive the approximate expression:
\begin{eqnarray}
{\mathcal K}_{(aa)}(\omega;\sigma,\sigma') &\sim& \int \frac{d^2k_\parallel}{(2\pi)^2} \, \frac{e^{i {\mathbf k}_\parallel
\cdot \partial_\alpha {\mathbf y}^{(a)}(\sigma)
(\sigma^\alpha-\sigma'^\alpha)}}{ 2 \sqrt{{\mathbf k}_\parallel^2 +
\omega^2}} \nonumber\\
&\sim& \frac{1}{4\pi \sqrt{g_{\alpha\beta}^{(a)}(\sigma)
\delta\sigma^\alpha \delta\sigma^\beta}} \, \exp\big[- |\omega|
\sqrt{g_{\alpha\beta}^{(a)}(\sigma)
\delta\sigma^\alpha \delta\sigma^\beta}\big] \;,
\end{eqnarray}
where ${\mathbf k}_\parallel$ is the projection of the momentum along the
tangent plane at the point ${\mathbf y}^{(a)}(\sigma)$, and
$\delta\sigma^\alpha \equiv \sigma^\alpha - \sigma'^\alpha$.
In the assumption that there is no appreciable momentum flux between the
different surface elements, we end up with the expression:
\begin{equation}
{\mathcal K}_{(aa)}(\omega;\sigma,\sigma') \;\sim \; \frac{1}{2
\sqrt{g^{(a)}(\sigma)} |\omega|} \,
\delta^{(2)}(\sigma-\sigma') \;.
\end{equation}
This yields:
\begin{equation}
G^{(a)}(\omega;\sigma,\sigma')\;\sim\; 2 \sqrt{g^{(a)}(\sigma)} |\omega| \, \delta^{(2)}(\sigma-\sigma')
\;\;\Rightarrow \; \eta(\omega,\sigma) = 2 |\omega| \,g^{(a)}(\sigma)\;.
\end{equation}
Let us first assume that we have two surfaces, $\Sigma^{(1)}$ and $\Sigma^{(2)}$,
and consider the second order expression for the interaction energy, using
the local approximation for the kernels $G^{(1)}$ and $G^{(2)}$.
We see that their interaction energy at this order becomes:
\begin{equation}
E^{(12)} \;=\; - \frac{2^2}{2} \int \frac{d\omega}{2\pi} \,
\omega^2 \, \int d^2\sigma \sqrt{g^{(1)}(\sigma)} \int d^2\sigma'
\sqrt{g^{(2)}(\sigma')} \big[{\mathcal
K}^{(12)}(\omega;\sigma,\sigma')\big]^2
\end{equation}
which, performing the integration over $\omega$, results in the following
expression:
\begin{equation}
E^{(12)} \;=\; \int d^2\sigma \sqrt{g^{(1)}(\sigma)} \int d^2\sigma'
\sqrt{g^{(2)}(\sigma')} V(\sigma,\sigma')
\end{equation}
where:
\begin{equation}
V(\sigma,\sigma') \;=\; - \frac{1}{32 \pi^3} \, \frac{1}{|{\mathbf
y}^{(1)}(\sigma) - {\mathbf y}^{(2)}(\sigma')|^5}
\end{equation}
which looks like a kind of local-potential, van
der Waals like interaction.
Finally, let us consider the case of infinite parallel plates, within the
quadratic approximation, using two different approaches.
Obviously, in this case, the planes cannot be regarded as small surfaces
and, even though the superposition approximation may be valid, certainly
the planes cannot be regarded as point-like objects.
It is clear that, using as parameters the coordinates ${\mathbf
x}^{(a)}_\parallel$ on each mirror, we have:
\begin{equation}
G^{(a)}(\omega;{\mathbf x}^{(a)}_\parallel,{\mathbf y}^{(a)}_\parallel)\;=\;
\int \frac{d^2k_\parallel}{(2\pi)^2} \; 2 \, \sqrt{k_\parallel^2 +
\omega^2} \; e^{i {\mathbf k}_\parallel \cdot ({\mathbf x}^{(a)}_\parallel -{\mathbf y}^{(a)}_\parallel)} \;,
\end{equation}
while for ${\mathcal O}$ the result is:
\begin{equation}
{\mathcal O}_{(ab)}(\omega;{\mathbf x}^{(a)}_\parallel,{\mathbf y}^{(b)}_\parallel)\;=\;
\int \frac{d^2k_\parallel}{(2\pi)^2} \; e^{-\sqrt{k_\parallel^2 + \omega^2}
|z^{(a)} - z^{(b)}|+ i {\mathbf k}_\parallel \cdot ({\mathbf x}^{(a)}_\parallel -
{\mathbf y}^{(a)}_\parallel)} \;,
\end{equation}
where $z^{(a)}$ is the position (on the third axis) of each plane. We see
that, even in this case, the norm of the operator is small.
Indeed, inserting this into (\ref{eq:quad}), we get for ${\mathcal E}_0$, the
energy per unit area:
\begin{equation}
{\mathcal E}_0 \;=\; - \frac{1}{2} \int \frac{d\omega}{2\pi} \,
\int \frac{d^2k_\parallel}{(2\pi)^2} \;e^{- 2 a \sqrt{{\mathbf
k}_\parallel^2 + \omega^2}} \;=\; \frac{1}{16 \pi^2 a^3} \;\simeq\; -0.00633
\, a^{-3} \;,
\end{equation}
to be compared with the exact result, that is ${\mathcal E}_{I;2} \simeq
-0.006854 \, a^{-3}$, what is a signal that the corrections are small.
If, on the other hand, we imagine each mirror as composed of
weakly interacting infinitesimal surface elements (not a conductor), and
apply the superposition result to a system composed of all the surface
elements, then the energy per unit area to the first non-trivial order, ${\mathcal
E}_{I;2}$, may be obtained by integrating the interaction energy between a
single point on a mirror and all the points in the other. This corresponds
to the following integral:
\begin{equation}
{\mathcal E}_{I;2}\;=\; 4 \, \int \frac{d\omega}{2\pi}\, \omega^2
\int d^2x_\parallel \, V(\omega; \sqrt{a^2 + {\mathbf x}_\parallel^2}) \;.
\end{equation}
The integral can be evaluated exactly, yielding:
\begin{equation}
{\mathcal E}_{I;2}\;=\; -\frac{1}{24 \pi^2 a^3} \;\simeq\; - 0.00422 \, a^{-3}
\end{equation}
which is different than the previously obtained result, as it corresponds
to a different material.
\section{Conclusions}\label{sec:concl}
We have obtained an expression that measures the departure from
superposition in the interaction Casimir energy corresponding due to a
massless scalar field in the presence of $N > 2$ Dirichlet surfaces. We
have found that the most general condition under which the
non superposition effects can be regarded as small corresponds to a number of small
surfaces separated by long distances.
Under this assumption, one may construct a perturbative expansion, as a
series in the operator ${\mathcal O}$.
The condition on that operator manifests itself in a
different fashion, depending on the number of spatial dimensions. In $d=1$,
since the size of the mirrors is zero, one is in the best possible
situation, namely, the perturbative expansion is always reliable.
In $d=2$ and $d=3$, on the other hand, one can always obtain conditions
under which the expansion should be reliable (although the rate of convergence depends
on $d$).
An interesting conclusion one can extract is that the knowledge of the
interaction energy for $N$ surfaces is useful to calculate the one for
$N+1$ surfaces only when all the surfaces are widely separated.
\section*{Acknowledgements}
C.C.T, C.D.F. and E.L.L. thank CONICET, ANPCyT and UNCuyo for financial support.
\newpage
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,777 |
The declaration that I'm offering you in my discovery of who I am, which came through the mind of Jesus and reminded me as he admonished me in the scripture, which to you appears to be perhaps two thousand years ago in his little sojourn in time, and I want you to repeat it with me, "All power is given unto me in Heaven and on earth." The acceptance of the fundamental necessity for the admission of the presence of Jesus with us now, here at this time, is the entire requirement of what I am offering you.
Shall we look together at it, just for a moment? All around the world are beginning demonstrations of conversions of body form which previously represented the fleshy idea that you were contained in that body. The entire message of our savior Jesus, and your willingness to accept it, depend on the simple admission that this is the time and place when it was accomplished. And it will be accomplished by your mind.
Now, here's some evidence of communication going on, because you've made an allowance when you decided to watch this video. You've heard reports about this old guy, that this old occupation of a body was beginning to perform, even on this visual video, miracles, with reports coming in from all over wherever they might be, that instances of re-identity were occurring. Look with me at this. This is from our savior Jesus. What we are offering each other is our true identity. Say to me, "I am whole and perfect as I was created." Did you say that? Yes, there, what was that? That was an idea. Say to me, "I've got an idea. I think I'll listen just for a moment to what this teacher of God is telling me and go along with the process that I just might be whole and perfect as I was created." Certainly the evidence within the scripture of Jesus Christ are that that is indeed a fact, along with the certainty that all power to heal the sick and raise the dead is given to you, isn't it?
Our shared recognition of the truth of what we are, through his mind, through the light of his mind and body and spirit, represents an instantaneous conversion of the forms of our former mis-identity. The time and space have come at last, and have always been, when the message of the New Testament of the resurrected man, Jesus, are coming into this continuum of time and it's impossible if you're watching this video that you are not a part of the healing process.
You've been walking along in this continuum of time for a very long time, looking for a solution that's not within the particulars of the time episode that you're representing. We intend to do a little more scripture. I got started on John and I promised Jesus, I had a long talk with him this morning.
Do you talk to Jesus? Would you like to try? Is Jesus in your mind? Say, "Jesus is in my mind." Would you like to share something else with me? Jesus is also in the space that I occupy, even though my body appears to be separate. Why? He's resurrected. He's representing the entirety of a whole body, momentarily in time, in the realization of a convergence of light form that I am offering to you. This is what healing is. Wow, did you see that? What happened to that tumor? Whoop, it's gone.
There are Christian healers that are out in the world proclaiming through the mind of Jesus Christ and the Holy Spirit that they can heal the sick and raise the dead – that was a demonstration of that occurrence. Would you like to have that be true? Then why don't you let it be true? The offering that I am giving you with my mind and with my heart does not require the particulars of the circumstances that represent who you think I am or who you think you are. If the identity of our savior Jesus in his entirety, and I assure you it is his entirety, is representing our moment of separation, why not let his light, there it is, the light of that revelation of the realization of you, come into the particulars that previously represented this body form.
It's important for you to remember that the fundamental teachings of Jesus direct your attention to the certainty that there's nothing outside of you. If we may review Matthew: 5, where in Sermon on the Mount, Jesus reminds you of the necessity to forgive the projections of your own mind, which you are using to represent the grievance and pain and loneliness that you hold against this world.
This directly from Jesus, listen carefully to me, this is important: there is no possibility whatsoever contained within this conflictual continuum of time that you don't at least admit to a fundamental dependence on an alternative, based on your defenselessness, based on a moment of you standing still and letting what you thought was your enemy share the love that we are expressing together through the mind of Christ.
With me now, his admonition: Thou shall love the Lord thy God with all of your heart. Say to me, "I'm going to love my Creator with all of my heart." Yes. Since your creator represents everything, what you're actually saying to me is, "I'm going to love everything." I'm going to feel the passion of the joy of the conversion of my mind that I am being offered now in the light of this idea of the healing process, with all of my heart, involved in the comprehension of his message that I will love with all of my mind. Suddenly it becomes very reasonably to me an expression of unconditional love, because I am not bound up in the conflict of the grievance that I suffer in order to express hatred for my brother, or in fact for God; With all of my soul; I am going to love my Lord, with all of my soul, which is what I am. I am a soulful realization in any time and space of what I am in all of the universe.
Remember our teaching for the program for today, that my self represents the entirety of universal mind. So, I am going to love the Lord my God with my heart, my mind and my soul, and now the crucial element: my neighbor as my self. Not my enemy, not my friend, not someone I have to study whether I like or not, but my neighbor. It's an indication that anyone who stands next to you in the image of your self is actually representing Jesus.
His entire teachings of saviorship are that the brother that you have previously represented in your denial of your own perfection can show you the alternative at this moment. Where is your neighbor standing? Next to you. Who is your neighbor? Your Christ.
What a lovely way to look at it, if you're in the circumference of space/time which was a momentary collapse down into a location of time that has disallowed you to see the entirety of your creative modality by using the definitions of your limited form and condemning your self to a reflection of the darkness that heretofore represented you.
Yes, your neighbor is you. There's nothing outside of you. What you've learned in this last hour, I hope, is that when you came into this contingency you brought with you all the ideas you have about your self as a body, but it's impossible that you also did not bring with you everything that has ever occurred since the beginning and the end of time. So that in the Second Coming of Jesus which we're now representing, we can see that time is about to be over, that you have come to a time and place where the healing of your mind and heart, through the forgiveness of your neighbor can show us the love that we share with the eternal mind of God. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,100 |
{"url":"https:\/\/taoofmac.com\/space\/com\/apple\/macos\/automation","text":"# macOS Automation (with JavaScript)\n\nWhile pondering some options for automating stuff on , I decided to take a look at the bridge. These are cursory notes on various odds and ends, without any real structure.\n\n## Retrieving the Current Wallpaper\n\nRun the below with osascript -l Javascript -i:\n\n\/\/ Import the bridge\nObjC.import('Cocoa');\n\n\/\/ Get a shared workspace\nsw = $.NSWorkspace.sharedWorkspace; \/\/ Get the first screen (yes, this is an NSArray) screen =$.NSScreen.screens.firstObject;\n\n\/\/ Log the pathname (NSURL) out\n\\$.NSLog(sw.desktopImageURLForScreen(screen).absoluteString)\n\n\nIf the above is a folder, you have to go into the Dock\u2019s desktoppicture.db database1 and take a look at what\u2019s there in the data table.\n\nSince the bridge seems to lack SQLite bindings, I haven\u2019t yet had the time to pursue this in depth, other than the data table doesn\u2019t seem to keep track of what wallpaper is on what display if you have multiple monitors (although I suspect that the last entry is always for the primary display).\n\n1. ~\/Library\/Application\\ Support\/Dock\/desktoppicture.db\u00a0\u21a9\ufe0e","date":"2022-08-15 18:11:35","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.2863142788410187, \"perplexity\": 2530.735306548648}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2022-33\/segments\/1659882572198.93\/warc\/CC-MAIN-20220815175725-20220815205725-00469.warc.gz\"}"} | null | null |
Le terme de sablière peut désigner :
sablière (architecture) : un élément de charpente ;
une carrière où on extrait du sable ;
sablière (chemins de fer) : un dispositif ferroviaire destiné à améliorer l'adhérence (physique) des locomotives.
Voir aussi
Sauvenière (homonymie)
la Sablière de Chateaubriant, où ont été exécutés les otages du Camp de Choisel, dont Guy Môquet | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,668 |
Antonio Boselli (1480-1532), peintre italien ;
Benoît-François Boselli (1768-1826), homme politique italien ;
Dino Boselli (né en 1958), joueur italien de basket-ball ;
Élisabeth Boselli (1914-2005), aviatrice française ;
Enrico Boselli (né en 1957), homme politique italien ;
Felice Boselli (1650-1732), peintre italien ;
Franco Boselli (né en 1958), joueur italien de basket-ball, frère de Dino ;
Giovanni Boselli (1924-2007), dessinateur italien de bandes dessinées ;
Mauro Boselli (né en 1953), scénariste italien de bande dessinée ;
Mauro Boselli (né en 1985), footballeur argentin ;
Paolo Boselli (1838-1932), homme d'État italien ;
Pietro Boselli (1988-), ingénieur, ancien maître de conférences en mathématiques à l'University College de Londres, et mannequin italien ;
Sebastián Boselli (né en 2003), footballeur uruguayen ;
Tony Boselli (né en 1972), joueur américain de football américain.
Voir aussi
Gouvernement Boselli, gouvernement du royaume d'Italie (1916-1917). | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,294 |
Лу́трини () — железнодорожный остановочный пункт на территории Салдусского края Латвии, на линии Елгава — Лиепая. Открыт 15 декабря 1928 года. В 1938 году здесь построили временное пассажирское здание.
Примечания
Ссылки
Страничка станции на сайте railwayz.info
Остановочные пункты Латвии
Бывшие остановочные пункты
Салдусский край | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 3,662 |
{"url":"http:\/\/aas.org\/archives\/BAAS\/v30n4\/aas193\/405.htm","text":"AAS Meeting #193 - Austin, Texas, January 1999\nSession 45. Spectral Observations of Stars\nDisplay, Thursday, January 7, 1999, 9:20am-6:30pm, Exhibits Hall 1\n\n## [45.12] A New Exploration of the Spectrum of CS 22892-052\n\nC. Sneden (U. Texas), G.M. Fuller (UCSD), S. Burles (U. Chicago), T.C. Beers (Michigan State U.), J.J. Cowan (U. Oklahoma)\n\nNew high resolution, high signal-to-noise spectra of the ultra-metal-poor, neutron-capture-rich halo giant CS~22892-052 have been obtained with the Keck~I 10m and McDonald 2.7m telescopes. The Keck spectra cover the near-UV spectral region (3100--4300\u00c5) and the McDonald spectra are most useful in the yellow-red region (5000--9000\u00c5). We have analyzed many new near-UV lines of previously studied neutron-capture elements (such as Y, Zr, Nd, and Dy) in CS~22892-052. These new transitions are used to increase the reliability of the abundances of those elements and to show that abundances deduced from near-UV features are the same as those from the visible spectral region. More importantly, with the new spectra we have identified transitions of several previously undetected neutron-capture elements in the range 41\\leqZ\\leq48 (especially Pd, Ag, and Cd), and elements of the third neutron-capture peak (Os, Ir, and Pt). We also detect, for the first time in metal-poor stars, a second line of Th~II at 4086\u00c5. The Th abundance deduced from this line is consistent with that obtained from the standard'' 4019\u00c5\\ Th~II line, increasing the confidence in the use of the Th as a cosmochronometer.","date":"2014-09-16 19:58:23","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 1, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.6719437837600708, \"perplexity\": 10315.632761171992}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2014-41\/segments\/1410657119220.53\/warc\/CC-MAIN-20140914011159-00335-ip-10-196-40-205.us-west-1.compute.internal.warc.gz\"}"} | null | null |
Scroll down to find all the sports we play at Birchfield.
Our Summer Term athletics programme is wide-ranging. All pupils from Pre-Prep upwards take part in age-appropriate training. Our extensive grounds allow us to keep a dedicated 400 metre track and permanent long jump facilities. The highlight of the athletics season is Sports Day when pupils from every year group compete in track and field events to win the coveted House Athletics Trophy and break records.
Cricket is a leading sport at Birchfield and is played by both boys and girls, separately and together in mixed teams. Our manicured cricket square provides a wonderful backdrop for long, sunny afternoon matches. Birchfield's sporting success in cricket has been outstanding on both a local and regional level, having twice won Cricket County Cup tournaments, beating schools from all over Shropshire at U12 and U13 level.
Birchfield works with cross country runners at all levels. We have twenty acres of grounds for running practice and the use of adjacent farm land on which our young runners really have to challenge themselves. Running is perfect for all round fitness and stamina and every child at Birchfield will train and run for their house during the school year.
Football is our Autumn Term boys' sport at Birchfield and a great school favourite with highly focused weekly training and hotly contested fixtures at home and away. The football season is dynamic and fast-paced and we see many successes for Birchfield each season at all age groups, resulting in cups, medals and awards for our cabinets.
Hockey at Birchfield is a main sport, being played by our girls and also, on occasion, with mixed boys' and girls' teams. We have a large astro-turf hockey facility which provides the perfect surface for training and matches. Our girls compete in hockey matches weekly in the season and have much success in deleting results against competing schools.
Netball is a hugely competitive sport at Birchfield. Our facilities provide a superb training ground with all our girls' teams undertaking focused training and practice weekly on the astro-turf and competing in external and home fixtures. Our success on the netball pitch grows every year with our girls developing teamwork, competition and fair play along the way.
PE lessons provide understanding of healthy lifestyles and the importance of looking after your body and your fitness and co-ordination. Classes are carefully balanced to deliver agility, flexibility and strength training exercises which form the basis of all other Birchfield sports.
In the Summer Term our girls play rounders, training weekly on our dedicated rounders pitch and competing against other schools regularly . Birchfield nurtures enthusiastic and competitive strong hitters and catchers of the rounders ball and this is wonderful for hand-eye co-ordination skills.
Rugby is a key Spring Term sport at Birchfield for our boys and is a very character-building experience for our young players. Boys learn age-appropriate tackling skills and compete weekly against other schools to consolidate their learning. We enjoy many successes each year on the rugby pitch, both at home on our two dedicated pitches and away.
Birchfield is very lucky to have its own outdoor heated swimming pool set in beautiful grounds. The pool is used in the Summer Term with pupils training regularly and gaining confidence ahead of the annual Swimming Gala in which they compete in a variety of events to gain points for their house.
Tennis goes from strength to strength at Birchfield. Our pupils are supported by superb tennis facilities with floodlit three astro-turf courts and our Summer programme provides many opportunities to play. Our tennis squad plays two prestigious inter-school tournaments each year and has an impressive record of success. | {
"redpajama_set_name": "RedPajamaC4"
} | 9,752 |
{"url":"http:\/\/zbmath.org\/?q=an:0686.35045","text":"# zbMATH \u2014 the first resource for mathematics\n\n##### Examples\n Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. \"Topological group\" Phrases (multi-words) should be set in \"straight quotation marks\". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. \"Quasi* map*\" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. \"Partial diff* eq*\" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.\n\n##### Operators\n a & b logic and a | b logic or !ab logic not abc* right wildcard \"ab c\" phrase (ab c) parentheses\n##### Fields\n any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)\nNonlinear second order elliptic partial differential equations at resonance. (English) Zbl\u00a00686.35045\n\nThe authors consider nonlinear second order elliptic partial differential equations at resonance. More precisely, they study the solvability of selfadjoint boundary value problems of the form\n\n$\\left(1\\right)\\phantom{\\rule{1.em}{0ex}}Lu+{\\lambda }_{1}u+g\\left(x,u\\right)=h\\phantom{\\rule{1.em}{0ex}}in\\phantom{\\rule{1.em}{0ex}}{\\Omega },\\phantom{\\rule{1.em}{0ex}}u\/\\partial {\\Omega }=0,$\n\n$\\left(2\\right)\\phantom{\\rule{1.em}{0ex}}Au+{\\lambda }_{1}u+g\\left(x,u\\right)=h\\phantom{\\rule{1.em}{0ex}}in\\phantom{\\rule{1.em}{0ex}}{\\Omega },\\phantom{\\rule{1.em}{0ex}}u\/\\partial {\\Omega }=0,$\nwhere h is a given function on ${\\Omega }$ and ${\\lambda }_{1}$ is the first (resp. principal) eigenvalue of a uniformly elliptic operator -L (resp. -A) on a bounded smooth domain ${\\Omega }\\subset {\u211d}^{N}:$\n$Lu=\\sum _{i,j}\\partial \/\\partial {x}_{i}\\left({a}_{ij}\\left(x\\right)\\partial u\/\\partial {x}_{j}\\right)-{a}_{0}\\left(u\\right)u,\\phantom{\\rule{1.em}{0ex}}Au=Lu+\\sum _{i}{b}_{i}\\left(x\\right)\\partial u\/\\partial {x}_{i},$\nwith the coefficients satisfying suitable regularity conditions. The objective is to show solvability of (1) or (2) for any h orthogonal to the first eigenfunction, in situations where the nonlinearity satisfies neither a monotonicity condition nor a Landesman- Lazer type condition. Instead, the nonlinearity is assumed to satisfy a sign condition g(x,u), $u\\ge 0$, and a linear growth allowing \u201cinteraction\u201d with the first and second eigenvalues. Moreover, some crossing of eigenvalues is allowed in certain cases.","date":"2013-12-06 00:00:28","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 7, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8284323811531067, \"perplexity\": 5657.6526352929595}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2013-48\/segments\/1386163048663\/warc\/CC-MAIN-20131204131728-00067-ip-10-33-133-15.ec2.internal.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.physicsforums.com\/threads\/problem-about-a-robotic-arm.680723\/","text":"# Problem about a robotic arm\n\n1. Mar 25, 2013\n\n### supermiedos\n\n1. The problem statement, all variables and given\/known data\n\nGiven the following robotic arm:\nhttp:\/\/i.imgur.com\/TIb1vOk.png\n\nand knowing that $x_{c}$ = Lcos\u03b8 and $y_{c}$ = Lsin\u03b8, find expressions for\n$x_{m}$ and $y_{m}$ and show that:\nd$x_{m}$ = -$y_{m}$d\u03b8 + ($y_{c}$-$y_{m}$)d$\\phi$\n\n2. Relevant equations\n\n(Shown on picture below)\n\n3. The attempt at a solution\nHere it is my attempt at a solution:\nhttp:\/\/i.imgur.com\/Ee7iZWk.png\n\nFirst I made a traslation to the origin and then I found the angles. Then, I got that triangle (4th pic) and found the relations between the angles and the sides. Next, I simplified both expressions using trigonometric identities and finally got d$x_{m}$.\n\nBut I don't get the book's answer!!! Could you help me please?","date":"2017-08-20 12:44:59","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 1, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.38134077191352844, \"perplexity\": 1353.0240797161734}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-34\/segments\/1502886106465.71\/warc\/CC-MAIN-20170820112115-20170820132115-00384.warc.gz\"}"} | null | null |
adidas Men's CF Lite Racer Running Shoe,Grey Two/Grey Three/White,10 M US Bridgeport, Connecticut 2019.
Basketball Shoes Best Sale – adidas Men's CF Lite Racer Running Shoe,Grey Two/Grey Three/White,10 M US Bridgeport, Connecticut 2019.
You'll feel like you're walking on a cloud in the Cloudfoam Lite Racer sneakers from adidas®.
Latest Collection 2019 – adidas Men's CF Lite Racer Running Shoe,Grey Two/Grey Three/White,10 M US, Bridgeport, Connecticut USA. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,235 |
\section{Introduction}
Image segmentation has become an essential technique in fields from medical imaging\cite{clarke-MRI1995, ji-Fuzzy2012, forouzanfar-Parameter2010} and autonomous driving\cite{feng-Deep2020} to robotic perception\cite{schwarz-RGBD2018} and image compression\cite{ratakonda-Lossless2002, sanderson-Image1995, liangshen-segmentationbased1997}. Through unsupervised segmentation of large data sets, trained algorithms can recognize and predict elements of new images. An appealing application of image segmentation is in the thickness identification of two-dimensional (2D) materials from their digital optical microscopy images. Current flake detection methods rely heavily on identification by trained researchers, a human-learning process, in which flakes are identified by their contrast difference on a substrate after significant trial and error. Automatic thickness identification would relieve this tedious, time-consuming screening process and possibly improve identification accuracy.
The easiest implementation of image segmentation for 2D materials is by thresholding. This is performed by analyzing image contrast, from reflectance or transmittance for example, and partitioning regions of an image based on contrast level difference. This technique has been widely and successfully employed in the identification and characterization of exfoliated 2D materials\cite{li-Rapid2013, bing-Optical2018, taghavi-Thickness2019, ni-Graphene2007, jung-Simple2007, wang-Optical2009, zhang-Optical2017, yu-Investigation2017, wang-Thickness2012, rubio-bollinger-Enhanced2015, jessen-Quantitative2018}. Thresholding techniques, while easily implemented, suffer from inaccuracy when contrast differences become relatively small, for example a single layer of graphene on a silicon/silicon dioxide (Si/SiO$_2$) substrate, and can be highly dependent on precise experimental conditions hindering universal application.
Recently, a variety of more advanced machine learning techniques have emerged to automate and improve the process of identifying exfoliated 2D materials\cite{yang-Automated2020, wu-twodimensional2019, masubuchi-Deeplearningbased2020, masubuchi-Classifying2019, lin-Intelligent2018, li-Rapid2019, greplova-Fully2020, cellini-Layer2019, hu2020rapid, dong20213d, aleithan2020toward}. These include techniques based on neural networks and data clustering but have been primarily applied to opaque substrates and almost entirely to standard Si/SiO$_2$. Transparent substrates are commonly used for exfoliation or experiments on 2D materials\cite{castellanos-gomez-Deterministic2014, island-Precise2016, lippert-Influence2017, nguyen-Visibility2020, chu-Linear2020, taghavi-Thickness2019}. A method that can be applied to identify the thickness of any material on any substrate is highly desirable.
Here we present an open source program\cite{github} written in Python 3 to automatically identify the thickness of exfoliated 2D flakes which can be universally applied to different materials and substrates. We combine three well-established clustering techniques to form a training script to segment layers of a flake, manually label the layers, and then use that training to test thicknesses of other flakes. The program presents roughly a 95\% pixel accuracy for graphene and transition metal dichalcogenides on silicon/silicon dioxide and polydimethylsiloxane (PDMS) substrates. Importantly, no change to the program's adjustable parameters are needed to identify different materials on different substrates, allowing simple and universal application to any material/substrate combination.
\section{Overview of the program}
An overview of the program applied to graphene on Si/SiO$_2$ is shown in Figure \ref{fig1}. The training stage begins with a set of optical microscopy images cropped to few-layer flakes whose thicknesses are determined using optical contrast methods\cite{li-Rapid2013}. Figure \ref{fig1}(a) shows a cropped optical image of a few-layer graphene flake on a Si/SiO$_2$ (300 nm SiO$_2$) substrate with each layer thickness labeled (1-4 layers). A scatter plot of the red, green, and blue (RGB) channel values (normalized to a range 0-1) for each pixel in the image is shown in Figure \ref{fig1}(b). The data points have been colored according to their RGB values. At this stage, the scatter plot shows only broad features that can be generally associated with the substrate (pink) and few-layer graphene (purple) but no clear correspondence to individual thicknesses can be made. The raw image is preprocessed using a bilateral filter to reduce noise and a background normalization using a planar fit. The result, after compression to roughly 10,000 total pixels, is shown in Figure \ref{fig1}(c). Preprocessing reveals the individual clusters of data in the scatter plot (Figure \ref{fig1}(d)) associated with the substrate and flake layers.
The location and distribution of these clusters in RGB space are found using a series of unsupervised clustering techniques summarized here and detailed further below. The centers are first located using mean shift and density-based spatial clustering. Once the centers are identified, fit characteristics such as the weight, mean position, and distribution of each cluster are found using a Gaussian mixture model. An image of the result of the fitting algorithm is shown in Figure \ref{fig1}(e). The pixels in the color plot have been colored according to the fit results and the scatter plot (Figure \ref{fig1}(f)) shows these fit assignments in more detail. Once the cluster characteristics are extrapolated for several training images, a master catalogue is created that ties the fit clusters to the predetermined flake thicknesses in our training images.
To determined accuracy of the training, we test the master catalogue on a set of images with identified thicknesses. An example of the testing results for graphene on Si/SiO$_2$ is shown in Figures \ref{fig1}(g-j). In the testing stage, untrained optical images (Figure \ref{fig1}(g-h)) are first preprocessed using the same procedure as in training but without cropping. The preprocessed images are then checked against the master catalogue for flake thickness assignment given the pixel location in RGB space. Figure \ref{fig1}(i) shows the result (cropped to show detail of flake of interest) with layer thicknesses identified by the color bar. The associated scatter plot in Figure \ref{fig1}(j) shows the corresponding clusters and layer assignments. In the following section we detail the implemenation of the clustering algorithms before presenting results of our program performed on other materials and substrates.
\begin{figure}
\includegraphics[width=6.6 in]{Fig_1}
\caption{\label{fig1} \textbf{Overview of the program composed of training and testing stages.}
(a-b) Raw optical image of a few-layer graphene flake on 300 nm of SiO$_2$ (a) and its corresponding scatter plot of each pixel in RGB color space (b). The scatter plot data points are colored to match their RGB value.
(c-d) The result after preprocessing the image in panel (a). The preprocessing reveals well-defined clusters in the associated scatter plot (d).
(e-f) A color plot of pixel-cluster association (e) and corresponding scatter plot (f). Each pixel is colored based on its most probable data cluster identity.
(g-h) Raw optical image of few-layer graphene flake with unknown thickness (g) used for testing and its corresponding RGB scatter plot (h).
(i-j) Crop of panel (g) around the flake of interest (i) and corresponding scatter plot after the testing stage (j).
}
\end{figure}
\section{Unsupervised clustering algorithms}
Our training script incorporates three clustering algorithms to identify the center of the data clusters and fit their distributions. Without explicitly knowing the number of clusters (layers) in the image, the script begins with an unsupervised method of determining the seed number. We use mean shift\cite{comaniciu-Mean2002, zhou-RegionBased2008, zhou-Mean2011} and density-based\cite{ester-densitybased1996, ruixu-Survey2005} algorithms to first find these cluster centers which are then fed to a Gaussian mixture model for fitting arbitrary ellipsoidal distributions.
Mean shift is an unsupervised machine learning algorithm that locates centers of high data density. The algorithm begins by populating color space with an array of points, referred to as "mean points" ($\vec{\rho}_k$). Figure \ref{fig2}(a) shows the same data as in Figure \ref{fig1}(d) but with red closed circles indicating the initial positions of the equally spaced mean points (an $8\times8\times8$ array). The next step groups all data points within a defined radius ($\epsilon$) of each mean point together. We define $\epsilon$ to be just large enough to overlap with its nearest neighbors. The average location of the data pixels within $\epsilon$ of a given mean point becomes the new position of that mean point ($\vec{\rho}_k'$) after one iteration of the algorithm. This is calculated by:
\begin{equation}
\vec{\rho}_k'=\frac{1}{M}\sum_i{\vec{x}_i} \textrm{ for } |\vec{x}_i-\vec{\rho}_k|<\epsilon,
\end{equation}
where $\vec{x}_i$ is the position of each data point and $M$ is the total number of data points within $\epsilon$ of $\vec{\rho}_k$. In this way, each mean point gradually shifts towards higher densities of data. Figure \ref{fig2}(b) shows one iteration of the algorithm. Several points have moved to their new mean positions according to the data within $\epsilon$ of each $\vec{\rho}_k$.
Mean shift is computationally slow, having to calculate the distance between every data point ($\approx$10,000 pixels) and every mean point (initially 512). To increase efficiency, mean points that have no data within $\epsilon$ after the first cycle, and thus make no contribution towards a data cluster, are deleted. Additionally, mean points may approach their local maximum at different rates. Per mean point, as soon as the number of data points within their radius starts to decrease, they are turned off and no longer involved in future calculations. Figure \ref{fig2}(c) shows the final state of the algorithm where all mean points have converged to their local density maxima. After this, outliers are removed before moving to the next algorithm.
Once mean shift is complete, several mean points will themselves be clustered in color space and some mean points will have converged to outliers. Due to the ellipsoidal shape of the clusters in RGB space after preprocessing, the mean points will tend to lie along lines. An efficient algorithm for grouping these lines is Density-Based Spatial Clustering of Applications with Noise (DBSCAN)\cite{ester-densitybased1996, ruixu-Survey2005}. DBSCAN groups data together by following the trajectory of nearby points. The algorithm starts by "visiting" a random mean point. A radius (we find $\epsilon/2$ works well) around it is checked for other mean points. If none are found, the starting point is labeled an outlier. If there are neighbors, they are grouped together. One of the other points in this group is visited next, checking the same radius around itself to find new points to add to the group. This repeats until no new points are added to the group and every point within the group has been visited. Once the group is finished, a new group starts at a randomly chosen mean point and the process repeats. The centers of each group are found by averaging their respective mean points. Figure \ref{fig2}(d) shows the result after running the DBSCAN algorithm on the mean points in Figure \ref{fig2}(c).
\begin{figure}
\centering
\includegraphics[width=3.3 in]{Fig_2}
\caption{\label{fig2} \textbf{Mean shift and DBSCAN clustering for identification of cluster centers.}
(a) The same data as in Figure \ref{fig1}(d) with red closed circles showing the initial positions of the mean points in the mean shift algorithm.
(b) Scatter plot after one cycle of mean shift; outlier mean points have been deleted and others have moved towards their local density maxima.
(c) The final state of the mean points after they have converged to their maxima.
(d) The RGB pixels plotted with the identified cluster centers (colored closed circles) after the DBSCAN algorithm.
}
\end{figure}
The combination of mean shift and DBSCAN presents an unsupervised method of determining how many clusters are in a given image and their centers. Following this step, this information can be used to seed a more powerful clustering technique for data with ellipsoidal distributions. The popular K-means clustering technique\cite{celebi-comparative2013, dhanachandra-Image2015, dhanachandra-Survey2017} for example is undesirable here as it assumes spherical clusters. Instead, we use a multivariate Gaussian Mixture Model (GMM)\cite{gupta-gaussianmixturebased1998, nguyen-Dirichlet2011, permuter-study2006, ribeiro-Hand2006, santosh-Tracking2013, ji-Fuzzy2012} that allows fitting of data with arbitrary normal distributions. This expands application of the program by automatically handling new materials and substrate combinations that may have different cluster distributions in RGB space.
In the GMM, each fitting ellipsoid has three characteristics developing throughout the process: the weight ($\phi_k$, defining the number of data points near ellipsoid $k$), the centroid ($\vec{\mu}_k$, defining the mean of the data points belonging to ellipsoid $k$), and the covariance matrix ($\Sigma_k$, defining the shape and orientation of ellipsoid $k$ in RGB space). These characteristics are used to calculate the probability $\gamma_{ik}$ of a data point ${\vec{x}_i}$ belonging to ellipsoid $k$. This probability is given by:
\begin{equation}
\gamma_{ik}=\frac{\phi_k\mathcal{N}(\vec{x}_i,\vec{\mu}_k,\Sigma_k)}{\sum_{j=1}^K\phi_j\mathcal{N}(\vec{x}_i,\vec{\mu}_j,\Sigma_j)},
\end{equation}
where $K$ is the total number of clusters and $\mathcal{N}$ is the three-variable (for 3-dimensional RGB space) Gaussian distribution given by:
\begin{equation}
\mathcal{N}(\vec{x}_i,\vec{\mu}_k,\Sigma_k)=[(2\pi)^3 |\Sigma_k| e^{(\vec{x}_i-\vec{\mu}_k)^T\Sigma_k^{-1}(\vec{x}_i-\vec{\mu}_k)}]^{-\frac{1}{2}}
\end{equation}
The weights, means, and covariance matrices used in these relations are calculated through:
\begin{equation}
\phi_k=\frac{1}{N}\sum_{i=1}^N\gamma_{ik},
\end{equation}
\begin{equation}
\vec{\mu}_k=\frac{\Sigma^N_{i=1}\gamma_{ik}\vec{x}_i}{\Sigma^N_{i=1}\gamma_{ik}},
\end{equation}
\begin{equation}\label{co}
\Sigma_k=\frac{\sum_{i=1}^N\gamma_{ik}|\vec{x}_i-\vec{\mu}_k|^2}{\sum_{i=1}^N\gamma_{ik}}.
\end{equation}
First we initialize each of the fitting ellipsoids by setting all initial weights to $1/K$. The centroids are taken directly from the results of DBSCAN $\vec{\mu}=\vec{\rho}$. The covariance matrices are initialized from the centroids using Equation \ref{co} with $\gamma_{ik}=1$. Figure \ref{fig3}(a) shows the initialization of the fitting ellipsoids for our example few-layer graphene data set from Figure \ref{fig1}(d) and Figure \ref{fig2}. The ellipsoids have been scaled to a 95\% confidence level.
An unsupervised machine learning algorithm, referred to as expectation-maximization (EM), is used to further optimize the ellipsoid parameters and fit the data. The expectation step determines $\gamma_{ik}$ based on the initialized weights, centroids, and covariance matrices calculated above. The maximization step uses these probabilities to re-calculate each cluster's weight, centroid, and covariance matrix. These two steps iterate and gradually the ellipsoid parameters converge. Figure \ref{fig3}(b) shows the algorithm results after 2 cycles and Figure \ref{fig3}(c) shows the results after 30 cycles. After 30 cycles, the ellipsoids resemble the distributions of the data with several small tight ellipsoids corresponding to the substrate and 1-4 layers of graphene, and two larger ellipsoids (purple and blue) accounting for noise. The max change of all cluster's weights between maximization steps ($\Delta\phi_k < 0.0001$) is used to define convergence and end the algorithm. Figure \ref{fig3}(d) shows the results of the algorithm after convergence (total 61 cycles) for this data set. Note that the large purple and blue ellipsoids are a product of over-fitting the data (fitting 7 ellipsoids to 5 data clusters). These ellipsoids do not contribute to the master catalogue, but are important for fitting data points associated with thicker layers ($>4$) and outliers. The over fitting also allows the primary ellipsoids to confine themselves to the core of their data clusters. Once convergence has been reached, only ellipsoids that fit well to known layer thicknesses are added to a catalogue.
The training process is repeated for multiple flakes of the same material and substrate (we trained around 5 for each material/substrate combination), saving their ellipsoid characteristics into the same catalogue. A master catalogue is then created by averaging together the characteristics of ellipsoids with like-thickness. This master catalogue is the tool with which we can test other images to determine their flake layer thicknesses (Figure \ref{fig1}(i-j)).
\begin{figure}[ht!]
\includegraphics[width=3.37 in]{Fig_3}
\caption{\label{fig3} \textbf{Cluster fitting with a Gaussian mixture model (GMM).}
The scatter plot from Figure \ref{fig1}(d) is superimposed with 95\% confidence ellipsoids based on the fit characteristics of the GMM-EM algorithm. (a) The initialized ellipsoids show little correspondence to the underlying data. (b) After two cycles of expectation-maximization, the ellipsoids better resemble the data clusters. (c) After 30 cycles, some ellipsoids have nearly converged on their data clusters. (d) The convergence condition is reached after 61 cycles.
}
\end{figure}
\section{General application to other materials and substrates}
Our script can be universally applied to the identification of other 2D material thicknesses on opaque and transparent substrates. This generality is achieved by analyzing all three dimensions of the color-space data and fitting the resulting clusters of arbitrary shape with our GMM-EM algorithm. Importantly, no change in the adjustable parameters ($\epsilon$ or GMM convergence) are required for the following results.
Figure \ref{fig4} displays the power of this generality by identifying the layer thickness of two additional materials, molybdenum disulfide (MoS$_2$) and molybdenum diselenide (MoSe$_2$), on opaque (Si/SiO$_2$) and transparent (polydimethylsiloxane (PDMS)) substrates. MoS$_2$ on Si/SiO$_2$ (Figure \ref{fig4}(a-e)) presents clusters very similar to those of graphene on Si/SiO$_2$ but they are separated further in RGB space (Figure \ref{fig4}(b)). Further training for this material/substrate combination would improve our testing results which only identify layer thicknesses of 1 and 2 (Figure \ref{fig4}(d-e)). From the covariance matrices we note that while all the data clusters are technically triaxial ellipsoids (none of the semi-axes are equal), the clusters for materials on Si/SiO$_2$ are roughly prolate spheroids with one axis (blue) an order of magnitude larger than the other two semi-axes (red and green).
MoS$_2$ on PDMS (Figure \ref{fig4}(f-j)) presents clusters again extending along the blue axis, though not as strongly as materials on Si/SiO$_2$. The clusters are similarly well-separated in RGB space as they are for MoS$_2$ on Si/SiO$_2$. Testing for this set identifies monolayer, bilayer and trilayer thicknesses (Figure \ref{fig4}(j)). Finally, MoSe$_2$ on PDMS presents the most spherical ellipsoids of our investigation still slightly extending along blue, (Figure \ref{fig4}(k-o)) and mono- through trilayer thicknesses are easily identified (Figure \ref{fig4}(o)).
\section{Discussion}
Our investigation focuses on the development of a program that can be universally applied to different 2D materials and substrates. This requirement invariably introduces computation time when compared with other recent segmentation methods\cite{masubuchi-Deeplearningbased2020, han-DeepLearningEnabled2020}. The training time, for example, reported in Ref. \cite{han-DeepLearningEnabled2020} for the entire program is roughly 31 hours. Computation times for the training stage of our program depend on the image composition. A single layer image can take about ten minutes but images with multilayer flakes (more clusters) take as long as 5 hours. Our program results here are from training sets of roughly 10 images corresponding to about 10 hour computation time. However, this is a single event time cost because once the master catalogue is trained for a particular material and substrate combination, it can then be used repeatedly in the testing step, which is more efficient.
Image testing requires roughly one minute to identify layer thicknesses of new images. Computation time is sufficiently short for testing because image pixels are simply compared with the master catalogue. This time would allow in-situ identification of flakes from images taken by human inspection of a substrate. The time spent scanning between images can take several minutes. The time may also be sufficient for an automated scanning system such as that presented in ref. \cite{masubuchi-Autonomous2018}. Improvements in computation time may be sought through further image compression or possibly reducing the testing step to two dimensions of the three-dimensional RGB space, possibly blue and either green or red, similar to algorithms presented in ref. \cite{masubuchi-Classifying2019}. Although, the dropped color dimension would have to be identified for a particular material/substrate combination.
For each material/substrate combination investigated in this study, the pixel accuracy was determined by creating a ground truth image and comparing it, pixel-by-pixel, with the testing images (see Figure S1 in the supplemental materials for details). Pixel accuracy was slightly better for materials on PDMS but overall the program achieves an average accuracy of 95\% for the materials and substrates investigated in this study. This pixel accuracy is comparable to that achieved in studies based on much larger training sets. Ref. \cite{han-DeepLearningEnabled2020} reports pixel accuracy of 97\% from a training set of 917 images. Based on these results, normalized confusion matrices for each combination were calculated showing the individual layer accuracy as well. Finally, we note that a clear advantage to our approach is the simplicity of our program which relies on well-known and proven clustering techniques with relatively high pixel accuracy from small training sets.
\section{Conclusion}
Summarizing, we have presented a code for the automatic identification of flake thicknesses that can be universally applied to a variety of 2D materials and substrates. The algorithm analyzes data clusters in RGB space of preprocessed optical microscopy images. It can accurately identify mono- and few-layer thicknesses with a pixel accuracy of 95\%. We anticipate the program will be of use for a wide variety of materials and substrates for the continued interest and investigation into the properties and characteristics of 2D materials.
\section{Acknowledgements}
The authors thank Jeffery Cloninger for technical support and Najme S. Taghavi and Dr. Andres Castellanos-Gomez for optical images of materials on PDMS.
\section{Author contributions statement}
J.O.I. conceived the project. R.M.S. coded the program with guidance from J.O.I.. R.M.S. and K.L.H. provided optical images of 2D materials. All authors wrote and reviewed the manuscript.
\begin{figure}
\includegraphics[width=6.6 in]{Fig_4}
\caption{\label{fig4} \textbf{General thickness identification of 2D materials on opaque and transparent substrates.}
(a-c) An example training process for MoS$_2$ flakes exfoliated onto Si/SiO$_2$ substrates. (a) Raw optical image before preprocessing. (b) RGB scatter plot of the identified clusters with pixels colored according to the cluster they belong to. (c) Reconstructed image of the MoS$_2$ flake in (a) after the training step.
(d-e) Testing process for MoS$_2$ on Si/SiO$_2$. (d) Raw optical image of an MoS$_2$ flake on Si/SiO$_2$. (e) Layer identification after testing the image in (d).
(f-h) An example training process for MoS$_2$/PDMS.
(i-j) An example testing process for MoS$_2$/PDMS.
(k-m) An example training process for MoSe$_2$/PDMS.
(n-o) An example testing process for MoSe$_2$/PDMS.
}
\end{figure}
\clearpage
\section{References}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,640 |
// Copyright (c) 2005, Regents of the University of California
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
// * Neither the name of the University of California, San Diego (UCSD) nor
// the names of its contributors may be used to endorse or promote products
// derived from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
// IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
// THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
// PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
// LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
//
// FILE
// GeneralAccount.java - edu.sdsc.grid.io.GeneralAccount
//
// CLASS HIERARCHY
// java.lang.Object
// |
// +-.GeneralAccount
//
// PRINCIPAL AUTHOR
// Lucas Gilbert, SDSC/UCSD
//
//
package edu.sdsc.grid.io;
/**
* An object to hold the user information used when connecting to a file system.
* This class does not actually connect to a filesystem. It only hold user
* connection information. Setting or getting this information only refers to
* the contents of the object.
*<P>
*
* @author Lucas Gilbert, San Diego Supercomputer Center
*/
public abstract class GeneralAccount extends Object implements Cloneable {
/**
* The home directory on the server
*/
protected String homeDirectory;
/**
* Constructs an object to hold the user information used when connecting to
* a file system.
* <P>
*
* @param homeDirectory
* home directory on the SRB
*/
public GeneralAccount(String homeDir) {
setHomeDirectory(homeDir);
}
/**
* Finalizes the object by explicitly letting go of each of its internally
* held values.
* <P>
*/
protected void finalize() {
if (homeDirectory != null)
homeDirectory = null;
}
/**
* Sets the home directory of this GeneralAccount.
*/
public abstract void setHomeDirectory(String homeDir);
/**
* Returns the homeDirectory used by this GeneralAccount.
*
* @return homeDirectory
*/
public String getHomeDirectory() throws NullPointerException {
if (homeDirectory != null)
return homeDirectory;
throw new NullPointerException();
}
/**
* @return a copy of this account object.
*/
public Object clone() {
try {
return super.clone();
} catch (CloneNotSupportedException e) {
// Shouldn't happen
throw new InternalError();
}
}
public abstract boolean equals(Object obj);
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,006 |
The Quarta Catalana is the 9th and last tier of the Spanish football league system and the fourth highest league in the autonomous community of Catalonia. The league was formed in 2011 to replace the Tercera Territorial as third level of Catalonia and was split into 31 groups. Every season, depending on budgets, each group can have from 12 to 18 teams.
Structure
Territorially, groups are divided as following:
Group 1 to 18 - Province of Barcelona
Group 19 and 20 - Terres de l'Ebre
Group 21 and 22 - Province of Lleida
Group 23 to 25 - Rest of the Province of Tarragona
Group 26 to 31 - Province of Girona
Groups (2021–22)
See also
Primera Catalana
Segona Catalana
Tercera Catalana
Divisiones Regionales de Fútbol
References
Catalan football competitions
Quarta Catalana | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 487 |
New memoir from the iconoclastic Edzard Ernst
By William M. London
William T. Jarvis, who served as president of the National Council Against Health Fraud from its founding in 1984 through 1999 described Germany as "a mothering ground of quackery." The herbalism of Paracelsus, magnetic healing, phrenology, homeopathy, aromatherapy, naturopathy, orgonomy, fresh cell therapy, electroacupuncture ("essentially transdermal electrical nerve stimulation masquerading as acupuncture"), anthroposophy, the Gerson cancer treatment protocol, and other ideologically-driven nonsense originated there. But Germany was also the mothering ground of one of the most influential opponents of quackery—and the most prominent opponent of the quackery-promoting efforts of Charles, Prince of Wales—during the last twenty years: Edzard Ernst.
Edzard Ernst in 2012. Image by Luiyo via Wikimedia Commons.
As he described in his new book A Scientist in Wonderland: A Memoir of Searching for Truth and Finding Trouble (ISBN 978-1-84540-777-3), Ernst grew up in Bavaria, where healing cults such as hydrotherapy, homeopathy, and naturopathy were "as accepted and unremarkable…as lederhosen." [p. 1] His mother was an enthusiast of such superstition as Sebastian Kneipp's naturopathic preaching about the salubrious value of ice cold baths and walking through dewy grass or snow. Such an upbringing could predispose many people to be future allies of Prince Charles, but Ernst was inclined to rebel against dogmatic authority.
I have imagined that Ernst's astonishingly productive record of scholarly and popular publications could be attributable to him having the luxury of a carefully charted career path that positioned him in consistently optimal work environments. But early on he was headed for a career as a jazz musician rather than as a medical researcher and, throughout most of his research career, he encountered—and often overcame— numerous obstacles to conducting scientific research.
His experience as a psychology student at University of Munich disappointed him. Instead of a curriculum emphasizing scientific discovery, he recalls exposure to postmodern concepts of truth, "a steady diet of speculation," "Freud, graphology, and a weird type of physiology," and classmates focused on "sorting out their own personal problems." [p. 17.]
He describes his medical school experience as offering an overwhelming amount of knowledge to absorb for the benefit of future patients, but with little opportunity for critically analyzing the facts he was expected to learn and little opportunity to develop as a researcher. However, by completing an M.D. thesis on blood clotting abnormalities in women experiencing septic abortion, he gained research skills that he would apply later in his career.
On his first job following medical school, as junior doctor at Germany's only homeopathic hospital, he practiced a range of so-called alternative therapies for which he would later provide evidence-based assessments. At the time, he recognized the implausibility of homeopathic preparations as therapy, but he observed that patients often got better with homeopathic treatment instead of nonsensical drugs they had been taking. This apparent paradox left him with questions he would try to answer in his future scientific investigations using proper controls for sources of bias.
After a distressing six-month stint working at a psychiatric hospital in the UK, he was hired to join a research team on blood rheology (the study of blood fluidity) at St. Georges Hospital in London. He writes that his roughly two years at St. Georges developing himself as a basic and applied research scientist with critical and analytic thinking skills was the happiest time of his life.
At his next position, a hospital near Munich, he expected that he would be able to continue his blood rheology research while also providing clinical services to patients with severe circulatory conditions. It turned out that the hospital was only interested in the image of being active in research and did not support his interest in conducting research in order to make important advancements in scientific knowledge.
He moved on to a university-based position in Munich emphasizing research with some clinical and teaching responsibilities. He completed his PhD, started the journal Perfusion, won an award for his research on naturopathic treatments on blood rheology, became a certified specialist in rehabilitation medicine, and began to investigate the egregious involvement of doctors and a medical journal he wrote for in experiments on concentration camp prisoners during the Third Reich.
As Professor of Rehabilitation Medicine at the Medical School of Hannover, his clinical responsibilities left little opportunity to continue his research. He moved on to the Vienna Medical School as the chair of Rehabilitation Medicine to lead the development of the largest department of its kind in Europe. He encountered corruption and enormous bureaucratic obstacles to moving his department into what was to be the largest hospital in Europe. Nevertheless, he managed to coordinate a large clinical service, conduct research on blood rheology, carry out clinical trials on some so-called alternative therapies, and found The European Journal of Physical Medicine. Most notably, he uncovered details of the shameful Nazi past of the Vienna Medical School. He considers his report of his findings published in the Annals of Internal Medicine to be the most important paper of his career.
After four years of enduring petty and sometimes vicious bureaucratic infighting among his colleagues in Vienna, he moved on to the University of Exeter as Laing Chair in Complementary Medicine, a position he held from 1993 to 2011. Ernst comes off as naïve in the book in his expressions of surprise about the intense resistance from so-called complementary and alternative medicine practitioners to his research agenda.
I say "so-called" because the buzzwords 'complementary' and 'alternative' are euphemisms used to misrepresent: (1) non-validated and invalidated health enhancement methods as worthwhile and (2) superstition-oriented practitioners as health experts. Not all quackery is promoted using the marketing doublespeak of 'complementary' and 'alternative.' (For example, the quackery of "John of God" and Ernest Angley is promoted without such language.) But when practitioners label themselves or their practices as 'complementary,' 'alternative,' 'holistic,' 'integrative,' 'natural,' etc., they engage in the popular semantics of quackery.
Just because a treatment is labeled complementary medicine does not mean it complements some other type of medicine to enhance health outcomes. (If all it is supposed to do is comfort patients rather than alter the course of illness and there is a plausible rationale for its use, it does not need to be labeled as if it is a special kind of palliative medicine.) And just because a treatment is labeled alternative medicine does not mean it is a viable alternative to a validated method for producing beneficial health outcomes.
Professor Ernst didn't create the language for his title at Exeter so he can't be blamed for taking a title that makes 'complementary medicine' seem like a bonafide field of medical specialty. The mission statement Professor Ernst wrote for his Department of Complementary Medicine should not have been controversial if 'complementary and alternative medicine (CAM)' practitioners are really concerned with accountability to consumers:
To conduct rigorous, inter-disciplinary and international collaborative research into the efficacy, safety and cost of complementary medicine.
To further analytical thinking in this area. [p. 90]
While I quibble with the term 'complementary medicine' and question the wisdom of carrying out efficacy research on supposed alternatives such as homeopathy of decidedly implausible value, Ernst's mission was laudable for its focus on scientific advancement. But practitioners who position themselves in the Neverland of 'CAM' and their admirers tend not to welcome scrutiny of their activities. Professor Ernst realized only in hindsight that he was asking for trouble—even when he tried to be accommodating.
For example, he worked with 'spiritual healers' in planning a study to test their abilities to reduce chronic pain. Although they approved of the design of the study, they objected when Ernst published results showing no significant difference in pain levels following 'spiritual healing' versus sham healing rituals performed by actors.
'CAM' practitioners would have preferred if his research simply served to document patient satisfaction with 'CAM.' However, over the years his research team published well over a thousand papers including around 40 clinical trials, more than 300 systematic reviews. Findings were predominantly negative. He found far less of value than he had initially expected.
Ernst's research team also investigated consumers' motivations to use 'alternative medicine,' practitioners' attitudes toward and knowledge of 'alternative medicine,' and advice given by 'alternative' practitioners regarding vaccination. As founder and editor-in-chief of the journal Focus on Alternative and Complementary Therapies, he became well acquainted with the work of other researchers and found little else in the literature indicating therapeutic value in the world of 'CAM.'
I'm glad that A Scientist in Wonderland includes clear, concise refutations of common arguments and tactics used by Ernst's hostile critics to defend 'CAM' methods despite the lack of validating evidence for them. 'CAM' proponents commonly: (1) fail to consider risks relative to benefits, (2) overrate their own expertise and denigrate the expertise of their critics, (3) question the integrity of those who disagree with them, (4) disregard rare, but serious risks [such as chiropractic neck twisting], (5) mistakenly equate "natural" with "safe," (6) design studies to make positive outcomes unavoidable, (7) claim 'CAM' methods cannot be tested scientifically, (8) claim 'CAM' is especially compassionate, (9) claim to be victims of conspiracies, and (10) make fallacious appeals to popularity, post hoc reasoning [after this, therefore because of this], ignorance, and tradition.
Many readers will be most interested in A Scientist in Wonderland for its extensive discussions of quackery passionately promoted by Prince Charles. Ernst makes a persuasive case that he behaved ethically in calling "Complementary Healthcare: A Guide for Patients" published by the Prince's Foundation for Integrated Medicine "frankly inaccurate and over-optimistically misleading" and in objecting to unfounded claims made in The Role of Complementary and Alternative Medicine in the NHS a report by retired economist Christopher Smallwood commissioned by the Prince.
Sir Michael Peat, the first private secretary of Prince Charles complained to the University of Exeter that Ernst broke a confidentiality agreement with Smallwood. Although an investigation cleared Ernst of wrongdoing, fundraising efforts to support Ernst's Department of Complementary Medicine ceased, leading to the closure of the department and to Ernst's retirement. However, Ernst has continued to write and speak out against quackery and for the need for promoters of health products and/or services to meet their moral obligation to be truthful, competent, and accountable.
The writing in A Scientist in Wonderland is clear and engaging. It combines good storytelling with important insights about medicine, science, and analytic thinking. Despite all the troubles Ernst encountered, I found his story to be inspirational. I enthusiastically recommend the book to scientists, health professionals, and laypersons who like to see nonsense and mendacity exposed to the light of reason.
William M. London is a professor of public health at California State University, Los Angeles, a co-author of the college textbook Consumer Health: A Guide to Intelligent Decisions, Ninth Edition (2013), associate editor of the free, weekly e-newsletter Consumer Health Digest, a North American editor of the journal Focus on Alternative and Complementary Therapies, and an anti-quackery activist since 1987 when he cofounded and served as president of the Ohio Council Against Health Fraud. On Twitter he is @healthgadfly. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,595 |
\section{Introduction}\label{sec:intro}
Circadian Rhythm (CR) is defined as the periodic quality of an organism's activity that follows a 24-hour cycle. Medical research has found that healthy individuals' day-to-day life exhibits a strong circadian rhythm, whereas deviations from such a rhythm are often indicators of potential health issues \cite{karatsoreos2012effects}. Traditionally, circadian rhythm is assessed by questionnaires, such as the Morning-Eveningness Questionnaire (MEQ) \cite{horne1976self} and the Munich Chronotype Questionnaire (MCTQ) \cite{roenneberg2003life}. These questionnaires are centered around the respondent's own recollection of their bed and wake time. With increasing amounts and varieties of sensor data available from daily life tracking devices, we have unprecedented capability to evaluate circadian rhythm objectively and passively, requiring minimal efforts from the user.
Multiple methods have been proposed for the purpose of CR characterization, using different sensor signals and different mathematical approaches. A straightforward approach is to automate the measurements of constructs solicited in the traditional CR surveys. As opposed to asking participants when a certain activity was performed in a day, we can instead find a digital marker in sensor signals that reflects the same event. For example, the first time in a day at which a person steps out of their home, while could be asked in a questionnaire, can be passively detected by their smartphone's GPS sensor. Higher on the scale of analytical complexity is the \textit{cosinor} method which was originally proposed in the 1960s \cite{halberg1969chronobiology} and continues to be improved upon \cite{marler2006sigmoidally}. Building on the assumption that a person's daily rest-activity pattern follows a sinusoidal shape, the cosinor method aims to fit a trigonometric function to the magnitude of a body-worn sensor signal (e.g., wrist-worn actigraphy) and extract coefficients that serve as CR descriptors such as amplitude and time of peak. To free CR analysis from complying to a rather strict sinusoidal assumption, non-parametric CR methods \cite{witting1990alterations, blume2016nparact} were proposed to directly compute metrics that quantify the variability of sensor signals within-day and across different days. Non-parametric methods have become popular due to their applicability to signals of all shapes without concerns of assumption violation. Last but not least, researchers have also employed Fourier analysis to characterize CR: by converting a signal to its frequency domain, one can examine the degree to which the signal follows a 24-hour cycle, thus quantifying the strength of its rhythmicity.
The methods outlined above produce different metrics that describe related, but distinct aspects of the circadian pattern. While these methods have been individually proposed and implemented with the sensing technology and sensor data of choice by the researcher, we find that evidence is limited in the extant literature that elucidates (1) the inter-relations between the circadian metrics extracted by different methods and (2) the relationship between the same circadian metric extracted from different types of mobile sensing data collected by companionship technology such as smartphones and smartwatches.
We aim to address these limitations in this paper. We base our analyses on smartphone tracking data we collected from 1584 college students in a major public university in the United States over three weeks in the 2018-2019 school year. We conduct CR analysis using the four major classes of methods outlined above (survey construct automation, cosinor, non-parametric, Fourier) on two types of smartphone sensor signals (GPS, accelerometer), and compare the same metrics extracted from different sensor signals as well as compare different metrics extracted from the same sensor signal.
\section{Related Work}\label{sec:related}
As introduced in Section \ref{sec:intro}, the Morning-Eveningness Questionnaire (MEQ) \cite{horne1976self} and the Munich Chronotype Questionnaire (MCTQ) \cite{roenneberg2003life} are typically used to assess the circadian rhythm in participants' sleep and wake schedule. Another survey instrument, called the Social Rhythm Metric \cite{monk1990social}, quantifies the circadian rhythm in other activities such as social interaction, attending school/work, and having dinner. The commonality between these surveys is their focus on the time in a day when a participant completes a certain number or proportion of a certain type of activity. Schoedel et al. \cite{schoedel2020challenge} sought to passively detect participants' sleep and wake schedule using smartphone usage events such as the action of snoozing, alarm settings, and the first and last time of smartphone usage during a day. The authors also recorded timestamps at which the participants completed 25\%, 50\%, and 75\% of smartphone usage to track its progression throughout the day. We call this approach \textbf{survey construct automation}, because it directly operationalizes survey-solicited activities as sensor-detected events.
Trigonometric functions naturally allow the modeling of periodicity. Researchers have leveraged this to fit cosine curves to sensor signals' temporal distribution over a 24-hour period to characterize the circadian rhythm therein \cite{cho2019mood}. The method is interchangeably called trigonometric regression, harmonic regression, or \textbf{cosinor regression}, for which multiple days of continuously or equidistantly sampled sensor signals serve as the input data. In the most basic cosinor setup, signal value $X$ at time $t$ is modeled by function $X(t) = mesor + amplitude \cdot cos(2\pi[t - \phi]/24)$, in which three parameters of the fitted curve are of primary interest: (1) $mesor$: short for Midline Estimating Statistic Of Rhythm, representing the mean value of the curve across cycles of the circadian rhythm; (2) $amplitude$: one half of the range of the curve within a cycle, and (3) $\phi$ or \textit{acrophase}: the time in a cycle at which the curve reaches its maximum value. In a transformed version of the cosinor method \cite{marler2006sigmoidally}, researchers aim to better mimic signal distributions that have a flatter or sharper peak or valley area than a normal cosine curve, which is prevalent in human actigraphy data, by plugging the cosinor function as an independent variable into a sigmoid link function such as the logistic function. Transformed cosinor methods introduce additional coefficients through the link function but mesor, amplitude, and acrophase are still the key parameters describing the shape. Besides the model parameters, another important metric to pay attention to is the goodness-of-fit, often the F-statistic, which indicates the degree to which the cosinor model explains the variance in the signal over the cycles.
For sensor signals that are largely sinusoidal in shape, cosinor method has been the gold standard approach to characterize circadian rhythm. However, for many other signals that fail to satisfy such an assumption, a set of metrics extracted by \textbf{non-parametric methods} have become popular \cite{blume2016nparact}. The non-parametric methods also take as input equidistantly sampled (at least hourly) sensor signals but aim to directly quantify notions such as fragmentation within cycle, contrast between rest and activity within cycle, and stability between cycles. Table \ref{tab:nonpar} lists five typical non-parametric descriptors of circadian rhythm which can be computed for sensor signals of any shape. Of the five metrics, Intradaily Variability (IV) quantifies fragmentation within a daily cycle. Its value increases when there exists a higher amount of switching between low and high activity each day (``varies more"). Interdaily Stability (IS), on the other hand, characterizes the extent to which the signal pattern remains similar across different days and takes a greater value when such similarity is high. The other three metrics, M10, L5, and Relative Amplitude (RA) are based on the periods of time during a day when the signal sees the lowest and highest intensity. M10 is the mean signal value over the 10 consecutive hours during which such value is the highest, whereas L5 indicates the mean signal value over the 5 consecutive hours during which such value is the lowest. Relative Amplitude quantifies the contrast between M10 and L5: when L5 is very small relative to M10, the RA approaches 1 but becomes zero when the signal's temporal distribution is uniform.
\begin{table}[]
\renewcommand{\arraystretch}{1.5}
\begin{tabular}{@{ }lllll@{ }}
\toprule
Descriptor & Formula & & \\ \midrule
Intradaily Variability (IV) & $\frac{\Sigma_{i=2}^{n}(X_i-X_{i-1})^2/(n-1)}{\Sigma_{i=1}^{n}(X_i-\bar{X})^2/n}$ & & \\
Interdaily Stability (IS) & $\frac{\Sigma_{h=1}^{24}(\bar{X}_h-\bar{X})^2/24}{\Sigma_{i=1}^n(X_i-\bar{X})^2/n}$ & & \\
Maximum 10-hour Activity (M10) & $\max_{h\in\{1,\ldots,24\}}[\Sigma_{h}^{min(h+9,24)}\bar{X}_h + \mathbf{1}(h>15)\Sigma_{1}^{h-15}\bar{X}_h ]/10$ & & \\
Minimum 5-hour Activity (L5) & $\min_{h\in\{1,\ldots,24\}}[\Sigma_{h}^{min(h+4,24)}\bar{X}_h +\mathbf{1}(h>20)\Sigma_{1}^{h-20}\bar{X}_h ]/5$ & & \\
Relative Amplitude (RA) & $\frac{M10-L5}{M10+L5}$ & & \\\bottomrule
\end{tabular}
\caption{Five non-parametric descriptors of circadian rhythm. In the formulas, $n$ represents the total number of sampled points. $X_i$ is the $i$-th sampled value of the signal. $\bar{X}$ is the mean value of all sampled points. $\bar{X}_h$ is the mean value of sampled points within hour $h \in \{1,\ldots,24\}$ across all days observed.} \label{tab:nonpar}
\end{table}
\textbf{Fourier analysis}, or spectral analysis, is another method to quantify circadian rhythm, specifically the strength of it. Using Fourier analysis, researchers first obtain the frequency spectrum of a signal, resulting in a periodogram. Then, the density of frequency that falls between a specific range can be used as an indicator of rhythmic strength, calculated as the area under the periodogram curve within the range. For circadian rhythm, this range should be a small neighborhood of 24 hours. Saeb et al. \cite{saeb2015mobile} first used this method on GPS location data collected from participants' smartphones. The authors created a Lomb-Scargle periodogram \cite{lomb1976least, scargle1982studies} for each participant's GPS coordinates, calculated the amount of energy that fell into the frequency bins within a 24±0.5-hour period, and used this measure as a circadian movement feature for further predictive modeling of depression symptoms.
Other standalone studies exist that seek to quantify the notion of circadian pattern in unique ways. Abdullah et al. \cite{abdullah2016automatic} used smartphone features such as distance traveled to predict CR scores obtained from the Social Rhythm Metric survey. Canzian et al. \cite{canzian2015trajectories} proposed a ``routine index" which quantifies the similarity between the geographic distribution of an individual's smartphone-tracked location traces within a period of time during a day and that of the location traces within the same period of time during other days. Huckins et al. \cite{huckins2019fusing} also focused on the similarity concept and computed ``circadian similarity" scores which are intra-class correlations between day-to-day variations in smartphone sensing features extracted over the same daily epochs (e.g., morning, afternoon). As opposed to using a trigonometric function to approximate for rest and activity, Huang et al. \cite{huang2018hidden} used a Hidden Markov Model to infer latent activity states from participants' accelerometer signal and computed cosinor-like circadian metrics based on the curve generated by latent state probabilities.
\section{Research Questions}\label{sec:rq}
We find that different circadian rhythm metrics produced by different methods may be characteristics of similar aspects of circadian rhythm. The first aspect is the \textbf{temporal distribution} of a signal within cycle, describing the signal's behavior with respect to time within each day. Both the traditional CR surveys and the method of automating CR survey constructs using sensor data aim to describe the temporal distribution of a signal. The acrophase parameter ($\phi$) from cosinor regression and the non-parametric, Intradaily Variability measure also fall in this category. The second aspect of CR is the \textbf{activity span} of a signal within cycle, describing the signal's behavior with respect to magnitude. This aspect concerns all the amplitude related metrics including the mesor and amplitude parameters from the cosinor method as well as M10, L5, and Relative Amplitude from the non-parametric approach. Lastly, we find both the periodogram density (near 24 hours) from Fourier analysis and the non-parametric Interdaily Stability are characteristics of \textbf{circadian disruption} and both decrease when a signal deviates from a 24-hour cycle, which can manifest as significantly altered patterns on different days.
\begin{itemize}
\item \textbf{RQ1}: How does the intradaily temporal distribution of magnitude differ between smartphone accelerometer and GPS signals?
\item \textbf{RQ2}: How does the level of circadian disruption differ between smartphone accelerometer and GPS signals?
\item \textbf{RQ3}: How do different CR metrics correlate with one another in both smartphone accelerometer and GPS signals?
\end{itemize}
We list our research questions above. Through answering RQ1 and RQ2, we examine the intradaily temporal distribution and the circadian disruption aspects of CR based on data from smartphone GPS and accelerometer, two heavily utilized sensors in ubiquitous computing research. We are interested in how CR manifests in the distinct yet related daily behavior captured by the two sensors: smartphone accelerometer data can reflect the user's interaction with their phone and physical activity (while the phone is carried on person), whereas GPS data reflects the user's location and mobility patterns. Magnitude can be straightforwardly calculated from accelerometer signals and is therefore used as their signal strength. GPS coordinates on the other hand do not straightforwardly lend to a signal magnitude measure, so we use \textit{displacement}, computed by differencing the GPS trace, as the signal strength of GPS. We will not compare GPS and accelerometer based on their activity span aspect of CR because of their inherently different definitions and scales of amplitude. Finally, through RQ3 we investigate the inter-relations between different CR metrics extracted from both smartphone accelerometer and GPS data.
\section{Data}
The data we use for this study come from the UT1000 Project \cite{10.1093/gigascience/giab044} we conducted at the University of Texas at Austin in two deployments, one in the Fall 2018 semester and the other during Spring 2019 semester. In this project we collected smartphone tracking data from 1584 student participants (in total) for three weeks, which included GPS, accelerometer, and phone usage data from the participants' primary smartphones in addition to real-time survey data including participants' responses to daily activity, mood, and sleep questions. Specifically, the GPS data contain timestamped coordinates (longitude and latitude). The GPS sensor was configured to scan for one minute every 10-minute break. The accelerometer data are sampled at a frequency of 10 Hz and contain a reading along the X, Y, and Z axes relative to the smartphone's position at each sampling. Both GPS and accelerometer data are subject to hardware constraints such as phone power-off or user deactivation.
\section{Methods}\label{sec:method}
To create the required input for CR analysis, we performed data preprocessing as follows. For accelerometer data, we first calculate a magnitude value $\sqrt{X^2+Y^2+Z^2}$ for each accelerometer reading. Then we divide each hour into six 10-minute bins and calculate the mean absolute deviation from unit gravity (rest state accelerometer magnitude) for each bin to serve as the activity value. For a day with complete accelerometer data we get to create an accelerometer activity vector of $6*24=144$ magnitude deviation values. For GPS, we use the same 10-minute bins and calculate the mean coordinate within each bin. Then we compute the haversine distance in meters between the previous bin's mean coordinate and the current bin's mean coordinate and use the distance as the activity value of the current bin. Similarly, for a day with complete GPS data we get to create a GPS activity vector of $6*24=144$ displacement values.
These 144-length vectors will be the input for further CR analysis. The CR methods outlined in Section \ref{sec:related} are highly sensitive to missing data and we do not want to fill in missing data by interpolation. As such, we retain participants who have at least five days of fully complete data (not necessarily consecutive), i.e., complete 144-length vectors of both accelerometer and GPS activity values. This is an extremely strict criterion because missing as little as 10 minutes worth of data on a day would disqualify the day as ``complete". Even so, our participant cohort is large enough that we can afford to restrict our dataset to the highest completeness of days and still provide a large enough sample size to conduct CR analysis. Our preprocessed dataset contains 162 participants from the 2018 deployment and 63 participants from 2019.
For each of the days with complete accelerometer and GPS data from each of the participants retained, we perform the following operations for both accelerometer and GPS data. First, we compute the cumulative activity at the increment of 10 minutes and find the timestamps at which 25\%, 50\%, and 75\% of cumulative activity has been reached (``quartile activity timestamps"). Activity is defined as mean absolute deviation from gravity for accelerometer and displacement for GPS. Second, we fitted a transformed cosinor model with a logistic link function \cite{marler2006sigmoidally} to the signals to learn parameters such as mesor, amplitude, acrophase, and the F-statistic. Third, we implement the formulas of Interdaily Stability and Intradaily Variability (Table \ref{tab:nonpar}). Finally, we follow the circadian movement calculation by Saeb et al. \cite{saeb2015mobile} and computed the frequency energy that falls between 23.5 and 24.5 hours on the Lomb-Scargle periodogram.
These computational efforts resulted in a list of metrics that we use to answer the research questions formulated in Section \ref{sec:rq}. To answer RQ1, we look into the differences between accelerometer and GPS in their quartile activity timestamps, acrophase and F-statistics from transformed cosinor modeling and Intradaily Variability. To answer RQ2, we look into the differences between accelerometer and GPS in their frequency energy and Interdaily Stability. For both RQ1 and RQ2, we use Welch's T test to compare values due to the likely different variance.
To answer RQ3, we put together 11 CR metrics (three quartile activity times, amplitude/mesor/acrophase, IV/IS/RA, and periodogram power near a 24 hour cycle) and apply a mixed graphical model \cite{haslbeck2020mgm} to learn their inter-relations. Specifically, we fit a LASSO regression model for each of 11 CR metrics with the remaining 10 metrics as predictors, using a regularization parameter $\lambda$ optimized by 10-fold cross validation. Through this double-round-robin operation, the relation between each pair of outcomes receives a coefficient in two models. We take the average of the two coefficients and use that value as the inter-relation value between the corresponding pair of metrics. The reason we undergo this process rather than simply calculating a correlation matrix is that we want to use the regularization functionality of LASSO models to reduce the visibility of inconsequential correlations between the CR metrics and accentuate the prominent ones; due to the inherently related nature of the CR metrics, simply calculating the pairwise correlations will return many significant results.
We repeat all procedures outlined above twice, once for the Fall 2018 group and once for the Spring 2019 group.
\begin{table}[]
\begin{tabular}{@{ }llll@{ }}
\toprule
Fall 2018 & Accelerometer (deviation) & GPS (displacement) & p-value \\ \midrule
25\%-time & 10.37 & 11.56 & \textbf{$<$0.001***} \\
50\%-time & 14.56 & 14.87 & \textbf{0.018*} \\
75\%-time & 18.51 & 17.89 & \textbf{$<$0.001***} \\
Acrophase & 16.22 & 16.34 & 0.532 \\
F-statistic & 24.86 & 49.95 & \textbf{$<$0.001***} \\
IV & 1.39 & 1.14 & \textbf{$<$0.001***} \\
\bottomrule
\end{tabular}
\caption{Comparing CR metrics that describe the intradaily temporal distribution of smartphone accelerometer and GPS activity, Fall 2018 participants.} \label{tab:result_temp_2018}
\bigskip
\begin{tabular}{@{ }llll@{ }}
\toprule
Spring 2019 & Accelerometer (deviation) & GPS (displacement) & p-value \\ \midrule
25\%-time & 10.45 & 11.2 & \textbf{0.011*} \\
50\%-time & 14.89 & 14.63 & 0.235 \\
75\%-time & 18.65 & 17.77 & \textbf{$<$0.001***} \\
Acrophase & 16.7 & 16.25 & 0.187 \\
F-statistic & 44.84 & 102.86 & \textbf{$<$0.001***} \\
IV & 1.36 & 0.92 & \textbf{$<$0.001***} \\
\bottomrule
\end{tabular}
\caption{Comparing CR metrics that describe the intradaily temporal distribution of smartphone accelerometer and GPS activity, Spring 2019 participants.} \label{tab:result_temp_2019}
\end{table}
\section{Results}
\subsection{RQ1}
Tables \ref{tab:result_temp_2018} and \ref{tab:result_temp_2019} show the results of comparing CR metrics that describe the intradaily temporal distribution of smartphone accelerometer and GPS activity, from the Fall 2018 and the Spring 2019 participants respectively. In both participant groups, the 25\% activity time is significantly earlier in accelerometer than GPS: the cumulative accelerometer activity reaches the first quartile between 10-11am while the cumulative GPS activity reaches the first quartile between 11am and noon. The 50\% or median activity time in accelerometer and GPS are quite similar in both groups, both falling between 2-3pm. Even though in the Fall 2018 group, the median activity time in GPS is significantly later than accelerometer (14.87 $>$ 14.56, p=0.018), such significance is not reproduced in the 2019 group. The 75\% activity time registers a significant difference between accelerometer and GPS again, with the latter significantly earlier. In both groups, cumulative accelerometer activity reaches 75\% of the day between 6-7pm while GPS activity does so between 5-6pm.
Moving on to the cosinor metrics, we see that the F-statistic is significantly greater for GPS than accelerometer in both groups, indicating that daily GPS activity follows a sinusoidal shape more closely than accelerometer. However, the acrophase, or predicted time of peak activity, shows little and insignificant difference between accelerometer and GPS in both groups. This indicates that the time when mobility behavior peaks and the time when physical activity peaks during a day converge. Note the clear difference between the acrophase time and the 50\% activity time in both groups and both sensors: acrophase falls between 4-5pm while 50\% activity time falls between 2-3pm. This temporal shift between median cumulative activity and peak activity during a day is tantamount to the difference between median and mode in the statistical context. The later acrophase than the 50\% activity time suggests a left skewed daily activity profile in both accelerometer and GPS.
Last but not least, Intradaily Variability is significantly greater in accelerometer than GPS in both groups, indicating that there exists more severe fragmentation, or switching between rest and activity, in accelerometer than GPS. This finding is not surprising because an individual tends to interact with their smartphone in ``fragments" -- picking it up, using it for a while, then leaving it unattended until the next use -- thus contributing to bouts of activity between periods of rest. However, in one's mobility pattern, such fragmentation is subject to the actual number of places the person visits and stays at during the day, which requires more effort and thus less likely to happen frequently.
\begin{table}[]
\begin{tabular}{@{ }llll@{ }}
\toprule
Fall 2018 & Accelerometer (deviation) & GPS (displacement) & p-value \\ \midrule
24±0.5h energy & 26.42 & 18.04 & \textbf{$<$0.001***} \\
IS & 0.26 & 0.09 & \textbf{$<$0.001***} \\
\bottomrule
\end{tabular}
\caption{Comparing CR metrics that describe the level of circadian disruption in smartphone accelerometer and GPS activity, Fall 2018 participants.} \label{tab:result_disr_2018}
\bigskip
\begin{tabular}{@{ }llll@{ }}
\toprule
Spring 2019 & Accelerometer (deviation) & GPS (displacement) & p-value \\ \midrule
24±0.5h energy & 32.60 & 22.31 & \textbf{$<$0.001***} \\
IS & 0.22 & 0.04 & \textbf{$<$0.001***} \\
\bottomrule
\end{tabular}
\caption{Comparing CR metrics that describe the level of circadian disruption in smartphone accelerometer and GPS activity, Spring 2019 participants.} \label{tab:result_disr_2019}
\end{table}
\subsection{RQ2}
Tables \ref{tab:result_disr_2018} and \ref{tab:result_disr_2019} show the results of comparing the level of circadian disruption in smartphone accelerometer and GPS activity, from the Fall 2018 and the Spring 2019 participants respectively. Both the energy within 24±0.5 hours on the Lomb-Scargle periodogram and Interdaily Stability are significantly higher in accelerometer than GPS for both participant groups. This result provides a straightforward answer to RQ2: there is a significantly stronger circadian rhythm, or a lower level of circadian disruption in daily accelerometer activity than GPS. The difference between Interdaily Stability between accelerometer and GPS is direct evidence that our participants followed a more homogeneous schedule of phone use and/or physical activity on different days as opposed to mobility patterns, which could vary greatly on different days depending the daily agenda.
\begin{figure}
\centering
\begin{subfigure}[b]{0.48\textwidth}
\centering
\includegraphics[width=\textwidth]{CR_RQ3_ACC_2018.png}
\caption{Accelerometer, Fall 2018}
\label{fig:acc_2018}
\end{subfigure}
\begin{subfigure}[b]{0.48\textwidth}
\centering
\includegraphics[width=\textwidth]{CR_RQ3_ACC_2019.png}
\caption{Accelerometer, Spring 2019}
\label{fig:acc_2019}
\end{subfigure}
\hfill
\begin{subfigure}[b]{0.48\textwidth}
\centering
\includegraphics[width=\textwidth]{CR_RQ3_GPS_2018.png}
\caption{GPS, Fall 2018}
\label{fig:gps_2018}
\end{subfigure}
\begin{subfigure}[b]{0.48\textwidth}
\centering
\includegraphics[width=\textwidth]{CR_RQ3_GPS_2019.png}
\caption{GPS, Spring 2019}
\label{fig:gps_2019}
\end{subfigure}
\caption{Inter-relations of CR metrics from smartphone accelerometer and GPS activity (see Section \ref{sec:method} for details). Each node represents a CR metric and edges represent relations between metrics. Color and weight of the edges indicate the direction (green: positive; red: negative) and magnitude of the pairwise relation. The blue part in the ring surrounding each node indicates the proportion of variance explained by other metrics. T25/T50/T75: time of 25\%/50\%/75\% cumulative activity; AMP/PHI/MES/FS: amplitude, acrophase, mesor, and F-statistics from the transformed cosinor modeling; IV/IS/RA: Intradaily Variability, Interdaily Stability, and Relative Amplitude from the non-parametric methods; E24: energy of frequency that falls within 24±0.5 hours on the Lomb-Scargle periodogram.}
\label{fig:RQ3}
\end{figure}
\subsection{RQ3}
Figure \ref{fig:RQ3} shows the inter-relations between 11 CR metrics extracted by four types of methods from smartphone accelerometer and GPS data collected from both the 2018 and the 2019 participant groups. Each node represents a CR metric and the edges in-between represent their inter-relations. The edges' color indicates the sign of the pairwise relation (green positive, red negative) and thickness is proportional to the magnitude. Overall, the inter-relations between CR metrics in both accelerometer and GPS are well-replicated between the two participant groups, with the 2019 group seeing slightly fewer inter-relations between the CR metrics in general.
Among the three quartile activity times, 50\% activity time is to a large extent explained by 25\% and 75\% activity times in both accelerometer and GPS, meaning that a person who arrives at median cumulative activity later (or earlier) in the day tends to complete 25\% and 75\% of sensor activity later (or earlier) as well. A surprising negative link exists between 25\% time and 75\% time unique to GPS, suggesting that in terms of mobility activity the participants who started their days early tend to be the ones who finished their days late.
Among the cosinor modeling measures, the only relation that stands out is a strongly positive one between mesor (MES) and amplitude (AMP). This is an expected pattern since both mesor and amplitude describe the signal's activity span and are supposed to be codependent. Interestingly, neither acrophase (PHI) nor the F-statistic (FS) is related to mesor or amplitude. This means that the time when accelerometer and GPS activity reach a peak and how closely the cosinor model fits activity data are both independent of how large the peak is.
The inter-relations between the three non-parametric CR metrics (IV, IS, RA) seem very weak in both accelerometer and GPS, except for a strong, positive association between IV and IS evident only in GPS. Also unique to GPS is a strong negative relation between IV and E24, the energy of frequency that falls between 23.5 and 24.5 hours on the Lomb-Scargle periodogram, of which we see none in accelerometer. This indicates that participants who have higher Intradaily Variability in mobility tend to have more disrupted CR in mobility across days.
Lastly, there exists a consistent positive relation between E24 and the F-statistics from cosinor modeling in both accelerometer and GPS, with that in accelerometer even stronger. This relation is evidence that better fit with the cosinor model translates to stronger rhythmicity with a 24-hour cycle.
\section{Discussion}
The relationship between the daily behavioral aspects captured by smartphone accelerometer and GPS is worth noting. Straightforwardly, the GPS sensor detects changes in geographic location, therefore captures the user's place visits and mobility patterns. However, we recognize at least three types of behavior that can lead to increased accelerometer signal activity (or greater deviation from gravity baseline): (1) interacting with the phone such as making phone calls and using mobile apps; (2) performing physical activities with phone carried on person while staying at the same place, such as cooking at home or walking around in an office, and; (3) traveling between places with phone carried on person, which is also reflected in GPS signals. In this sense, accelerometer captures a wider range of daily behavior than GPS.
\section{Conclusion}
In this study, we used smartphone tracking data from 225 college student participants with at least five full days of complete data to investigate inter-relations between circadian patterns extracted from accelerometer and GPS sensors. We used four analytical approaches, namely survey construct automation, transformed cosinor modeling, non-parametric methods, and Fourier analysis, to characterize circadian rhythm using both data types. We conceptually categorized CR metrics into three categories, namely temporal distribution, activity span, and circadian disruption. We asked three research questions: RQ1 and RQ2 compared CR metrics of the temporal distribution category and the circadian disruption category between smartphone accelerometer and GPS activity, whereas RQ3 examined the inter-relations between different CR metrics within the same sensor.
We found that, compared to GPS signals, the intradaily distribution of smartphone accelerometer activity follows a pattern that starts earlier in the day; winds down later; reaches half cumulative activity about the same time, which is about two hours earlier than when it reaches maximum activity; conforms less to a sinusoidal wave; and exhibits more intradaily fragmentation. Moreover, GPS activity exhibited a stronger circadian rhythm and interdaily stability than accelerometer, revealing differences in the daily behavioral aspects that manifest in the two sensor signals. Finally, the inter-relations between different CR metrics have their respective peculiarities in accelerometer and GPS activity. A notable one is the negative relation between intradaily variability and circadian rhythm strength, which is present in GPS but not in accelerometer.
Our explorations reported in this paper demonstrated the reactivity of passive circadian monitoring and computation to mobile sensor choices (thus daily behavioral aspects) and offered empirical evidence for the inter-relations between a comprehensive set of different circadian rhythm measures.
\section*{Funding}
This work was supported by Whole Communities—Whole Health, a research grand challenge at the University of Texas at Austin.
\bibliographystyle{plain}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 655 |
\section{Introduction}\label{intro}
With an increasing submission of academic papers in recent years, the task of making final decisions manually incurs significant overheads to the program chairs, it is desirable to automate the process.
In this study, we aim at utilizing document-level semantic analysis for paper review rating prediction and recommendation.
Given the reviews of each paper from several reviewers as input, our goal is to infer the final acceptance decision for that paper and the reviewers' evaluation with respect to a numeric rating (e.g., 1-10 points).
Paper review rating prediction and recommendation is a practical and important task in AI applications which will help improve the efficiency of the paper review process. It is also intended to enhance the consistency of the assessment procedures and outcomes, and to diversify the paper review process by comparing human recommended rating with machine recommended rating.
In the literature, most of existing studies cast review rating prediction as a multi-class classification/regression task ~\cite{pang2005seeing}.
They build a predictor by using supervised machine learning models with review texts and corresponding ratings.
Due to the importance of features, most researches focus on extracting effective features such as context-level features \cite{qu2010bag} and user features \cite{gao2013modeling} to boost prediction performance.
However, feature engineering is time-consuming and labor-intensive.
Recently, with the development of neural networks and its wide applications, various deep learning-based models have been proposed for automatically learning features from text data \cite{bengio2013representation}.
Existing deep learning models usually learn continuous representations of different grains (e.g., word, phrase, sentence, document) from text corpus \cite{pennington2014glove,lai2015recurrent,kim2014convolutional,conneau2016very,wang2018disconnected,qiao2018new}.
Although deep learning models can automatically learn extensive feature representation, they cannot efficiently capture the hierarchical relationship inherent to the review data.
To address this problem, \newcite{yang2016hierarchical} studied a hierarchical architecture and implemented it in deep learning framework to learn a better document-level representation.
Also, with the success of attention mechanism in many tasks such as machine translation, question answering and so on \cite{vaswani2017attention},
\newcite{shen2018disan} designed a directional self-attention network to gain context-aware embeddings for words and sentences.
Despite great progress made by these models, they do not focus on the task of paper review rating recommendation and are not effective enough to be directly used for this task because of the following reasons:
First, the review data is hierarchical in nature.
There exists a three-level hierarchical structure in the review data: word level, intra-review level and inter-review level, while previous models only capture two-levels (i.e., the word level and intra-review level) of this hierarchy.
Second, paper reviews are usually much longer than other reviews (e.g., product reviews, movie reviews, restaurant reviews, etc.), while most of these models are working on those shorter reviews stated above and they do not leverage the up to date representation techniques such as BERT \cite{devlin2018bert} and SciBERT \cite{beltagy2019scibert}.
In this paper, we propose a novel neural network framework for paper review rating recommendation by taking word, intra-review and inter-review information into account.
Specifically, inspired by HAN \cite{yang2016hierarchical} and DiSAN \cite{shen2018disan}, we introduce a Hierarchical Bi-directional self-Attention Network ({HabNet}) framework to effectively incorporate different levels of hierarchical information.
The proposed framework consists of three main modules in end-to-end relationship: sentence encoder, intra-review encoder and inter-review encoder, which can consider hierarchical structures of review data as comprehensive as possible.
The outputs of inter-review encoder are leveraged as features to build the rating predictor without any feature engineering.
We release the code and data collected by us to enable replication and application to new tasks, available at \emph{https://github.com/RingBDStack/HabNet}.
The contributions of this work are as follows:
\begin{itemize}
\item We present a novel framework to guide the investigation and assessment of the effects of hierarchies on review data.
To our best knowledge, this is the first work that incorporates different levels of semantic information into a hierarchical neural network to perform paper review rating recommendation.
\item We introduce two new metrics to better evaluate models when the distributions of classes are highly imbalanced (such as the paper review data we are working with).
\item Empirical results on OpenReview (ours) and extended PeerRead datasets demonstrates the effectiveness of the proposed method in automatically making final acceptance decisions and helping reveal the rating inconsistency between the semantic review content and the numerical review ratings.
\end{itemize}
\section{Related Work}
\subsection{Review Rating Prediction}
Review rating prediction is a basic task in sentiment analysis.
It was initially studied by \newcite{pang2005seeing} who cast this problem as a multi-class classification/regression task.
In the literature, most of studies following this approach used supervised machine learning models to do review rating prediction.
Since the features used by these models are critical for prediction performance, more refined textual features are exploited.
\newcite{qu2010bag} introduced bag of opinions representation, where an opinion was composed of a root word, a set of modifier words and one or more negation words.
\newcite{gao2013modeling} used user-specific and product-specific features to increase the reliability of sentiment classification.
With the popularity of deep learning model, instead of hand-crafted features, many works were proposed to automatically learn features from text corpora.
\newcite{lai2015recurrent} applied a recurrent structure for convolutional neural network to capture contextual information for learning word representation.
\newcite{conneau2016very} used very deep convolutional networks to learn hierarchical representations of whole sentences.
\newcite{johnson2017deep} studied deepening word-level CNNs to capture global representations of text.
\newcite{peng2018large} designed a deep Graph-CNN to learn both non-consecutive and long-distance features of text.
\newcite{kangetal2018dataset} collected a dataset of peer reviews from several conferences and predicted paper acceptance decision by using paper draft.
\newcite{gaoetal2019rebuttal} focused on predicting after-rebuttal scores by using their presented corpus.
\newcite{huaetal2019argumentmining} applied argument mining on their AMPERE dataset to assess the efficiency of reviewing process.
\newcite{li2019neural} designed a neural model to predict citation count of accepted papers.
\newcite{yang2018automatic} designed a hierarchical attention-based CNN for automatic academic paper rating by using source paper, it adopts original attention mechanism which cannot capture the interactions between elements in the same level.
\newcite{leng2019deepreviewer} proposed DeepReviewer for automatic paper review utilizing paper's grammar and innovation to help learn better representation and predict paper's final review score.
Different from above works, we aim at predicting the final acceptance decisions for papers and ratings for reviews with self-attention based framework using raw review texts. And our collected dataset contains the rating score of each review and the final decision of each paper.
\subsection{Attention Mechanism}
Attention mechanism was proposed by researchers to improve the performance of different NLP tasks.
There are two common attention mechanisms: additive attention \cite{bahdanau2014neural} and multiplicative attention \cite{rush2015neural,vaswani2017attention,peng2019hierarchical}, they use different compatibility functions to compute the attention weights.
\newcite{lin2017structured} introduced self-attention to extract an interpretable sentence embedding.
\newcite{yang2016hierarchical} proposed a hierarchical attention network for document classification, which applied attention mechanism at word and sentence level.
\newcite {vaswani2017attention} built a simple network architecture based only on attention mechanism without convolutions and recurrence.
\newcite{yin2018attentive} proposed an attentive convolution network which enables deriving higher-level features for a word from information extracted from nonlocal context.
\newcite{shen2018disan} designed a new attention mechanism which is directional and multi-dimensional, and a neural network solely based on this attention mechanism was proposed to learn sentence embedding.
\newcite{shen2018bi} proposed a memory-efficient bi-directional self-attention network which splits sequence into blocks to save memory.
Our framework is also based on self-attention mechanism, which makes use of the hierarchical characteristic of HAN \cite{yang2016hierarchical} and the ability of capturing relationships between words from two directions in DiSAN \cite{shen2018disan}.
\section{Methodology}
In this section, we first describe the problem setting, and then present the details of our proposed framework for paper review rating prediction and recommendation.
\subsection{Problem Setting}
We consider the problem of paper review rating prediction and recommendation from a dataset containing $K$ papers, where each paper has $M$ reviews associated with the corresponding ratings and a decision class. Concretely, given the set $R = \{(r_1,c_1),...,(r_M,c_M), y\}$ for a scientific paper, where $r_i$ is the $i$-th reviewer's text review and $c_i$ is its associated numeric rating and $y$ is the final decision (i.e., accept or reject). Assume that each text review $r_i$ has $N$ sentences $S = \{\mathbf{s}_{i,1}, \mathbf{s}_{i,2}, \cdots, \mathbf{s}_{i,N}\}$ and each sentence contains $L$ words,
let $\mathbf{w}_{i, j, t}$ with $i \in [1, M], j \in [1, N], t \in [1, L]$ denotes the $t$-th word in the $j$-th sentence of the $i$-th review document. Given a new paper with a set of reviews $R = \{r_1,...,r_M\}$, our goal is to predict the decision class $y$ which enables the program chairs to automatically make the final decision/recommendation, and also generate a rating $c$ for each review $r$ that is consistent with text sentiment as an aid to reviewers for discovering the rating inconsistency between ratings and review sentiments in the review process.
Similar to \cite{zhang2010comparison,hassan2020multi}, here we treat paper review rating prediction problem as a multi-class classification problem, where the class labels are the rating scores $c$. We treat the final decision prediction as a binary classification problem, where the class labels are the decisions $y$.
\subsection{Our Approach}
The proposed framework takes raw review texts as input and mainly consists of four components: sentence encoder, intra-review encoder, inter-review encoder and rating predictor, as shown in Figure \ref{fig:framework_architecture}.
Before describing the details of each component, we introduce the multi-dimensional source2token self-attention module by following \cite{shen2018disan} and taking this module in the sentence encoder as an example. The attention weight of each word $\mathbf {we}_{i,j,t}, t \in [1, L]$ is obtained by applying softmax on the scores $f(\mathbf{we}_{i,j,t}), t \in [1, L]$ calculated by Eq. (\ref{eq:source2token}), $W^T, W^{(1)}, b^{(1)}, b$ are trainable parameters. The output of this module is the weighted sum of the inputs (e.g., $\mathbf {we}_{i,j,t}, t \in [1, L]$ in sentence encoder).
\begin{equation}\label{eq:source2token}
f(\mathbf{we}_{i,j,t}) = W^T\sigma(W^{(1)}\mathbf{we}_{i,j,t}+b^{(1)})+b.
\end{equation}
\noindent{\bf $\bullet$ \emph{Sentence Encoder.}}
Sentence encoder is designed to capture the relationships between words in a sentence and the importance of each word to the meaning of that sentence. It is shown in the first part of Figure \ref{fig:framework_architecture}.
It first generates context-aware embedding for each word in a sentence by using bi-directional self-attention module (Bi-SAN) \cite{shen2018disan}.
Based on these context-aware embeddings of words, the encoding for that sentence, which contains all words' information and relations between words, is then obtained from the multi-dimensional source2token self-attention module \cite{shen2018disan} which aims at generating the sentence encoding by combining the context-aware word embeddings.
Specifically, the input of sentence encoder are pre-trained word embeddings obtained from raw review texts by using GloVe pre-trained word embedding \cite{pennington2014glove}, or using BERT \cite{devlin2018bert} or SciBERT \cite{beltagy2019scibert}.
Each word (e.g., $\mathbf{w}_{i,j,1}$, $\mathbf{w}_{i,j,2}$) is represented by a $d_e$-dimensional vector.
These vectors are fed into Bi-SAN, which includes a forward self-attention network and a backward self-attention network. Each of these two networks outputs a refined embedding for each word and then the two refined embedding of each word are concatenated by Bi-SAN as the final context-aware embedding for each word (e.g., $\mathbf{we}_{i,j,1} \in \mathbb{R}^{2d_e}$).
The context-aware embedding for each word has $2d_e$ dimension because of the two networks (i.e., forward and backward) in Bi-SAN.
After obtaining the context-aware embedding of each word, sentence encoder can generate encoding $\mathbf{s}_{i,j} \in \mathbb{R}^{2d_e}$ for each sentence through the multi-dimensional source2token self-attention module.
\begin{figure}
\centering
\includegraphics[scale=0.76]{framework_architecture.pdf}
\caption{The architecture of HabNet framework.}
\label{fig:framework_architecture}
\end{figure}
\noindent{\bf $\bullet$ \emph{Intra-Review Encoder.}}
Sentences in one review may have temporal orders, causality and other logic relationships, and some sentences contain more information for the review.
Therefore, intra-review encoder is designed to capture these relations existing in each individual review itself.
The input is the sentence embedding $\mathbf{s}_{i,j}$ generated by the first-level sentence encoder.
The structure of intra-review encoder is similar to sentence encoder where it first feeds sentence embedding to the Bi-SAN module, which captures the relations between sentences and the importance of one sentence to another from two directions by generating forward embedding $\mathbf{s}_{i,j}^{fw}$ and backward embedding $\mathbf{s}_{i,j}^{bw}$ for sentence $\mathbf{s}_{i,j}$.
The final embedding $\mathbf{se}_{i,j} \in \mathbb{R}^{4d_e}$ for each sentence $\mathbf{s}_{i,j}$ in $i$-th review is generated by concatenating $\mathbf{s}_{i,j}^{fw}$ and $\mathbf{s}_{i,j}^{bw}$.
We have $\mathbf{se}_{i,j} =[\mathbf{s}_{i,j}^{fw}||\mathbf{s}_{i,j}^{bw}]$, where $||$ denotes concatenation operation.
Next, the multi-dimensional source2token self-attention module takes $\mathbf{se}_{i,j}$ as input and generates encoding $\mathbf{r}_i \in \mathbb{R}^{4d_e}$ for $i$-th review by combining all $\mathbf{se}_{i,j}$ in this review according to their importance weights, i.e., attention weights. As shown in the second part of Figure \ref{fig:framework_architecture}, intra-review encoder can generate encoding $\mathbf{r}_i$ for each review of the same paper.
The dimension of $\mathbf{r}_i$ is $4d_e$, which is double of sentence encoding because of Bi-SAN.
\noindent{\bf $\bullet$ \emph{Inter-Review Encoder.}}
The integration of different reviews is essential for performing comprehensive analysis and supporting final decision-making on a paper. We use the inter-review encoder as the third level of our framework to integrate information from different reviews of each paper, as shown in the third part of Figure \ref{fig:framework_architecture}. It first feeds the second-level encoding $\mathbf{r}_i$ of $i$-th review of a paper to a bi-directional GRU \cite{bahdanau2014neural} layer, and then uses a Bi-SAN to model the relations between reviews from two directions by generating refined encoding $\mathbf{re}_i$ for this review.
Thus $\mathbf{re}_i$ contains the information from other reviews. Then, a multi-dimensional source2token self-attention module is applied on these encoding $\mathbf{re}_i$ to get a final compact vector representation $\mathbf{rs}$ of the paper.
This encoder can handle papers having different number of reviews by using padding.
The whole process above is formulated as follows:
\textbf{Step1}: Feeding encoding $\mathbf{r}_i$ of each review of a paper generated by intra-review encoder to the bi-directional GRU layer, it outputs a new encoding for each review (we still use $\mathbf{r}_i$ to denote the new encoding of $i$-th review). Then these new encodings are fed to the following Bi-SAN module.
\textbf{Step2}: Bi-SAN has a forward self-attention network and a backward self-attention network.
Two attention matrices, denoted as $\mathbf{P}^{i(fw)} \in \mathbb{R}^{4d_e\times M}$ and $\mathbf{P}^{i(bw)} \in \mathbb{R}^{4d_e\times M}$, for $i$-th review are calculated in these two networks respectively.
Then the forward encoding $\mathbf{re}_i^{fw}$ and backward encoding $\mathbf{re}_i^{bw}$ for this review are generated as follows ($\odot$ denotes element-wise multiplication):
\begin{equation}\label{eq:forward&backward}
\mathbf{re}_i^{fw} = \sum_{o=1}^M \mathbf{P}^{i(fw)}_{\cdot o}\odot \mathbf{r}_o, ~~ \mathbf{re}_i^{bw} = \sum_{o=1}^M \mathbf{P}^{i(bw)}_{\cdot o}\odot \mathbf{r}_o,
\end{equation}
where $M$ is the number of reviews for one paper.
$\mathbf{P}^{i(fw)}_{\cdot o}$ and $\mathbf{P}^{i(bw)}_{\cdot o}$ denote the $o$-th column in attention matrix $\mathbf{P}^{i(fw)}$ and $\mathbf{P}^{i(bw)}$ respectively.
The refined encoding $\mathbf{re}_i$ for $i$-th review, which contains the information from other reviews of the same paper, is generated in the following equation.
\begin{equation}\label{eq:re}
\mathbf{re}_i =[\mathbf{re}_i^{fw}|| \mathbf{re}_i^{bw}], \mathbf{re}_i \in \mathbb{R}^{8d_e}.
\end{equation}
\textbf{Step3}: The multi-dimensional source2token self-attention module takes the encodings of all reviews of one paper outputed from Bi-SAN as input, and computes the importance weight for each review encoding $\mathbf{re}_i$, and then combines all these review encodings to get the final vector representation $\mathbf{rs}$ of the paper based on the importance weights in the similar way as shown in Eq. (\ref{eq:forward&backward}).
\noindent{\bf $\bullet$ \emph{Rating Prediction and Recommendation.}}
With the three levels of encoding above, a fully connected layer with softmax function is designed to make rating prediction and final recommendation. Specifically, we take the compact representation $\mathbf{rs}$ from all reviews as its input to predict the final decision, and the encoding $\mathbf{r}_i$ for $i$-th review as its input to predict the corresponding rating, respectively. It is worth noting that the predicted review ratings are consistent with text sentiment conveyed by reviewers, thus it can serve as a guidance to reviewers for finding the inconsistencies between semantic review content and numerical review ratings in the review process.
\subsection{Model Variants}
To understand the contribution of different components in the proposed framework, we derive different variants for ablation study. Below are three variants implemented in our experiments.
\textbf{{HabNet}-V1:} After obtaining the encoding $\mathbf{r}_i$ of each review for a paper which is outputed from intra-review encoder, we sum them up using equal weight and then use the result as the final encoding $\mathbf{rs}$ of that paper, i.e., $\mathbf{rs} = \frac{1}{M}\sum_{i=1}^M\mathbf{r}_i$.
Thus the inter-review encoder is removed in this variant.
\textbf{{HabNet}-V2:} We remove the sentence encoder in the proposed framework as the second variant to verify the contribution of sentence encoder to the framework.
Specifically, for a sentence, we use the average of all words' pre-trained embeddings as its encoding, and feed such sentence encodings to intra-review encoder.
Therefore, this variant cannot encode the relations between words in a sentence.
\textbf{{HabNet}-V3:} We remove the intra-review encoder as the third variant to understand how effectively this encoder captures the interactions between sentences in a review document and to demonstrate the importance of intra-review encoder to the proposed framework.
To be specific, the encoding of a review document is the mean of sentence embeddings in that review.
\section{Experiments and Results}
\subsection{Dataset}
We conduct experiments on two datasets to validate our approach for scientific paper decision recommendation and review rating prediction.
One is called OpenReview dataset which is collected by us.
The other one is a dataset extended from PeerRead which is originally published by \newcite{kangetal2018dataset}. Table \ref{table:stats_of_datasets} shows the statistics of OpenReview and Extended PeerRead.
For all the experiments on these two datasets, all samples are randomly shuffled before splitting the dataset.
\noindent{\bf $\bullet$ \emph{OpenReview.}}
This collection contains all reviews for ICLR conference and workshop's papers from 2017 to 2019.
Generally, each paper has 3-5 reviews with corresponding ratings, the rating is a numeric value from 1 to 10 (10 being the highest rating). There is also a decision (accept or reject) associated with each paper.
The number of accepted and rejected papers are 1341 and 1962.
For paper decision recommendation, we use 2293, 491 and 492 papers as training, validation and testing set respectively.
For review rating prediction, 7600, 1000, 1000 reviews are used as training, validation and testing set respectively.
As shown in Table \ref{table:stats_of_datasets}, the number of reviews with different ratings are highly imbalanced.
\noindent{\bf $\bullet$ \emph{Extended PeerRead.}}
The majority of papers with reviews in the original PeerRead dataset are accepted papers collected from NIPS 2013-2017, as shown in Table \ref{table:stats_of_datasets}, the number of accepted and rejected papers are 2054 and 0, respectively. Thus the original PeerRead dataset cannot be used directly for predicting final decisions on accepted/unaccepted papers due to the severe imbalance problem stated above. Therefore, we further collect 2211 papers from ICLR 2020 conference and corresponding reviews from the openreview website to extend the PeerRead dataset.
Finally, the extended PeerRead dataset has 4265 papers and 13721 reviews in total. However, since most review ratings are not available in the original PeerRead, we only use this extended dataset to predict the final decision.
\newcommand{\tabincell}[2]{\begin{tabular}{@{}#1@{}}#2\end{tabular}}
\begin{table}[h!]
\small
\centering
\begin{tabular}{m{1.4cm}|m{2.2cm} m{1.0cm} m{1.1cm} m{1.3cm}|m{0.2cm} m{0.2cm} m{0.2cm} m{0.5cm} m{0.5cm} m{0.5cm} m{0.5cm} m{0.2cm} m{0.2cm} m{0.2cm}}
\hline
\multirow{2}{*}{Dataset} & \multirow{2}{*}{Section} & \multirow{2}{*}{\#Papers} & \multirow{2}{*}{\#Reviews} & \multirow{2}{*}{\#Acc/Rej} & \multicolumn{10}{c}{Review Rating Distribution} \\
\cline{6-15}
& & & & & 1 & 2 &3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
\hline
OpenReview & ICLR 2017-2019 & 3,303 & 9,600 & 1,341/1,962 & 37 & 205 & 851 & 1,816 & 1,943 & 2,154 & 1,875& 563 & 158 & 16 \\ [0.5ex]
\hline
\multirow{3}{0.2cm}{Extended PeerRead} & NIPS 2013-2017 & 2,054 & 7,006 & 2,054/0 & - \\ [0.5ex]
& ICLR 2020 & 2,211 & 6,715 & 687/1,524 & - \\ [0.5ex]
\cline{2-15}
& Total & 4,265 & 13,721 & 2,741/1,524 & - \\ [0.5ex]
\hline
\end{tabular}
\caption{Statistics of OpenReview and Extended PeerRead, - means the rating distribution is unavailable.}
\label{table:stats_of_datasets}
\end{table}
\subsection{Evaluation Metrics and Baselines}
We use Accuracy, Macro-F1 and Micro-F1 to evaluate the effectiveness of our framework on the task of paper decision recommendation.
For review rating prediction, due to the imbalanced distribution of ratings (shown in Table \ref{table:stats_of_datasets}) and ineffectiveness of methods dealing with imbalanced problem (such as the oversampling technique and reducing rating range we tried), two new metrics with better discernibility are designed to better evaluate the performance of our framework and baselines apart from Accuracy.
\textbf{Distance Measure (DM).} The distance between true label and predicted label is crucial for evaluating a model when there are multiple labels as in our task of review rating prediction.
The smaller the distance, the better a model works.
Thus we design a new metric which incorporates the distance between predicted rating and true rating.
This metric can distinguish a better model from a more reasonable perspective.
For example, models which predict a rating of 8 as 7 are much better than models that predict it as 3.
Let $p_i$ and $r_i$ be the predicted rating and true rating for $i$-th sample respectively, and $n$ be the total number of samples.
We define $DM$ as follows:
\begin{equation}\label{eq:dm}
DM = \frac{1}{n}\sum_{i=1}^n(1-\frac{d_i}{d_{max}}),\quad \text{where}\quad d_i = |p_i - r_i|.
\end{equation}
It first calculates the distance $d_i$ for each sample and then takes an average over all samples according to Eq. (\ref{eq:dm}).
When the predictions for all samples are correct, the value of $DM$ achieves its best which is $1$.
When all predictions are wrong and the distances between predicted ratings and true ratings are all maximum distances $d_{max}$ (in our case $d_{max}=9$), the value of $DM$ is $0$.
When the distances become smaller, the value of $DM$ becomes larger.
Thus it can evaluate the performance of models appropriately.
The range of $DM$'s value is $[0,1]$. The larger its value is, the better the algorithm works.
\textbf{Optimized Precision (OP).} It is important to correctly predict all classes when the data is imbalanced. Inspired by \newcite{hossin2015review}, we combine accuracy and recall of all classes into a unified measure, which allows to better deal with imbalanced data environments.
Let $ACC$ be the accuracy,
$N$ be the number of classes, and $R_i$ be the recall for $i$-th class, $i=1, \cdots, N$. We define $OP$ as follows:
\begin{equation}\label{eq:op}
OP = ACC -\frac{\sum_{i,j=1}^N|R_i-R_j|}{2(N-1)\sum_{k=1}^N R_k}.
\end{equation}
As shown in Eq. (\ref{eq:op}), $OP$ first computes the absolute differences between recalls of each pair of classes and sum them up, and then normalizes it by using the sum of all recalls.
In this way, this metric measures the model's ability to predict the highest score of both accuracy and recall for all classes. The higher the value of $OP$, the better the model fits the data.
We compare our proposed method with fourteen other state-of-the-art methods and three variations of our proposed model: (1). 10 flat baselines: three are traditional text classification models, including Support Vector Machines (SVM), Logistic Regression (LR) and Naïve Bayes (NB); five are deep learning models, including RNN (i.e., Bi-GRU) \cite{cho2014learning,bahdanau2014neural}, TextCNN \cite{kim2014convolutional}, TextRCNN \cite{lai2015recurrent}, VDCNN \cite{conneau2016very} and DPCNN \cite{johnson2017deep}; two are attention-based models, including Transformer \cite{vaswani2017attention} and SA-Sent-EM \cite{lin2017structured}, which exploit various relationships existing in review text.
(2). 4 hierarchical baselines which leverage the hierarchical structure of the dataset: HAN-extended is an extension of HAN \cite{yang2016hierarchical} re-implemented by us; we also implement three Bert-based baselines \cite{devlin2018bert,beltagy2019scibert} using large pre-trained contextual embeddings. Specifically, Bert-base and Bert-large use 768 and 1024-dimensional Bert embedding respectively, while SciBert utilizes 768-dimensional SciBert embedding. For our proposed framework {HabNet}, apart from using GloVe embedding, we also conduct experiments by using the above three Bert-based contextual embeddings. (3). To demonstrate the contribution of each encoder ingredient, we also implement three variants of our proposed framework.
\subsection{Experimental Settings}
We use raw review texts as input for all models.
For the decision recommendation task, 50-dimensional pre-trained GloVe word embedding is used for the models of our framework and HAN-extended, while 100-dimensional one is adopted for other deep learning models except bert-based baselines which utilize corresponding bert-embeddings.
The number of training epochs is set to 100.
For the rating prediction task, except bert-based baselines using bert embeddings, 100-dimensional pre-trained GloVe word embedding is used for all models. The number of training epochs is set to 50 since all models converge quickly.
We use cross entropy as objective function to train all deep learning models.
The common parameters, such as learning rate and batch size, are empirically set.
For all the experiments on {HabNet} and its variants, we train each of them 10 times and use the average results to evaluate them.
\subsection{Experimental Results and Discussion}
The experimental results are shown in Table \ref{table:results_binary_cls}.
For the paper decision recommendation task, {HabNet} achieves the best performance results
no matter which kind of embedding is used.
This demonstrates the effectiveness of our framework and its generality.
To be specific,
compared with flat baselines, our framework with GloVe embedding, i.e., {HabNet} (Glove), performs much better, which demonstrates that our framework can make good use of the hierarchical structure in the dataset.
While compared with hierarchical baselines, {HabNet} (Bert-base), {HabNet} (Bert-large) and {HabNet} (SciBert) obtain good performance gain (5.4\%, 8.2\%, 5.4\% and 8.2\%, 8.0\%, 4.1\% in terms of accuracy on both datasets) over corresponding bert-based baseline respectively.
The improvement indicates that our framework can capture the relationships between words, sentences, and reviews existing in the dataset. Although the three bert-based baselines can obtain contextual word embeddings, they cannot capture intra-review level and inter-review level relationships as our framework does.
Even {HabNet} (Glove) still performs better than the three bert-based baselines using pre-trained contextual embedding and HAN-extended, which further demonstrates the ability of the encoders on capturing the three-level relationships.
In addition, the best performance of our framework on both datasets validates its generality, and {HabNet} with different embedding outperforming all the baselines consolidates this.
It is worth noting that the performance results of all models on the extended PeerRead dataset are higher than that on the OpenReview dataset. The reason may be that the review texts (especially those from NIPS 2013-2017) in the PeerRead dataset are much shorter and less complex than those in the OpenReview dataset. This demonstrates that our framework can work on long review text much better than other models.
Note that in Table \ref{table:results_binary_cls}, there are only results on OpenReview dataset for review rating prediction, as PeerRead does not contain ratings.
{HabNet} with various embedding (including GloVe and bert embeddings) achieving the best performance demonstrates the effectiveness and generalization ability of our framework again, because {HabNet} has a similar performance improvement as in the paper decision recommendation task when compared with flat and hierarchical baselines.
Furthermore, the ratings predicted by {HabNet}, although not completely correct, can still be used as an aid to find inconsistencies between given ratings and text sentiments conveyed by reviewers.
\begin{table}
\small
\centering
\begin{tabular}{c|c| c c c| c c c| c c c}
\hline
\multirow{3}{*}{} & \multirow{3}{*}{Models} &\multicolumn{6}{c|}{Scientific Paper Decision Recommendation} & \multicolumn{3}{c}{Review Rating Prediction} \\ \cline{3-11}
& & \multicolumn{3}{c|}{OpenReview} & \multicolumn{3}{c|}{Extended PeerRead} & \multicolumn{3}{c}{OpenReview} \\ \cline{3-11}
& & ACC & Ma-F1 & Mi-F1 & ACC & Ma-F1 & Mi-F1 & ACC & DM & OP \\ [0.5ex]
\hline
\multirow{10}{0.4cm}{\rotatebox{90}{\tabincell{c}{Flat Baselines}}}
& NB & 0.599 & 0.375 & 0.449 & 0.643 & 0.391 & 0.504 & 0.225 & 0.854 & -0.772 \\ [0.5ex]
& LR & 0.699 & 0.635 & 0.671 & 0.794 & 0.763 & 0.789 & 0.316 & 0.883 & -0.401 \\ [0.5ex]
& SVM & 0.686 & 0.603 & 0.643 & 0.790 & 0.757 & 0.783 & 0.318 & 0.883 & -0.392 \\ [0.5ex]
\cline{2-11}
& RNN \cite{bahdanau2014neural} & 0.606 & 0.404 & 0.472 & 0.697 & 0.628 & 0.679 & 0.250 & 0.856 & -0.318 \\ [0.5ex]
& TextCNN \cite{kim2014convolutional} & 0.677 & 0.606 & 0.638 & 0.820 & 0.802 & 0.821 & 0.284 & 0.861 & -0.356 \\ [0.5ex]
& TextRCNN \cite{lai2015recurrent} & 0.648 & 0.595 & 0.624 & 0.816 & 0.803 & 0.819 & 0.271 & 0.854 & -0.364 \\ [0.5ex]
& VDCNN \cite{conneau2016very} & 0.616 & 0.551 & 0.584 & 0.667 & 0.456 & 0.565 & 0.233 & 0.849 & -0.350 \\ [0.5ex]
& DPCNN \cite{johnson2017deep} & 0.642 & 0.478 & 0.551 & 0.831 & 0.828 & 0.835 & 0.295 & 0.874 & -0.230 \\ [0.5ex]
\cline{2-11}
& Transformer \cite{vaswani2017attention} & 0.602 & 0.381 & 0.458 & 0.720 & 0.658 & 0.705 & 0.212 & 0.841 & -0.322 \\ [0.5ex]
& SA-Sent-EM \cite{lin2017structured} & 0.699 & 0.662 & 0.683 & 0.831 & 0.821 & 0.834 & 0.323 & 0.885 & -0.204 \\ [0.5ex]
\hline
\multirow{4}{0.4cm}{\rotatebox{90}{\tabincell{c}{Hierarchical\\ Baselines}}}
& HAN \cite{yang2016hierarchical}-extended & 0.713 & 0.709 & 0.716 & 0.833 & 0.816 & 0.834 & 0.338 & 0.887 & -0.187 \\ [0.5ex]
\cline{2-11}
& Bert-base \cite{devlin2018bert} & 0.735 & 0.702 & 0.721 & 0.814 & 0.806 & 0.817 & 0.331 & 0.887 & -0.208 \\ [0.5ex]
& Bert-large \cite{devlin2018bert} & 0.736 & 0.706 & 0.725 & 0.816 & 0.803 & 0.816 & 0.330 & 0.884 & -0.270 \\ [0.5ex]
& SciBert \cite{beltagy2019scibert} & 0.746 & 0.730 & 0.743 & 0.845 & 0.831 & 0.844 & 0.341 & 0.887 & -0.176 \\ [0.5ex]
\hline
\multirow{4}{0.4cm}{\rotatebox{90}{\tabincell{c}{Ours}}}
& {HabNet} (Glove) & \textbf{0.753} & \textbf{0.730} & \textbf{0.745} & \textbf{0.876} & \textbf{0.863} & \textbf{0.877} & \textbf{0.356} & \textbf{0.890} & \textbf{-0.061} \\ [0.5ex]
& {HabNet} (Bert-base) & \textbf{0.775} & \textbf{0.766} & \textbf{0.776} & \textbf{0.881} & \textbf{0.870} & \textbf{0.880} & \textbf{0.375} & \textbf{0.901} & \textbf{0.019} \\ [0.5ex]
& {HabNet} (SciBert) & \textbf{0.786} & \textbf{0.779} & \textbf{0.787} & \textbf{0.880} & \textbf{0.869} & \textbf{0.879} & \textbf{0.365} & \textbf{0.899} & \textbf{-0.013} \\ [0.5ex]
& {HabNet} (Bert-large) & \textbf{0.796} & \textbf{0.787} & \textbf{0.796} & \textbf{0.881} & \textbf{0.873} & \textbf{0.882} & \textbf{0.379} & \textbf{0.900} & \textbf{0.032} \\ [0.5ex]
\hline
\end{tabular}
\caption{Performance results of all models on OpenReview and Extended PeerRead datasets. ``ACC", ``Ma-F1" and ``Mi-F1" denote Accuracy, Macro-F1 and Micro-F1 respectively.}
\label{table:results_binary_cls}
\end{table}
\subsection{Ablation Study}
We conduct ablation study of our framework to evaluate the contribution of each component.
The results are shown in Table \ref{table:ablation_study}.
For the paper decision recommendation task, the better performance of {HabNet} over {HabNet}-V1 on both datasets indicates that the inter-review encoder can integrate information from different reviews of one paper well which helps the decision recommendation. While {HabNet} performs better than {HabNet}-V2 verifies the importance of sentence encoder which can encode the relationships between words in a sentence. And {HabNet} outperforming {HabNet}-V3 demonstrates the ability of intra-review encoder to capture sentence-level relations in a review text and that such relations between sentences contribute much information to the meaning of the review document. The results of {HabNet} and the variants on the review rating prediction task have a similar trend which further validates the contribution of different encoders to the framework. In conclusion, the three encoders help {HabNet} capture three-level relationships in the dataset which plays a vital role on improving prediction performance.
\begin{table}[h!]
\small
\centering
\begin{tabular}{m{0.5cm}|m{1.5cm}|m{1.3cm} m{1.3cm} m{1.3cm}|m{1.3cm} m{1.3cm}|m{1.3cm} m{1.3cm} m{1.3cm}}
\hline
\multirow{2}{*}{Task} & \multirow{2}{*}{Models} & \multicolumn{5}{c|}{OpenReview Dataset} & \multicolumn{3}{c}{Extended PeerRead Dataset} \\ \cline{3-10}
& & Accuracy & Macro-F1 & Micro-F1 & DM & OP & Accuracy & Macro-F1 & Micro-F1 \\
\hline
\multirow{4}{0.2cm}{\rotatebox{90}{\tabincell{c}{Decision\\ Prediction}}} & {HabNet}-V1 & 0.735 & 0.705 & 0.723 & - & - & 0.858 & 0.846 & 0.860 \\ [0.5ex]
& {HabNet}-V2 & 0.736 & 0.716 & 0.730 & - & - & 0.861 & 0.843 & 0.860 \\ [0.5ex]
& {HabNet}-V3 & 0.726 & 0.700 & 0.717 & - & - & 0.859 & 0.846 & 0.861 \\ [0.5ex]
& {HabNet} & \textbf{0.753} ($\uparrow$) & \textbf{0.730} ($\uparrow$) & \textbf{0.745} ($\uparrow$) & - & - & \textbf{0.876} ($\uparrow$) & \textbf{0.863} ($\uparrow$) & \textbf{0.877} ($\uparrow$) \\ [0.5ex]
\hline
\multirow{3}{0.2cm}{\rotatebox{90}{\tabincell{c}{Rating\\ Prediction}}} & {HabNet}-V2 & 0.335 & - & - & 0.886 & -0.218 & - & - & - \\ [0.5ex]
& {HabNet}-V3 & 0.336 & - & - & 0.887 & -0.210 & - & - & - \\ [0.5ex]
& {HabNet} & \textbf{0.356} ($\uparrow$) & - & - & \textbf{0.890} ($\uparrow$) & \textbf{-0.061} ($\uparrow$) & - & - & - \\ [0.5ex]
\hline
\end{tabular}
\caption{Results of ablation study of our framework on OpenReview and Extended PeerRead datasets. Accuracy, Macro-F1 and Micro-F1 are the metrics used for the decision prediction/recommendation task; while Accuracy, DM and OP are used for the rating prediction task, and there are no results for this task on the extended PeerRead dataset because this dataset does not have rating for each review. {HabNet} achieves the best results which are in bold, arrow $\uparrow$ indicates statistical significance ($p < 0.05$).}
\label{table:ablation_study}
\end{table}
\subsection{Case Study}
To gain a view over the ability of our proposed framework on capturing the importance of words in the scientific paper decision recommendation task, we visualize the top-15 approbatory words for accepted and rejected papers, as shown in Figure~\ref{fig:top15words}.
One can see that for the accepted papers, the attention on positive words such as ``excellent", ``competitive" and so on are much higher than other words.
For the rejected papers, negatives words such as ``unsatisfactory", ``incoherent" and so on have higher attention weight than others.
Intuitively, reviewers can express their tendency towards the result of article more clearly through the above keywords.
Moreover, compared to the attention weights of words in accepted papers, the attention weights of words in rejected papers are generally greater.
The possible reason is that reviewers' comments on the rejected articles are more consistent than that of accepted articles.
\begin{figure}[t]
\centering
\includegraphics[height = 1.3in,width=5.15in]{top15words.png}
\caption{Attention weights of the top 15 approbatory words for accepted and rejected papers, left sub-figure is for accepted papers, right one is for rejected papers.}
\label{fig:top15words}
\end{figure}
We also visualize the sentence-level attention on one accepted paper and rejected paper respectively, as shown in Figure \ref{fig:sent-level-attn}, the deeper the color, the bigger the attention weight. For the accepted paper, the sentence with the deepest color expresses strong positive attitude towards the acceptance decision, while other sentences without strong sentiment have smaller attention weights (i.e., the color is much lighter). The same trend also appears in the rejected paper. This result shows that our framework can capture the most important sentence-level signal within a review for predicting the final decisions for papers.
\begin{figure*}[htbp]
\centering
\subfigure[A review for an accepted paper.]{
\begin{minipage}[t]{1.0\linewidth}
\centering
\includegraphics[height = 0.95in,width=6in]{accept_sent_level_attn.png}
\end{minipage}%
}%
\subfigure[A review for a rejected paper.]{
\begin{minipage}[t]{1.0\linewidth}
\centering
\includegraphics[height = 1.7in,width=6in]{reject_sent_level_attn.png}
\end{minipage}%
}%
\centering
\caption{Sentence-level attention visualization for accepted and rejected papers.}
\label{fig:sent-level-attn}
\end{figure*}
\subsection{Error Analysis}
We investigate the error cases that {HabNet} did not predict correctly on OpenReview dataset and find that: (1) 67\% of them are predicted by {HabNet} as rejected papers, but they are actually accepted paper; (2) 33\% of them are predicted as accepted but are in fact rejected.
We randomly select 20 examples from (1) and read the review text carefully, we find that: a). 18 of them have many negative keywords and phrases, like ``unclear", ``limited", ``hard to interpret", ``not provable" and so on. Although there are also positive expressions such as ``looks good", ``interesting", majority of the content contains negative ones. Thus the overall sentiment of the review text is classified as negative by {HabNet}.
b). 2 of them have indicator of acceptance, like the keyword ``accepted" or ``acceptance", but meanwhile there are also many negative words, such as ``confusing", ``no comparison". All of these positive and negative information together make the model unable to make correct prediction.
We also randomly select 20 examples from (2). There are three cases: a). 7 of them contain very strong acceptance keywords and sentences, such as ``pretty impressive", ``promising", ``I recommend acceptance". Because of these strong indicators, {HabNet} predict them as accepted papers. b). 2 of them have strong indicators of rejection, such as ``The novelty of the paper is not enough to justify its acceptance", but they also have several strong positive keywords which deviate the overall sentiment of the review text and thus affect {HabNet}'s prediction.
c). 11 of them have many positive and negative keywords and sentences at the same time, and there is no strong indicator of rejection. {HabNet} can not deal with them very well, because it takes all the positive and negative information into consideration.
\section{Conclusion}
In this paper, a scientific paper review dataset called OpenReview is collected from ICLR openreview website and released.
We observe that there is a three-level hierarchical structure in this dataset (i.e., word level, intra-review level and inter-review level) -- the information and relationships between reviews of one paper may affect the final decision, and so may relationships between words and sentences in each review.
Based on these observations, a hierarchical bi-directional self-attention network (HabNet) framework is proposed for paper review rating prediction and recommendation that can model the interactions among words, sentences, intra- and inter-reviews in an end-to-end manner. Moreover, considering the imbalanced distribution of different classes (i.e., ratings from 1 to 10) in the review rating prediction task, we design two new metrics to better evaluate models.
It is seen that both experimental results of predicting final decisions for submitted papers and identifying ratings for reviews on two datasets (OpenReview and extended PeerRead) demonstrate our proposed framework has sufficient ability to capture the hierarchical structures of words, sentences and reviews in the datasets and outperforms other models.
In the future, we plan to investigate multi-task learning for paper review rating recommendation.
\section*{Acknowledgements}
The corresponding author is Hao Peng. This work is supported by the NSFC NO.62002007 and 61872022, NSF of Guangdong Province (2017A030313339), and in part by NSF under grants III-1763325, III-1909323, and SaTC-1930941.
We thank the reviewers for their constructive comments.
\input{coling2020.bbl}
\bibliographystyle{coling}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 761 |
When women do time
By Jim Bencivenga Staff writer of The Christian Science Monitor
August 11, 1988 | Bedford Hills, N.Y.
AN inmate at New York's Bedford Hills prison, a maximum-security facility for women, laughs when she thinks of how little people really know about women in prison. B.J. Close recalls a phone call from a couple who are friends of hers. ``He's a university professor,'' she says, ``and he and his wife wanted to come and visit, take me out for dinner. They wanted me to just tell them where a nearby restaurant was and they'd be sure to get me back in on time.'' The visit took place inside the prison in the visitors' room.
The steel-bar doors in women's prisons clang just as loud as in men's. Concertina wire (a ribbon of looped, razor-blade steel) scrapes the tops of walls and fences and snakes along the ground at the outer perimeter of the facility. Electronic searches of visitors for weapons and contraband are just as thorough, just as impersonal. All movement is confined and controlled.
But differences are quickly apparent. Some are grounds for sex discrimination lawsuits, criminal-justice experts say. Others offer possibilities for change in the premises for which people are imprisoned.
Overcrowding is not the problem for women that it is for men. Fewer than 28,000 women are doing hard time in a state or federal prison, compared with 542,500 men in similar institutions.
But fewer women behind bars means the cost of rehabilitation per inmate is greater for women than men. ``You just don't have the economy of scale for women that you do for men,'' says Kay Monaco, a lawyer in Santa Fe, N.M., who is a former state deputy secretary for corrections. The result is fewer education programs and pre-release work opportunities for women, she says.
``Women get the short end of the stick when it comes to prison industries,'' Ms. Monaco says. ``Lots of resources go into men's programs. There's an inequality for women.'' The qualities that should be rewarded with more opportunities result in fewer, because in the competition for scarce resources men win out each time, she says.
``They didn't come in with high job skills,'' says Christine J. Herlinger, executive director of the Guilford County Women's Residential/Day Center, an alternative setting for incarceration of women. If they spend 10 years in prison, where education programs are limiteas and they'd be sure to get me back in on time.'' The visit took place inside the prison in the visitors' room.
The rate of increase in incarceration for women last year was 12.3 percent, more than double that for men. If this rate continues, a crisis in overcrowding will occur very quickly for women, and it will be difficult to manage, because state systems have far fewer options for shifting female populations among prisons.
Incarceration plays itself out differently for women in terms of self-respect, says Michael A. Millemann, a professor of law at the University of Maryland. Men inmates preserve an element of dignity that does not exist in women's prisons. The guards know how potentially violent men are, and there are sections (especially in the residential cellblocks) where ``treaties'' are reached between inmate and guard. Not so in women's facilities, he says.
``The biggest problem by far,'' says Mr. Millemann, ``is that our perception of women inmates is distorted in that we do not, and cannot, relate to the idea of a woman as inmate.'' Women's records suggest that more women offenders could be given alternative sentences or paroled, he says. But because society confuses them with male inmates, it is not willing to take what it considers risks in releasing them, he says.
This problem is endemic to modern corrections, says Anthony Travisono, executive director of the American Correction Association. ``We equate punishment with putting someone someplace,'' he says. This mentality limits alternative forms of sentencing better suited to the offense and the offender.
Few women in prison ever dreamed they would be incarcerated. Many men, especially the 60 percent who are repeat offenders, knew they faced such a possibility. And although the majority of women do their crime with a man, they do their time without one. Rarely, if ever, are there any men in the visiting room. Sisters, mothers, daughters, aunts - but seldom men.
In most cases, locking up a woman means locking up a family. ``When a woman does time, her entire family does time,'' says Bedford Hills inmate Karen Ely. Child custody reverts to the state except in the rare instance when a father is present.
This increases the potential ripple effect for children entering the criminal-justice cycle as offenders themselves, says Jo Ann Potter, an advocate for women's correctional issues at the Edna McConnell Clark Foundation in New York City.
It would take five to 10 years to verify, says Ms. Monaco, but she is convinced fewer kids would turn up in juvenile-justice court if fewer mothers were locked up.
Violence is less likely in women's prisons.
``The violence isn't there, so you don't have the same atmosphere in women's prisons,'' Mr. Travisono says. Although there's always a hard-core element intimidating other women, the smaller number of women prisoners allows prison officials to isolate these predators and maintain a (physically) violence-free facility, he says.
``Idle men often lead to trouble in prisons. Women bring less attention to themselves, in that they do not deal with idleness in a violent way,'' says John DiIulio of Princeton University's Wilson School of Government.
``Women are not going to riot,'' says Susan Hallett, an inmate at Bedford Hills. ``We'll just nest.'' It is common to see curtains in a cell, or find one inmate surprising another with a hot meal or a handcrafted gift.
In a perverse way this works against the best interests of women inmates, Ms. Potter says. Riots and court intervention have resulted in better rehabilitation programs for men. In contrast, the absence of violence in facilities for women has let state corrections departments be more responsive to male than to female inmates, she says.
Ironically, a little-known fact in the history of corrections is that many humanizing innovations originated in women's prisons at the turn of the century: These include education classes, libraries, art and music programs, work release, recreation, vocational training, and placement by age, offense, and length of sentence.
The high price tag on corrections (average annual cost of keeping an inmate in a state medium- or maximum-security prison is $17,500; in some industrialized states costs reach $30,000) is forcing many states to consider alternative modes of punishment and incarceration, Travisono says, adding they are much more likely to be adopted for women than for men, because women present less of a threat to others.
``One of the current catches of the criminal-justice system is that murderers of a spouse or lover are not a risk to you or me,'' says Monaco. ``We are talking about a serious crime, certainly,'' she says, ``but how many years is enough?'' ``Ten, 15, 25?'' If the risk is near zero that a 45- to 55-year-old inmate would injure anyone else or commit another crime, punishment becomes the only reason, not safety at all, she says.
A series on prison problems ran in the Monitor July 26, 27, and 28.
The story of prisoner 5770102414
More lawmakers agree: feminine hygiene products should be free for prisoners
California sterilization ban: Why it was needed
https://www.csmonitor.com/1988/0811/djail.html | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,448 |
Borderline Fortune (Penguin Poets) (Paperback)
By Teresa K. Miller, Carol Muske-Dukes (Selected by)
On Our Shelves Now.
Green Apple Books on Clement
On hand as of Jan 30 12:19am
Books on the Park on 9th Avenue
On hand as of Jan 29 11:45pm
Kobo eBook (October 4th, 2021): $11.99
A collection that explores inherited trauma on an individual and communal level, from a National Poetry Series–winning poet who "refus[es] the mind's limits" (Carol Muske-Dukes)
Borderline Fortune is a meditation on intangible family inheritance—of unresolved intergenerational conflicts and traumas in particular—set against the backdrop of our planetary inheritance as humans. As species go extinct and glaciers melt, Teresa K. Miller asks what we owe one another and what it means to echo one's ancestors' grief and fear. Drawing on her family history, from her great-grandfather's experience as a schoolteacher on an island in the Bering Strait to her father's untimely death, as well as her pursuit of regenerative horticulture, Miller seeks through these beautifully crafted poems to awaken from the intergenerational trance and bear witness to our current moment with clarity and attention.
A graduate of Barnard College and the Mills College MFA program, Teresa K. Miller is the author of sped (Sidebrow) and Forever No Lo (Tarpaulin Sky) as well as co-editor of Food First: Selected Writings from 40 Years of Movement Building (Food First Books). Her poems and essays have appeared in ZYZZYVA, AlterNet, Entropy, DIAGRAM, and elsewhere. Originally from Seattle, she tends a mini orchard near Portland, Oregon.
Advance praise for Borderline Fortune:
"Borderline Fortune is a poetry book with a voice in a dying world." —NPR's Bookworm
"Though short, these poems haunt at length." —The Oregonian
"Full of meditative and sharp lyric moments, these poems are alive with complexity and critique. Acoustically, they enact the swell and crash of water: 'the wish/ you'd unwhisper,' 'friction/ on the flint.' Thematically, they prod the undercurrents of society and the expectations of American life . . . These are valuable, urgent poems of witness." —Publishers Weekly
"Miller will be a new and invigorating voice, fully conversant with the ambiguities of our present day." —Library Journal
"I'm so impressed with this new book, with the condensation of syntax, the music, the interior rhyme and off-rhyme, echoey sequences, and the ethical and aesthetic insistence on a lack of resolution. I'm fascinated by the way the 'you' to whom so many of the poems are directed begins to take on aspects of a landscape. In fact, all through the book, the nonhuman and the human seem to be merging. W. S. Merwin implied that elegy is always written for someone who can't read it, but Miller's poems suggest that elegy is a modality that can conjure presence again and that the poem resurrects the dead in some sense." —Forrest Gander, winner of the Pulitzer Prize, on Borderline Fortune at the Montana Book Festival
"Teresa K. Miller explores startling territories in Borderline Fortune. She addresses the lines we've drawn and erased for centuries on the earth—that conform to the borders we cross and uncross in the mind. Yet: 'I'm asking you to believe in what you've never seen or heard,' she writes, refusing the mind's limits. Here is the dark power of climate change where she finds 'the future all danger, heat, & scarcity.' Blake, Dickinson, and Hopkins' Terrible Sonnets hover ('birds build—but not I build'), above trees cut down and hope with feathers. The damage done to the earth echoes the damages to the protean mind of the poet—but Miller remains radiantly elusive, an escape artist in these marvelous poems of altered terra firma and revelation." —Carol Muske-Dukes, author of Blue Rose
"In Borderline Fortune, Teresa K. Miller claws her way to and through her subject—loss in the form of 'shrapnel and good intention.' Awareness: It's a hard journey. The human voice calls in ragged gasps, how did we get here? But unlike Rumi who blithely says, 'Whoever brought me here will have to take me home,' Miller's voice has been dragged to this shore and pressed under. To write is to imagine, and Miller discovers in the going, in the moment when we remember that 'every river had a first day to flow.' Through Miller's poems, we are given that first day, no matter what comes after. We find hope for another way of being in the world." —David Romtvedt, National Poetry Series–winning author of A Flower Whose Name I Do Not Know and Dilemmas of the Angels
"The poems in Teresa K. Miller's Borderline Fortune emphasize the greater context of our existence as individuals, as family members, and as cultures. Miller mines family as a construct, whether naturally related or collected. She interrogates relationships with the lens of a geologist, exploring the physical, chemical, and biological properties of the gravitational fields that pull us together and the elements that erode us. Several ages are explored by the poems, acknowledging the violence that must be present for eloquent transition and rebirth. The poems in Borderline Fortune are so sharply crafted, they serve as the pick and axe that dig deep into the granite of the past. Miller questions specific characters, many ghosts from the past that hold secrets to a history she is rebirthing. The poems shape a world created from the knowledge and the mythology Miller has extracted." —Elmaz Abinader, author of This House, My Bones and cofounder of VONA
"Borderline Fortune feels like a book that was written to save oneself, to enact through poetry a means of salvation. Teresa K. Miller weaves together transcendent astonishments, precise images of the natural world, histories of horrors still present in the land, & personal revelations as intimate as bruises, weaving them into a single, entangled whole. Borderline Fortune is not a book that solves a problem, but a book that creates a net, a thing made of both solidity & gaps, open enough to be pulled through the dangers, strong enough to haul a body up to the air. This salvation happens in the reading, how the reader creates the net along with the poem, hand-in-hand, each one pulling the other to the surface, ceaselessly, with every memory of beauty & of grief. The book is a reminder that salvation is an ongoing work, for, as Miller writes, 'In the end, there was no end.'" —Mathias Svalina, creator of the Dream Delivery Service and author of The Wine-Dark Sea
"In the sweeping expanses of Borderline Fortune, Teresa K. Miller grapples with the complexity of inheritance, the complicated legacies of family, history, and place. What created us, and what do we in turn create? How closely twined are belonging and betrayal? Here, history, identity, and the natural world meet and merge: 'a riven nausea in the cambium, / some needle-leafed private anguish.' Geography itself is sentient and responsive: 'lies twine into granite, brine / into mineral creatures made of lace.' In the end, the poems form a landscape we must immerse ourselves in, their movement as dark and unpredictable as the ocean or tectonic plates, and their story one we don't navigate as much as survive: 'Haul / yourself out, / one frozen leg at a time.'" —Laura Walker, author of swarm lure and psalmbook
Series: Penguin Poets
Poetry / Subjects & Themes / Nature
Poetry / Subjects & Themes / Family
Poetry / Women Authors | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 263 |
Roads Less Traveled: 3 Unusual Audio CDs
Experiments in Bellydance by Rebecca Wolf-Nail
Passages by Middle-Earth Ensemble
Desert Winds by Transition
Review by Tracy Benton
Here's a collection of music for those searching for something off the beaten path! It can be difficult for a dancer to decide to spend money on dance music by lesser-known bands, particularly while trying to avoid adding the eighteenth cover of "Zeina" to a personal collection. If the band and the music are utterly unknown to you, how can you open your wallet? Perhaps these reviews will help you make up your mind. The 3 audio CDs reviewed here range from the traditional to the cutting edge.
Transition is a small ensemble featuring three musicians–Souren Baronian, Haig Manoukian, and Cornelia Kraft–performing on a range of instruments from clarinet to kaval, oud to saxophone. Although the ensemble is billed mainly as a Middle Eastern jazz ensemble, its "Desert Winds" album feels steeped in Armenian and Turkish traditional influences. This CD is well-recorded and is full of virtuoso playing, from complicated runs and riffs to soulful taxim. Sometimes I thought the sound was a bit spare, but three musicians are three musicians, after all. I found the album particularly notable in that it offers tracks in less common time signatures: 10/8, 9/8, 7/8, even 5/4. (Trust the jazz musicians to challenge you rhythmically; the track listing kindly shows this information.)
My favorite tracks on this CD included the 8-minute "Karshlama Medley", a lively mix of melodies and taxim over a steady, moderate 9/8 beat, perfect for the dancer wanting to explore theTurkish style. The clarinet and the oud trade the lead lines, offering a lot of variety for a dancer wishing to experiment. Another was the more jazzy-feeling "Seasoning", an original by drummer/vocalist Cornelia Kraft. Kraft scat-sings the melody over the top of the instruments; the end result is akin to Enya turning her hand to Middle Eastern music, producing a fusion track complete with a fast introduction, an ethereal slow section, and an exciting finish. On some tracks the musicians clearly want to hang out in their jazz mode; the last song, "New Dawn," is a good example of this. If you like both jazz and Armenian music, and are intrigued by the idea of putting them together, you will definitely enjoy this album.
Available for purchase here on CDBaby
Souren on our Musical Instrument Tour page here
Rating: Three Zils
The Middle-Earth Ensemble is a five-piece band whose sound I would classify as "renaissance faire." I don't mean this in a disparaging way; I think they are an excellent example of the types of versatile musical groups one hears at ren faires. They have a wide repertoire of music that pulls from many different ethnic influences. Their album Passages displays their voyages into many different sounds: Arabic, jazz, Turkish, Balkan… luckily, not all in one track! At first, I found listening to their instrumentation a little startling. Oud, violin, and traditional percussion were not surprising, but the electric bass seemed out of place to my ear, and doubling the violin melody lines on flute sounded like too much on the top end. However, I have no doubt that this band would be a fun dance experience in a live show or hafla. Their sound is upbeat and pulls you in; it's "in your face" and delightful.
More than half the tracks on Passages are originals. The drum solo, "Cairo Beats," is a well-varied solo, with several rhythmic changes, but it avoids the cut-and-paste structure that makes so many drum solos sound alike. I have to admit that while I found pieces like "Galiciana" to be breezy and entertaining, their fusion with Middle Eastern music is very loose. A dancer looking for ren-faire-like fusion will like these original tracks, but not one seeking a strong Middle Eastern feel to the music. However, the cover tracks on Passages are well worth a listen if more traditional music is to your taste. "El Helwa Di," in particular, is arranged to great effect with tempo changes and a lyrical flute solo. If the idea of a less traditional ensemble's take on
Middle Eastern dance music intrigues you, you might check out Passages.
Frank's GS Bio Page with his GS articles listed
Rebecca Wolf-Nail's Experiments in Bellydance goes much further into fusion territory than the previous two albums. At first, I was disappointed to see no musician credits printed on the liner notes… then realized that she is apparently supplying all the instrumentation herself. Most of this CD sounds synthesized, so if "unreal" instruments bother you, this album won't be your favorite. The entirely original tracks vary in flavor from Native American to Zambra Mora stylings. Several tunes, such as the "Nocturne Suite", are quite Western and orchestral in nature, but they are limited by the synthesizer. They sound as if they've been recorded inside a small box, and this lack of resonance detracts from the music.
Most successful are the tracks in which the composer explored themes far away from traditional music for Bellydance. Her "Sol Bloom Jam" is perfectly designed to appeal to fusion dancers exploring the vaudeville and circus themes now becoming popular, complete with a nod to the "Snake Charmer" tune, circus calliope, and music box dancer. (In fact, I can't wait to see this in a performance somewhere.) "When Clowns Attack" is a more pared-down composition along this line, featuring a sound like a toy piano. Dancers in search of the truly unusual are those who will most appreciate Experiments in Bellydance.
Available for purchase on artist's site here
Rating: Two zils
When you're ready to take the plunge and investigate some music that's not your everyday baladi, keep all three of these CDs in mind. Depending on what you're searching for, one of them just might be the perfect fit.
Have a comment? Use or comment section at the bottom of this page orSend us a letter!
7-12-09 Heartbeat of the Dance: Review of 4+ Drum Solo CDs Reviewed by Amina Goodyear
Sabla Tolo 1 & 2 by Hossam Ramzy, Drum Attack by Tony Chamoun, Pulse of the Sphinx by Henkesh Brothers
4-17-09 Two Dance CDS for Performance and Listening, "The Soul of Cairo" & "The Masters of Bellydance Music" 2 CDs reviewed by Amina Goodyear
This family is dedicated to producing (and also finding) the latest and most popular bellydance music as well as reissuing classic albums in a remastered format with updated liner notes.
11-14-08 Unveiled Musical Gems, 3 CD Reviews by Joette Sawall
Raqs El Qamar by Chris Marashlian, Rhythms of Turkey by Tayyar Akdeniz, Angelika Unveiled, by Angelika Nemeth and Raul Ferrando
11-6-08 "Aheb Masr, Music and Songs for Oriental Dance" CD Review by Catherine Barros
produced by Nader Zakaria, at Merryland Studio Heliopolis, Artistic direction by Yasmina. Depending on your mood and tastes, there should be something for just about everyone on this CD.
4-15-08 Bellylicious Raks CD review by Andrea
So many other songs end abruptly and leave you hanging or just take too long to finish–not unlike an unsatisfying lover. Hasan, however, is truly satisfying. It will be my next new entrance piece for 2008!
3-15-08 The Magic Sounds Studio of Cairo, 3 Albums reviewed and Compared by Amina Goodyear
CDs- Oriental Fantasy #12- Talisman, Nesma:Del Nilo al Guadalquivir (From the Nile to the Guadalquivir),Nesma, Memories of Cairo. In a world where Egyptian dancers dance in the "less is more" tradition, the world of musicians seemed to be – more is better and lots more is best. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 2,335 |
Subscribe to our newsletter for the latest and greatest in luxury, delivered to your inbox.
Recibe nuestros últimos artículos, eventos, promociones e invitaciones.
We are committed to respecting your privacy. Click here to view our Privacy Policy.
Estamos comprometidos a respetar tu privacidad. Lee nuestra Política de Privacidad para más información.
AzureAzure.com
Luxury Global Magazine
EventsA carefully crafted teaser with no more than two lines on a mobile device.
SUBSCRIBESUSCRÍBETE
Cruises, Trains
Curated Trips
CHEFS & RESTAURANTS
Gourmet & Organic
Accessories, Parfums
Designers, Boutiques
Watches & JewelryThe best jewelry and watches in the world, with news about the latest collectible pieces and their stories.
EventsThe best events of international high society, its guests, behind the scenes details and photos.
FAIRS & EXHIBITS
Curated Trips / Travel
Bespoke London: Personalized London Tours Away From The Crowds
By Barbara Geier
Bespoke London: Personalized London Tours…
London is so much more than Buckingham Palace, the Houses of Parliament or – god forbid – shopping hell on Oxford Street. A new service known as "Bespoke London," offers unique, exclusive opportunities for discerning travelers.
Beating the crowd in London is hard, some might even say impossible. In recent years, the signs of increased tourism have become more obvious, with hordes of people congregating in the same spots. However, it is possible to beat the crowds – with the right person by your side and plenty of unique London insights:
As a long-standing London dweller and lover, I have been exploring the city on foot for decades, away from the overcrowded tourist spots. I have also written a couple of London guide books and shown friends and family another side of London. My London, which includes nooks and crannies that people don't usually see. All of this has now culminated in the launch of "Bespoke London," a service offering exclusive private tours that are designed as a "walk with a friend." Highly personalized and full of surprises, the tours can contain rural spots and urban wilderness, hidden gardens, Victorian cemeteries, cool galleries, stunning architecture, quirky shops, street food, fine dining, shopping or fancy houses – depending on the person's interest and curiosity.
Orangery Gunnersbury Park – one of the many places to see in London
Apart from curating personalized tours and creating unique London moments for anyone prepared to leave the usual tourist hotspots behind, "Bespoke London" also puts the spotlight on the city's unique neighborhoods. London is essentially a conglomeration of many little villages which is all too often forgotten. Exploring these and venturing beyond tube zone 1 that a lot of visitors stick to will reveal hidden gems and unusual sights. Such as the former mansion of the Rothschild family in Gunnersbury Park in London's west side. The building, which reopened this year after extensive renovation, also houses a fascinating museum of local history and is set in beautiful parklands.
Lassco Brunswick House
Turning south, architecture and antique lovers will delight in "Lassco Brunswick House," a treasure chest of architectural salvage pieces, in a beautiful Georgian mansion in Vauxhall. The surroundings might be far from promising, but boy, the interior is something to marvel over. You can easily get lost here and rummage around for hours. Luckily, there is the delightful Brunswick House Café in the same building to stock up on food and drinks. The café and restaurant are decked out in relics and decorative ornaments gathered by Lassco over forty years of operating in the London salvage trade. Only a 15-minute walk away, Damien Hirst's Newport Street Gallery has turned a somewhat industrial looking street into a destination for art lovers. The gallery in a converted former theatre carpentry and scenery production workshop is a stunning space and regularly hosts top exhibitions. (Not to mention "Pharmacy 2," a rather stylish restaurant).
Moving north, bohemian Hampstead, the neighborhood of choice for writers, intellectuals and thinkers, is not only home to one of the most charming cafés in London (think: Budapest, c. 1950) but also to one of the few examples of Modernist architecture in London: The Isokon Building is a pioneering modern apartment block where, among others, Agatha Christie, Bauhaus founder Walter Gropius or design icon Marcel Breuer lived. The fabulous free gallery telling its story is a must for anyone only remotely interested in Modernist design.
Go east and you'll find an example of something that London does particularly well, i.e., extremes. In Walthamstow, another former village, the "William Morris Gallery" Arts and Crafts treasure chest, and "God's Own Junkyard," a neon wonderland showcasing the work of the late neon artist Chris Bracey including pieces that were used in "Captain America" or "Eyes Wide Shut," exist within less than 20 minutes walking distance. More? How about the world's oldest, surviving music hall, "Wilton's," hiding a few minutes away from the Tower at the end of a tiny, residential road. Its crumbling charm is irresistible. Settle down in the bar to soak up the atmosphere or get a ticket for one of the shows – anything from theatre to music – on offer. Last but not least, let's not discriminate against central London (because there are plenty of exclusive places here, too, away from the tourist crowds): If you like shopping, don't miss "The Shop," in Covent Garden. It not only has one of the best of luxury fashion and of-the-moment brands – retail spaces simply don't come much more beautiful than this concept store in a 19th-century Grade II listed building.
Wilton's Music Hall
For more information about Bespoke London Tours, including tour options & prices go to: www.bconnects.net/bespoke-london. ■
Kona Kai Resort & Spa: A Reclusive Getaway in San Diego
Beautiful and Unprecedented Gardens
7 Top Ski Hills in North America
PreviousPrevious post:Fake Luxury: For The Eco-Conscious FashionistaNextNext post:Award-Winning Japanese Whiskeys With History
Unique And Spectacular Places To Ring In The New Year
You still have time to book a one of a kind new years celebration! Take a look at these suggestio...
Maria Cristina Hotel: The Historic Jewel Of San Sebastian
After a $33 million dollar renovation, the Maria Cristina is an exclusive five-star hotel with mo...
Hong Kong: The Multicultural Destination That You Can't Miss
Hong Kong, known as a city that blends Eastern and Western views with traditional and modern amen...
Abalone: The Best And Rarest Seafood In The World?
Almas: The Most Expensive Caviar in the World
Luxury Gastronomy
The Most Expensive Liquor, Starting at One Million Dollars
Join us as we discover the best the world can offer.
We are committed to respecting your privacy. View our Privacy Policy for more information.
Subscribe to our email newsletter and see the best the world can offer.
We are commited to respecting your privacy. See our Privacy Policy for details.
© Copyright 2019 azureazure, LLC, a subsidiary of Grove Multimedia USA Corp. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 952 |
\section{INTRODUCTION}
The development of lasers of high-intensity and high-frequency
made possible the experimental investigations of many atomic
systems and revealed new phenomena. For example, the strong
electromagnetic coupling of two autoionizing states and their
coherent interaction, in some cases, could lead to partial
stabilization and population trapping in the ground
state~\cite{PL81}. The interaction of atomic autoionizing states
with an external electromagnetic field has been considered in a
number of papers~\cite{PL81,And82,Ba86,Lam89,TN99}. An
experimental and theoretical investigation of the effects of the
strong electromagnetic coupling of two autoionizing states on the
photoionization properties of Mg demonstrated the coherent
interaction between the autoionizing states~\cite{Kar95}.
Many experiments involving autoionizing states, have been performed
over the last years and the observed dynamics present very
interesting features. In this study, we consider the case of helium
atom in which the ground state is coupled to the 2s2p ${^1}P^o$
autoionizing state, through a laser with frequency $\omega_1$. A
second laser, with frequency $\omega_2$, couples the 2s2p ${^1}P^o$
state to the $2p^2~{^1}S$ autoionizing state. The latter has not
been observed in any photoexcitation experiment and the results of
the present study can be used for a new experimental investigation.
A similar system involving double autoionization resonance, has been
studied theoretically in detail, in connection with laser-induced
transitions between triply excited hollow states~\cite{LBM20}. Here
we present only the essential formulae of our approach, since the
the complete theoretical treatment has been published
elsewhere~\cite{PL81,LBM20}. The atomic parameters of the states
involved are calculated by an {\it ab-initio} approach. In Sec. 2 we
give a short description of our theoretical methodology and the
basic dynamic equations describing the problem. In Sec. 3 we solve
the equations and present and analyze our results. Finally, we
conclude in Sec. 4 with suggestions for prospective experimental
investigations.
\section{Theoretical approach}
We consider Helium atom subject to two linear polarized laser
fields with frequencies $\omega_1$ and $\omega_2$, respectively.
The relative phase between them is ignored and the total laser
field has the form:
\begin{equation}
E(t) = E_1 (t)\exp (i\omega _1 t) + E_2 (t)\exp (i\omega _2 t) +
c.c. .
\end{equation}
The frequencies $\omega_1$ and $\omega_2$ are chosen so as to be
tunable around the selected resonance transitions, namely
$1s^2~{^1}S \rightarrow 2s2p~{^1}P^o$ and $2s2p~{^1}P^o
\rightarrow 2p^2~{^1}S$. For the time-dependent field amplitudes
$E_i(t),~i=1,2$ we choose a convenient form for the pulse
envelope, namely a $\sin^2$, avoiding the long tails of a Gaussian
which make the numerics more difficult, without significantly
affecting the results. The explicit form is:
\begin{equation}
E_i(t)=
{\cal E}_i^{(0)}
\sin^{2}(\frac{\pi t}{\tau _i} ),
\quad
\textrm{with}~
0 \leq t \leq {\tau _i},
\end{equation}
with ${\cal E}_i^{(0)}$ the the maximum field strength and
${\tau}_i/2$ is the Full Width at Half Maximum (FWHM). We assume
that ${\tau}_i$ is few picoseconds and the simultaneous action of
$E_i(t), i=1,2$, i.e. ${\tau}_1$=${\tau}_2$.
The next step is to solve the time-dependent Schr\"{o}dinger
equation. In the following sections we use the notation $ \left| g
\right\rangle$ for the ground state $1s^2~{^1}S$ of He, and
$\left| a \right\rangle$, $\left| {E_a } \right\rangle $ and
$\left| b \right\rangle$, $\left| {E_b } \right\rangle $ for the
discrete and continua parts belonging to the $2s2p~{^1}P^o$ and
$2p^2~{^1}S$ doubly excited states, respectively. Note that these
autoionizing states are single channel Feshbach resonances. The
wave function for this standard model system shown in fig.1, can
be expressed as:
\begin{eqnarray}
\left| {\Psi (t)} \right\rangle &=& C_g(t)\left| g \right\rangle +
C_a(t)\left| a \right\rangle + C_b(t)\left| b \right\rangle \nonumber \\
&+& \int {dE_a C_{E_a } (t)\left| {E_a } \right\rangle } + \int
{dE_b C_{E_b } (t)\left| {E_b } \right\rangle } .
\end{eqnarray}
The Hamiltonian operator of the system is written as: $H=H_0 + V +
V_d$, with $ H_0\left| {\mu} \right\rangle = E_{\mu}\left| {\mu}
\right\rangle , ~\mu=a,b,g$, and $V$ being the configuration
interaction coupling the discrete parts of the doubly excited states
to the continua and $V_d = V_d(t)$ is the field-atom interaction.
Projection of the individual states in the expansion of $\left|
{\Psi (t)} \right\rangle$ leads to a set of coupled differential
equations containing amplitudes for the discrete parts as well as
for the continua. The introduction of (i) the slowly varying
amplitudes $c_{i} (t)$ which are defined by $c_{i} (t)$ = $C_{i}
(t)e^{i(E_i/\hbar+\Delta \omega)t}$ and $\Delta \omega$ is the sum
of the frequencies of the absorbed photons, (ii) the application of
the rotating wave approximation(RWA), and (iii) the adiabatic
elimination of the continua lead to the following set of equations
for the discrete-state amplitudes:
\begin{equation}
{i \hbar} \frac{{\partial }}{{\partial t}} {\bf c}(t) = {\bf H}(t)
{\bf c}(t),
\end{equation}
where
\begin{equation}
{\bf H}(t) = \left[
\begin{array}{ccc} {S_g - \frac{i}{2}\gamma _g } & \tilde \Omega _{ga} &
{S_{gb} - \frac{i}{2}\gamma _{gb} } \\
\tilde \Omega_{ag} & -\delta _1 - \frac{i}{2}(\Gamma _a +
\gamma _a ) & \tilde \Omega _{ab} \\
{S_{bg} - \frac{i}{2}\gamma _{bg} } & \tilde \Omega _{ba} &
-{\delta _1 - \delta _2 - \frac{i}{2}(\Gamma _b + \gamma _b )}
\end{array} \right],
\label{eq:H}
\end{equation}
and ${\bf c}(t) = \left[ c_{g}(t), c_{a}(t), c_{b}(t) \right]^T$.
In equation (5) $ \delta _1 = \omega _1 - (E_a^{(0)} + S_a -
E{}_g - S_g) $, $ \delta _2 = \omega _2 - (E_b^{(0)} + S_b -
E_a^{(0)} - S_a )$ are the detunings, $E_a^{(0)}$, $E_b^{(0)}$
and $\Gamma _a$, $\Gamma _b$ the resonance energy and width of the
doubly excited states, $S_g$, $S_a$, $S_b$, $S_{gb}$ and $\gamma
_g$, $\gamma _a$, $\gamma _b$, $\gamma_{gb}$ the laser induced
shifts and widths. The generalized complex Rabi frequencies
$\tilde \Omega _{ga} $ and $\tilde \Omega _{ab}$ are defined as:
\begin{equation}
\tilde \Omega _{ga} = \Omega _{ga} \left( {1 - \frac{i}{{q_a }}}
\right) = \frac{1}{2}E_1 (t)D^{(z)}_{ga} \left( {1 - \frac{i}{{q_a
}}} \right)
\end{equation}
and
\begin{equation}
\tilde \Omega _{ab} = \Omega _{ab} \left( {1 - \frac{i}{{q_{ab}
}}} \right) = \frac{1}{2}E_2 (t)D^{(z)}_{ab}\left( {1 -
\frac{i}{{q_{ab} }}} \right)
\end{equation}
with $D^{(z)}$ being the dipole along the polarization direction
$z$, and $q_a$ and $q_{ab}$ the Fano line shape parameter for the
transition $\left| g \right\rangle \rightarrow \left| a
\right\rangle$ and its generalization for the transition $\left|
a \right\rangle \rightarrow \left| b \right\rangle$. Obviously the
Hamiltonian of equation (\ref{eq:H}) is \emph{Non-Hermitian}. The
coefficients $c_{i}(t)$ are slowly varying in the sense that the
transformation $c_{i} (t)$ = $C_{i} (t)e^{i(E_i/\hbar+\Delta
\omega)t}$ has removed their rapid variation.
\begin{figure}
\includegraphics[width=12cm]{fig1.eps}
\caption{Schematic representation of the coupling between the
ground, the two autoionizing states and the continua entering the
problem.}
\end{figure}
For the derivation of the above equations the laser induced
continuum-continuum couplings have been neglected. It has been
shown that the line shapes are not affected by continuum-continuum
transitions and the same is true and for the total photoionization
rate~\cite{Cav95}. Also, preliminary calculations showed that we
can ignore the laser-induced couplings between the discrete parts
$\left| a \right\rangle$ and $\left| b \right\rangle$ of the
resonance states and the non-resonant part of the continua $\left|
E_b \right\rangle$ and $\left| E_a \right\rangle$ respectively,
and the second order effect of the laser induced coupling of the
ground state $\left| g \right\rangle$ to $\left| b \right\rangle$
via the non-resonant part of the continua $\left| E_a
\right\rangle$. By solving the above equations the ionization
yield into each channel and the total ionization probability can
be calculated. The total ionization probability is:
\begin{equation}
P{\rm{ (}}t{\rm{) }} = {\rm{ 1 }} - \left| {{\rm{c}}_{\rm{g}} (t)}
\right|^2 - \left| {{\rm{c}}_{\rm{a}} (t)} \right|^2 - \left|
{{\rm{c}}_{\rm{b}} (t)} \right|^2
\end{equation}
\begin{table}
\begin{tabular}{ccccccccc}
\hline \hline ~~~$q_a$~~~ & ~~~$q_{ab}$~~~&
~~~~$E_a^{(0)}$~~~~&~~~~ $\Gamma _a$~~~~&$~~~~E_b^{(0)}$~~~~ &
~~~~$\Gamma _b$~~~~
&~~~~$\Omega _{ga}$~~~~ & ~~~~$\Omega _{ab}$~~~~ & ~~~~$\gamma _g$~~~~ \\
\hline
-2.79&-714 &-0.6928&1.37 $\times 10{^{-3}}$ &-0.6214 &
2.15$\times 10{^{-4}}$
& $ 0.038 \frac{E_{1}(t)}{2} $ & $ 2.14 \frac{E_{2}(t)}{2} $ & $ 0.47 \frac{I_{1}(t)}{4} $ \\
\hline
\hline
\end{tabular}
\caption{Coupling of the states involved in the 3$\times$3 model
examined here. All values are given in atomic units. $E_a^{(0)}$,
$E_b^{(0)}$ and $\Gamma _a$, $\Gamma _b$ are the energies and the
widths of the 2s2p${^1}P^o$ and $2p^2~{^1}S$ states,
respectively.}
\end{table}
{\emph{Atomic structure parameters}}. We have calculated all of the
parameters pertaining to the atomic levels coupled by the process
described above, through an {\it ab initio} approach. In order to
take into account the electron correlation, very accurately, a large
number of configurations were selected. The MCHF
method~\cite{CFF2000} has been used to perform the present
calculations. The MCHF wave-function expansion for the ground state
of He was over a set of 15 configuration states coupled to form a
$^{1}S$ term. The radial wave functions for the different orbitals
were obtained by the MCHF procedure, varying all the orbitals
simultaneously. Minimization of the total energy yielded an energy
of -2.9033 a.u. to be compared to the accurate value of -2.903724
a.u. from extensive variational calculations. The autoionizing
states 2s2p ${^1}P^o$ and $2p^2$~${^1}S$ of He are calculated using
a partition of the function space within the framework of the
Feshbach formalism~\cite{Fes62}. Using appropriate $\it Q$ and $ \it
P$ projection operators, we can represent these resonances as
quasibound states embedded in a continuum. The localized
wavefunctions and of these states are also calculated by a MCHF
approach. For 2s2p ${^1}P^o$ we used 27 configuration states and the
energy obtained for this state is: -0.69256 a.u. For the
$2p^2$~${^1}S$ state we used 30 two-electron configuration states
and the energy obtained for this state is: -0.62218 a.u. The
correlation effects are important for an accurate description of
these states. This can be seen from their configuration expansion,
which for the 2s2p ${^1}P^o$ is of the form:
\[
\psi(2s2p~ {^1}P^o) = 0.953 (2s2p) - 0.291 (2p3d) - 0.076 (3s3p)
+ ...
\]
while for the $2p^2$~${^1}S$ state we have:
\[
\psi(2p^{2}~{^1}S) = 0.787 (2p^2) - 0.554 (2s^2) + 0.173 (3s^2) -
0.139 (3p^2) + 0.179 (3d^2) + ...
\]
The autoionization widths of these states are calculated by the
well known complex-coordinate method~\cite{Byl98}. We choose the
open channel component of the resonant wavefunctions to be:
\begin{equation}
u(1s\varepsilon \ell~ ^{1}L^{\pi}) = \hat{ \cal A} \left( \phi_
{1s}(r_1) \sum_{i} c_i \chi_i ( \rho_2 ^{*}) Y_{\ell m}(\Omega_2)
\right)
\end{equation}
with $\chi_i ( \rho ^{*}) = (\rho ^{*})^{k_i} e^{-a_i \rho ^{*}}$.
The radial function $\phi_ {1s}(r)$ was kept fixed to the
hydrogen-like orbital of He$^+$ whereas, in the variant of the
complex-coordinate approximation followed here, for $\chi_i ( \rho
^{*})$ the radial coordinate takes the form $\rho_i ^{*}=r_i
e^{-i\theta}$. The non-linear parameters $a_i$ and the expansion
coefficients $c_i$ are subject to a variational optimization for
the calculation of the complex energy eigenvalues pertaining to
the autoionizing resonant states.
Our results for the energy position, including the energy shift,
and the width, of the autoionizing states presented here, can be
compared to other more elaborate calculations~\cite{Lind94}. The
wave-functions described above were also used for the calculation
of the dipole moments for the various transitions involved. All
the parameters that enter in the calculation are shown in table 1.
We note here that the use of the complex-coordinate method
provides a powerful tool for the calculation of the complex Rabi
frequency $\tilde \Omega _{ab}$ for a transition between
autoionizing states.
\section{Results and discussion}
\begin{figure}
\includegraphics[width=10cm]{fig2.eps}
\caption{He$^+$ photoion yield as a function of the detuning
${\delta}_1$, associated with the transition between the ground
state and the 2s2p ${^1}P^o$ doubly excited state. The laser
coupling the 2s2p ${^1}P^o$ and $2p^2$~${^1}S$ states is on
resonance (${\delta}_2$=0). We clearly see that the laser coupling
induces an Autler-Townes doublet.}
\end{figure}
The solution of the system of differential equations given by Eq.
(4) can provide us the information about the temporal evolution of
the system under consideration. We have chosen to study the
response of the system under the simultaneous action of the
electric field $E_1$ with frequency $\omega_1$ and a pulse
duration ${\tau _1}$=5 ps and of the electric field $E_2$ with
frequency $\omega_2$ and of the same duration.
Figures 2 and 3 show the photoionization yield of He$^+$ as a
function of the detunings of the laser sources for a series of
intensities and detunings. As it can be seen from Fig. 2 the line
shape changes significantly with the intensity of the laser
coupling the 2s2p ${^1}P^o$ and $2p^2$~${^1}S$ doubly excited
states. At low intensities we have a line shape for the lowest
${^1}P^o$ Feshbach resonance of He which is a typical Beutler-Fano
profile~\cite{Fan61}. As the intensity is increased a doublet
appears due to the ac Stark splitting as a result of the laser
induced oscillation between 2s2p ${^1}P^o$ and $2p^2$~${^1}S$.
This structure is known as an Autler-Townes doublet and the
separation between the two peaks carries information about the
dipole matrix element coupling the doubly excited states. In Fig.
3 the frequency $\omega_1$ is on resonance (${\delta}_1$=0) while
the laser frequency $\omega_2$ is varied (${\delta}_2 \ne 0$). In
this case the coupling of the doubly excited states reveals a
window resonance on the photoionization cross section.
\begin{figure}
\includegraphics[width=10cm]{fig3.eps}
\caption{He$^+$ photoion yield as a function of the detuning
${\delta}_2$, associated with the 2s2p ${^1}P^o$ $\rightarrow$
$2p^2$~${^1}S$ transition. The laser coupling the ground state
with the 2s2p ${^1}P^o$ doubly excited state is on resonance
(${\delta}_1$=0). We clearly see that the appearance of a window
resonance as the laser intensity increases.}
\end{figure}
The number of the electrons emitted in the energy region of each
autoionizing state is proportional to the ionization signal given
by the formula:
\begin{equation}
S_i = \int\limits_{ - \infty }^{ + \infty } {\left| {c_i (t)}
\right|^2 \Gamma _i dt}
\end{equation}
with $i=a, b$. The magnitude of $S_i$ depends on the time
evolution of the coefficients $c_i$ and, in a more crucial way, on
the values of the autoionizing widths of the resonant states. We
have calculated $S_a$ and $S_b$ for various values of $I_2$
ranging from $10^8 W/cm^2$ to $2 \times 10^{11} W/cm^2$ and for
(${\delta}_1 \ne 0$, ${\delta}_2=0$) and our results are shown in
fig. 4a and 4b.
\section{CONCLUSIONS}
To our knowledge the autoionizing state $2p^2$~${^1}S$ of He has not
been observed in any multiphoton process. There has not been any
detection of this state by two-photon processes and the energy
position of this resonance is measured only in scattering
experiments. In this study we showed that, the coupling of this
state via a laser field of moderate intensity to another
autoionizing state, has significant and detectable results in the
photoionization cross section of He. The prospective pump-probe two
color experiments utilizing sources as, for example, the Deutsches
Elektronen-Synchrotron Free Electron Laser (DESY FEL) provide an
apparatus for the detection of the resonant coupling of autoionizing
states as these described here~\cite{Mey01}. The laser intensities
used in our study are attainable and proposed experiments with
Free-Electron Laser (FEL) sources are readily
available~\cite{Andr00,Fel03}.
\begin{figure}
{\bf (a)} \includegraphics[width=7.cm]{fig4a.eps} \hskip0.1cm {\bf
(b)}\includegraphics[width=7.cm]{fig4b.eps} \caption {The
ionization signal in the energy range of the autoionizing states
(a) 2s2p ${^1}P^o$ and (b) $2p^2~{^1}S$, for various values of the
laser intensity $I_2$. The laser coupling the 2s2p ${^1}P^o$ and
$2p^2$~${^1}S$ states is on resonance (${\delta}_2$=0).}
\end{figure}
\begin{acknowledgments}
The author is indebted to Prof. P. Lambropoulos for fruitful and
inspiring discussions which initiated the project.
\end{acknowledgments}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,034 |
Q: d3.js rainbow chart animation enhancements I've created this arc chart. I'd like to animate the labels better, have them tween with the arc animations. I've placed the labels inside to avoid being covered up.
jsFiddle
var arcGenerator = {
radius: 100,
oldData: "",
init: function(data){
var clone = jQuery.extend(true, {}, data);
this.oldData = this.setData(clone, false);
this.setup(this.setData(data, true));
},
update: function(data){
var clone = jQuery.extend(true, {}, data);
this.animate(this.setData(data, true));
this.oldData = this.setData(clone, false);
},
animate: function(data){
var that = this;
var chart = d3.select(".arcchart");
that.generateArcs(chart, data);
},
setData: function(data, isSorted){
var diameter = 2 * Math.PI * this.radius;
var localData = new Array();
var displacement = 0;
var oldBatchLength = 0;
$.each(data, function(index, value) {
var riseLevels = value.segments;
var riseLevelCount = riseLevels.length;
if(oldBatchLength !=undefined){
displacement+=oldBatchLength;
}
var arcBatchLength = 2*Math.PI;
var arcPartition = arcBatchLength/riseLevelCount;
$.each(riseLevels, function( ri, value ) {
var startAngle = (ri*arcPartition);
var endAngle = ((ri+1)*arcPartition);
if(index!=0){
startAngle+=displacement;
endAngle+=displacement;
}
riseLevels[ri]["startAngle"] = startAngle;
riseLevels[ri]["endAngle"] = endAngle;
});
oldBatchLength = arcBatchLength;
localData.push(riseLevels);
});
var finalArray = new Array();
$.each(localData, function(index, value) {
$.each(localData[index], function(i, v) {
finalArray.push(v);
});
});
return finalArray;
},
generateArcs: function(chart, data){
var that = this;
//_arc paths
//append previous value to it.
$.each(data, function(index, value) {
if(that.oldData[index] != undefined){
data[index]["previousEndAngle"] = that.oldData[index].endAngle;
}
else{
data[index]["previousEndAngle"] = 0;
}
});
var arcpaths = that.arcpaths.selectAll("path")
.data(data);
arcpaths.enter().append("svg:path")
.attr("class", function(d, i){
return d.machineType;
})
.style("fill", function(d, i){
return d.color;
})
.transition()
.ease("elastic")
.duration(750)
.attrTween("d", arcTween);
arcpaths.transition()
.ease("elastic")
.style("fill", function(d, i){
return d.color;
})
.duration(750)
.attrTween("d",arcTween);
arcpaths.exit().transition()
.ease("bounce")
.duration(750)
.attrTween("d", arcTween)
.remove();
function arcTween(b) {
var prev = JSON.parse(JSON.stringify(b));
prev.endAngle = b.previousEndAngle;
var i = d3.interpolate(prev, b);
return function(t) {
return that.getArc()(i(t));
};
}
//_arc paths
var r = that.radius - 50;
var ir = that.radius + 90;
//__labels
var labels = that.labels.selectAll("text")
.data(data);
labels.enter()
.append("text")
.attr("text-anchor", "middle")
labels
.attr("x", function(d) {
var a = d.startAngle + (d.endAngle - d.startAngle)/2 - Math.PI/2;
d.cx = Math.cos(a) * (ir+((r-ir)/2));
return d.x = Math.cos(a) * (r + 20);
})
.attr("y", function(d) {
var a = d.startAngle + (d.endAngle - d.startAngle)/2 - Math.PI/2;
d.cy = Math.sin(a) * (ir+((r-ir)/2));
return d.y = Math.sin(a) * (r + 20);
})
.text(function(d) {
return d.color;
})
.each(function(d) {
var bbox = this.getBBox();
d.sx = d.x - bbox.width/2 - 2;
d.ox = d.x + bbox.width/2 + 2;
d.sy = d.oy = d.y + 5;
})
.transition()
.duration(300)
labels
.transition()
.duration(300)
labels.exit().remove();
//__labels
//__pointers
that.pointers.append("defs").append("marker")
.attr("id", "circ")
.attr("markerWidth", 6)
.attr("markerHeight", 6)
.attr("refX", 3)
.attr("refY", 3)
.append("circle")
.attr("cx", 3)
.attr("cy", 3)
.attr("r", 3);
var pointers = that.pointers.selectAll("path.pointer")
.data(data);
pointers.enter()
.append("path")
.attr("class", "pointer")
.style("fill", "none")
.style("stroke", "black")
.attr("marker-end", "url(#circ)");
pointers
.attr("d", function(d) {
if(d.cx > d.ox) {
return "M" + d.sx + "," + d.sy + "L" + d.ox + "," + d.oy + " " + d.cx + "," + d.cy;
} else {
return "M" + d.ox + "," + d.oy + "L" + d.sx + "," + d.sy + " " + d.cx + "," + d.cy;
}
})
.transition()
.duration(300)
pointers
.transition()
.duration(300)
pointers.exit().remove();
//__pointers
},
setup: function(data){
var chart = d3.select("#threshold").append("svg:svg")
.attr("class", "chart")
.attr("width", 420)
.attr("height", 420)
.append("svg:g")
.attr("class", "arcchart")
.attr("transform", "translate(200,200)");
this.arcpaths = chart.append("g")
.attr("class", "arcpaths");
this.labels = chart.append("g")
.attr("class", "labels");
this.pointers = chart.append("g")
.attr("class", "pointer");
this.generateArcs(chart, data);
},
getArc: function(){
var that = this;
var arc = d3.svg.arc()
.innerRadius(function(d, i){
return that.radius;
})
.outerRadius(function(d){
var maxHeight = 100;
var ratio = (d.height/maxHeight * 100)+that.radius;
return ratio;
})
.startAngle(function(d, i){
return d.startAngle;
})
.endAngle(function(d, i){
return d.endAngle;
});
return arc;
}
}
$(document).ready(function() {
var dataCharts = [
{
"data": [
{
"segments": [
{
height: 10,
color: "grey"
},
{
height: 40,
color: "darkgrey"
},
{
height: 33,
color: "grey"
},
{
height: 50,
color: "darkgrey"
},
{
height: 33,
color: "grey"
},
{
height: 10,
color: "darkgrey"
},
{
height: 50,
color: "grey"
},
{
height: 45,
color: "darkgrey"
},
{
height: 10,
color: "grey"
},
{
height: 40,
color: "darkgrey"
}
]
}
]
},
{
"data": [
{
"segments": [
{
height: 50,
color: "red"
},
{
height: 100,
color: "yellow"
},
{
height: 10,
color: "green"
}
]
}
]
}
];
var clone = jQuery.extend(true, {}, dataCharts);
arcGenerator.init(clone[0].data);
$(".testers a").on( "click", function(e) {
e.preventDefault();
var clone = jQuery.extend(true, {}, dataCharts);
var pos = $(this).parent("li").index();
arcGenerator.update(clone[pos].data);
});
});
A: There are two parts for this. First, the animation of the pointer lines. This is relatively easy and the only thing you're missing is that the .transition() is in the wrong place:
pointers
.transition()
.duration(300)
.attr("d", function(d) {
// etc
The second part is the animation of the text labels. This is a bit more difficult because their computation includes some side effects that allow the correct computation of the pointer lines. This comes in two parts -- the computation of the position and the computation of the extent of the displayed text. With that in mind, the changes are relatively straightforward, we just need to make sure that those computations take place before the transition starts:
labels.text(function(d) {
return d.color;
}).each(function(d) {
var a = d.startAngle + (d.endAngle - d.startAngle)/2 - Math.PI/2;
d.cx = Math.cos(a) * (ir+((r-ir)/2));
d.cy = Math.sin(a) * (ir+((r-ir)/2));
d.x = d.x || Math.cos(a) * (r + 20);
d.y = d.y || Math.sin(a) * (r + 20);
var bbox = this.getBBox();
d.sx = d.x - bbox.width/2 - 2;
d.ox = d.x + bbox.width/2 + 2;
d.sy = d.oy = d.y + 5;
})
First, the text itself is set. This is required to be able to use .getBBox() to determine its dimensions. Then, all the values required by the pointer paths are computed -- these bits of code were previously in the computation of the position of the text, but that's what we want to transition to so those values are set later (except for new text labels that don't have coordinates set).
All that remains now is to animate the change of coordinates of the text in the same way as before:
.transition()
.duration(300)
.attr("x", function(d) {
var a = d.startAngle + (d.endAngle - d.startAngle)/2 - Math.PI/2;
return d.x = Math.cos(a) * (r + 20);
})
.attr("y", function(d) {
var a = d.startAngle + (d.endAngle - d.startAngle)/2 - Math.PI/2;
return d.y = Math.sin(a) * (r + 20);
});
Complete example here.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 789 |
Il termine moderno sopranista, assente nella trattatistica storica preottocentesca, è stato talvolta usato per indicare i cantori evirati soprani. Pertanto, è impreciso denominare gli attuali falsettisti sopranisti perché gli uomini che oggi cantano le parti di soprano non sono cantori eunuchi, o castrati; questi ultimi sono scomparsi nel Novecento con Alessandro Moreschi.
In Cappella Sistina, dove sono stati in servizio appunto fino al Novecento, sia i falsettisti che i cantori castrati erano detti semplicemente soprani.
Nella traduzione de La musique mise a la portée de tout le monde, pubblicata in Italia con il titolo La musica accomodata alla intelligenza di tutti, François-Joseph Fétis chiama sopranisti Giacinto Fontana (soprannominato Farfallino), Antonio Pasi e Pier Francesco Tosi, celebri soprani castrati; inoltre, indica con il termine 'soprano' sia le donne che altri castrati, come Andrea Martini, detto Senesino (1761-1819, diverso dal più noto Senesino Francesco Bernardi vissuto tra il 1686 e il 1758), anch'egli evirato. Fétis usa la parola francese sopraniste per riferirsi a due insegnanti di canto di Benedetta Rosamunda Pisaroni, entrambi castrati (Moschini, al servizio del viceré d'Italia a Milano, e Marchesi; p. 54 di Curiosités historique de la musique, complemento a La musique mise a la portée de tout le monde).
I moderni falsettisti praticano oggi soprattutto il repertorio che va dalla fine del XVI secolo e il XVIII secolo perché fu quello il periodo aureo nel quale prosperarono i più famosi cantanti evirati, come il celebre Farinelli, e i maggiori compositori scrissero un considerevole numero di opere musicali per queste voci, spesso con parti virtuosistiche.
Il famosissimo cantante e didatta Pier Francesco Tosi scrisse nel 1723 il primo trattato sulla tecnica del canto, Opinioni de' cantori antichi e moderni, riferendo molte interessanti notizie su questi straordinari cantori del passato; Tosi non usò mai la parola 'sopranista', né per riferirsi a sé, né agli altri cantanti. Piuttosto, i soprani evirati erano detti anche 'soprani naturali' per distinguere la condizione 'naturalmente' acuta della loro voce. Infatti, già nel 1640 Pietro della Valle scriveva nella nota epistola a Lelio Guidiccioni, Della musica dell'età nostra: «Ma lasciando delle altre voci, per dire un poco de' soprani, che sono il maggiore ornamento della musica, V. S. vuol paragonare i falsetti di quei tempi co' i soprani naturali de' castrati che ora abbiamo in tanta abbondanza».
Note
Bibliografia
Castrati, in Dizionario Enciclopedico Universale della Musica e dei Musicisti, ISBN 88-02-03732-9
Canto (II-IV), Ibidem
Pier Francesco Tosi, Opinioni de' Cantori Antichi e Moderni, Bologna, Lelio Dalla Volpe, 1723 (un esemplare d'epoca privo di indicazioni editoriali è reperibile digitalizzato presso Internet Archive) – Ristampa con note ed esempi di Luigi Leonesi, Napoli, Di Gennaro & Morano, 1904; ristampa anastatica, Bologna, Forni, 1985.
Voci correlate
Muta vocale
Voci bianche
Castrato
Contraltista
Registri vocali | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,259 |
/**
* @typedef {Object} sap.ui.layout.BlockRowColorSets
* @typedef {Object} sap.ui.layout.BlockLayoutRow
*/
sap.ui.define(['jquery.sap.global', 'sap/ui/core/Control', './library', 'sap/ui/layout/BlockLayoutCellData'],
function(jQuery, Control, library, BlockLayoutCellData) {
"use strict";
// shortcut for sap.ui.layout.BlockBackgroundType
var BlockBackgroundType = library.BlockBackgroundType;
// shortcut for sap.ui.layout.BlockRowColorSets
var BlockRowColorSets = library.BlockRowColorSets;
/**
* Constructor for a new BlockLayoutRow.
*
* @param {string} [sId] ID for the new control, generated automatically if no ID is given
* @param {object} [mSettings] Initial settings for the new control
*
* @class
* The BlockLayoutRow is used as an aggregation to the BlockLayout. It aggregates Block Layout cells.
* The BlockLayoutRow has 2 rendering modes - scrollable and non scrollable.
* @extends sap.ui.core.Control
*
* @author SAP SE
* @version ${version}
*
* @constructor
* @public
* @since 1.34
* @alias sap.ui.layout.BlockLayoutRow
* @ui5-metamodel This control/element also will be described in the UI5 (legacy) designtime metamodel
*/
var BlockLayoutRow = Control.extend("sap.ui.layout.BlockLayoutRow", {
metadata: {
library: "sap.ui.layout",
properties: {
/**
* Sets the rendering mode of the BlockLayoutRow to scrollable. In scrollable mode, the cells get
* aligned side by side, with horizontal scroll bar for the row.
*/
scrollable: {type: "boolean", group: "Appearance", defaultValue: false},
/**
* Defines background type for that row.
* There might be several rows with the same type
* @since 1.42
*/
rowColorSet: {type: "sap.ui.layout.BlockRowColorSets", group: "Appearance"}
},
defaultAggregation: "content",
aggregations: {
/**
* The content cells to be included in the row.
*/
content: {type: "sap.ui.layout.BlockLayoutCell", multiple: true, singularName: "content"}
},
associations: {
/**
* Cells that would be accented.
* *Note:* This association has visual impact only for BlockLayouts with background types "Mixed" and "Accent".
*
* Mixed: In this type, areas of 25% (on desktop) can have a dark background color. Per section one area can be dark.
* Accent: Every section can contain multiple gray blocks, which are used alternately, beginning with the bright one
*
* @since 1.42
*/
accentCells: {type: "sap.ui.layout.BlockLayoutCell", multiple: true, singularName: "accentCell"}
},
designtime: "sap/ui/layout/designtime/BlockLayoutRow.designtime"
}
});
BlockLayoutRow.prototype.init = function () {
this._applyLayoutData = {};
};
BlockLayoutRow.prototype.addContent = function (oContent) {
this._ensureLayoutData(oContent);
return this.addAggregation("content", oContent);
};
BlockLayoutRow.prototype.insertContent = function(oContent, index) {
this._ensureLayoutData(oContent);
return this.insertAggregation("content", oContent, index);
};
/**
* Performs guidelines check
*/
BlockLayoutRow.prototype.onBeforeRendering = function () {
var aCells = this.getContent(),
that = this;
aCells.forEach(function (oCell, index) {
oCell._setParentRowScrollable(that.getScrollable());
});
this._calculateBreakpointRendering();
};
/**
* Changes dynamically row color set
* Note: this might invalidate cells inside and also change color sets of the other BlockLayoutRow-s below it.
* @public
* @method
* @param {sap.ui.layout.BlockRowColorSets} sType
* @since 1.42
* @returns {sap.ui.layout.BlockLayoutRow}
*/
BlockLayoutRow.prototype.setRowColorSet = function (sType) {
// Apply here so if there's an exception the code bellow won't be executed
var aArgs = Array.prototype.slice.call(arguments),
oObject = Control.prototype.setProperty.apply(this, ["rowColorSet"].concat(aArgs)),
sClassName = "sapUiBlockLayoutBackground" + sType,
oBlockLayout = this.getParent(),
sBackground = oBlockLayout && oBlockLayout.getBackground(),
iThisIndexInParent = oBlockLayout && oBlockLayout.indexOfAggregation("content", this),
aParentContent = oBlockLayout && oBlockLayout.getContent(),
oPrevBlockRow = (iThisIndexInParent && aParentContent[iThisIndexInParent - 1]) || null,
oNextBlockRow = (aParentContent && aParentContent[iThisIndexInParent + 1]) || null,
oBlockRowColorSets = BlockRowColorSets,
aColorSets = Object.keys(oBlockRowColorSets).map(function (sKey) {
return oBlockRowColorSets[sKey];
}),
bInvertedColorSet = false;
if (oPrevBlockRow && oPrevBlockRow._hasStyleClass(sClassName, sBackground, bInvertedColorSet, sType)) {
sClassName += "Inverted";
bInvertedColorSet = true;
}
aColorSets.forEach(function (sCurType) {
var sColorSetStyle = "sapUiBlockLayoutBackground" + sCurType,
sInvertedColorSetStyle = sColorSetStyle + "Inverted";
if (this._hasStyleClass(sColorSetStyle, sBackground, false, sCurType)) {
this.removeStyleClass(sColorSetStyle, true);
} else if (this._hasStyleClass(sInvertedColorSetStyle, sBackground, true, sCurType)) {
this.removeStyleClass(sInvertedColorSetStyle, true);
}
}, this);
this.addStyleClass(sClassName, true);
// If the next row is of the same type and has the same CSS class, recalculate it and cascade
if (oNextBlockRow && oNextBlockRow._hasStyleClass(sClassName, sBackground, bInvertedColorSet, sType)) {
oNextBlockRow.setRowColorSet.apply(oNextBlockRow, aArgs);
}
// Invalidate the whole row as the background dependencies, row color sets and accent cells should be resolved properly
this.invalidate();
return oObject;
};
BlockLayoutRow.prototype.addAccentCell = function (vId) {
var oObject,
sId = vId && vId.getId ? vId.getId() : vId,
args = Array.prototype.slice.call(arguments),
oBackgrounds = BlockBackgroundType,
oBlockLayout = this.getParent(),
sLayoutBackground = oBlockLayout && (oBlockLayout.getBackground() || "");
oObject = this.addAssociation.apply(this, ["accentCells"].concat(args));
if (!oBlockLayout) {
return this;
}
if ([oBackgrounds.Accent, oBackgrounds.Mixed].indexOf(sLayoutBackground) === -1) {
jQuery.sap.log.warning(sId + " was not se as accent cell. Accent cells could be set only for 'Accent' and 'Mixed' layout backgrounds.");
return this;
}
if (oBackgrounds.Mixed === sLayoutBackground) {
this._processMixedCellStyles(sId, this.getContent());
} else if (oBackgrounds.Accent === sLayoutBackground) {
this._processAccentCellStyles(this.getAccentCells(), this.getContent());
}
return oObject;
};
BlockLayoutRow.prototype._ensureLayoutData = function (oContent) {
var oOldData = oContent.getLayoutData();
if (!oOldData || !(oOldData instanceof BlockLayoutCellData)) {
oContent.setLayoutData(new BlockLayoutCellData());
}
};
BlockLayoutRow.prototype._onParentSizeChange = function (currentSize) {
this._currentSize = currentSize;
this._calculateBreakpointRendering();
this.invalidate();
};
BlockLayoutRow.prototype._getCellArangementForCurrentSize = function () {
if (!this._arrangements || !this._currentSize) {
return null;
}
return this._arrangements[this._currentSize];
};
BlockLayoutRow.prototype._calculateBreakpointRendering = function () {
if (!this._currentSize) {
return;
}
this._arrangements = {
//For S we take the data from the LayoutData of the cells
"S": this._calcArrangementForSize("S"),
//For M we take the data from the LayoutData of the cells
"M": this._calcArrangementForSize("M"),
//For L we take the data from the LayoutData of the cells
"L": this._calcArrangementForSize("L"),
//For Xl we take the data from the LayoutData of the cells
"XL": this._calcArrangementForSize("Xl")
};
};
/**
* Calculates each row for the corresponding arrangement size.
* @private
* @method
* @param {string} sSizeName The size that needs to be calculated
* @returns {[*]}
*/
BlockLayoutRow.prototype._calcArrangementForSize = function (sSizeName) {
var aContent = this.getContent();
if (aContent.length >= 3 && sSizeName === "M" && aContent.length < 5) {
return this._generateArrangementForMCase();
} else {
return this._generateArrangement(sSizeName);
}
};
BlockLayoutRow.prototype._generateArrangement = function (sSizeName) {
var oLayoutData,
iIndex = 0,
aFlatData = [],
aBreakOn = [],
aArrangement = [[]],
aContent = this.getContent();
aContent.forEach(function (oCell) {
oLayoutData = oCell.getLayoutData();
aBreakOn.push(oLayoutData["breakRowOn" + sSizeName + "Size"]);
aFlatData.push(oLayoutData["get" + sSizeName + "Size"]());
});
aFlatData.forEach(function (iData, i) {
aArrangement[iIndex].push(iData);
if (aBreakOn[i + 1]) {
iIndex++;
aArrangement[iIndex] = [];
}
});
return aArrangement;
};
BlockLayoutRow.prototype._generateArrangementForMCase = function () {
var aContent = this.getContent();
if (aContent.length === 3 && this._isAllCellsHasSameWidth("M")) {
return [[1, 1, 1]];
} else if (aContent.length === 3) {
return [[1, 1], [1]]; // This is the case where we have for example 25% 25% 50%
} else if (aContent.length === 4) {
return [[1, 1], [1, 1]];
}
};
BlockLayoutRow.prototype._isAllCellsHasSameWidth = function (sSizeName) {
var iCurrentRowSize,
aContent = this.getContent(),
iFirstRowSize = aContent[0].getLayoutData()["get" + sSizeName + "Size"]();
for (var i = 1; i < aContent.length; i++) {
iCurrentRowSize = aContent[i].getLayoutData()["get" + sSizeName + "Size"]();
if (iCurrentRowSize !== iFirstRowSize) {
return false;
}
}
return true;
};
/**
* Adjusts accents cells for Mixed background layout
* @private
* @method
* @param {string} sId The ID of the row that will be processed
* @param {Array} aCells Cells in the current row
* @returns {sap.ui.layout.BlockLayoutRow}
*/
BlockLayoutRow.prototype._processMixedCellStyles = function (sId, aCells) {
var oBlockLayout, bProcessAccentCells;
if (!aCells || !aCells.length) {
jQuery.sap.log.warning("No accent cells were set");
return this;
}
oBlockLayout = this.getParent();
bProcessAccentCells = oBlockLayout && (oBlockLayout.hasStyleClass("sapUiBlockLayoutSizeL") || oBlockLayout.hasStyleClass("sapUiBlockLayoutSizeXL"));
aCells.forEach(function (oCell) {
var oColorSets, bUseContrast2;
// Accent only on a cell with 25% width and L, XL sizes
if (bProcessAccentCells && oCell.getId() === sId && oCell.getWidth() === 1) {
oCell.addStyleClass("sapContrast").addStyleClass("sapContrastPlus");
oColorSets = BlockRowColorSets;
bUseContrast2 = this._hasStyleClass("sapUiBlockLayoutBackground" + oColorSets.ColorSet1, BlockBackgroundType.Mixed, false, oColorSets.ColorSet1) ||
this._hasStyleClass("sapUiBlockLayoutBackground" + oColorSets.ColorSet1, BlockBackgroundType.Mixed, true, oColorSets.ColorSet1);
if (bUseContrast2) {
oCell.addStyleClass("sapUiBlockLayoutBackgroundContrast2");
}
} else if ((!bProcessAccentCells || oCell.getId() !== sId) && (oCell.hasStyleClass("sapContrast") || oCell.hasStyleClass("sapContrastPlus"))) {
oCell.removeStyleClass("sapContrast").removeStyleClass("sapContrastPlus").removeStyleClass("sapUiBlockLayoutBackgroundContrast2");
this.removeAssociation("accentCells", oCell);
jQuery.sap.log.warning(sId + " was removed as accent cell. Only one cell at a time could be accented for Mixed layout background");
}
}, this);
return this;
};
/**
* Adjusts accents cells for Accent background layout.
* @private
* @method
* @param {Array} aAccentCells Cells with accent contrast
* @param {Array} aRowCells All cells in the row
* @returns {sap.ui.layout.BlockLayoutRow}
*/
BlockLayoutRow.prototype._processAccentCellStyles = function (aAccentCells, aRowCells) {
var oCell, sCellId, sCalculatedStyleClass,
iIndex = 0,
iInvertCellColorsModulo = 0,
aAccentCellsCopy = Array.prototype.slice.call(aAccentCells);
if (!aAccentCells || !aAccentCells.length) {
jQuery.sap.log.warning("No accent cells were set");
return this;
}
// Find the index of current accented cell and check if it should be of Accent type 1 OR 2
for (iIndex = 0; iIndex < aRowCells.length; iIndex++) {
oCell = aRowCells[iIndex];
sCellId = oCell.getId();
if (!aAccentCellsCopy.length) {
break;
}
if (aAccentCellsCopy.indexOf(sCellId) > -1) {
iInvertCellColorsModulo++;
sCalculatedStyleClass = "sapUiBlockLayoutBackgroundColorSetGray" + ((iInvertCellColorsModulo % 2) + 1);
// If the cell already has the expected class, shouldn't loop further as everything below is already adjusted
if (oCell.hasStyleClass(sCalculatedStyleClass)) {
continue;
}
// Optimise a bit the next loop iteration
aAccentCellsCopy.splice(aAccentCellsCopy.indexOf(sCellId), 1);
oCell
.removeStyleClass("sapUiBlockLayoutBackgroundColorSetGray1")
.removeStyleClass("sapUiBlockLayoutBackgroundColorSetGray2")
.addStyleClass(sCalculatedStyleClass);
}
}
return this;
};
/**
* Checks for specific cases when two row color sets share the same colors e.g. Light and Mixed backgrounds.
* @private
* @method
* @param {string} sStyleClass
* @param {sap.ui.layout.BlockBackgroundType} sLayoutBackground Background type of the <code>BlockLayout</code>
* @param {boolean} bIsColorInverted Determines if the color inverted
* @param {sap.ui.layout.BlockRowColorSets} sType The current color set of the given row
* @returns {boolean} Determines if the row contains the class
*/
BlockLayoutRow.prototype._hasStyleClass = function (sStyleClass, sLayoutBackground, bIsColorInverted, sType) {
var oBackgrounds = BlockBackgroundType,
oColorSets = BlockRowColorSets,
i, aStyleClasses, aEqualSets;
// Check if this is NOT Mixed or Light background and just do the normal check
if ([oBackgrounds.Light, oBackgrounds.Mixed].indexOf(sLayoutBackground) === -1) {
return this.hasStyleClass(sStyleClass);
} else if (this.hasStyleClass(sStyleClass)) { // Check if this class is there and don't continue further
return true;
}
// Define array with equal sets
aEqualSets = [
[oColorSets.ColorSet1, oColorSets.ColorSet3],
[oColorSets.ColorSet2, oColorSets.ColorSet4]
];
// Find on which index is sType
for (i = 0; i <= aEqualSets.length; i++) {
if (aEqualSets[i] && aEqualSets[i].indexOf(sType) > -1) {
break;
}
}
// If it's not found there, then return false, as if the class was inside, it would fulfill the first hasStyleClass above
if (!aEqualSets[i]) {
return false;
}
// Build class strings to check against
aStyleClasses = aEqualSets[i].map(function (sColorSet) {
return "sapUiBlockLayoutBackground" + sColorSet + (bIsColorInverted ? "Inverted" : "");
});
// Check if any of the classes is inside
return aStyleClasses.some(this.hasStyleClass, this);
};
return BlockLayoutRow;
});
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,660 |
ulreullib
=========
When you want to use that combined between a Non-Korean noun clause and Korean postposition(은/는, 을/를, 이/가, 으로/로, 와/과), The Korean first postposition character should be chosen by whether a consonant in aspect of the pronunciation of the noun clause is or not. This project helps you who want to generate a statement like this automatically.
| {
"redpajama_set_name": "RedPajamaGithub"
} | 1,112 |
package com.imc.mobile.android;
import java.util.ArrayList;
import java.util.HashMap;
import com.imc.mobile.android.R;
import android.app.Activity;
import android.content.Context;
import android.graphics.Typeface;
import android.view.LayoutInflater;
import android.view.View;
import android.view.ViewGroup;
import android.widget.BaseAdapter;
import android.widget.ImageView;
import android.widget.TextView;
public class IMCPostAdapter extends BaseAdapter{
private Activity activity;
private ArrayList<HashMap<String,Object>> data;
private static LayoutInflater inflater=null;
public ImageLoader imageLoader;
public Typeface face;
public IMCPostAdapter(Activity a, ArrayList<HashMap<String,Object>> d) {
activity = a;
data=d;
inflater = (LayoutInflater)activity.getSystemService(Context.LAYOUT_INFLATER_SERVICE);
face=Typeface.createFromAsset(a.getAssets(), "Roboto-Light.ttf");
imageLoader=new ImageLoader(activity.getApplicationContext());
}
public int getCount() {
return data.size();
}
public Object getItem(int position) {
return position;
}
public long getItemId(int position) {
return position;
}
public View getView(int position, View convertView, ViewGroup parent) {
View vi=convertView;
if(convertView==null)
vi = inflater.inflate(R.layout.postlist_item, null);
TextView title = (TextView)vi.findViewById(R.id.Title);
TextView excerpt = (TextView)vi.findViewById(R.id.Excerpt);
TextView PostID = (TextView)vi.findViewById(R.id.ID);
ImageView thumb_image=(ImageView)vi.findViewById(R.id.PostImg);
TextView CmtCnt = (TextView)vi.findViewById(R.id.CmtCnt);
TextView LikeCnt = (TextView)vi.findViewById(R.id.LikeCnt);
HashMap<String, Object> post = new HashMap<String, Object>();
post = data.get(position);
// Setting all values in listview
title.setText(post.get(ConstUtilities.Node_Title).toString());
excerpt.setText(post.get(ConstUtilities.Node_Excerpt).toString());
PostID.setText(post.get(ConstUtilities.Node_ID).toString());
CmtCnt.setText(post.get(ConstUtilities.Node_CommentCnt).toString());
LikeCnt.setText(post.get(ConstUtilities.Node_LikeCnt).toString());
//Setting up font
title.setTypeface(face);
excerpt.setTypeface(face);
CmtCnt.setTypeface(face);
LikeCnt.setTypeface(face);
imageLoader.DisplayImage(post.get(ConstUtilities.Node_Image).toString(), thumb_image);
return vi;
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 5,953 |
Jürg Häusermann (born 1951) is a Swiss-German media scholar and emeritus professor. He studied Germanic, Russian language and literature and French linguistics at the University of Zurich and the Moscow State Linguistic University. Häusermann doctorate in 1977 in Zurich. 1985 to 1989 he was visiting professor at the University of Trieste in Italy. From 1993 to 2017, Häusermann was professor of media analysis and production at the University of Tübingen. He was director of the German seminar at Tübingen.
Works
Journalistisches Texten. 3rd edition. Konstanz: UVK, 2011.
Radio. Tübingen: Niemeyer, 1998.
External links
http://www.rhet.de/
1951 births
Living people
People from Winterthur
Linguists from Switzerland
Swiss mass media scholars
Academic staff of the University of Trieste
Academic staff of the University of Tübingen
University of Zurich alumni | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 6,113 |
Domenick Ammirati
Justine Kurland, SCUMB Manifesto
Justine Kurland's latest exhibition "SCUMB Manifesto" found her swerving for the first time from photography to a more plastic medium and a loosely conceptual framework, yet with her usual mode of expression still in mind. Kurland has taken up collage, but with a provocative and very specific set of raw materials: The artist culled her extensive photo-book library of its roughly 150 volumes by white men and went at them with an X-Acto. SCUMB (Society for Cutting Up Men's Books) is, obviously, a tribute to Valerie Solanas's hilarious, violent, and critically perspicacious SCUM Manifesto (1967). As a kind of coup de grâce, when showtime rolled around Kurland offered to sell each of the sixty-five artworks she'd completed to the man whose imagery she'd reconfigured. Not a single one took her up on the offer.
If Kurland had scripted that response herself, it could not have been more perfect. A geek-macho culture has pervaded photography throughout what one might call its classical postwar form—that is, the cargo-vest, it's-an-art, women-are-beautiful, put-us-in-MoMA, tenure-us-at-Yale form, with a champagne coupe of fashion sleaze on the side. Sure, the executor of, say, Roman Vishniac's estate may have been befuddled to receive Kurland's unexpected sales pitch. But half the artists are living, and many of them are, I would hazard, of Kurland's acquaintance. Come on, gentlemen. I know money is tight these days, but we all nearly just died in a pandemic. Can't you take a joke?
The collages make an impressive addition to Kurland's already exceptional oeuvre, with its explorations of girl- and womanhood, the American landscape, marginal characters, and dilapidated fantasies of freedom. The new works are skillful, versatile, and refreshingly analog—yes to the cut-and-paste of Jess or Linder, no to the aesthetics of Photoshop (in keeping with the artist's continuing dedication to film). The splayed, stripped-off covers from the mostly hardbound volumes—each one comprising the tome's full front, spine, and back—serve as grounds for the books' diced-up contents. The results show off a vibrant array of logics and styles. Paris by Night, 2020, for example, turns an image of a sinuous cobblestoned gutter on its side, making it the central arch of an elegant, mysterious composition that evokes a machinic form of Surrealism. Think of England, 2021, with its synthetic colors, canned goods, and bisected Pegasus, has a Pop feel, pace Richard Hamilton. Hustlers, 2019, and Hustlers (Kate's Copy), 2021—made from Philip-Lorca diCorcia's portraits of sex workers—the subjects absent from their sidewalks and motel rooms, are intricate yet ghostly memento mori.
Despite the rigorous formalism on display, the exhibition does feature many moments of satire and critique. Take the ironically titled Exhibit A, 2020, which reconstitutes Guy Bourdin's work as a long splay of women's body parts, mostly legs, with a trained seal begging for a fish in the upper-right corner. The Man, the Image, & the World, 2020, riffs on the objectivist impulse, classifying clipped limbs, faces, and so on into columns bracketing a tondo of headless, suit-clad men who orbit a cadre of rifles. In Nudes, 2021, a welter of dissected female bodies spell out the artist's first name, with a nipple dotting the I. Twilight, 2021, rooted in a familiar suburban gothic, studs a thin landscape of clunky trees and lampposts with taxidermied fauna, while moody empty interiors lurk below in the universal psychic basement. Meanwhile, at center, a pregnant woman with a distended belly is just missed by the rays of an anxious moon.
In the end, "SCUMB Manifesto" made an incisive point about art history and history in general. The virtuous gallerygoer, the conscientious citizen, is trained to see what's in front of them in light of the past. But for an exhibition that, Solanas style, cuts an antique, patriarchal history down to size, how relevant should yesterday be? Kurland's staging of this conundrum, dismissing the male figures behind her images while consistently calling them to account, makes yet another incisive point: The past can't just vanish with a finger snap, but rather must be dealt with in a complex case-by-case way—preferably a gleeful one, and maybe involving a razor. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,619 |
Q: Is there a way to sync Dynamics CRM contacts to surveymonkey? Is there a way to sync Dynamics CRM contacts to surveymonkey? I would like to find a syncing app which can automatically import all my Dynamics CRM contacts to Surveymonkey. It would make my workflow much easier, instead of uploading CSV files... Any ideas? Someone?
A: Power Automate would be a good solution for what you're looking to achieve.
Power Automate will effectively let you integrate practically any service that uses an API using a concept of connectors. survey monkey has a connector for power Automate, however you may have to create a custom connector to perform bulk data uploads - I checked the survey monkey connector and it does not have a lot of actions - https://learn.microsoft.com/en-gb/connectors/surveymonkey/#actions
Your Power Automate flow can be created to run on a daily basis to move data between dynamics and Survey Monkey
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,094 |
Q: How to Implement Values for New Registered User Based On Their Score? What I'm trying to code for my advanced software project is the program filling random integer values depending on the value of the user's overall score into my SQL database once a user has registered an account. I'm having trouble on how to generate these values and put them into my database.
I've tried to give one of the values a random number within a certain range, but Java Eclipse has been giving me errors.
This is the method code that I have so far:
public void setUser(String user, Stage registerStage) throws Exception {
String userlist = "INSERT INTO users (uid, username, email, password) VALUES(?, ?, ?, ?)";
String overviewlist = "INSERT INTO user_overview (pid, gamertag, score, wins, goals, saves, shots, assists) VALUES(?, ?, ?, ?, ?, ?, ?, ?)";
int uid = 1;
int pid = 1;
double minScore = 400000.0;
double maxScore = 10000000.0;
int minWins = 500;
int maxWins = 15000;
int minGoals = 500;
int maxGoals = 15000;
int minSaves = 500;
int maxSaves = 15000;
int minShots = 500;
int maxShots = 15000;
int minAssists = 500;
int maxAssists = 15000;
try {
Class.forName("com.mysql.cj.jdbc.Driver");
// Class.forName("com.mysql.jdbc.Driver");
System.out.println("Driver is Loaded");
String strConnect = "jdbc:mysql://localhost/RLDATA";
Connection connection = DriverManager.getConnection(strConnect,"root","");
System.out.println("Database connected");
PreparedStatement userstmt = connection.prepareStatement(userlist, Statement.RETURN_GENERATED_KEYS);
PreparedStatement overviewstmt = connection.prepareStatement(overviewlist, Statement.RETURN_GENERATED_KEYS);
String username = tfUsername.getText();
String email = tfEmail.getText();
String password = pfCPassword.getText();
double ranScore = ThreadLocalRandom.current().nextDouble(minScore, maxScore + 1);
if (ranScore <= 1000000.0) {
}
userstmt.setInt(1, uid);
userstmt.setString(2, username);
userstmt.setString(3, email);
userstmt.setString(4, password);
overviewstmt.setInt(1, pid);
overviewstmt.setString(2, username);
overviewstmt.setDouble(3, ranScore);
overviewstmt.setString(2, username);
overviewstmt.setString(2, username);
overviewstmt.setString(2, username);
overviewstmt.setString(2, username);
overviewstmt.setString(2, username);
ResultSet rs = userstmt.getGeneratedKeys();
ResultSet rs2 = overviewstmt.getGeneratedKeys();
if(rs.next()) {
uid = rs.getInt(1);
}
if(rs2.next()) {
pid = rs2.getInt(1);
}
userstmt.executeUpdate();
Alert alert = new Alert(AlertType.INFORMATION);
alert.setTitle("Successful Registration");
alert.setHeaderText("Successful Registration");
String s = "You have successfuly registered as " + user;
alert.setContentText(s);
alert.showAndWait();
System.out.println("Sucess");
registerStage.close();
}
catch(SQLException ex) {
ex.printStackTrace();
}
}
Here is the database table for my project:
DROP DATABASE IF EXISTS RLData;
CREATE DATABASE RLData;
USE RLData;
DROP TABLE IF EXISTS `overview` ;
CREATE TABLE IF NOT EXISTS `users` (
`uid` INT NOT NULL,
`username` VARCHAR(45) NOT NULL,
`email` VARCHAR(50) NOT NULL,
`password` VARCHAR(30) NOT NULL,
PRIMARY KEY (`uid`))
ENGINE = InnoDB;
CREATE TABLE IF NOT EXISTS `user_overview` (
`pid` INT NOT NULL,
`gamertag` VARCHAR(45) NOT NULL,
`score` DECIMAL(10, 1) NOT NULL,
`wins` INT(10) NOT NULL,
`goals` INT(10) NOT NULL,
`saves` INT(10) NOT NULL,
`shots` INT(10) NOT NULL,
`assists` INT(10) NOT NULL,
PRIMARY KEY (`pid`))
ENGINE = InnoDB;
CREATE TABLE IF NOT EXISTS `player_overview` (
`pid` INT NOT NULL,
`gamertag` VARCHAR(45) NOT NULL,
`score` DECIMAL(10, 1) NOT NULL,
`wins` INT(10) NOT NULL,
`goals` INT(10) NOT NULL,
`saves` INT(10) NOT NULL,
`shots` INT(10) NOT NULL,
`assists` INT(10) NOT NULL,
PRIMARY KEY (`pid`))
ENGINE = InnoDB;
INSERT INTO users (uid, username, email, password) VALUES
(0, 'sushhhiii', 'rocketleagueuser@gmail.com', 6543654365);
INSERT INTO user_overview (pid, gamertag, score, wins, goals, saves, shots, assists) VALUES
(0, 'sushhhiii', 2688518.2, 3032, 14811, 9918, 28633, 1920);
INSERT INTO player_overview (pid, gamertag, score, wins, goals, saves, shots, assists) VALUES
(1, 'TheCar', 3803677.6, 7744, 25550, 17305, 52249, 6777),
(2, 'Savvy', 5482247.6, 10131, 29975, 24410, 66393, 10946),
(3, 'oKhaliD', 2043555.4, 2480, 8448, 9192, 17931, 2485),
(4, 'xXander', 1631656.8, 5845, 22639, 13709, 43530, 4656),
(5, 'SML', 5372512.7, 11719, 30564, 27461, 71700, 13486),
(6, 'Killerican', 3784957.5, 9597, 42526, 26680, 82977, 8781),
(7, 'Zeldris', 832783.2, 982, 3359, 2311, 6980, 853),
(8, 'mectos', 2761034.4, 3391, 14711, 11522, 29624, 2472),
(9, 'Scrub Killa', 1053493.9, 11791, 40630, 31134, 86571, 12014),
(10, 'kuxir97', 3993712.8, 12911, 43379, 31458, 95550, 15677),
(11, 'Emre', 999486.9, 1396, 3473, 3651, 7434, 1210),
(12, 'BuZayed', 1458886.4, 2175, 7220, 4209, 14018, 1644),
(13, 'kinseh', 711179.4, 943, 4425, 2639, 7799, 367),
(14, 'King Ranny', 5991440.5, 13871, 58022, 37892, 119366, 13149),
(15, 'Brisky', 2067200.1, 2709, 7845, 5804, 17035, 2402),
(16, 'Firstkiller', 3044781.2, 6253, 19687, 20052, 43381, 7180),
(17, 'Mijo.', 4777480.5, 9107, 25237, 19222, 57470, 10461),
(18, 'Tuster', 873322.3, 1044, 4058, 2503, 8277, 890),
(19, 'eekso', 4969356.2, 7904, 31823, 21032, 62533, 7039),
(20, 'DanielAlmelo', 437627.9, 547, 1636, 1623, 3672, 472),
(21, 'Jwols', 3519406.0, 7365, 20147, 17157, 44556, 7551),
(22, 'Roll Dizz', 4865837.5, 10653, 30799, 27807, 67736, 11034),
(23, 'Oghma', 524124.3, 741, 2207, 1777, 4678, 706),
(24, 'OSM', 490561.7, 622, 2493, 1898, 4605, 462),
(25, 'Tx0', 1914821.8, 4948, 13266, 8940, 26778, 4407);
-- Create a user named mgs_user
GRANT SELECT, INSERT, UPDATE, DELETE
ON *
TO mgs_user@localhost
IDENTIFIED BY 'pa55word';
Also, here is my database table with the players and their score values:
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,337 |
\section{Introduction} \label{Introduction}
The de Rham-Hodge theory reveals that the cohomology of an oriented closed Riemannian manifold can be represented by harmonic forms. It also holds for an oriented compact Riemannian manifold with boundary by forcing certain boundary conditions, such as absolute and relative cohomology~\cite{ray1971r}. This theory has been proved to be fundamentally important throughout algebraic geometry. It studies differential geometry and algebraic topology with partial differential equations (PDEs). The understanding of the de Rham-Hodge theory requires a variety of contemporary mathematical techniques including differential geometry, algebraic geometry, elliptic PDE, abstract algebra, topology, et al.
The de Rham-Hodge theory has a wide range of applications, including not only mathematics, but also graphics/visualization~\cite{tong2003discrete, zhao20193d}, physics/fluids~\cite{foster1996realistic}, vision/robotics~\cite{gao2010singular,mochizuki2009spatial} and astrophysics/geophysics~\cite{mansour2004turbulence,akram2010regularisation}. Among all these applications, most of them rely upon the Hodge theory result, i.e., the Helmholtz-Hodge decomposition. It is one of the fundamental theorems in dynamical problems, describing a vector field into the gradient and curl components.
Due to the orthogonal decomposition, the analysis of vector fields becomes easier since certain properties such as incompressibility and vorticity of fluid dynamics can be studied on the orthogonal subspace. Such an orthogonal decomposition was first applied on a finite-dimensional compact manifold without boundary~\cite{hodge1989theory}, and then was developed for manifolds with boundaries~\cite{shonkwiler2009poincare}. Pushed by the visualization community, the implementation of orthogonal decomposition integrates a variety of boundary conditions with discrete vector fields expressed as discrete differential forms into two potential fields and harmonic fields~\cite{zhao20193d}. The boundary conditions of the decomposition preserve orthogonality. The duality revealed by tangential and normal boundary conditions provides compact spectral representations of the Laplace operators in the de Rham-Hodge theory. The spectra of de Rham-Laplace operators provide a quantitative approach to understanding topological spaces and geometry characteristics of manifolds and have been applied to biomolecular modeling and analysis \cite{zhao2019rham}. The development of discrete exterior calculus (DEC) is the driving force for de Rham-Hodge theory analysis and application \cite{arnold2006finite,desbrun2008discrete}.
Over half a century ago, Kac asked a famous question, ``can one hear the shape of a drum?'' \cite{kac1966can}. Zelditch noticed that different drums may be distinguished by imposing restrictions with analytic boundary \cite{zelditch2000spectral}. However, the traditional spectral analysis cannot fully resolve the shape of a drum due to the isospectrum from different geometric shapes. Innovative theoretical development is required to solve this long-standing spectral geometry problem.
In the last few decades, geometric analysis has made great progress in understanding shapes that evolve in time. Geometric flows~\cite{willmore2013introduction} or geometric evolution equations have been extensively studied in mathematics~\cite{spruck1991motion,gomes2001using,mikula2004direct}, and many processes by which a curve or surface can evolve, such as the Gauss curvature flow and the mean curvature flow. Numerical techniques based on level sets were devised by Osher and Sethian~\cite{osher1988fronts} and have been extended and applied by many others in geometric flow analysis~\cite{wei2010differential,cecil2005numerical,du2004phase}. More recently, as the progress in contemporary life sciences, a large number of problems of unveiling the structure-function relationship of biomolecules and understanding of biomolecular systems, requires multiscale geometric modeling and analysis ~\cite{bates2008minimal,wei2010differential,chen2011differential}. However, compared with the investigations on curves and surfaces, a small amount of geometric explorations focuses on the evolution of compact manifolds specific to $\mathbb{R}^3$ due to the difficulty of computations. Additionally, it is rare to resolve topology from a nonlinear geometric PDE. Using a minimal molecular surface model \cite{bates2008minimal}, Wang and Wei studied the topological persistence via the evolutionary profiles of the Laplace-Beltrami flow~\cite{wang2016object}. As a result, features of topological invariants are computed from the geometric PDE based filtration. In fact, there has been much effort in pure mathematics to understand the convergence of Riemannian manifolds in terms of sequences of submanifolds in metric spaces. However, the involved Gromov-Hausdorff distance can be computationally very difficult.
With the advancements in data development and computational software, persistent homology has been promoted as a new multiscale approach for data analysis~\cite{zomorodian2005computing,edelsbrunner2010computational}. The traditional topological approaches describe the topology of a given object without invoking the metric or coordinate representations. Whereas, persistent homology bridges algebraic topology and multiscale analysis. The essential difference is that persistent homology analyzes the persistence of the topological space through a filtration process, which is a family of simplicial complexes under a series of inclusion maps. Therefore a series of complexes is constructed based on filtration, which captures topological features changing over a range of spatial scales and reveals the features' topological persistence. In some sense, persistent homology can embed geometric information to topological invariants such that ``birth" and ``death" of connected components, rings, or cavities can be monitored by topological measurements during geometric scale changes. The original idea of varying scales was introduced by Frosini and Landi~\cite{frosini1999size} and by Robins in 1990s~\cite{robins1999towards}. Edelsbrunner et al. formulated the persistent homology and developed the first efficient computational algorithm \cite{edelsbrunner2000topological}. Zomorodian and Carlsson generalized the mathematical theory ~\cite{zomorodian2005computing}. Persistent homology has stimulated much theoretical development\cite{carlsson2009zigzag,edelsbrunner2010computational,chowdhury2018persistent,cang2018evolutionary,meng2019weighted, wang2019persistent}. Among them, persistent spectral graph generates both topological persistence and spectral analysis \cite{wang2019persistent}. Persistent homology has been applied to a variety of fields, including image analysis~\cite{carlsson2008local,pachauri2011topology,singh2008topological,bendich2010computing}, image retrieval~\cite{frosini2013persistent}, chaotic dynamics verification~\cite{mischaikow1999construction,kaczynski2006computational}, sensor network~\cite{de2005blind}, complex network~\cite{lee2012persistent,horak2009persistent}, data analysis~\cite{niyogi2011topological,wang2011branching}, computer vision~\cite{singh2008topological}, shape recognition~\cite{di2011mayer}, and computational biology~\cite{yao2009topological,xia2014persistent,xia2015persistent,gameiro2015topological,kovacev2016using}.
One of the first integrations of persistent homology and machine learning was developed for protein classification in 2015~\cite{cang2015topological}. Since then, persistent homology has been utilized as one of the most successful methods for the multiscale representation of complex biomolecular data~\cite{cang2017topologynet,cang2018integration,cang2018representability}. Two other multiscale representations of complex biomolecular data have also been proposed and found tremendous success in worldwide competitions in computer-aided drug design~\cite{nguyen2019mathematical,nguyen2019mathdl}. One of them is based on multiscale graphs~\cite{opron2015communication}, or more precisely, multiscale weighted colored graphs~\cite{bramer2018multiscale}. Eigenvalues of the graph Laplacians of multiscale weighted colored graphs were shown to provide some of the most powerful representations of protein-ligand binding interactions~\cite{nguyen2019agl}. The other representation utilizes the curvatures computed from multiscale interactive molecular manifolds~\cite{nguyen2019dg}. The multiscale shape analysis offers an efficient means to discriminate similar geometries. A common feature which is crucial to the success of the aforementioned three mathematical data representations is that they either create a family of multiscale topological spaces, or generate a family of multiscale graphs, or construct a family of manifolds, indicating the importance of the multiscale analysis in the representation of complex data with intricate internal structures.
Inspired by the aforementioned ideas, we introduce an evolutionary de Rham-Hodge method for data representation. The present evolutionary de Rham-Hodge method is developed by integrating differential geometry, algebraic topology, and multiscale analysis. It is noted that the fusion of algebraic topology and multiscale analysis leads to persistent homology, the combination of differential geometry and multiscale analysis renders manifold convergence \cite{sormani2010riemannian}, while the union of differential geometry and algebraic topology results in the de Rham-Hodge theory. For a given dataset, using the evolutionary filtration developed in early work \cite{wang2016object}, we construct a sequence of evolving manifolds that lead to a geometry-embedded filtration under inclusion maps. The evolutionary de Rham-Hodge method is established on this sequence of manifolds. In general, the evolution of the manifolds can be either topological persistence which involves topological changes or geometric progression which does not involve topological changes. We are interested in both the data analysis by evolutionary Hodge decompositions associated with various differential forms and the data representations via the evolutionary spectra of de Rham Laplace operators defined on the sequence of manifolds. The evolutionary spectra reveal both the topological invariants and the geometric shapes of evolving manifolds. Such an evolutionary spectral analysis has great potential to ``hear the shape of a drum''.
In this work, we concern both close 2-manifolds and compact manifolds in $\mathbb{R}^3$ with boundaries, which require the enforcement of appropriate boundary conditions on differential forms to ensure topological properties. Much effort has been given to the understanding and implementation of appropriate boundary conditions for the evolutionary de Rham-Hodge method, which results in three sets of unique evolutionary Hodge Laplacians. The multiplicities of the zero eigenvalues of these evolutionary Hodge Laplacians provide the 0th, 1st, and 2nd persistent Betti numbers. Their non-zero eigenvalues further portray the geometric shape and topological characteristics of data.
The rest of this paper is organized as follows. Section~\ref{primerDHT} is devoted to a brief review of the de Rham-Hodge theory, which includes the topics of the de Rham complex and Hodge decomposition. Then, the discrete forms and spectra generated by de Rham-Hodge theory are discussed in Section~\ref{primerDHT}. Readers familiar with the content in the above primer are recommended to start from Section~\ref{evoDHT}, where the evolutionary de Rham-Hodge method is formulated. To demonstrate the utility and usefulness of the present method, we present the evolutionary de Rham-Hodge analysis of geometric shapes in Section~\ref{resDHT}. Finally, a conclusion is given in Section~\ref{conclusion}.
\section{A primer on de Rham-Hodge theory} \label{primerDHT}
To introduce the evolutionary de Rham-Hodge method, we briefly review the de Rham-Hodge theory to establish notation. We first discuss differential geometry and de Rham complex on smooth manifolds before reviewing the Hodge decomposition. Then, we illustrate the DEC discretization of the de Rham-Laplace operators and analyze their spectra.
\subsection{Differential geometry and de Rham complex}
Differential geometry is the study of shapes that can be represented by smooth manifolds of an arbitrary dimension.
A differential $k$-form $\omega^k \in \Omega^k(M)$ is an antisymmetric covariant tensor of rank $k$ on manifold $M$. Roughly speaking, at each point of $M$, it is a linear map from an array of $k$ vectors into a number, which switches sign if any two of the vectors are swapped. In general, it gives a uniform approach to define the integrals over curves, surfaces, volumes or higher-dimensional oriented submanifolds of $M$. More precisely, the antisymmetric rank-$k$ covariant tensor linearly maps $k$ edges from the first vertex of each $k$-simplex in a tessellation of the $k$-submanifold into a number, creating a Riemann sum that converges to an integral independent of the tessellation.
In $\mathbb{R}^3$, $0$-forms and $3$-forms can be recognized as scalar fields, as the antisymmetry permits one degree of freedom (DoF) per point, whereas $1$-forms and $2$-forms are considered vector fields as they require three DoFs per point. Our following discussion is specific to 3-dimensional (3D) volumes bounded by 2-manifolds in $\mathbb{R}^3$.
The \emph{differential} operator (i.e., exterior derivative) $d^k$ maps from the space of $k$-form on manifold, $\Omega^k(M)$ to $\Omega^{k+1}(M)$. It can be regarded as an antisymmetrization of the partial derivatives of a $k$-form. As such, it is a linear map $d^k:\Omega^k(M) \rightarrow \Omega^{k+1}(M)$ that satisfies the Stokes' theorem over any ($k\!+\!1$)-submanifold $\mathcal{S}$ in $M$:
\begin{equation}
\label{eqn:stokesThm}
\int_{\mathcal{S}} d^k \omega^k = \int_{\partial\mathcal{S}} \omega^k,
\end{equation}
where $\partial\mathcal{S}$ is the boundary of $\mathcal{S}$ and $\omega^k\in\Omega^k(M)$ is an arbitrary $k$-form.
Consequently, a key property of differential operator, $d^k d^{k-1}=0$, follows from that boundaries are boundaryless ($\partial\partial \mathcal{S}=0$). This implies that an \emph{exact} form (image of a $(k\!-\!1)$-form under differential) is \emph{closed} (i.e., is in the kernel of differential). The differential operator indeed provides a unification of a number of commonly used operators in 3D vector field analysis. Depending on the degree $k$ of differential forms, $d^k$ can be regarded as gradient ($\nabla$), curl ($\nabla\times$) and divergence ($\nabla\cdot$) operators for $0$-, $1$- and $2$-forms, respectively, e.g., $d^0$ takes the gradient of a scalar field (representing a $0$-form) to a vector field (representing a $1$-form).
With the linear spaces of $k$-forms treated as abelian groups under addition and the linear maps $d$ treated as group homomorphisms, they form a sequence that fits the definition of a \emph{cochain complex} as $d^k d^{k-1}=0$. This cochain complex of differential forms on a smooth manifold $M$ is known as the \emph{de Rham complex}:
\begin{center}
\begin{tikzcd}
0 \arrow{r} & \Omega^0(M) \arrow{r}{d^0} & \Omega^1(M) \arrow{r}{d^1} & \Omega^2(M) \arrow{r}{d^2} & \Omega^3(M) \arrow{r}{d^3} & 0.
\end{tikzcd}
\end{center}
Note that $d^3$ maps $3$-forms to $4$-forms, but $k$-forms for $k>3$ are always zero in $\mathbb{R}^3$ due to antisymmetry.
The \emph{Hodge $k$-star} $\star^k$ (also called \emph{Hodge dual}) is linear map (and hence also a group isomorphism) from a $k$-from to its dual form, $\star^k : \Omega^k(M)\rightarrow\Omega^{n-k}(M)$. Due to the antisymmetry, both $k$-forms and their dual $(n\!-\!k)$-forms have the same DoF ${n \choose k}={n \choose n-k}$. More specifically, for an orthonormal basis $(\mathbf{e}_1,\mathbf{e}_2, \dots, \mathbf{e}_n)$, $\star^k(\mathbf{e}_{i_1}\wedge{\mathbf{e}_{i_2}}\wedge\cdots\wedge{\mathbf{e}_{i_k}})=\mathbf{e}_{j_1}\wedge{\mathbf{e}_{j_2}}\wedge\cdots\wedge{\mathbf{e}_{j_{n-k}}}$, where $\wedge$ denotes the antisymmetrized tensor product, and $(i_1,...,i_k,j_1,...,j_{n-k})$ is an even permutation of $\{1,2,...,n\}$. The associated $(\mathbf{e}_1,\mathbf{e}_2, \dots, \mathbf{e}_n)$ is a basis for $1$-forms, and $\mathbf{e}_{i_1}\wedge\dots\wedge\mathbf{e}_{i_k}$ form a basis for $k$-forms.
As $\star^k$ and $d^k$ can only operate on $k$-forms, we can omit the superscript of the forms or the operators when the dimension is clear from the context. The ($L_2$-)inner product of differential forms for two $k$-forms $\alpha, \beta \in \Omega^k(M)$ can be defined as
\begin{equation}
\label{eqn:innerProduct}
\langle \alpha , \beta \rangle = \int_M\alpha\wedge\star\beta = \int_M\beta\wedge\star\alpha.
\end{equation}
Under these inner products, the adjoint operators of $d$ are the \emph{codifferential} operators $\delta^k$: $\Omega^k(M)\rightarrow\Omega^{k-1}(M)$ , $\delta^k=(-1)^k\star^{4-k}d^{3-k}\star^k$ for $k=1,2,3$. In 3D, they can be identified with $-\nabla\cdot$, $\nabla\times$ and $-\nabla$ for $\delta^k$, $k= 1, 2, 3$ respectively in vector field analysis. Equipped with codifferential operators $\delta^k$, the spaces of differential forms now constitute a bi-directional chain complex,
\begin{center}
\begin{tikzcd}
\Omega^0(M) \arrow[r, shift left, "d^0"] &
\Omega^1(M) \arrow[r, shift left, "d^1"] \arrow[l, shift left, "\delta^1"] &
\Omega^2(M) \arrow[r, shift left, "d^2"] \arrow[l, shift left, "\delta^2"] &
\Omega^3(M) \arrow[l, shift left, "\delta^3"].
\end{tikzcd}
\end{center}
\begin{table}
\small
\caption{Exterior (odd rows) vs. traditional (even rows) calculus in $\mathbb{R}^3$. $f^0$, $\mathbf{v}^1$, $\mathbf{v}^2$ and $f^3$ stand for $0$-, $1$-, $2$- and $3$-forms with their components stored in either a scalar field $f$ or vector field $\mathbf{v}$.}
\begin{center}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{|c| l| l| l| l|}
\hline
& order $0$ & order $1$ & order $2$ & order $3$ \\
\hline
\hline
form & $f^0$ & $\mathbf{v}^1(\mathbf{a})$ & $\mathbf{v}^2(\mathbf{a},\mathbf{b})$ & $f^3(\mathbf{a},\mathbf{b},\mathbf{c})$ \\
& $f$ & $\mathbf{v}\cdot \mathbf{a}$ & $\mathbf{v}\cdot(\mathbf{a}\times\mathbf{b})$ & $f[(\mathbf{a}\times\mathbf{b})\cdot\mathbf{c}]$ \\
\hline
$d$ & $df^0$ & $d \mathbf{v}^1$ & $d \mathbf{v}^2$ & $d f^3$ \\
& $(\nabla f)^1$ & $(\nabla \times \mathbf{v})^2$ & $(\nabla \cdot \mathbf{v})^3$ & $0$ \\
\hline
$\star$ & $\star f^0$ & $ \star \mathbf{v}^1$ & $\star \mathbf{v}^2$ & $\star f^3$ \\
& $f^3 $ & $\mathbf{v}^2$ & $\mathbf{v}^1$ & $f^0$ \\
\hline
$\delta$ & $\delta f^0$ & $\delta \mathbf{v}^1$ & $\delta \mathbf{v}^2$ & $\delta f^3$ \\
& $0$ & $(- \nabla \cdot \mathbf{v})^0$ & $(\nabla \times \mathbf{v})^1$ & $(-\nabla f)^2$ \\
\hline
$\wedge$ & $f^0\!\wedge\! g^0$ & $f^0\!\wedge\!\mathbf{v}^1$ & $f^0\!\wedge\!\mathbf{v}^2$, $\mathbf{v}^1\!\wedge\!\mathbf{u}^1$ & $f^0\!\wedge\!g^3$, $\mathbf{v}^1\!\wedge\!\mathbf{u}^2$\\
& $(fg)^0$ & $(f\mathbf{v})^1$ & $(f\mathbf{v})^2$, $(\mathbf{v}\!\times\!\mathbf{u})^2$ & $(fg)^3$, $(\mathbf{v}\cdot\mathbf{u})^3$\\
\hline
\end{tabular}
\end{center}
\label{tb:ECoperator}
\end{table}
Finally, the exterior calculus notations and their counterparts in traditional calculus are summarized in Table~\ref{tb:ECoperator}. The exterior calculus operations are strictly equivalent to the vector calculus operation in flat 3-dimensional space. A 0- or 3-form can be identified as a scalar function $f:M\subset\mathbb{R}^3\rightarrow\mathbb{R}$, while a 1- or 2-form is identified with a vector field $\mathbf{v}:M\to \mathbb{R}^3$. Thus, we can use $f^0$, $\mathbf{v}^1$, $\mathbf{v}^2$ or $f^3$ to denote a scalar field $f$ or vector field $\mathbf{v}$ regarded as a 0-, 1-, 2- or 3-form, respectively.
\subsection{Hodge decomposition for manifolds}
Hodge theory can be seen as the study of nonintegral parts (cohomology) of (scalar/vector) fields through the analysis of differential operators. Thus, it is often conveniently and concisely described by differential $k$-forms and the exterior calculus of these forms, as discussed in the previous section.
We first establish the aforementioned adjointness between the differential and codifferential operators.
Through integration by part and the Stokes' theorem Eq.~(\ref{eqn:stokesThm}),
\begin{equation}
\label{eqn:integralPart}
\langle d\alpha, \beta\rangle=\langle \alpha, \delta\beta\rangle + \int_{\partial M} \alpha \wedge \star \beta.
\end{equation}
Thus, either for a boundaryless manifold ($\partial M=\emptyset$) or for forms that vanish on boundary ($\alpha|_{\partial M}=0$ or $\star\beta|_{\partial M} = 0$), the boundary integral vanishes, i.e., $\int_{\partial M} \alpha \wedge \star \beta = 0$. In such cases, the adjointness, $\langle d\alpha, \beta\rangle=\langle \alpha, \delta\beta\rangle$, implies that $d$ and $\delta$ satisfy the important property of adjoint operators---the kernel of a linear operator is the orthogonal complement of the range of its adjoint operator.
If we denote the space of \emph{normal forms} as $\Omega^k_n=\{\omega\in\Omega^k|\omega|_{\partial M} = 0\}$, and the space of \emph{tangential forms} as $\Omega^k_t=\{\omega\in\Omega^k|\star\omega|_{\partial M} = 0\}$, the orthogonal complementarity can be expressed as $\Omega^k=\ker\delta^k \oplus d \Omega^{k-1}_n$ and $\Omega^k=\ker d^{k}\oplus \delta\Omega^{k+1}_t$. With $\mathrm{im}\;{d^{k-1}}\subset \ker d^k$ (based on the property of the cochain complex $d^k d^{k-1}=0$), the complementarity restricted to $\ker d^k$ implies
\begin{equation}
\label{eqn:kernelDecom}
\ker d^{k}=\mathcal{H}^k \oplus d\Omega^{k-1}_n,
\end{equation}
where $\mathcal{H}^k=\ker d^k\cap \ker \delta^k$ is the space of \emph{harmonic forms}, which are defined to be both closed and coclosed. Substituting the above equation into $\Omega^k=\ker d^{k}\oplus \delta\Omega^{k+1}_t$, we obtain the three-component Hodge decomposition,
\begin{equation}
\label{eqn:decomposition1}
\Omega^k = d\Omega_n^{k-1} \oplus \delta \Omega_t^{k+1} \oplus \mathcal{H}^k.
\end{equation}
Thus, any $\omega \in \Omega^k$ can be uniquely expressed as a sum of three $k$-forms
from the three orthogonal subspaces,
\begin{equation}
\label{eqn:orthogonalDiscription}
\omega = d\alpha_n + \delta\beta_t + h,
\end{equation}
where $\alpha_n \in \Omega_n^{k-1}$, $\beta_t \in \Omega_t^{k+1}$, and $h \in \mathcal{H}^k$. Note that the potentials $\alpha$ and $\beta$ do not have to be unique, and a variety of gauge conditions can be specified to make them unique.
\subsubsection{Boundaryless manifolds}
When $\partial M\!=\!\emptyset$, $\Omega^k=\Omega^k_t=\Omega^k_n$, we can establish an isomorphism between the cohomology (of the de Rham complex described in the previous section) and the harmonic space, as was developed by Hodge.
In this case, Eq.~(\ref{eqn:kernelDecom}) can be written as
\begin{equation}
\label{eqn:kernelDecom1}
\ker d^{k}=\mathcal{H}^k \oplus \mathrm{im}\; d^{k-1}.
\end{equation}
Thus, we can find a unique element in $\mathcal{H}^k$ that corresponds to each equivalence class in the \emph{de Rham cohomology} $H^k_{dR}=\ker d^k/\mathrm{im}\;{d^{k-1}}$ (quotient spaces induced by the de Rham cochain complex). This bijection implies $\mathcal{H}^k \cong H^k_{dR}$, which indicates $\mathcal{H}^k$ is a finite-dimensional space with its dimension determined by the topology of the manifold.
Moreover, we can identify $\mathcal{H}^k$ as the kernel of a particular second-order differential operator, the \emph{de Rham-Laplace operator}, or \emph{Hodge Laplacian}, defined as $\Delta^k\equiv d^{k-1}\delta^k+\delta^{k+1} d^k$. Through the adjointness between $d$ and $\delta$, we have
\begin{equation}
\label{eqn:Laplace2form}
\langle \Delta \alpha, \alpha \rangle=\langle (d\delta+\delta d)\alpha, \alpha\rangle = \langle d\alpha, d\alpha \rangle + \langle \delta\alpha, \delta\alpha \rangle.
\end{equation}
Denoting $\mathcal{H}^{k}_{\Delta} \equiv \ker\Delta^k$, the above equation implies that $\mathcal{H}^k_{\Delta} = \ker\Delta^k = \ker{d^k}\cap\ker{\delta^k}=\mathcal{H}^k$ for boundary-less manifolds.
As a direct consequence, we rewrite Eq.~(\ref{eqn:decomposition1}) as
\begin{equation}
\label{eqn:decomposition2}
\Omega^k = \mathrm{im}\; d^{k-1} \oplus \mathrm{im}\; \delta^{k+1} \oplus \mathcal{H}^k_\Delta.
\end{equation}
The importance of the decomposition lies in that the first two components can be expressed as the derivatives of some potential functions, and the last non-integral part is spanned by the finite-dimensional harmonic space, whose dimension is determined by the topology of the domain due to the above-mentioned isomorphism. For example, for $\Omega^k$ with $k=1,2$, this decomposition is often recognized as the Helmholtz-Hodge decomposition of vector calculus in 3D, $\mathbf{v}^1 = \nabla f^0 + \nabla \times \mathbf{u}^2 + \mathbf{h}^1$, and $\mathbf{v}^2 = -\nabla f^3 + \nabla \times \mathbf{u}^1 + \mathbf{h}^2$.
\subsubsection{Manifolds with boundary}
For 3-manifolds with 2-manifold boundary, we need additional boundary conditions to have a finite dimensional kernel for the Laplacians, as in this case, $\mathcal{H}=\ker{d}\cap\ker{\delta}\subsetneq \mathcal{H}_{\Delta}$.
Through integration by part with the boundary, we have
\begin{equation}
\label{eqn:LaplacePart}
\langle \Delta \alpha, \alpha \rangle=\langle (d\delta+\delta d)\alpha, \alpha\rangle = \langle d\alpha, d\alpha \rangle + \langle \delta\alpha, \delta\alpha \rangle+ \int_{\partial M} (\delta \alpha \wedge \star \alpha- \alpha \wedge \star d\alpha).
\end{equation}
Thus, if we can eliminate the boundary integral by restricting the space of forms, the kernel of $\Delta$ will be the intersection of the kernel of $d$ and $\delta$. Indeed, there are a variety of choices to satisfy boundary conditions, e.g., forcing the support of the differential form to be in the interior of manifolds. However, an option that is consistent with common physical boundary conditions is to restrict the differential form $\alpha$ in the decomposition
to be tangential to the boundary $\star\alpha|_{\partial M}=0$ or normal to the boundary $\alpha|_{\partial M}=0$ as we have required for the potentials.
Then, one natural choice to eliminate both terms in the boundary integral is to force $d \alpha$ to be tangential when $\alpha$ is tangential and force $\delta \alpha$ to be normal when $\alpha$ is normal. In other words, we modify the definition $\Omega_t$ to be the space of tangential forms with tangential differential, i.e., $\alpha_t\in\Omega_t$ if and only if
\begin{equation}
\label{eqn:tangentialBoundary}
\star \alpha_t |_{\partial M}=0, \quad \star d\alpha_t |_{\partial M}=0.
\end{equation}
Similarly, we modify the definition of $\Omega_n$ to be the space of normal forms with normal codifferential, i.e., $\alpha_n\in\Omega_n$ if and only if
\begin{equation}
\label{eqn:normalBoundary}
\alpha_n |_{\partial M}=0, \quad \delta\alpha_n |_{\partial M}=0.
\end{equation}
\begin{table}
\caption{Boundary conditions of tangential and normal form}
\begin{center}
\renewcommand{\arraystretch}{1.3}
\begin{tabular}{|l|l|l|l|l|}
\hline
type & $f^0$ & $\mathbf{v}^1$ & $\mathbf{v}^2$ & $f^3$ \\
\hline \hline
tangential & {\footnotesize unrestricted} & $\mathbf{v}\cdot \mathbf{n} = 0$ & $\mathbf{v} \parallel \mathbf{n}$ & $f|_{\partial M} = 0$ \\
normal & $f|_{\partial M} = 0$ & $\mathbf{v} \parallel \mathbf{n}$ & $\mathbf{v} \cdot \mathbf{n}=0$ & {\footnotesize unrestricted} \\
\hline
\end{tabular}
\end{center}
\label{tb:boundary}
\end{table}
To illustrate the boundary conditions explicitly, we consider a moving frame, which is formed at each boundary point by two tangent vectors of the boundary surface $\mathbf{t}_1$ and $\mathbf{t}_2$ and the normal vector to the surface $\mathbf{n}$, with the typical convention that they form a right-hand orthonormal frame with the normal pointing outward. As a 1-form $\mathbf{v}^1$ is tangential if $\star\mathbf{v}^1(\mathbf{t}_1,\mathbf{t}_2)=\mathbf{v}^2(\mathbf{t}_1,\mathbf{t}_2)= \mathbf{v}\cdot(\mathbf{t}_1\times \mathbf{t}_2) = \mathbf{v}\cdot\mathbf{n} = 0$, it matches the condition that the corresponding vector field is tangential to the boundary. Similarly, a 1-form $\mathbf{v}^1$ is normal to the boundary, if $\mathbf{v}^1(\mathbf{t}_i)=\mathbf{v}\cdot\mathbf{t}_i = 0$ for $i=1,2$, thus it is the equivalent to $\mathbf{v}$ is normal to the boundary. For a $2$-form $\mathbf{v}^2$, its normal (tangential) boundary condition is the same as the tangential (normal) boundary condition of $\mathbf{v}^1$. Therefore, normal (tangential) $2$-forms should have their corresponding vector fields tangential (normal, resp.) to the boundary. Additionally, tangential $3$-forms (normal $0$-forms) are zero on the boundary whereas normal $3$-forms (tangential $0$-forms) automatically satisfy the boundary condition. In Table~\ref{tb:boundary}, we summarized these choices of the boundary conditions for tangential and normal $k$-forms in 3D.
In vector field representation, the boundary conditions Eqs.~(\ref{eqn:tangentialBoundary}) and (\ref{eqn:normalBoundary}) are equivalent to the following. The choice of a $1$-form in $\Omega^1_t$ (a $2$-form in $\Omega^2_n$) is equivalent to enforcing a tangential vector field $\mathbf{v}$ to have its curl to be normal to the boundary, i.e., adding two homogeneous Neumann boundary conditions to the (Dirichlet-type) tangentiality,
\begin{equation}
\label{eqn:bdyT1form}
\mathbf{v}\cdot\mathbf{n}=0, \quad \nabla_{\mathbf{n}}(\mathbf{v}\cdot\mathbf{t}_1)=0,\quad \nabla_{\mathbf{n}}(\mathbf{v}\cdot\mathbf{t}_2)=0.
\end{equation}
For a normal vector field $\mathbf{v}$ ($1$-forms in $\Omega^1_n$ or $2$-forms in $\Omega^2_t$), it amounts to adding one homogeneous Neumann boundary condition derived from the zero divergence on the boundary to the (Dirichlet-type) orthogonality constraints,
\begin{equation}
\label{eqn:bdyT2form}
\mathbf{v}\cdot\mathbf{t}_1=0,\quad \mathbf{v}\cdot\mathbf{t}_2=0,\quad \nabla_{\mathbf{n}}(\mathbf{v}\cdot\mathbf{n})=0.
\end{equation}
For an unrestricted function $f$ (tangential $0$-forms or normal $3$-forms), it amounts to forcing its gradient to be tangential at the boundary (Neumann-type),
\begin{equation}
\label{eqn:bdyT0form}
\nabla_{\mathbf{n}} f|_{\partial M}=0,
\end{equation}
and a function $f$ for tangential $3$-forms (normal $0$-forms) satisfies the homogeneous Dirichlet boundary condition
\begin{equation}
\label{eqn:bdyT3form}
f|_{\partial M}=0.
\end{equation}
With these modified boundary conditions, we still have the same Hodge decomposition,
\begin{equation}
\label{eqn:decomposition4}
\Omega^k = d\Omega_n^{k-1} \oplus \delta \Omega_t^{k+1} \oplus \mathcal{H}^k.
\end{equation}
This is due to the fact that $d\Omega_n$ (or $\delta\Omega_t$) remains the same regardless of whether $\Omega_n$ (or $\Omega_t$) contains the additional boundary conditions, as they can be seen as part of the gauge condition that restricts the potentials but not their differential (codifferential).
As mentioned above, with the boundary, $\mathcal{H}^k$ is no longer finite dimensional or the kernel of of Laplacians $\mathcal{H}^k_\Delta$. However, if we restrict $\Delta$ to $\Omega_t$ or $\Omega_n$ and denote the corresponding operator as $\Delta_t$ and $\Delta_n$ respectively, we can still find finite dimensional kernels $\mathcal{H}^k_{\Delta_t}$ and $\mathcal{H}^k_{\Delta_n}$ that correspond to $\mathcal{H}^k\cap \Omega_t$ or $\mathcal{H}^k\cap \Omega_n$ orthogonal to $\mathrm{im}\; d$ and $\mathrm{im}\; \delta$.
In fact, the harmonic space $\mathcal{H}^k$ can be further decomposed into tangential, normal harmonic forms and exact-coexact harmonic forms $\mathcal{H}^k=(\mathcal{H}^k_{\Delta_t} + \mathcal{H}^k_{\Delta_n}) \oplus (d\Omega^{k-1}\cap \delta\Omega^{k+1})$ as proposed by Friedrichs~\cite{friedrichs1955differential}. Moreover, in flat 3D space, all three subspaces are orthogonal to each other. The third space can be seen as the infinite-dimensional space of solutions to Laplace equations in dimension $k\pm 1$ with either normal or orthogonal boundary conditions. Thus, we can focus on the Laplacian operators that are either tangential or normal for analysis.
In total, there are 8 different Hodge Laplacians ($\Delta^k_{t}$ and $\Delta^k_{n}$ for $k=0,1,2,3$)
and 8 associated finite dimensional harmonic spaces. Friedrichs also noted that for manifolds with boundary, the tangential harmonic spaces are isomorphic to the absolute de Rham cohomology $\mathcal{H}^k_{\Delta_t} \cong H^k(M)$, and the normal harmonic spaces are isomorphic to the relative de Rham cohomology $\mathcal{H}^k_{\Delta_n} \cong H^k(M,\partial M)$. From the dimensionality of the corresponding homology (Betti numbers) of the manifold $M$, together with the Hodge duality between $\mathcal{H}^k_{\Delta_t}$ and $\mathcal{H}^{3-k}_{\Delta_n}$,
we can obtain the dimensions of all these harmonic spaces: $\beta_k=\dim \mathcal{H}^k_{\Delta_t} = \dim \mathcal{H}^{3-k}_{\Delta_n}$. Roughly, speaking, $\beta_0$ is the number of connected components, $\beta_1$ is the number of rings, $\beta_2$ is the number of cavities, and $\beta_3$ is 0 as $M$ in flat 3D cannot contain any noncontractible topological 3-sphere.
\subsection{Discrete forms and spectral analysis} \label{Discreteformandspectrumanalysis}
In practical applications, the de Rham-Hodge theory is often computed for decompositions and spectral analysis. In both cases, the discretization of exterior derivatives is required. We follow one typical discretization of the exterior calculus on differential forms, the discrete exterior calculus (DEC)~\cite{desbrun2008discrete}. A major technical aspect is the handling of arbitrarily complex geometric shapes in 3D. In spectral analysis, the Hodge Laplacian operators and their boundary conditions are to be implemented such that the key topological property of $d\circ d=0$, which defines the de Rham cohomology, is preserved in the discrete version by DEC in complex computational domains. First, the domain of differential forms, in this case, a 3-manifold embedded in 3D Euclidean space is tessellated into a 3D simplicial complex, i.e., a tetrahedral mesh. Any $k$-form $\omega$ is represented by its integral on oriented $k$-D elements ($k$-simplex) of the mesh, listed as a vector $W$ with the length equaling the number of $k$-simplices. More specifically, a discrete $0$-form is the assignment of one real number per vertex, a discrete $1$-form is the assignment of one value per oriented edge, a discrete $2$-form is the assignment of one value per oriented triangle, and a discrete $3$-form is the assignment of one value per tetrahedron (tet). The choice of orientation per $k$-simplex is arbitrary since the antisymmetry of a $k$-form guarantees that the integral on that $k$-simplex only changes its sign.
Now the linear operator $d^k$ is represented by a sparse matrix ${D}_k$, which is implemented as the transpose of the signed incidence matrix between $k$-simplices and $(k\!+\!1)$-simplices, with the sign determined by mutual orientation. This can be seen as the consequence of the aforementioned Stokes' theorem, because the integral of $d\omega$ on each $(k\!+\!1)$-simplex is exactly the sum of the integral of $\omega$ on the boundary of the $(k\!+\!1)$-simplex, which is the union of its consistently oriented $k$-simplex faces.
Thus, the defining property in de Rham-Hodge theory ${D}_{k+1}{D}_{k}=0$ is preserved through as the boundary of the boundary is empty. As shown in Fig.~\ref{fig:discretedR}, the adjoint operator $\delta^k$ is implemented as ${S}_{k-1}^{-1}{D}^T_{k-1}{S}_{k}$, where ${S}_k$ is discretization of the $L_2$-inner product between two discrete $k$-forms such that $(W_1^k)^TS_k W_2^k$ is an approximation of $\langle\omega_1^k,\omega_2^k\rangle$. In this work, we use the lowest order diagonal matrices for $S_k$ for simplicity, but higher-order Galerkin matrices for $k$-form basis can be developed with proper treatment on matrix inversion for better accuracy. Such a discrete Hodge star operator can also be seen as a mapping from a discrete $k$-form to a discrete dual $(3\!-\!k)$-form defined on the basis associated with dual elements of a dual mesh to the tet mesh. Obviously, this field needs more effort from the computational mathematics community
With both the differential operators and the Hodge stars discretized, the discrete counterpart of a Hodge Laplacian $\Delta^k$ is defined as $S_k^{-1}L_k$ through products and summations of these matrices following the continuous version, here
\begin{equation}
\label{eqn:discreteLaplacian}
L_k=D_k^TS_{k+1}D_k+S_kD_{k-1}S^{-1}_{k-1}D^T_{k-1}S_k.
\end{equation}
The reason that $L_k$ is used frequently as the discrete Hodge Laplacian instead of $S_k^{-1}L_k$ is its symmetry. Alternatively, we can also see $L_k$ as the quadratic form on the space of discrete $k$-forms, such that $W^T L_k W$ is an approximation of $\langle \omega, \Delta \omega\rangle$.
In our analysis of volumetric shapes, we conjecture that the evolution of topological and geometric structures is related not only to the null spaces of Hodge Laplacians, but also to the general spectra of these operators, in particular, those eigenvalues that are close to zero. The associated eigen differential forms can be found through a generalized eigenvalue problem for the discrete Hodge Laplacian and Hodge star operators.
\begin{equation}
\label{eqn:genEigval}
L_k W^k=\lambda^k S_k W^k.
\end{equation}
\begin{figure}
\begin{center}
\begin{tikzcd}
\text{0-form} \arrow[r, "{D}_0"] \arrow[d, xshift=0.7ex, "{S}_0"] &
\text{1-form} \arrow[r, "{D}_1"] \arrow[d, xshift=0.7ex, "{S}_1"] &
\text{2-form} \arrow[r, "{D}_2"] \arrow[d, xshift=0.7ex, "{S}_2"] &
\text{3-form} \arrow[d, xshift=0.7ex, "{S}_3"] \\
\text{dual 3-form} \arrow[u, xshift=-0.7ex, "{S}_0^{-1}"] &
\text{dual 2-form} \arrow[u, xshift=-0.7ex, "{S}_1^{-1}"] \arrow[l, "D_0^{T}"] &
\text{dual 1-form} \arrow[u, xshift=-0.7ex, "{S}_2^{-1}"] \arrow[l, "D_1^{T}"] &
\text{dual 0-form} \arrow[u, xshift=-0.7ex, "{S}_3^{-1}"] \arrow[l, "D_2^{T}"]
\end{tikzcd}
\caption{Discrete de Rham cohomology; $D_k$ is the combinatorial operators such that
${D}_{k+1}{D}_{k}=0$; ${S}_k$ is the discrete Hodge stars.}
\label{fig:discretedR}
\end{center}
\end{figure}
For illustration purpose, we can reformulate Eq.~(\ref{eqn:genEigval}) as a regular eigenvalue problem,
\begin{equation}
\label{eqn:genRegular}
\bar{L}_k\bar{W}^k=\lambda^k \bar{W}^k,
\end{equation}
where $\bar{L}_k = S_k^{-1/2}L_kS_k^{-1/2}$ and $\bar{W}^k=S_k^{1/2} W^k$.
Then, to partition the spectrum of the modified discrete Hodge Laplacian, we express it as the sum of two semi-positive-definite matrices,
\begin{equation}
\label{eqn:modifiedLaplacian}
\bar{L}_k=\bar{D}_k^T\bar{D}_k+\bar{D}_{k-1}\bar{D}_{k-1}^T,
\end{equation}
where $\bar{D}_k=S^{1/2}_{k+1}D_kS_k^{-1/2}$. We can observe that the cohomology structure is maintained as $\bar{D}_{k+1}\bar{D}_k=0$. Moreover, now the adjoint operator of $\bar{D}_k$, in the $L_2$ inner products defined by the Hodge stars, is simply its transpose $\bar{D}^T_k$. Thus, the entire spectrum of $\bar{L}_k$ can be studied through the singular value decomposition of the discrete differential operator
\begin{equation}
\label{eqn:SVDdisdiffoperator}
\bar{D}_k=U_{k+1}\Sigma_kV_k^T,
\end{equation}
where $U_{k+1}$ and $V_k$ are orthogonal matrices, and $\Sigma_k$ is a rectangular diagonal matrix with non-negative real elements. We can recognize the nonzero spectra of the modified Hodge Laplacian as the union of the squares of the nonzero entries from $\Sigma_k$ and $\Sigma_{k-1}$, since
\begin{equation}
\label{eqn:SVDmodifiedLaplacian}
\bar{L}_k=V_k\Sigma_{k}^2V^T_k+U_k\Sigma_{k-1}^2U^T_k.
\end{equation}
Note that for $0$- or $3$-forms, one of the $\Sigma$'s contains only zeros.
Based on the Hodge decomposition Eq.~(\ref{eqn:decomposition4}), we can also notice that the columns of $V_k$ that correspond to nonzero singular values in Eq.~(\ref{eqn:SVDmodifiedLaplacian}) are orthogonal to those of $U_k$, which means the entire $k$-form space is spanned by harmonic forms (eigen form with eigenvalue 0), and those column vectors of $V_k$ and $U_k$.
For domains with boundaries, the tangential or normal forms are restricted by Dirichlet and/or Neumann boundary conditions, which can be implemented by whether to include the boundary elements or not for $D_k$.
We denote the discrete differential operator for tangential (normal) $k$-forms as $D_{k,t}$ (respectively $D_{k,n}$).
For the detail on the construction of these matrices, readers are referred to our previous work~\cite{zhao20193d}.
In summary, for the four types of $k$-form ($k=0,1,2,3$) with two boundary conditions, there are 8 different discrete Hodge Laplacians ($L_{k,t}$ and $L_{k,n}$) in total, such that
\begin{equation}
\label{eqn:Laplacianktn}
\begin{split}
L_{k,t}&=D_{k,t}^TS_{k+1}D_{k,t}+S_kD_{t,k-1}S^{-1}_{k-1}D^T_{t,k-1}S_k,\\
L_{k,n}&=D_{k,n}^TS_{k+1}D_{k,n}+S_kD_{n,k-1}S^{-1}_{k-1}D^T_{n,k-1}S_k.
\end{split}
\end{equation}
Based on the above singular value analysis, the non-zero spectrum of $\bar{L}_k$ is the union of squared singular values of $\bar{D}_k$ and those of $\bar{D}_{k-1}$. Therefore, for each type of boundary conditions, the spectra of the four discrete Hodge Laplacians only depend on the singular spectra of $\bar{D}_0$, $\bar{D}_1$ and $\bar{D}_2$. Furthermore, in Table~\ref{tb:boundary}, the same set of boundary conditions is shared between tangential $1$-forms and the normal $2$-forms, between tangential $2$-forms and normal $1$-forms, between normal $3$-forms and tangential $0$-forms, and between tangential $3$-forms and normal 0-forms. This duality between tangential $k$-forms and normal ($3\!-\!k$)-forms is also present in the corresponding operators between these forms, more specifically, the equivalence exists between $\bar{D}_{0,t}$ and $\bar{D}_{2,n}^T$,
$\bar{D}_{1,t}$ and $\bar{D}_{1,n}^T$, and
$\bar{D}_{2,t}$ and $\bar{D}_{0,n}^T$.
We thus reduce the 8 different spectra of Hodge Laplacians to 3 distinct sets of different singular spectra. We denote the set of singular values of $\bar{D}_{0,t}$ for the tangential gradient eigen field by $T$, the set of the singular values of $\bar{D}_{1,t}$ for the curl eigen field by $C$, and the set of the singular value set of $\bar{D}_{2,t}$ for tangential divergent eigen field by $N$.
Although each of the 8 spectra for Hodge Laplacians defined on smooth manifolds can be represented by the combination of one or two sets of the $T$, $C$ and $N$, the numerical calculations of the singular values of the equivalent differential operators can deviate from these due to the different DoFs in the representations for different discrete forms, as well as the inaccuracy introduced by the approximation of Hodge star and differential operators. While the numerically computed singular values of tangential $k$-forms $\bar{D}_{k,t}$ can deviate from those of normal $(3\!-\!k)$-forms $\bar{D}_{2-k,n}^T$, as the observation in previous work~\cite{zhao2019rham}, with increased resolution, the low frequencies converge reasonably well.
\section{Evolutionary de Rham-Hodge method}\label{evoDHT}
In this section, we introduce the evolutionary de Rham-Hodge method to analyze the topological and geometric properties throughout the evolution of manifolds. We first discuss the existing data that motivates the present theoretic formulation. Then, we provide the mathematical description of manifold evolution, followed by the definitions of the associated persistence and progression. We extend the usual study of cohomology (associated to zero eigenvalues of Hodge Laplacians) to employing the leading small non-zero eigenvalues to facilitate the concepts of persistence and progression so that the variations of topological spaces ($\beta_0$, $\beta_1$ and $\beta_2$) can be traced to the changes in the eigenvalues away from or towards zero as the geometry evolves.
\subsection{Data and their de Rham-Hodge analysis}
Most commonly occurred data are closed manifolds, such as star surfaces, earth surfaces, brain surfaces, and molecular surfaces. The de Rham Laplace operator can be applied to compute eigenfunctions and eigenvalues for the geometric shape analysis. Another interesting type of data includes scalar or vector functions defined on closed manifolds, such as temperature or ocean currents on the earth's surface and in compact manifolds with boundaries, such as the electron densities or electrostatic potentials in proteins or the magnetic fields around the earth. The Hodge decomposition can be directly applied to these functions. For smooth scalar functions, surface contours can be specified to generate compact manifolds with boundaries. The geometric shape analysis via the de Rham Laplace operator can be carried out. A special class of data is the density distributions, either obtained from cryogenic electron microscopy (cryo-EM), magnetic resonance imaging (MRI) or created from quantum mechanical calculations. In this situation, one can render a family of inclusion surfaces by systematically varying the density isovalues. The de Rham-Hodge analysis and modeling of this family of inclusion surfaces are the objects of the present theoretical development.
The evolutionary de Rham-Hodge method developed in this work can also be applied to point cloud data, such as stars in the universe, atoms in biomolecules, and the output of 3D scanning processes. In this situation, one can carry out a discrete to continuum map to create volumetric density functions from point clouds \cite{xia2014multiscale,nguyen2016generalized}. Then, a family of inclusion surfaces can be obtained for the evolutionary de Rham-Hodge analysis.
Flexibility rigidity index (FRI) density is a useful tool to construct a continuous density distribution from a set of discrete point cloud data inputs. By selecting an isovalue from the FRI density, one can further generate a boundary surface, which composes the 3-manifold with a 2-manifold boundary. FRI density has been shown to be particularly straightforward to implement and computationally stable on any point cloud~\cite{nguyen2016generalized} and is defined by the following position-dependent rigidity (or density) function~\cite{xia2014multiscale}
\begin{equation}
\label{eqn:densityFcn}
\rho(\mathbf{r}, \eta) = \sum_{j=1}^{N}\Phi(\|\mathbf{r}-\mathbf{r}_j\|; \eta)
\end{equation}
where $\mathbf{r}$ is a point in space, $N$ is the number of particles, $\mathbf{r}_j$ is the location of a data point $j$, $\eta$ is a scaling parameter, and $\Phi(\cdot;\eta)$ is a correlation function, i.e., a real-valued monotonically decreasing function with the following admissibility conditions
\begin{equation}
\label{eqn:densityCond}
\begin{split}
\Phi(\|\mathbf{r}-\mathbf{r}_j\|;\eta) &= 1, \text{ as } \|\mathbf{r}-\mathbf{r}_j\| \rightarrow 0,\\
\Phi(\|\mathbf{r}-\mathbf{r}_j\|;\eta) &= 0, \text{ as } \|\mathbf{r}-\mathbf{r}_j\| \rightarrow \infty,
\end{split}
\end{equation}
One used families of correlation functions is the generalized exponential functions
\begin{equation}
\label{eqn:expFcn}
\Phi(\|\mathbf{r}-\mathbf{r}_j\|;\eta) = \exp({-(\|\mathbf{r}-\mathbf{r}_j\|/\eta )^\kappa}), \quad \kappa>0.
\end{equation}
Here, the weight $\eta$ is application-dependent, e.g., the multiplication of a scaling parameter and the van der Waals radius $r_{{\rm vdw}_j}$ of the atom at $\mathbf{r}_j$ for molecular data. In fact, $\eta$ can be chosen as anisotropic function to induce a multidimensional persistent homology filtration \cite{xia2015multidimensional}. In our numerical tests, we use the generalized exponential function with $\kappa=2$, which is known as the Gaussian function. A family of 3-manifolds can be defined by a varying level set parameter (isovalue) $c\in(0,c_\text{max})$, where $c_\text{max}=\max{\rho(\cdot, \eta)}$,
\begin{equation}
\label{eqn:manifolds}
M_c=\{\mathbf{r}|\rho(\mathbf{r}, \eta) \leq c_\text{max}-c\},
\end{equation}
which has the level-set of $\rho$ as its boundary $\partial M_c = \{\mathbf{r}|\rho(\mathbf{r}, \eta) = c_\text{max}-c\}$.
\subsection{Manifold evolution}
Hodge theory studies the de Rham cohomology groups of a smooth manifold $M$, and established the bijection from equivalence classes in a cohomology group to a harmonic differential form in the null space of the corresponding Hodge Laplacian. While these harmonic forms associated with the zero eigenvalues in the spectra of Hodge Laplacians carry some geometric information in addition to the topology, the non-zero spectra provide richer geometric information than the multiplicity of zero. However, the geometry is not uniquely determined by the spectra of the Hodge Laplacians (even for planar shapes), as one cannot hear the shape of a drum~\cite{kac1966can}. Thus, we propose to extend the study of de Rham-Hodge theory to a family of smooth manifolds instead of one specific manifold and track the spectral changes in a sequence of manifolds. Such a family of manifolds controlled by a continuous filtration parameter is sometimes called the evolution of manifolds embedded in an ambient manifold, which in our case is the 3D Euclidean space.
The evolution of manifolds is often defined through a smooth map from a basic manifold $B$ to a family of submanifold $\{M_c\}$ of an ambient manifold $M$ at a given instant (the value of parameter $c$ treated as time). More precisely, it is the smooth map $F: B \times [0,c_\text{max}] \rightarrow M$ such that $F^c=F(\cdot, c)$ is an immersion for every $c$. The one-parameter family of subsets of $M$, $\{F^c(B)\}_{c\geq 0}$ is then called the \emph{evolving manifold}. However, such a Hodge Lagrangian description makes it hard to handle topological changes, especially if each mapping is restricted to be an embedding. Therefore, in this work, we directly use the Eulerian representation described by $M_c$ in Eq.~(\ref{eqn:manifolds}). This level-set bounded volume evolution handles both the geometric progression and topological changes in a consistent fashion. As Morse functions are dense in continuous functions, we can assume $\rho(\mathbf{r},\eta)$ to be a Morse function without loss of generality, since otherwise, we can use symbolic perturbation to make it a Morse function. We can regularly sample the interval $(0,c_\text{max})$ at $n$ sample locations, forming an index set $I=\{c_0,c_1,...,c_n\}$, such that none of the parameters are one of the isolated critical values through symbolic perturbation if necessary. Noting that $M_c$ are only non-manifold when $c$ is a critical point of the Morse function, the snapshots of the evolving manifold, $\{F^c\}_{c\in I}$, are all manifolds. Thus, they form a filtration of manifold $M$, with the inclusion map $\mathfrak{I}_{l,l+1}: M_{l}\hookrightarrow M_{l+1}$ linking each pair of consecutive manifolds and
\begin{center}
\begin{tikzcd}
M_{0} \arrow[r, "\mathfrak{I}_{0,1}"] &
M_{1} \arrow[r, "\mathfrak{I}_{1,2}"] &
M_{2} \arrow[r, "\mathfrak{I}_{2,3}"] &
\cdots \arrow[r, "\mathfrak{I}_{n-1,n}"] &
M_{n} \arrow[r, "\mathfrak{I}_{n,n+1}"] &
M=M_{c_\text{max}}.
\end{tikzcd}
\end{center}
If $(c_l,c_{l+p})$ does not contain any critical points of $\rho(\mathbf{r}, \eta)$ and the largest critical value smaller than $c_l$ is $c_c$, the inclusion map $\mathfrak{I}_{l,l+p}:M_l\hookrightarrow M_{l+p}$ is also homotopic to a homeomorphism from $M_{l}$ to $M_{{l+p}}$, which can be constructed by moving every point $\mathbf{r}$ with $\rho(\mathbf{r},\eta)>c_{\max}-c_c$ along the gradient integral line of $\rho(\cdot, \eta)$ to a point $\hat\mathbf{r}$ such that {$\rho(\mathbf{r},\eta)-\rho({\hat\mathbf{r}}, \eta)=(c_{l+p}-c_l)e^{1-\frac{c_l-c_c}{\rho(\mathbf{r}, \eta)-c_{\max}-c_c}}$}. When the two parameter values are similar, one can also see that the above map is nearly isometric since the deformation is close to an identity map.
When $(c_l,c_{l+p})$ contains critical points of the Morse function, there is no smooth homeomorphism between $M_l$ and $M_{l+p}$ as the level set underwent topological changes. Without loss of generality, we can assume that there is only one critical point, which can be classified as (local) minimum, 1-saddle, 2-saddle, or (local) maximum, based on the signature of the Hessian of $\rho$. As all minima of $\rho$ is at the value of $0$, the interval may only contain the latter three types: if it is a maximum, one 2nd homology generator in $M_l$ will be mapped to $0$ in $M_{l+p}$ for the mapping induced by the inclusion; if it is a 2-saddle, either $M_l$ has a 1st homology generator mapped to $0$ or $M_{l+p}$ contains a 2nd homology generator not in the image of the induced mapping from $H(M_l)$ to $H(M_{l+p})$; similarly, if it is a 1-saddle, either $M_l$ has a 0th homology generator mapped to $0$ or $M_{l+p}$ contains a 1st homology generator, not in the image of the induced mapping. Through the isomorphisms among the de Rham cohomology, singularly homology, simplicial homology, and simplicial cohomology, we can use the persistent homology to study the mapping between the de Rham cohomologies indirectly. However, we found that direct construction can reveal some additional insight on the relation and persistence of the harmonic forms across different manifolds, as we discuss next.
\subsection{Persistence of harmonic forms}
\subsubsection{Normal harmonic forms}
Drawing an analogy from persistent homology, we first attempt to construct a homomorphism from closed forms on $M_l$ to closed forms on $M_{l+p}$, i.e., from $\ker d_{l}$ to $\ker d_{l+p}$, if we use the subscript $l$ to denote the operator defined on $M_l$. For manifolds with boundary, one realizes that this is not possible for tangential forms through the isomorphism relations to cochain and chain spaces on simplicial complexes, but rather straightforward for normal forms in the discrete case. More specifically, we can map $k$-forms in $M_l$ by setting values for simplices in $M^c_{l,p}=M_{l+p}\backslash M_l$ to $0$, i.e., a 0-padded $k$-cochain on $M_{l+p}$ as the image of a $k$-cochain on $M_l$ assuming that $M_l$ has a tessellation that is a subcomplex of the tessellation of $M_{l+p}$. The reason that the image of $\omega_l \in \ker d_{l}$ remains in $\ker d_{l+p}$ is that the value of $d\omega_{l+p}$ on any $({k\!+\!1})$-simplex with one or more faces in $\partial M_l$ is still $0$, as $\omega_{l}|_{\partial M_l} = 0$.
However, in the continuous case, setting $\omega$ to $0$ in $M^c_{l,p}$ creates either discontinuity or at least large $\delta\omega$ near the boundary. A smoother extension of the $\omega$ from $M_l$ to $M_{l+p}$ can be defined by minimizing the Dirichlet energy $\langle d\omega,d\omega\rangle + \langle \delta \omega,\delta \omega\rangle$ in $M^c_{l,p}$, which leads to simply a Laplace equation $\Delta \omega = 0$. The boundary of $M^c_{l,p}$ is the union of $\partial M_{l}$ and $\partial M_{l+p}$ with the orientation of the former flipped. Recall that when $\omega$ is normal to the boundary i.e., $\omega_l|_{\partial M_l}=0$, we also impose the condition that $\delta \omega$ is normal to the boundary ($\delta\omega_l|_{\partial M_l}=0$). For the extension, we keep this condition on $\partial M_{l+p}$, while on $\partial M_l$ we impose the continuity instead, $\omega_{l+p}|_{\partial M_l} = \omega_l|_{\partial M_l}$. Note that the resulting Laplace equation has a finite kernel identical to that of $\Delta_n$ on $M^c_{l,p}$, so we can find a unique solution by forcing the solution to have 0 projection to this kernel~\cite{zhao20193d}.
For instance, if we have a normal 1-form $\omega_l$ to extend, we can impose the homogeneous boundary condition for the proxy vector field $\mathbf{v}$ on $\partial M_{l+p}$ as in Eq.~(\ref{eqn:bdyT2form}),
\begin{equation}
\label{eqn:bc_ext_n}
\mathbf{v}_{l+p}\cdot\mathbf{t}_1=0,\quad \mathbf{v}_{l+p}\cdot\mathbf{t}_2=0,\quad \nabla_{\mathbf{n}}(\mathbf{v}_{l+p}\cdot\mathbf{n})=0;
\end{equation}
whereas on $\partial M_l$, we use a Dirichlet boundary condition for continuity $\mathbf{v}_{l+p}=\mathbf{v}_l$, i.e.,
\begin{equation}
\label{eqn:bc_ext_n_1}
\mathbf{v}_{l+p}\cdot\mathbf{n}=\mathbf{v}_{l}\cdot\mathbf{n}, \quad \mathbf{v}_{l+p}\cdot\mathbf{t}_1=0,\quad \mathbf{v}_{l+p}\cdot\mathbf{t}_2=0.
\end{equation}
We denote the map through this harmonic extension as $\mathfrak{E}_{l,p}$, i.e., $\omega_{l+p} = \mathfrak{E}_{l,p}(\omega_l)$. However, the minimization of Dirichlet energy does not imply $\delta \omega_{l+p} = 0$ even when $\delta \omega_l = 0$. Nevertheless, $d \omega_{l+p} = 0$ is always possible, since otherwise, one would be able to perform a Hodge decomposition to find a tangential $(k\!+\!1)$-form $\beta_t$ in $M^c_{l,p}$ and remove $d\omega_{l+p}$ by subtracting $\delta\beta_t$ from $\omega_{l+p}$. An alternative is to restrict the extension to minimize $\langle \delta\omega,\delta\omega\rangle$ under the constraint $d\omega_{l+p}=0$ in $M^c_{l,p}$, which results in a fourth-order bi-Laplace equation. Since this discussion is mainly for theoretical purposes, we assume the simple harmonic extension followed by a decomposition to enforce $d\omega_{l+p}=0$ instead of a biharmonic extension. In Fig.~\ref{fgr:normalTangentialVF} (a), we illustrate the implementation of boundary conditions for the extension of normal harmonic forms to the interior cavity. In this evolving process, the outside surface is fixed and the inner cavity shrinks to null in order that the manifold with a cavity extends into a solid ball. Under the boundary condition Eq.~(\ref{eqn:bc_ext_n_1}) on the interior surface, the input normal harmonic forms (thin lines) are extended into the cavity, which also preserve curl-free properties shown as thick lines in Fig.~\ref{fgr:normalTangentialVF} (a).
Note that $d\mathfrak{E}(\omega)$ is a solution to the equation for solving the extension of $d\omega$, by the uniqueness we impose, it must be $\mathfrak{E}(d\omega)$. Thus, we can construct the following commutative diagram on the de Rham complexes for normal forms on the filtration of $M$:
\begin{center}
\begin{tikzcd}
\Omega^0_n(M_{0}) \arrow[d, "\mathfrak{E}_{0,1}"]
\arrow[r, shift left, "d^0"] &
\Omega^1_n(M_{0}) \arrow[d, "\mathfrak{E}_{0,1}"]
\arrow[r, shift left, "d^1"] &
\Omega^2_n(M_{0}) \arrow[d, "\mathfrak{E}_{0,1}"]
\arrow[r, shift left, "d^2"] &
\Omega^3_n(M_{0}) \arrow[d, "\mathfrak{E}_{0,1}"] \\
\Omega^0_n(M_{1}) \arrow[d, "\mathfrak{E}_{1,1}"] \arrow[r, shift left, "d^0"] &
\Omega^1_n(M_{1}) \arrow[d, "\mathfrak{E}_{1,1}"]
\arrow[r, shift left, "d^1"] &
\Omega^2_n(M_{1}) \arrow[d, "\mathfrak{E}_{1,1}"]
\arrow[r, shift left, "d^2"] &
\Omega^3_n(M_{1}) \arrow[d, "\mathfrak{E}_{1,1}"] \\
\Omega^0_n(M_{2}) \arrow[d, "\mathfrak{E}_{2,1}"] \arrow[r, shift left, "d^0"] &
\Omega^1_n(M_{2}) \arrow[d, "\mathfrak{E}_{2,1}"]
\arrow[r, shift left, "d^1"] &
\Omega^2_n(M_{2}) \arrow[d, "\mathfrak{E}_{2,1}"]
\arrow[r, shift left, "d^2"] &
\Omega^3_n(M_{2}) \arrow[d, "\mathfrak{E}_{2,1}"] \\
\cdots &
\cdots &
\cdots &
\cdots
\end{tikzcd}
\end{center}
which places the de Rham complex in the horizontal direction and the filtration-induced extensions in the vertical direction.
\begin{figure*}[t!]
\centering
\includegraphics[height=2in]{fig15}
\begin{picture}(17,0)
\put( -175, 17){\text{(a) Normal harmonic forms}}
\put( 61, 17){\text{(b) Tangential harmonic forms}}
\end{picture}
\caption{Illustration of normal and tangential harmonic field extensions. Thick lines are the inputs and thin lines are the extended outputs. Left charts in both (a) and (b) show harmonic fields and their extensions while right charts give meticulous detail of interior parts. (a) Normal harmonic forms. A solid ball with a cavity extends inward to a solid ball without cavity. The outside surface is fixed. (b) Tangential harmonic forms. A torus extends to a solid ball.}
\label{fgr:normalTangentialVF}
\end{figure*}
Now, we can discuss the direct relation of bases of normal harmonic forms induced by $\mathfrak{E}$. First, $\omega_n \in \ker d_l$ implies $\mathfrak{E}_{l,p}(\omega_n) \in \ker d_{l+p}$. Thus, there is an injective homomorphism from $\ker d_l$ to $\ker d_{l+p}$. This induces a homomorphism from the cohomology group $\ker d^k_l/ \mathrm{im}\; d^{k-1}_l$ to $\ker d^k_{l+p}/ \mathrm{im}\; d^{k-1}_{l+p}$, which, through de-Rham isomorphism between cohomology and harmonic spaces in $M_l$ and $M_{l_p}$, is equivalent to a homomorphism from the harmonic space $\mathcal{H}^k_{\Delta_n, l}$ to $\mathcal{H}^k_{\Delta_n, l+p}$. Instead of using the mapping between the equivalence classes, we can actually directly pick the unique harmonic representative $h_{n}\in \ker d^k \cup \ker \delta^{k+1}=\mathcal{H}^k_{\Delta_n}$ for each equivalence class in the cohomology, as we can pick the closed form that is orthogonal to $\mathrm{im}\; d^{k-1}$ which is $\ker \delta^{k}$ due to the adjointness between $d$ and $\delta$. However, for $h_n\in\mathcal{H}^k_{\Delta_n, l}$, its extension $\mathfrak{E}_{l,p}(h_n)$ is not necessarily an element of $\mathcal{H}^k_{\Delta_n, l+p}$. Nevertheless, composed with the simple $L_2$ projection onto the finite dimensional normal harmonic space $P_{\mathcal{H}^k_{\Delta_n, l+p}}$, we have the linear map (also a homomorphism) $\Psi_{n,l,p}=P_{\mathcal{H}^k_{\Delta_n, l+p}}\circ\mathfrak{E}_{l,p}:\mathcal{H}^k_{\Delta_n, l}\to \mathcal{H}^k_{\Delta_n, l+p}$.
The map between these two normal harmonic spaces is neither necessarily injective nor necessarily surjective. In fact, if $h_n \in \mathcal{H}^k_{\Delta_n,l}$ is not in $\mathrm{im}\; \Psi_{n,l-1,1}$, it is said to be born at index $l$; if $p$ is the smallest integer such that $\Psi_{n,l,p}(h_n)=0$, it is said to die at index $l+p$, with a persistence of $p$. This is consistent with the persistence of the relative cohomology $H^k(M,\partial M)$ and the (absolute) homology $H_{3-k}(M)$.
\subsubsection{Tangential harmonic forms}
As there is a one-to-one correspondence between tangential $k$-forms and normal $(3\!-\!k)$-forms, it is indeed sufficient to study the tangential forms only. For completeness and flexibility in numerical implementation, we provide a brief discussion on this dual case.
We first note that there is a homomorphism from coclosed forms on $M_l$ to coclosed forms on $M_{l+p}$, i.e., from $\ker \delta_{l}$ to $\ker \delta_{l+p}$ when restricted to tangential forms $\Omega_t(M_l)$. The same harmonic extension $\mathfrak{E}_{l,p}$ can be obtained through the minimization of the Dirichlet energy $\langle d\omega,d\omega\rangle + \langle \delta \omega,\delta \omega\rangle$ in $M^c_{l,p}$. For tangential forms, $\star\omega_l|_{\partial M_l}=0$, we also impose the condition that $d \omega$ is tangential to the boundary ($\star d \omega_l|_{\partial M_l}=0$). We keep this condition on $\partial M_{l+p}$, on $\partial M_l$ we impose continuity $\omega_{l+p}|_{\partial M_l} = \omega_l|_{\partial M_l}$ and $ d\omega_{l+p}|_{\partial M_l} = d \omega_l|_{\partial M_l}$. A unique solution is again found by forcing it to have 0 projection to the kernel of a mixed-type boundary condition Laplace equation~\cite{zhao20193d}.
To illustrate it with a tangential 1-form $\omega_l$, we can impose the homogeneous boundary condition for the proxy vector field $\mathbf{v}$ on $\partial M_{l+p}$ as in Eq.~(\ref{eqn:bdyT1form}),
\begin{equation}
\label{eqn:bc_ext_t_1}
\mathbf{v}_{l+p}\cdot\mathbf{n}= 0 , \quad \nabla_{\mathbf{n}}(\mathbf{v}_{l+p}\cdot\mathbf{t}_1)=0,\quad \nabla_{\mathbf{n}}(\mathbf{v}_{l+p}\cdot\mathbf{t}_2)=0;
\end{equation}
whereas on $\partial M_l$, the Dirichlet boundary condition $\mathbf{v}_{l+p}=\mathbf{v}_l$ is equivalent to
\begin{equation}
\label{eqn:bc_ext_t}
\mathbf{v}_{l+p}\cdot\mathbf{t}_1=\mathbf{v}_{l}\cdot\mathbf{t}_1,\quad \mathbf{v}_{l+p}\cdot\mathbf{t}_2=\mathbf{v}_{l}\cdot\mathbf{t}_2,\quad \mathbf{v}_{l+p}\cdot\mathbf{n}=0.
\end{equation}
In this case, we can enforce $\mathfrak{E}_{l,p}(\ker \delta_l)\subset \ker \delta_{l+p}$. For example, Fig.~\ref{fgr:normalTangentialVF} (b) shows the extension of tangential harmonic forms from a torus to a solid sphere where both boundary conditions Eqs.~(\ref{eqn:bc_ext_t_1}) and (\ref{eqn:bc_ext_t}) are applied. The inputs (thick lines) are only circulations shown in the right chart of Fig.~\ref{fgr:normalTangentialVF} (b), while the extended outputs (thin lines) are tangential harmonic forms as well. Therefore, we can construct the following commutative diagram on the de Rham complexes for tangential forms on the filtration of $M$:
\begin{center}
\begin{tikzcd}
\Omega^0_t(M_{0}) \arrow[d, "\mathfrak{E}_{0,1}"]
&
\Omega^1_t(M_{0}) \arrow[d, "\mathfrak{E}_{0,1}"]
\arrow[l, shift left, "\delta^1"] &
\Omega^2_t(M_{0}) \arrow[d, "\mathfrak{E}_{0,1}"]
\arrow[l, shift left, "\delta^2"] &
\Omega^3_t(M_{0}) \arrow[d, "\mathfrak{E}_{0,1}"]
\arrow[l, shift left, "\delta^3"] \\
\Omega^0_t(M_{1}) \arrow[d, "\mathfrak{E}_{1,1}"] &
\Omega^1_t(M_{1}) \arrow[d, "\mathfrak{E}_{1,1}"]
\arrow[l, shift left, "\delta^1"] &
\Omega^2_t(M_{1}) \arrow[d, "\mathfrak{E}_{1,1}"]
\arrow[l, shift left, "\delta^2"] &
\Omega^3_t(M_{1}) \arrow[d, "\mathfrak{E}_{1,1}"] \arrow[l, shift left, "\delta^3"] \\
\Omega^0_t(M_{2}) \arrow[d, "\mathfrak{E}_{2,1}"] &
\Omega^1_t(M_{2}) \arrow[d, "\mathfrak{E}_{2,1}"]
\arrow[l, shift left, "\delta^1"] &
\Omega^2_t(M_{2}) \arrow[d, "\mathfrak{E}_{2,1}"]
\arrow[l, shift left, "\delta^2"] &
\Omega^3_t(M_{2}) \arrow[d, "\mathfrak{E}_{2,1}"] \arrow[l, shift left, "\delta^3"] \\
\cdots &
\cdots &
\cdots &
\cdots
\end{tikzcd}
\end{center}
Similar to the normal form case, through the composition with the simple $L_2$ projection onto the finite dimensional tangential harmonic space $P_{\mathcal{H}^k_{\Delta_t, l+p}}$, we have a linear map (also a homomorphism) between the tangential harmonic spaces of different manifolds in the filtration, $\Psi_{t,l,p}=P_{\mathcal{H}^k_{\Delta_t, l+p}}\circ\mathfrak{E}_{l,p}:\mathcal{H}^k_{\Delta_t, l}\to \mathcal{H}^k_{\Delta_t, l+p}$. If $h_t \in \mathcal{H}^k_{\Delta_t,l}$ is not in $\mathrm{im}\; \Psi_{t,l-1,1}$, it is said to be born at index $l$. If $p$ is the smallest integer such that $\Psi_{t,l,p}(h_t)=0$, it is said to die at index $l+p$, with a persistence of $p$. This is consistent with the persistence of the (absolute) cohomology $H^k(M)$ and the relative homology $H_{3-k}(M,\partial M)$.
\subsubsection{Relation among persistent cohomologies under different boundary conditions}
As discussed in section~\ref{Discreteformandspectrumanalysis}, with the duality through Hodge star,
there are only three independent singular spectra $T$, $N$ and $C$ for the three differential/codifferential operators (two for gradient operators under tangential or normal conditions, and one curl operator with either tangential or normal boundary condition). The unions of these spectra produce all the eigenvalues of the eight possible Hodge Laplacians on an arbitrary compact manifold $M$ embedded in a flat 3D space. Moreover, the intersections of spaces spanned by left or right singular vectors of singular value 0 for these operators form the tangential and normal harmonic spaces. Thus, we can restrict our discussion to either normal or tangential fields without loss of generality.
We now discuss the persistence from the perspective of evolving Hodge Laplacian operators. Note that the following discussion is to provide theoretical backgrounds for our proposed use of the evolution of eigenvalues, but not for implementations, since some of the operators discussed may not be sparse matrices when discretized. Recall that for any two manifolds $M_l$ and $M_{l+p}$ in any type of filtration, there is an inclusion map $\mathfrak{I}_{l,p}:M_l \hookrightarrow M_{l+p}$. We call $M_{l+p}$ the \emph{$p$-evolution manifold} of $M_{l}$. We can directly investigate whether a harmonic form in $M_l$ survived in its $p$-evolution manifold, by defining a restricted subset $\tilde{\Omega}^{k}_{p}(M_l)$ of $\Omega^k(M_{l+p})$ and using it to define modified differential and codifferential operators on $M_l$. This restricted subset is given by
\begin{equation}
\label{eqn:strictionSet}
\tilde{\Omega}^{k}_{p}(M_l)=\{\omega\in\Omega^{k}(M_{l+p}) | d^{k}_{l+p}\omega \in \mathfrak{E}_{l,p}(\ker d^{k+1}_{l}) \}.
\end{equation}
This space can be equipped with a modified operator $\tilde{d}^{k}_{l+p}$ that maps it to $\Omega^{k+1}(M_l)$, which is defined as the compound of $d^{k}_{l+p}$ followed by the pullback through the inclusion, i.e., $\tilde{d}^k_{l+p}=\mathfrak{I}_{l,p}^*\circ d^k_{l+p}$. Assuming that we use normal differential forms, we have $d^{k+1}_{l}\tilde{d}^{k}_{l+p}=0$ on $\tilde{\Omega}^k_p(M_l)$ as a result of the definition of the restricted space.
For $\omega\in \Omega^{k-1}(M_l)$, we have $d^{k-1}_{l+p} \mathfrak{E}_{l,p}(\omega)=\mathfrak{E}_{l,p}(d^{k-1}_{l+p}\omega)\in \mathfrak{E}_{l,p}(\ker d^k_l)$, thus $\mathfrak{E}_{l,p}(\Omega^{k-1}(M_l)) \subseteq \tilde{\Omega}^{k-1}_{p}(M_l)$ for $p\geq 0$. Therefore, we can construct the following the $p$-evolution differential form diagram
\begin{center}
\begin{tikzcd}
\Omega^0(M_{l }) \arrow[r, shift left, "d^0_l"] \arrow[dd,"\mathfrak{E}_{l,p}"] &
\Omega^1(M_{l }) \arrow[ldd, shift left, "\tilde{\delta}^1_{l+p}"]
\arrow[r, shift left, "d^1"] \arrow[l, shift left, "\delta^1_l"] \arrow[dd,"\mathfrak{E}_{l,p}"] &
\Omega^2(M_{l }) \arrow[ldd, shift left, "\tilde{\delta}^2_{l+p}"]
\arrow[r, shift left, "d^2_l"] \arrow[l, shift left, "\delta^2_l"] \arrow[dd,"\mathfrak{E}_{l,p}"] &
\Omega^3(M_{l }) \arrow[ldd, shift left, "\tilde{\delta}^3_{l+p}"]
\arrow[l, shift left, "\delta^3_l"] \\
& & & \\
\tilde{\Omega}^{0}_{p}(M_l) \arrow[ruu, shift left, "\tilde{d}^0_{l+p}"] &
\tilde{\Omega}^{1}_{p}(M_l) \arrow[ruu, shift left, "\tilde{d}^1_{l+p}"] &
\tilde{\Omega}^{2}_{p}(M_l) \arrow[ruu, shift left, "\tilde{d}^2_{l+p}"] &
\end{tikzcd}
\end{center}
where $\tilde{\delta}^k_{l+p}$ denotes the adjoint operator of $\tilde{d}^k_{l+p}$. Based on this diagram,
the $p$-evolution Hodge Laplacian $\Delta^{k}_{l,p}$: $\Omega^k(M_l)\rightarrow\Omega^k(M_l)$ can be defined on $M_l$ as
\begin{equation}
\label{eqn:restrictLaplacian}
\Delta^{k}_{l,p} = \delta^{k+1}_{l} d^k_l+\tilde{d}^{k-1}_{l+p}\tilde{\delta}^{k}_{l+p},
\end{equation}
which leads to the definition of the $p$-evolution harmonic space as $\mathcal{H}^k_{l,p}=\ker{\Delta^{k}_{l,p}}=\ker{d^k_l}\cap\ker{\tilde{\delta}^{k}_{l+p}}$. The $p$-evolution (tangential) $k$-form spectra are the sets of $\Delta^{k}_{l,p}$'s eigenvalues for $k=0,1,2,3$. By comparing the $p$-evolution Laplace operator $\Delta^{k}_{l,p}$
and the Laplace operator $\Delta^{k}_{l,0}$, the eigenvalues of the unmodified part, $\delta^{k+1}_{l} d^k_l$, are preserved, and the eigenvalues involving the pullback of the restricted operators are varying with $p$. Next, we examine the part involving $\tilde{d}^{k-1}_{l+p}\tilde{\delta}^{k}_{l+p}$. For any $\alpha\in \ker \tilde{\delta}^k_{l+p},$ and any $\tilde\beta\in \tilde{\Omega }_p^{k-1}(M_l)$, we have $0=\langle\tilde{\delta}^k_{l+p}\alpha,\tilde{\beta}\rangle = \langle\alpha,\tilde{d}^{k-1}_{l+p}\tilde\beta\rangle$. For any $\beta \in\Omega^{k-1}(M_l)$, we have $\langle\delta^k_l \alpha,\beta\rangle = \langle\alpha,d^{k-1}_{l}\beta\rangle = \langle\alpha,\tilde{d}^{k-1}_{l+p}\mathfrak{E}_{l,p}(\beta)\rangle=0$. Therefore, $\ker\tilde{\delta}^k_{l+p}\subset\ker\delta^k_l\subset\Omega^k(M_l)$.
\begin{figure*}[t!]
\centering
\includegraphics[height=3.7in]{fig2}
\begin{picture}(17,0)
\put( -150, 147){\text{(a) Persistence}}
\put( 53, 147){\text{(b) Persistence and progression}}
\put( -150, 17){\text{(c) Identity map}}
\put( 85, 17){\text{(d) Progression}}
\end{picture}
\caption{Persistence and progression on benzene.}
\label{fgr:persistenceProgression}
\end{figure*}
Thus, in terms of persistent cohomology, we may examine the kernel of $p$-evolution Laplace operator for the persistence of topological features of $M_l$ in $M_{l+p}$. In the perspective of spectral analysis, this change is reflected in the multiplicity of the eigenvalue $0$, which changes if $\dim{(\ker\tilde{\delta}^k_l)}<\dim{(\ker\delta^k_l)}$, or remains unchanged when $\dim{(\ker\tilde{\delta}^k_l)}=\dim{(\ker\delta^k_l)}$. In the former case, as shown in Fig.~\ref{fgr:persistenceProgression} (a), multiplicity of 0 (the number of connected components) is reduced for $\Delta^0_{l,p}$, whereas $\Delta^1_{l,p}$ has a new 0 (a tunnel) that is not present in $\Delta^1_{l,p}$. For the latter case, the inclusion map is homotopic to a geometrical deformation of the manifold, which implies the same topology. Fig.~\ref{fgr:persistenceProgression} (d) illustrate an example where the size of tunnel shrinks, and the cohomology groups are isomorphic.
The spectra are continuous when corresponding manifolds are continuously deforming, since, as discussed above, when the level set values are close, the deformation is close to an isometric, and the eigenvalues of Hodge Laplacian is determined by the metric tensor. In particular, the smallest non-zero eigenvalues are continuous if the dimension of null space is stable, but are typically non-differentiable when the multiplicity of eigenvalue 0 is changed. The birth of non-zero eigenvalues is the death of topological features, which signals the death of harmonic basis fields; whereas the birth of zero eigenvalues indicates the birth of topological features. Moreover, the changes in leading smallest non-zero eigenvalues can thus indicate possible pending topological changes as well as the geometric properties when the manifold evolves without topological changes.
For instance, for the $l$-th manifold of the filtration of $M$, $\{\lambda^{T}_{l,i}\}$, $\{\lambda^{C}_{l,i}\}$ and $\{\lambda^{N}_{l,i}\}$ give the eigenvalues of the $T$, $C$ and $N$ sets respectively. In particular, the multiplicities of the zero eigenvalues in $\lambda^{T}_{l,0}$, $\lambda^{C}_{l,0}$, and $\lambda^{N}_{l,0}$ are associated with Betti numbers $\beta_0, \beta_1$ and $\beta_2$, respectively. Additionally, $\lambda^{T}_{l,1}$, $\lambda^{C}_{l,1}$, and $\lambda^{N}_{l,1}$ are the first non-zero eigenvalues, which are known as the Fiedler values in graph theory, an indicator of how well the graph is connected.
In summary, the correspondence established by the spectral analysis provides us with tools to investigate both types of manifold evolution, with persistence for topological features and spectral progression for the geometric properties.
\section{Evolutionary de Rham-Hodge analysis of geometric shapes}\label{resDHT}
In this section, we present the application of the proposed evolutionary de Rham-Hodge method. We demonstrate the spectral analysis with evolutionary de Rham Laplace operators and illustrate their topological persistence and geometric progression associated with submanifolds in $\mathbb{R}^3$. The evolving manifolds in our studies are generated by applying Eq.~(\ref{eqn:manifolds}) to point cloud datasets with a varying level set $c$, with a fixed scaling parameter $\eta$.
For clarity, the first three examples are simple point sets consisting of few points. The two-body set has the location coordinates in $\{(-1.5, 0, 0), (1.5, 0, 0)\}$, and for the four-body and eight-body sets. We duplicate the two-body set by translating $\pm 1.5$ along the $y$-axis, and duplicate the four-body set by translating $\pm 1.5$ along the $z$-axis respectively. Next, we present two concrete molecular examples with interesting topological and geometric features, benzene ($\text{C}_6\text{H}_6$) and fullerene ($\text{C}_{60}$). We show in these proof-of-concept examples that the evolution of leading smallest eigenvalues provides additional information to that of the persistent Betti numbers, which are the same as those of persistent homology analysis. That is, we propose to extend the evaluation of the manifold evolution from persistent Betti numbers (i.e., the multiplicity of the zero eigenvalues of evolutionary de Rham Laplace operators) to a larger subset of the spectra.
\subsection{Two-body system}
\begin{figure}
\centering
\includegraphics[height=1.7in]{fig3}
\begin{picture}(0,0)
\put( -485, 110){\textbf{a}}
\put( -370, 110){\textbf{b}}
\put( -250, 110){\textbf{c}}
\put( -135, 110){\textbf{d}}
\end{picture}
\caption{Snapshots of evolving manifold with the two-body system. {\bf a}, {\bf b}, {\bf c} and {\bf d} are snapshots from the beginning to the end. {\bf b} and {\bf c} show the transition of the Betti-0 number from 2 to 1.
}
\label{fgr:twoAtoms}
\end{figure}
\begin{figure}
\centering
\includegraphics[height=1.82in]{fig4}
\begin{picture}(0,0)
\put(-160, 135){\textbf{i}}
\put( 5, 135){\textbf{ii}}
\put( 165, 135){\textbf{iii}}
\end{picture}
\caption{ Eigenvalues and Betti numbers vs isovalue ($c$) of the two-body system with $\eta = 1.19$ and $\max(\rho)\approx 1.0$.
{\bf i} shows the smallest eigenvalues of the $T$ set.
The drops at $c=0.6$ correspond to snapshots in Figs.~\ref{fgr:twoAtoms} {\bf b} and {\bf c}.
{\bf ii} and {\bf iii} show the smallest eigenvalues of the $C$ and $N$ sets respectively.
}
\label{fgr:twoAtomsEigBetti}
\end{figure}
Our first example illustrates the evolving manifold with a two-body system, in which the initial two connected components merge into one. In this evolution, only the number of components persistent $\beta_0$ changes from 2 to 1, with the other Bettie numbers remain at $0$ throughout. As shown in Fig.~\ref{fgr:twoAtoms}, the two connected components gradually approach each other as the isovalue grows and eventually touch each other as more volume is enclosed.
The change in topology can be observed directly from the blue circle plots in Fig.~\ref{fgr:twoAtoms}, where persistent $\beta_0$ is dropped from 2 to 1 when $c$ increased to around 0.6, and the curves for persistent $\beta_1$ and $\beta_2$ remained flat due to the lack of tunnels or cavities in the system. However, the persistent Betti numbers do not provide any information about the volume increase of the manifold during the evolution, or the increase in the size of the tube-like structure between the two blobs around the body centers after they touch. In contrast, the orange triangles in Fig.~\ref{fgr:twoAtomsEigBetti} show how the first nonzero eigenvalues (Fiedler values) in the three singular spectra ($T$, $C$ and $N$) demonstrated both the topological transition and geometric progression in the evolving manifold.
First, one may observe that the discontinuity for the Fiedler values of the tangential gradient fields $T$ coincides with the jump of persistent $\beta_0$ in Fig.~\ref{fgr:twoAtomsEigBetti} {\bf i}, whereas the Fiedler values of the tangential/normal curl fields $C$ and that of the normal gradient fields $N$ are both smooth as shown in Figs.~\ref{fgr:twoAtomsEigBetti} {\bf ii} and {\bf iii}. These behaviors are consistent with the evolution process only having changes in the number of connected components. More precisely, the multiplicity of the eigenvalue zero in $T$ is $\beta_0=2$ at the beginning, so the Fiedler values can be seen as the third eigenvalue, whereas after the merging, it is switched to be the second eigenvalue, which contributes to the discontinuity in its value. As we will see in later examples, this behavior for the persistence to be directly observable in the discontinuity of Fiedler values happening at the same isovalue when the Betti numbers jump to different integers is generic, which indicates that the birth of non-zero eigenvalue and the death of the harmonic basis are both linked to the death of topological features (homology generators). Moreover, as the tube between the two blobs is created, the extreme values of the first oscillation mode can be placed further apart along the line connecting the two atoms. Thus, $\lambda^T_{l,1}$ jumps to a small value. It grows as the structure becomes stiffer when the narrow tube turns thicker before it eventually decays again as the entire shape turns softer as a ball with a growing radius. Figs.~\ref{fgr:twoAtomsEigBetti} {\bf ii} and {\bf iii} show the smoothness of $\lambda^C_{l,1}$ and $\lambda^N_{l,1}$ which is consistent with the invariant 1st and 2nd Betti numbers.
\subsection{Four-body system}
\begin{figure}
\centering
\includegraphics[height=3.2in]{fig5}
\caption{ Snapshots of evolving manifolds with the four-body system. {\bf a} is the initial point of four components; {\bf b} and {\bf c} show the transition of a ring formed and the persistent Betti-0 number changes from 4 to 1. {\bf g} and {\bf h} show the vanishing of the ring and the persistent Betti-1 number changes from 1 to 0.
}
\label{fgr:fourAtoms}
\begin{picture}(0,0)
\put( -240, 255){\textbf{a}}
\put( -120, 255){\textbf{b}}
\put( -5, 255){\textbf{c}}
\put( 120, 255){\textbf{d}}
\put( -240, 150){\textbf{e}}
\put( -120, 150){\textbf{f}}
\put( -5, 150){\textbf{g}}
\put( 120, 150){\textbf{h}}
\end{picture}
\end{figure}
\begin{figure}
\centering
\includegraphics[height=1.82in]{fig6}
\begin{picture}(0,0)
\put(-160, 135){\textbf{i}}
\put( 5, 135){\textbf{ii}}
\put( 165, 135){\textbf{iii}}
\end{picture}
\caption{Eigenvalues and Betti numbers vs isovalue ($c$) of the four-body system with $\eta = 1.19$ and $\max(\rho)\approx 1.2$.
{\bf i} shows the smallest eigenvalues of the $T$ set. At near $c=0.80$, the persistent Betti-0 number changes from 4 to 1.
{\bf ii} shows the smallest eigenvalues of the $C$ set. At around $c=1.02$, the persistent Betti-1 number changes from 1 to 0.
{\bf iii} shows the smallest eigenvalues of the $N$ set.
}
\label{fgr:fourAtomsEigBetti}
\end{figure}
As another example, we explore an evolution that involves changes in both the number of components persistent $\beta_0$ and the number of tunnels $\beta_1$. With two points added to the two-body set to form a planar square, the evolving manifold can contain a tunnel for a range of isovalues, when each of the four components touches two neighbors to form a ring, which will eventually disappear as the level set value increases to the point that the tunnel in the middle is filled. During the same process, persistent $\beta_0$ drops from four to one when persistent $\beta_1$ increased to one with the formation of the tunnel, but persistent $\beta_0$ stays at $1$ when persistent $\beta_1$ changes back to zero with the disappearance of the tunnel. The persistent Betti number $\beta_2$ remains unchanged as there is no cavity in the system.
In terms of the geometric measurements, the total volume continuously increases, and once the tunnel appears, the size of the handle dual to the tunnel also increases. Finally, at the time of disappearing of the tunnel, two concave surfaces are formed on each side of the blocked tunnel with the concavity decreases with an increasing level set parameter.
Fig.~\ref{fgr:fourAtomsEigBetti} shows all the Fiedler values varying over time, along with the relevant Betti numbers.
As both $\beta_0$ and $\beta_1$ change during the evolution, $\lambda^T_{l,1}$ and $\lambda^C_{l,1}$ are non-differentiable for this example. On the other hand, $\beta_2$ is invariant and thus $\lambda^N_{l,1}$ is smooth. Fig.~\ref{fgr:fourAtomsEigBetti} {\bf i} exhibits a similar pattern as the two-body case of $\lambda^T_{l,1}$. As the volume of the manifold increases, $\lambda^T_{l,1}$ decays until the four components are connected, at which point $\lambda^T_{l,1}$ drops to a much smaller value. After the discontinuity, the increasing handle size leads to an initial growth of $\lambda^T_{l,1}$ due to the increased stiffness of the system, before returning to the decreasing trend as the system becomes more flexible with the increase in the overall volume. In Fig.~\ref{fgr:fourAtomsEigBetti} {\bf ii}, one may observe the difference compared with the first case as we introduce the changes in persistent $\beta_1$. When $\beta_1$ changes from zero to one through the connection of the four components, $\lambda^C_{l,1}$ does not actually change much, because the tangential/normal curl field is not largely influenced when the handle size is nearly zero. In stark contrast, $\lambda^C_{l,1}$ is discontinuous when $\beta_1$ changes back down to zero as the hole disappears. The behavior of $\lambda^C_{l,1}$ after the discontinuity is similar to that of $\lambda^T_{l,1}$, an initial increase in stiffness and then a decrease again. Moreover, by comparing Figs.~\ref{fgr:fourAtomsEigBetti} {\bf i} and {\bf ii}, we observe that the value of $\lambda^T_{l,1}$ starts to decrease just when $\lambda^C_{l,1}$ is discontinuous, as the structural change in the tunnel also contributed to the ``stiffness'' of the tangential gradients. Finally, Fig.~\ref{fgr:fourAtomsEigBetti} {\bf iii} shows the smooth Fiedler values $\lambda^N_{l,1}$ with an unchanged persistent $\beta_2$.
In summary, from the second example, one can notice that $\lambda^C_{l,1}$ can reveal the information of persistent $\beta_1$
and some geometric properties after the disappearance of the hole. In addition, the coincidental topological changes, the birth of hole that coincides with the death of a few connected components, can be distinguished by the spectral functions $\lambda^T_{l,1}$ and $\lambda^C_{l,1}$.
\subsection{Eight-body system}
\begin{figure}
\centering
\includegraphics[height=2.4in]{fig7}
\begin{picture}(0,0)
\put( -487, 157){\textbf{a}}
\put( -410, 157){\textbf{b}}
\put( -465, 83){\textbf{b}'}
\put( -333, 157){\textbf{c}}
\put( -357, 83){\textbf{c}'}
\put( -255, 157){\textbf{d}}
\put( -244, 83){\textbf{d}'}
\put( -176, 157){\textbf{e}}
\put( -125, 83){\textbf{e}'}
\put( -98, 157){\textbf{f}}
\end{picture}
\caption{Snapshots of evolving manifold with the eight-body system.
{\bf a} presents the initial state with eight components.
{\bf b} and {\bf c} show the formation of 6 tunnels when the persistent Betti-0 number changes from 8 to 1, and the persistent Betti-1 number changes from 0 to 5.
{\bf d} and {\bf e} illustrate that a cavity appears, so the persistent Betti-1 number drops to 0 and the persistent Betti-2 number increases to 1.
{\bf f} shows a solid volume without cavity. The gray planes cut manifolds to create cross-section views to illustrate the process of the formation of cavity as shown in {\bf b'}, {\bf c'}, {\bf d'} and {\bf e'}.
}
\label{fgr:eightAtoms}
\end{figure}
\begin{figure}
\centering
\includegraphics[height=1.82in]{fig8}
\begin{picture}(0,0)
\put(-160, 135){\textbf{i}}
\put( 5, 135){\textbf{ii}}
\put( 165, 135){\textbf{iii}}
\end{picture}
\caption{ Eigenvalues and Betti numbers vs isovalue ($c$) of the eight-body system with $\eta = 1.53$ and $\max(\rho)\approx1.1$.
{\bf i} shows the Fiedler values of the $T$ set and persistent Betti-0 numbers.
{\bf ii} shows the Fiedler values of the $C$ set and persistent Betti-1 numbers.
{\bf iii} illustrates the comparison of $\lambda_{l,1}^C$ and persistent $\beta_2$.
}
\label{fgr:eightAtomsEigBetti}
\end{figure}
We constructed the simple eight-body system to analyze the behavior of Hodge Laplacian spectra with an evolving cavity in the filtration. In this system, not only multiple connected components and multiple tunnels are involved, but a cavity also appears after the isovalue reaches a certain level before disappearing eventually. Thus, the dimension-2 Betti number $\beta_2$, which measures the number of cavities, changes during this process.
As shown in Fig.~\ref{fgr:eightAtoms}, the eight symmetric components start as blobs around eight vertices of a cube. Then they expand as the isovalue increases until they touch each other and form 6 rings, one for each face of the cube. At this point, persistent $\beta_0$ drops from 8 to 1, when persistent $\beta_1$ increases from 0 to 5 (as five of the six tunnels are independent homology generators). As the level set value increases to the point that the tunnels are filled, persistent $\beta_1$ drops back to 0, but persistent $\beta_2$ increases to $1$ as a cavity formed inside the manifold. The cavity is filled up eventually, and persistent $\beta_2$ drops back to 0.
In Fig.~\ref{fgr:eightAtomsEigBetti}, the Fiedler values as functions of isovalue are shown in Figs.~\ref{fgr:eightAtomsEigBetti} {\bf i} and {\bf ii}, which exhibit similar behaviors as in the first two examples.
As in the previous example, the comparison between Figs.~\ref{fgr:eightAtomsEigBetti} {\bf i} and {\bf ii} shows that at $c=0.3$ the spectral function $\lambda^T_{l,1}$ starts to decay when $\lambda^C_{l,1}$ is discontinuous. Different from the previous examples, the smallest eigenvalues in {\bf iii} is no longer differentiable as persistent $\beta_2$ changes from one to zero near isovalue 0.5. Fig.~\ref{fgr:eightAtomsEigBetti} {\bf iii} also indicates that at the isovalue where $\lambda^N_{l,1}$ is non-differentiable, $\lambda^C_{l,1}$ starts to decrease. Moreover, the simultaneous topological changes, the disappearance of tunnels and the appearance of the cavity, can be observed in $\lambda^C_{l,1}$. The disappearance of the cavity can be observed from $\lambda^N_{l,1}$.
From these preliminary results of the evolutionary de Rham-Hodge method, one may observe that the singular values in different spectra taken as functions of the isovalue $c$ not only illustrate the changes of topological features of different dimensions throughout the evolution of the manifold but also reveal the geometric features in different dimensions.
Therefore, empirically, the importance of low frequencies rather than the multiplicity of the zeroth frequency can already be observed in these simplistic constructions for features of different dimensionality. In the following, we demonstrate similar characteristics of spectral functions in two molecular systems.
\subsection{Benzene molecule}
Benzene ($\text{C}_6\text{H}_6$) is a small organic chemical compound which consists of six carbon atoms in a planar hexagon ring and six hydrogen atoms each connected with one carbon atom. In this system, atoms have
different van der Waals radii, one for carbon and another for hydrogen. The carbon atoms are closer to each other than the hydrogen atoms and form the benzene ring. Thus, benzene is a perfectly simple yet realistic example to illustrate the evolutionary de Rahm-Hodge method. With the benzene data, we use $\eta=0.45$ to generate evolving manifolds.
\begin{figure}
\centering
\includegraphics[height=3.1in]{fig9}
\begin{picture}(0,0)
\put( -480, 210){\textbf{a}}
\put( -360, 210){\textbf{b}}
\put( -240, 210){\textbf{c}}
\put( -120, 210){\textbf{d}}
\put( -480, 110){\textbf{e}}
\put( -360, 110){\textbf{f}}
\put( -240, 110){\textbf{g}}
\put( -120, 110){\textbf{h}}
\end{picture}
\caption{ Manifold evolution of benzene with $\eta=0.45\times r_{\rm vdw}$.
{\bf a} through {\bf h} are snapshots from the start to the end.
{\bf a} and {\bf b} show the transition of the persistent Betti-0 number from 12 to 6.
{\bf c} and {\bf d} show the formation of a ring;
The Betti-0 number changes from 6 to 1 and remains at one to the end, whereas
the Betti-1 number changes from zero to one.
{\bf d}, {\bf e}, {\bf f} and {\bf g} illustrate the deformation of the hexagonal tunnel to a round tunnel.
From {\bf g} to {\bf h}, the ring disappears and the Betti-1 number changes from 1 back to 0.
}
\label{fgr:benzene45}
\end{figure}
The first evolving manifold of benzene is generated at $\eta=0.45$. In the beginning, there are 12 components, with each smooth component center around one atom location as shown in Fig.~\ref{fgr:benzene45} {\bf a}. The van der Waals radius of carbon atoms is larger than that of hydrogen atoms, so the components associated with the carbon atoms are larger. From Fig.~\ref{fgr:benzene45} {\bf b} to Fig.~\ref{fgr:benzene45} {\bf c}, the originally separated components of the atoms start to connect pairwise, with a narrow tube formed between each hydrogen to its bonded carbon and thus, the persistent Betti-0 number is reduced to 6. The behavior of the manifold is similar to essentially six copies of our first example, the two-body system, until the six components of Fig.~\ref{fgr:benzene45} {\bf c} start to form a hexagonal ring, as shown in Fig.~\ref{fgr:benzene45} {\bf d}. At this point, there are six narrow tubes, one for each bond between two adjacent carbon atom pairs. As the density function continues to expand, the hexagonal ring evolves into a round cycle around a tunnel with a shrinking diameter. As the diameter of the tunnel reduces to zero at some parameter value between those of Fig.~\ref{fgr:benzene45} {\bf g} and Fig.~\ref{fgr:benzene45} {\bf h}, the noncontractible cycle disappears. During this topological change, the tiny cycle in the middle of the manifold in Fig.~\ref{fgr:benzene45} {\bf g} is filled up to form two concave surface patches in the middle of the manifold in Fig.~\ref{fgr:benzene45} {\bf h}. The final topology of this system remains as a single component with a volume larger than that of Fig.~\ref{fgr:benzene45} {\bf h}.
\begin{figure}
\centering
\includegraphics[height=1.82in]{fig10}
\begin{picture}(0,0)
\put(-160, 135){\textbf{i}}
\put( 5, 135){\textbf{ii}}
\put( 165, 135){\textbf{iii}}
\end{picture}
\caption{ Eigenvalues and Betti numbers vs isovalue ($c$) of the benzene system with $\eta = 0.45$ and $\max(\rho)\approx1.1$.
{\bf i} shows the smallest eigenvalues of the $T$ set.
The drops at $c=0.12$ correspond to snapshots in Figs.~\ref{fgr:benzene45} {\bf a} and {\bf b}.
The drops at $c=0.22$ correspond to snapshots in Figs.~\ref{fgr:benzene45} {\bf c} and {\bf d}.
{\bf ii} shows the smallest eigenvalue of the $N$ set.
The drops at $c=0.9$ correspond to snapshots in Figs.~\ref{fgr:benzene45} {\bf g} and {\bf h}.
{\bf iii} shows the smallest eigenvalues of the $C$ set.
}
\label{fgr:benzene45EigBetti}
\end{figure}
Fig.~\ref{fgr:benzene45EigBetti} shows the Fiedler values of the $T$, $N$ and $C$ sets and their relations with the persistent Betti numbers when seen as a function of varying isovalues. First, for the $T$ set, $\lambda^T_{l,1}$ has two jumps at $c=0.12$ and $c=0.22$, which divide the $\lambda^T_{l,1}$ to three curve segments. Both discontinuities correspond to the decreases of the persistent Betti 0, from twelve to six, and then to one. As shown in Figs.~\ref{fgr:benzene45EigBetti} {\bf i}, $\lambda_{l,1}^T$ cannot only tell the topological changes but also give some additional information of a continuous portion of the evolution. After $c=0.22$, $\lambda_{l,1}^T$ increases first and reaches its maximum at $c=0.9$ when the ring just disappears, at which point the structure (for tangential gradients) starts to grow softer as an expanding blob instead of a thicker ring. Fig.~\ref{fgr:benzene45EigBetti} {\bf ii} presents the jump of $\lambda_{l,1}^C$, which is correlated to the disappearance of the hole as indicated by the change of Betti-1 number from one to zero.
After the jump, $\lambda_{l,1}^C$ also increases slightly first and decays in the end. There is no cavity involved, so the spectral function shows a steady progression for the $C$ set as in our four-body example. One difference from that example is the finer grid used in the calculation, in order to handle the initial small components for the hydrogen atoms.
\subsection{Buckminsterfullerene}
The buckyball ($\text{C}_{60}$) has a beautiful structure composed of sixty carbon atoms.
It has twenty hexagons and twelve pentagons that resemble the pattern on a soccer ball, which has a rich structure with both geometric symmetries and topology features. With our continuous density function, at certain values of $\eta$, the manifold evolution covers all the possible values of the persistent Betti-1 number allowed by the symmetry.
However, it is difficult to cover all the topological space for a density function associated with a single kernel size $\eta$. Thus we propose to use a multiscale (with a few different kernel sizes) analysis of the manifold evolution.
By using different $\eta$'s to capture different sets of snapshots for the evolving manifolds, we can compare the spectra across different kernel sizes $\eta$ as well as different control parameters $c$. We use the buckyball as an example for the multiscale analysis of manifold evolution, and demonstrate how the spectra provide information on the evolution of their topological spaces and geometric features.
\begin{figure}
\centering
\includegraphics[height=4in]{fig11}
\begin{picture}(0,0)
\put( -235, 265){\textbf{a}}
\put( -120, 265){\textbf{b}}
\put( -5, 265){\textbf{c}}
\put( 115, 265){\textbf{d}}
\put( 90, 135){\textbf{d}'}
\put( -240, 135){\textbf{e}}
\put( -75, 135){\textbf{e}'}
\end{picture}
\caption{Illustration of fullurene ($\text{C}_{60}$) manifold evolution with $\eta=0.5\times r_{\rm vdw}$.
{\bf a} presents sixty components around carbon atom positions.
{\bf a} and {\bf b} show that the components connect if they share a pentagonal hole, and persistent $\beta_0$ changes from 60 to 12 and persistent $\beta_1$ changes from 0 to 12.
{\bf c} shows the hexagonal holes are formed, resulting in the change of persistent $\beta_0$ to 1 and persistent $\beta_1$ to 31. (There are 32 rings, but only 31 are independent in terms of homology.)
{\bf c} and {\bf d} show that the 12 pentagonal rings disappear and the persistent Betti-1 number drops from 31 to 19.
{\bf d} and {\bf e} show that the 20 hexagonal rings disappear and a cavity forms inside, so that persistent $\beta_1$ drops to $0$ and persistent $\beta_2$ increases to 1.
The vertical plan cuts the manifolds that gives an illustration of cavity in {\bf d'} and {\bf e'}.
}
\label{fgr:fullerene50}
\end{figure}
\begin{figure}
\centering
\includegraphics[height=1.82in]{fig12}
\begin{picture}(0,0)
\put(-160, 135){\textbf{i}}
\put( 5, 135){\textbf{ii}}
\put( 165, 135){\textbf{iii}}
\end{picture}
\caption{Eigenvalues and Betti numbers vs isovalue ($c$) of the fullurene ($\text{C}_{60}$) system with $\eta = 0.5\times r_{\rm vdw}$ and $\max(\rho)\approx1.3$.
{\bf i} gives the Fiedler values of the $T$ set and persistent $\beta_0$.
{\bf ii} presents the comparison of $\lambda^C_{l,1}$ and persistent $\beta_1$.
{\bf iii} shows the Fiedler values of the $N$ set and persistent $\beta_2$.
}
\label{fgr:fullerene50EigBetti}
\end{figure}
For kernel scaling parameter $\eta=0.5\times r_{\rm vdw}$, the manifold evolution starts with 60 components as shown in Fig.~\ref{fgr:fullerene50} {\bf a}. The components start the expansion, each around the position of one carbon atom, and merge into larger connected components if they share a common pentagon in the skeleton structure as shown in Fig.~\ref{fgr:fullerene50} {\bf b}. This leads to the changes in persistent $\beta_0$ (from 60 to 12) and persistent $\beta_1$ (from 0 to 12). Fig.~\ref{fgr:fullerene50} {\bf c} shows the snapshot right after the appearance of twenty hexagonal holes. Next, each hole starts to shrink. As each pentagonal hole has a smaller size than that of a hexagonal hole, we observe in Fig.~\ref{fgr:fullerene50} {\bf c} to Fig.~\ref{fgr:fullerene50} {\bf d}, the pentagonal holes disappear before the hexagonal holes also disappear. Simultaneous to the disappearance of hexagons, a cavity is created. In Fig.~\ref{fgr:fullerene50} {\bf e} after the formation of the cavity, both the outer surface and the inner surface contain numerous regions of concavity and gradually, the shape evolves to resemble a slightly dented thick spherical shell.
For analysis of this evolution, Fig.~\ref{fgr:fullerene50EigBetti} illustrates the eigenvalues and Betti numbers versus the isolvaue $c$. Fig.~\ref{fgr:fullerene50EigBetti} {\bf i} gives the Fiedler values (smallest eigenvalue) of the $T$ set and $\beta_0$. This Betti number has two drops, from 60 to 12, and then to 1. Within each interval of isovalues with the same persistent Betti number, $\lambda_{l,1}^T$ is changing smoothly as expected from our discussion on homeomorphic shapes with a slowly evolving metric. Fig.~\ref{fgr:fullerene50EigBetti} {\bf ii} presents the information that the Fiedler values of the $C$ set can offer. For the interval, $c\in [0.16,0.5]$, persistent $\beta_1$ remains at $31$, and the continuous decrease in $\lambda^C_{l,1}$ shows that the geometric structure is ``softer'' for the curl fields as the handles grow thicker. Similarly, for intervals within which persistent $\beta_1$ equals to 19 or 1, $\lambda^C_{l,1}$ is a smooth function within each interval but is discontinuous at the boundary of these intervals where the topology transitions.
The Fiedler values of the $N$ set are given in Fig.~\ref{fgr:fullerene50EigBetti} {\bf iii}, which, although mostly smooth, also has changed in slope at isovalues associated with changes in connected components and tunnels.
As the examples become more complex, the spectral functions also exhibit richer structure, with the advantage of indicating both topological persistence and geometric progression.
\begin{figure}
\centering
\includegraphics[height=4in]{fig13}
\begin{picture}(0,0)
\put( -235, 265){\textbf{a}}
\put( -120, 265){\textbf{b}}
\put( -5, 265){\textbf{c}}
\put( 115, 265){\textbf{d}}
\put( 90, 135){\textbf{d}'}
\put( -240, 135){\textbf{e}}
\put( -71, 135){\textbf{e}'}
\end{picture}
\caption{Illustration of fullurene ($\text{C}_{60}$) manifold evolution with $\eta=0.8\times r_{\rm vdw}$.
{\bf a} shows 12 initial solid pentagonal components.
{\bf b} and {\bf c} show the formation and contraction process of the 20 rings.
{\bf d} is the snapshot right after the formation of the cavity.
{\bf e} shows the final stage as a solid ball of this example.
}
\label{fgr:fullerene80}
\end{figure}
\begin{figure}
\centering
\includegraphics[height=1.82in]{fig14}
\begin{picture}(0,0)
\put(-160, 135){\textbf{i}}
\put( 5, 135){\textbf{ii}}
\put( 165, 135){\textbf{iii}}
\end{picture}
\caption{ Eigenvalues and Betti numbers vs isovalue ($c$) of the fullurene ($\text{C}_{60}$) system with $\eta = 0.8\times r_{\rm vdw}$; $\max{\rho}\approx2.5$.
{\bf i} gives the Fiedler values of the $T$ set and persistent $\beta_0$.
{\bf ii} presents the comparison of $\lambda^C_{l,1}$ and persistent $\beta_1$.
{\bf iii} shows the Fiedler values of the $N$ set and persistent $\beta_2$.
}
\label{fgr:fullerene80EigBetti}
\end{figure}
For large and dense point sets as in this fullerene, the shape of the manifold evolution is heavily influenced by the kernel size $\eta$. To show the importance of multiscale analysis, we create a second evolution with $\eta=0.8\times r_{\rm vdw}$ and generate the snapshots in Fig.~\ref{fgr:fullerene80}. For the initial isovalue, as seen in Fig.~\ref{fgr:fullerene80} {\bf a}, the manifold consists of twelve pentagonal components. Unlike the evolution with $\eta=0.5\times r_{\rm vdw}$, which contains pentagonal holes alongside hexagonal holes, here the pentagonal components are already with the holes filled before the hexagonal holes are even formed. Thus, the two evolutions cannot find a homeomorphism between their stages even if any isovalues are allowed, which implies that they can reveal different information regarding the system. As the components connect, twenty rings show up as in Figs.~\ref{fgr:fullerene80} {\bf b} and \ref{fgr:fullerene80} {\bf c}, with decreasing diameters for increasing isovalues. Once the cavity is formed, the large inner surface shown in Fig.~\ref{fgr:fullerene80} {\bf d} starts to contract, and the manifold ends up as a solid ball in Fig.~\ref{fgr:fullerene80} {\bf e}. As for the spectral functions, Fig.~\ref{fgr:fullerene80EigBetti} shows three plots of the Fiedler values of the $T$, $C$ and $N$ sets and the persistent Betti numbers against the isovalues, respectively. Since the components connect right after first two snapshots, Fig.~\ref{fgr:fullerene80EigBetti} {\bf i} shows the drop of $\lambda_{l,1}^T$ in the third snapshot as persistent $\beta_1$ changes from 12 to 1. The Fiedler values $\lambda_{l,1}^T$ then increases before starting to decrease when persistent $\beta_1$ drops to 0 when the system can be seen as a shell growing softer with thicker membrane instead of a structure growing stiffer with thicker supporting handles. Similarly, there are only a few snapshots for the evolving manifold to have rings as they are quickly filled up. In Fig.~\ref{fgr:fullerene80EigBetti} {\bf ii}, the Fiedler values $\lambda_{l,1}^C$ already decreases quickly before plunging to a small number at the point when holes disappear. During the period of the inner surface contracting and outer surface expanding, $\lambda_{l,1}^C$ increases first as the structure grows stiffer for curl fields, and then grows softer eventually near the very end of the manifold evolution. In the last plot of Fig.~\ref{fgr:fullerene80EigBetti}, $\lambda_{l,1}^N$ slightly increases at beginning and then decreases smoothly. The disappearance of the cavity is captured at the end of snapshots, thus there is a non-differentiable point at end of this spectral function. We see in this evolution again, that the progression of the manifold evolution can be observed in the spectral functions as well as the topological transitions.
\section{Conclusion} \label{conclusion}
While persistent homology has had tremendous success in data science and machine learning via a multiscale analysis, it does not capture geometric progression when there are no topological changes. In contrast, although de Rham-Hodge theory provides a simultaneous geometric and topological analysis, it lacks multiscale information. We introduce an evolutionary de Rham-Hodge method to offer a unified multiscale geometric and topological representation of data. The evolutionary de Rham-Hodge method is applied to analyze the topological and geometric characteristics through the evolution of manifolds which are a family of 3D multiscale shapes constructed from an evolutionary filtration process. In addition to exactly the topological persistence that would be obtained from persistent homology, the analysis of the evolutionary spectra of Hodge Laplacian operators portrays geometric progression. Specifically, appropriate treatments of the Hodge Laplacian boundary conditions gives rise to three unique sets of singular spectra associated with the tangential gradient eigen field ($T$), the curl eigen field ($C$), and the tangential divergent eigen field ($N$). The multiplicities of the zero eigenvalues corresponding to the $T$, $C$, and $N$ sets of spectra are exactly the persistent Betti-0 ($\beta_0$), Betti-1 ($\beta_1$), and Betti-2 ($\beta_2$) numbers one would obtain from persistent homology. Using discrete exterior calculus in close manifolds or compact manifolds with boundary, we show that investigating the first non-zero eigenvalues, i.e., Fiedler values, of the $T$, $C$, and $N$ sets of evolutionary spectra unveil both the persistence for topological features and the geometric progression for the shape analysis. For a proof-of-concept analysis, the evolutionary de Rham-Hodge method is applied to a few benchmark examples, including the two-body system, four-body system, eight-body system, benzene (C$_{6}$H$_{6}$), and buckminsterfullerene (C$_{60}$). Extensive numerical experiments demonstrate that the present evolutionary de Rham-Hodge method captures the multiscale geometric progression and topological persistence of data.
In the present proof-of-concept analysis, only the first non-zero eigenvalues are presented. However, in practical applications, both eigenfunctions and high-order eigenvalues are needed in de Rham-Hodge modeling and analysis as shown in our recent work \cite{zhao2019rham}. The proposed evolutionary de Rham-Hodge method provides a solid foundation for a wide variety of applications, including shape analysis, image processing, computer vision, pattern recognition, computer aided design, network analysis, computational biology, and drug design. Since the evolutionary de Rham-Hodge method can reveal both topological persistence and geometric progression, it will offer a powerful multiscale representation of data for machine learning, including deep learning.
Finally, the present evolutionary de Rham-Hodge method opens new opportunities in further theoretical developments in differential geometry, such as the introduction of multiscale analysis to Riemannian connection, tensor bundle, index theory, and K theory.
\section{Acknowledgments}
This work was supported in part by NSF Grants DMS1721024, DMS1761320, IIS1900473, NIH grants GM126189 and GM129004, Bristol-Myers Squibb, and Pfizer. GWW thanks Vidit Nanda for useful discussion.
\bibliographystyle{alpha}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,055 |
Warrior Wraps can help you design and wrap your Store Front. We offer full wraps, partial wraps, cut decals, and more. Your Store Front shows your customers who you are. With our help we can turn the ordinary to extraordinary. We offer solid vinyl. window perf, and frosted vinyl. Make a statement before your customers even open the door. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,246 |
Q: sam local start-api cannot be accessed from outside I am using aws sam local to developer few lambdas/nanoservices
I start the lambda container with:
sudo sam local start-api --docker-network db-pros
where db-pros is the database container
when I go to 127.0.0.1:3000/lambda-name everything works fine however when I try to connect from the test device (Android phone which is connected to WiFi) I cannot.
Tried to use the IP (both Ethernet and docker0) from ifconfig and I still can't connect.
I do not know if it's possible and if yes how.
A: Use sam local start-api --host 0.0.0.0 instead.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 2,592 |
from __future__ import division, print_function, absolute_import
import os
from os.path import join
from scipy._build_utils import numpy_nodepr_api
def configuration(parent_package='',top_path=None):
from numpy.distutils.misc_util import Configuration
from scipy._build_utils.system_info import get_info
config = Configuration('integrate', parent_package, top_path)
# Get a local copy of lapack_opt_info
lapack_opt = dict(get_info('lapack_opt',notfound_action=2))
# Pop off the libraries list so it can be combined with
# additional required libraries
lapack_libs = lapack_opt.pop('libraries', [])
mach_src = [join('mach','*.f')]
quadpack_src = [join('quadpack', '*.f')]
lsoda_src = [join('odepack', fn) for fn in [
'blkdta000.f', 'bnorm.f', 'cfode.f',
'ewset.f', 'fnorm.f', 'intdy.f',
'lsoda.f', 'prja.f', 'solsy.f', 'srcma.f',
'stoda.f', 'vmnorm.f', 'xerrwv.f', 'xsetf.f',
'xsetun.f']]
vode_src = [join('odepack', 'vode.f'), join('odepack', 'zvode.f')]
dop_src = [join('dop','*.f')]
quadpack_test_src = [join('tests','_test_multivariate.c')]
odeint_banded_test_src = [join('tests', 'banded5x5.f')]
config.add_library('mach', sources=mach_src,
config_fc={'noopt':(__file__,1)})
config.add_library('quadpack', sources=quadpack_src)
config.add_library('lsoda', sources=lsoda_src)
config.add_library('vode', sources=vode_src)
config.add_library('dop', sources=dop_src)
# Extensions
# quadpack:
include_dirs = [join(os.path.dirname(__file__), '..', '_lib', 'src')]
if 'include_dirs' in lapack_opt:
lapack_opt = dict(lapack_opt)
include_dirs.extend(lapack_opt.pop('include_dirs'))
config.add_extension('_quadpack',
sources=['_quadpackmodule.c'],
libraries=['quadpack', 'mach'] + lapack_libs,
depends=(['__quadpack.h']
+ quadpack_src + mach_src),
include_dirs=include_dirs,
**lapack_opt)
# odepack/lsoda-odeint
odepack_opts = lapack_opt.copy()
odepack_opts.update(numpy_nodepr_api)
config.add_extension('_odepack',
sources=['_odepackmodule.c'],
libraries=['lsoda', 'mach'] + lapack_libs,
depends=(lsoda_src + mach_src),
**odepack_opts)
# vode
config.add_extension('vode',
sources=['vode.pyf'],
libraries=['vode'] + lapack_libs,
depends=vode_src,
**lapack_opt)
# lsoda
config.add_extension('lsoda',
sources=['lsoda.pyf'],
libraries=['lsoda', 'mach'] + lapack_libs,
depends=(lsoda_src + mach_src),
**lapack_opt)
# dop
config.add_extension('_dop',
sources=['dop.pyf'],
libraries=['dop'],
depends=dop_src)
config.add_extension('_test_multivariate',
sources=quadpack_test_src)
# Fortran+f2py extension module for testing odeint.
config.add_extension('_test_odeint_banded',
sources=odeint_banded_test_src,
libraries=['lsoda', 'mach'] + lapack_libs,
depends=(lsoda_src + mach_src),
**lapack_opt)
config.add_subpackage('_ivp')
config.add_data_dir('tests')
return config
if __name__ == '__main__':
from numpy.distutils.core import setup
setup(**configuration(top_path='').todict())
| {
"redpajama_set_name": "RedPajamaGithub"
} | 7,881 |
{"url":"http:\/\/amu.sci.am\/archives\/1634","text":"# Some relations between the self-commutator and the numerical range of operators\n\n25 April 2014, a general meeting of AMU was held. Prof. Levon Gevorgyan from the State Engineering University of Armenia have presented\u00a0\u00a0a talk \u201cSome relations between the self-commutator and the numerical range of operators\u201d.\n\nAbstract:\nFor a Hilbert space bounded linear operator the norm of its self-commutator\u00a0\u00a0\u00a0\u00a0 shows \u00abhow far\u00bb is it from being normal. For some classes of operators different estimates of that norm from above (Putnam\u2019s inequality, Berger-Shaw theorem) and from below (Khavinson, Ferguson ttheorems) are known.In the report similar problems will be discussed for finite-dimensional operators (the tensor product of two Hilbert space elements, 2\u00d72 complex matrices, tri-diagonal Toeplitz matrices, SOR matrices), as well for infinite-dimensional oerators (composition operators, acting in the Dirichlet sace, the Volterra integration operator).It turned out that the above mentioned norm is connected with the numerical range of the operator. Solving an isoperimetric-type problem for compact subsets of the complex plane, the norm of the self-commutator is bounded from above by the multiple of numerical range\u2019s area.|Based on the numerical evidence, two more precise conjectures on the value of that norm are formulated.\n\nThis entry was posted in Sessions. Bookmark the permalink.","date":"2017-10-22 04:22:02","metadata":"{\"extraction_info\": {\"found_math\": false, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 0, \"mathjax_asciimath\": 0, \"img_math\": 0, \"codecogs_latex\": 0, \"wp_latex\": 0, \"mimetex.cgi\": 0, \"\/images\/math\/codecogs\": 0, \"mathtex.cgi\": 0, \"katex\": 0, \"math-container\": 0, \"wp-katex-eq\": 0, \"align\": 0, \"equation\": 0, \"x-ck12\": 0, \"texerror\": 0, \"math_score\": 0.8856328725814819, \"perplexity\": 1754.5145038223761}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 20, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2017-43\/segments\/1508187825141.95\/warc\/CC-MAIN-20171022041437-20171022061437-00336.warc.gz\"}"} | null | null |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.