prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What are some fields in which the inverse problem is encountered?

Read the following text and answer briefly.

Context 1: \section{Introduction}
Given a data set and a model with some unknown parameters, the inverse problem aims to find the values of the model parameters that best fit the data   
In this work, in which we focus on systems of interacting elements,
 the inverse problem concerns  the statistical inference
 of the underling interaction network and of its coupling coefficients from observed data on the dynamics  of the system  
 Versions of this problem are encountered in physics, biology (e g , \cite{Balakrishnan11,Ekeberg13,Christoph14}), social sciences and finance (e g ,\cite{Mastromatteo12,yamanaka_15}), neuroscience (e g , \cite{Schneidman06,Roudi09a,tyrcha_13}), just to cite a few, and are becoming more and more important due to the increase in the amount of data available from these fields \\
 \indent 
 A standard approach used in statistical inference is to predict the interaction couplings by maximizing the likelihood function 
 This technique, however, requires the evaluation of the  
 
   partition function that, in the most general case, concerns a number of computations scaling exponentially with the system size 
  
  
    Boltzmann machine learning uses Monte Carlo sampling to compute the gradients of the Log-likelihood looking for stationary points \cite{Murphy12} but this method is computationally manageable only for small systems  A series of faster approximations, such as naive mean-field, independent-pair approximation \cite{Roudi09a, Roudi09b}, inversion of TAP equations \cite{Kappen98,Tanaka98}, small correlations expansion \cite{Sessak09}, adaptive TAP \cite{Opper01}, adaptive  cluster expansion \cite{Cocco12} or Bethe approximations \cite{Ricci-Tersenghi12, Nguyen12}  have, then, been developed  These techniques take as input means and correlations of observed variables and most of them assume a fully connected graph as underlying connectivity network, or expand  around it by perturbative dilution   In most cases, network reconstruction turns out to  be not accurate for small data sizes and/or when couplings are  strong or, else, if the original interaction network is sparse \\
\indent
 A further method, substantially improving performances for small data, is the so-called Pseudo-Likelyhood Method (PLM) \cite{Ravikumar10}  In Ref  \cite{Aurell12} Aurell and Ekeberg performed a comparison between PLM and some of the just mentioned mean-field-based algorithms on the pairwise interacting Ising-spin  ($\sigma = \pm 1$) model, showing how PLM performs sensitively better, especially on sparse graphs and in the high-coupling limit, i e , for low temperature 
 
 In this work, we aim at performing statistical inference  on a model whose interacting variables are continuous $XY$ spins, i e , $\sigma \equiv \left(\cos \phi,\sin \phi\right)$ with $\phi \in [0, 2\pi )$  The developed tools can, actually, be also straightforward applied  to the $p$-clock model  \cite{Potts52} where the phase $\phi$ takes discretely equispaced $p$ values  in the $2 \pi$ interval, $\phi_a =  a 2 \pi/p$, with $a= 0,1,\dots,p-1$  The $p$-clock model, else called vector Potts model, gives a hierarchy of discretization of the $XY$ model as $p$ increases  For $p=2$, one recovers the Ising model, for $p=4$ the Ashkin-Teller model \cite{Ashkin43}, for $p=6$ the ice-type model \cite{Pauling35,Baxter82} and the eight-vertex model \cite{Sutherland70,Fan70,Baxter71} for $p=8$   
It turns out to be very useful also for numerical implementations of the continuous $XY$ model  
Recent analysis on the multi-body $XY$ model has shown that for a limited number of discrete phase values ($p\sim 16, 32$) the thermodynamic critical properties of the $p\to\infty$ $XY$ limit are promptly recovered \cite{Marruzzo15, Marruzzo16}   
Our main motivation to study statistical inference is that these kind of models have recently turned out to be rather useful in describing the behavior of optical systems, 
including standard mode-locking lasers \cite{Gordon02,Gat04,Angelani07,Marruzzo15} and random lasers \cite{Angelani06a,Leuzzi09a,Antenucci15a,Antenucci15b,Marruzzo16}  
In particular, the inverse problem on the pairwise XY model analyzed here might be of help in recovering images from light propagated through random media  


      This paper is organized as follows: in Sec  \ref{sec:model} we introduce the general model  and we discuss its  derivation also  as a model for light transmission through random scattering media  
    In Sec  \ref{sec:plm} we introduce the PLM with $l_2$ regularization  and with decimation, two variants of the PLM respectively introduced in Ref  \cite{Wainwright06} and \cite{Aurell12} for the inverse Ising problem  
    Here, we analyze these techniques for continuous $XY$ spins and we test them on thermalized data generated by Exchange Monte Carlo numerical simulations of the original model dynamics  In Sec  \ref{sec:res_reg} we  present the results related to the PLM-$l_2$  In Sec  \ref{sec:res_dec} the results related to the PLM with decimation are reported and its performances are compared to the PLM-$l_2$ and to a variational mean-field method analyzed in Ref  \cite{Tyagi15}  In Sec  \ref{sec:conc}, we outline conclusive remarks and perspectives 

        \section{The leading $XY$ model}
      \label{sec:model}
 The leading model we are considering is defined, for a system of $N$ angular $XY$ variables, by the Hamiltonian 
 \begin{equation}
  \mathcal{H} = - \sum_{ik}^{1,N} J_{ik} \cos{\left(\phi_i-\phi_k\right)} 
  \label{eq:HXY}
 
  \end{equation} 
  
  The $XY$ model is well known in statistical mechanics, displaying important physical
  insights, starting from the Berezinskii-Kosterlitz-Thouless
  transition in two dimensions\cite{Berezinskii70,Berezinskii71,Kosterlitz72} and moving to, e g , the
  transition of liquid helium to its superfluid state \cite{Brezin82}, the roughening transition of the interface of a crystal in equilibrium with its vapor \cite{Cardy96}  In presence of disorder and frustration \cite{Villain77,Fradkin78} the model has been adopted to describe synchronization problems as the Kuramoto model \cite{Kuramoto75} and in the theoretical modeling of Josephson junction arrays \cite{Teitel83a,Teitel83b} and arrays of coupled lasers \cite{Nixon13} 
  Besides several derivations and implementations of the model in quantum and classical physics, equilibrium or out of equilibrium, ordered or fully frustrated systems, Eq  (\ref{eq:HXY}), in its generic form,
  has found applications also in other fields  A rather fascinating example being the behavior of starlings flocks  \cite{Reynolds87,Deneubourg89,Huth90,Vicsek95, Cavagna13} 
  Our interest on the $XY$ model resides, though, in optics  Phasor and phase models with pairwise and  multi-body interaction terms can, indeed, describe the behavior of electromagnetic modes in both linear and nonlinear optical systems in the analysis of problems such as light propagation and lasing \cite{Gordon02, Antenucci15c, Antenucci15d}  As couplings are strongly frustrated, these models turn out to be especially useful to the study of optical properties in random media \cite{Antenucci15a,Antenucci15b}, as in the noticeable case of random lasers \cite{Wiersma08,Andreasen11,Antenucci15e}  and they might as well be applied to linear scattering problems, e g , propagation of waves in opaque systems or disordered fibers  
  
  
  \subsection{A propagating wave model}
  We briefly mention a derivation of the model as a proxy for the propagation of light through random linear media  
 Scattering of light is held responsible to obstruct our view and make objects opaque  Light rays, once that they enter the material, only exit  after getting scattered multiple times within the material  In such a disordered medium, both the direction and the phase of the propagating waves are random  Transmitted light 
 yields a disordered interference pattern typically  having low intensity, random phase and almost no resolution, called a speckle  Nevertheless, in recent years it has been realized that disorder is rather a blessing in disguise \cite{Vellekoop07,Vellekoop08a,Vellekoop08b}  Several experiments have made it possible to control the behavior of light and other optical processes in a given random disordered medium,  
 by exploiting, e g ,  the tools developed for wavefront shaping to control the propagation of light and to engineer the confinement of light \cite{Yilmaz13,Riboli14} 
 \\
 \indent
 In a linear dielectric medium, light propagation can be described through a part of the scattering matrix, the transmission matrix $\mathbb{T}$, linking the outgoing to the incoming fields  
 Consider the case in which there are $N_I$ incoming channels and $N_O$ outgoing ones; we can indicate with $E^{\rm in,out}_k$ the input/output electromagnetic field phasors of channel $k$  In the most general case, i e , without making any particular assumptions on the field polarizations, each light mode and its polarization polarization state can be represented by means of the $4$-dimensional Stokes vector  Each $ t_{ki}$ element of $\mathbb{T}$, thus, is a $4 \times 4$ M{\"u}ller matrix  If, on the other hand, we know that the source is polarized and the observation is made on the same polarization, one can use a scalar model and adopt Jones calculus \cite{Goodman85,Popoff10a,Akbulut11}:
   \begin{eqnarray}
 E^{\rm out}_k = \sum_{i=1}^{N_I}  t_{ki} E^{\rm in}_i \qquad \forall~ k=1,\ldots,N_O
 \label{eq:transm}
 \end{eqnarray}
  We recall that the elements of the transmission matrix are random complex coefficients\cite{Popoff10a}  For the case of completely unpolarized modes, we can also use a scalar model similar to Eq  \eqref{eq:transm}, but whose variables are  the intensities of the outgoing/incoming fields, rather than the fields themselves \\ 
In the following, for simplicity, we will consider Eq  (\ref{eq:transm}) as our starting point,
where $E^{\rm out}_k$, $E^{\rm in}_i$ and $t_{ki}$ are all complex scalars  
If Eq  \eqref{eq:transm} holds for any $k$, we can write:
  \begin{eqnarray}
  \int \prod_{k=1}^{N_O} dE^{\rm out}_k \prod_{k=1}^{N_O}\delta\left(E^{\rm out}_k - \sum_{j=1}^{N_I}  t_{kj} E^{\rm in}_j \right) = 1
  \nonumber
  \\
  \label{eq:deltas}
  \end{eqnarray}

 Observed data are a noisy representation of the true values of the fields  Therefore, in inference problems it is statistically more meaningful to take that noise into account in a probabilistic way, 
 rather than looking  at the precise solutions of the exact equations (whose parameters are unknown)  
 To this aim we can introduce Gaussian distributions whose limit for zero variance are the Dirac deltas in Eq  (\ref{eq:deltas}) 
 Moreover, we move to consider the ensemble of all possible solutions of Eq  (\ref{eq:transm}) at given $\mathbb{T}$, looking at  all configurations of input fields  We, thus, define the function:
 
   \begin{eqnarray}
  Z &\equiv &\int_{{\cal S}_{\rm in}} \prod_{j=1}^{N_I}  dE^{\rm in}_j \int_{{\cal S}_{\rm out}}\prod_{k=1}^{N_O} dE^{\rm out}_k 
  \label{def:Z}
\\
    \times
  &&\prod_{k=1}^{N_O}
   \frac{1}{\sqrt{2\pi \Delta^2}}  \exp\left\{-\frac{1}{2 \Delta^2}\left|
  E^{\rm out}_k -\sum_{j=1}^{N_I}  t_{kj} E^{\rm in}_j\right|^2
\right\} 
\nonumber
 \end{eqnarray}
   We stress that the integral of Eq  \eqref{def:Z} is not exactly a Gaussian integral  Indeed, starting from Eq  \eqref{eq:deltas}, two constraints on the electromagnetic field intensities must be taken into account  

  The space of solutions is  delimited by the total power ${\cal P}$ received by system, i e , 
  ${\cal S}_{\rm in}: \{E^{\rm in} |\sum_k I^{\rm in}_k = \mathcal{P}\}$, also implying  a constraint on the total amount of energy that is transmitted through the medium, i  e , 
  ${\cal S}_{\rm out}:\{E^{\rm out} |\sum_k I^{\rm out}_k=c\mathcal{P}\}$, where the attenuation factor  $c<1$ accounts for total losses 
  As we will see more in details in the following, being interested in inferring the transmission matrix through the PLM, we can omit to explicitly include these terms in Eq  \eqref{eq:H_J} since they do not depend on $\mathbb{T}$ not adding any information on the gradients with respect to the elements of $\mathbb{T}$ 
  
 Taking the same number of incoming and outcoming channels, $N_I=N_O=N/2$, and  ordering the input fields in the first $N/2$ mode indices and the output fields in the last $N/2$ indices, we can drop the ``in'' and ``out'' superscripts and formally write $Z$  as a partition function
    \begin{eqnarray}
        \label{eq:z}
 && Z =\int_{\mathcal S} \prod_{j=1}^{N} dE_j \left(   \frac{1}{\sqrt{2\pi \Delta^2}} \right)^{N/2} 
 \hspace*{- 4cm} \exp\left\{
  -\frac{ {\cal H} [\{E\};\mathbb{T}] }{2\Delta^2}
  \right\}
  \\
&&{\cal H} [\{E\};\mathbb{T}] =
-  \sum_{k=1}^{N/2}\sum_{j=N/2+1}^{N} \left[E^*_j t_{jk} E_k + E_j t^*_{kj} E_k^* 
\right]
 \nonumber
\\
&&\qquad\qquad \qquad + \sum_{j=N/2+1}^{N} |E_j|^2+ \sum_{k,l}^{1,N/2}E_k
U_{kl} E_l^*
 \nonumber
 \\
 \label{eq:H_J}
 &&\hspace*{1 88cm } = - \sum_{nm}^{1,N} E_n J_{nm} E_m^*
 \end{eqnarray}
 where ${\cal H}$ is a real-valued function by construction, we have introduced the effective input-input coupling matrix
\begin{equation}
U_{kl} \equiv \sum_{j=N/2+1}^{N}t^*_{lj} t_{jk} 
 \label{def:U}
 \end{equation}
 and the whole interaction matrix reads (here $\mathbb{T} \equiv \{ t_{jk} \}$)
 \begin{equation}
 \label{def:J}
 \mathbb J\equiv \left(\begin{array}{ccc|ccc}
 \phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}\\
 \phantom{()}&-\mathbb{U} \phantom{()}&\phantom{()}&\phantom{()}&{\mathbb{T}}&\phantom{()}\\
\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}\\
 \hline
\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}&\phantom{()}\\
 \phantom{()}& \mathbb   T^\dagger&\phantom{()}&\phantom{()}& - \mathbb{I} &\phantom{()}\\
\phantom{a}&\phantom{a}&\phantom{a}&\phantom{a}&\phantom{a}&\phantom{a}\\
 \end{array}\right)
 \end{equation}
 
 Determining the electromagnetic complex amplitude configurations that minimize the {\em cost function} ${\cal H}$, Eq   (\ref{eq:H_J}),  means to maximize the overall distribution peaked around the solutions of the transmission Eqs  (\ref{eq:transm})  As the variance $\Delta^2\to 0$, eventually, the initial set of Eqs  (\ref{eq:transm}) are recovered  The ${\cal H}$ function, thus, plays the role of an Hamiltonian and  $\Delta^2$ the role of a noise-inducing temperature  The exact numerical problem corresponds to the zero temperature limit of the statistical mechanical problem  Working with real data, though, which are noisy, a finite ``temperature''
  allows for a better representation of the ensemble of solutions to the sets of equations of continuous variables  
  

  
  
  Now, we can express every phasor in Eq  \eqref{eq:z}  as $E_k = A_k e^{\imath \phi_k}$  As a working hypothesis we will consider the intensities $A_k^2$ as either homogeneous or as \textit{quenched} with respect to phases 
The first condition occurs, for instance, to the input intensities $|E^{\rm in}_k|$ produced by a phase-only spatial light modulator (SLM) with homogeneous illumination \cite{Popoff11} 
With \textit{quenched} here we mean, instead, that the intensity of each mode is the same for every solution of Eq  \eqref{eq:transm} at fixed $\mathbb T$ 
We stress that, including intensities in the model does not preclude the inference analysis but it is out of the focus of the present work and will be considered elsewhere  

If all intensities are uniform in input and in output, this amount to a constant rescaling for each one of the four sectors of matrix $\mathbb J$ in Eq  (\ref{def:J}) that will not change the properties of the matrices 
For instance, if the original transmission matrix is unitary, so it will be the rescaled one and the matrix $\mathbb U$ will be  diagonal 
Otherwise, if intensities are \textit{quenched}, i e , they can be considered as constants in Eq  (\ref{eq:transm}),
they are inhomogeneous with respect to phases  The generic Hamiltonian element will, therefore, rescale as 
  \begin{eqnarray}
  E^*_n J_{nm} E_m = J_{nm} A_n A_m e^{\imath (\phi_n-\phi_m)} \to J_{nm} e^{\imath (\phi_n-\phi_m)}
  \nonumber
  \end{eqnarray}
  and the properties of the original  $J_{nm}$ components are not conserved  in the rescaled one  In particular, we have no argument, anymore, to possibly set the rescaled $U_{nm}\propto \delta_{nm}$ 
  Eventually, we end up with the complex couplings $XY$ model, whose real-valued Hamiltonian is written as
 \begin{eqnarray}
  \mathcal{H}& = &  - \frac{1}{2} \sum_{nm} J_{nm} e^{-\imath (\phi_n - \phi_m)}  + \mbox{c c } 
    \label{eq:h_im}
\\    &=&  - \frac{1}{2} \sum_{nm} \left[J^R_{nm} \cos(\phi_n - \phi_m)+
  J^I_{nm}\sin (\phi_n - \phi_m)\right] 
  \nonumber
 \end{eqnarray}
where $J_{nm}^R$ and $J_{nm}^I$ are the real and imaginary parts of $J_{nm}$  Being $\mathbb J$  Hermitian, $J^R_{nm}=J^R_{mn}$ is symmetric and $J_{nm}^I=-J_{mn}^I$ is skew-symmetric 

\begin{comment}
\textcolor{red}{
F: comment about quenched:
I think that to obtain the XY model, it is not necessary that the intensities are strictly quenched (that is also a quite unfeasible situation, I guess) 
Indeed eq (2) does not deal with the dynamics of the modes, but just connect the in and out ones 
For this, what it is necessary to have the XY model, it is that the intensities are always the same on the different samples
(so that the matrix $t_{ij}$ is the same for different phase data)  If the intensities are fixed, then they can be incorporated in $t_{ij}$ and eq (2) can be written just for phases as described  \\
}
\end{comment}


  \section{Pseudolikelihood Maximization}
  \label{sec:plm}
The inverse problem consists in the reconstruction of the parameters $J_{nm}$ of the Hamiltonian, Eq  (\ref{eq:h_im})   
Given a set of $M$ data configurations of $N$ spins
 $\bm\sigma = \{ \cos \phi_i^{(\mu)},\sin \phi_i^{(\mu)} \}$, $i = 1,\dots,N$ and $\mu=1,\dots,M$, we want to \emph{infer} the couplings:
 \begin{eqnarray}
\bm \sigma  \rightarrow  \mathbb{J} 
\nonumber
 \end{eqnarray}
 With this purpose in mind,
 in the rest of this section we implement the working equations for the techniques used  
 In order to test our methods, we generate the input data, i e , the configurations, by Monte-Carlo simulations of the model 
 The joint probability distribution of the $N$ variables $\bm{\phi}\equiv\{\phi_1,\dots,\phi_N\}$, follows the Gibbs-Boltzmann distribution:
 \begin{equation}\label{eq:p_xy}
 P(\bm{\phi}) = \frac{1}{Z} e^{-\beta \mathcal{H\left(\bm{\phi}\right)}} \quad \mbox{ where } \quad Z = \int \prod_{k=1}^N d\phi_k  e^{-\beta \mathcal{H\left(\bm{\phi}\right)}}  
 \end{equation}
 and where we denote $\beta=\left( 2\Delta^2 \right)^{-1}$ with respect to Eq  (\ref{def:Z}) formalism 
 In order to stick to usual statistical inference notation, in the following we will rescale the couplings by a factor $\beta / 2$: $\beta J_{ij}/2 \rightarrow J_{ij}$  
 The main idea of the PLM is to work with the conditional probability distribution of one variable $\phi_i$ given all other variables, 
 $\bm{\phi}_{\backslash i}$:
 
  \begin{eqnarray}
	\nonumber
   P(\phi_i | \bm{\phi}_{\backslash i}) &=& \frac{1}{Z_i} \exp \left \{ {H_i^x (\bm{\phi}_{\backslash i})
  	\cos \phi_i + H_i^y (\bm{\phi}_{\backslash i}) \sin \phi_i } \right \}
	\\
 \label{eq:marginal_xy}
	&=&\frac{e^{H_i(\bm{\phi}_{\backslash i}) \cos{\left(\phi_i-\alpha_i(\bm{\phi}_{\backslash i})\right)}}}{2 \pi I_0(H_i)}
  \end{eqnarray}
  where $H_i^x$ and $H_i^y$ are defined as
   \begin{eqnarray}
   H_i^x (\bm{\phi}_{\backslash i})  &=& \sum_{j (\neq i)} J^R_{ij} \cos \phi_j  - \sum_{j  (\neq i) } J_{ij}^{I} \sin \phi_j \phantom{+  h^R_i} \label{eq:26} \\
   H_i^y  (\bm{\phi}_{\backslash i})  &=&  \sum_{j  (\neq i)} J^R_{ij}  \sin \phi_j  + \sum_{j  (\neq i) } J_{ij}^{I}   \cos \phi_j \phantom{ + h_i^{I} }\label{eq:27}
   \end{eqnarray}
and $H_i= \sqrt{(H_i^x)^2 + (H_i^y)^2}$, $\alpha_i = \arctan H_i^y/H_i^x$   and we introduced the modified Bessel function of the first kind:
  \begin{equation}
  \nonumber
   I_k(x) = \frac{1}{2 \pi}\int_{0}^{2 \pi} d \phi e^{x \cos{ \phi}}\cos{k \phi}
  \end{equation}
  
   Given $M$ observation samples $\bm{\phi}^{(\mu)}=\{\phi^\mu_1,\ldots,\phi^\mu_N\}$, $\mu = 1,\dots, M$, the
   pseudo-loglikelihood for the variable $i$ is given by the logarithm of Eq  (\ref{eq:marginal_xy}),
   \begin{eqnarray}
   \label{eq:L_i}
   L_i &=& \frac{1}{M}  \sum_{\mu = 1}^M  \ln P(\phi_i^{(\mu)}|\bm{\phi}^{(\mu)}_{\backslash i})
   \\
   \nonumber
   & =&  \frac{1}{M}  \sum_{\mu = 1}^M  \left[ H_i^{(\mu)} \cos( \phi_i^{(\mu)} - \alpha_i^{(\mu)}) - \ln  2 \pi I_0\left(H_i^{(\mu)}\right)\right] \,  
    \end{eqnarray}
The underlying idea of PLM is that an approximation of the true parameters of the model is obtained for values that maximize the functions $L_i$ 
The specific maximization scheme differentiates the different techniques 


   
   
   \subsection{PLM with $l_2$ regularization}
   Especially for the case of sparse graphs, it is useful to add a regularizer, which prevents the maximization routine to move towards high values of 
   $J_{ij}$ and $h_i$ without converging  We will adopt an $l_2$ regularization so that the Pseudolikelihood function (PLF) at site $i$  reads:
   \begin{equation}\label{eq:plf_i}
  {\cal L}_i = L_i
  - \lambda \sum_{i \neq j} \left(J_{ij}^R\right)^2 - \lambda \sum_{i \neq j} \left(J_{ij}^I\right)^2  
   \end{equation}
   with $\lambda>0$ 
   Note that the values of $\lambda$ have to be chosen arbitrarily, but not too large, in order not to overcome $L_i$ 
   The standard implementation of the PLM consists in maximizing each ${\cal L}_i$, for $i=1\dots N$, separately  The expected values of the couplings are then:
   \begin{equation}
   \{ J_{i j}^*\}_{j\in \partial i} :=  \mbox{arg max}_{ \{ J_{ij} \}}
    \left[{\cal L}_i\right]
   \end{equation}
   In this way, we obtain two estimates for the coupling $J_{ij}$, one from maximization of ${\cal L}_i$, $J_{ij}^{(i)}$, and another one from ${\cal L}_j$, say $J_{ij}^{(j)}$ 
    Since the original Hamiltonian of the $XY$ model is Hermitian, we know that the real part of the couplings is symmetric while the imaginary part is skew-symmetric  
   
     The final estimate for $J_{ij}$ can then be obtained  averaging the two results:
  
  
  
   \begin{equation}\label{eq:symm}
   J_{ij}^{\rm inferred} = \frac{J_{ij}^{(i)} + \bar{J}_{ij}^{(j)}}{2} 
   \end{equation}
   where with $\bar{J}$ we indicate the complex conjugate 
   It is worth noting that the pseudolikelihood $L_i$, Eq  \eqref{eq:L_i}, is characterized by the
   following properties: (i) the normalization term of Eq \eqref{eq:marginal_xy} can be
   computed analytically at odd with the {\em full} likelihood case that
   in general require a computational time which scales exponentially
   with the size of the systems; (ii) the $\ell_2$-regularized pseudolikelihood
   defined in Eq \eqref{eq:plf_i} is strictly concave (i e  it has a single
   maximizer)\cite{Ravikumar10}; (iii) it is consistent, i e  if $M$ samples are
   generated by a model $P(\phi | J*)$ the maximizer tends to $J*$
   for $M\rightarrow\infty$\cite{besag1975}  Note also that (iii) guarantees that  
   $|J^{(i)}_{ij}-J^{(j)}_{ij}| \rightarrow 0$ for $M\rightarrow \infty$ 
   In Secs  \ref{sec:res_reg}, \ref{sec:res_dec} 
   we report the results obtained and we analyze the performances of the PLM having taken the configurations from Monte-Carlo simulations of models whose details are known 
   

   
   \subsection{PLM with decimation}
   Even though the PLM with $l_2$-regularization allows to dwell the inference towards the low temperature region and in the low sampling case with better performances that mean-field methods, in some situations some couplings are overestimated and not at all symmetric  Moreover, in the technique there is the bias of the $l_2$ regularizer 
   Trying to overcome these problems, Decelle and Ricci-Tersenghi introduced a new method \cite{Decelle14}, known as PLM + decimation: the algorithm maximizes the sum of the $L_i$,
   \begin{eqnarray}
    {\cal L}\equiv \frac{1}{N}\sum_{i=1}^N \mbox{L}_i
    \end{eqnarray}  
    and, then, it recursively set to zero couplings which are estimated very small  We expect that as long as we are setting to zero couplings that are unnecessary to fit the data, there should be not much changing on ${\cal L}$  Keeping on with decimation, a point is reached where ${\cal L}$ decreases abruptly indicating  that relevant couplings are being decimated and under-fitting is taking place 
   Let us define  by $x$  the fraction of non-decimated couplings  To have a quantitative measure for the halt criterion of the decimation process, a tilted ${\cal L}$ is defined as,
   \begin{eqnarray}
  \mathcal{L}_t &\equiv& \mathcal{L}  - x \mathcal{L}_{\textup{max}} - (1-x) \mathcal{L}_{\textup{min}} \label{$t$PLF} 
   \end{eqnarray}
   where 
   \begin{itemize}
   \item $\mathcal{L}_{\textup{min}}$ is the pseudolikelyhood of a model with independent variables  In the XY case: $\mathcal{L}_{\textup{min}}=-\ln{2 \pi}$ 
   \item
   $\mathcal{L}_{\textup{max}}$ is the pseudolikelyhood in the fully-connected model and it is maximized over all the $N(N-1)/2$ possible couplings  
   \end{itemize}
   At the first step, when $x=1$, $\mathcal{L}$ takes value $\mathcal{L}_{\rm max}$ and  $\mathcal{L}_t=0$  On the last step, for an empty graph, i e , $x=0$, $\mathcal{L}$ takes the value $\mathcal{L}_{\rm min}$ and, hence, again $\mathcal{L}_t =0$  
   In the intermediate steps, during the decimation procedure, as $x$ is decreasing from $1$ to $0$, one observes firstly that $\mathcal{L}_t$ increases linearly and, then, it displays an abrupt decrease indicating that from this point on relevant couplings are being decimated\cite{Decelle14}  In Fig  \ref{Jor1-$t$PLF} we give an instance of this behavior for the 2D short-range XY model with ordered couplings  We notice that the maximum point of $\mathcal{L}_t$ coincides with the minimum point of the reconstruction error, the latter defined as 
   \begin{eqnarray}\label{eq:errj}
   \mbox{err}_J \equiv \sqrt{\frac{\sum_{i<j} (J^{\rm inferred}_{ij} -J^{\rm true}_{ij})^2}{N(N-1)/2}} \label{err}
   \end{eqnarray}
  We stress that the ${\cal L}_t$ maximum is obtained ignoring the underlying graph, while the err$_J$ minimum can be evaluated once the true graph has been reconstructed  
   
     \begin{figure}[t!]
   	\centering
   	\includegraphics[width=1\linewidth]{Jor1_dec_tPLF_new eps}
   	\caption{The tilted likelyhood ${\cal L}_t$ curve and the reconstruction error vs the number of decimated couplings  for an ordered, real-valued J on 2D XY model with $N=64$ spins  The peak of ${\cal L}_t$ coincides with the dip of the error }  
   	\label{Jor1-$t$PLF}
   \end{figure} 
       
   
   In the next sections we will show the results obtained on the  $XY$ model analyzing the performances of the two methods and comparing them also with a mean-field method \cite{Tyagi15} 
   
  
    
   \section{Inferred couplings with PLM-$l_2$}
    \label{sec:res_reg}
    \subsection{$XY$ model with real-valued couplings}
    
    In order to obtain the vector of couplings, $J_{ij}^{\rm inferred}$ the function $-\mathcal{L}_i$ is minimized through the vector of derivatives ${\partial \mathcal{L}_i}/\partial J_{ij}$  The process is repeated for all the couplings obtaining then a fully connected adjacency matrix  The results here presented are obtained with $\lambda = 0 01$ 
   For the minimization we have used the MATLAB routine \emph{minFunc\_2012}\cite{min_func}  
      
      \begin{figure}[t!]
    	\centering
    	\includegraphics[width=1\linewidth]{Jor11_2D_l2_JR_soJR_TPJR}
    	\caption{Top panels: instances of single site coupling reconstruction for the case of $N=64$ XY spins on a 2D lattice with ordered $J$ (left column) and bimodal distributed $J$ (right column)  
    	
    	Bottom panels: sorted couplings }
    	\label{PL-Jor1}
    \end{figure}

   
To produce the data by means of numerical Monte Carlo simulations a system with $N=64$  spin variables  is considered on a deterministic 2D lattice with periodic boundary conditions  
Each spin has then connectivity $4$, i e , we expect to infer an adjacency matrix with $N c = 256$ couplings different from zero  
The dynamics of the simulated model is based on the Metropolis algorithm and parallel tempering\cite{earl05} is used to speed up the thermalization of the system 
The thermalization is tested looking at the average energy over logarithmic time windows and
the acquisition of independent configurations
starts only after the system is well thermalized 

   For the values of the couplings we considered two cases: an ordered case, indicated in the figure as  $J$ ordered (e g , left column of Fig  \ref{PL-Jor1}) where the couplings can take values $J_{ij}=0,J$, with $J=1$, 
   and a quenched disordered case, indicated in the figures as  $J$ disordered (e g , right column of Fig  \ref{PL-Jor1})
   where the couplings can take also  negative values, i e , 
    $J_{ij}=0,J,-J$, with a certain probability   The results here presented were obtained with bimodal distributed $J$s: 
   
    $P(J_{ij}=J)=P(J_{ij}=-J)=1/2$   The performances of the PLM have shown not to depend on $P(J)$  
   
    We recall that in Sec  \ref{sec:plm} we used the temperature-rescaled notation, i e , $J_{ij}$ stands for $J_{ij}/T$  
   
    To analyze the performances of the PLM, in Fig  \ref{PL-Jor1} the inferred couplings, $\mathbb{J}^R_{\rm inf}$, are shown on top of the original couplings,  $\mathbb{J}^R_{\rm true}$ 
     The first figure (from top) in the left column shows  the $\mathbb{J}^R_{\rm inf}$ (black) and the $\mathbb{J}^R_{\rm tru}$ (green) for a given spin
     at temperature $T/J=0 7$ and number of samples  $M=1024$  PLM appears to reconstruct the correct couplings, though zero couplings are always given a small inferred non-zero value  
     In the left column of Fig   \ref{PL-Jor1},  both the $\mathbb{J}^R_{\rm{inf}}$ and the $\mathbb{J}^R_{\rm{tru}}$ are sorted in decreasing order and plotted on top of each other  
     We can clearly see that $\mathbb{J}^R_{\rm inf}$ reproduces the expected step function  Even though the jump is smeared, the difference between inferred couplings corresponding to the set of non-zero couplings 
     and to the set of zero couplings can be clearly appreciated 
     Similarly, the plots in the right column of Fig  \ref{PL-Jor1} show the results obtained for the case with  bimodal disordered couplings, for the same working temperature and number of samples  
     In particular, note that the algorithm infers half positive and half negative couplings, as expected 
     
     
\begin{figure}
\centering
\includegraphics[width=1\linewidth]{Jor11_2D_l2_errJ_varT_varM}
\caption{Reconstruction error $\mbox{err}_J$, cf  Eq  (\ref{eq:errj}), plotted as a function of temperature (left) for three values of the number of samples $M$ and  as a function $M$ (right) for three values of temperature in the ordered system, i e , $J_{ij}=0,1$  
The system size is $N=64$ }
\label{PL-err-Jor1}
\end{figure}

In order to analyze the effects of the number of samples and of the temperature regimes, we plot in Fig  \ref{PL-err-Jor1} the reconstruction error, Eq  (\ref{err}), as a function of temperature for three different sample sizes $M=64,128$ and $512$  
The error is seen to sharply rise al low temperature, incidentally, in the ordered case, for  $T<T_c \sim 0 893$, which is the Kosterlitz-Thouless transition temperature of the 2XY model\cite{Olsson92}  
 However, we can see that if only $M=64$ samples are considered, $\mbox{err}_J$ remains high independently on the working temperature  
 In the right plot of Fig  \ref{PL-err-Jor1},  $\mbox{err}_J$ is plotted as a function of $M$ for three different working temperatures $T/J=0 4,0 7$ and $1 3$  As we expect, 
 $\mbox{err}_J$  decreases as $M$ increases  This effect was observed also with mean-field inference techniques on the same model\cite{Tyagi15} 

To better understand the performances of the algorithms, in Fig  \ref{PL-varTP-Jor1} we show several True Positive (TP) curves obtained for various values of $M$ at three different temperatures $T$  As $M$ is large and/or temperature is not too small,  we are able to reconstruct correctly all the couplings present in the system (see bottom plots) 
The True Positive curve displays how many times the inference method finds a true link of the original network  as a function of the index of the vector of sorted absolute value of reconstructed couplings $J_{ij}^{\rm inf}$  
The index $n_{(ij)}$ represents the related spin couples $(ij)$  The TP curve is obtained as follows: 
first  the values $|J^{\rm inf}_{ij}|$ are sorted in descending order and  the spin pairs $(ij)$ are ordered according to the sorting position of $|J^{\rm inf}_{ij}|$  Then,
     	a cycle over the ordered set of pairs $(ij)$, indexed by $n_{(ij)}$, is performed, comparing with the original network coupling $J^{\rm true}_{ij}$ and verifying whether it is zero or not  The true positive curve is computed as
\begin{equation}
\mbox{TP}[n_{(ij)}]= \frac{\mbox{TP}\left[n_{(ij)}-1\right] (n_{ij}-1)+ 1 -\delta_{J^{\rm true}_{ij},0}}{n_{(ij)}}
\end{equation}
As far as $J^{\rm true}_{ij} \neq 0$, TP$=1$  As soon as the true coupling of a given $(ij)$ couple in the sorted list is zero, the TP curve departs from one  
In our case, where the connectivity per spin of the original system is  $c=4$ and there are $N=64$ spins, we know that we will have  $256$ non-zero couplings   
     	If the inverse problem is successful, hence, we expect a steep decrease of the TP curve when  $n_{ij}=256$ is overcome 

In Fig  \ref{PL-varTP-Jor1}
it is  shown that,  almost independently of $T/J$, the TP score improves as $M$ increases  Results are plotted for three different temperatures, $T=0 4,1$ and $2 2$, with increasing number of samples $M = 64, 128,512$ and $1024$ (clockwise)  
We can clearly appreciate the improvement in temperature if the size of the data-set is not very large: for small $M$, $T=0 4$ performs better  
When $M$ is high enough (e g , $M=1024$), instead, the TP curves do not appear to be strongly influenced by the temperature 

\begin{figure}[t!]
	\centering
	\includegraphics[width=1\linewidth]{Jor11_2D_l2_TPJR_varT_varM}
	\caption{TP  curves  for 2D short-range ordered $XY$ model with $N=64$ spins at three different values of $T/J$ with increasing - clockwise from top - $M$ }
	\label{PL-varTP-Jor1} 
\end{figure} 

\subsection{$XY$ model with complex-valued couplings}
For the complex $XY$ we have to contemporary  infer $2$ apart coupling matrices,  $J^R_{i j}$ and $J^I_{i j}$   As before, a system of $N=64$ spins is considered on a 2D lattice 
For the couplings we have considered both ordered and bimodal disordered cases 
In Fig  \ref{PL-Jor3}, a single row of the matrix $J$ (top) and the whole sorted couplings (bottom) are displayed for the ordered model (same legend as in Fig  \ref{PL-Jor1}) for the real, $J^R$ (left column), and the imaginary part, $J^I$   

\begin{figure}[t!]
	\centering
\includegraphics[width=1\linewidth]{Jor3_l2_JRJI_soJRJI_TPJRJI}
	\caption{Results related to the ordered complex XY model with $N=64$ spins on a  2D lattice  Top: instances of  single site reconstruction for the real, JR (left column), and
		the imaginary, JI (right column), part of $J_{ij}$  Bottom: sorted values of JR (left) and JI (right) }
		
	\label{PL-Jor3}
\end{figure}
 
 
  \section{PLM with Decimation}
 \label{sec:res_dec}
 

\begin{figure}[t!]
   	\centering
   	\includegraphics[width=1\linewidth]{Jor1_dec_tPLF_varT_varM}
    	\caption{Tilted Pseudolikelyhood, ${\cal L}_t$, plotted as a function of decimated couplings  Top: Different ${\cal L}_t$ curves obtained for different values of $M$ plotted on top of each other  Here $T=1 3$  The black line indicates the expected number of decimated couplings, $x^*=(N (N-1) - N c)/2=1888$  As we can see, as $M$ increases, the maximum point of ${\cal L}_t$ approaches $x^*$  Bottom: Different ${\cal L}_t$ curves obtained for different values of T with $M=2048$  We can see that, with this value of $M$, no differences can be appreciated on the maximum points of the different  ${\cal L}_t$ curves }
   	\label{var-$t$PLF}
   \end{figure}

\begin{figure}[t!]
    \centering
    \includegraphics[width=1\linewidth]{Jor1_dec_tPLF_peak_statistics_varM_prob eps}
    	\caption{Number of most likely decimated couplings, estimated by the maximum point of $\mathcal{L}_t$, as a function of the number of samples $M$  We can clearly see that the maximum point of $\mathcal{L}_t$ tends toward $x^*$, which is the right expected number of zero couplings in the system }  
    	\label{PLF_peak_statistics}
    \end{figure}
      
      For the ordered real-valued XY model we show in Fig  \ref{var-$t$PLF}, top panel, the outcome on the tilted pseudolikelyhood, $\mathcal{L}_t$ Eq  \eqref{$t$PLF}, of the progressive decimation: from a fully connected lattice  down to an empty lattice  The figure shows the behaviour of $\mathcal{L}_t$ for three different data sizes $M$  A clear data size dependence of the maximum point of  $\mathcal{L}_t$, signalling the most likely value for decimation, is shown  For small $M$ the most likely number of  couplings is overestimated and for increasing $M$ it tends to the true value, as displayed in Fig  \ref{PLF_peak_statistics}   In the bottom panel of Fig  \ref{var-$t$PLF} we display instead different 
 $\mathcal{L}_t$ curves obtained for three different values of $T$ 
  Even though the values of $\mathcal{L}_t$ decrease with increasing temperature, the value of the most likely number of decimated couplings appears to be quite independent on $T$ with $M=2048$ number of samples 
In Fig  \ref{fig:Lt_complex} we eventually display the tilted pseudolikelyhood for a 2D network with complex valued ordered couplings, where the decimation of the real and imaginary coupling matrices proceeds in parallel, that is, 
when a real coupling is small enough to be decimated its imaginary part is also decimated, and vice versa 
One can see that though the apart errors for the real and imaginary parts are different in absolute values, they display the same dip, to be compared with the maximum point of $\mathcal{L}_t$ 
     
       \begin{figure}[t!]
    	\centering
      	\includegraphics[width=1\linewidth]{Jor3_dec_tPLF_new}
      	\caption{Tilted Pseudolikelyhood, ${\cal L}_t$, plotted with the reconstruction errors for the XY model with $N=64$ spins on a 2D lattice  These results refer to the case of  ordered and complex valued couplings  The full (red) line indicates ${\cal L}_t$  The dashed (green) 
      		and the dotted (blue) lines show the reconstruction errors (Eq  \eqref{eq:errj}) obtained for the real and the imaginary couplings respectively  We can see that both ${\rm err_{JR}}$ and ${\rm err_{JI}}$ have a minimum at $x^*$ }
          	\label{fig:Lt_complex}
    \end{figure}

\begin{figure}[t!]
   	\centering
   	\includegraphics[width=1\linewidth]{Jor1_dec_JR_soJR_TPJR}
   	\caption{XY model on a 2D lattice with $N=64$ sites and real valued couplings  The graphs show the inferred (dashed black lines) and true couplings (full green lines) plotted on top of each other  The left and right columns refer to the
   		 cases of ordered and bimodal disordered couplings, respectively  Top figures: single site reconstruction, i e , one row of the matrix $J$  Bottom figures: couplings are plotted sorted in descending order }  
   	\label{Jor1_dec}
   \end{figure}
   
\begin{figure}[t!]
    	\centering
    	\includegraphics[width=1\linewidth]{Jor3_dec_JRJI_soJRJI_TPJRJI}
    	\caption{XY model on a 2D lattice with $N=64$ sites and ordered complex-valued couplings 
    		The inferred and true couplings are plotted on top of each other  The left and right columns show the real and imaginary parts, respectively, of the couplings  Top figures refer to a single site reconstruction, i e , one row of the matrix $J$  Bottom figures report the couplings sorted in descending order }
    	\label{Jor3_dec}
    \end{figure}
    
       







       \begin{figure}[t!]
     	\centering
     	\includegraphics[width=1\linewidth]{MF_PL_Jor1_2D_TPJR_varT}
     	\caption{True Positive curves obtained with the three techniques: PLM with decimation, (blue) dotted line,  PLM with $l_2$ regularization, (greed) dashed line, and mean-field, (red) full line   These results refer to real valued ordered couplings with $N=64$ spins on a 2D lattice  The temperature is here $T=0 7$ while the four graphs refer to different sample sizes: $M$ increases clockwise }
     	\label{MF_PL_TP}
     \end{figure}
    
    \begin{figure}[t!]
    	\centering
    	\includegraphics[width=1\linewidth]{MF_PL_Jor1_2D_errJ_varT_varM}
    	\caption{Variation of reconstruction error, ${\rm err_J}$, with respect to temperature as obtained with the three different techniques, see Fig  \ref{MF_PL_TP}, for four different sample size:  clockwise from top   $M=512,1024, 2048$ and $4096$ } 
    	\label{MF_PL_err}
    \end{figure}
    
     Once the most likely network has been identified through the decimation procedure, we perform the same analysis displayed in Fig  \ref{Jor1_dec}  for ordered and then quenched disordered real-valued couplings
and in Fig  \ref{Jor3_dec} for  complex-valued ordered couplings   In comparison to the results shown in Sec  \ref{sec:res_reg},
  the PLM with decimation leads to rather cleaner results  In Figs  \ref{MF_PL_err} and \ref{MF_PL_TP} we compare the performances of the PLM with decimation in respect to ones of the PLM with $l_2$-regularization  These two techniques are also analysed in respect to a mean-field technique previously implemented on the same XY systems\cite{Tyagi15} 
  
    For what concerns the network of connecting links, in Fig  \ref{MF_PL_TP} we compare the TP curves obtained with the three techniques  The results refer to the case of ordered and real valued couplings, but similar behaviours were obtained for the other cases analysed  
  The four graphs are related to different sample sizes, with $M$ increasing clockwise  When $M$ is high enough, all techniques reproduce the true network  
  However, for lower values of $M$ the performances of the PLM with $l_2$ regularization and with decimation drastically overcome those ones of the previous mean field technique  
  In particular, for $M=256$ the PLM techniques still reproduce the original network while the mean-field method fails to find more than half of the couplings  
  When $M=128$, the network is clearly reconstructed only through the PLM with decimation while the PLM with $l_2$ regularization underestimates the couplings  
  Furthermore, we notice that the PLM method with decimation is able to clearly infer the network of interaction even when $M=N$ signalling that it could be considered also in the under-sampling regime $M<N$   
 
 
In Fig  \ref{MF_PL_err} we compare the temperature behaviour of the reconstruction error 
In can be observed that for all temperatures and for all sample sizes  the reconstruction error, ${\rm err_J}$, (plotted here in log-scale) obtained with the PLM+decimation is always smaller than 
that one obtained with the other techniques  The temperature behaviour of ${\rm err_J}$ agrees with the one already observed for Ising spins in \cite{Nguyen12b} and for XY spins  in \cite{Tyagi15} with a mean-field approach:  ${\rm err_J}$ displays a minimum around $T\simeq 1$ and then it increases for very lower $T$; however,
 the error obtained with the PLM with decimation is several times smaller  than the error estimated by the other methods 



 
 

     
     \section{Conclusions}
     \label{sec:conc}


Different statistical inference methods have been applied to the inverse problem of the XY model 
After a short review of techniques based on pseudo-likelihood and their formal generalization to the model we have tested their performances against data generated by means of Monte Carlo numerical simulations of known instances
with diluted, sparse, interactions 

The main outcome is that the best performances are obtained by means of the  pseudo-likelihood method combined with decimation  Putting to zero (i e , decimating) very weak bonds, this technique turns out to be very precise for  problems whose real underlying interaction network is sparse, i e , the number of couplings per variable does not scale with number of variables 
The PLM + decimation method is compared to the PLM + regularization method, with $\ell_2$ regularization and to a mean-field-based method  The behavior of the quality of the network reconstruction is analyzed by looking at the overall sorted couplings and at the single site couplings, comparing them with the real network, and at the true positive curves in all three approaches  In the PLM +decimation method, moreover, the identification of the number of decimated bonds at which the tilted pseudo-likelihood is maximum allows for a precise estimate of the total number of bonds  Concerning this technique, it is also shown that the network with the most likely number of bonds is also the one of least reconstruction error, where not only the prediction of the presence of a bond is estimated but also its value 

The behavior of the inference quality in temperature and in the size of data samples is also investigated, basically confirming the low $T$ behavior hinted by Nguyen and Berg \cite{Nguyen12b} for the Ising model  In temperature, in particular, the reconstruction error curve displays a minimum at a low temperature, close to the critical point in those cases in which a critical behavior occurs, and a sharp increase as temperature goes to zero  The decimation method, once again, appears to enhance this minimum of the reconstruction error of almost an order of magnitude with respect to other methods 
 
The techniques displayed and the results obtained in this work can be of use in any of the many systems whose theoretical representation is given by Eq  \eqref{eq:HXY} or Eq  \eqref{eq:h_im}, some of which are recalled in Sec  \ref{sec:model}  In particular, a possible application can be the field of light waves propagation through random media and the corresponding problem of the  reconstruction of an object seen through an opaque medium or a disordered optical fiber \cite{Vellekoop07,Vellekoop08a,Vellekoop08b, Popoff10a,Akbulut11,Popoff11,Yilmaz13,Riboli14} 

 	
Context 2: UT College of Liberal Arts: College of Liberal Arts University of Texas at Austin Departments Graduate Resources Undergraduate Resources Courses Online Courses Dean's Office Alumni & Giving Faculty by Department Search the College of Liberal Arts
next profile Jeffrey Tulis Associate Professor — Ph D ,
E-mail: tulis@austin utexas edu
Office: MEZ 3 152
Political Theory and American Politics
Professor Tulis's interests bridge the fields of political theory and American politics, including more specifically, American political development, constitutional theory, political philosophy and the American presidency  His publications include The Presidency in the Constitutional Order (LSU, 1981; Transaction, 2010), The Rhetorical Presidency (Princeton, 1987), The Constitutional Presidency (Johns Hopkins 2009), The Limits of Constitutional Democracy (Princeton, 2010) and recent journal articles and chapters on constitutional interpretation, the logic of political change, and the meaning of political success  Four collections of essays on The Rhetorical Presidency with responses by Tulis have been published, including a special double issue of Critical Review: An Interdisciplinary Journal of Politics and Society, (2007), where his book is described as "one of the two or three most important and perceptive works written by a political scientist in the twentieth century "
He has served as President of the Politics and History Section of the American Political Science Association  He received the President's Associates Teaching Excellence Award at the University of Texas  He has held research fellowships from NEH, ACLS, Olin Foundation, Harvard Law School, and the Mellon Preceptorship at Princeton University, where he taught before moving to Texas  He has held visiting positions at Notre Dame and Harvard  He has served as associate chair of the Department of Government from 1989-2001 and was acting chair during 1992-93  and for part of each year between 1989 and 2001  During the academic year 2008-09, he was a Laurance S  Rockefeller Visiting Fellow at the University Center for Human Values at Princeton  During Spring 2016, he was a Dahrendorf Visiting Fellow at the London School of Economics and Political Science 
His forthcoming books include: Legacies of Losing in American Politics, with Nicole Mellow (University of Chicago Press, Fall 2017), and an expanded edition of The Rhetorical Presidency in the Princeton Classics series (Princeton, Fall 2017)  For two decades he served as co-editor of the Johns Hopkins Series in Constitutional Thought, and he currently co-edits (with Sanford Levinson) Constitutional Thinking, a Series at the University Press of Kansas 
GOV 370L • Pres In Constitutional Ord 38840 • Spring 2017 Meets MW 2:30PM-4:00PM CAL 221 show description
GOV 370 Seminar: The Presidency in the Constitutional Order
Spring 2017 Unique # 38840
MW 2:30 to 4pm GDC 2 402
Jeffrey K  Tulis
In this Seminar we will discuss a series of constitutional problems including: the problem of executive energy in the American Constitution; presidential selection and the problem of political legitimacy; separation of powers; delegation of powers, the constitutional status of war and foreign affairs, administration and bureaucracy and the meaning of leadership in the constitutional order 
Seminar will meet twice a week and regular attendance and thorough preparation for discussion is expected  Unexcused absence from more than three classes will result in failure of the participation component of the course  There will also be pop quizzes on the reading that will count as part of your participation grade  In addition to class participation, course requirements include four short analytic essays, and one in-class test  The course grade will be calculated as follows:
Seminar participation: 20%
In-class test: 20%
Three analytic essays 60% (20% each)
Class participation is especially important  Preparation for seminar and for your in-class test will be enhanced by careful note taking on the readings  If students appear to be unprepared, pop quizzes will be given and the grades on them will affect the participation component of your course grade 
Texts: (tentative)
Joseph M  Bessette and Jeffrey K  Tulis, The Constitutional Presidency
Michael Nelson, The Presidency in the Political System (tenth edition)
Richard Ellis and Michael Nelson, Debating the Presidency (third edition)
The Federalist (any edition, or online) GOV 310L • American Government-Honors 38335 • Fall 2016 Meets TTH 3:30PM-5:00PM BEN 1 106 show description
GOV 310 (Honors) (38335) Fall 2016
TTH 3:30-5:00pm, BEN 1 106
This honors seminar offers an introduction to American politics that emphasizes the confluence of ideas, mores, institutions, and interests, in the constitutional system  This course covers more theory, and the readings are more demanding, than other versions of GOV 310  One of the main objectives of the course is to deepen your understanding of the practical aspects of contemporary public affairs by developing your ability to understand the theoretical foundations of American politics  Although we cover the nuts and bolts of politics there is much more theory in this version of GOV 310  If you have registered for this section mainly because 310 is a legislative requirement that you need to fulfill, this is not the right version for you  There is a substantial workload in this class 
Regular attendance, thorough and timely preparation, and active participation are all necessary to do well 
Four essays (approximately 1000 words each)  Three of these will be assigned analytic essay topics  The last will be a book review of a title chosen by the student from a long list of provided possibilities  (15% each essay, 60% of total course grade)
Two in-class tests  These will count 15% each, 30% of total course grade 
Class participation  (10% of course grade)  Both informed participation and occasional leadership of the seminar will be graded 
No make-up exams or late papers, except for documented medical or other emergencies 
Mark Landy and Sidney M  Milkis, American Government: Enduring Principles, Critical Choices, Third Edition
Mary Nichols and David Nichols, Readings in American Government, Ninth Edition
Thomas Mann and Norman Ornstein, Its Even Worse Than It Looks: How the American Constitutional System Collided With the New Politics of Extremism
Bruce Ackerman,Before the Next Attack: Preserving Civil Liberties in an Age of Terrorism GOV 381L • Constitutional Conflict 38660 • Fall 2016 Meets W 3:30PM-6:30PM BAT 5 102 show description
GOV 381L Fall 2016
Constitutional Conflict
W 3:30-6:30pm, BAT 5 102
Many of the most important debates regarding the nature and character of contemporary American politics are essentially arguments regarding the structure of separation of powers  In this seminar we will consider such questions as whether the American system is prone to deadlock of stalemate in the construction of national policy; whether conflict is a hindrance to institutional responsibility or an essential attribute of responsibility; whether there are “political questions” especially suitable to resolution between President and Congress; how one can distinguish salutary from pathological conflict, and whether it is truly possible to harness the ambition of office holders to the duties of their office 
More specifically, we will review literature and arguments regarding constitutional reform; divided government; separation of powers theory; and case studies of Supreme Court appointments; the budget process; and war powers and foreign affairs  In these contexts we will also discuss current controversies surrounding war authorization, intelligence and secrecy, sequestration, government shut downs and budget resolutions, and debt ceiling politics 
The course is designed to accommodate two different student needs: it will provide a good overview of important literature relevant to the comprehensive examination in American politics and it will provide opportunities for research  This subject area is a treasure trove of “hot” topics, publication possibilities, subjects for MA theses and Ph D  dissertations  I will tailor the written requirements to the objectives of individual students 
1  All students will prepare a short analytic essay early in the semester, and an annotated bibliography at mid-semester  These assignments will count (30%) of the grade 
2  Students interested primarily in exam preparation will complete an examination near the end of the semester based on study questions assigned in advance  OR
Students interested in research will write a 20-25 page paper  (60%)
3  A basic requirement of the course is that students prepare for each seminar by carefully reading the material assigned for that week  Class discussion is an essential component of the course  (10%)
Tentative Texts:
Jones, Separate But Equal Branches
Silverstein, Imbalance of Powers
Wilson & Schram, Separation of Powers and Good Government
Burgess, Contest for Constitutional Authority
Farrier, Passing the Buck: Congress, the Budget and Deficits
Weissman, A Culture of Deference
Zeisberg, War Powers: The Politics of Constitutional Authority
Fisher, Congressional Abdication on War and Spending
Lowi, The End of Liberalism GOV 379S • Regime Persp Amer Poltc-Honors 38105 • Spring 2016 Meets TH 3:30PM-6:30PM GAR 1 134 (also listed as CTI 335, LAH 350) show description
GOV 379S Regime Perspectives on American Politics
This is a seminar on American politics and culture  Two purposes govern the selection of texts for the course and guide our discussion of them  All of our texts attempt to look at American politics as a whole  Most books and courses on America look at only a part, such as the Presidency, or elections, or popular culture  Here we attempt to think about how the parts of America fit together  Even when these texts speak about a part, for example an institution such as the presidency or the Congress, they present the topic from a vantage point on the whole polity  To see the polity as a whole also means that we will have to revisit and rethink aspects of our political life that we take for granted – that we don’t examine because those parts have become so natural or familiar to us  Seeing the polity whole enables us to render the familiar unfamiliar, to make what we take for granted strange and new 
To see the polity as a whole requires that we get some distance from our subject, much as to see the planet earth as a whole requires one to look at it from outer space  Just as it is difficult to get visual perspective on a place living within it, it is difficult to understand the promise or pathologies of a regime from within  To get critical distance from our politics, we will closely study three sets of texts that look at American politics from a distance  The first part of the course will recover the perspective of the founding debate between Federalists and Anti-federalists  This fundamental debate reveals what is a stake in the basic architecture of the American regime  The second part of the course is a close study of Tocqueville’s Democracy in America  Regarded by many as the best book ever written on democracy and the best book written on America, Tocqueville sees our polity whole because he looks at it from the vantage point of Europe, in general, and France, in particular  In the third part of the seminar we think about American politics from the perspective of thoughtful commentators who feel only nominally included in the polity  Half in and half out, these extraordinary black American writers reveal fissures and fault lines in the American regime  We end the class with a discussion of America’s place in the world today – examining a speech by a writer who articulately raises challenges to our self-understanding that are inarticulately expressed today in rage and ranting from enemies of the United States 
Three take home analytic essays, chosen from a list of topics I provide, each weighted 25% of the course grade  Late essays will not be accepted, except with a doctor’s excuse or a Dean’s excuse for family emergency 
OR as an option: you may write the two short essays (both together weighted 25%) and do a longer 15 page paper on a topic of your choice in consultation with me (weighted 50% of your course grade)  Government honors students who are thinking of doing an honors thesis next year may prefer this option to begin to develop research and writing skills for longer work  Students who prefer this option will need to designate their preferred third short essay and have discussed with me a topic for their long paper by March 30  Texts:
Selected Anti-Federalist writings
Tocqueville, Democracy in America
Essays, speeches and articles by Frederick Douglass, W E B  Dubois, Booker T  Washington, James Baldwin and Ralph Ellison GOV 382M • Democratic Theory 38120 • Spring 2016 Meets M 3:30PM-6:30PM BAT 1 104 show description
GOV 382M (38120)
Democratic Theory Spring 2016
This is a graduate seminar on contemporary topics in democratic theory  Topics to be covered include: democratic epistemology; deliberative democracy; the meaning of the people; oracular democracy; agonistic democracy; and possibly new theories of republicanism, representation and partisanship 
Texts (tentative)
Helene Landemore, Democratic Reason
Jeffrey Edward Green, The Eyes of the People
Amy Gutmann and Dennis Thompson, Why Deliberative Democracy?
Alan Keenan, Democracy in Question
Jason Frank, Constituent Moments
Jason Frank, Publius and Political Imagination
Nadia Urbanati, Democracy Disfigured
Russell Muirhead, Partisanship in a Polarized Age
Bryan Garsten, manuscript
Active seminar participation; an annotated bibliography or review essay; a research/analytic paper  GOV 310L • American Government-Honors 37615 • Fall 2015 Meets TTH 2:00PM-3:30PM BEN 1 106 show description
TTH 2-3:30/BEN 1 106
Bruce Ackerman,Before the Next Attack: Preserving Civil Liberties in an Age of Terrorism GOV 370L • Presidency In Constitutl Order 37845 • Fall 2015 Meets TTH 5:00PM-6:30PM PAR 310 show description
GOV 370L (37845)
TTH 5-6:30 PAR 310
The Presidency in the Constitutional Order
A study of the place of the presidency in the American political order that stresses tension between power and accountability inherent in the office and the system  Topics include: separation of powers, presidential selection, impeachment, relations with Congress and bureaucracy, emergency powers, presidential character, and leadership 
This is a very demanding writing flag class  If you are enrolling in this class just in order to satisfy the writing flag, you are in the wrong class  Interest in political theory and willingness to work very hard are necessary for success in this class 
Joseph M  Bessette, The Constitutional Presidency
Andrew Rudalevige, The New Imperial Presidency
Bruce Ackerman, The Rise and Decline of the American Republic
Michael Nelson, ed , The Presidency in the Political System
Michael Nelson, ed , The Evolving Presidency
Louis Fisher, Constitutional Conflicts Between Congress and the President
Active and prepared class participation
Regular quizzes on the reading
Four analytic essays (approximately 1200 words) 
One term paper, (approximately 5000 words)  GOV 379S • Regime Persp On Amer Politics 38100 • Spring 2015 Meets T 3:30PM-6:30PM MEZ 1 104 (also listed as LAH 350) show description
Essays, speeches and articles by Frederick Douglass, W E B  Dubois, Booker T  Washington, James Baldwin and Ralph Ellison GOV 382M • Tocqueville 38135 • Spring 2015 Meets M 3:30PM-6:30PM BAT 5 102 show description
This graduate seminar will be devoted to close readings of two principal writings of Tocqueville: Democracy in America and The Ancien Regime and the Revolution  We will also assess some of the best secondary studies of Tocqueville, including work by Sheldon Wolin, Harvey Mansfield, Delba Winthrop, Jon Elster, Francois Furet, and a book by Pierre Manent 
Course requirements will include two very short analytic essays and one seminar paper (20-25 pages)  GOV 310L • American Government-Honors 38722 • Fall 2014 Meets TTH 2:00PM-3:30PM GAR 2 112 show description
Joseph M  Bessette and John J  Pitney, American Government and Politics: Deliberation, Democracy and Citizenship
Mary Nichols and David Nichols, Readings in American Government
Bruce Ackerman,Before the Next Attack: Preserving Civil Liberties in an Age of Terrorism GOV 370L • Presidency In Constitutl Order 38977 • Fall 2014 Meets TTH 9:30AM-11:00AM CBA 4 332 show description
A study of the place of the presidency in the American political order that stresses
tension between power and accountability inherent in the office and the system 
Topics include: separation of powers, presidential selection, impeachment,
relations with Congress and bureaucracy, emergency powers, presidential
character, and leadership 
This is a very demanding writing flag class  If you are enrolling in this class just in order
to satisfy the writing flag, you are in the wrong class  Interest in political theory and willingness
to work very hard are necessary for success in this class 
One term paper, (approximately 5000 words)  GOV 379S • Regime Persp On Amer Politics 39395 • Spring 2014 Meets T 3:30PM-6:30PM MEZ 1 104 (also listed as CTI 335, LAH 350) show description
Essays, speeches and articles by Frederick Douglass, W E B  Dubois, Booker T  Washington, James Baldwin and Ralph Ellison GOV 381L • Constitutional Conflict 39415 • Spring 2014 Meets M 3:30PM-6:30PM BAT 1 104 show description
Lowi, The End of Liberalism GOV 330K • The American President 39140 • Fall 2013 Meets MW 3:00PM-4:30PM MEZ B0 306 show description
This course offers an over view of the place of the presidency in the American political order  Topics covered include: constitutional design of the office; nominations and elections; legislative leadership; leadership of the bureaucracy; staffing and organizing the White House; the presidency and the judiciary; war and emergencies  We will spend extra time this fall on the presidential campaign and election of 2012 
Two in-class examinations (50% of the final grade)
One short (1000 word) take-home essay (30% of the final grade)
Class participation and quizzes (20% of the final grade)
Richard J  Ellis, The Development of the American Presidency (Routledge, 2012)
Richard J  Ellis and Michael Nelson, eds, Debating the American Presidency, (2nd edition, CQ Press, 2009)
Packet of selected primary texts (to be linked or posted on Blackboard)  GOV 330K • The American President 39145 • Fall 2013 Meets MW 5:00PM-6:30PM MEZ B0
Context 3: A Brief History of Benjamin Franklin's Residences on Craven Street, London: 1757 - 1775 - Journal of the American Revolution
Benjamin Franklin House, 36 Craven St, London  (Photo by Elliott Brown | Wikimedia Commons)
If one looked into Benjamin Franklin’s time on Craven Street, they might initially believe he lived at 36 Craven Street the entirety of his two stays in London based on the plethora of articles on the internet that say so  If they dug a little deeper they might read that he lived at No  27 Craven Street, previously numbered 7, but now numbered 36; or that he lived exclusively at No  7 Craven Street; or that he lived in multiple residences on Craven Street; or that he moved out of No  36 to another house on Craven Street and then moved back into No  36 the last year of his residence  What is one to believe with all of the conflicting accounts? What does the historical record have to say about Franklin’s time on Craven Street?
Figure 1  Spur Alley 1685  “A map of the parish of St Martins in the Fields, taken from ye last survey, with additions (1685)”  (© The British Library Board, Shelfmark: Maps Crace Port  13 2, Item number: 2)
Before Craven Street existed there was Spur Alley, a narrow passageway sandwiched between the Hungerford Market to the north (now Charing Cross Station) and Scotland Yard and the Northumberland House and Garden to the south  It was flanked on both ends by major thoroughfares, the Strand on the west, connecting Westminster to London by road, and the River Thames on the east, not only connecting the two cities to each other and to Southwark on the south side of the Thames, but connecting the entire metropolis to the rest of the world  Being located in the City of Westminster, Spur Alley had escaped the devastation of the Great Fire of London in 1666 leaving its wooden structures, built in the early part of seventeenth century, intact, but also in dire need of restoration or demolition  “The ratebooks show that during the last thirty years or so of their existence the houses in Spur Alley were in a very bad condition  Few of them were rated at more than a few shillings and many of them were unoccupied ”[1] The landowner, William, 5th Baron Craven, desiring to increase the profitability of his assets, tore down the derelict structures on Spur Alley around 1730 and leased the newly established lots to builders  By 1735, twenty brick houses in the Georgian style had been built on the west side and sixteen on the east side of the way now called Craven Street [2]
Figure 2  Craven Street 1746  (John Rocque London, Westminster and Southwark, First Edition 1746, Motco Enterprises Limited, motco com)
Letters to Franklin during his residence with Mrs  Margaret Stevenson, his landlady on Craven Street, were addressed rather vaguely; “Craven Street/Strand”, “Mrs  Stevensons in Craven Street”, or “Benjamin Franklin Esqr ” are but a few examples  Letters from Franklin referenced “London,” or sometimes “Cravenstreet,” but never included a number  Despite the absence of numbered addresses in Franklin’s correspondence, there was a sense of one’s place in the neighborhood based on entries in the Westminster Rate Books (tax assessments)  The Rate Books did not list house numbers during Franklin’s time there, but they did list the residents of Craven Street in a particular order that became the default numbering system for the street  Number one was associated with the first resident listed under “Craven Street” in the Rate Books and was the northernmost house on the west side of the street  The numbers increased counter-clockwise down the west side and up the east side in accordance with the list of residents  In 1748, the first year of Margaret Stevenson’s (Stevens in the Rate Books for that year) residence on Craven Street, she is listed as the twenty-seventh resident, the second house north of Court Street (later Craven Court, now Craven Passage) on the east side of the street [3]
In 1766, Parliament passed the London Paving and Lighting Act (6 Geo  3 c  26), “An act for the better paving, cleansing, and enlightening, the city of London, and the liberties thereof; and for preventing obstructions and annoyances within the same; and for other purposes therein mentioned ”[4] One of the other purposes therein mentioned was the numbering of houses  With an aim to bring order to the chaotic numbering systems or lack thereof on London streets the Act provided that “… the said commissioners … may also cause every house, shop, or warehouse, in each of the said streets, lanes, squares, yards, courts, alleys, passages, and places, to be marked or numbered, in such manner as they shall judge most proper for distinguishing the same ”[5] This was quite an undertaking that took years to accomplish  It was a decade later before numbered addresses on Craven Street in the City of Westminster appeared in The London Directory (1776)  The London Directory and its competitors were published primarily by booksellers or printers to supplement their income and were highly profitable  To say they were competitive is an understatement  “Some of the most hotly disputed struggles over copyright in the century concerned guidebooks  Many were optimistically emblazoned with a royal license and a notice that the work had been entered at Stationers’ Hall  Various struggles between rival guides intensified as the potential for profits became clear ”[6] The London Directory boldly proclaimed to contain “An ALPHABETICAL LIST OF THE NAMES and PLACES of ABODE of the MERCHANTS and PRINCIPAL TRADERS of the Cities of LONDON and WESTMINSTER, the Borough of SOUTHWARK, and their Environs, with the Number affixed to each House ”[7] Kent’s Directory made a similar proclamation: “An Alphabetical LIST OF THE Names and Places of Abode OF THE DIRECTORS of COMPANIES, Persons in Public Business, MERCHANTS, and other eminent TRADERS in the Cities of London and Westminster, and Borough of Southwark WITH THE NUMBERS as they are affixed to their Houses agreeable to the late Acts of Parliament ”[8] Mrs  Stevenson wasn’t included in the directories because she didn’t meet the criteria of being a merchant or trader, not because she was a woman  Although it is rare to see women listed in the directories, some examples do exist [9] If Mrs  Stevenson had appeared in the directories in 1776 it would not have been on Craven Street as she had moved to Northumberland Court, a stone’s throw away, the previous year [10] A comparison of Craven Street residents whose names and addresses do appear in the directories with the same residents as they appear in the Westminster Rate Books determines if the numbering systems were congruent  For the most part they were  For example, Joseph Bond at No  30, William Rowles at No  31, Samuel Sneyd at No  32, and Jonathan Michie at No  35 in The London Directory coincide with their places of residence in the Westminster Rate Books; however, errors did occur  The 1776 edition of The London Directory lists Brown & Whiteford, wine merchants, at No  9 Craven Street while the Westminster Rate Books list them as the twenty-ninth residents  Obviously, it makes no sense to have Brown & Whiteford at No  9 in The London Directory and their next-door neighbor, Joseph Bond, at No  30  The same error appears in Baldwin’s The New Complete Guide for 1783  The New Complete Guide may have “borrowed” the error from The London Directory  It was not uncommon for the owner of one directory to copy entries from another to save both time and money  Beginning in 1778 and contrary to The London Directory, Kent’s Directory faithfully followed the numbering system of the Westminster Rate Books in all of its editions and listed Brown & Whiteford at No  29 as did Bailey’s Northern Directory in 1781  Perhaps realizing their error, The London Directory changed their listing of Brown & Whiteford from No  9 to No  29 in their 1783 edition and maintained that listing thereafter 
Sometime prior to 1792, the embankment on the Thames at the south end of Craven Street had been sufficiently extended allowing for the construction of ten new houses below the original houses: “ … four houses, Nos  21–24, were built on the west side, and six houses, Nos  25–30, on the east side of the way ”[11] In a note in the same report, the new numbering system is explained  “The houses in the street, which had previously been numbered consecutively down the west side and up the east side, were then renumbered on the same system to include the additional houses ”[12] Because the new houses (21-24) on the west side were built below the existing houses (1-20), houses 1-20 retained their original numbering 
Figure 4  Craven Street 1799  (Richard Horwood’s Map of London, Westminster and the Borough of Southwark 1799, Motco Enterprises Limited, motco com)
One would think that the numbers of the sixteen original houses on the east side, Nos  21 – 36, would simply increase by ten with the addition of the ten new houses, but such was not the case; they increased by nine  How could that be? The only possible explanation is that No  21 of the original houses was demolished to make way for the construction of the northernmost of the six new houses on the east side (No  30)  Evidence of No  21’s demolition appears in the lease granted to Charles Owen by William, 7th Baron Craven, in 1792, which describes No  22 as: “All that messuage in Craven Street late in the occupation of Francis Deschamps undertaker … being the Southernmost house in the Old Buildings on the East Side of the said Street numbered with the No  22 ”[13] The lease describes No  22 as being the southernmost house in the old buildings on the east side of Craven Street  Clearly the house previously at No  21 did not exist when the lease granted to Charles Owen was written in 1792 as it used to be the southernmost house  It is also worth noting that in 1790, The London Directory listed Jacob Life at No  21 (original numbering)  In 1791-2, it listed him at No  6  With No  21 vacated, it would allow for its demolition and the construction of the tenth new house  By utilizing lot No  21 for the new construction, only nine additional lots were needed to build the ten houses, hence, Margaret Stevenson’s former residence at 27 became 36 (27 + 9) in the renumbering and not 37 
For nearly a century and a half after Franklin departed London for America in March of 1775 the scales were tipped heavily in favor of his residence having been No  7 Craven Street  As early as 1807 in London; Being An Accurate History And Description Of The British Metropolis And Its Neighborhood, Volume 4, one would have read: “In Craven Street is a house, No  7, remarkable for having been the residence of Dr  Benjamin Franklin [14] In 1815, the identical phrase appeared in The Beauties of England and Wales [15] After 23 editions of not mentioning Franklin, his name finally appeared in the 24th edition of The Picture of London in 1826: “The house, No  7, Craven Street, in the Strand, was once the residence of Dr  Benjamin Franklin ”[16] In 1840, Jared Sparks referred to Franklin’s Craven Street residence appearing in London guide books in his voluminous The Works of Benjamin Franklin: “In the London Guide Books, ‘No  7, Craven Street,’ is still indicated as the house in which Dr  Franklin resided ”[17] In 1846, George Gulliver F R S , in his book, The Works of William Hewson, wrote: “She [Polly] had been upon terms of the warmest friendship with Dr  Franklin
Figure 5  No  7 Craven Street with Memorial Tablet  (Photo courtesy of British History Online, and the Survey of London)
since she was eighteen years of age  That eminent philosopher resided with her mother, Mrs  Margaret Stevenson, at No  7, Craven Street, Strand, during the fifteen years of his abode in London ”[18] Guide books mentioning Franklin at No  7 continued to proliferate throughout the century: Handbook for London; Past and Present, Volume I (1849);”[19] Handbook for Modern London (1851);”[20] The Town; Its Memorable Characters and Events (1859);”[21] London and Its Environs (1879) [22] There was an anomaly when London In 1880 Illustrated With Bird’s-Eye Views of the Principal Streets, Sixth Edition (1880) placed Franklin at 27 Craven street [23] The anomaly lasted for six years until his place of residence was changed to No  7 in the revised edition, London  Illustrated by Eighteen Bird’s-Eye Views of the Principal Streets (1886) [24] London Past and Present; Its History, Associations, and Traditions, Volume 1 (1891), copied the 1849 Handbook for London almost word-for-word and included, “The house is on the right from the Strand ”[25] In October of 1867, The Society of Arts in London declared that: “In order to show how rich the metropolis is in the memory of important personages and events, which it would be desirable to mark by means of tablets on houses, the Council have caused an alphabetical list to be prepared, … ”[26] Franklin had been elected a corresponding member to the Society in 1756 and was a popular choice among Council members deciding who they were to memorialize [27] By January of 1870, a tablet honoring him was affixed to the house they believed to have been his residence while in London, No  7 Craven Street in the Strand on the west side of the street [28] A majority of historians writing about Franklin in the nineteenth and early twentieth century placed him at No  7: O  L  Holley, The Life of Benjamin Franklin (1848); E  M  Tomkinson, Benjamin Franklin (1885); John Torrey Morse, Benjamin Franklin (1891); Paul Elmer More, Benjamin Franklin (1900); John S  C  Abbot, Benjamin Franklin (1903); Sydney George Fisher, The True Benjamin Franklin (1903)  A notable exception is D  H  Montgomery’s His Life Written by Himself published in 1896  He has Franklin at No  27 Craven Street  It seems then that depending upon the source, Franklin was thought to have lived at either No  7 or No  27, but not both, the overwhelming majority favoring No  7  As late as 2011, Franklin is still mentioned as living at No  7 [29]
In 1913, No  7 was scheduled to be torn down  An article in the March 1914 edition of The Book News Monthly, describes the situation:
As is well known to informed American pilgrims, it has been possible for all admirers of the famous philosopher and statesman to pay their respects to his memory before that house, No  7 Craven Street, just off the Strand, which was his chief home during his two sojourns in the British capital, but even as these lines are being written the London newspapers are recording that that interesting shrine is soon to be pulled down to make room for a restaurant  It is some mitigation of this misfortune to remember that at the most the Craven Street house was nothing more than a reproduction of the one in which Franklin had his suite of four rooms, for the structure has been rebuilt since Franklin’s time  When, then, some one makes a piteous plea that at least the philosopher’s bedroom shall be preserved, the soothing answer is that the apartment in question is only a replica of that in which the illustrious American enjoyed his well-earned slumbers in 1757-62 and 1764-75  The restaurant-builder, however, with an eye doubtless to possible American patronage, has assured the world that every effort will be made to preserve as much as possible of the entire structure [30]
Concerned with the possible demolition of Franklin’s residence, the Royal Society of Arts (formerly the Society of Arts[31]) initiated an inquiry into the matter [32] The London County Council, having taken over the responsibility of placing memorial tablets on notable houses from the Royal Society, was charged with the investigation  It ultimately fell to Sir George Laurence Gomme, a clerk to the Council, to come up with a response  A few years earlier Sir George had discovered Margaret Stevenson residing at No  27 Craven Street in the Westminster Rate Books  He must have wondered why No  7 on the west side of Craven Street was being celebrated as Franklin’s residence when the evidence clearly showed otherwise 
Sir George and his staff examined the various London directories discussed earlier and came up with a novel explanation for the discrepancy  They concluded that there had been two numbering systems on Craven Street  An anonymous author echoes Sir George’s conclusion about the two numbering systems in an article in The Journal of the Royal Society of Arts:
…an inspection of the directories of that time proves that there were at least two systems of numbering in Craven Street before the erection of the additional houses  According to one of these the numbers started from the top (Strand end) on the west side of the street, and ran down to the bottom to No  20, then crossed over and went back to the Strand along the east side – 21 to 36  According to the other system, the east side of the street was numbered from the bottom upwards, starting at No 1  This was not apparently in general use, but there is evidence that this numbering was at all events occasionally used 
The evidence of these two systems of numbering, and for believing that Mrs  Stevenson’s house was first No  7 under the oldest system, next No  27 under the second system, and finally No  36 under the latest and existing system, is to be found in the various directories and the Westminster rate-books [33]
The “evidence” mentioned above consisted of The London Directory’s listing of Brown & Whiteford at No  9: “The rate-books for 1781 and 1786 show the house next but one to the north of Mrs  Stevenson’s house as in the occupation of Brown and ‘Whiteford,’ while the old directories mention the business of the firm as wine merchants, and give their address as 9, Craven Street – then a little later, down to 1791, as 29, Craven Street  Curiously enough, in the years 1778 to 1780, or 1781, Lowndes gives it as No  9, and Kent as 29 ”[34] Ignoring Kent’s Directory having Brown and Whiteford as 29 and The London Directory (Lowndes) having Brown and Whiteford “a little later” as 29, and knowing that Mrs  Stevenson lived two doors south of them, Sir George concluded that her house must have been numbered 7, even though there is no listing in any of the directories of her residence ever being No  7  He surmised that the No  7 on the west side of Craven Street with the memorial tablet thought to have been Franklin’s residence had simply been confused with number 7 (27) on the east side  Again from The Journal of the Royal Society of Arts:
Taking all the evidence together, there cannot be any doubt whatever that Mrs  Stevenson’s house, in which Franklin lodged, was the house two doors north from Craven Court, first numbered 7, afterwards 27, and finally 36, and consequently that the house in which Franklin lived was that now numbered 36, not the one now numbered 7, on which the tablet is placed [35]
A response to The Royal Society of Arts was issued: “… the London County Council … informed the Society that it had made a mistake and that No  36 Craven street was the building that deserved commemoration ”[36] The Society accepted the Council’s conclusion, and despite assurances of preservation by the restaurant builder, No  7 was torn down the following year 
Sir George’s assertion “that Mrs  Stevenson’s house, in which Franklin lodged, was the house two doors north from Craven Court” was correct, however, his assertion that it was “first numbered 7, afterwards 27”, was not  It was only by association with the errant entry of Brown & Whiteford at No  9 from 1776-1782 in The London Directory that Mrs  Stevenson’s address was conjured to be No  7  The problem with associating her address exclusively with that of Brown & Whiteford at No  9 during those years is that, as previously demonstrated, The London Directory also listed four other Craven Street residents, Bond, Rowles, Sneyd, and Michie, who’s addresses did conform to the numbering system in The Westminster Rate Books  If Brown & Whiteford at No  9 was indicative of a numbering system different from The Westminster Rate Books, Bond, Rowles, Sneyd, and Michie would have been listed as Nos  10, 11, 12, and 15, respectively  So on one hand Sir George was relying on the Westminster Rate Books to establish Mrs  Stevenson at No  27 and on the other hand he was dismissing the Westminster Rate Books to establish her at No  7  Instead of using the anomalous listing of Brown & Whiteford at No  9, he could have just as easily, and more logically, used the Bond et al  listings, or the post-1782 Brown & Whiteford listing in the London Directory at No  29 to establish Mrs  Stevenson at No  27  Even if there had been two numbering systems, his assertion that No  27 was first numbered 7 would still be false  The earliest numbering system was the Westminster Rate Books dating from the early 1730s when the houses were constructed  Brown & Whiteford at No  9 didn’t appear until 46 years later and then only for a brief period 
There is ample evidence in Franklin’s correspondence and in a memoir by Polly Hewson (Mrs  Stevenson’s daughter) that Benjamin and Mrs  Stevenson lived in not one, but two houses on Craven Street  On July 6, 1772, Polly wrote to Benjamin from her house at Broad Street North in London: “My Mother I must tell you went off last friday week, took our little Boy with her and left Mr  Hewson [Polly’s husband, William] the care of her House [27 Craven Street]  The first thing he did was pulling down a part of it in order to turn it to his own purpose, and advantage we hope  This Demolition cannot affect you, who at present are not even a Lodger [Benjamin was traveling at the time], your litterary apartment remains untouch’d, the Door is lock’d …”[37] In a memoir about her husband written after his death Polly writes: “He [William Hewson] began his Lectures Sept  30, 1772, in Craven-street, where he had built a Theatre adjoining a house which he intended for the future residence of his family ”[38] On October 7, 1772, Benjamin wrote to his son William: “I am very well  But we [Mrs  Stevenson and I] are moving to another House in the same street; and I go down tomorrow to Lord LeDespencer’s to [stay a] Week till things are settled ”[39] To his son-in-law, Richard Bache, on the same day he wrote: “We are moving to another House in the [street] leaving this to Mr  Hewson ”[40] Writing to a friend on October 30, 1772 he explained: “I should sooner have answered your Questions but that in the Confusion of my Papers, occasioned by removing to another House, I could not readily find the Memorandums …”[41] On November 4, 1772 Benjamin informed his wife Deborah of the move  “We are removed to a more convenient House in the same street, Mrs  Stevenson having accommodated her Son-in-Law with that we lived in  The Removing has been a troublesome Affair, but is now over ”[42]
An agreement had been struck between the parties  Margaret and Benjamin would move to another house on Craven Street and allow Polly and William to move into No  27, the large yard behind the house being spacious enough to accommodate the anatomy school William wished to build [43] Perhaps the idea was inspired by Margaret’s next-door neighbor at No  26, Dr  John Leake, a man-midwife and founder of the Westminster Lying-in Hospital, who had built a theater adjoining his residence in which he practiced anatomy and taught midwifery [44]
After Margaret and Benjamin vacated No  27, Polly, William, their son William Jr , and William’s younger sister, Dorothy Hewson, took up residence there [45] In the 1773 Westminster Rate Books for Craven Street, Mrs  Stevenson’s (Stephenson in the Rate Books) name has been crossed out and replaced with “William Hewson ”[46] Further proof that the Hewsons had indeed moved into 27 Craven Street has been confirmed by the discovery of human and animal remains buried in the basement of No  36 (formerly No  27 and now the Benjamin Franklin House), a by-product of the dissections that took place at William’s anatomy school [47]
So what house on Craven Street did Mrs  Stevenson and Benjamin move into after vacating No  27? An examination of the Westminster Rate Books for the years 1774 and 1775 reveal them living not at No  7 on the west side of Craven Street as one might expect from the overwhelming consensus of nineteenth century guidebooks and biographies, but surprisingly at No  1 [48] The controversy of No  7 being torn down was all for naught as it had never been Franklin’s residence  Sir George was correct on that point  Unfortunately, No  1 was torn down as well in the early part of the twentieth century  The first time No  1 is mentioned as Franklin’s second residence is in the Survey of London: Volume 18, St Martin-in-The-Fields II: the Strand published by the London County Council in 1937, ironically the same County Council that had declared No  36 as Franklin’s only residence twenty-four years earlier 
From 1748 until 1772 Margaret ‘Stephenson’ occupied this house [No  27 (36)], and it was there that Benjamin Franklin settled after his arrival in London in 1757 as Agent to the General Assembly of Pennsylvania … In October, 1772, Mrs  Stevenson and Franklin removed to No  1, Craven Street (now demolished), and No  36 was for the next two years occupied by William Hewson, surgeon, who had married Mary Stevenson



ground_truth: Physics, biology, social sciences, finance, and neuroscience are some fields in which the inverse problem is encountered.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is Professor Tulis's forthcoming book?

Read the following text and answer briefly.

Context 2: 306 show description
Packet of selected primary texts (to be linked or posted on Blackboard)  GOV 381L • American Founding 39040 • Spring 2013 Meets T 6:30PM-9:30PM BAT 1 104 show description
NOTE WELL: Course meets Tuesdays, 6:30 to 9:30pm
Batts Hall 1 104
This is a seminar on American political thought and constitutional design  It is designed for students of American politics and political theory  The principal themes include: 1) the nature of founding and its constitutive significance; 2) the relation of structure and power in American politics; 3) the meaning and significance of the Federalist/Anti-Federalist debate; 4) the philosophic background of the American founding; and 5) the relevance of the founding to debate to prospects for, and pathologies of, American politics today 
We will conduct a close reading of the Madison’s Notes, of The Federalist, and selected Anti-Federalist writings  We will also study a larger and growing body of secondary literature on the constitutional convention, ratification and early American political thought 
James Madison, Notes of the Debates: In the Federal Convention of 1787
The Federalist (Rossiter, ed )
The Anti-Federalist (Storing, ed )
David Brian Robertson, The Constitution and America’s Destiny (2005)
Pauline Maier, Ratification (2012)
Gordon Wood, The Idea of America (2011)
Jack Rakove, Original Meanings: Politics & Ideas in the Making of the Constitution
Herbert Storing, What the Anti-Federalists Were For (1981)
Numerous essays and articles (to be posted on line or gathered in packet)
Grading: Active seminar participation, including three short papers and presentations (40%) and one article-length seminar paper (60%) T C 357 • Amer Founding/Probs Const Des 43095 • Spring 2013 Meets M 3:30PM-6:30PM CRD 007B show description
The American Founding and Problems of Constitutional Design
Jeffrey Tulis, Associate Professor, Department of Government
Sanford Levinson, Professor, School of Law
This Plan II seminar will be built around a close reading of the debates that informed the drafting and ratification of the U S  Constitution  We aim to recover the perspective of these founding thinkers -- their way of thinking -- as much as their concrete ideas, in order to raise fundamental questions about the American political order today  Are some of the most important pathologies of American politics today rooted in design features of our original political architecture? Are the original answers to basic founding questions (such as "how democratic is our Constitution?) still adequate for contemporary circumstances? What features of the Constitution should we preserve and what features should we amend, if possible? Would it be good for the polity as a whole to reconsider these questions in a new constitutional convention today, or would such an event be a political nightmare? Our reading will include notes from the founding conventions, writings by Federalists and Anti-Federalists, and present-day critiques of the American political order  Our aim will be to generate a dialogue between the thought of the founders and some of the best present day critics and supporters of the Constitution 
James Madison, Notes of the Debates in the Federal Convention
The Federalist, ed  Clinton Rossiter
The Anti-Federalist, ed  Herbert Storing
Pauline Maier, Ratification: The People Debate the Constitution, 1787-1788
Sanford Levinson, Framed: America’s 51 Constitutions and the Crisis of Governance
Bruce Ackerman, The Decline and Fall of the American Republic
Robert Goldwin, ed  How Democratic is the Constitution?
a course packet of selected articles, essays, and additional primary materials 
Class participation, including at least one presentation of a short discussion paper 25%
One take-home analytic essay 25%
One term paper 50%
About the Professors:
Professor Tulis's interests bridge the fields of political theory and American politics, including more specifically, American political development, constitutional theory, political philosophy and the American presidency  He received the President's Associates Teaching Excellence Award at the University of Texas  He has held research fellowships from NEH, ACLS, Olin Foundation, Harvard Law School, and the Mellon Preceptorship at Princeton University, where he taught before moving to Texas  He has held visiting positions at Notre Dame and Harvard  During the academic year 2008-09, he was a Laurance S  Rockefeller Visiting Fellow at the University Center for Human Values at Princeton 
Proefessor Levinson holds the W  St  John Garwood and W  St  John Garwood, Jr  Centennial Chair in Law, he joined the University of Texas Law School in 1980  Previously a member of the Department of Politics at Princeton University, he is also a Professor in the Department of Government at the University of Texas  The author of over 350 articles and book reviews in professional and popular journals--and a regular contributor to the popular blog Balkinization  He received the Lifetime Achievement Award from the Law and Courts Section of the American Political Science Association in 2010  He has been a visiting faculty member of the Boston University, Georgetown, Harvard, New York University, and Yale law schools in the United States and has taught abroad in programs of law in London; Paris; Jerusalem; Auckland, New Zealand; and Melbourne, Australia 
GOV 330K • The American President 38675 • Fall 2012 Meets MW 3:00PM-4:30PM MEZ B0 306 show description
Packet of selected primary texts (to be linked or posted on Blackboard)  GOV 330K • The American President 38675 • Fall 2011 Meets MW 3:30PM-5:00PM WAG 420 show description
see syllabus GOV 330K • The American President 38680 • Fall 2011 Meets MW 5:30PM-7:00PM UTC 1 146 show description
see syllabus GOV 379S • Regime Persp On Amer Polit-Hon 39110 • Spring 2011 Meets W 3:30PM-6:30PM BAT 5 102 (also listed as CTI 326, LAH 350) show description
To see the polity as a whole requires that we get some distance from our subject, much as to see the planet earth as a whole requires one to look at it from outer space  Just as it is difficult to get visual perspective on a place living within it, it is difficult to understand the promise or pathologies of a regime from within it  To get critical distance from our politics, we will closely study three sets of texts that look at American politics from a distance  The first part of the course will recover the perspective of the founding debate between Federalists and Anti-federalists  This fundamental debate reveals what is a stake in the basic architecture of the American regime  The second part of the course is a close study of Tocqueville’s Democracy in America  Regarded by many as the best book ever written on democracy and the best book written on America, Tocqueville sees our polity whole because he looks at it from the vantage point of Europe, in general, and France, in particular  In the third part of the seminar we think about American politics from the perspective of thoughtful commentators who feel only nominally included in the polity  Half in and half out, these extraordinary black American writers reveal fissures and fault lines in the American regime  We end the class with a discussion of America’s place in the world today – examining a speech by a writer who articulately raises challenges to our self-understanding that are inarticulately expressed today in rage and ranting from enemies of the United States 
Four take home writing assignments  Analytic essays, each 1000-1500 words  (Grades weighted: 10%, 25%, 25%, and 25%) Late essays will not be accepted, except with a doctor’s excuse or a Dean’s excuse for family emergency  Regular preparation and class participation: 15% 
OR as an option: By prior arrangement with me by the due date of the second analytic essay, students may substitute one longer research paper (15 – 20 pages) for two of the last three analytic papers This paper will be on a topic of the students choosing , if I approve, and the due date will be the same as the last assigned analytic essay  This project would count 50% of the students course grade 
Selected writings by Frederick Douglass, W E B  Dubois, Ralph Ellison, James Baldwin
Solzhenitsyn, “A World Split Apart”
Tocqueville, Democracy in America GOV 382M • Tocqueville 39150 • Spring 2011 Meets T 6:30PM-9:30PM BAT 5 102 show description
See syllabus GOV 370L • President, Congress, And Court 38695 • Fall 2010 Meets TTH 8:00AM-9:30AM UTC 3 112 show description
Course Description: A Study of the political relationship of the President, Congress and Court in the American constitutional order  Has this relationship changed over the course of American history? Is American national politics prone to stalemate or deadlock between the branches regarding major issues of public policy? Do we have a new “imperial presidency?” Should the Court arbitrate disputes between the President and Congress over custody of their respective powers? Has Congress abdicated its constitutional responsibilities? We will examine questions like these in light of practical problems such as executive privilege and secrecy, the war on terror, budget politics and controversies regarding appointments to the Supreme Court  Grading:Three in class essay tests, for which study questions will be distributed in advance  The exam questions will be chosen from the list of study questions  (25% each) One short take home essay (10% each)  Class participation and attendance (15%)  Tentative Texts: The FederalistFisher, Congressional Abdication on War and SpendingRudalevige, The New Imperial PresidencyBessette and Tulis, The Constitutional PresidencySkowronek, Presidency in Political TimeGoldsmith, The Terror PresidencyA course packet of articles and essays GOV 370L • President, Congress, And Court 38700 • Fall 2010 Meets TTH 5:00PM-6:30PM UTC 3 122 show description
Course Description: A Study of the political relationship of the President, Congress and Court in the American constitutional order  Has this relationship changed over the course of American history? Is American national politics prone to stalemate or deadlock between the branches regarding major issues of public policy? Do we have a new “imperial presidency?” Should the Court arbitrate disputes between the President and Congress over custody of their respective powers? Has Congress abdicated its constitutional responsibilities? We will examine questions like these in light of practical problems such as executive privilege and secrecy, the war on terror, budget politics and controversies regarding appointments to the Supreme Court  Grading:Three in class essay tests, for which study questions will be distributed in advance  The exam questions will be chosen from the list of study questions  (25% each) One short take home essay (10% each)  Class participation and attendance (15%)  Tentative Texts: The FederalistFisher, Congressional Abdication on War and SpendingRudalevige, The New Imperial PresidencyBessette and Tulis, The Constitutional PresidencySkowronek, Presidency in Political TimeGoldsmith, The Terror PresidencyA course packet of articles and essays GOV 312L • Iss & Policies In Amer Gov-Hon 38698 • Spring 2010 Meets MW 3:30PM-5:00PM UTC 3 104 show description
Government 312L satisfies the second half of the mandated six hours of government that every UT student must take  Course covers analysis of varying topics concerned with American political institutions and policies, including the United States Constitution, and assumes basic knowledge of government from GOV 310L, which is a prerequiste  May be taken for credit only once  GOV 370L • President, Congress, And Court 38966 • Spring 2010 Meets MW 5:00PM-6:30PM MEZ B0 306 show description
Prerequisite: Six semester hours of lower-division coursework in government 
GOV 370L • President, Congress, And Court 39295 • Fall 2009 Meets TTH 2:00PM-3:30PM UTC 3 112 show description
GOV 370L • President, Congress, And Court 39435 • Spring 2008 Meets MW 3:00PM-4:30PM PAR 203 show description
GOV 312L • Iss & Policies In Am Gov-Hon-W 38615-38620 • Spring 2007 Meets MW 11:00AM-12:00PM MEZ B0 306 show description
Government 312L satisfies the second half of the mandated six hours of government that every UT student must take  Course covers analysis of varying topics concerned with American political institutions and policies, including the United States Constitution, and assumes basic knowledge of government from GOV 310L, which is a prerequiste  May be taken for credit only once  GOV 312L • Iss & Policies In Am Gov-Hon-W 37600-37605 • Spring 2006 Meets MW 11:00AM-12:00PM MEZ B0 306 show description
Government 312L satisfies the second half of the mandated six hours of government that every UT student must take  Course covers analysis of varying topics concerned with American political institutions and policies, including the United States Constitution, and assumes basic knowledge of government from GOV 310L, which is a prerequiste  May be taken for credit only once  GOV 312L • Iss & Policies In Am Gov-Hon-W 34900-34905 • Spring 2004 Meets MW 11:00AM-12:00PM BUR 134 show description
Government 312L satisfies the second half of the mandated six hours of government that every UT student must take  Course covers analysis of varying topics concerned with American political institutions and policies, including the United States Constitution, and assumes basic knowledge of government from GOV 310L, which is a prerequiste  May be taken for credit only once  GOV 312L • Iss & Policies In Am Gov-Hon-W 34495-34500 • Spring 2003 Meets MW 11:00AM-12:00PM UTC 1 130 show description
Government 312L satisfies the second half of the mandated six hours of government that every UT student must take  Course covers analysis of varying topics concerned with American political institutions and policies, including the United States Constitution, and assumes basic knowledge of government from GOV 310L, which is a prerequiste  May be taken for credit only once  Publications
Tulis, JK (2011), "Plausible Futures," in Dunn, Charles W  (ed ) The Presidency in the Twenty-First Century, University Press of Kentucky Tulis, J K  and Macedo, S  (2010) The Limits of Constitutional Democracy, Princeton University Press Tulis, J K  and Macedo, S  (2010) "Constitutional Boundaries," in The Limits of Constitutional Democracy, Princeton University Press Tulis, JK (2010), "The Possibility of Constitutional Statesmanship," in Tulis, JK and Macedo, S (eds ) The Limits of Constitutional Democracy, Princeton University Press Tulis, J  (2009) The Constitutional Presidency  Johns Hopkins University Press Tulis, J  (2009) Impeachment in the Constitutional Order  In J  Tulis & J M  Bessette (Eds ), The Constitutional Presidency  Johns Hopkins University Press Tulis, J  & Bessette, J M  (2009) On the Constitution, Politics, and the Presidency  In J  Tulis & J M  Bessette (Eds ), The Constitutional Presidency  Johns Hopkins University Press Tulis, J (and Bessette, J M) (2010) The Presidency in the Constitutional Order: Historical Perspectives, Reissued Classics Series, Transaction Publishers,Tulis, J and Bessette, J M  (2010, "Introduction to the Transaction Edition," The Presidency in the Constitutional Order: Historical Perspectives, Transaction Publishers 
Tulis, JK, (2009) "The Two Constitutional Presidencies," in Nelson, Michael (ed ) The Presidency in the Political System, Congressional Quarterly Press Tulis, J  & Mellow, N  (2007) Andrew Johnson and the Politics of Failure  In S  Skowronek & M  Glassman (Eds ), Formative Acts: Reckoning with Agency in American Politics  Philadelphia: University of Pennsylvania Press Tulis, J  (2007, September) The Rhetorical Presidency in Retrospect  Critical Review: An Interdisciplinary Journal of Politics and Society, 19(2&3)  Curriculum Vitae
Context 3: [49]
In the spring of 1774, William Hewson died unexpectedly of septicemia two weeks after cutting himself while dissecting a cadaver  Polly was left to care for their two young sons and was pregnant with a daughter she would give birth to in August of the same year  Is it possible that Margaret and Benjamin moved back into No  27 to assist Polly after the death of her husband as suggested in The Americanization of Benjamin Franklin?[50]
If the Westminster Rate Books are to be believed, the answer is no  For the year 1774, the Rate Books list Margaret Stevenson at No  1 and William Hewson at No  27  For the year 1775, they list Margaret Stevenson at No  1 and Magnus Falkner (Falconer/Falconar) at No  27  Magnus was William’s assistant at the anatomy school and fiancé to William’s sister, Dorothy  On his death bed, William instructed Polly, “let Mr  Falconar be my successor ”[51] Magnus would immediately take over the running of the anatomy school and continue William’s unfinished research  Four months later, he and Dorothy would marry [52] Essentially only two things changed at 27 Craven Street after William’s death: Polly gave birth to her daughter, and Magnus replaced William as the lease holder, so even if Margaret and Benjamin had wished to move back into No  27, there would have been no room for them  It is also interesting to note that considering the multiple times Benjamin wrote of his move out of No  27 (and complained of it), he never once mentioned moving back into No  27 in any of his correspondence after Mr  Hewson’s death 
Figure 6  No  36 Craven Street  (Photo courtesy of David Ross, britainexpress com)
In sum, based on the Westminster Rate Books[53] and Franklin’s correspondence, Mrs  Stevenson is known to have resided at No  27 (36) Craven Street from 1748 to 1772  It follows that, aside from the two years Franklin spent in Philadelphia from 1762 to 1764, he resided there from 1757 to 1772  Franklin’s correspondence also reveals that in the autumn of 1772, he and Mrs  Stevenson moved to another house on Craven Street  The 1773 Westminster Rate Books show her name crossed off at No  27 and William Hewson’s inserted  The following year the Rate Books list her at No  1 Craven Street  Evidence for Mrs  Stevenson and Benjamin remaining at No  1 after William’s death appears in the Westminster Rate Books for 1775 which have Mrs  Stevenson still residing at No  1 and Magnus Falkner residing at No  27  Further evidence can be construed from the lack of any mention of a move back into No  27 in Franklin’s correspondence  Despite the many theories one could devise as to why Franklin was thought to have lived at No  7 Craven Street by so many guide books and Franklin biographers of the nineteenth century, one thing is certain; at some point after Franklin’s departure to America in March of 1775, and no later than 1807, someone mistakenly associated him with No  7 on the west side of Craven Street, and it soon became his de facto residence  Credit must go to D  H  Montgomery in 1896 and Sir George in 1913 for setting the record partially straight by placing Franklin at No  27(36)  In 1937, the London County Council gave us the first accurate account of Franklin’s residences on Craven Street in the Survey of London at No  27(36) and No  1  It has been shown conclusively that No  27 was never previously numbered 7  It was, however, renumbered 36 in 1792 after ten additional houses were built at the southern end of the street and remains No  36 to this day 
[1] “Craven Street and Hungerford Lane”, in Survey of London: Volume 18, St Martin-in-the-Fields II: the Strand, ed  G H Gater and E P Wheeler (London, 1937), 27-39, Early History of the Site 
http://www british-history ac uk/survey-london/vol18/pt2/pp27-39
[2] “England, Westminster Rate Books, 1634-1900,” from database with images, Craven Street – 1735, FamilySearch from database by FindMyPast and images digitized by FamilySearch; citing Westminster City Archives, London 
[3] Ibid , Craven Street – 1748 
[4] The Statutes at Large, From Magna Charta to the End of the Eleventh Parliament of Great Britain  Anno 1761 Continued, Vol  XXVII, ed  Danby Pickering, (Cambridge, John Archdeacon, 1767), 96 
[6] James Raven, Publishing Business in Eighteenth-Century England, (Woodbridge: The Boydell Press, 2014), 201 
[7] The London Directory For the Year 1776, Ninth Edition, (London: T  Lowndes, 1776), title page 
[8] Kent’s Directory For the Year 1778, Forty-Sixth Edition, (London: Richard and Henry Causton, 1778), title page 
[9] A listing in Kent’s Directory for the Year 1882 on p  28 reveals, “Brown Sarah, Leather-seller, 1, Westmoreland-buildings, Aldersgate-street”, and in Kent’s Directory for the Year 1883 on p  175, “Whiteland Mary, Wine & Brandy Mercht  Jermyn-str  St  James ”
[10] “The Papers of Benjamin Franklin,” Sponsored by The American Philosophical Society and Yale University, Digital Edition by The Packard Humanities Institute, 22:263a 
http://franklinpapers org/franklin
Mrs  Stevenson wrote to Benjamin Franklin a letter from her new home at 75 Northumberland Court on November 16, 1775: “In this Court I have a kind friend, Mr  Lechmoen he comes and seats with me and talks of you with a hiy regard and friendship ”
[11] Survey of London, Early History of the Site 
[12] Survey of London, Footnotes/n 10 
[13] Survey of London, Historical Notes/No  31 
[14] David Hughson, LL D , London; Being An Accurate History And Description Of The British Metropolis And Its Neighbourhood, To Thirty Miles Extent, From An Actual Perambulation, Vol  IV, (London: W  Stratford, 1807), 227 
[15] The Reverend Joseph Nightingale, The Beauties of England and Wales: Or, Original Delineations, Topographical, Historical, and Descriptive, of Each County, Vol  X, Part III, Vol  II (London: J  Harris; Longman and Co ; J  Walker; R  Baldwin; Sherwood and Co ; J  and J  Cundee; B  and R  Crosby and Co ; J Cuthell; J  and J  Richardson; Cadell and Davies; C  and J  Rivington; and G  Cowie and Co , 1815), 245 
[16] John Britton, F S A  & Co , ed , The Original Picture of London, Enlarged and Improved: Being A Correct Guide For The Stranger, As Well As For the Inhabitant, To The Metropolis Of The British Empire Together With A Description Of The Environs, The Twenty-Fourth Edition (London: Longman, Rees, Orme, Brown, and Green, 1826), 479 
[17] Jared Sparks, The Works of Benjamin Franklin, Vol  VII, (Philadelphia: Childs & Peterson, 1840), 151 
[18] George Gulliver, F R S , The Works of William Hewson, F  R  S , (London: Printed for the Sydenham Society, MDCCCXLVI), xx 
[19] Peter Cunningham, Handbook for London; Past and Present, Vol  I, (London: John Murray, 1849), 245 
[20] F  Saunders, Memories of the Great Metropolis: or, London, from the Tower to the Crystal Palace, (New York: G P  Putnam, MDCCCLII), 138 
[21] Leigh Hunt, The Town; Its Memorable Characters and Events, (London: Smith, Elder and Co , 1859), 185 
[22] K  Baedeker, London and Its Environs, Including Excursions To Brighton, The Isle of Wight, Etc : Handbook For Travelers, Second Edition, (London: Dulau and Co , 1879), 133 
[23] Herbert Fry, London In 1880 Illustrated With Bird’s-Eye Views of the Principal Streets, Sixth Edition, (New York: Scribner, Welford, & Co , 1880), 50 
[24] Herbert Fry, London  Illustrated By Eighteen Bird’s-Eye Views of the Principal Streets, (London: W  H  Allen and Co , 1886), 40 
[25] Henry B  Wheatley, F S A , London Past and Present; Its History, Associations, and Traditions, Vol  1, (London: John Murray, New York: Scribner & Welford, 1891), 473 
[26] The Journal of the Society of Arts, Vol  XV, No  778, (October 18, 1867): 717 
[27] D  G  C  Allen, “Dear and Serviceable to Each Other: Benjamin Franklin and the Royal Society of Arts,” American Philosophical Society, Vol  144, No  3, (September 2000): 248-249 
Franklin was a corresponding member in 1756 because he was still residing in Philadelphia  He became an active member the following year when he moved to London 
[28] The Journal of the Society of Arts, Vol  XVIII, No  894, (Jan  7, 1870): 137 
“Since the last announcement, the following tablets have been affixed on houses formerly occupied by – Benjamin Franklin, 7 Craven-street, Strand, W C ”
[29] Franklin in His Own Time, eds  Kevin J  Haytes and Isabelle Bour, (Iowa City, University of Iowa Press, 2011), xxxvii 
“Takes lodgings with Margaret Stevenson at No  7 Craven Street ” It is unknown if the editors are referring to No  7 on the west side of Craven Street or No  36 on the east side using Sir George’s explanation of No  36 being previously numbered 7 
[30] Henry C  Shelly, “American Shrines on English Soil, III  In the Footprints of Benjamin Franklin,” in The Book News Monthly, September, 1913 to August, 1914, (Philadelphia: John Wanamaker, 1914), 325 
[31] The Journal of the Royal Society of Arts, Vol  LVI, No  2,880, (Jan  31, 1908): 245 
http://babel hathitrust org/cgi/pt?id=mdp 39015058423073;view=1up;seq=251
“His Majesty the King, who is Patron of the Society, has granted permission to the Society to prefix to its title the term ‘Royal,’ and the Society will consequently be known in future as the ‘Royal Society of Arts ’”
[32] Nineteenth Annual Report, 1914, of the American Scenic and Historic Preservation Society, (Albany: J  B  Lyon Company, 1914), 293 
http://babel hathitrust org/cgi/pt?id=wu 89072985302;view=1up;seq=4;size=150
[33] The Journal of the Society of Arts, Vol  LXII, No  3,183, (Nov  21, 1913): 18 
http://babel hathitrust org/cgi/pt?id=mdp 39015058422968;view=1up;seq=26
[36] Allen, “Dear and Serviceable,” 263-264 
[37] Papers of Benjamin Franklin, 19:20 
[38] Thomas Joseph Pettigrew, F  L  S , Memoirs of the Life and Writings of the Late John Coakley Lettsom With a Selection From His Correspondence, Vol  I, (London: Nichols, Son, and Bentley, 1817), 144 of Correspondence 
[39] Papers of Benjamin Franklin, 19:321b 
[40] Ibid , 19:314 
[41] Ibid , 19:353a 
[43] Simon David John Chaplin, John Hunter and the ‘museum oeconomy’, 1750-1800, Department of History, King’s College London  Thesis submitted for the degree of Doctor of Philosophy of the University of London , 202 
“Following Falconar’s death [1778] the lease [27 Craven Street] was advertised, and the buildings were described as:
A genteel and commodious house, in good Repair, with Coach-house and Stabling for two Horses…consisting of two rooms and light closets on each floor, with outbuildings in the Yard, a Museum, a Compleat Theatre, and other conveniences  (Daily Advertiser, 27 August 1778)”
[44] Simon Chaplin, “Dissection and Display in Eighteenth-Century London,” in Anatomical Dissection in Enlightenment England and Beyond: Autopsy, Pathology and Display, ed  Dr  Piers Mitchell, (Burlington: Ashgate Publishing Company, 2012), 108 
“Given that a nearby building at 35 [ No  26 in Franklin’s time] was occupied by the man-midwife John Leake, who advertised lectures – including lessons in the art of making preparations – at his ‘theatre’ between 1764 and 1788, it is possible that some facilities were shared  In both cases, however, the buildings [Leake’s residence at No  26 and Hewson’s residence next door at 27] served a dual function as domestic accommodation and as sites for lecturing and dissection ”
[45] George Gulliver, F R S , The Works of William Hewson, F  R  S , (London: Printed for the Sydenham Society, MDCCCXLVI), xviii 
[46] Westminster Rate Books, Craven Street – 1773, courtesy of the City of Westminster Archives 
[47] S W  Hillson et al , “Benjamin Franklin, William Hewson, and the Craven Street Bones,” Archaeology International, Vol  2, (Nov  22, 1998): 14-16 
http://dx doi org/10 5334/ai 0206
[48] Westminster Rate Books, Craven Street – 1774, 1775, courtesy of the City of Westminster Archives 
[49] Survey of London, Historical Notes/No  36, Craven Street (not sourced) 
[50] Gordon S  Wood, The Americanization of Benjamin Franklin, (New York: The Penguin Press, 2004), 261 
[51] Pettigrew, Memoirs, 146 of Correspondence 
[52] http://founders archives gov/documents/Franklin/01-22-02-0178, note 7  “Falconar married Hewson’s sister five months after the Doctor’s death; most of the Craven Street circle attended the wedding, and BF gave away the bride: Polly to Barbara Hewson, Oct  4, 1774, APS” (American Philosophical Society); “England Marriages, 1538–1973 ,” database, FamilySearch (https://familysearch org/ark:/61903/1:1:V52W-TGS : accessed September 15, 2015), Magnus Falconar and Dorothy Hewson, September 12, 1774; citing Saint Martin In The Fields, Westminster, London, England, reference ; FHL microfilm 561156, 561157, 561158, 942 B4HA V  25, 942 B4HA V  66 
[53] I chose to rely on the Westminster Rate Books for the numbering system on Craven Street  The books were consistent throughout the eighteenth century in the ordering of residents on the street and were used as the basis for the 1792 re-numbering  For the most part, commercial directories aligned with them as well  If by chance a directory didn’t initially align, it would inevitably produce future editions that did 
Benjamin Franklin, Benjamin Franklin House, London
More from David Turnquist
If one looked into Benjamin Franklin’s time on Craven Street, they might   
I think it’s very ironic that on the street maps included in your excellent article, Craven Street is so close to Scotland Yard  Because following the back and forth juxtapositions of numbers 7, 27 and 36 Craven Street (throw in 75 Northumberland Court and 1 Craven Street, too) was a case that could confound Sherlock Holmes 
Excellent job of deciphering street renumbering material spanning sixty years, including that of a wrong house number (# 7) being erroneously identified and then perpetuated in subsequent street map printings  It’s gratifying at least to know that the present day #36 Craven Street is the correct house for Ben Franklin tourists to visit  Except for #1 Craven Street for the last three years Franklin was in London, but we won’t get into that 
Again, excellent article, David!



ground_truth: Legacies of Losing in American Politics and an expanded edition of The Rhetorical Presidency in the Princeton Classics series.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What did the London Directory proclaim to contain?

Read the following text and answer briefly.

Context 4:  Our training uses REINFORCE   Pascal VOC Game We further evaluate the complexity of compositional communication with a Pascal VOC   This is a two-agent referential game similar to the Cifar game but requires the prediction of multiple classes 
During each episode, each agent observes a random image from the Pascal VOC dataset containing exactly two unique labels  Each agent must encode information given only the raw pixels from the original image such that the other agent can recognize the two class labels in the original image  An agent receives a reward of 0 25 per correctly chosen class label and will receive a total reward of 1 if both agents guess all labels correctly 
See figure 2  Our training uses heterogeneous agents trained with PPO (modified from MAPPO repository)  For simplicity of setup, we consider images with exactly two unique labels from a closed subset of size five labels of the original set of labels from the Pascal VOC data  Furthermore, these images must be of size 375 × 500 pixels 
Thus, the resultant dataset comprised 534 unique images from the Pascal VOC dataset 

Baselines

To evaluate our methodology, we compare our method to the following baselines: (1) no-comm, where agents do not communicate; (2) rl-comm, which uses a baseline communication method learned solely through policy loss ; (3) ae-comm, which uses an autoencoder to ground communication in input observations ; (4) VQ-VIB, which uses a variational autoencoder to ground discrete communication in input observations and a mutual information objective to ensure low entropy communication  
We provide an ablation of the loss parameter β in table 1 in the blind traffic junction scenario  When β = 0, we use our compositional message paradigm without our derived loss terms  We find that higher complexity and independence losses increase sample complexity  When β = 1, the model was unable to converge 
However, when there is no regularization loss, the model performs worse (with no guarantees about referential representation)  We attribute this to the fact that our independence criteria learns a stronger causal relationship  There are fewer spurious features that may cause an agent to take an incorrect action 
In order to understand the effect of the independent concept representation, we analyze the emergent language's capacity for redundancy  A message token m l is redundant if there exists another token m k that represents the same information  With our methodology, the emergent 'language' converges to the exact number of observations and intents required to solve the task 
With a soft discrete threshold, the independent information loss naturally converges to a discrete number of tokens in the vocabulary  Our β ablation in table 1 yields a bijection between each token in the vocabulary and the possible emergent concepts, i e , the enumerated observations and intents  Thus for β = 0 1, there is no redundancy 
Sparse Communication In corollary 4 3, we assume that there is no mutual information between tokens  In practice, the loss may only be near-zero  Our empirical results yield independence loss around 1e − 4  In table 1, the size of the messages is automatically compressed to the smallest size to represent the information 
Despite a trivially small amount of mutual information between tokens, our compositional method is able to reduce the message size in bits by 2 3x using our derived regularization, for a total of an 8x reduction in message size over non-compositional methods such as ae-comm  Since the base unit for the token is a 32-bit float, we note that each token in the message may be further compressed 
We observe that each token uses three significant digits, which may further compress tokens to 10 bits each for a total message length of 20 bits 

Communication Utility Results

Due to coordination in MARL, grounding communication in referential features is not enough  Finding the communication utility requires grounding messages in ordinal information  Overall, figure shows that our compositional, contrastive method outperforms all methods focused on solely input-oriented communication grounding 
In the blind traffic junction, our method yields a higher average task success rate and is able to achieve it with a lower sample complexity  Training with the contrastive update tends to spike to high success but not converge, often many episodes before convergence, which leaves area for training improvement 
That is, the contrastive update begins to find aligned latent spaces early in training, but it cannot adapt the methodology quickly enough to converge  The exploratory randomness of most of the early online data prevents exploitation of the high utility f + examples  This leaves further room for improvement for an adaptive contrastive loss term 
Regularization loss convergence After convergence to high task performance, the autoencoder loss increases in order to represent the coordination information  This follows directly from the information bottleneck, where there exists a tradeoff between utility and complexity  However, communication, especially referential communication, should have an overlap between utility and complexity 
Thus, we should seek to make the complexity loss more convex  Our compositional communication complexity loss does not converge before task performance convergence  While the complexity loss tends to spike in the exploratory phase, the normalized value is very small  Interestingly, the method eventually converges as the complexity loss converges below a normal- ized 0 3 
Additionally, the contrastive loss tends to decrease monotonically and converges after the task performance converges, showing a very smooth decrease  The contrastive f − loss decreases during training, which may account for success spikes prior to convergence  The method is able to converge after only a moderate decrease in the f + loss 
This implies empirical evidence that the contrastive loss is an optimal critic for messaging  See figure 3 

Heterogeneous Alignment Through Communication

In order to test the heterogeneous alignment ability of our methodology to learn higher-order concepts from highdimensional data, we analyze the performance on the Pascal VOC game  We compare our methodology against ae-comm to show that concepts should consist of independent information directly from task signal rather than compression to reconstruct inputs 
That is, we show an empirical result on pixel data to verify the premise of the information bottleneck  Our methodology significantly outperforms the observation-grounded ae-comm baseline, as demonstrated by figure 4  The ae-comm methodology, despite using autoencoders to learn observation-grounded communication, performs only slightly better than no-comm 
On the other hand, our methodology is able to outperform both baselines significantly  It is important to note that based on figure 4, our methodology is able to guess more than two of the four labels correctly across the two agents involved, while the baseline methodologies struggle to guess exactly two of thew four labels consistently 
This can be attributed to our framework being able to learn compositional concepts that are much more easily discriminated due to mutual independence 

Social Shadowing

Critics of emergent communication may point to the increased sample complexity due to the dual communication and action policy learning  In the social shadowing scenario, heterogeneous agents can learn to generate a communication policy without learning the action policy of the watched expert agents  To enable social shadowing, the agent will alternate between a batch of traditional MARL (no expert) and (1st-person) shadowing an expert agent performing the task in its trajectory 
The agent only uses the contrastive objective to update its communication policy during shadowing  In figure , the agent that performs social shadowing is able to learn the action policy with almost half the sample complexity required by the online reinforcement learning agent  Our results show that the structured latent space of the emergent communication learns socially benevolent coordination 
This tests our hypothesis that by learning communication to understand the actions of other agents, one can enable lower sample complexity coordination  Thus, it mitigates the issues of solely observing actions 

Discussion

By using our framework to better understand the intent of others, agents can learn to communicate to align policies and coordinate  Any referential-based setup can be performed with a supervised loss, as indicated by the instant satisfaction of referential objectives  Even in the Pascal VOC game, which appears to be a purely referential objective, our results show that intelligent compression is not the only objective of referential communication 
The emergent communication paradigm must enable an easy-to-discriminate space for the game  In multi-agent settings, the harder challenge is to enable coordination through communication  Using contrastive communication as an optimal critic aims to satisfy this, and has shown solid improvements  Since contrastive learning benefits from good examples, this method is even more powerful when there is access to examples from expert agents 
In this setting, the communication may be bootstrapped, since our optimal critic has examples with strong signals from the 'social shadowing' episodes  Additionally, we show that the minimization of our independence objective enables tokens that contain minimal overlapping information with other tokens 
Preventing trivial communication paradigms enables higher performance  Each of these objectives is complementary, so they are not trivially minimized during training, which is a substantial advantage over comparative baselines  Unlike prior work, this enables the benefits of training with reinforcement learning in multi-agent settings 
In addition to lower sample complexity, the mutual information regularization yields additional benefits, such as small messages, which enables the compression aspect of sparse communication  From a qualitative point of view, the independent information also yields discrete emergent concepts, which can be further made human-interpretable by a post-hoc analysis  
This is a step towards white-box machine learning in multi-agent settings  The interpretability of this learned white-box method could be useful in human-agent teaming as indicated by prior work   The work here will enable further results in decision-making from high-dimensional data with emergent concepts 
The social scenarios described are a step towards enabling a zero-shot communication policy  This work will serve as future inspiration for using emergent communication to enable ad-hoc teaming with both agents and humans 

Appendix

A 1  Proofs Proposition 4 1 For the interaction information between all tokens, the following upper bound holds: Proof  Starting with the independent information objective, we want to minimize the interaction information, which defines the conditional mutual information between each token and, Let π i m (m l |h) be a variational approximation of p(m l |h), which is defined by our message encoder network 
Given that each token should provide unique information, we assume independence between m l   Thus, it follows that our compositional message is a vector, m = [m 1 ,       , m L ], and is jointly Gaussian  Moreover, we can define q( m|h) as a variational approximation to p(m|h) = p(m 1 ;       , m L |h) 
We can model q with a network layer and define its loss as || m − m|| 2   Thus, transforming equation 4 into variational form, we have, it follows that q( m|h) log q( m|h)d m ≥ q( m|h) log Thus, we can bound our interaction information, Proposition 4 2 For the mutual information between the composed message and encoded information, the following upper bound holds:
Proof  By definition of mutual information between the composed messages M and the encoded observations H, we have, Substituting q( m|h) for p( m|h), the same KL Divergence identity, and defining a Gaussian approximation z( m) of the marginal distribution p( m), it follows that, In expectation of equation 1, we have,
This implies that, for m = [m 1 ,       , m L ], there is probabilistic independence between m j , m k , j = k  Thus, expanding, it follows that, where z(m l ) is a standard Gaussian  Proposition 5 1  Utility mutual information is lower bounded by the contrastive NCE-binary objective, Proof  We suppress the reliance on h since this is directly passed through 
By definition of mutual information, we have, Our network model learns π R + (y|m) from rolled-out trajectories, R + , using our policy  The prior of our network state, π R − (y), can be modeled from rolling out a random trajectory, R−  Unfortunately, it is intractable to model π R + (y|m) and π R − (y) directly during iterative learning, but we can sample y + ∼ π R + (y|m) and y − ∼ π R − (y) directly from our network during training 
It has been shown that log p(y|m) provides a bound on mutual information , with the expectation over l p(m l , y l )  However, we need a tractable understanding of the information Y   In the information bottleneck, Y represents the desired outcome  In our setup, y is coordination information that helps create the desired output, such as any action a −  
This implies, y =⇒ a −   Since the transition is known, it follows that a − =⇒ s − f , a random future state  Thus, we have, π This is similar to the proof for lemma A 5, but requires assumptions on messages m from the emergent language  We note that when m is random, the case defaults to lemma A 5  Thus, we assume we have at least input-oriented information in m given sufficiently satisfying equation 2  Given a sufficient emergent language, it follows that y =⇒ a + , where a + is an intention action based on m 
Similarly, since the transition is known, a + =⇒ s + f , a desired goal state along the trajectory  Thus, we have, π R + (y|m) = p(s = s + f |y, m)  Recall the following (as shown in ), which we have adapted to our communication objective, Proposition A 3 (rewards → probabilities)  The Q-function for the goal-conditioned reward function r g (s t , m t ) = (1 − γ)p(s = s g |y t ) is equivalent to the probability of state s g under the discounted state occupancy measure:
and Lemma A 4  The critic function that optimizes equation 8 is a Q-function for the goal-conditioned reward function up to a multiplicative constant 1 The critic function f (s, m, s f ) = y enc(s f ) represents the similarity between the encoding y = enc(s, m) and the encoding of the future rollout s f  
Given lemmas A 5 A 6 A 8 and proposition A 7, it follows that equation 8 is the NCE-binary (InfoMAX ) objective, Î(M j , Y i ) = log σ(f (s, m, s + f )) + log 1 − σ(f (s, m, s − f )) which lower bounds the mutual information, I(M j , Y i ) ≥ Î(M j , Y i )  The critic function is unbounded, so we constrain it to [0, 1] with the sigmoid function, σ( * ) 
We suppress the reliance on h since this is directly passed through  By definition of mutual information, we have, Our network model learns π R + (y|m) from rolled-out trajectories, R + , using our policy  The prior of our network state, π R − (y), can be modeled from rolling out a random trajectory, R− 
Unfortunately, it is intractable to model π R + (y|m) and π R − (y) directly during iterative learning, but we can sample y + ∼ π R + (y|m) and y − ∼ π R − (y) directly from our network during training  It has been shown that log p(y|m) provides a bound on mutual information , with the expectation over l p(m l , y l ) 
However, we need a tractable understanding of the information Y   Lemma A 5  π R − (y) = p(s = s − f |y)  In the information bottleneck, Y represents the desired outcome  In our setup, y is coordination information that helps create the desired output, such as any action a −   This implies, y =⇒ a −   Since the transition is known, it follows that a − =⇒ s − f , a random future state 
Thus, we have, π R − (y) = p(s = s − f |y)  Lemma A 6  π R + (y|m) = p(s = s + f |y, m)  This is similar to the proof for lemma A 5, but requires assumptions on messages m from the emergent language  We note that when m is random, the case defaults to lemma A 5  Thus, we assume we have at least input-oriented information in m given sufficiently satisfying equation 2  Given a sufficient emergent language, it follows that y =⇒ a + , where a + is an intention action based on m 
Similarly, since the transition is known, a + =⇒ s + f , a desired goal state along the trajectory  Thus, we have, π R + (y|m) = p(s = s + f |y, m)  Recall the following (as shown in ), which we have adapted to our communication objective, Proposition A 7 (rewards → probabilities)  The Q-function for the goal-conditioned reward function r g (s t , m t ) = (1 − γ)p(s = s g |y t ) is equivalent to the probability of state s g under the discounted state occupancy measure:
and Lemma A 8  The critic function that optimizes equation 8 is a Q-function for the goal-conditioned reward function up to a multiplicative constant 1 p(s f ) : exp(f * (s, m, s f ) = 1 p(s f ) Q π s f (s, m)  The critic function f (s, m, s f ) = y enc(s f ) represents the similarity between the encoding y = enc(s, m) and the encoding of the future rollout s f  
Given lemmas A 5 A 6 A 8 and proposition A 7, it follows that equation 8 is the NCE-binary (InfoMAX ) objective, which lower bounds the mutual information, I(M j , Y i ) ≥ Î(M j , Y i )  The critic function is unbounded, so we constrain it to [0, 1] with the sigmoid function, σ( * ) 



ground_truth: An alphabetical list of names and places of abode of the merchants and principal traders of the cities of London and Westminster, the Borough of Southwark, and their environs, with the number affixed to each house.