Welcome to Total Transformers where you will find a large selection of LED drivers, magnetic and electronic transformers, Class 2 transformers, General Purpose Transformers, Commercial Transformers and Transformer Accessories such as photo cells and timers.
Because of the almost limitless configurations of our transformer and driver offering some units are assembled in California as needed. In most cases we ship within 1-3 days. If you have special time constraints please contact us before ordering to insure that delivery meets your needs. In addition, transformers ordered incorrectly and returned will be charged a 25% RESTOCKING CHARGE. Please be sure to order correctly and make sure you are getting the exact transformer you need. Pay special attention if your needs are AC or DC. Need help? Don't hesitate to contact us.


The Federal Ministry for Sustainability and Tourism intends to introduce a mandatory national indication of origin for processed foods (meat products, milk, egg products, processed products and dairy products).
fleischwirtschaft.com — AUSTRIA, Vienna. Katharina Koßdorff, Managing Director of the Association of the Food Industry, comments on the plan of labelling processed foods.
The Federal Ministry for Sustainability and Tourism intends to introduce a mandatory national indication of origin for processed foods (meat products, milk, egg products, processed products and dairy products). This planned regulation goes far beyond the EU food legislation already in force and applies only to domestic manufacturers. The industry is against this discrimination of Austrian companies by the government project.
"Food safety is the top priority and must be observed by all participants along the food chain, from the stable to the plate. Only if all market participants comply with the laws can incidents such as those currently occurring in Poland be prevented. A national, mandatory labelling of origin for Austrian manufacturers would certainly not improve the safety of food, as some voices from agriculture now claim. It is crucial that the multitude of existing rules for food in all countries and by all partners in the food chain is observed, controlled and sanctioned. Labelling cannot replace proper production in agriculture and processing. We are asking for more prudence in the public debate", explains Koßdorff.
She specifies: "The safety of food and its origin must not be mixed up in the Austrian debate. That would be untrustworthy, because ne has nothing to do with the other. A nationally compulsory labelling of processed food does not create more safety; it cannot compensate for careful and lawful production in one's own country and in other countries. Every food must be safe, no matter where it comes from. Consumers rightly expect this."


Description: Humans and androids crowd the raucous streets of New Beijing. A deadly plague ravages the population. From space, the ruthless lunar people watch, waiting to make their move. No one knows that Earth's fate hinges on one girl. . . .
"Iko rolled to her side, clasping her metal grippers over her chest. "Prince Kai! Check my fan, I think I'm overheating."
"I'm sure I'll feel much more grateful when i find a guy who thinks complex wiring in a girl is a turn-on."
"And yet, the memory of his fingers against her skin refused to fade."
I enjoyed the audio of this one, surprisingly. I'm not a huge YA reader but loved this take on Cinderella.


"[error] Failed to create ASO for aspect 'Aes Controller Variable Table'" in CBM while doing any modifications/deletion in hardware tree. what is the reason behind this error?
kindly see the attached screen shot for more information.
I have seen another similar case but the IP Value holder is showing correct IP address and also the Profibus/HART extensions are installed in this station.
A DCT Software Compare will show that this client does not have all system extensions installed. I suspect Engineering Studio to be missing or improperly installed.
Rule of thumb is: "All system extensions goes everywhere" (=into every node).
Thanks for the response. The DCT report indicates the extension in both the aspect server and this client is the same except for one package "ABB SCL Component V2.9.80". I don't think this should be the issue.
Should reinstallation of Engineering Studio solve this problem?
The System Extensions aspect can also be checked; does Engineering Studio show up as "Installed on this node"?
Engineering studio is also installed on this node.
The only extension missing in this node "ABB Function Designer for AC800M". This was intentionally not installed because we are not using function designer. Could this be the potential reason?
"Aes Controller Variable Table" is as far as I can tell an aspect belonging to Function Designer.
If you do not intend to use Function Designer you should not have loaded it as a system extension.
Once you load a system extension you are *MANDATORY OBLIGED* to see to that it is installed into *EVERY NODE* of the system.
Less is more... don't load what you don't need.
The worst part of loading something you don't need is that you sign a perpetual contract to keep you updated on rollups, etc. released for the system extensions you load.
Back in version 4 we had a lot of problems with system backup when Parameter and Document Manager silently "trashed" the system backups making them impossible to restore.


A Finnish 10 Year Old Boy, have actually hacked into a platform which actually is not eligible to register on. This literally means , he is not in the platform, but he understands what is happening on the platform more than those using the platform.
A Finnish Boy have hacked into Instagram and yea, he went away with $10,000.
This have actually made him the youngest to have hacked into one of Facebook's platform that they aren't technically eligible to register on since most of Facebook's platform makes it known for users to be above 13.
While trying to figure out what he should not have done, he realized that he could hack into Instagram's server and delete people's posts on the platform.This was also confirmed by Facebook, after using a test account which was patched in February said Forbes.
Though it is great how Facebook encourage Hackers that try to detect loop Holes on the platform, i think the case of Jani is more of just giving him some cool cash to encourage him as i could imagine what would have happened if this was performed by someone who have come of age and then, has hos identity hidden.
Over to you, What do you think about this 10 year old hacker?


Trigard Burial Vault and Funeral Service: Packed and ready for Tampa!
Have you ever wondered how our team takes an idea for a convention booth and turns it into the experience that you see when you attend? Needless to say, it involves a lot of planning, checklists and teamwork!
One of the most important parts of the process is proofing the panels. If you've ever created a custom wall display with our Marketing team, you understand what this process is all about. With a showroom wall display, our Marketing team will mock up the panel on slat wall - or sometimes even use a photo of your actual showroom - to help you visualize the finished product.
With a convention booth, our team uses Google SketchUp to create a 3-D model of the booth so we can all visualize it. And here's a sneak peek at the Memorials side of our booth at ICCFA.
Want to see the rest? You'll have to come to Tampa! Or keep watching this newsletter for post-convention photos.


Julie Tomaino's lively production of HAIR is just the sunny panacea for the January doldrums. On stage at Hart House Theatre until Feb 2. Details in our review.
"This musical feels like a labour of love, and we can't wait to share it with you!" ~ Kyle Blair makes a scene-stealing YPT debut as beloved song-and-dance chimney sweep Bert in Disney & Cameron Mackintosh's "Mary Poppins", now onstage at YPT.
A leader in the COC's Scotiabank Summer Opera Camps, Composer Chris Thornborrow mentors young people to acquire skills, express creativity, and form friendships within a vibrant, interactive operatic experience.
Anika Johnson & Barbara Johnston's ONE SMALL STEP is a new musical about high-school students mounting a musical, "The Hadfield Follies: An Out of This World Musical Journey into the Life and Times of Astronaut Chris Hadfield".


text:
\section{Introduction}
\label{submission}
Graphical models are a way of efficiently representing the  conditional independence relationships satisfied by a collection of random variables. They form the starting point for many efficient estimation and inference algorithms. Thus, learning the graphical model of a collection of random variables is a fundamental, and very well-studied problem.

For jointly Gaussian random variables, the graphical model is given by the non-zeros in the inverse of the covariance matrix, also known as the precision matrix. We ask a natural variant of this fundamental problem: suppose we observe the random variables with independent additive noise. Thus, in the infinite sample limit, rather than knowing the covariance matrix, $\Sigma$, we have access only to $M = \Sigma + D$, the sum of the covariance matrix and a diagonal matrix. In general, $(\Sigma + D)^{-1}$ does not share the sparsity structure of $\Sigma^{-1}$. In the language of probability, if two random variables $X$ and $Y$ are independent conditioned on $Z$, then we do not expect that $(X+W_1)$ and $(Y+W_2)$ are independent when conditioned on $(Z+W_3)$, even when $W_1$, $W_2$ and $W_3$ are independent.

We ask: when is it possible to recover the conditional independence structure (graphical model) of the underlying variables, i.e., when can we recover the sparsity pattern of $\Sigma^{-1}$? Despite the voluminous literature on Gaussian graphical models, to the best of our knowledge, there has been no answer to this question.

{\bf Contributions of this paper}. We show the following:
\begin{itemize}
\setlength\itemsep{0em}
    \item A negative result of unidentifiability (Theorem \ref{thm_unident}): Even for a simple Markov chain on three nodes, the problem is unidentifiable even when an arbitrarily small amount of independent noise is added. That is, there are covariance matrices that differ only on their diagonal entries, and yet whose inverses have different sparsity patterns.
    \item A positive result of limited unidentifiability (Theorem \ref{thm_limited_unident}): While unidentifiable, even for large independent noise, the ambiguity is highly limited. Specifically, we show that for tree-structured graphical models, distinguishing leaves from their immediate neighbors is impossible, but the remaining structure of the graph is identifiable (see Figure \ref{fig:identifiability} for an illustration).
    \item Identifiability with Side Information:
    \begin{itemize}

    \setlength\itemsep{0em}
        \item (Theorem \ref{noise_ident}) We characterize an upper bound on the noise which, if given as side information, makes the problem identifiable.
        \item (Theorem \ref{diag_major_ident}) If there is side information that in the precision matrix, for a leaf node, the diagonal entry is greater than the absolute value of the other non-zero entry, the problem is identifiable.
        \item (Theorems \ref{min_eig_ident}, \ref{min_eig_unident}) Given a lower bound on the minimum eigenvalue of the true covariance matrix as side information, we characterize the upper bound on the noise for which the problem is identifiable. We also characterize a lower bound on the noise which makes the problem unidentifiable.
    \end{itemize}
    \item We provide, an $\mathcal{O}(n^3)$ algorithm that identifies the equivalence class of the underlying tree (Section \ref{sec:algorithm}).
\end{itemize}
\subsection*{Related Work}
Estimating Gaussian graphical models has been a very widely explored topic. Various algorithms based on the $\ell^1$ penalized log likelihood maximization have been used in, e.g., \cite{banerjee2008model, raskutti2009model, friedman2008sparse, yuan2007model, rothman2008sparse}. A parameter free Bayesian approach was presented in \cite{wong2013adaptive}. In \cite{meinshausen2006high} and \cite{yuan2010high}, another approach was proposed which finds conditional independence relations by regression using one random variable as output and the remaining random variables as input. The output variable is conditionally independent of the input variables with regression coefficient zero.

For learning the special class of tree structured Gaussian graphical models a classical algorithm is proposed in \cite{chow1968approximating}, now known as the Chow-Liu algorithm. The authors prove that the maximum likelihood estimate of Markov tree structure is given by the maximum-weight spanning tree (MWST) where the edge weights are the empirical mutual information. If the number of samples is infinite, this algorithm provides the exact tree structure. This algorithm inherently induces some robustness against additive independent Gaussian noise. This is because the MWST estimate remains the same if the ordering of mutual information from smaller to larger remains the same. Therefore, if the noise does not alter the order of mutual information, the algorithm still correctly identifies the tree structure. However, this is not the case in general as we show in Section \ref{sec:examples}. Moreover, whether the noise has or has not altered the MWST is not checkable from the data.

In \cite{tan2009learning}, an error analysis of the Chow-Liu algorithm is presented which considers the statistical error due to finite samples.
There are other papers which study the class of tree structured Gaussian graphical models based on the Chow-Liu algorithm \cite{choi2011learning, li2016chernoff, mossel2013robust}. None of these, however, are able to offer guarantees in the face of noise.

There has been a lot of research on the robust estimation of graphical models \cite{loh2011high, yang2015robust, wang2017robust, kolar2012estimating, lounici2014high, wang2014robust, liu2012high}. However, the robustness is against outliers or missing data or Gaussian noise with known covariance or bounded noise. To the best of our knowledge, there is no work that addresses the natural setting of (unknown) additive independent Gaussian noise. This is precisely the setting that we tackle in this paper.

The algorithm in \cite{janzamin2014high} comes closest to our setting, and in fact is complementary. In that work, the goal is to recover the graph structure in the presence of corruption in those off-diagonal terms of the covariance matrix which are not conditionally independent. Specifically, the results there do not consider (and cannot address) noise in the diagonal elements. Thus, this setting considers a perfectly complementary setting, as in this work there is noise only in the diagonal elements of the covariance matrix and not in the off diagonal elements. It would be interesting to consider if these results can be merged to obtain a general result.

\section{Problem Statement}
Let $X = [X_1, X_2 \dots, X_n]^T$ denote a jointly Gaussian random variable whose conditional independence structure is given by a tree. We call this the {\em true tree} $T^*$. We denote the covariance matrix of $X$ by $\Sigma^*$ and the precision matrix by $\Omega^*$. That is, $X\sim \mathcal{N}(0, \Sigma^*)$. We denote the noise covariance matrix by $D^*$. This is a non-negative diagonal matrix. We denote the observed noisy covariance matrix by:
\begin{equation*}
    \Sigma^o = \Sigma^*+D^*.
\end{equation*}
Given $\Sigma^o$ as an input, recovering $\Sigma^*$ exactly is never possible. Consider, for instance, independent noise added only to a leaf node. Instead, we would like to recover the underlying tree $T^*$. We show that in general, recovering $T^*$ exactly is not possible. However, we show that the ambiguity is limited to an equivalence class of trees. We characterize this explicitly. That is, we characterize the set of possible trees $T'$ that correspond to a covariance matrix, $\Sigma'$, and a nonnegative diagonal matrix $D'$ such that $\Sigma^o = \Sigma'+D'$.
\subsection*{Notation}
For any matrix $\Sigma$, $(\Sigma)^T$ represents the transpose of the matrix. $\Sigma_{ij}$ denotes the element at the $i,j$ position. $\Sigma_{:,i}$ represents the $i^{th}$ column. $\Sigma_{-i, -j}$ represents the submatrix after deleting row $i$ and column $j$ from $\Sigma$. $\Sigma_{-i, j}$ represents the $j^{th}$ column without the $i^{th}$ element. Similarly, $\Sigma_{i, -j}$ represents the $i^{th}$ row without the $j^{th}$ element. We use $\det(\Sigma)$ to represent the determinant of the matrix. For a random vector $X = [X_1, X_2, \dots, X_n]^T$, $X_i$ denotes the $i^{th}$ component and $X_{-i}$ denotes the subvector after removing the $i^{th}$ component.

\section{Identifiability Result}
Let the set of all the leaf nodes of $T^*$ be $\mathcal{L}$:
\begin{equation*}
    \mathcal{L} = \{a \mid \text{node } a \text{ is a leaf node in } T^*\}.
\end{equation*}
Consider all the subsets of $\mathcal{L}$ such that no two nodes in the subset share a common neighbor. Let $p$ be the number of such subsets. Let $\mathcal{S}^q$ be the $q^{th}$ subset. Let $T^q$ be the tree obtained by exchanging the position of nodes in $\mathcal{S}^q$ with their neighbor node in $T^*$. Therefore, for every tree $T^q$, there is a corresponding set $\mathcal{S}^q$. We define a set of these trees as $\mathcal{T}_{T^*}$.
\begin{equation*}
\mathcal{T}_{T^*} = \{ T^q \mid q \in \{1, 2, \hdots p\}  \}.
\end{equation*}
Figure \ref{fig:identifiability} gives an example of $\mathcal{T}_{T^*}$.
\begin{figure
    \centering
    \includegraphics[scale = 0.5]{identifiability.jpg}
    \caption{For this $T^*$, $\mathcal{T}_{T^*}$ is the set of all the trees obtained by permuting the nodes within each of the dotted regions. We prove that while $T^*$ is unidentifiable, under our noise model, we can recover $\mathcal{T}_{T^*}$. In other words, the tree structure is recoverable up to permutation of leaves with their neighbors.}
    \label{fig:identifiability}
\end{figure}
\subsection{Identifiability Results without Side Information}
\begin{theorem}\label{thm_unident}
(Negative Result - Unidentifiability) Consider a covariance matrix $\Sigma^*$ whose independence structure is given by the tree $T^*$. Suppose we are given a noisy covariance matrix $\Sigma^o = \Sigma^* + D^*$ where $D^*_{ii} > 0$ when $i$ is a neighbor of a leaf node. For any tree $T^q\in \mathcal{T}_{T^*}$, it is always possible to decompose $\Sigma^o = \Sigma^q + D^q$ where the conditional independence for $\Sigma^q$ is given by the tree $T^q$ and $D^q$ is a non-negative diagonal matrix.
\end{theorem}

\textit{Proof Outline. }We give an explicit construction that demonstrates that any tree $T^q\in \mathcal{T}_{T^*}$ is achievable.
Consider any tree $T^q \in \mathcal{T}_{T^*}$ and its corresponding leaf subset $\mathcal{S}^q$. The required decomposition of $\Sigma^o = \Sigma^q + D^q$ is given as follows:
\begin{equation}\label{main_sig_q}
    \Sigma^q_{ij} =
    \left \{
    \begin{array}{lr}
          \Sigma^*_{ij} - \frac{1}{\Omega^*_{ij}} & \text{if $i=j\in \mathcal{S}^q$} \\
          \Sigma^*_{ij} + c_{1}^i & \text{if $i=j\in Neighbor(\mathcal{S}^q) $} \\
          \Sigma^*_{ij}  & \text{otherwise},
    \end{array}
    \right.
\end{equation}
where $Neighbor(\mathcal{S}^q)$ is the set of neighbor nodes of all the nodes in $\mathcal{S}^q$. Also, $c_{1}^i$ is chosen such that $0 < c_{1}^i \leq D^*_{ii}$.
\begin{equation}\label{main_d_q}
    D^q_{ii} =
    \left \{
    \begin{array}{lr}
          D^*_{ii} + \frac{1}{\Omega^*_{ii}}& \text{if $i \in \mathcal{S}^q$} \\
          D^*_{ii} - c_{1}^i & \text{if $i \in Neighbor(\mathcal{S}^q)$} \\
          D^*_{ii}  & \text{otherwise}.
    \end{array}
    \right.
\end{equation}
The full proof which includes arriving at this decomposition and showing that the conditional independence structure of $\Sigma^q$ is given by $T^q$ is in Appendix A.

\begin{theorem}\label{thm_limited_unident}
(Positive Result - Limit on unidentifiability) Consider any decomposition $\Sigma^o = \Sigma'+D'$ such that the conditional independence for $\Sigma'$ is given by a tree $T'$ and $D'$ is a non-negative diagonal matrix. Then $T'\in \mathcal{T}_{T^*}$. Equations \ref{main_sig_q} and \ref{main_d_q} provide a decomposition that results in this $T'$.
\end{theorem}

\textit{Proof Outline.} The proof of the theorem relies on showing that the off-diagonal terms of the covariance matrix suffice to specify the structure of the underlying tree up to the equivalence set $\mathcal{T}_{T^*}$. Our proof is constructive, and hence can be considered as a proto- or conceptual- algorithm for recovering $\mathcal{T}_{T^*}$. As any construction suffices to prove the result, we ignore questions of computational complexity. The ideas of this proof are then used and refined in order to provide an efficient algorithm in Section \ref{sec:algorithm}.

The main building block of this proof and of the algorithm presented in Section 5 is to categorize any set of 4 nodes as a {\it star-shape} or a {\it non-star-shape} (we define this below). Moreover, if it is a non star shape, we show that it is always possible to partition the four nodes into two pairs that each lie in separate connected components of the tree.
\begin{definition}\label{def:starShape}
\begin{itemize}
\setlength\itemsep{0em}
    \item Four nodes $\{i_1, i_2, i_3, i_4\}$ form a \textbf{non-star shape} if there exists a node $i_k$ in the tree $T^*$\footnote{Note that nothing prevents $i_k$ to be one of the four nodes.} such that exactly two nodes among the four lie in the same connected component of $T^* \setminus i_k$.
    \item If $\{i_1, i_2, i_3, i_4\}$ do not form a non-star shape, we say they form a \textbf{star shape}.
\end{itemize}
\end{definition}
\noindent
It is easy to see that in the event that a set of 4 nodes forms a non star, there exists a grouping such that the 2 nodes in the same connected component form the first pair and the other 2 nodes form the second pair.
\begin{figure}
    \centering
    \includegraphics[scale = 0.5]{starnonstareg.jpg}
    \caption{Examples of classification of 4 nodes as star shape or non star shape. If they form a non star shape, the nodes are grouped in pairs of 2.}
    \label{fig:main_eg_star_nonstar}
\end{figure}
 Figure \ref{fig:main_eg_star_nonstar} gives examples of star shape and non star shape. This categorization is done using only the off-diagonal elements of the covariance matrix, hence this property remains invariant to diagonal perturbations, that is, every set of 4 nodes falls in the same category in any tree obtained from the decomposition of $\Sigma^o = \Sigma' + D'$ as $\Sigma'_{ij} = \Sigma^*_{ij}$  $\forall$  $i\neq j$.
The proof of this theorem is split in 3 parts:
\begin{enumerate}[(i)]
\setlength\itemsep{0em}
    \item Prove that it is possible to categorize any set of 4 nodes as star shape or non star shape using only off diagonal elements of the covariance matrix. Moreover, if the 4 nodes have a non star shape, we can find their grouping  in two halves.
    \item Prove that this categorization of all the possible sets of 4 nodes completely defines all the possible partitions of the original tree in 2 connected components such that the connected components have at least 2 nodes.
    \item Prove that these partitions of a tree into connected components completely define the tree structure up to the equivalence set $\mathcal{T}_{T^*}$.
\end{enumerate}
For part (i), we prove that a set of 4 nodes $\{i_1, i_2, i_3, i_4\}$ forms a non star shape such that nodes $i_1$ and $i_2$ form one pair and $i_3$ and $i_4$ form the second pair if and only if:
\begin{equation}\label{eq:nonstar_cond}
\begin{aligned}
 \frac{\Sigma^*_{i_1i_3}}{\Sigma^*_{i_1i_4}} &= \frac{\Sigma^*_{i_2i_3}}{\Sigma^*_{i_2i_4}}, \\
\frac{\Sigma^*_{i_2i_1}}{\Sigma^*_{i_3i_1}} &\neq \frac{\Sigma^*_{i_2i_4}}{\Sigma^*_{i_3i_4}}, \\
\frac{\Sigma^*_{i_2i_1}}{\Sigma^*_{i_4i_1}} &\neq \frac{\Sigma^*_{i_2i_3}}{\Sigma^*_{i_3i_4}}.
\end{aligned}
\end{equation}
We also prove that a set of 4 nodes $\{i_1, i_2, i_3, i_4\}$ forms a star if and only if:
\begin{equation}\label{eq:star_cond}
\begin{aligned}
 \frac{\Sigma^*_{i_1i_3}}{\Sigma^*_{i_1i_4}} &= \frac{\Sigma^*_{i_2i_3}}{\Sigma^*_{i_2i_4}}, \\
\frac{\Sigma^*_{i_2i_1}}{\Sigma^*_{i_3i_1}} &= \frac{\Sigma^*_{i_2i_4}}{\Sigma^*_{i_3i_4}}, \\
\frac{\Sigma^*_{i_2i_1}}{\Sigma^*_{i_4i_1}} &= \frac{\Sigma^*_{i_2i_3}}{\Sigma^*_{i_3i_4}}.
\end{aligned}
\end{equation}

For part (ii), we first define a subtree.\\
\begin{definition}
Let $\mathcal{A}$ denote the set of all the nodes in $T^*$. A \textbf{subtree} $\mathcal{B}$ of a tree $T^*$ is a set of nodes such that $\mathcal{B}$ and $\mathcal{A}\setminus \mathcal{B}$ both form connected components in $T^*$. The pair of subtrees $\mathcal{B}$ and $\mathcal{A}\setminus \mathcal{B}$ are called \textbf{complementary subtrees}.
\end{definition}

We prove that if we start with a set of nodes $\{i_1, i_2, i_3, i_4\}$ that form a non star such that nodes $i_1$ and $i_2$ form a pair, we can get a partition of $T^*$ into the smallest subtree containing $i_1$ and $i_2$ and the remaining tree. This is done using the function \textsc{SmallestSubtree}($\Sigma^o, \{i_1, i_2, i_3, i_4\}$), the details of which are provided in Appendix B.2. Upon doing this for different initializations, we get all the possible partitions of the tree such that each partition has at least 2 nodes.

For part (iii) we define equivalence clusters and edges between equivalence clusters as follows:
\begin{definition}
A set containing an internal node and all the leaf nodes connected to it forms an \textbf{equivalence cluster}. We say that there is an edge between two equivalence clusters if there is an edge between any node in one equivalence cluster and any node in the other equivalence cluster.
\end{definition}
The subtrees obtained from part (ii) completely specify the equivalence clusters and the edges between the equivalence clusters. This gives us the set $\mathcal{T}_{T^*}$.
\begin{figure}
    \centering
    \includegraphics[scale = 0.5]{partition_ec_combined.jpg}
    \caption{(a) Suppose $\{i_1, i_2, i_3, i_4\} = \{7, 9, 5, 2\}$, part (ii) partitions the nodes in group 1 and group 2. All the equivalence clusters are also shown. (b) Edges between equivalence clusters. }
    \label{fig:partition_EC}
\end{figure}
Partitioning in part (ii) and equivalence clusters in part (iii) are illustrated in Figure \ref{fig:partition_EC}.
The detailed proof of each part is presented in Appendix B.

\subsection{Identifiability Results with Side Information}
\begin{theorem}\label{noise_ident}
(Maximum Noise Identifiability Condition) Suppose the noise is upper bounded by
\begin{equation}\label{noise_cond}
    D^*_{aa} < \frac{1}{\Omega^*_{aa}},\text{ }\forall \text{ }a\in \mathcal{L}
\end{equation}
and suppose that this upper bound is known as side information. In this case, the decomposition of $\Sigma^o = \Sigma' + D'$ results in $\Sigma'$ whose independence structure is given by $T^*$.
\end{theorem}
\begin{proof}
From Equation \ref{main_d_q}, for a leaf node $a$ to exchange position with its neighbor, we need:
\begin{equation*}
    D'_{aa} \geq \frac{1}{\Omega^*_{aa}}.
\end{equation*}
The constraint in Equation \ref{noise_cond} makes this solution infeasible. Hence any feasible solution cannot have a leaf node exchanged with its neighbor.
\end{proof}
\begin{theorem}\label{diag_major_ident}
(Leaf Diagonal Majorization Identifiability Condition) Suppose $\Omega^*$  satisfies the condition that for any leaf node $a$ and its neighbor node $b$ in $T^*$, $\Omega^*_{aa} > |\Omega^*_{ab}|$. Then for any decomposition of $\Sigma^o = \Sigma' + D'$ which satisfies the same property, the tree structure of $\Sigma'$ is the same as that of $\Sigma^*$, that is, $T' = T^*$.
\end{theorem}

\textit{Proof Outline.} To prove this claim, we consider the decomposition of $\Sigma^o = \Sigma' + D'$ such that the conditional independence structure $T'$ for $\Sigma'$ has leaf node $b$ and its neighbor node $a$. We show that $\Omega'_{bb} < |\Omega'_{ab}|$, that is, the leaf node $b$ in $T'$ violates the constraint. Hence, any decomposition of $\Sigma^o$ which results in an exchange of a leaf node with its neighbor is infeasible. Hence the problem becomes identifiable.
\par
Relabeling if necessary, assume that node $n$ is a leaf node connected to node $n-1$ in $T^*$. From Equation \ref{main_sig_q}, the decomposition of $\Sigma^o = \Sigma' + D'$ to obtain a tree structure $T'$ in which node $n-1$ is a leaf node connected to node $n$ is given by:
\begin{equation*}
    \Sigma'_{ij} =
    \left \{
    \begin{array}{ll}
          \Sigma^*_{ij} - \frac{1}{\Omega^*_{ij}} & \text{if $i = j = n$}\\
          \Sigma^*_{ij} + c_1^i & 0<c_1^i<D^*_{n-1n-1}\text{ if $i = j = n-1$} \\
          \Sigma^*_{ij} & \text{otherwise}.
    \end{array}
    \right.
\end{equation*}
We derive the expression of $\Omega' = (\Sigma')^{-1}$. We denote $B^1$ and $B^2$ as follows:
\begin{align*}
    B^1_{ij} &=
    \left \{
    \begin{array}{ll}
          c_1^i & 0<c_1^i<D^*_{n-1n-1}\text{ if $i = j = n-1$} \\
          0 & \text{otherwise}
    \end{array},
    \right.\\
    B^2_{ij} &=
    \left \{
    \begin{array}{ll}
          - \frac{1}{\Omega^*_{nn}} & \text{if $i = j = n$}\\
          0 & \text{otherwise}
    \end{array}.
    \right.
\end{align*}
This gives us $\Sigma' = \Sigma^* + B^1 + B^2$. The calculation of $\Omega' = (\Sigma')^{-1}$ is presented in Appendix C.
At positions $(n-1, n-1)$ and $(n-1,n)$ of $\Omega'$, we get:
\begin{align*}
    \Omega'_{n-1n-1} &= \frac{1}{c_1^{n-1}},\\
    \Omega'_{n-1n} &=\frac{\Omega^*_{nn}}{c_1^{n-1}\Omega^*_{n-1n}}.
\end{align*}
By the original assumption we have $\Omega^*_{nn} > |\Omega^*_{n-1n}|$, hence
$\Omega'_{n-1n-1} < |\Omega'_{n-1n}|$. Therefore any exchange of leaf node with its neighbor gives an infeasible solution.

\begin{theorem}\label{min_eig_ident}
(Minimum Eigenvalue Identifiability Condition) Suppose that a lower bound on the minimum eigenvalue $\lambda_{\min}$ of $\Sigma^{\ast}$ is such that for every neighbor node $b$ of a leaf node $a$ in $T^*$, $D^*_{bb} < \lambda_{min}$. Then for any decomposition of $\Sigma^o = \Sigma' + D'$ such that the minimum eigenvalue of $\Sigma'$ is at least $\lambda_{min}$, the tree structure of $\Sigma'$ is the same as that of $\Sigma^{\ast}$, i.e., $T' = T^{\ast}$.
\end{theorem}

\begin{corollary}
If the smallest eigenvalue of $\Sigma^{\ast}$ is larger than every element of the diagonal noise matrix $D^{\ast}$, {\em and we know that this fact holds as side information}, then $T^{\ast}$ is identifiable.
\end{corollary}

\begin{proof}
Relabeling if necessary, assume that node $n$ is a leaf node and node $n-1$ is its neighbor in $T^*$. We again consider the decomposition of $\Sigma^o = \Sigma' + D'$ such that the conditional independence structure $T'$ for $\Sigma'$ has leaf node $n-1$ and its neighbor node $n$. In order to prove this theorem we first consider an intermediate matrix $\Sigma^I$:
\begin{equation*}
    \Sigma^I = \Sigma^* + B^2.
\end{equation*}
$\Sigma^I$ has minimum eigenvalue 0 (This is proved in the Appendix A during the proof of Theorem \ref{thm_unident}). $\Sigma'$ is obtained as follows:
\begin{equation*}
    \Sigma' = \Sigma^I + B^1.
\end{equation*}
We denote the minimum eigenvalue of $\Sigma'$ by $\lambda'_{min}$ and $\Sigma^I$ by $\lambda^I_{min}$. Using a standard result in matrix perturbation theory for symmetric matrices \cite{perturbation} we have:
\begin{align*}
    \lambda'_{min} &\leq  \lambda^I_{min} + c_1^{n-1}\\
    &= c_1^{n-1} \\
    &\leq D^*_{n-1n-1}.
\end{align*}
If $D^*_{n-1n-1} < \lambda_{min}$ then $\lambda'_{min} < \lambda_{min}$ making this decomposition infeasible. Hence any decomposition resulting in the exchange of a leaf node $a$ with its neighbor $b$ is infeasible if $D^*_{bb} < \lambda_{min}$.
\end{proof}
Theorem \ref{min_eig_ident} gives a sufficient condition on the noise for identifiability if the minimum eigenvalue is lower bounded. Next, we present a sufficient condition for unidentifiability in the same setting.\\
Before the theorem statement, we define the following quantities for any pair of a leaf node $a$ and its neighbor $b$ in $T^*$:
\begin{equation}\label{definitions}
\begin{aligned}
    e^{ab} &= 1+\frac{\Omega^*_{aa}}{|\Omega^*_{ab}|},\\
    f^{ab} &= \frac{(\Omega^*_{aa})^2}{(\Omega^*_{ab})^2} + \frac{\Omega^*_{aa}}{|\Omega^*_{ab}|},\\
    g^{ab} &= \frac{\Omega^*_{aa}(\Omega^*_{aa}\Omega^*_{bb} - (\Omega^*_{ab})^2)}{(\Omega^*_{ab})^2} + \sum_{\substack{j=1 \\j\neq a,b}}^n \frac{\Omega^*_{aa}|\Omega^*_{bj}|}{|\Omega^*_{ab}|},\\
    h^{ab} &= \max_{\substack{i=1\dots n \\ i\neq a,b}} \Big(\sum_{\substack{j=1 \\ j\neq a,b}}^{n}|\Omega^*_{ij}| + \frac{\Omega^*_{aa}|\Omega^*_{bi}|}{|\Omega^*_{ab}|}\Big).
\end{aligned}
\end{equation}
\begin{theorem}\label{min_eig_unident}
(Minimum Eigenvalue Unidentifiability Condition)
Suppose that a lower bound on the minimum eigenvalue of $\Sigma^*$ is $\lambda_{min}$. If for any decomposition of $\Sigma^o = \Sigma' + D'$, the same constraint holds, the problem will be unidentifiable if, for a leaf node $a$ and its neighbor $b$, the noise in node $b$ is lower bounded as follows:
\begin{equation*}
    D^*_{bb} \geq
    \left \{
    \begin{array}{ll}
          e^{ab}\lambda_{min} & \text{ if $\lambda_{min} \leq \frac{(e^{ab} - f^{ab})}{e^{ab}g^{ab}}$, }\\
          \frac{f^{ab}}{1/\lambda_{min} - g^{ab}} & \text{ if $\frac{(e^{ab} - f^{ab})}{e^{ab}g^{ab}} < \lambda_{min}< \frac{1}{g^{ab}}, \frac{1}{h^{ab}}$. } \\
    \end{array}
    \right.
\end{equation*}
If this holds, there exists a feasible $\Sigma'$ with conditional independence structure $T'$ which has node $b$ as a leaf node and node $a$ as its neighbor.
\end{theorem}
\textit{Proof Outline.} Suppose $\Sigma'$ has node $b$ as leaf node and node $a$ as its neighbor and the rest of the structure is the same as $T^*$. We provide a lower bound on the minimum eigenvalue of $\Sigma'$ by upper bounding the maximum eigenvalue of $\Omega'$ using Gerschgorin's Theorem \cite{perturbation}. The details are provided in Appendix D.\\
Note that a lower bound on the noise for unidentifiability can be given only below a threshold of $\lambda_{min}$. If $\lambda_{min}$ is above this threshold, we cannot draw a conclusion about identifiability using this theorem.

\section{Examples and Illustrations}\label{sec:examples}
In this section we provide an example to illustrate the theorem statements.\\
Consider a Markov Chain (MC) on 4 nodes whose covariance matrix is given as follows:
\begin{equation*}
    \Sigma^* =
    \begin{bmatrix}
    1.1508 &  -0.1885 &   0.0548 &  -0.0069 \\
   -0.1885 &   0.2356 &  -0.0686 &   0.0086 \\
    0.0548 &  -0.0686 &   0.7472 &  -0.0934 \\
   -0.0069 &   0.0086 &  -0.0934 &   0.1367 \\
    \end{bmatrix},
\end{equation*}
Then its precision matrix is:
\begin{equation*}
    \Omega^* =
    \begin{bmatrix}
    1  &  0.8  &       0   &      0 \\
    0.8  &  5  &  0.4   &      0 \\
         0  &  0.4  &  1.5   & 1 \\
         0  &       0  &  1   & 8 \\
    \end{bmatrix}.
\end{equation*}
and $T^*$ is given in Figure \ref{example}(a).
Let the noise matrix be:
\begin{equation*}
    D^* =
    \begin{bmatrix}
    0.1 &  0 &  0 &  0 \\
   0 &   10 &  0 &  0 \\
   0 &  0 &   0.5 &  0 \\
   0 &  0 &  0 &   0.1 \\
    \end{bmatrix}.
\end{equation*}
We have $\Sigma^o = \Sigma^* + D^*$.
\subsection{Example for Theorem \ref{thm_unident}}
By Theorem \ref{thm_unident}, there exists a decomposition of $\Sigma^o = \Sigma' + D'$ such that the conditional independence structure of $\Sigma'$ is given by a tree $T'$ with node 2 as a leaf node. A possible decomposition is as follows:
\begin{equation}\label{eg_decom}
\begin{aligned}
    \Sigma' &=
    \begin{bmatrix}
    0.1508 &  -0.1885 &   0.0548 &  -0.0069 \\
   -0.1885 &   10.2356 &  -0.0686 &   0.0086 \\
    0.0548 &  -0.0686 &   0.7472 &  -0.0934 \\
   -0.0069 &   0.0086 &  -0.0934 &   0.1367 \\
    \end{bmatrix},\\
    D' &=
    \begin{bmatrix}
   1.1 &  0 &  0 &  0 \\
   0 &  0 &  0 &  0 \\
   0 &  0 &   0.5 &  0 \\
   0 &  0 &  0 &   0.1 \\
    \end{bmatrix}.
\end{aligned}
\end{equation}
The precision matrix $\Omega'$ is then:
\begin{equation}\label{eg_new_prec}
    \Omega' =
    \begin{bmatrix}
    6.9687 &   0.1250 &  -0.5 &   0 \\
    0.1250 &   0.1 &   0 &  0 \\
    -0.5 &   0 &   1.5 &   1 \\
    0  &  0  &  1 &   8 \\
    \end{bmatrix}.
\end{equation}
Thus, in the conditional independence structure of $\Sigma'$, node 2 is a leaf node attached to node 1 as shown in Figure \ref{example}(b).

{\bf Chow-Liu}. We now note that running the Chow-Liu algorithm on $\Sigma^o$ gives a MC as shown in Figure $\ref{example}$(c). This tree does not belong to $\mathcal{T}_{T^*}$. This is an example of how the Chow-Liu algorithm can give an infeasible solution.
\begin{figure}
    \centering
    \includegraphics[scale = 0.5]{example_fig1.jpg}
    \caption{(a) $T^*$ is a Markov Chain on 4 nodes. (b) $T'$ is an element of $\mathcal{T}_{T^*}$, thus $\exists \Sigma', D'$ such that $\Sigma^o = \Sigma'+ D'$, $D'$ is diagonal with non-negative entries and the conditional independence structure of $\Sigma'$ is given by $T'$. (c) Running the Chow-Liu algorithm on the $\Sigma^o$ gives a tree which is not in $\mathcal{T}_{T^*}$, hence it gives an infeasible solution.}
    \label{example}
\end{figure}
\subsection{Example of Theorem \ref{noise_ident}}
The noise matrix $D^*$ satisfies the condition of Theorem \ref{noise_ident}:
\begin{equation*}
    D^*_{11} < \frac{1}{\Omega^*_{11}}, D^*_{44} < \frac{1}{\Omega^*_{44}}.
\end{equation*}
Hence by the theorem statement, with side information that $D'_{11} < 1$, the decomposition in Equation \ref{eg_decom} is no longer feasible. Similarly a decomposition with node 3 as a leaf node is also not feasible. Hence the only feasible solutions have the same structure as $T^*$ and the problem is identifiable.\\
\subsection{Example of Theorem \ref{diag_major_ident}}
$\Omega^*$ satisfies the condition of Theorem \ref{diag_major_ident}, that is, for leaf nodes 1 and 4:
\begin{equation*}
  \Omega^*_{11} > |\Omega^*_{12}|,  \Omega^*_{44} > |\Omega^*_{34}|.
\end{equation*}
In the presence of side information that for any leaf node $b$ connected to node $a$ in $T'$, $\Omega'_{bb} > |\Omega'_{ab}|$, the decomposition in Equation \ref{eg_decom} becomes infeasible as $\Omega'_{22} < |\Omega'_{12}|$. Similarly, exchanging nodes 3 and 4 also results in an infeasible $\Sigma'$. Hence the problem becomes identifiable with this side information.
\subsection{Example of Theorem \ref{min_eig_ident}.}
A lower bound on the minimum eigenvalue of $\Sigma^*$ is $\lambda_{min} = 0.6$. The noise in node 2 does not satisfy the condition of Theorem \ref{min_eig_ident}, that is:
\begin{equation*}
    D^*_{22} > \lambda_{min}.
\end{equation*}
Therefore, we cannot say anything about the feasibility of the decomposition when node 2 becomes a leaf node connected to node 1. However, the condition of Theorem \ref{min_eig_ident} is satisfied by node 3, that is:
\begin{equation*}
    D^*_{33} < \lambda_{min}.
\end{equation*}
Therefore any decomposition which results in node 3 becoming a leaf node violates the minimum eigenvalue constraint (if $\Sigma'$ were such that node 3 were a leaf node, the minimum eigenvalue of $\Sigma'$ could at most be 0.0046  $< \lambda_{min}$).
\subsection{Example of Theorem \ref{min_eig_unident} }
In order to illustrate Theorem \ref{min_eig_unident}, we consider leaf node 1 and its neighbor node 2. The values $e^{12}, f^{12}, g^{12}, h^{12}$ for the current example are:
\begin{equation*}
    e^{12} = 2.25, f^{12} = 2.8125, g^{12} = 7.3125, h^{12} = 9.
\end{equation*}
If $\lambda_{min} = 0.6$, we cannot draw a conclusion about the identifiability of the problem using Theorem \ref{min_eig_unident} as $\lambda_{min}>1/h^{12}$. If instead $\lambda_{min} = 0.1$, it satisfies $\lambda_{min}<1/h^{12}, 1/g^{12}$. Hence we can arrive at a lower bound on the noise for unidentifiability using Theorem \ref{min_eig_ident} which is given as follows:
\begin{equation*}
    D^*_{22} > 1.0465.
\end{equation*}
In Figure \ref{eg_bound}, we present noise regions for node 2 for sufficient conditions of identifiability and unidentifiability.
\begin{figure}
    \centering
    \includegraphics[scale = 0.15]{min_eigenvalue.jpg}
    \caption{Suppose the lower bound on the minimum eigenvalue is $\lambda_{min}$. If the noise in node 2 lies in the unidentifiable region for a given $\lambda_{min}$, there exists a $\Sigma'$ with minimum eigenvalue greater than $\lambda_{min}$ and node 2 as a leaf node. If the noise in node 2 lies in the identifiable region for a given $\lambda_{min}$, any $\Sigma'$ with node 2 as a leaf node will have minimum eigenvalue less than $\lambda_{min}$.}
    \label{eg_bound}
\end{figure}

\section{Algorithm}\label{sec:algorithm}
In this section we present an algorithm which takes the noisy covariance matrix $\Sigma^o$ as an input and outputs $\mathcal{T}_{T^*}$. We use the classification of 4 nodes as a star shape or non star shape, the concept of subtrees, complementary subtrees and equivalence cluster (EC) that we introduced in the proof of Theorem \ref{thm_limited_unident}.
\begin{enumerate
\setlength\itemsep{0em}
    \item We start by obtaining a subtree $\mathcal{B}$ and a node from the closest EC outside of this subtree $i_{outside_{B}}$. To do so:
    \begin{enumerate}
    \setlength\itemsep{0em}
        \item We partition all the nodes into complementary subtrees $\mathcal{B}$ and $\mathcal{B'}$ with at least 2 nodes using only the off diagonal terms of $\Sigma^o$. This is implemented in \textsc{PartitionNodes}$(\Sigma^o)$.
        \item We pick any node $i_B$ in $\mathcal{B}$.
        \item  We find the EC in $\mathcal{B'}$ that has an edge with a node in $\mathcal{B}$ in $T^*$ by calling  \textsc{GetClosestEquivalenceCluster}. We select one node from this EC, $i_{outside_{B}}$.

    \end{enumerate}
    \item We learn all the ECs and the edges between ECs in $\mathcal{B}$ by calling \textsc{LearnEdges} which uses a node from the closest EC outside $\mathcal{B}$. The sets of ECs and edges are initialized as null sets. We perform the following steps:
    \begin{enumerate}
    \setlength\itemsep{0em}
        \item We first call \textsc{GetClosestEquivalenceCluster} to obtain $EC_{close}$, the EC closest to $i_{outside_{B}}$. We add this EC to the set of ECs and select one node $i_{close}$.
        \item We add the edge between the EC containing $i_{outside_{B}}$ and $EC_{close}$ in the edge set.
        \item We then call \textsc{SplitRootedTree} to split $\mathcal{B}\setminus EC_{close}$ into the subtrees $\mathcal{B}_1, \dots, \mathcal{B}_k$.
        \item For any $\mathcal{B}_j$, $i_{close}$ is a node from the closest EC. We recursively call \textsc{LearnEdges} on all the subtrees.

    \end{enumerate}
    \item We repeat 1.b) - 2.d) with $\mathcal{B'}$ instead of $\mathcal{B}$.
\end{enumerate}
This is illustrated in Figure \ref{fig:algo}.
\begin{figure}
    \centering
    \includegraphics[scale = 0.5]{algo.jpg}
    \caption{One recursive step of \textsc{LearnEdges}.}
    \label{fig:algo}
\end{figure}
We next present the implementation and proof overview of all the functions.
\subsection{Algorithm to partition all the nodes into two subtrees - \textsc{PartitionNodes}}
The function \textsc{PartitionNodes} can be split in two parts:
\begin{enumerate}[(i)]
\setlength\itemsep{0em}
    \item Find a set of 4 nodes which forms a non star. Let this set be $\{i_1, i_2, i_3, i_4\}$ such that nodes $i_1$ and $i_2$ form a pair.
    \item Call the function \textsc{SmallestSubtree} to obtain complementary subtrees $\mathcal{B}$ and $\mathcal{B'}$ such that $\mathcal{B}$ is the smallest subtree containing $i_1$ and $i_2$.
\end{enumerate}
For part (i), we fix two nodes and scan through all the pairs of the remaining nodes. If there exists a set of 4 nodes which forms a non star shape, this procedure finds that set. If there is no such set, $T^*$ has a single EC.\\
Part (ii) is the same as discussed in the proof of Theorem \ref{thm_limited_unident}.
In Appendix E, we give the pseudo-code, proof of correctness and prove that this function is $\mathcal{O}(n^2)$
\subsection{Algorithm to find the closest equivalence cluster - \textsc{GetClosestEquivalenceCluster}}
As an input, \textsc{GetClosestEquivalenceCluster} takes the set of the nodes of the subtree $\mathcal{B}$, an external node $i_{outside_B}$ which belongs in $\mathcal{A} \setminus \mathcal{B}$, and the observed covariance matrix $\Sigma^o$. It outputs the EC in $\mathcal{B}$ closest to $i_{outside_{B}}$.

We first find a node from the closest EC. We initialize its estimate $i_{close}$ to be the first node of $\mathcal{B}$. We notice an important fact:
if $\{i_{outside_B}, i_2, i_3, i_4\}$ forms a non-star shape, nodes from the closest EC always pair with $i_{outside_B}$. Therefore, we can compare two nodes $i_{close}$ and $i_{candidate}$: if there exists a node $j$ in $\mathcal{B}$ such that $\{i_{outside_B}, i_{close}, i_{candidate}, j\}$ forms a non-star shape and $i_{candidate}$ is paired with $i_{outside_B}$, then $i_{close}$ is ruled out and $i_{candidate}$ becomes the next estimate $i_{close}$. We use this fact to find a node $i_{close}$ in the closest EC to $i_{outside_{B}}$, by scanning through all the values of $i_{candidate}$ and $j$.

Further, we find the remaining nodes in the EC of $i_{close}$. A node $i_{equivalent}\in \mathcal{B}$ is in the EC of $i_{close}$ if  $\{i_{outside_B}, i_{close}, i_{equivalent}, j \}$ forms a star shape $\forall j \in \mathcal{B} \setminus \{i_{close} \}$.
In Appendix E, we give the pseudo-code, proof of correctness and prove that this function is $\mathcal{O}(n^2)$.

\subsection{Algorithm to split a subtree - \textsc{SplitRootedTree}}
As inputs, \textsc{SplitRootedTree} takes the subset $\mathcal{B}$, an external node $i_{outside}$, the EC to be removed $EC_{close}$, and the observed covariance matrix $\Sigma^o$. It outputs a list of the largest subtrees  $\mathcal{B}_1, \dots, \mathcal{B}_k$ containing all the nodes of $\mathcal{B}\setminus EC_{close}$.

Choose any $i_{close}\in EC_{close}$. To get these subtrees, we notice an important fact: $i_1$ and $i_2$ belong in the same subtree of $\mathcal{B}\setminus EC_{close}$, if and only if $\{i_{outside}, i_{close}, i_1, i_2\}$ forms a non-star shape. Therefore, we pick any node of $\mathcal{B} \setminus EC_{close}$, and use it to initialize $\mathcal{B}_1$. Then, for each new node $j$ in $\mathcal{B}$, for each subset $\mathcal{B}_i$ containing a node $i_{\mathcal{B}_i}$ we check if $\{i_{outside}, i_{close}, j, i_{\mathcal{B}_i}\}$ forms a non-star shape. If it does, we add $j$ to $\mathcal{B}_i$. Otherwise, we create a new subset containing only $j$. In Appendix E, we give the pseudo-code, proof of correctness and prove that this function is $\mathcal{O}(n^2)$
\subsection{Algorithm to find equivalence clusters and edges between equivalence clusters - \textsc{LearnEdges}}
We use \textsc{GetClosestEquivalenceCluster} and \textsc{SplitRootedTree} to find the ECs and the edges between the ECs.

As inputs, \textsc{LearnEdges} takes a subtree $\mathcal{B}$, an external node $i_{outside_B}$ which is a node in the EC in $\mathcal{A} \setminus \mathcal{B}$ closest to $\mathcal{B}$ and the observed covariance matrix $\Sigma^o$. The set of ECs ($equivalence\_clusters$) and the edges between ECs ($cluster\_{edges}$) are initialized as empty sets. This function updates these sets.

This is done in the following steps:
\begin{enumerate}
\setlength\itemsep{0em}
    \item Use \textsc{GetClosestEquivalenceCluster} to get the equivalence cluster $EC_{close}$ in $\mathcal{B}$ closest to $i_{outside_B}$. Add $EC_{close}$ to $equivalence\_clusters$ and the edge between $EC_{close}$ and the EC containing $i_{outside_B}$ in $cluster\_{edges}$.
    \item Use \textsc{SplitRootedTree} to split $\mathcal{B}\setminus EC_{close}$ into subtrees $\mathcal{B}_1, \dots, \mathcal{B}_k$.
    \item For each of these subtrees $\mathcal{B}_j$, $i_{close}\in EC_{close}$ is a node from the closest EC in $\mathcal{A}\setminus \mathcal{B}_j$. Recursively call \textsc{LearnEdges} with $\mathcal{B}_j$, $i_{close}$ and $\Sigma^o$ as inputs.
\end{enumerate}

\subsection{Complete Algorithm - \textsc{LearnClusterTree}}
Finally, we describe \textsc{LearnClusterTree}, the complete algorithm which learns all the ECs of a tree $T^*$ and the edges between them from the observed covariance matrix $\Sigma^o$.\\
As input, it takes the observed covariance matrix $\Sigma^o$. It populates the ECs, $equivalence\_clusters$, and the edges between ECs, $cluster\_edges$. \textsc{LearnClusterTree} performs the following steps:
\begin{enumerate}
\setlength\itemsep{0em}
    \item Partition all the nodes in complementary subtrees $\mathcal{B}$ and $\mathcal{B'}$ using the \textsc{PartitionNodes} function.
    \item Using the \textsc{GetClosestEquivalenceCluster} function, it finds a node $i_{outside_B}$ from the closest EC (respectively $i_{outside_{B'}}$) to $\mathcal{B}$ in $\mathcal{B'}$ (respectively to $\mathcal{B'}$ in $\mathcal{B}$).
    \item It finally learns all the ECs and the edges between ECs by recursively calling \textsc{LearnEdges}$(i_{outside_B}, \mathcal{B}, \Sigma^o)$ followed by \textsc{LearnEdges}$(i_{outside_{B'}}, \mathcal{B'}, \Sigma^o)$.
\end{enumerate}
In Appendix E, we give the pseudo-code, proof of correctness and prove that this function is $\mathcal{O}(n^3)$, hence the algorithm is $\mathcal{O}(n^3)$.

\newpage
\balance

redpajama_set_name: RedPajamaArXiv


text:
Петре́нкове — село в Україні, у Валківській міській громаді Богодухівського району Харківської області. Населення становить 17 осіб. До 2020 орган місцевого самоврядування — Шарівська сільська рада.

Географія
Село Петренкове знаходиться на правому березі річки Карамушина, примикає до села Шевченкове, на відстані 2 км розташовані села Хворостове, Рогівка і Коверівка, поруч знаходиться лісовий масив (дуб), за 2 км проходить залізниця, станція Хворостове.

Історія
12 червня 2020 року, розпорядженням Кабінету Міністрів України № 725-р «Про визначення адміністративних центрів та затвердження територій територіальних громад Харківської області», увійшло до складу Валківської міської громади.

17 липня 2020 року, в результаті адміністративно-територіальної реформи та ліквідації Валківського району, село увійшло до складу Богодухівського району.

Примітки

Посилання
 Погода в селі Петренкове

Села Харківської області
Населені пункти Богодухівського району

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text:
Nick Cave and The Bad Seeds Announce European Tour in Support of New Album "Ghosteen"
Following the surprise release of their spellbinding seventeenth studio album Ghosteen, Nick Cave & The Bad Seeds have announced a European tour taking place next spring in support of the critically acclaimed record.
The tour begins April of 2020 with two nights in Lisbon, Portugal, and continues through Spain and into the Netherlands and Belgium before heading over to the UK, with the first show in Birmingham.
Next on the itinerary are gigs in Cardiff, Glasgow, Manchester, Ireland, Leeds before closing out the UK leg of the tour with two nights in London at the O2.
After dates in Germany, Switzerland, Scandinavia (including two nights in Denmark), Italy and Eastern Europe, Cave and the band have boldly decided to end the tour with a concert in Tel Aviv, Israel, a decision that will certainly court more controversy, as Cave had previously clashed with musicians such as Brian Eno, and Roger Waters over the BDS movement boycotting performances in the Middle-Eastern Country.
Cave had previously alluded to the controversy in a recent post in his Personal AMA blog, The Red Hand Files issue #66, expounding on his opinions of free speech and "Woke" culture.
See the full dates, below.
Nick Cave & The Bad Seeds Tour Dates:
Europe Part 1:
22 April – Campo Pequeno, Lisbon, Portugal
25 April – WiZink Center, Madrid, Spain
26 April – Palau Sant Jordi, Barcelona, Spain
29 April – Ziggo Dome, Amsterdam, Holland
30 April – Sportpaleis, Antwerp, Belgium
2 May – Arena Birmingham, Birmingham, UK
3 May – Motorpoint Arena, Cardiff, UK
5 May – The SSE Hydro, Glasgow, UK
6 May – Manchester Arena, Manchester, UK
8 May – 3Arena, Dublin, Ireland
12 May – First Direct Arena, Leeds, UK
14 May – The O2, London, UK
17 May – Lanxess Arena, Cologne, Germany
18 May – Barclaycard Arena, Hamburg, Germany
20 May – Royal Arena, Copenhagen, Denmark
23 May – Ericsson Globe, Stockholm, Sweden
25 May – Spektrum, Oslo, Norway
27 May – Mercedes-Benz Arena, Berlin, Germany
28 May – Arena Gliwice, Gliwice, Poland
30 May O2 – Arena, Prague, Czech Republic
1 June – Stadthalle, Vienna, Austria
2 June – László Papp Budapest Sportaréna, Budapest, Hungary
4 June – Stark Arena, Belgrade, Serbia
6 June – Olympiahalle, Munich, Germany
8 June – Hallenstadion, Zurich, Switzerland
9 June – Mediolanum Forum, Milan, Italy
11 June – Cavea Auditorium Parco della Musica, Rome, Italy
14 June – AccorHotels Arena, Paris, France
17 June – Bloomfield Stadium, Tel Aviv, Israel
Lynchian Songstress Kat Koan Bathes in Iridescent Light in "White"
Avant-garde Electronic Music Auteur Autumns Announces New Cassette Album "Foyle Living" and Tour Dates
The Sisters of Mercy add Second Date in Los Angeles and Headlining Concert in Las Vegas
New Order Announce US Live Dates This March
Berlin-based Post-Punk Outfit ERRORR Debuts Video for "Innocent" Starring Gloria De Oliveira and Henryk Gericke
Cruel World 2023 Announces Siouxsie, Love and Rockets, Adam Ant, Iggy Pop, Billy Idol, Gary Numan and More
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Sit on interchange fabrics long sufficient till you locate one that is right for you. This is especially important if it is going to be "the sofa," that special one that is used every the time. taking into account examination for fabric, you should then check to see if it wrinkles easily or stretches. If it wrinkles easily, it will be difficult to preserve its looks for a long time. Sagging fabric will create it see dilapidated extremely quickly.


text:
I am a writer of romances and mysteries – a little bit of something for everyone.
Love a historical Western romance with steamy love scenes? Try Cera's Place.
Love a historical romance with mild love scenes? Try Venice in the Moonlight.
Love a contemporary romance filled with angst and mild love scenes? Try First Crush, Last Love.
Love a cozy mystery with just a splash of romance akin to Nancy Drew? Try The Great Jewel Robbery.
Love a dark mystery filled with murder and a bit of romance? Try Killer Resolutions.
Killer Resolutions (Novella)
For fans of Agatha Christie's And Then There Were None . . .
Five years ago, a tragedy shattered the friendship between Dani, her older brother, and their college pals. When her brother invites the old gang for a weekend of outdoor winter fun at a remote lodge, she sees it as a chance to reconnect and heal. But when her friends are murdered one-by-one, Dani must determine whom she can trust before she becomes the next victim.
Goodreads – 4.5 stars "Killer Resolutions is another exciting suspense filled mystery by Elizabeth McKenna…I did not find it to be predictable and was surprised who the killer was in the end. There is quite a bit of twists and turns that left my head spinning. I never knew what was going to happen next."
The Great Jewel Robbery (Novel)
A Front Page Mystery – Book 1
For fans of cozy mysteries . . .
Chicago Tribune reporters Emma and Grace have been best friends since freshman year of college despite coming from different worlds. When Grace is assigned to cover an annual charity ball and auction being held at a lakeside mansion and her new boyfriend bails on her, she brings Emma as her plus one. The night is going smoothly until Emma finds the host's brother unconscious in the study. Though at first it is thought he was tipsy and stumbled, it soon becomes clear more is afoot, as the wall safe is empty and a three-million-dollar diamond necklace is missing. With visions of becoming ace investigative journalists, Emma and Grace set out to solve the mystery, much to the chagrin of the handsome local detective.
Goodreads – 5 stars "I really enjoyed this book! There were fun characters to meet and watch develop throughout the story. Both the characters and the plot kept me guessing who would be the robber…This really is a great read for everyone from teenagers to adults."
Murder up to Bat (Novel) – Coming Soon!
After falling in love with the quiet lake life and a certain police detective, former Chicago Tribune reporter Emma Moore trades interviewing jocks for chasing champion cows at the county fair. As a small-town newspaper reporter, she covers local topics both big and small, but when her friend Luke is arrested for the murder of the head coach of his club softball team, she'll need to hone her investigative skills to clear his name. Emma calls up best friend Grace for help, and together the women go up against cutthroat parents willing to kill for a chance to get their daughters onto a premier college sports team.
It's the bottom of the ninth with bases loaded, and murder is up to bat. Can Emma and her friends bring the heat and win the game?
First Crush, Last Love (Novel)
Remember your first crush? How your heart raced and your cheeks flushed whenever you saw him? Jessie Baxter does, and it's happening again. Ten years ago, despite her best efforts, Lee Archer wanted to be just friends. Now, he wants more, but Jessie's still recovering from a psycho ex-husband. Can she learn to trust again and make her first crush into her last love?
Elizabeth McKenna's latest novel will have you remembering the angst of high school, the grief of a failed relationship, and the happiness of true love.
Goodreads – 5 stars "The story was captivating and drew me in from the start. I loved the character development that both Jessie and Lee went through as they grew up and discovered what they wanted from life. The struggles they went through were extremely well written and kept me, as a reader, invested in their story. The tension caused by the undertones of violence and abuse provided an edge to counteract the sweet romantic elements."
Venice in the Moonlight (Novel)
A young widow discovers her father's murderer is related to the man she's falling in love with and must decide between vengeance, forgiveness, and love.
Goodreads – 5 stars "A delightful book in which the author captures the essence of Venice in the eighteenth century…The romance is extremely well done and it just shows that it doesn't need to be graphic to be steamy. If you like Italy, romantic heroes or history you'll love this book."
Chosen as Best Historical Romance 2013 by Escape with Dollycas Into a Good Book
Cera's Place (Novel)
Sparks fly when a feisty saloon owner crosses paths with a scarred Civil War hero.
Goodreads – 5 stars "The love story between Jake and Cera is gradual, leading up to some pretty awesome love scenes that left me tingling and wanting more."
The Gypsy Casts a Spell (Short Story)
Vadoma turns to desperate measures (and a handsome Marquis) to save her kin from the gallows.
Read it for free.
Published in the February 2012 edition of eFiction Magazine.
6 thoughts on "Welcome"
Angela Joseph (@trincity) said:
Intriguing, Elizabeth! Sounds like the kind of book I would love to read.
elizabethmckennaauthor said:
I hope you – and others – will like it. It's been fun to write so far!
Judith Post said:
I really enjoyed The Gypsy Casts a Spell. Two great characters. I fell for each of them.
Thank you, Judith!
Thaveesa said:
Totally my kinda novels
Elizabeth McKenna - Romance Author said:
Thank you for stopping by, Thaveesa!


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text:
Q: Prevent state reloading when changing states ui-router I understand this has been asked and answered in multiple posts but I have attempted the solutions and still can't quite get there yet.
I have a few components that I'm routing between with ui-router and one is a contact form which, if a user enters data to and moves to another route then back to the contact form the state is reloaded and the form contents gone.
I saw another way of doing this by having a parent state and child states but couldn't recreate this in my code.
Maybe there's a simpler solution by using ui-router-extras with the sticky option although I attempted this and could't get it working either. I'll post the code as it works now.
(function () {
    angular.module('personalPortfolio')
        .config(['$stateProvider', '$urlRouterProvider', function ($stateProvider, $urlRouterProvider) {

            $stateProvider
                .state('about', {
                    sticky: true,
                    url: '/about',
                    template: '<pg-about></pg-about>'
                })

                .state('development', {
                    sticky: true,
                    url: '/work',
                    template: '<pg-dev></pg-dev>'
                })

                .state('contact', {
                    sticky: true,
                    url: '/contact',
                    template: '<pg-contact></pg-contact>'
                });

            $urlRouterProvider.otherwise('/about');
        }]);
})();

A: You can create a service when You will store unsaved form data.

redpajama_set_name: RedPajamaStackExchange


text:
Diocese releases names of clergy accused of child sexual abuse
Lyle Peterson leads Trump, a Belgian horse at Red Ridge Ranch Riding Stable that survived an influx of hay contaminated from toxic blister beetles. Of the surviving 110 horses, 100 were sickened.
JOHN HART, STATE JOURNAL
Cindy Kanarowski-Peterson has been riding horses since she was 2 years old and has had her own ranch for 20 years, but has never endured the death of 14 horses from toxic hay. She's now trying to heal her remaining herd and is trying to bring awareness about the potential problems of buying hay from Wyoming and South Dakota.
Lyle Peterson moves one of the few good bales of hay at Red Ridge Ranch Riding Stable. It was grown on the 355-acre ranch, but most of the 2019 crop was hampered by rains and floods, forcing the ranch to purchase hay elsewhere.
These large bales of hay are useless for Cindy Kanarowski-Peterson, who had 14 horses die from the toxic hay. She's now looking for other sources of hay to get her 110 horses through the winter.
Horse blankets were draped last week over a fence at Red Ridge Ranch Riding Stable near Mauston. The blankets, once worn by some of the 14 horses who died over the last four months from eating toxic hay purchased from South Dakota and Wyoming, were being aired out by Cindy Kanarowski-Peterson, who owns the ranch along with her husband, Lyle Peterson. "Our winter hay is a total loss and we are left with a barn full of poisonous hay," Kanarowski-Peterson said.
Horses at Red Ridge Ranch Riding Stable near Mauston are on the mend after being sickened by toxic blister beetles that contaminated loads of hay purchased from out-of-state vendors.
This pile of hay was among six loads of hay purchased from farmers in South Dakota and Wyoming that was contaminated by blister beetles, which when crushed during the harvest, secrete a toxin that can be deadly to horses.
The outpouring of support has been overwhelming for Cindy Kanarowski-Peterson, seen here with longtime friend Rick Short, who was dropping off a $100 donation and another $500 check from a neighbor to help the ranch purchase hay.
Small but toxic beetles kill 14 horses on Mauston horse ranch
BARRY ADAMS badams@madison.com
MAUSTON — Cindy Kanarowski-Peterson thought she was set for the winter.
Steady rains over the summer and flooding had left much of the 252 acres of hay fields at her Red Ridge Ranch Riding Stable unusable and in some cases under water. So in late August, she and her husband, Lyle Peterson, purchased six semi-tractor trailer loads of hay and alfalfa from farms in South Dakota and Wyoming with the hope that it would be enough to make it through the first cutting of hay in June.
But what appeared to be a problem solved has turned into a heart-wrenching disaster.
A blister beetle, a bug that when crushed during harvest secrets a deadly toxin, is being blamed for the deaths of 14 of their beloved horses at Red Ridge. The beetles, typically not an issue for Wisconsin-grown hay, also sickened another 100 horses on the ranch and has the couple scouring the region for new sources of hay to keep their 110 horses fed. At some point they'll likely be looking for an attorney.
Blankets, once worn for warmth by the now-dead horses, hung on a fence last week in effort to air them out, but they also served as a cold and painful reminder of the equines who began dying shortly after Labor Day. The Belgian, Mustang, Appaloosa, Percheron and other breeds sported names like Jill, Bell, Leo, Brown Beauty, Elvira and Breeze. Sir Bob the 4th, Charlie and Talley are gone, too, along with Little Nick. Big Nick died Jan. 3.
"I need to get rid of them," Kanarowski-Peterson said of the blankets. "It's just sickening that we've had to go through this."
Kanarowski-Peterson is now trying to bring awareness to other ranchers about blister beetles, and she's launched a Go Fund Me campaign with a goal of $50,000 to help cover the costs of buying new hay and paying for veterinarian bills. While insurance would cover the loss of harvested hay due to a fire or tornado, the ranch's insurance policy does not cover blister beetles. A $5,000 load of hay arrived Friday, but they passed on a load they looked at on Thursday that was for sale near Westfield for $150 per bale, which are 3 feet high, 3 feet wide and 8 feet long. The $40,000 worth of hay purchased this fall from farms out west cost about half of what it would cost to buy the hay now in Wisconsin.
"We thought we were doing the right thing," Kanarowski-Peterson said. "That was the better deal we thought. But not after 14 dead horses."
As of Saturday, 408 people have donated nearly $21,000 to the online campaign, while other donations have come in from both longtime customers and those who have never mounted a horse or taken a wagon or sleigh ride on the sprawling ranch located along Highway 82 just north of the Lemonweir River.
Rick Short, a longtime friend of Kanarowski-Peterson and her husband, stopped by on Thursday to donate $100 and to drop off a $500 check from one of his neighbors, a frequent customer who rode Talley, one of the horses that died.
"Everyone out here can't believe it. It's just one of those wild things," Short said from the seat of his pickup truck as it idled in the driveway of the ranch. "Who would have thought it would have been from little bugs."
According to PJ Liesch, director of the UW-Madison Insect Diagnostic Lab, blister beetles comprise an entire family of beetles that can be found worldwide. There are around 400 species in North America, including almost 30 species in Wisconsin that aren't typically on hay and alfalfa during harvest. In general, Liesch said, blister beetles are oblong, not particularly hard or crunchy, with somewhat softer exoskeletons, similar to fireflies.
"In the grand scheme of things, blister beetles are not uncommon in Wisconsin. However, they are rarely an issue in hay," Liesch wrote Friday in an e-mail to the Wisconsin State Journal. "In my nearly six years as director of the UW Insect Diagnostic Lab, the recent incident in the state is the only time I've encountered an issue with horses and blister beetles. Having multiple horses die is an unusual occurrence."
Dr. Dave Kolb, an equine veterinarian with Lodi Veterinary Care, one of the largest veterinary clinics in the state, said this is the first time in his 32-year career that he has dealt with the deaths of horses from blister beetles. Kolb, who performed necropsies on two of the horses at Red Ridge, said that when blister beetles are ingested by horses (cows are less affected) the toxin, called cantharidin, is "very irritating" to the linings of the stomach and intestines. Kolb said that the beetles in the hay were likely crushed by harvesting machinery, but the cantharidin remains toxic on the hay. Adding to the problem is that horses are unable to vomit to clear their systems.
"Both of (the horses necropsied) had holes in (their stomachs) and that's what causes the death," said Kolb, who believes the surviving horses have a good shot at recovering. "The GI system and kidneys are affected, but with time the lesions are going to heal up and the kidneys should get back to normal as well."
Kanarowski-Peterson initially thought the first cases were just colic. But as the problems grew she considered it to be bad grain and then thought it was worms. Her surviving horses are now getting a mineral lick supplement to help them recover, heal from the inside out and gain weight that was lost over the last four months.
Red Ridge — located just west of Woodside Sports Complex, which hosts youth baseball, softball, soccer and other sporting events — opened 20 years ago with 10 horses and 20 acres of land. Kanarowski-Peterson, 51, a graduate of Mauston High School, has been riding horses since she was 2 years old, and her mother used to trick ride. Kanarowski-Peterson started the ranch as a way to have her own horses. She competes in barrel racing, along with a sister who also trains and sells barrel horses, while two other sisters are also into horses.
At Red Ridge, Kanarowski-Peterson and her husband make their livelihood offering up year-round trail rides to the tourists that flock from around the country to nearby Wisconsin Dells. Muscovy ducks waddle around the ranch, chickens cluck, roosters crow and the cats romp and play, but the horses are the draw here, along with Bonnie, the lone mule.
"I love horses," Kanarowski-Peterson said. "It doesn't matter what breed, what color, what size. I love them all, but I don't know if I can ever begin to replace what I lost."
Barry Adams covers regional news for the Wisconsin State Journal. Send him ideas for On Wisconsin at 608-252-6148 or by email at badams@madison.com.
Cindy Kanarowski-peterson
Dave Kolb
Red Ridge Ranch
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text:
Murder Mystery Review
Originally published in Student Life.
All Student Theatre gathered for a performance this past Friday night. But, instead of a show they had rehearsed weeks for, the performance was acted out by the audience, as the nautical-themed murder mystery unfolded in three rooms in the Danforth University Center. The event is timed to get students in the Halloween spirit and to fundraise for their spring show, which will be "Expecting Isabel" this year.
Clad in outlandish costumes from ball gowns and crowns to a hole-filled jean jumpsuit, mystery-goers were cast into characters the night before. Through lengthy biographies and objectives that read like stage directions for each round of the night, the attendees became their characters over the course of the evening and investigated their fellow boat passengers as suspects, after character Candy Cann was killed.
Lindsay Tracy | Student Life
A student plays dead. All Student Theatre presented "Cruising for Murder!" on Oct. 22.
"What I think is really fun about the murder mystery is that it's like a one-hit wonder," junior Kate Biddle, the organizer of the event, said. "It just has to work."
All Student Theatre (AST) created the event two years ago to engage students in AST's theater before their spring show. After the votes were cast and the murderer was revealed, AST announced that their spring show will be "Expecting Isabel," a dramedy about a couple trying to have a child, and will be directed by senior Rose Shapiro.
The night started in the Orchid Room, where the audience mingled with fellow passengers and AST board members, dressed as boat crew. After the death of a showgirl character, the group moved to the Goldberg Formal Lounge, for more food and intense discussions and cross-examinations of the other characters. After the police character, played by Shapiro, announced additional evidence, the group moved to the Harvey Media Center, where the audience cast their votes on who the murderer was and then revealed the true culprit. Throughout the night, characters used fake money, distributed in envelopes at the beginning of the night, to bribe information from others in order to solve the puzzle.
Though they don't get to act in the murder mystery, the AST members still get the thrill of the show during the course of the night, as they interact with the characters and manage behind-the-scenes work. At the end of the night, the audience members walked away with a better understanding of acting and one heck of a story to tell.
December 28, 2016 by lindsaytracy	Journalism, Murder Mystery, Photography, Photojournalism, Student Life, Videography


text:
Века () је врста птице нелетачице из породице барских кока (лат. -{Rallidae}-). Ендемит је Новог Зеланда. Признате су четири подврсте, али само за две (северна и јужна) постоје генетски докази. Века је птица смеђе боје, отприлике величине кокошке. Сваштојед је и храни се углавном бескичмењацима и воћем. Века обично полаже јаја између августа и јануара; оба пола учествују у инкубацији.

Опис
Века је велика барска кока. Перје јој је смеђе боје прошарано црним и сивим мрљама; смеђа нијанса варира од бледе до тамне у зависности од подврсте. Мужјак је већи од женке, достиже дужину од 50–60 cm и тежину од 532–1,605 g. Женке су дуге 46-50 cm и тешке 350-1,035 g. Распон крила креће се од 50 до 60 cm.

Релативно велики, црвенкасто-смеђи кљун дугачак је око 5 cm, чврст је и узак, а користи га као оружје. Шиљати реп готово непрестано помера, што је знак нелагодности карактеристичан за породицу барских кока. Века има чврсте ноге и смањена крила.

Таксономија и распрострањеност
Народно име, века, потиче из маорског језика, а научни назив, -{Rallus australis}-, дао јој је 1789. Андерс Ериксон Спарман. Спарман је опис врсте, четири фасцикле на основу примерака прикупљених током путовања са капетаном Џејмсом Куком између 1772. и 1775. објавио у музеју Карлсонијанум (-{Museum Carlsonianum}-). -{Australis}- је латинска реч, која значи "јужна". Био је усвојен предлог Јохана Георга Ваглера из 1830, да подврсте веке буду признате као посебне врсте и смештене у род -{Ocydromus}-. Међутим, века је касније класификована као једна врста са четири подврсте и смештена у род -{Gallirallus}-.

Подврсте:
 Мркожута века (-{Gallirallus australis hectori}-) раније је насељавала источне дистрикте Јужног острва, али је данас ограничена на острво Чатам и острво Пит на које је уведена почетком 1900-их, а где је лов на њу у јесен широко распрострањен, због употребе у исхрани (лов на њу је прихватљив јер је на ова острва уведена). Поновно увођење у Кантербери до сада је било неуспешно, али су увођење на острво Мао Вахо (у језеру Ванака 2004. године) и одатле на острво Пиџ`н и Пиг (у језеру Вакатипу 2005/2006) била много успешнија. Перје ове подврсте много је светлије од осталих подврста.

 Северна века (-{Gallirallus australis greyi}-) представљена је изворним популацијама у Нортленду и заливу Пав`рти, као и пренетим јединкама на друге локације, а које потичу из тих популација. Ова подврста се разликује по сивљим доњим деловима тела и смеђим, а не црвенкастим ногама.

 Западна века (-{Gallirallus australis australis}-) насељава углавном северне и западне регионе Јужног острва од Нелсона до Фјордленда. Одликује се тамноцрвено-смеђим и црним пругама на грудима, западна века има два различита обрасца боја, код најјужнијих популација присутнија је црна боја, док је код осталих присутнија кестењаста.

 Ракијурска века (-{Gallirallus australis scotti}-) је мања од других подврста и попут западне веке, има два обрасца боја; кестењаста форма, слична је кестењастој западној веки, док црна форма није толико тамна као црна западна века. Поново уведене популације ограничене су на острво Стјуарт / Раки(ј)уру и околна острва, као и на острво Капити на које је уведена. Века је домаћин две врсте птичјих ваши (-{Rallicola harrisoni}- и -{Pseudomenopon pilgrimi}-) које показују исту структуру популације север-југ виђену код њихових домаћина.

Понашање

Станиште и исхрана
Века насељава шумска станишта, субалпијске травњаке, пешчане дине, камените обале и измењено полуурбано окружење. Она је сваштојед, а исхрана садржи 30% животињске хране и 70% биљне хране. Животињска храна укључује глисте, ларве, бубе, вете (-{Anostostomatidae}- и -{Rhaphidophoridae}-), мраве, пужеве, јаја инсеката, мокрице, жабе, пауке, пацове, мишеве и мале птице. Ракијурска века (-{G. a. scotti}-) примећено је како лови јаја и пилиће гараве бурнице (-{Ardenna grisea}-, syn. -{Puffinus griseus}-).

Биљна храна укључује лишће, траву, бобице и семење. Века је важна због расејавања семена, она шири семе превелико за мање птице које једу бобичасто воће. Тамо где је века релативно честа, њена прикривена радозналост наводи је да око кућа или кампова тражи остатке хране или било шта што јој је непознато и преносиво. Познато је да узима сјајне предмете.

Размножавање

Сезона гнежђења варира, али када хране има у изобиљу, века може у току целе године да одгаји до четири легла. Гнезда прави на земљи под окриљем густе вегетације, гради их тако што траву (или сличан материјал) свије тако да чини гнездо облика посуде, у које могу да стану ~ четири јаја. У просеку, женка веке полажи три јаја кремасте или ружичасте боје са смеђим и лиластим мрљама. Оба пола учествују у инкубацији. Пилићи се излегу након месец дана, а оба родитеља их хране док одрасту (између шест и десет недеља од излегања).

Заштита
Века је на црвеној листи МУЗП () наведена као рањива врста. План опоравка веке новозеландског "Одељења за заштиту", који је одобрен 1999. године, имао је за циљ побољшање стања угрожености веке (прелазак у категорију са мањим ризиком од изумирања), разјашњење статуса популација веке за које постоји недостатак података, задржавање статуса врсте која није угрожена за друге популације веке и на крају враћање веке на њену целу традиционалну територију (на којој је била значајна компонента екосистема).

Заштита веке је проблематична; неке подврсте су угрожене, али су представљале проблем другим угроженим дивљим животињама на мањим острвима, нарочито на острвима на које су уведене, а природно их нису настањивале. Века није у стању да издржи тренутне притиске са којима се суочава ни на Северном ни на Јужном острву. Међутим, може бити врло продуктивна када постоје добри услови и обиље хране. На неколико локација забележено је гнежђење у току целе године, са укупно 14 излежених птића по пару. Популације веке могу да опстану у прилично измењеним стаништима, али су нестале са огромних делова свог некадашњег подручја, што сугерише да се могу прилагодити широком спектру услова, али су посебно осетљиве на претње.

Претње

"Одељење за заштиту" идентификује осам главних претњи веки. Грабљивци, као што су твор, мачка и пас претња су одраслој веки; Велика ласица и твор претња су птићима; велика ласица и пацов претња су за јаја. Суочава се са конкуренцијом за храну (воће и бескичмењаци) са уведеним врстама и трпи штетне последице од утицаја животиња које брсте на састав и регенерацију шума. Исцрпљивање станишта узроковано је модификовањем и деградацијом шума и мочвара. Болести и паразити повезани су са смањењем њене бројности, иако се мало зна о овом проблему. Суша је допринела нестанку веке из неких подручја. У неким регионима моторна возила узрокују велики број смртних случајева. Операције сузбијања штеточина понекад доводе до тровања веке, јер храну прикупља на земљи и осетљива је на мамце, а замке се постављају тако да их века може дохватити. Генетска разноликост може се изгубити током преноса гена кроз генерације, што лоше утиче на изоловане популације.

Повезаност са људима
Нека маорска племена уважавају веку и диве се њеној радозналости, одлучности и храбрости. Одважност је један од разлога због кога ју је лако ухватити. Века је Маорима била извор хране, користили су је за израду мириса и лековитих уља коришћених за упале, перје је коришћено за израду одеће, а коришћена је и као мамац за хватање паса. Први европски истраживачи и досељеници често су наилазили на веку и користили је; звали су је "кокошка из дивљине".

Извори

Спољашње везе

Барске коке


text:
#include <shogun/base/SGObject.h>
#include <shogun/base/range.h>
#include <shogun/lib/SGMatrix.h>
#include <shogun/lib/SGSparseMatrix.h>
#include <shogun/lib/SGSparseVector.h>
#include <shogun/lib/SGVector.h>

namespace shogun
{
	/** @brief Mock class to test clone and equals for SGObject.
	 * Serves as a parameter of type SGObject for @see CloneEqualsMock.
	 */
	template <class T>
	class CloneEqualsMockParameter : public SGObject
	{
	public:
		CloneEqualsMockParameter()
		{
			SG_DEBUG("Creating new {}, at {}.\n", get_name(), fmt::ptr(this))
			m_was_cloned = false;
			m_some_value = 1;

			watch_param("some_value", &m_some_value);
		}
		const char* get_name() const override
		{
			return "CloneEqualsMockParameter";
		}

		virtual std::shared_ptr<SGObject> create_empty() const override
		{
			return std::make_shared<CloneEqualsMockParameter>();
		}

		virtual std::shared_ptr<SGObject> clone(ParameterProperties pp = ParameterProperties::ALL) const override
		{
			auto clone = SGObject::clone(pp);
			auto casted = clone->template as<CloneEqualsMockParameter>();
			casted->m_was_cloned = true;
			return clone;
		}

		bool m_was_cloned;
		T m_some_value;
	};

	/** @brief Mock class to test clone and equals for SGObject.
	 * Has members that cover (hopefully) all possibilities of parameters.
	 */
	template <class T>
	class CloneEqualsMock : public SGObject
	{
	public:
		CloneEqualsMock()
		{
			init_single();
			init_sg_vector_matrix();
			init_sg_sparse_vector_matrix();
			init_raw_vector();
			init_raw_matrix();
		}

		~CloneEqualsMock()
		{
			free_single();
			free_raw_vector();
			free_raw_matrix();
		}

		void init_single()
		{
			m_basic = 1;
			watch_param("basic", &m_basic);

			m_object = std::make_shared<CloneEqualsMockParameter<T>>();
			watch_param("object", &m_object);

			m_string = "Shogun rocks!";
			watch_param("string", &m_string);
		}

		void free_single()
		{
			m_object.reset();
		}

		void init_sg_vector_matrix()
		{
			m_sg_vector = SGVector<T>(2);
			m_sg_vector.set_const(m_basic);
			watch_param("sg_vector", &m_sg_vector);

			m_sg_matrix = SGMatrix<T>(3, 4);
			m_sg_matrix.set_const(m_basic);
			watch_param("sg_matrix", &m_sg_matrix);
		}

		void init_sg_sparse_vector_matrix()
		{
			m_sg_sparse_vector = SGSparseVector<T>(4);
			for (auto i : range(m_sg_sparse_vector.num_feat_entries))
			{
				SGSparseVectorEntry<T> entry;
				entry.feat_index = i * 2;
				entry.entry = 2;
				m_sg_sparse_vector.features[i] = entry;
			}
			watch_param("sg_sparse_vector", &m_sg_sparse_vector);

			m_sg_sparse_matrix =
			    SGSparseMatrix<T>(m_sg_sparse_vector.num_feat_entries, 6);
			for (auto i : range(m_sg_sparse_matrix.num_vectors))
			{
				SGSparseVector<T> vec(m_sg_sparse_matrix.num_features);
				for (auto j : range(vec.num_feat_entries))
				{
					SGSparseVectorEntry<T> entry;
					entry.feat_index = i * 2;
					entry.entry = 3;
					vec.features[j] = entry;
				}
				m_sg_sparse_matrix.sparse_matrix[i] = vec;
			}
			watch_param("sg_sparse_matrix", &m_sg_sparse_matrix);
		}

		void init_raw_vector()
		{
			m_raw_vector_basic_len = 5;
			m_raw_vector_basic = new T[m_raw_vector_basic_len];
			for (auto i : range(m_raw_vector_basic_len))
				m_raw_vector_basic[i] = m_basic;
			watch_param(
			    "raw_vector_basic", &m_raw_vector_basic,
			    &m_raw_vector_basic_len);

			m_raw_vector_sg_vector_len = 7;
			m_raw_vector_sg_vector =
			    new SGVector<T>[m_raw_vector_sg_vector_len];
			for (auto i : range(m_raw_vector_sg_vector_len))
			{
				m_raw_vector_sg_vector[i] = SGVector<T>(i + 1, true);
				for (auto j : range(m_raw_vector_sg_vector[i].vlen))
					m_raw_vector_sg_vector[i].vector[j] = 1;
			}
			watch_param(
			    "raw_vector_sg_vector", &m_raw_vector_sg_vector,
			    &m_raw_vector_sg_vector_len);

			m_raw_vector_object_len = 6;
			m_raw_vector_object =
			    new std::shared_ptr<CloneEqualsMockParameter<T>>[m_raw_vector_object_len];
			for (auto i : range(m_raw_vector_object_len))
				m_raw_vector_object[i] = std::make_shared<CloneEqualsMockParameter<T>>();
			watch_param(
			    "raw_vector_object", &m_raw_vector_object,
			    &m_raw_vector_object_len);
		}

		void free_raw_vector()
		{
			delete[] m_raw_vector_basic;

			for (auto i : range(m_raw_vector_object_len))
				m_raw_vector_object[i].reset();
			delete[] m_raw_vector_object;

			delete[] m_raw_vector_sg_vector;
		}

		void init_raw_matrix()
		{
			m_raw_matrix_basic_rows = 2;
			m_raw_matrix_basic_cols = 3;
			auto size =
			    int64_t(m_raw_matrix_basic_rows) * m_raw_matrix_basic_cols;
			m_raw_matrix_basic = new T[size];
			for (auto i : range(size))
				m_raw_matrix_basic[i] = 1;
			watch_param(
			    "raw_matrix_basic", &m_raw_matrix_basic,
			    &m_raw_matrix_basic_rows, &m_raw_matrix_basic_cols);
		}

		void free_raw_matrix()
		{
			delete[] m_raw_matrix_basic;
		}

		const char* get_name() const override
		{
			return "CloneEqualsMock";
		}

		virtual std::shared_ptr<SGObject> create_empty() const override
		{
			return std::make_shared<CloneEqualsMock>();
		}

		T m_basic;
		std::shared_ptr<CloneEqualsMockParameter<T>> m_object;

		SGVector<T> m_sg_vector;
		SGMatrix<T> m_sg_matrix;

		SGSparseVector<T> m_sg_sparse_vector;
		SGSparseMatrix<T> m_sg_sparse_matrix;

		T* m_raw_vector_basic;
		index_t m_raw_vector_basic_len;

		SGVector<T>* m_raw_vector_sg_vector;
		index_t m_raw_vector_sg_vector_len;

		std::shared_ptr<CloneEqualsMockParameter<T>>* m_raw_vector_object;
		index_t m_raw_vector_object_len;

		T* m_raw_matrix_basic;
		index_t m_raw_matrix_basic_rows;
		index_t m_raw_matrix_basic_cols;

		std::string m_string;
	};

	/** @brief Used to test the tags-parameter framework
	 * Allows testing of registering new member and avoiding
	 * non-registered member variables using tags framework.
	 */
	class MockObject : public SGObject
	{
	public:
		MockObject() : SGObject()
		{
			init_params();
		}

		virtual ~MockObject()
		{
		}

		const char* get_name() const override
		{
			return "MockObject";
		}

		void set_watched(int32_t value)
		{
			m_watched = value;
		}

		int32_t get_watched() const
		{
			return m_watched;
		}

		auto get_object() const
		{
			return m_object;
		}

		int some_method() const
		{
			return 42;
		}

	protected:
		void init_params()
		{
			float64_t decimal = 0.0;
			register_param("vector", SGVector<float64_t>());
			register_param("int", m_integer);
			register_param("float", decimal);

			watch_param(
			    "watched_int", &m_watched, AnyParameterProperties("Integer"));

			watch_param(
			    "watched_object", &m_object, AnyParameterProperties("Object"));
			SG_ADD(
			    &m_constrained_parameter, "constrained_parameter", "Mock parameter to test constraints.",
                ParameterProperties::CONSTRAIN, SG_CONSTRAINT(positive<>(), less_than(10)));

			watch_method("some_method", &MockObject::some_method);
		}

		virtual std::shared_ptr<SGObject> create_empty() const
		{
			return std::make_shared<MockObject>();
		};

	private:
		int32_t m_integer = 0;
		int32_t m_watched = 0;
		int32_t m_constrained_parameter = 1;

		std::shared_ptr<MockObject> m_object = nullptr;
	};
} // namespace shogun

redpajama_set_name: RedPajamaGithub


Interested in learning about photography in Harrison MT? Whether you are a professional, beginner, or hobbyist, the best approach to improving your photography skills is through hands-on training with skilled instructors.
There are many accredited photography schools in Montana. Photography classes cover subjects like lighting techniques, digital capture, outdoor photography, exposure, composition, and many other basic and advanced camera techniques. Becoming an experienced photographer can lead to a prosperous professional career or lifelong hobby.


text:
Advocacy Program Celebrates Nationwide Success
The Texas A&M University School of Law Advocacy Program is celebrating recent victories from mock trial, negotiation and dispute resolution competitions from the East to West Coast.
Elizabeth Anderson
2L Elizabeth Anderson won Best Direct Examination at the Lone Star Classic Mock Trial Competition in San Antonio on Oct. 13-15. This is the law school's first individual mock trial award.
"I am humbled and proud, but especially thrilled for the school," she said. "We want to elevate our competitiveness in mock trial and become a known, respected trial advocacy program."
Anderson and her teammates 3Ls Ashu Balimba, Greg Franklin and Jessica Lesnau were coached by Justice Lee Gabriel, who is also the mock trial coordinator. This award follows a new 18-hour summer training program implemented by Justice Gabriel this year.
This was Anderson's first mock trial competition, and although she has experience in public speaking, she said she had a lot to learn.
"I practiced about 120 hours between Aug. 22 and Oct. 12," she said. "Nothing works better than constant rehearsal and repetition; Justice Gabriel emphasized the value of practicing each element (direct, cross examination, opening, and closing) as though it was the real thing."
She said this made a huge difference in her learning and delivery.
Jonathan Heathman, Diny Chang and Paul Manigrasso
The team of 2Ls Diny Chang and Paul Manigrasso, and 3L Jonathan Heathman, coached by Professor Kay Elliott, won the Best Mediation Award, placing 2nd overall, at the FINRA Securities Dispute Resolution Triathlon in New York City on Oct. 15-16. The competition consists of rounds in mediation, arbitration, and negotiation. The complex subject matter at this competition requires intense practice and learning.
Christopher Hamilton and Jessica Holtman
2Ls Jessica Holtman and Christopher Hamilton, coached by Elliott, placed second at the Sports Law Negotiation Competition in San Diego, Calif. on Sept. 23-25. Other Aggie Law teams finished 6th and 8th respectively, out of 40 teams.
Director of Advocacy Jennifer Ellis said the students and coaches have worked very hard, and she is glad their work was rewarded.
"Winning our first individual mock trial award demonstrates that our new initiatives and training in mock trial are working," she said. "And it's wonderful to have continued success at the FINRA competition, where we won the mediation award in 2014."
- Article by Jennifer Nassar, Communications Specialist, Texas A&M University School of Law


As International Women's Day approaches on March 8 and my time as NSW Premier's Woman of the Year draws to a close, I have been thinking about diversity in the workplace, and in particular, the relationship between diversity and innovation.
We don't have to look far from our own backyard to see examples of this. The rapid global expansion of wireless communications is in part possible because of the now widely acknowledged work by John O'Sullivan and his team at the CSIRO. Wi-Fi is now estimated to be used in more than 3 billion devices worldwide.
Reports also suggest that advances in gender equality correlate positively with higher Gross National Product (GNP) and that increasing women's labour force participation and earnings generates greater economic benefits for a family's health and education. Surely this can only be a good thing.
The Australian Businesswomen's Network says that women are starting small businesses at twice the rate of men. Despite this, a US study has found that female-owned companies are less likely to attract private investment compared to male-owned companies.
But I have a new reason. As the traditional "social organisers" women bring a lot to the table. Business and science success is all about relationships and networking. You have to meet to do business.
When you look at the reason for the delay, it is often when the development gets caught up in what is often called the "valley of death" or a black hole in the commercialisation process which can add years to transitioning time. Translating a discovery in the science lab to the engineering and development, then finally securing industry adoption can be a tortuous process.
If women's participation is a demonstrated element for business success and innovation is the essential ingredient for businesses to flourish, then why have we not embraced the opportunity to boost the role of women in science and business? Perhaps if we did we would witness greater translation of research to industry and our economic success would grow even more.


text:
A MUSEUM FOR NAT TURNER
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Birding columnist goes on the road to look for rare Steller's sea eagle in Maine
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NAVY FINDS BODY OF SEAL
HAMPTON'S BLACKBEARD'S POINT WAS PIRATE'S FINAL RESTING PLACE
42nd Annual Bid 'n Buy Auction to benefit more than 1,400 children
By Amelia Heymann
Virginia Gazette |
The Child Development Resources Center is holding its 42nd Annual Bid 'n Buy Auction on March 15.
CDR serves more than 1,400 young children and their families in the Historic Triangle according to Nancy Wigley, an event organizer. They serve children with special needs, developmental delays or those at-risk for delays.
"The one thing I like to say too is we are a complete resource for anyone who has a question about the development of a baby or a young child," said Jenny O'Donnell, spokeswoman.
Wigley said this is CDR's largest fundraiser of the year and usually brings in $175,000 for the group. O'Donnell said the money raised would go towards children services, such as therapies, parents as teachers program and developmental playgroup.
"Because we don't ever deny services to anyone for an inability to pay," she said. "There's lots of need out there and there are things that even when we do get insurance coverage ... there are more things that are not covered and that's why we fundraise, to support these services."
The auction is made possible by donations and sponsorships found around the area, and the event's sponsors, such as Ferguson Enterprises.
"We just couldn't pull it off without all of the sponsors who step forward and help us do this great event," Wigley said.
"I think a lot of it is they understand the importance of what we do and therefore are willing to help us out," O'Donnell said.
There will be 500 items up for auction that Saturday ranging from dining gift certificates and home decor to event tickets and a full birthday party with cake, live entertainment and a petting zoo.
"We've got an ultimate Cubs experience where you to can go to Wrigley Field and watch the Cubs play," O'Donnell said.
"And have an on-field experience," Wigley added.
However, not all the prizes are extravagant. One of the more popular auction categories is children's toys.
"It doesn't matter what your budget is because there's something small just about anyone can grab," O'Donnell said.
Williamsburg-James City County reports 1,301 confirmed COVID cases, 422 students in quarantine
Letter to the editor: Recent presidential news conference left much to be desired
The event is 11:30 a.m.-2 p.m. March 15 at Jamestown High School, 3751 John Tyler Highway. Entry is free. To donate items to the auction, or for more information about sponsorship opportunities, email nancyw@cdr.org. Find more information online at cdr.org.
Networking events this week
This month the Greater Williamsburg Chamber and Tourism Alliance are holding three networking events.
The first is #WORKWMBG Career Fair & Networking Event. In addition to face to face recruiting there will be resume coaching and online application stations to apply for jobs on site. It is 9 a.m.-2 p.m. March 11, the Cascades Ballroom of the Hotel Conference Center, Woodlands Hotel & Suites, 105 Visitor Center Drive. Free and open to the public.
The following week is the Morning Blend, a breakfast event where you can pitch your business to those in attendance. 8-9:30 a.m. March 17, London Co. Coffee & Tea/The Meadows Original Frozen Custard, 1222 Richmond Road. $5-$10; RSVP online at williamsburgcc.com.
Finally, they are holding Business After Hours at the end of the month. There will be networking, prizes and giveaways. 5-7 p.m. March 23, Baeplex, 500 Bulifants Blvd. $10-$15; RSVP online at williamsburgcc.com.
bid n buy
child develoupment resources
Amelia Heymann
Amelia Heymann covers arts and culture in the Historic Triangle. A Virginia native, she graduated from Virginia Commonwealth University. In her free time, Amelia loves traveling and eating good food.
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