text:
\section{Introduction}
In the study of real complex network systems, information about the system components is often incomplete, unreliable, or unknown.
Recently proposed methods to infer the likelihood of links in a network take advantage of node similarities or network structures \cite{2008_Clauset, 2009_Guilerma, 2010_Lu, 2013_Ravasz,Yu_2018,2019_Pech}.
Combined with statistical inference, such methods have demonstrated remarkable success in a variety of real-world networks with heterogeneous errors \cite{2018_Peixoto}.
Other approaches include observing links present in reconstructed networks after perturbations  \cite{2015_Lu},  applying the inverse problem to generative models for networks with predicted hyperbolic structures \cite{2012_Papadopoulos}, and inferring missing nodes from community detection algorithms \cite{2016_Hric}.
Statistical measures of correlation and causation have also been used to infer links from observations \cite{2012_Wu,2015_Liao,lunsmann2017transition,casadiego2017model}.

In addition to the topology of their connections, links and nodes often carry parameters that encode their properties.  In models of physical networks, such parameters must be determined through measurements of observables, which may be costly and limited.  In some cases, while the topology of the network is known in principle, parameters such as link weights can only be estimated for a relatively small proportion of the network.  Nevertheless, if the network is derived from a knowledge-based model (i.e., it is believed to include all relevant details and is physically well motivated), it is usually assumed that individual parameters can be measured accurately through targeted experiments.

The key problem in such cases is not to determine which nodes and links are present, but rather,  which of them are most important to include in the model.  ``Weak'' nodes and links may be systematically neglected to reduce the number of parameters and derive minimal models, but it is unclear how these missing elements may affect the estimated parameters, and hence the predicted dynamics, of the parts of the network that are retained. That is, it remains largely unknown what impact missing and deliberately omitted structural information may have  on the relevant dynamical processes predicted or described by a network model.

\begin{figure}[b]
\includegraphics[width=\columnwidth]{fig1}
\caption{Impact of missing information in a simple electric network. (a)~Network of four resistors, where $V_1=1$V is fixed and $V_{\mathrm{adj}}$ differs in different experiments. The resistance of the blue resistor ($R_1=1\Omega$) is unknown to the experimenter and is determined through measurements of the currents $I_{1,2}$ while the red resistor ($R_2=10\Omega$) is missing in the model.  (b)~Estimate of resistor value vs adjustable voltage, as given by the least squares fit. The blue dashed line shows the actual value, and the black dotted line shows where the currents become insensitive to the estimate.
\label{fig1}}
\end{figure}

Here, in contrast to previous studies focused on solely network structure, we explore the impact of network incompleteness on the  parameters governing the system dynamics. To motivate this work, consider the simple electric network of resistors shown in Fig.~\ref{fig1}(a). Suppose an experimenter attempts to fit an incomplete model of the system (in which the red resistor is absent) to current measurements in order to determine the resistance $R_1$ of the blue resistor. Since the missing resistor is relatively large, little current passes through it.  From the network perspective, the links in the network should be given a weight proportional to their admittance (inverse resistance) and, intuitively, a model that neglects small weighted links would still be expected to be good at predicting the dynamics.  The absence of the red resistor results in a systematic error due to the modeling approximation, and we assume for simplicity that the measurements are perfect and no additional errors are present.

The currents drawn from the voltage sources are measured, and the resistance $R_1$ in the model is adjusted until the model's predicted currents minimize the deviations from the measured currents, resulting in a least squares estimate (see Appendix \ref{acircuit} for details). Figure \ref{fig1}(b) shows how this estimated resistance $R_{\mathrm{est}}$ depends on the voltage value $V_{\mathrm{adj}}$ that the experiment is conducted under. Crucially, two experimenters who operate with different values of $V_{\mathrm{adj}}$ can obtain substantially different estimates for $R_{\mathrm{est}}$ and may falsely conclude that the resistance changes with the experimental conditions. The apparent variability of a constant in this example is actually quite easy to understand. Essentially no current passes through the blue resistor when $V_{\mathrm{adj}}\approx V_1$, so the measured currents are not sensitive to changes in the value of $R_1$ (as quantified by local sensitivity in Appendix \ref{acircuit}). Thus, the error introduced by the incomplete  model is amplified around the dotted line in Fig.~\ref{fig1}(b), and therefore the measure of link importance based on the admittance (link weight) does not adequately reflect the impact of link removal on parameter estimation.

While the errors induced by the estimation procedure in Fig.~\ref{fig1} are easy to understand in terms of local sensitivities, subtler challenges arise in more complex networks, especially when the network dynamics are nonstationary. In the remainder of the paper, we show that for complex chemical reaction networks in particular, missing information about the underlying network can lead to significant variations in rate constants estimated under different conditions even when the local sensitivities for the neglected links are small compared to those for the links being measured.
Given that network models of chemical reactions will necessarily be incomplete (since additional short-lived radical species and rare reactions could always be added to a given model), this variability poses a serious challenge to the efforts to reliably determine rate constant through experiments.

To illustrate this challenge, we focus on important chemical reaction networks involved in natural gas combustion in Section \ref{combustion} and ethylene pyrolysis in Section \ref{pyrolysis}, which have been carefully developed for decades, primarily through experiments employing shock tubes and laminar flame speed measurements \cite{2003_Simme,2004_Li_Frederick,2004_Conaire_Charles,2005_Baulch,2012_Ranzi}. We compare the results for these processes in Section \ref{comparison}, and find in particular that local sensitivity analysis, which is a commonly used methods for determining reaction importance \cite{1980_Dougherty_Herschel,1990_Turanyi,2013_Tomlin}, correlates weakly with the reactions impact on rate constant measurements in all cases.  We conclude in Section \ref{discussion} with a discussion of implications and directions for future research.

\begin{figure*}
\includegraphics[width=2\columnwidth]{fig2}
\caption{{Natural gas ignition in simulations. (a) Mole fractions vs time, with water, methane, and oxygen shown in green, blue, and orange, respectively, and all other species shown in gray. (b) Temperature (red line) and pressure (blue line) vs time, where the sharp rises at $1.5\si{ms}$ corresponds to ignition.(c) Network of chemical species in the natural gas network, where colored nodes show species, black nodes show prominent reactions, and links show reaction flux, with the weight showing the time-integrated reaction rate and the node size showing the time-integrated concentration, both on a logarithmic scale. The node and link color indicate the time that the species and reactions are most prominent, as measured by the time of the maximum reaction flux and the time at which the integrated species  concentration reaches half its ultimate value.  Nodes with identical chemical formulae are isomers, and species with no links weighted above a threshold ($\ce{C3H8}$, $\ce{CH3CHO}$, $\ce{C3H7}$, $\ce{HCCOH}$, $\ce{HCNN}$, $\ce{H2CN}$, $\ce{AR}$, $\ce{HCNO}$, $\ce{HOCN}$, $\ce{HCN}$, $\ce{CN}$, $\ce{HNCO}$, $\ce{NCO}$, $\ce{NH3}$, $\ce{NH2}$, $\ce{NH}$, $\ce{N2O}$, $\ce{N}$, $\ce{HNO}$, $\ce{NO2}$, $\ce{NNH}$, $\ce{NO}$) are shown together in the node labeled ``Others'' with their mean size (and color).  An animation of the temporal evolution of this network is available in the Supplemental Material \cite{SM}.  \label{fig2} }}
\end{figure*}
\section{Natural gas combustion}
\label{combustion}
We first consider the impact of unknown network reactions in the case of natural gas combustion.
We model the chemical process with a coupled set of kinetic equations, which corresponds to a network of chemical species, elementary reactions, and physical parameters, including the rate constants that relate species concentrations to the rate of reactions (see Appendix~\ref{akinetic}).
To emulate the effects of missing information in models of real processes, we take a specific network (which we regard as the complete network) as our ``ground truth'' from which measurement values (regarded to be exact) are generated using simulations.
We employ the GRI 3.0 network \cite{1999_Smith} as our ``complete'' natural gas network, which is then simulated using the open source software Cantera to integrate a continuously stirred reactor with an accurate time stepping method for stiff ordinary differential equations \cite{cantera,SM2}.
The GRI 3.0 network is a specification of $53$ chemical species and $325$ elementary reactions and rate constants, which have been curated  carefully from the body of experiments in the literature. Despite extensive curation, this network is not reliable for general purposes across different conditions when the parameters are fixed, which our analysis will suggest to be due to incompleteness of the network model itself. But for the purpose of this analysis, we regard this network as complete and evaluate our hypothesis by  quantifying the impact of further removing information from the network. Specifically, starting with this network, we  produce plausible models for the process by removing some reactions from the complete network and use the resulting ``incomplete'' networks to determine parameter values from measurements.

Figure \ref{fig2}(a) shows the evolution of the chemical compositions in a mixture of natural gas and oxygen.  The  reactants combine explosively as the reaction proceeds and ultimate produce water and a variety of other products. During this process, the temperature and pressure of the gas increase sharply as the fuel ignites, as shown in Fig.~\ref{fig2}(b).  This ignition is the result of a chain reaction process taking part in the complex network of species which are connected by elementary reactions.  The network structure of this process can be represented as a hypergraph, where nodes are chemical species and directed hyperedges are reactions, with weights proportional to the reaction flux.  This hypergraph can be visualized by its bipartite incidence graph, where the hyperedges are replaced with reaction nodes, as shown in Fig.~\ref{fig2}(c).

A traditionally employed measure of reaction importance in chemical reaction networks is the local sensitivity, which quantifies changes in  the concentration with changes in the rate constant (see Appendix \ref{akinetic}).
To assess the reliability of this metric, we generate new incomplete networks from the complete network by randomly removing reactions that are deemed unimportant while retaining reactions presumed to be important, where reaction importance is assessed on the basis of local sensitivities. Rate constants in these incomplete networks are then fit to simulated measurements from the complete network to assess the impact of network incompleteness on parameter estimation.

For our measurement simulations, we consider two reactions whose rate constants are to be determined,
\begin{align}
\ce{H + O_2 <=> O + OH},  \label{eqn1} \tag{I} \\
\ce{CH_4 + H <=> CH_3 + H_2},  \label{eqn2} \tag{II}
\end{align}
taking all other rate constants at the fixed values given in the natural gas network.  Equation \eqref{eqn1} is a chain branching reaction, which helps to populate the radical pool that leads to ignition.  Equation \eqref{eqn2} is a propagation reaction, which helps to diversify this pool of radicals.

We perform a numerical optimization to minimize an error $\epsilon$ in order to fit the incomplete network to the measurements. The error we use quantifies the discrepancy in the peak oxygen radical concentration and ignition time, as described in Appendix~\ref{acombustion}.
This particular quantity is employed in order to emulate the data available in real experiments, such as shock tube experiments based on oxygen radical concentration peaks \cite{2005_Baulch}.
Furthermore, the reactions in Eqs.~\eqref{eqn1} and \eqref{eqn2} are known to be important for combustion modeling, and their local sensitivities $S_{\ce{O} \mathrm{I}}$ and $S_{\ce{O} \mathrm{II}}$ are among the largest of all the reactions in the network during the ignition events, as shown in Fig.~\ref{fig3}(a).
\begin{figure}[b]
\includegraphics[width=\columnwidth]{fig3}
\caption{{Simulated rate constant measurement for Eqs.~\eqref{eqn1} and \eqref{eqn2}. (a)  Local sensitivity $S_{\ce{O} \ell}$ vs time during ignition for Eq.~\eqref{eqn1} (green line), Eq.~\eqref{eqn2} (red line), and the other eight most sensitive reactions (dashed lines).  (b) Oxygen radical mole fraction $X_{\ce{O}}$ vs time during the ignition event corresponding to Experiment $14$ (see Table \ref{conditions} in Appendix \ref{acombustion}) for the complete network and a fitted incomplete network with $N_{\mathrm{ret}}=N_{\mathrm{rem}}=40$. The value of the rate constant for the fitted network provides an estimate for the rate constants $k_{\mathrm{est}}$.  \label{fig3} }}
\end{figure}

\begin{figure}[t]
\includegraphics[width=\columnwidth]{fig4}
\caption{{Average values of $\left \lvert \log_{10} \left({k_{\mathrm{est}}}/{k_0} \right) \right \rvert$ (top row), $S_{\mathrm{r}}/S_{\mathrm{m}}$ (center row), and $\log_{10} \left(\epsilon \right)$ (bottom row) as a function of $N_{\mathrm{rem}}$ and $N_{\mathrm{ret}}$ for Eq.~\eqref{eqn1} (left column) and Eq.~\eqref{eqn2} (right column). The averages follow similar trends, with magnitudes increasing for increasing $N_{\mathrm{rem}}$ and decreasing $N_{\mathrm{ret}}$. \label{fig4} }}
\end{figure}

Incomplete networks are generated randomly by removing reactions with small oxygen sensitivity from the network. In order to quantify how the sensitivity of the removed reactions impacts the variability of the rate constant estimate, we retain from the $N_{\mathrm{tot}}$ total reactions a tunable number of reactions, $N_{\mathrm{ret}}$, with the largest $\ce{O}$-sensitivities, which are not candidates for removal in the generation of the incomplete networks.  Incomplete networks are then generated by randomly selecting a tunable number of reactions $N_{\mathrm{rem}}$ from the remaining $N_{\mathrm{tot}}-N_{\mathrm{ret}}$ reactions and removing them from the network.  For each value of $N_{\mathrm{ret}}$ and $N_{\mathrm{rem}}$, multiple incomplete networks are generated with differing random seeds, which allows us to statistically study the effects of missing information.
Rate constant estimates are obtained from fits minimizing $\epsilon$. The fit of one sample realization is shown in Fig.~\ref{fig3}(b), but the quality of this fit varies significantly with each randomly realized incomplete network for fixed $N_{\mathrm{rem}}$ and $N_{\mathrm{ret}}$.

Under any particular thermodynamic condition, minimizing the error results in a rate constant estimate $k_{\mathrm{est}}$ for Eq.~\eqref{eqn1} or Eq.~\eqref{eqn2}, but these estimates will vary with the thermodynamic conditions. For example, for one incomplete network generated with $N_{\mathrm{ret}}=40$ and $N_{\mathrm{rem}}=40$, the estimate for Eq.~\eqref{eqn1} varied considerably among the $27$ thermodynamic conditions described in Appendix \ref{acombustion}, with values ranging from $0.06$ to $4.71$ times as large as the actual rate constant $k_0$.
Each estimate made in this fashion uses only a single observational data point, and so we may hope to eliminate the variation in the estimate by combining many observations in a single fit to produce an estimate.

To test if measurements of multiple data points will improve the estimate, we performed $1000$ rate constant estimates for Eqs.~\eqref{eqn1} and \eqref{eqn2} for incomplete networks generated with $N_{\mathrm{rem}}$ and $ N_{\mathrm{ret}}$ varying from $10$ to $160$ by increments of $15$ (in total, $2.42\times10^5$ estimates), where each estimate was obtained by minimizing the aggregated error over all $27$ thermodynamic conditions. Figure \ref{fig4} shows how the average results from these simulations vary with $N_{\mathrm{rem}}$ and $N_{\mathrm{ret}}$. For each estimate, we consider the ratio of the sensitivities of the removed and measured reactions, $S_{\mathrm{r}}/S_{\mathrm{m}}$, the magnitude of logarithmic deviation of the rate constant estimate (representing the orders-of-magnitude difference between the rate constant estimate and the actual rate constant), $\left \lvert \log_{10} \left({k_{\mathrm{est}}}/{k_0} \right) \right \rvert$, and the logarithm of the error, $\log_{10} \left(\epsilon \right)$.
It is clear from these results that after increasing the amount of observational data in the rate constant estimates, there can still be significant variation in the estimates even when relatively few of the least sensitive reactions are missing from the network and the fit appears adequate.
\begin{figure}[t]
\includegraphics[width=\columnwidth]{fig5}
\caption{Rate constant estimate with argon dilution vs rate constant estimate without argon dilution for (a) Eq.~\eqref{eqn1} and (b) Eq.~\eqref{eqn2}.  The same incomplete network is used in each pair of measurements, and the color code indicates the ratio of the sensitivities between the removed reactions and the measured reaction. \label{fig5}}
\end{figure}
\begin{figure*}
\includegraphics[width=2\columnwidth]{fig6}
\caption{Counterpart of Fig.~\ref{fig2} for ethylene pyrolysis. The ethylene fuel breaks down in the absence of oxygen in a slower and more temporally distributed process than in the case of combustion, where oxygen is present.
\label{fig6}}
\end{figure*}

Having incorporated multiple thermodynamic conditions in each estimate, it is interesting to study how the estimates change under yet different conditions.
We performed a second set of rate constant measurements using the same set of incomplete networks described above under slightly different experimental conditions by diluting the gas with about ten percent argon.  Argon, a neutral buffer which does not react chemically, is sometimes used in shock-tube experiments to adjust conditions, such as pressure, under the assumption that its presence will not alter the results.  However, besides deviating again from the true rate constants, the same incomplete networks also exhibit substantial differences between rate constant measurements performed in air with and without argon dilution, as shown in Fig.~\ref{fig5}. Among all the paired measurements, the Pearson correlation coefficient between rate constant estimates with no argon and with argon dilution was $0.93$ for Eq.~\eqref{eqn1} and $0.78$ for Eq.~\eqref{eqn2}, while the fraction of variance unexplained by a linear regression between the two conditions was, respectively,  $14\%$ and $39\%$.  Furthermore, while networks with small removal sensitivities tend to produce rate constant estimates closer to the real value, the scatter in Fig.~\ref{fig5} is not substantially smaller when the estimates are good or when the removal sensitivity is small. Thus, network incompleteness can clearly result in variable rate constant estimates under differing conditions even when the reactions being measured have large sensitivities compared to the neglected reactions and the change in conditions is seemingly innocuous.

\section{Ethylene pyrolysis}
\label{pyrolysis}
\begin{figure}[b]
\begin{center}
\includegraphics[width=\columnwidth]{fig7}
\caption{{Counterpart of Fig.~\ref{fig3} for pyrolysis reactions in Eqs.~\eqref{eqn3}-\eqref{eqn4}, with $N_{\mathrm{rem}}=N_{\mathrm{ret}}=200$. Incomplete network models are fitted to the observed yields of $X^{\mathrm{o}}_{\ce{H2}}$ and $X^{\mathrm{o}}_{\ce{CH4}}$ to simulate measurements of the rate constants. \label{fig7}}}
\end{center}
\end{figure}
\begin{figure}[b]
\includegraphics[width=\columnwidth]{fig8}
\caption{{Counterpart of Fig.~\ref{fig4} for ethylene pyrolysis. The rate constant estimate $k_{\mathrm{est}}$, removal sensitivity $S_r$, and error $\epsilon$ follow the same general trends as for natural gas combustion, but estimates are generally better for Eq.~\eqref{eqn3} and worse for Eq.~\eqref{eqn4}. \label{fig8}}}
\end{figure}
To illustrate that these results generalize beyond combustion, we next consider a different complex reaction network describing ethylene pyrolysis. Pyrolysis is a common industrial chemical process involving the burning of organic compounds in the absence of oxygen.  In this process, larger organic molecules like $\ce{C2H4}$ (ethylene) break down into smaller molecules such as $\ce{H2}$ and $\ce{CH4}$.  We employ a recent model of light hydrocarbon pyrolysis consisting of $84$ species and $1698$ reactions as our complete pyrolysis network \cite{2012_Ranzi}. Figure \ref{fig6} shows the evolution of the process and network structure in the pyrolysis case, as in Fig.~\ref{fig2}.

\begin{figure*}
\includegraphics[width=2\columnwidth]{fig9}
\caption{Distributions of rate constant estimates for Eqs.~\eqref{eqn1}-\eqref{eqn4}. (a-d) Histograms of the rate constant estimates for Eqs.~\eqref{eqn1}-\eqref{eqn4}, with the red-green color blend indicating the proportion of removed and retained reactions for each set of histograms. (e-f) Relative sensitivity of the removed reactions vs rate constant estimates for Eqs.~\eqref{eqn1}-\eqref{eqn4}, with all data divided into $25$ evenly-occupied bins in each axis and with error bars showing the $90\%$ quantiles for each bin.  \label{fig9}}
\end{figure*}

For ethylene pyrolysis, we consider rate constant measurements based on net yields of $\ce{H2}$ and $\ce{CH4}$ rather than the peak $\ce{O}$ concentration and ignition time used previously.
We allow the reaction to evolve until the $\ce{H2}$ concentration reaches its steady state with $27$ different thermodynamic conditions relevant to low pressure chemical vapor deposition.  We consider two reactions,
\begin{align}
\ce{H + C2H4 -> H2 + C2H3},  \label{eqn3} \tag{III} \\
\ce{C2H5 + C2H4 -> C2H6 + C2H3},  \label{eqn4} \tag{IV}
\end{align}
each of which has large sensitivity with respect to the $\ce{H2}$ and $\ce{CH4}$ net yields.  The  error $\epsilon$ was minimized as before to obtain the rate constant estimates.
Appendix~\ref{apyrolysis} describes details for these pyrolysis simulations. Figures \ref{fig7}-\ref{fig8} show counterparts to Fig.~\ref{fig3}-\ref{fig4} in the case of pyrolysis. It is clear from these results that, as was the case for methane combustion, rate constant estimates may vary considerably for ethylene pyrolysis when relatively few reactions are missing even if the missing reactions have small sensitivities and the fit errors are small.

\section{Combustion/Pyrolysis Comparisons}
\label{comparison}
\begin{table}[b]
\begin{tabular}{l  c  r  r  r  r}
$x$ & $y$ & ~\eqref{eqn1}~ & ~\eqref{eqn2}~ & ~\eqref{eqn3}~ & ~\eqref{eqn4}~ \\
\hline \phantom{.} & \phantom{.} & \phantom{.} & \phantom{.} &\phantom{.} &  \phantom{.} \\[0.05em]
${S_{\mathrm{r}}}/{S_{\mathrm{m}}}$ & $\log_{10}\left( \epsilon \right)$ & $0.48$ & $0.49$ & $0.59$ & $0.47$ \\
${S_{\mathrm{r}}}/{S_{\mathrm{m}}}$ & $\left \lvert \log_{10} \left({k_{\mathrm{est}}}/{k_0}\right) \right\rvert$  & $0.43$ & $0.46$ & $0.47$ & $0.45$ \\
$\left \lvert \log_{10} \left({k_{\mathrm{est}}}/{k_0}\right) \right\rvert$ & $\log_{10}\left( \epsilon \right)$  & $0.30$ & $0.38$ & $0.32$ & $0.64$ \\
\end{tabular}
\caption{Pearson correlation coefficients between quantities $x$ and $y$ for the distribution of simulated rate constant measurements in the combustion reactions in Eqs.~\eqref{eqn1} and \eqref{eqn2} and the pyrolysis reactions in Eqs.~\eqref{eqn3} and \eqref{eqn4}. \label{table2}}
\end{table}
\begin{figure}[b]
\includegraphics[width=\columnwidth]{fig10}
\caption{{Acceptable and unacceptable regions of network completeness for (a) the combustion network and (b) the pyrolysis network. The rate constant estimates are deemed acceptable only if more than $95\%$ of incomplete network fits result in rate constant estimates which differ from the actual rate constant by less than a factor of two.
Thin lines show how the boundary varies as the acceptable threshold is reduced to $90\%$,  $85\%$,  $75\%$, and $70\%$. }\label{fig10}}
\end{figure}
The distributions of rate constant estimates for the combustion and pyrolysis networks are broadly similar, as summarized by the histograms in Fig.~\ref{fig9}(a)-(d). The rate constant estimates typically deviate much more than the error or the removal sensitivities in all cases, despite the differing measurement targets and reaction networks. Table \ref{table2} shows the correlation coefficients between measurement quantities for each reaction in each process; there are moderate to weak correlations between all quantities.  Thus, in both these processes, the local sensitivity metric correlates weakly with the rate constant estimates and is not a very reliable measure of link importance. Even when the removed reactions have local sensitivity totaling to much less than the sensitivity of the measured links, the rate constant estimates can vary considerably, as shown in Fig.~\ref{fig9}(e)-(f).  In the networks we generated, for example, the smallest values of $S_r/S_m$ leading to order-of-magnitude changes with $|\log_{10} (k_{\mathrm{est}}/k_0)| > 1$ are just $0.005$ for Eq.~\eqref{eqn1}, $0.0046$ for Eq.~\eqref{eqn2}, $0.019$ for Eq.~\eqref{eqn3}, and $0.0024$ for Eq.~\eqref{eqn4}.  While computational costs prohibit us from testing all reactions in these networks, less systematic simulations suggest that other reactions typically exhibit even greater variations in rate constant estimates, as expected given that the reactions \eqref{eqn1}-\eqref{eqn4} are among the most sensitive ones in the networks.

To compare the two processes in more detail, we consider the effect of varying the number of removed and retained reactions in the simulated measurements. We divide the plane spanned by $N_{\mathrm{ret}}$ and $N_{\mathrm{rem}}$ into an acceptable region (in which more than $95\%$ of the rate constant estimates from fits of incomplete networks deviate from the actual value by less than a factor of two) and an unacceptable region (in which this is not the case).  Figure \ref{fig10} compares the acceptable regions in the combustion and pyrolysis cases by normalizing the axes by $N_{\mathrm{tot}}$, the total number of reactions in each network.
In order to achieve acceptable measurements  with just $10\%$ of reactions missing for all cases, the retained reactions must amount to more than $15\%$ of the network.  While somewhat smaller $N_{\mathrm{ret}}/N_{\mathrm{tot}}$ is adequate for acceptable measurements for Eqs.~\eqref{eqn1}-\eqref{eqn3} in this case, the proportion of retained reactions required for acceptable measurements rises to about $15\%$ in all cases when $50\%$ of the reactions are missing.

Interestingly, the natural gas network shows a stronger dependence on the proportion of removed reactions than the pyrolysis network, indicating that the pyrolysis network has a greater proportion of reactions that are unimportant to the dynamics of the measurement. This may result from the more complex chain reaction involved in ignition compared to the slower and more temporally distributed pyrolysis process.

\section{Discussion}
\label{discussion}
Our results show that observed variations in rate constants of combustion and pyrolysis networks can be largely attributed to the use of incomplete network models that are missing reactions that were presumed to be negligible. We demonstrated that even when the neglected reactions have small cumulative sensitivity compared to the sensitivity of the measured reaction, rate constant estimates in incomplete networks can vary by one order of magnitude. Furthermore, rate constant estimate deviations and local sensitivity analysis showed weak statistical correlations. While these results highlight significant challenges in constructing a reliable and transferable kinetic model for these important chemical processes, they also reveal that current observations of variability in rate constant estimates are not necessarily an indication that a complete network model applicable across all conditions is unattainable.  Yet, since measurements of individual rate constants using the current incomplete network models cannot produce reliable results, iteratively refining individual parameters through targeted experiments is unlikely to ever produce accurate estimates.  It would therefore be desirable to accumulate large data sets from measurements across all relevant conditions in order to simultaneously estimate all rate constants in the model.

Our results also have implications for other processes described by complex chemical reaction networks, including atmospheric processes \cite{2008_Atkinson,runge2015identifying, 2016_Debiagi} as well as biochemical processes, such as those mediated by metabolic networks \cite{2013_Chakrabarti, 2014_Khodayari,2014_Link}. Compared to the combustion and pyrolysis networks considered here, parameter estimation in metabolic networks in particular is still in its infancy and could benefit significantly from more informed formulations at the outset. One promising direction for improvement is suggested by information-geometric and sloppy modeling approaches \cite{2014_Transtrum, 2015_Transtrum, 2016_White}.  Using such methods, it may be possible to identify measurement targets as algebraic combinations of rate constants that are more robust to the variations caused by missing network links. Another promising information theoretic approach for predicting network parameters from data would be to employ maximum entropy models, whose degeneracy issues have been recently addressed \cite{2015_Horvat}. Alternatively, it may be possible to directly estimate reaction fluxes rather than species concentrations in order to disentangle reactions.   In principle, molecular dynamics simulations can be used to estimate fluxes even if they are experimentally inaccessible, provided that the molecular force fields can be modeled realistically \cite{2015_Dontgen,2017_Alaghemandi}.

Beyond chemical reaction networks, social networks \cite{2004_Eubank,2007_Liben, 2018_Jorgensen} and  infrastructure networks may also benefit from our findings.   In power grids \cite{2013_Backhaus, 2013_motter}, for example, the network components are assumed to be  known but  can involve uncertainties and the network itself may also vary, as not all components are necessarily operational at all times. Our results suggest that power-grid models may become unreliable even if the component parameters are accurate unless they are updated in real time to account for missing components.   In other applications, our results also emphasize an important trade-off between model accuracy and parameter accuracy when dimension reduction is implemented by network trimming. That is, trimmed networks may lead to accurate results under specific conditions at the cost of requiring parameter values that differ significantly from their actual values and that may change substantially as conditions change. We anticipate that the impact of missing information on parameter estimation will ultimately depend on the class of networks under consideration, much in the same way as optimal link detection varies across scientific domains \cite{2020_Ghasemian}.

\acknowledgments{The authors thank Igor Mezi\'{c} for insightful discussions. This work was supported by MURI Grant No.\ W911NF-14-1-0359 and ARO Grant No.\ W911NF-19-1-0383.}

\begin{appendix}
\section{Electric circuit analysis}
\label{acircuit}
We first derive the measured currents for the circuit Fig.~\ref{fig1} using Kirchhoff's laws. The voltage across the blue resistor is known, so the current moving from left to right across the blue resistor is $I_3 = (V_{\mathrm{adj}}-V_1)/R_1$. Since the black nodes are neither sources nor sinks of current, the current from top to bottom across the red resistor must be $I_2+I_3 = ( V_{\mathrm{adj}} - V_3)/R_2$. This same current must pass through the horizontal $1\Omega$ resistor, so that $I_2+I_3 = V_3/(1\Omega)$.  It follows that $V_3 = V_{\mathrm{adj}}/(R_2+1\Omega)$ and $I_2 = V_{\mathrm{adj}}/(R_2+1\Omega) - (V_{\mathrm{adj}}-V_{1})/R_1$. Similarly, the current across the vertical $1 \Omega$ resistor must be $I_1-I_3 = V_1 / (1\Omega)$, and thus $I_1 = V_1/(1\Omega) + (V_{\mathrm{adj}}-V_1)/R_1$.

Next, we consider the model of the experimenter who neglects the red resistor. According to this model, all the current drawn through the adjustable voltage source travels across the blue resistor, so that the estimated current is $I_2' = -(V_{\mathrm{adj}}-V_{1})/R_{\mathrm{est}}$, where $R_{\mathrm{est}}$ is the estimate of the resistance of the blue resistor. Similarly, the experimenter estimates the current drawn from the left voltage source to be  $I_1' = V_1/(1\Omega) + (V_{\mathrm{adj}}-V_1)/R_{\mathrm{est}}$. The square error for the incomplete model, $\epsilon^2 \equiv (I_1'-I_1)^2 + (I_2'-I_2)^2$, is thus
\begin{align}
\epsilon^2 &= \Delta^2  + \left(\frac{V_{\mathrm{adj}}}{R_2+1\Omega} + \Delta \right)^2,
\end{align}
where $\Delta=({V_{\mathrm{adj}}-V_1})(1/{R_{\mathrm{est}}}-1/{R_1})$. The least square estimate for the resistance in Fig.~\ref{fig1}(b) follows by minimizing $\epsilon^2$ with respect to $R_{\mathrm{est}}$. The local sensitivity $S_{ij}\equiv({R_j}/{I_i})({\partial I_i}/{\partial R_j})$ quantifies how the $i$th current varies with the $j$th resistor.  It seems intuitive that the least square estimate derived from the model that omits $R_2$ can become unreliable when $S_{i2}$ becomes large compared to $S_{i1}$. Indeed, for this circuit, the ratio $S_{22}/S_{21}=(R_2+1\Omega)^2(V_{\mathrm{adj}}-V_1)/R_1R_2V_{\mathrm{adj}}$ approaches zero as $V_{\mathrm{adj}}$ approaches $V_1$, where the estimate in Fig.~\ref{fig1}(b) becomes unreliable.
\renewcommand{\thetable}{C\arabic{table}}
\setcounter{table}{0}
\begin{table*}[t]
\begin{tabular}{| c | c | c | c | c | c | c |}
\hline & & & & & & \\
 \hspace{1em} Exp. \# \hspace{1em} & \hspace{1em} $T (\si{K}) $ \hspace{1em} & \hspace{1em} $P (\si{atm})$ \hspace{1em} & \hspace{1em} $\phi$  \hspace{1em} & \hspace{2em} $t^\mathrm{o}_{\mathrm{ig}} (\si{s})$ \hspace{2em} & \hspace{2em} $X^\mathrm{o}_{\ce{O}_\mathrm{peak}}$ \hspace{2em} &  \hspace{1em} $k_{\mathrm{est}}/k_0$ \hspace{1em} \\[0.5em]
\hline & & & & & & \\
$1$ & $1300$ & $0.1$ & $0.5$ &  $6.3\times10^{-2}$ & $1.5\times10^{-2}$ & $1.02$ \\
$2$ & $1300$ & $0.1$ & $1.0$ &  $9.0\times10^{-2}$ & $2.7\times10^{-4}$ & $1.01$ \\
$3$ & $1300$ & $0.1$ & $2.0$ &  $1.4\times10^{-1}$ & $1.8\times10^{-5}$ & $4.71$ \\
$4$ & $1300$ & $1.0$ & $0.5$ &  $1.2\times10^{-2}$ & $1.3\times10^{-2}$ & $1.03$\\
$5$ & $1300$ & $1.0$ & $1.0$ &  $1.7\times10^{-2}$ & $7.8\times10^{-5}$ & $1.09$ \\
$6$ & $1300$ & $1.0$ & $2.0$ &  $2.5\times10^{-2}$ & $1.0\times10^{-5}$ & $2.27$ \\
$7$ & $1300$ & $5.0$ & $0.5$ &  $2.9\times10^{-3}$ & $7.4\times10^{-3}$ & $1.11$ \\
$8$ & $1300$ & $5.0$ & $1.0$ &  $4.1\times10^{-3}$ & $7.6\times10^{-5}$ & $1.30$ \\
$9$ & $1300$ & $5.0$ & $2.0$ &  $6.3\times10^{-3}$ & $6.8\times10^{-6}$ & $0.30$ \\

$10$ & $1500$ & $0.1$ & $0.5$ &  $7.6\times10^{-3}$ & $1.7\times10^{-2}$ & $1.03$ \\
$11$ & $1500$ & $0.1$ & $1.0$ &  $9.0\times10^{-3}$ & $4.2\times10^{-4}$ & $1.02$ \\
$12$ & $1500$ & $0.1$ & $2.0$ &  $1.2\times10^{-2}$ & $3.3\times10^{-5}$ & $2.00$ \\
$13$ & $1500$ & $1.0$ & $0.5$ &  $1.1\times10^{-3}$ & $1.5\times10^{-2}$ & $1.04$ \\
$14$ & $1500$ & $1.0$ & $1.0$ &  $1.5\times10^{-3}$ & $3.2\times10^{-4}$ & $1.03$ \\
$15$ & $1500$ & $1.0$ & $2.0$ &  $2.2\times10^{-3}$ & $2.1\times10^{-5}$ & $0.06$ \\
$16$ & $1500$ & $5.0$ & $0.5$ &  $3.3\times10^{-4}$ & $1.1\times10^{-2}$ & $1.07$ \\
$17$ & $1500$ & $5.0$ & $1.0$ &  $4.5\times10^{-4}$ & $2.0\times10^{-4}$ & $1.09$ \\
$18$ & $1500$ & $5.0$ & $2.0$ &  $6.6\times10^{-4}$ & $1.5\times10^{-5}$ & $0.14$ \\

$19$ & $1700$ & $0.1$ & $0.5$ &  $1.9\times10^{-3}$ & $1.8\times10^{-2}$ & $1.03$ \\
$20$ & $1700$ & $0.1$ & $1.0$ &  $1.9\times10^{-3}$ & $5.9\times10^{-4}$ & $1.05$ \\
$21$ & $1700$ & $0.1$ & $2.0$ &  $2.2\times10^{-3}$ & $5.4\times10^{-5}$ & $2.17$ \\
$22$ & $1700$ & $1.0$ & $0.5$ &  $2.2\times10^{-4}$ & $1.6\times10^{-2}$ & $1.05$ \\
$23$ & $1700$ & $1.0$ & $1.0$ &  $2.5\times10^{-4}$ & $5.0\times10^{-4}$ & $1.05$ \\
$24$ & $1700$ & $1.0$ & $2.0$ &  $3.2\times10^{-4}$ & $4.0\times10^{-5}$ & $1.87$ \\
$25$ & $1700$ & $5.0$ & $0.5$ &  $5.7\times10^{-5}$ & $1.3\times10^{-2}$ & $1.08$ \\
$26$ & $1700$ & $5.0$ & $1.0$ &  $6.9\times10^{-5}$ & $3.5\times10^{-4}$ & $1.10$ \\
$27$ & $1700$ & $5.0$ & $2.0$ &  $9.4\times10^{-5}$ & $2.9\times10^{-5}$ & $0.11$ \\
\hline
\end{tabular}
\caption{Simulated experimental observations for natural gas combustion.  The temperature $T$, pressure $P$, and the fuel to air ratio $\phi$ are varied, resulting in different observed ignition times $t^\mathrm{o}_{\mathrm{ig}}$ and peak $\ce{O}$ radical mole fraction $X^\mathrm{o}_{\ce{O}_\mathrm{peak}}$. An example of the estimated rate constant $k_{\mathrm{est}}/k_0$  for fits of the corresponding observation for a network with $40$ reactions removed is shown in the last column. \label{conditions} }
\end{table*}

\section{Kinetic models and reaction sensitivity}
\label{akinetic}
The chemical reaction networks we consider are described by state variables corresponding to the molar fraction $X_{\ce{A_i}}$ of the $i$th species with name $\ce{A_i}$ in an ideal gas and thermodynamic variables including the temperature $T$ and pressure $P$, with volume held fixed and under adiabatic conditions. For simplicity, we consider well-mixed systems, so that there is no spatial dependence on variables.  Molar fractions vary because of elementary chemical reactions between species, such as the $\ell$th reaction  $\ce{ \sum_i \nu_{i \ell} A_{i} -> \sum_j \eta_{j_\ell} A_j}$, which is assumed to occur at a rate governed by mass-action kinetics (i.e., proportional to a rate constant $\kappa_\ell$ times the product of the reactants molar concentrations raised to their stoichiometric coefficients).  Each molar fraction increases at a rate given by the reactions that produce it and decreases at a rate given by the reactions that consume it, as ${{\mathrm d}X_{A_i}}/{{\mathrm d}t} = \sum_\ell \kappa_\ell \left( \eta_{i \ell} - \nu_{i \ell} \right)\prod_{j} X_{A_j}^{\nu_{j \ell}}$.  The energy released or consumed from each reaction (determined from thermodynamic data about the species) is converted to heat, which enters an energy conservation equation governing the evolution of the temperature, and the pressure and temperature are related through a constitutive relation, which we take as the ideal gas law.  Each rate constant has temperature dependence which is based on a modified Arrhenius equation $\kappa = k T^b \exp(-E/RT)$ where $k$, $b$, and $E$ are model parameters. Some three-body reactions also depend on pressure with a Troe falloff, and reversible reactions have rate constants derived from detailed balance.  The local sensitivity, $S_{i\ell} \equiv \kappa_\ell/X_i\times\partial X_i/\partial \kappa_\ell$, quantifies how  the state variable $X_i$ changes as the parameter $\kappa_\ell$ varies \cite{1990_Turanyi}. Small changes in the rate constants for reactions with large sensitivities produce large changes in the species molar fractions, indicating that sensitivity may be a useful metric for reaction importance.

\renewcommand{\thetable}{D\arabic{table}}
\setcounter{table}{0}
\begin{table*}[t]
\begin{center}
\begin{tabular}{| c | c | c | c | c | c | c| }
\hline & & & & & & \\[0.1em]
\hspace{1em} Exp. \# \hspace{1em} & \hspace{1em} $T (\si{K}) $ \hspace{1em} & \hspace{1em} $P (\si{atm})$ \hspace{1em} & \hspace{1em} $\phi$  \hspace{1em} & \hspace{2em} $X^\mathrm{o}_{\ce{H2}}$ \hspace{2em} & \hspace{2em} $X^\mathrm{o}_{\ce{CH4}}$ \hspace{2em} &  \hspace{1em} $k_{\mathrm{est}}/k_0$ \hspace{1em} \\[0.5em]
\hline & & & & & & \\[0.1em]
$1$ & $1000$ & $0.01$ & $0.5$ &  $2.8\times10^{-1}$ & $1.2\times10^{-2}$ & 0.93 \\
$2$ & $1000$ & $0.10$ & $0.5$ &  $2.6\times10^{-1}$ & $3.2\times10^{-2}$ & 0.96 \\
$3$ & $1000$ & $1.00$ & $0.5$ &  $2.1\times10^{-1}$ & $6.5\times10^{-2}$ & 0.95 \\
$4$ & $1000$ & $0.01$ & $1.0$ &  $4.0\times10^{-1}$ & $1.9\times10^{-2}$ & 0.93 \\
$5$ & $1000$ & $0.10$ & $1.0$ &  $3.7\times10^{-1}$ & $4.7\times10^{-2}$ & 0.95\\
$6$ & $1000$ & $1.00$ & $1.0$ &  $3.1\times10^{-1}$ & $9.5\times10^{-2}$ & 0.93 \\
$7$ & $1000$ & $0.01$ & $2.0$ &  $5.1\times10^{-1}$ & $2.6\times10^{-2}$ & 0.93 \\
$8$ & $1000$ & $0.10$ & $2.0$ &  $4.7\times10^{-1}$ & $6.2\times10^{-2}$ & 0.94 \\
$9$ & $1000$ & $1.00$ & $2.0$ &  $4.0\times10^{-1}$ & $1.2\times10^{-1}$ & 0.91 \\

$10$ & $1100$ & $0.01$ & $0.5$ &  $2.8\times10^{-1}$ & $1.0\times10^{-2}$ & 0.95 \\
$11$ & $1100$ & $0.10$ & $0.5$ &  $2.7\times10^{-1}$ & $2.4\times10^{-2}$ & 0.94 \\
$12$ & $1100$ & $1.00$ & $0.5$ &  $2.3\times10^{-1}$ & $5.4\times10^{-2}$ & 0.93 \\
$13$ & $1100$ & $0.01$ & $1.0$ &  $4.0\times10^{-1}$ & $1.7\times10^{-2}$ & 1.04 \\
$14$ & $1100$ & $0.10$ & $1.0$ &  $3.8\times10^{-1}$ & $3.7\times10^{-2}$ & 0.93 \\
$15$ & $1100$ & $1.00$ & $1.0$ &  $3.3\times10^{-1}$ & $8.0\times10^{-2}$ & 0.92 \\
$16$ & $1100$ & $0.01$ & $2.0$ &  $5.1\times10^{-1}$ & $2.3\times10^{-2}$ & 1.05 \\
$17$ & $1100$ & $0.10$ & $2.0$ &  $4.8\times10^{-1}$ & $5.1\times10^{-2}$ & 0.93 \\
$18$ & $1100$ & $1.00$ & $2.0$ &  $4.2\times10^{-1}$ & $1.1\times10^{-1}$ & 0.91 \\

$19$ & $1200$ & $0.01$ & $0.5$ &  $2.8\times10^{-1}$ & $8.9\times10^{-3}$ & 0.92 \\
$20$ & $1200$ & $0.10$ & $0.5$ &  $2.7\times10^{-1}$ & $2.0\times10^{-2}$ & 0.98 \\
$21$ & $1200$ & $1.00$ & $0.5$ &  $2.4\times10^{-1}$ & $4.4\times10^{-2}$ & 0.93 \\
$22$ & $1200$ & $0.01$ & $1.0$ &  $4.0\times10^{-1}$ & $1.5\times10^{-2}$ & 1.30 \\
$23$ & $1200$ & $0.10$ & $1.0$ &  $3.8\times10^{-1}$ & $3.1\times10^{-2}$ & 0.97 \\
$24$ & $1200$ & $1.00$ & $1.0$ &  $3.4\times10^{-1}$ & $6.7\times10^{-2}$ & 0.92 \\
$25$ & $1200$ & $0.01$ & $2.0$ &  $5.0\times10^{-1}$ & $2.1\times10^{-2}$ & 1.43 \\
$26$ & $1200$ & $0.10$ & $2.0$ &  $4.8\times10^{-1}$ & $4.3\times10^{-2}$ & 0.97 \\
$27$ & $1200$ & $1.00$ & $2.0$ &  $4.3\times10^{-1}$ & $8.9\times10^{-2}$ & 0.91 \\
\hline
\end{tabular}
\end{center}
\caption{Simulated experimental observations for ethylene pyrolysis. The temperature $T$, pressure $P$, and fuel purity $\phi$ are varied, resulting in different net yields $X^\mathrm{o}_{\ce{H2}}$ and $X^\mathrm{o}_{\ce{CH4}}$. An example of the estimated rate constant $k_{\mathrm{est}}/k_0$  for fits of the corresponding observation for a network with $200$ reactions removed is shown in the last column. \label{conditions2}}
\end{table*}

\section{Simulated combustion measurements}
\label{acombustion}
We consider $27$ thermodynamic conditions for our measurement simulations that evenly span the range of thermodynamic values over which the GRI network was designed to model ignition, as listed in Table \ref{conditions}.  The initial concentrations in the simulation are a mixture of air and methane, with 8 parts $\ce{N2}$, 2 parts $\ce{O2}$, and $\phi$ parts fuel $\ce{CH4}$.  For the measurements in air diluted with argon, an additional $1$ part $\ce{Ar}$ was added to the initial conditions.

Experiments cannot generally observe the concentration of all species or reaction fluxes during the course of ignition.  Instead, specific targets are identified to measure and fit.  For this study, we consider the ignition time $t_{\mathrm{ig}}$ and the peak in the oxygen radical mole fraction $X_{\ce{O}_\mathrm{peak}}$ that occurs at ignition, where $t_{\mathrm{ig}}$ is taken as the time of the oxygen peak.   For simplicity, we fix the values of $b$ and $E$ in the rate constants to their values in the original network and optimize only over the pre-exponential factor $k$. We optimize over the error quantity
\begin{equation}
\epsilon^2 \equiv  {\left(\frac{t^\mathrm{o}_{\mathrm{ig}}-t^\mathrm{f}_{\mathrm{ig}}}{t^\mathrm{o}_{\mathrm{ig}}}\right)^2+\left(\frac{X^\mathrm{o}_{\ce{O}_\mathrm{peak}}-X^\mathrm{f}_{\ce{O}_\mathrm{peak}}}{X^\mathrm{o}_{\ce{O}_\mathrm{peak}}}\right)^2}, \label{error}
\end{equation}
where the superscripts $\mathrm{o}$ and $\mathrm{f}$ indicate the observed and fitted values, respectively.
When the observation from multiple thermodynamic conditions are combined to produce a rate constant estimate, the square errors are totaled to give the aggregated error.
The particular optimization target in Eq.~\eqref{error} is intended to emulate choices made in real combustion experiments \cite{2005_Baulch}.

We use a Brent optimization algorithm, with a bracket found from an initial interval of $[k_0/2, 2k_0]$, where $k_0$ is the original network's rate constant value. To simulate dynamics, we used the open-source software Cantera to numerically integrate the coupled ordinary differential equations in the combustion and pyrolysis networks. The $2$-norm (over the time indexes) of the local sensitivity $S_{\ce{O} \ell}$ (and $S_{\ce{H2} \ell}$ in the case of pyrolysis below) was calculated for all reactions and averaged over all experimental conditions to rank reactions by their sensitivity.  The removal sensitivity $S_{\mathrm{r}}$ is the total sensitivity of all reactions removed to generate the incomplete network, and the measurement sensitivity $S_{\mathrm{m}}$ is the sensitivity of the reaction whose rate constant is being estimated.

\section{Simulated pyrolysis measurements}
\label{apyrolysis}
Table \ref{conditions2} shows the experimental conditions for the pyrolysis rate constant measurements.  The fuel purity $\phi$ in this case indicates the ratio of ethylene to $\ce{N2}$ in the initial condition. These conditions were chosen for their applicability to low pressure chemical vapor deposition.  For ethylene pyrolysis, we optimize over the measurement error
\begin{equation}
\epsilon^2 \equiv {\left(\frac{X^\mathrm{o}_{{\ce{CH4}}}-X^\mathrm{f}_{{\ce{CH4}}}}{X^\mathrm{o}_{{\ce{CH4}}}}\right)^2+\left(\frac{X^\mathrm{o}_{{\ce{H2}}}-X^\mathrm{f}_{{\ce{H2}}}}{X^\mathrm{o}_{{\ce{H2}}}}\right)^2}, \label{error2}
\end{equation}
where the yield concentrations are evaluated at a time that the $\ce{H2}$ concentration has attained its equilibrium value.  The particular optimization target in Eq.~\eqref{error2} based on methane and hydrogen yields is intended to represent the kinds of limited data that are available in chemical vapor deposition experiments.

\end{appendix}

redpajama_set_name: RedPajamaArXiv


text:
THE STRUMBELLAS Announce New Album 'Rattlesnake'
February 2, 2019 February 2, 2019 by Kristin
ANNOUNCE NEW ALBUM
OUT MARCH 29TH VIA GLASSNOTE RECORDS
'SALVATION'
NEW SINGLE OUT NOW
EUROPEAN HEADLINE DATES IN MARCH
The Strumbellas have announced their fourth album, Rattlesnake, out March 29th via Glassnote Records. Last week the band released the video for 'Salvation', the first single to be taken from the album.
Rattlesnake marks a stylistic turn from their melancholy, introspective releases, to an uplifting album with songs that focus more on optimism. Produced by Tim Pagnotta (Elle King, Walk the Moon), co-produced and engineered by Brian Phillips, the album was recorded on the band's home turf, at the legendary Bathouse Recording Studio outside of Kingston, Ontario, and at Revolution Recording in Toronto.
The nine-track body of work is the sunny side of the street follow-up to The Strumbellas' Billboard-charting third album, Hope, which featured the hit single 'Spirits'.
"Well, after the last tour, Izzy had a baby, I got an English Bulldog, Darryl travelled to Bali, Jon built a cottage, Jer drove all the way across Canada in his 85' Camper Van, Dave grew a mustache and we made an album that we are REALLY proud of," commented Simon Ward. "Everyone in the band is SO excited to get back on the road to show everyone some new music."
The release of Rattlesnake will come after a string of European headline shows, including a show at London's Bush Hall on the 25th, and will be followed by an extensive US headline tour starting on the 1st May. Full European dates can be found below.
The Strumbellas are Simon Ward (vocals, acoustic guitar), David Ritter (keys), Jeremy Drury (percussion), Isabel Ritchie (strings), Jon Hembrey (guitar) and Darryl James (bass).
In 2017, they won the iHeartRadio Music award for Best New Alternative Rock Artist of the Year, and collected the JUNO Award for Single of the Year in their native Canada ahead of Drake, The Weeknd and Shawn Mendes.
From the onset the band received critical praise from the press, including from The New York Times, who said "The Strumbellas have perfected a story arc that's summed up in the title of their new album 'Hope," and Forbes, who declared "The Strumbellas aren't just taking on the US, they are taking on the world."
Rattlesnake Tracklist:
1) Salvation
2) I'll Wait
3) One Hand Up
4) Running Scared (Desert Song)
5) We All Need Someone
6) We Were Young
7) The Party
8) High
9) All My Life
EUROPEAN TOUR DATES MARCH 2019
17th – Cologne, Studio 672
18th – Berlin, Privatclub
19th – Hamburg, Molotow
21st – Amsterdam, Het Zonnehuis
23rd – Paris, Les Etoiles
25th – London, Bush Hall
Tickets are available here – http://thestrumbellas.ca/tour/
THE STRUMBELLAS | Official Channels
Website | Facebook | Twitter | Instagram
alternative music Bathouse Recording Studio blog blogger blogging Brian Phillips Canada Darryl James David Ritter Glassnote Records iHeartRadio Isabel Ritchie Jeremy Drury Jon Hembrey Music new music New York Times Rattlesnake Revolution Recording Salvation Simon Ward The Strumbellas Tim Pagnotta
FERRIS & SYLVESTER Release Dramatic New Single 'Sickness'
ALITA: BATTLE ANGEL | Super Bowl Video Spot Released | In theaters February 14, 2019!

redpajama_set_name: RedPajamaCommonCrawl


Inspired by my meal at Kopapa, I decided to have a go at my own slow-cooked lamb dish. Slathered in a pomegranate molasses marinade, and roasted until it fell from the bone in tender chunks of caramelised meat, this went perfectly with a chickpea and pomegranate dish (roughly based on a recipe from my mother's Moro cookbook) and a refreshing salad of cucumber, pomegranate seeds, fresh coriander and lime juice.
Place the lamb in a large dish, and drizzle generously with pomegranate molasses. Massage the molasses into the lamb, using as much as you need to ensure the meat is well coated. If you want to, cut slits into your lamb (this allows the pomegranate molasses to penetrate the meat), and place a clove of peeled garlic into each slit.
Leave your lamb to marinade in the fridge for a few hours, removing 30 minutes or so before cooking in order to bring the meat back to room temperature. Alternatively, if you're strapped for time, you can simply marinade the lamb for 15 minutes while the oven is heating up (this is what I did, and it didn't seem to have a particularly adverse affect on my finished dish!).
Preheat the oven to 150C. Transfer the lamb to a roasting dish, pouring over the pomegranate molasses marinade (and adding more as needed - I think I used about twice as much as was recommended by any recipe...which probably helped make up for my shorter marinading time). Add 100ml or so of water to the roasting tin, and cover with silver foil.
Remove your lamb from the oven, discarding the silver foil, and pour off any juices into a seperate bowl. Other recipes recommend that you leave the juices to cool for half an hour before skimming off any fat, and returning them to the roasting tin.
If you don't want to wait for half an hour, you can do what I did: pour off any grease (and remove any large chunks of fat from the surface of your lamb). Then add more pomegranate molasses and a dash more water to the roasting tin, before returning the lamb (uncovered this time) to the oven.
Turn the temperature up to 190C, and cook until the meat is nicely caramelised (around 30 minutes). Upon removing the lamb from the oven, stand for a few minutes to cool, before tearing into rough chunks with two forks (OK, or your fingers), and serving.
Begin the day before, by soaking the chickpeas overnight in cold water. (If you don't have time to do this, you can always used canned chickpeas, but the dried ones are much nicer!). Rinse thoroughly, and prepare according to the instructions on the packet - I boiled mine for about an hour and a half, until tender.
Infuse a few strands of saffron in a tea cup with some boiling water. Meanwhile, heat the olive oil in a saucepan and briefly fry the sliced garlic* before adding the drained chickpeas and pomegranate molasses. Add the 200ml of boiling water, the stock cube (if using - this isn't in the original recipe, but I think it adds flavour) and the saffron-infused water to your pan, and simmer gently for ten minutes or so, until you are left with just a small amount of flavourful sauce.
Use the ten minutes cooking time to de-seed your pomegranate. This is my least favourite part of the cooking process - not only is it quite time consuming, but I am incapable of extracting the seeds without covering myself (and everything else in my kitchen) with brightly-coloured juice**.
Cut the cucumber into two lengthways and use a dessert spoon to scoop out the juicy seeded centre. Discard (or eat...) as this will make your salad too watery. Roughly dice the remaining cucumber, and place the chunks into a bowl. Add the seeds of half a pomegranate (more tedious de-seeding required!), the juice of one small lime, and chopped fresh coriander. Season to taste, and serve.
Serve the three dishes together, alongside a pile of flatbreads or toasted pittas and an assortment of dips (hummus, baba ganoush, tzatziki...) for an impressive Middle Eastern feast.
*Be careful not to let your garlic get too brown, as it will develop an unpleasant acrid taste.
**I've actually started de-seeding pomegranates in my underwear - not because I am some sort of sensual domestic goddess, a la Nigella...but because I've ruined too many tops with spatters of pomegranate juice.


text:
Water protesters face surveillance from firm
By Fiachra Ó Cionnaith
Irish Examiner Political Correspondent
Follow @ocionnaith
A local authority has met with a surveillance company run by former soldiers to discuss ways to monitor water charge protesters after council workers were subjected to a spate of "bullying and harassment" attacks.
Officials from Dublin City Council's water works department met with Risk Management International (RMI) last month in a move that has been heavily condemned by protesters.
Details obtained by People before Profit councillor John Lyons and confirmed by the council show that, on Thursday, April 16, up to 15 supervisors from the department held a meeting with RMI, which has previously performed surveillance work for Irish Water and which was involved in the recent jailings of water charge protesters.
The discussions — which took place at the council's water division offices on Marrowbone Lane and led to RMI offering "surveillance expertise" — took place after the local authority raised concerns over a number of "incidents of bullying and harassment" linked to water charge protests.
During the meeting, RMI offered its services to the local authority to help address what a council spokesperson said are "health and safety" issues.
However, while the council ultimately rejected the deal, water charge protesters have claimed the meeting shows they are being unfairly targeted by State institutions.
In a statement to the Irish Examiner, a Dublin City Council spokesperson said: "There has been an increase in the number of incidents of bullying and harassment associated with anti-meter installation protests reported by Dublin City Council employees working in the delivery of drinking water services.
"Dublin City Council discussed this, as it is obliged to, with Irish Water under the Service Level Agreement.
"Irish Water suggested that their specialist adviser could meet with Dublin City Council to provide some advice as to how best to mitigate the risks to the health and safety of the workforce."
While RMI has previously performed work for Irish Water, this is the first known instance of the company meeting directly with a State body — a development Mr Lyons said is "disturbing".
News of the meeting comes as the Right2Water campaign holds a national conference today for anyone who wishes to be a general election candidate for the umbrella group.
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Wrist and hand injuries are commonplace in sporting activities. Sports-related hand injuries vary greatly, and include injuries that are acute and traumatic in nature, as well overuse injuries where by stress to the damaged structure/s has accumulated over time.
Injuries like these may not seem serious at first, but left untreated, can put athletes of all levels on the sidelines for months, and have a lasting effect on function. It is important to seek help as soon as possible as delaying treatment may result in long-term problems or even a permanent disability.
Sprains: This is damage to ligaments of the fingers, thumb, wrist and elbow. There are different grades of sprains from a minor tear to complete rupture. A common example is a volar plate injury.
Injuries to the bone: Bones can be fractured or dislocated. A fracture is a crack or break in a bone, and a dislocation is when a bone is pushed out of place so that they no longer line up correctly at the joint. Fractures and dislocations can occur to the metacarpals (the bones in the hand just before your knuckles), the phalanges (the bones between the joints of your fingers), the carpals (the eight small bones that make up your wrist), the radius and ulna (the two long bones in your forearm) and the humerus (the long bone in your upper arm).
Soft tissue injuries: Tendons are a type of connective tissue that attaches muscle to bone. A common injury of the tendon is called tendinitis (an acute irritation of the tissue), or tendinosis (chronic degeneration of the tendon). These injuries are commonly referred to as overuse injuries because they happen over time, usually from repetitive training.
Closed-tendon injuries: The most common example being Mallet Finger.
Treatment and recovery time for these injuries greatly vary and depend on a range of factors, including the severity of the injury, how long ago the injury occurred, personal factors such as age, health, other activities (such as work and hobbies) and compliance.
At Hand Works we understand that sport is a valued occupation. We are committed to providing high quality treatment, which is tailored to suit your individual demands, to ensure a prompt, safe return to field.


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DTS Publishing
Buses & Trolleybuses
Fleetbooks
Tramways & Light Rail
Shipping & Maritime
None Transport
Buses & Trams
abc Rail Guide 2020
abc Rail Guide has established itself as the most comprehensive, detailed, accurate and reliable guide to the rolling stock used on the railway networks of the British Isles. The new 2020 edition of this best-selling annual publication has been thoroughly revised and updated and reverts to its original format in providing a complete overview of all of the railway, metro, light rail and tramway systems, London Underground and heritage lines in the UK and Ireland. The book offers the most accurate listings, in operator order, of the locomotives, multiple units and stock used on the railways of Britain and Ireland. Entries are also separately cross-referenced to their operators. There has been a huge amount of investment in recent years in the rolling stock fleet and all these new types are described and illustrated to maintain the in depth coverage of all motive power for which abc Rail Guide is renowned.
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text:
Great War Association
Schipperfabrik
Designs by Alyssa
Navvy Boots
This is the typical working mans boot of the late victorian and edwardian era. Built much heavier than the more common balmoral style. Most were sold with out eyelets. Ours is made of 6 oz bridle leather and lined with leather. Firm toe with a stiffener.
Size : 7 7 1/2 8 8 1/2 9 9 1/2 10 10 1/2 11 11 1/2 12 12 1/2 13
Width : D EE
Eyelets : None Eyelets + $5.00
Please allow at least 12 weeks for us to make and ship your order
U.S. 1903 High Quarter Marching Shoes
QMD specification number 599 dated 1903. As the 1898 calf skin shoe proved too light in the field this is one of a number of improvements the army sought. The QMD also thought to replace leggings with this type boot. This boot was about 40 years ahead of its time. With a small production run this boot still shows up in 1906 QMD prints but is gone by the 1916 QMD list.
Size : 6 7 8 9 10 11 12
Sole : All leather heel Rubber heel
1904 Russet Marching Shoe
These were first issued in 1898 in light weight black calf as the dress shoe. In 1904 they were listed as two items, the russet marching shoe and the dress shoe. In 1912 they were modified for the Munson last and given a heavier weight vamp. The black dress shoe was gone by then. They were supposed to be replaced in 1919 by the Service Shoe but were issued until stocks ran out about 1928. Ours are built on Munson lasts of american bridle leather tallowed and waxed. They are dyed the correct army russet.
Size : 8 8 1/2 9 9 1/2 10 10 1/2 11 11 1/2 12 12 1/2 13
1900 Boer War Shoe
This was copied from pictures supplied by Edouard DeVillers R.S.A. . It seems to be the most common type of ankle boot worn in that era. It is available in either sewn sole or pegged as both types were used.
Size : 7 7 1/2 8 8 1/2 9 9 1/2 10 10 1/2 11 11 1/2
Sole : Sewn Pegged
Field Boot
This version of the field boot has many names sometimes called a motor patrol boot for the motorcycle policemen who have always worn them, also known as Lord Strathcona"s boot for the canadian officer who led troops in the Boer war. This type of boot was also favored by many allied pilots in the first world war. It is also the dress boot for the RCMP. Ours is made of bridle leather tanned in America in either black or brown. The boot may be had on a european style last as pictured or on a U.S. military spec Munson last. This boot is fitted and requires careful measurements before ordering you must be very careful and double check if you have any questions please e-mail us and we will be glad to help.
Size : 6 6 1/2 7 7 1/2 8 8 1/2 9 9 1/2 10 10 1/2 11 11 1/2 12 12 1/2
Contact for Measuring Sheet
Website Design by Josh Mann Designs


karvind writes "According to story at law.com, 'lawmakers in Washington are considering changes to the patent code that would bring U.S. law closer to intellectual property standards in the rest of the industrialized world.' The stated result of Patent Reform Act of 2005, HR 2795 is supposed to make the system work 'more efficiently' and be 'less prone to litigation.'"
What's your point bro? Just wondering what it is? Give us an opinion, please.
all i know about that crap is it has my dad working till like midnight every night.


Laurel Burch was an American self taught artist who sadly died in 2007. She is known for her use of bright colours and mythical interpretations of fauna and flora. Immediately recognisable, her paintings translate well onto fabric and these bags are gorgeous!


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Shopping-Mall CEO's $6.6 Million Sale
Alexander Eule
Updated Sept. 24, 2008 11:59 pm ET
Tables: Buyers | Sellers
AS RETAILERS NERVOUSLY AWAIT the holiday shopping season, one shopping-mall executive is getting a jump on the selling spree.
Arthur Coppola, chairman and chief executive officer of regional-mall owner Macerich (ticker: MAC), sold $6.6 million in his company's stock on Friday. Coppola sold 100,000 shares at an average...
Barron's Online's John Kimelman reports that insiders at the Gap clothing chain and the CEO of mall owner Macerich sold shares following recent gains in the stock.


TORONTO — The Canadian Media Guild / CWA Canada is welcoming a $35-million class actionfiled by law firm Cavalluzzo on behalf of hundreds of reality and factual TV workers who have worked at Cineflix, which produces such TV shows as Property Brothers and Mayday.
The Fairness in Factual TV campaign began five years ago when a group of reality and factual TV workers decided enough was enough and sought the support of the Canadian Media Guild / CWA Canada. More than 400 people have signed up as supporters since the campaign began.
The Guild is urging people in the industry to talk about this issue at work and join the FairnessInFactualTV.ca campaign. If you feel your work conditions have been unfair, contact the union at factualtv@cmg.ca . Write a few lines about your experience and attach a recent contract. It will be held in complete confidence.
Those who have worked at Cineflix, Boat Rocker Media, Insight Productions or other companies who want more information about class actions can visit the Cavalluzzo LLP website or email factual-television-classaction@cavalluzzo.com .


text:
@interface HJYAppDelegate : UIResponder <UIApplicationDelegate>

@property (strong, nonatomic) UIWindow *window;

@end

redpajama_set_name: RedPajamaGithub


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Nelson says he will not renew contract as CEO of NAIC
The term for former U.S. Senator Ben Nelson will end on January 31, 2016.
By Melissa Hillebrand | October 09, 2015 at 07:50 AM
Sen. Ben Nelson in 2009 (Thinkstock file photo)
Former U.S. Senator Ben Nelson announced Thursday that he will not renew his contract as CEO of the National Association of Insurance Commissioners (NAIC). Nelson, who represented Nebraska as a democrat from 2001 to 2013, joined NAIC as CEO in January of 2013. His term will end Jan. 31, 2016.


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Printed from https://ideas.repec.org/a/wly/emetrp/v82y2014i1p41-88.html
Optimal Taxes on Fossil Fuel in General Equilibrium
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Mikhail Golosov
Per Krusell
Aleh Tsyvinski
We analyze a dynamic stochastic general‐equilibrium (DSGE) model with an externality—through climate change—from using fossil energy. Our central result is a simple formula for the marginal externality damage of emissions (or, equivalently, for the optimal carbon tax). This formula, which holds under quite plausible assumptions, reveals that the damage is proportional to current GDP, with the proportion depending only on three factors: (i) discounting, (ii) the expected damage elasticity (how many percent of the output flow is lost from an extra unit of carbon in the atmosphere), and (iii) the structure of carbon depreciation in the atmosphere. Thus, the stochastic values of future output, consumption, and the atmospheric CO 2 concentration, as well as the paths of technology (whether endogenous or exogenous) and population, and so on, all disappear from the formula. We find that the optimal tax should be a bit higher than the median, or most well‐known, estimates in the literature. We also formulate a parsimonious yet comprehensive and easily solved model allowing us to compute the optimal and market paths for the use of different sources of energy and the corresponding climate change. We find coal—rather than oil—to be the main threat to economic welfare, largely due to its abundance. We also find that the costs of inaction are particularly sensitive to the assumptions regarding the substitutability of different energy sources and technological progress.
Mikhail Golosov & John Hassler & Per Krusell & Aleh Tsyvinski, 2014. "Optimal Taxes on Fossil Fuel in General Equilibrium," Econometrica, Econometric Society, vol. 82(1), pages 41-88, January.
Handle: RePEc:wly:emetrp:v:82:y:2014:i:1:p:41-88
File URL: http://hdl.handle.net/10.3982/ECTA10217
Other versions of this item:
Mikhail Golosov & John Hassler & Per Krusell & Aleh Tsyvinski, 2011. "Optimal Taxes on Fossil Fuel in General Equilibrium," NBER Working Papers 17348, National Bureau of Economic Research, Inc.
Golosov, Mikhail & Hassler, John & Krusell, Per & Tsyvinski, Aleh, 2011. "Optimal taxes on fossil fuel in general equilibrium," CEPR Discussion Papers 8527, C.E.P.R. Discussion Papers.
Daron Acemoglu & Philippe Aghion & Leonardo Bursztyn & David Hemous, 2012. "The Environment and Directed Technical Change," American Economic Review, American Economic Association, vol. 102(1), pages 131-166, February.
Daron Acemoglu & Philippe Aghion & Leonardo Bursztyn & David Hemous, 2009. "The Environment and Directed Technical Change," NBER Working Papers 15451, National Bureau of Economic Research, Inc.
Acemoglu, Daron & Aghion, Philippe & Bursztyn, Leonardo & Hemous, David, 2011. "The Environment and Directed Technical Change," CEPR Discussion Papers 8660, C.E.P.R. Discussion Papers.
Acemoglu, Daron & Aghion, Philippe & Bursztyn, Leonardo & Hemous, David, 2010. "The Environment and Directed Technical Change," Seminar Papers 762, Stockholm University, Institute for International Economic Studies.
Acemoglu, Daron & Aghion, Philippe & Bursztyn, Leonardo & Hemous, David, 2010. "The Environment and Directed Technical Change," Sustainable Development Papers 92839, Fondazione Eni Enrico Mattei (FEEM).
Daron Acemoglu & Philippe Aghion & Leonardo Bursztyn & David Hemous, 2010. "The Environment and Directed Technical Change," Working Papers 2010.93, Fondazione Eni Enrico Mattei.
Bovenberg, A Lans & Smulders, Sjak A, 1996. "Transitional Impacts of Environmental Policy in an Endogenous Growth Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(4), pages 861-893, November.
Bovenberg, A.L. & Smulders, J.A., 1994. "Transitional impact of environmental policy in an endogenous growth model," Discussion Paper 1994-50, Tilburg University, Center for Economic Research.
Bovenberg, A.L. & Smulders, J.A., 1996. "Transitional impacts of environmental policy in an endogenous growth model," Other publications TiSEM e002b2ed-f04f-4ffc-98f8-0, Tilburg University, School of Economics and Management.
Thomas Sterner & U. Martin Persson, 2008. "An Even Sterner Review: Introducing Relative Prices into the Discounting Debate," Review of Environmental Economics and Policy, Association of Environmental and Resource Economists, vol. 2(1), pages 61-76, Winter.
Sterner, Thomas & Persson, U. Martin, 2007. "An Even Sterner Review: Introducing Relative Prices into the Discounting Debate," Discussion Papers dp-07-37, Resources For the Future.
Angeletos, George-Marios & Calvet, Laurent-Emmanuel, 2006. "Idiosyncratic production risk, growth and the business cycle," Journal of Monetary Economics, Elsevier, vol. 53(6), pages 1095-1115, September.
George-Marios Angeletos & Laurent E. Calvet, 2002. "Idiosyncratic Production Risk, Growth and the Business Cycle," Harvard Institute of Economic Research Working Papers 1952, Harvard - Institute of Economic Research.
Laurent-Emmanuel Calvet & George-Marios Angeletos, 2006. "Idiosyncratic Production Risk, Growth and the Business Cycle," Post-Print halshs-00119533, HAL.
Laurent-Emmanuel Calvet & George-Marios Angeletos, 2003. "Idiosyncratic Production Risk, Growth and the Business Cycle," Working Papers hal-00593392, HAL.
George-Marios Angeletos & Laurent Calvet, 2003. "Idiosyncratic Production Risk, Growth, and the Business Cycle," NBER Working Papers 9764, National Bureau of Economic Research, Inc.
Laurent Calvet & George-Marios Angeletos, 2012. "Idiosyncratic Production Risk, Growth and the Business Cycle," Working Papers hal-00674230, HAL.
repec:cup:cbooks:9780521700801 is not listed on IDEAS
Tol, Richard S. J., 2008. "The Social Cost of Carbon: Trends, Outliers and Catastrophes," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 2, pages 1-22.
Richard S.J. Tol, 2007. "The Social Cost Of Carbon: Trends, Outliers And Catastrophes," Working Papers FNU-144, Research unit Sustainability and Global Change, Hamburg University, revised Aug 2007.
Tol, Richard S. J., 2007. "The Social Cost of Carbon: Trends, Outliers and Catastrophes," Economics Discussion Papers 2007-44, Kiel Institute for the World Economy (IfW).
Lans Bovenberg, A. & Smulders, Sjak, 1995. "Environmental quality and pollution-augmenting technological change in a two-sector endogenous growth model," Journal of Public Economics, Elsevier, vol. 57(3), pages 369-391, July.
Bovenberg, A.L. & Smulders, J.A., 1995. "Environmental quality and pollution-augmenting technological change in a two-sector endogenous growth model," Other publications TiSEM 6784bb12-71fb-45a5-bf7e-8, Tilburg University, School of Economics and Management.
Eyckmans, Johan & Tulkens, Henry, 2003. "Simulating coalitionally stable burden sharing agreements for the climate change problem," Resource and Energy Economics, Elsevier, vol. 25(4), pages 299-327, October.
EYCKMANS, Johan & TULKENS, Henry, 1999. "Simulating coalitionally stable burden sharing agreements for the climate change problem," CORE Discussion Papers 1999026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
EYCKMANS, Johan & TULKENS, Henry, 2003. "Simulating coalitionally stable burden sharing agreements for the climate change problem," CORE Discussion Papers RP 1677, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
Hassler, John & Krusell, Per & Olovsson, Conny, 2012. "Energy-Saving Technical Change," CEPR Discussion Papers 9177, C.E.P.R. Discussion Papers.
John Hassler & Per Krusell & Conny Olovsson, 2015. "Energy-Saving Technical Change," Discussion Papers 1529, Centre for Macroeconomics (CFM).
Hassler, John & Krusell, Per & Olovsson, Conny, 2015. "Energy-saving technical change," LSE Research Online Documents on Economics 86280, London School of Economics and Political Science, LSE Library.
John Hassler & Per Krusell & Conny Olovsson, 2012. "Energy-Saving Technical Change," NBER Working Papers 18456, National Bureau of Economic Research, Inc.
Martin L. Weitzman, 2009. "On Modeling and Interpreting the Economics of Catastrophic Climate Change," The Review of Economics and Statistics, MIT Press, vol. 91(1), pages 1-19, February.
Weitzman, Martin L., 2009. "On Modeling and Interpreting the Economics of Catastrophic Climate Change," Scholarly Articles 3693423, Harvard University Department of Economics.
van der Ploeg, Frederick & Withagen, Cees, 2012. "Is there really a green paradox?," Journal of Environmental Economics and Management, Elsevier, vol. 64(3), pages 342-363.
Frederick van der Ploeg & Cees Withagen, 2010. "Is there really a Green Paradox?," Tinbergen Institute Discussion Papers 10-020/3, Tinbergen Institute, revised 27 Aug 2012.
Rick van der Ploeg & Cees Withagen, 2010. "Is There Really a Green Paradox?," OxCarre Working Papers 035, Oxford Centre for the Analysis of Resource Rich Economies, University of Oxford.
Frederick Van der Ploeg & Cees A. Withagen, 2010. "Is There Really a Green Paradox?," CESifo Working Paper Series 2963, CESifo Group Munich.
Grimaud, André & Lafforgue, Gilles & Magné, Bertrand, 2011. "Climate change mitigation options and directed technical change: A decentralized equilibrium analysis," Resource and Energy Economics, Elsevier, vol. 33(4), pages 938-962.
GRIMAUD André & LAFFORGUE Gilles & MAGNE Bertrand, 2008. "Climate change mitigation options and directed technical change: A decentralized equilibrium analysis," LERNA Working Papers 08.10.254, LERNA, University of Toulouse.
André Grimaud & Gilles Lafforgue & Bertrand Magné, 2009. "Climate Change Mitigation Options and Directed Technical Change: A Decentralized Equilibrium Analysis," CESifo Working Paper Series 2875, CESifo Group Munich.
Grimaud, André & Lafforgue, Gilles & Magné, Bertrand, 2009. "Climate Change Mitigation Options and Directed Technical Change: A Decentralized Equilibrium Analysis," TSE Working Papers 09-063, Toulouse School of Economics (TSE).
GRIMAUD Andre & LAFFORGUE Gilles & MAGNE Bertrand, 2009. "Climate change mitigation options and directed technical change: A decentralized equilibrium analysis," LERNA Working Papers 09.20.296, LERNA, University of Toulouse.
Grimaud, André & Lafforgue, Gilles & Magné, Bertrand, 2008. "Climate Change Mitigation Options and Directed Technical Change: A Decentralized Equilibrium Analysis," IDEI Working Papers 510, Institut d'Économie Industrielle (IDEI), Toulouse, revised Nov 2009.
Pizer, William A., 1999. "The optimal choice of climate change policy in the presence of uncertainty," Resource and Energy Economics, Elsevier, vol. 21(3-4), pages 255-287, August.
R. M. Solow, 1974. "Intergenerational Equity and Exhaustible Resources," Review of Economic Studies, Oxford University Press, vol. 41(5), pages 29-45.
R. M. Solow, 1973. "Intergenerational Equity and Exhaustable Resources," Working papers 103, Massachusetts Institute of Technology (MIT), Department of Economics.
Kelly, David L. & Kolstad, Charles D., 1999. "Bayesian learning, growth, and pollution," Journal of Economic Dynamics and Control, Elsevier, vol. 23(4), pages 491-518, February.
Saint-Paul, Gilles, 2002. "Environmental Policy and Directed Innovation in a Schumpeterian Growth Model," IDEI Working Papers 153, Institut d'Économie Industrielle (IDEI), Toulouse.
Uzawa,Hirofumi, 2009. "Economic Theory and Global Warming," Cambridge Books, Cambridge University Press, number 9780521066594, December.
Joseph Stiglitz, 1974. "Growth with Exhaustible Natural Resources: Efficient and Optimal Growth Paths," Review of Economic Studies, Oxford University Press, vol. 41(5), pages 123-137.
S. Illeris & G. Akehurst, 2002. "Introduction," The Service Industries Journal, Taylor & Francis Journals, vol. 22(1), pages 1-3, January.
Goulder, Lawrence H. & Mathai, Koshy, 2000. "Optimal CO2 Abatement in the Presence of Induced Technological Change," Journal of Environmental Economics and Management, Elsevier, vol. 39(1), pages 1-38, January.
Withagen, Cees, 1994. "Pollution and exhaustibility of fossil fuels," Resource and Energy Economics, Elsevier, vol. 16(3), pages 235-242, August.
Chakravorty, Ujjayant & Roumasset, James & Tse, Kinping, 1997. "Endogenous Substitution among Energy Resources and Global Warming," Journal of Political Economy, University of Chicago Press, vol. 105(6), pages 1201-1234, December.
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E0 - Macroeconomics and Monetary Economics - - General
Q5 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics
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The principal staff officer for all matters concerning military intelligence (MI), counterintelligence, security operations, and military intelligence training. An intelligence officer is located at every echelon from battalion through corps.
Disseminating intelligence to commanders and other users in a timely manner. Collecting, processing, producing, and disseminating intelligence. Conducting and coordinating intelligence preparation of the battlefield (IPB). Recommending unit area of interest and assisting the staff in defining unit battlespace. Describing the effects of the battlefield environment on friendly and enemy capabilities. Evaluating the threat (their doctrine, order of battle factors, high-value targets (HVTs), capabilities, and weaknesses).
Determining enemy most probable and most dangerous courses of action. Coordinating with the entire staff and recommending PIR for the commander's critical information requirements. Integrating staff input to IPB products for staff planning, decision making, and targeting.Coordinating with the S3 and Provost Marshall (PM) for processing (for intelligence purposes) materials taken from EPWs and civilian internees. Coordinating ground and aerial reconnaissance and surveillance operations with other collection assets. Participating in targeting meeting. Debriefing personnel returning from enemy control. Analyzing, in coordination with the S3 (engineer coordinator (ENCOORD), enemy capability to use environmental manipulation as a means to impede friendly forces or jeopardize long-term objectives. Coordinating technical intelligence activities and disseminating information.
Assisting the S3 in planning target acquisition activities for collection of target information. Coordination with the chemical officer to analyze the enemy's capability and predictability of using nuclear, biological, and chemical (NBC) weapons. Coordinating with the S1 the enemy situation that may affect evacuation or hospitalization plans. Coordinating with the S4 the enemy situation that may affect logistics operations. Coordinating with the G5 the enemy situation that may affect civil-military operations. Assisting the S3 (deception officer) in preparing deception plans by recommending the target and objective based on assessed enemy collection capability and susceptibility to deception. Assisting the S3 in information operations, to include command and control warfare (C 2 W).
Planning and managing intelligence collection operations in coordination with the S3 and fire support planners. Recording, evaluating, and analyzing collected information to produce all-source intelligence that answers the commander's priority intelligence requirements and information requirements (IR), including battle damage assessments (BDAs). Maintaining the current situation regarding the enemy and environmental factors and updating IPB and the intelligence estimate.Determining map requirements and managing the acquisition and distribution of map and terrain products.
Identifying enemy intelligence collection capabilities, such as human intelligence (HUMINT), signals intelligence (SIGINT), imagery intelligence (IMINT), and efforts targeted against the unit. Evaluating enemy intelligence capabilities as they affect the areas of OPSEC, countersurveillance, signals security (SIGSEC), security operations, deceptions planning, psychological operations (PSYOP), rear area operations, and force protection. Conducting counterintelligence liaison for security and force protection. Conducting counterintelligence force protection source operations.
Supervising the command and personnel security program. Evaluating physical security vulnerabilities to support the S3. Coordinating security checks for indigenous personnel.
Preparing the command intelligence training plan and integrating intelligence, counterintelligence, operational security, enemy (organization, equipment, and operations), and intelligence preparation of the battlefield considerations into other training plans. Exercising staff supervision of MI support to the commands intelligence training program.


Haiyan Lee, The Stranger and the Chinese Moral Imagination Stanford: Stanford University Press, 2014. vi, 362 pp. $50.00. ISBN: 9780804785914 (cloth); ISBN: 9780804793544 (ebook).
In the introduction to her Strangers and the Chinese Moral Imagination, Haiyan Lee lays out an ambitious theoretical framework for investigating the border zones of "self and other" in Chinese literature, a figure she calls the "stranger." Lee's definition of the stranger follows Georg Simmel's notion of "the wanderer who comes today and stays tomorrow—the potential wanderer, so to speak, who although he has gone no further, has not quite got over the freedom of coming and going" (10). The "stranger" for Lee opens up an ethical discussion in Chinese literature of class, gender, race, ethnicity, and ideology and treats a wide variety of literary and cultural texts. Those texts range from literature to television, public exhibitions, and film where the lines between self and other become legible in the figures of ghosts, animals, women, domestic servants, sent-down youth, racialized class enemies, migrant workers, and, of course, foreigners. Lee uses these encounters to chart the historical, evolving relationship between what she calls Confucian "kinship sociality" and "stranger sociality," an evolution the author sees as essential for developing a robust civil society in China.
To underscore the importance of developing a stronger civil society in China, Lee begins the book with examples of moral breakdown. She notes "two consecutive hit-and-run incidents in a narrow market street that left a toddler girl named Yueyue lying in a pool of blood, crushed, inert, and ignored by over a dozen passers-by." She relays a gut-wrenching synopsis of Blind Shaft, a film about unsuspecting migrant workers killed for their life insurance payouts. She discusses public signs admonishing travelers "not to talk to strangers," and these episodes set the stage for Lee's primary notion that the moral failings of the public sphere "have roots in both the Confucian tradition of kinship sociology and the modern state management of stranger sociality" (2).
Lee argues that neither the received Confucian kinship morality nor the "state management of stranger sociality," paradigmatically embodied by Lei Feng (a model soldier who selflessly serves the people), have been able to offer a moral foundation for China's urbanizing population. She argues that the Party has "furnished the alibi for the state-sponsored suspension of stranger sociality and the attendant atrophy of the moral imagination" (2). There is hope, however; Lee shows the potential of literature (as well as film, TV, etc.) to incubate and nourish an "emerging civil society that can and should sustain moral proximity, wherein the face to face is cultivated by individuals qua individuals and wherein rules and sanctions are a mater of negotiation rather than imposition" (29).
Lee encourages readers to think about how reading literature and other forms of cultural production will bring attention not only to the historical conditions that undergirded "kinship sociality" in the past, but also to how and why many sociologists still label Chinese society "low trust" today. Like Lee, many sociologists wonder aloud what might be done to usher in a more organic Chinese civil society in the future.
The book is organized into three parts: "Alien Kind," "The Benighted and the Enchanted," and "Friends and Foes." Part I explores important moments in modern Chinese literature where "superstitious peasant beliefs" in ghosts, spirits, gods, etc. embed peasants and minority groups within a traditional cosmology that "makes them and their deities strangers to secular modernity" represented in the figure of the modern intellectual narrator (31). Lee argues that these literary moments draw readers' attention to the fact that "modernity does not have all the answers to existential questions" and that banishing such superstitions can paradoxically expose these vulnerable groups to "the predation of uneven development" (31). Part I then continues in this vein by tracing out how human-animal relations become indexical to a wider paradigmatic shift from the premodern vertical cosmic order (where animals could be viewed as "marvelous creatures with fabulous powers") to the modern order in which they are helpless victims of human development, reduced to pets, game, livestock, etc. (31).
Part II begins with chapter 3, "The Power and Pollution of the Stranger Woman," which explores the gendering of strangers within the Confucian kinship sociality, and continues with chapter 4, "The Country and the City," where the evolving encounters between urbanites and the migrant working class (maids, transient tenants) in Chinese cities or the experiences of sent-down youth in the countryside reveal how Chinese urbanization is transforming discourses of civility on a personal, narrative scale. The final section, "Friends and Foes," is comprised of chapters that explore the evolving discourses of the stranger as "enemy." The book ends with a conclusion entitled "Literature and the Veil of Ignorance," which for this reader failed to deliver on the promise of the earlier chapters.
Throughout the book, Lee offers fresh and illuminating readings of canonical texts like Wu Cheng'en's Journey to the West, modern best sellers like Jiang Rong's Wolf Totem, Mo Yan's Life and Death Are Wearing Me Out, and Gao Xingjian's Soul Mountain, films like Blind Shaft, and television serials such as 28 Maids at Professor Tian's and Nannies for Foreigners. Each reading offers genuinely productive insights into historically-specific moments where encounters with outsiders both structure and disrupt existing gender, race, class, and ethnicity commitments. While the introduction could have benefited from a deeper engagement with questions of moral agency highlighting the tension between human agency as individual ethics vs. a collective historical dynamic (a point I will return to), any one of Lee's individual chapters make up for these missed opportunities. While all six chapters ostensibly focus on one particular register of "strangers," each builds upon the next, revealing a multi-vectored reinforcing network of othering. Take for instance Lee's critical reading of Jiang Rong's novel Wolf Totem, where she shows how the novel's ostensibly clear demarcation line between human and animal others actually conflates species and ethnic scales of otherness (wolves and Mongols) to reveal a "profoundly Han-centric and anthropocentric" hearkening "back to the century-old racial-nationalist question: how can China attain wealth and power and avert the fate of extinction in the Darwinian jungle" (109). Or chapter 5, "The Enemy Within," arguably the book's most powerful chapter, wherein Lee reveals how concepts of class and ethnic/racial difference became conflated in ways that expose how the logic of "racism" need not hinge upon biological notions of difference.
The buoyant rigor of Lee's prose outweighs the occasional awkward turns of phrase in these chapters (a fault I would find more with the editors than the author) but still falls flat in the conclusion with an awkward invocation of Roland Barthe's binary of writerly vs. readerly texts. I was left scratching my head at Lee's unproved assertion that "writerly" (disjunctive, non-linear, or otherwise non-absorptive) works are somehow complicit with authoritarian "commitment politics," whereas the more absorptive "readerly" texts can offer a moral theater within which a civil society can be practiced and strengthened. I am on board with the idea that fully absorbing narrative prose can enable us to experience morally challenging situations, but there are strengths offered by so-called writerly texts that are not only ignored here but excluded with such a reductive choice. Despite this awkwardness, Lee's conclusion does communicate a vision for an engaged humanities, one where literary criticism can validate its value propositions against the encroachments of big data and other structures of knowledge gaining strength in academia and beyond.
Hegel's argument hinges on the idea that history progresses through a dialectical relationship among the family (kinship), the state, and civil society and that the Chinese culture at present (ca. early nineteenth century) cannot extend ethics beyond the substance of the family to the state. Hegel's model reduces ethics to filial obligations and deprives people of moral subjectivity (differentiation), the required ethical conditions for developing modern civil society. Rather than unmasking the reductive teleology of such logic that measures sociological progress along a continuum toward a culturally coded definition of progress, this reader instead found these recalcitrant paradigms reaffirmed and emotionally redoubled. No longer excluded from dialectical "progress," according to Lee, Chinese literature can serve as a powerful tool to help "evolve" Chinese society away from the problematic non-individuatedness of Confucian kinship sociality toward models that we associate with the West's idea of modern liberal democracy.
To help make the stakes of this problem easier to grasp, imagine for a moment reading a work of literary criticism that started with a spattering of horror stories drawn from the more-seedy corners of America's nursing home industry followed by an analysis that reads these incidents as causally linked to the dominance of "stranger sociality" (or lack of kinship sociality). Now imagine that readers are asked to see these behaviors as existing on an evolutionary continuum where the outmoded worldview of stranger sociality can no longer cope with societal changes more capably addressed by Confucian filial piety/kinship sociality. The fact that we can reverse the poles of such dichotomies not only reveals the existence of a reductive cultural logic at play, but perhaps more importantly reveals a need for a more nuanced comparative cultural framework that acknowledges both shortcomings to be avoided and strengths to be drawn on when addressing contemporary (trans-cultural) social phenomena. In the example above, it arguably calls for a deeper, more complete study of causes of ageism without relying on ideologically-coded indices, especially those emanating from a single culture or world view.
I would argue that Levinas would have been a more fruitful framework for Lee than the sociological one she ultimately chose to frame the book as a whole if only because a larger treatment of Levinas would likely have come with a wider canvas of Levinasian studies in China. Citing key arguments in works like the 2008 volume Levinas: Chinese and Western Perspectives (edited by Nicholas Bunnin, Dachun Yang, Linyu Gu) would have provided the kind of nuanced theoretical background able to match the rigor we find in Lee's powerful close readings.
Finally, it is worth restating how right Lee is to insist on placing literature and literary criticism at the heart of the challenges facing China and the West. Because interpretation puts forward a thesis and marshals supports to back it up, we are forced to foreground the argumentative nature of our work and we do this by rigorously engaging our own motivations as deeply as the ideologically contingent, culturally- and historically-specific discourses being interpreted. There is certainly no reason to avoid drawing on the tools of sociology, for instance, as long as concepts like "stranger" or "kinship sociality" are employed with an understanding of their dependence on the very dynamic potentiality of our own cultural contingencies (not separate from them). In other words, literature and literary criticism may not be an ideal place to validate or disprove hypotheses developed by sociologists, but we should feel free to engage this work as long as we resist falling into the evidential logic that condition their conceptual limitations. Having said this, there are few literary critics better prepared to carry out this work than Haiyan Lee, as she has proven by her keen interpretive analysis here and elsewhere, and I am looking forward to her next work.