text:
\section{Methods}
\import{./}{2A_CompProcedures.tex}
\import{./}{2B_Sources_prediction_errors.tex}
\import{./}{2C_define_bserror}
\section{results}
\import{./}{3_0_this_work_details.tex}
\import{./}{3A_scatter.tex}
\import{./}{3B_ao_error.tex}
\import{./}{3C_ao_correction.tex}
\import{./}{3D_Truncation_error.tex}
\import{./}{3E_Vibrational.tex}
\import{./}{3F_benzene_pyridine.tex}
\import{./}{4_conclusion.tex}

\section*{Acknowledgement}
O.A.v.L. acknowledges funding from the Swiss National Science foundation (200021\_175747) and from the European Research Council (ERC-CoG grant QML). This work was partly supported by the NCCR MARVEL,
funded by the Swiss National Science Foundation.

\section{References}

\section{Introduction}
Chemical space, the ensemble of all possible molecule that constitute matter, is unfathomably large. The number of molecules in chemical space is estimated to be higher than $10^{60}$ just considering small organic molecules \cite{ccs,ccs2}.
The size of this problem makes it impossible to enumerate and assess a significant portion of chemical space with standard quantum chemistry methods alone. Therefore, modern approaches in materials design have the need for computationally less demanding, yet sufficiently accurate methods \cite{ccsLilienfeld}.
Promising results were obtained for instance through quantum machine learning models \cite{qml1,qml2,qml3,qml4,qml5,qml6}. Provided that the machine has been trained on a sufficiently large number of molecules, quantum machine models can provide fast yet accurate predictions. For example, in 2017 machine learning models were trained to predict multiple electronic properties for thousands of organic molecules reaching DFT accuracy in milli-second prediction time\cite{Faber1,Faber2}.

Alchemical perturbation density functional theory (APDFT) aims at a similar goal, namely to obtain a rapid screening of chemical space. The approach is fundamentally different though: While machine learning models require thousands or millions of training instances in order to interpolate towards similar systems, APDFT relies on a single explicit calculation on a reference system to give approximate, but still accurate predictions for properties of a multitude of isoelectronic and similar target compounds. \cite{Lilienfeld2009,Chang2018,benzene2013,Lilienfelds_bn_doped_graphene,c60_2018}
APDFT yields consistent predictions of both energies and electron densities\cite{apdft}. Its reliability has been shown in several applications such as energies in BN-doped aromatic systems and non-covalent interactions thereof\cite{apdft}, decomposition of energy contributions\cite{Rudorff2019a} or estimation of deprotonation energies\cite{Rudorff2020,Cardenas}.
Through the use of pseudopotentials, quantum alchemy can be a powerful tool in solid state chemistry \cite{marzari_94,Lilienfeld2009,Lilienfeld2010,Solovyeva_crystals_2016,Chang2018}, with possible application in catalysts design \cite{Keith2017,Keith2019,Keith2020} .
In recent applications, it has been shown that APDFT---if applied to high level CCSD \cite {ccsd1,ccsd2,ccsd3} calculations for the reference molecule---can outperform\cite{apdft} widely used methods in computational chemistry (e.g.  HF\cite{1935,slater1951}, MP2\cite{Moller1934} and DFT\cite{becke1993,lee1988,vosko1980,pbe})
This approach holds the promise to shift the computational cost from many medium-quality calculations throughout chemical compound space to a few select high-quality calculations which serve as a subsequent basis to obtain alchemical estimates of electronic observables for a combinatorially larger number of molecules in one shot.

APDFT is straight-forward: The non-degenerate electronic ground state in the Born Oppenheimer approximation $E_0(\mathbf{R}_I,Z_I,N_e)$ is a continuous function of (i) the positions of the nuclei $\mathbf{R}_I$, (ii) the nuclear charges $Z_I \le 0$, and (iii) the number of electrons $N_e$ of a molecule.
Partial derivatives  of observables such as $E_0$ with respect to the nuclear charges (constant $\mathbf{R}_I$ and $N_e$) are called alchemical derivatives and can be used to perturb a reference molecule and obtain efficient estimates of solutions for multiple target molecules via the Taylor series expansion.
As such, iso-electronic alchemical changes take place within the same Hilbert space populated by all the solutions to Schr\"odinger's equation for {\em any} combination of real values for $\{Z_I,{\mathbf{R}_I}\}$.  Obviously, comparison to experimental realizations are only meaningful when all nuclear charges assume integer positive values.

Due to the Hellmann-Feynman theorem, the first alchemical derivative can be obtained analytically and typically at negligible additional cost. \cite{4DEDF,Levy1978}
The second derivatives of the ground state energy with respect to $N_e$, $R$ and $Z$ and their mixed partial derivatives constitute a unified Hessian matrix \cite{anm} which is a generalization of the "geometrical" Hessian matrix, in which only the derivatives with respect to the nuclear coordinates are included, and which can be diagonalized in order to generate a complete basis in which chemical compound space can be expanded.
Rigorously rooted in Rayleigh-Schr\"odinger-perturbation theory, APDFT is an approximate method in practice.
While other (uncontrolled) approximations are common in DFT, the approximate nature of APDFT has not yet been explored in full. As such, it is highly desirable to obtain at least an estimate of the error associated with alchemical estimates for given reference calculations and given perturbation orders.
Control of prediction errors represent an important goal for computational materials design efforts,
as meaningful trade-offs between a calculation's cost and its accuracy can be established.

Note that while in principle the concept of alchemical prediction applicable to all electronic properties\cite{apdft}, here we focus on the ground state energy $E_0$.
More specifically, we give a comprehensive discussion of the sources of errors from a practical point of view, i.e. also including those sources of errors which are not necessarily inherent to APDFT \textit{per se} but rather result from restrictions in present quantum chemistry codes. We explain the relevance of the various sources of errors and give a correction for the error in energy resulting from atomic basis sets (validated on pyridine, bipyridine and triazine). Based on a set of diatomics, we calibrate a measure for the error of quantum alchemy. Finally, we demonstrate that APDFT calculations of vibrational frequencies in dimers can be nearly as good as the reference method employed (CCSD), and more accurate than common DFT approximations.
\subsection{\label{sec:level1}Alchemical Perturbation Density Functional Theory}
Following earlier work\cite{apdft} where details on the derivation are given, we  define the alchemical coordinate $0 \le \lambda \le 1$ as a linear transformation of the nuclear charges from the reference vector of nuclear charges $Z^\text{R}$ to the target $Z^\text{T}$. For atom $I$:
\begin{equation}
  \begin{aligned}
  Z_I(\lambda) &\equiv Z_I^\text{R} + \lambda (Z_I^\text{T}-Z_I^\text{R}) = Z_I^\text{R} + \lambda  \Delta Z_I
\end{aligned}
\end{equation}

For isoelectronic changes, the total electronic ground state energy of the molecule is continuous and differentiable in $\lambda$. \cite{Lilienfeld2009} The function $E(\lambda)$ can be expanded as Taylor series centered at $\lambda=0$, i.e. at the reference molecule. With the energy of the reference molecule $E^\text{R} = E(\lambda=0)$ and its derivatives, we can approximate the energy of the target molecule $E^\text{T}= E(\lambda=1)$.

\begin{equation}
  \begin{aligned}
   E^\text{T} &= \sum_{n=0}^{\infty}{ \frac{1}{n!} \left.\frac{\partial^n E(\lambda)}{\partial \lambda^n}\right|_{\lambda=0}}= E^\text{R} + \sum_{n=1}^{\infty}{ \frac{1}{n!} \left.\frac{\partial^n E(\lambda)}{\partial \lambda^n}\right|_{\lambda=0}}
\end{aligned}
\end{equation}
The first derivative can be evaluated via the Hellmann-Feynman theorem\cite{HF_theorem_Feynman}:
\begin{equation}
\begin{aligned}
\label{firstderiv}
\left.\frac{\partial E}{\partial \lambda}\right|_{\lambda=0} & = \bra{\psi_\text{R}}\hat{H}_\text{T} - \hat{H}_\text{R} \ket{\psi_\text{R}} \\
\end{aligned}
\end{equation}
which can be evaluated analytically for any wavefunction-based or density-based quantum chemistry method. Given the electron density, one finds~\cite{Lilienfeld2009}:
\begin{equation}
\begin{aligned}
\label{eq_1st_deriv_int}
\frac{\partial E}{\partial \lambda} & = \int_\Omega d \mathbf{r}(v_\text{T}(\mathbf{r})-v_\text{R}(\mathbf{r})) \rho(\mathbf{r},\lambda)
\end{aligned}
\end{equation}
with the external potentials $v_\text{R}$ and $v_\text{T}$ corresponding to reference and target systems, respectively.
From this it is clear that Eq.~\ref{eq_1st_deriv_int} can be written in terms of higher order perturbations of the electron density alone~\cite{apdft}
\begin{equation}
\begin{aligned}
\label{rho_deriv_eq}\frac{\partial^{n+1} E}{\partial \lambda^{n+1}}
=\int_\Omega d \mathbf{r}(v_\text{T}(\mathbf{r})-v_\text{R}(\mathbf{r})) \frac{\partial^n \rho(\mathbf{r},\lambda)}{\partial \lambda^n}
\end{aligned}
\end{equation}
Combining Eqs.~\ref{rho_deriv_eq} and 2, one obtains
\begin{equation}
E^\text{T} = E^\text{R} + \int_\Omega d \mathbf{r}(v_\text{T}(\mathbf{r})-v_\text{R}(\mathbf{r}))
\tilde{\rho(\mathbf{r})}
\end{equation}
---an orbital free density functional which is exact provided that (i) $E^\text{R}$ is exact and that (ii) the Taylor expansion converges, and where the averaged density $\tilde{\rho}$ is given by
 $\tilde{\rho(\mathbf{r})} = \sum_{n=1}^\infty \frac{1}{n!} \frac{\partial^{n-1} \rho(\mathbf{r},\lambda)}{\partial \lambda^{n-1}}|_{\lambda = 0} $.

The integrals \ref{eq_1st_deriv_int} and  \ref{rho_deriv_eq} can be obtained from numerical integration by projecting the one particle electron density on an integration grid
or analytically by contracting the one particle density matrix with the nuclear attraction operator in atomic orbital basis. Both method are equivalent provided a suitable integration grid is used.

In this work, we evaluate the derivatives of the electron density via finite differences on an evenly spaced five point stencil with $\Delta\lambda= 0.05$. Based on previous results, this stencil yields good numerical stability\cite{apdft}. The stencil coefficients have been calculated\cite{FDcoeffs} such that the leading error term is $\mathcal{O}(\Delta\lambda^5)$.
In practice, the infinite sum from the Taylor expansion is truncated after the perturbation order $n$. Estimates made using all terms up to order $n$ are denoted by APDFT$n$.
\subsection{Sources of prediction errors}
Calculating the alchemical derivatives via finite differences requires the evaluation of the density derivatives in the basis set of the reference. While plane wave calculations use the same basis set for target and reference, atom-centered orbital basis sets do not. Atomic orbitals are commonly chosen because are a reliable and inherently local way to represent the wave function in molecules.

Consequently, using atom-centered basis sets means that APDFT derivatives actually build up the energy of the target molecule in the basis set of the reference molecule. With atomic orbital basis sets being optimized for each element, this results in a potentially noticeable error in the target energy.

The energy of the target molecule with the basis set of the reference $E^\text{T[R]}$ is in general different and usually higher than the energy of the target with its  optimized basis set $E^\text{T[T]}$. We define the energy error due to the use of the reference basis set $\Delta E_\text{BS}$ as the difference between these energies.
\begin{equation} \label{dEbs_def}
     \Delta E_{\textrm{BS}} \equiv E^\text{T[R]} - E^\text{T[T]}
\end{equation}

In contrast to this error, the truncation of the Taylor series to a certain number of leading terms introduces other errors. This error contribution is equal to the difference between the predicted energy $E^\text{APDFT}n$ and the energy of the target molecule $E^\text{T[R]}$ evaluated with the basis set of the reference molecule:
\begin{equation}
     \Delta E_\text{trunc} \equiv E^\text{APDFT} -E^\text{T[R]}
\end{equation}

Besides these higher order terms, practical implementation details commonly introduce two more sources of error: i) the error in the estimation of derivatives due to the finite difference scheme and ii) the error from numerical integration of the Coulomb interaction with the perturbed densities. These two errors can potentially be minimized by choosing a more numerically stable integration grid or a more accurate finite difference stencil.

As such, we view the intrinsic error of APDFT$n$ as the sum of two dominating contributions, one due to the truncation of the Taylor series at order $n$, and the other one due to using the basis set of the reference molecule:
\begin{equation}
    \begin{aligned}
     \Delta E_{\textrm{APDFT}}&=E^{\textrm{APDFT}}-E^{\textrm{T[T]}}\\
     &=   E^{\textrm{APDFT}}-E^{\textrm{T[R]}}+E^{\textrm{T[R]}}-E^{\textrm{T[T]}}\\
     &= \Delta E_{\textrm{trunc}}+\Delta E_{\textrm{BS}}
    \end{aligned}
\end{equation}
While the truncation order can be controlled through increase of $n$ (as long as the Taylor expansion converges), basis set effects have been studied less.

\subsection{Correction for Atom-Centered Orbital Basis Sets} \label{bsc_def_sect}
For small to medium atomic basis sets, the error contributions $\Delta E_\text{BS}$ which arise from representing the density derivatives in the basis set of the reference molecule dominate the total deviation from a self-consistent evaluation of the target molecule. Technically, the exact error $\Delta E_\text{BS}$ can be recovered by including alchemical derivatives w.r.t. the basis set coefficients\cite{zachara2012}. This, however, would substantially increase the computational cost as we go to higher orders in the perturbation. While the error vanishes in the complete basis set limit (see numerical evidence below), a correction constitutes a worthwhile alternative, enabling accurate absolute energy estimates while remaining cost-effective. Note that relative energies, such as atomization energies, are less affected by this problem due to a cancellation of all those error-contributions which are independent of the atomic environment.

To motivate the correction, we observe that the largest contribution to the total electrostatic energy of the molecule is given by the core orbitals, thus we can also assume that the main contribution in $\Delta E_\text{BS} $ is due to the change in the core orbitals' coefficients. This is both because the core orbitals have a larger contribution to the total energy than valence orbitals and because they are less flexible than their valence counterparts.\\

If $\Delta E_\text{BS} $ is predominantly unaffected by the chemical environment we can approximately estimate it using the full dissociation limit, i.e.~the individual free atoms. For each  atom $I$, an atomic contribution $\Delta E_\text{BS,I}$ is collected, the sum of which amounts to our approximate correction of $\Delta E_\text{BS}$

\begin{equation}
\Delta E_\text{BS} \approx \sum_{I} E^\text{T[R]}_I-E^\text{T[T]}_I \equiv  \sum_{I} \Delta E_{\text{BS},I}
\end{equation}
For every atom, $E_{\text{BS},I}$ is the difference between the free atom energy with the basis set of the reference element for that site minus the energy of the free atom with its proper basis set.\\

This correction has no effect on the shape of the potential energy surface, it does improve total energies with limited and constant additional computational effort, namely a single free atom calculation for each target element is required. For example, in order to study BN-doping in $sp^2$-hybridized carbon sites, four such elemental calculations are necessary, regardless of the number of target compounds: $E^\text{B[B]},E^\text{B[C]},E^\text{N[N]},E^\text{N[C]} $. Here, all free atom calculations have been performed in their their lowest electronic spin state. While certainly of interest, the study of alchemical changes involving other spin-state combinations is so substantial that it warrants a separate publication.

\subsection{Error From Reference Basis Set}
\begin{figure}[h!]
\includegraphics[width=\linewidth]{figures/Scatterplot_alchemy_vs_BasisSet.pdf}
\caption{The scatter plot shows the correlation between $\Delta E_\text{BS}$ and $\Delta E_{\text{APDFT}}$ for alchemical transmutations with $|\Delta Z|= 1$ (solid markers) and $|\Delta Z| = 2$ (hollow markers). Every pair of reference-target molecules within the 14 electron diatomic series is represented by a point for each APDFT order. The error shown is the median of all considered geometries. }
 \label{scatter_plt}
\end{figure}

For all alchemical absolute energy estimates within the diatomic iso-electronic series ($N_e$=14) for which the nuclear charges of reference and target molecule differ at most by 2, Figure~\ref{scatter_plt} shows the comparison between the basis set error $\Delta E_\text{BS}$ and the total error for all the different contributions for APDFT perturbation orders ranging from 2 to 5. Each panel corresponds to a different basis-set.
For all basis sets and perturbation orders,
we see substantially larger errors for $\Delta Z = \pm 2$ than for $\Delta Z = \pm 1$.
This is not surprising since the former also constitutes a much larger perturbation than the latter.
In view of the scales and the correlation between the overall APDFT error and the basis set contribution thereto, this suggests that the basis set contribution constitutes the dominating source of error. Moreover, the results indicate that the contribution is highly systematic especially when it comes to the smaller perturbation ($\Delta Z = \pm 1$).

For some basis sets (3-21G, 6-31G*, aug-cc-pVQZ), we observe clusters of errors, due to $\Delta E_\text{BS}$ being mostly constant for neighboring elements. In the case of aug-cc-pVQZ, the cluster is subdivided, as the contribution for $\Delta E_\text{BS}$ for elements within the second period is smaller than the contribution for those in the third period.
Also as $|\Delta Z|$ increases, we see less correlation between the total error and the basis set contribution. This is predominantly caused by the truncation of the Taylor series as shown by the higher order predictions being much more consistently off. In rare cases those two contributions become comparable in magnitude.

The convergence with expansion orders is slower with the minimal STO or Pople basis sets. Interestingly, one consequence is that higher order energies are not always an improvement over lower orders. As shown below, we attribute this to the representability of the alchemical density derivatives in those basis sets. Consequently, the overall magnitude of the errors in these basis sets is significantly higher than for e.g. the Karlsruhe basis sets, and we note that due to such erratic behavior, the use of APDFT in small basis-set calculations is {\em not} to be recommended.

In the cases of aug-cc-pVQZ, def2-TZVP and def2-QZVPP we obtained some negative basis set error. Those correspond to the alchemical transformations BeNe$\xrightarrow{}$ HeMg, BeNe$\xrightarrow{}$LiNa, BF$\xrightarrow{}$LiNa. In these transformations, the total number of core electrons decreases from target to reference. Since we used frozen core CCSD,a reduction of the correlation energy is observed, consequently leading to a total basis set error of negative sign.

For some noticeable outliers in Figure \ref{scatter_plt}, HeMg$\xrightarrow{}$BeNe and HAl$\xrightarrow{}$LiNa), even fourth order contributions for the largest basis set still yield significant residual differences. Note that in all these cases, an atom from the first period is used as a reference for an atom from the second period with a substantially increased electronic extend.
Consequently, we must caution against the use of APDFT across periods when using nuclear charges only.
\subsection{Quantifying the Basis Set Derivative Error} \label{AOerror}
\begin{figure}
\includegraphics[width=\linewidth]{figures/bs_error_stats.pdf}
\caption{Dependence of $\Delta E_{\text{BS}}$ on basis set type and size.
For alchemical transmutations within diatomics containing elements of the second period (BeNe, BF, CO, and NN) grouped by $|\Delta Z|$ are shown the median, the 10$^\text{th}$ and 90$^\text{th}$ percentile of $\Delta E_{\text{BS}}$. }
\label{bs_error_stat}
\end{figure}

\begin{table}
\begin{tabular}{lrrr}
\toprule
Basis set &  \ \ \ \ $\Delta Z=\pm 1 $ & \ \ \ \ $\Delta Z =\pm 2$ & \ \ \ \  HAl $ \leftrightarrow $ HeMg \\
\hline
\midrule
        STO-3G\rule{0pt}{12pt}  &       2215 &     8519 &    1684 \\
        STO-6G &       2238 &     8460 &    1687 \\
         3-21G &       1855 &     6956 &      1775 \\
        6-31G* &       1862 &     6947 &     1762 \\
      cc-pVTZ &        553 &     2382 &      1260 \\
  aug-cc-pVQZ &         23 &      190 &        1144 \\
    def2-TZVP &        105 &      552 &    1081 \\
   def2-QZVPP &         12 &       89 &     100 \\
\end{tabular}
\label{tab_bse}
\caption{Median of $\Delta E_{\text{BS}}$[mHa] for second period diatomics with $\Delta Z = \pm 1,2$ and for the pair HAl, HeMg ($\Delta Z = \pm 1 $).}
\end{table}

All sources of error depend on the basis set chosen for the reference calculation. By and large, the basis set error tends to be smaller for more expanded basis sets, approaching zero in the complete basis set limit. Since for some dimer pairs in this work the number of core electrons is not constant under alchemical transformation which can lead to an additional error for frozen-core CCSD, we  divided our dimer set into two subsets: HAl, and HeMg as well as BeNe, BF, CO, and NN. Within each subset, the number of core electrons remains constant under alchemical transformation between any set element.
As shown in Figure~\ref{bs_error_stat} and Table \ref{tab_bse}, we find Karlsruhe def2 basis sets to be the most reliable in the context of alchemical changes as they outperform any other basis set family, in particular considering their number of basis functions. \\
The Karlsruhe basis set def2-TZVP has a basis set contraction scheme (11s,6p,2d,1f) $\rightarrow$ [5s,3p,2d,1f] similar to the cc-pVTZ basis set (10s,5p,2d,1f) $\rightarrow$ [4s,3p,2d,1f]. Even though they differ only by one $s$ base function the error for second row elements in cc-pVTZ is five fold higher than in def2-TZVP. \\
If we look at the quadruple-zeta basis set, def2-QZVPP with a second period contraction scheme of (15s,8p,3d,2f,1g) $\rightarrow$ [7s,4p,3d,2f,1g] is a substantially smaller basis set than aug-cc-pVQZ with a contraction scheme of (16s,10p,6d,4f,2g) $\rightarrow$ [9s,8p,6d,4f,2g]. Despite def2-QZVPP being smaller in number of basis functions, it performs better than aug-cc-pVQZ for APDFT, with typically half the error for $\Delta E_\text{BS}$.
The reasons for this may be found in the optimization procedures of these basis sets. For example, the first order energy derivative for vertical changes by virtue of the chain rule can be written as
\begin{align}
    \frac{\partial E}{\partial \lambda} = \sum_I \frac{\partial E}{\partial Z_I} + \sum_i \frac{\partial E}{\partial c_i}
\end{align}{}
where the second sum represents the contribution of the basis set coefficients $c_i$ as they change from the reference to the target molecules. By construction\cite{def2tz,def2qz}, the first order terms for HF are zero for the def2 basis set family which might contribute to the good performance in the context of APDFT.

As discussed above, we treated the alchemical transmutation  HAl $ \leftrightarrow $ HeMg  independently. In that case, the best results were obtained  with def2-QZVPP basis set, as shown in the SI. In this case, the basis set error is 100\,mHa, one order of magnitude smaller than the error for any other basis set.
\subsection{Correcting the Basis Set Derivative Error} \label{AOcorrection}
As shown above, choosing appropriate atomic orbitals basis sets can significantly reduce the overall error in APDFT. Still, even in our best case (def2-QZVPP), such error is on the order of tens of milli-Hartree, while for other smaller basis sets the error is up to two orders of magnitude larger. With the simple correction (see section \ref{bsc_def_sect}), however, this error can be substantially reduced for all basis sets, as shown in Figure~\ref{bs_corr}.

\begin{figure}[t]
    \includegraphics[width= \linewidth]{figures/boxplot.pdf}
    \caption{Systematic reduction in signed error $E^\text{T[T]}-E^\text{T[R]}$ due to the basis set correction we suggest, here shown for def2-QZVPP and the diatomic pairs of the  second period. For every alchemical transmutation (labeled reference/target in the figure) different interatomic distances lead to slightly different errors shown in boxplots. The red line is the median of the distribution, and the arrows indicate the shift due to the correction outlined in section~\ref{bsc_def_sect}.}
    \label{bs_corr}
\end{figure}

Due to the inclusion of several interatomic distances for each dimer in our data set, we always have a distribution of errors that covers the thermally accessible range. Since the correction is based on free atoms, it is independent of the interatomic distances. Consequently, the correction always moves the whole error distribution. As shown in Figure~\ref{bs_corr}, the signed error is consistently improved, since the largest error source is approximately corrected for. It is remarkable that for the cases with $\Delta Z = \pm 1$, the basis set error can be reduced to few milli-Hartree for our large span of interatomic distances.
With the exception of the case BeNe $\rightarrow $ BF, the correction generally overestimates the error. In molecules the orbitals placed on different atoms can overlap (superposition). As a consequence the basis set for each atom is more complete and thus the $\Delta E_\text{BS}$ is lower for molecular species than for isolated atoms.
\subsection{Truncation Error}
\begin{figure}[ht]
\includegraphics [width=\linewidth]{figures/trunc_err_plot.pdf}
\caption{Correlation between $ \Delta E_\text{trunc}$ and the electron density displacement $\left\lVert \Delta \rho \right\rVert$. Each panel shows the median of the error for one basis set for the different truncation orders in APDFT. For comparison, horizontal lines denote the mean absolute error of Hartree Fock and MP2 calculations, respectively. }
\label{median_error}
\end{figure}

As with any truncated series expansion, APDFT suffers from truncation errors, i.e. the total contribution from higher order terms in the series expansion:
\begin{align}
    \Delta E_\text{trunc} = E^\text{APDFT} -E^\text{T[R]}
\end{align}{}
An \textit{a priori} estimation of the truncation error would be highly valuable to judge the accuracy of APDFT estimations and, consequently, to define a trust region  similar to a convergence radius where the extent of the region is derived from the required accuracy with regards to the reference method.

Based on earlier work for crystal systems \cite{Chang2018}, we propose to use the integrated absolute electron density difference $\Delta \rho \equiv \rho^{\mathrm{T}}(\mathbf{r}) - \rho^{\mathrm{R}}(\mathbf{r})$ between reference and target as proxy of the error:
\begin{align}
\label{deltarho}
    \left\lVert \Delta \rho \right\rVert\equiv
    \int_\Omega d\mathbf{r} |\Delta \rho (\mathbf{r})|
\end{align}{}

Since alchemical energy derivatives are evaluated through the alchemical perturbations of the electron density, two systems are close to each other if and only if they possess similar electron densities. In this way, a small density change in the alchemical path results in a small error. In the limit of $\left\lVert \Delta \rho \right\rVert  =0 $, reference and target are identical and the error in alchemical energy prediction is zero. Note that this integral is only weakly sensitive to changes in level of theory or basis set, as the corresponding differences in electron density are minute. This allows for simple evaluations in practice where the electron density of a low level of theory  or even  atomic densities can serve as substitute of the self-consistent electron density for the purpose of error estimation.

Figure \ref{median_error} shows that the error of APDFT correlates with $\left\lVert \Delta \rho \right\rVert$ for APDFT2 to APDFT5  for representative basis sets. The consistent trends observed in that figure allow us to give an empirical formula for the unsigned truncation error. We see that this error increases exponentially with the integrated absolute charge difference for diatomic molecules. Different expansion orders yield different steepness of this relation only.

To put the focus of the empirical error estimation on small truncation errors, we propose to fit a linear function to the logarithmized data:

\begin{equation}
\label{alpha_beta_eq}
    \log(|\Delta E_{\mathrm{trunc}}|) \approx  \alpha + \beta \left\lVert \Delta \rho \right\rVert
\end{equation}
where the coefficients $\alpha$ and $\beta$ are found via a fit for each APDFT order and basis set. Table~\ref{alpa_beta_coeffs} shows the resulting fits. With this empirical fit, we can estimate the expected error for APDFT numbers without any additional DFT calculations. It is of great value in practise to have an expected uncertainty associated with every APDFT energy.

For more complex molecules we can consider the size-consistency of APDFT and of its error. If more than one transmutation is done on non-interacting independent sites, the total error is decomposed in a sum of site-defined contributions.

\begin{table}[ht]
    \begin{tabular*}{\linewidth}{lr @{\extracolsep{\fill}} rrr}
    \toprule
      Basis set &  $n$ & $\alpha$ [$\log(\text{Ha})$]  & $\beta$ [$\log(\text{Ha})e^{-1}$] & $R^2$ \\
\hline
\midrule
STO-6G & \rule{0pt}{12pt} 5 & -3.161 &  0.522   &  0.95     \\
6-31G* &              5 &     -3.572 &  0.480   &  0.97     \\
aug-cc-pVQZ &        5 &     -3.743 &  0.416    &  0.97     \\
def2-QZVPP &         1 &      0.047 &  0.172     &  0.88 \\
def2-QZVPP &         2 &     -2.355 &  0.273    &  0.84    \\
def2-QZVPP &         3 &     -2.806 &  0.314    &  0.98    \\
def2-QZVPP &         4 &     -3.643 &  0.388    &  0.94    \\
def2-QZVPP &         5 &     -3.973 &  0.442    &  0.92    \\
    \end{tabular*}
    \caption{The fitting parameters $\alpha$  and $\beta$ which describe the total truncation error for APDFT of order $n$ according to Eq.~\ref{alpha_beta_eq} the data are extracted from the binned values shown in Figure~\ref{median_error}. }
    \label{alpa_beta_coeffs}
\end{table}

Due to symmetry of the dimers\cite{apdft}, the error is similar for second and third order as well as for fourth and fifth order.
For small $\left\lVert \Delta \rho \right\rVert$, higher order APDFT performs substantially better than lower order ones, while for large $\left\lVert \Delta \rho \right\rVert$ the error obtained with different APDFT orders becomes comparable. We attribute this to the finite precision of the density derivatives as obtained from finite differences where for larger changes in $\Delta Z$ numerical noise is amplified.

In Figure \ref{median_error} the comparison of the truncation error between different basis sets gives results similar to those obtained for the basis set error earlier. In fact, more expanded basis sets yield lower $\Delta E_\text{trunc}$ than smaller ones and the triple and quadruple zeta basis set give very good results: for APDFT4 with $\left\lVert \Delta \rho \right\rVert < 5e $ the error is less than 10\,mHa. The best performance again was obtained with the def2 basis set: for def2-QZVPP APDFT performs better than MP2 up to $\left\lVert  \Delta \rho \right\rVert=6e$ (indicative of $\Delta Z\le 2$) and performs better than HF up to $\left\lVert \Delta \rho \right\rVert=8e$ ($\Delta Z =3$).
\subsection{Vibrational Frequencies\label{pes_sect}}

\begin{figure}[ht]
    \centering
    \includegraphics[width=\linewidth,height=300pt]{figures/freq_graph.pdf}
    \caption{Homolytic bond dissociation energy $E_{\text{BD}}$ and harmonic vibrational frequencies $\nu_{\text{harm}}$ of CO, NN and BF calculated at  CCSD, MP2, HF, PBE, B3LYP and APDFT5 level of theory. For APDFT the basis set correction from section \ref{bsc_def_sect} is included. All data shown for the def2-QZVPP basis set.}
    \label{pes_curves}
\end{figure}
\begin{table}[ht]
    \begin{tabular*}{\linewidth }{lrr@{\extracolsep{\fill}}r}
\toprule
\vspace{5pt} Method & \ \ \ \ Bond Energy  & \ \ \ \ \ Bond Length  &    $\nu_\text{{harm}}$  \\
\midrule
\hline
\textbf{CO $\rightarrow $ NN} &\rule{0pt}{12pt} & &\\
APDFT1 &  1827.97 &  1.90 &  3118 \\
APDFT2 &  -210.76 &  2.07 &  2425 \\
APDFT3 &  -219.71 &  2.08 &  2388 \\
APDFT4 &  -214.22 &  2.07 &  2445 \\
APDFT5 &  -214.29 &  2.07 &  2444 \\
HF &  -117.32 &  2.01 &  2728 \\
MP2 &  -235.28 &  2.10 &  2197 \\
PBE &  -243.22 &  2.08 &  2347 \\
B3LYP &  -228.07 &  2.06 &  2453 \\
\vspace{5pt} CCSD &  -213.43 &  2.07 &  2439 \\
\hline
\textbf{NN $\rightarrow $ CO} &\rule{0pt}{12pt} & &\\
APDFT1 &  1805.18 &  1.93 &  2954 \\
APDFT2 &  -250.73 &  2.12 &  2270 \\
APDFT3 &  -250.73 &  2.12 &  2270 \\
APDFT4 &  -248.22 &  2.13 &  2222 \\
APDFT5 &  -248.22 &  2.13 &  2222 \\
HF &  -175.58 &  2.08 &  2427 \\
MP2 &  -269.41 &  2.14 &  2133 \\
PBE &  -268.94 &  2.14 &  2134 \\
 B3LYP &  -254.52 &  2.12 &  2211 \\
 \vspace{5pt} CCSD &  -247.87 &  2.12 &  2234 \\
\hline
\textbf{BF $\rightarrow $ CO} &\rule{0pt}{12pt} & &\\
APDFT1 &  1781.15 &  1.97 &  2800 \\
APDFT2 &  -232.08 &  2.10 &  2358 \\
APDFT3 &  -252.25 &  2.13 &  2247 \\
APDFT4 &  -250.84 &  2.13 &  2218 \\
\vspace{5pt} APDFT5 &  -249.58 &  2.13 &  2228 \\
\hline
\textbf{CO $\rightarrow $ BF }& \rule{0pt}{12pt}& & \\
APDFT1 &  1893.64 &  2.08 &  2250 \\
APDFT2 &  -195.06 &  2.44 &  1314 \\
APDFT3 &  -183.34 &  2.42 &  1340 \\
APDFT4 &  -174.49 &  2.38 &  1441 \\
APDFT5 &  -174.34 &  2.38 &  1420 \\
    HF &  -137.70 &  2.35 &  1508 \\
   MP2 &  -188.87 &  2.39 &  1417 \\
   PBE &  -186.79 &  2.41 &  1350 \\
 B3LYP &  -179.79 &  2.38 &  1399 \\
   CCSD &  -176.17 &  2.39 &  1421 \\
    \end{tabular*}
    \caption{Comparison of dissociation profile in terms of homolytic bond dissociation energy [kcal/mol], bond length [Bohr] and vibrational frequencies [cm $^{-1}$] for different APDFT orders, HF, MP2, CCSD and the DFT functionals PBE and B3LYP.}
    \label{vibr_tabel}
\end{table}

Accurate estimates of potential energy surfaces  open up access to the application in vibrational spectroscopy. Even more so if the residual errors from either higher order terms or basis set intricacies are systematic around the minimum geometry configuration. \cite{Chang_bonds}
Starting from a scan of interatomic distances for one molecule, we have tested this application for APDFT energies at the same interatomic distance of a different isoelectronic molecule from our set. We then interpolated these points with a cubic spline to obtain both curvature and minimum of the target molecule. From the curvature, we calculated vibrational frequencies in the harmonic approximation.

Figure \ref{pes_curves} shows the error made by APDFT in comparison with the result that can be obtained with other computational methods. The alchemical prediction is accurate up to 2\,kcal/mol for the dissociation energies while the equilibrium bond distance is correct up to 0.01\,Bohr. Consequently, the dissociation profiles of the alchemical estimations overlay with the self-consistent CCSD profiles. In part, this is achieved thanks to the basis set correction described in section \ref{bsc_def_sect} that shifts the profile by a fixed energy, leaving minimal bond distances and the vibrational frequencies unchanged.

The dissociation profiles for other methods do not agree well with CCSD results. In particular MP2 and PBE yield errors for dissociation energies of up to 20\,kcal/mol compared to CCSD. In the right part of Figure~\ref{pes_curves} we can see that vibrational frequencies from APDFT are closer to the CCSD reference calculations than other established methods. For both energies and vibrational frequencies we observe that APDFT using perturbations of a higher level of theory can consistently outperform self-consistent results of lower levels of theory, as reported in Table~\ref{vibr_tabel}. This is particularly remarkable for vibrational frequencies which are much less affected by relative errors then total energies. Among the APDFT predictions, those are more accurate when reference and target have similar electronic structures, as example the predictions from CO to N$_2$ and \textit{vice versa} are better than the predictions from CO to BF and from BF to CO.
\subsection{APDFT derivatives on benzene \label{rings_sect} }
Finally, we show how the results from the dimer case can be transferred to larger molecules. To this end, we investigate three  targets: pyridine, pyrimidine and triazine.

With the reference molecule benzene being of D$_\text{6h}$ symmetry, and all sites being equivalent, we can reduce the number of derivatives that need to be calculated. For a APDFT3 only three derivatives of the electron density are needed to predict all targets, namely the first $\frac{\partial \rho}{\partial Z_1}$, the second $\frac{\partial^2 \rho}{\partial Z_1^2}$ and the second mixed $ \frac{ \partial^2 \rho}{\partial Z_1\partial Z_2}$, all of which were obtained by finite differences. \\

The basis set correction described in section \ref{bsc_def_sect} was obtained subtracting the CCSD energy of a nitrogen atom with its proper basis functions from the CCSD energy of an isolated nitrogen atom with the basis set of a carbon atom and a ghost hydrogen:
\begin{equation}
    \Delta E_{\text{corr}} = E^{\text{[N][C-H]}}-E^{\text{[N][N]}}
\end{equation}

The value of $\Delta E_{\text{corr}}$ was subtracted once for every CH to N transmutation in the alchemical transformation.
Based on the results in section \ref{AOerror}, we chose the def2-TZVP basis set as a compromise between cost and accuracy.
\begin{figure}[ht]
    \centering
     \includegraphics[width=\linewidth,keepaspectratio]{figures/benz_pyr.pdf}
    \caption{ $\Delta E$ in the prediction of the total energies of pyridine, pyrimidine and triazine. APDFT3 energies are calculated from a benzene reference. The results were obtained using CCSD/def2-TZVP.}
    \label{rings}
\end{figure}

\begin{table}[ht]
    \centering
    \begin{tabular*}{\linewidth}{{l @{\extracolsep{\fill}} rrr}}
    \toprule
     \vspace{5pt}& Pyridine & Bipyridine & Triazine \\
    \hline
    \midrule
     $\Delta E_\text{trunc}$ \rule{0pt}{12pt}   & -8.73 & -17.98 &  -27.74  \\
    $\Delta E_\text{BS}$   & 55.09 & 110.37 & 165.90 \\
    $\Delta E_\text{APDFT}$  & 46.35 & 92.38 & 138.16 \\
    Correction  & -65.64 & -131.28 & -196.92 \\
    Error after correction  & -19.28 & -38.90 & -58.76 \\
    \end{tabular*}
    \caption{Errors and corrections in the APDFT3 predictions of pyridine, pyrimidine, triazine from benzene, using CCSD/def2-TZVP, as shown in Figure \ref{rings}.}
    \label{tab:rings}
\end{table}

Figure \ref{rings} and Table \ref{tab:rings} show errors and corrections for the predictions of pyridine, bipyridine, and triazine.

From the results we can see that $\Delta E_\text{BS}$ is roughly six times larger than $\Delta E_{\text{trunc}}$ and constitutes the dominating source of error, both errors increase with an approximately linear trend with the number of transmuted atoms.
The basis set correction obtained overestimates the basis set error by a sixth, as observed earlier in section \ref{AOcorrection}. The truncation error is negative in sign therefore after the correction it cancels to some degree with the error in the correction, nevertheless corrected prediction is still improved by a factor of 3.\\
If we consider the total difference in the energy of benzene and pyridine of 16.019 Ha, it is remarkable that the error with APDFT3 of 19.28\,mHa constitutes 0.12\,\% of the  total energy difference.
\section{Conclusion}
In this work we analysed prediction errors in APDFT\cite{Lilienfeld2009,apdft} in terms of atomic basis set effects as well as perturbation order in the context of its application to energetics and vibrational frequencies in iso-electronic diatomics, as well as for mutating benzene to pyridine, pyrimidine, and triazine.

Our numerical results indicate that absolute energy estimates are dominated by two main sources of error: Truncation of the Taylor expansion and differences in basis sets between reference and target compound. The error due to basis set can be considerable for small basis sets, while parametrically optimized basis sets such as the Karlsruhe basis sets yield reasonably accurate alchemical derivatives. For this error source, we proposed a single atom correction which is easily implemented.

The error due to the Taylor expansion truncation has been shown to be related to the total displacement of electronic charge between reference and target molecule. We provide linear fits as an empirical relation between the two which can help to estimate the expected accuracy of an APDFT energy up to order $n = 5$ . We show that this error for small $|| \Delta \rho ||$ and for APDFT5 can  be as small as 1\,kcal/mol for the largest basis set considered.

Regarding the prediction of vibrational frequencies, we have observed that APDFT based on CCSD calculations can reproduce the shape of dissociation curves better than GGA (at second order for $\Delta Z=1$) and B3LYP or MP2 (at fifth order). Consequently, quantities derived from these curves, such as equilibrium distances or vibrational frequencies, are also more predicted more accurately using APDFT than using DFT.

While obtaining the alchemical derivatives from finite differences is expensive for higher orders, we showed in that good predictions can regularly be achieved already at APDFT3 level--even for vibrational frequencies. In this work, we use $n+1$ additional single points for all APDFT terms up to and including $n$-th order. APDFT becomes cost effective for problems with a large number $N $ of transmutation sites. APDFT3 requires $1+N+N^2$ single point calculations without any symmetry, while the number of possible targets increases in a combinatorial manner ($\simeq 2^N$). Symmetry can be used to further reduce the required number of reference QM calculations\cite{apdft}. This scaling behaviour renders APDFT suitable for exploring large chemical spaces from much fewer reference calculations than potential targets.

redpajama_set_name: RedPajamaArXiv


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text:
Q: A Theorem On Compact Connected Metric Spaces by Stadje I recently came across a surprising theorem, due to Wolfgang Stadje, a special case of which states that:

Let $(X,d)$ be a compact connected metric space. Then there exists a unique real number $c$ such that for any positive integer $n$, and for any $x_1,\ldots,x_n\in X$, there exists $x\in X$ such that $$c=\frac{1}{n}\sum_{i=1}^n d(x,x_i)$$

The original proof of the general statement can be found here.
This proof is unaccessible to me.
Since this proof was published in 1981, it is possible that simpler proofs have been found in subsequent years, especially for the special case mentioned above.
I haven't been able to find any other proof on the internet though.
Does anybody know a more accessible proof of the result mentioned above?

A: $\newcommand{\mc}{\mathcal}$
$\newcommand{\lrset}[1]{\left\{#1\right\}}$
$\newcommand{\set}[1]{\{#1\}}$
$\newcommand{\R}{\mathbf R}$
We will just show the existence of $c$.
For a fixed $n$ and a tuple $x=(x_1 , \ldots, x_n)\in X^n$, define
$$
\mc I(x) =
\lrset{
\frac{1}{n}\sum_{i=1}^n d(x_i, p):\ p\in X
}
$$
The compactness and connectedness of $X$ implies that $\mc I(x)$ is a closed interval.

Lemma 1. Let $x=(x_1 , \ldots, x_n)$ and $y=(y_1 , \ldots, y_n)$ be points in $X^n$.
  Then $\mc I(x)$ and $\mc I(y)$ have non-empty intersection.

Proof.
Suppose not.
Then without loss of generality assume that $\sup \mc I(x)< \inf \mc I(y)$.
Then for all $p$ and all $q$ in $X$ we have that
$$
\sum_{i=1}^n d(x_i, p)< \sum_{j=1}^n d(y_j, q)
$$
This implies
$$
\sum_{i=1}^n d(x_i, y_k) < \sum_{j=1}^n d(y_j, x_\ell)
$$
for all $1\leq k, \ell\leq n$.
Therefore
$$
\sum_{k=1}^n\sum_{i=1}^n d(x_i, y_k) < \sum_{\ell=1}^n\sum_{j=1}^n d(y_j, x_\ell)
$$
But this is a contradiction since LHS and RHS are equal in the last expression.

Lemma 2.
  Let $x=(x_1 , \ldots, x_m)\in X^m$ and $y=(y_1 , \ldots, y_n)\in X^n$.
  Then $\mc I(x)$ and $\mc I(y)$ have non-empty intersection.

Proof.
Suppose not.
Then one of the following two happen
$$
\frac{1}{m}\sum_{i=1}^m d(x_i, p)< \frac{1}{n}\sum_{j=1}^n d(y_j, q), \quad \forall p, q\in X
$$
or
$$
\frac{1}{n}\sum_{j=1}^n d(y_j, q) < \frac{1}{m}\sum_{i=1}^m d(x_i, p), \quad \forall p, q\in X
$$
Without loss of generality suppose the first happens.
Define the tuples
$$
\tilde x= (x_1 , \ldots, x_1,\ x_2 , \ldots, x_2,\ldots,\ \underbrace{ x_i , \ldots, x_i}_{n \text{ times}},\ \ldots,\ x_m , \ldots, x_m)
$$
$$
\tilde y= (y_1 , \ldots, y_1,\ y_2 , \ldots, y_2,\ldots,\ \underbrace{ y_j , \ldots, y_j}_{m \text{ times}},\ \ldots,\ y_n , \ldots, y_n)
$$
By our assumption, it follows that $\mc I(\tilde x)$ and $\mc I(\tilde y)$ do not intersect.
This contradicts Lemma 1.

Lemma 3.
  Let $\set{\mc I_\alpha}_{\alpha \in J}$ be a collection of closed intervals in $\R$, each contained in $[0, D]$, where $D$ is a positive constant.
  Then the intersection $\bigcap_{\alpha\in J}I_\alpha$ is non-empty.

Proof.
It is easy to prove that every finite subcollection of $\set{I_\alpha}_{\alpha\in J}$ have a non-empty intersection.
Then by the compactness of $[0, D]$ we infer that the desired intersection is also non-empty.
Now we are in a position to finish the proof of the theorem.
By Lemma 2 we have that for any $m$ and $n$ the intervals $\mc I(x)$ and $\mc I(y)$ intersect for any $x\in X^m$ and $y\in X^n$.
Now by Lemma 3 we infer that the intersection $\mc I:=\bigcap_{x\in \mathbf X}I(x)$ is non-empty, where $\mathbf X=\bigcup_{n=1}^\infty X^n$.
Any point $c$ chosen in $\mc I$ satisfies the requirement of Theorem.

redpajama_set_name: RedPajamaStackExchange


I'm impressed at how much Susie has taught my young daughter in just a few months. Susie is patient and encouraging. She gives her the confidence to excel. She is excited to go to her lesson every week!
My son practiced piano with Susie for several months when he was 3 1/2 years old. Although he was on the younger side, Susie welcomed him into her studio and worked patiently with him. Susie did a great job tailoring the lessons to his level and introduced fun and creative games to make learning music fun for him and keep him engaged. Susie is warm, sweet, and very easy to talk to. She will make you and your child feel immediately at ease when you walk into her studio. Her lessons offer the perfect balance of rigor and fun with the comfort that Susie is there to support your musical interests. Susie is a wonderful kind and creative piano teacher and I would recommend her enthusiastically to anyone looking for piano lessons.
I had piano lessons with Susie for a few months before I moved out of the area. In that short time my playing improved far beyond the plateau I'd reached on my own. This was the fastest progress I've ever made at the piano.
As an adult (lazily) pursuing the piano as a hobby, lessons normally take the fun out of playing. Susie had no problem adapting to my casual relationship with the instrument. She was able to help me with music theory, mechanical problems in my left hand, and finger placement, but all of this learning took place within the context of a piece that I really enjoyed. This was much more effective than lessons I've had in the past, where theory and technique were isolated from the learning of actual music.


On one those perfect sunny days of Summer, pack up the family and venture out to a local farm. Farm stands are great places for kids of all ages. Many offer hayrides, playgrounds, tours and other outdoor activities. Some farms offer "pick you own" programs, where you and the family can wander the fields and select your own fruits and vegetables to take home.
Talk to the people who work on the farm. They may offer to give you a special tour and to teach your children about farming. While you are shopping let each child pick out something new to try. If you have a baby, show them all the different colors, shapes and textures. Make it fun! One visit to a farm may inspire you to start your own garden at home!
Asking questions at the farm or farmers market: Ask open-ended questions. Instead of yes or no questions like – Do you use pesticides? Or, is your beef grass-fed? How about – How do you grow your strawberries (or corn, or tomatoes)? Or, How do you raise your beef (or chicken, or lamb)? Let the farmer tell you about what he does, most of them are more than happy to tell you all about what they do.
When were these fruits or vegetables picked?
What is the best way to cook or eat this?
What do you grow or raise?


Africans and the youth in particular are engaging much more actively in topics that impact us every day such as race and politics. One area that needs more focus and attention among the African youth is economics. The economy of Africa, the cornerstone of its renaissance, has more impact on the African individual, however we find external parties scrutinise and analyse the economy more than those directly affected by it. The onus is on us to do our research and share informed opinions.
This month Professor Mthuli Ncube, Professor of Public Policy at Oxford University and former Chief Economist at the African Development Bank, shared his views in a lecture in Johannesburg. He gave a diagnosis and possible solutions on African regions, their bottlenecks and their opportunities and pointed out 3 things that will impact Africa's economic outlook in the short to medium term: the Chinese economy, US interest rates movements and Commodities market.
East Africa is a prime example of how inter-regional activity can insulate global economic volatility. The rising stars in the region include Rwanda – Dubbed the 'Singapore of Africa', their success has been largely attributed to leadership and good governance. Kenya, Tanzania and Ethiopia, which grew at 10% in 2014, are also countries to watch.
In the West, Professor Ncube is particularly enthusiastic about Cote d'Ivoire, en route to becoming an emerging nation by 2020, their services industry has contributed significantly to GDP. Ghana and Nigeria will continue to be strong despite debt challenges and other economic issues.
Countries like Nigeria, Ghana and Angola have been negatively affected by the drop in the oil price. Nigeria's economy in particular is highly dependent on the oil price movement and has suffered currency depreciation. Further, China, the world's second largest crude oil consumer, is experiencing a slowdown in growth.
As a net exporter of commodities, Sub-Saharan Africa has been hurt by lower prices, however according to Makhtar Diop, World Bank Vice President for Africa, "The end of the commodity super-cycle has provided a window of opportunity to push ahead with the next wave of structural reforms and make Africa's growth more effective at reducing poverty".
Since 2008, SA's GDP has slowed to 1.8% per year, with unemployment hovering around the 25% mark. Labour issues, energy constraints and a weak currency have contributed to the contraction of the economy by 1.4% in the first quarter of 2015.
McKinsey Global Institute released a report in September identifying 5 opportunities that should reverse the negative trend, growing GDP by 1.1% per year and creating 3.4 million jobs. These opportunities include advanced manufacturing, infrastructure productivity, natural gas, service exports and raw and processed agricultural exports. The effective implementation of these various initiatives and SA's National Development Plan are central to achieving the growth figures Cyril Ramaphosa, the deputy president has claimed.
The United Nations (UN) estimates that Africa will have a population of 2.5 billion by 2050 – The Next Billion. "Currently 41% of the population is below the age of 15 and another 19% are between the ages of 19 and 24", the UN director of the Population Division, John Wilmoth has stated. These statistics present a great opportunity, provided the proper planning for and management of this population growth takes place.
The African Diaspora are a very important factor in the rise of the continent. Africans in various parts of the world can come back home and exercise their school of thought, build businesses, provide services and invest in their countries. Together, leaders and the diaspora should develop innovative solutions for growth.
An example of this is the Grand Ethiopian Renaissance Dam (GERD) that used what is termed as 'Diaspora Bond' to raise finance for the construction of a hydro power dam in Ethiopia. While it has its challenges, it's a great step involving those scattered across the globe.
China recently suffered a knock in its financial markets due to the slowdown of growth in its economy. Contagion resulted and the stock markets across the globe and emerging markets currencies plummeted (In SA, R14 to the dollar!), on what analysts have called 'Black Monday'.
The traditional trade relationship between Africa and China has been that Africa exports raw materials and imports manufactured goods from China. They are also the leading partner in our infrastructure development, these deals are linked to extractive industries proving China's slowing growth is unfavourable to African countries.
That said, Africa needs to make sure it gets "the best deal possible" for its natural resource exports, particularly with its largest trading partner China, to protect itself from global market turbulence, according to the new president of the African Development Bank, Akinwumi Adesina.
In the US, there's been speculation about the rise of interest rates, which after the recent plunge in financial markets and a strong US dollar, would be especially detrimental to African countries as, among other factors, debt commitments will be more painful to service.
An overall trend observed recently is that the world's developed economies and their markets are converging upwards, whereas emerging markets are slowing down and vulnerable.
The infrastructure deficit is commonly referred to as the single most important factor stifling Africa's growth. If we don't have adequate roads, buildings, commercial hubs, public transport systems, industrial plants such as power plants etc. we won't be able to unlock all our opportunities. Lack of access to suitable funding (structures), inadequate strategies and collaborative and integrated planning are probably the most important challenges in infrastructure development.
Critical however is, the structural transformation of the economy with growth strategies sensitive to equity and sustainability. This will help diversify the economy and pull the continent out of the commodity-dependent state it's in right now. This involves a value addition/beneficiation focus, investing in the services and manufacturing sectors (sometimes at the cost of the economy in the short-run). Of significance is education and skills development with investment in social infrastructure for health and well-being of the populace.
Hi Lilitha, excellent article! Yes, the world should be looking at Africa as the new emerging markets!
Awesome article! I enjoyed the fact that it talks about economics, us who are still studying can save it for next year and as well as international relations.
It has opened my eyes on how important it is as youth to fight in improving our country's economy and question the decision that are taken by our leaders where we kind of not going to benefit. However it is also important as youth to think out of the box and be more creative with our ideas in being more innovative in order to improve our economy and the lives of the South Africans.
Well Done Nolitha, great article and well researched.


Run for your little Sheep life and look dashing doing it!
Plan B is on the way, but for now we need to hit 'em good with Plan C!
Launch a Hobo out of a circus cannon!
Control different points of view as you work your way through a spooky jungle, and an eerie dungeon.


text:
Richard Gable Hovannisian (), né à Tulare (Californie) le , est un historien arméno-américain connu pour son histoire de la Première République d'Arménie en quatre volumes. Il est professeur émérite de l'Université de Californie à Los Angeles (UCLA).

Biographie

Origines familiales
Richard Hovannisian naît et grandit à Tulare, en Californie, au sein d'une famille ayant survécu au génocide arménien. Son père, Gaspar Gavroian, est né en 1901 dans le village de Bazmashen (ou Pazmashen, aujourd'hui Sarıçubuk), près de Kharpert, dans l'Empire ottoman. Il fuit le génocide et s'installe aux Etats-Unis vers 1920, où il adopte le nom de famille Hovannisian d'après le prénom de son père Hovhannes. En 1926, il se marie avec Siroon (Sarah) Nalbandian, elle aussi descendante de survivants des massacres. Ils ont ensemble trois fils : John (né en 1928), Ralph (né en 1930), et Richard Gable en 1932 (en hommage à Clark Gable).

Formation et carrière
Il fait ses études à l'Université de Californie à Berkeley, où il obtient son Bachelor of Arts en 1954, puis à l'Université de Californie à Los Angeles (UCLA) où il obtient son Master of Arts en histoire en 1958 et son doctorat en 1966.

Il commence à travailler à l'Université de Californie à Los Angeles en 1962 et est associate professor au Mount St. Mary's College (Los Angeles) de 1966 à 1969. Formé selon la méthode de l'historien allemand Leopold von Ranke, ses premiers travaux abordent le sujet de la Première République d'Arménie (1918-1920). Sa thèse de doctorat, qui devait au départ être une histoire complète de cet État, finit par ne constituer que la première partie d'une histoire en quatre volumes. Elle est publiée sous le titre Armenia on the Road to Independence en 1967, tandis que les tomes suivants sont publiés entre 1971 et 1996.

En 1986, Richard Hovannisian est nommé premier titulaire de la chaire d'histoire arménienne contemporaine à l'UCLA. En 2011, il reçoit de la part de l'association des élèves de l'UCLA le titre de « Professeur le plus inspirant » (« Most Inspiring Teacher »).

Il est membre du conseil d'administration d'un certain nombre d'organisations universitaires et humanitaires, notamment la Fondation Facing History and Ourselves Foundation, l'International Institute on the Holocaust and Genocide, International Alert, la Fondation pour la Recherche sur l'architecture arménienne (Foundation for Research on Armenian Architecture) ou encore l'Armenian National Institute (ANI).

Il décroche la Bourse Guggenheim et a reçu au cours de sa carrière un certain nombre de récompenses. Il est entré dans les versions américaine et mondiale du Who's Who.

Vie privée
Richard Hovannisian épouse Vartiter Kotcholosian en 1957 à la Holy Trinity Armenian Church de Fresno. Ils ont ensemble quatre enfants : Raffi, Armen, Ani et Garo. Raffi est Ministre des Affaires étrangères d'Arménie en 1991-1992 puis président du parti d'opposition arménien Héritage depuis 2013.

Positions politiques
Lors d'une interview en 2006, il critique le gouvernement du président arménien Robert Kotcharian, dont il dénonce la nature autoritaire ; il ajoute que  ().

Il prend part aux manifestations qui suivent l'élection présidentielle arménienne de 2013 lors de laquelle son fils Raffi arrive en deuxième position.

Œuvre

Sélection d'ouvrages

Direction d'ouvrages

Sélection d'articles

Notes et références

Voir aussi

Bibliographie

Liens externes

 Liste des œuvres

Naissance en novembre 1932
Naissance à Tulare (Californie)
Étudiant de l'université de Californie à Berkeley
Docteur de l'université de Californie à Los Angeles
Historien du génocide arménien
Historien contemporain
Historien américain du XXe siècle
Historien américain du XXIe siècle
Arménologue américain

redpajama_set_name: RedPajamaWikipedia


To a visitor, the small town of Lonoke, Ark., may be remarkable only in its unremarkable similarity to the other small farming communities that dot the map here along old Highway 70.
Life for its 4,000 residents centers on rice farming, commercial goldfish raising, and other modest agrarian-related businesses.
But since 1994 Lonoke has been known less for tilling of the soil and more as the hometown of Paula Jones, the president's accuser in a sexual-harassment lawsuit.
Even though Ms. Jones now lives in California and her allegations stem from a time when she was a state employee in Little Rock, Ark., the town feels the strain with each twist in the notorious case. The latest, this week, are reports that cast doubt on state-trooper accounts of then-Gov. Bill Clinton's marital infidelities.
The Jones matter has turned lives upside down and tarnished Lonoke's reputation, residents complain.
"The [media] came here looking for dirt and didn't find any, so they made it up," says Mary Louise Nisbett, who teaches English at the high school this reporter attended until 1982.
Locals say Lonoke is, in fact, a backdrop for the sort of idyllic life not available in big cities. Limbs of massive oak trees create canopies over quiet streets and neatly trimmed lawns. Commuters are moving here from Little Rock 30 minutes to the west for the schools, minimal crime, and absence of traffic.
Yet people who have never been here have felt free to give a less charitable view of the place. Clinton defender James Carville suggested that "trailer trash" could be found here by dragging hundred-dollar bills through trailer parks. But no trailer- park communities exist in the town.
The single most-complained-about newspaper article, one that townsfolk here believe set the tone for subsequent negative coverage, was published by U.S. News & World Report after Jones filed her civil suit.
It set Jones's story in "a world that is both unpredictable and menacing." Lonoke was a "land of big hair and tight jeans and girls whose dreams soar no further than a stint at hairdressers school."
The sting of such accounts would perhaps be easier to soothe if residents - many of whom know Jones or Clinton personally - weren't themselves so divided about the case.
Take Pam Blackard. She is the first person Jones spoke to on the infamous night of May 8, 1991, after Jones allegedly came downstairs from meeting Mr. Clinton at a hotel in Little Rock. Ms. Blackard would be central to any successful Jones case.
Yet she has more concerns about denim than depositions these days: Her dry-cleaning business has been hurt by a quiet boycott. "I've had customers ask why I am standing up for Paula," she says.
A cousin and staunch defender of Jones, speaking on condition of anonymity, said she recently traveled to Washington to receive an award for her service to a national volunteer organization. She was congratulated by Clinton in the Oval Office. The woman failed to acknowledge her hometown of Lonoke or her relationship with Jones to the president and even to her co-workers. "I chose to bury it," she says.
Gwen Standridge, married to a cousin of Jones, says she's skeptical of Jones's suit. But she believes the negative media attention actually has had some positive effects locally. "The civic groups banded together and ... worked really hard on trying to correct any area of our downtown, or businesses" that needed fixing up, she says.
But even if there have been benefits, residents like Carolyn Bransford, who along with her husband has had close ties to Clinton since he was governor, are looking forward to resolution of the Jones suit.
As if on cue to help demonstrate Ms. Bransford's view of small-town life, Charles "Spanky" Gilliam walks up the driveway, stopping by for a visit. Bransford says her family has helped him since he was a boy, but she won't specify the kind of help. It's just the way people here "do for each other," she says.


This page displays sold house prices for Bearbridge Road in Bristol.
Bearbridge Road in Bristol BS13 consists predominantly of semi-detached houses. Properties on Bearbridge Road typically have values around £150,000 - £200,000, with larger terraced houses and townhouses valued at around £200,000.
Map showing Bearbridge Road in Bristol.


I just got word that the "Real Cowboys" show I did for the History Channel last week is supposed to air beginning in February. It's going to be a six-part series with one episode playing each month. The one Sherry Monahan and I did is supposed to air in April. I think they are starting with the Lonesome Dove one, the Billy the Kid one, then ours.
Last night I got to meet one of the legends of Woodstock: Adolfo "Fito" de la Parra, the drummer for Canned Heat. Fito flew into Phoenix for a gig at the Dead Goat Saloon in Mesa, and then he had a benefit show in Casa Grande yesterday for "Bikers Against Diabetes." He and his ex, Sheri Riley (who works for me, and by the way, they get along famously), met me at El Encanto last night for dinner. We sat at the bar, ordered the mole enchiladas and talked about drumming and documentaries. He's just finished a doc on "The History of Mexican Rock 'N' Roll," which he produced. Both of us are left-handed so we had some comparing to do on customizing drum sets to meet our peculiar predicaments. Great talking with him about all things percussion and, of course, he has crazy stories of being on the road.
The most famous Canned Heat tune is probably "Goin' Up The Country" which is the signature song of the Woodstock film. They also had a million seller with "Let's Work Together." Other hits include "Got My Mojo Workin'" and "Spoonfull."
"In painting, as in the other arts, there's not a single process, no matter how insignificant, that can be reasonably made into a formula. You come to nature with your theories, and she knocks them all flat."


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The four main components of LifeDesign: sight lines, traffic patterns, room placement, and windows and light.
Long before anyone actually moves into a David Weekley home, the team at David Weekley works to anticipate how the home will be used — the ways in which the family will move around the home, the potential purposes of different rooms, and how the home will continue to grow to meet the changing needs of the people who live in it.
How do they do this? When designing a home, David Weekley Homes keeps in mind their four main components of LifeDesign: sight lines, traffic patterns, room placement, and windows and light. By keeping the importance of sight lines in mind, designers can make spaces seem larger without actually increasing square footage.
Instead of fretting about how a design looks on paper, designers at David Weekley Homes try to anticipate how people will actually move around the home, what their traffic patterns will be like. They use rooms as transition spaces instead of hallways to make spaces feel larger and more open while at the same time ensuring that traffic patterns won't interfere with the purpose of the space. Rooms are placed in areas that allow for smooth transitions while also keeping in mind the importance of having some spaces in which to congregate and some in which to retreat. And last but certainly not least, David Weekley Homes recognizes the importance of natural light and thinks carefully about window placement — both how the windows will help light the home and how views can make the exterior environment part of the interior environment, enlivening the space.
The company's purpose, "Building Dreams, Enhancing Lives," is embedded in everything David Weekley Homes strives for, from the different elements they consider when designing a home to the creative ways the company consistently finds to give back to their communities. Over the past 20 years, David Weekley Homes has donated more than $70 million to charitable causes, and employees have volunteered in a variety of ways — from building homes with Habitat for Humanity to collecting back-to-school supplies for low-income students.


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Romania - Sighetu Marmaţiei
europe-east.com > Romania > Sighetu Marmaţiei Sitemap How to use Guestbook
Basic factsSights »Surroundings »Accommodation »WWW »
Sighetu Marmaţiei, which means "Sighet in Maramureş". The town was formerly known as Sighetul Maramuresului, the Hungarian name Marmaros-Sziget is just a translation of the Romanian name. Locals usually refer to the town simply as Sighet. This means "Fortress".
Sighet is the northernmost town of Romania and stretches along the border to the →Ukraine. The capital →Bucharest is more than 400 km away. The small river Iza crosses the town before it eventually flows into the long river Tisa (Tisza), which originates in the Ukraine and passes →Hungary and →Serbia before it flows into the river Danube. The town is tucked away in the river valley in the middle of the Wooded Carpathians
Around 40,000. Sighet is the local centre of the area.
The train station and the bus terminal are conveniently located next to each other and several hundred metre north of the centre of town. It takes less than 10 minutes to walk from the train station along Str. Iuliu Maniu southwards to get to the centre. There you will find the two roads Str. Traian & Str. Ioan Mihaly de Apşa running parallel to each other. Everything concentrates along these two roads, including some churches, hotels and restaurants. The centre itself is surprisingly beautiful and features several baroque buildings. A small park occupies the narrow stretch between the two streets. Sighet is quite a green town.
Sighet is only two, three kilometres away from the Ukrainian border, but as a matter of fact foreigners are not allowed to cross the border in or near Sighet. Which is really a pity. Unfortunately, the railroad was built during the Habsburg period, which means that two out of three railway lines lead into the →Ukraine. These lines are out of service. The third line leads to →Borşa in the mountains and further to →Cluj-Napoca. If you want to get to the closest big cities, ie Baia Mare and →Satu Mare, you will have to take the bus. To Satu Mare it takes around 125,000 Lei (€ 3), to →Vişeu de Sus 1½ hrs (50,000 Lei).
Basic facts »SightsSurroundings »Accommodation »WWW »
Sighet is an old market town, which was founded during the 14th. It's the local centre of the northern part of Maramureş, a remote and rather rural area in Romania. Many of the villages around Sighet are unique and reflect Europe as it has already vanished in most areas some hundred years ago. Sighet itself is a small, sleepy town which has somehow managed to keep an atmosphere as of around the year 1900 or so.
The beautiful old town of Sighet
One thing visitors will soon notice is the large number of churches in the centre of town, among them the Gothic Hungarian Reformed Church built in the 15th century and the slightly younger Romanian Catholic Church. A synagogue and a Jewish cemetary tell the visitor something about the Jewish past of the town. Almost all Jews of Sighet were deported and murdered in extermination camps. Among one of the few survivors was Elie Wiesel, Nobel-prize winner and author of the famous and shocking novel 'Night'.
Inside the old high security prison
In the centre of town, on Str. Corneliu Coposu, there's a museum with the long name Muzeu al Gândirii Arestate şi Centru Internaţional de Studii asupra Totalitarismului. It doesn't need profound understanding of the Romanian language to guess what this is about. During the 1950ies, the building was used as a high security prison. The former prime minister as well as many other members of the anticommunist intelligentsia were imprisoned in Sighet and forced to very heavy labour. Many of them did not survive the following years.
Memorial in the courtyard of the prison
Nowadays, the prison houses a highly interesting museum about the history of suppression of free speech and ethnic minorities as well as about some of Ceauşescu's lunatic projects, eg the Danube canal, mass deportations etc. The cells are used as exhibition rooms, with each room specialising in a specific issue. Unfortunately, very few explanations are in English. Nevertheless it's a very interesting place to visit. There are several impressive monuments in the two courtyards of the large building, among them a group of sculptures. Admission fee for foreigners is 4 Lei, a photo permit costs an extra 3 Lei. The price includes a very short tour through the building (something like "here's the toilet, there's the exhibition, have fun") in English.
Basic facts »Sights »SurroundingsAccommodation »WWW »
Vişeu de Sus
The road from Sighet direction south-east is very scenic. After passing some wooded mountains and old villages, the road enters the valley of the small river Vişeu. Some 75 km away from Sighet, there's the small but very long town of Vişeu de Sus with a traditional wooden church, very typical for this area, in the centre of town. Forestry is the traditional business in the area, and there's a special narrow-gauge railroad from Vişeu to the mountains for bringing down the wood. Occasionally, steam locomotives are still used here. The centre of Vişeu is quite small and green and not particularly interesting - except for the above-mentioned church.
The wooden church in the centre of Viseu des Sus
About 20 km away from Vişeu de Sus in the same valley and almost in the mountains, there's the chic holiday resort of Borşa with several large hotel complexes. The small town is located at the foot of the up to 2,300 metres high Rodna Mountains, where snow in late spring is quite a common sight. Borşa and the area around it could be anywhere in the Alps - it looks completely different to other rural areas in the country. When you continue to the south-east, you will get to the →Prislop-Pass, which is the gateway to the historical region Southern Bukovina (lit: country of the beeches), see also →Suceava.
Borşa and the Rodna mountains
In the Southern Bukovina as well as in Maramureş you will notice old villages with partially brand new luxurious villas on the one hand and countless horse carts on the other hand, forming a sharp contrast. Poverty? At first sight, poverty doesn't seem to exist. And when you talk to the people, they don't mention things like that. Most people are very kind and interested towards strangers. Things look very different in the cities. A small restaurant in Sighet was record-breaking (as far as my personal experiences are concerned): Eight beggars in 30 minutes. Half of them were children. Among the others, there was a man presenting a nasty wound on his belly while we were eating.
Still a common sight: Horse carts. And friendly drivers.
Basic facts »Sights »Surroundings »AccommodationWWW »
There aren't many choices - at least not in Sighet, but as far as I've heard in some villages around Sighet. One option is the Hotel Tisa right in the middle of town. It's an old, time-honoured hotel. A double room with balcony and bathroom costs 450,000 Lei (€ 11) per person, including breakfast. Since staff at the hotel tends to forget to tell it to the customers, I should better mention it here: There's no running water at all between midnight and 5 am. Here's the address: Piaţa Libertăţii 8, Tel.: (062)-312 645.
Basic facts »Sights »Surroundings »Accommodation »WWW
http://www.johnrausch.com/Maramures Very nice and extensive website about the Maramureş and many of the villages there. Incl. many pictures. English.
home.t-online.de/home/maramures Interesting website about Sighet and nearby villages. In German.
Do you have or do you know a good website about Sighet? Don't hesitate, let me know! After checking it, I would love to add it to the link list. You can submit a link by using the →contact form. Note that commercial websites will be treated differently.
alston wrote:
It is now an option to enter into Ukraine from Sighet. Worth it just to visit Solotvino on a day trip.
Posted by alston on January 20, 2011 11:47
Cinci Mănăstiri

redpajama_set_name: RedPajamaCommonCrawl


RGCCISD Child Nutrition Program held a decorating contest recently among all of the district cafeteria's. The criteria for the contest was that designs had to be original and provide nutritious information. Grulla Elementary Staff demonstrated great skills as they hung their three dimensional giant size veggies in vibrant colors. The decor is in an effort to promote healthy eating habits for the students. All Child Nutrition staff members are congratulated for their efforts and for their dedication to the students. Congratulations Grulla Staff for a job well done. Pictured from left to right; front row: Corina Vela, Lupita Fernandez, Frances de Luna, Maria Bazan, back row: Hernan Cortez, Conchita Reyna, Camelia Palomares. (RGCCISD Photo).


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❶Computers have emerged as one of the best technologies which have not only reduced the manual burden but improved the work quality as well.
These technologies benefit man in numerous ways. Computer education has gained much importance in modern world. It is being used in every field. Today, we can easily find computers being used in offices, libraries, banks, schools and even at homes. The present world and the upcoming generation should look forward to acquire computer education so that they can be updated with worldwide news and information. Computer education can help in maintaining a contact between people that may be acquaintances, colleagues, or close relations.
With the help of computer and advanced technology, internet everyone can send any text, messages, images, and videos from one place to another anywhere in the world. So that is a reason everyone likes to work on computers.
Every person gives more preference to computers for their work. Nowadays people are more dependent on computers for earning purposes. People sell their product online and earn commissions through online businesses. Apart from that people advertise their products through advanced technology computers and internet. Besides in hospitals, offices, banks computers software are used for billing and for account purposes. So we cannot neglect the role of computers in our life.
On the flip side, some students prefer to do study course online through computers without the help of the teacher. It is clear that when students use computers as a study source.
Then they do not interact, share ideas as well as thoughts, problems related to topics with their classmates. As a result, they become less social and lack self-confidence. Moreover, the concepts of topics are not clear to the students. If you compare this to India our people here are busier in talking about politics and corruption instead of doing something becoming better than yesterday. The level computer education in India is very low.
You can check this: Top 11 Most important Computer Skills to learn for career development. Maybe I am wrong, but the computer education we are providing in colleges and university level such as programming, designing, apps development etc. We Indians are creative, intelligent, hardworking, honest and innocent. We are happy in taking what is served to us by developed countries.
We are not grouped because of selfish reasons that are why the level of new inventions is very low. We are implementing almost everything from other countries instead of creating something that is for India and developed in India. Our computer teachers are on strikes most of the time. They are helpless because of policies produce to them by less computer literate people such as politicians.
Computer education in schools provided by private companies, CEO and operators are known or linked up with politicians.
There is no law and quality testing system of computer education in schools. They are learning a more theoretical portion of the computer then practical knowledge of computers and internet. What we need to do is to empower and educate our kids and students.
We need to educate them to become more powerful, creative and confident that they can lead India. Our government is also trying to improve the education level but not fully focused towards the education and for the development of unemployed youth. Industrialisation is not only one formula or overseas investment we can believe that it can lower down the rate of unemployed educated youth of India.
It can help but only for few people who are highly skilled and have enough money to invest to get a job. Yes, there are many skills India kind of programs run by the government of India but the level of education or supply of high-quality individual is lower than the demands.
Importance of computer technology in the field of education The significance of computers in the field of education still remains a matter of debate. While some claim that it interferes with the enhancements of the learning skills of children, some argue that it helps them to be good learners. Know more about the importance of computer education. Computer teaching plays a key role in the modern systems of education. Students find it easier to refer to the Internet than searching for information in fat reference books.
Dec 20, · Apart from this, computer is playing a great role in the field of business. The one who knows about computer and its use can easily carry out all the calculations, statistical work and other programming within seconds. A person who has the knowledge of computers can use various software for the completion of various tasks. Computers can by an important tool to optimize young children's potential, and help aid the learning process. Before deciding to introduce children to computers, it is important to address the potential benefits and dangers the machines have on youths.


text:
Q: 2d and 3d arrays in objective-c...HELP? Im new to objective-c programming and im currently working on an iPhone project and my task has to deal with 2d and 3d arrays, I have actually been trying for a while but im not sure if im on the right track. Im trying to achieve the following:
1)Trip 1 must be in index 0 of array1
2)Trip 1 has departure time, arrival time and trip instructions
3)now im trying to have the departure in array2 index 0 that's being pointed to by trip1 in array1 in index zero, and arrival in array2 index 1
4)array2 will have array3 that has instructions for trip one
I have for loops and everything is working perfectly i just need to know how to do the above, in other words how to save these information in the manner i have described in the  above steps?
i have done this but not sure if im right or wrong:
Array1 = [[NSmutableArray] init];
Array2 = [[NSmutableArray] inti];
[Array1 insertObject:Array2 atIndex:0];
[Array1 addObject:ObjectToAdd, i]
[Array2 addObject:ObjectToAdd, i]
Note: "i" starts from zero
Thank you,

A: You can use a NSMutableArray and insert different objects into it.
For example you have 3 classes say A, B, C
NSMutableArray mainArray = [NSMutable array];
A array1 = [A new];
B array2 = [B new];
C array3 = [C new];

[mainArray addObject:array1];
[mainArray addObject:array2];
[mainArray addObject:array3];

Now you can access these objects via your mainArray.


text:
General Dynamics Elects Cecil Haney to Board of Directors
FALLS CHURCH, Va., March 6, 2019 /PRNewswire/ -- The board of directors of General Dynamics (NYSE: GD) has elected Cecil D. Haney to be a director of the corporation, effective March 6.
Cecil D. Haney, pictured here, was elected to the General Dynamics board of directors on March 6. Haney is a retired four-star admiral, a career Navy submariner, and former commander of the U.S. Strategic Command.
Haney, age 63, is a retired U.S. Navy admiral who previously served as commander of the United States Strategic Command, where he was responsible for the global command and control of U.S. strategic forces including nuclear forces, missile defense, space, cyberspace and electronic warfare. He also served as the commander of the U.S. Pacific Fleet, leading the U.S. Navy's operations from the West Coast of the United States to the Indian Ocean.
A career U.S. Navy submariner, Haney held a series of leadership positions in the submarine force and in joint assignments during his nearly four decades of service. He also served as a member of the Congressionally-mandated Military Leadership Diversity Commission. He retired from the Navy in 2017.
Haney serves on the Johns Hopkins University Applied Physics Board of Managers, the Naval Studies Board of the National Academy of Sciences, the Center for New American Security board of directors, and as co-chair for the China-U.S. Dialogue on Strategic Nuclear Dynamics for the Pacific Forum.
"Cecil's wealth of experience as a national security leader will help General Dynamics continue to deliver the products and services our nation needs to remain a preeminent global power," said Phebe Novakovic, chairman and chief executive officer. "He is a visionary leader and thinker who will be a valuable addition to our board of directors."
A graduate of the U.S. Naval Academy, Haney also holds Master's degrees in National Security Strategy from the National Defense University and in Engineering Acoustics and System Technology from the Naval Post Graduate School. Among his many commendations and medals, Haney was a 1998 recipient of the Vice Admiral James Bond Stockdale Leadership Award.
General Dynamics, headquartered in Falls Church, Va., is a global aerospace and defense company that offers a broad portfolio of products and services in business aviation; combat vehicles, weapons systems and munitions; IT services; C4ISR solutions; and shipbuilding and ship repair. General Dynamics employs more than 100,000 people worldwide. More information about the company is available at www.generaldynamics.com.
SOURCE General Dynamics
http://www.generaldynamics.com
General Dynamics to Webcast 2019 Second-Quarter Financial Results ...
General Dynamics Awarded $2 Billion U.S. Department of State...


Pittsburgh guard Ramon Foster is asking his ex-teammates to stop the criticism of current Steelers players. The latest social-media salvo was fired early Thursday morning by former Steelers running back Rashard Mendenhall, who called quarterback Ben Roethlisberger a racist in a series of tweets. Mendenhall, who played for Pittsburgh from 2008-12, was addressing accusations that wideout Antonio Brown quit on the team when he did not play in the 2018 season finale.
Steelers vs. Saints live stream: Watch NFL Week 16 game online originally appeared on nbcsportsboston.com The Pittsburgh Steelers beat the New England Patriots last week at Heinz Field, and it's very possible they will determine who the Pats play in the Wild Card round of the AFC playoffs. The Steelers entered Week 16 atop the AFC North at 8-5-1, but after the Baltimore Ravens beat the Los Angeles Chargers on Saturday night, Pittsburgh needs to beat the New Orleans Saints on the road Sunday to remain in first place in their division. A Steelers win over the Saints would keep the Ravens in the No.
Green Bay Packers @ Chicago Bears The NFL's longest winless streak on the road belongs to the Green Bay Packers, who have gone eight games without tasting victory on their travels. Packers running back Aaron Jones needs 280 yards in his team's final three games to become Green Bay's first 1,000-yard rusher since Eddie Lacy managed the feat four years ago. Dallas Cowboys @ Indianapolis Colts Indianapolis are seeking a fifth home win in a row for the first time since they won seven on the spin between October 2012 and September 2013.
As the high-profile holdout of Steelers running back Le'Veon Bell continues, more reports are surfacing about past Pittsburgh offers that the two-time All-Pro has apparently turned down. The three-time 1,000-yard rusher nixed an offer from the Steelers with the team pledging $47 million to Bell over three years, Pro Football Talk reported Friday. An NFL source told PFT that the package had the potential to guarantee Bell $20 million -- a $10 million signing bonus plus another $10 million bonus soon after the agreement.
Pittsburgh Steelers wide receiver Antonio Brown said Thursday that his frustration on the sideline during Sunday's game and his tweet toward a critic on Monday came from his desire to win. Meeting with reporters for the first time since the team's 42-37 loss to the Kansas City Chiefs, Brown made it clear he does not want a trade, but rather for his team to start performing at the level it has previously. "We were losing the game... we haven't won a game yet," Brown said.
The Browns rallied from a 14-point deficit in the fourth quarter against the rival Steelers and snapped a 17-game losing streak with a 21-21 result that left fans celebrating in the rain. For a while, it seemed the Steelers would cruise to another easy win over the Browns even without Le'Veon Bell. Backup James Conner had 135 yards rushing and two touchdowns and caught five passes for 57 yards.


Byron White, CEO of the online content marketing platform WriterAccess, spearheads a conference that provides tools, tactics, and strategies to transform businesses into content marketing machines.
Responding to the ever-increasing demand for hands-on, actionable tools and techniques to ramp up content marketing capabilities, WriterAccess is spearheading a brand new, industry-transforming, educational conference. Designed to help attendees fortify their content marketing "smartitude," the Content Marketing Conference will be held May 12 to 14 at the Rio All-Suites Hotel in Las Vegas.
WriterAccess CEO Byron White, who serves as the Chair of the Conference, is packing the event with superior speakers, case studies and in-depth industry knowledge to provide attendees with transformational knowledge that can immediately be put to work. "Content marketing is transforming the way businesses communicate," commented White. "Businesses are producing more content now than they did just a year ago, and that trend just grows stronger every year. If a business doesn't have the tools to compete effectively, it will fall behind. This conference will provide the skills and information necessary to succeed." WriterAccess will bring about half of its team to network with writers and clients, and introduce newcomers to the benefits of content marketing.
The conference kicks off May 12 with a full-day content marketing workshop led by White and Arnie Kuenn of Vertical Measures. Entitled "Content Marketing Intensified," the workshop will cover the proven eight-step process that defines how to successfully leverage content marketing to generate more traffic, and grant attendees a Content Marketing Certification. There will also be a "Lost Ball" Charity Golf Tournament to raise money for the Jimmy Fund, which funds cancer research and drives awareness for early cancer detection.
Over the next two days attendees will have the opportunity to attend 27 sessions organized around the content marketing concepts of planning, creation, optimization, management, distribution and performance. In addition to White, some of the proven professional and content marketing speakers scheduled to present include Ardath Albee of Marketing Interactions, Inc., Bruce Rogers - Chief Insights Officer at Forbes and Mike Roberts of SpyFu, Inc. Sessions will cover case studies, tactics, and the latest methodologies. Keynote speakers are Douglas Van Praet of Unconscious Branding and Tim Ash of Site Tuners.
A "Tool Talk" networking opportunity on Wednesday, May 13, is an industry first. Attendees will have the opportunity to get the inside scoop on the 100 most powerful content marketing tools available from peers that put the tools to work every day.
WriterAccess is an online marketplace connecting customers directly with expert writers. It's a Platform-as-a-Service developed by ideaLaunch, a leading provider of content marketing services and solutions. The company's mission is to streamline content creation with great writers and editors that all have the passion, expertise and experience needed to help grow a business organically—the content marketing way. Visit the website or call 617-227-8800 for further information.