text:
\section{Introduction}
Deep generative models have shown outstanding sample quality in a wide variety of modalities. Generative Adversarial Networks (GANs) \cite{goodfellow2014generative, karras2021alias}, Autoregressive models \cite{ramesh2021zero}, Variational Autoencoders \cite{kingma2013auto, rezende2014stochastic}, Normalizing Flows \cite{grathwohl2018ffjord, chen2019residual} and Energy-based models \cite{xiao2020vaebm} show impressive abilities to synthesize objects. However, GANs are not robust to the choice of architecture and optimization method \cite{arjovsky2017wasserstein, gulrajani2017improved, karras2019style, brock2018large}, and they often fail to cover modes in data distribution \cite{zhao2018bias, thanh2020catastrophic}. Likelihood-based models do not suffer from collapse modes, but may overestimate the probability in low-density regions \cite{zhang2021understanding}.

\begin{figure}[t]
    \centering
    \begin{minipage}{\columnwidth}
        \centering
        \includegraphics[width=\columnwidth]{images/teaser_ddpm.png}
        \subcaption{Denoising Diffusion Probabilistic Models}

    \end{minipage}
    \begin{minipage}{\columnwidth}
        \centering
        \includegraphics[width=0.8\columnwidth]{images/teaser_ss.png}
        \subcaption{Star-Shaped Denoising Diffusion Probabilistic Models}
    \end{minipage}
    \caption{Forward processes of DDPM and SS-DDPM.}
    \label{fig:teaser}
\end{figure}

Recently, diffusion probabilistic models \cite{sohl2015deep, ho2020denoising} have received attention. These models generate samples using a trained Markov process that starts with white noise and iteratively removes noise from the sample. Recent works have shown that diffusion models can generate samples comparable in quality or even better than GANs \cite{song2020score, dhariwal2021diffusion}, while they do not suffer from mode collapse by design, and also they have a log-likelihood comparable to Autoregressive models \cite{kingma2021variational}. Moreover, diffusion models show these results in various modalities such as images \cite{saharia2021image}, sound \cite{popov2021grad, liu2022diffgan} and shapes \cite{luo2021diffusion, zhou20213d}.

The main principle of diffusion models is to destroy information during the forward process and then restore it during the reverse process.
In conventional diffusion models like denoising diffusion probabilistic model (DDPM) destruction of information occurs through the injection of Gaussian noise, which is reasonable for some types of data, such as images.
However, for data distributed on manifolds, bounded volumes, or with other features, the injection of Gaussian noise can be unnatural, breaking the data structure.
For such data, one might want to use non-Gaussian noise that takes the data structure into account.

Unfortunately, it is not clear how to replace the noise distribution within traditional diffusion models. The problem is that we have to maintain a connection between the distributions defining the Markov noising process that gradually destroys information and its marginal distributions. While some papers explore other distributions, such as delta functions \cite{bansal2022cold} or Gamma distribution \cite{nachmani2021denoising}, they provide ad hoc solutions for special cases that are not easily generalized.

In this paper, we present Star-Shaped Denoising Diffusion Probabilistic Models (SS-DDPM), a new approach that generalizes Gaussian DDPM to an exponential family of noise distributions.
In SS-DDPM, one only needs to define marginal distributions at each diffusion step (see Figure~\ref{fig:teaser}).
We provide a derivation of SS-DDPM, design an efficient sampling and training algorithms, and show its equivalence to DDPM \cite{ho2020denoising} in the case of Gaussian noise.
Then, we outline a number of practical considerations that aid in training and applying SS-DDPMs.
In Section~\ref{sec:experiments}, we demonstrate the ability of SS-DDPM to work with distributions like von Mises--Fisher, Dirichlet and Wishart.
Finally, we define and train a Beta diffusion model on CIFAR-10, achieving results, comparable to a Gaussian DDPM.

\section{Theory}
We start by briefly reminding the definition of DDPM \cite{ho2020denoising} and describing its limitations.
We then introduce SS-DDPM by challenging one of the main design principles behind DDPMs.

\subsection{DDPMs}
The Gaussian DDPM \cite{ho2020denoising} is defined as a forward (diffusion) process $q^{\scriptscriptstyle\mathrm{DDPM}}(x_{0:T})$ and a corresponding reverse (denoising) process $p_\theta^\DDPM(x_{0:T})$.
The forward process is defined as a Markov chain with Gaussian conditionals:
\begin{align}
    q^{\scriptscriptstyle\mathrm{DDPM}}(x_{0:T})&= q(x_0){\prod_{t=1}^T} q^{\scriptscriptstyle\mathrm{DDPM}}(x_t|x_{t-1})\label{eq:ddpm-1}\\
    q^{\scriptscriptstyle\mathrm{DDPM}}(x_t|x_{t-1})&= \Normal{x_t; \sqrt{1-\beta_t}x_{t-1}, \beta_t\mathbf{I}}\label{eq:ddpm-2}
\end{align}
where $q(x_0)$ is the data distribution.
Parameters $\beta_t$ are typically chosen in advance and fixed, defining the noise schedule of the diffusion process. The noise schedule is chosen in such a way that the final $x_T$ no longer depends on $x_0$ and follows a standard Gaussian distribution $q^{\scriptscriptstyle\mathrm{DDPM}}(x_T)=\Normal{x_T;0,\mathbf{I}}$.

The reverse process $p_\theta^\DDPM(x_{0:T})$ follows a similar structure and constitutes a generative part of the model:
\begin{align}
p_\theta^\DDPM(x_{0:T})&= q^{\scriptscriptstyle\mathrm{DDPM}}(x_T){\prod_{t=1}^T}p_\theta^\DDPM(x_{t-1}|x_t)\\
p_\theta^\DDPM(x_{t-1}|x_t)&=  \Normal{x_{t-1}; \mu_\theta(x_t, t), \Sigma_\theta(x_t, t)}
\end{align}
The forward process $q^{\scriptscriptstyle\mathrm{DDPM}}(x_{0:T})$ of DDPM is typically fixed, and all the parameters of the model are contained in the generative part of the model $p_\theta^\DDPM(x_{0:T})$.
These parameters are tuned to maximize the variational lower bound (VLB) on the likelihood of the training data:
\begin{gather}
\mathcal{L}^{\scriptscriptstyle\mathrm{DDPM}}(\theta)=\mathbb{E}_{q^{\scriptscriptstyle\mathrm{DDPM}}}\left[\log p_\theta^\DDPM(x_0|x_1)-\phantom{{\sum_{t=2}^{T}}}\right.
\\
\label{eq::KL}
\!\!\!\!\!\!\left.-{\sum_{t=2}^{T}}\KL{q^{\scriptscriptstyle\mathrm{DDPM}}(x_{t-1}|x_t, x_0)}{p_\theta^\DDPM(x_{t-1}|x_t)}\right]
\\
\mathcal{L}^{\scriptscriptstyle\mathrm{DDPM}}(\theta)\to\max_{\theta}
\end{gather}
DDPM can also be defined for categorical \cite{hoogeboom2021argmax} and Gamma \cite{nachmani2021denoising} distributions.

\subsection{Limitation of DDPMs}
Suppose we are tasked with constructing a generative model for data that is distributed on some manifold, e.g. on a unit sphere. While it may be tempting to consider utilizing a conventional DDPM, such a model would treat our data as points in Euclidean space and thereby noisy objects would no longer lie on a unit sphere. Consequently, the generative model would expend a significant portion of its resources to learn what is already known from the specifics of the given problem---that the real-world data resides on a sphere.

A more efficient way would be to inject a noise such that the noisy objects remain on the same sphere.
Then the model will not waste its limited resources in learning the manifold, and generate objects lying on it by design.
One possible method of generating such noise is through the von Mises--Fisher distribution. In order to construct a DDPM, we must define the transition between two neighboring steps of diffusion, $x_{t-1}$ and $x_t$. For instance, we could sample from the von Mises--Fisher distribution, $q(x_t|x_{t-1})$, with a mode of $x_{t-1}$ and some large concentration parameter $\kappa$.

However, a problem arises when attempting to complete the DDPM, as we also require the explicit form of the marginals, $q(x_t|x_0)$. This is needed for computation of $q(x_{t-1}|x_t,x_0)$ that is a key ingredient in equation \eqref{eq::KL}.
Those marginals can be computed for Gaussian or Gamma noise due to the fact that these distributions are a conjugate prior to itself, and for categorical distributions in the case of discrete data. In general, however, we cannot know both the transition and marginal distributions in explicit form, which is a crucial requirement for constructing a DDPM.
As such, the conventional DDPM framework is currently unable to process the injection of noise other than Gaussian, Gamma or categorical.
To overcome this limitation, we must alter the way we build the diffusion model by bypassing the explicit definition of the transition distribution, $q(x_t|x_{t-1})$, and starting from the marginal distribution, $q(x_t|x_0)$, instead.

\subsection{Star-Shaped DDPMs}

\begin{figure*}[t!]
    \centering
    \begin{minipage}[b]{\columnwidth}
        \centering
        \includegraphics[width=\columnwidth]{images/ddpm.png}

        \vspace{1em}
        \subcaption{Denoising Diffusion Probabilistic Models}
    \end{minipage}
    \begin{minipage}[b]{\columnwidth}
        \centering
        \includegraphics[width=\columnwidth]{images/ss.png}
        \subcaption{Star-Shaped Denoising Diffusion Probabilistic Models}
    \end{minipage}
    \caption{Model structure of DDPM and SS-DDPM.}
    \label{fig:model-structure}
\end{figure*}

As previously discussed, extending the DDPM model to other distributions poses significant challenges. Specifically, we must define the steps, $q(x_t|x_{t-1})$, in a manner that enables us to compute the explicit form of the marginals, $q(x_t|x_0)$, and also compute the posterior distributions, $q(x_{t-1}|x_t, x_0)$, which is only feasible for simple distributions such as Gaussian, Gamma \cite{nachmani2021denoising}, and categorical \cite{hoogeboom2021argmax}.

In light of these difficulties, we propose to construct a model that only relies on marginal distributions, $q(x_t|x_0)$, in its definition and the derivation of the loss function.

We define a star-shaped diffusion with the \emph{non-Markovian} forward process $q^\SS(x_{0:T})$ that has the following structure:
\begin{equation}
\label{eq:ss-forward}
    q^\SS(x_{0:T})= q(x_0){\prod_{t=1}^T} q^\SS(x_t|x_0),
\end{equation}
where $q(x_0)$ is the data distribution. We note that in contrast to DDPM all noisy variables $x_t$ are conditionally independent given $x_0$ instead of constituting a Markov chain. This structure of the forward process allows us to utilize other noise distributions, which we discuss in more detail later.

\subsection{Defining the reverse model}

\begin{figure}[t]
\centering
\includegraphics[width=\columnwidth]{images/ReverseProcessComparison.png}
\caption{
    Markov reverse process fails to recover realistic images from star-shaped diffusion, while a general reverse process produces realistic images.
    }
\label{fig:markov-vs-general}
\end{figure}

In DDPMs the true reverse model $q^{\scriptscriptstyle\mathrm{DDPM}}(x_{0:T})$ has a Markovian structure \cite{ho2020denoising}, allowing for an efficient sequential generation algorithm:
\begin{align}
   q^{\scriptscriptstyle\mathrm{DDPM}}(x_{0:T})&=q^{\scriptscriptstyle\mathrm{DDPM}}(x_T){\prod_{t=1}^{T}} q^{\scriptscriptstyle\mathrm{DDPM}}(x_{t-1}|x_t).
\end{align}
For a star-shaped diffusion, however, the Markovian assumption breaks:
\begin{align}
q^\SS(x_{0:T})&=q^\SS(x_T){\prod_{t=1}^{T}} q^\SS(x_{t-1}|x_{t:T})
\end{align}

Consequently we now need to approximate the true reverse process by a parametric model which is conditioned on the whole tail $x_{t:T}$.
\begin{equation}
    p_\theta^\SS(x_{0:T})= p_\theta^\SS(x_T){\prod_{t=1}^T} p_\theta^\SS(x_{t-1}|x_{t:T})
\end{equation}
It is important to use the whole tail $x_{t:T}$ rather than just $x_t$ when predicting $x_{t-1}$ in star-shaped model.
As we show in Appendix~\ref{app:true-reverse}, if we try to approximate the true reverse process with a Markov model, we introduce a substantial irreducible gap into the variational lower bound.
More crucially, such sampling procedure fails to generate realistic samples, as can be seen in Figure~\ref{fig:markov-vs-general}.
Intuitively, in DDPMs the information about $x_0$ that is contained in $x_{t+1}$ is nested into the information about $x_0$ that is contained in $x_t$. That is why knowing $x_t$ allows us to discard $x_{t+1}$.
In star-shaped diffusion, however, all variables contain independent pieces of information about $x_0$ and should all be taken into account when making predictions.
A similar effect was observed in Cold Diffusion \cite{bansal2022cold}, which also required a modified sampling scheme.

We can write down the variational lower bound as follows (see Appendix~\ref{app:vlb} for details):
\begin{equation}
\begin{split}
    &\mathcal{L}^\SS(\theta)=\mathbb{E}_{q^\SS}\left[\log p_\theta(x_0|x_{1:T})-\phantom{{\sum_{t=2}^T}}\right.
    \\
    &\left.-{\sum_{t=2}^T}\KL{q^\SS(x_{t-1}|x_0)}{p_\theta^\SS(x_{t-1}|x_{t:T}}\right]
    \label{eq:ss-elbo}
\end{split}
\end{equation}
With this VLB we only need the marginal distributions $q(x_{t-1}|x_0)$ to define and train the model, which allows us to use a wider variety of noising distributions.
Since conditioning the predictive model $p_\theta(x_{t-1}|x_{t:T})$ on the whole tail $x_{t:T}$ is typically not practical, we propose a more efficient way to implement the reverse process next.

\subsection{Efficient tail conditioning}
Instead of using the full tail $x_{t:T}$, we would like to define a variable $G_t=\mathcal{G}_t(x_{t:T})$ that would extract all information about $x_0$ from the tail $x_{t:T}$.
Formally speaking, we would like for the following equality to hold:
\begin{equation}
    q^\SS(x_{t-1}|x_{t:T})=q^\SS(x_{t-1}|G_t)
\end{equation}
One way to define $G_t$ is to concatenate all the variables $x_{t:T}$ into a single vector.
This, however, is impractical, as its dimension would grow with the size of the tail $T-t+1$.

The role of $G_t$ is that of a sufficient statistic for the tail $x_{t:T}$.
The Pitman–Koopman–Darmois \cite{pitman_1936} theorem (PKD) states that exponential families admit a sufficient statistic with constant dimensionality.
It also states that no other distribution admits one: if such statistic were to exist, the distribution has to be a member of the exponential family.

Inspired by the PKD, we turn to the exponential family of distributions.
In the case of star-shaped diffusion, we cannot apply the PKD directly, as it was formulated for i.i.d. samples and our samples are not identically distributed.
However, we can still define a \emph{sufficient tail statistic} $G_t$ for a specific subset of exponential family, which we call an \emph{exponential family with linear parameterization}:

\begin{restatable}{theorem}{memory}
\label{theorem:memory}
Given
\begin{align}
    \!\!q^\SS(x_t|x_0)&=h_t(x_t)\exp\left\{\eta_t(x_0)^\mathsf{T}\mathcal{T}(x_t)-\Omega_t(x_0)\right\}\label{eq:exponential-family}\\
    \eta_t(x_0)&=A_tf(x_0)+b_t\label{eq:linear-parameterization}\\
    G_t&=\mathcal{G}_t(x_{t:T})={\sum_{s=t}^T} A_s^\mathsf{T} \mathcal{T}(x_s)
    \label{eq:tail-statistic}
\end{align}
the following holds:
\begin{equation}
    q^\SS(x_{t-1}|x_{t:T})=q^\SS(x_{t-1}|G_t)
\end{equation}
\end{restatable}
We prove this equality in Appendix~\ref{app:proof-1}.
When $A_t$ is scalar, we denote it as $a_t$ instead.

For the most part, the premise of Theorem~\ref{theorem:memory} restricts the parameterization of the distributions rather than the family of the distributions involved.
As we discuss in Appendix~\ref{app:different-families}, we found it easy to come up with linear parameterization for a wide range of distributions in the exponential family.
For example, we can obtain a linear parameterization for the Beta distribution $q(x_t|x_0)=\mathrm{Beta}(x_t; \alpha_t, \beta_t)$ using $x_0$ as the mode of the distribution and introducing a new concentration parameter $\nu_t$:
\begin{align}
    \alpha_t&=1+\nu_tx_0\\
    \beta_t&=1+\nu_t(1-x_0)
\end{align}
In this case $\eta_t(x_0)=\nu_tx_0$, $\mathcal{T}(x_t)=\log\frac{x_t}{1-x_t}$, and we can use \eqref{eq:tail-statistic} to define the tail statistic $G_t$.
We provide more examples in Appendix~\ref{app:different-families} and summarize these results in Table~\ref{tab:different-families}.

We suspect that, just like in PKD, this trick is only possible for a subset of exponential family.
In general case the dimensionality of $G_t$ would grow with the size of the tail $x_{t:T}$.
It is still possible to apply SS-DDPM in this case, however, crafting the (now only approximately) sufficient statistic $G_t$ would require a more careful consideration and we leave it for future work.

\subsection{Final model definition}
To maximize the VLB~\eqref{eq:ss-elbo}, each step of the reverse process should approximate the true reverse distribution:
\begin{equation}
\begin{split}
    p_\theta^\SS(x_{t-1}|x_{t:T})\approx q^\SS(x_{t-1}|x_{t:T})=
    \\
    =\int q^\SS(x_{t-1}|x_0)q^\SS(x_0|x_{t:T})dx_0
\end{split}
\end{equation}
Similar to DDPM \cite{ho2020denoising}, we choose to approximate $q^\SS(x_0|x_{t:T})$ with a delta function centered at the prediction of some model $x_\theta(\mathcal{G}_t(x_{t:T}), t)$.
This results in the following definition of the reverse process of SS-DDPM:
\begin{equation}
    p_\theta^\SS(x_{t-1}|x_{t:T})=\left.q^\SS(x_{t-1}|x_0)\right|_{x_0=x_{\theta}(\mathcal{G}_t(x_{t:T}), t)}
\end{equation}

The distribution $p_\theta^\SS(x_0|x_{1:T})$ can be fixed to some small-variance distribution $p^\SS(x_0|x_1)$ centered at $x_1$, similar to the dequantization term, commonly used in DDPM.

Together with the forward process~\eqref{eq:ss-forward} and the VLB objective~\eqref{eq:ss-elbo}, this concludes the general definition of the SS-DDPM model.
The model structure is illustrated in Figure~\ref{fig:model-structure}.
The corresponding training and sampling algorithms are provided in Algorithms~\ref{alg:training}~and~\ref{alg:sampling}.

\begin{algorithm}[tb]
   \caption{SS-DDPM training}
   \label{alg:training}
\begin{algorithmic}

   \REPEAT
      \STATE $x_0\sim q(x_0)$
      \STATE $t\sim \mathrm{Uniform}({1, {\dots}, T})$
      \STATE $x_{t:T}\sim q^\SS(x_{t:T}|x_0)$
      \STATE $G_t =  \sum_{s=t}^TA_s^\mathsf{T} \mathcal{T}(x_s)$
      \STATE Move along $\nabla_{\theta}\mathrm{KL}(q^\SS(x_{t-1}| x_0)\|p_\theta^\SS(x_{t-1}| G_t))$
   \UNTIL{ Convergence }
\end{algorithmic}
\end{algorithm}

\begin{algorithm}[tb]
   \caption{SS-DDPM sampling}
   \label{alg:sampling}
\begin{algorithmic}

   \STATE $x_T\sim q^\SS(x_T)$
   \STATE $G_T= A_T^\mathsf{T} \mathcal{T}(x_T)$
   \FOR{$t=T$ to $2$}
      \STATE $\tilde{x}_0 = x_\theta(G_{t}, t)$
      \STATE $x_{t-1}\sim \left.q^\SS(x_{t-1}|x_0)\right|_{x_0=\tilde{x}_0}$
      \STATE $G_{t-1}= G_{t} + A_{t-1}^\mathsf{T} \mathcal{T}(x_{t-1})$
   \ENDFOR
   \STATE $x_0\sim p_\theta^\SS(x_0|G_1)$
\end{algorithmic}
\end{algorithm}

The resulting model is similar to DDPM in spirit.
We follow the same principles when designing the forward process: starting from a low-variance distribution, centered at $x_0$ at $t=1$, we gradually increase the entropy of the distribution $q^\SS(x_t|x_0)$ until there is no information shared between $x_0$ and $x_t$ at $t=T$.

We provide concrete definitions for Beta, Gamma, Dirichlet, von Mises, von Mises--Fisher, Wishart, Gaussian and Categorical distributions in Appendix~\ref{app:different-families}.
We also present these results in form of a cheat-sheet in Table~\ref{tab:different-families}.

\subsection{Connection to DDPMs}
The tail statistics $G_t$ form a diffusion-like Markov process that can be seen as dual to the star-shaped process on $x_t$.
Interestingly, in Gaussian SS-DDPM this dual process is itself a Gaussian DDPM with a particular noising schedule:
\begin{restatable}{theorem}{equivalence}
\label{theorem:equivalence}
Let $\overline{\alpha}_t^{\scriptscriptstyle\mathrm{DDPM}}$ define the noising schedule for a DDPM model~(\ref{eq:ddpm-1}--\ref{eq:ddpm-2}) via $\beta_t=(\overline{\alpha}^{\scriptscriptstyle\mathrm{DDPM}}_{t-1}-\overline{\alpha}^{\scriptscriptstyle\mathrm{DDPM}}_t)/\overline{\alpha}^{\scriptscriptstyle\mathrm{DDPM}}_{t-1}$.
Let $q^\SS(x_{0:T})$ be a Gaussian SS-DDPM forward process with the following noising schedule and tail statistic:
\begin{align}
q^\SS(x_t|x_0)&=
\Normal{x_t; \sqrt{\overline{\alpha}_t^\SS}x_0, 1-\overline{\alpha}_t^\SS},\\
\mathcal{G}_t(x_{t:T})&=
\frac{1-\overline{\alpha}^{\scriptscriptstyle\mathrm{DDPM}}_{t}}{\sqrt{\overline{\alpha}^{\scriptscriptstyle\mathrm{DDPM}}_{t}}}\sum_{s=t}^T\frac{\sqrt{\overline{\alpha}^\SS_s}x_s}{1-\overline{\alpha}^\SS_s},\text{ where}\\
\frac{\overline{\alpha}^\SS_t}{1-\overline{\alpha}^\SS_t}&=
\frac{\overline{\alpha}^{\scriptscriptstyle\mathrm{DDPM}}_{t}}{1-\overline{\alpha}^{\scriptscriptstyle\mathrm{DDPM}}_{t}}-\frac{\overline{\alpha}^{\scriptscriptstyle\mathrm{DDPM}}_{t+1}}{1-\overline{\alpha}^{\scriptscriptstyle\mathrm{DDPM}}_{t+1}}.
\label{eq:schedule-transform}
\end{align}

Then the tail statistic $G_t$ follows a Gaussian DDPM noising process $q^{\scriptscriptstyle\mathrm{DDPM}}(x_{0:T})|_{x_{1:T}=G_{1:T}}$ defined by the schedule $\overline{\alpha}_t^{\scriptscriptstyle\mathrm{DDPM}}$.
Moreover, the corresponding reverse processes and VLB objectives are also equivalent.
\end{restatable}
We show this equivalence in Appendix~\ref{app:gaussian-equivalence}.
Since the Gaussian SS-DDPM is equivalent to a Gaussian DDPM, the SS-DDPM can be seen as a direct generalization of the DDPM model.
We make use of this connection when choosing the noising schedule for other distributions, as discussed in Appendix~\ref{app:noise-schedule}.

In the general case, the explicit description of Markov diffusion process for $G_t$ is problematic and it is easier to work directly with star-shaped model for $x_t$. We leave the derivation of general description of diffusion process for $G_t$ for future research.

\section{Practical considerations}
While the model is properly defined, there are several practical considerations that are important for the efficiency of star-shaped diffusion.

\begin{figure}[t]
\centering
\includegraphics[width=\columnwidth]{images/schedule-gauss.pdf}
\caption{
    The noising schedule $\overline{\alpha}_t^\SS$ for Gaussian star-shaped diffusion, defined for different numbers of steps $T$ using~\eqref{eq:schedule-transform}.
    All the corresponding equivalent DDPMs have the same cosine schedule $\overline{\alpha}_t^{\scriptscriptstyle\mathrm{DDPM}}$.
}
\label{fig:ss-vs-ddpm-schedule}
\end{figure}

\begin{figure}[t]
\centering
\includegraphics[width=\columnwidth]{images/ForwardProcessesComparison.png}
\caption{
    Top: samples $x_t$ from a Gaussian DDPM forward process with a cosine noise schedule.
    Bottom: samples $G_t$ from a Beta SS-DDPM forward process with a noise schedule, obtained by matching the mutual information as described in Appendix~\ref{app:noise-schedule}.
    Middle: corresponding samples $x_t$ from that Beta SS-DDPM forward process.
    The tail statistics have the same level of noise as $x_t^{\mathrm{\scriptscriptstyle DDPM}}$, while the samples $x_t^{\mathrm{\scriptscriptstyle BetaSS}}$ are diffused much faster.
}
\label{fig:ss-vs-ddpm-schedule-viz}
\end{figure}

\paragraph{Choosing the right schedule}
It is important to choose the right noising schedule for a SS-DDPM model.
It significantly depends on the number of diffusion steps $T$, and behaves differently given different noising schedules, typical to DDPMs.
This is illustrated in Figure~\ref{fig:ss-vs-ddpm-schedule}, where we show the noising schedules for Gaussian SS-DDPMs that are equivalent to DDPMs with the same cosine schedule.

Since the variables $G_t$ follow a DDPM-like process, we would like to somehow reuse those DDPM noising schedules that are already known to work well.
For Gaussian distributions we can transform a DDPM noising schedule into the corresponding SS-DDPM noising schedule analytically by equating $I(x_0; G_t)=I(x_0; x_t^{\scriptscriptstyle\mathrm{DDPM}})$.
In general case we look for schedules that have approximately the same level of mutual information $I(x_0; G_t)$ as the corresponding mutual information $I(x_0; x_t^{\scriptscriptstyle\mathrm{DDPM}})$ for a DDPM model for all timesteps $t$.
We estimate the mutual information using Kraskov \cite{kraskov2004estimating} and DSIVI \cite{molchanov2019doubly} estimators, and build a look-up table to match the noising schedules.
This procedure is described in more detail in Appendix~\ref{app:noise-schedule}.
The resulting schedule for the Beta SS-DDPM is illustrated in Figure~\ref{fig:ss-vs-ddpm-schedule-viz}.

\paragraph{Implementing the sampler}
During sampling, we can grow the tail statistic $G_t$ without any overhead, as described in Algorithm~\ref{alg:sampling}.
However, during training we need to sample the tail statistic for each object to estimate the loss function.
For this we need to sample the full tail $x_{t:T}$ from the forward process $q^\SS(x_{t:T}|x_0)$, and then compute the tail statistic $G_t$.
In practice this does not add a noticeable overhead, and can be computed in parallel to the training process if needed.

\paragraph{Reducing the number of steps}
We can sample from DDPMs more efficiently by skipping some timestamps.
This wouldn't work for SS-DDPM, because changing the number of steps would require to change the noising schedule and, consequently, to retrain the model.

However, we can still use a similar trick to reduce the number of function evaluations.
Instead of skipping some timestamps $x_{t_1+1:t_2-1}$, we can draw them from the forward process using the current prediction $x_\theta(G_{t_2}, t_2)$, and then use these samples to obtain the tail statistic $G_{t_1}$.
For Gaussian SS-DDPM this is equivalent to skipping these timestamps in the corresponding DDPM.
In general case it amounts to approximating the reverse process with a different reverse process:
\begin{equation}
\begin{split}
    \!\!\!\!p_\theta^\SS(x_{t_1:t_2}|G_{t_2})&={\prod_{t=t_1}^{t_2}} \left.q^\SS(x_t|x_0)\right|_{x_0=x_\theta(G_{t}, t)}\approx
    \\
    &\approx{\prod_{t=t_1}^{t_2}} \left.q^\SS(x_t|x_0)\right|_{x_0=x_\theta(G_{t_2}, t_2)}
\end{split}
\end{equation}
In practice we observe a similar dependence on the number of function evaluations for SS-DDPMs and DDPMs.
See Appendix~\ref{app:change-discretization} for more details.

\paragraph{Time-dependent tail normalization}
As defined in Theorem~\ref{theorem:memory}, the tail statistics can have vastly different scales for different timestamps.
The values of coefficients $a_t$ can range from thousandths when $t$ approaches $T$ to thousands when $t$ approaches zero.
To make the tail statistics suitable for use in neural networks, proper normalization is crucial.

As we show in Figure~\ref{fig:tail-normalization}, normalizing the tail statistics by the sum of coefficients $\sum_{s=t}^Ta_s$ is not enough.
Instead, we collect the time-dependent means and variances of the tail statistics across the training dataset, and normalize the tail statistics to zero mean and unit variance.

Proper normalization is also crucial for the visualization of the tail statistics.
After matching the mean and the variance of the tail statistics to those of the sufficient statistics of the training data $\mathcal{T}(x_0)$, we can map the normalized tail statistics $\tilde{G}_t$ into the data domain using $\mathcal{T}^{-1}(\tilde{G}_t)$, and visualize them there.
The effects of normalization in this case are illustrated in Figure~\ref{fig:tail-visualization}.

\paragraph{Architectural choices}
To make training the model easier, we make some minor adjustments to the neural network architecture and the loss function.

Our neural networks $x_\theta(G_t, t)$ take the tail statistic $G_t$ as an input and are expected to produce an estimate of $x_0$ as an output.
In SS-DDPM the data $x_0$ might lie on some manifold, like the unit sphere or the space of positive definite matrices.
Therefore, we need to map the neural network output to that manifold.
We do that on a case-by-case basis, as described in the corresponding subsections.

Different terms of the VLB can have drastically different scales.
For this reason it is common practice to train DDPMs with a modified loss function like $L_{simple}$ rather than the VLB to improve the stability of training \cite{ho2020denoising}.
We follow a similar intuition and optimize a reweighted variational lower bound, as described in Section~\ref{sec:experiments}.

\section{Experiments}
\label{sec:experiments}
First, we apply SS-DDPM to various manifolds by considering the von Mises--Fisher, Dirichlet and Wishart diffusion processes.
We train and sample from the Dirichlet and Wishart SS-DDPM using $T = 64$ steps, and use $T=100$ steps for the von Mises--Fisher SS-DDPM.
We use a MLP with 3 hidden layers of size 512, swish activations and residual connections through hidden layers \cite{he2015deep}.
We use sinusoidal positional time embeddings \cite{vaswani2017attention} of size $32$ and concatenate them with the normalized tail statistics $\tilde{G}_t$.
On top of the network we add a mapping to the corresponding domain.
We use noise schedule parameterization described in Table~\ref{tab:different-families} and use time-dependent tail normalization in all experiments with SS-DDPM.
The corresponding forward processes are illustrated in Figures~\ref{fig:dirichlet-forward},~\ref{fig:vmf-forward}~and~\ref{fig:wishart-forward}.

The results of these experiments are presented in
Table~\ref{tab:experiment-results}.
This demonstrates the ability of SS-DDPM to work with different distributions and generate data from exotic domains.

\begin{table*}[h!]
\begin{center}
    \caption{Experiments results. The first row is real data and the second are generated samples. For von Mises--Fisher and Dirichlet models we show two-dimensional histograms of samples. For the Wishart model we draw ellipses, corresponding to the p.d. matrices $x_0$ and $x_\theta$. The darker the pixel, the more ellipses pass through that pixel.}
    \label{tab:experiment-results}
    \begin{tabular}{ccccc}
    \toprule
    &
    \makecell[c]{von Mises--Fisher}
    &
    \makecell[c]{Dirichlet}
    &
    \makecell[c]{Wishart}
    \\ \midrule
    \rotatebox[origin=c]{90}{Real}&
    \makecell[c]{\vspace{-0.5em}\includegraphics[width=53mm, height=30mm]{images/geodesic_real.png}}
    &
    \makecell[c]{\vspace{-0.5em}\includegraphics[width=30mm, height=30mm]{images/DirichletOriginal.pdf}}
    &
    \makecell[c]{\vspace{-0.5em}\includegraphics[width=30mm, height=30mm]{images/WishartOriginal.pdf}}
    \\

    \rotatebox[origin=c]{90}{Generated}&
    \makecell[c]{\includegraphics[width=53mm, height=30mm]{images/geodesic_generated.png}}
    &
    \makecell[c]{\includegraphics[width=30mm, height=30mm]{images/Dirichlet_SS-DDPM.pdf}}
    &
    \makecell[c]{\includegraphics[width=30mm, height=30mm]{images/Wishart_SS-DDPM.pdf}}
    \\ \bottomrule
    \end{tabular}
\end{center}
\end{table*}

\subsection{Geodesic data}
We apply SS-DDPM to a geodesic dataset of fires on the Earth surface \cite{fire2020dataset} using a three-dimensional von Mises--Fisher distribution as defined in Table~\ref{tab:different-families}.
We optimize a simplified loss function, defined as $\sum_{t=1}^T(1-x_0^\mathsf{T} x_\theta(G_t, t))$.
To map the prediction to the unit sphere, we normalize the three-dimensional output of the MLP.
We train the MLP using the AdamW \cite{loshchilovdecoupled} optimizer with learning rate of $2 \times 10^{-4}$ for 500k iterations and batch size 100.
We use EMA weights with decay of $0.9999$ for inference, and use $100$ steps of the reverse process to produce the resulting samples.

\subsection{Synthetic data}
We evaluate Dirichlet SS-DDPM on a synthetic problem of generating objects on a three-dimensional probabilistic simplex.
We use a mixture of three Dirichlet distributions with different parameters as training data.
To map the predictions to the domain, we put a \texttt{Softmax} function on the top of the MLP.
We optimize the VLB without any modifications.
We train the MLP using Adam \cite{adam} with learning rate of $10^{-4}$ for 60k iterations and batch size 128.
We use gradient clipping and EMA weights to improve stability.

We evaluate Wishart SS-DDPM on a synthetic problem of generating symmetric positive definite matrices of size $2 \times 2$.
We use a mixture of three Wishart distributions with different parameters as training data.
For the case of symmetric positive definite matrices $V$, MLP predicts a lower triangular factor $L_{\theta}$ from the Cholesky decomposition $V_{\theta} = L_{\theta} L_{\theta}^\mathsf{T}$.
For stability of sampling from the Wishart distribution and estimation of the loss function, we add a scalar matrix $10^{-4}\mathbf{I}$ to the predicted symmetric positive definite matrix $V_{\theta}$.
In Wishart SS-DDPM we use analogue of $L_{simple}$ as a loss function.
To improve the training stability we also divide each KL term corresponding to a timestamp $t$ by $n_t$, the de-facto concentration parameter from the used noising schedule (see Table~\ref{tab:different-families}).
We train MLP similar to the Dirichlet case and additionally use an exponential learning rate scheduler to mitigate training instabilities.
We use a base learning rate of $10^{-4}$ with an exponential scheduler with $\gamma = 0.99996$, batch size $128$ and train the MLP for 100k iterations.
Since positive definite $2\times 2$ matrices can be interpreted as ellipses, we visualize the samples by drawing the corresponding ellipses.

\subsection{Images}
\label{exp:beta-cifar}
Finally, we evaluate the Beta SS-DDPM on CIFAR-10.
Beta diffusion can be applied to images because the training data is typically constrained to a $[0, 1]$ segment.
We use NCSN++ neural network architecture and train strategy from \cite{song2020score}.
We put a sigmoid function on the top of NCSN++ to map the predictions to the data domain.
We train Beta SS-DDPM with $T = 1000$.
We matched the noise schedule in Beta SS-DDPM to the cosine noise schedule in Gaussian DDPM \cite{nichol2021improved} in terms of mutual information, as described in Appendix~\ref{app:noise-schedule}.
Following Improved DDPM \cite{nichol2021improved}, we evaluate our model with various numbers of generation steps, as described in Appendix~\ref{app:change-discretization}, and report the resulting FID scores \cite{heusel2017gans} in Figure~\ref{fig:ddpm-vs-beta}.
Beta SS-DDPM achieves comparable quality with the Improved DDPM model, and is slightly better on fewer number of steps.
The best FID score achieved by Beta SS-DDPM is $3.17$ at $T=1000$.

\begin{figure}[t]
\centering
\includegraphics[width=\columnwidth]{images/DDPM_vs_BetaSS.pdf}
\caption{Quality of images, generated using Beta SS-DDPM and DDPM with different numbers of sampling steps, as measured by FID (Fréchet Inception Distance, \cite{heusel2017gans}). Models are trained and evaluated on CIFAR-10. DDPM results taken from \cite{nichol2021improved}.}
\label{fig:ddpm-vs-beta}
\end{figure}

\section{Related works}
Our work builds upon Denoising Diffusion Probabilistic Models \cite{ho2020denoising}. Interest in diffusion models has increased recently due to their impressive results in image \cite{ho2020denoising, song2020score, dhariwal2021diffusion} and audio \cite{popov2021grad, liu2022diffgan} generation. However, conventional diffusion models are limited to using Gaussian noise to specify generative process. These limitations and the high quality of samples has spearheaded a series of papers exploring ways to extend diffusion models to more flexible distributions of noise.

The authors of DDIM \cite{song2020denoising} proposed an approach to build an implicit diffusion model that allows to build a non-Markovian forward process. This formulation greatly simplifies the problem of building a connection between distributions that form a forward process and marginal distributions. Later, the authors of \cite{zhang2022gddim} have formulated this approach in a more general form. However, implicit diffusion models still rely on Gaussian distributions.

To the best of our knowledge, for the first time, an approach for constructing diffusion without a consecutive process was proposed in \cite{rissanen2022generative}. In this work, the authors used a similar formulation of the model and an objective to build diffusion process based on blurring instead of noise injection. Later in \cite{daras2022soft, hoogeboom2022blurring} this approach was combined with standard Gaussian diffusion.

The authors of Cold Diffusion \cite{bansal2022cold} proposed a heuristic non-probabilistic approach to reversing almost any degradation process. The authors of Flow Matching \cite{lipman2022flow} developed an alternative probabilistic framework that works with any differentiable degradation process. However, the generative process in both of these approaches is deterministic.

In \cite{de2022riemannian} the authors proposed an approach to build diffusion on the manifold on which the data lies by projecting the stochastic differential equation onto it. By design, Riemannian diffusion only works with continuous time diffusion, which makes this approach expensive to apply to high-dimensional data.

In \cite{vahdat2021score} the authors proposed to run a diffusion model in the latent space of a Variational Autoencoder \cite{kingma2013auto, rezende2014stochastic}. Extending this idea, the authors of \cite{kim2022maximum} proposed to run diffusion in the latent space of a Normalizing Flow \cite{grathwohl2018ffjord, chen2019residual}. Latent diffusion is another way to apply diffusion to different domains. However, under the hood these approaches still apply a conventional Gaussian diffusion.

The authors of \cite{zhang2021diffusion} extended the idea of modifying the diffusion model latent space and proposed a way to build a fully trainable diffusion model that reduces the total number of diffusion steps due to more flexible dynamics. However, at training stage such approach requires backpropagation through the whole forward Markov process, significantly slowing down the training procedure. Moreover, the forward Markov process in \cite{zhang2021diffusion} still uses Gaussian noise.

In \cite{nachmani2021denoising}, the authors extend the DDPM to the case of the Gamma distribution. They demonstrate that for the Gamma diffusion, it is possible to compute the marginal distributions, $q(x_t|x_0)$, and the posterior distributions, $q(x_{t-1}|x_t, x_0)$, in a closed form. However, the resulting expressions are cumbersome, necessitating the utilization of an approximation for the variational lower bound. Furthermore, the approach employed by the authors is ad hoc and not generalizable to other cases.

\section{Conclusion}
We propose an alternative view on diffusion-like probabilistic models. We reveal the duality between star-shaped and Markov diffusion processes that allows us to go far beyond Gaussian noise by switching to a star-shaped formulation. This duality provides us with insights of how to set the noise schedules in star-shaped diffusion models regardless of the choice of the noising distribution which would be problematic otherwise.
It allows us to define diffusion-like models with arbitrary noising distributions and to establish diffusion processes on specific manifolds.
We propose an efficient way to construct a reverse process for such models in the case when the noising process lies in a general subset of the exponential family and show that star-shaped diffusion models can be trained on a variety of domains with different noising distributions.
On image domain star-shaped model with Beta distributed noise shows comparable performance to Gaussian DDPM which is known to attain state-of-art performance on that domain.
The star-shaped formulation opens new applications of diffusion-like probabilistic models, especially for data from exotic domains where domain-specific non-Gaussian diffusion is more appropriate.
Any star-shaped model implicitly defines a dual Markov diffusion process in the space of tail statistics.
The explicit description and analysis of this process remains an interesting open problem.

redpajama_set_name: RedPajamaArXiv


text:
Q: How to embed code to medium blog which doesn't disappear I'm using the medium blogging system and I need to insert some code (cli commands, scripts in JS, ...)
I'm using the Keyboard shortcuts but when I press Ctr + Alt + 6 the selected code dissapears.
Is there any other way to insert any code (single or multiline) or some code snippets in our medium publishing process?

A: For embedding scripts/snippets in JS in my Medium blog, I use gist. After you create the gist, select "clone via HTTPS" and get the .git link (e.g https://gist.github.com/ab056e7d7d521b5e90b6747bbfd8bac4.git).
Then in Medium blog page, just paste that .git URL from Gist and press Enter. Wait a second or so and the code will appear, perfectly formatted.

A: As mentioned by @Rohan Paul you can use gist for adding code snippets and the Steps for Adding Gist is as follows:
Step 1:Click on the + button on the left side and select Add Embed
Step 2:Simply copy the link of the gist from the browser
Step 3:Paste the link inside the Add Embed
Cheers its done

A: Both answers are given above direct us to embed gist but the question itself said he needs to add some CLI commands. So there is no point of using gist for just for simple CLI command. I also came across this issue with my Windows PC ctrl + alt + 6 short key is not worked as expected. This might happen because of some cashing problem in the browser. but refresh the page also doesn't work. So just open a new incognito window and try the same short key ctrl + alt + 6 and it worked for me.

Note:
Short key for windows: ctrl + alt + 6
Short key for Mac: command + option + 6

redpajama_set_name: RedPajamaStackExchange


text:
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redpajama_set_name: RedPajamaCommonCrawl


Well, we survived. 500 or so in Maharashtra, 80 or so in Mumbai did not. Three feet of rain within a few hours are no joke. As of this morning, we have water and electricity again, but of course no phone. I love my Blackberry though, which strangely seemed to work most of the time, and I am writing this from the Blackberry browser.
More on this little adventure in a few days, but it was quite something. I ended up walking home through 7km/5miles/5hours of knee to hip deep (and sometimes chest deep) sewage floods, at one spot with quite a strong current.
There were no street lights, it was dark evening, there were thousands of laughing people and hundreds of abandoned flooded cars and busses everywhere – and the intermittent thunder of lightening gave the whole scene a bizarrely apocalyptic touch.
When Ksenia reached home, a few hours before me, our apartment was in two inch deep waters from the overflowing terrace. The two miniature drains proved useless and our upstair neighbors having a penchant for throwing newspapers, plastic bags and sometimes even food from their balconies didn't help matters.
Tagged food, maharashtra, mumbai, ny, people, the flood, walking, water. Bookmark the permalink.


Haocool provides customers with proper design and cold storage construction program.
With many years of work experience, our engineers have always maintained a long-term and stable accumulation of related knowledge. Based on the team of engineers, Haocool designs plans of the whole program, equipment layout and process flow chart in early stage of the project.
There is a professional cold storage design team in Haocool to provide you with one-stop service. According to diverse client's requirements, we will formulate a project plan and quote so that you can compare similar equipment. After that, we complete professional installation by our engineers and after-sales services to ensure the machinery meets all of your needs.
2. Design basis: The design specifications and standards followed by design engineers.
3. Cold storage equipment selection calculation: Design and configuration of equipment units are determined according to the cold storage operation requirements. Appropriate calculation is also carried out.
5. Main configuration table of the selected unit: optional configurations are listed in detail.
7. Control system: Control system includes control modes, alarm and protection functions, data monitoring and history record, system parameters menu and so on.
After fully understanding the customers' purpose of the project, Haocool's business staffs communicate with customers and guide them to plan cold storage projects in order to provide reasonable and market competitive programs. The construction is designed to meet the needs of users and investors.
Design department carries out a long-term accumulation of electronic drawings, models and design programs. The accumulated design experience covers most categories of refrigeration industry, so it has become standardized and efficient to inherit and accumulate design experience. It is the most important part in cold storage project design to fully understand the needs of investors.


on our offense. Whether we win or lose depends on the performance of our OL. Charone Peake is not Sammy but he's still very good. There'll be minimal drop off there. Our OL going against a VERY good DL will determine who wins this game.
If they can make up for some weakness our Oline might bring and keep us in the game, then I think we still pull it out. Can't wait to see where we stack up-pretty nervous right now.
Love to see Peake have a tremendous game but MINIMAL???
True freshman all-american loss is a bit more than minimal.
lose. We don't beat AU last year without him, or FSU or UMD.
I think we win a close one, but Sammy's the best player on our team, the ACC, and one of the top 5 in the country, imo.


NEW YORK – Reports of the death of the regional mall are greatly exaggerated. Heading into the all-important holiday selling season soon upon us, the format is evolving to encompass multiple uses amid changes in both the retail landscape and consumer demand, says "Deep Dive: The Mall Is Not Dead – Part 1," the first in a three-part series that analyzes the state of U.S. retail real estate industry from international think tank Fung Global Retail & Technology.
Top malls continue to attract new and varied tenants as their role in showcasing and even launching new brands cannot be underestimated. In addition, operators of entertainment and dining outlets have returned to the mall in search of higher traffic. However, declining traffic, increasing competition from e-commerce and outlet centers, oversaturation and obsolescence.
The retail real estate industry remains on a post-recession upswing, and occupancy rates have stabilized at about 94 percent since 2014, after hitting a low of 89 percent in 2009. Mall owners say that productivity at top properties is up. Though traffic has steadily declined for the past 42 months, including a 9.1 percent drop since 2015, conversion rates continue to rise, indicating that shoppers are concentrating their purchases into fewer trips.
Some companies are looking to benefit from these shifts. Tesla Motors has moved its showrooms into malls to take advantage of the traffic they generate rather than locating in outlying suburban locations. Many restaurants, once located in mall parking lots, are moving back inside centers. Cinemas that had moved out of the malls also are returning.
"Even though some stores have closed, many new ones are opening and creating hybrid formats we have not seen before," Weinswig writes.
But the retail landscape has continued to evolve, with new modes of shopping, including e-commerce, consignment services, the sharing economy, subscription packages and even factory outlet centers taking share from the traditional mall. The result is a form of retail Darwinism, with top producers attracting ever more business, and weaker properties continuing to decline. Just 20 percent of malls (approximately 270), categorized as Class A based on productivity, generate 72 percent of all mall sales. The top 10 malls in the U.S. average sales of more than $1,000 per square foot, 2.5 times the industry average. In addition, these properties have seen sales productivity increases of more than 10 percent over the past 10 years. Class B and C centers total about 550 in the U.S., but represent just 28 percent of mall sales. Fewer than 80 Class D malls account for just 0.2 percent of all mall sales. The current total of 1,221 malls in the U.S. according to the International Council of Shopping Centers simply is too many.
The full report can be found here. Future reports in the series will analyze department stores in malls, trends impacting malls, malls' evolution and store concepts that are expanding.
Previous reports issued by Fung Global Retail & Technology include: "US Furniture Market 2016: Preferences and Trends" and "Deep Dive: The Changing Retail Landscape & the Evolving Opportunity for Better Demand Planning." Fung Global Retail & Technology's reports and analyses can be found at www.FungGlobalRetailTech.com and www.deborahweinswig.com. Subscribe here to Deborah Weinswig's daily news and analysis on retail, fashion and technology.


text:
Q: Reading Sentinel-2 L2A product footprint (valid data) from metadata as shapely polygon? Is the valid data footprint of Sentinel-2 products stored somewhere in the SAFE products metadata and if yes, how do I read it and convert it to a shapely.geometry.Polygon object in python?
EDIT: by valid data I mean the portion of the frame that is not 0

A: Answering first part of the question - yes, there is raster footprint in MTD_MSIL1C.xml (or MTD_MSIL2A.xml for L2A products) metadata file. See <Global_Footprint> tag. The first value is Y coordinate and the second is X.
Picture 1:

Picture 2:

Answering second part of the question - yes, you could convert it easily. I recommend that you start by reading this documentation.
from shapely.geometry import Polygon
polygon = Polygon([(0, 0), (1, 1), (1, 0)])
polygon.area  # equals 0.5
polygon.length  # equals  3.4142135623730949

You may also be interested in reading this question: The term for determining the pixels of a raster image.

A: Adding the snippet I wrote to parse the xml and build the polygon in case someone ends up here:
import xml.etree.ElementTree as ET
from shapely.geometry import Polygon

# product_path is the path to the .SAFE folder
fname = os.path.join(product_path, 'MTD_MSIL2A.xml')
root = ET.parse(fname).getroot()

text = root[1][0][0][0][0].text.strip().split()
coords = [(float(text[i]), float(text[i + 1])) for i in range(0, len(text) - 1, 2)]
geom = Polygon(coords)


In the process of combing through original art that some of my Patreon backers won through their support of my comic, I came across a gem that I had entirely forgotten about.
This was an illustration that I had created to run the the Philadelphia Daily News. Unfortunately, it never ran, but I was always really happy with how it turned out.
With Wizard World Philadelphia right around the corner, I figured this would be a great time to make this the next original art offered on eBay.
Just a thought, but this would make a great print, especially for the hometown show.


On Magnolia Avenue between Van Buren Blvd. & Jackson St.
Arlington's annual Chili Cook-Off and Car/Cycle Show is one of Riverside's largest community events that continues to grow year-after-year drawing thousands of attendees from all over the Inland Empire and contributing to an economic impact of over $225,000 dollars. The event is held along a ½ mile stretch of Magnolia Ave. from Van Buren Blvd. to Jackson Street in Arlington Village. With the event being a thrilling success in Arlington, community members from across the Inland Empire castes votes in The Press Enterprise's Best of the Inland Empire Reader's Choice Awards and voted Arlington Business Partnership's Chili Cook-off & Car/Cycle Show a Hometown Favorite: Best Community Event.
Join us for some amazing fun in the sun, exciting sounds of live music, delicious foods, and a wide variety of street vendors and classic cars. The Chili Cook-Off & Car/Cycle Show is a free, family friendly event offering tons of activities for children and adults alike. Adults are sure to enjoy their visit to our beer garden featuring a selection of beers and wines. Younger attendees can explore the Kid's Zone that features a petting zoo, jumpers, crafts, rock climbing, games, and so much more! While in Arlington, be sure to enjoy the unique shops and restaurants of the Arlington Business District.
Come and be a part of the fun! The Arlington Business Partnership is actively seeking sponsors, vendors, chili cooks, car/cycle show participants, and volunteers.
For more information on Arlington Business Partnership or the Chili Cook-Off & Car/Cycle Show event, please email info@riversideabp.com or call (951) 509.1100.


text:
Joaquín Rodrigo Vidre (Sagunto, Valencia, 22 november 1901 - Madrid, 6 juli
1999), I Marqués de los Jardines de Aranjuez (1e Markies van de tuinen van Aranjuez), was een Spaans componist. Zijn bekendste compositie is het Concierto de Aranjuez voor gitaar en orkest.

Levensloop
Rodrigo was de jongste van tien kinderen van een koopmansfamilie. Hij was net drie jaar oud, toen hij als gevolg van difterie blind werd. In 1906 vertrok de familie naar Valencia, waar hij aan de blindenschool zijn eerste muziekles kreeg. Hij wilde componist worden nadat hij de opera Rigoletto van Giuseppe Verdi had gehoord.

Van 1917 tot 1922 studeerde hij compositie bij Francisco Antich aan het Conservatorio Superior de Música in Valencia, dat later zijn naam zou krijgen. Zijn eerste werken schreef hij in 1922; twee jaar later werd zijn orkestwerk Juglares uitgevoerd. In 1922 ging hij naar Duitsland om te studeren. In deze tijd werd hij lid van een avant-gardistische componistengroep in Madrid. Dit intermezzo eindigde in 1925, nadat hem de Premio Nacional de Música als gevolg van dit lidmaatschap onthouden werd. Vervolgens vertrok hij naar Parijs (1927), waar hij bij Paul Dukas studeerde aan de École Normale de Musique. Hier onderhield hij vriendschappen met Maurice Ravel, Darius Milhaud, Arthur Honegger, Igor Stravinsky en Manuel de Falla.

In 1933 trouwde hij met de Turkse pianiste Victoria Kamhi, lerares aan het Conservatoire de Paris.

Terug in Spanje (1934) ontving hij de titel Conde de Cartagena (Graaf van Cartagena). In 1935 schreef Rodrigo zijn Sonata de adiós voor piano ter herinnering aan zijn leermeester Dukas. Nog eens ging hij naar Parijs om zijn studie af te ronden aan de Sorbonne. Daarna reisde hij door Duitsland, Oostenrijk en Zwitserland. Pas na het aflopen van de Spaanse Burgeroorlog op 1 april 1939 keerde hij terug naar Spanje en vestigde zich definitief in Madrid.

In januari 1939, nog in Parijs, was Rodrigo gestart met het componeren van zijn meesterwerk Concierto de Aranjuez, het eerste concert voor klassieke gitaar met symfonieorkest. Hij rondde het werk af na zijn terugkeer in Madrid. De première was op 9 november 1940 in Barcelona door de solist Regino Sáinz de la Maza met het Philharmonisch Orkest van Barcelona onder leiding van César Mendoza Lasalle.

Tijdens de franquistische dictatuur (1939 - 1975) vertegenwoordigde Rodrigo met zijn composities de (quasi klassieke) Spaanse muziek in het buitenland. Met de uitvoering van zijn Fantasía para un gentilhombre in 1958 in San Francisco door de gitarist Andrés Segovia, aan wie dit werk was opgedragen, bereikte hij het hoogtepunt van zijn internationale carrière. Terug in Spanje werd hij medewerker van de radio en later docent aan de Madrileense universiteit.

In 1960 werd hij in Parijs als Officier van de kunst en literatuur onderscheiden.
Van de Universiteit van Puerto Rico ontving hij in 1963 het "Legión de Honor". In 1964 kreeg hij een eredoctoraat aan de Universiteit van Salamanca en in 1978 aan de Universiteit van Valencia. Koning Juan Carlos I van Spanje verhief hem in 1991 opnieuw in de adelstand, met de titel 'Marqués de los jardines de Aranjuez' (Markies van de tuinen van Aranjuez) voor zijn bijdrage aan de Spaanse muziek en als erkenning van zijn meest bekende werk het Concierto de Aranjuez. Na zijn overlijden op 6 juli 1999 werd zijn dochter Cecilia Rodrigo Kamhi de tweede 'Marquesa de los Jardines de Aranjuez'.

Composities

Werken voor orkest
 1923 Cançoneta, voor strijkorkest
 1923 Juglares
 1924 Cinco piezas infantiles
 Son chicos que pasan
 Después de un cuento
 Mazurka
 Plegaria
 Gritería final
 1926-1929 Tres viejos aires de danza
 1927-1930 Zarabanda lejana y Villancico
 Zarabanda Lejana
 Villancico
 1928 Preludio para un poema a la Alhambra
 1929 Dos miniaturas Andaluzas
 1934 Per la flor del Lliri Blau, symfonisch gedicht
 1945 Dos piezas Caballerescas
 1953 Soleriana, Suite para orquesta
 Entrada
 Fandango
 Tourbillon
 Pastoral
 Passepied
 Fandango a lo alto
 Contradanza
 Boleras
 1955 Homenaje a Sagunto
 1955 Pavana Real
 1957 Música para un jardín [orkestratie van twee Berceuses voor piano]
 1963 Sones en la Giralda
 1966 Dos danzas españolas
 1975 Pasodoble para Paco Alcalde
 1976 A la busca del más allá, symfonisch gedicht voor de viering van 200 jaar onafhankelijkheid van de Verenigde Staten
 1982 Palillos y panderetas

Werken voor orkest met soloinstrument
 1939 Concierto de Aranjuez, voor gitaar en orkest
 1943 Concierto heroico, voor piano en orkest
 1944 Concierto de estío, voor viool en orkest
 1949 Concierto in modo galante, voor cello en orkest
 1954 Concierto serenata, voor harp en orkest
 1958 Fantasía para un gentilhombre, voor gitaar en orkest
 1960 Aria antigua, voor fluit en orkest
 1966 Concierto madrigal, voor twee gitaren en orkest
 1967 Concierto Andaluz, voor vier gitaren en orkest (opgedragen aan Los Romeros)
 1978 Concierto pastoral, voor dwarsfluit en orkest (opgedragen aan James Galway)
 1982 Concierto para una fiesta, voor gitaar en orkest
 1990 Rincones de España, voor gitaar en orkest

Werken voor harmonieorkest
 1934 Per la flor del lliri blau (verplicht werk in de "Seción Especial" tijdens het Certamen Internacional de Bandas de Música - Ciudad de Valencia in 2002)
 1939 Homenaje a la tempránica, marcha
 1955 Homenaje a Sagunto, marcha
 1966 Adagio, para instrumentos de viento (voor blazers)
 Adagio
 Allegro Moderato - Adagio - Allegro Moderato
 Adagio
 1975 Paso-doble para Paco Alcalde
 1978 Fantasía para un Gentilhombre

Oratoria, cantates en gewijde muziek
 1953 Música para un códice salmantino, cantate voor bas, gemengd koor en orkest - tekst: Miguel de Unamuno, Oda a Salamanca - gecomponeerd voor de feestelijkheden van 700 jaar Universiteit van Salamanca
 1960 La Azuzena de Quito, oratorium
 Ave María, voor vijfstemmig gemengd koor

Muziektheater

Zarzuela

Balletmuziek

Toneelmuziek
 1954 La destrucción de Sagunto, voor de komedie van José Pemán en Francisco Sánchez-Castañer, naar Gaspar Zavala y Zamora, (1762-1824)

Werken voor koor
 1982 Cántico de San Francisco de Asís, voor gemengd koor en orkest - gecomponeerd ter gelegenheid van de 800e verjaardag van de Heilige Franciscus van Assisi.
 Ave María, voor gemengd koor

Vocale muziek met orkest of instrumenten
 1948 Ausencias de Dulcinea, voor bas, vier sopranen en orkest
 1952 Retablo de Navidad, voor sopraan, bas, gemengd koor en orkest - tekst: Victoria Kamhi
 Cantan por Belén Pastores
 Duérmete, Niño
 Aire y Donaire
 Pastorcito Santo
 Coplillas de Belén
 A la Chiribirivuela
 La Espera
 A la Clavelina
 1965-1974 Himnos de los neófitos de Qumrán, voor drie sopranen, mannenkoor en kamerorkest - tekst: Victoria Kamhi, naar uittreksels uit de Qumran-rollen, die in 1947 aan de Dode Zee gevonden werden
 Rezaré día y noche en todos los instantes
 Y caminaré sobre las Ilanuras sin límites
 Te doy las gracias, O Señor
 Album Centenario Canto y Piano, voor zang en piano
 Aranjuez, Ma Pensée, voor zang en gitaar
 Canción del Grumete, voor zang en piano
 Canciones, voor zang en piano
 Canço del Teuladí i Trova, voor zang en piano
 Cánticos Nupciales, voor drie sopranen en orgel
 Cantos de Amor y de Guerra, voor zang en piano
 Coplas del Pastor Enamorado, voor sopraan en gitaar

Kamermuziek
 7 Canciones Valencianas, voor viool en piano

Werken voor piano
 Deux Berceuses
 Suite para Piano
 Canción y Danza
 Bagatela
 Pastoral
 Preludio al Gallo Mañanero
 Zarabanda Lejana
 Air de ballet sur le nom d'une jeune fille
 Serenata española
 Sonada de adiós
 Cinco piezas del Siglo XVI
 Cuatro piezas para piano
 Tres danzas de España
 À l'Ombre de Torre Bermeja
 Cuatro Estampas Andaluzas
 El Álbum de Cecilia
 Cinco Sonatas de Castilla
 Tres Evocaciones
 Preludio de Añoranza
 Atardecer, vierhandig
 Cinco Piezas Infantiles, voor twee piano's

Werken voor gitaar
 Concierto Andaluz, voor 4 gitaren
 Concierto-madrigal, voor 2 gitaren

Bibliografie

 Francisco Alia Miranda: Índice de Autores e Intepretes, in: La música en la radio: radio Ciudad Real EAJ 65 y sus discos de pizarra, Cuenca: Ediciones de la Universidad de Castilla-La Mancha, 2000, 378 p., ISBN 978-84-8427-046-1
 Colin Larkin: The encyclopedia of popular music, Third edition, New York: Macmillan, 1998, 8 v., ISBN 978-1561592371
 Arístides Incháustegui, Blanca Delgado Malagón: Índice Onomástico, in: Vida musical en Santo Domingo (1940-1965), Banco de Reservas, Publicación Especial, Editora Corripio, C. por A. Santo Domingo, D. N., 1998. 529 p., ISBN 9945-036-01-7
 Luis Iglesias de Souza: El Teatro Lírico Español: Tomo I-Catálogo: A-E, 1991. 994 p./ Tomo II-Catálogo F-O / Tomo III-Catálogo O-Z, 1994. 1045 p. / Tomo IV-Libretistas y compositores 1996. 742 p.; Coruña: Editorial Deportación Provincial, 1991-1996, ISBN 8-489-65219-8
 Stewart Gordon: Spanish, Portuguese, and Latin Keyboard Music in the Twentieth Century, in: A History of Keyboard Literature. - Music for the Piano and its Forerunners, New York: Schirmer Books, 1996, 566 p., ISBN 978-0534251970
 Tomas Marco, Cola Franzen: Spanish music in the twentieth century, Cambridge, Mass: Harvard University Press, 1993, 261 p.
 Jacqueline Cockburn, Richard L. Stokes, Graham Johnson: The Spanish song companion, London: Victor Gollancz, 1992
 Maurice J. Summerfield: Its composers, in: The classical guitar: its evolution and players since 1860, Newcastle-upon-Tyne: Ashley Mark Publishing, 1992, 333 p.
 Wolfgang Suppan, Armin Suppan: Das Neue Lexikon des Blasmusikwesens, 4. Auflage, Freiburg-Tiengen, Blasmusikverlag Schulz GmbH, 1994, ISBN 3-923058-07-1
 Paul E. Bierley, William H. Rehrig: The heritage encyclopedia of band music: composers and their music, Westerville, Ohio: Integrity Press, 1991, ISBN 0-918048-08-7
 Piero Sonti: Repertorio di musica sinfonica - Gli autori, le composizioni dal Seicento a oggi, Ricordi, 2001, 1060 p., ISBN 978-8809022553
 Lamberto Trezzini: Indice Dei Nomi, in: Due secoli di vita musicale storia del teatro comunale di Bologna, Seconda edizione, Nuova Alfa Editoriale, 1987, 362 p., ISBN 978-8877790026
 Matthias Henke: Joaquin Rodrigo: Concierto de Aranjuez, Neue Zeitschrift für Musik. 145 (1984) H. 7/8, S. 31-34.
 Roger Alier, Xosé Aviñoa: El libro de la zarzuela, Madrid: Ediciones Daimon, 1982, ISBN 84-231-2677-3
 David Ewen: Composers since 1900 - A biographical and critical guide, First supplement, New York: H. W. Wilson Company, 1981, 328 p., ISBN 978-0824206642
 Margaret Campbell: Rodrigo's cello concerto, The Strad. 92 (1981/82), S. 892-893.
 Linton Elzie Powell: A history of Spanish piano music, Bloomington, Indiana: Indiana University Press, 1980
 Jozef Powrozniak: Gitarrenlexikon, Berlin: Verlag Neue Musik, 1979, 185 p.
 Martin Giertz: Liten uppslagsbok, in: Den klassiske Gitarren: Instrumentet musiken mastarna, Stockholm: P. A. Norstedt & Soners Forlag, 1979
 Gösta Morin, Carl-Allan Moberg, Einar Sundström: Sohlmans musiklexikon - 2. rev. och utvidgade uppl., Stockholm: Sohlman Förlag, 1975-1979, 5 v.
 Gösta Morin, Carl-Allan Moberg, Einar Sundström: Sohlmans musiklexikon: nordiskt och allmänt upplagsverk för tonkonst, musikliv och dans, Stockholm: Sohlmans Förlag, (1951-)
 José María Ruiz Gallardón, Antonio Fernández-Cid: Cien Años de teatro musical en España 1875-1975, Madrid: Real Musical Editores, 1975, 610 p., ISBN 978-8-438-70021-1
 Antonio Fernández-Cid: La música española en el siglo XX, Madrid: Publicaciones de la Fundacion Juan March, 1973
 Antonio Fernández-Cid: Lieder y canciones de España; pequeña historia de la música nacional, 1900-1963, Madrid: Editora Nacional, 1963, 531 p.
 Storm Bull: Index to biographies of contemporary composers, Vol. II, Metuchen, N.J.: Scarecrow Press, 1974, 567 p., ISBN 0-8108-0734-3
 John Vinton: Dictionary of contemporary music, New York: E.P. Dutton, 1974, 834 p., ISBN 978-0525091257
 Paul Frank, Burchard Bulling, Florian Noetzel, Helmut Rosner: Kurzgefasstes Tonkünstler Lexikon - Zweiter Teil: Ergänzungen und Erweiterungen seit 1937, 15. Aufl., Wilhelmshaven: Heinrichshofen, Band 1: A-K. 1974. ISBN 3-7959-0083-2; Band 2: L-Z. 1976. ISBN 3-7959-0087-5
 Marc Honneger: Dictionnaire de la musique, Paris: Bordas, 1970-76
 Antonio Iglesias: Joaquín Rodrigo. Su obra para piano, Orense, Conservatorio de Música 1965. 297 S.
 Bernard Gavoty, Daniel Lesur: Pour ou contre la musique moderne?, Paris: Flammarion, Editeur, 1957, 340 p.
 Philip James Bone: The guitar and mandolin: biographies of celebrated players and composers, London: Schott, 1954, 388 p.
 Joaquín Pena, Higinio Anglés, Miguel Querol Gavalda: Diccionario de la Música LABOR, Barcelona: Editorial Labor, 1954, 2V, 2318P.
 Gilbert Chase: The music of Spain, New York: W.W. Norton, 1941, 375 p.
 Carlo Schmidl: Dizionario universale dei musicisti: Supplemento, Milan: Sonzogno, 1938, 806 p.

Trivia
 In de jaren tachtig is een fragment uit het derde gedeelte van Fantasía para un gentilhombre gebruikt als leader voor het NOS-televisieprogramma Paspoort voor Spanjaarden.

Externe link
  Joaquín Rodrigo internetpagina

Spaans componist
20e-eeuws componist
Spaans muziekpedagoog
Spaanse adel

redpajama_set_name: RedPajamaWikipedia


text:
/*
 * Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except
 * in compliance with the License. You may obtain a copy of the License at
 *
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 * or implied. See the License for the specific language governing permissions and limitations under
 * the License.
 */
/*
 * This code was generated by https://github.com/googleapis/google-api-java-client-services/
 * Modify at your own risk.
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package com.google.api.services.integrations.v1alpha.model;

/**
 * Mapped field is a pair of input field and output field. Next Id: 3
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 This is the Java data model class that specifies how to parse/serialize into the JSON that is
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 * explanation see:
 * https://developers.google.com/api-client-library/java/google-http-java-client/json
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 *
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redpajama_set_name: RedPajamaGithub


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text:
Home Latest News Exposure to air pollution may increase risk of Covid death, major study...
Exposure to air pollution may increase risk of Covid death, major study says
Long-term exposure to air pollution may increase the risk of death from Covid-19, according to a large study by the Office for National Statistics.
It analysed more than 46,000 coronavirus deaths in England and showed that a small, single-unit increase in people's exposure to small-particle pollution over the previous decade may increase the death rate by up to 6%. A single-unit increase in nitrogen dioxide, which is at illegal levels in most urban areas, was linked to a 2% increase in death rates.
These increases are smaller than found in other research; a US study found an 8% increase and an analysis of the Netherlands found a 15% rise. This may be because those studies assessed earlier stages of the pandemic when the virus was mostly spreading in cities.
Data is so far only available as averages for groups of people and the ONS said this meant no definitive conclusion on the link between dirty air and the worst impacts of Covid-19 could yet be made. Instead, individual-level data would have to be examined to rule out other possible factors. The ONS has begun this work for patients in London.
The ONS also found that air pollution could be a factor in explaining why people from BAME backgrounds suffer more from coronavirus.
"The effects of long-term exposure to air pollution as a factor that increases coronavirus mortality appear smaller than those reported in previous studies, though our upper estimates are similar in magnitude to some," the ONS report said. "[But] it must be accepted that the true picture will likely only emerge once data are available for highly detailed individual-based modelling."
There are good reasons to suspect that air pollution worsens Covid-19. "Consistent exposure to air pollution is a known cause of breathing difficulties and other long-term conditions in the lungs and heart," the ONS report said.
"Our data show that 35% of deaths involving Covid-19 had a respiratory or cardiovascular disease as the main pre-existing health condition."
However, towns and cities have both high air pollution and also high rates of coronavirus infections, deprivation, poor health and dense population. The ONS report was able to take some account of these factors, but teasing out the impact of each factor alone is a difficult statistical challenge.
This is particularly true for minority ethnic populations as they are exposed to higher levels of dirty air than others. The ONS said it was currently impossible to entirely separate the effects of race and pollution. But it said: "If there is a causal link between air pollution and Covid-19-related mortality, it would partially explain the disparities in outcomes for minority ethnic groups."
The ONS used a novel approach to help take account of the other factors. Instead of using postcodes or other geographical areas for the analysis, it grouped together areas across the country that shared socioeconomic and demographic characteristics.
Prof Matthew Cole, at the University of Birmingham and who conducted the analysis of the Netherlands, said: "The ONS study uses a very unconventional way of grouping the data. This is a real shame as it means we can't be sure if the estimated results are driven by this unconventional method.
"In the absence of individual level data, fine regional data is the only way to examine these issues," he said. "It's a shame therefore that this study uses 175 relatively large regional groupings. This means the characteristics of each region risk being averaged out."
Geraint Davies MP, chair of the all-party parliamentary group on air pollution, said: "The study neither proves nor disproves the hypothesis that air pollution worsens outcomes in Covid-19. However, we know air pollution leads to 62,000 premature deaths each year and weakens people prior to catching coronavirus. Therefore the government has a duty to act and this should be a call to action, not an excuse for further inaction."
In July, the detailed and comprehensive Netherlands analysis concluded there was "compelling" evidence that air pollution significantly increases coronavirus infections, hospital admissions and deaths. There is also evidence from Europe, the US and China.
The UK government's expert air pollution advisers stated at the start of July that air pollution was likely to be increasing the number and severity of Covid-19 infections. They said further investigation of the link between dirty air and the coronavirus pandemic was urgently required and may be relevant to how the pandemic is managed.
Also in July, a study of 400 hospital patients in Birmingham linked the severe impacts of Covid-19 on people from ethnic minorities to air pollution and overcrowded and poor-standard homes.
Ninety parliamentarians led by Davies have urged the government to back action on air pollution to help avoid a second wave of coronavirus, while an air pollution inquiry by a select committee of MPs is examining delays in the rollout of clean air zones in cities as a result of the pandemic.
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Robertson Memorials is one of the oldest and largest memorial masons and stone suppliers in the UK. Established in 1876, they have over 30 branches across the UK and hundreds of hand-crafted products.
We designed and developed their new website with a product-driven content management system that is easily operated within each branch to manage orders from initial enquiry to memorial erection. A business management module built into the backend allows head office to view orders and performance statistics from each branch at the touch of a button.
In conjunction with the website development, we carried out a brand improvement project, art directed a new photo library for use across all external and internal marketing material, designed and produced all print assets and updated their branch signage.
We are a full service design, digital and advertising agency based in London. We create intelligent, inspired and effective design and communications for business.


text:
Home Life Equestrian Goldstein Scores Big Victory In $384,000 Rolex CSI 5*
Goldstein Scores Big Victory In $384,000 Rolex CSI 5*
Danielle Goldstein of Israel rides Lizziemary to victory. Photo by Ashley Neuhof
In the second five-star Grand Prix of the season, Danielle Goldstein was victorious riding Lizziemary in the $384,000 Rolex Grand Prix on Saturday, Feb. 24 at the Winter Equestrian Festival at the Palm Beach International Equestrian Center in Wellington.
There were 39 entries in the Saturday night event, and six found the key to a clear round to advance to the Anthony D'Ambrosio-designed jump-off. First in was Liubov Kochetova on her own Veneno, a 10-year-old Oldenburg gelding. They took their time to produce a clear round in 45.77 seconds, which would hold up for second place.
"He's still young for me," said Kochetova of the horse she found five years ago at the Paul Schockemöhle auction. "He started to jump big Grand Prix just like half a year ago. He's getting better and better. It's a very good horse for the future and big classes; he just needs more experience in night classes because he's looking at all this and the jumps. Today, of course, he was amazing. I'm so happy he did two clear rounds."
Jessica Springsteen and RMF Swinny du Parc, owned by Rushy Marsh Farm, were next in, but had eight faults in 37.24 seconds for sixth place. Goldstein and Lizziemary, a 12-year-old AES mare owned by Goldstein and the Golden Group, contested next and put down a blazing time of 35.92 seconds, but even more importantly, the only other clear round in the jump-off.
"I got a good shot at the skinny, and I saw it, and I thought, 'Alright, it's there. I'm just going to kick and hope it works out,'" Goldstein said. "The horse jumped great, so tonight, it worked!"
Three more would chase Goldstein's time and end up with four faults. Yuri Mansur and Louise Weber's Babylotte had a time of 39.28 seconds for fifth place, and Eric Lamaze and the Chacco Kid Group's Chacco Kid finished in 37.23 seconds for fourth place.
Going last in the jump-off, Olympic gold medalist McLain Ward and HH Azur, owned by Double H Farm, were on pace to win, but a front rail at the final Rolex oxer relegated them to third place in 36.60 seconds.
"Azur was brilliant," Ward said. "Dani put up a great jump-off round. It wasn't easy to beat. She did eight [strides] to the last, which I actually hadn't walked. I thought it was nine. When I rolled back on the skinny, it didn't show up exactly the way I wanted. I thought the mare made a great move to clear it, but we landed very far to the left. I just didn't see the line to do it, and I chickened out and did the nine. I knew the nine was too slow, so I was trying to do the nine quickly, and I just drove her through the front rail."
Goldstein has been building up Lizziemary's program this winter to aim for the five-star competitions.
"The horse had a big summer," she said of her European Championships mount. "I was gearing her toward one of these classes, specifically tonight. I jumped an easy class on Wednesday, and then she had a couple days to recover and prepare. I thought she came out tonight and jumped beautifully. I was thrilled with her."
This was the second five-star Grand Prix victory at the 2018 WEF for an Israeli rider, following Daniel Bluman's win during week five.
"It's huge," said Goldstein of the success for Israel. "Winning any Grand Prix in Wellington is a big deal, but winning one of the five stars is really unbelievable. Daniel has won two Grand Prix this season, so it's been a big season first of all, which I think is wonderful. We've been building for a few years, trying to get a number of riders up to this level. We're a bit of a close-knit group. It means the world to us. All we want to do is go to the Olympics and represent our country well. OK, everybody wants to win a medal, but for us, for Israel, it's a huge deal. I think the country has never fielded an equestrian team at the Olympics.'"
Goldstein was also presented with the Martha Jolicoeur Leading Lady Rider Award by Martha Jolicoeur of Douglas Elliman Real Estate for week seven. For winning the Grand Prix, Goldstein received a stay in a luxury studio at the Brazilian Court Hotel in Palm Beach.
The Saturday Night Lights series continues throughout the 12-week WEF circuit, held at the Palm Beach International Equestrian Center in Wellington. Hunter, jumper and equitation competition at WEF continues through April 1, offering more than $9 million in prize money. For more info., visit www.pbiec.com.
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Check out some of my articles around the web.
There's a lot of encouragement to dream big, but more important than the size of the dream is where it's really coming from and why. Is your dream really God's vision for your life?
The difference between a talented leader and a truly inspiring one can be measured by how far we're willing to follow them.


text:
Youngsters speak out as part of 'I Heart Wisbech' campaign
Published: 3:29 PM July 25, 2019 Updated: 6:26 AM November 4, 2020
Young people learned how they could have a positive impact on the future of their town when more than 150 students gathered together as part of the 'I Heart Wisbech' campaign. Picture: AMY AMPS - Credit: Archant
Young people learned how they could have a positive impact on the future of their town when more than 150 students gathered together as part of the 'I Heart Wisbech' campaign.
Wisbech's Thomas Clarkson Academy hosted an engagement event earlier this month so students could hear the results of the 'I Heart Wisbech' community survey - and find out how they can get involved in the campaign.
More than 1,000 people have taken part in the survey over the past six months, giving their ideas on what was good about the town, not so good and what could be changed.
Now the results are being shared with the community to inform residents how feedback will be used to help develop future services and projects in the town.
The Thomas Clarkson event was the fourth engagement event in the town, following others at the Oasis Centre, Queen Mary Centre and Rosmini Centre.
The survey feedback has also been shared with consultants producing Fenland's four Growing Fenland Masterplans, to help inform the draft Masterplan for Wisbech.
Tim Mann, the professional artist behind the Crowded Room Wisbech project, was invited to present the Thomas Clarkson event.
He highlighted what other students had said in the survey, and what was important to them as younger people living in Wisbech.
Friendship and respect topped the most important things, closely followed by support networks (including teachers), diversity, community events, facilities and family.
Students also took part in a lively debate to discuss what they could do to help improve the town.
Russell Rolph, of Support Cambridgeshire, who is managing the project on behalf of the I Heart Wisbech team, said: "The next step is all about working even more closely with residents who wanted to be contacted after the community survey and want to do something positive for their town.
"We need to work with these people through the partnership and give them the opportunity to become involved, and to ensure they have the confidence, skills and support to be able to do so.
"There's a lot already happening in Wisbech which residents young and old can get involved in and exciting plans for the future they can play a role in too." Councillor Chris Boden, leader of Fenland District Council, said: "It's essential that the voice of Wisbech's young people is included in the I Heart Wisbech campaign, and that we are all involved in shaping future services and resident-led activities in the town. Young people's views are valued and will have a positive impact on our community."
The I Heart Wisbech team is made up of Cambridgeshire County Council, Fenland District Council, Wisbech Town Council, Support Cambridgeshire, Care Network Cambridgeshire, Clarion, CPSL Mind, Ferry Project, HealthWatch, Hunts Forum of Voluntary Organisations, Living Sport and the Oasis Community Development Trust.


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The first day of the PassivHaus conference in Dresden showed some clear similarities in the Home Performance Industry in Europe and America as well as some huge differences.
1. The industry on both continents is developing with a strong reliance on subsidies, either government grants or tax credits, or utility rebates. Testing and certification is essential to this approach and is a backbone of both industries.
2. The early adopters of deep energy retrofits are usually very expensive. One home that was showcased today had a $574,000 Euro price tag for the retrofit. This obviously takes significant subsidy or a "true believer" with plenty of money to act on their beliefs about peak oil, climate change or stewardship of the planet. … and there are more and more of those folks. This expensive retrofit was a combination of a government grant and a true believer with money to spend.
3. Later, Energy Efficient building gets systemized and the craftsmen learn the craft, and the building gets a lot cheaper. A factory built wood Passive House from Norway was demonstrated.
4. Occupant behavior is essential to the success of a Home Performance project. Occupant education and buy in has as much impact on performance as the quality of the work. This is especially true in the multi family projects that were demonstrated.
2. Europeans are really serious about ventilation. More like Canadians. I saw more ERV-HRV's and "Magic Boxes" (all in one, vent and heat) than I had ever seen in my life.
3. Europe is way ahead of the US on using rigid foam. They have in all configurations with the fittings & flashings to make it last 100 years.
In sum, there are more similarities than differences. The main difference is that Europe is ahead of America on almost all of the technology. I'll write more on that after the conference.
It was good to see several California friends and a few GreenEarthEquities Planetsavers here at the conference. But it's also good to start up a conversation with a German or a Bulgarian. This of course depends on their English, but most attendees have at least some English. Some dont, but they are still nice. One German couldn't speak to me but he gave me a big pretzel and a smile. There is a camaradarie among Energy Geeks from all continents. It is kind of like a family and kind of like a religeon. Like in religeon and family, you do things for long term gain, rather than just short term "best for me right now" thinking. Everyone is willing to share and everyone seems happy with other's success. It's a good place to be.
This entry was posted on Friday, May 28th, 2010 at 10:40 pm and is filed under G.E.A.R. MEMBERSHIP, Home Performance, Politics and Programs, Regulators and Regulations, RENOVATORS. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.
Good blog Dave, good intro analysis, expand it even further. Any more pictures of exhibits? keep it up.


text:
Building a Legacy for our Community
Funded on Spacehive 23 July 2019
By St Paul's Church & Parish Centre Chichester Delivery stage
By St Paul's Church & Parish Centre
Initial preparatory work including sketch plans, purchase and installation of automatic sliding doors (disabled-friendly) in order to provide a fit for purpose disabled access entrance.
Chichester Delivery stage
23 Jul 2019!
This project was funded on 23 Jul 2019!
St Paul's Church & Parish Centre
St Paul's Church & Centre is used for both church and non church events in the community. Our aim is to improve and provide a fit for purpose disabled access by providing an automatic entrance for the disabled and their carers and parents with push chairs/buggies. This will be of benefit to over 300 people every week (comprising of the disabled both young and old, mums and toddlers on pushchairs, those struggling to walk, those on wheel chairs, those taking part in our activities for the community to combat social isolation and build a stronger community and activities provided by other groups such Say Aphasia, those who have suffered stroke ). This is part of a larger project which we have decided to do in phases because of the cost. The overall project will provide a fit for purpose disable access.
Initial preparatory work
appropriate sketch plans and elevations
Dismantling
Purchase disable friendly automatic sliding doors
Installation of automatic sliding doors
We seek to be more inclusive by ensuring that our centre is easily accessible and safe for all who currently use it and those who may use it in the future.
Further Consultation
Sketch plan and preparatory work
Purchase of automatic doors
Demolition and Installation
To improve access to our church and parish centre building (from the east and west of the parish centre). Making them more inclusive, safe and welcoming, as well as offering new facilities so that we are better able to serve our community. This project will provide the necessary upgrading and refurbishment of a busy parish centre and church.
Location Chichester
Building a Legacy for our Community hit its fundraising target!6 months ago
Brilliant news, thanks everyone!
Skipton Charitable Foundation pledged £3,0006 months ago
We're Overfunding!
We hit our funding goal!
1 Pledge worth £1206 months ago
Building a Legacy for our Community has reached 70% of its target!7 months ago
West Sussex County Council pledged £1,7507 months ago
2 people liked Building a Legacy for our Community8 months ago
Building a Legacy for our Community started fundraising!8 months ago
Building a Legacy for our Community verified by Locality.8 months ago
West Sussex Crowd
How will the money be spent?Total £12,249
Purchase automatic sliding doors, installation etc - £6,205 (51%)
All Initial preparatory work - £4,335 (35%)
Sketch plans and elevation - £1,440 (12%)
Purchase automatic sliding doors, installation etc
All Initial preparatory work
Sketch plans and elevation
Overfunding
This project is enabled for overfunding. If the project hits its funding goal before the end of the campaign period, any extra funds raised will be spent (in order of priority) on: Other elements of the project such as the ramp
Total £12,249
http://www.stpaulschichester.org
St Paul's church and parish centre is a registered charity (No. 1133785) situated near the Chichester Festival Theatre, just to the north of the city centre. The church and parish centre are open every day to all the community. It is very much used for community events and local activities, for example the NHS Blood Transfusion Service and the local parliamentary elections. The main church is used for Christian worship but is also a popular venue for secular activities including meetings, music examinations, and (musical) concerts. The parish centre is already used for many varied purposes, with and without any religious element. Increased, better quality, flexible space, which is accessible to all, will better meet the needs of the community we seek to serve. Our service to the community includes a weekly refugee drop in, weekly homeless breakfast, weekly parent and toddlers, elderly meet and socialisation group etc.
Project Delivery Manager: St Paul's Church & Parish Centre The Project Delivery Manager takes legal responsibility for receiving and spending the funds raised and ensuring the project is delivered.


text:
2019 1/4 oz British Gold Queen's Beast Falcon of the Plantagenets Coin (BU)
Ships within 1 business day of cleared payment
This product is in stock and available to ship. Please note that items will not ship until payments clear as per the below:
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Same or Next Business Day
Paper Check:
4-6 Business Days After Deposit
Bank Wire:
Upon Receipt of Wire
Bitcoin/Bitcoin Cash:
1-24	 $386.85	 $390.88	 $402.97
25-49	 $383.85	 $387.85	 $399.84
50+	 $380.85	 $384.82	 $396.72
As low as $107.96 per oz over spot!
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On the obverse of 2019 1/4 oz British Gold Queens Beast Falcon of the Plantagenets Coin is the effigy of Queen Elizabeth II. This latest-generation design of Her Majesty comes from Jody Clark and was created for British coinage in 2015. It captures the Queen in right-profile relief at the age of 89.
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Mint: The Royal Mint (United Kingdom)
Condition: Brilliant Uncirculated
Weight: 1/4 oz
Purity: .9999 pure gold
Picture is an example only. Actual item is subject to change, but will always correlate with title and description.
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