text:
\section{\label{sec:intro}Introduction}

Modern astronomical and cosmological surveys consist of enormous raw dataset too large to be
interrogated directly. Most of the time, cosmological analyses require that raw data be compressed to
a computationally tractable set of summaries \citep{ Tegmark_1997,alsing2018_general}. Physical understanding can often guide the choice of this compression, such as light curve compression
and power spectrum computation. However, for data for which the physical processes are poorly
understood, choosing an optimal compression that preserves the maximal amount of information from the
raw data is tricky. Existing techniques such as Principal Component Analysis \citep{Connolly1994ph, francis_pca} and power spectrum
estimation have proven successful for astrophysical problems, but due to the sheer size of some
datasets, even summary sets prove too large to work with in the context of likelihood computation.
Surveys such as Euclid are forecast to produce $10^4$ summary statistics \citep{massive_Heavens_2017}. Upcoming astrophysical surveys such as Euclid \citep{laureijs2011euclid}, the Legacy Survey of Space and time (LSST) \citep[]{lsstdarkenergysciencecollaboration2012large} and the Square Kilometre Array \citep[]{ska_Weltman_2020} will allow the
cosmological field to be interrogated directly in the context of dark energy measurement and
large-scale structure formation. For these non-Gaussian fields the power spectrum alone is not
sufficient to describe galaxy clustering, posing a challenge for cosmologists. Recent advances in deep learning have made interpreting large swaths of cosmological data more tractable, from emulators \citep{shirleyd3m, Kodi_Ramanah_2020, moster2020galaxynet, deoliveira2020fast} to systematics and foreground removal \citep{makinen2020deep21, Puglisi_2020, Petroff_2020} (see \cite{ntampaka2021role} for a recent review).

We study Information Maximising Neural Networks (IMNNs) \citep{Charnock_IMNN} in the context of computing posteriors for cosmological parameters from cosmological fields. IMNNs are neural networks that compress data to informative nonlinear summaries, trained on simulations to maximise the Fisher information. Training such networks automatically gives Gaussian approximation uncertainties from the summary Fisher information, and score estimates for parameters can then be used for efficient implicit likelihood inference. Beyond cosmology, IMNNs perform massive dimensionality reduction, even for highly non-Gaussian problems, such as galaxy type identification from multiband images \citep{livet2021catalogfree}.

Other studies have investigated neural techniques for point estimate cosmological parameter extraction from cosmological fields via regression networks trained on simulation-parameter pairs \citep{pan2020cosmological, ravanbakhsh2017estimating, Kwon_2020, prelogovic2021machine, Fluri_2019lensing, Fluri_2018, Matilla_2020, ribli2018improved, Gillet_2019} with squared loss. As reviewed in \cite{villaescusanavarro2020neural}, these techniques can estimate the posterior mean of parameters. This implies they require simulations drawn from a prior, specified at the time of training, not just near the parameters favored by the data. This adds to the variability that needs to be fit by the network.

We show that IMNNs, trained on simulations at a fiducial point in parameter space, can compress cosmological fields to maximally informative score estimates \citep{alsing2018_general} without specifying a prior at the training stage.  Lossless field-level inference--equivalent to using all pixels in an image--can then be performed without evaluating an explicitly specified (or expensive or intractable) likelihood and while specifying the prior at the following inference stage. We first introduce IMNNs within a differentiable framework when exact simulation gradients are accessible.
We  compare inference with IMNN-compressed parameters to a computationally expensive yet exact full field-level
inference for  Gaussian fields, demonstrating
that a convolutional neural network can be trained to extract the maximal amount of information from Gaussian fields using a modest number of simulations. Although simplistic, Gaussian fields are relevant to early cosmological density fields such as the Cosmic Microwave Background (CMB) as measured by \cite{planck_collab}. We verify through Approximate Bayesian Computation \citep{grazian2020review,Cranmer30055} with these summaries that we recover the exact analytic posterior. We then
demonstrate an extension to log-normal fields generated with a  cosmological power
spectrum.  We demonstrate that IMNN compression extracts the maximal amount of information
from raw
field inputs, and produces Fisher matrices that allow for efficient Density Estimation Likelihood Free Inference (DELFI), recovering simulation-generated posteriors with a moderate number of simulations. Finally, we show that IMNN compression is robust to the choice of the fiducial model - even for poor choices of fiducial model a single re-training iteration on score estimates recovers optimality.

After reviewing and defining additions to our IMNN framework in Section \ref{sec:imnn} and outlining simulation-based inference techniques in Section \ref{sec:sbi} we proceed to applying our framework to progressively more difficult problems to verify our techniques in Sections \ref{sec:benchmark} and conclude in \ref{sec:cosmo}.

\section{Information Maximising Neural Networks}\label{sec:imnn}

\begin{figure*}[ht!]
    \centering
    \includegraphics[width=\textwidth]{figures/imnn-scheme.png}
    \caption{Cartoon of the information maximising neural network scheme. Raw real-space field
    values are fed directly to the network compressor. We compute field simulations $\textbf{d}^{\rm s fid}_i$ at
    the fiducial model and pass the data through the network to produce $n_{\rm summaries} = 2$
    summary statistics $\textbf{{x}}_i^{\rm s fid}$, for each simulation. This is done for $n_s$ independent simulations evaluated at $\boldsymbol{\theta}_{\rm fid}$. Since both the simulator and compression steps are numerically differentiable, the gradients with respect to input parameters are readily obtained to compute equation \ref{eq:autograd-enabled} which are used to compute the covariance $\textbf{C}_f$ and derivatives of the summaries $\boldsymbol{\mu}_{f,\alpha}$. The output of the IMNN is Fisher information matrix, computed via equation \ref{eq:fisher-compressed}. The network is trained via gradient back-propagation, with the $\det \textbf{F}$ and $\textbf{C}_f$ contributing to the scalar loss function.}
    \label{fig:conv-scheme}
\end{figure*}

The IMNN framework is presented in full in \cite{Charnock_IMNN},
but we review the formalism here for completeness, as well as
introduce two new aspects to the technique. The sharper the peak of
an informative likelihood function $\mathcal{L}(\textbf{d} |
\boldsymbol{\theta} )$ for some data $\textbf{d}$ with $n_{\textbf{d}}$ data
points and $n_{\boldsymbol{\theta}}$ parameters at a given value of $\boldsymbol{\theta}$,
the better $\boldsymbol{\theta}$ is known. The Fisher information matrix
describes how much information $\textbf{d}$ contains about the
parameters, and is given as the second moment of the score of the
likelihood
\begin{equation}
    \textbf{F}_{\alpha \beta} = \int d \textbf{d}\ \mathcal{L}(\textbf{d} | \boldsymbol{\theta}) \frac{\partial \ln \mathcal{L}(\textbf{d} | \boldsymbol{\theta})}{\partial \theta_\alpha} \frac{\partial \ln \mathcal{L}(\textbf{d} | \boldsymbol{\theta})}{\partial \theta_\beta},
\end{equation}
and can be written as
\begin{equation}\label{eq:fisher-def}
    \textbf{F}_{\alpha \beta} = -\left\langle \frac{\partial^2 \ln \mathcal{L}}{\partial \theta_\alpha \partial
\theta_\beta} \right\rangle \Big|_{\boldsymbol{\theta} = \boldsymbol{\theta}_{\rm fid}} .
\end{equation}
A large Fisher information for a set of data indicates that the data is very informative about the model
parameters attributed to it. Fisher forecasting for a given model is made possible by the Cram\'er-Rao bound \citep{cramerharald_1946, rao_1945}, which states that the minimum variance of the value of an estimator $\boldsymbol{\theta}$ is given by
\begin{equation}\label{eq:cramer-rao}
    \langle (\theta_\alpha - \langle \theta_\alpha \rangle ) (\theta_\beta - \langle \theta_\beta
    \rangle) \rangle \geq \textbf{F}^{-1}_{\alpha \beta}.
\end{equation}

We will write the compression as a function $f:\textbf{d} \rightarrow \textbf{{x}}$. For large datasets, data compression is essential for inference to avoid the curse of dimensionality. The MOPED formalism \citep{Heavens_2000} gives optimal score compression for cases where the likelihood is  well-approximated by a Gaussian form.

IMNNs are neural networks that optimize data compression and compute the Fisher information of a data set even if the data likelihood is unknown or intractable, simply based on having simulations of the data at a given fiducial parameter point and local information about how the parameters change the data distribution. It can be shown (Wandelt, 2021, in preparation) that the optimality of the IMNN summaries holds for any unknown or intractable data likelihood even though the IMNN maximizes Fisher information assuming the Gaussian likelihood form for the IMNN summaries
\begin{equation}\label{eq:og-moped-like}
    -2 \ln \mathcal{L}(\textbf{{x}} | \textbf{d}) = (\textbf{{x}} - \boldsymbol{\mu}_f(\boldsymbol{\theta}))^T \textbf{C}_f^{-1}(\textbf{{x}} - \boldsymbol{\mu}_f(\boldsymbol{\theta}))
\end{equation}
where
\begin{equation}
    \boldsymbol{\mu}_f(\boldsymbol{\theta}) = \frac{1}{n_s} \sum_{i=1}^{n_s} \textbf{{x}}_i^s
\end{equation}
is the mean of the compressed summaries $\textbf{x}_i^s$, with $\{\textbf{x}^s_i | i \in [1, n_s] \}$. Here $i$ indexes the random initialisation of $n_s$ simulations. The data are obtained via simulation $\textbf{d}^s_i = \textbf{d}_i^s(\boldsymbol{\theta}, i)$ via the compression scheme $f:\textbf{d}_i^s \rightarrow \textbf{x}_i^s$. The covariance of the summaries is computed from the data as well:
\begin{equation}
    (\textbf{C}_f)_{\alpha \beta} = \frac{1}{1- n_s}\sum_{i=1}^{n_s} (\textbf{{x}}_i^s - \boldsymbol{\mu}_f)_\alpha (\textbf{{x}}_i^s - \boldsymbol{\mu}_f)_\beta.
\end{equation}
A modified Fisher matrix can then be computed from the likelihood in equation \ref{eq:og-moped-like}:
\begin{equation}\label{eq:fisher-compressed}
    \textbf{F}_{\alpha \beta} =  \tr [\boldsymbol{\mu}_{f,\alpha}^T C^{-1}_f \boldsymbol{\mu}_{f, \beta}],
\end{equation}
where we introduce the notation $\bm{y}_{,\alpha}\equiv\frac{\partial \bm{y}}{\partial\theta_\alpha}$ for partial derivatives with respect to parameters. If the compression function $f$ is a neural network parameterized by layer weights $\textbf{w}^\ell$ and biases
$\textbf{b}^\ell$ (with $\ell$ the layer index), the summaries (and respective mean and covariance) then become
functions of these new parameters $\textbf{{x}}(\boldsymbol{\theta}) \rightarrow \textbf{{x}}(\boldsymbol{\theta}, \textbf{w}^\ell, \textbf{b}^\ell)$. To evaluate equation \ref{eq:fisher-compressed} for a neural compression, we must compute
\begin{equation}
    \boldsymbol{\mu}_{f,\alpha} = \frac{\partial}{\partial \theta_\alpha} \frac{1}{n_s}\sum^{n_s}_{i=1} \textbf{{x}}^{s\ \rm fid}_i
\end{equation}

One way of computing the derivatives of the summary means with respect to the parameters is to define a finite difference gradient dataset by altering simulation fiducial values by a small amount, yielding
\begin{equation}\label{eq:discrete-deriv}
    \left( \frac{\partial \hat\mu_i}{\partial \theta_\alpha} \right)^{s\ \rm fid} \approx \frac{1}{n_s}\sum^{n_s}_{i=1} \frac{\textbf{{x}}^{s\ \rm fid +}_i - \textbf{{x}}^{s\ \rm fid -}_i}{\Delta \theta^+_\alpha - \Delta \theta^-_\alpha}.
\end{equation}
However, this discrete numerical differentiation requires more memory ($\theta_\alpha^{\rm fid \pm}$ datasets), as well as the hyperparameter tuning for the size of the numerical derivatives.

An alternative we will explore in this paper is to calculate the adjoint gradient of the simulations as well as the derivatives of the network parameters with respect to the simulations:
\begin{equation}\label{eq:autograd-enabled}
    \boldsymbol{\mu}_{f,\alpha} =  \frac{1}{n_s}\sum^{n_s}_{i=1} \left( \frac{\partial \textbf{{x}}}{\partial \theta_\alpha} \right)_i^{s\ \rm fid} = \frac{1}{n_s} \sum^{n_s}_{i=1} \sum^{n_d}_{k=1} \frac{\partial \textbf{{x}}^{s\ \rm fid}_i}{\partial d_k}\frac{\partial \textbf{d}^{s\ \rm fid}_i}{\partial \theta_\alpha} .
\end{equation}
If the gradient of the simulations can be computed efficiently, this technique for computing the compression Fisher information eliminates the need for hyperparameter tuning of the finite difference derivative size, $\Delta \theta_\alpha$.

The network compression is trained to maximise the determinant of the Fisher information, computed via equation \ref{eq:fisher-compressed}.
As described in \citeauthor{Charnock_IMNN} and \citeauthor{livet2021catalogfree}, the Fisher information is invariant to nonsingular linear transformations of the summaries. To remove this ambiguity, a term driving covariance to the identity matrix is added
\begin{equation}
    \Lambda_C = \frac{1}{2} \left( \left|\left|(\textbf{C}_f-\mathbf{1})\right|\right|^2_\mathcal{F} + \left|\left|(\textbf{C}^{-1}_f-\mathbf{1})\right|\right|^2_\mathcal{F} \right),
\end{equation}
where  $||\bm{A}||_\mathcal{F}\equiv \sqrt{\tr{\bm{AA}^T}}$ denotes the Frobenius norm. This yields the loss function
\begin{equation}\label{eq:imnn-loss}
\Lambda = -|\det \textbf{F} | + r_{\Lambda_C} \Lambda_C,
\end{equation}
with regularization parameter
\begin{equation}
    r_{\Lambda_C} = \frac{\lambda \Lambda_C}{\Lambda_C + \exp(-\alpha \Lambda_C)},
\end{equation}
where $\lambda$ and $\alpha$ are user-defined parameters. When the covariance is far from identity, the $r_{\Lambda_C}$ function is large and the optimization focuses on bringing the
covariance and its inverse back to identity. The network is trained until the Fisher information stops increasing for a pre-determined number of iterations.

\subsection{On-the-fly training }
For this study we introduce some modifications to the IMNN implementation, including sampling and simulations written in \texttt{Jax}. The \texttt{Jax} XLA backend allows for efficient GPU-enabled numerical differentiation. If simulations are exactly and efficiently differentiable, equation \ref{eq:autograd-enabled} can be used to eliminate the need for the two copies of derivatives needed for $\{ \theta_\alpha^{\rm fid \pm} \}$ in equation \ref{eq:discrete-deriv}. For cheap simulators, \texttt{Jax}'s auto-differentiation allows simulation realizations and their derivatives to be generated anew each epoch for neural network training, additionally eliminating the need for a validation dataset.

\subsection{Iterative IMNN training}\label{subsec:iterative-training}
In cases where the fiducial model is poorly chosen for the compression, e.g. $\boldsymbol{\theta}_{\rm target}$ is very far from $\boldsymbol{\theta}_{\rm fid}$, we still wish our IMNN to be able to estimate the correct posterior. In these circumstances, an iterative training scheme can be adopted, namely
\begin{enumerate}
    \item Train IMNN on $\boldsymbol{\theta}_{\rm fid}$ and perform a Gaussian Approximation on target data using the IMNN's Fisher matrix and score estimation
    \item If $\boldsymbol{\theta}_{\rm MLE}$ is more than $ 1\sigma$ from $\boldsymbol{\theta}_{\rm fid}$, retrain the IMNN using $\boldsymbol{\theta}_{\rm fid} \gets \boldsymbol{\theta}_{\rm MLE}$. If not, stop.
\end{enumerate}
We explore this method in the context of dark-matter-like field inference in Section \ref{sec:cosmo}.

\section{Simulation-Based Inference Techniques}\label{sec:sbi}
For many astronomical and cosmological problems, it can become too difficult to write down analytic likelihood functions to describe both physics and survey instrumental effects. In these situations, Approximate Bayesian Computation (ABC) can make inference possible when a likelihood is not available \citep{grazian2020review}. ABC is a technique in which parameters are sampled from a prior and used to forward simulate mock data to be compared to the real data, and accepted if the corresponding mock data (or compressed summaries) are ``close enough'' by a pre-defined metric to the target data or summaries. \citep{Cranmer30055}.

However, ABC methods can scale poorly with large prior volumes and high parameter dimensionality, making the forward simulation step expensive for large simulations like N-body grids. Methods like Population Monte Carlo can improve convergence by drawing from a weighted prior each iteration \citep{kitagawa96}, but are still highly simulation-intensive. Density Estimation Likelihood Free Inference (DELFI) \citep{pydelfiAlsing_2019} instead leverages neural density estimators to parameterize the \textit{summary data likelihood}, $p(\textbf{{x}} | \boldsymbol{\theta})$. These neural networks can be trained efficiently on a smaller number of parameters drawn from the prior and their respective compressed forward simulations. Once $p(\textbf{{x}} | \boldsymbol{\theta})$ is learned, the likelihood can be evaluated at $\textbf{{x}}_{\rm target}$ and multiplied by the prior to yield the posterior $p(\boldsymbol{\theta} | \textbf{{x}}) = p(\textbf{{x}} | \boldsymbol{\theta})\times p(\boldsymbol{\theta})$. In this work we primarily consider Conditional Masked Autoregressive Flows (CMAFs). CMAFs are stacks of neural autoencoders carefully masked to parameterize the summary-parameter likelihood. This can be seen by noting that any probability density can be factored as a product of one-dimensional conditional distributions via the chain rule of probability:
\begin{equation}
    p(\textbf{x} | \boldsymbol{\theta}) = \prod_{i=1}^{\dim(\textbf{x})} p({\rm x}_i | \textbf{x}_{1:i-1}, \boldsymbol{\theta}).
\end{equation}
Masked Autoencoders for Density Estimation (MADE) \citep{papa_mafs2017, papamakarios2019sequential} model each of these one-dimensional conditionals as Gaussians with mean and variance parameters parameterized by neural network weights, $\textbf{w}$. The neural network layers are masked in such a way that the autoregressive property is preserved, e.g. the output nodes for the density $p({\rm x}_i | \textbf{x}_{1:i-1}, \boldsymbol{\theta})$ only depend on $\textbf{x}_{1:i-1}$ and $\boldsymbol{\theta}$, satisfying the chain rule. MADEs can then be stacked into CMAFs for stable summary likelihood estimation \citep{pydelfiAlsing_2019}. CMAFs are trained to minimize the log-probability, $-\ln U = -\sum_i \ln p(\textbf{{x}}_i | \boldsymbol{\theta}_i; \textbf{w})$, where $i$ indexes over a training batch of $\{\textbf{{x}}, \boldsymbol{\theta} \}_i$ pairs.

\section{Benchmarking Inference with 2D Gaussian Fields}\label{sec:benchmark}
\begin{figure}[h!]
    \centering
    \includegraphics[width=0.4\textwidth]{figures/bhm-gauss-fields.png}
    \caption{Diagram of the Bayesian hierarchical model and inference techniques for inferring parameters from Gaussian fields. Yellow shaded boxes indicate probability distributions, while arrows denote deterministic connections. The inference schemes considered in this work are denoted by dashed boxes and correspond to their respective contours in figure \ref{fig:128x128-inference}.}
    \label{fig:bhm-gauss}
\end{figure}
We begin verifying a convolutional neural network (CNN) compression scheme within the IMNN framework on 2D Gaussian fields generated from the toy power spectrum model
\begin{equation}\label{eq:toy-powerspec}
    P (k) = Ak^{-B}
\end{equation}
where $\boldsymbol{\theta} = \{A,B \}$ are the two ``cosmological'' parameters of interest in the field measurement. The parameter $A$ controls the amplitude of the power in Fourier space, while $B$ describes the scale-dependency of the power modes. We compare the implicit likelihood inference using the IMNN compression to a full field-level data assimilation (DA) inference, in which all measured field values are used in the inference to hand.

\subsection{Field-Level Inference via Data Assimilation}
Field-level inference aims to obtain posterior distributions for $A$ and $B$ using all field values $\textbf{d}$, indicated by the orange box in the hierarchical model in figure \ref{fig:bhm-gauss}. The likelihood for an $N_{\rm pix}\times N_{\rm pix}$ Gaussian field can be explicitly written down for the Fourier transformed data, $\boldsymbol{\Delta}$ as:
\begin{equation}\label{eq:field-like}
    \mathcal{L}{}(\boldsymbol{\Delta} | \boldsymbol{\theta}) = \frac{1}{ \det(2\pi\textbf{C})^{1/2}}\exp{\left(-\frac{1}{2} \boldsymbol{\Delta}^T \textbf{C}^{-1} \boldsymbol{\Delta} \right)}
\end{equation} where the covariance matrix $\textbf{C} = P(k)$ is just the target power spectrum.
It is helpful to picture ``unwinding'' the gridded data as
a vector of pixel values of shape $\boldsymbol{\Delta} \in
\mathbb{R}^{N_p}$, where $N_p = N^2$. At this point our
likelihood is a function of the observed data and the
parameters $\boldsymbol{\theta}$ governing our theoretical model. Since the entire field is used for the parameter estimation with no intermediate compression step,
this can be viewed as the exact solution to the inference problem.

\subsubsection{Analytic Fisher Matrix}
To test our compression scheme, it is also of interest to obtain the exact information content of the Gaussian Field. For the DA likelihood of equation \ref{eq:field-like}, the Fisher Matrix for parameters indexed by $\alpha, \beta$ is given by \citep{Dodelson_2003}:
\begin{equation}\label{eq:fisher}
    \textbf{F}_{\alpha \beta} = \langle \mathcal{F} \rangle= \frac{1}{2} \tr (\textbf{C}_{, \alpha} \textbf{C}^{-1} \textbf{C}_{, \beta} \textbf{C}^{-1}),
\end{equation}
where $\textbf{C}$ is the full-rank covariance matrix appearing in equation \ref{eq:field-like} (see Appendix \ref{app:fisher-field-comp} for a detailed calculation).

For our simple power law case, the covariance between modes is given as:
\begin{equation}
    \textbf{C}_{k_i, k_j} = \left( P (k_i) \right) \delta_{ij} .
\end{equation}
To compute the Fisher information for the two-parameter model $\boldsymbol{\theta} = (A,B)$, only the first derivatives of the covariance,
\begin{align}
    \frac{\partial P}{\partial A} &= \left( k_i^{-B} \right)\delta_{ij} \\
    \frac{\partial P}{\partial B} &= \left( -Ak_i^{-B}\ln k_i \right) \delta_{ij}
\end{align}
are needed. Evaluating Eq. \ref{eq:fisher} numerically for an $N_{\rm pix}=128$ field in grid units with a $\textbf{k}\in [0.5 / 128, 1.0]$ and $\boldsymbol{\theta}_{\rm fid} = \{1.0, 0.5\}$ yields a Fisher Information matrix of
\begin{equation}
    \textbf{F} = \begin{pmatrix}
     2047.5  & -1556.2 \\
    -1556.2  & 1743.1
    \end{pmatrix},
\end{equation}
which yields a determinant of 1147281, or a Shannon entropy $\frac{1}{2}\ln \det \textbf{F}= 6.9765$ nats, for $\theta_{\rm fid} = \{1.0, 0.5\}$
We note that we compute this value for all unique modes of the Fourier-transformed field excluding the first (zero) mode.

\subsection{Approximate Bayesian Computation with Optimal Compression}

To test the IMNN compression framework, we also wish to infer $A$ and $B$ via simulation
based-inference with a compression step. The ABC scheme is illustrated in figure \ref{fig:bhm-gauss} via the orange box, with the IMNN compression step denoted by the grey box, yielding summaries $\textbf{x}$. Once an IMNN is trained on a fiducial model, the network
mapping is used to compress raw field data to maximally informative summaries that can be used for learning the likelihood, as in DELFI, or performing
Approximate Bayesian Computation (ABC). Given target data $\textbf{d}$ and its corresponding summaries \textbf{\textbf{{x}}}, parameters are drawn from the priors, in our case the uniform $\mathcal{P}(A)$ and $\mathcal{P}(B)$, used to generate field simulations, which are then fed directly into the network to produce corresponding summaries. The optimal distance measure $\varrho_k^t$ obtained in \cite{alsing2018_general} can be defined using attributes of the IMNN:
\begin{equation}\label{eq:abc-distance}
    \varrho_k^t = \sqrt{(\textbf{x}^{s,t}_{ik}-\textbf{x})^T \textbf{F}_{\rm IMNN} (\textbf{x}^{s,t}_{ik} - \textbf{x})},
\end{equation} where $s$ indexes the summaries, and $i$ labels the random initialisation. Parameter draws are accepted or rejection if the distance $\varrho_k^t$ between simulation and target summaries is within some threshold, $\epsilon$.

\begin{figure}[h!]
    \centering
    \includegraphics[width=0.35\textwidth]{figures/incept-block-small.png}
    \caption{Inception block architecture. We adopt stride-4 downsampling before filter concatenation to quarter the spatial dimensions of the simulations.}
    \label{fig:incept-block}
\end{figure}

\subsubsection{Neural Network Architecture}
With the analytic Fisher Information known, we can test a neural compression scheme within the IMNN framework for the $N_{\rm pix}^2$ field dataset. The network takes as input an $N_{\rm pix}\times N_{\rm pix}$ field, and extracts information via a convolutional compression scheme. We tested several architectures for our chosen $N=128$ simulations, but found an inception-block CNN to be most efficient in training \citep[e.g][]{szegedy2016inceptionv4}. For each inception block, data is passed through $5^2$, $3^2$, $1^2$ convolutions and a \texttt{maxpool} layer in parallel, with outputs concatenated and passed to the next block, shown graphically in figure \ref{fig:incept-block}. We adopt three stride-4 inception blocks, each with $n_f=55$ filters, quartering the output spatial dimensions, each followed by a Leaky \texttt{ReLU} nonlinear activation function. Once spatial dimensions are of shape $(2,2)$, we adopt a stride-2 inception block with $1^2$ kernels followed by a $1^2$ convolution to $n_{\rm summaries} = n_{\rm params} = 2$ summaries.

To train the network, we generate 200 new simulation realizations on-the-fly each epoch. We make use of \texttt{Jax}'s autograd feature to implement equation \ref{eq:autograd-enabled}, obtaining both simulations and exact derivatives with respect to simulation parameters each epoch for the Fisher information computation. We train the network with the \texttt{Adam} optimizer \citep{kingma_adam_2014} and coupling parameters $\lambda=10$ and $\alpha=0.95$ until the Fisher information stopped increasing for 500 epochs.

\subsection{Numerical Results}
\begin{figure}[htp!]
    \centering
    \includegraphics{figures/128x128-training.png}
    \caption{On-the-fly IMNN training using $128\times128$ field simulations.  Within 550 epochs, the network is able to extract 90 \% of the theoretical Fisher information (dashed black line), saturating to $98\%$ by 1500 training epochs.}
    \label{fig:training}
\end{figure}

In this section we present the numerical results obtained from the two inference methods.

\begin{figure}[htp!]
    \centering
    \includegraphics{figures/128x128/128x128-inference-contours-3sig-col.png}
    \caption{Inference for power spectrum-generated $128\times128$ Gaussian random field. The target
    field ({top right panel}) was generated using a $\boldsymbol{\theta}_{\rm target} = (0.9,0.6)$, shown
    via the dashed black lines. The Gaussian approximation ({green contour}) and ABC
    computation ({purple histogram}) were made using an IMNN-calculated Fisher matrix, trained on a
    fiducial
    $\boldsymbol{\theta}_{\rm fid}=(1.0, 0.5)$, ({dashed grey crosshairs}). Accepted ABC simulations are displayed in the scatterplot, coloured by ABC distance. The ABC computation overlaps
    with the full field likelihood along the entire prior range, indicating that the convolutional
    network has effectively summarised the field data for exact inference.}
    \label{fig:128x128-inference}
\end{figure}

We begin by analysing a single Gaussian field realization generated by $\theta_{\rm target} = \{0.8,
0.8 \} $, shown in the top right panel of figure \ref{fig:128x128-inference}. We first compute the
field-level likelihood from equation \ref{eq:field-like} over the prior range $\mathcal{P}(A) = \mathcal{U}(0.1,
2.0)$ and $\mathcal{P}(B) = \mathcal{U}(0.1, 2.0)$, displayed by the orange contours in figure
\ref{fig:128x128-inference}. We then trained an IMNN from simulations generated from the fiducial model $\boldsymbol{\theta}_{\rm fid} = \{1.0, 0.5 \} $ until the extracted $\det \textbf{F}$ stopped increasing for 500 epochs (matching the theoretical saturation limit in figure \ref{fig:training}).  Using the trained IMNN, we then use the compressed summaries' Fisher matrix to compute first a Gaussian approximation to $\boldsymbol{\theta}_{\rm target}$, shown by the green contours in the figure. We then use the IMNN Fisher as a proposal distribution for constructing the simulation-based inference contours via ABC and equation \ref{eq:abc-distance} with $\varepsilon = 0.05$, with accepted points histogrammed in purple. We run 20,000 simulations until a cumulative 1279 proposal parameters were accepted, which takes approximately 20 minutes on a single GPU.

The IMNN posterior is almost as tight as the field-level inference, indicating that the nonlinear
compression has successfully summarized the field data at the same precision level as using all of the data to hand.

For this example we verified our technique with Approximate Bayesian Computation, but for the next example we find a massive reduction in the number of simulations needed by employing DELFI techniques for inference.

\section{Cosmological Parameters from Mock Dark Matter Fields}\label{sec:cosmo}
Here we consider an application of the differentiable IMNN framework making use of a more cosmologically-relevant power spectrum in the context of inferring parameters from a dark matter field. Log-normal fields are often used as an approximation to late-time cosmological overdensity fields \citep[][]{ln-coles-jones, leclercq2021accuracy}. Specifically, we simulate log-normal fields from Gaussian noise \textit{to have a specified power spectrum}, $P_{\rm LN}(k)$ (see Appendix \ref{sec:logfromgauss}). Since the lognormal field is a bijective mapping of the Gaussian field it must conserve the information it contains.  Therefore we can  calculate the theoretical Fisher information content contained in the lognormal field by  equation \ref{eq:fisher} with the covariance of the underlying Gaussian field.  To do so we need to obtain the underlying Gaussian field's power spectrum, $P_{\rm G}$, since this spectrum is diagonal in $k$-space. We employ the backwards conversion formula, presented in \cite{Greiner_2015} to obtain
\begin{equation}\label{eq:backwards-conv}
    P_{\rm G} = \int d^u x e^{i \textbf{k} \cdot \textbf{x}} \ln \left( \int \frac{d^u q}{(2\pi)^u} e^{i \textbf{q} \cdot \textbf{x}} P_{\rm LN}(\textbf{q}) \right),
\end{equation}
where $u=N_{\rm pix}$ is the dimensionality of the space. Once calculated, we can proceed to take derivatives of $P_{\rm G}$ to evaluate equation \ref{eq:fisher} as before.

We simulate scaled log-normal fields with the Eisenstein-Hu linear matter power spectrum \citep[]{Eisenstein_1999} as our $P_{\rm LN}$, implemented differentiably in the \texttt{jax-cosmo} module \citep{jax_cosmo_2020}. We seek to infer the critical matter density parameter, $\Omega_c$, as well as $\sigma_8$, the r.m.s. fluctuation of density perturbations at the 8 $\rm h^{-1} Mpc$ scale. Implementing the simulator and power spectrum in \texttt{Jax} means exact numerical derivatives can be computed for $P_{{\rm G},\Omega_c }$ and $P_{{\rm G},\sigma_8 }$. Evaluating equation \ref{eq:fisher} with these expressions at the fiducial model $(\Omega_c, \sigma_8) = (0.6, 0.6)$ yields a Shannon information of 6.2056.

We generate four target fields each with cosmological volume $V = L^2 = (250 \ \rm h^{-1}\ Mpc)^2$ on a $128^2$ grid using Planck 2015 parameters \citep[][]{planck2015} at redshift $z=0$ (present day). For this example, we explore the iterative
training method introduced in Section
\ref{subsec:iterative-training}. We adopt an IMNN
pipeline with a neural network identical to the
InceptNet used in the Gaussian Fields example, trained on-the-fly with $n_s = n_d = 200$ at a deliberately far-away fiducial model, $\boldsymbol{\theta}_{\rm fid, 1} = (0.6, 0.6)$. We train the IMNN until the Fisher information from compressed summaries stops increasing for 500 epochs, and then proceed to making score estimates on the target fields, adopting a new fiducial model, $\boldsymbol{\theta}_{\rm fid, 2}$ at the mean of the four target estimates. We find that in both training cases the network saturates to above $90\%$ of the respective theoretical field information content.

\subsection{DELFI Setup}
\begin{figure}[h!]
    \centering
    \includegraphics[width=0.39\textwidth]{figures/delfi-plate-diagram.png}
    \caption{DELFI training setup with IMNN summaries. We train $N_{\rm MAF}=4$ MAFs per target data, first on 1000 simulations from parameters drawn from the prior, then on 3 subsequent subsequent draws from the posterior to produce the blue contours in figure \ref{fig:cosmo-inference}.}
    \label{fig:delfi-setup}
\end{figure}
For this inference we construct Conditional Masked Autoregressive Flows (CMAFs) \citep{papa_mafs2017, papamakarios2019sequential} to perform DELFI posterior estimation for the cosmological parameters, shown graphically in figure \ref{fig:delfi-setup}. For each target field, we utilize an ensemble of 4 networks \citep{deep_ens, pydelfiAlsing_2019} consisting of 5 MADEs, each with two hidden layers of 50 neurons. For our training scheme we first sample 1000 simulations from the prior, simulate fields, compress with an IMNN, and train each DELFI ensemble on batches of 100 $\{\textbf{{x}}, \boldsymbol{\theta} \}$ pairs (with a 75-25\% train-validation split) for 1000 epochs with an \texttt{Adam} optimizer with learning rate $10^{-3}$. We then sample the posterior following \citep{papamakarios2019sequential} for new parameters using a  Tensorflow affine-invariant MCMC sampler (adapted from \citep{Foreman_Mackey_2013} and implemented in the \texttt{pydelfi} package \citep{pydelfiAlsing_2019}). Then we simulate  fields from these parameters and compute their compressed summaries. We append the new training data and re-train the CMAFs iteratively until $-\ln U$ stops decreasing significantly.

\subsection{Results}

\begin{figure}[htp!]
    \centering
    \includegraphics{figures/cosmo-IMNN-training.png}
    \caption{On-the-fly IMNN training using $128\times128$ cosmological field simulations at the initial fiducial model $(\Omega_c, \sigma_8)=(0.6,0.6)$.  Within 1600 epochs of on-the-fly sets of 200 simulations, the network is able to extract $90\%$ of the theoretical Fisher information (dashed black line), saturating to $100\%$ by 3000 training epochs.}
    \label{fig:cosmo-training}
\end{figure}

\begin{figure*}[htp!]
    \centering
    \includegraphics[width=\textwidth]{figures/new-four-cosmo-field-comparison.png}
    \caption{Field-based inference comparison for four independent log-normal cosmological fields (top row). Using IMNN compression immediately gives estimates and Gaussian Approximation uncertainties (black contours) for cosmological parameters, even for a poorly-chosen fiducial model. Even a single iteration of IMNN compression (circle and star) gives summaries that are nearly maximally informative compared to theoretical estimates. Using IMNN summaries, both ABC (orange) and DELFI (blue) methods give consistent posterior contours. DELFI matches ABC compression but requires $\gtrsim$100 times fewer simulations. }
    \label{fig:cosmo-inference}
\end{figure*}

We display target log-normal dark matter fields and inference results in figure \ref{fig:cosmo-inference}. We first train the IMNN on the poor fiducial cosmological model $\boldsymbol{\theta}_{\rm fid} = (\Omega_c, \sigma_8) = (0.6, 0.6)$, with all other power spectrum parameters consistent with Planck15. Training saturated at $100\%$ of the Shannon information content of the field at the fiducial model, shown in figure \ref{fig:cosmo-training}. We then performed a Gaussian Approximation on the four target fields using the IMNN's Fisher matrix. Since the IMNN's parameter estimates move more than 1$\sigma$ from the fiducial model, we train a new IMNN at the score estimates, $\boldsymbol{\theta}_{\rm fid, 2} = (0.229, 0.745)$, saturating to 98\% of the corresponding Shannon information. With the compression closer to the target, we then train a DELFI ensemble for each target data over the wide priors $\mathcal{P}(\Omega_c) = \mathcal{U}(0,1.5)$ and $\mathcal{P}(\sigma_8) = \mathcal{U}(0, 1.5)$ for 4 iterations, recovering the blue posteriors needing a total of only 4000 simulations per target data inference. We also compare the DELFI estimates to more expensive ABC sampling, for which we ran 50,000 simulations per target datum with an acceptance parameter $\epsilon=0.1$. Accepted points ($\approx 250$ per field) are coloured according to the log of the distance calculation in equation \ref{eq:abc-distance}.

\section{Discussion \& Conclusion}

In this study, we compared posteriors obtained from implicit likelihood inference via optimally compressed nonlinear summaries to exact likelihood computation for Gaussian field inference. We show that nonlinear summaries from sufficiently expressive convolutional neural networks saturate the known Fisher information content in Gaussian fields. Implicit likelihood inference with this optimal compression yields the exact analytic posterior obtained via the full-field analytic likelihood computation, meeting the benchmark for implicit likelihood inference. We then apply the same network to log-normal fields generated by a more realistic cosmological power spectrum, demonstrating the applicability of our pipeline.

We also introduced new aspects to the IMNN framework. Implementing the network and simulator in \texttt{Jax}'s fully-differentiable framework meant having exact derivatives of simulation parameters with respect to the compression network, eliminating the need for validation and finite difference derivative datasets, significantly reducing the amount of memory needed for network training.

We also demonstrated IMNN training in an iterative fashion where the initial fiducial model is poorly chosen. Since the IMNN compression is trained at a parameter point (rather than using parameters drawn from a prior) a network trained far from the target data cannot be expected to be maximally informative about the target, leading to suboptimal inference. To address this, we performed a single iteration of  IMNN training for four mock dark matter log-normal fields. Although initially trained far from the target, the target data parameter estimates obtained from the first IMNN allowed the new compression to be trained much closer to the posterior mean, yielding tighter posteriors with the updated IMNN.

The results of this work hold several implications for cosmological parameter estimation. With a Fisher information-maximizing nonlinear compression, the full information of a cosmological field can be represented by optimal summaries, allowing for likelihood-free or simulation-based inference, resulting in posteriors for cosmological or astrophysical parameters. The equivalence of these posteriors based on  IMNN summaries to the analytic solution for Gaussian fields demonstrates that given a sufficiently expressive convolutional network compression, implicit likelihood inference with nonlinear summaries can yield near-exact posteriors.

\cite{leclercq2021accuracy} raised the question whether implicit likelihood, or simulation-based, approaches can give results that are comparable to full field-based implementations of Bayesian Hierarchical Models, especially for non-Gaussian fields with heavy tail probabilities, such as log-normal data. While we do not directly study the specific example used in that work, our results seem to provide evidence that IMNNs provide near-optimal summaries for  correlated log-normal fields with cosmological power spectra. It can therefore be hoped that the massive compression techniques we describe here remain promising for cosmological parameter estimation as a complement to bespoke sampling implementations that  marginalize high-dimensional latent parameters in  Bayesian Hierarchical Models with complex physical modeling and observational effects \citep[see e.g.][]{jasche_bayesian_2013,jasche2015,lavaux_unmasking_2016,Jasche2019_PM,pydelfiAlsing_2019}.

Follow-up study is warranted on much larger (e.g. three-dimensional) datasets and with more parameters,  with a view to readying this framework for application to inference from detailed physical simulations and, ultimately, realistic datasets.

\section{Code Availability}
The code used for this analysis is available at \url{https://github.com/tlmakinen/FieldIMNNs}. Full documentation for the IMNN software is available at \url{https://www.aquila-consortium.org/doc/imnn/index.html}.

\begin{acknowledgments}
T.L.M acknowledges the hospitality of SISSA, Trieste, where part of this work was completed; and Master's scholarship funding from Sorbonne University.
B.D.W. acknowledges support by the ANR BIG4 project, grant ANR-16-CE23-0002 of the French Agence Nationale de la Recherche;  and  the Labex ILP (reference ANR-10-LABX-63) part of the Idex SUPER, and received financial state aid managed by the Agence Nationale de la Recherche, as part of the programme Investissements d'avenir under the reference ANR-11-IDEX-0004-02.
The Flatiron Institute is supported by the Simons Foundation. T.C. acknowledges financial support from the Sorbonne Univ. Emergence fund, 2019-2020. J.A. was supported by the research project grant Fundamental Physics from Cosmological Surveys funded by the Swedish Research Council (VR) under Dnr 2017-04212.
\end{acknowledgments}

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The YOUNG PEOPLE'S CHAMBER ORCHESTRA was founded in 1982 by beloved music teacher Ellen Mindell. This year Young People's Chamber Orchestra celebrates its 31st anniversary! Originally a single all-strings orchestra for young musicians, YPCO now includes the Chamber Orchestra and the Advanced Ensemble. Our musicians come from all parts of the Bay Area– Berkeley, Albany, Kensington, Oakland, Lafayette, Richmond, El Cerrito, San Pablo, Marin, Santa Clara and San Francisco.
YPCO's mission is to provide a musical learning experience for young musicians in the community. As a teaching orchestra, YPCO promotes a non-competitive and cooperative philosophy, welcoming the skills and talents of all our members with equal warmth. We believe that, through music, our students develop their abilities to cooperate, focus, communicate and work towards a common goal. Of course, we also work hard to develop musical skills, including technique, rhythm, intonation, dynamic control, interpretation, and expression. For many of our young musicians, the transition from individual lessons and practice to ensemble playing with YPCO introduces an exciting and tremendously motivating dimension of the world of music. There are performances several times a year, combining pieces for small chamber groups with pieces for the whole orchestra. Each chamber group has a coach, which allows us to give individual attention and encouragement to each young musician. More than anything, YPCO is about giving young musicians the opportunity to discover the joy of making music together.
Rem Djemilev has been the Music Director and Conductor for YPCO since 1998. Under Rem's gifted leadership, the orchestra has further solidified its reputation as a nurturing environment where young musicians can build their ensemble playing skills.


A magazine of poised prose, precarious poetry, and photography to pilot our own realms again.
"From A Friend" is a collection of poems promoting self-worth. It serves as a method of coping and spreading awareness of various themes.


text:
Citizens of Italy unleash mass protests against mandatory vaccination law
Monday, July 17, 2017 by: Cassie B.
Tags: anti-vaccine protests, Italy, measles outbreak, peaceful protests, vaccine laws, vaccine mandates
(Natural News) Italy's controversial new measure that requires young students to get vaccines against 12 common illnesses is not going over too well with the people, who have taken to the streets to protest the rule.
In May, officials ruled that kids will not be allowed to enroll in state-run schools until they've gotten the vaccines for measles, chicken pox, mumps, hepatitis B, tetanus and polio. Parents who send non-vaccinated kids to schools or even child care facilities will be given steep fines, and repeat offenders could even lose custody of their children. The parents will have to present proof of vaccinations each school year.
Last year, Italy introduced its "no jab, no pay" policy that took child benefits away from parents who failed to get their kids vaccinated. This resulted in 200,000 more kids getting vaccinated. Despite this increase, measles is on the rise in Italy, and the government is taking the opportunity to blame the jump in cases on not enough kids being vaccinated in an attempt to try to scare more people into getting shots. They have conveniently failed to point out the possible contribution of the shedding of the virus from those who have been vaccinated since that policy was instituted to the current epidemic.
Italy making some concessions in response to protests
People have been protesting for more than a month, and now it appears that their voices are being heard as the Italian Senate has appeared to soften its stance. A new proposal sees lighter penalties for those who do not get on board if the legislation passes and the original 12 required vaccines being reduced to ten. The amendments would also drop the requirement to report those parents who do not comply to authorities, which could have caused some parents to lose custody of their children. Meanwhile, the maximum penalty for older children who are already in school but haven't been vaccinated will be decreased from 7,500 Euros to 2,500 Euros.
While this is certainly an improvement, most Italians remain unhappy with the idea of any amount of forced vaccinations, and some people are criticizing the Italian government for its close relationship with vaccine maker Glaxo Smith Kline.
Italians' vaccine skepticism hardly surprising
The mainstream media, of course, has largely failed to cover the anti-vaccine protests, despite the presence of millions of people in major Italian cities shouting "We want freedom!" It's only natural that the people would want to have the freedom to choose whether they put their children's lives at risk with vaccines that contain all manner of horrific ingredients like thimerosal and formaldehyde.
In addition, it is not surprising that Italians would be skeptical of vaccines. On top of the growing body of evidence showing a link between vaccines and several scary side effects as well as autism, a flu vaccine made headlines in the country in 2014 when 13 people died after being given the jab. This prompted the Italian government to ban the batches that were behind the deaths.
The new decree must now pass through Italy's Chamber of Deputies, where it is expected to be approved, although there is the possibility that further amendments might be added.
Similar legislation was recently passed in France, where children will be required to get 11 vaccines despite widespread doubts among the population regarding vaccine safety and efficacy.
WakingTimes.com
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More news on anti-vaccine protests
New Jersey parents and lawmakers slam mandatory flu jabs for students
https://www.naturalnews.com/2017-07-17-citizens-of-italy-unleash-mass-protests-against-mandatory-vaccination-law.html
Citizens of Italy unleash mass protests against mandatory vaccination law

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What started by snapping images during holidays has over the past few years developed into a full love for the craft.
My focus is to document people and places in a natural way, highlighting the beauty of fleeting moments by creating timeless, yet fresh and original images.
I typically shoot lifestyle, travel and adventure. If you feel a connection with my photographs, please feel free to get in touch to explore the possibilities.
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Criminal Minds brought Season 12 to an explosive end earlier this month, and fans have had to wonder if everybody actually survived the events of the finale. Well, recent contract negotiations have revealed that two characters' fates are still up in the air. Negotiations between CBS and members Kirsten Vangsness and A.J. Cook have stalled with neither actress signing on for a Season 13 return just yet. Garcia and J.J. may not be back in the fall.
Kirsten Vangsness and A.J. Cook are negotiating together to seek higher pay for any subsequent seasons of Criminal Minds. The two actresses are seeking parity with their male cast members, who have historically made significantly more than them on the series. This is the second times Vangsness and Cook have joined forces to stand for a bump in salary; back in 2013, they held out on re-signing with the series because they were paid less than half of some of the men in the cast, including Shemar Moore and Matthew Gray Gubler. A deal was obviously struck back then, but Deadline states that both actresses will walk from Criminal Minds if they don't get some degree of parity with other actors this time.
The negotiations between CBS and the actresses reportedly did not even begin with Kirsten Vangsness and A.J. Cook until after the negotiations with Joe Montegna and Matthew Gray Gubler had concluded. Given that Kirsten Vangsness has been in the second most episodes of any Criminal Minds actor and both actresses have been on board longer than Joe Montegna, I'd say it's easy to see why they're sticking together for a salary bump. Garcia and J.J. are pivotal and popular characters on the show, which has already seen some major shakeups in the last couple of years due to the departures of Shemar Moore and Thomas Gibson.
Criminal Minds has made news in years past due to its treatment of female characters. Back in 2010, the show elected not to renew A.J. Cook for another season and reduced the episode count for Paget Brewster, who played Emily Prentiss, which resulted in Kirsten Vangsness as the only full-time female member of the cast. Both Cook and Brewster ultimately returned, and other female characters debuted over the years, but it makes sense that Cook and Vangsness are sticking together for Season 13.
Given the gigantic cliffhanger at the end of Season 12, the stalled negotiations will undoubtedly come as bad news for fans who were hoping for hints of who survived Mr. Scratch's finale trap. Garcia obviously won't have died, as she wasn't involved in the crash, but J.J. could very well be killed in the Season 13 premiere if CBS doesn't work something out with the actresses. That said, we shouldn't start panicking for J.J. or Garcia just yet. This isn't the first time that actresses on a hit CBS show have held out for parity, and negotiations may still be worked out to everybody's satisfaction. We'll have to wait and see.
It's unfortunate that Criminal Minds stars may be leaving the show. However, if you are looking to add all of your favorite seasons with the original cast to your dvd or blu-ray collection, you can check that out here.


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Non-Debate Debates
Who Won the YouTube Debate?
By retired, July 24, 2007 in Non-Debate Debates
Which candidate won?
1. Which candidate won?
Mike Gravel
Anderson Cooper / You!
retired 2208
Fermenting Revolution!
So, who won?
supersteph6590 10
I think there could be a potential debate as to who won the debate but I think it is fair to say Hilary lost. If that even makes sense, she spoke so much but really said nothing. I believe the only question she answered was the one asked if she would meet with the leaders of Iran, North Korea, Syria and Venezuela. Other than that I heard alot of nothing.
I think we need a female president but Hillary Clinton is NOT the right person for the job.
Lockesdonkey 421
Liberal Jihadist
I agree that BaraCk Obama won.
What can I say, I'm a stickler...On top of that, "Barak" makes me think of the leader of Ha'Avoda...
p.s. You can edit your poll options.
Lynn C. Thompson 1904
Warrior Lifestyle
I really do think that Barack stepped up in this one. I was dissapointed in the last few "unofficial" debates. However a political debate is hardly a debate more than everyone just saying what they think then going on to another question.
slcathena 629
Name:Sara
School:Lexington
Barack did a really good job staying on message, and didn't feel the need to yell every time he made a point like Hillary did. I was really pleased with his performance. Hillary's moment of pointing out the preliminaries to talking with dictators looked petty to me, particularly given how short their responses were.
i was tempted to say biden, richardson, or dodd. they all seemed to learn from their warm ups.
Sonic-Jihad 475
Name:Rob
School:Emory
I don't think these debates have winners...
Hillary is still the best candidate, without question.
why rob? why... What is the meaning of this word, best? Electability?
As in she would be the "best" president. Most people won't spend the time to learn about her Healthcare Plan, but it would have gone a long way to solving some of the major problems with the US healthcare system.
She's not stupid, she has experience both in national politics and the white house - she's the best candidate for the job.
tshuman 1763
Nobody, really...
Name:Terrance Shuman
School:Atlantic High School
I think Biden did well. I think he would be a good nominee and probably a pretty decent president. Not left-wing enough to get the party's nomination, though. I was less impressed with Richardson (probably because he's been blanketing Iowa with media buys for months and I'm tired of his shtick) and Dodd...
She's not stupid
No, she isn't. She is, however, ruthless, vindictive, and petty...
she has experience both in national politics and the white house
If you mean her administration would have their corruption, law-breaking, secrecy, and spin-control operations ready to hit the ground running, you're probably right!
[Note to the humor-impaired: Please spare me the "Bush is worse" retorts, okay? When it comes to that sort of stuff, the current administration is a bunch of rank amateurs compared to Hillary's folks...]
she's the best candidate for the job.
I'm not sure how you define "best," but she doesn't bring anything to the table you don't get with Biden other than her sex. Obama is a media candidate; if a white guy with his bio and accomplishments were running, no one would ever have heard of the guy. Edwards is a hothouse flower, not a national candidate. Richardson probably has more talent than most of these others (he is better spoken, more comfortable on TV, has that "gravitas" thing, etc.), but his positions come across as Gore/Kerry Redux. Dodd? Give me a freakin' break, okay?
TLF 2147483647
Name:dylan
sorry shu, i gotta ask. what makes "hillary's folks" worse than the bushies? and i'm asking for some very specific comparisons here - what corruption and lies have come from hillaries campaign/administrations, and why are they worse than the litany of lies and slew of corruptions that we've seen over the last 7 years?
if all you meant was that they are amateurs, as in they - their corruption/lies are only less sophisticated, that i think i'll spot you.
sorry shu, i gotta ask. what makes "hillary's folks" worse than the bushies?
We aren't going to have that conversation, I suspect, because we won't be able to agree on benchmarks for measurement. For instance, I don't recall anyone in the Bush administration being caught going through hundreds of confidential FBI files, but since it was mostly Republicans being researched you're probably okay with that (or think that it goes on all the time anyway). Whole books have been written about the Clintons' escapades in the White House; if those haven't been sufficient to convince you that things were pretty bad (both from a public policy and from a ethical perspective), nothing I say here is going to make any difference...
papak_06 237
I did!
We aren't going to have that conversation, I suspect, because we won't be able to agree on benchmarks for measurement.
probably true. i'd have to suspect the measurements used for someone who's as big an apologist for the white house
look i'm not trying to tell anyone the clinton's were spotles. obviously both administrations have done bad things. i'm just wondering where your comparison comes down. i was thinking ethically, mostly.
For instance, I don't recall anyone in the Bush administration being caught going through hundreds of confidential FBI files, but since it was mostly Republicans being researched you're probably okay with that (or think that it goes on all the time anyway).
is it worse than the privacy violations that come from the war on terror? or maybe it's that they were FBI files that's got you irked. so it's just a sort of flaunting of the justice system that's made the clinton's more unethical. sort of like bush white house reps saying "i dont know what you mean by equal justice under the law" or stonewalling inverstigation after investigation into it's people.
Whole books have been written about the Clintons' escapades in the White House; if those haven't been sufficient to convince you that things were pretty bad (both from a public policy and from a ethical perspective), nothing I say here is going to make any difference...
right. neither is wearing a white hat. i bet for every book on clinton there's one on bush. that's not really what i was asking.
Idon't see anything wrong with putting a relative political tyro like Obama in the Presidency, especially one with a pretty good group of people around him.
I would like to remind everyone that were an election held in Britain tomorrow, it is quite possible--perhaps likely--that a certain David Cameron would come out PM (the Tories have been doing very well in the polls, and outside South-East England, too). Cameron has been an MP for six years--two years longer than Obama would have were he to become President. And he would have been a frontbencher (which is the real equivalent of being a Senator in British politics) for a mere four years, and party leader for two. Obviously, an election isn't about to happen tomorrow, or this year. But if the UK Conservative Party is willing to entrust this (politically) young man with this very good organization around with the leadership, and if the British people are willing to award that party with that organization with a plurality in the opinion polls and an almost-certain increase of seats and maybe even the Premiership come the next election, then why can't the US entrust its Presidency to a man with similar experience? (Heck, Cameron has less experience in government as a whole; Obama was in local and state government for years, while Cameron went straight from party functionary to party candidate in '01). And don't talk about how the US presidency is unique. Yes, it is, I and recognize that.
I also recognize, however, that a President is no longer a single human being but rather the organization that he brings with him. The people who support him, advise him, and guide him are, put together, about as important as the man himself. While he does make the final decisions, most presidents--especially relatively inexperienced ones--will tend to govern in consultation with advisors. In addition, if Obama picks an experienced VP candidate (Joe Biden, Chris Dodd, and Carl Levin spring to mind...I won't say Richardson, though), that should shore up any concerns, I would imagine.
The president is not a man. He is an institution. And institutions can get very old and very experienced in a very short period of time.
Latent sexism aside, this really isn't the point.
No one would say that Obama is an idiot, or that he couldn't *eventually* be a good president...the point is that he doesn't have the lawmaking experience to become the president NOW.
There are some things that people have to learn about the political system, interacting with Foreign leaders, communicating to the American public and managing a huge portion of the government. Obama has little experience in most of those categories. His platform is idealistic, Clinton's is a bit more pragmatic. This is probably informed by her experience in the Governor's Mansion, White House, and Senate.
JFK is another example of a politically inexperienced person being president...and while everyone loves him because he was charismatic and got killed, he wasn't a great president. Obama would probably fall into the same trap.
Now - the critcism stemming from Obama's inexperience isn't that "Inexperience = no president." But rather, "Obama's inexperience has lead to a mediocre campaign, along with some problems in his ability to govern." If some political upstart jumped into the field and had EXCELLENT ideas along with a good uderstanding of the system, people would vote for him or her in a heartbeat. The point is that Obama isn't a great candidate, his inexperience contributes to that.
brorlob 1369
Name:Brett
Your nominee will be chosen for you.
I take it that you are referring to the healthcare plan from 15 years ago that failed? She has yet to release one this time. Although her bullet pointed memo was almost impressive.
Pressure of time, sorry...
I'll address the rest of the post later (pressure of time again).
At this point, she is too deep in the pockets of the insurance industry to really do anything meaningful. If you want decent nationalized healthcare, vote Socialist.
Pepsi One 57
Because People Are Idiots
Name:Kunal A.
School:West Bloomfield
gravel took the fuckin train
he wins...
I take it that you are referring to the healthcare plan from 15 years ago that failed?
Without being too nitpicky, the plan didn't fail - it failed to be enacted. This is an important distinction, because most people who have no knowledge of the healthcare system (or this plan specifically) would say the plan would have been a failure. That is factually inaccurate. There have been numerous studies done concerning the viability of the plan, and nearly all of them conclude that the plan would have reduced healthcare costs across the board, reduced institutional redundancy, improved the quality of healthcare, and given access to many more people.
It's all irrelevant - We're not getting universal health care from either of the major parties. Remember, it's not the republicans that killed the Clinton plan in 94.
There have been numerous studies done concerning the viability of the plan, and nearly all of them conclude that the plan would have reduced healthcare costs across the board, reduced institutional redundancy, improved the quality of healthcare, and given access to many more people.
I'm game. Post some links to such studies, if possible. My default position about social science research making such claims is severe skepticism...


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Sodagreen (chino: 蘇打綠, pinyin: Suda lǜ; estilizado como Sodagreen) es una banda de indie rock taiwanés formado en 2001. Su formación ha sido modificado desde 2003. Sodagreen surgió en la escena musical del generop rock indie, después de recibir un Premio en el "Festival Hohaiyan Gongliau Rock" en 2004, tras lo cual firmaron un contrato con el sello discográfico de "Willlin Music". La banda se destacaba por el gran talento de su vocalista principal y compositor Wu Tsing-Fong, quien se destacó por sus composiciones y letras poéticas, siendo el único estilo en su rendimiento y amplio rango vocal.

Historia

Sodagreen fue nombrado por Shih, entonces líder de la banda y Wu, el vocalista. La banda fue originalmente llamado Soda (苏打), pero Shih sentía que la banda necesitaba un nombre con tres caracteres de origen chinos. Wu, cuyo color favorito era el color verde, sugirió que se añadiera la palabra verde (绿) detrás del nombre, por lo tanto el nombre de la banda quedó así.

En mayo del 2001, Sodagreen compitió en la "Golden Melody Cup", organizado por la Universidad Nacional de Chengchi y ganaron popularidad por su canción titulada "Peeping". La obtención de la apreciación de Shiao-Ying, uno de los jueces, ellos grabaron dicha canción, para una compilación llamado " Taiwan independent compilation 2001", que fue publicado por TCM. En abril del próximo año, después de varios de cambios en la alineación de la banda como en las guitarristas, Sodagreen participó en la  "Golden Melody Cup", una vez más, esta vez siendo nuevamente ganadores denominados como el mejor grupo musical por sus letras y composiciones, de la propia autoría de sus integrantes.

Discografía

Álbumes

Singles

Enlaces externos
  Official site
  Introduction of Sodagreen at G-Music
 Sodagreen photo and video

Grupos de música de Taiwán
Grupos de rock de Taiwán
Grupos de indie rock de Taiwán
Grupos de indie pop de Taiwán
Grupos de música de los años 2000
Grupos de música formados en 2001

redpajama_set_name: RedPajamaWikipedia


text:
Q: AngularJS UI freeze during polling $timeout $scope updates I have an app with a simple view that contains a list of a few items.
   <ion-view view-title="App">
    <ion-content>

                    {{group.name}}

    </ion-content>
</ion-view>

I fetch these items from a service that makes a $http get of a json array from the server, and inside the controller I need to update this list every 10 seconds.
.config(function ($stateProvider, $urlRouterProvider) {
    $stateProvider
        .state("home", {
            url: "/home",
            templateUrl: "home.html",
            controller: "homeCtrl",
            resolve: {
                data: function(appDataService){
                    return appDataService.getData();
                }
            }
        })

    ;
    $urlRouterProvider.otherwise("/home");
});
    .factory('appDataService', function ($http) {
        return {
            getData: function () {
                return $http.get(HOST + "/ionic-proof.ashx").then(function (response) {
                    return response;
                });
            },
        };
    })

    .controller("homeCtrl", function($state, $scope, data, appDataService, $timeout){
        $scope.groups = data.data.groups;
        (function refresh(){
            appDataService.getData().then(function(response){
                $scope.groups = response.data.groups;
                $timeout(refresh, 10000);
            });
        })();
        $scope.live = function(id){
            $state.go("event", {id: id});
        };
    })

The problem is, everytime the $scope.groups inside the refresh() function is executed, I get a short "freeze" in the UI, which is quite noticeable (e.g. if I am scrolling the list up and down).
Any ideas what I might be doing wrong?
Thanks in advance

redpajama_set_name: RedPajamaStackExchange


V2801S is 1GE Secure ONU designed for fulfilling FTTH ultra-broadband access request of home and SOHO users.
G/EPON 1GE Safe ONU is support Dual mode(EPON and GPON), It can also be applied to a wide temperature environment, and also has a powerful firewall function.
G/EPON 1GE ONU meets telecom operators FTTO (office), FTTD (Desk), FTTH(Home) broadband speed, SOHO broadband access, video surveillance and other requirements and design a GPON/EPON Gigabit Ethernet products. The box is based on the mature Gigabit GPON/EPON technology, highly reliable and easy to maintain, with guaranteed QOS for different service. And it is fully compliant with technical regulations such as ITU-T G.984.x and IEEE802.3ah.


Andy requires a Shure SM58 or similar vocal microphone on a mic stand for vocals.
He plays 3 bouzoukis, mandola(s), and a digitally produced drone for which he requires five DI boxes essential, six if possible.
He also uses a condenser mic on these instruments to be mixed in. He can supply his own Audix condenser mic but requires a mic stand and a cable.
He requires at least one monitor and an armless chair. Please DO NOT provide water on stage! Thank you!


22 Oct - min - Uploaded by Warsidi CA On a trip to the South of France, the shy heroine of Rebecca falls in love with Maxim de Winter. 12 Aug - 31 min - Uploaded by Learning GO PLEASE DO NOT CLICK HERE! ▻firstclasscareacademy.com ✌learninggo Send Learninggo Ur Vids. Rebecca Audible Audiobook – Unabridged. Daphne du Maurier (Author), Anna Massey (Narrator), Hachette Audio (Publisher) & 1 more. The novel begins in Monte Carlo, where our heroine is swept off her feet by the dashing widower Maxim de Winter and his sudden proposal of marriage.
Written by Daphne du Maurier, Audiobook narrated by Anna Massey. Sign-in to download and listen to this audiobook today! First time visiting Audible? Get this. Rebecca by Daphne Du Maurier by Alex Kingston, released 22 December 1. Part One 2. Part Two 3. Part Three 4. Part Four 5. Part Five 6. Part Six 7. Listen to Rebecca audiobook by Daphne du Maurier. Stream and download audiobooks to your computer, tablet or mobile phone. Bestsellers and latest.
Audio+Book: 'Rebecca' Daphne du Maurier. Number 47 of 75 in C1/2 - ADVANCED+. New English word? Translate any word using double click. Rebecca. Listen to a sample or download Rebecca (Unabridged) by Daphne du Maurier in iTunes. Read a description of this audiobook, customer reviews and more.


You're overseas for an extended period, and you need a little taste of home. It's time for a Netflix binge of your favorite TV series.
You sit down, open your laptop and fire up the Avast Secureline VPN app to open a pipe up to Netflix back stateside. You load Netflix, click "Play" and - "Whoops, Something Went Wrong…"?
Well, hell. Netflix has blocked Avast Secureline again!
Avast offers a 30-day money-back guarantee, so it's nice and easy to switch to ExpressVPN (which I think is the best VPN provider for unblocking Netflix).
Some days you feel like the whole world is against on you - especially when you can't watch your favorite Netflix content. But don't worry, it's nothing personal (well, not when it comes to Netflix, at least): the streaming provider is just following the rules.
Netflix's licensing agreement with movie studios and television networks require them to block access to anyone who attempts to access the licensed content from outside of the licensed areas. That means your favorite film or TV series might not be available where you're currently residing.
It would be great if movie studios and other content owners would come into the 21st century with the rest of us, making their content available wherever people are willing to pay to see it. However, they insist on holding onto their old ways.
Netflix has become quite adept at detecting and blocking VPN connections to their servers. This has led many VPN providers to give up on providing Netflix access to their users.
While many VPN providers still claim Netflix compatibility, they aren't reliable and don't respond quickly when their servers are blocked by the streaming service.
The battle between VPNs and Netflix is somewhat like an elaborate game of Battleship. Netflix finds a VPN connection coming into their servers, sinks it, and the VPN provider then sends another set of IP addresses out into the battle, hoping this battleship won't be sunk.
Here's how it works. A VPN sets up servers for their customers to use. The clients that access these servers will share a single IP address. This is common practice and is designed to help protect a user's anonymity. A bunch of those users start accessing Netflix content in another country.
Netflix notices multiple viewers connecting to their service via the same IP address. Netflix reacts by blocking that IP address, no longer allowing it to access their servers. VPN customers cry foul to their VPN provider. The provider then sets up new servers with fresh IP addresses.
Once again, Netflix detects those, blocks them, and the game is once more afoot.
If this constant back-and-forth has led your VPN provider to give up the Netflix ghost, it's time to find a better provider. I recommend ExpressVPN.
I have found ExpressVPN to be the best VPN provider for reliable access to Netflix. The provider does an excellent job of hiding their "battleships" from Netflix.
In addition to persistent access to Netflix, the VPN provider also offers access to a large number of other streaming providers and other types of services, including BBC iPlayer, Hulu and many others.
ExpressVPN also offers a goodly amount of Netflix-related information on their website, such as helpful FAQ's, tricks and tips, and links to Netflix-related browser plugins.
In addition, the provider offers 24/7 customer support, comprehensive global server coverage, great privacy protections, fast connection speeds and more.
If you're using ExpressVPN, you won't have any worries about meeting Netflix's bandwidth requirements. You also won't have any issues finding the fastest available VPN server, either, thanks to the ExpressVPN app's built-in speed test feature.
I've found that, on average, this provider offers connection speeds measuring in at within 20% of my ISP-only connections. Of course, this all depends on your usual connection speeds, but ExpressVPN should easily be up to handling Netflix content requirements.
Readers who use all of their devices to view Netflix will be happy to learn that ExpressVPN offers apps for every popular device platform.
$8.32 is somewhere around the cost of a large coffee and a cronut. Give those up one day each month, and you'll cover the cost of an ExpressVPN subscription (and your waistline will thank you). It'll come out to $99.95 per year. A monthly payment option is available too, but it will run you $12.95 per month.
Don't worry: the provider doesn't pack all of its income into an offshore bank account. They pour a good bit of that money back into improving their services.
A 30-day money-back guarantee is available, but I'm reasonably certain you're going to like ExpressVPN enough to stay.
I always received quick replies to my support inquiries, and the provider's 24/7 live support chat feature means you'll never have an issue getting help when you need it.
No matter your location, you should have access to the Netflix content of your dreams via ExpressVPN's over 1,500 servers, well-located in 94 different countries around the world.
Privacy protection is top-notch at ExpressVPN thanks to its being located in the privacy-friendly British Virgin Islands. The government there doesn't have any data retention requirements for VPN services, so there isn't any information being saved about your online travels.
Bitcoin is an option for users looking to protect their payment information, as they can use the cryptocurrency to pay for their subscription.
If and when Avast Secureline VPN lets you down, no worries. You can find a better VPN - just look in the direction of ExpressVPN.
The provider offers fast connection speeds, reliable access to Netflix, optimal global server coverage, top-notch customer support, comprehensive privacy protections and so much more.


text:
Canyon Dreams
A Basketball Season on the Navajo Nation
The moving story of a Navajo high school basketball team, its members struggling with the everyday challenges of high school, adolescence, and family, and the great and unique obstacles facing Native Americans living on reservations.
Deep in the heart of northern Arizona, in a small and isolated patch of the vast 17.5-million-acre Navajo reservation, sits Chinle High School. Here, basketball is passion, passed from grandparent to parent to child. Rez Ball is a sport for winters where dark and cold descend fast and there is little else to do but roam mesa tops, work, and wonder what the future holds. The town has 4,500 residents and the high school arena seats 7,000. Fans drive thirty, fifty, even eighty miles to see the fast-paced and highly competitive matchups that are more than just games to players and fans.
Celebrated Times journalist Michael Powell brings us a narrative of triumph and hardship, a moving story about a basketball team on a Navajo reservation that shows how important sports can be to youths in struggling communities, and the transcendent magic and painful realities that confront Native Americans living on reservations. This book details his season-long immersion in the team, town, and culture, in which there were exhilarating wins, crushing losses, and conversations on long bus rides across the desert about dreams of leaving home and the fear of the same.
Michael Powell:
Michael Powell has been a writer at the New York Times since 2007, and a "Sports of The Times" columnist since 2014. Before joining the Times, he worked for the Washington Post from 1996 to 2006, where he covered the 2000 presidential campaign and later served as New York bureau chief. He has been part of teams that won the Pulitzer Prize and the Polk Award. Powell began his career in 1984 at the Burlington Free Press, going on to positions with the Bergen Record, New York Newsday, and the New York Observer. He studied American and African history at SUNY Purchase College, worked as a tenant organizer in East Flatbush, and received his master's degree from Columbia University's Graduate School of Journalism in 1984. Powell and his wife have two sons. They live in Ditmas Park, Brooklyn.
Imprint Blue Rider Press
Sport & Outdoor » Ball sports / ball games » Basketball
History & Archaeology » History » History of the Americas
History & Archaeology » History » History: specific events & topics » Social & cultural history
Social Sciences » Society & culture: general » Social groups » Ethnic studies » Ethnic minorities & multicultural studies » Indigenous peoples


Amity Institute of Biotechnology (AIB) in association with Amity Academic Staff College (AASC) organized two weeks DBT Sponsored Short Term Refresher Training Course on "Application of Metagenomic Tools for Bioremediation towards Environmental Restoration" at University Campus, Sector 125 Noida.
The aim of the workshop was to train mid-career Scientists and UG & PG Faculty on the advanced level courses by updating them with practical aspects of biotechnology related research techniques encompassing metagenomics and meta-data analysis.
Welcoming the guests, Prof.(Dr.) Chanderdeep Tandon, Director, Amity Institute of Biotechnology saidthat the course provided lab based hands-on training in research techniques tothe participants who can subsequently apply them in their research or teachingprogramme. He shared that the course aimed to enhance the understanding of theBioinformatics Data analysis which has been aligned with the experimental workto weave the complete framework of the workshop's theme.
Addressing the gathering, DrArvinder Singh, Country Manager, Human Diagnostics said that technology hasbrought the communities together. Without technology, Science couldn't havedeveloped and Life Sciences field is entirely dependent on technology and itsdevelopments. He mentioned that now a days, every research work requires teamof researchers from different domains. He averred that it is important forresearchers to be cohesive and work as a team for an outcome in research. Dr.Singh stressed that need of the hour is to have an Advanced Instrumentationcourse in Biotechnology in educational institutions. He called upon theeducational institutions to organize more such workshops to develop moreresourceful and trained human resources in this field.
Sharing her experience, Dr CharuThapliyal, participant from IIT Delhi said that her field of research isMolecular Biophysics and during the workshop, she gained knowledge aboutMolecular Modeling which she will further use in her research work. Sheemphasized that the talks during the workshop were very informative and willhelp her in achieving the research goal.
Speaking on the occasion, Dr.R.B. Lal, Joint Director, Ministry of Environment, Forest and Climate Change talked on management of Hazardous Substances/Wastes and apprised about challenges during waste management with regards to Solid Waste, Plastic Waste,Biomedical Waste, Hazardous Waste and E waste. He mentioned that Ministry has laid down water management rules for various industries so that most of the waste generated can be recycled or re used.
The Training course consisted of 14 hours of lectures and 70 hours of practical training in Metagenomic tools, PCR and Expression cloning. Lectures on Advanced topics were delivered by highly experienced scientists from IIT, JNU and Delhi University along with Internationally Trained Faculty and Instructors of Amity Institute of Biotechnology.


If you are lucky enough to visit Southern West Virginia, you may feel you have stepped back in time to the beauty of an early 1900's farming village as you enter Forest Hill, near the border of Monroe and Summers Counties, the home of Wake Robin Gallery.
Within the gallery, you will find many treasures. Gallery owner Marcia Springston Dillon will greet you, most likely accompanied by her companion German Shepherd. While the beauty of her work is immediately apparent, you may not realize that Marcia has created these amazing pieces while being blind since birth.
Marcia's passion for pottery began during her independent study in high school. She discovered that she really loved pottery, particularly the magic of the wheel.
Later, Marcia decided to obtain a graduate degree. While applying to graduate schools, she took a job at an historical museum as a tour guide in the glassworks and pottery studios. Working closely with artisans at the museum provided her the inspiration to focus on ceramics and sculpture. After graduating, Marcia returned to her home state of West Virginia and eventually established her gallery in Forest Hill. As explanation for choosing Forest Hill, Marcia says "We mostly thought of it as a good place to work and a great place to live."
Originally, she focused on making fine functional pieces like mugs, platters, bowls and dinnerware. Over the years she continued to attend workshops with other successful ceramic artists to enhance her techniques and artistic growth, and now finds that by spending part of her time on more unique sculptural pieces, she feels more challenged and fulfilled.
In addition to Marcia's stoneware and ceramic pieces, the gallery also offers jewelry, wooden utensils, stained glass, baskets and other interesting items from talented local artisans. Marcia's pieces beckon to be held and used. Her glazes are beautiful renditions of colors from nature - celadon shades and cool and dark blues blended with stone tones. The motto on her business card is an apt description of her work: "Pleasing to the hand, as well as the eye."


Home > News > Latest News > Most properties sold year to date!
zoopla most solds year to date july 21It's official! Carters Estate Agents have sold more properties, year to date in CV11 than any other agent. Whether you are selling or buying, to be part of our sucess call a member of our dedicated team on 02476 388863.


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Love|Rebecca Flatow, George Zornick
https://nyti.ms/22G4pHy
Rebecca Flatow, George Zornick
Rebecca Bernice Flatow and George Lawrence Zornick III were married June 4. Mathew E. Flatow, the brother of the bride who became a minister of American Marriage Ministries for the occasion, officiated at the Sequoia restaurant in Washington.
Mrs. Zornick, 32, is a lead analyst for policy, planning and innovation at the Substance Abuse and Mental Health Services Administration in the Department of Health and Human Services; she works in Rockville, Md. She graduated and received a law degree from the University of North Carolina and has a master's degree in social work from Columbia.
The bride is the daughter of Nelida M. Flatow and Michael Flatow of Charlotte, N.C.
Mr. Zornick, 33, is the Washington editor of The Nation, the weekly magazine. He graduated from the State University of New York at Buffalo.
He is a son of Margaret J. Milliron of Buffalo and the late George L. Zornick Jr.
The couple were introduced in 2014 through the dating app Hinge.