text:
\section{Introduction}

The conventional decision tree  induction is to recursively partition the training set.
During the tree induction, the training set is divided into smaller and smaller subsets according to the test functions of minimum split criteria
until a stopping criterion is reached.
As a result, it can be represented graphically as a tree and we call the terminal subsets leaf nodes.
The terminal/leaf nodes take the mode of its ground truth set as the prediction value.
It is greedy and data-driven.
However, the trained decision tree is always implemented as a collection of `if-else-then' sentences in computer.
In another word, it is rule-based, which makes it friendly for us to understand and interpret.
In contrast, this implementation  is unfriendly for computers to execute.
The duality, greedy data-driven training and hard-coded rule-based implementation, does not occur in other supervised machine learning such as deep learning methods.

To overcome the duality, there are some end-to-end training schemes for decision trees
such as \cite{norouzi2015efficient, kontschieder2015deep, yang2018deep, hehn2019end} instead of the greedy training methods.
Additionally we can vectorize the implementation of decision trees
such as QuickScorer\cite{dato2016fast, lettich2016gpu, lucchese2015quickscorer, lucchese2017quickscorer} and RapidScorer\cite{ye2018rapidscorer}.
These advances drive us to take the advantages of non-greedy training and efficient vectorized implementation in purpose of boosting all the tree-based algorithms.

It is a long history to find more compact and clearer representation of decision trees \cite{brent1991fast}.
In the section 2 of \cite{fridedman1991multivariate}, there is an equivalent model of recursive partitioning in in the form of an
expansion in a set of basis functions (as products of different step functions)
by replacing the geometrical concepts of regions and splitting with the arithmetic notions of adding and multiplying.
And it is to transform each tree into a well-known polynomial form in \cite{kuralenok2019monoforest}.
There are also some schemes to translate the decision trees into neural networks such as \cite{EntropyNet, welbl2014casting, biau2019neural}.
Guang-He Lee and Tommi S. Jaakkola \cite{lee2020oblique} induce oblique decision trees from the derivatives of neural models.
New representation form of the decision trees would bring or require new optimization and implementation methods for decision trees.

Here we show the possibility to reuse the deep learning tool kits to implement the decision trees.
Our main contributions  are:
\begin{itemize}
	\item an algorithm to represent binary trees in analytic form;
	\item a new interpretation of binary decision trees in the error correcting output codes framework;
	\item an approximation of binary decision trees for non-greedy induction in the from of attention mechanism;
	\item a novel learning scheme to unify decision trees, mixture models and attention mechanism.
\end{itemize}

The rest  is organized as follows: section \ref{sec2} introduces the new  conversion and interpretation;
section \ref{sec3} extends decision trees to differentiable trees and connects the binary trees with artificial neural network.
Finally, section \ref{sec4} summarizes future trend and presents our conclusions.

\section{Logical Decision Machines}\label{sec2}

As mentioned before, the decision trees take the mode of the ground truth within each terminal/leaf node as the output prediction.
In another word, it is the terminal/leaf node which the input samples eventually reach that determines the prediction rather than the non-terminal nodes.
Note that the nature of decision tree prediction is tree traversal
thus it is possible to vectorize the prediction if we can navigate the input samples to appropriate terminal/leaf nodes.

The input sample follows a path from the root to the appropriate terminal/leaf node, which we call the decision path to the leaf node.
\begin{quote}\label{theorem_zhang}
Each decision path is equivalent to a sequence of test in decision tree.
\end{quote}

We call the above fact \emph{the zeroth law of decision trees}
and it is so intuitive and obvious that we do not need a word to prove it.

\subsection{Construction of  Logical Decision Machines}
Based on the fact\eqref{theorem_zhang},
we will show how to represent the binary decision trees in the analytic form.
The core idea is that true path is maximum likelihood path over all possible decision paths given an input.
In the rest of section, we will show how to convert the given decision trees to analytic mappings.

We start with the following example.
\begin{figure}[H]
\centering
\includegraphics[width=0.9\textwidth]{trees.png}
\caption{A Binary Decision Tree}
\label{Fig.main1}
\end{figure}

For example, if a sample arrives at the leaf node $v_3$ in \ref{Fig.main1},
it must traverse the first, the second, the fourth and the fifth non-terminal nodes
and it must pass the first and the second tests and fail the fourth and the fifth tests.
Additionally, it does not take the third test for the leaf node $v_3$.
In another word, it is not necessary for the leaf node $v_3$ to know the results of the third test.
There are only 2 results for each test while  3 types of signal for the terminal/leaf nodes as below
\begin{enumerate}
  \item $-1$ to represent the passed tests;
  \item $+1$ to represent the failed tests;
  \item $0$ to represent the absent tests.
\end{enumerate}
For example, it is best to use $(-1, -1, 0, +1, +1)$ to represent the leaf node $v_3$ in \ref{Fig.main1}.

Based on the fact \eqref{theorem_zhang}, each leaf corresponds to a ternary row vector, so-called template vector of the leaf node,
where the positive ones ($+1$) indicate the tests  its travelers must pass;
the negative ones($-1$) indicate the tests its travelers must fail;
the zeroes ($0$) indicate the tests its travelers are absent.
Template matrix $B$ of the binary decision tree consists of the template vectors of the leaf nodes as its row vectors.
Here the travelers of the leaf node $n$ is referred to the input samples which eventually reach the node $n$.
The template vectors are distinct from each other because each decision path is unique in the decision trees.

For simplicity, we firstly  consider the numerical variables to test.
In decision trees, it is only to test if the numerical variables is no greater than some given specific threshold as shown in \eqref{Fig.main1}.
The results of all tests are boolean, i.e., true or false.
We want to replace the test procedure with analytical representation.
The ad hoc choice is the $\operatorname{sgn}(x)$  while  it returns 0 when $x=0$, which contradicts with our boolean result.
We can observe that the signum function $\operatorname{sgn}(x)$ is the subgradient of the absolute value function $|x|$
when $x\not=0$ in $\mathbb{R}$, i.e.,
\begin{equation}\nonumber
\operatorname{sgn}(x)=\partial |x|=\begin{cases}
-1 &\text{if $x<0$}\\
1  &\text{if $x>0$}
\end{cases}.
\end{equation}
Additionally, $0$ belongs to subgradient of absolute value function at $0$.
Thus the $\operatorname{sgn}(x)$ is a special type of subgradient of absolute value function.
In order to  represent the results of passed tests as $-1$s, we take $-1$ to substitute $0$ in $\operatorname{sgn}(x)$ when $x=0$.
Note that it is still a special type of subgradient of absolute value function
so we define a $\operatorname{sgn}(x)$ in our context
  \begin{equation}\label{signum}
  \operatorname{sgn}(x)=\begin{cases}
  -1 &\text{if $x\leq 0$}\\
  1 &\text{if $x>0$}
  \end{cases}.
  \end{equation}

Now suppose that we want to predict the response value of the input $x$, the input $x$ takes a series of successive tests  as a path from the root to the terminal node.
If two inputs reach different leaf nodes, they must take different paths, where there is at least one different results of the tests.
It is the results of all tests rather than the orders of  tests that determine the prediction value of the decision trees for a specific input.
The travelers of a leaf node must share a common sequence of tests and the corresponding results of these tests.

If the input takes all the tests and obtains all the results, it is supposed to follow the `maximum likelihood path'.
The key step is  to match the test result vector $h\in\mathbb{H}$ with the template vector $b^T\in\mathbb{H}$,
where $\mathbb{H}=\{\pm 1, 0\}^{L-1}$.
We must take two numbers into consideration:
(1) the total number of the nonzero elements in template vector $b$ associated with the leaf node and
(2) the total number of test results $h_i$ which agree with the template vector $b$.
We need to count the number of agreements.
Here if $h_i=b_i$, we say they match with each other, i.e., the input sample and the leaf node achieve consensus on the $i$th test.
If these  numbers are equal, it means the input would follow the corresponding path of the template vector $b$ to the leaf node.
In another word, the input samples take all the tests and meet the requirements of the  template vector.
If the template vector match with the result vector in all non-zero position, this template vector corresponds to the maximum likelihood path.
Otherwise, the template vector does not correspond to the maximum likelihood path of the input.

The inner product $\left<h,b^T\right>=b\cdot h$, as a common measure of similarity, does not take the number of the tests into consideration
while the cosine similarity  $\frac{b\cdot h}{\|h\|_2\|b\|_2}$, takes the distances of both vectors into consideration.
We modify the cosine similarity into so-called logical similarity
\begin{equation}\label{zhang_similarity}
LS(b, h)=\frac{b\cdot h}{\|b\|_1}.
\end{equation}
Here note that the $\ell_1$ norm is equal to the $\ell_0$ norm for $h\in\{\pm1\}^{L-1}, b\in\{\pm1, 0\}^{L-1}$.
This logical similarity\eqref{zhang_similarity} is limited in $[-1, 1]$ as the cosine similarity.
And $\frac{\alpha b\cdot  b}{\alpha\|b\|_1}=\frac{\|b\|_2^2}{\|b\|_1}=1$ for any $b\in\mathbb{H}$ and $\alpha>0$;
$\frac{ b\cdot \alpha b}{\|b\|_1}=\frac{-\|b\|_2^2}{\|b\|_1}=-1$ for any $b\in\mathbb{H}$ and $\alpha<0$.
In contrast to symmetric distance, it is asymmetric, i.e., $LS(b, h)\not=LS(h, b)$.

In order to find the maximum likelihood path, it is necessary to compute the `likelihood' of all possible paths.
In another word, we need to compute the logical similarities between the result vector $h$ and the template vectors associated with the leaf nodes.
Then we can find the maximum likelihood path of the input and output the prediction value.

In summary, we can reorganize the binary decision trees as following
\begin{equation}\label{tree}
\begin{split}
    h & = \operatorname{sgn}(Sx-t)), \\
    p & = \operatorname{diag}(\|B_1\|_1,\cdots, \|B_L\|_1)^{-1}Bh, \\
    v[i] & =v[\arg\max{p}],
\end{split}
\end{equation}
where  $\operatorname{diag}(\cdot)$ maps a vector to a diagonal matrix;
the vector $x$ and $t$ are real vectors in $\mathbb{R}^n$;
the matrix $S$ is the selection matrix of the decision tree in $\mathbb{R}^{(L-1)\times  n}$;
the element-wise transformation $\operatorname{sgn}$ is the sign or signum function;
the matrix $B$ is the template matrix of the decision tree in $\{\pm 1, 0\}^{L\times(L-1)}$;
the vector $B_i$ is the $i$th row of the matrix $B$ for $i=1,2,\cdots, L$;
$\|\cdot\|_1$ is the $\ell_1$ norm of real vector, i.e. the sum of absolute values;
the integer $L$ is the total number of terminal/leaf nodes;
the function $\arg\max(x)$ returns the first index of  maximums in the vector $x$,
i.e., $i=\arg\max(\vec{v})=\min\{j\mid \vec{v}_j=\max(\vec{v})\}$;
the output $v[i]$ is the $i$th component of vector $v$ for $i=1,2,\cdots, L$.
In a compact form, the equation\eqref{tree} is re-expressed as
\begin{equation}\label{Tree}
\begin{split}
     i &=\arg\max(\tilde{B}\operatorname{sgn}(\tilde{S}\tilde{x})),\\
     T(x)   & = v[i],
\end{split}
\end{equation}
where $\tilde{B}=\operatorname{diag}(\|B_1\|_1,\cdots, \|B_L\|_1)^{-1}B$;
the augmented matrix $\tilde{S}=[S \,\,\vec{b}]\in\mathbb{R}^{L\times(n+1)}$;
the augmented vector $\tilde{x}=(x^T \,\, -1)^T\in\mathbb{R}^{n+1}$.
We call the new expression of binary decision trees \emph{logical decision machines}.
Note that $\max(\tilde{B}\operatorname{sgn}(\tilde{S}\tilde{x}))=1$
and each row is a unit vector in $\tilde{B}$.

And we can embed the class labels into row vectors to make a value matrix $V$.
We can define the decision trees in a compact form:
\begin{equation}\label{def: one-hot tree}
\begin{split}
      c  & =\arg\max_{h\in\Delta}\left<h,\tilde{B}\operatorname{sgn}(\tilde{S}\tilde{x})\right>,\\
     & T(x) =Vc,
\end{split}
\end{equation}
where $\Delta$ is the probability simplex defined as $\Delta=\{h\mid h>0,h^T\vec{1}=1\}$;
$c$ is a one-hot vector with the element $1$ in the position of maxima, i.e., $c=\text{one-hot}[\arg\max_{i} z]$;
each column of $V$ is the class label embedding vector associated with some terminal leaf for classification.

In order to extend our procedure for categorical variables,
we need more tricks.
The direct one is to use dummy or indicator variable as used in many cases.
The indirect one is to embed the categorical values to real numbers such as the hashing function.
The only test of categorical variable is to judge if it is equal to some value.
And categorical variables are always discrete and of finite values.
For example, assume that the categorical variable is embedded in the finite number set $E=\{e_1,\cdots, e_m\}\subset\mathbb{R}$,
we need a function $\mathbb{I}$ so that $\operatorname{sgn}(\mathbb{I}(x))=-1$ if $x=e$
and $\operatorname{sgn}(\mathbb{I}(x))=1$ if $x\not=e$ where $e\in E$.
Inspired by \cite{O'Sullivan1991multivariate}, we consider the Lagrange polynomial
$L(x;e_i)=\prod_{e_j\not=e_i}\frac{x-e_j}{e_i-e_j}$ for $e_i\in E$.
Thus we define $\mathbb{I}(x) =1- L(x;e_i)$ and get
\begin{equation}\nonumber
\mathbb{I}(x) =1- L(x;e_i)=
     \begin{cases}
     0 &\text{if $x=e_i$}\\
     1 &\text{if $x\not=e_i$}.
     \end{cases}.
\end{equation}
And we can use this technique to deal with each categorical variable in decision trees.

\subsection{An Example of Binary Decision Trees}

Suppose the input variable $x$ has 4 numerical features and
the trained decision tree is as shown in the figure \ref{Fig.main1},
we will take a specific example to show how logical decision machine\eqref{Tree} works.

The threshold vector is $t=(1,4,3,2,5)^T$.
The value vector is  categorical or numerical,
such as $v=(v_1, v_2, v_3, v_4, v_5, v_6)^T$.
The selection matrix $S$ and  bit-vector matrix $B$ is
$$S=\begin{pmatrix}
1 & 0 & 0 & 0\\
0 & 1 & 0 & 0\\
0 & 0 & 1 & 0\\
0 & 1 & 0 & 0\\
0 & 0 & 0 & 1
\end{pmatrix},\quad
B=\begin{pmatrix}
-1 & -1 & 0 & -1 & 0\\
-1 & -1 & 0 & +1 & -1\\
-1 & -1 & 0 & +1 & +1\\
-1 & +1 & 0 & 0 & 0\\
+1 & 0 & -1 & 0 & 0\\
+1 & 0 & +1 & 0 & 0\\
\end{pmatrix},$$
respectively.

Suppose input vector $x=(2,1,2,2)^T$, its prediction is $v_5$ according to the figure \ref{Fig.main1}.
The computation procedure is as following
$$\tilde h=Sx-t=\begin{pmatrix}
1\\ -3\\ -1\\ -1\\ -3
\end{pmatrix},\quad
h=\sigma(\tilde h)=\begin{pmatrix}
+1\\ -1\\ -1\\ -1\\ -1
\end{pmatrix},$$
$$b=\operatorname{diag}(\|B_1\|_1^{-1},\cdots,\|B_L\|_1^{-1})B\operatorname{sgn}(h)=\begin{pmatrix}
\frac{1}{3}\\ 0\\ -\frac{1}{2}\\ 0\\ 1\\0
\end{pmatrix},$$
$$i=\arg\max(b)=5,v[i]=v_5,$$
thus then the output is given by $$T(x)=v[\arg\max(B\,\operatorname{sgn}(Sx-t))]=v_5.$$
Here we do not specify the data types of the elements in the value vector.
For regression, the value vector $v$ is numerical;
for classification, it is categorical \footnotemark.
\footnotetext{See more differences of classification trees and regression trees in \cite{loh2011classification}.}

\subsection{Template Matrix}

The matrix $B$ in \eqref{Tree} is called template matrix which consists of the template vectors of the leaf nodes as its row vectors.
This matrix is related with the structure of decision tree.
The sibling  leaves share the same parent and ancestor nodes
thus their template vectors share the same zero elements
and the results of tests except the one corresponding to their parent node.
From the computation perspective, the difference of sibling template vectors is parallel to certain unit vector(one-hot vector).

The number of non-zeroes in template vector is equal to the depth of the corresponding leaf node to the root plus 1.
And the depth of binary tree is equal to the $\infty$-norm of the template matrix plus 1.
And the following theorem is obvious.
\begin{quote}\label{depth}
	The sum of the binary tree depth  is equal to the trace of the $BB^{T}$ plus the number of leaf nodes.
\end{quote}

Based on the fact that only the sibling terminal nodes share all the tests and  the only different result is returned by their parent node,
We observe some facts on the template  vector:
(1) the template  vectors associated with sibling terminal nodes are linearly independent
even they share the same elements except the one corresponding to their parent node.
(2) the sibling template  vectors are independent of other template  vectors
according to the  nonzero elements  associated with their parent node in the sibling column vectors,
which we cannot combine the zero elements in other  vectors to generate.
The common elements in two template vector correspond  to the common ancients of leaf nodes associated with these vectors.

Another observation is that the root node will test all samples
so that its corresponding results  are not zero in all template vectors.
In another word, there is an column vector without any 0 in the template matrix.
The column vector corresponds to the results, which a nonterminal node returns for all template vectors.
For example, the first column of $B$ in the above subsection corresponds to the test associated with the root node,
which means the test is true for the first four leaves and false for the last two ones.
Thus it implies that the first four leaves belongs to left subtree of the root node and
the last two ones belong to the right subtree of the root node.
Every test will produce two results so each column must have at least one $1$ and $-1$.
In another word, each test must be involved with at least two decision path.
The number of nonzero elements in the column  vectors is the number of decision path associated with the corresponding non-terminal node.
The $-1$ ($1$) of row vector means that leaf is in the left(right) subtree of the corresponding non-terminal node.

Note that the template matrix $B$ is of full column rank in the above subsection.
In another word, the rank of template matrix is equal to the number of nonterminal nodes.
We conjecture that
\begin{quote}\label{rank}
	The template matrix $B$ is of full column rank for any binary decision tree.
\end{quote}
It is to say that we can use basic column operation
to preserve an unique element in each column, which are in different row.
Note that it is equivalent to prove the terminal nodes can be separated by the vertical line across the non-terminal nodes.
In another word, each terminal node is constrained in the cell fenced on the right and left sides.

Based on these observation, it is not too difficult to recover the kinship of all nodes in binary decision methods
when the template matrix is given.

Additionally, we can find the subtree is associated with the  submatrix of the template matrix.
For example, we can find  the template matrix of the left subtree in \ref{Fig.main1} as following
$$\begin{pmatrix}
      -1  & -1 & 0 \\
      -1  & +1 & -1\\
      -1  & +1 & +1\\
      +1  & 0  & 0 \\
\end{pmatrix}.$$

\subsection{Theoretical Interpretation}

Now we prove the correctness of the conversion algorithms \eqref{tree}.
\begin{theorem}\label{correctness}
     The conversion algorithms \eqref{tree} is correct.
\end{theorem}
\begin{proof}
We only need to prove that (1) the true path always obtains the  maximum logical similarity;
(2) the maximum is unique in the vector $p$ in the equation\eqref{tree}.
Here the true path refers to the path which the input sample really follows from the root to the exit leaf node.

The logical similarity \eqref{zhang_similarity} $LS(b, h)$ get the maximum if and only if $(b-h)^Tb=\vec{0}$ for $b,h\in\{\pm 1, 0\}^{L-1}$.
The true path of the input $x$ is the path which $x$ follow from the root node to the exit leaf
thus the binary test in the true path will return the same results as in the true template vector $b(x)$.
Note that the elements $0$es  in the template vector will ignore the tests absent in its decision path
so it is not necessary for the input samples to take the same results of all tests if they reach the same leaf.
In another word, the true template vector $b(x)$ coincide the non-zero  element with the result vector $h$ at the same position,
So the logical similarity between them is equal to 1, i.e. $LS(b(x), h)=\max(\tilde{B}\operatorname{sgn}(\tilde{S}\tilde{y}))=1$.

Every decision node returns the unique result: if it is true, the $-1$ is returned;
if it is false, the $1$ is returned.
And we modified the original  $\operatorname{sgn}$ function to \eqref{signum} in order to meet this requirement.
And the uniqueness of the maxima of vector $p$ is because of the facts
that only the true path share the same results of all binary test in its path.
If the template vector is not the corresponding vector of the maximum likelihood path,
then  at least one result in this path conflicts with the result in the result vector $p$.

The correctness of our procedure is based on above facts.
\end{proof}

We call this \emph{template matching interpretation} of decision trees\eqref{Tree}
because it is to select the prediction value based on similarity between  template vectors of leaf nodes and the tests results of input samples.

In one hand,  if two input samples arrive at the same terminal node,
they must take the same path, i.e., they must take the same sequence of tests and get the same results.
In notation, if two input sample $x, y$ arrive at the same terminal node,
then $\arg\max(\tilde{B}\operatorname{sgn}(\tilde{S}\tilde{x}))=\arg\max(\tilde{B}\operatorname{sgn}(\tilde{S}\tilde{y}))$.
In another hand, if the samples take all the tests and share the same maximum similarity decision path,
they must reach the same leaf associated with maximum likelihood path.
In notation, if $\tilde{B}_{i}\operatorname{sgn}(\tilde{S}\tilde{x})=\tilde{B}_i\operatorname{sgn}(\tilde{S}\tilde{y})=1$,
then two input sample $x, y$ arrive at the same terminal node $i$.

And according to the proof of \ref{correctness}, we can reformulate the \eqref{Tree} as following
\begin{equation}\label{delta}
     \begin{split}
          h &=\tilde{B}\operatorname{sgn}(\tilde{S}\tilde{x}),\\
          T(x)   & = \sum_{i=1}^{L}\delta(1-h_i)v[i],
     \end{split}
\end{equation}
where $\delta(x)=\begin{cases}1 &\text{ if $x=0$} \\ 0 &\text{otherwise}\end{cases}$.

Based on \ref{delta}, we can rewrite the additive models such as \cite{breiman2001random, chen2015xgboost} in analytic form
\begin{equation}\label{forest}
F(x)=\sum_{i=1}^N w_iT_i(x)
\end{equation}
where $w_i\in\mathbb{R}$ and the tree $T_i$ is formulated as \eqref{delta}.
There is another representation of additive trees via block matrix.
For example, suppose we have two decision trees $T(x)$ and ${T}_{\ast}(x)$ as following
\begin{equation}\nonumber
     \begin{split}
          h &=\tilde{B}\operatorname{sgn}(\tilde{S}\tilde{x}),
          T(x)    = \sum_{i=1}^{L}\delta(1-h_i)v[i], \\
          h^{\ast} &=\tilde{B}_{\ast}\operatorname{sgn}(\tilde{S}_{\ast}\tilde{x}),
          {T}_{\ast}(x)    = \sum_{i=1}^{L_{\ast}}\delta(1-\tilde{h}^{\ast}_i)\tilde{v}^{\ast}[i], \\
     \end{split}
\end{equation}
then we can add them as following
\begin{equation}\nonumber
     \begin{split}
          h &=(B\operatorname{sgn}[S\tilde{x})],\\
          {T}_{\ast}(x)   & = \frac{1}{2}\sum_{i=1}^{L}\delta(1-h_i)v[i]+\frac{1}{2}\sum_{i=1+L}^{L+L_{\ast}}\delta(1-\tilde{h}^{\ast}_i)\tilde{v}^{\ast}[i-L] , \\
     \end{split}
\end{equation}
where
$$S=\begin{pmatrix}
     \tilde{S} \\
     \tilde{S}_{\ast}
\end{pmatrix}$$
and
$$B=\begin{pmatrix}
     \tilde{B} & 0 \\
     0 &\tilde{B}_{\ast}
\end{pmatrix}.$$

It is also similar to  the  error correcting output codes (ECOC)\cite{dietterich1994solving, Kong95error-correctingoutput, allwein2001reducing} framework,
which is a powerful tool to deal with multi-class categorization problems.
The basic idea of ternary ECOC is to  associate each class $r$ with a row of a coding matrix $M \in \{-1, 0, +1\}^{k \times \ell}$.
We briefly introduce ECOC in the algorithms\eqref{ECOC}.

\begin{algorithm}[h]\label{ECOC}
	\caption{Ternary Error Correcting Output Codes}
          \begin{enumerate}
          \item  Train the binary classifier $f_s$ for each column $s=1,\cdots, \ell$.
          \item  For training classifier $s$, example labeled $y$ is mapped to $M(y,s)$. Omit examples for which $M(y,s) = 0$.

          \item  Given test example $x$, choose the row $y$ of $M$ that is "closest" to binary predictions $(f_1(x),…, f_{\ell}(x))$
                    according to some distance (e.g. modified Hamming).
          \end{enumerate}
\end{algorithm}

The bitvector corresponds to the error-correcting code $h$ and
the bitvector matrix $B$ corresponds to the error-correcting code matrix $M$.
All intermediate nodes are associated with binary test,
which are parameterized by $S$ and $t$.
And each binary test corresponds to one dichotomizer.
In fact, there is a ternary variant of the error-correcting output codes such as \cite{allwein2001reducing}.
The main difference between \ref{ECOC} and \eqref{Tree} is that the row in the code matrix $M$ corresponds to a specific class
while the row in the template matrix $B$ corresponds to a specific leaf which is attached with label.
In one hand, we can consider our method as another coding strategy of  ternary error-correcting output codes.
In another hand, the coding strategy such as \cite{escalerasergio2010on} will help to find new induction methods of decision tree.

Their main difference is that each class is attached with a single codeword in ECOC
while each class may be associated with multiple leaves in decision trees.

\section{Analytical Decision Machines}\label{sec3}

The operator $\arg\max(\cdot)$ and $\operatorname{sng}$ make the decision trees different from the  differentiable models such as deep neural networks.

In \cite{norouzi2015efficient}, the sign/signum function is formulated as  following:
$$\operatorname{sgn}(\tilde{h})=\arg\max_{h\in\mathbb{H}}\left<h,\tilde{h}\right>\quad \forall \tilde{h}\in\mathbb{R}^{L-1}$$
where $\mathbb{H}$ is  $\{1,-1,0\}^{L-1}$.
And it is obvious that $\operatorname{sgn}(\tilde{h})_i=\frac{(\tilde{h})_i}{|(\tilde{h})_i|}$ except $(\tilde{h})_i=0$
where the number $\operatorname{sgn}(\tilde{h})_i$ is the $i$th component of the real vector $\tilde{h}$
and $|(\tilde{h})_i|$ is the absolute value of $\tilde{h}$.
However, it is not compatible with our definition in \eqref{signum}.
For example, suppose $\tilde{h}=(1,-1, 0)^T$, we will obtain
$$\arg\max_{h\in\mathbb{H}}\left<h,\tilde{h}\right>=\{(1,-1, 0)^T, (1,-1, 1)^T, (1,-1, -1)^T\}$$
where the maximizers are not unique and only the $(1,-1, 0)^T$ is our expected result\footnotemark.
And we formulate the sign/signum function as solution to the following minimization problem
$$\operatorname{sgn}(\tilde{h})=\arg\min_{h\in [-1, 1]^{L-1}}\left<h,\vec{1}\right> \quad
\text{subject to }\quad |\tilde{h}|=\left<h,\tilde{h}\right>,\forall \tilde{h}\in\mathbb{R}^{L-1}.$$
And we can formulate the decision tree in  3-splitting way as following
\begin{equation}\label{def:LPOM}
\begin{split}
T(x) &=Vc,\\
\text{subject to } & c=\arg\max_{h\in\Delta}\left<h,\tilde{B}z\right>,\\
     &z=\operatorname{sgn}(\tilde{S}\tilde{x}).
\end{split}
\end{equation}
Here $\Delta$ is the probability simplex and $\mathbb{H}=\{\pm 1, 0\}^{L-1}$.
Other notations are explained in \ref{def: one-hot tree}.

We formulate the dependence of prediction on binary tests explicitly
\begin{equation}\label{navigation}
T(x)=v f((\tilde{B}\operatorname{sgn}(\tilde{S}\tilde{x})))
\end{equation}
where the mapping $f:\mathbb{R}^L\mapsto\mathbb{H}$ maps its maximum component to $1$ and other components to $0$.
The only non-zero of $f(\cdot)$ is at the index of the selected leaf.
And we can obtain the  upper bound on empirical loss in \cite{norouzi2015efficient}
and use the non-greedy methods therein to train the decision trees.

\footnotetext{As convention, the sign/signum function maps the $0$ to $1$ in artificial neural network community
while the sign function is defined to be $0$ at the original point in mathematics.}

\subsection{Construction of Analytical Decision Machines}

Inspired by the soft decision tree \cite{irsoy2012soft}, a node redirects instances to its children with some confidence calculated by a scoring function.
In another word, we substitute the $\operatorname{sgn}$ with some differentiable functions as the following formula.
\begin{equation}\label{Soft Tree}
   i=\arg\max(\tilde{B}\sigma(\tilde{S}\tilde{x})), T(x)=v[i],
\end{equation}
where $\sigma$ is monotonic, $-\sigma(x)=\sigma(-x)$ and $\lim_{x\to\infty}\sigma(x)=1$.
Note that we can translate any cumulative density function to the scoring function
such as  the hyperbolic tangent function $\sigma(x)=2\frac{1}{1+\exp(-2x)}-1$.

Saturated linear function $\sigma$, an alternative to sign/signum function, is defined as following
\begin{equation}\nonumber
     \sigma(x)=\begin{cases}1, &\text{if $x>\epsilon$}\\
\frac{1}{\epsilon}x, &\text{if $-\epsilon\leq x\leq\epsilon$}\\
-1, &\text{if $x<-\epsilon$}\end{cases},
\end{equation}
and we can obtain
$$\arg\max(\tilde{B}\operatorname{sgn}(\tilde{S}\tilde{x})) = \arg\max(\tilde{B}\sigma(\tilde{S}\tilde{x}))) $$
if each component does not belong to the gap interval$(-\epsilon, \epsilon)$.
Here $\epsilon$ is conventionally set to be $1$ as in \cite{blondel2001stability}.
The gap interval $(-\epsilon, \epsilon)$ makes \eqref{Soft Tree} dfficult to deal with the categorical attributes.
And $\max(\tilde{B}\sigma(\tilde{S}\tilde{x}))\leq 1$ so that we cannot extend \eqref{delta} directly.

Note that in \eqref{Tree} the prediction phase can be regarded as an inner product
$$v[i
=\sum_{n=1}^{L}v[n] \delta_{in}$$
where $\delta_{in}=1$ if $i=n$ otherwise $\delta_{in}=0$.
The operator $\arg\max$ is equivalent to choose an one-hot vector,
and such a vector is only non-zero at the index of the selected leaf.
Here we do not specify the data type or any requirement on the value vector $v$.
The element $v[i]$ can be anything such as function.
Usually it is numerical for regression and categorical/discrete for classification.

In order to make \eqref{Soft Tree} differentiable, we  apply $\operatorname{softmax}$ to approximate the one-hot vector:
\begin{equation}\label{GT2}
 T(x)

      =\sum_{i=1}^{L}e_i v_i.
\end{equation}
Here $(e_1,\cdots,e_L)^T=\operatorname{softmax}(\frac{\tilde{B}\, \sigma(Sx-b)}{\tau})$;
the hyperparameter $\tau>0$  is the temperature parameter.
In another word we use the softmax function as an alternative to the  navigation function in \cite{norouzi2015efficient}.
Additionally, there are a few alternatives of softmax  such as \cite{jang2016categorical,  Sigsoftmax1, laha2018controllable}.

We can regard the representation formulae \eqref{GT2} as the smooth version of \eqref{delta} if we rewrite \eqref{GT2} as following
\begin{equation}\label{smooth delta}
\begin{split}
     \vec p & = \operatorname{softmax}(\frac{\tilde{B}\, \sigma(Sx-b)}{\tau}), \\

     T(x) &=\sum_{i=1}^{L}p_i v[i].
\end{split}
\end{equation}
Here $e_i>0$ and $\sum_{i=1}^L e_i=1$.

\iffalse
\begin{table}  \label{Tab1}

  \caption{Approximation of the Index Finding Function}
  \begin{center}
  \begin{tabular}{p{3cm}|p{7cm}}
  \hline
  Mapping  & Definition \\
  \hline
  \hline

  Softmax\cite{Campbell_onthe} & $\operatorname{softmax}_i(z)=\frac{\exp(z_i)}{\sum_{j}\exp(z_j)}$ \\
  \hline

  Gumbel-softmax\cite{jang2016categorical} & $z=\operatorname{softmax}(\frac{\log(\pi)+g}{\tau})$\\
  \hline

  Weighted softmax\cite{zhang2018weighted} & $\operatorname{softmax}_i(z)=\frac{\alpha_i\exp(z_i)}{\sum_{j}\alpha_j\exp(z_j)}$\\
  \hline
  Smoothed max operator\cite{niculae2017regularized} & $\prod_{f}(z)=\arg\min_{p\in \triangle^{L-1}}p^Tz-\gamma f(p)$\\
  \hline
  Sparsemax\cite{martins2016softmax} & $\operatorname{sparsemax}(z)=\arg\min_{p\in \triangle^{L-1}}\|p-z\|$ \\
  \hline
  Sigsoftmax\cite{Sigsoftmax1} & $\operatorname{Sigsoftmax}_i(z)=\frac{\exp(z_i)\sigma(z_i)}{\sum_{j}\exp(z_j)\sigma(z_j)}$ \\
  \hline
  sparsegen\cite{laha2018controllable} & $\rho(z)=\arg\min_{p\in \triangle^{L-1}}\|p-g(z)\|_2^2-\lambda \|z\|_2^2$\\
  \hline
  $\alpha$-Entmax\cite{correia2019adaptively} & $\alpha-\operatorname{entmax}(z)=[(\alpha-1)z-\tau\vec{1}]_{+}^{\frac{1}{\alpha}-1}$\\

  \hline
  \end{tabular}
  \end{center}
\end{table}
\fi

\subsection{Connection with Attention Mechanism}

We compute the similarities between the hidden vector $\sigma(Sx-b)$ and all template vectors
\begin{equation}\nonumber
\begin{split}
\tilde{B}\, \sigma(Sx-b)) &=\operatorname{diag}(\|B_1\|_1,\cdots, \|B_L\|_1)^{-1}B\, \sigma(Sx-b)) \\
&= (\frac{B_1 h}{\|B_1\|_1}, \cdots, \frac{B_L h}{\|B_L\|_1})^T \\
& = (LS(B_1, h), \cdots, LS(B_L, h))^T
\end{split}
\end{equation}
where $L$ is the number of the leaves;$h=\sigma(Sx-b)$.
Here $LS(\cdot, \cdot)$ is the logical similarity defined in \eqref{zhang_similarity}.

And we find that the decision tree \eqref{Tree} is in the form of hard attention mechanism\cite{xu2015show}.
Generally, the ECOC \ref{ECOC} takes the form of hard attention mechanism.
although the code matrix of ECOC is to design via training diverse classifiers and code matrix is usually  binary or ternary.

And we can reformulate the equation \ref{GT2} in the terms of soft attention mechanism \cite{vaswani2017attention, mino-etal-2017-key}
\begin{equation}\label{def:NN}
\begin{split}
     h    &=\sigma(\tilde{S}\tilde{x}),\\
     T(x) &=\operatorname{Attention}(B, h, v).
\end{split}\end{equation}
Here we adapt the scaled dot-product attention to the logical similarity
$$\operatorname{Attention}(B, h, v)=v\operatorname{softmax}(\tilde{B}\sigma(\tilde{S}\tilde{x})).$$
The first layer is a common fully connected layer with special activation function.
In the terms of attention mechanism,
the hidden vector $h$ is the query, and template vectors $\{B_1,\cdots, B_L\}$ are the keys.
Additionally $v$ is the value vector.
And it is key-value attention.
In this setting, it is exactly a shallow  neural network with attention mechanism.

The expression \eqref{def:NN} describe the logical decision trees \eqref{def: one-hot tree}
if we set $\sigma=\operatorname{sgn}$ and substitute the attention with the hard attention\cite{serra2018overcoming}.
The logical decision machines \ref{sec2}  are the exact translation of decision trees
while soft attention mechanism\eqref{def:NN} is an approximation and generalization framework of decision trees.
All the operators are common in deep learning such as matrix multiplication and softmax.
We call those models `analytic decision machines' because we describe the decision tree in the analytic way.
Analytic decision machines are continuous so it is not suitable to the categorical features/attributes.
And we can take advantages of the mature software infrastructure to implement  decision machines at large scale.
As a cost, we cannot interpret the analytic decision machines in the ECOC framework.

The representation \eqref{def:NN} is `mixed-precision'
because only $B$ is 0-1 valued\footnotemark and the rest are real.
\footnotetext{In a vanilla binary decision tree, the selection matrix is also 0-1 valued.
Here we focus on oblique/multivariate decision trees.}

The work \cite{vaswani2017attention} inspires diverse variants of attention mechanism via modifying  $\operatorname{softmax}$ such as \cite{malaviya2018sparse, zhang2018weighted, niculae2017regularized, martins2016softmax,  correia2019adaptively}.
So that we can use these variants to replace the  $\operatorname{softmax}$ in \ref{GT2}.
Note that we use $\operatorname{softmax}$ to approximate the one-hot vector so we prefer the sparse alternatives to $\operatorname{softmax}$.
And  a generalized attention equation is proposed in \cite{katharopoulos_et_al_2020} for any similarity function as following
\begin{equation}\label{alg_attention}
     Attention(q, K, V)=\sum_{i=1}^n \frac{sim(K_i, q)}{\sum_{i=1}^n sim(K_i, q)}V_i.
\end{equation}
Thus we say that the decision machines belong to generalized attention  mechanism.

\subsection{Extension of Decision Machines}

The large scale piece-wise linear model or mixed logistic regression in \cite{gai2017learning} is also interpreted as generalized attention mechanism:
\begin{equation}\label{mlr}
\begin{split}
     f(x) &=\left<g(Mx),\operatorname{softmax}(Wx)\right>\\
          &=\sum_{i=1}^m\frac{\exp(\left< W_j^T, x\right>)}{\sum_{j=1}^m \exp(\left< W_j^T, x\right>)}g_i(x)
\end{split}\end{equation}
where $g=\sigma(Mx)$, $g_i=\sigma(M_i x)$ and $\sigma$ is the element-wise sigmoid function.
And $\left< W_j^T, x\right>$ is the inner product.
Here the value term, query term and key term is $g$, $x$, $W$, respectively.
Note that the value term $h$ is the generalized linear model with the respect to the input $x$.

And its counterpart of decision trees is the generalized linear model trees in \cite{seibold2018generalised}
where each leaf is associated with a generalized linear model rather than a constant.
In the framework of \eqref{Tree}, we can formulate the generalized linear model trees as following
\begin{equation}\label{glmt}
     \begin{split}
          i &=\arg\max(\tilde{B}\operatorname{sgn}(\tilde{S}\tilde{x})),\\
          T(x)   & = g_i(x),
     \end{split}
\end{equation}
where $g_i$ is a generalized linear model.
And we can approximate the \eqref{glmt} in the framework of analytic decision machines \eqref{GT2}
\begin{equation}\label{sglmt}
     T(x)  = \sum_{j} \frac{\exp(\tilde{B}_j\, \sigma(Sx-b))}{\sum_{i} \exp(\tilde{B}_j\, \sigma(Sx-b))} g_j(x)
\end{equation}
where $g_j(x)$ is the generalized linear model associated with the leaf $j$ and $\sigma$ is the modified sign function \eqref{signum}.

Both methods  \eqref{sglmt} and \eqref{mlr} share the selection and prediction procedure.
Its belief is that distinct partition corresponds to different models
and each model only approximates the global true model in a local region.
In the selection stage, we compute weights for different models via softmax regression.
Then the prediction models vote for the final result with the weights in the selection stage.
They are conditional aggregation and  mixture models.
In the term of \eqref{alg_attention}, they choose different similarities in the selection stage.

If the model $g_i$ is the Gaussian distribution function, then we derive the mixture density network \cite{bishop1994mixture}.

Combining the advantages of these methods, we derive the selection-prediction model
\begin{equation}\label{spt}
     T(x)=\sum_{i=1}^n \frac{sim(W_j, f(x))}{\sum_{j=1}^n sim(W_j, f(x))}g_i(x),
\end{equation}
where $g_i$ is the prediction formula and the similarity function $sim(\cdot, \cdot)$ is always non-negative.
Clearly it is a  weighted linear combination of diverse models.
And for different tasks, we can find the proper prediction formula $g_i$ for the samples clustered at the leaf $i$.

Based on above equation, we can unify ECOC\eqref{ECOC}, generalized attention\eqref{alg_attention}, mixed logitisc model \eqref{mlr}, decision machines\eqref{glmt}, mixture density network \cite{bishop1994mixture}.
As an example, we can rewrite the logical decision machine \ref{delta}
\begin{equation} \nonumber
     \begin{split}
          h &=\tilde{B}\operatorname{sgn}(\tilde{S}\tilde{x}),\\
          T(x)   & = \sum_{i=1}^{L}\frac{\delta(1-h_i)}{\sum_{j=1}^{L}\delta(1-h_j)}v[i],
     \end{split}
\end{equation}
where the notations share with the \ref{delta}.
Here the $sim(\cdot, \cdot)$ is defined in implicit way:  $sim(x, B_i)=\delta(1-B_i\operatorname{sgn}(\tilde{S}\tilde{x}))$.

And we can use other similarity function $sim(\cdot, \cdot)$ as an alternative to the Dirac delta function.
For example, we can extend the \eqref{mlr} in the selection-prediction framework
\begin{equation}\label{elr}
     y(x)=\sum_{i=1}^n\frac{\exp(-\frac{\|x-W_i\|^2}{\tau})}{\sum_{j=1}^n \exp(-\frac{\|x-W_j\|^2}{\tau})} g_i(x)
\end{equation}
where $\tau>0$ and $g(\cdot)$ is a generalized linear model or generalized additive model.

\subsection{Decision Machines as Mixtures of Experts}

Decision trees are viewed as a model combination method \cite{PRML2006} in a descriptive way.
Here we clarify this statement in an analytic way.
In fact, ECOC is always as an ensemble methods to combine classifiers.
In the term of model combination, the logical decision machine is exactly the model selection;
the analytic decision machine belongs to the model averaging.
In the perspective of model selection, we define the logical similarity\eqref{zhang_similarity} as the model selection criteria in \eqref{Tree}.
We encode the partitioning or the sequential decision in the selection matrix.
And the extension of decision machines above are a weighted sum of different models.
The extended scheme \ref{spt} is a mixtures-of-experts,
which is closer to  model averaging than the hierarchical mixtures of experts \cite{jordan1994hierarchical, bishop2002bayesian}.

Here we derive the mixtures of experts \cite{6215056} as an extension of decision trees.
In fact they have the common basic idea -- divide-and-conquer principle.
The model averaging is the generalization of the mixtures-of-experts.
Generally model averaging is to aimed to handle the uncertainty of models
while decision machines are originally designed as an analytic representation form of decision trees.

So the formulation \ref{spt} is a simple framework to unify decision machines, attention mechanism, model averaging and model selection.
We can invent different scheme to mix the models by taking different similarity function.
The component $g_i(\cdot)$ in \ref{spt} is designed according to the learning tasks.
This interpretation of decision trees helps us to extend it to learn more tasks other than regression and classification.
And it also helps us to combine the ensemble learning methods.

\section{Discussion and Conclusion}\label{sec4}

We represent the binary decision tree in an analytic form \eqref{tree}, \eqref{Tree}.
We illustrate this representation with a concrete example and explore some intrinsic properties in theory.
Then  we prove the equivalence of binary decision trees and two-layer networks with sign activation function \ref{correctness}.
As a byproduct we find that binary decision tree share the implementation approach with the ECOC framework.
Based on the proof of \ref{correctness} we represent the additive trees in analytic form \eqref{forest}.
By explicitly formulating the decision tree, we can obtain the  upper bound on empirical loss proved in \cite{norouzi2015efficient}.

In order to make decision trees continuous we modify the logical decision machines\eqref{tree}, \eqref{Tree} via softening the $\operatorname{sgn}$ and $\arg\max$ in \eqref{tree}.
And we find that the analytic decision machines \eqref{Soft Tree} \eqref{GT2} are  related with generalized attention mechanism\ref{alg_attention}.
And in the term of attention mathematics, we extend the value terms into generalized linear/additive models.
We propose the selection-prediction scheme\eqref{spt} to unify analytic decision machines\eqref{def:NN}, generalized attention mechanism \ref{alg_attention},
mixed logistic regression \cite{gai2017learning} and mixture density network \cite{bishop1994mixture}.

It is hard for the analytic decision trees to deal with the categorical attribute and missing or incomplete data.

The future trends are to find more robust and efficient implementation of decision trees.
As shown the analytic form of decision trees may help to apply regularization techniques
and mixed integer programming to tree construction.
It also provides some insights on the interpretation of deep learning models.

\bibliographystyle{plain}

redpajama_set_name: RedPajamaArXiv


text:
Q: Developing a Home Server - Install full-blown Ubuntu on Laptop or Ubuntu Server I want to "develop" a Home Server for Web Developement and other network stuff, for that i want reporpuse my old Laptop as Server machine. Now i want to ask if you recommend to install full-blown Ubuntu or Ubuntu Server ?
I am asking this, because i don't see the graphical interface as an advantage, as i will SSH into the machine.
Are there other major differences between the two version.
And by the way i can operate with both versions.
Ps This is only temporary, because later this year i will build a raspberry pi (Zero Maybe?) Cluster, but until then i want to "construct" the server enviroment.

A: Unlike most Linux distros Ubuntu is unusual in that there are versions or editions that are technically entirely different distros like Kubuntu. However this is not the case with Ubuntu Server which is more or less a repackaging of Ubuntu.
Ubuntu Server uses a different installer but uses the same repositories as Ubuntu and can easily be converted to a Ubuntu desktop by installing packages.
Incidentally going from Ubuntu to Ubuntu server wouldn't be as easy as it involves removing lots of packages.
Installing a distro like Debian for example however gives you the option in the installer to add features like servers and desktop environments that are all selectable. I mention that because not all distros take the approch of having "editions."
The Ubuntu Server edition is also commercially supported on certain VPS services while Ubuntu may not.

A: If you are sure you want to go headless (no graphical UI, no Desktop) then definitely use the server version. There'a also a server (minimal) version for the Raspberry Pi.
The server version does not install GUI-Apps like Editors that require a user interface to work, and also does not install X11 and its dependencies.
On a Raspberry Pi, I once uninstalled all UI-related stuff (I think in Feb.2015 there was no server/minimal version avaliable). The SD-card was initially 94% full, after deleting all X11-stuff it was 41% full (apt-get remove --auto-remove --purge libx11-.*). Too bad I don't remember the size of the card, I guess it was 2GB, the default image size. There are also X11-related processes running in the background which you will never use when only using SSH.

redpajama_set_name: RedPajamaStackExchange


The blessings of salvation are made free to all by the Gospel of Christ. The cost of salvation is all on God's side. That cost includes the sufferings of Jesus, who "tasted death for every man" (Hebrews 2:9). "But of him are ye in Christ Jesus, who of God is made unto us wisdom, and righteousness, and sanctification, and redemption" (I Corinthians 1:30).
The Great Commission, Matthew 28:18-20, demands a belief that all can be saved.
I. LET IT FIRST BE UNDERSTOOD THAT ALL MEN NEED GOD'S SALVATION.
To believe otherwise is to charge God with foolishness.
How else can the suffering of Jesus and the death of the cross be explained? (Romans 3:23; 6:23).
II. GOD OFFERS SALVATION TO ALL MEN -none are excluded.
"And it shall come to pass, that whosoever shall call on the name of the Lord shall be saved" (Acts 2:21 and Acts 17:30).
III. IT IS THE DUTY OF MAN TO ACCEPT THE BLESSINGS OF THE GOSPEL OF FAITH.
1. Jesus is a provisional Saviour to all men, and a special Saviour to all them that believe (I Timothy 4:10).
2. God is no respecter of persons (Romans 2:11).
3. Jesus is the only satisfier of Divine justice for men. "And he is the propitiation for our sins: and not for our's only, but also for the sins of the whole world" (I John 2:2; Romans 3:26).
4. Nothing prevents the salvation of the greatest sinner on earth but his own inherent depravity and rejection of the Gospel of Christ (John 5:40).
IV. WHAT IS THE GOSPEL?
The Gospel is not the Word of God. The Word of God sets forth the Gospel. I Corinthians 15:1-4 tells what the Gospel is.
V. WHAT IS FAITH IN JESUS?
1. It is not an historical faith. "Thou believest that there is one God; thou doest well: the devils also believe and tremble" (James 2:19).
2. It is a trusting faith (Ephesians 1:11-14).
3. It is a receiving of Jesus Christ for what He is (John 1:11,12).


text:
Posik: Hillary's Exploitation of Maine
Jacob Posik
When you're a conceited, self-centered elitist like Hillary Clinton, you often believe you can sidestep the rules of law.
Take no surprise then, in what the Clinton campaign is doing in states like Maine to funnel out-of-state funds back into the Democratic National Committee (DNC) and her presidential campaign.
The Hillary Victory Fund (HVF) is a joint fundraising committee composed of 33 state Democratic parties, Clinton's campaign, and the DNC. The HVF receives large individual contributions from out-of-state donors and sends them back to the DNC, circumventing campaign contribution limitations.
According to this Pine Tree Watchdog article, as a state party accepting donations through the HVF, Maine's Democratic Party received $93,552 from 14 out-of-state donors alone. Six of those 14 donors gave the maximum state party contribution of $10,000.
Some of the donors to Maine's HVF include sugar tycoons, entertainment moguls, and hotel heirs. In October and November of 2015, the HVF made two transfers totaling $39,000 to the Maine Democratic Party. In less than 48 hours, that money was then wired to the DNC.
Maine isn't the only state to fall victim to the Clinton campaign's efforts to maximize campaign contributions. Alaska's Democratic Party accepted $43,500 in donations through their state's HVF. Not so coincidentally, the party then transferred all of those contributions back to the DNC as well.
The same party that preached for the need of transparency in campaign finance laws in November is using out-of-state-donors, who have more than likely maxed out their individual contribution limits in other states, to funnel money through Maine's version of the joint fundraising committee and back to the DNC.
This flies in the face of everything the Maine Democratic Party supposedly stands for, but perhaps just association with someone of the surname "Clinton" exempts you from upholding any of your moral obligations.
Usually, joint fundraising committees are established after a party has selected its nominee. Both President Obama and Mitt Romney created joint fundraising committees after earning their respective party nominations in 2012. Without even receiving the Democratic nomination, the Clinton campaign has already shown that it's dedicated to getting the dirty money flowing early and often for the 2016 presidential election.
Jeremy Kennedy, Executive Director of the Maine Democratic Party, told Pine Tree Watchdog, "The money we raise for those campaigns is in hopes of making the state of Maine the best place to live for our families."
It's weird, Mr. Kennedy, how the money you're "raising" is coming from wealthy, out-of-state donors. It's also strange how, according to your interpretation, this dirty, out-of-state money makes Maine "the best place to live for our families."
That's not the only controversy the Clinton campaign created in Maine last week. Supposedly offered as a community service opportunity, students at Marshwood High School in South Berwick received emails from the Clinton campaign, urging them to sign up for positions as unpaid fellows for "Hillary for New Hampshire." The emails were sent without parents' knowledge or consent. Students are required to complete 50 hours of community service at Marshwood in order to graduate.
Tim and Elita Galvin were furious that their son was being targeted by the campaign at school, especially without the school making the opportunity known to parents beforehand. After Superintendent Mary Nash heard of the complaint, she reviewed her school board's policies to find that it does prohibit this type of solicitation to students.
"I immediately convened an investigation where I first reviewed the Board's policies regarding the acceptable (and prohibited) uses of the district's computers and internet/email services and found that the Board's policy titled Employee Computer and Internet Use Rules are very clear and they strictly prohibit: "Any use as a forum for communicating by email or any other medium with other school users or outside parties to solicit, proselytize, advocate or communicate the views of an individual or non-school-sponsored organization; to solicit membership in or support of any non-school-sponsored organization; or to raise funds for any non-school sponsored purpose whether profit or not-for-profit," Nash wrote in a letter on the school district's website.
She also added that similar opportunities to work on campaigns have been offered in the past, but parents were given additional information about the opportunities in those instances.
It's not surprising that this was passed along to students without the knowledge or consent of parents, as the world of academia has long been in the back pocket of the Democratic Party.
What we've learned about Clinton's involvement with our state in the last week is quite clear: We are little more to her campaign than an additional source of income to be exploited by weakened campaign finance laws, and that her above-the-law persona has carried itself all the way to our public school systems.
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About Jacob Posik
Jacob Posik, of Turner, is the director of communications at The Maine Heritage Policy Center (MHPC) and the editor of The Maine Wire. He formerly served as a policy analyst at MHPC. Posik can be reached at jposik@mainepolicy.org.
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Clinton's Pattern of Dishonesty is Alarming

redpajama_set_name: RedPajamaCommonCrawl


Larry Mullen, Head Composter, Saskatchewan Waste Reduction Council, will be hosting a composting and soil quality workshop from 6:30-7:30 pm, August 11, 13, and 14 at CHEP's Railside Community Garden at 222 Avenue K South. The garden employs drip irrigation and various composting methods.
Ken Compton, local wind and solar installer, will answer questions about solar voltaic energy systems for home, business, and co-housing ventures at 7 pm, August 20, at Nature's Best, Regina (co-hosted by Nature's Best and Prairie Spruce Commons).
Nature Regina and the Lumsden Valley Community Association will be hosting Nature Saskatchewan's Fall Meet on September 19 and 20, 2014. The meeting will feature Friday evening at the Royal Saskatchewan Museum and Saturday field trips to Nature Conservancy of Canada sites in the Qu'Appelle Valley.
The Saskatchewan Environmental Society is holding their 9th annual fundraising dinner on September 27 at the Saskatoon Club. The Sustainable Gourmet dinner features local food prepared by local chefs.
David Suzuki will be in Saskatoon (October 26) and Regina (October 27) as part of the Blue Dot tour. Check out the Blue Dot website for more information.
Brie Bennett is offering a closer look at environmental sustainability in Regina on her Green Guerrilla website. Brie is the Waste Minimization Specialist for the City of Regina and a graduate of the School of Environment and Sustainability.
Looking for art supplies? Why not check out the Alt Art Depot, an alternative art supply and materials shop that supports upcycled art with recycled materials.


2013 Jeep Wrangler Sport - Meyer Drive Pro 6' 8"
This is a 2013 Jeep Wrangler Sport we installed a Meyer Drive Pro 6' 8" plow on. We also did an EZ Plus conversion from the standard Meyer Single Pull design. This was to make it easier for the customer to mount and dismount. Nice little Jeep with soft top and sliding windows in the doors. Never saw these on a Wrangler before.
Bumper and grille removed. Opening the hood to rest on the windshield frame makes things MUCH easier.
Watch the window washer hose, it may need more slack to open that far, just unclip it and move it.
This is a stock 2013 Jeep Wrangler JK Sport. The lowest point of the mount is about 9.5" to the ground. The notch in the Clevis is at 10-3/4" which is perfect.
Meyer says 9.5" for the notch in the Clevis, but around 11" is perfect.
This is the measurement from the ground to the bottom of the frame of a stock 2013 Jeep Wrangler JK Sport. It is about 22-3/4".
From this we get that it is about 10-3/4" to the notch in the 19836 Drive Pro Universal Clevis, and it is about 10" from the notch to the bottom of the 2013 Wrangler JK frame. IF I used a 19943 1/2 ton Universal Drive Pro Clevis, it would be 2" lower. Hopefully this helps someone with a lifted Wrangler JK understand how to get 2" of drop.
As I mentioned above, this Meyer Drive Pro 6'8" was converted from a Single Pull to an EZ Plus. This eliminates the cross bar that connects the two pins of the Single Pull, which can make mounting and dismounting the plow harder. Espeically if the notch in the Drive Pro Universal Clevis was a little lower. The cross bar would hit the Drive Pro Universal Clevis and unlock the pins making it impossible to get it on the Wrangler JK without a fight, EVERY time.
Bumper back on. 1 Piece Plug mounted on custom bracket.


At IMAOG, our friendly, professional staff is ready to help you meet all of your healthcare needs. Our board certified physicians can assist you in overall health maintenance as well as more complicated medical issues.PREVENTION is the best prescription for overall good health.
Located in the heart of the Gastonia medical community Internal Medicine Associates of Gastonia cares about our citizens. Whether you prefer a male or female healthcare provider, we have got you covered. Dr. Jaime Villarreal and Dr. Kelly Shedd are accepting new patients at this time. Your appointment is just a phone call away.
In the event of inclement weather, please tune into WBTV for weather related closings or delays.


The Health Transformation Learning Laboratory is a collaboration of the National Maternal and Child Health Workforce Development Center at UNC Chapel Hill (the Center) and the MCH Navigator; it serves as a repository for universal training resources/online learning materials in support of the Center's activities.
The Center currently focuses on three main topics: Change Management and Adaptive Leadership, Evidence-Based Decision Making, and Systems Integration. In addition, the Center has developed a number of learning resources focused on topics during its first funding cycle (2013 - 2016) that include Access to Care and Quality Improvement. In addition, the Center offers a Pipeline Program to enhance training and networking opportunities for graduate and undergraduate students and promotes Family Engagement and Health Equity in all of its activities.
Visit the Health Transformation Learning Laboratory.
Mallorie McKinnon, UF PPC Nursing Trainee: "Being a UF PPC trainee has allowed me to learn not only the importance of patient and family centered care, but also how to advocate for and apply it in my own clinical nursing practice. Working with my fellow PPC trainees, I have come to better understand the benefits of interdisciplinary collaboration and communication within both outpatient and inpatient settings to provide superior care to our pediatric patients. It has been a pleasure learning from such an enthusiastic and knowledgeable faculty, knowing that they are passionate about their work and their responsibilities within the PPC, making them a wonderful sounding board for difficult decisions and an advisor to turn to in times of need."
Taylor Gonzalez, Nardley Docteur, Sonnie Mayewski, UF PPC Social Work Trainees: "As social work trainees, being a part of the interdisciplinary team has given us the opportunity to learn from other disciplines and in doing so, provide the best and most comprehensive care to our patients. We have experienced that attending to various aspects of an individual's functioning improves health outcomes. We believe that our discussions in Core Curriculum meetings have helped us become stronger leaders and communicators outside of this traineeship as well as helped us become better members of the PPC team. This opportunity has allowed us to be immersed in the pediatric healthcare setting while having the resources of fellow trainees and professionals. Having had the experience of being PPC trainees will guide and strengthen our future practice as social workers. We have grown into practitioners who effectively collaborate with numerous team members from a variety of disciplines, sharing ideas and increasing knowledge."
Parent Attitudes Toward Enhancing Cognition and Clinical Research Trials in Down Syndrome - This research project is an exploratory study which focuses on understanding parent attitudes towards scientific efforts such as the use of drug therapies that target intellectual functioning and cognition in individuals with Down syndrome. We expect there to be many factors that influence the range of these attitudes and interest in clinical drug trials, and hope to gain insight on the complexities associated with this decision-making process. The goal of this project is to delineate family attitudes regarding clinical trials in order to inform and advance the development and trajectory of treatments for Down syndrome in a way that is consistent with parent values. The project will continue after the 2016-2017 LEND program is over, with data collection, analyzation, and manuscript write-up continuing throughout the summer.
There is a paucity of research relating to parent opinions on ameliorating or treating certain symptoms associated with developmental disabilities, such as cognitive impairment. Little is known about the factors that contribute to a parent deciding whether treatments such as medication to "cure" their child's disability are warranted, and the ethical and personal concerns pertaining to those perspectives and opinions. Multidisciplinary collaboration in both clinical and research work within the field of neurodevelopmental and related disabilities is imperative; this cooperative framework allows for a better understanding of the issues and treatment of the individual. Throughout LEND, I have learned the importance of continuing to act as an ally and advocate for individuals with disabilities, and to continue learning about the clinical, research, and policy work being conducted in this area.
Community Based Organizations Somali Development Center - At the Somali Development Center, I did a variety of legal work and assistance, as well as some other work for the organization. I was able to figure out legal issues from loan forgiveness to a cease and desist letter for a patent infringement. These are opportunities that are truly not available to many law students and I feel fortunate to have been able to experience this. I also helped produce a grant proposal that the SDC will be using to show the need for Congressional funding. I loved working at the SDC and look forward to helping there in the future.
I learnt the value of offering your time to an organization who truly needs it. It was very rewarding to help the Somali and African refugee community at the SDC.
Community Based Organizations Somali Development Center - Throughout the year, I had the pleasure of volunteering with Partners for Youth with Disabilities (PYD) in their Access to Theatre program. The program included weekly acting classes that provided children and adolescents with the opportunity to develop skills in teamwork, selfexpression, and creativity. The participants, who have a myriad of disabilities, absolutely thrived in this setting, which was beautifully adapted to meet their needs. Each week, I was so impressed by the ideas and interactions of these participants. I always left with a smile on my face and cannot wait to continue my involvement with this organization in the future.
LEND completely changed my life in so many ways. First, through the weekly seminars, I learned a great deal about services, health policy, cultural competencies, and other issues related to Developmental Disabilities (DD). Second, because my colleagues hail from various disciplines, I gained a global understanding of the diverse resources available to individuals with DD and their families. Third, through the Disability Policy Seminar experience, I developed competency in advocacy at a political level and realized how powerful conversations with legislators can be. Finally, LEND has not only given me a new network of colleagues, but it has also given me a new group of best friends. The people that I have met through LEND are some of the most wonderful, compassionate, and enthusiastic professionals that I have ever met. I will always be thankful for what I have learned from them.
Partners for Youth with Disabilities (PYD) – Helped organize a sensory friendly Santa event at the Prudential Center, worked with children to make holiday cards for veterans, and worked on fundraising for the annual party for PYD.
Research - Practical Aspects and Implications of Variant Interpretation in the Clinical Setting investigated the implications of genetic variant interpretation and review in pediatric and oncology clinical settings to better understand the impact on medical management of patients.
Clinical - Genetic counseling intern at Seattle Children's Hospital (general pediatrics and pediatric oncology), Boston Medical Center (in oncology and prenatal settings), and Beth Israel Deaconess medical center (in the center for Maternal-Fetal Medicine).
My time at LEND has been an invaluable experience. It has expanded my understanding of the disability community and allowed me to become a stronger advocate for my patients and families. It has also highlighted the effectiveness of an interdisciplinary team and helped me understand how my role as a genetic counselor fits in. I've not only made some wonderful connections within the medical field, but developed lifelong friendships with all of the fellows! I couldn't be more thankful to have had this opportunity.
Birth to Three Family Center, Ipswich, Massachusetts - Attended playgroups of children ages 0 - 5 years old, developed and presented a parent training entitled, "Letting Go of Their Little Hand: Preschool A Child's First Step Towards Independence." This presentation was geared towards parents of rising three-year-olds both transitioning from Early Intervention services and typically developing children.
Before LEND, as a mother of a child with communication, neurological, and learning disabilities, as well as, using my education background as a special education advocate and educational consultant, I was doing my part to help families on their respective IEP/504 journeys. In many cases, I was learning as I was navigating the school systems and doing my best to learn about Medicaid, DDS, DMH, etc. as needed. Throughout LEND, my understanding of these programs has broadened to a deep understanding about referral, applications, and processes. I learned of DPH programs that I did not know existed and can directly benefit my family and clients. I have already connected two families with MASSSTART. Being a LEND fellow has given me critical information that will directly impact families in the community and has helped me to form a network of professionals that I will rely on in the future and I hope will rely on me if I can help them in any way.
Upon learning that BookShare, a program for individuals with print disabilities was a proposed federal budget cut, began to focus my efforts at the Disability Policy Seminar and beyond to advocate to save this invaluable program. This included speaking to staffers from Massachusetts Congress members and attending local town hall meetings.
Residency - My involvement in the Boston Children's LEND program has been in collaboration with the Boston Children's Hospital's Occupational Therapy Residency program and places my participation throughout this year within the clinical track. The residency program is approved and supported by the American Occupational Therapy Associated and is detailed as an opportunity for advanced post-professional clinical experience, designed to develop clinical experts and leaders in specific areas of occupational therapy practice. The Boston Children's Hospital's OT Residency is specific to pediatric practice and has been an incredible experience for both my professional and personal development. The program, which I began in September 2016, is an eleven-month opportunity organized by a 5-module rotation. Upon completion, I will have spent time in each setting of BCH occupational therapy inclusive of inpatient, outpatient, early intervention, augmentative communication/assistive technology, psychiatry, and pain rehabilitation. I have had the distinct pleasure and incredible fortune to work with and learn from esteemed mentors and leaders in order to advance my clinical skills and my ability to provide collaborative and all-inclusive care to the complex and unique children we see in practice at BCH.
The LEND program has been an invaluable compliment to my clinical work as the occupational therapy resident. The ability to work within an interdisciplinary team of enthused, motivated and talented individuals has facilitated a degree of vigor in my practice and opened lines of communication that will undoubtedly foster ongoing collaboration in the future. It has been a pleasure to return to a learning environment each Friday and to then implement new knowledge into my practice throughout the week. I recognize now, the power of the the Association of University Centers on Disabilities (AUCD) and University Centers for Excellence in Developmental Disabilities Education, Research, and Service (UCEDD) and how huge a difference a group of dedicated professionals can make for the children we work with. My clinical practice, research efforts, advocacy experience and community engagement across this year within the residency and LEND have taken my work to the next level and will continue to shape what I do and how I work for the rest of my career.
Third year UCSD DBP Fellow Dr. Sai Iyer is highlighted in Pediatric News for her research on the 10-item Early Literacy Assessment Tool (ELSAT), which is used to screen preschool children for delayed literacy skills.
I recently had the privilege of connecting with many other MCH trainees and former trainees at this year's Making Lifelong Connections (MLC) Meeting. I had the opportunity to attend the conference as a member of a team from the Trainee Ambassador Group that is working on a new trainee mentoring initiative. I must admit that I was not sure what to expect going in to the meeting, but after experiencing the event, I was inspired to comment on how meaningful it proved to be for me as a Developmental Pediatrician in training.
Prior to the MLC meeting, I did not have a full understanding of the different MCHB trainee programs or their various attributes. While at MLC, I had the chance to meet others in each of the training programs, to better understand our respective roles, and to consider how we can work together as an interdisciplinary force for maternal and child health. I heard about creative projects being completed by my colleagues, which led to the generation of new ideas that I could take back to my home program.
Getting the opportunity to consider issues alongside peers from different disciplines pushes one to think creatively and often introduces a new perspective. This can prove to be invaluable, and as one who practices medicine, I found that hearing from my colleagues outside of my specific discipline led me to consider approaches to problems or ideas that were "outside of the box." As I sat down at tables next to my peers, I discovered that, while our day to day schedules may look completely different, we were all working toward a common purpose, and this was extremely encouraging.


Hello, bookish creatures! Welcome to my stop on the blog tour for Paranoia by J.R. Johansson, the sequel to Insomnia! Jenn and I put together a very, er, interesting post for you today, plus there's all the info on the books, where you can stalk find Jenn, and there's a giveaway. Really, if you miss out on the all awesome in this post, then you're going to feel at least a little bit paranoid. So give yourself some insomnia and check all this out!
When I hosted Jenn last year for Insomnia's blog tour, I wanted to do something a bit different for the post. What that ended up being was a dream sequence that we made up, and it was really fun to do! This year, Jenn wanted to do something kind of similar, so this time we did a paranoia sequence. Or something like that. Really, this is something you just have to read for yourself (I'm not even kidding), so read away!
Rachel: You're on your way to the bookstore to see Paranoia on shelves for the first time (woohoo!). But oops, you step on a crack in the sidewalk. What happens?
Jenn: I realize that it isn't really a crack, but a long line of deadly spiders. And now I've squished some of them and they're angry and start swarming up my pant leg...now what?
Jenn: So I pick up a set of striped balls from a nearby table and remind myself to thank my mom later for signing me up for juggling lessons when I was twelve. Dodging left and right, I try not to look any clown directly in their creepy faces before I can escape out through a nearby doorway...but then I find myself stuck in one of those bizarre mirrored funhouses.
Rachel: In the mirrored not-so-fun house, your appearance changes. (And at one point you may look like Miley Cyrus, which is so totally weird.) But then you find a mirror with no reflection, and when you touch it (because you were investigating like Nancy Drew) you fall into...a room full of black cats. (Sheesh, I hope you're wearing sleeves.) What happens next?
Jenn: When I fell there was glass on the floor and my arms and legs are all scratched up and now the cats all licked me and it healed me. Somehow, now I'm one of them.
So, naturally, I change into a skin-tight black leather outfit I find hanging nearby (because it just seems like something I should be wearing). And I walk out the back door--my many, many black cats in tow--and head toward a black motorcycle I see back there. One problem, to get to it, I HAVE to walk under a ladder, and the motorcycle has a red number 13 on the license plate.
Rachel: Because you're Catwoman and you have to save the world, you go under the bad-luck ladder and head for the bad-numbered motorcycle, of course. Unfortunately for you and your kitty gang, it starts to rain, and cats do not like rain. This causes you to run to the store--all the while, the rain is making you melt into your normal self--to get an umbrella. Which you mistakenly open. INSIDE.
Rachel: ...Keeping yourself off the aliens' radar. (People are paranoid about that, you know.) It's a good thing you bought that foil when you did, because reports of aliens are EVERYWHERE! "Extra-Terrestrials Break Out of Area 51!" "ET Phoned His Friends to Take Us All!" But really, all that foil on your head is great for shining sun into people's faces (the rain stopped, FYI), so you get hit by a car and pass out. And when you wake up...My gosh! It's a zombie apocalypse!
Jenn: Oddly, my bad luck apparently is good luck with the zombies because the only things that appear to repel Zombies? Wet-cat smell and sunlight glinting off of tin foil. I start to run, only to discover that the zombies are tripping over themselves trying to get away from me--literally. The only downside to this whole scenario is that a large group of humans has discovered my zombie-proof state and is starting to gather behind me. They're using me as a sort of shield to keep the zombies away...and there are so many of them that it's making me feel kind of claustrophobic.
Rachel: What do people do when they're feeling overwhelmed by a crowd? They imagine people in their underwear. GUESS HOW WELL THAT GOES, JENN. Yet, you are in luck: copies of Paranoia appear out of nowhere and cover the people--and shield you from them--so that you can make a quick escape (and yay, look at all the people with your book!). What on earth could possibly happen next, hmm?
Jenn: Now that all the humans have copies of my book, they start reading (naturally). And I being the pro-reading author that I am, use my tin foil hat and the power of the sun to drive all the zombies away. Thus making a nice reading sanctuary that is safe from all zombies from this time forth.
And then we wake up from the dream sequence, with an intense hunger for...PARANOIA.
If you like eBooks, you may want to look this up on some retailers ('cause rumor has it it's only $1.99 for a limited time)!


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The practices were picked from a shortlist of nine outfits vying for jobs on the Urbed- masterplanned riverside scheme.
Riches Hawley Mikhail beat local studio +3 Architecture and Metropolitan Workshop to be named the lead architect.
Paris-based AWP and Feix Merlin were meanwhile chosen to design a new cycle hub and café.
Featherstone Young meanwhile won a residential block with mixed-use units below.
Other outfits which failed to win work were Mawson Kerr, Konishi Gaffney Berlin-based Magma.
Work began on the first phase of the regeneration scheme – a 76-home eco-housing project designed by Ash Sakula – last year.
The winning schemes are expected to start on site in spring 2015.
London-based Riches Hawley Mikhail and Metropolitan Workshop are up against local practice +3 Architecture in the race to become the lead architect on the Urbed-designed masterplan (pictured).
Mawson Kerr, Konishi Gaffney, Featherstone Young, Feix & Merlin, Paris-based AWP and Berlin-based Magma Architecture are all working on plans for a smaller part of the scheme.
The work up for grabs includes two housing projects each comprising 50 apartments, a café, a restaurant and a cycle hub.
David Roberts, development director at Igloo, said: 'As the gateway to Ouseburn, Malmo Quay will be a high-profile development and we are looking for imaginative ideas that combine the character of the Quayside with the creativity of the Ouseburn Valley.


text:
Were the Mauryans vassals of the Seleucids?
Thread starter Raghavendra
Salaminia
Aupmanyav said:
Selucus was not interested in this (arid and far-off) region, he just wanted peace on his eastern borders so that he could concentrate on the western border. I do not think anyone denies influence.
This is true. It was apparent in the aftermath of Alexander's death that control of territory so far east was very problematic. In fact, the establishment of Taxila as a client kindom and, more so, the enlarging of Poros' client kingdom was the solution adopted by Alexander as his method of doing so without committing too costly numbers of Macedonian troops. Seleukos, with major unresolved military matters in his western rear, was not ever going to be able to hold down lands that far east. As the crisis in the west (producing the decisive showdown of Ipsos) developed, a negotiated agreement was the natural solution to stable eastern borders. A border which remained stable.
The Wiki article needs to be read with caution (as always). There are problems with its view. Alexander is described as having "retreated" but more indicative of the author's prejudices are statements such as the following:
Chandragupta's mercenaries may have assassinated two of Alexander's governors, Nicanor and Philip. He probably fought Alexander's satraps, including Eudemus – who left the territory in 317 BCE; and Peithon, who governed cities near the Indus River until he left for Babylon in 316 BCE.
No evidence exists which provides backing to the claim that Nikanor and Philip were killed by Chandragupta's mercenaries. In fact, it is clear that Philip was killed by the mercenaries appointed as part of his satrapal troops. Nikanor was killed in 326 in an uprising of the Assakenians and was hardly dispatched by Chandragupta's supposed mercenaries.
With Eudamos and Peithon, the clear implication of the author's statement is that this pair left because of supposed inroads by Chandragupta. Both these men did leave their satrapies but hardly for any such reason. Eudamos murdered Poros (sometime between 321 and 318) and headed west to join a satrapal coalition to fight against the aggrandising Peithon (not he mentioned above). Nothing indicates he was planning not ever to return for this coalition was soon taken over by Eumenes in the great struggle against Antigonos; the end of which saw Eudamos' murder. Peithon, now gover of Para[amisodai, was subsequently summoned by the victor, Antigonos and made satrap of Babylonia in place of Seleukos.
I would not contest all your points, but I would like to mention that retreat of Selucus was not the end of Greeks in India. After the decline of Mauryan empire, the Bactrian Greeks again ruled North-West India (Starting with Menander) for more than a 100 years before they were replaced by Scythians.
Very true. While I would say that Seleukos hardly "retreated", he most certainly returned with some alacrity; alacrity fueled by the impending battle on his western marches. Had Seleukos not returned it was certain Antigonos will have won and will have subsequently invaded Seleukos' heartland.
I would add that it is much easier to maintain a hold on these Indian territories from a base in Bactria (or modern Afghanistan) than what would be Seleukos' "centre".
Yeah, either from Bactria or even more conveniently from Purushapura (Peshawar) or Kabul. But the capital of Indo-Greeks was Sagala (Sakala, modern Sialkot, Pakistan), much deeper in Punjab. By that time they had lost Bactria to Scythians. That was the pattern in Central Asia from times immemorial, pressure from tribes in the North and movement into India, one after the other. That happened with Aryans too. Later, the Greeks lost Sagala too to Scythians, Rajuvula.
(and perhaps retreaded to Himalayas). A few tribes in India and Pakistan are supposed to have Greek connection.
Aelfwine
After the decline of Mauryan empire, the Bactrian Greeks again ruled North-West India (Starting with Menander) for more than a 100 years before they were replaced by Scythians.
The Bactrian Greek conquest of India surely began during the reign of the Bactrian king, Euthydemos, some time before 195 BC. The actual first campaign seems to have been conducted by Demetrius, the king`s son, which took the provinces of Pushkalavati and Gandhara . Euthydemos died about the year 195 to be succeeded by Demetrius whose first coins depict him wearing the elephant crown of Alexander with Heracles, the patron deity of the dynasty, on the reverse in the act of crowning himself. It is the elephant crown on the coins which symbolizes Demetrius`s Indian conquests. Menander didn`t appear on the scene until much later, possibly about 150 BC.
No Bias FTW
Minor addendum for the sake of the facts. It seems more accurate to say that they ruled only a small portion of the North-West since they were only relegated to Punjab for any 'durable' period of time (at the duration of time when the Sungas, Kanvas, and Satavahannas were ruling substantially West from Pataliputra and Amaravati respectively). The Indo-Greek rule of the North-Western portion of the Gangetic plains (Mathura) was apparently quickly replaced at first by a '-mitra' or '-datta' dynasty. They were the ones who were apparently in turn replaced by the Scythians that originated from the North.
Reactions: Bharata
What I meant was that the Indo-Greeks in their principality were replaced by Scythians after some time. I did not say that they ruled the whole Indo-Gangetic plains.
Wikipedia has a nice time-line at Indo-Greek Kingdom - Wikipedia
Himalay Singh
It was most likely other way around as giving up your daughter to your enemy is considered most humiliating thing in India as we see from Mughal-Rajput relationships.
Selucids invaded India for more lands, Mauryans defeated them, took daughter of king to further humiliate him and 1/3 of his Empire.
And made his now father in law his autonomous vassal and allowed him to go home.
Was that woman Selucus' daughter? Mentioned earlier also, Selucus was not at all Interested in Indian territories. He perhaps had his eyes on Greece.
Were the Crusades waged as a 'total war' Middle Eastern History Saturday at 7:58 AM
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Were the Crusades waged as a 'total war'
How likely were you to meet a minority in Europe in the Middle Ages?
In Greece, graves were built 3500 years ago.
How rich Ancient cities were?


Volunteers are one of our most important assets. You do make a difference! Help to keep this special green oasis alive.
Our 2019 Spring Clean-up and Volunteer Tea is scheduled for Saturday and Sunday, May 4 and 5. There will be sessions from 10–12 and 1–3 each day, and a Volunteer Tea (both for workers, and for people wanting to know more!) on Sunday from 3 to 4:30. Learn about the different volunteer opportunities and all the wonderful things happening at the gardens.
Thanks for your interest and see you at the gardens!
Also, To prepare for the season, we are putting together a Volunteer Committee to help plan a super volunteer experience for Season 2019. If you are interested please contact Deb at ddteag1@comcast.net. Please email any new ideas and suggestions you may have.


« A Continuing look at specific procurement goals and resolutions for the New Year.
Part Five of continuing looks at specific procurement goals and resolutions for the New Year.
In yesterday?s blog post, we looked at the procurement resolution or goal of taking a close look at your supplier chain, where you can find ways to save money by reevaluating what suppliers are charging. Today we are going to discuss goal number three. Make training a priority because talented workers want to be challenged. Keep them happy by helping them develop new skills.
This author began his career as a teacher. In fact, a history teacher. One of my favorite quotes comes from Aristotle who lived from 384 BC to 322 BC and nearly 2500 years later this quote it is still appropriate. ?Excellence is an art won by training and habituation. We do not act rightly because we have virtue or excellence, but we rather have those because we have acted rightly. We are what we repeatedly do. Excellence, then, is not an act but a habit.?
The challenge with the above quote for all leaders of procurement knowledge workers is to provide an ongoing educational environment as part of the daily routine so that what was discussed during yesterdays post where we see coworkers every day that just like to come to work, do what they perceive to be their job and then head home. One reason this happens is because there is no challenge or fun it what they are doing. Repetitive tasks become boring. Training and education can provide the spark necessary to open a world of creativity that will benefit the entire company going forward.
The following are some creative ways to create a procurement departmental educational program without spending a lot of time or money.
If education is perceived to be fun and the entire team is involved in developing and participating in the program, the quality of the team will improve as will team communication and moral. It is however important not to rank individual team members or publish individual scores. This is not a competition. This exercise is about the team.


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Allergy types
Allergy tests
Home > Drug Allergy
The purpose of drugs is to combat, alleviate, or prevent illnesses. But unfortunately, sometimes they can also cause allergic reactions of varying intensity, depending on the hypersensitivity reactions of each person. At our specialized allergy clinic in Barcelona, the objective is to re-establish the patient's quality of life and treat the affliction. To do so, we carry out a detailed evaluation that helps us to avoid, minimize, or reverse the negative consequences of the allergy.
How do I know if I have a drug allergy?
Drugs, like other substances, can produce allergic reactions. At PB Clinical, we perform tests specific to the drugs involved in the reaction to determine the cause, so the allergist can decide which treatment should be carried out.
Can you be allergic to more than one drug?
Though rare, it is possible to be allergic to different drugs. You can be allergic, for example, to penicillin and also allergic to Ibuprofin or other medications in its group.
What's the difference between an allergy and a side effect?
Drug allergies are produced by an immunological mechanism that consists of the generation of antibodies against the substance and the presentation of certain characteristic symptoms. For example, when a person takes an aspirin and his or her lips swell up (lip angioedema), we are talking about an allergy. By contrast, secondary effects are produced when a drug, in addition to producing the desired therapeutic effect, also produces other effects like nausea, vomiting, dizziness, etc. For example, if you take an aspirin and subsequently experience stomach pain, we are talking about a side effect and not an allergy.
If I'm allergic to penicillin, will I be allergic to other drugs?
In principle, your risk of presenting with allergic reactions to other drugs is not heightened after being diagnosed as allergic to penicillin. That's why at PB Clinical we perform an exhaustive study including the different epicutaneous drug tests to eliminate other possible allergies.
Specialists in clinical immunology and allergy treatment in Barcelona.
PBClinical Allergology Clinic Rambla de Catalunya, 120 2º 2ª Barcelona (Spain) Email: info@pbclinical.com Phone :+34 936 394 559 / +34 609 034 039 WhatsApp: +34 609 034 039


Our main headquarters are located in Veldhoven, the Netherlands, and we also have 18 office locations around the United States- including main offices in Wilton, CT, Chandler, AZ, San Jose, CA and San Diego, CA.We are proud of bringing together the brightest minds all over the world to tackle the most challenging problems in making faster and smaller chips. As part of our team, you will have the opportunity to go beyond yourself in developing more advanced techniques and push the technology boundaries.ASML San Jose, CA is an industry leader in computational lithography for integrated circuits. Our Tachyon platform enables capabilities that address chip design, photomask making and wafer printing for semiconductor manufacturing and the LithoTuner platform enables lithography optimization for ASML's leading photo lithography tools, known as 'scanners'.
Brion Technologies is a division of ASML and an industry leader in computational lithography for integrated circuits. Brion's Tachyon™ platform enables capabilities that address chip design, photomask making and wafer printing for semiconductor manufacturing. Brion's Fab Products enable lithography optimization for ASML's leading photo lithography tools.
In the software research and development (R&D) team, you will be a key member to develop high quality software and contribute to all phases of the development process from designing to release. You must be responsible for independently developing and testing the algorithms and turn general requirement definitions into functioning modules. A good candidate should exhibit strategic thinking, be self-motivated and collaborative with team members. You will review and analyze requirements, assess the impact of changes to software, provide estimates of work effort, design and develop software, and write unit-tests.
Ph.D. or M.S. in physics (computational physics preferred), computer science, electrical engineering, applied mathematics, or related areas, or equivalent experience.
3+ years experience – numerical simulation, modeling, or similar (academic or industry).
Experience developing object oriented software in Python.
Knowledge of software design principles and software engineering processes.
Experience with C++, Git, JIRA, or similar.


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Під покриття́м розуміється шар матеріалу, утворений природним або штучним шляхом на поверхні елемента, виконаного з іншого матеріалу.
Покриття найчастіше застосовуються з метою захисту металів від корозії. Досить широко також використовуються в техніці для підвищення зносостійкості, поверхневої твердості виробів і з метою відновлення робочих поверхонь, пошкоджених внаслідок зношування, корозії, ерозії, кавітації. Знаходять певне застосування з метою декорування (прикраси) виробів і виконують часто захисно-оздоблювальну функцію.

Див. також
 Антикорозійні поліуретанові покриття

Примітки

Посилання

 ЗАХИСНІ ПОКРИТТЯ //

Матеріалознавство
Триботехніка
Виробничі процеси
Катодний захист
Дизайн

redpajama_set_name: RedPajamaWikipedia


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Mask insurance policy for sports star
Tuesday October 20th 2009
Italian footballer David Grassi is fighting back after he suffered a triple cheekbone fracture and is now wearing a facemask showing-off the Aberdeen team's colours.
The defender was injured during last month's Co-operative Insurance Cup defeat at Dundee and following surgery returned wearing a carbon-based face mask which is decorated in the style of the Dons' new home kit.
The 23-year-old wore the mask after a trip to his native Italy. He hopes to begin training again in two weeks' time.
Grassi told his club's official website, www.afc.co.uk: "I decided to get it done in Aberdeen's colours because they are now my team. I then asked if they could add the logo.
"I like it. I think it looks great, I hope to be here for a long time and hope the fans are as pleased as I am with how the mask looks."
Grassi's operation included having a titanium plate fixed on to the top part of his broken cheekbone.
The Aberdeen-based surgeon also inserted a screw, via an incision through the roof of his mouth, to the bottom end of the bone to offer more support.
Grassi added: "I'm due to see the surgeon who did the operation next Friday.
"If he gives me the all-clear, I will be looking to get back in to training very soon, maybe in two weeks' time."
Exercise or playing your favourite sport is good for you, but it's surprising how easy it is to hurt yourself. Sport Injury Protection from helpucover provides you with cash lump sums towards your expenses in the event of a sports injury.


"An intervention is made to a small-scale amorphous building accommodating an individual house. The interventions and additions made over time created a garage and a series of annexes in different shapes and sizes, placed without any particular rule in mind. The project aims to perfect the house filling it with functional spaces while also cleansing and organising the exterior space of the patio. The main volume of the house and the garage are thus further preserved.
In the interior space, the intervention brings a spacious living area, attached to the main volume at the same time opening towards the exterior on all its three sides. The shape is so conceived in order to generate an ample interior space while directing it to the light and overlooking the exterior. Natural light is the starting point of the project; the most significant element is the "screen" towards the garden which allows for an opening on the entire wall. This has a double purpose: one the one hand, it facilitates the view from the living room to the exterior space of the garden, allowing natural light inside, while at the same time, it displays the daily activities on the screen of family life.
The old wing of the building, which was left unaltered, houses the night spaces and the kitchen, an area directly connected with the living room.