text:
\section{Conclusion}

We present an analysis of the delayed feedback problem based
on the assumption that the relationships between post-click behaviors
and conversions are relatively stable.
Our results indicate that to improve the performance of learning under delayed feedback,
we should utilize post-click information as complements.
Therefore,
we propose a generalized delayed feedback model to incorporate
general user behaviors and a re-weighting method to utilize
behavior information efficiently.
Experiments on public datasets validate
the effectiveness of our method.

\section{Experiments}

\subsection{Datasets and data analysis}

We use two large-scale real-world datasets:
1) \textbf{Criteo Conversion Logs\footnote{\url{https://labs.criteo.com/2013/12/conversion-logs-dataset/}\label{url:criteo}}}
is collected from an online display advertising service within 60 days
and consists of about 16 million samples with conversion labels and timestamps\cite{dfm}.
2) \textbf{Taobao User Behavior\footnote{\url{https://tianchi.aliyun.com/dataset/dataDetail?dataId=649&userId=1&lang=en-us}\label{url:taobao}}}
is a subset of user behaviors on Taobao collected within 9 days and
consists of more than 70 million samples and 1 million users\cite{taobao_nips}.
Taobao dataset provides user behaviors within (page-view, buy, cart, favorite).

\begin{figure}[!htb]
  \centering
  \includegraphics[width=0.9\linewidth]{figure/statistic.pdf}
  \caption{(Left)
    Conditional entropy (orange) and temporal gap (blue) changes
    along with time in Criteo dataset.
    (Right) In Taobao dataset, the conditional distribution $p(\mathbf{a}|\mathbf{y})$ (bar) is stabler than conversion rate (line).\label{fig:data_statistic}}
\end{figure}

We conduct data analysis on the datasets to validate our assumption on GDFM.
The results are depicted in \reffig{fig:data_statistic}.
First, we investigate the change of conversion rate distribution $p(\mathbf{y}|\mathbf{x})$.
Since exact $p(\mathbf{y}|\mathbf{x})$ is not available,
we train a CVR model on the first 30 days to estimate the conversion rate
at the 30th day, which is denoted as $p^0(\mathbf{y}|\mathbf{x})$.
Then we fine tune this model day by day to estimate the conversion rate
at $p^t(\mathbf{y}|\mathbf{x})$, here $t$ denotes the $t$th day.
In this way, we can estimate the temporal gap between $p^0(\mathbf{y}|\mathbf{x})$ and
$p^t(\mathbf{y}|\mathbf{x})$ by their Kullback-Leibler divergence $D_{KL}(p^0||p^t)$.
In \reffig{fig:data_statistic} (Left) we can see that the temporal gap
grows along with time, which necessitate the analysis of time dependent
conversion distribution $p^t(\mathbf{y}|\mathbf{x})$ in \refsec{sec:gdfm}.
Secondly, we investigate the information quality of actions with
conditional entropy as proposed in \refsec{sec:entropy}.
Specifically, we use the observed conversion at revealing time $\delta$
as post-action $A_{\delta}$, and vary the revealing time from 0 to 30 days.
We can infer from \reffig{fig:data_statistic} (Left) that the information
carried by this action steadily increase (the conditional entropy decrease)
along with time, which is intuitive that the latter actions are more informative.
Thirdly, we investigate the relationship between post-click actions and
conversions. We plot the conversion rate and the proportion of cart and favorite
actions in converted samples
(which corresponds to $p(\mathbf{a}=1|\mathbf{y}=1)$) in the Taobao dataset in \reffig{fig:data_statistic} (Right).
We can see that the action distribution $p(\mathbf{a}=1|\mathbf{y}=1)$ is stabler comparing to conversion rate,
which conforms our assumption of stable action distribution in \refsec{sec:gdfm}.

\subsection{Evaluation}

\paragraph*{Streaming evaluation}
We follow a streaming evaluation protocol proposed by \citet{esdfm}.
Specifically, the datasets are split into pretraining and
streaming datasets. An initial conversion rate prediction model
as well as auxiliary models
(e.g., the importance weighting model in ESDFM and action distribution model $q_{\phi}$ in GDFM)
are trained on this pretraining dataset to simulate a stable state after
a long time of streaming training in real-world recommender systems.
Then the models are evaluated and updated hour by hour in the streaming dataset.
Each method is trained with the available information at the corresponding timestamps.
Following practice in \cite{defer_kdd,mt_dfm,iw_www,esdfm},
we report the receiver operating characteristic curve (AUC), precision-recall curve (PR-AUC)
and negative log-likelihood (NLL).
The metrics are calculated within each hour.
We report the average performance on the streaming dataset.

\paragraph*{Baseline methods}
To evaluate the performance of GDFM, we compare with the following methods:
1) \textbf{Pretrain}: The CVR model is trained on the pretraining dataset,
then fixed in streaming evaluation. The following methods start
with this pre-trained model at the beginning of the streaming evaluation.
2) \textbf{Vanilla}: Wait for $\delta_y$ time, then use conversion labels
to train the model.
3) \textbf{Oracle}: Use conversion labels to train without delay.
The oracle method corresponds to the upper bound of performance with feedback delay.
We compare two representative importance sampling methods.
4) \textbf{FNW}\cite{fnw}:
A sample is labeled as negative on arrival,
and a duplicate is inserted once its conversion is observed.
The fake negative weighted (FNW) loss adjusts the loss function;
5) \textbf{ES-DFM}\cite{esdfm}:
After waiting for a predefined time, a sample is labeled as negative if
conversion has not been observed.
If a sample converts after the waiting time, a duplicate is inserted.
The loss function is adjusted by the ES-DFM loss.
We also compare with a multi-task learning method based on DFM.
6) \textbf{MM-DFM}\cite{mt_dfm}:
Treating predicting the observed conversion label as a multi-task
learning problem, the tasks are optimized jointly using streaming data.
\input{table_main}

\paragraph*{Implementation}
Following \cite{esdfm,defer_kdd}, we discretize and treat numerical features the same
as categorical features in the Criteo dataset.
Since the Taobao dataset does not provide user features,
we use the last 5 user behaviors as features\cite{taobao_nips}.
Inspired by \citet{hashing}, we hash user ID and item ID into bins and
use an embedding to represent each bin.
We use the same architecture for all the methods to ensure a fair comparison.
All the methods are carefully tuned.
We use $\alpha=2$, $\beta=1$, $\lambda=0.01$, $lr=10^{-3}$ for GDFM.
Because of the page limit, the details of implementation and code
are provided in the supplementary material.

The performance is reported in \reftab{tab:main}.
Following \cite{esdfm,defer_kdd,iw_www},
we report the relative improvement of each method to
the performance gap between the Pre-trained model and the Oracle model.
From the results, we can infer that,
1) GDFM performs significantly better than compared methods.
2) It is noteworthy that FNW and
ES-DFM brings a significant negative impact to NLL
on the Taobao dataset, which is caused by the
fake negative samples introduced by them;
3) The performance of FNW and MM-DFM has a more considerable variance compared
with ES-DFM and GDFM (especially NLL on Taobao), since ES-DFM uses a fixed weighting model
to re-weight its loss, which has a similar effect to GDFM's explicit regularizer
that can stabilize training;
4) On the Criteo dataset, GDFM outperforms other methods
without using post-click information other than conversion labels,
which indicates that our information measure is effective
for early conversions;
5) On the Taobao dataset, GDFM also utilizes post-click information
such as cart and favorite.
The results indicate that introducing rich post-click information
into GDFM can improve the performance of CVR prediction.

\subsection{Experimental analysis of GDFM}

To further investigate the source of performance gain of GDFM,
we construct several experiments.
First, we remove the effect of information weights and
the regularizer loss by setting the coefficients to zeros correspondingly.
The results reported in \reftab{tab:abl} indicate that
the performance of GDFM is a combined effect of different
components.
Without $\alpha$ and $\lambda$,
the performance drops significantly,
which indicates that sample complexity and training
variance are influential factors in the Criteo dataset.
Dropping $\beta$ has relatively little influence to
performance, which indicates that the temporal gap
in the Criteo dataset has a weaker influence.

\input{table_aux}

Secondly, to validate the capacity of GDFM to deal with more actions,
we construct an additional user action in the Criteo dataset.
This action is set to the same as $\mathbf{y}$ with a probability $p$,
and set to $1-\mathbf{y}$ with probability $1-p$.
In this way, we can investigate how the information
measure influences the performance of GDFM.
We report the results with different $p$ in \reftab{tab:aux}.
When $p=0.5$, the newly inserted action does not contain
information about $y$, and the performance does not decrease,
which indicates that GDFM can extend to more actions safely;
When $p > 0.5$, the action becomes more informative,
and the performance of GDFM steadily improves,
\begin{wrapfigure}{r}{0.4\textwidth}
  \begin{center}
    \includegraphics[width=0.4\textwidth]{figure/weights.pdf}
  \end{center}
  \caption{Information weights on the Criteo dataset.\label{fig:weights}}
\end{wrapfigure}
which indicates that GDFM can utilize the information carried by
actions efficiently;
When $p=0.95$, the action is highly informative to $y$,
the performance approaches Oracle, which indicates
that GDFM can efficiently extract information from
high-quality action features.

Thirdly, we plot the weigths $w_{\text{info}}$, $w_{\text{time}}$ and $w$
corresponding to different revealing time $\delta$,
with $\alpha=2,\beta=1$ as in other experiments.
We can infer from the \reffig{fig:weights} that
1) the information carried by actions increases as
the revealing time increases;
2) the temporal gap enlarges as the revealing time increases;
3) the combined information weights $w$ reaches its maximum value
on the 7th day, which indicates that the information revealed on the 7th day
is most informative to conversion prediction.
Information revealed at other times still has non-negligible weights
that influence training.

\section{Introduction}

Conversion rate (CVR) prediction has become a core problem in display advertising
with the prevalence of the cost-per-conversion (CPA) payment model\cite{cvr_14,cvr_adv,cvr_kdd}.
With CPA, advertisers bid for predefined user behaviors such as purchases or downloads.
Similar demands also arise from online retailers that aim to improve sales volume\cite{cvr_survey},
which need to recommend items with high conversion rates to users.
However, conversions (e.g., purchases) may happen after a long delay~\cite{dfm},
which leads to a delay in conversion labels.
The adverse impact of such a delayed feedback problem becomes increasingly
significant with a rapidly changing market,
where the features of users and items are updated every second.
Thus, how to timely update the CVR prediction model with delayed feedback
attracts much attention in recent years \cite{dfm,fnw,fsiw,esdfm,defer_kdd,mt_dfm,mt_sigir}.

Since conversions are gradually revealed after click events,
previous literature concentrates on utilizing available conversion labels that
reveal earlier.
Inserting early conversions into the training data stream will also introduce many
fake negative samples \cite{fnw}, which will eventually convert but have not converted yet.
To mitigate the adverse impact of fake negatives,
\citet{dfm} proposes a delayed feedback model (DFM) to model
conversion rate along with expected conversion delay,
then the model is trained to maximize the likelihood of observed labels.
The delayed feedback model is further improved by introducing kernel
distribution estimation method \cite{dfm_kde} and more expressive neural
networks \cite{dfm_entier_space,attention_dfm,mt_dfm}.
However, the need to maintain a long time scale offline dataset impedes
training efficiency of DFM based methods
in large scale recommender systems\cite{fnw}.
To enable efficient training in a streaming manner,
\citet{fnw} proposes to insert a negative sample once a click sample arrives and
re-insert a duplicated positive sample once its conversion is observed.
The fake negative samples are supposed to be corrected by an importance sampling\cite{importance_sampling_review} method.
Importance sampling based methods are further improved by adopting different
sampling strategies \cite{fsiw,esdfm,defer_kdd,iw_www}.

Besides the conversion labels, many events related with conversion exist
in real-world recommender systems\cite{post_click_sigir20,post_click_sigir21,user_behavoir_1}.
For example, after clicking through an item,
a user may decide to add this item to a shopping cart.
Statistical data reveals that such post-click behaviors have a strong relationship with
conversions: About 12\% of items in a shopping cart will finally be bought,
while the proportion is less than 2\% without entering a shopping cart\cite{post_click_sigir20}.
Intuitively, utilizing post-click behaviors can potentially mitigate
the delayed feedback problem in CVR prediction since the time delay of
post-click behaviors is usually much shorter than conversions.
However, the corelations between post-click behaviors and conversions
are far more complex than only considering conversions,
and the problem is further complicated
by the streaming nature of training with delayed feedback.

In this work, we propose a Generalized Delayed Feedback Model (GDFM)
which generalizes the delayed feedback model (DFM)\cite{dfm} to unify
post-click information and early conversions.
Based on GDFM, we establish a novel view on learning with delayed feedback.
We argue that training using post-click information in the delayed feedback problem
is intrinsically different from traditional learning problems
from three perspectives:
(\textbf{i})
Estimating conversion rates via post-click actions requires
more samples than using conversion labels directly,
which highlights the importance of sample complexity.
(\textbf{ii}) The post-click actions bring information of
past distributions, which incurs a temporal gap.
(\textbf{iii}) The signals provided by post-click actions are
highly stochastic and lead to large variance on the target model
during training, which may instead hinder the performance of the conversion rate
prediction.
Inspired by our analysis, we propose to (\textbf{i}) measure the
information carried by a post-click action with conditional entropy,
which we empirically show is related to the sample complexity of
estimating the conversion rate;
(\textbf{ii}) measure the temporal distribution gap by time delay;
(\textbf{iii}) stabilize streaming training with a regularizer trained on past data distribution.
We conduct various experiments on public datasets with delayed feedback under
a streaming training and evaluation protocol.
Experimental results validate the effectiveness of our method.
To summarize,

\begin{itemize}
  \item We propose a generalized delayed feedback model (GDFM) to support various user behaviors
        beyond conversion labels and arbitrary revealing times of
        user actions.
  \item From a novel perspective,
        we attribute the difficulty of efficiently utilizing user behaviors to
       a sampling gap and a temporal gap in delayed feedback problems.
  \item Based on our analysis, we propose a re-weighting method that
        could selectively use the user actions that are most informative to
        improve performance.
        Our method achieves stable improvements compared to baselines.
\end{itemize}

\section{Background}

\begin{figure}[!htb]
  \centering
  \includegraphics[width=\linewidth]{figure/intro.pdf}
  \caption{
    (Left) Different post-click information can be revealed at different times.
    (Right) Depending on available information,
    GDFM is updated with different objectives accordingly.\label{fig:intro}}
\end{figure}

In recommender systems, the data stream is collected from user behavior
sequence.
Without loss of generality, we take an E-Commerce search engine as an example,
while a similar procedure also holds for display advertising\cite{cvr_adv,cvr_kdd} and
personalized recommender\cite{cvr_survey}.
When a user searches for a keyword, the search engine will provide several items
for this user. Here, a (user-keyword-item) tuple is called an \textit{impression},
which corresponds to a sample $\mathbf{x}$.
After viewing an item's detail page,
the user may purchase it.
The probability that a user will buy after clicking is called conversion rate (CVR).
Conversion can be any desired user behavior, such as registering an account or
downloading a game.
Without loss of generality,
we only consider one type of conversion in the rest of this paper,
while our method can be applied to multi-class case\cite{mt_cvr} without modification.
If an impression sample $\mathbf{x}$ is finally converted,
it will be labeled as $\mathbf{y}=1$ and $\mathbf{y}=0$ otherwise.
The conversion rate of $\mathbf{x}$ corresponds to $p(\mathbf{y}=1|\mathbf{x})$.

The distribution $p(\mathbf{x})$ and $p(\mathbf{y}|\mathbf{x})$ changes rapidly in real-world recommender
systems. For example, when a promotion starts, the conversion rate may increase
steeply for items with a large discount, and such promotion happens every day.
The CVR model has to be updated timely to capture such distribution change.
However, the ground-truth conversion labels are available only after a long delay:
A user may purchase several months later after a click event $\mathbf{x}$.
Usually, a sample will be labeled as negative after a long enough waiting time,
e.g., 30 days\cite{dfm}, this delay time of conversion label is denoted as $\delta_y$.
Besides conversion labels, post-click actions (behaviors) are denoted as
$\mathbf{a}_j, j \in \{1, ..., m\}$.
Each action $\mathbf{a}_j$ is paired with a revealing time $\delta_j$,
which means the value of $\mathbf{a}_j$ is determined after a $\delta_j$ delay.
For example, we can query the database to see whether a user has put an item
into the shopping cart 10 minutes ($\delta_j$) after clicking.
If true, this action is labeled as $\mathbf{a}_j=1$, and $\mathbf{a}_j=0$ otherwise.
There can be several revealing times for a single type of action,
e.g., we may choose to reveal the shopping cart information at 10 minutes,
30 minutes and 1 hour, they are treated as different actions since
the revealing time is different.
It is noteworthy that revealing the conversion labels is also treated
as a type of action.
The sequential relationship of available information is depicted in
\reffig{fig:intro} (Left).
To capture the characteristic that the data distribution changes along with time,
the data distribution is denoted by $p^t(\mathbf{x}, \mathbf{y})=p^t(\mathbf{x})p^t(\mathbf{y}|\mathbf{x})$ at time $t$.
Our goal is to predict $p^t(\mathbf{y}|\mathbf{x})$ at time $t$ by training a model $q_{\theta}(\mathbf{y}|\mathbf{x})$,
where $\theta$ denotes model parameters.
Without data distribution shift, it is straightforward to optimizing
likelihood by sampling from $p^t$.
However, in delayed feedback setting,
the latest available labels have a $\delta_y$ delay.
Thus simply training using available labeled data will lead to
$q_{\theta}(\mathbf{y}|\mathbf{x})=p^{t-\delta_y}(\mathbf{y}|\mathbf{x})$ instead.

\section{Generalized Delayed Feedback Model\label{sec:gdfm}}

We propose following generalized delayed feedback model to describe the
relationship between data features $\mathbf{x}$, conversion labels $\mathbf{y}$,
post-click actions $\mathbf{a}$, revealing time of actions $\delta$,
and data distribution at time $t$:
\begin{align}
  p^t(\mathbf{x}, \mathbf{y}, \mathbf{a}, \delta) = p^t(\mathbf{y}|\mathbf{x}) p(\mathbf{a}|\mathbf{x}, \mathbf{y}, \delta) p(\delta) p^t(\mathbf{x}) \label{GDFM}
\end{align}
Our formulation unified previous delayed feedback
models\cite{dfm,mt_dfm,mt_sigir,dfm_kde} while enable
more general feedbacks and revealing times.
$p^t(\mathbf{y}|\mathbf{x})$ is the target CVR distribution,
we assume that $p^t(\mathbf{y}|\mathbf{x})$ is independent to user actions $\mathbf{a}$,
which enable us to extend existing CVR prediction framework seamlessly.
To model the post-actions,
we introduce a post-action distribution $p(\mathbf{a}|\mathbf{x}, \mathbf{y}, \delta)$, which
depends on
sample features $\mathbf{x}$, the conversion label $\mathbf{y}$, and the revealing time $\delta$.
We assume the post-action distribution $p(\mathbf{a}|\mathbf{x}, \mathbf{y}, \delta)$ is fixed or
changes much slower than $p^t(\mathbf{y}|\mathbf{x})$, so that the post-action distribution does
not depend on time $t$.
This assumption is critical for learning under delayed feedback since the
relationship between post-actions and conversion should be stable so that
post-actions can be informative.
Previous literature also relies on similar assumptions implicitly,
for example, a predictable delay time of conversion\cite{dfm} or
a loss function that depends on a stable post-action distribution in our formulation\cite{defer_kdd,esdfm,defer_kdd}.
Our formulation decouples the post-action distribution and the conversion distribution,
which enables us to formulate this assumption explicitly and conduct further analysis based
on this assumption.
An alternative but more intuitive definition is to define
$p^t(\mathbf{x}, \mathbf{y}, \mathbf{a}, \delta)=p^t(\mathbf{a}|\mathbf{x}, \delta) p(\mathbf{y}|\mathbf{x}, \mathbf{a}, \delta) p(\delta) p(\mathbf{x})$,
which requires to sum out $\mathbf{a}$ and $\delta$ to make prediction.
This approach not only increases the prediction cost but also introduces large
variance in sampling.
We discuss this approach in the supplementary material.
We further introduce a revealing time distribution of post-actions $p(\delta)$,
which is independent of other variables.
$\delta$ is also known as the elapsed time in previous literature \cite{dfm,esdfm}.
The revealing time enables us to inject action information at time $\delta$, which is
typically less than $\delta_y$ so that the model can be updated much earlier.
We introduce a streaming training method of GDFM in the next section.

\subsection{Training GDFM}

We introduce an action prediction model $q_{\phi}(\mathbf{a}|\mathbf{x}, \mathbf{y}, \delta)$
to estimate the action distribution $p(\mathbf{a}|\mathbf{x}, \mathbf{y}, \delta)$,
the CVR prediction model is denoted as $q_{\theta}(\mathbf{y}|\mathbf{x})$, which
will be used to predict the conversion rate $p^t(\mathbf{y}|\mathbf{x})$.
In the data stream, not all the information in GDFM defined in \refeq{GDFM}
is available at that same time, so we propose a streaming training method
for GDFM that can utilize available information in the data stream.
According to the availability of $\mathbf{a}$, $\mathbf{y}$,
there are several different cases.
We assume the current timestamp is $t$.

\paragraph*{When $\mathbf{a}, \mathbf{x}, \mathbf{y}$ is available} The action prediction model $q_{\phi}(\mathbf{a}|\mathbf{x}, \mathbf{y}, \delta)$ can be
trained with following loss when $\mathbf{a}$, $\mathbf{x}$ and $\mathbf{y}$ are available.
\begin{align}
  \mathcal{L}_{\text{action}} =
  -\mathbb{E}_{p^{t - \delta_y}} \log q_{\phi}(\mathbf{a}_j|\mathbf{x}, \mathbf{y}, \delta_j)\label{axy_train_loss}
\end{align}
Note that with the assumption that $p(\mathbf{a}_j|\mathbf{x}, \mathbf{y}, \delta_j)$ is invariant with respect to $t$,
loss \refeq{axy_train_loss} will be minimized when $p(\mathbf{a}_j|\mathbf{x}, \mathbf{y}, \delta_j)=q_{\phi}(\mathbf{a}_j|\mathbf{x}, \mathbf{y}, \delta_j)$.

\paragraph*{When $\mathbf{y}, \mathbf{x}$ is available}
When we have the ground-truth label of $\mathbf{y}$, we are able to update
the CVR model directly by minimizing cross entropy.
\begin{align}
  \mathcal{L}_{\delta_y} = -\mathbb{E}_{p^{t - \delta_y}}\log q_{\theta^{t - \delta_y}}(\mathbf{y}|\mathbf{x})\label{y_loss}
\end{align}
Note that this loss is minimized when $p^{t - \delta_y}(\mathbf{y}|\mathbf{x})=q_{\theta^{t - \delta_y}}(\mathbf{y}|\mathbf{x})$.

\paragraph*{When $\mathbf{a}, \mathbf{x}$ is available}
Since the delay times of user actions ($\delta_j$) are smaller
than the conversion label delay
$\delta_y$, we can update the CVR model once a user action is observed.
When we observe the $j$th user action $\mathbf{a}_j$ at revealing time $\delta_j$,
we can update the prediction model $q_{\theta}(\mathbf{y}|\mathbf{x})$ using following loss:
\begin{align}
  \mathcal{L}^\prime_{\delta_j} & = -\mathbb{E}_{p^{t - \delta_j}} \log q(\mathbf{a}_{j}|\mathbf{x}, \delta_j)
  = - \mathbb{E}_{p^{t - \delta_j}}
   \log \sum_\mathbf{y} q_{\phi}(\mathbf{a}_j|\mathbf{x}, \mathbf{y}, \delta_j)
  q_{\theta}(\mathbf{y}|\mathbf{x})\label{stream_xy_loss}
\end{align}
Training GDFM with different losses is depicted in \reffig{fig:intro} (Right).
However, it is unclear whether minimizing \refeq{stream_xy_loss}
will help learning $p^t(\mathbf{x}|\mathbf{y})$.

\subsection{Narrowing the delayed feedback gap with post-actions}

The training objective of GDFM can be viewed as a multi-task training
problem, which is also explored by \citet{mt_dfm} and \citet{mt_sigir}.
However, learning with delayed feedback is different
from general multi-task learning problems without delayed feedback.
In learning with delayed feedback, since we are training on
different data distribution at different times,
the tasks are intrinsically conflicted, which may be harmful to
the target \cite{mt_dfm,mt_survey}.
We analyze its effect in the following sections.

\subsubsection{Post-actions can be informative\label{sec:info_action}}
Since in GDFM we are using post-actions from $t - \delta_j$ instead of $t - \delta_y$,
we have a chance to do better.
But will optimizing \refeq{stream_xy_loss}
improve the performance of $q(\mathbf{y}|\mathbf{x})$?
Without loss of generality, we consider an action $\mathbf{a} \in \{a_1, ..., a_k\}$,
and $p(\mathbf{a}|\mathbf{x})=\sum_{\mathbf{y}} p(\mathbf{y}|\mathbf{x}) p(\mathbf{a}|\mathbf{x}, \mathbf{y})$, $\mathbf{y} \in \{y_1, ..., y_n\}$.
Assuming we can estimate $p(\mathbf{a}|\mathbf{x})$ accurately and $k \ge n$, we have following results:
\begin{lemma}\label{lemma_rec}
  Use a matrix $\mathbf{M_x} \in \mathbb{R}^{k \times n}$ to denote
  the conditional probability $p(\mathbf{a}|\mathbf{x}, \mathbf{y})$, where
  $(\mathbf{M_x})_{ji}=p(\mathbf{a}=a_j|\mathbf{x}, \mathbf{y}=i)$.
  We can recover $p(\mathbf{y}|\mathbf{x})$ from $p(\mathbf{a}|\mathbf{x})$
  if and only if $\operatorname{rank}(\mathbf{M_x})=n$.
\end{lemma}
\textbf{Proof sketch}: $p(\mathbf{a}|\mathbf{x})$ is a linear transformation from
$p(\mathbf{y}|\mathbf{x})$ and the
transform matrix is given by $\mathbf{M_x}$.
By construction a solution exists, and
$\operatorname{rank}(\mathbf{M_x})=n$
guarantees that the solution is unique.

\reflemma{lemma_rec} highlights the benefits of utilizing post-actions:
if the relationship between a post-action and the target is predictable
(we can train a model $q(\mathbf{a}|\mathbf{x}, \mathbf{y})$ to approximate $p(\mathbf{a}|\mathbf{x}, \mathbf{y})$)
and informative ($\operatorname{rank}(M)=n$)
we can recover the target distribution even without the ground-truth label $\mathbf{y}$.
Since $\operatorname{rank}(\mathbf{M})<n$ requires that some rows of $\mathbf{M}$ are
linear combination of the others, which rarely happens in real-world problems,
we assume the assumption holds true in the next section.
We discuss the case that this assumption fails in \refsec{sec:reg}.
However, even if $\operatorname{rank}(\mathbf{M})=n$,
this result is still overly optimistic.
Because we are estimating $p(\mathbf{a}|\mathbf{x})$ using samples from $p(\mathbf{a}|\mathbf{x})$,
and the difficulty of estimating $p(\mathbf{y}|\mathbf{x})$ via estimating $p(\mathbf{a}|\mathbf{x})$
also depends on properties of $p(\mathbf{a}|\mathbf{x}, \mathbf{y})$.

\subsubsection{Measuring information carried by actions\label{sec:entropy}}

Not all actions carry the same amount of information about $p(\mathbf{y}|\mathbf{x})$.
For example, an action may carry zero information about $\mathbf{y}$ if it is
constant and irrelevant to $\mathbf{y}$; it may carry full information
if it always equals $\mathbf{y}$.
The general relationship between $\mathbf{a}$ and $\mathbf{y}$ is far more complex,
which lies between non-informative and fully informative.
We want to estimate the information quantity of each action to utilize actions
more efficiently.
To this end, we propose to use conditional entropy to measure information
carried by actions. The conditional entropy of $\mathbf{y}$ given $\mathbf{a}$ can by
calculated by
\begin{align}
  H(\mathbf{y}|\mathbf{a}) = \sum_{\mathbf{a}, \mathbf{y}} p(\mathbf{y}, \mathbf{a}) \log \frac{p(\mathbf{a})}{p(\mathbf{y}, \mathbf{a})}\label{eq:entropy}
\end{align}
Conditional entropy measures the amount of information needed to describe
$\mathbf{y}$ given the value of $\mathbf{a}$.
When $\mathbf{a}$ is non-informative to $\mathbf{y}$, that is $p(\mathbf{a}, \mathbf{y})=p(\mathbf{a})p(\mathbf{y})$,
we have $H(\mathbf{y}|\mathbf{a})=H(\mathbf{y})$, which is the maximum value of $H(\mathbf{y}|\mathbf{a})$;
when $\mathbf{a}$ determines value of $\mathbf{y}$, that is, there is a function $\mathbf{y}=f(\mathbf{a})$,
we have $H(\mathbf{y}|\mathbf{a})=0$. Since the scale of $H(\mathbf{y}|\mathbf{a})$ only depends on
$p(\mathbf{y})$, this information metric is comparable among different $\mathbf{a}$,
which is a desired property.

\begin{wrapfigure}{r}{0.35\textwidth}
  \begin{center}
    \includegraphics[width=0.35\textwidth]{figure/dtv_and_h.pdf}
  \end{center}
  \caption{Conditional entropy and transformed distance.\label{fig:dtv}}
\end{wrapfigure}

Empirically, we found that conditional entropy is also related to the sample complexity
of estimating $p(\mathbf{y}|\mathbf{x})$ via $p(\mathbf{a}|\mathbf{x})$.
In learning with delayed feedback, we are sampling
from different distribution $p^t$ at different time stamp $t$, which indicates
that to perform well, we should be able to learn fast.
Thus, analysis that is based on a large amount of i.i.d samples from a fixed distribution
can't capture the difficulty of learning with delayed feedback.
Property testing~\cite{property_testing_survey} considers sample complexity of
learning distributions.
Specifically,
distinguishing between two discrete distribution $p$ and $q$ with probability at least
$1 - \epsilon$ requires
$\Omega (\frac{1}{D^2_{\text{TV}}(p, q)} \log \frac{1}{\epsilon})$ samples from $q$
and $p$.
Where $D_{TV}$ is the total variance distance which is defined by
$D_{\text{TV}}(p, q)=\sum_i |p(i) - q(i)|$.
Since we are estimating $p(\mathbf{y}|\mathbf{x})$ through a proxy distribution $p(\mathbf{a}|\mathbf{y})$,
the sample complexity depends on how close the transformed distribution $p(\mathbf{a}|\mathbf{x})$ is.
Empirically, we found that using $p(\mathbf{a}|\mathbf{x})$ will make $p(\mathbf{y}|\mathbf{x})$
more difficult to learn,
that is, the distance of two distribution $p_1(\mathbf{y}|\mathbf{x})$ and $p_2(\mathbf{y}|\mathbf{x})$ will
decrease when they are transformed to $p_1(\mathbf{a}|\mathbf{x})$ and $p_2(\mathbf{a}|\mathbf{x})$ correspondingly.
So the difficulty of learning $p(\mathbf{y}|\mathbf{x})$ via $p(\mathbf{a}|\mathbf{x})$ depends on the change of distribution
distance incurred by the stochastic transformation $p(\mathbf{a}|\mathbf{y})$.
We empirically investigate the relationship between the change of distribution distance and
conditional entropy by Monte Carlo sampling, the results in \reffig{fig:dtv} indicate that
as the conditional entropy increases, the transformed distribution distance decreases
exponentially, which motivates the following information weights
\begin{align}
  w_{\text{info}}(p(\mathbf{a}_j, \mathbf{y})) = e^{-\alpha H(\mathbf{y}|\mathbf{a}_j)}\label{info_weight}
\end{align}
where $\alpha$ is a hyper-parameter. \refeq{info_weight} roughly measures the
reciprocal of sample complexity of learning $p^{t-\delta_j}(\mathbf{y}|\mathbf{x})$ via $p^{t-\delta_j}(\mathbf{a}_j|\mathbf{x})$,
so that actions are weighted based on their effective information carried by each sample.

\subsubsection{Measuring temporal gap}

Besides the sample complexity of estimating $p^{t-\delta_j}(\mathbf{y}|\mathbf{x})$ via
action distribution, the intrinsic temporal gap
between $p^t$ and $p^{t - \delta_j}$ also influence the predicting performance.
Even if we have unlimited samples from $p^{t-\delta_j}$
we are only able to recover $p^{t - \delta_j}(\mathbf{y}|\mathbf{x})$ instead of $p^t(\mathbf{y}|\mathbf{x})$.
So we also need to take the revealing time $\delta_j$ into consideration.
However, we can't estimate the gap between $p^{t-\delta_j}$ and $p^{t}$
accurately since the exact distribution is unknown and changes along with time.
Empirically (\reffig{fig:data_statistic}) we found that the gap measured by KL divergence tends to increase
as the time gap increases.
So we propose the following temporal weight
\begin{align}
  w_{\text{time}}(\delta_j) = e^{-\beta \delta_j}\label{gap_weight}
\end{align}
which measures the gap between $p^t$ and $p^{t-\delta_j}$.
$\beta$ is a hyper-parameter which reflects the expected changing speed of
data distribution during time, larger value of $\beta$ indicates that
we discard more information from stale data.
Overall, we introduce a weight on loss \refeq{stream_xy_loss} as follows:
\begin{align}
  \mathbf{w}_j = w(p(\mathbf{a}_j, \mathbf{y}), \delta_j) = w_{\text{info}}(p(\mathbf{a}_j, \mathbf{y}))w_{\text{time}}(\delta_j)
  \label{eq:weights}
\end{align}
For simplicity, our $\mathbf{w}_j$ does not depend on $\mathbf{x}$,
the extension to $\mathbf{x}$ dependent weights is straightforward.
The weight $\mathbf{w}_j$ can be decomposed into two components,
the first component $w_{\text{info}}$ measures how informative
action $\mathbf{a}_j$ is to the target $\mathbf{y}$.
The second component $w_{\text{time}}$ measures the gap between $p^t$
and $p^{t-\delta_j}$.
The procedure of calculating weight vector $\mathbf{w} \in \mathbb{R}^{m}$ is summarized in \refalg{algo:weight}.
\begin{minipage}{0.49\textwidth}
\begin{algorithm}[H]
  \caption{Streaming training of GDFM\label{algo:gdfm}}
  \begin{algorithmic}[1]
    \FOR{$\{\mathbf{x}, \mathbf{y}, \mathbf{a}, \delta\}$ in data stream}
    \FOR{$\{\mathbf{x}, \mathbf{y}, \mathbf{a}\}$ that $\mathbf{y}$ is unlabeled}
    \STATE Update $q_{\theta}(\mathbf{y}|\mathbf{x})$ with \refeq{loss:all}.
    \ENDFOR
    \FOR{$\{\mathbf{x}, \mathbf{y}, \mathbf{a}\}$ that $\mathbf{y}$ is labeled}
    \STATE Update $q_{\phi}(\mathbf{a}|\mathbf{x}, \mathbf{y}, \delta)$ with \refeq{axy_train_loss}.
    \STATE Update $q_{\theta^{t-\delta_y}}(\mathbf{y}|\mathbf{x})$ with \refeq{y_loss}.
    \ENDFOR
    \ENDFOR
  \end{algorithmic}
\end{algorithm}
\end{minipage}
\begin{minipage}{0.49\textwidth}
\begin{algorithm}[H]
  \caption{Estimating $w_j$\label{algo:weight}}
  \textbf{Input}: Dataset $\{\mathbf{y}, \mathbf{a}\}$ \\
  \textbf{Parameter}: $\alpha$, $\beta$. \\
  \begin{algorithmic}[1]
    \STATE Estimate $p(\mathbf{a}, \mathbf{y})$ by counting.
    \STATE Calculate $H(\mathbf{y}|\mathbf{a})$ with \refeq{eq:entropy}.
    \STATE Calculate $w_{\text{info}}$ with \refeq{info_weight}.
    \STATE Calculate $w_{\text{time}}$ with \refeq{gap_weight}.
    \STATE Calculate weights $\mathbf{w}_j$ with \refeq{eq:weights}.
    \STATE Normalize $\mathbf{w}$ to have $\operatorname{mean}(\mathbf{w})=1$.
  \end{algorithmic}
\end{algorithm}
\end{minipage}

\subsubsection{Reducing variance by delayed regularizer}\label{sec:reg}

Estimating probability with sampling will incur instable variance during stream training,
which may harm performance.
Since we are estimating using a stochastic proxy $p(\mathbf{a}|\mathbf{x})$,
the variance will be even higher.
To reduce variance and stabilize training, we introduce a regularizer loss \refeq{eq:reg_loss}
that constraints update step during training,
where $q_{\theta^{t - \delta_y}}(\mathbf{y}|\mathbf{x})$ is trained with loss \refeq{y_loss}.
\begin{align}
  \mathcal{L}_{\text{reg}} = \operatorname{KL}(q_{\theta^{t - \delta_y}}(\mathbf{y}|\mathbf{x})||q_{\theta}(\mathbf{y}|\mathbf{x}))\label{eq:reg_loss}
\end{align}
Besides reducing variance during training,
another critical function of $\mathcal{L}_{reg}$ is to make GDFM \textit{safe}
to introduce more actions.
The analysis in \refsec{sec:info_action} shows that if an action is informative,
we can learn $p(\mathbf{y}|\mathbf{x})$ through $p(\mathbf{a}|\mathbf{x})$.
However, if $\operatorname{rank}(\mathbf{M})<n$ (typically because $k<n$) or
the information carried by $p(\mathbf{a}|\mathbf{x})$ is too weak to recover $p(\mathbf{y}|\mathbf{x})$
as analyzed in \refsec{sec:entropy}, GDFM may fail to learn $p(\mathbf{y}|\mathbf{x})$
because of interference from action signals.
The regularizer loss $\mathcal{L}_{reg}$ introduces the ground-truth labels
of $\mathbf{y}$ from $p^{t-\delta_y}$,
which guarantees that the performance learned by GDFM will
not be much worse than $p^{t-\delta_y}$ (the Vanilla method in experiments).
In this perspective, $\mathcal{L}_{reg}$ make it safer to introduce various post-click information
into our training pipeline without worrying about sudden performance drop,
which is critical in production environments.
The overall loss function with revealing time $\delta_j$ is
\begin{align}
  \mathcal{L}_{\delta_j} = \mathbf{w}_j \mathcal{L}^\prime_{\delta_j} + \lambda \mathcal{L}_{\text{reg}}\label{loss:all}
\end{align}
The streaming training procedure of GDFM is summarized in \refalg{algo:gdfm}.
\section{Related work and discussion\label{sec:related_work}}

Delayed feedback model (DFM) \cite{dfm} firstly introduces
survival analysis\cite{survival_analysis,survival_www}
to deal with the delayed feedback problem.
However, learning the delay time distribution in survival analysis
is intrinsically harder than the original CVR prediction task
since DFM further needs to predict when a user will convert.
To side-step such a difficulty,
the following methods predict the probability of whether a user converts before
a predefined waiting time\cite{mt_dfm,defer_kdd,esdfm}.
However, how to define the strategy of duplicating training
samples varies among previous literatures\cite{mt_dfm,defer_kdd,esdfm,iw_www}.
On the contrary, the revealing time distribution is explicitly defined in
GDFM, which indicates that each sample should be duplicated once at a revealing time.
The information weight $\mathbf{w}$ in GDFM is effectively
adjusting the revealing time with the aid of GDFM's information measure,
while in existing methods,
the revealing time is treated as a hyper-parameter.
We further discuss how GDFM unifies and extends existing methods in the supplementary.

To the best of our knowledge, we are the first to analyze the
property of learning with delayed feedback with a time-varying distribution.
Existing analysis\cite{esdfm,defer_kdd,iw_www,dfm} assumes
the distribution is stable (unlimited samples from $p(\mathbf{x}, \mathbf{y})$)\cite{dfm},
or the action distribution $p(\mathbf{a}|\mathbf{x})$ can be estimated accurately\cite{esdfm,defer_kdd,iw_www}.
Since $p^t(\mathbf{x}, \mathbf{y})$ indeed varies along with time (otherwise streaming training is unnecessary),
assuming a static $p(\mathbf{x}, \mathbf{y})$ can not capture the property of the delayed feedback problem;
The action distribution
$p(\mathbf{a}|\mathbf{x})=\sum_{\mathbf{y}} p(\mathbf{a}|\mathbf{x}, \mathbf{y})p(\mathbf{y}|\mathbf{x})$ also changes following $p^t(\mathbf{y}|\mathbf{x})$.
Thus, GDFM can be a better model for understanding and analyzing the delayed feedback problem.

Delayed feedback problem has also attracted attention from bandit
learning communities\cite{bandit_icml20_intermediate,bandit_icml21,bandit_icml18},
where the objective is to minimize regret in a decision problem.
\citet{bandit_icml20_intermediate} introduces a similar idea of using
intermediate observations before getting rewards
and shows that such intermediate observations can improve regret,
which agrees with our analysis from a different perspective.

A limitation of GDFM is that the training cost grows linearly with
the number of different revealing time $\delta_j$,
which may be a potential bottleneck in large-scale streaming training.
Intuitively, we may use the information weights to prune some revealing times,
which will be our future work.

redpajama_set_name: RedPajamaArXiv


text:
Where Are Jim and Ron Watkins Now?
Viswa Vanapalli
Image Credit: Business Insider
'Q: Into the Storm' is a documentary series from HBO that explores the QAnon conspiracy theory and its origins. Directed and produced by Cullen Hoback, the series features Jim and Ron Watkins, who own 8kun (formerly 8chan), Fredrick Brennan, who is the creator of 8chan, QAnon believers, and right-wing personalities. After Brennan's exit from the company, Jim and Ron Watkins have landed in a lot of controversies and have been accused of helping spread misinformation. But what is the truth, and where they are now? Let's find out.
Who Are Jim and Ron Watkins?
Jim Watkins is a 57-year-old businessman who is currently the operator of the websites 8kun and 2channel. An ex-army man, he moved to Manila, Philippines, in the early 2000s, getting married soon after. His foray into business happened when he was still in the Army. He set up a Japanese porn site that was hosted from the US to skirt Japanese censorship laws. Eventually, he founded NT Technology, which made money through advertising and web hosting services.
Image Credit: ABC News, YouTube
Sometime in late 2014, Watkins spoke with Fredrick Brennan about providing help with hosting the website since he was struggling with a surge in traffic. Brennan accepted and moved to Manila as well. Watkins chose not to charge Brennan but instead was given 60% of the profits the website made. In addition, Watkins also has other business investments ranging from a pig farm to a news organization.
Ron Watkins, the son of Jim, became the administrator of 8chan once Brennan resigned from the role. (In fact, Ron was the one who talked to his father about Brennan in the first place after he watching a documentary about the creator). Ron served as the administrator for 8chan from 2016 to 2020, at which point he resigned. Many have also alleged that Ron Watkins, directly or indirectly, has had a huge hand in spreading misinformation regarding the discredited QAnon conspiracy theory.
The theory states that the world is run by a group of Satan-worshipping pedophiles. Starting off in 2017 on 4chan, posts from an anonymous user who went by the name of "Q Clearance Patriot" have fueled misinformation. The user claimed to have classified government data. The discredited theory then found a following on 8chan, another website that was heavily criticized for the kind of content it allowed its users to post.
In August 2019, Jim Watkins was asked to testify by The House of Representatives Homeland Security Committee in connection to 8chan's part in "the proliferation of extremist content, including white supremacist content." This was a result of gunmen from three separate shooting incidents posting their manifestos on 8chan.
Ron Watkins has also played a significant part in spreading conspiracy theories regarding the 2020 Presidential elections. He tweeted false information about the tampering of the election results. In another bizarre turn of events, the Trump campaign's former attorney, Sidney Powell, had listed Ron Watkins as an expert witness in a case to overturn the election results in Georgia. Throughout the Presidential elections in 2020, President Donald Trump had retweeted Ron Watkins' tweets alluding to voter fraud. As the support for QAnon increased, it culminated with an attack on the Capitol building with multiple QAnon believers being arrested for the riot.
Sidney Powell has just offered an affidavit from Ron Watkins – administrator of the QAnon hangout 8kun – as evidence in her Georgia lawsuit. pic.twitter.com/u49GhgS7PN
— Brad Heath (@bradheath) December 1, 2020
Many journalists and researchers believe that Jim and Ron Watkins might know the identity of Q or are Q themselves. Researcher Marc-Andre Argentino stated, "There are similarities between the type of content that Watkins posts on his own Twitter account that echoes very closely to what Q has started posting in his drops. The echoes are a little too close for it to be accidental." Brennan himself also believed that Jim or Ron Watkins could be the ones posing as Q, or the mysterious figure is someone hired by them. However, both Jim and Ron have opposed these claims.
As per a report from September 2020, Jim Watkins had left for the United States from the Philippines in the same month, but his current whereabouts are unknown. NBC News reported in 2021 that Ron Watkins has been living in Japan. Not much else is currently known about the father and son, especially since Twitter permanently banned their accounts. This was done as the social media giant believed that these accounts, along with a few others, were "solely dedicated to sharing QAnon content." However, Ron did tell a few journalists after his resignation from 8chan that he wanted to write a book about constitutional law.
Read More: Where is Fredrick Brennan Now?

redpajama_set_name: RedPajamaCommonCrawl


Or so I thought. When I try, Windows says "Error copying file or folder. Leo Davidson says: October 12, 2011 at 4:13 am @Anonymous Coward: I don't know how VS2010 manages to have such a bug but it has been confirmed. And to my surprise that worked flawlessly, transferring whole folders without any error and any delay.
To solve the problem, I use Picasa to import my iPhone photos, instead of using Windows Explorer copy. Reply Bobby says: February 27, 2016 at 1:13 am Doh!!! If your disk is almost full, the conversion process might not succeed. NTFS or ReFS.This error-87 can also occur when copying files to a SharePoint server and the file is of a restricted type.
Does the drive refuse to mount until I change the setting? GSCopyPro also comes with an open file agent which can copy files that are locked/ opened by other processes. It certainly caused me some headaches. The former is what you're supposed to use with NTFS, but it will enable write caching.
Reply Aidan Formosa says: February 12, 2015 at 2:25 pm This will do the trick. Any idea what is going on? We've just sent you an email to . It doesn't need flush.
The drives I'm copying to are NTFS. For some reason, every time I tried doing something with those files it returned this error. It gets translated to STATUS_IO_TIMEOUT, which gets translated to ERROR_SEM_TIMEOUT, and gives: "The semaphore timeout period has expired.". Proffitt Forum moderator / June 2, 2007 10:55 PM PDT In reply to: Cannot copy file : parameter is incorrect You'll see that now and then.
Create a password I agree to the Terms of Service Signed in as (Sign out) Close Close Sign in Sign in Sign up Cancel Technical Articles Information to include for technical Using the same backside-USB as I use for a removable hard disk (for backup) and a Sandisk USB-stick without any problems. Well "best" - let's say least worst. Perhaps I have to just use the basic Windows importer rather than my preferred application that is smarter.
If you lack a flush you don't even really get isolation, because if it crashes in the middle than a process that starts after the restart isn't isolated from the intermediate The last time I had a similar error I was copying MP3 files from DVDs to my hard drive. I have nearly 4GB of photos and videos on my phone, and I want to put them into my computer's pictures folder. If you believe this post is offensive or violates the CNET Forums' Usage policies, you can report it below (this will not automatically remove the post).
I don't know where it's coming from, but my guess is that somewhere inside the copy command, it tries to create the destination file and set its file size. Cesar says: October 11, 2011 at 8:06 am Another option is UDF: superuser.com/…/using-udf-on-a-usb-flash-drive Unless you are trying to write to it from Windows XP (which should cease to be a problem A solution is to reformat the drive using the NTFS file system, which supports larger file sizes. God forbid you unplugged them without invoking "safe removal".
If I tried to copy somewhere else, it produced this error, if I tried to delete then it produced this error. Disruptive posting: Flaming or offending other usersIllegal activities: Promote cracked software, or other illegal contentOffensive: Sexually explicit or offensive languageSpam: Advertisements or commercial links Submit report Cancel report Track this discussion I am not sure iCloud will help me because it would duplicate rather than move the pics, and I want to modify the files after download anyway. (Also, iCloud requires an How could it be a file with unrecognized attributes when it is already on a Windows 7 machine?
Clear search results Contact support Knowledge Base Frequently Asked Questions47 articles Sales15 articles Technical Articles426 articles Web Store9 articles Legal6 articles Education and Non-Profit3 articles All articles 2BrightSparks Homepage 2BrightSparks Homepage Not reasonable for the file system to be trashed which was my initial impression upon reading about this requirement. Reply Speak Your Mind Cancel reply Name * Email * Website Keep me updated with Tubblog posts and the monthly newsletter! Reply Richard Tubb says: January 4, 2016 at 5:02 pm My pleasure Stephen.


In Chachaji's cup, talented children's book author Uma Krishnaswami, dearly loved and admired here on Saffron Tree, tells the story of a warm and initimate relationship a little boy and his father's old uncle, Chachaji share. Through skillful storytelling surrounding a simple, yet precious teacup, Uma masterfully ties in a subject you won't come across often in children's literature - the partition of 1947 between India and Pakistan.
Teatime with Chachaji is very special. Sipping his chai, Chachaji often spins tales from Hindu mythology and Bollywood movies for his grand nephew, Neel. And during teatime, Chachaji always drinks his chai from a special teacup. But, the teacup holds much more than chai. It is a family heirloom holding some very special memories. Memories of partition and the story of a family and a country divided in two.
The flowered piece of china traveled with Chachaji's mother (Neel's great grandmother) as she migrated with young Chachaji from Pakistan to India. One day, in one careless moment, Neel accidentally breaks the teacup. Following this, Chachaji coincidentally falls ill. Neel feels devastated, but eventually comes up with a neat idea to fix the broken pieces of the cup and even find a special use for it. In the process, he also reconnects with Chachaji and grows to appreciate more the value of family and heritage.
I've been fortunate to come across several wonderful picture books written by Uma. In all her books, the prose has a certain charm that is hard to miss. The lyrical quality of her text never fails to lure me back to her picture books. I have delighted in reading her book, Monsoon, at my daughter's school. Chachaji's Cup is no exception. The poetic style awakens your senses, much like the sweet fragrance of cardamom chai. The description of the curly, swirling steam, sure enough, left me craving for a cup of chai. That, of course, I promptly made myself right after reading the book.
The drawings are lush, vividly colored and radiant. The close-ups and expressions pop out of the page leaving a lasting impression of the human faces and the family setting.The full-page and double-page illustrations, especially of the partition with refugees walking in long lines with their bags and belongings rendered a poignant feel. But overall, the book with its positive appeal is a real treasure useful in explaining to children a difficult topic in history. Uma's lucid description on the back of the book about partition provides an opportunity to take the topic for further discussion with older children.
In her books, Uma has the knack of capturing and integrating details about Indian culture and traditions. Stories illuminating the experiences of Indian-American families come as a rare and delightful treat in the world of children's literature. Especially, considering the scarcity of picture books featuring stories set in the Indian backdrop, here in the west.
Perfectly brewed with a balance of history, family and traditions, Chachaji's Cup played host to several warm and cozy read-aloud sessions, while I cuddled with my little girls. And trust me, it is even more delightful when paired with a cup of steaming chai!
Awesome pick and review P! I can see how there is a drive in you to handpick the ones that will feel the homiest for our children.
"Deepa's Special Day", a Diwali story in the Ladybug magazine was a delight to my then 3 yr old daughter and that was how we were introduced to the author.
I recently read about how this book has also turned into a musical "Tea with Chachaji", that must be quite an experience (to see the book come alive), right Uma?
Will definitely add this to our list. Thanks!
Came across this book very recently and love your review P. The book is indeed unique in what it addresses.
Praba, your review has as much a poetic touch as you describe Uma's work :-). Wonderful pick and a great review. I think I need to look out for all her books, after reading your review ! Will check them out in my library.
You have brought the book alive for us, Prabha. Would love to get my hands on this cup, certainly- as partition of India is yet another pet topic of mine.
Thanks Praba and thank you all for your kind words about my writing.
Meera, I got to see a tech rehearsal of Tea With Chachaji (the wonderful musical produced by Making Books Sing) that ran at the start of this year in New York City and Palo Alto.
I did not alas make the opening: my blog posts from the time speak a little bit about that.
Thank you again. It's my belief that books, especially children's books, are incomplete until they have been in the hands of readers.
Just as your reviews is now P! How coincidental is it that I am just now reading it as I sip my afternoon ginger chai! I don't have that special cup like Chachaji's to go with it, but that is where your review and our memories of the book make up for it. We have read it and enjoyed it and loved the way it ended! Thanks Uma for such a sensitive look at some complex human emotions.
We have read Chachaji's Cup a year back. This is definitely a book we will revisit soon. Now that the girls have a grasp that there are multiple religions, India-Pak partition, India's freedom and such.
Lovely review P. Have read many books on partition but never came across any for children. Will soon pick this one up. My mother's family had to migrate from Shekhupura which is now in Pakistan to this side of India during that time,and had to face the 'katl-e-aam' period once in which my grandmother lost her right arm. It was so hard to come to terms with having nothing, not even complete families and all body parts. We grew up listening to those stories.
Oh Vibha...that's so heart rendering to hear. What an agony it must have been for the entire family.
Truly amazed by how such complex topics and emotions are distilled to a child's level. Kudos to Uma! Will pick this up and read it.


Chocolate espresso banana bread is deliciously flavored with coffee and chocolate, loaded with nuts and has the goodness of bananas in it. Made without any butter, this yogurt banana bread is perfect for a morning or afternoon pick me up and a beautiful way to treat your mother this Mother's day!
"food is love made edible"!
Thanks Ms.Child for this wonderful quote that truly sums up y obsession with food in such a succinct manner! The very reason why most of cook, apart from feeding and staying alive is coz its such a simple way to show how much you love. I dare say, not even diamonds are as priceless as a meal cooked just for you by your spouse, or your child. Remember your proposal? Ours wasnt very official..after having been together for six years it was understood we would marry and till date I can't remember when and how he asked, or when I said yes. Maybe its just the innate romantic in me that finds this more lovely than a staged proposal! But if he had to propose, I would expect him to cook me a meal , splurge on some really good wine and set a table fit to sweep a princess off her feet!
As far as I am concerned( and I am sure you too), love isn't limited to our spouse. It definitely includes our family and friends. Family, that drives us mad on holidays with their idiosyncrasies and knows all our wretched past,and friends with whom you have shared more than you ever thought possible! The bond between family and friends is sacred to me. And if there was ever a chance of me doing something to make them happy, I do it in a heart beat! And how can we forget mom? Mothers are the single thread that hold entire families together, mothers are what we wish to be most like (or may be not, either ways we do love them). So this Mother's day I have decided to show just how utterly blessed I feel I am to have her as my mom by cooking up a delicious storm in the kitchen.
She is not the kinds who likes icing. Neither am I. I detest frosting or icing unless its reallly good and my standards are a little too high. So yes, you wont see me swooning after clouds of buttery frosting like a seven yr old or even eating one for that matter. But banana breads without any butter!?? Well..that's definitely more me! And that is something I know my mom (and most of ours) would LOVE. What's not to like in it?
Made of yogurt – check.
Has coffee in it -check.
Has chocolate chunks – check.
Does that read like a dream or what! If someone wrapped that in a pretty parchment paper, and tied it with a string that had some foraged flowers looped in it, and gifted me this with a favorite book of mine, that person would be instantly my favorite person in the whole wide world!
Often when I think of my childhood and my mother, I have a bazillion sweet thoughts floating around in my head, leaving a gentle smile on my face. Today, I wanted something easy and comfortable as a mother's hug or her warm wide smile that lights up my entire world. I just wanted to make Mother's day as easy for you guys as it is for me. Just like sitting in the balcony in the morning, with a hot cup of coffee in one hand and a slice of this delicious, moist and fluffy bread in the other. Yup..that sounds like a good plan to me! These muffins are mocha in flavor rather than a knock out espresso, and the banana is not over powering at all. The chocolate chunks add a great contrast in texture and make the bread taste incredible when one bites into a molten piece of chocolate. But the nuts? So not optional guys! Load it up with nuts. I added salted peanuts and some almond flakes in the batter and all over the top, and it made the bread fabulous in every bite.
Overall, this was a great variation to my Banana Strawberry bread and Orange yogurt muffins that are currently ruling the roost at my home. We keep getting requests for them every 2 weeks from D's friends and P himself.
So make these for you mom or anyone you love this Mother's day and show them just how much you love and care for them. Its easy and takes barely 20 mins to whip up, then let the oven do all the hard work while you enjoy that cup of coffee with your mom and pinch yourself for being so lucky to have her!
PS: This recipe has been approved by my sister,brother and brother in law who enjoyed these in muffin form.
Chocolate espresso banana bread is deliciously flavored with coffee and chocolate, loaded with nuts and has the goodness of bananas in it. Made without any butter, this yogurt banana bread is perfect for a morning or afternoon pick me up and a beautiful way to treat your mother this Mother's day!
1 banana, whole, slit length wise.
Start by keeping everything measured and ready before you get started.
In a large mixing bowl, add the egg, yogurt, oil, vanilla, both the sugar and mix well till thoroughly combined.
In another bowl, sieve the flour, cocoa, cinnamon add the baking powder and salt and mix.
Start adding the dry mix into the wet mix(egg yogurt mix) little by little till combined. Don't over mix. Add the bananas and espresso and fold gently to combine.
Spray a baking pan (9 *5 inch loaf) with oil and dust with flour. I use a baking paper too.
Next, pour the batter into the pan. Add the chocolate chunks and half the nuts.
Now take a skewer and swirl the dough.
Make the topping by tossing together brown sugar, chopped nuts, and chocolate chips in a small bowl, then sprinkle evenly on top of the batter.
Place the slit banana on the top.
Put the pan into a pre-heated oven. Bake at 180 C for 55-60 mins till a skewer inserted in the centre comes out clean.
Take it out when done, and let it cool in the pan for 15 mins. Remove to a wire rack and let cool completely before serving.
Dust with icing sugar (optional) and serve with your morning cuppa!
Batter should be on the thicker side. If it's not, you may wish to add up to ¼ cup additional flour. All bananas vary in their moisture content and the consistency of batters will vary.
Make the coffee as strong as you like. This is just right with nothing being over powering.
Watch your bread in the last 10 mins and tent it with foil, if its starting to brown too quickly.
That bread just looks fantastic!! I love that used yogurt, makes it nice and moist! Agreed! Cooking is showing your love for someone! No card, flowers or presents say it as well!
I'm not a fan of frosting either! More a savory girl and thats why I love this recipe! Your photos are beautiful and I love your story!
If I could just get my hand through this screen to taste this deliciousness. Oh my!! Yum!!
This banana bread looks divine!! Wish I had it for breakfast today!
I've been drooling over this ever since you teased me with the photo on facebook, now I've seen the recipe I'm even more excited to try it! It looks sooooo yummy!
My dear mother and I would both love this banana bread. Whenever we are out and about, just the two of us, we always have to sit down to a good cup of coffee because neither of our husbands love coffee like we do.
And I really love the presentation of the whole banana on top of the loaf. Just beautiful!
how do I substitute egg?


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Home > Insights > 5G Automation and Intelligent Edge
CxO Insight
Virtualisation and automation will bring a shared future to benefit all
5G Automation and Intelligent Edge
Abdallah Nassar, Chief Engineering and Network Officer at Orange Cameroon, talked to Contributing Editor Annie Turner about the long but fast-moving journey from telco to techco.
Abdallah Nassar has been in his job at Orange Cameroon for four years. In that time, he's won two Awards and been nominated as running the Best Network by nPerf (2019, 2020) and by Ookla as Best Mobile Coverage (2019, 2020), Fastest Mobile Network (2020) and Best Mobile Network (2020).
He stressed that virtualisation is the future of the network, so automation of the network, tools or process must be talked about in that context. He explained that his company began to pay serious attention to virtualisation when it was looking at how best to provide content to customers, how to combine content with data services, how to gain greater speed and agility – and ensure quality of services.
Abdallah Nassar is a speaker at FutureNet Middle East & Africa, regsiter today!
As is common in many markets, customers typically have more than one SIM card and switch between them depending on what they are doing. He says, "In terms of [absolute numbers] we are not claiming we are first in the market" with about 12 million customers but claims to lead the market in terms of coverage, service quality and products. The population of Cameroon is a little over 27.5 million.
Most notably, the operator offers mobile banking services across its African operating companies under the Orange Money brand. In July, Emmanuel Tassembedo, the former Head of Orange Money Cameroon, announced his company has a 70% market share of the mobile banking market on Orange Money's tenth anniversary of operations in Cameroon.
Previously Tassembedo estimated that the operator's cumulative monthly transactions amount to CFA800 billion ($1.37 billion) during this year, making an estimated total of CFA9.6 trillion ($16.414 billion) for the year or about twice Cameroon's state budget for 2021.
Meeting demands
Demand for data on Orange Cameroon's network is growing at 200% year on year, which results in the infrastructure becoming increasingly challenging in terms of maintenance, capacity, technology updates and more. Nassar says, "We realised this complexity cannot continue in the same way, using the same type of equipment, dimensioning, and legacy technology…we started to look how we can deal with all this.
He says, "So the first step was we needed to invest but also lower operational costs – how could we create a significant cost saving while we're investing? That started the idea of virtualisation, of putting all our system in a virtual environment, because it comes with more agility, more flexibility and on a bigger scale than normal legacy equipment."
What exactly does Nassar mean when he talks about virtualisation – network functions virtualisation (NFV) or full-blown cloud native? He says it's an evolving mixture and explains that while some operators use public clouds like AWS, Google Cloud or IBM Cloud, Orange chose a different way. Nassar says, "We are investing in our own cloud and recently launched our first vEPC [virtual evolved packet core] on it: we built our own public cloud infrastructure using systems from different vendors." .
This first vEPC is to help Orange Cameroon handle data more efficiently on 3G and 4G infrastructure, but Nassar adds, "We need to be independent…this kind of an investment gives us a different position versus the competition which also has vEPCs, but they use vendors' infrastructure or a vendor's virtualised system. We want to be independent because when we talk about scaling, we mean different kinds of scaling: we can use this infrastructure for investment in our own systems and we can even offer it to the public. That's why we call it Orange public cloud."
Think global, act local
While building and controlling its own telco cloud is in line with group-level strategy, Nassar says that execution is "country by country. We are talking about virtual environments, but you still need a certain type of infrastructure in place and in Africa there is a lot of limitations on international transit, so it's much better to put things in place locally and reserve international connectivity for customers' use.
"This is why we cache content in the country – things like Meta, so Facebook, Instagram and WhatsApp – to lower the costs of international transit and give our customers better experience. Also, [we cache] the entire Google platform, from YouTube to all the others, and recently we put Netflix in place."
How does the virtualisation and keeping-it-local strategy work for the enterprise or B2B market in Cameroon? Nassar explains there are two sectors. At the moment, the much larger one is private businesses, most especially micro financial institutions and banks, as well as logistics including local transport and sea-borne and other international transport. Almost all of them have systems hosted on Orange's own public cloud, using the operator's equipment in its own data centres
He elaborates, "We're talking about big players in the market and in various domains such as transport, banking, micro-finance and breweries". He notes, "The public or government sector is totally different," displaying natural caution regarding issues like security and the maturity of technology, but Orange Cameroon expects the pace to pick up here too.
Enter automation
Having got that first vEPC up and running, Nassar says, "The second step is to virtualise all [the EPC] and new services, along with classic services for a mobile operator such as VAS [value-added services] and triple-play services. Step by step we are increasing the scalability of this public cloud system to virtualise our whole environment."
Is this move to cloud and virtualisation preparing the way for 5G? He states, "It is one of many steps that we are taking to prepare the ground for 5G. It is an ambition, but a difficult ambition for this continent because there are many dependencies. We are trying to benefit from each step, although the virtualisation and automation are essential steps toward 5G."
Nassar says, "The idea of having a virtual environment really is to simplify our operational method…but this virtual system will require a lot of frequent maintenance. To do that manually is very painful and human error could have a huge impact. When we talk about virtualisation, we cannot ignore that we need certain types of automation to be in place too.
Fault management, predictive maintenance
What automation is Nassar talking about? "We are talking about orchestration [by which I mean] an automated system that will eventually harmonise and simply the workflow of our systems, which will give us the ability to better analyse, anticipate and correct," he says.
"There is also automation from robots which experience the network, products and services like a customer and tests them nonstop. We are not sitting in the office waiting for the customer to inform us something is not working. Our robots run all the time to identify particular types of service interruption by simulating certain situations, for example during a high utilisation period, so we can do preventive maintenance while the orchestration tries to harmonise the functionality of different nodes to make it all work together."
Does Orange Cameroon build its own artificial intelligence (AI) models for fault management and predictive maintenance? Nassar says his company aims to develop support for ongoing maintenance and simulations of maintenance on its own cloud but is still in the process of evolving from a classic telco to a data-driven company, relying on vendors' AI and automation solutions in the meantime.
He describes this shift as "a very long journey" but adds, "We are moving very fast. We even recently opened our Open RAN Lab, which is unique – we are asking the other operators to come and test and experiment with us. The idea is that it will help all the operators to go faster with their deployments."
Nassar says the motivation behind Open RAN is to allow operators to act faster in the future, and to lower operational costs while using the RAN as platform for innovation in business and operational models. He explains, "The future of the current Open RAN will not only provide interoperability and standardisation of RAN elements, but also it will allow different dimensioning of your network. You will have a better control on your resources – that is, frequency, radio, equipment and power resources."
He continues, "Open RAN will open the door to wider competition between vendors and if we continue that way, not only will the operators benefit from this interoperation between vendors' equipment and more network flexibility at a lower cost, but also it enables the operators to come together. The future O-RAN will have the capability to merge the environment – allow it to act as a single operator with potentially many operators and vendors at the same site to offer a universal platform."
Nassar says, "I see the future where all the resources in terms of vendors, equipment, frequencies and passive infrastructure, such as towers, will be shared by many operators that differentiate themselves based on the services they run on those platforms."


The most common complaint I hear in my office is anxiety. Actually, this is also the most common complaint I hear around the community with family, friends, and coworkers. Our culture is full of anxious people and is in desperate need of change.
In answering this question, the first thing I ask is "Does your anxiety impair your ability to function?" You may be thinking, please do not use clinical jargon with me. I understand. Let's break this down. Ability to function simply means are you able to do the things you need to do throughout the day. If your anxiety makes it difficult for you to live out your day, then it is a problem. Below I have listed common daily activities that are impaired by anxiety. If you suffer from any of these issues, your anxiety needs to be addressed.
1. SLEEP – You have difficulty falling asleep, staying asleep, and/or waking too early.
2. APPETITE – You have either increased or decreased appetite. You do not eat healthy meals on a regular basis. You may skip meals or eat junk food daily. You have a significant increase or decrease in weight.
3. CLASS/WORK – You find your work, either occupational or school-related, slipping. You arrive late to class. You completely miss a meeting. Your grades drop or you are written up at work.
4. RELATIONSHIPS – You are unable to keep steady relationships in your life. You struggle to talk to others and listen to their concerns. You are distracted by your anxiety to the point that you are disengaged from people. This could be your friends or your family relationships.
5. FOCUS – When anxiety comes, you are unable to consider anything else. Your mind is completely wrapped up in whatever is causing distress. You have difficulty relaxing and emptying your mind.
If you are like most people, reading these symptoms alone causes anxiety. The good news is that you are reading this article and becoming aware that you suffer from a disease that needs to be addressed in many of us. Awareness is the first step to healing.
Anxiety is one of the most common problems I see in my office. Fortunately, through counseling anxiety levels can decrease within a few sessions. Counseling gives people tools for battling their anxious thoughts. Do not continue to let anxiety impair your life. Give us a call and schedule an appointment today.


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Q: How to improve the visibility of light without increasing the brightness? I am not sure whether or not this is the right SE site to post this question on but I'm sure someone will inform me of my mistake soon enough if it is wrong.
Basically I am an Electronic Engineer and I am creating a circuit that has a notification LED that will flash when there is a problem with the system. The circuit is in a casing that has a 'light rod' coming out of it that allows the flashes to be seen when the device is mounted to the ceiling.
The image below is a rough sketch and some pictures of what I am talking about in case it is not quite clear.
The rod that I have mentioned is what my question is about, currently it is made of plastic and is shaped quite similarly to the picture above  - I am no physicist but I assume that the reason for the top of it being shaped like a rectangular based pyramid is to refract the light so it can be more clearly seen from most angles.
From an electronics point of view I want the circuit to take as little current as possible while still allowing the LED flashes to be seen clearly so I was wondering if there was a way to 'amplify' the light from the LED using the rod to the end of the rod so the LED itself could be a bit less bright but still have good visibility at the end of the rod?
Failing that, there is a fair amount of light lost through the sides of the rod before it reaches the end, would a different coloured coating around the clear plastic help prevent this? Or maybe even having a different shaped / coloured top in order to make it clearer at the end of the rod? (I thought having a translucent white shade at the top might make it more clear but then I thought it might not be 'eye catching' unless looking directly at it)
Again I apologise if this is on the wrong SE but I remember doing prisms and light refraction in physics at college and school, hence my reasons for putting it here.

A: Suppose the LED was mounted where the tip of the plexiglass is. How visible would it be? Would you need to make it brighter? Contrast with the background color? Reduce ambient light around it? Would it be more noticeable if it flashed than if it was steady?
When light strikes an interface between two materials, some of it is absorbed, some transmitted, and some reflected. Absorption is controlled by indices of refraction and properties of the material. Reflection and Transmission are controlled by angle of incidence and indices of refraction.
For an optical imaging system, these are everything. People spend enormous effort on them. Surfaces must be designed and manufactured with tolerances less than a wavelength of light. Surfaces must be polished so scratches are smaller than a wavelength.
Fortunately, your application should not require as much care as making a lens would. And absorption should not be a problem for a few inches of plexiglass and visible light.
The first problem is to get as much light into the rod as possible. Find out if there are LEDs that are designed for this. For example, you don't want an LED that emits light in all directions. You will lose light that goes sideways. If it only sent light upwards and had a flat top, you could put a flat plexiglass right on the surface.
You will have two interfaces: LED to air, and air to plexiglass. Each typically costs 4% of the light. Probably not a big deal. If it is and you have a budget, you could use antireflection coatings.
Once light is in plexiglass, it will travel in a straight line to the next surface. If this is the side of the plexiglass, the angle of incidence should be small if you have designed it properly. A grazing angle will cause total internal reflection. You will loose no light.
Notice the notch you have directly above the LED. Light will strike that at normal incidence, and mostly be transmitted. You will want to pay attention to the angle of the bend.
When light gets to the top, you do not want a smooth flat surface. Light would travel through it and be refracted in one predictable direction. You would have to put your eye in the path of the light to see it.
Instead, you want a rough surface. Many scratches create surfaces in all directions. Light is refracted in all directions, and is therefore visible from all directions.

A: You could wrap the pipe in reflective foil for a start. Also, have you considered reducing the duration/period of the flashing and using the same energy dumped into the LED in a shorter time via a reservoir capacitor ?

A: Rather than wrapping in foil as Dirk suggested, I would see if you can't coat the pipe with reflective paint. The problem with foil is that it will always have microcreases which act as light traps.
Now, as to visibility at the top: If you want visibility over a wide range of viewing angles, then your best bet is either a polished spherical dome (difficult) or a roughened surface (easy).  The former directs light uniformly in all angles and the latter scatters light slightly less efficiently -- see "Lambertian Surface" at the usual reference websites.
As to power saving: typical LED displays actually pulse at 30-60Hz or so to reduce power use (and thermal strain on the device) while appearing 'steady state' to our integrating retinals.  You may want to dig through some manufacturer's data sheets to get an idea of the luminosity vs. peak and average current for your LED.

redpajama_set_name: RedPajamaStackExchange


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Oregon's Only National Park
Plan your vacation or day trip to Crater Lake National Park In the mood for a scenic road trip starting in Bend, Oregon and ending in one of the most pristine national parks on earth? Crater Lake National Park features towering cliffs, stunning volcanic islands, and water so shockingly blue, … read more
http://www.nps.gov/crla/index.htm
Crater Lake, OR 97604
Plan your vacation or day trip to Crater Lake National Park
In the mood for a scenic road trip starting in Bend, Oregon and ending in one of the most pristine national parks on earth? Crater Lake National Park features towering cliffs, stunning volcanic islands, and water so shockingly blue, you'll stand blinking in the sun trying to clear your vision in case the whole thing is one big, beautiful mirage.
Where is Crater Lake National Park
Located two hours, eight minutes, and thirty four seconds from Bend Oregon (give or take), Crater Lake is an incredible must-see day trip from your Bend home base. At 1,943-feet deep, it's the deepest lake in the United States, and the seventh deepest in the world. Crater Lake formed when Mt. Mazama erupted approximately 7,700 years ago in a massive volcanic eruption. Then the whole thing collapsed on itself, creating a big hole that eventually filled with water to become the amazing lake you see today.
What to Do at Crater Lake National Park in the Winter or Summer
You can visit Crater Lake any time of year, though some of the roads and facilities are closed during the winter when the area gets an average of 44 feet of snow. But all that snow makes it a great time to enjoy Crater Lake's popular ranger-guided snowshoe walks between November and April. The walks last two hours over a mile of moderately strenuous terrain, while exploring forests and meadows along the rim of Crater Lake. You can also bring snowshoes or your cross country skis from home and set out exploring on your own. The park's north entrance is closed during the winter months, but the national park can still be accessed by using the southern entrance.
Summer is the most popular season for visiting Crater Lake, and for good reason. Hiking, camping, fishing, picnicking, swimming – and even scuba diving – are popular pastimes in the warmer months. The lake makes an incredible backdrop for family reunions. Keep in mind the season is short, generally spanning from June until the first snowfall in September. The average lake temperature below 300 feet is a chilly 38 degrees, but the surface can warm to 55 or 60 degrees during the summer months. There's only one spot where it's safe and legal to access the lake shore for swimming. The Cleetwood Cove Trail opens mid to late June, is 1.1 miles long, and drops nearly 700 feet to the shoreline where you can safely swim in the chilly water. If you dare, dive into the crystal clear lake water from the 20-foot rock ledge, which has become a ritual for many brave swimmers.
CRATER LAKE LODGE
Over a hundred years ago, many travelers were not able to experience the beauty of Crater Lake due to a remote location far from paved roads. Then along came William Gladstone Steel who constructed the historic Crater Lake Lodge in 1915 and even spearheaded the park's designation as a national park in 1902.
The Crater Lake Lodge you visit today is nothing compared to the 1915 version. The National Park Service had to completely reconstruct the Lodge due to structural impacts from snow and substandard construction practices. On May 20, 1995, the Lodge reopened to the public and offers fine and
casual dining, lodging, visitor information, a gift shop, and, of course, endless blue vistas.
Crater Lake Lodging
Crater Lake lodging is fairly limited when it comes to hotels and lodging so many visitors choose to stay at hotels and motels in nearby Bend, the largest city closest to Crater Lake National Park. The historic Crater Lake Lodge is the only Oregon hotel located within the national park and it fills quickly. Camping, RV sites, and cabins are available seven miles from the lake rim, near the south entrance, at Mazama Village Campground and RV Park.Whether you are on vacation in Bend or taking a road trip across Oregon, plan a day to explore one of the nation's most stunning national parks.
Driving Directions | Crater Lake Map | Things to Do & See | FAQs & Park Facts
Established in 1902, Crater Lake National Park is in the Cascade Mountains of southern Oregon, about 90 miles south of Bend. Formed 7,700 years ago by the eruption of the now-collapsed volcano, Mount Mazama, Wizard Island is a cinder cone near the western edge of the lake. The Rim Drive around the lake offers views of the volcanic formations. The park has a number of trails, including Sun Notch, with views of the Phantom Ship, a small island. Fed by rain and snow, it's the deepest lake in the USA and perhaps the most pristine on earth with its deep blue water. The park is open year-round, 24 hours a day. However many of the park's roads, trails, and facilities are closed seasonally due to snow. Check the website's current conditions page to find out what's open in the park each day. Rim Drive becomes a trail for skiing and snowshoeing. The North Entrance road becomes a snowmobile trail. These roads close for the season with the first big October snowstorm, or on November 1, whichever comes first.
Payment can be made by cash, check, or credit card. Currently, the park sells the Crater Lake Annual Pass and America the Beautiful Annual Interagency Pass at the visitor center during operating hours (10 a.m. to 4 p.m.). Other special passes may be available weekdays as staffing allows. Cell reception in the park and surrounding areas is limited. Be sure to carry a map or GPS.
The park does not have a physical street address, so it can be hard to locate us using GPS. Try entering "Crater Lake" or "Rim Village" as a town or waypoint. The Park Headquarters is 3 miles south of Rim Village.
Crater Lake, OR 97604 Get Directions
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Released on Label: MxPx Global Enterprises LLC.
MxPx's ninth single was just released on label MxPx Global Enterprises LLC and can be streamed on Spotify. The single is not yet on Last.FM, indicating it's not all that popular or needs some time to get played.
Since MxPx began making music in 1992 back in Bremerton in United States of America, they have released a truckload of albums (twenty-one in total) and nine singles. MxPx's previous album 'Left Coast Live' from July 2017 was quite popular and well received. MxPx is probably best known for the tracks Wrecking Hotel Rooms, Heard That Sound and Responsibility.
MxPx is a duo of Mike Herrera and Tom Wisniewski. MxPx has a good amount of followers on Twitter, currently topping out at 34,909.


Want to know who will win today? In Today's Dream11 Fantasy Cricket Prediction MI vs KXIP 50th T20 Match IPL 2018, we will cover playing 11, pitch report Wankhede Stadium, Mumbai, toss prediction.
We will also cover players recent and past performance, all the latest news and updates of Mumbai Indians vs Kings XI Punjab, dream11 guru prediction, the best choice for captain and vice-captain, weather report of Mumbai, dream 11 best team, where to watch live match of KXIP vs MI and details of live streaming.
All the details and statistics that we provide are taken from very reliable sources. Make sure to read the complete post to get 100% benefit. Read all the sections of this post as every section contains some tips and tricks to win in any fantasy leagues. All the details in this post are absolutely free of cost. You don't have to pay a single penny for that.
Where Can You Watch the Live Streaming of MI vs KXIP or Channels to Watch?
Who Will Win the 50th Match of IPL 2018 Between MI vs KXIP and Toss Prediction?
What is the best combination of players for Dream11 in 50th Match?
Match: Indian Premier League, KXIP vs MI, IPL 2018.
The pitch of Mumbai, Wankhede Stadium is a batting beauty. It has a good bounce on it and the batsmen can trust on the bounce and can play straight shots. They can also play on the rise shots easily as the wicket has even bounce. The seamers also get some benefit from the pitch. Today fast bowler will get some swing in the initial overs if they bowl at the right areas. We can expect a high scoring match on this ground.
The average first inning score of this ground is 187.
The average second inning score of this ground is 183.
Highest total on this ground is 230/8 in 19.4 overs by ENG vs SA.
Lowest total on this ground is 172/10 in 20 overs by AFG vs SA.
Sunny, Sunny and mostly sunny. This is how the weather will be of Mumbai on 16th May, throughout the day. The sky will be clear and no rain is expected today. The cricket fans and fantasy users can see the complete match. The temperature is expected to be 30-Degree Celsius and humidity to be 78%, which may rise up to 80%. In the latter half of the game, dew is expected.
In the last five matches, MI won three matches out of five matches whereas KXIP won two games out of five games. In overall encounters, MUM won 11 matches and PUN won 10 matches. At this venue, Mumbai Indians won three games and Kings XI Punjab won four games.
Star Sports has paid a huge amount of INR 16,347.50 Crores to get exclusive rights of IPL 2018 for live coverage for five years starting from 2018 to 2022. Star Sports has all the media rights including TV and all Digital Rights. You can watch the full match of Kings XI Punjab vs Mumbai Indians, 50th match on Star Sports.
In this section, we will provide you with the squad of Mumbai Indians vs Kings XI Punjab.
Ravichandran Ashwin (c), Aaron Finch, Lokesh Rahul (wk), Pardeep Sahu, Chris Gayle, Yuvraj Singh, Manoj Tiwary, Karun Nair, Mujeeb Ur Rahman, Mohit Sharma, Marcus Stoinis, Mayank Dagar, David Miller, Mayank Agarwal, Akshdeep Nath, Axar Patel, Barinder Sran, Manzoor Dar, Andrew Tye, Ben Dwarshuis, Ankit Rajpoot.
Ishan Kishan (wk), Rohit Sharma (c), Krunal Pandya, Suryakumar Yadav, Mitchell McClenaghan, Sharad Lumba, Evin Lewis, Aditya Tare, Hardik Pandya, Pradeep Sangwan, Adam Milne, Ben Cutting, Saurabh Tiwary, Tajinder Singh, Jean-Paul Duminy, Jasprit Bumrah, MD Nidheesh, Mustafizur Rahman, Mayank Markande, Siddhesh Lad, Anukul Roy, Kieron Pollard, Akila Dananjaya, Rahul Chahar, Mohsin Khan.
If Mumbai Indians loses today's match, they will be out of the tournament. On the other hand, Kings XI Punjab may get a chance to play in the playoffs if they lose the match on Wednesday. However, both the team will definitely want to win the match. It will be interesting to see how MUM and PUN make their playing 11 combinations. We will provide you with the playing 11 in the next section.
At this stage of the tournament, MI cannot afford to lose the game. They are in a do-or-die situation. If they want to win, Rohit Sharma has to strike today. The only change MUM can think of is to bring Pollard in, in place of JP Duminy as they find it difficult to use Duminy. Except for this change, MI should play with the same playing 11.
Evin Lewis, Rohit Sharma (capt), Hardik Pandya, Ben Cutting, Mitchell McClenaghan, Mayank Markande, Suryakumar Yadav, Ishan Kishan (wk), Krunal Pandya, JP Duminy/Kieron Pollard, Jasprit Bumrah.
Kings XI Punjab had a great start at this season of IPL but after they returned back after a week's break, they lost their momentum. They lost 4 matches out of five matches. They have heavily relied on their top-order batsman and their middle-order batsman failed continuously. If they want to win their middle-order have to perform today.
KXIP can make a couple of changes in their team. If Mujeeb Zadran is fit to play then he will replace Stonis. Yuvraj Singh or Manoj Tiwari may get a chance in place of Mayank Agarwal.
Chris Gayle, Karun Nair, Marcus Stoinis/Mujeeb ur Rahman, R Ashwin (capt), Mohit Sharma, KL Rahul (wk), Mayank Agarwal/Yuvraj Singh/Manoj Tiwari, Aaron Finch, Axar Patel, Andrew Tye, Ankit Rajpoot.
Pro tips: Both the wicket-keepers are in good form. You can take anyone on your team. Try to keep KL Rahul in your team. Make a combination of the above players for multiple teams.
Pro tips: The above batsmen has a good chance of performing in this match. Make a combination of the above players for multiple teams.
Pro tips: Make a combination of the above players. The right combination can make you a winner in the grand league.
Pro tips: The above bowlers are most likely to take wickets. Make a combination of the bowlers for multiple teams. You can also take bowlers from playing 11.
Pro tips: The above players are most likely to perform today. You can take them as a captain and vice captain. You can also take captains from playing 11.
Kings XI Punjab will get 2 points and will go to 14 points. It will make things easier for KXIP. MI is on a do-or-die situation. They have to win this match as this is the last chance for them. Both the teams will give their best to win today's match. As per the cricket experts, MI will win the match but according to our astrology prediction, KXIP will win.
The team winning the toss will love to bowl first as defending a total is very difficult on this ground and dew will also come into the play at the latter half of the match. According to our astrology prediction, MI will win the toss and ask KXIP to bat first.
Suryakumar Yadav is one of the top scorers. Try to keep him in your teams. Ben Cutting can contribute you points which can make or break. Try to pick players who are consistent. KL Rahul, Chris Gayle, Suryakumar Yadav can give you maximum points. Our astrology team has predicted that Rohit will strike today.
Conclusion: This is it for Today's Dream11 Fantasy Cricket Match Prediction of MI vs KXIP, 50th T20 Match, IPL 2018 which will be played on Wednesday 16th May. You can give your valuable feedback in the comment section. Subscribe to our notification of latest updates. GOODBYE!
Superb website, good at predictions ????


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GAME GOLF Launches Free App Featuring Real-Time Shot, Game Tracking and Rangefinder for iOS and Android Phones
SAN FRANCISCO, April 15, 2015 /PRNewswire/ -- GAME GOLF, the first wearable device that automatically tracks and graphically displays a golfer's round with valuable game data and statistics, today announced the new GAME GOLF Tracking App enabling golfers to track their game and club distances in real-time, and manage their game with a built-in GPS rangefinder, all from their iOS or Android (News - Alert) device. No purchase of the GAME GOLF physical device is required to use the new App.
In celebration of GAME GOLF's newest free app and its Irish roots, the company is giving away a once-in-a-lifetime Irish golf vacation. Two players and one guest each, who post a minimum of three 18-hole golf rounds with either the GAME GOLF wearable device or the new GAME GOLF Tracking App from now through June 30, 2015, will be eligible to receive an all-expense paid golf trip to Ireland. For contest rules, lg on to GAMEGOLF.com.
"If you don't truly understand your game it's hard to improve. The free GAME GOLF Tracking App allows golfers to see their shot performance in real-time, something which many amateur golfers will never have had access to before," said John McGuire, CEO of GAME GOLF. "Further, it affords everyone access to the GAME GOLF platform to gather stats, collect data and share their game with friends, family, coaches and instructors."
The GAME GOLF Tracking App can be downloaded and put in play just before teeing off. The App provides golfers with an aerial view of each hole, distances to key locations using the GPS Rangefinder feature, and the ability to "tag (News - Alert)" each shot by selecting the club used. You'll be able to see - greens in regulations, fairway accuracy, scrambling percentage, putts per hole, club distances and more. Golfers can view their platform profile and data on their mobile device or at GAMEGOLF.com.
The GAME GOLF TRACKING App can be downloaded for free on iOS in the App Store or on Android at the Google (News - Alert) Play Store.
About GAME GOLF:
GAME GOLF is dedicated to bringing innovative ways for golfers to connect to their game, PGA Professionals and their friends through the wearable GAME GOLF device and the GAME GOLF Tracking App. Golfers can then see their game and club performance to help them improve online at GAMEGOLF.com and on the GAME GOLF Tracking App.
The development company behind GAME GOLF is Active Mind Technology, a privately held company pioneering the gamification of sport through its development of the GAME platform.
GAME GOLF has strategic partnerships with Golf Channel, The PGA of America and British PGA. GAME GOLF is in use in 104 countries with over 36,000 worldwide golf courses mapped. For information, visit www.gamegolf.com.
Photo - http://photos.prnewswire.com/prnh/20150414/198723
To view the original version on PR Newswire (News - Alert), visit:http://www.prnewswire.com/news-releases/game-golf-launches-free-app-featuring-real-time-shot-game-tracking-and-rangefinder-for-ios-and-android-phones-300066120.html
SOURCE GAME GOLF