text:
\section*{introduction}

Computational methods for quantum chemistry and quantum physics have proven to be invaluable tools in modern scientific research and technological innovation. The application space of such methods is vast, ranging from the prediction of novel high-temperature superconductors~\cite{duan2019ab} to the acceleration of drug discovery~\cite{cavasotto2018quantum}; from the study of catalytic processes for e.g. CO$_2$ sequestration~\cite{yu2017co2} and plastic recycling~\cite{jones2016computational} to the design of nanomaterials~\cite{boschetto2021exploring}, solar cells~\cite{frost2014atomistic}, and batteries~\cite{urban2016computational}.

In the landscape of quantum-based computational methods, density functional theory (DFT) especially stands out due to its ability to produce accurate results for a wide range of systems at a relatively low computational cost~\cite{jones2015density}. Accordingly, an impressive amount of computational research utilizes DFT calculations each year. For instance, the US National Energy Research Scientific Computing Center (NERSC) reported that nearly 30\% of their supercomputer resources in 2018 were spent on DFT calculations alone~\cite{nersc10}. Widespread research and development effort is continuously devoted towards optimizing the performance and accuracy of DFT calculations, giving rise to a plethora of open-source and commercial DFT software packages~\cite{talirz2021trends}. Several packages can leverage specialized hardware, such as general-purpose graphics processing units (GPUs), for most of the workload~\cite{huhn2020gpu,seritan2021terachem,nwchem,gaussian,abinit,bigdft,vasp_gpu}.
However, in conventional DFT implementations, i.e., without specific sparsity assumptions for the density matrix or Hamiltonian matrix, the computational cost scales as the third power of the number $N$ of orbitals used to describe the system (referred to $O(N^3)$ DFT throughout this work), and this cubic scaling often makes simulating large systems, such as protein-ligand complexes or metal-organic frameworks~\cite{wu2017metal}, prohibitively expensive.

\addtocounter{edit}{-1}

\begin{figure
\includegraphics[width=.45\textwidth]{figures/multihost_benchmark.pdf}
\centering
\caption{TPU v3 wall time for $O(N^3)$ density matrix purification, Eqs. \eqref{eq:transfH}-\eqref{eq:DD}, as a function of the number $N$ of orbitals, for clusters of water molecules, both in single (squares) and double (triangles) precision. A full TPU v3 pod with 2048 cores \edit{and 32 TB of memory is expected to handle $N \sim 500\,000$ orbitals in our current implementation (extrapolated results necessitated by temporary resource unavailability)}
}
\label{fig: multihost_benchmark}
\end{figure}

\addtocounter{edit}{-1}
\input{multihost_table}

Google's Tensor Processing Units (TPUs) are application-specific integrated circuits originally designed to accelerate large-scale machine learning workloads ~\cite{TPUinfo, jouppi2017datacenter, jax, Frostig-Leary2018, Abadi-Zheng2016}. By leveraging the JAX library ~\cite{jax, Frostig-Leary2018, Abadi-Zheng2016}, it is nevertheless possible to repurpose TPUs for other computational tasks ~\cite{Belletti-Anderson2020, Wang-Anderson2021, Pan-Mishra2021, Lu-Ma2020, TPUFFT1, TPUFFT2, huot2019highresolution, morningstar2022simulation, tpu_qphys, tpu_algebra, tpu_Z2field, ganahl2022density}. In this work, we demonstrate the use of TPUs as quantum chemistry supercomputers by accelerating the $O(N^3)$ computational bottleneck of DFT approaches which use an auxiliary single-particle kinetic energy approximation, such as Kohn-Sham (KS)~\cite{hohenberg1964inhomogeneous,kohn1965self} and generalized KS (gKS)~\cite{seidl1996generalized} DFT, where gKS admits hybrid DFT functionals. This enables the systematic study of quantum chemistry problems at unprecedented scales. As a concrete demonstration, we performed end-to-end $O(N^3)$ DFT calculations on large clusters of water molecules, reaching a total of $N = 247\,848$ DFT orbitals, corresponding to $10\,327$ water molecules with $103\,270$ electrons, see Fig.~\ref{fig: multihost_benchmark} and Table~\ref{tab: multihost table}. To our knowledge, this is the largest $O(N^3)$ DFT calculation to date, with the previously largest computation consisting of a single $O(N^3)$ DFT iteration with $N\approx 230\,000$ orbitals on Fujitsu's K computer~\cite{hasegawa2014performance}.

Some variants of DFT, most notably linear-scaling DFT~\cite{prentice2020onetep, bowler2010calculations, soler2002siesta, vandevondele2005quickstep}, avoid the $O(N^3)$ bottleneck altogether and can thus reach an even larger number of orbitals. However, these variants rely on additional approximations and conditions, such as truncating density matrix elements ~\cite{cole2010protein}, or on special properties of only a subset of density functionals (such as semilocal density functional approximations). In turn, this results in restricted applicability, with e.g. linear-scaling DFT being suitable for insulating systems but not for metals or systems with a small energy gap~\cite{prentice2020onetep}. In practice, conventional $O(N^3)$ DFT is a more preferable choice since it alleviates technical complexity and problem space restrictions associated with current lower-scaling methods, greatly extending the domain of problems to which DFT can be applied reliably and with relative ease.

There are many aspects that go into an $O(N^3)$ DFT calculation. Throughout we focus on atom-centered basis sets with all electrons treated explicitly, that is we do not consider e.g. plane waves or pseudopotentials. At a high level, one can identify two main computational steps: (a) building the DFT Hamiltonian matrix (with cost $O(N)$ to $O(N^2)$) and (b) computing the ground state density matrix ($O(N^3)$), see Fig.~\ref{fig:cpu_tpu_graphic}.

(a) \textit{DFT Hamiltonian build}: Given a choice of $N$ atom-centered basis functions
$\chi_i(\mathbf{r})$,
one needs to compute the DFT Hamiltonian matrix $H$ and the overlap matrix $S$, with coefficients given by
\begin{equation}
    H_{ij} = \bra{\chi_i} \mathcal{H} \ket{\chi_j}, ~~~~~~~~ S_{ij} = \braket{\chi_i| \chi_j},
\label{eq: H and S}
\end{equation}
where $\mathcal{H}$ represents the DFT Hamiltonian in the continuum and each matrix coefficient requires computing one or several integrals.
Over the past few decades much effort has been devoted to optimizing the build of the $N\times N$ matrix $H$. Naively, the computational time here scales as $O(N^4)$, however, in many implementations the scaling is effectively reduced to $O(N^2)$ due to two-electron integral screening methods. The scaling can be further reduced to almost $O(N)$ if other strategies, such as fast multipole methods~\cite{white1996linear} or fast fourier transform
based methods~\cite{vandevondele2005quickstep}, such as the Ewald method for periodic systems, are employed. In this work we do~\emph{not} attempt to accelerate the Hamiltonian or overlap matrix build times with TPUs. Instead, we simply use a well-established all-electron DFT package, the \textit{Fritz Haber Institute ab initio molecular simulations package} (FHI-aims)~\cite{huhn2020gpu,BLUM20092175,FHI}, which we run using CPUs.

\begin{figure}[tbp]
\centering
\includegraphics[width=1.0\linewidth]{figures/cpu_tpu_graphic.pdf}
\caption{The two main steps of our implementation of an $O(N^3)$ DFT computation, the Hamiltonian build and computing the ground state density matrix, which we run on CPUs and TPUs, respectively. The DFT code FHI-aims~\cite{BLUM20092175, FHI} is used to set up the Hamiltonian and the ELSI library~\cite{yu2020elsi,yu2018elsi} is used to facilitate the integration of the TPU-based solver to FHI-aims.
\label{fig:cpu_tpu_graphic}
}
\end{figure}

(b) \textit{Density matrix purification:} The pair of matrices $H$ and $S$ define a generalized eigenvalue problem, the so-called KS equations,
\begin{equation} \label{eq:generalized}
H \ket{\phi_\alpha} =e_{\alpha} S \ket{\phi_\alpha},
\end{equation}
with $\ket{\phi_{\alpha}}$ and $e_{\alpha}$ the KS orbitals and energies. Our goal is to compute the ground state density matrix
\begin{equation}
    D \equiv \sum_{\alpha=1}^N \theta(\mu-e_{\alpha}) \ket{\phi_{\alpha}}\bra{\phi_{\alpha}},
\end{equation}
where $\theta(x)$ is the step function and $\mu$ is the chemical potential, chosen such that $\sum_{\alpha=1}^N \theta(\mu-e_{\alpha}) = N_e$, for $N_e$ the number of electrons in the system. The density matrix $D$ can be obtained by solving the KS equations \eqref{eq:generalized} using standard linear algebra libraries, such as LAPACK~\cite{laug} or Intel MKL~\cite{intel-alt}. An alternative route, which we follow in this work, is to use a density matrix purification scheme~\cite{hole_particle_purify, purify_review}. First, by computing the inverse square root of $S$,
\begin{equation} \label{eq:invSquareRoot}
    S \mapsto S^{-\frac{1}{2}}
\end{equation}
we can write the Hamiltonian in an orthonormal basis,
\begin{equation} \label{eq:transfH}
    H \mapsto \tilde{H} \equiv S^{-\frac{1}{2}} H S^{-\frac{1}{2}}.
\end{equation}
and re-express \eqref{eq:generalized} as a standard eigenvalue problem $\tilde{H} \ket{\tilde{\phi}_\alpha} =e_{\alpha}\ket{\tilde{\phi}_\alpha}$,
where $\ket{\tilde{\phi}_{\alpha}} \equiv S^{1/2}\ket{\phi_{\alpha}}$. Next we compute the density matrix $\tilde{D}$,
\begin{equation} \label{eq:purify}
    \tilde{H} \rightarrow \tilde{D} \equiv \theta(\mu I - \tilde{H})= \sum_{\alpha=1}^{N_e} \theta(\mu - e_{\alpha}) \ket{\tilde{\phi}_{\alpha}}\bra{\tilde{\phi}_{\alpha}},
\end{equation}
and finally re-express it in the original basis,
\begin{equation} \label{eq:DD}
    \tilde{D} \mapsto D \equiv  S^{-\frac{1}{2}} \tilde{D} S^{-\frac{1}{2}}.
\end{equation}
\edit{The transformation in Eq.~\eqref{eq:purify} is obtained using a standard density matrix purification scheme that is suitable for TPUs, namely the hole-particle canonical purification scheme~\cite{hole_particle_purify}, which we elaborate on later in the paper.}

If no further modifications are made (e.g., density matrix truncations in linear-scaling DFT), then the cost of computing $D$, whether by solving Eq. \eqref{eq:generalized} or performing the four matrix transformations in Eqs. \eqref{eq:invSquareRoot}-\eqref{eq:DD}, scales as $O(N^3)$. This constitutes what is known as the \textit{cubic wall} of DFT.

The density matrix $D$ is used to derive several important quantities. The real-space electron density $n({\bf r})$ is given by
\begin{equation}
    n({\bf r}) = \sum_{i, j}^N \chi_i({\bf r}) D_{ij} \chi_j({\bf r}) \, ,
\end{equation}
which can be computed on a real-space grid ~\cite{BLUM20092175}.
The sum of occupied KS eigenvalues, given by $\mathrm{Tr}(H \, D)=\mathrm{Tr}(\tilde{H} \, \tilde{D})$, is also used to compute the total ground-state energy.
Additionally, the~\emph{energy weighted density matrix}~$Q$,
\begin{equation} \label{eq: energy weighted density matrix}
    Q = D \, H \, D \, ,
\end{equation}
is also useful to compute atomic forces analytically~\cite{BLUM20092175}.

\section*{Results}
\subsection*{DFT with TPUs}
The main result of our work is the successful use of TPUs to perform the four matrix transformations \eqref{eq:invSquareRoot}-\eqref{eq:DD}, thereby tackling the $O(N^3)$ computational bottleneck of DFT. We employed TPUs of the third generation, denoted v3. A single TPU v3 core contains two matrix multiply units (MXUs) to formidably accelerate matrix-matrix multiplication (matmul), resulting in about 10 teraFLOPS (floating point operations per second) of measured single-core matmul performance in single precision. \edit{Importantly for our purposes, matmuls are also available in double precision using a software-emulated 57-bit floating point format. In this approach, utilized algorithms require many more single precision floating point operations when operating in our emulated double precision than in single precision, and as a result matmuls in double precision take $\sim 11\times$ longer than in single precision.}

The smallest available TPU configuration consists of 8 TPU v3 cores with a total of 128 GB of dedicated high bandwidth memory (HBM), controlled by a single host with 48 CPU cores. The largest configuration is a pod with 2048 TPU v3 cores and 32 TB of HBM, controlled by 256 hosts.
Given a choice of configuration, the available TPU cores are directly connected to nearest neighbors in a 2D torus network through fast inter-core interconnects (ICIs), see Fig.~\ref{fig:cpu_tpu_graphic}. The ICIs are critical to maintaining high performance when distributing matmuls and other dense linear algebra operations over all available TPU cores. In this work we used the JAX library ~\cite{jax, Frostig-Leary2018, Abadi-Zheng2016} to write \textit{single program multiple data} (SPMD) code and executed it on configurations made of $p$ TPU cores, denoted v3-$p$, for $p=8,32,128$ and $512$.

\edit{
The TPU hardware architecture is especially suited for dense large-scale matmuls, which we perform in distributed form using the SUMMA algorithm \cite{SUMMA}, as recently demonstrated in Ref. \cite{tpu_algebra}.
Here it was shown that for sufficiently large matrices a v3-512 TPU can perform dense matmuls at near-optimal efficiency: the performance per TPU core (measured in single-precision FLOPS) is maintained at roughly $93\%$ of the single TPU core maximum performance~\cite{tpu_algebra}.}
\edit{It is important to emphasize that TPUs are often ill-suited for other tasks, and hence the algorithms utilized in this work and those in Ref.~\cite{tpu_algebra} had to be picked carefully and may differ from more conventional choices used in CPUs or GPUs.
The use of DM purification algorithms, rather than direct diagonalization, is especially attractive for TPUs since all steps can be evaluated from a series of matmuls.
Clearly, transformations \eqref{eq:transfH} and \eqref{eq:DD} require large-scale matmuls.} Transformations \eqref{eq:invSquareRoot} and \eqref{eq:purify} are implemented by an iteration involving matrix polynomials of small degree, where each polynomial requires a short sequence of matrix additions and multiplications. Specifically, the matrix inverse square root in \eqref{eq:invSquareRoot} is implemented using a standard Newton-Schulz iteration \cite{higham1997stable}, whereas for the density matrix purification in \eqref{eq:purify} we implemented the hole-particle canonical purification scheme~\cite{hole_particle_purify}. Further algorithm details can be found in the Supporting Information.

For benchmarking purposes, we have performed end-to-end DFT computations on a sequence of increasingly large water clusters \edit{with geometries obtained from standard molecular dynamics simulations (see Supporting Information)}.  We leverage the DFT code FHI-aims~\cite{BLUM20092175, FHI} to set up and drive calculations using CPUs, then use the TPUs to tackle the $O(N^3)$ dense linear algebra bottlenecks \eqref{eq:invSquareRoot}-\eqref{eq:DD}. We also utilize the \textit{ELectronic Structure Infrastructure} (ELSI) library~\cite{yu2020elsi,yu2018elsi} to facilitate the integration of FHI-aims and the TPU solver. In particular, the DFT Hamiltonian build time and associated computational scaling and parallelization are dictated exclusively by the FHI-aims code,
which uses numeric atom-centered orbitals (NAOs) with an explicit finite spatial extent, and a truncated multipole expansion to accomplish low prefactor and efficient scaling of the Hamiltonian matrix build.
\edit{While the computational time required to build the DFT Hamiltonian may vary greatly between different systems with the same total number of orbitals $N$ (due to possible differences in the resulting sparsity in the systems), the computational time required for the $O(N^3)$ DM purification step performed on the TPU has much less variability since dense matrix operations are assumed, which do not utilize any sparsity present (see Supporting Information for more discussion). Thus, we emphasize that the TPU wall times, which are reported throughout only for water clusters, are fairly robust with respect to different systems with the same total number of orbitals.}

\begin{figure}[ht]
\includegraphics[width=.45\textwidth]{figures/fhi_singlehost_timings.pdf}
\centering
\caption{Wall times for a single DFT iteration on water clusters, using a TPU board composed of a CPU host (48 CPU cores) and 8 TPU cores with 128 GB of HBM.
Green and purple curves correspond to using single and double precision in the TPU solver, respectively. The dashed blue curve corresponds to the CPU time spent on FHI-aims (always in double precision), and should be subtracted from the other curves in order to obtain the time spent on the TPU solvers.  For reference, in red we also plot the time required for a CPU-only computation using the \textit{Eigenvalue soLvers for Petaflop Applications} (ELPA), a highly parallelized eigensolver library \cite{kuus2019optimizations,marek2014elpa}, run on 48 CPU cores.
}
\label{fig: timing_benchmark}
\end{figure}

\edit{Throughout this work we perform all-electron calculations using the PBE exchange-correlation functional and utilize an NAO basis set such that each H$_2$O molecule contributes 10 electrons, represented by 24 orbitals (5 for each hydrogen atom and 14 for the oxygen atom).}
First we consider a single TPU board with 8 TPU v3 cores controlled by a host with 48 CPU cores, and we run FHI-aims on the host. Fig.~\ref{fig: timing_benchmark} shows the wall time for a single DFT iteration (including both Hamiltonian build on CPUs and density matrix purification on TPUs) as a function of the size of the water cluster, which ranges from a few thousand to $N \approx 50\,000$ orbitals. When using the TPU solver in single precision (green curve) we see that
the $O(N)$ Hamiltonian build on 48 CPU cores takes longer than the $O(N^3)$ density matrix purification run on 8 TPU cores, thus shifting the bottleneck. Using the TPU solver in double precision is an order of magnitude slower and saturates the TPU's HBM for $N \approx 36\,000$ orbitals.

Then we consider larger TPU configurations, of up to 512 TPU v3 cores, to perform end-to-end DFT computations on larger clusters, of up to $10\,327$ water molecules (or $N= 247\,848$ orbitals). Fig. \ref{fig: multihost_benchmark} shows the TPU wall time for the $O(N^3)$ density matrix purification for one DFT iteration. These include 350 (5\,434) seconds for a density matrix purification in single (double) precision on the largest cluster, demonstrating feasibility of DFT computations at that scale of a quarter of a million orbitals.

\begin{figure}[ht]
\includegraphics[width=.45\textwidth]{figures/water247848_bifdyn_512_dyn_prec_plot.pdf}
\centering
\caption{Convergence trajectory of an end-to-end dynamic precision DFT calculation on a (H$_2$O)$_{10327}$ cluster. The absolute total energy differences between subsequent DFT iterations, $i$ and $i-1$, are plotted (top). The corresponding difference in real-space densities within the L$^1$ norm is plotted (bottom).}
\label{fig:water247848_bifdyn_512_dyn_prec_plot}
\end{figure}

\subsection*{Dynamic precision on TPUs}

In our implementation, early DFT iterations are treated with single precision and later ones in double precision. This \emph{dynamic precision} approach allows us to cut down on the use of double precision matmuls on TPUs (which are significantly slower than single precision ones) without sacrificing accuracy of the final converged DFT result. Our criteria to switch precision is based on relative density changes, using the L$^1$ norm, defined as $L^1[f(\mathbf{r})] \equiv \int d^3r \, |f(\mathbf{r})| $, and relative energy changes:
\begin{align} \label{eq:converge_density}
    \frac{1}{N_e} L^1[n^{[i]}(\mathbf{r}) - n^{[i-1]}(\mathbf{r})] &< \epsilon \hspace{10mm} \text{and} \, \\
    |E^{[i]} - E^{[i-1]}|/|E^{[i]}| &< \epsilon \, , \label{eq:converge_energy}
\end{align}
where $n^{[i]}(\mathbf{r})$ is the real-space density at DFT iteration $i$, $E^{[i]}$ is the corresponding total ground-state energy, and we use $\epsilon = 5 \times 10^{-7}$ for single precision.

Fig.~\ref{fig:water247848_bifdyn_512_dyn_prec_plot} shows the convergence trajectory of a dynamic precision DFT calculation for the largest cluster we have considered.
We are able to converge such a DFT calculation to a fairly tight convergence threshold using first $9$ single precision DFT iterations, followed by $7$ double precision DFT iterations. In a smaller cluster, (H$_2$O)$_{1481}$ with $N = 35\,544$ orbitals, a smaller number of double precision iterations are required for convergence, resulting in an overall DFT calculation time that is under $5$ hours on a single TPU board (v3-8), see Supporting Information.

\section*{Discussion}

This work has successfully demonstrated that TPUs can both \textit{accelerate} and \textit{scale up} DFT computations. Significant \textit{acceleration} is already achieved using only a single TPU board with 8 TPU v3 cores, see Fig.~3. For instance, an end-to-end dynamic precision DFT computation with N = 35$\,$544 orbitals consisting of 12 iterations in single precision and 4 iterations in double precision yields converged results in under 5 hours. For context, using \edit{double precision only and the highly optimized ELPA $O(N^3)$ solver with 48 CPUs, the same water cluster calculation required 20 hours to achieve $16$ DFT iterations}.

In order to \textit{scale up} the size of DFT computations while retaining high performance two main ingredients are involved: (i) a larger amount of high bandwidth memory, scaling as $O(N^2)$, to be able to store dense $N\times N$ matrices; (ii) a larger number of cores, with state-of-the-art inter-core connectivity, to more effectively execute the $O(N^3)$ floating point operations involved in the required distributed matrix transformations. As shown in Fig.~1,
by using a number of cores that scales as $O(N^2)$ and commensurate amounts of HBM, we can scale up to $N = 500\,000$ orbitals with wall times that only grow proportional to $N$.

\edit{Once the main ingredients (i) and (ii) are satisfied, the Input/Output (IO) time, i.e. the end-to-end communication time between the TPU and CPU, can become an important (and possibly limiting) factor.
This IO step is not exclusive to TPUs, for instance, it is also relevant and analogous in GPU setups that require communication with CPUs.
This step is parallelizable, such that by using a number of TPU and CPU cores that scales as $O(N^2)$, the total IO time remains constant $O(1)$.
However, in this context, obtaining such optimality will depend on specific implementation details of the DFT code utilized, such as the matrix distribution pattern on the CPU processor grid.
Our current prototype implementation is modular and generalizeable and IO times scale unfavorably as $O(N^2)$, even becoming the rate-limiting step in some cases (see Supporting Information).
Less-general (but straightforward) engineering approaches are expected to be much more optimal, but are beyond the scope of this work which aims to demonstrate the use of TPUs in a more general context.
}

We emphasize that other hardware accelerators, most notably GPUs, can also accelerate and scale up DFT computations in a similar manner as discussed above, and Ref.~\cite{das2022dft} recently presented a useful and positive development in this direction.
\edit{
Modern distributed GPU configurations are expected to achieve similar performance to TPUs in this regard, however, a direct comparison is complicated by the highly diverse nature of distributed GPU configurations found in practice. On the Summit supercomputer configuration, it has been reported that 432 distributed Nvidia V100 GPUs can perform matmuls for dense $N > 500\,000$ matrices with a performance per GPU (measured in FLOPS) that is roughly 85\% of the single V100 GPU maximum performance~\cite{herault2019generic}.
}

Here we have focused, for simplicity, on applying DFT to clusters of water molecules. More complicated systems may present additional difficulties. For instance, protein-ligand complexes often require more elaborate schemes, such as including solvation to facilitate the convergence of the DFT iteration~\cite{lever2013electrostatic,rudberg2012difficulties}. Work in progress shows that our TPU-based large-scale DFT computations can also successfully address protein-ligand complexes with explicit solvents,
as well as in a variety of other large systems, including DNA segments, carbon nanotubes, and graphene surfaces. In addition to single-point DFT energy calculations, analytical forces can also be extracted from the TPU-calculated ~\emph{energy-weighted density matrix}, enabling large-scale geometry optimization or Ab initio molecular dynamics calculations.

DFT is a highly successful quantum-based method, but it is ultimately a consistent-field approximation, which may not be accurate enough for certain applications. Fortunately, TPUs can also accelerate and scale up other, more accurate quantum chemistry approaches where the computational bottleneck is again given by dense linear algebra operations. For example, in density matrix renormalization group (DMRG)~\cite{white_density_1992} calculations, TPUs can be used to reach an unprecedentedly large bond dimension $D = 65\,536$~\cite{ganahl2022density}. Similarly, we anticipate that TPUs will thrive in other methods such as coupled cluster~\cite{fales2020performance} and Møller–Plesset perturbation theory~\cite{vogt2008accelerating}. Even when applying such higher-level methods, large-scale DFT may still be a crucial piece in simulations that require a quantum-mechanically treated region that embeds a subsystem treated with higher-level correlated methods~\cite{sun2016quantum}.

To conclude, in this work we have successfully repurposed TPUs as quantum chemistry supercomputers by tackling the $O(N^3)$ computational bottleneck of density functional theory. We demonstrated performance and scalability with a water cluster with $N = 247\,848$ orbitals, which to our knowledge is the largest $O(N^3)$ DFT computation to date. We remark that cloud-based TPUs, and other hardware accelerators such as GPUs, are more accessible and affordable than traditional supercomputer resources. Our work thus paves the way towards accessible and straightforward use of quantum chemistry computational methods for much larger systems than were previously possible. \\

\textbf{Competing Interests}: V.B. received compensation as an advisor from Google during part of this work. V.B. is also a board member of MS1P e.V., the non-profit organization that licenses the FHI-aims electronic structure code used in this work. He does not receive any financial gains from this position.

\begin{acknowledgments}

The authors would like to thank Toru Shiozaki and Garnet Kin-Lic Chan for suggesting to investigate the use of TPUs to accelerate mean-field quantum chemistry methods (by accelerating matrix multiplications for a diagonalization-free construction of the density matrix, as in the density matrix purification used in this paper), and Toru Shiozaki, Garnet Kin-Lic Chan, Chase Roberts and Stefan Leichenauer for previous exploratory work in this direction. Also, special thanks to Xing Zhang and Garnet Kin-Lic Chan for work adjusting PySCF, as part of an on-going integration of our TPU solver, to be described elsewhere, and to David Bowler, Tsuyoshi Miyazaki, and Jun-ichi Iwata for help documenting the largest DFT computation run on the K computer.
Fianlly, the authors would also like to thank
Giuseppe M. J. Barca,
Anudhyan Boral,
Michael Brenner,
Kieron Burke,
Rafael Gomez-Bombarelli,
JW Feng,
Filipp Furche,
Andreas Goeller,
Stephan Hoyer,
Olivier Lacombe,
Stefan Leichenauer,
Lin Lin,
Ruben Martin Romo,
Todd Martinez,
Anders M. N. Niklasson,
Nicholas Rubin,
Zak Stone,
Matthias Tan,
Keiran Thompson,
Edward Valeev,
and
Jae Yoo
for useful discussions and comments.
Research supported with Cloud TPUs from Google's TPU Research Cloud (TRC).
Sandbox is a team within the Alphabet family of companies, which includes Google, Verily, Waymo, X, and others.
G.V. is a CIFAR fellow in the Quantum Information Science Program, a Distinguished Invited Professor at the Institute of Photonic Sciences (ICFO), and a Distinguished Visiting Research Chair at Perimeter Institute. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Research, Innovation, and Science. R.S. and Y.Y. were partially supported by the National Science Foundation (NSF), USA under Award No. 1450280.
\end{acknowledgments}

\clearpage

\section*{Supporting information}

\subsection{orthogonalization details}
\label{sec: orthogonalization details}

The original set of $N$ basis functions $\chi_i(\mathbf{r})$, corresponding in our current FHI-aims implementation to numeric atom-centered orbitals (NAOs), are not orthogonal, in the sense that the overlap matrix $S$, with coefficients
\begin{equation}
    S_{ij} = \braket{\chi_i| \chi_j} = \int d^3r ~\chi_i(\mathbf{r})\chi_j(\mathbf{r})
\end{equation}
is not the identity matrix, but some non-trivial, positive definite matrix.
To identify the linear combinations of orbitals that are occupied in the ground state of the system, we need to account for overlaps between the orbitals.
This can be done using the L\"{o}wdin decomposition, where the Hamiltonian matrix $H$, with coefficients
\begin{equation}
    H_{ij} = \braket{\chi_i| \mathcal{H}| \chi_j} = \int d^3r ~\chi_i(\mathbf{r}) \mathcal{H}(\mathbf{r})\chi_j(\mathbf{r}),
\end{equation}
is transformed into an orthonormal basis as $H \mapsto \tilde{H} = S^{-\frac{1}{2}} H S^{-\frac{1}{2}}$. The transformed Hamiltonian $\tilde{H}$ can then be purified, as described in the next section, to yield the density matrix $\tilde{D}$, which is then transformed back into the original orbitals basis,
\begin{equation}
    \tilde{D} \mapsto D = S^{-\frac{1}{2}} \tilde{D} S^{-\frac{1}{2}}.
\label{eq:orthogonal D}
\end{equation}
For this purpose, the inverse square root $S^{-\frac{1}{2}}$ of the overlap matrix is needed.
To compute it efficiently on TPUs, we need an algorithm for computing the matrix inverse square root for which the computational bottleneck reduces to repeated matrix multiplications. As discussed in~\cite{higham1997stable}, this can be achieved using Newton-Schulz iterations. The iteration
\begin{align}
    \label{eq:newton-schulz}
    X_{[n+1]} = \frac{1}{2} X_{[n]} (3I - X_{[n]}^2), \quad X_{[0]} = A,
\end{align}
converges to the matrix sign function of $A$, which turns positive eigenvalues to $+1$ and negative eigenvalues to $-1$. Notice that two matrix multiplications are needed for each iteration. These matrix multiplications can be executed very quickly when distributed over a set of TPUs. The inverse square root can in turn be cast as a sign function as
\begin{align}
    \label{eq:block-signum}
    \operatorname{sgn}\left( \begin{bmatrix} 0 & S \\ I & 0 \end{bmatrix} \right) = \begin{bmatrix} 0 & S^{\frac{1}{2}} \\ S^{-\frac{1}{2}} & 0 \end{bmatrix}.
\end{align}
Applying the iteration \eqref{eq:newton-schulz} to the block matrix in \eqref{eq:block-signum} results in the Denman-Beavers iteration for computing the inverse square root.

In single (double) precision, the above procedure typically converges in about 35-50 (65-90) iterations, depending on how small the absolute value of the smallest (in absolute value) eigenvalue of matrix $A$ is. In order to further accelerate this computation, we introduce the pre-conditioning polynomial iteration (which we described and justified in Sect. III.D of \cite{tpu_algebra} in the related context of the matrix sign function for singular values),
\begin{align}
    \label{eq:rogue}
    X_{[n+1]} = aX_{[n]} (I - \frac{4}{27} a^2 X_{[n]}^2), \quad X_{[0]} = A,
\end{align}
where $a = \frac{3}{2} \sqrt{3} - s_-$ for some choice of small $s_->0$. [Notice that for $a=3/2$, that is $s_- = 3(\sqrt{3}-1)/2$ we recover \eqref{eq:newton-schulz}.] This pre-conditioning polynomial accelerates the growth of small eigenvalues of $A$, until they become of size at least $s_{-}$. From then on, the regular Newton-Schulz iteration is used to bring all the positive eigenvalues to 1, with quadratic convergence.  For $s_- = 0.1$, in single (double) precision we need 15-20 (35) iterations of the pre-conditioning polynomial and 10 (10) iterations of the regular polynomial, for a total of 25-30 (45) iterations.

The inverse of $S$ is of course very sensitive to poor conditioning of $S$, which for the overlap matrix corresponds to (nearly) linearly dependent orbitals, a common occurrence when dealing with large molecules.
The danger of instability and poor accuracy due to small eigenvalues of $S$ is especially pressing if operating in low numerical precision.
Consequently we always compute $S^{-\frac{1}{2}}$ in double precision.
Because TPUs do not operate natively in double precision but rather rely on software emulation, this incurs a significant time cost.
However, in a full DFT simulation that cost gets amortized:
the overlap matrix does not change between DFT iterations (only the Hamiltonian does), and thus we only need to compute $S^{-\frac{1}{2}}$ once at the first iteration, write the result to disk, and reread and use it at all the successive iterations with negligible cost.

\subsection{purification details}
\label{sec: purification details}
By \textit{density matrix purification} we mean the map from a Hermitian matrix $\tilde{H}$ of linear size $N$  to a certain density matrix $\tilde{D}$, itself a projector into the subspace corresponding to the $N_e$ smallest (or most negative) eigenvalues of $\tilde{H}$, where $N_e$ is the number of electrons in the system. [As in the rest of the paper, the tilde in the Hamiltonian $\tilde{H}$ and density matrix $\tilde{D}^{(k)}$ denotes that these matrices are expressed in an orthonormalized basis of orbitals, as described in the previous section.] In symbols, let
\begin{equation}
    \label{eq:Hdecomp}
    \tilde{H} = V \Sigma V^H
\end{equation}
be the ascendingly sorted eigendecomposition of $\tilde{H}$, and let $\rho \equiv \mathrm{diag}(1_1, 1_2, \ldots, 1_{N_e}, 0_{N_e+1}, 0_{N_e+2}, \ldots, 0_N)$ be a diagonal matrix with $N_e$ 1's followed by $N - N_e$ 0's on the main diagonal. Then $\tilde{D}$ is defined by
\begin{equation}
    \label{eq:Ddecomp}
    \tilde{D} \equiv V \rho V^H.
\end{equation}
It follows identically that $\tilde{D}^2 = \tilde{D}$, so that $\tilde{D}$ is indeed a projector.

With the decomposition \eqref{eq:Hdecomp} in hand, $\tilde{D}$ is trivially computed by the manual substitution $\Sigma \to \rho$. Unfortunately an efficient algorithm for Hermitian eigendecomposition is not presently available in a distributed-TPU context. Instead, we turn to matrix-multiplication based purification algorithms originally developed in the context of linear scaling methods (see \cite{purify_review} for a review; note that since our matrices are dense and are not truncated, our implementations scale as $N^3$ despite the name).

Density matrix purification algorithms can be divided into two classes \cite{canonical_purify} by the manner in which $N_e$ is specified. In \textit{grand canonical purification}, a so-called \textit{chemical potential} $\mu$ is given, and $\tilde{D}$ found so that the $N_e+1$'th most negative entry of $\Sigma$ is the first to exceed $\mu$. This can be achieved by shifting the spectrum of $\tilde{H}$ by $\mu$ so that the latter divides negative from positive eigenvalues, and then computing a polar decomposition using the methods of \cite{tpu_algebra}.

In the \textit{canonical purification} used in this work, $N_e$ is instead specified directly. Compared to the grand canonical case this is more directly relevant to computations of molecular electronic structure, where $\mu$ is unknown but the number $N_e$ of electrons is provided.

Various algorithms for canonical purification have been proposed in the literature. The original scheme is presented in \cite{canonical_purify}, and is variously referred to as \textit{canonical purification} (in which case other algorithms are given a different name), \textit{trace-preserving purification}, or the \textit{Palser and Manolopoulos scheme}. The \textit{trace-resetting} schemes proposed in \cite{trace_resetting_purify1, trace_resetting_purify2} are probably most common in practical use. We use the \textit{generalized} or \textit{hole-particle} scheme presented in \cite{hole_particle_purify}. In our TPU experiments this iteration yields  performance comparable to that of \cite{trace_resetting_purify1, trace_resetting_purify2}, but avoids certain branching conditionals which are awkward to phrase efficiently on the TPU.

All such schemes work by first mapping the input $\tilde{H}$ to some initial $X_{[0]}$ with eigenvectors unchanged but eigenvalues bound in $[0, 1]$, and then repeatedly applying a matrix-multiplication based iteration which also preserves eigenvectors. This iteration is chosen so that the eigenvalues of its fixed point $X_{[\infty]}$ are \emph{exactly} either 0 or 1 with $\mathrm{Tr}(X_{[\infty]}) = N_e$; $X_{[\infty]}$ then satisfies \eqref{eq:Ddecomp} and it is thus equal to $\tilde{D}$, up to numerical error. \edit{In practice, the number of purification iterations required for convergence varies across different Hamiltonians and the numerical precision desired. Relevant factors include the size of the energy gap and the fraction of occupied to unoccupied states. Typically, less than $50$ purification iterations are required~\cite{hole_particle_purify}. Calculations performed to double precision tend to require more purification iterations, up to twice as many as the same calculation performed to single precision.}

Details of the specific iteration we use are given in \cite{hole_particle_purify}. It can be reproduced by the initialization
\begin{subequations}
\begin{align}
    X_{[0]} &= \beta_1 I + \beta_2(\mu I - \tilde{H}), \\
    \mu &= \frac{\mathrm{Tr}\tilde{H}}{N}, \\
    \beta_1 &= \frac{k / N}{e_{+} - \mu}, \\
    \beta_2 &= \frac{1 - k/N}{\mu - e_{-}},
\end{align}
\end{subequations}
where $e_{+}$ and $e_{-}$ are estimates of the largest and smallest eigenvalues of $\tilde{H}$ obtained by e.g. the Gershgorin circle theorem. Note that in practice we use the slightly more complicated initialization referred to as \textit{HPCP+} in \cite{hole_particle_purify}, which gives moderately improved performance when $N_e$ is far from $N / 2$. In either case, the iterate $X_{[n+1]}$ is found from its predecessor $X_{[n]}$ via
\begin{subequations}
\begin{align}
    X_{[n]}^{\prime} &= I - X_{[n]}, \\
    X_{[n + 1]} &= X_{[n]} + 2 \left(X_{[n]}^2 X_{[n]}^{\prime} - \frac{\mathrm{Tr}(X_{[n]}^2 X_{[n]}^{\prime})}{\mathrm{Tr}(X_{[n]} X_{[n]}^{\prime})} X_{[n]} X_{[n]}^{\prime}\right).
\end{align}
\end{subequations}
Once $\tilde{D}$ is found, its counterpart in the non-orthogonal basis, $D$, is found by applying \eqref{eq:orthogonal D}.

In Fig.~\ref{fig: purify_benchmark} we demonstrate the computational scaling of density matrix purification on TPUs using dense random Hermitian matrices and single precision. In this benchmark we scale both the system size (dimension of the matrix, $N$) and the number of TPU v3 cores used. Starting with a single TPU board, consisting of 8 TPU v3 cores, we can systematically scale up to hundreds (or thousands) of TPU v3 cores. Using a full TPU v3 pod (consisting of $2048$ TPU v3 cores), we project that we can address dense systems of $N = 500\,000$ orbitals within 30 minutes using single precision.

\begin{figure}[ht]
\includegraphics[width=.45\textwidth]{figures/purify_benchmark.pdf}
\centering
\caption{Average wall times for TPU density matrix purification (normalized to a total of $50$ purification iterations) in single precision using dense random Hermitian matrices of dimension $N$. Open-circle data points (v3-2048 results) are a linear extrapolation from v3-512 results.}
\label{fig: purify_benchmark}
\end{figure}

For dense linear algebra, the computational scaling here is cubic. If suitable sparsity is assumed, and the density matrix is correspondingly truncated, sparse linear algebra can be used to obtain linear scaling. Such linear scaling approaches have been implemented and used in practice within computational quantum chemistry packages, however their practical application is limited to systems whose density matrix has a sufficient sparsity structure to ensure accurate results.

\subsection{FHI-aims TPU integration details}
\label{sec: fhi-aims}

We outline the practical details of integrating a TPU-based density matrix solver with the CPU-based DFT package FHI-aims. The platform and integration described here is a prototype.
Its main purpose is to illustrate, in actual end-to-end DFT computations, the viability of accelerating the $O(N^3)$ bottleneck using TPUs.

The software ELSI~\cite{yu2020elsi,yu2018elsi} is used to facilitate the connection between FHI-aims and the TPU by providing an interface and abstraction in which FHI-aims, or other codes, such as Siesta~\cite{garcia2020siesta} and DFTB+~\cite{hourahine2020dftb+}, can utilize external eigensolvers launched within ELSI. We implement in-house routines to launch the TPU-based density matrix purification (instead of an eigensolver) using the ELSI standard. In all calculations, we use an off-the-shelf FHI-aims code with \emph{no} modifications (version 210226).

In the course of a DFT calculation, FHI-aims utilizes the following matrices: the overlap matrix $S$, the DFT Hamiltonian $H$, and the density matrix $D$. FHI-aims distributes each matrix across CPU processes and memory using a 2D block-cyclic distribution pattern. On the other hand, in our current TPU implementation which utilizes SUMMA (Scalable Universal Matrix Multiplication Algorithm), our TPU-based solver requires matrices to be distributed across a TPU processor grid as 2D blocks in a \emph{checkerboard} distribution, see~\cite{tpu_algebra} for more details. This poses a practical matrix communication challenge between the CPU-based and TPU-based schemes since their matrix distribution patterns differ in both cyclicity and the number of processors. A simple solution to communicate such matrices between CPU and TPU is to serialize and transfer the respective matrices and deserialize and redistribute them in the desired scheme. Specifically, we utilize available MPI processes on the CPU to serialize (and deserialize) to a network disk using the ELSI IO module and compressed sparse column (CSC) format with no cyclicity. Double precision is used throughout. We note that each process (CPU and TPU) calculates where its data should be within the serialized CSC representation of the whole matrix and reads (writes) to (from) only that portion of the matrix representation on the centralized network drive. That is, our implementation incurs some algorithmic overhead but only communicates the data that is needed.

This is not the most performant solution, however, it is generalizable, makes use of existing tooling within ELSI, and avoids the complexity of the various distribution patterns. Due to the use of the CSC format, serializing (writing) dense matrices to disk is especially costly and dominates the total CPU-TPU communication time for large system sizes. For transparency, in Fig.~\ref{fig: io_times} we plot the average observed total end-to-end CPU-TPU communication time (excluding the TPU density matrix purification time) incurred in our current implementation. There are, however, several ways to further optimize the current integration. For instance, we are currently using an off-the-shelf network file system (NFS) share, and replacing it with a different implementation of a portable operating system interface (POSIX) compliant distributed file system (one designed for high-performance applications) would result in a much higher throughput and would not require any changes to our code. In addition, further algorithmic optimizations are likely possible.

\begin{figure}[ht]
\includegraphics[width=.45\textwidth]{figures/io_times.pdf}
\centering
    \caption{Total end-to-end CPU-TPU communication time per DFT iteration (excluding the TPU density matrix purification time) incurred in current integration with FHI-aims.}
\label{fig: io_times}
\end{figure}

Within FHI-aims all calculations are performed using the all-electron ``light defaults'' numeric atom-centered basis set~\cite{BLUM20092175}. This results in $5$ basis functions per H atom and $14$ basis functions per O atom in the water cluster calculations. All calculations are non-periodic with open boundary conditions and utilize the PBE~\cite{perdew1996generalized} XC functional. The geometries of water clusters are \edit{directly obtained from Ref.~\cite{ergoscf_waterclusters} which were generated by taking spherical cutouts of varying radii from a large molecular dynamics simulation of bulk water at standard pressure and an average temperature of 300K (further details can be found in Ref.~\cite{rudberg2018ergo}).}

In our implementation with FHI-aims, hybrid functionals can also be used without any modification, but simply result in longer DFT Hamiltonian build times on CPUs. Analytical forces are also available from FHI-aims using TPU-computed energy-weighted density matrices, which are also communicated using the above scheme and facilitated using ELSI.\\

\subsection{dynamic precision on smaller water clusters}

The dynamic precision approach illustrated in Fig.~4 of the main text for 10\,327 water molecules, when applied to smaller systems, allows for a larger part of the computation to be performed in single precision. For instance, an end-to-end converged DFT calculation on (H$_2$O)$_{1481}$ cluster with $N = 35\,544$ orbitals  required 11 iterations in  single  precision  and  4  iterations  in  double  precision, with an overall time of under 5 hours on a single TPU (v3-8) board, see Fig.~\ref{fig:water35544_bifdyn_8_dyn_prec_plot}.

\begin{figure}[ht]
\includegraphics[width=.45\textwidth]{figures/water35544_bifdyn_8_dyn_prec_plot.pdf}
\centering
\caption{Convergence trajectory of an end-to-end dynamic precision DFT calculation on a (H$_2$O)$_{1481}$ cluster with $N = 35\,544$ orbitals. The absolute total energy differences between subsequent DFT iterations, $i$ and $i-1$, are plotted (top). The corresponding difference in real-space densities within the L$^1$ norm is plotted (bottom).}
\label{fig:water35544_bifdyn_8_dyn_prec_plot}
\end{figure}

\clearpage

redpajama_set_name: RedPajamaArXiv


text:
Q: Ajax uploading dom gets slower until chrome crashes I have a page loaded in via Ajax (long story but I need multiple pages in a single html file for javascript enabled browsers and for them not to be loaded if js disabled). The pages loaded via Ajax also have additional ajax links. So the page gets loaded in and if you click links within that page it loads content and updates the dom. This all works fine but if you keep clicking the Ajax links to update the content the page gets slower and slower until the browser crashes so I'm guessing it has to be a memory link (particularly bad in Chrome but this may be because its a bit more of a resource hog than Firefox).
I'm wondering whether it could be because within the ajax callback I'm calling the function again - I'm doing this otherwise the links within the ajax content won't have the ajax event applied to them (even though I thought .on was supposed to do this in a similar way to .live did). Anyway I'm thinking the below may be obvious to someone, any help very much appreciated.
function ajaxContent() {
    $('.ajaxContentWrapper').on('click', 'a.ajaxContentTrigger', function(event){
        event.preventDefault();
        var myUrl = $(this).attr("href") + " .ajaxContent";
        $(".ajaxContentWrapper").load(myUrl,function(){
            ajaxContent();
        });

    return false;
    });
};

A: Have you tried looking at the ajax calls in chrome developer tools?
Also i don`t understand the function you provide, what is wrong with this approach?:
$('.ajaxContentWrapper').on('click', 'a.ajaxContentTrigger', function(event) {
    event.preventDefault();
    var myUrl = $(this).attr("href") + " .ajaxContent";
    $(".ajaxContentWrapper").load(myUrl);
});

redpajama_set_name: RedPajamaStackExchange


Ida B. Wells-Barnett, born in 1862, was an activist, teacher, and writer who, despite death threats and the destruction of her self-built newspaper, never stopped demanding an end to racial injustice. She was one of the leading voices in exposing the terrorism that white people inflicted on Black families through lynching, threats, and Jim Crow laws.
After returning to the U.S., she helped organize the National Association of Colored Women, and was one of two women who helped found the NAACP. She died in Chicago in 1931.
Ida B. Wells-Barnett contributed greatly to the future civil rights movement, to the end of Jim Crow laws, and to the movement to end lynching. Yet Black families continue today to experience threats, struggle, and violence—whether state-sanctioned or from individuals. Modern voices that echo Ida B. Wells-Barnett are critical.
Women who have made history influence women who will make history, and Ida is surely no exception. I encourage you to read from Echoing Ida's ever-growing body of work, and support the women who are continuing Ida's legacy of justice.
As Advocacy Director for Legal Voice, Sara Ainsworth is committed to reproductive and racial justice, and to honoring and following the leadership of people of color. She is a huge fan of the Idas and jumped at this chance to promote their work.
Photo of Ida B. Wells-Barnett from Wikimedia Commons.


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According to census bureau, in 2008, there were 27,281,452 small businesses.
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Business license, assumed business name certificate, tax resale number. Plus your location, rent/utilities/phone. And some cars to sell.
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A lot of people, the exact number cannot be determined.
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text:
Reset Button Pressed
JP Landman – Political Analyst
The overall poll participation dropped from 73,5% in 2014 to 66%. A lot of people stayed home.
The ANC got 1,4 million fewer votes than in 2014, dropping from 62% to 57%. Voters have made it clear that they do not condone the shenanigans of the last few years. The party will face further vote losses in the future if it does not take its own renewal project seriously. The impunity of the Zuma years has been called to order.
Yet the 57% is an improvement on the poor 2016 local government results and as such is a turnaround for the ANC. Predictions that their support would drop to 51% did not materialise. The party also held on to Gauteng, avoiding the need for another destabilising coalition. Overall a rebuke, but not to the extent that stability is undermined.
How much of the 57% is due to Cyril Ramaphosa as an individual is unclear, but he certainly saved the ANC's bacon. Fikile Mbalula, the ANC head of elections, said that without Ramaphosa the ANC may only have achieved 40%. Perhaps a typical Mbalula flourish, but there is no doubt that Ramaphosa helped the ANC. (Ace Magashule first wanted to argue the point with Mbalula, but on Saturday morning he recanted. This is in itself interesting as it was his second recant in 24 hours.)
GAUTENG IS RISING
Gauteng is the province with the largest population and the largest number of registered voters. It is now also the biggest contributor to ANC votes. It delivered 24% of the party's total, overtaking KZN, which used to be the ANC's biggest province. (KZN contributed 20% now, compared to 22% in the last election.
The ANC margin in Gauteng is now so thin (50,2%) that there is little room for mismanagement and corruption in Gauteng, or indeed in other provinces or by ANC individuals that could cause reputational damage in Gauteng. It is a pressure point for the ANC in general.
KZN AND OTHERS ARE DECLINING
In KZN the ANC's share of the vote dropped from 64% to 54%. The IFP reclaimed ground lost to the NFP, garnering enough support to replace the DA as official opposition in the province. Behind the DA in fourth position is the EFF with just under 10%. The ANC government in KZN will now face more opposition from parties to its right than to the left. The party's dismal performance is likely to weaken the Zuma faction in KZN and further diminish the ex- president's position.
The decline in ANC votes in KZN was repeated in the other Zuma-supporting provinces of the Free State, North West and Mpumalanga. The decline shifts the balance of power in the ANC further to the other five provinces, which are strong Ramaphosa supporters. The 'Ramaphosa provinces' contributed nearly 60% of the total ANC vote.
Of course, the internal ANC balance of power is determined by branches and membership, and not by votes in national elections, but the party cannot divorce itself from the electoral reality out there (as both Ramaphosa's election in 2017 and this election amply illustrate).
CR'S POSITION
These factors constitute a good base for Cyril Ramaphosa. They certainly deprive the Ace Magashule faction of room to try and dump him, as the rumour mill would have it. All other things being equal (health, physical protection and a reasonable economy), Ramaphosa is set to serve as president for ten years. It gives the country time to reset and get back on course – generating economic growth faster than population growth; jobs; better management; and stronger social cohesion. This election has finally put the Zuma years behind us.
This does not mean that the Magashule faction will simply lie down and die. But they dare not threaten the renewal of the ANC and its reconnection with the voters. The balance of forces has shifted fundamentally in Ramaphosa's favour.
TRADE UNION PARTY IS NOT TAKING OFF
It is worth noting that the Socialist Revolutionary Workers Party (SRWP) launched by the trade union NUMSA failed miserably. It garnered 0,14% or 24 400 votes. NUMSA is one of the oldest and strongest trade unions in the country with more than 300 000 members and considerable funds and organisation. Clearly, the union could not get too many of its members to vote for SRWP. This may focus the minds of COSATU members that are considering establishing a party in opposition to the ANC.
REFLECTION TIME FOR ALL PARTIES
The election is a wake-up call for all political parties.
The ANC will have to look at governance and building a more capable state. As much as voters appreciate what has been done, they want to see better delivery and management. The party will also have to re-connect with the voters. The impunity and arrogance of the last few years is a proven recipe for how not to win support.
The DA got 470 000 less votes than in 2014, dropping from 22,3% to 20,8%. 250 000 votes seem to have gone to the FF+ and arguably another 73 000 to Patricia de Lille's GOOD Party. That leaves 150 000 or so lost votes to explain. It is very conceivable that they are DA voters who 'voted for Cyril'. These numbers describe where the lost votes went, but they do not explain the reasons behind those very different choices. The party will have to do some soul searching. Paradoxically, the departure of 250 000 supporters to the FF+ may make it easier, but we will see.
Going by their own claims and predictions, the EFF must be very disappointed with the election. They improved their vote count by 707 000 (or 60%) and their share of the vote from 6,3% to 10,78% This is good by any standard, but the party expected much more. Malema boldly claimed that the EFF would be 'kingmakers' after the elections. They do not come near kingmaker status in any of the nine provinces. Some pre-election polls gave them 14% to 15%, but they only achieved 10,8% (another 707 000 votes short of 15%). The EFF was the official opposition in two provinces. They added Mpumalanga by getting 12,8% of the provincial vote, overtaking the DA. The militant message did not do as well as many predicted. South Africa's voters are not into radical politics, whatever the latest outrage on Twitter.
The three biggest parties corralled 89% of the vote. Eleven smaller parties share the remaining 11%. There will be fourteen parties in parliament.
Two small parties disappeared from parliament (Agang and the African Peoples' Convention) and three new parties will enter parliament (Patricia de Lille's GOOD Party, Mzwanele Manyi's ATM and Al Jama ah).
Gauteng has moved into pole position as the largest single provider of ANC votes (24%), despite the party capturing just over 50% of the votes in the province.
This shift puts paid to the narrative that the ANC will become a rural party.
Cyril Ramaphosa is now free to revitalise SA and pursue a balanced agenda of economic growth and social justice for the next ten years. He will push the reset button.
The first sitting of the new parliament is scheduled for Wednesday 22 May, when the new president will be elected by parliament. This should be a formality.
On Saturday 25 May the president will be inaugurated.
On Monday 27 May the new cabinet will be announced and on Tuesday 28 May the new cabinet members will be sworn in. Expect this cabinet to be substantially smaller with about 25 cabinet members compared to 35 currently.
A cabinet lekgotla will be held on 12 to 14 June.
Parliament will be opened with the State of the Nation Address on Thursday evening the 20th of June, when the President will outline the government's programme of work.
JP Landman
Political Analyst

redpajama_set_name: RedPajamaCommonCrawl


Sedum 'Beach Party' | TERRA NOVA® Nurseries, Inc.
Blooming plants look like mounding pink dunes in the garden – very compact. The prolific flowers are star-shaped and light rose-pink. Spring leaves are a showy yellow-green, edged with red. Needs good sun and drainage.
10" / 19" / 14"
It is very low and compact with very large flower heads of light pink.
Obligate long day plant. Pinch 1 week after transplant. Grow with 60°-65° F nights, 75°-80° F days. Provide night interruption or day-length extension to force flowering under natural short days. Supplemental lighting during cloudy days has proven beneficial for flower production. AVOID CHEMICAL SPRAYS. Received the highest rating at MSU for container culture.


text:
Is a website sidebar a user blind spot?
I've seen studies about how ad blindness can prevent users from even noticing ads exist on a website, but are there any studies that perform the same research for the entire sidebar?
On some sites, like this one, I use the sidebar quite frequently as it has it has useful content relevant to the main content on the page. On other sites, like blogs, I find I very rarely ever use or even look at the sidebar. While these are my own personal browsing habits, I'd love to see some empirical data on what kinds of sidebar content is most engaging and whether there is such a thing as sidebar blindness.
website-design content sidebar
Virtuosi MediaVirtuosi Media
You can't get empirical data on sidebar blindness without doing your own testing. The data will be about someone else's sidebar, and the design makes all the difference; your design is different, and you'll need to do testing on your site to see whether the layout is inducing users to miss the content. – Myrddin Emrys Apr 20 '12 at 22:27
@MyrddinEmrys - I definitely agree that it's always best to test your own site because every site is different. That said, perhaps there is some helpful data from someone else's study that could help me. – Virtuosi Media Apr 21 '12 at 5:36
It can be, if you answer yes to anyone of these questions:
Has your sidebar remained the exact same for the last 3 months?
Does your sidebar exhibit signs of "sidebar creep" ?
Was there a time when people clicked around in your sidebar, but now you're thinking you might have dreamed it?
Do you have more than 4 affiliate buttons showing at one time? (not a guarantee of sidebar-blindness, but a possible indicator)
Do you have 3 or more of your own offers and specials showing at one time?
Do you have more than 1 social media feed in your sidebar? (ex: latest tweets, latest Flickr photos, latest Facebook statuses)
Do you have anything in your sidebar that makes you look less cool than you really are? (ex: I have 40 Twitter followers! 12 people subscribe to this blog!)
Is anything in your sidebar boring, unimaginative, or physically painful to look at?
All from Sarah J. Bray who wrote the post "How to avoid a devastating case of sidebar-blindness (gasp!)"
When I read it I realized I scored 6 of 8 just because I use the sidebar as "the place for everything else, that isn't really valid, but I need to fill the space with something-area". Leading to the fact that no one reads it (me included).
Probably it's better to leave this area empty, if one doesn't have anything valid to put there which could be related links to the content in the middle or great images. I'm going back to the drawing table with mywebsite.com.
Benny SkogbergBenny Skogberg
Human beings have a narrow, 15-degree arc of vision, that directs their focus. Outside this arc, the eye's ability to resolve colour and shape drastically diminishes. In fact, at the edges of vision, humans are effectively colourblind. The only visual signs that humans can resolve effectively across all directions are animations, especially tracking animations where objects enter the visual field, travel and leave it. But these are so powerful, users have trouble progressing any further than spotting the animated element - no matter what copy you write underneath. This makes it hard for visual elements to garner attention in this space.
But the real question is: is this really a bad thing? Sidebars and right-hand content are typically used for secondary content, and that allows users to employ a handy heuristic to avoid right-hand content in high-strain tasks. Humans have a narrow field of vision because they're bad at multitasking, and that's not something any kind of content is going to fix.
I wouldn't recommend swapping left-hand content with right-hand sidebars, either. I have seen a multi-variant test where a site put a secondary 'request a quote' form in left-hand space. It didn't turn out well. Lots of users converted and submitted the form, but phone surveys conducted afterwards indicated that nearly all the users had no intention of actually requesting any kind of quote. The quote form was positioned as though it were another step in the 'primary' workflow; users presumably completed it because they assumed it was necessary, not because they engaged with the content.
One contributing factor that I have found to be true over the years is "What side of the page is the sidebar on?" Believe it or not users are much more likely to pay attention to a sidebar that is on the left side vs the right side.
This is due to the fact that more often than not, the left sidebar is for navigation and the right side is for adds.
It all has to do with conditioning.
PL3XPL3X
Not the answer you're looking for? Browse other questions tagged website-design content sidebar or ask your own question.
Sidebars - How useful are they?
Best practices for a sidebar on a blog
One scrollbar or two for content + sidebar?
Keyboard shortcuts overriding default browser action
Menu in right sidebar vs left sidebar
Switching which side a sidebar is on
Fixed Sidebar with Accordions
How to avoid "Loading fatigue"
Interactive documents v websites. What research/studies exist to cover when one should be used over the other?
Should emotion-neutral fonts be used for user-submitted content?
Home link inside sidebar. Sidebar opens on click. Clicking home should open sidebar or home?


Marie and Chris talk about how we decide what new features get added to CodePen, and get into the process of taking them from a "lightbulb moment" to building them out on the app.
Get ready for Web Unleashed! October 1 - 2, 2018 in Toronto, Canada.
Save 50% off the price of tickets with code CODEPEN!
23:40 Why you can't build from feature requests alone.
26:50 Study on how much a person could be paid to lose access to a net feature.


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text:
Governor's May 15 Extension Makes No Sense
While the health and safety of New Mexicans are the top priority, Gov. Lujan Grisham's decision to extend her stay-at-home order to at least May 15 demonstrates she has no solid plan to get New Mexico moving again.
A third of our counties have fewer than 10 COVID-19 cases, some none at all, yet the governor has offered no real statewide strategy, while putting a stranglehold on New Mexico's economy: it's business or bust for hundreds of thousands of New Mexicans, as local economies drown, unemployment soars and Main Streets become ghost towns.
The governor continues to permit national chains to remain open, sending millions of New Mexico dollars out of state, while crippling our locally-owned mom and pop businesses. The Republican Party of New Mexico implores the governor to use common sense and to help all New Mexicans to get back to work. Now. Social distancing can work at small establishments, and reopening them will kickstart New Mexico. Social distancing is not working at big box stores, where people are rubbing elbows in the aisles.
Let's be fair, governor. We're all in this together, remember?
"The governor cannot pick and choose winners and losers in this dire situation. She fails to understand that we can responsibly social distance at small businesses and do what's right to protect our citizens while saving our economy," said Steve Pearce, Republican Party of New Mexico Chairman. "Our state is going under, and peoples' livelihoods are being lost. We may never recover from this unless the governor reopens New Mexico for the little guy. They make this state run. And it's all about fairness."
The governor's establishment of an "economic council" to decide how to phase in business activity is a poor excuse to "resolve" the problem. How will decisions be made? Which businesses will get priority? Why should they get priority? Where in the state?
No answers. The governor seems to be passing the buck to a group that will now advise her.
Again, no solid plan.


text:
Home/Frank Buncom, San Diego Chargers/The Best of Times
Buzz Ponce, author of the book-in-progress, Finding Frank; Full Circle in a Life Cut Short, gives us another brief look into the life of linebacker, Frank Buncom, and another chapter of his upcoming book!
#156 – Frank Buncom
Frank Buncom's career with the San Diego Chargers mirrors the team's overall best of times in its entire 52 year history. His tenure with San Diego – 1962 to 1967 — reflected not just his best years as a football player but also the Chargers' best, all-time seasons. The fact that the team's lone championship came in 1963, Buncom's second year, helps to bolster that hypothesis.
Strikingly, at no other time in the team's history has it accumulated a better winning percentage than during those six years that Buncom played for San Diego. The Chargers rolled up 47 wins in those seasons and while that number exactly matches six-year runs by future Chargers teams (coached by Bobby Ross and Marty Schottenheimer), those seasons saw a 16-game schedule, while the Sid Gillman era saw a regular season of only 14 games. From 2007 to 2011, the team went on an all-time best ride with 49 wins under Norv Turner, but again, that's with an additional two games per year, meaning a total of 10 games more overall than during Buncom's reign with San Diego.
That all-time high winning percentage takes into account the team's dreary record in 1962, dipping to a low of just 4 wins versus 10 losses – by far Gillman's worse year as the head coach in the American Football League. The '62 season was an anomaly when compared to the two years it was sandwiched between; 1961 saw the team go 12-2, 1963 brought the AFL Championship with its 11-3 mark.
If one were to put a microscope on Buncom's overall football career, including his playing days at USC, and make a judgment on what his best season was, 1965 would stand out like a beacon in spite of his team's embarrassing season ending loss. The Chargers led the AFL in both defense and offense that year and were heavily favored to beat the Buffalo Bills in the league championship game, having already bested them 34-3 in their first match-up earlier in the season, and then playing to a 20-20 tie in their second meeting.
As the football gods would have it though, the Bills trashed San Diego for the AFL title in front of the Chargers' home crowd at Balboa Stadium. The Chargers offense – and defense for that matter — didn't show up that day as Buffalo's Jack Kemp (later Republican Congressman Jack Kemp of supply-side economics fame and a future vice presidential running mate with presidential candidate Bob Dole in 1996) threw two touchdown passes and Hungarian soccer-style kicker Pete Gogolak added three field goals.
The Chargers were clearly caught feeling immensely over confident in their '65 title game. In an Associated Press article the day prior, the opening line was, "The San Diego Chargers are taking a relaxed and confident attitude toward Sunday's American Football League championship game." Tight end Dave Kocourek, a key cog for the team throughout the early '60's, was quoted as saying, "Our team is in a relaxed state of mind. I think that's a good sign. Maybe it's the season – green trees, green money. Whatever the reason, everyone's in a really good mood." [1]
That good mood didn't last long once the game started as the Bills romped 23-0.
Gillman, revered as a football strategist par-excellence and one of the very early pioneers of the so-called West Coast offense, may have contributed largely to his team's state of over confidence and subsequent loss. He predicted a San Diego blowout and told columnist Larry Felser of the Buffalo Evening News before the game, "You know, there is no way we can lose this game."
Gillman, an eventual Hall of Fame coach, said the reason was, "Because of Kemp. We're going to win this game because Kemp has the maturity of a 10-year-old girl."[2]
Kemp, still smarting from Gillman's release of him from the Chargers three years earlier, found his comeuppance.
A sobering sidebar for the city of San Diego in that '65 game (as well as the Chargers' loss the previous year in the AFL championship game to Buffalo) is the fact that the Chargers' title in 1963 still stands as the only major sports crown won by any sports team for San Diego. No other metropolitan area with at least two professional sports teams has gone longer than "America's Finest City" between championships. Adding salt to the wound, the 1963 win is also the only time the Chargers have beaten the New England (Boston) Patriots in a postseason game.
If it was the best of times during Buncom's six years in San Diego, just how valuable was Buncom as a football player? How significant was his success for the Chargers during their wonder years?
His rookie season in 1962 saw him crack the team's starting lineup as an outside linebacker, moving from the defensive line as a collegiate, and quickly becoming known as a bruising force on an already punishing defense. He was smart, quick, very agile, and "hit like a mule" as teammates later recounted.
Buncom joined an already stalwart defensive lineup that included middle linebacker Chuck Allen and outside linebacker Emil Karras. Allen, Karras and Buncom formed a linebacking trifecta that year that would last three seasons; Buncom and Allen would team together until '68. Buncom led that corps in interceptions his rookie season with five – an impressive number by any standard, and speaks of his quickness and agility.
That same defense also featured the game's original "Fearsome Foursome." Although the New York Daily News ran a feature story way back in 1957 profiling the New York Giants' defensive group and headlined, "A Fearsome Foursome," it wasn't until the Los Angeles/San Diego Chargers came along in 1960 that the term gained popular acceptance. The Fearsome Foursome saw several different versions with the Chargers, but in 1962 was composed of behemoth lineman Ernie Ladd, defensive end Earl Faison, and linemen Ron Nery, and Bill Hudson.
Though seemingly nearly invisible to most fans and followers throughout his career and throughout the AFL, Buncom did receive the "Charger of the Year" award in 1964 from a group calling itself "The Fan-Attics," a spin-off of the notable Chargers Backers club. In a letter to Buncom dated February 1, 1965, the Fan-Attics explained that, "Our choice was unanimous…it was Frank Buncom all the way! We hope you will accept this award in the spirit in which it is given – a token of appreciation for your outstanding performance. Congratulations on an outstanding year and good luck and good health to you." [3]
By 1965 he had established his bonafides as a certifiable key player for the San Diego Chargers; hardly a headline generating name but roundly recognized by his peers as one of the best and most dependable players in the American Football League. Still largely unheralded by the average fan, he was nevertheless named to his first AFL All Star team (to differentiate from the rival National Football League, the AFL used the term "All Star" during its time versus the NFL's "All Pro" designation) in 1964, duplicating that honor again in '65 and '67.
Sports Illustrated confirmed Buncom's status as a team leader in its "Pro Football 1965" edition, saying, "The linebacking should be the best in the Chargers' history, with Chuck Allen in the middle and Frank Buncom on the right…"[4]
As San Diego galloped through its'65 schedule going 9-2-3 tripped up only by losses to the Patriots and the Chiefs and ties (this was before the introduction of pro football's sudden-death format to determine tie-breakers) to Kansas City, Boston, and Buffalo, the Chargers were clearly the class of the AFL, outscoring their opponents 380 to 227 and ending with a winning percentage of .818, far ahead of the Bills' .769. Then their meltdown to Buffalo occurred in the title game and their dream season evaporated. But Buncom's role throughout the year as a team spearhead was solid and noteworthy, culminating on his selection to the league's All-Star team as a starting linebacker.
The AFL, always preemptive for something different and unusual to set itself apart from its fierce rivals in the NFL, radically departed from the traditional East vs West format for that season's All Star game. In a one-year experiment, the league pitted its champion Buffalo Bills against an opposing team comprised of standout players from the other seven teams in the league.
As was typical of the AFL, the game proved to be a rock 'em, sock 'em, high scoring contest. The 35,572 fans that shuffled into Houston's Rice Stadium and the NBC national television audience with Curt Gowdy and Paul Christman calling the action, were treated to rookie quarterback Joe Namath's come-from-behind theatrics. The All Star team thumped the Bills 30-19 with Namath, resplendent in his white shoes and swashbuckling manner throwing for two touchdowns, being named the game's offensive MVP.
And it was the original number 55 for the Chargers — a guy with the unheralded name of Frank Buncom — playing the entire game at right linebacker and being credited with five tackles and one sack, who was named by sportswriters as the All Star game's defensive MVP.
Frank Buncom
By any measure, 1965 was Buncom's finest hour as a football player. It was his zenith, his time to shine as one of the game's best. Though he again attained All Star status in 1967, Buncom's football light never shined as bright as in '65.
The Chargers slipped to a sloppy 7-6-1 record in 1966, finishing a distant third in the AFL Western Division. Probably the highlight of that season was the team's swan song at run-down and outdated Balboa Stadium. They moved into sparkling new San Diego Stadium (later named Jack Murphy Stadium and later still, Qualcomm Stadium) the next year. That season also was the debut of the AFL-NFL World Championship Game where the AFL champs Kansas City Chiefs met the NFL's Green Bay Packers in January of 1967 in the Los Angeles Coliseum, marking the beginning of the phenomenon forever since called the Super Bowl.
The next year saw San Diego slightly improve to 8-5-1 in its new home, but still languishing in third place in the tough AFL West of the time. The team lost its final four consecutive games that year, sealing its fate as an also-ran. The highlight for Buncom, in his final year with the Chargers, was being selected for his third — and last — time to the AFL All Star team.
The largest crowd in AFL All Star history saw the East squad squeak out a 25-24 victory at the Gator Bowl in Jacksonville, Florida, with Namath again being named MVP for his offensive heroics. San Diego Charger Speedy Duncan was named defensive MVP based on his record-breaking All Star game touchdown punt return.
Buncom, playing for the last time as a Charger, packed up after the game, returned to San Diego, and began hearing rumors of his status in the upcoming AFL draft that spring that was being put in place to seed the league's newest team. Unknowingly at the time for him, he would be wearing a Cincinnati Bengal uniform in 1968.
Frank Buncom's – and the Chargers' – best of times were over. His six year tenure with San Diego had come to an end.
[1] Associated Press, December 25, 1965
[2] Buffalo News, December 25, 1965
[3] Letter from Sarah Buncom's journals
[4] Sports Illustrated, September 13, 1965
By Todd Tobias|2013-01-14T06:29:53-08:00January 14th, 2013|Frank Buncom, San Diego Chargers|18 Comments
Lance Alworth, a Great for the Ages…
Remembering the Chargers Don Norton
San Diego's Glory Years – the 1960s
Los Angeles Chargers Season Ticket Brochure
Eddie Arminio January 14, 2013 at 11:19 AMLog in to Reply
I really enjoy your Charger stories. I'm from the Boston area , and a life long Patriot fan. The early Chargers intrigued me because of Sid Gillman and the great teams he put together. He definately was way ahead of his time. A great plus for them also, was the fantastic powder blue uniforms ,and the helmet with players number on it. The best uniform in the history of professional football. Thanks for a great website.Eddie Arminio Franklin,Ma.
1967 January 14, 2013 at 2:51 PMLog in to Reply
Frank Buncom's move from SD to CINN 1968 expansion draft continued the Chargers loss of defensive talent (Ernie Ladd, Earl Faison, Miller Farr among them), and a failure to replace them that resulted in a showing on field best described as "muy stinko". Seems personalities – both player & coaching side – sometimes be the impetus moves, rather than merely diminishing talent.
Pop-offs…
Everybody wants to rule the world (or at least be 'The Greatest' aka 'The Mouth That Roared') but there was only one Cassius Clay / Muhammad Ali, who stated various occasions what he would do, even the round that pugilist would fall all lipped to Louisville's own home-spun 'poemage' – originals are always better an sequel, however many.
My dad hated him – I rooted for Sonny Liston in their first fight – Clay prevailed.
Joe Namath? My sire also hated Joe's 'white shoes'. Namath was Clay Lite; in fact had his team not prevailed Superbowl III, Joe might have ended up more a joke than the savior a league according some (I think his signing '65 & SB III win was a bit overblown as well re: his impact.)
Sid Gillman? I prefer to remember Sid's "get him out of there because he 'has' no hands" quip re: missing appendages his player (it ranks up there with McKay's, "I'm in favor of it" retort the post game query 'what do you think of your team's execution'.)
KC Head Coach Hank Stram was quoted as saying, "we'll tear apart the NFL" in reference playing GB Superbowl 1 aft the Chiefs buried BUF AFL Championship Game (Stram denied his statement but it was a directly attributed quote in an Sports Illustrated magazine the time.) Which made his chastisement Fred 'The Hammer' Williamson for Fred's pre-Superbowl bluster about him dropping the hammer' on the Packers somewhat hypocritical, hindsight.
Back to those 1967 Chargers, they stood 8-1-1 before losing those last 4 games in a row, their defense – had none – gave up 37 points per those last 4 including 41 to that powerhouse offense the 4-10 Dolphins (who SD had shut out less than a month earlier.) What a waste of an fantastic offense the Chargers, via a defense that was downright criminal.
Tom January 14, 2013 at 5:27 PMLog in to Reply
Buzz as it is public record the 1956 LA City Street Directory gives the address of an Elnora Buncom as 3624 10th Av, it's 5 blocks east of Crenshaw Bl between Jefferson Bl and Exposition Bl. The old LATL J street car loop was at Jefferson Bl and 10th ave. If Frank needed to get to school he could walk to the corner and ride the J car to USC or when he attended Dorsey down to Exposition Bl and hop the freight car on Exposition Bl. Today the J car has been replaced with buses and the freight train with the spanking new Exposition passenger rail line. The Expo Line.
A few others who were from the LA area include Mike Gaechter Lancaster, Bruce Snyder El Monte, both played with San Diegans Dave Grayson, HD Murphy and Roscoe Cook at Oregon a couple of years after their hometown heroes Willie West and Alden Kimbrough starred for the Duckes, Dave Kopay No Hollywood Notre Dame HS and Dick Post who was born in San Pedro but raised in Oklahoma. Marv Luster CFL HOF Belmont HS and Dick Norman from Lynwood with Chris Burford set passing records at Stanford.
Buzz Ponce January 14, 2013 at 6:35 PMLog in to Reply
Tom: Yes, Frank Buncom's mother's name was Eleanor. His father, Frank Sr;, died in 1958, the same year Frank II graduated from Dorsey. Eleanor went on to earn a teaching credential and taught elementary school for a number of years in the LAUSD.
Thanks for the information!
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The Socceroos have hit the track ahead of their do-or-die Round of 16 clash against Uzbekistan. ... Graham Arnold's men enter Tuesday morning's (1:00am AEDT) match having scored six goals in their last two AFC Asian Cup UAE 2019™ games with five different scorers on target.
With four goals in his first seven Socce...�appearances, Awer Mabil is fast becoming a fan-favourite for the national team.


After reading Peter's post on this subject I thought I'd weigh in with some thoughts.
In a previous life I worked at a school as a webby-techie sort. This was back in the days before fast internet and the school had serious problems with the speed of the internet with all the children surfing for the same things at the same time. In addition the ISP filtering (and this article isn't going to discuss whether filtering is good or bad) was fairly rudimentary.
Being a fairly adventurous sort I snagged an old machine and installed Squid (a GPL licenced caching web proxy with filtering support) on it. The school then changed the proxy settings of all PCs to go through the new proxy and we gained a slightly faster system for frequently visited sites, and had the means to block other sites totally.
Once the system had proved how valuable it was, the school decided it needed something better than a random old PC to handle the web cache. Rather than buy a more fit for purpose machine for me to repeat my installation, they promptly paid through the nose for a black-box solution from RM. After basic investigation it turned out that this black-box solution was running nothing other than Squid. The school however had more confidence in a commercially obtained solution than some free thing downloaded and installed in-house.
It is this sort of "nobody ever got fired for buying IBM equipment" mentality that seriously hampers the take-up of free and open source software (FOSS) within schools. To some extent this isn't surprising. The people making the decisions aren't usually technical experts, and want to make a decision that they think won't backfire on them.
What we need are trustworthy organisations to advise and guide schools away from closed proprietary systems and towards open source, and to do so consistently rather than give mixed messages. Maybe a focused single perspective on this issue that saved money could have helped BECTA from being closed down. Maybe not.
If you're FOSS savvy and know how to install and support this sort of thing but you aren't prepared to get a job in a school doing this (or volunteer many hours of your time) then it is easy (but not necessarily helpful) to look on the problem from the outside and say something must be done.
The real problem is how do we get the relevant expertise into our schools in a sustainable way? For this I really think the government needs to lead, and in a time of financial cuts across the board, I believe real savings can be made by guiding a lot of the public sector over to FOSS.
resolving bad maths record. high sms costs, low bandwidth costs. Mxit – South African company, 7 million users, software is free. So can Mxit be used possitively in education? 'Dr Maths' homework hotline using Mxit. help with maths homework up to grade 12. 14:00 – 20:00 sundays-thursdays. over 2000 kids use it. 20 students from Uni of Pretoria are the tutors (anonymous), some physics and chemistry help too. mostly english, some africaans support too. approx 2000 students using the service. no advertising, growth via word of mouth.
pocket pc program to help staff development – staff doing collaborative development to teach different modules each year.
HP pocket pcs. vodcasts. mlessons (thinking skills curriculums).
provide guides and access to computers so that students can convert the powerpoint slides to videos for their own hardware – rather than teachers doing the conversion for the students. that way each student with a different device can make the best material for their device.
useful webapps running in mobile safari.
Site blurb: Everybody with an interest in 21st Century learning and teaching practice is invited.
The rules are simple. Anybody can present but you're allowed 20 images that you show for 20 seconds each giving you a total of 6 minutes and 40 seconds before the next presenter is up. You can't spend 6:40 on one image/slide or 2:20 or any other denomination you can only spend 20 seconds on each image/slide. It's all part of the fun and keeps presentations concise. If the facilitator decides then the presentation may be open for discussion with the audience otherwise it's straight on to the next presenter.
Each presentation is pre-loaded onto a laptop (Powerpoint or Keynote) and then is ready to go. The facilitator will make a brief introduction of the presenter and then the talk begins. Each presentation must be pre-configured to advance every 20 seconds, so it's up to the speaker to keep pace with their slides.