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Mark Lancaster Lusk became a member of the Penn State faculty in 1986. Prior to his appointment, he enjoyed a varied career with such diverse groups as the Woody Herman Thundering Herd, the Chicago Symphony Orchestra, the Eastman Wind Ensemble, and the Chicago Contemporary Chamber Players.
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iClock990 is a 3.5-inch TFT screen Time Attendance & Access Control Terminal. It has a very user-friendly interface with the new firmware and latest core board. Users can easily manage data via RS232/485, TCP/IP and USB-host. Most importantly, the built-in 2000mAh backup battery can eliminate the trouble of power failure.


Some game genres only exist as desktop games, board games, or mobile games, and not as multiplayer games. Even with the best artificially intelligent player, though, there's something special about playing against human opponents.
One such genre is business games, typically simulations where you can run an airline or a transport company, as in Transport Tycoon Deluxe, or TTD. There are two open source versions: openTTD and Simutrans. OpenTTD has a multiplayer mode for up to 255 players, but Simutrans is only available on the desktop.
The one I'd really like to see is a multiplayer version of a 1990s era PC game called Detroit. This is a simulation where you manage an automobile manufacturer, starting in 1908 and going on for 100 years. Game play includes designing new cars, testing them, then manufacturing and selling them and making enough profit to keep running and growing the business. It was a little bit buggy, but a great game all the same.
For a game designer, the period of play is recent history and very well documented. Today, Numerous automobile inventions that we take for granted all appeared during the last hundred years. Not just seat belts, flashing indicators, windscreen wipers or engine management units, but new types of engines such as the Wankel Rotary. Automobiles changed enormously from the humble Model T Ford to Google's self driving cars and the game should encompass that.
Game play includes deciding when to introduce these innovations. Do you spend a fortune developing them and licensing them to rivals? How much do you spend on marketing, offering dealer incentives or even setting up your own dealer chains?
As with most new business sectors, there were dozens of small manufacturers at the start. But failures, mergers and takeovers within 20 years shrank it down and now only a handful are left. So, the game should let you buy up other automobile manufacturers.
Add in two world wars and a few smaller conflicts to stimulate demand, but make it easy to play and above all enjoyable. At heart it's still a business simulation so you have to take control of the finances, build or expand factories for manufacturing, set staffing levels and decide how much to spend on research and marketing, and set the prices of vehicles. Then there's dealing with domestic and overseas markets, manufacturing and sales, maybe even issuing dividends or arranging credit lines to pay for expansion.
If you want to develop that game, you've got a beta tester just waiting for your invite. Just don't keep me waiting too long!


For the six-month period ended September 30, 2011, Ubisoft reported a loss of €37.1 million (around $50 million), compared to a loss of €89.8 million in the same period the previous year. Essentially, Ubisoft emphasized the fact that it lost less money this year than last. Ubisoft attributed the lower loss to improved back-catalog sales and a reduction in development expenses (mostly due to the fact that the company released fewer high-definition games).
This page contains a single entry by Editor published on November 8, 2011 10:37 AM.
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text:
\section{Introduction}
In the past decade, there has been an exponential growth in the scope of data science and machine learning.
This has led to new learning problems as well as novel principles for learning from different types of unstructured data, such as medical records, social media content, or surveys to only mention a few.
A type of data that has recently gained some traction in the context of crowdsourcing and psychometrics is \emph{comparisons} \citep{stewart2005absolute,agarwal2007generalized}, particularly in the form of:
\begin{itemize}
\item \textbf{Triplet comparison}: Binary response to the query---is object $i$ more similar to object $j$ than to object $k$?
\item \textbf{Quadruplet comparison}: Binary response to the query ---are objects $i$ and $j$ more similar to each other than objects $k$ and $l$?
\end{itemize}
Comparisons have been used in the psycho-physics literature for more than 50 years since it is known that humans can provide relative measurements better than absolute ones \citep{shepard1962theanalysis,stewart2005absolute}. It led to a surge of popularity of comparisons in the context of crowdsourcing information about objects that cannot be easily represented by Euclidean features, such as food \citep{wilber2014hcomp} or musical artists \citep{daniel2002quest}, or objects for which humans cannot robustly estimate a pairwise similarity, for instance cars \citep{kleindessner2017kernel} or natural scenes \citep{heikinheimo2013crowd}.
The purpose of collecting comparisons is often to learn patterns in the objects, such as latent clusters, or use them for prediction, as in classification.
Hence, there has been significant development of algorithms for comparison based learning \citep{agarwal2007generalized,heikinheimo2013crowd,haghiri2017comparison,kazemi2018comparison,perrot2019boosting}.

The present paper focuses on comparison-based hierarchical clustering.
Clustering---partitioning a dataset into groups of similar objects---is a fundamental machine learning problem.
It is natural to wonder how one can group similar objects when neither features nor pairwise similarities are available, and one only has access to triplet or quadruplet comparisons.
Several comparison-based clustering algorithms have been developed \citep{kleindessner2017kernel,ukkonen2017crowdsourced,perrot2020near}.
Hierarchical clustering is the problem of finding partitions of the data at different levels of granularity. For instance, the objects in the food dataset \citep{wilber2014hcomp} can be broadly categorised into `sweets or desserts' and `main or savoury dishes', but the latter can be further sub-divided into meat dishes, soups and others.
\citet{ghoshdastidar2019foundations} observed that two widely used hierarchical clustering algorithms---single and complete linkage---can be computed using only actively chosen quadruplet comparisons, that is without explicit knowledge of the pairwise similarities between the objects.
There are, however, limited practical settings where the learning algorithm can actively decide which comparisons should be queried, and the most relevant case in crowdsourcing is that of learning from a set of  \emph{passively collected} comparisons. Hierarchical clustering algorithms based on passive comparisons (triplets or quadruplets) have already been proposed in the literature \citep{kleindessner2017kernel,ghoshdastidar2019foundations}.
These methods use the given comparisons to compute pairwise similarities between objects or clusters, which are further used by a linkage function to construct the hierarchy.

\paragraph{Motivation.} As it is common in clustering, evaluating the goodness of a learned hierarchy is challenging when no ground truth is available. Nevertheless, a cost minimisation formulation of hierarchical clustering was introduced by \citet{dasgupta2016cost}, where any hierarchy, also called a dendrogram, on a dataset is assigned a cost based on pairwise similarities.
This formulation, along with an equivalent revenue maximisation formulation \citep{moseley2017approximation},
has led to new methods and insights into hierarchical clustering \citep{cohenaddad2018hierarchical,alon2020hierarchical}.
However, the requirement of access to pairwise similarities makes Dasgupta's cost or revenue inapplicable for comparison-based hierarchical clustering. Hence, existing works evaluate the meaningfulness of the hierarchies learned using comparisons either by visual inspection of the dendrograms or in an artificial setting, where comparisons are computed from pairwise similarities. Neither solution is useful in practice, where one only has access to comparisons.

The lack of a formal cost or revenue also has implications on the fundamental limits of comparison-based hierarchical clustering. \citet{emamjomeh2018adaptive} study the problem of recovering a latent hierarchy among $n$ objects using triplets comparisons. They show that $\Omega(n^3)$ \emph{passively obtained} triplets (a constant fraction of all triplets) are necessary for exact recovery of the latent hierarchy, whereas only $O(n\log n)$ triplets are sufficient for exact recovery, if they are \emph{actively queried}.
This raises the question whether one can obtain a good approximation to the latent hierarchy using fewer comparisons. One requires a comparison-based quantification of the goodness of a dendrogram (or hierarchy) to address this problem.

\paragraph{Contributions.}
In this paper, we propose new revenue functions for dendrograms that are only based on triplet or quadruplet comparisons (Section \ref{compcost}).
This not only allows us to evaluate the goodness of hierarchies (without ground truth),  but also helps to design new comparison-based hierarchical clustering algorithms based on the maximisation of the proposed revenue functions. We show that the proposed comparison-based revenues are equivalent to Dasgupta's cost or revenue applied to particular pairwise similarities that can be computed from comparisons.
Interestingly, the pairwise similarities that arise from this equivalence are known in the comparison-based clustering literature \citep{perrot2020near}.

In Section \ref{sec:theory-latent}, we demonstrate the significance of our revenue function through the problem of recovering a latent hierarchy among $n$ objects using passive triplets \citep{emamjomeh2018adaptive}.
We show that, when all triplets are available, the dendrogram corresponding to the latent hierarchy maximises the revenue function.
Moreover, only $O(n^2 \log n / \epsilon^2)$ passive triplets suffice to obtain a $(1-\epsilon)$-approximation of the optimal revenue.

In Section \ref{sec:algorithms}, we further use the connection of the proposed revenue functions to the \emph{additive similarities} in \citet{perrot2020near} and present two variants of average linkage hierarchical clustering based on passive triplet or quadruplet comparisons.
The performance of these approaches are empirically compared in Section \ref{sec:experiments} with state of the art baselines using synthetic and real datasets.

\section{Related Work}
\label{sec:related}
While, to the best of our knowledge, this paper is the first one to propose a principled way to evaluate the goodness of dendrograms when only comparisons are available (and without using ground truth clusters), several approaches have been proposed or adapted in the literature to learn dendrograms using only comparisons. We review some of them here.

The most widely used principle in comparison-based learning is ordinal embedding, where the underlying idea is to retrieve Euclidean representations of the objects that respect the available comparisons as well as possible, and that can subsequently be used with standard hierarchical clustering algorithms such as average linkage (see \citet{vankadara2019large} for an extensive review of ordinal embedding approaches). This kind of approaches have the advantage of being flexible in terms of clustering methods that may be used. However, they also assume that the data is Euclidean, and when this is not the case, the embedded data might be far from the original one and the learned clusters might be less relevant compared to methods that do not make this assumption \citep{ghoshdastidar2019foundations}.

To avoid learning a restrictive Euclidean embedding, a solution is to use the comparisons to compute general pairwise similarities. It is then possible to apply most of the standard hierarchical clustering algorithms, such as average linkage. This principle has been successfully used in hierarchical clustering \citep{kleindessner2017kernel,ghoshdastidar2019foundations}. In this paper, we show that our revenue function allows us to derive new algorithms that can be summarized as applying average linkage to two similarities that are known to perform well in standard clustering \citep{perrot2020near} but have not yet been studied in the context of hierarchical clustering.

There exists a third kind of approaches in comparison-based hierarchical clustering where the idea is to directly learn from the comparisons without a proxy similarity or an embedding \citep{emamjomeh2018adaptive,addanki2021design}. However, these methods use actively queried triplets which might not be suitable in practice. In this paper, we focus on passively obtained comparisons that are easier to obtain from a crowd. Finally, \citet{ukkonen2017crowdsourced} derives a direct method for standard clustering by defining a comparison-based cost function that should be minimized. In this paper, we consider a similar approach in the sense that we maximize a revenue. However, rather than clustering, we consider the problem of hierarchical clustering where the goal is to learn the entire hierarchy and not simply the ground clusters.

\section{Preliminaries}
\label{sec:background}

We consider the problem of hierarchical clustering of a set of $n$ objects, denoted by $[n] = \{1,2,\ldots,n\}$.
A hierarchy or dendrogram on $[n]$ is a binary tree $H$ whose root node is the set $[n]$ and each node represents a set $C\subseteq [n]$ with its two children, $C_1$ and $C_2$, denoting a split of $C$ such that $C = C_1 \cup C_2$ and $C_1 \cap C_2 = \emptyset$.
For node $C$, we use $H(C)$ to denote the subtree rooted at $C$ and $|H(C)|$ represents the number of leaves in the subtree, or equivalently, the number of objects in the set $C$. For objects $i,j\in [n]$, let $i\lor j$ and $H(i \lor j)$ respectively denote the smallest node in the tree and the smallest subtree containing both $i$ and $j$.
The goal of hierarchical clustering is to find a dendrogram $H$ that is \emph{optimal}, or at least \emph{good}, in some sense.
In the next subsections, we recall Dasgupta's cost for hierarchical clustering that allows ones to measure the goodness of a dendrogram given full access to pairwise similarities, and then describe the comparison-based learning framework, where only triplet or quadruplet comparisons are available.
In the paper, we use the standard Landau notations $O(\cdot), \Omega(\cdot), o(n)$, where the asymptotics are defined with respect to $n$.

\subsection{Dasgupta's Cost for Hierarchical Clustering}
\label{Dcost}
Suppose one has access to a function $s: [n] \times [n] \to \mathbb{R}$, symmetric, such that $s_{ij} = s(i,j)$ denotes the pairwise similarity between objects $i,j\in[n]$. Dasgupta's cost function \citep{dasgupta2016cost} for a dendrogram $H$ on $[n]$, with respect to the pairwise similarity $s$,  is defined as
\begin{align}
Dcost(H,s) &= \sum_{{i,j \in [n], \ i<j}} s_{ij} \cdot |H(i \lor j)| \,.
\end{align}
To find a good dendrogram, \citet{dasgupta2016cost} proposed to minimize this cost over all trees. While it is NP-hard to find the optimal solution, several relaxations are known to have constant factor approximation guarantees for Dasgupta's cost or related quantities.
In particular, \citet{moseley2017approximation} defined Dasgupta's revenue function,
\begin{align}
Drev(H, s) =  n \sum_{i,j \in [n], \ i<j}s_{ij} - Dcost(H, s).
\end{align}
Note that since $\sum s_{ij}$ is fixed, maximising $Drev(H,s)$ over all binary trees is equivalent to minimising $Dcost(H,s)$.
It can then be shown that the tree $H$ obtained from average linkage achieves $Drev(H,s) \geq \frac13$-optimal revenue, provided that the similarity function $s$ is non-negative.

\subsection{Comparison-based Learning}
\label{comp_framework}
In the present paper, we assume that the pairwise similarities $\{s_{ij}\}_{i,j\in[n]}$ are not available.
Instead the algorithm has access to either a set of triplets $\mathcal{T}$, which is a subset of
\begin{align*}
  \mathcal{T}_{all} = \{(i,j,k) \in [n]^3 : s_{ij}>s_{ik},\ i,j,k \ \text{distinct}\},
\end{align*}
or a set of quadruplets $\mathcal{Q} \subseteq \mathcal{Q}_{all}$, where
\begin{align*}
    \mathcal{Q}_{all} = \{(i,j,k,l) \in [n]^4 :~ &s_{ij}>s_{kl},i < j, \ k < l, \ (i,j) \neq (k,l)\}.
\end{align*}
Assuming $i<j,k<l$ avoids counting the same comparison multiple times.
We note that the number of possible comparisons is high---$|\mathcal{Q}_{all}| =O(n^4)$ and $|\mathcal{T}_{all}| =O(n^3)$---but, in practice, the observed comparisons, $\mathcal{T} $ or $\mathcal{Q}$, are fewer, ranging between $O(n\cdot\text{polylog}(n))$ up to $O(n^2)$.
Note that whenever a triple $(i,j,k)$ is considered,  $\mathcal{T}$ contains either $(i,j,k)$ or $(i,k,j)$, depending on whether $s_{ij} \lessgtr s_{ik}$. The same holds for quadruplets.
We further assume that  $\mathcal{T}$, or $\mathcal{Q}$, is passively collected---the algorithm cannot decide which comparisons should be queried.

\section{Comparison-based Revenue}
\label{compcost}

We present two comparison-based revenue functions for hierarchical clustering, one in the triplets framework and the other for quadruplet comparisons.

\paragraph{Triplet comparisons.} We first consider the case of triplets and assume that the algorithm has access to a passively collected set of triplets $\mathcal{T}$. In the following, let $\mathbb{I}_E$ denote the indicator of event $E$, that is, $\mathbb{I}_E= 1$ if $E$ happens, and 0 otherwise.
We define the triplet comparison revenue of a binary tree (dendrogram) $H$ on $[n]$, using triplets $\mathcal{T}$, as
\begin{equation}
Trev(H,\mathcal{T}) =\sum_{(i,j,k)\in\mathcal{T}}\Big(|H(i \lor k)| - |H(i \lor j)|\Big).
\label{eqn_Trev}
\end{equation}
For every $(i,j,k)\in \mathcal{T}$, we know that $i$ is more similar to $j$ than to $k$, and hence, we prefer to merge $i,j$ before merging $i$ and $k$, which leads to $|H(i \lor k)| > |H(i \lor j)|$.
Hence, it is desirable to maximise $|H(i \lor k)| - |H(i \lor j)|$ for every observed triplet $(i,j,k)\in\mathcal{T}$.
We then propose to formulate triplets comparison-based hierarchical clustering as the problem of maximizing $Trev(H,\mathcal{T})$ over all binary trees.

\paragraph{Quadruplet comparisons.} The above formulation can be similarly stated in the quadruplets setting.
Assuming that the algorithm has access to a passively collected set of quadruplets $\mathcal{Q}$,
we define the quadruplet comparison revenue of a binary tree $H$ on $[n]$ as
\begin{equation}
Qrev(H,\mathcal{Q}) =\sum_{(i,j,k,l)\in\mathcal{Q}} \Big(|H(k \lor l)| - |H(i \lor j)|\Big).
\label{eqn_Qrev}
\end{equation}
Similar to the triplet setting, every $(i,j,k,l)\in \mathcal{Q}$ indicates that $i,j$ should be merged earlier than $k,l$ in $H$, and we prefer trees such that $|H(k \lor l)| > |H(i \lor j)|$. We propose to achieve this by finding a tree that maximises $Qrev(H,\mathcal{Q})$.

\paragraph{Connection with Dasgupta's cost.} While one may try to directly maximise the above comparison-based revenue functions, the following equivalence to Dasgupta's cost and revenue allows us to employ existing methods for hierarchical clustering that require pairwise similarities.

\begin{theorem
\label{thm_equivalence}
For any given set of triplets $\mathcal{T}$ and any dendrogram $H$ on $[n]$,
\begin{displaymath}
Trev(H,\mathcal{T}) = - Dcost(H,s^{AddS3}) = Drev(H,s^{AddS3}),
\end{displaymath}
where $s^{AddS3}$ refers to the additive similarity from triplets (AddS3) defined by \citet{perrot2020near}
\begin{displaymath}
s^{AddS3}_{ij} = \sum_{k\neq i,j}  \mathbb{I}_{(i,j,k)\in\mathcal{T}} - \mathbb{I}_{(i,k,j)\in\mathcal{T}} + \mathbb{I}_{(j,i,k)\in\mathcal{T}} - \mathbb{I}_{(j,k,i)\in\mathcal{T}}
\end{displaymath}
Similarly, for any set of quadruplets $\mathcal{Q}$ and dendrogram $H$,
\begin{displaymath}
Qrev(H,\mathcal{Q}) = - Dcost(H,s^{AddS4}) = Drev(H,s^{AddS4}),
\end{displaymath}
where $s^{AddS4}$ is the additive similarity from quadruplets (AddS4) defined by \citet{perrot2020near}
\begin{displaymath}
s^{AddS4}_{ij} = \sum_{k \neq l, \ (k,l) \neq (i,j)}  \mathbb{I}_{(i,j,k,l)\in\mathcal{Q}} - \mathbb{I}_{(k,l,i,j)\in\mathcal{Q}} \;.
\end{displaymath}
\end{theorem}

\begin{proof}[Proof sketch (details in appendix)]
Proving $Trev(H,\mathcal{T}) = - Dcost(H,s^{AddS3})$ involves a rearrangement of terms, with the observation that, for every $i,j$, the term $|H(i \lor j)|$ appears in the summation in \eqref{eqn_Trev} with coefficient $-1$ when $(i,j,k)\in\mathcal{T}$ or $(j,i,k)\in\mathcal{T}$ and with coefficient $+1$ when $(i,k,j)\in\mathcal{T}$ or $(j,k,i)\in\mathcal{T}$. Adding these coefficients for all $k\neq i,j$ gives us $-s^{AddS3}_{ij}$, and proves the equality.
The second equality $- Dcost(H,s^{AddS3}) = Drev(H,s^{AddS3})$ simply follows from the observation that $\sum_{i<j} s^{AddS3}_{ij} = 0$.
The proof for quadruplets is similar.
\end{proof}

\section{Recovering a Latent Hierarchy by Triplet Revenue Maximisation}
\label{sec:theory-latent}

In this section, we consider the problem of recovering a latent hierarchy from triplet comparisons, earlier studied in \citet{emamjomeh2018adaptive}.
Let $H_0$ be a hierarchy on $[n]$, from which we derive a set of triplets\footnote{%
\citet{emamjomeh2018adaptive} consider triples of the form $\{i,j,k\}$ that imply $i,j$ are closer to each other than $k$, with respect to $H_0$.  Each such triple $\{i,j,k\}$ correspond to two triplets $(i,j,k)$ and $(j,i,k)$ in our setting.}
\begin{displaymath}
\mathcal{T}_0 = \{(i,j,k), (j,i,k) ~:~ i,j \text{ are merged before } k \text{ in } H_0\}.
\end{displaymath}
One can show that any rooted tree $H'$ that satisfies all triplets in $\mathcal{T}_0$ is equivalent to $H_0$, up to isomorphic transformations, and hence, one can exactly recover $H_0$ given $\mathcal{T}_0$.
\citet{emamjomeh2018adaptive} further show one cannot exactly recover $H_0$ from any passively obtained $\mathcal{T} \subseteq \mathcal{T}_0$ if $|\mathcal{T}| = o(n^3)$.
This raises the question---can one approximately recover $H_0$ from a smaller set of triplets $\mathcal{T}$?

We use the proposed triplet based revenue to answer this question in the affirmative.
Before providing an approximation guarantee, we first show the significance of our formulation in this context by proving that one can recover $H_0$ from $\mathcal{T}_0$ by maximising $Trev$.

\begin{proposition}
\label{thm-H0-maxrev}
Consider the aforementioned setting, where $H_0$ is a latent hierarchy on $[n]$ objects, and $\mathcal{T}_0$ is the corresponding set of triplets as defined above. Then
\begin{displaymath}
H_0 = \argmax_{H} Trev(H,\mathcal{T}_0),
\end{displaymath}
where the maximisation is over all binary trees $H$ on $[n]$.
\end{proposition}

\begin{proof}[Proof sketch (details in appendix)]
The proof is in two steps. First, we show that $\mathcal{T}_0$ is the optimal set of triplets to maximize the revenue for the tree $H_0$, that is
$\mathcal{T}_0 = \argmax_{\mathcal{T}} Trev(H_0,\mathcal{T})$.
Then, we show that, given two trees $H_0$ and $H_1$ such that $\mathcal{T}_0$ and $\mathcal{T}_1$ are the corresponding sets of triplets then we have that $Trev(H_0,\mathcal{T}_1) = Trev(H_1,\mathcal{T}_0)$. Combining these two results, we obtain that $Trev(H_0,\mathcal{T}_0) > Trev(H_0,\mathcal{T}_1) = Trev(H_!,\mathcal{T}_0)$ for any tree $H_1$ and corresponding set of triplets $\mathcal{T}_1$. This directly implies Proposition~\ref{thm-H0-maxrev}.
\end{proof}

\citet{emamjomeh2018adaptive} prove the uniqueness of the hierarchy that satisfies all the triplets in $\mathcal{T}_0$, that is, $H_0$ maximises the function
\begin{displaymath}
f(H,\mathcal{T}_0) =\sum_{(i,j,k)\in\mathcal{T}_0} \mathbb{I}_{|H(i \lor k)| > |H(i \lor j)|}.
\end{displaymath}
While maximising $Trev(H,\mathcal{T}_0)$ seems to be a relaxation of maximising $f(H,\mathcal{T}_0)$ in this context, Proposition \ref{thm-H0-maxrev} shows that both problems have the same optimal solution $H_0$.

\subsection{Approximate Recovery of $H_0$ Using Passive Triplets}

We consider the setting, where $\mathcal{T}_0$ is not completely available but one has access to a uniformly sampled subset $\mathcal{T} \subseteq \mathcal{T}_0$.
We show that $|\mathcal{T}| = O(n^2 \log n / \epsilon^2)$ triplets suffice to obtain a tree $\widehat{H}$ such that $Trev(\widehat{H},\mathcal{T}_0) \geq (1-\epsilon)\cdot Trev(H_0,\mathcal{T}_0)$,
that is, we get a good approximation of $H_0$
with much fewer than $n^3$ samples, although we may not exactly recover $H_0$.

We consider the following uniform sampling to obtain $\mathcal{T}$. Let $p_n \in (0,1]$ denote a sampling probability, depending on $n$.
For every pair of triplets $(i,j,k),(j,i,k) \in \mathcal{T}_0$, we add the pair to $\mathcal{T}$ with probability $p_n$. One can use standard  concentration inequalities to show that, with high probability, $|\mathcal{T}| = O(p_n n^3)$.
We state the following approximation guarantee for trees derived using $\mathcal{T}$.

\begin{theorem}
\label{thm-approx}
Let $p_n \in (0,1]$ that depends on $n$, and $\mathcal{T}$ be as defined above.
Given access to $\mathcal{T}$, consider the hierarchy
\begin{displaymath}
\widehat{H} = \argmax_{H} Trev(H,\mathcal{T}).
\end{displaymath}
For any $\epsilon \in (0,1)$, there exist constants $n_0,c>0$ (depending on $\epsilon$) such that for $n> n_0$ and $p_n > c\log n/n\epsilon^2$,
\begin{equation}
Trev(\widehat{H},\mathcal{T}_0) \geq (1-\epsilon)\cdot Trev(H_0,\mathcal{T}_0)
\label{eqn-approx}
\end{equation}
with probability at least $1-n^{-O(1)}$.
Setting $p_n$ at its smallest allowable value, \eqref{eqn-approx} holds for $|\mathcal{T}| = O(n^2 \log n / \epsilon^2)$.
\end{theorem}

\begin{proof}[Proof sketch (details in appendix)]
Using concentration results, we show that with probability $1-n^{-O(1)}$,
$\big| Trev(H, \mathcal{T}) - p_n Trev(H,\mathcal{T}_0) \big| = O\left(n^3 \sqrt{p_n n\log n}\right)$ for every tree $H$.
Using this concentration for both $H_0$ and $\widehat{H}$, and noting that $Trev(\widehat{H},\mathcal{T}) \geq Trev(H_0,\mathcal{T})$, we have
\begin{displaymath}
Trev(\widehat{H},\mathcal{T}_0) \geq Trev(H_0,\mathcal{T}_0) - O\left(\sqrt{\frac{n^7\log n}{p_n}}\right).
\end{displaymath}
Finally, we show that $Trev(H_0,\mathcal{T}_0) = \Omega(n^4)$ to arrive at the $(1-\epsilon)$-approximation for $p_n = \Omega(\log n/n\epsilon^2)$.
\end{proof}

The result in \citet[][Proposition 2.2]{emamjomeh2018adaptive}---that $\Omega(n^3)$ is necessary to exactly recover $H_0$---hinges on the fact that it impossible to correctly guess the hierarchy at the lowest level of the tree $H_0$ using fewer comparisons.
Since errors in the lowest level do not significantly affect $Trev$, we can achieve the $(1-\epsilon)$-approximation in Theorem \ref{thm-approx}. However, note that $\widehat{H}$ may not be efficiently computable as it requires exhaustive search over all trees.
We discuss practical algorithms in the next section.

\section{Comparison-based Algorithms for Hierarchical Clustering}
\label{sec:algorithms}

The equivalence between comparison-based revenues and Dasgupta's revenue, stated in Theorem~\ref{thm_equivalence}, implies that one may simply employ standard hierarchical clustering algorithms using the pairwise similarities AddS3 or AddS4, depending on whether one has access to triplets or quadruplets.
This makes it possible to use the well-established literature on hierarchical clustering with pairwise similarities.
In fact, as mentioned before, previous works on passive comparison-based hierarchical clustering also follow this philosophy using other kind of pairwise similarities obtained from the comparisons  \citep{kleindessner2017kernel,ghoshdastidar2019foundations}.
Unlike previous works, our use of AddS3 or AddS4 stems from a revenue maximisation formulation that allows us to consider an approach based on the average linkage (AL) clustering algorithm, that is, the following procedure:

\noindent\hrulefill
\\
\textbf{AddS3-AL (or AddS4-AL)}
\begin{itemize}
    \item[] \hskip-2.5ex\textbf{Given:} A set of triplets $\mathcal{T}$ (or quadruplets $\mathcal{Q}$) on $[n]$
    \item[\bf1.] Compute the pairwise similarity function $s^{AddS3}$ (or $s^{AddS4}$) for every pair of objects
    \item[\bf2.] Run average linkage algorithm with $s^{AddS3}$ (or $s^{AddS4}$)
    \item[] \hskip-2.5ex\textbf{Output:} The tree or dendrogram $H$ on the objects, $[n]$
\end{itemize}
\vskip-2ex\hrulefill\vskip1ex

\paragraph{Remark on approximation guarantee.} Average linkage enjoys strong theoretical guarantees under the assumption that the similarities are always positive.
In particular, \citet{moseley2017approximation} show that average linkage achieves a worst-case $\frac13$-approximation for revenue maximisation. Unfortunately, this result does not readily extend to AddS3-AL and AddS4-AL as these similarities may be negative in some cases. A possible approach could be to add a positive constant to all the similarities to ensure that they are positive. Although this does not change the optimal tree or the one obtained from average linkage, a $\frac13$-approximation for the modified revenues (considering revised similarities) does not imply a $\frac13$-approximation for the original revenues.

Based on the proof of \citet{moseley2017approximation}, one can show that AddS3-AL (or AddS4-AL) returns a tree with non-negative triplet (or quadruplet) comparison revenue. Whether approximation guarantees may also be derived for AddS3-AL and AddS4-AL remains open.

\section{Experiments}
\label{sec:experiments}

In this section, we propose two sets of experiments\footnote{The code is available at \url{https://github.com/jitaishik/Revenue_ComparisonHC.git}} to demonstrate the practical relevance of our new revenue function and the corresponding algorithm. On the one hand, we consider synthetic data and show that our function indeed gives higher revenue to dendrograms that are closer to the ground truth. On the other hand, we apply our new algorithms on real datasets and show that they obtain trees with revenues that are on par with state of the art approaches in comparison-based hierarchical clustering.

\subsection{Planted Model}
In this first set of experiments, we study the behaviour of our new revenues in a controlled setting. Hence, we generate data using a planted model for comparison-based hierarchical clustering \citep{ghoshdastidar2019foundations} and we use 3 triplets based and 2 quadruplets based methods to learn dendrograms.

\paragraph{Data.} To generate the data in this first set of experiments, we use a standard planted model in comparison-based hierarchical clustering~\citep{balakrishnan2011noise,ghoshdastidar2019foundations}. More precisely, given $n$ objects, we create a similarity matrix as $M+R$ where, $M = (\mu _{ij})_{1 \leq i,j \leq n}$ is an ideal symmetric matrix characterizing the planted hierarchy among the examples and $R =(r_{ij})_{1 \leq i,j \leq n}$ is the symmetric perturbation matrix which accounts for the noise in the data. We generate $r_{ij} \sim \mathcal{N}(0,\sigma ^2)$ where the variance is fixed. To compute $M$, we assume that there are $2^L$ pure clusters, each of size $n_0$ denoted as $\mathcal{C}_{1},\mathcal{C}_{2},...,\mathcal{C}_{2^L}$, and the planted hierarchy on the pure clusters is a complete binary tree of height $L$. The total number of points (leaves) in the planted tree is $n = n_{0}2^L$. Let the root of the tree be at level $0$ and the pure clusters be at level $L$. Then, given two examples $i,j$ such that $H(i\lor j)$ is rooted at level $\ell$, we define $\mu_{ij} = \mu -(L-\ell)\delta$ where $\mu$ and $\delta$ are constants that control the hardness of the problem. In particular, smaller values of $\delta$ make the similarities between examples that belong to the same cluster to be more difficult to distinguish from similarities between examples that belong to different clusters. Overall, given two examples $i,j$, we obtain the similarity $s_{ij} = \mu _{ij} + r_{ij}$ for all $j<i$ which implies that $s_{ij} \sim \mathcal{N}(\mu _{ij},\sigma ^2)$ for all $j<i$. The hardness of the problem is dependent on the signal-to-noise ratio $\frac{\delta}{\sigma}$. In all the experiments, we set $\mu = 0.8$, $\sigma = 0.1$, $n_{0}=30$, $L=3$ and we vary $\delta \in \{0.02,0.04,...,0.2\}$.

Since we are in a comparison based setting, we do not directly use the similarities of the planted model to learn dendrograms but instead generate comparisons. Given $\mathcal{T}_{all}$ and $\mathcal{Q}_{all}$ the sets containing all possible triplets and quadruplets (see preliminaries), we obtain $\mathcal{T} \subseteq \mathcal{T}_{all}$ and $\mathcal{Q} \subseteq \mathcal{Q}_{all}$ by uniformly sampling $kn^2$ comparisons with $k>0$.

\begin{table*}[]
\centering
\caption{Revenue and AARI of various methods for a fixed signal to noise ratio of $1.5$ and increasing amounts of comparisons. In each line the highest revenue and AARI are underlined, showing that the two measures are well aligned.}
\begin{tabular}{@{}clrllrllrl@{}}
\toprule
\multirow{2}{*}{\begin{tabular}[c]{@{}c@{}}Value of $k$\\ ($kn^2$  comparisons)\end{tabular}} &
  \multirow{2}{*}{} &
  \multicolumn{2}{c}{AddS3-AL} &
   &
  \multicolumn{2}{c}{tSTE-AL} &
   &
  \multicolumn{2}{c}{MulK3-AL} \\ \cmidrule(lr){3-4} \cmidrule(lr){6-7} \cmidrule(l){9-10}
 &
   &
  \multicolumn{1}{c}{Revenue} &
  \multicolumn{1}{c}{AARI} &
  \multicolumn{1}{c}{} &
  \multicolumn{1}{c}{Revenue} &
  \multicolumn{1}{c}{AARI} &
  \multicolumn{1}{c}{} &
  \multicolumn{1}{c}{Revenue} &
  \multicolumn{1}{c}{AARI} \\ \midrule
1  &  & $4.303 \times 10^6$           & $0.664$          &  & $\underline{4.564\times 10^6}$  & $\underline{0.859}$  &  & $3.701\times 10^6$  & $0.534$ \\
2  &  & $8.904\times 10^6$           & $0.739$          &  & $\underline{9.093\times 10^6}$  & $\underline{0.851}$ &  & $8.462\times 10^6$  & $0.683$ \\
3  &  & $1.352\times 10^7$          & $0.794$          &  & $\underline{1.363\times 10^7}$ & $\underline{0.853}$ &  & $1.316\times 10^7$ & $0.775$ \\
4  &  & $1.812\times 10^7$          & $0.845$          &  & $\underline{1.817\times 10^7}$ & $\underline{0.867}$ &  & $1.784\times 10^7$ & $0.825$ \\
5  &  & $2.275\times 10^7$          & $0.844$          &  & $\underline{2.278\times 10^7}$ & $\underline{0.865}$ &  & $2.252\times 10^7$ & $0.841$ \\
6  &  & $\underline{2.733\times 10^7}$ & $\underline{0.885}$ &  & $2.723\times 10^7$          & $0.856$           &  & $2.705\times 10^7$ & $0.847$ \\
7  &  & $\underline{3.194\times 10^7}$ & $\underline{0.890}$ &  & $3.181\times 10^7$          & $0.866$          &  & $3.167\times 10^7$ & $0.856$ \\
8  &  & $\underline{3.674\times 10^7}$ & $\underline{0.911}$ &  & $3.648\times 10^7$          & $0.858$          &  & $3.636\times 10^7$ & $0.857$  \\
9  &  & $\underline{4.113\times 10^7}$ & $\underline{0.889}$  &  & $4.089\times 10^7$          & $0.855$          &  & $4.081\times 10^7$ & $0.856$ \\
10 &  & $\underline{4.567\times 10^7}$ & $\underline{0.918}$ &  & $4.534\times 10^7$          & $0.856$          &  & $4.536\times 10^7$ & $0.864$ \\ \bottomrule
\end{tabular}%

\label{tab:triplets_planted_revenue_aari}
\end{table*}

\begin{figure}[ht]
  \centering
  \begin{subfigure}[b]{0.45\linewidth}
    \includegraphics[width=\linewidth]{Plots/New_Plots/cost_n2_tri_bar.pdf}
    \caption{Revenue (Triplets)}
  \end{subfigure}
  \begin{subfigure}[b]{0.45\linewidth}
    \includegraphics[width=\linewidth]{Plots/New_Plots/aari_n2_tri_bar.pdf}
    \caption{AARI (Triplets)}
  \end{subfigure}

  \begin{subfigure}[b]{0.45\linewidth}
    \includegraphics[width=\linewidth]{Plots/New_Plots/cost_n2_quad_bar.pdf}
    \caption{Revenue (Quadruplets)}
  \end{subfigure}
  \begin{subfigure}[b]{0.45\linewidth}
    \includegraphics[width=\linewidth]{Plots/New_Plots/aari_n2_quad_bar.pdf}
    \caption{AARI (Quadruplets)}
  \end{subfigure}

  \caption{Revenue and AARI (higher is better) of several triplets (a--b) and quadruplets (c--d) based methods using $n^{2}$ comparisons. Given various signal to noise ratios, a higher revenue implies higher AARI values (better dendrograms).}
  \label{fig:triplets_planted_revenue_aari}
\end{figure}

\paragraph{Evaluation Function.} To measure the closeness between the dendrograms obtained by the different approaches and the ground truth trees, we use the Averaged Adjusted Rand Index \citep{ghoshdastidar2019foundations}. The AARI is an extension to hierarchies of a well known measure in standard clustering called Adjusted Rand Index~\citep{hubert1985comparing}. The underlying idea is to average the ARI obtained over the top $L$ levels of the tree. This measure takes values in $[0,1]$ with higher values for more similar hierarchies, an AARI of $1$ implying identical trees. Our goal is to empirically verify that higher revenues imply higher AARI. Indeed, this would show that our revenue function is appropriate to evaluate the goodness of a dendrogram and that maximizing the revenue is indeed a good unsupervised way to select hierarchies. The results reported are averaged over $10$ independent trials.\footnote{The randomness stems from three sources: the noise in the similarities (we use the time + 42 as the seed), the triplets selection (we use the time as the seed), and the optimization procedure (initialization, batch selection) in tSTE (we use the time as the seed).} We defer the standard deviations to the appendix for the sake of readability.

\paragraph{Methods.}
We compare AddS3-AL and AddS4-AL, the two methods proposed in this work to various comparison-based algorithms for learning dendrograms, such as 4K-AL \citep{ghoshdastidar2019foundations}, a quadruplets based method, along with two triplets based approaches MulK3-AL \citep{kleindessner2017kernel,perrot2020near} and tSTE-AL \citep{van2012stochastic}. The former two are similarity based approaches where the idea is use the comparisons to learn a similarity. The latter is an ordinal embedding approach where the idea is to recover a representation of the data that respects the comparisons as well as possible, we can then use the cosine similarity
$\displaystyle s_{ij} = \frac{\langle x_i,x_j\rangle}{||x_i||^2 _2 ||x_j||^2 _2}$
to compare the examples. To learn the dendrograms we then apply standard average linkage to the various similarities.

\begin{table*}[t]
\centering
\caption{Experiments on real datasets. For the triplets based methods, AddS3-AL tends to obtain the dendrograms with the best revenues. For the quadruplets based approaches, AddS4-AL and 4K-AL obtain comparable results. Using the original Cosine similarities only yields slightly better hierarchies than the comparison-based methods.}
\begin{tabular}{@{}l@{}llllll@{}rrr@{}}
\toprule
\multirow{2}{*}{Dataset} &  & \multicolumn{4}{c}{Triplet}                                    &  & \multicolumn{3}{c}{Quadruplet}                     \\ \cmidrule(lr){3-6} \cmidrule(l){8-10}
 &
   &
  \multicolumn{1}{c}{AddS3-AL} &
  \multicolumn{1}{c}{tSTE-AL} &
  \multicolumn{1}{c}{MulK3-AL} &
  \multicolumn{1}{c}{Cosine-AL} &
   &
  \multicolumn{1}{c}{AddS4-AL} &
  \multicolumn{1}{c}{4K-AL} &
  \multicolumn{1}{c}{Cosine-AL} \\ \midrule
Zoo                      &  & $2.845\text{$\times$}10^5$           & $2.287\text{$\times$}10^5$  & $2.129\text{$\times$}10^5$  & $\underline{2.879\text{$\times$}10^5}$ &  & $2.988\text{$\times$}10^5$  & $2.966\text{$\times$}10^5$          & $\underline{3.032\text{$\times$}10^5}$  \\
Glass                    &  & $\underline{2.182\text{$\times$}10^6}$ & $1.993\text{$\times$}10^6$ & $1.479\text{$\times$}10^6$ & $2.115\text{$\times$}10^6$         &  & $2.427\text{$\times$}10^6$ & $2.447\text{$\times$}10^6$         & $\underline{2.493\text{$\times$}10^6}$ \\
MNIST                    &  & $1.876 \text{$\times$}10^9$                  & $\underline{2.028\text{$\times$}10^9}$         & $1.749\text{$\times$}10^9$         & $2.027\text{$\times$}10^9$                 &  & $1.935\text{$\times$}10^9$         & $1.910\text{$\times$}10^9$                 & $\underline{2.062\text{$\times$}10^9}$                  \\
Car                      &  & $1.521\text{$\times$}10^5$  & $\underline{1.562\text{$\times$}10^5}$  & $1.264\text{$\times$}10^5$  & -                 &  & $\underline{1.521\text{$\times$}10^5}$  & $1.125\text{$\times$}10^5$ & - \\

Food                      &  & $\underline{6.137\text{$\times$}10^6}$  & $5.993\text{$\times$}10^6$  & $6.096\text{$\times$}10^6$  & -                 &  & $\underline{6.137\text{$\times$}10^6}$  & $\underline{6.137\text{$\times$}10^6}$ & -\\

Vogue                      &  & $\underline{2.722\text{$\times$}10^4}$  & $2.104\text{$\times$}10^4$  & $3.022\text{$\times$}10^3$  & -                 &  & $\underline{2.722\text{$\times$}10^4}$  & $2.549\text{$\times$}10^4$ & -\\

Nature                      &  & $\underline{2.650\text{$\times$}10^5}$  & $2.056\text{$\times$}10^5$  & $1.231\text{$\times$}10^5$  & -                 &  & $\underline{2.650\text{$\times$}10^5}$  & $2.228\text{$\times$}10^5$ & -\\

Imagenet                      &  & $\underline{7.179\text{$\times$}10^7}$  & $6.571\text{$\times$}10^7$  & $3.440\text{$\times$}10^7$  & -                 &  & $\underline{7.179\text{$\times$}10^7}$  & $6.994\text{$\times$}10^7$ & -
\\ \bottomrule
\end{tabular}%

\label{tab:comparisons_real}
\end{table*}

\begin{table}[]
\centering
\caption{Description of Datasets used in experiments.}
\label{tab:datasets}
\begin{tabular}{@{}llrrr@{}}
\toprule
Dataset  & Query                & \#Objects & \#Triplets \\ \midrule
Zoo      & Cosine Similarity    & 101       & 10201      \\
Glass    & Cosine Similarity    & 214       & 45796      \\
MNIST    & Cosine Similarity    & 2000      & 4000000    \\ \midrule
Car      & Most Central Triplet & 60        & 14194      \\
Food     & Standard Triplet     & 100       & 190376     \\
Vogue    & Odd-out Triplet      & 60        & 2214       \\
Nature   & Odd-out Triplet      & 120       & 6710       \\
Imagenet & Rank 2 to 8          & 1000      & 328549     \\ \bottomrule
\end{tabular}%
\end{table}

\paragraph{Results.} In Figure~\ref{fig:triplets_planted_revenue_aari}, we present the AARI and Revenue of our various methods for several signal to noise ratios using $n^2$ comparisons.\footnote{Note that we also considered other amounts of comparisons. However, the trends were similar to the ones observed here and thus we chose to defer these results to the appendix.} We observe that, given a set signal to noise ratio, the ordering between the methods remains the same for the revenue and the AARI, that is the method with the highest revenue is also the one with the highest AARI. In other words, a higher revenue indicates that the corresponding dendrogram is better. In Table~\ref{tab:triplets_planted_revenue_aari}, we verify that this remains true for a constant signal to noise ratio of $1.5$ and various number of observed comparisons. On each line, the highest revenue and AARI are underlined. We can notice that when the revenue of AddS3-AL becomes higher than the revenue of tSTE-AL, that is using more than $6n^2$ triplets, the AARI also follows the same trend, thus confirming that selecting the dendrogram with the highest revenue is indeed a good way to select meaningful hierarchies. In the appendix, we show that the same behaviour can be observed for various signal to noise ratios.

\subsection{Real Data}
The previous experiments establish that our revenue functions are good at identifying meaningful dendrograms in an unsupervised way. In the following experiments, we investigate the behaviour of the proposed approaches on real data. In particular, we show that they are competitive with standard comparison based hierarchical clustering approaches on various datasets.

\paragraph{Data.} We consider 8 different datasets. On the one hand, we consider 3 standard clustering datasets: Zoo, Glass, and MNIST \citep{heller2005bayesian,lecun2010mnist,vikram2016interactive}. For Zoo and Glass, we use the same pre-processing as \citet{ghoshdastidar2019foundations} while for the MNIST dataset we use the one of \citet{perrot2020near}. Since we are in a comparison-based setting, we generate $n^2$ comparisons using the cosine similarity. To model mistakes from human annotators, we randomly and uniformly flip $5\%$ of the comparisons~\citep{emamjomeh2018adaptive}, for example if one should observe the triple $(i,j,k)$ that is object $x_i$ is closer to $x_j$ than to $x_k$ then one observes $(i,k,j)$ instead. On the other hand, we consider 5 comparison-based datasets, Car, Food, Vogue Cover, Nature Scene and ImageNet Images v0.1, from the cblearn repository.\footnote{\url{https://github.com/dekuenstle/cblearn}} The number of objects, the kind of query used to obtain comparisons are summarized in Table~\ref{tab:datasets}.
The comparisons are transformed into triplets (final number of triplets noted in Table \ref{tab:datasets}), which are also used in the quadruplet setting.

\paragraph{Evaluation Function.} Since the datasets considered here do not come with a ground truth hierarchy, we cannot compute the AARI. Hence, we only report the revenue. The results reported are averaged over $10$ independent trials\footnote{The randomness stems from two main sources: the triplets generation in the Zoo, Glass, and MNIST dataset (we use the time as the seed for the triplets selection and the time + 42 as the seed for the random flips) and the optimization procedure (initialization, batch selection) in tSTE (we use the time as the seed). For all the other datasets and methods, every step is deterministic and, thus, we only need to report the results of a single run.} and defer the standard deviations to the appendix.

\paragraph{Methods.} Besides the methods already used in the planted setting, we also consider the Cosine baseline where it is assumed that the pairwise cosine similarities are available, and we apply average linkage directly on the similarities used to generate the comparisons. This baseline is not applicable to the comparison-based datasets where we only have access to the comparisons and not to the similarities.

\paragraph{Results.} The results are reported in Table~\ref{tab:comparisons_real}. We can notice that AddS3-AL tends to be better than tSTE-AL and MulK3-AL while AddS4-AL and 4K-AL are comparable. As is expected, the Cosine baseline based on the original similarities obtains the best performances in most cases, but it only seems to yield slightly better hierarchies than the comparison-based methods. This would tend to confirm that hierarchical clustering with average linkage is indeed a problem that can be solved using only a limited number of comparisons, instead of using all similarities.

\section{Conclusion}
\label{conclusion}
In this paper, we proposed novel revenue functions that allow us to measure the goodness of a dendrogram in an unsupervised way using only triplet or quadruplet comparisons. This suggest natural algorithms for hierarchical clustering based on the maximization of such revenues. Drawing theoretical connections with existing work on cost and revenue functions in standard hierarchical clustering, we propose two average linkage based algorithms for hierarchical clustering using only comparisons. We empirically show that our revenue functions successfully identify the dendrograms that are closest to the ground truth. We also show that the proposed approaches to learn hierarchies perform well on real datasets and are competitive with state of the art methods.

We further used the proposed revenue function to resolve an open theoretical problem of recovering a latent hierarchy using fewer than $\Omega(n^3)$ passive triplets.
We showed that $O(n^2 \log n / \epsilon^2)$ passive triplets suffice to obtain a $(1-\epsilon)$-approximation of the optimal triplet revenue.
We conclude with the following open questions:
(i) Are $\Omega(n^2 \log n)$ passive triplets necessary for a $(1-\epsilon)$-approximation?
(ii) Can a polynomial time algorithm, such as average linkage, achieve a constant factor approximation of the triplet revenue?

\bibliographystyle{abbrvnat}

redpajama_set_name: RedPajamaArXiv


text:
The Miller / Packan Doc Fund
The Miller / Packan Film Fund.
We learn from each other.
The Miller / Packan* Film Fund supports documentaries that Educate, Embrace and Inspire. The Fund is financed through the Rogovy Foundation. We believe in the transformational power that comes from enlightening narratives and inspiring characters.
The Fund begins granting in 2016. In its first year, grants totaling $150,000 will be awarded to between six and ten filmmakers. The fund operates an open rolling submission process, and awards will be announced bi-annually. The first grants will be awarded in July 2016.
Each grant will be one-time only and offered in amounts of between $5,000 to $25,000. Due to the large number of submissions, our selection process will be highly competitive.
Submissions will be reviewed in the first round by Rogovy Foundation staff. Final selections will be chosen by an Awards Committee which includes notable members within the film industry.
We believe in a more perfect world. The Miller / Packan Documentary Film Fund provides grants to feature-length non-fiction projects that address social issues and inspire others.
Our planet is wonderfully diverse. We support film as an instrument for change, delivering greater knowledge, compassion and awareness. Listening and understanding bring us together.
Subject Categories / Areas of Interest:
At the highest level, the Fund's subject categories are Education, the Environment and Civics. Please review our Ideals and Values for a sense of what types of topics we might support. Grants will be awarded to filmmakers who most closely match our defined areas of interest.
We back a variety of styles that drive a film's narrative. This might include character-driven storytelling, a fact-based exposé or an informational point-of-view upon a controversial subject.
We look for quality filmmaking comprised of inspiring characters, a fascinating story, a strong visual style, tight editing and generally high production values.
We seek projects that open our eyes through a strong premise, critical thinking, detailed analysis and competing views.
We like investigations into the cost structures of our social institutions, such as healthcare and education. We appreciate the celebration of public heroes and find inspiration through their stories. We favor topics that bring our global community together.
Your success in winning a grant will depend upon how well your film matches up with our mission and the strength of your proposal.
Supported Activities / Stages of Production:
The Fund supports filmmaking in advanced development (up to $10,000), production and post-production stages (up to $25,000).
If your film is in advanced development, you will need to provide a detailed synopsis (or shooting script), along with supporting research and legal clearances to use your material. You will also need to include at least 7 minutes of footage, which helps us understand your project in relation to your vision.
If your film is in production or post-production, we will evaluate your project based upon the application details and progress of your project. You must also submit footage (seven minutes minimum) or a rough cut of your project. The more footage submitted, the better we can understand your story and evaluate your proposal.
We do not fund outreach or audience engagement activities. Nor do we fund expenses related to fund-raising, distribution, publicity or marketing.
• The applicant must be the producer and/or director, and at least 18 years of age
• The film must be feature length of no less than 70 minutes.
• The film addresses a social issue that reflects the Foundation's Ideals and Values
• The film is commercially viable and capable of reaching a large audience
• The project must have IRS 503(c)(3) status or a Fiscal Sponsor
• Non-English language films are eligible but must have English subtitles.
• Student films are ineligible
• Completed films are ineligible
Application Guidelines:
Applications are accepted online only. Your submission will include details about your project, links to view footage and examples of past work. Once your proposal is successfully received, an acknowledgement email will be sent to you.
Proposals go through two stages of evaluation: Finalists and Award Winners. During the first stage, Rogovy Foundation staff will review your submission to determine if it qualifies as a Finalist. If your package does not make this round, we will notify you within three months of your submission.
The Finalist round will be reviewed by our staff along with notable members within the film community. The first Award Winners will be announced in July 2016.
You may make one submission per Open Call. No project updates will be accepted once we have received your proposal. If you are denied an award, you are welcome to re-submit your application during another Open Call period. You are only allowed two submissions per project.
Proposal Considerations:
The Fund evaluates your application based upon the following criteria: How compelling your Story is, the Issue areas being addressed and the Strength of your proposal.
We look for stories that engage an audience, propelling a narrative forward. The issue area should align with the Fund's Ideals and Values. We also consider the filmmaker's previous experience and the soundness of the proposal.
Proposal checklist:
• Logline (2-3 Sentences)
• Story Summary / Synopsis (Approximately 1-2 pages)
What is your story and story structure? Give an overview of your story, introducing the main characters and potential plot points. Describe the anticipated story structure and narrative trajectory, or potential character arcs for your project. Discuss your access to the story and characters.
• Topic Summary (Approximately 1-2 pages)
Why is this topic important, timely, or relevant? Why are you the best person to make a film about this? Explain the cultural or social relevance and context for the topic, and why this project is timely or urgent. Detail the topics, issues, themes, challenges, stakes, or questions that your project will cover.
• Artistic Approach (Approximately ½ page)
How are you going to tell this story? Describe your creative vision for the finished project – its visual look and feel. Explain your intended use of cinematic language or any particular artistic approach that informs the storytelling.
• Project Stage (Approximately 1 paragraph)
Outline the projected production timeline from the project's current state to the anticipated completion date. Your timeline should cover both the creative and production processes and should detail major project activities, production schedules, and anticipated post production and release dates.
• Key Creative Personnel (Approximately 1 paragraph/bio)
Provide brief biographies (50-150 words) for the director(s), and if attached, the producer(s), cinematographer, or editor. Include notable credits and/or major recognition or award information. For each key creative, include information about relevant expertise and the individual's role in the project.
• Audience and Distribution Strategies (approximately 1 paragraph for each)
◦ Distribution and Marketing Strategy
Characterize the intended distribution life for your film. Specify plans for festival, theatrical, and/or community screenings, as well as plans for securing national broadcast and/or distribution.
◦ Audience Engagement
Describe the anticipated audience for your project, including any underserved audiences. How do you plan to reach your target audience? Not all films are suited for social engagement, but if yours is, what actions do you hope for viewers to take after seeing your film?
• Financial Info (1 paragraph for each)
◦ Fundraising Strategy
Describe the strategy for raising the additional funds necessary to complete the project. Include all sources and amounts raised to date. Clearly distinguish between potential sources of funding and secured amounts. List the status of other sources of funding currently under consideration, whether to be applied for or pending.
Example:
Foundation A: $X Secured
Private Donations: $X Secured
Foundation B: $X Applied
Broadcast License A: $X In Negotiation
Crowdfunding: $X In Process (Campaign end date MM/DD/YY)
◦ Grant Impact
Amount requested? If you were to receive a grant, describe how the funds would be spent. In light of your total budget, how would these funds help you move forward with your project?
In the online application form, you'll be asked to briefly address the following question: How does your project relate to the Ideals and Goals of the Rogovy Foundation?
3. Comprehensive Line Item Expense Budget:
• Top Sheet
Provide a single page budget top sheet/summary.
• Line Item Budget
Provide a comprehensive line item budget including all documentary related expenses. The budget should be broken down on a line item basis in the form of a spreadsheet. A budget cover sheet or narrative budget summary alone is not adequate. Please include detailed budget notes for any areas that may be viewed as out of the ordinary or which requires further explanation.
4. Visual Sample and Description:
A current work sample is required. Provide a link and password to a streaming version of your work sample as part of the application. There is no specific length required. Submit the sample that you feel best represents your project at its current phase of production. While samples may be any length, for longer samples we will only guarantee to consider the first 10 minutes. The sample provided must be for the project you are applying for. Include a paragraph giving your work sample context and background information.
When all of your materials are gathered and prepared, you are invited to submit your grant application via our online system.
You will receive an automated email confirmation acknowledging receipt of your application. If your film does not qualify as a finalist, you will be notified within three months of your submission.
If I'm a first-time filmmaker, can I still apply?
We do consider both first-time and accomplished filmmakers. However bear in mind our selection criteria includes strength of proposal. Your experience will be a factor in our evaluation.
Do you accept International productions?
Yes, we accept International productions as long as the film is either in English or includes English subtitles. If you are based internationally and do not have IRS 501(c) (3) status, you will need to work with a Fiscal Sponsor who does.
You may submit your film without 501(c) (3) status and without a Fiscal Sponsor. However you will need one should your application be accepted.
We will only consider submissions which are written in English.
What is a Fiscal Sponsor?
A Fiscal Sponsor is an organization that qualifies as an IRS public charity 501 (c) (3) and can accept funds on your behalf. The funds are then re-distributed to your project, thus ensuring a tax-efficient transaction for the Film Fund.
How many times may I re-apply?
You may re-apply if your first application is denied. However we will only accept two submissions per project.
If my application is denied, when can I submit it?
You can re-submit your application during any Open Call period.
Can I make changes or update my application?
If a decision is still pending and you have more information that would make a material difference to our evaluation, you are welcome to send us the update and we will do our best to incorporate that information into our evaluation process.
Can I check on the application progress or discuss?
Unfortunately, we are unable to respond verbally to any inquiries. You best option to contact us is via email: inquiries@rogovy.org
Are animated documentary films eligible?
Yes we do consider animated films for awards.
Do I need to request a specific amount of money with my application?
Yes. We want to best match the grant to your requirements.
Can the funding be allocated to marketing and distribution expense?
No we do not fund outreach or audience engagement activities. Nor do we fund expenses related to fund-raising, distribution, publicity or marketing.
When are the awards announced?
The awards are announced bi-annually, in January and July.
Can I send materials on a DVD?
No, we do not accept materials sent by mail. All submission material must be sent via our online application system.
What is the best way to be in touch with you?
If you have additional questions, we are happy to discuss them with you. The best option to reach us is via email: inquiries@rogovy.org
Selection Process / Committee:
The applications for funding will be initially reviewed and vetted by the staff of the Rogovy Film Fund. Finalists will be reviewed by a Committee comprised of Foundation staff and notables within the film industry.
If you are selected for a grant, you will be required to list the Fund and its logo within the film credits.
*Miller / Packan represent two legendary Ohio High School teachers: Sally G Miller and Mae Packan. Teaching is the noblest of professions. To learn more about these two legendary For We honor the profession … etc etc….
About Miller / Packan
Who are Sally Miller & Mae Packan? It's nearly certain you've never heard of these outstanding educators. Locally, they left a mark on several generations of high school students. Yet there are no major awards given to them, no buildings named after them, not a statue nor even a plaque. Like many exceptional educators, their impact goes largely unrecognized.
It's in their honor, and in honor of all the other exceptional yet unheralded educators, that we dedicate this Fund. The Miller / Packan Film Fund supports documentaries that perpetuate the Idealism and Critical Thinking they brought to their students.


The key difference between neurons and glia is that neurons are 'excitable'. This means that they produce electrical events called action potentials, which are also known as nerve impulses, or spikes. Nerve impulses are the basic currency of the brain. They allow neurons to communicate with each other, computations to be performed, and information to be processed.
When a neuron spikes it releases a neurotransmitter, a chemical that travels a tiny distance across a synapse before reaching other neurons (Fig 1). Any time a neuron spikes, neurotransmitters are released from hundreds of its synapses, resulting in communication with hundreds of other neurons.
What do these neurons hear as they listen to other neurons talking? That depends on the language being spoken—or the identity of the neurotransmitter that is released. Although some research has revealed exceptions, the vast majority of neurons are currently thought to be monolingual—they can only release one type of neurotransmitter.
Neuronal communication is exquisitely regulated as a balance between excitatory and inhibitory influences (Fig 2). A given neuron receives hundreds of inputs, almost exclusively on its dendrites and cell body. These inputs add and subtract in a constantly evolving pattern, depending on what the brain is thinking. This is a process called synaptic integration, which determines whether a neuron becomes active.
In order to become active, the total input must reach a threshold at which excitation outweighs inhibition enough. Only at this point will the receiving neuron spike, adding its voice to the conversation by releasing its own neurotransmitter.
Neurons aren't all the same; for starters, they release different neurotransmitters. Moreover, several different subclasses of neurons can use the same transmitter. These different subclasses seem to be suited to different tasks in the brain, although we don't fully know yet what those tasks are. One major goal of contemporary neuroscience is to understand the extent of this diversity.
How many different types of neuron are there (and how can we define a "type" of neuron)? What do they all do? Are particular types more important than others in various diseases, and can we target them for therapies?
The ongoing genetic revolution has made these questions more addressable than ever before, yet we still have a long way to go. Once you appreciate this diversity and combine it with the fact that there are 86 billion neurons (plus at least as many glia!) you can begin to understand why we still have much more to discover about how brains work.


GFC Beautiful | Beautiful Conference hopes to empower women of all ages, backgrounds and cultures.
Welcome to the Beautiful Conference!
Special Pricing now thru Sunday, February 3.
Women 18+ and Young Women 14+ in High School.
*Special registration price for High School and College Students 14 to 22.
Lisa Bevere has spent nearly three decades empowering women of all ages to find their identity and purpose. She is a New York Times bestselling author and internationally known speaker. Her books, which include Adamant, Lioness Arising, Girls with Swords, and Without Rival, are in the hands of millions worldwide.
Lisa and her husband, John, are the founders of Messenger International, an organization committed to developing uncompromising followers of Christ who transform their world. Messenger International has given away nearly 20 million resources in 106 languages.
If you are tired of running away from your life or tired of running ragged toward the next thing you think will make you feel complete, Hannah's new book Come Matter Here will help you do whatever it takes to show up for the life God has for you.


The Lunar New Year is a day when families gather for an annual reunion dinner to mark the beginning of a prosperous year. Lunar festivals are celebrated here in the Philippines with elaborate meals and traditional feast with friends and family.
Certain dishes are staples during the Chinese New Year for their auspicious, symbolic meaning. Food is the cornerstone of the Chinese New Year celebrations Most families serve lucky food during this festive season, believed to bring good luck for the coming year. The food preparation, and ways of serving and eating is expected to attract a year of good health, prosperity, luck, happiness and peace this Year of the Fire Rooster.
Food Exchange Chef Alen Meng from China has curated 3 sumptuous Lauriat Family Set Menus to share with people close to your heart. And I joined in and sampled one of the three special Lauriat feast created for the upcoming Year of the Rooster earlier today.
We were treated to a revelry of good fortune, and great food at the Novotel Manila Araneta Center's all-day dining restaurant. We savored a bounty of Chinese culinary from the Fortune Set (P 18,888++) that features 15 specially prepared dishes.
This includes: Assorted Chinese Cold Cuts, Sweet and Sour Squid & Garlic Fungus and Cucumber Salad, Jilin Black Chicken Ginseng Soup, Xinjiang Spicy Stewed Chicken, Taiwanese Stir Fried Beef with Sha Cha Sauce, Steamed Grouper Fish in Light Soy Sauce with Ginger and Spring Onion, Dalian Style Stir-Fried Mixed Seafood, Dimsum Sets, Cantonese Wok Fry Noodles, and Wagyu Beef Fried Rice.
The Chinese dumplings, made to look like Chinese silver ingots, meant an opportunity to make more money when eaten during the Lunar New Year celebrations.
I so love the steamed dumplings with minced pork (Siomai) and diced shrimp (hakao) wrapped in a thin and elastic dough skin.
Chinese New Year always includes Fish as it equates to an increase in Prosperity. The steamed grouper was light but savory to the palette.
It was a first for me to sip a wonderful soup made of black chicken. They this to us in individual bowls.
Our next dose of protein came as the Xinjiang Spicy Stewed Chicken and Taiwanese Stir-Fried Beef was served.
The Cantonese Wok Fry Noodles, and Wagyu Beef Fried Rice came in next to complement these yummy dishes. The Noodles symbolizes a wish for longevity and its length is symbolic of the eater's life. The longer and uncut the noodles are, the better.
After a healthy protein fix, we were offered sweet treats to cap off a hearty meal. We were served Sweet Rice Roll with Black Sesame Seed in Rice Wine, Almond Lychee, Mango Sago, plus Tikoy Roll to cap our indulgence.
I loved the Sweet Rice Roll with Black Sesame Seed in Rice Wine as it tasted really good! In Chinese people's minds, eating food made with sticky rice meant an increase in rise in business success, promotions at work, better positions year-after-year by year. In addition, the round shape is favored by the Chinese during the New Year celebrations as is signifies "being together".
Eating round Fruits and those "golden" in color during the Chinese New Year implies Fullness and Wealth. Indulging in the Fruit Platter is believed to bring in more wealth.
Food Exchange Manila features all 3 Lauriat Set menus for a limited time only. Gather around and delight in specialty dishes from Chef Allan Meng to usher in good fortune, happiness, wealth and longevity until January 29, 2017!
When you are at Novotel Manila Araneta Center , have your photo taken beside the Money Tree with red envelopes to remind you of good fortune all year long. The Chinese give away red envelopes that contain money because red is the symbol of energy, happiness and good luck. The color red is believed to bestow happiness and blessings on the receivers.
Make a wish at the Prosperity Tree as the new energy of the Year of the Rooster will make way for new beginnings.
Stay at Novotel Manila Araneta Center from Jan 23-30 starting from P 6,888 nett.
A relaxing weekend staycation in a Superior Room (P 6,888) entitles you, your partner plus 2 kids ages 15 and below to a sumptuous Buffet Breakfast plus Chinese Prosperity Buffet Dinner at the Food Exchange.
Avail of Wish N Treat promo and get to pamper yourself and a friend to a well-deserved one-hour massage for two (2) at In Balance Spa worth P 3,000!
Check out the Gourmet Bar from January 25 to 29 and enjoy an Auspicious High Tea (P 1,874 for 4 pax) which features premium tea with Chinese delicacies such as Mini Pao, Siomai, Tikoy Roll, Rice Mango, Cake Roll and Gulameka.
Call (02) 9907888 now for reservations or visit www.novotel.com and www.accorhotels.com to know more about these Chinese New Year packages.
We love how Novotel notch up their menu to suit the needs of their guests.
Their facilities are superb! They have something to offer for all the members in the family.
Yay! :) Belated Kiong Hee! Last time we had a family lauriat was during our temple's saint's birthday. Auntie paid for a whole table of sumptuous though not in Novotel. Just brings a lot of memories to be feasting with the family.
Everything looks yummy! We don't prepare dor CNY unlike the calendar new year but yes to dining out and feast on Asian food!
What I missed from chinese food is their dumplings, the street foods are also good.
I wonder how much the lauriat menus cost.
What is a garlic fungus??haha! But I love Chinese food. I always eat a lot when we dine at a Chinese resto.
Sweet rice roll with black sesame seed in rice wine sounds insteresting. Never had it before, what does it taste like?
It was like biting into a supersoft and smooth "bilu-bilo". Its flavorful, clear soup was served lukewarm.
Chinese foods are really delightful. My family loves visiting chinese food chains kasi asian na asian eh. Patok talaga sa panlasang pinoy!
Yummy!!! I hope you enjoyed your stay!
Would have loved to partake on something like this during the lunar new year but we decided to stay home because of the baby. The only way we celebrated was by having tikoy at home. Haha!
When I saw photos of my friends who had an R&R at Novotel, I got jealous and wanted to try it for myself. Seeing your food shots is like a sign that Novotel would be our next R&R destination.
Their Chinese New Year lauriat meals look scrumptious! It would be nice to experience Chinese New Year celebrations like this.
I used to hate Chinese food. But now that I am older and hopefully wiser, I get to love their food and even could eat them everyday. I particularly love Century Egg and pancit. Their dim sum are also love, same with their chicken cooked in a very different way we prepare and cook. Seems like celebrating Chinese New Year at Novotel is a great treat. Love the spread of food, as usual.
That really is a fortune set, you were so fortunate to taste it! Parang masarap lahat.
This must've been an awesome experience. I love all the food, too! :D I have tried celebrating Chinese New Year in Binondo and it was festive and grand! I loved the dragon dance and the fireworks. I would love to try that again soon.


text:
Periodični gibi udov v spanju so motnja, za katero so značilni stereotipni gibi spodnjih in lahko tudi zgornjih okončin med spanjem. Praviloma gre za premike spodnjih delov telesa (palci, gležnji, kolena, tudi kolki).

Najpogosteje se kaže s kratkotrajnimi epizodami nenadnih, periodično ponavljajočih se stereotipnih zgibkov okončin, ki ponavadi povzročijo popolno ali nepopolno prebujanje.

Gre za drugo vrsto motnje, kot je sindrom nemirnih nog. Pri sindromu nemirnih nog gre hoteni odziv na občutek nelagodja v nogi, medtem ko so periodični gibi udov v spanju nehoteni ter se jih bolnik  pogosto sploh ne zaveda.

Znaki in simptomi
Za periodične gibe udov v spanju so značilni nehoteni premiki zlasti spodnjih udov med spanjem. Bolniki premikajo zlasti palce, gležnje, kolena, tudi kolke, redkeje tudi zgornje okončine. Taki periodični zgibki pogosto povzročijo popolno ali nepopolno prebujanje, zato so lahko bolniki zaradi pomanjkanja kakovostnega spanca čez dan pretirano utrujeni.  Praviloma se nočnih prebujanj zaradi periodičnih gibov udov sploh ne spominjajo.

Sklici

Motnje spanja

redpajama_set_name: RedPajamaWikipedia


text:
All issues Volume 9 (2003) EAS Publications Series, 9 (2003) 359 Abstract
Magnetism and Activity of the Sun and Stars
https://doi.org/10.1051/eas:2003121
J. Arnaud and N. Meunier (eds)
EAS Publications Series, 9 (2003) 359
XMM-Newton observation of ρ Oph dark cloud
H. Ozawa1, T. Montmerle1 and N. Grosso2
1 Service d'Astrophysique, Centre d'Études de Saclay, France : Laboratoire d'Astrophysique de Grenoble, France
2 Max-Planck-Institut für extraterrestrische Physik, Garching bei München, Germany : Laboratoire d'Astrophysique de Grenoble, France
We observed the ρ Ophiuchi dark cloud around core F, an active star-forming region, with the XMM-Newton observatory for 30 ks. We detected 107 X-ray sources within the 30' diameter field-of-view of the XMM-Newton observatory. We compared the positions of the XMM-Newton X-ray sources with the Chandra X-ray sources and found 43 X-ray sources detected with both satellites. We had a high rate of X-ray detection of Class I protostars of ~70%. We extracted light curves and spectra from bright 4 Class I sources, YLW16A, EL29, YLW15, and IRS51. They did not show X-ray flare during the observation time of 30 ks. Their X-ray spectra showed high temperature and heavy absorption, which is typical for Class I protostars.
© EAS, EDP Sciences, 2003
The X-ray emission from Young Stellar Objects in the ρ Ophiuchi cloud core as seen by XMM-Newton
Activity of protostars and brown dwarfs
Magnetism and Activity of the Sun and Stars J. Arnaud and N. Meunier (eds) EAS Publications Series, 9 (2003) 307p. 307
ROSAT-HRI detection of the Class I protostar YLW16A in the Ophiuchi dark cloud
A&A 370, L22-L25 (2001)
The physics of young stellar objects: X-rays, magnetism, and high-energy phenomena
Star Formation and the Physics of Young Stars: Summer school on Stellar Physics X J. Bouvier and J.-P. Zahn (eds) EAS Publications Series, 3 (2002) 85-109p. 85
Results from DROXO — II. [Ne II] and X-ray emission from ρ Ophiuchi young stellar objects


Rajjo, 16 Jun 2012is this a dual sim phone? can anyone comfirm plsNo, get Samsung galaxy ace duos for dual sim.
It's lauched in at 14.5 k INR.
Really expensive for a budget device with below average specs.
Sony's live with walkman is much better option at 13 k INR with much better specs.
Does this phone has Corning Gorilla Glass protection?.
What is beats audio hand free?.
what is "beats audio hand free"?
Think is between the following models HTC Desire C, ZTE Skate 4.3, Huawei Ascend G300 and Samsung Galaxy Fit. For now, the closest I buy a HTC-but I worry a little bit negative comments to the dispute and not a good choice. Are those users with higher demands and deeper pockets do not know, but these are the models of which I want to choose the best ... I ask for any advice that will help me in the decision.
shashank, 12 Jun 2012Hey....all visitors....i dont understand why all of them speak about a processor without knowi... moreShashank's posting is one of the best, well informed and useful comments of late.
This comment is written with the HTC right now it is one of the best Budget phones I have ever tested. It is not the fastest surely, the screen lags a bit behind, when I type. But the screen is nice, the size of the devife is just right and the battery runtime blows you away. I was able to get nearly two days out of the device - with a constant e-mail connection (i mean IMAP idle on). Today i am going one step further and set the screen to always on.
seems to be a good lightweight phone. Only gripe is that the quality of the pictures are not sharp most of the time...auto focus plm I dont know...I'm told by shop to get a more powerful phone but this should not be happening. it doesnt matter wherether its 3mp or 8mp, it should have been sharpish. Note there is NO led flash so useless in a disco or dim place.
Rajjo, 16 Jun 2012is this a dual sim phone? can anyone comfirm plsDear friend, this is not a dual sim device. But if you are interested to buy a budget dual sim phone, you may wait for a while for the upcoming budget phone - "Sony Xperia tipo dual," which has dual sim support, 2.9 GB internal storage, Adreno 200 GPU for gaming, supports full flash player, HVGA screen resolution, and runs on Ice Cream Sandwich, etc................ "Sony Xperia tipo dual" will be released in the 3rd quarter of 2012.
Not recommended for playing games. Beats audio is crap! camera have no touch focus like others phone. Other than that it is the same as other icecream sandwich phone.
External speaker is so so. Battery life I have not yet test it.
Reason why i bought: my mum likes the form factor, short and fat! while the sony was long and skinny. Even though it is 26gram lighter than the sony, you can feel it when you hold both on hand.
If you are using call and sms only, this is good for your pocket when u wear tight jeans. Surf web, NO. because no gpu and is only 600mhz... just 600.


We have a wide range of deposit products with maturity periods ranging from three months to thirty six months. We have two types of term deposit schemes: Monthly Interest Scheme and Cumulative Scheme.
Copyright © 2015 Welfare Group. Conceptualized by Ads Creations.


text:
Muhammad Abdallah Kounta (ur. 27 października 1994 w Paryżu) – francuski lekkoatleta sprinter i płotkarz, medalista halowych mistrzostw Europy, olimpijczyk.

Specjalizuje się w biegu na 400 metrów i biegu na 400 metrów przez płotki. Odpadł w eliminacjach sztafety 4 × 400 metrów na igrzyskach olimpijskich w 2020 w Tokio.

Zdobył srebrny medal w sztafecie 4 × 400 metrów na halowych mistrzostwach Europy w 2023 w Stambule.

Był wicemistrzem Francji w biegu na 400 metrów przez płotki w 2018 i w biegu na 400 metrów w 2021, a w hali wicemistrzem w biegu na 400 metrów w 2023.

Osiągnięcia

Rekordy życiowe
 bieg na 200 metrów – 21,15 (30 kwietnia 2022, Tucson)
 bieg na 200 metrów (hala) – 21,73 (27 stycznia 2018, Reims)
 bieg na 400 metrów – 46,05 (21 czerwca 2021, Angers)
 bieg na 400 metrów (hala) – 46,28 (19 lutego  2023, Aubière)
 bieg na 400 metrów przez płotki – 49,41 (8 lipca 2018, Albi)

Przypisy

Bibliografia

Francuscy sprinterzy
Francuscy płotkarze
Francuscy olimpijczycy
Lekkoatleci na Letnich Igrzyskach Olimpijskich 2020
Ludzie urodzeni w Paryżu
Urodzeni w 1994


text:
Our Services to Yatris best in the country: Dir Health
By Reader Correspondent on July 16, 2018 Comments Off on Our Services to Yatris best in the country: Dir Health
'Have been able to save lives of hundreds of Yatris'
SHEIKH UZAIR
SRINAGAR: Director General Health Services, Kashmir, Dr Saleem-Ur-Rehman on Saturday said the department is providing state-of-art facilities and services to Amarnath Yatra pilgrims which are "far better than any place in the country".
The Director Health expressed these views while talking to the media persons during a press briefing over the healthcare management during the ongoing Amarnath Yatra at the division of Epidemiology & Public Health, Barzulla Srinagar.
The Department of Health is entrusted with provisioning of health facilities during all pilgrimages and public events and this mandate includes doing the same for the Amarnath Yatra which takes place from the two routes from North (Sonamarg) and South (Pahalgam).
According to the Director, among various other organisations, institutes and departments, the health department has an important role to play during the Yatra period – of providing medical facilities suited for adverse high altitude conditions.
Dr Saleem-Ur-Rehman said the health department has been striving and making all out efforts to keep Yatris in good health en-route and to provide them all necessary medical attention.
"We have state-of-art facilities available at the altitude of almost 12,000 feet and have established medical camps equipped with modern infrastructure and high tech equipment all along the routes," he said. "We have base hospitals at five places along the Yatra routes with facilities like Intensive Care Units, ABG Analyzers and all the highest level of equipment which is available at the other big hospitals."
The Director said they have three-tier healthcare system in place to deliver smooth healthcare facilities. Specialised facilities were set up at strategic locations at Baltal, Chandanwari, Holy Cave, Sheshnag and Panjtarni. "These designated hospitals have the facilities for consultations in medicine, surgery, orthopaedics, cardiology and critical care backed up with all required equipment, diagnostics, nursing and referral facilities," he said.
The second tier of Medical Aid Centres, according to the Director, was created which are manned by trained medical officers and has basic diagnostics and treatment facilities including for the treatment of emergencies. They were set up at 10 locations along both routes focusing on the areas where incidences of morbidity were high, he said.
The third tier of Emergency Aid Centres, Dr Saleem said, were created providing health facility at every 2 kilometres distance along the routes leading to the holy cave which include defibrillators, cardiac monitors, hyperbaric oxygen chambers, pulse oxymeters, automated CPR machines, transport ventilators and portable oxygen concentrators.
Dr Saleem-Ur-Rehman said the doctors and paramedics are vigorously trained in Pahalgam and Baltal before sending them to their posts.
"This has helped in decreasing mortality and morbidity drastically. Our staff is fully trained to handle medical emergencies. We are using HYPO bags (hyperbaric chambers) to transfer critically sick to descending camps and have saved hundreds of lives up there," he said. "We have saved hundreds of lives up there. Only two deaths have occurred this year at our facilities which is very low compared to the causalities of last year."
However, the Director advocated the adoption of minimum fitness protocols for intending Yatris who he said should get Compulsory Health Certificate (CHC) which was made mandatory for registration of any intending pilgrim. He said that people above 50-55 years of age should be fully prepared before embarking the journey and that the cardiac compromised patients should not embark the journey.
The Director thanked the Government of India for providing the additional requirement of doctors and paramedics which were requested by the department.
"The department has full support of the state government and the Amarnath Shrine Board," Dr Saleem-Ur-Rehman said.
Amarnath Yatra, Governor NN Vohra, Governor rule, HEALTHCARE
Our Services to Yatris best in the country: Dir Health added by Reader Correspondent on July 16, 2018
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Height 14 3/4 in. by Width 13 in.
Period frame but not original to painting. The painting has been waxed, relined, and placed on new stretchers. Top of head 1/2 inch by 1/2 inch touch up at edge of head with ground. Left cheek with 1/4 inch touch up at edge of ground. There is a 2 1/2 by 2 1/2 inch area to the right side adjacent to neck and several significant areas of inpainting going into the collar and dress. Right arm with significant inpainting. Frame: Height 20 in. by Width 18 in.