Todd was born in Tulsa and graduated from Jenks High School in 1992. After high school, he graduated from Texas Christian University and then the University of Texas School of Law. After spending the majority of seven years below the Red River, he knew it was time to come home. Since starting his legal career in his home town of Tulsa, he met his amazing wife Christina, a Catoosa native, and added a indefatigable son, Duncan, to his family in 2011.
Besides his family, Todd's other great passion is music. He has sung and acted in dozens of productions with wonderful groups like Theatre Tulsa and Tulsa Opera. Tulsa Opera is particularly dear to Todd and led him to serving on their Board of Directors for several years. It's also where he met his wife Christina. Todd and his family are also very active at their church, Harvard Avenue Christian Church, where he serves as an Elder, Sunday school leader and choir member.


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BRUSSELS (Reuters) -- The European Parliament on Wednesday began a year-long investigation into the Volkswagen emissions scandal and whether regulators could have done more to prevent it.
EU regulation of the car industry has been under scrutiny since Volkswagen admitted last September it rigged U.S. tests for nitrogen oxide emissions in some diesel vehicles.
In a first closed-door session, the committee of inquiry elected its chair from the Socialists and Democrats and four vice-presidents to represent the political range of the European Parliament.
Some EU sources question how effective the inquiry will be as the risk is it will degenerate into political point-scoring and the main political group, the center-right European People's Party, said it should not be "a witch hunt."
The Green Party said that was not the aim and the committee would make a real difference if it could expose years of alleged close ties between the car industry, the European Commission and some politicians.
"In this year, it is crucial that we perform our process in an organized and transparent way so that the conclusions cannot be denied by European Commission and national authorities," Dutch Green politician Bas Eickhout said.
"That is the crux. If we do our job poorly, they can just ignore the reports. That is going to be the biggest challenge."
The Green Party has pushed for change and, together with some centrist lawmakers, wanted to tear up a compromise deal that allows diesel cars to continue producing above agreed limits.
In the end, they narrowly failed to get a veto, but setting up the parliamentary enquiry secured cross-party support.
On Wednesday, the European People's Party said it welcomed the work of the committee, but would cease to support it if it turned into a political blame game.
"We will not accept that the committee turns into a detrimental witch hunt on the European automotive industry, diesel technology or the European Commission," EPP spokesman Krisjanis Karins of Latvia, said.
The Green Party said it expected the committee to hear from representatives of all sides, including the industry, the Commission and national authorities.
The European Commission has also asked the industry and national authorities for information and proposed a radical reform of legislation that would give the EU executive enforcement powers that until now have been in the hands of member states that tended not to use them.


text:
Economy July 16, 2021 <July 16, 2021
US assessment: Amazon may avoid global tax deal
by Thalia Vaughn
Status: 07/16/2021 8:35 AM
The world's 100 largest and most profitable corporations are to be taxed more in the future. However, according to the US government, Amazon may not be affected by the new regulation.
US online retailer Amazon may not have to pay the planned global minimum tax. This is evident from the statements of the US government. "It depends on whether the company reaches profitability, and I'm not sure about that," U.S. Treasury Secretary Janet Yellen said in an interview with CNBC, when asked whether the agreement would reach 130. Will reallocate taxation rights to more states. Amazon.
Finance ministers of 20 largest trading and industrialized countries (G20) recently agreed That companies with an annual turnover of at least 750 million euros will have to pay a minimum tax rate of 15 percent on their profits in the future. was already under the umbrella of the OECD 130 states voted in favor of the plans. Amazon also falls in this category.
Also, a more equitable distribution of taxation is planned so that in future companies pay taxes not only in their home country, but where they do good business.
On the other hand, one of the so-called pillars of the deal is about the question of which country will receive more tax payments from the 100 largest and most profitable corporations in the future – whether, for example, emerging countries can claim the share. of tax revenue in which a corporation provides services. For example, regulation could replace national taxes on digital services.
READ German economy not growing in spring
The prerequisite is a ten percent return on sales
This pillar would affect corporations or their business sectors that achieve a minimum turnover of 20 billion euros and a profit of ten percent of income.
At least at Amazon, the requirements were not met last year. Amazon sold $386 billion. Profit was a good $21 billion, the return on sales was a good five percent.
However, in the first quarter of the current year, the group came in slightly closer to the 10 per cent limit. Profited $8.1 billion with sales of $108 billion, This corresponds to a return of 7.5 percent.
The background to Yellen's statement is clearly that a group like Amazon can be taxed as entire groups or as individual divisions. Amazon Web Services, a subsidiary of cloud computing, is especially extremely profitable.
Thalia Vaughn
Reader. Organizer. General creator. Zombie fanatic. Alcohol advocate. Food junkie. Bacon ninja.
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Easily reheat by placing the bag directly in boiling water or microwave. To microwave, cut corner of bag to vent and place on microwave safe dish.
DO NOT reuse bags if they have been used to store any of the following. - Raw meats - Fish - Oily Foods Do not reuse bags if they have been boiled or microwaved. Bags containing other food items can be washed in warm, soapy water, or the dishwasher (if desired). To wash bags in dishwasher, turn bags inside out and spread over top rack. Allow bags to dry completely before using.
Pull out one end of spring loaded bag roll holder.
Remove cardboard from empty roll.
Slide replacement roll onto holder. Make sure roll is positioned to dispense from the bottom.
Place end of holder back into slot.
Please note: for VS120 and VS125 series the built-in bag roll holder and cutter is located at the back of the unit. Open bag roll cover and follow instructions above. Click here for detailed troubleshooting information.


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text:
HomeCover ArtistsAbout the Artist: June Valentine-Ruppe
About the Artist - Ali Leja
January 2021 Issue
About the Cover Artist — Ali Leja
By Meredith M. Deal
Artist Ali Leja of Johns Creek, Georgia, wants her audience to smile. Carefully weaving her personal story into modern, upbeat paintings, Ali is creating positivity and happiness. The many happy subjects in her art reflect hopefulness and laughter.
Our January cover is titled "Island Life". "I love painting women and figures who look elegant and fun. I do a lot of women paintings in summery clothes or bathing suits with really big hats. I like that they don't have faces so people can imagine them to be whoever they want," Ali explained.
Ali's artworks, which cover a variety of subjects, come to life from mediums of acrylics, charcoal, oil, pastels and ink, each emblazoned with bold lines and bright colors. Her portfolio also includes animals, such as beguiling bees and foxes. "I love painting woodland creatures. We don't live on a farm, but we collect animals. We have a cat and three dogs. I love bringing animals to life." Other favorite portfolio subjects include many cocktails, lemons and stylish shoes.
The self-taught, instinctual painter came into her art after serving her community for 20 years as a school counselor. Deciding she needed a change, she explored painting as a creative outlet. "I've loved art my whole life. I enjoyed buying art and have always been creative, but never thought I had the skills to be a painter."
Nine years ago, to combat some of her school counselor stress, Ali decided to learn to paint. Consulting with several artists about becoming one herself, they all told her the same thing: "Paint every day." Taking their advice, Ali painted every day for three years—approximately 10,000 hours! Her talents blossomed quickly as she started producing meaningful works of art.
At first, selling her art was challenging. But, as an experienced problem solver and new business owner, she used her personal Facebook page for sales, expanding into a website and Instagram feed. "Each time I sold a piece, I was motivated to create more," Ali explained. She started attending craft shows and arranged for her art to be placed into small local shops, then into larger galleries and high-end boutiques. "Before I knew it, I had a very diversified way of selling art."
Ali says she is an introspective person striving to be just a little bit better each day. "It's about being positive. I don't want people to see my art as just whimsical. There's a lot more to it; my art is meaningful and spiritual. It's really about smiling on the inside."
Ali says she used to consult by listening, but "Now I paint with a touch of joy. I collect art, too, and get excited to open and display my new artworks when they arrive. I always want that feeling of excitement for my clients when they open my art."
Find Ali's Art: View and purchase Ali Leja's artworks, including our cover piece, at Camellia Art Custom Framing and Fine Art Gallery on Hilton Head Island (www.camelliaart.com). Original pieces are also represented by Viola's Market on St. Simons Island. Visit www.alilejaart.com online to learn more about Ali's gallery collections, commission pieces and portraits and find her on Instagram @alilejaart.


text:
Home World U.S. Brazil's President Bolsonaro offers US ambassador job to son
Brazil's President Bolsonaro offers US ambassador job to son
Eduardo (L), the third son of Mr Bolsonaro (R), has a strong influence on his father
Jair Bolsonaro, the far-right president of Brazil, has invited his son to become ambassador to the US.
Eduardo Bolsonaro, 35, who is currently serving as a congressman and advises his father on foreign affairs, told reporters he would accept the post if it were offered.
The position of ambassador has been vacant since April.
Mr Bolsonaro was elected last year after a successful campaign he said had been inspired by Donald Trump.
Eduardo would have to resign as a congressman if he did take up the position of ambassador.
The appointment hinges on his son accepting the position, the president said
"I don't want to decide his future for him if the legislation says he has to renounce his position," Mr Bolsonaro was quoted as saying by Reuters news agency.
Eduardo Bolsonaro has been dubbed Brazil's "shadow foreign minister" at the Brazilian foreign ministry because of the strong influence he has on his father's foreign policy ideas, BBC Americas editor Candace Piette reports.
Both the president and his son have a pro-US stance, breaking with Brazil's traditionally more cautious position, and Eduardo is openly pro-Israeli, whereas in the past Brazil has been careful not to offend Arab nations.
Mr Bolsonaro uses several of his family members as official advisers. His eldest son, Flavio, is a senator, while Carlos Bolsonaro is a Rio de Janeiro city council member.
Mr Trump is also known for appointing family members to political positions. On the White House website, his daughter Ivanka Trump is listed as an adviser to the president, focussing on "the education and economic empowerment of women and their families as well as job creation and economic growth".
Brazils
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There's Another Movie That's Earned More Views Per Theater Than Avengers: Endgame 2019-07-16
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We're stating the obvious when we say that when Avengers: Endgame first hit theaters earlier this summer, it broke a lot of records....
There's Another Movie That's Earned More Views Per Theater Than Avengers:...


text:
Q: How to safely call setState function from async function in flutter? I have a download button in my flutter application that will show Text("download") before button is pressed CircularProgressIndicator() when file is downloading, and Text("Open") when file is downloaded.
_FileStatus status = _FileStatus.EMPTY;

RaisedButton raisedButton() {
  var child;
  if (status == _FileStatus.EMPTY) {
    child = Text("download");
  } else if (status == _FileStatus.DOWNLOADING) {
    child = CircularProgressIndicator();
  } else {
    child = Text("Open");
  }
  return RaisedButton(
    child: child,
    onPressed: () {
      if (status == _FileStatus.EMPTY) {
        setState(() {
          status = _FileStatus.DOWNLOADING;
        });
        download().then((bool isDownloaded) {
          if (isDownloaded) {
            //setState status=>Downloaded
          } else {
            //setState status=>Empty
          }
        });
      } else {
        print("Open");
      }
    },
  );
}

Future<bool> download() async {
  var response = await Future<bool>.delayed(Duration(seconds: 5), () {
    print("Downloading ...");
    return true;
  });
  if (response) {
    print("Downloaded");
    return true;
  } else {
    print("Download Failed!");
    return false;
  }
}

But this button lies in second page of application. So one might press download button and then go back to first page. Normally if I press download button and then wait for it to complete then setState will update status to DOWNLOADED; no problem whatsoever. But if I press download button and then go back, then download() will run in background and when it completes it tries to run one of the setState methods that I've commented out. This either gives error, or says memory leak problem.
I've tried to solve this problem by using isLoaded variable.
@override
void initState() {
  isLoaded = true;
  super.initState();
}
@override
void dispose() {
  isLoaded = false;
  super.dispose();
}

and then checking if isLoaded is true before calling setState method.
if (isLoaded) {
  setState(() {
    status = _FileStatus.DOWNLOADING;
  });
}

But this feels like hacky method, and I know there must be a better way to tackle this. I've searched to other similar question but couldn't quite find what I was looking for.

A: Just add a condition to check whether your state is mounted or not, and when it's not - do not call setState:
          download().then((bool isDownloaded) {
            // Checking if widget is mounted
            if (!mounted) {
              return;
            }

            ...

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The FMDS-University of West England (UWE) degree programme offers all its Advanced Diploma graduates an accelerated degree pathway with a 12-month "top-up". This programme is designed to endow students with analytical,conceptual and research skills that serve to up their ante in the diverse areas of professional design practice.
FMDS aims to engage students' senses and minds with its series of classroom and out learning activities that include overseas university visits, leadership training (through Passage to ASEAN mobility programmes) and participation in social and community work.
Harness the power of good design thinking. Start your tomorrow, today.


The Telupid District (Malay: Daerah Telupid) is an administrative district in the Malaysian state of Sabah, part of the Sandakan Division which includes the districts of Beluran, Kinabatangan, Sandakan and Tongod. The capital of the district is in Telupid Town. The district is formerly a part of Beluran District.
Telupid was firstly settled around 1940s and became the major route for the Sandakan Death Marches during World War II. At the time, it was mainly inhabited by the Dusun people. The present district was formed around 1965, shortly after Sabah became part of Malaysia. The district was developed following the agreement between the Australian and Malaysian government to jointly build road. Following the availability of road, a number of infrastructures start to be built there. Under the administration of United Sabah National Organisation (USNO) in 1970, Telupid was made a sub-district. In 2015, Telupid was elevated into a full district with a district council are proposed to be established.
^ "Sejarah Pewujudan Daerah" (in Malay). Telupid District Office. Retrieved 12 March 2018.
^ "Study on district council for Tongod and Telupid". Daily Express. 28 September 2015. Archived from the original on 12 March 2018. Retrieved 12 March 2018.
^ "Study on creating Tongod, Telupid district councils – Hajiji". The Borneo Post. 28 September 2015. Retrieved 12 March 2018.
This page was last edited on 24 January 2019, at 11:28 (UTC).


Guess what? They changed the word "Toolbar" to "Search App". Is that supposed to make the program more palatable? Giving the program a different name doesn't change its nature. Nor does it change the fact that it's an opt out, rather than an opt in third-party program.
Last week, I was updating Java on a computer when I got the following pop-up. Although I'm not 100% certain, I believe the box next to "Install the Ask Toolbar in Internet Explorer" was checked, thus installing a toolbar into the browser of any unwary user. This situation is not news; Oracle has been doing this for over a year already. Nevertheless, I thought I'd take a moment to remind everyone not to click those "next" buttons in program installers without reading what you're agreeing to.


text:
Luther C. Carter
Chairman of the U.S. House Committee on the District of Columbia
Member of the U.S. House of Representatives
from New York's 1st district
March 4, 1859 – March 3, 1861
John A. Searing
Edward H. Smith
(1805-02-25)February 25, 1805
Bethel, Maine
New York City, New York
Resting place
Green-Wood Cemetery, Brooklyn, New York
Mary L. Converse (m. 1829)
Luther Cullen Carter (February 25, 1805 – January 3, 1875) was a U.S. Representative from New York.
Carter was born in Bethel, Maine on February 25, 1805, the son of Dr. Timothy Carter and Frances "Fanny" (Freeland) Carter. He was educated in Maine, and a business and mercantile career in Saco. At age 20, he moved to New York City, where he continued his business career and served as president of the Market Savings Bank.
In addition to his business career, Carter served as a member of the Board of Education of New York City for several years beginning in 1853. He later moved to Long Island City, where he lived in semi-retirement as a gentleman farmer.
Carter was elected as a Republican to the Thirty-sixth Congress (March 4, 1859 – March 3, 1861). He served as chairman of the Committee on the District of Columbia (Thirty-sixth Congress). He was an unsuccessful candidate for reelection in 1860 to the Thirty-seventh Congress.
YouTube Encyclopedic
✪ Martin Luther's Reformation | 500 Year Anniversary of the Reformation (Mike Wittmer, PhD)
✪ Lift Every Voice and Sing - David W. Carter Choir
✪ Uncharted Territory: David Thompson on the Columbia Plateau
Death and burial
He died in New York City January 3, 1875. He was interred in Brooklyn's Green-Wood Cemetery, Section 113, Lot 18623.
On September 29, 1829, Carter married Mary L. Converse (d. 1882) of Palmer, Massachusetts.
Carter's siblings included Timothy J. Carter, who also served in Congress.
United States Congress. "Luther C. Carter (id: C000198)". Biographical Directory of the United States Congress.
Luther C. Carter at Find a Grave
U.S. House of Representatives
John A. Searing Member of the U.S. House of Representatives
from New York's 1st congressional district
This article incorporates public domain material from the Biographical Directory of the United States Congress website http://bioguide.congress.gov.
<abbr style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;" title="Discuss this template">t</abbr>
Chairmen of the United States House Committee on the District of Columbia
Van Horne
Bouldin
W. Johnson
Ficklin
Conkling
B. Johnson
Zihlman
Focht
Palmisano
Dirksen
Diggs
Dellums
US Congress: C000198
WorldCat Identities (via VIAF): 26912975
This page was last edited on 16 May 2019, at 09:24


text:
\section{Introduction}

\subsection{Convex Clustering, Bi-Clustering, and Co-Clustering}

In recent years, there as been a surge of interest in the expression of classical statistical problems as penalized estimation problems. These convex re-formulations have many noteworthy advantages over classical methods, including improved statistical performance, analytical tractability, and efficient and scalable computation. In particular, a convex formulation of clustering \citep{Pelckmans:2005,Hocking:2011,Lindsten:2011} has sparked much recent research, as it provides theoretical and computational guarantees not available for classical clustering methods \citep{Zhu:2014,Tan:2015,Radchenko:2017}. Convex clustering combines a squared Frobenius norm loss term, which encourages the estimated centroids to remain near the original data, with a convex fusion penalty, typically the $\ell_q$-norm of the row-wise differences, which shrinks the estimated centroids together, inducing clustering behavior in the solution:
\begin{equation}
    \hat{\bm{U}} = \argmin_{\bm{U} \in \mathbb{R}^{n \times p}} \frac{1}{2}\|\bm{X} - \bm{U}\|_F^2 + \lambda \sum_{\substack{i, j = 1 \\ i < j}}^n w_{ij} \|\bm{U}_{i\cdot} - \bm{U}_{j\cdot}\|_q \label{eqn:clust}
\end{equation}
Observations $i$ and $j$ are assigned to the same cluster if $\hat{\bm{U}}_{i\cdot} = \hat{\bm{U}}_{j\cdot}$.

For highly structured data, it is often useful to cluster both the rows and the columns of the data. For example, in genomics one may wish to simultaneously estimate disease subtypes (row-wise clusters of patients) while simultaneously identifying genetic pathways (column-wise clusters of genes). While these clusterings can be performed independently, it is often more efficient to jointly estimate the two clusterings, a problem known as \emph{bi-clustering}. Building on \eqref{eqn:clust}, \citet{Chi:2017} propose a convex formulation of bi-clustering, given by the following optimization problem:
\begin{equation}
\begin{aligned}
\hat{\bm{U}} &= \argmin_{\bm{U} \in \mathbb{R}^{n \times p}} \frac{1}{2}\|\bm{X} - \bm{U}\|_F^2 \\ & +\lambda \left(\sum_{\substack{i, j = 1 \\ i < j}}^n w_{ij} \|\bm{U}_{i\cdot} - \bm{U}_{j\cdot}\|_q \right.  \left.+ \sum_{\substack{k, l = 1 \\ k < l}}^p \tilde{w}_{kl}\|\bm{U}_{\cdot k} - \bm{U}_{\cdot l}\|_q\right)
\end{aligned} \label{eqn:bclust}
\end{equation}
for fixed $\lambda \in \mathbb{R}_{\geq 0}$, $\bm{w} \in \mathbb{R}^{\binom{n}{2}}_{\geq 0}$, and $\tilde{\bm{w}} \in \mathbb{R}^{\binom{p}{2}}_{\geq 0}$. As with standard convex clustering, the fusion penalties fuse elements of $\bm{U}$ together, but here the rows and columns are both fused together, resulting in a characteristic checkerboard pattern in $\hat{\bm{U}}$

Extending this, \citet{Chi:2018b} propose a convex formulation of \emph{co-clustering}, the problem of jointly clustering along each mode of a tensor (data array). Their estimator is defined by the following optimization problem, where both $\mathcal{X}$ and $\mathcal{U}$ are order $J$ tensors of dimension $n_1 \times n_2 \times \cdots \times n_J$ and $\mathcal{X}^{j/i}$ denotes the $i$\textsuperscript{th} slice of $\mathcal{X}$ along the $j$\textsuperscript{th} mode:
\begin{equation}
  \hat{\mathcal{U}} = \argmin_{\mathcal{U}} \frac{1}{2}\|\mathcal{X} - \mathcal{U}\|_F^2 + \lambda \sum_{j=1}^J \sum_{\substack{k, l = 1 \\ k < l}}^{n_J}w^j_{k, l}\|\mathcal{U}^{j/k} - \mathcal{U}^{j/l}\|_q \label{eqn:cclust}
\end{equation}
for fixed $\lambda \in \mathbb{R}_{\geq 0}$ and $\bm{w}^j \in \mathbb{R}^{\binom{n_j}{2}}_{\geq 0}, j = 1, \dots, J$, and where $\|\mathcal{X}\|_q$ denotes the $\ell_q$-norm of the vectorization of $\mathcal{X}$. While many algorithms have been proposed to solve Problem \eqref{eqn:clust}, there has been relatively little work on efficient algorithms to solve Problems \eqref{eqn:bclust} and \eqref{eqn:cclust}. Operator splitting methods have been shown to be among the most efficient algorithms for convex clustering \citep{Chi:2015} and, as we will show below, they are highly-efficient for bi-clustering and co-clustering as well.

\subsection{Operator Splitting Methods}

Many problems in statistical learning, compressive sensing, and sparse coding can be cast in a ``loss + penalty'' form, where a typically smooth loss function, measuring the in-sample accuracy, is combined with a structured penalty function (regularizer) which induces a simplified structure in the resulting estimate to improve performance. The popularity of this two-term structure has spurred a resurgence of interest in so-called operator splitting methods, which break the problem into simpler subproblems which can be solved efficiently \citep{Glowinski:2016}. Among the most popular of these methods is the Alternating Direction Method of Multipliers (ADMM), which is typically quite simple to implement, has attractive convergence properties, is easily parallelizable and distributed, and has been extended to stochastic and accelerated variants \citep{Boyd:2011,Ouyang:2013,Goldstein:2014}.

The ADMM can be used to solve problems of the form
\(\argmin_{(\bm{u}, \bm{v}) \in \mathcal{H}_1 \times \mathcal{H}_2} f(\bm{u}) + g(\bm{v}) \quad \text{ subject to } \quad \mathfrak{L}_1\bm{u} + \mathfrak{L}_2\bm{v} = \bm{b} \label{eqn:two_block}\) where $\bm{u}$, $\bm{v}$ take values in arbitrary (real, finite-dimensional) Hilbert spaces $\mathcal{H}_1$, $\mathcal{H}_2$, $\mathfrak{L}_i: \mathcal{H}_i \to \mathcal{H}_*, i = 1, 2$ are linear operators from $\mathcal{H}_i$ to a common range space $\mathcal{H}_*$, $\bm{b}$ is a fixed element of $\mathcal{H}_*$, and $f, g$ are closed, proper, and convex functions from $\mathcal{H}_1$ and $\mathcal{H}_2$ to $\overline{\mathbb{R}} = \mathbb{R} \cup\{\infty\}$. The ADMM proceeds by Gauss-Seidel updates of the augmented Lagrangian
\begin{align*}
  \mathscr{L}_{\rho}(\bm{u}, \bm{v}, \bm{z}) &= f(\bm{u}) + g(\bm{v}) + \langle \bm{z}, \mathfrak{L}_1\bm{u} + \mathfrak{L}_2\bm{v} - \bm{b}\rangle_{\mathcal{H}_*} \\ &\quad + \frac{\rho}{2}\|\mathfrak{L}_1\bm{u} + \mathfrak{L}_2\bm{v} - \bm{b}\|_{\mathcal{H}_*}^2.
\end{align*} The ADMM steps are given by:
\begin{subequations}
\renewcommand{\theequation}{\theparentequation.\arabic{equation}}
\begin{align}
  \bm{u}^{(k+1)} &= \argmin_{\bm{u} \in \mathcal{H}_1} \mathscr{L}_{\rho}(\bm{u}, \bm{v}^{(k)}, \bm{z}^{(k)}) \label{eqn:admm_1}\\
  \bm{v}^{(k+1)} &= \argmin_{\bm{v} \in \mathcal{H}_2} \mathscr{L}_{\rho}(\bm{u}^{(k+1)}, \bm{v}, \bm{z}^{(k)})  \label{eqn:admm_2} \\
  \bm{z}^{(k+1)} &= \bm{z}^{(k)} + \rho(\mathfrak{L}_1\bm{u}^{(k+1)} + \mathfrak{L}_2\bm{v}^{(k+1)} - \bm{b}).
\end{align}
\end{subequations}
While this level of generality is not typically required in applications, we will see below that judicious use of the general formulation is key to developing efficient ADMMs for the co-clustering problem.

While the simplified sub-problems are often much easier to solve than the original problem, they may still be impractically expensive. \citet{Deng:2016} consider a \emph{generalized} ADMM, which augments the subproblems (\ref{eqn:admm_1}-\ref{eqn:admm_2}) with positive-definite quadratic operators $\mathfrak{A}$ and $\mathfrak{B}$ to obtain the updates:
\begin{subequations}
\renewcommand{\theequation}{\theparentequation.\arabic{equation}}
\begin{align}
  \bm{u}^{(k+1)} &= \argmin_{\bm{u} \in \mathcal{H}_1} \mathscr{L}_{\rho}(\bm{u}, \bm{v}^{(k)}, \bm{z}^{(k)}) + \mathfrak{A}(\bm{u} - \bm{u}^{(k)})\label{eqn:gadmm_1}\\
  \bm{v}^{(k+1)} &= \argmin_{\bm{v} \in \mathcal{H}_2} \mathscr{L}_{\rho}(\bm{u}^{(k+1)}, \bm{v}, \bm{z}^{(k)}) + \mathfrak{B}(\bm{v} - \bm{v}^{(k)})\label{eqn:gadmm_2} \\
  \bm{z}^{(k+1)} &= \bm{z}^{(k)} + \rho(\mathfrak{L}_1\bm{u}^{(k+1)} + \mathfrak{L}_2\bm{y}^{(k+1)} - \bm{b}).
\end{align}
\end{subequations}
If $\mathfrak{A}$ and $\mathfrak{B}$ are appropriately chosen, the generalized subproblems (\ref{eqn:gadmm_1}-\ref{eqn:gadmm_2}) may be easier to solve than their standard counterparts.

The wide adoption of the ADMM has lead to many attempts to extend the ADMM to objectives with three or more terms.
Recently, \citet[Algorithm 8]{Davis:2017} proposed an operator-splitting method for the three-block problem:
\begin{equation}
\begin{aligned}
  \argmin_{(\bm{u}, \bm{v}, \bm{w}) \in \mathcal{H}_1 \times \mathcal{H}_2 \times \mathcal{H}_3} & \quad f(\bm{u}) + g(\bm{v}) + h(\bm{w})\\ \text{ subject to } & \quad  \mathfrak{L}_1\bm{u} + \mathfrak{L}_2\bm{v} + \mathfrak{L}_3\bm{w} = \bm{b}.
\end{aligned} \label{eqn:three_block}
\end{equation} Like the standard ADMM, the Davis-Yin scheme alternately updates the augmented Lagrangian in a Gauss-Seidel fashion:
\begin{align*}
    \mathscr{L}_{\rho}(\bm{u}, \bm{v}, \bm{w}, \bm{z}) =& f(\bm{u}) + g(\bm{v}) + h(\bm{w}) \\ &+ \frac{\rho}{2}\|\mathfrak{L}_1\bm{u} + \mathfrak{L}_2\bm{v} + \mathfrak{L}_3\bm{w} - \bm{b} - \rho^{-1}\bm{z}\|_{\mathcal{H}_*}^2
\end{align*}
The Davis-Yin iterates bear similarities to the standard ADMM and the Alternating Minimization Algorithm \citep{Tseng:1991}, both of which are special cases:
\begin{subequations}
\renewcommand{\theequation}{\theparentequation.\arabic{equation}}
\begin{align*}
  \bm{u}^{(k+1)} &= \argmin_{\bm{u} \in \mathcal{H}_1} f(\bm{u}) + \langle \bm{z}^{(k)}, \mathfrak{L}_1\bm{u}\rangle\\
  \bm{v}^{(k+1)} &= \argmin_{\bm{v} \in \mathcal{H}_2} \mathscr{L}_{\rho}(\bm{u}^{(k+1)}, \bm{v}, \bm{w}^{(k)}, \bm{z}^{(k)}) \\
  \bm{w}^{(k+1)} &= \argmin_{\bm{w} \in \mathcal{H}_3} \mathscr{L}_{\rho}(\bm{u}^{(k+1)}, \bm{v}^{(k+1)}, \bm{w}, \bm{z}^{(k)}) \\
  \bm{z}^{(k+1)} &= \bm{z}^{(k)} + \rho(\mathfrak{L}_1\bm{u}^{(k+1)} + \mathfrak{L}_2\bm{v}^{(k+1)} + \mathfrak{L}_3\bm{w}^{(k+1)} - \bm{b})
\end{align*}
\end{subequations}
Like the AMA, the Davis-Yin three block ADMM requires strong convexity of $f(\cdot)$. Unlike the standard ADMM, which allows $\rho$ to be arbitrarily chosen or even to vary over the course of the algorithm, both the AMA and Davis-Yin ADMM place additional constraints on $\rho$ to ensure convergence.

\section{Operator-Splitting Methods for Convex Bi-Clustering} \label{sec:algs}
In this section, we present three operator-splitting methods for convex co-clustering. For simplicity of exposition, we focus only on the bi-clustering (second-order tensor) case in this section and suppress the fusion weights $\bm{w}, \tilde{\bm{w}}$. The bi-clustering problem \eqref{eqn:bclust} then becomes
\begin{equation}
\begin{aligned}
\hat{\bm{U}} &= \argmin_{\bm{U} \in \mathbb{R}^{n \times p}} \frac{1}{2}\|\bm{X} - \bm{U}\|_F^2 +\lambda \left(\|\bm{D}_{\text{row}}\bm{U}\|_{\text{row}, q} + \|\bm{U}\bm{D}_{\text{col}}\|_{\text{col}, q}\right)
\end{aligned} \label{eqn:bclust2}
\end{equation} where $\bm{D}_{\text{row}}$ and $\bm{D}_{\text{col}}$ are directed difference matrices implied by the (non-zero) fusion weights and $\|\cdot\|_{\text{row}, q}$ and $\|\cdot\|_{\text{col}, q}$ are the sums of the row- and column-wise $\ell_q$-norms of a matrix. The extension of our methods to to tensors of arbitrary order is natural and discussed in more detail in Section \ref{sec:tensor}.

\subsection{Alternating Direction Method of Multipliers}
Because the convex bi-clustering problem \eqref{eqn:bclust2} has three terms, it is not immediately obvious how a standard two-block ADMM can be applied to this problem. However, if we take $\mathcal{H}_1 = \mathbb{R}^{n \times p}$ to be the natural space of the primal variable and $\mathcal{H}_2 = \mathcal{H}_{\text{row}} \times \mathcal{H}_{\text{col}}$ to be the Cartesian product of the row- and column-edge difference spaces, we can obtain the ADMM updates:
\begin{align*}
  \bm{U}^{(k+1)} &= \argmin_{\bm{U} \in \mathbb{R}^{n \times p}} \frac{1}{2}\|\bm{X} - \bm{U}\|_2^2 + \frac{\rho}{2}\left\|\bm{D}_{\text{row}}\bm{U} - \bm{V}^{(k)}_{\text{row}} + \rho^{-1}\bm{Z}^{(k)}_{\text{row}}\right\|_F^2 \\ &\qquad +  \frac{\rho}{2}\left\|\bm{U}\bm{D}_{\text{col}} - \bm{V}^{(k)}_{\text{col}} + \rho^{-1}\bm{Z}^{(k)}_{\text{col}}\right\|_F^2 \\
  \begin{pmatrix} \bm{V}^{(k+1)}_{\text{row}} \\ \bm{V}^{(k+1)}_{\text{col}} \end{pmatrix} &= \begin{pmatrix} \prox_{\lambda / \rho \, \|\cdot\|_{\text{row}, q}}(\bm{D}_{\text{row}}\bm{U}^{(k+1)} + \rho^{-1}\bm{Z}^{(k)}_{\text{row}}) \\
  \prox_{\lambda / \rho \, \|\cdot\|_{\text{col}, q}}(\bm{U}^{(k+1)}\bm{D}_{\text{col}} + \rho^{-1}\bm{Z}^{(k)}_{\text{col}}) \end{pmatrix}  \\
  \begin{pmatrix} \bm{Z}^{(k+1)}_{\text{row}} \\ \bm{Z}^{(k+1)}_{\text{col}} \end{pmatrix} &= \begin{pmatrix} \bm{Z}^{(k)}_{\text{row}} + \rho(\bm{D}_{\text{row}}\bm{U}^{(k+1)} - \bm{V}^{(k+1)}_{\text{row}}) \\ \bm{Z}^{(k)}_{\text{col}} + \rho(\bm{U}^{(k+1)}\bm{D}_{\text{col}} - \bm{V}^{(k+1)}_{\text{col}}) \end{pmatrix}
\end{align*}
The $\bm{V}$- and $\bm{Z}$-updates are straightforward to derive and parallel those of the ADMM for the convex clustering problem \citep[Appendix A.1]{Chi:2015,Weylandt:2019}. Additionally, we note that, due to the separable Cartesian structure of $\mathcal{H}_2$, the $\bm{V}$ and $\bm{Z}$-updates can be applied separately, and potentially in parallel, for the row and column blocks. As we will see, this separable structure holds for all algorithms considered in this paper and for tensors of arbitrary rank.

The $\bm{U}$-update is somewhat more difficult as it requires us to solve
\begin{equation*}
\begin{aligned}
&\bm{X} + \rho\bm{D}_{\text{row}}^T(\bm{V}^{(k)}_{\text{row}} - \rho^{-1}\bm{Z}^{(k)}_{\text{row}}) + \rho(\bm{V}^{(k)}_{\text{col}} - \rho^{-1}\bm{Z}^{(k)}_{\text{col}})\bm{D}_{\text{col}}^T \\ &\quad = \bm{U} + \rho\bm{D}_{\text{row}}^T\bm{D}_{\text{row}}\bm{U} + \rho \bm{U}\bm{D}_{\text{col}}\bm{D}_{\text{col}}^T.
\end{aligned} \label{eqn:sylvester}
\end{equation*}
This is a Sylvester equation with coefficient matrices $\frac{1}{2}\bm{I} + \rho \bm{D}_{\text{row}}^T\bm{D}_{\text{row}}$ and $\frac{1}{2}\bm{I} + \rho \bm{D}_{\text{col}}\bm{D}_{\text{col}}^T$ and can be solved using standard numerical algorithms \citep{Bartels:1972,Golub:1979}. Typically, the most expensive step in solving a Sylvester equation is either a Schur or Hessenberg decomposition of the coefficient matrices, both of which scale cubically with the size of the coefficient matrices. Since the coefficient matrices are fixed by the problem structure and do not vary between iterations, this factorization can be cached and amortized over the ADMM iterates, though, as we will see below, it is often more efficient to modify the $\bm{U}$-update to avoid the Sylvester equation entirely.

\subsection{Generalized ADMM}

To avoid the Sylvester equation in the $\bm{U}$-update, we turn to the Generalized ADMM framework of \citet{Deng:2016} and augment the $\bm{U}$-update with the quadratic operator $\mathfrak{A}(\bm{U}) = \frac{1}{2}(\alpha\|\bm{U}\|_F^2 - \rho\|\mathfrak{L}_1\bm{U}\|_{\mathcal{H}_*}^2)$. The constant $\alpha$ must be chosen to ensure $\mathfrak{A}$ is positive-definite so that sub-problem \eqref{eqn:gadmm_1} remains convex. The smallest valid $\alpha$ depends on $\rho$ and the operator norm of $\mathfrak{L}_1$ which can be bounded above by
\[\|\mathfrak{L}_1\|_{\mathcal{H}_1 \to \mathcal{H}_*} \leq \sigma_{\max}(\bm{D}_{\text{row}}) + \sigma_{\max}(\bm{D}_{\text{col}})\]
where $\sigma_{\max}(\cdot)$ is the maximum singular value of a matrix. To avoid expensive singular value calculations, an upper bound based on the maximum degree of any vertex in the graph can be used instead \citep[Section 4.1]{Anderson:1985,Chi:2015}.

With this augmentation, the $\bm{U}$-update \eqref{eqn:gadmm_1} becomes:
\begin{align*}
  \bm{U}^{(k+1)} &= \left(\alpha \bm{U}^{(k)} + \bm{X} + \rho\bm{D}_{\text{row}}^T(\bm{V}^{(k)} - \rho^{-1}\bm{Z}^{(k)}_{\text{row}} - \bm{D}_{\text{row}}\bm{U}^{(k)}) \right. \\ &\left.\qquad+ \rho(\bm{V}^{(k)}_{\text{col}} - \rho^{-1}\bm{Z}^{(k)}_{\text{col}} - \bm{U}^{(k)}\bm{D}_{\text{col}})\bm{D}_{\text{col}}^T \right)/(1+\alpha)
\end{align*}
We note that this can be interpreted as a weighted average of a standard update and the previous estimate of $\bm{U}$. This update does not require solving a Sylvester equation and can be performed in quadratic, rather than cubic, time. As we will see in Section \ref{sec:experiments}, this update significantly decreases the computational cost of an iteration without significantly slowing the \emph{per iteration} convergence rate, resulting in much improved performance.

\subsection{Davis-Yin Splitting}

The three-block structure of the convex bi-clustering problem \eqref{eqn:bclust2} naturally lends itself to the Davis-Yin three-block ADMM, which has provable convergence due to the strongly convex squared Frobenius norm loss. We take $\mathcal{H}_1$ as before, but now split the row- and column-edge differences into two spaces ($\mathcal{H}_2 = \mathcal{H}_{\text{row}}$ and $\mathcal{H}_3 = \mathcal{H}_{\text{col}}$). The joint range space, which also contains the dual variable, is still the Cartesian product $\mathcal{H}_* = \mathcal{H}_2 \times \mathcal{H}_3$. The Davis-Yin iterates have the same $\bm{V}$- and $\bm{Z}$-updates as before, but yield a simpler $\bm{U}$-update:
\begin{align*}
  \bm{U}^{(k+1)} &= \bm{X} - \bm{D}_{\text{row}}^T\bm{Z}^{(k)}_{\text{row}} - \bm{Z}^{(k)}_{\text{col}}\bm{D}^T_{\text{col}}
\end{align*}
Unlike the ADMM, the Davis-Yin updates require $\rho$ to be less than $1 / \|\mathcal{L}_1\|_{\mathcal{H}_1 \to \mathcal{H}_*}$. The same bound used for $\alpha$ in the Generalized ADMM can be used here.

We note that, due to the ``Cartesian'' structure of the linear operators $\mathcal{L}_2\bm{V} = (-\bm{V}_{\text{row}}, \bm{0}_{\mathcal{H}_{\text{col}}})$ and $\mathcal{L}_3\bm{W} = (\bm{0}_{\mathcal{H}_{\text{row}}}, -\bm{V}_{\text{col}})$, the Davis-Yin updates have the same separable structure as the ADMM and Generalized ADMM updates. In fact, it is not hard to see that the Davis-Yin updates can also be derived as updates of the Alternating Minimization Algorithm (AMA) \citep{Tseng:1991}. The AMA is known to be equivalent to proximal gradient on the dual problem, which \citet{Chi:2018b} recommended to solve Problem \eqref{eqn:cclust}.

As \citet{Chi:2015} note for the convex clustering problem, Moreau's decomposition \citep{Moreau:1962} can be used to eliminate the $\bm{V}$-update by replacing the proximal operator with a projection onto the dual norm ball, giving the simplified $\bm{Z}$-updates
\begin{align*}
  \bm{Z}^{(k+1)}_{\text{row}} &= \proj_{\lambda / \rho \mathbb{B}_{\|\cdot\|^*_{\text{row}, q}}}(\bm{Z}^{(k)} + \rho \bm{D}_{\text{row}}\bm{U}^{(k+1)}) \\
  \bm{Z}^{(k+1)}_{\text{col}} &= \proj_{\lambda / \rho \mathbb{B}_{\|\cdot\|^*_{\text{col}, q}}}(\bm{Z}^{(k)} + \rho \bm{D}_{\text{col}}\bm{U}^{(k+1)}).
\end{align*}
This simplification lowers the computational cost of the Davis-Yin updates, but it does not improve their per iteration convergence which, as we will see in the next section, is not competive with the ADMM variants.

\section{Simulation Studies} \label{sec:experiments}
In this section, we compare the performance of the three algorithms considered on the presidential speeches data set ($n = 44$, $p = 75$) of \citet{Weylandt:2019} and log-transformed Level III RPKM gene expression levels from 438 breast cancer samples collected by The Cancer Genome Atlas (TCGA) ($n = 438$, $p = 353$)  \citep{TCGA:2012}. In addition to the three algorithms discussed above, we also compare to the {\tt COBRA}\xspace algorithm of \citet{Chi:2017}, an application of the \emph{Dykstra-Like Proximal Algorithm} of \citet{Bauschke:2008} to Problem \eqref{eqn:bclust}, which works by solving alternating convex clustering problems \eqref{eqn:clust} on the rows and columns of $\bm{U}$ until convergence. For each method, we compare a standard version and a version using the acceleration techniques proposed in \citet{Goldstein:2014}. (For {\tt COBRA}\xspace, acceleration was applied to both the row and column sub-problems.)

We show results for the rotationally-invariant $q = 2$ penalty with $\lambda = 1\times 10^4$ for the presidents data and $\lambda = 1\times 10^6$ for the breast cancer data, though our results are similar for other penalty functions and values of $\lambda$. For the ADMM variants, we fixed $\rho = 1$. The Davis-Yin step size and the Generalized ADMM coefficient ($\alpha$) were both set to twice the maximum degree of the row- or column-indicidence graph. The default sparse Gaussian kernel weights of the {\tt clustRviz}\xspace package \citep{Weylandt:2019-pkg} are used for each data set.

\begin{figure*}[t]
  \centering
  \includegraphics[width=\textwidth]{iteration.png}\vspace{-0.35in}
  \caption{Per iteration convergence of the ADMM, Generalized ADMM, Davis-Yin Splitting, and {\tt COBRA}\xspace on the presidential speech and TCGA breast cancer data sets. {\tt COBRA}\xspace clearly exhibits the fastest \emph{per iteration} convergence, appearing to exhibit super-linear convergence. The ADMM and Generalized ADMM have similar convergence rates, while the Davis-Yin iterates converge much more slowly.}
  \label{fig:iter_conv}
\end{figure*}

As can be seen in Figure \ref{fig:iter_conv}, the {\tt COBRA}\xspace algorithm clearly has the fastest \emph{per iteration} convergence, rapidly converging to the optimal solution. (The slower convergence near optimality appears to be an artifact of the inexact solution of the sub-problems rather than an inherent behavior of the DLPA.) The ADMM and Generalized ADMM exhibit relatively fast convergence, while the Davis-Yin iterates are the slowest to converge. The standard ADMM appears to have slightly faster convergence than the Generalized ADMM near initialization, but the two methods appear to eventually attain the same convergence rate. Acceleration provides a minor, but consistent, improvement for all methods except {\tt COBRA}\xspace, where the acceleration is applied within each sub-problem.

The apparent advantage of {\tt COBRA}\xspace disappears, however, when we instead consider total elapsed time, as shown in Figure \ref{fig:iter_time}, as the {\tt COBRA}\xspace updates require solving a pair of expensive convex clustering sub-problems at each step. On a wall-clock basis, the Generalized ADMM performs the best for both problems, followed by the standard ADMM, {\tt COBRA}\xspace, and Davis-Yin splitting in that order.

Practically, the Generalized ADMM and Davis-Yin updates have essentially the same cost and are both three to four times faster per iteration than the standard ADMM with caching. Precise numerical results are given in Table \ref{tab:results}. These results suggest that our Generalized ADMM scheme attains the best of both worlds, achieving both the high per iteration convergence rate of a standard ADMM with the low per iteration computational cost of the Davis-Yin / AMA updates, consistent with our theoretical analysis in the next section.

\begin{figure*}[t]
  \centering
  \includegraphics[width=\textwidth]{elapsed.png}\vspace{-0.35in}
  \caption{Wall clock speed of the ADMM, Generalized ADMM, Davis-Yin Splitting, and {\tt COBRA}\xspace on the presidential speech and TCGA data sets. Despite its rapid per iteration convergence, {\tt COBRA}\xspace is less efficient than the ADMM and Generalized ADMM due to the complexity of its iterations.  Davis-Yin Splitting remains the least efficient algorithm considered for this problem.}
  \label{fig:iter_time}
\end{figure*}

\section{Complexity Analysis}
Both the ADMM and AMA are known to exhibit $O(1/K)$ convergence in general, \citep{He:2012,He:2015,Goldstein:2014}, but the ADMM obtains a superior convergence rate of $o(1/K)$ for strongly convex problems \citep{Davis:2017b}. This rate can be further improved to linear convergence if certain full-rank conditions are fulfilled by the problem-specific $\bm{D}_{\text{row}}$ and $\bm{D}_{\text{col}}$ matrices \citep{Deng:2016}. As \citet{Deng:2016} show, the Generalized ADMM achieves essentially the same convergence rate as the standard ADMM. Consequently, theory suggests that the two-block ADMM variants have superior per iteration convergence, consistent with our experimental results.

The computational cost of the Generalized ADMM and Davis-Yin  $\bm{U}$-updates are essentially the same, both being dominated by matrix multiplications giving $\mathcal{O}(np\max(\#\text{rows}, \#\text{columns}))$ complexity, where $\#\text{rows}$ and $\#\text{columns}$ are the number of non-zero row and column fusion weights respectively. For sparse weighting schemes, we typically have $\#\text{rows} = \mathcal{O}(n)$ and $\#\text{columns} = \mathcal{O}(p)$, yielding an overall per iteration complexity of $\mathcal{O}(\max(np^2, n^2p))$ for the $\bm{U}$-update. A naive implementation of the ADMM update requires $\mathcal{O}((\#\text{rows})^3 + (\#\text{columns})^3)$ to solve the Sylvester equation, but if the initial factorization is cached, the per iteration complexity is again reduced to $\mathcal{O}(\max(np^2, n^2p))$ under a sparse weight scheme.

To the best of our knowledge, a convergence rate for the DLPA, on which {\tt COBRA}\xspace is based, has not been established.
Experimentally, the DLPA exhibits very rapid convergence, consistent with known rates for Dykstra's alternating projections algorithm. Despite this, the high per iteration cost makes it impractical on larger problems.

\begin{table*}
\begin{center}
\begin{tabular}{lS[table-format=3.2]rrS[table-format=3.2]rr}
\toprule
\multirow{2}{*}{Method}& \multicolumn{3}{c}{\emph{Presidential Speeches}} & \multicolumn{3}{c}{\emph{TCGA Breast Cancer}} \\
& {Iter/sec} & {Total Time (s)} & {Total Iterations} & {Iter/sec} & {Total Time (s)} & {Total Iterations} \\
\midrule
Generalized ADMM & 663 & 3.98 & 2639 & 2.58 & 1318 & 3411\\
\phantom{AB} Accelerated & 645 & 4.69 & 3025 & 2.55 & 835 & 2135\\
Davis-Yin / AMA & 657 & \textsuperscript{\textdagger}15.23 & \textsuperscript{\textdagger}10000 & 2.60 & \textsuperscript{\textdagger}3850 &  \textsuperscript{\textdagger}10000\\
\phantom{AB} Accelerated & 653 & \textsuperscript{\textdagger}15.31 & \textsuperscript{\textdagger}10000 & 2.58 & \textsuperscript{\textdagger}3879 & \textsuperscript{\textdagger}10000\\
ADMM & 189 & 8.12 & 1536 & 0.84 & 1521 & 1277\\
\phantom{AB} Accelerated & 188 & 7.08 & 1334 & 0.84 & 1324 & 1107\\
\midrule
{\tt COBRA}\xspace & 5.06 & 37.20 & 188 (29581 total) & 0.054 & 5994 & 325 (16519 total)\\
\phantom{AB} Accelerated & 6.89 & 27.15 & 187 (21362 total) & 0.065 & 4953 & 323 (13549 total)\\
\bottomrule
\end{tabular}
\end{center}\vspace{-0.15in}
\caption{Performance of the ADMM, Generalized ADMM, Davis-Yin Splitting, and {\tt COBRA}\xspace on the presidential speech and TCGA data sets. For {\tt COBRA}\xspace, the numbers in parentheses are the total number of sub-problem iterations taken. The $\dagger$ indicates that the method was stopped after failing to converge in 10,000 iterations.}
\label{tab:results}
\end{table*}

\section{Extensions to General Co-Clustering} \label{sec:tensor}

In Section \ref{sec:algs}, we restricted our attention to co-clustering tensors of order two, \emph{i.e.}, bi-clustering. In this section, we show how the ADMM, Generalized ADMM, and Davis-Yin (AMA) algorithms can be extended to the general problem of co-clustering order-$K$ tensors \eqref{eqn:cclust}. As before, we can re-express the co-clustering problem using directed difference tensors $\mathcal{D}_j$ as
\[\hat{\mathcal{U}} = \argmin_{\mathcal{U}} \frac{1}{2}\|\mathcal{X} - \mathcal{U}\|_F^2 + \lambda \sum_{j=1}^J\|\mathcal{U} \times_j \mathcal{D}_j\|_{j, q}\] where $\|\mathcal{X}\|_{j, q}$ is the sum of the $\ell_q$-norms of the vectorization of each slice of $\mathcal{X}$ along the $j$\textsuperscript{th} mode. For all three methods, the $\mathcal{V}$ and $\mathcal{Z}$-updates are straightforward extensions of the bi-clustering case:
\begin{align*}
  \mathcal{V}^{(k+1)}_j &= \prox_{\lambda/\rho \|\cdot\|_{j, q}}\left(\mathcal{U}^{(k+1)} \times_j \mathcal{D}_j + \rho^{-1} \mathcal{Z}{(k)}_j\right) \\
  \mathcal{Z}^{(k+1)}_j &= \mathcal{Z}^{(k)}_j + \rho(\mathcal{U}^{(k+1)}\times_j \mathcal{D}_j - \mathcal{V}^{(k+1)}_j).
\end{align*}
As with the bi-clustering case, we have separate $\mathcal{V}$ and $\mathcal{Z}$ variables for each term in the fusion penalty (\emph{i.e.}, each mode of the tensor), each of which can be updated in parallel. For the standard ADMM, the $\mathcal{U}$-update requires solving the following tensor Sylvester equation, where $(\cdot)^{\mathcal{T}}$ denotes a transpose, with the direction implied by context:
\[\mathcal{X} + \rho\sum_{j=1}^J (\mathcal{V}^{(k)}_j - \rho^{-1}\mathcal{Z}^{(k)}_j) \times_j \mathcal{D}_j^{\mathcal{T}} = \mathcal{U} + \rho\sum_{j=1}^J \mathcal{U} \times_j \mathcal{D}_j \times_j \mathcal{D}_j^\mathcal{T}.\] As above, the $\mathcal{U}$-update can be solved explicitly for our other methods:
\begin{align*}
  \mathcal{U}^{(k+1)} &=\frac{\alpha}{1+\alpha}\mathcal{U}^{(k)} + \frac{\mathcal{X}}{1+\alpha} \tag{Generalized ADMM} \\ &\quad + \frac{\rho}{1+\alpha}\sum_{j=1}^J(\mathcal{V}^{(k)}_j - \rho^{-1}\mathcal{Z}^{(k)}_j - \mathcal{U}^{(k)}\times_j\mathcal{D}_j)\times_j\mathcal{D}_j^{\mathcal{T}}  \\
  \mathcal{U}^{(k+1)} &= \mathcal{X} -\sum_{j=1}^J \mathcal{Z}^{(k)}_j \times_j (\mathcal{D}_j)^{\mathcal{T}}. \tag{Davis-Yin / AMA}
\end{align*}
\section{Discussion}
We have introduced three operator-splitting methods for solving the convex bi-clustering and co-clustering problems: a standard ADMM, a Generalized ADMM, and a three-block ADMM based on Davis-Yin splitting. The Davis-Yin three-block ADMM was found to be equivalent to the AMA which is in turn equivalent to the dual projected gradient recommended by \citet{Chi:2018b}. The standard ADMM achieves the fastest per iteration convergence, but requires solving a Sylvester equation at each step. The Generalized ADMM avoids the expensive Sylvester equation while still maintaining the rapid convergence of the ADMM. Unlike \citet{Chi:2015}, we do not find that the AMA performs well, perhaps due to the more complex structure of the bi- and co-clustering problems. On the TCGA breast cancer data, the Generalized ADMM was able to find a better solution in three and a half minutes than the AMA could in over an hour. All three of our methods can be extended to co-cluster tensors of arbitrary order, with the advantages of the Generalized ADMM becoming even more pronounced as it avoids a tensor Sylvester equation.

Our ADMM and Generalized ADMM methods provide a unified and efficient computational approach to convex co-clustering of large tensors of arbitrary order, but several interesting methodological questions remain unanswered. In particular, the conditions under which the co-clustering solution path is purely agglomerative, enabling the construction of dendrogram-based visualizations of the kind proposed for convex clustering by \citet{Weylandt:2019}, remain unknown. While not discussed here, our algorithms can naturally be extended for missing data handling and cross-validation, using a straight-forward extension of the Majorization-Minimization (MM) imputation scheme proposed by \citet{Chi:2017}. Our algorithms make convex bi- and co-clustering practical for large structured data sets and we anticipate they will encourage adoption and additional study of these useful techniques.

\section{References}
\printbibliography[heading=none]
\clearpage
\onecolumn

redpajama_set_name: RedPajamaArXiv


They each boast a large dial, 1.5 inch and 1.7 inch in diameter, and come in a striking case embellished with the Ferrari Shield. Fitted with straps detailed with grooves inspired by the front grille of racing cars, these accessories are infused with a strong sporting spirit via the bright color contrasts and the racing-inspired design. They are personalized with the iconic Ferrari Shield at the 12 o'clock position. A perfect complement to every outfit, the new RedRev watches have their own unique personality and inimitable spirit. Alternate yours as a constant symbol of your passion for Scuderia Ferrari.


Come see who we are and what God is doing across our Association!
Visit through our website or come see first hand for yourself.
Listen to hear how God speaks to you about your role in missions in Virginia & beyond!


If you haven't invested in an Ultrasonic Aromatherapy Diffuser for your home yet, here's what one will do for you, how to use it & why it would make a wonderful addition to your home.
If you're not sure what you can do with Essential Oils, or how to add them to your life, here are 101 answers.
You might love the way that Essential Oils smell, but you might not know just how powerful Essential Oils are.
If you haven't heard of a hydrosol before, this article will explain what one is & why you'll want to start adding hydrosols to your life & natural beauty regimen.
What should you be on the look out for when it comes to purchasing Essential Oils? Spoiler alert: it has nothing to do with "therapeutic grade" oils.
What exactly are Essential Oils? Find out here.


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April 28, 2019 by vicky in Uncategorized
Tourist attractions in Tel Aviv
Tourists have long chosen Israel for various reasons. The language barrier is practically not a problem here, since a huge number of our compatriots live in this country. Where, if not in Israel we can get acquainted with different cultures. This country is known for its color, a mixture of diverse cultures, a considerable number of nationalities, traditions and cultural and historical attractions. All this together with the incredible beauty of nature and the Dead Sea make the resorts of Israel especially popular. But the legendary tourist attractions in Tel Aviv will bring real pleasure from your trip. There are a lot of unique things to do in Tel Aviv.
Holidays with children or with friends in this country is always unforgettable. The main feature of Israel is undoubtedly a vacation in various resorts of the Red and Mediterranean Seas. The reason for such popularity among tourists is great hotels, many restaurants, discos and bars, developed infrastructure and much more. Here, both lovers of a more passive pastime can fully relax, basking in the sun and swimming in the waters of the Mediterranean Sea, and those who prefer tourist attractions in Tel Aviv. It will be interesting to see the rich underwater world, rocky mountains, coral reefs and much more.
If you have just arrived, you can visit the Vicky Cristina restaurant. It is a popular tourist attraction in Tel Aviv. It is worth noting that you use the tapas technology. This is a variation of the Spanish wines from around the world. Become a tourist destination in Tel Aviv Vicky Cristina to get some incredible experiences for a lifetime. Enjoy your trip!
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CHAMPAGNE FRANCE GOLAN HEIGHTS ISRAEL ITALY OTHER PRIORAT REDS RED WINE REST OF THE WORLD RIBERA DEL DUERO RIOJA SPAIN SPARKLING UPPER GALILEE WHITES WHITE WINE YEHUDA REGION גליל עליון רמת הגולן שאר העולם


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25 Musical Tours Offer Great Last-Minute Gift Ideas
If you need gifts in the last moments of the holiday, why not treat someone with the gift of live music? Below, we've highlighted 25 major tours taking place in the new year for which tickets are still available. Furthermore, the majority of these tours take place at outdoor venues, so you'll be able to enjoy a show with limited viewing risks. However, if you are attending an indoor prom, please be sure to wear a mask.
Also, be sure to check out the Consequence Shop, where all our CBD products and merchandise are on sale with up to 50% off. This includes the popular Protect Live Music shirt capsule and premium face coverings, as well as GWAR's Bud of Gods and Flower Lab CBD/Delta-8 products.
Editor's Note: By purchasing tickets via the affiliate links below, Consequence receives a portion of the transaction.
Red Hot Chili Peppers '2022 World Stadium Tour'
The Red Hot Chili Peppers (with John Frusciante back in the fold!) will be out on a 32-date tour of the field next summer. Even more exciting, they will be joined on the road by a rotating cast of all-star inaugural stars, including The Strokes, Beck, St. Vincent, HAIM, A$AP Rocky, Anderson .Paak, Thundercat, and King Princess.
Get tickets via Ticketmaster
Rage against the "public service announcement tour" of the machine
Rage Against the Machine meets on their first run together in over a decade. The PSA Tour, which runs for more than 40 days, runs from late March through mid-August. As an added bonus, they will be joined by Run the Jewels throughout the journey.
Foo Fighters "Live in North America 2022"
In support of their latest album, Medicine in the middle of the nightThe Foo Fighters have charted a North American tour for 2022. The 17-history swing features the newly inducted Rock and Roll Hall of Fame playing massive stadium shows in New York City, Philadelphia, Denver, Seattle, Los Angeles, and more.
Jack White "The Supply Chain Issues Tour"
In 2022, Jack White hit the road for the first time in four years on a massive tour in support of his upcoming albums. The Supply Chain Issues Tour consists of 57 performances taking place in North America, the United Kingdom and Europe between April and August 2022.
Eddie Vader "Earths Tour 2021"
Eddie Vader charted a US tour in 2022 in support of his new solo album, lightingAnd he has formed an All-Star Support Squad to join him on the road. Also debuting at Vedder's Ohana Fest earlier this fall, The Earthlings features drummer Chad Smith (from Red Hot Chili Peppers), guitarist/keyboarder Josh Klingover (from Pearl Jam), and bassist Chris Chaney (from Red Hot Chili Peppers). Addiction Jane), guitarist/vocalist Glen Hansard (from The Swell Season), and producer/guitarist Andrew Watt. Hansard will pull double duty into the round, where he will also unlock every show.
Kraftwerk movie "3D North America 2022"
After Kraftwerk was recently inducted into the Rock and Roll Hall of Fame, the pioneers of electronic music are planning a 2022 North American tour in 24 cities between May 27 and July 10. Each date will contain a 3D rendering of the group launch.
Roger Waters "This Isn't a Training Tour"
Roger Waters will play 36 dates across North America in the summer of 2022. The tour is billed as the "first farewell tour" of Pink Floyd's co-founder and promises a playlist of "dozens of great songs from Pink Floyd's golden age". The race begins in Pittsburgh, Pennsylvania on July 6 and travels from coast to coast — including a few Canadian stops — before concluding in Dallas, Texas on October 8.
Tyler the Creator Tour 2022 with Kali Uchis and Vince Staples
Tyler the Creator has announced a North American tour in 2022 in support of his new album, Call me if you lose. Launching in February, the 34-date circuit tour will also feature Kali Uchis, Vince Staples and Teezo Touchdown.
Dua Lipa "Nostalgia for the Future" tour
The future is close: Dua Lipa has announced that her "Future Nostalgia Tour" will arrive in North America in 2022. The pop star "brings the perfect girl gang with me," as Megan Thee Stallion, Caroline Polachek and Lulu Zwach will be supporting her.
Tame Impala "Slow Rush Tour (2022)"
Tame Impala has charted an early tour of North America for 2022, which includes stops at the Scotiabank Arena in Toronto, Barclays Center in Brooklyn, TD Garden in Boston, and Bridgestone Arena in Nashville, as well as two dates at ExploreAsheville.com Arena in Asheville, North Carolina.
HAIM "One More HAIM Tour"
Next year, the HAIM sister trio will embark on the "One More HAIM Tour," a 27-date outing featuring performances alongside Waxahatchee, Faye Webster, Princess Nokia and more.
RUSH's Greeting Tour in Primus
Primus has expanded its celebratory RUSH tour with the addition of 46 new dates taking place in the spring and summer of 2022. "A Tribute to Kings Tour" features a full performance of RUSH's 1977 album, Farewell to the kings, as well as opening groups from the likes of Battles, Black Mountain, and The Black Angels
"Legacy of the Beast" by Iron Maiden
Iron Maiden recently expanded its "Legacy of the Beast" world tour with a new series of North American shows in 2022. The short, 30-day tour kicks off in Mexico City on September 7 and runs through the end of October. Even better, you'll join Iron Maiden on the road by Trivium and within Temptation.
Tears for Fears "The Tipping Point World Tour" features trash
In February 2022, Tears For Fears will be released The turning pointTheir first studio album in two decades. To mark the occasion, the British duo will embark on their first US tour in five years, taking trash throughout the trip. The runway tour spans 21 dates and will begin in Cincinnati on May 20 before stopping in cities like Denver, Los Angeles, Atlanta, Philadelphia, and Boston.
New order and "unity tour" for boys from pet store
The New Order and Pet Shop Boys will join forces in fall 2022 for "The Unity Tour," a 13-date back-to-back trip that includes stops in Toronto, Boston, Brooklyn, Chicago, Los Angeles and beyond. Grammy-nominated DJ Paul Oakenfold will support the entire tour.
"Weird Al" Yankovic "The Unfortunate Return of a Self-Tolerant Vanity and Ridiculous Advice Tour"
Jankovi? "Weird Al" Jankovi? plans to spend the vast majority of 2022 on the road. The tour officially kicks off April 26 in Poughkeepsie, New York and runs through the end of October, stopping virtually everywhere you can think of—from Saskatoon and Saskatchewan to Midwest City, Oklahoma—before wrapping up October 29 at Carnegie Hall in New York City. Finally, "Weird Al" will have 133 shows.
The Killers "Imploding the Mirage Tour"
The Killers have announced "Imploding the Mirage Tour" in support of their latest album of the same name. The all-around arena tour takes place between August and September 2022, and will feature Johnny Greenwood in a supporting role.
Netflix Prank: The Festival
Netflix inaugural joke: The festival will feature over 100 comedians performing at 25 venues in the Los Angeles area between April 28 and May 8, 2022. Among the confirmed talents: Dave Chappelle, John Mulaney, David Letterman, Conan O'Brien, Jerry Seinfeld, Tina Fey , Amy Poehler, Chris Rock, Larry David, Bill Burr, Kevin Hart, Seth Rogen, Pete Davidson, and more.
"Crash The Live Tour 2022" by Charlie XCX
Charli XCX has charted an extensive tour in support of her upcoming album, Collide. With nearly 40 dates on the agenda, the pop star will perform across North America and Europe between March and June 2021.
Robert Plant and Allison Krause Tour 2022
After reuniting for their second album raise the roof, Robert Plant and Allison Krause are on the way to an international tour next year. The duo will embark on their first cruise in 12 years starting June 1 in the US before heading across the pond to a British and European stop from June 26 through July 20.
"Freedom Tour 2022" for the trip with Billy Idol and Toto
Next year, Journey will be on an intense North American tour alongside Billy Idol and Toto. From late February through mid-May, the "Freedom Tour 2022" will stop in 40 cities across the United States and Canada. Idol will open the first leg of the tour, before Toto takes over those duties starting in April.
Live 2022 by Nick Cave and Warren Ellis
One year after the release of their album massacre This past March, Nick Cave and Bad Sid member Warren Ellis were headed out on a North American tour. The 17-times itinerary includes two nights runways in Austin, Auckland, and Montreal, as well as four nights cruising around Brooklyn and Manhattan in New York.
The reunion tour 2022 in Pavement
He hits the pavement in 2022 on a worldwide reunion tour. After major appearances at Primavera Sound and NOS Primavera Sound in June, alternative rock will be on a 23-date US tour beginning in September, followed by dates in the UK, France, Germany and more.
Kacey Musgraves movie "Star Crossed: Unveiled"
Kacey Musgraves has announced a major tour in support of her newly announced album, through the stars. The 15-city arena tour, titled "Star Crossed: Unveiled," officially kicks off in January. Over the next month, she will play shows at major venues including United Center in Chicago, TD Garden in Boston, Madison Square Garden in New York City, and American Airlines Center in Dallas before concluding with a party at Staples in Los Angeles Center on the 20th February. The King Princess and MUNA will provide support for the entire tour.
John Mulaney "From Scratch"
John Mulaney has announced "From Scratch," a new slate of dates for 2022. Our former comedian will be back on the road beginning March 11th in Wilkes Barre, Pennsylvania. The 33-date trip appears designed to increase frequent flyer miles, with a performance in Ohio followed by a layover in Maine, a two-night layover at Foxwoods Casino in Connecticut giving way to a run through Texas, and what could have been a California stretch that was interrupted by layovers in Denver, CO, Omaha, Northeast, and St. Paul, Minnesota.
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WADE'S WORLD: Fancy a holiday in a lighthouse?
Do you fancy holidaying somewhere different in 2013? How about a lighthouse on an island? Or maybe a castle or a Victorian folly?
You don't need to go far either as you can rent out buildings like these and many more for holidays around the UK, courtesy of the Landmark Trust.
The trust has been restoring historic and architecturally interesting buildings since 1965 and giving them a new lease of life by letting them out for holidays. Some are for just two people, others are for 12 or more.
So instead of a caravan, you could try the Old Light on Lundy island in the Bristol Channel. Snug in your keepers' cottage, built of 'Cyclopean blocks of granite' you could explore the delights of this haven of wildlife, which also boasts a pub.
While not needing a ferry crossing to get there, the Martello Tower in Aldeburgh, Suffolk also looks a likely spot for an adventurous break with a nautical feel.
Martello Towers were built to deter French invasion during the Napoleonic Wars, but this intriguing spot now boasts a teak floor, a restored, vaulted interior and 'an intriguing echo'.
They're not always pricey either.
Beckford's Tower, a Victorian folly in Bath could be yours for four nights for £344, and as it sleeps four, that makes a tidy £21.50 per person, per night. Visitors can enjoy the sumptuous Scarlet Drawing Room, the fine circular staircase and admire what Beckford called 'the finest prospect in Europe'.
And closer to home is Clytha Castle near Abergavenny. Built in 1790, this magnificent home stands on the summit of a small hill with deer known to wander its grounds. Small as castles go, it only sleeps five, but with some imagination, that should be more than enough for an exotic weekend away.
What's more, your holiday will be helping preserve these parts of our heritage for many years to come .


Oh Janet.....I think I buy the most Disney Dollars of any guest there! We have used them since they began many, many years ago for a family game at each meal. My kids who are now 31 and 29 still insist we play the Disney Dollar game!
Your best luck at purchasing the Disney Dollars is at any of the park's Guest Service windows. They will have all three of the denominations available: ones, fives, and tens. I purchase a great amount at one time and know that they will put a limit on how much you can charge to a credit card so be prepared for that. The resort front desks and concierges will sometimes have them as but you might not find all denominations at one place. Downtown Disney has a Guest Service desk as well that can help you with this purchase.
When it is time to head home and you still have some Disney Dollars left you can simply turn them in at your resort for the "real" paper money or any other location on property. Disney Dollars at Walt Disney World work as cash for anything from dining, souvenirs, and even tips. (Although the valets are not real fond of Mickey and friends faces on their money...alas).


Mark EA8FF bought one of the first SunSDR2 PRO HF, 6m and 2m tranceivers from SunSDR.eu. Mark is a demanding operator with a very special interest in low signal DXing, both on HF, VHF and UHF. In his own words, this is Mark's initial review after using his new SunSDR2 PRO for a few weeks.
I have not being doing any absolute measurements on the SunSDR2 PRO but compared its ability to receive weak signals in general with a few other tranceivers, connecting both receivers to the same antenna trough a good 3 dB splitter and listening to, or decoding the same signal at the same time.
The results were all but one well in favor of the SunSDR2 PRO. In fact, no other receiver ever comes close by on the bands were I have antennas for. I have been specially looking for weak signals close to interference or digged in the noise. Weak beacons, perfectly readable on the SunSDR2 PRO were barely detectable on all other equipment. So all other tranceivers have gone out by now, I wouldn't switch them on anymore anyway. 100 MHz broadcast sounds distorted, but thats probably a software issue and I don't need broadcast reception.
I am building a 23 cm EME station and want to use K1JT's MAP65 software. This allows you to receive and decode all JT65 signals simultaneously in a 90 kHz part of the band. To get familiar with the software I implemented MAP65 in the ExpertSDR2 software as CWSkimmer, using the I/Q output over Virtual Audio Cable. At first I couldn't get enough signal level to MAP65, but discovered that in the last versions of Virtual Audio Cable you can enable volume control to boost the signal from the SunSDR2 PRO.
The reception of JT65 signals on 14.076 is exeptional: I see people exchanging reports down to -21 but I get many perfect decodes down to -27 and even far below, all this without Deep Search.
Frequency stability and accuracy is excellent, I connected my GPSDO at 10 MHz and found a difference of 20 Hz on 144 MHz, and the internal frequency standard walks away from this no more than 10 Hz a day. So no need for external frequency references unless you want to have a very precise frequency using WSPR.
On SSB transmit the sound is crystal clear, you can make lot's of adjustments to adapt your voice to the transmitter.
I connected a bug and tried some CW keying. Super keying, perfect vox keying , clean signal, nothing to comment.
I mounted a 12 x 12 cm 12 volt computer blower on top of the SunSDR2 PRO with a 100 Ohm resistor in series. This lowers the temperature in this warm climate down to 35 C without extra noise in the shack.
A nice thing about the SunSDR2 PRO unlike some other SDR receivers is that you don't see birdies when you disconnect the antenna.
I like the concept of the SunSDR2 PRO tranceiver: Small size, enough power to drive modern solid state PA's, good quality connectors. The only tranceiver you need to everything!
More information on the SunSDR2 PRO high performance HF, 6m and 2m SDR transceiver is found here.


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Mt. Wilson Observatory
When the US Forest Service suggested that we scout the Mt. Wilson Observatory as a site for our AW21 runway show, I didn't appreciate the significance of the location. Travelling up the windy roads of the Angeles National Forest in the San Gabriel mountains, I started researching the Observatory on my iPhone until my signal ultimately dropped as we drove a mile above Los Angeles.
When we got to the top, we were given a tour of the grounds and the Observatory by Executive Director of the Mount Wilson Institute, Tom Meneghini, who calls the Observatory the "Sistine Chapel of Astronomy." I now understand why.
I learned that most advances in astrophysics in the modern era have emanated from here. Built in the early 1900s led by George Ellery Hale, the Observatory is home to 100-inch Hooker telescope where Edwin Hubble made the groundbreaking discovery confirming that the Andromeda Galaxy was indeed its own galaxy--proving the universe was bigger than anyone ever knew and more importantly, that it was expanding. These discoveries became the foundation for the Big Bang Theory and other great scientific achievements. Visited by Einstein and other preeminent scholars, Mt. Wilson has been the cornerstone of advanced astronomy.
What's so special about this site for me is that it is nestled in some of the most beautiful forests I have easy access to from LA. You can go for a day hike and stumble upon the Observatory or view it in the distance from the hundreds of miles of trails throughout the forest.
For more information about the Observatory visit www.mtwilsdon.edu.
The Institute is a non-profit and donations can be made by clicking here.
For more information about the trails and surround areas visit the USDA Forest Service here.


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Connect Trade Union Ireland's largest Craft Union elects new General Secretary Designate
Connect Trade Union Ireland's largest…
Paddy Kavanagh, the South-East Regional Secretary of the Connect Trade Union has been elected General Secretary Designate to succeed Eamon Devoy as leader of Ireland's largest craft union. He will take up office as General Secretary from July 24th, 2016. Speaking after the Executive Council at the weekend where the election result was announced, Mr Devoy said that, "Paddy Kavanagh is highly regarded in the trade union movement and has extensive experience of both the private and public sectors.
"He is from a mechanical engineering background. Besides currently being Regional Secretary in the Connect Trade Union's South-East Region based in Waterford, he has national responsibility for our members in the Public Service and brings a vast amount of experience to the role."
Mr Kavanagh said. "I look forward to the challenges of leading the Connect Trade Union. I particularly welcome the fact that I had support and nominations from all sectors of the union, across the country. I am very proud of the confidence my fellow members have placed in me and makes me all the more committed to championing their interests."
He has been a trade union activist representing workers for over 30 years. His recent achievements include leading the Connect Trade Union team in national negotiations on the Croke Park, Haddington Road and Lansdowne Road agreements, recruiting, organising and securing union recognition in many private sector companies and protecting defined benefit pension schemes for members.
He comes from Clogh, Castlecomer, in County Kilkenny, which has a strong trade union tradition and said he had been inspired to become active by his parents who had both been very active in the labour movement. He has an avid interest in labour history and now lives in Kilkenny. He is married with three children, two boys and a girl.
In a separate election Alan Douglas (cousin of Mandate General Secretary John Douglas) was elected as a full time paid official of the union. He will commence employment in January 2016 and will be based in the Connect Trade Union's Limerick office. He will have a dual role, supporting members in the Connect Trade Union Limerick Branch and supporting Brian Nolan, the National Construction Official in the Mechanical and Electrical Contracting sector on the western seaboard.
Mr Douglas has an electrical engineering background and is currently Organiser for the Electrical Branch based in Dublin. He is Chairperson of the Connect Trade Union's National Youth Forum and a member of the Irish Congress of Trade Unions' Youth Network.
PreviousPrevious post:Connect Trade Union & SIPTU Local Authority Water Workers vote of Industrial ActionNextNext post:Connect Trade Union Condemns Commission for Energy Regulations Decision on ETCI


The VERASEC-KIT1 comes with a VeraSecure controller, two 2GIG door/window sensors and two 2GIG motion detectors.
The VeraSecure controller brings together security and home automation in a flexible and affordable system that allows for self-monitored security, control and automation with NO monthly fees, by using the free Vera Cloud service.
You can arm & disarm the system, self-monitor and get alerts on your smartphone or tablet with the free iOs and Android apps from Vera. VeraSecure has a loud onboard siren.
The 2GIG-DW10-345 wireless thin door/window sensors make an aesthetically pleasing security solution for almost any point of entry or valuable enclosure with it slim and unobtrusive design. They have a maximum range of up to 350 feet.
The 2GIG-PIR1-345 wireless passive infrared motion detectors are pet immune and can be set between modes for pets either up to 33lbs or 55lbs. A high sensitivity mode can also be set which ignores pet immunity altogether.
Note: We recommend having your home's Internet gateway/router on a UPS so it will also continue to function during a power failure. VeraSecure service is available with no monthly fees right now. The optional Vera Sentinel and Vera Protect services are NOT currently available in Canada but we hope they will offer these add-on features for Canada in early 2018.


surfin estate, our journal: NOW.
This is the lastest video from Analog. Although a perfect mix of progressive surfing. stunning images, outfits and rock music, it doesn't smell so good. Sequences are reduced to spectacular single tricks (air reverse, air reverse, air reverse) and skip the whole riding.
Have a look and tell us what you think on our Facebook page.


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Is Judas Priest rock?
Is Judas Priest progressive rock?
Is Judas Priest hair metal?
When did KK Downing join Judas Priest?
How much is Judas Priest worth?
10. Judas Priest, "Victim of Changes" (1976) Long before they conquered America with concise heavy rockers like "Breaking the Law," "Living After Midnight" and "You've Got Another Thing Comin'," metal gods Judas Priest stood for years at the crossroads between prog and metal.
Additionally, some established hard rock and heavy metal bands of the era such as Scorpions, Whitesnake, Dio, Aerosmith, Kiss, Alice Cooper, Ozzy Osbourne, Judas Priest, Saxon and Accept began incorporating hair metal elements into their sounds and images, as the genre's popularity skyrocketed in 1985–1986.
Release contributions
Al Atkins 1969–1973 none
K. K. Downing 1970–2011 all Judas Priest releases from Rocka Rolla (1974) to A Touch of Evil: Live (2009)
John Ellis 1970–1971 none
Alan Moore 1971–1972 1975–1977 Sad Wings of Destiny (1976)
The Birmingham-based heavy metal band Judas Priest was formed in 1969. So far, they have sold more than 50 million copies of their entire albums, while receiving several Grammy nominations with them. Judas Priest's net worth is $80 million, which is making them the 4th richest metal band worldwide.
IT IS INTERESTING: You asked: How do Christians remember the Trinity?


Gather 'round ... it's time to visit te Chocolate Factory!!!
The wild symbol of this game is Doctor Chocolate. He substitutes for only the candy symbols (there are 6 candy symbols) in this game. This symbol is also the "big payer" of the game ... get 5 on a payline and get awarded 8,000 coins!!!
The BonBon Bonus Game is triggered when you get 3, 4, or 5 of the bon bon bonus symbols on a payline. You will be presented with 10 different chocolates. Click on a chocolate to see what your win is. If you get a number value, you continue on to pick again and again and again, until you click one that says "collect" .... that ends the bonus game.


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How does a player released by Bournemouth end up in Finland? Ask Begovic, Stacey and Antti Niemi
While Calum Ward's story over the past year has been up and down, it's rarely been dull. From being stuck in Frankfurt to isolating in Helsinki, the goalkeeper is now settled in Finland following his release from Bournemouth
Updated 19:54, 30 MAR 2022
Ward playing for HIJK in the derby last season (Image: Photo: HIJK/Calum Ward)
"They officially released me in April. But they tell you early. I kind of saw it coming because they weren't having me at Bournemouth before that. Probably from Christmas onwards."
It is December 2021 and DorsetLive sits down with Calum Ward almost a year after he first received official news of his release from the club he had been at for eight years. The festive period also provided a period of apt reflection on the previous 12 months. It had seen Ward enter a new phase in his life and career. At just 21 years of age, the goalkeeper has already become well-versed in the lessons of living away from home.
Ward's permanent residence is now in Finland, Helsinki, where he's currently settling into his second club in the country. It is an unusual footballing trajectory for someone so young and naturally, leads to several colourful stories.
READ MORE: Which Bournemouth player boasts the best points per Championship match record?
Most who end up being released have a gut instinct long beforehand. It turns out to be a prescient feeling and Ward was no different. He had expected the news weeks, months, before it was confirmed. It came to be an intangible sense that often leads to a sense of trepidation causing you to prepare for the worst sometime before it actually arrives.
Ward had risen through the club's academy age groups and at under-16 level, had first begun to train with the first team under Eddie Howe. By the time he reached the scholarship phase, he was a staple of the training sessions at Kings Park.
An influential loan spell at Weymouth in the 2019/20 season should have shown Ward was on the right path. But that sixth sense kept kicking in - he knew his time at the Cherries was coming to an end.
"I was at Weymouth and we got promotion," says Ward. "I came back for the next season having played every single game on loan. I returned for pre season but didn't play because of the number of goalkeepers all needing minutes at the club and it was tough to get back in.
"I wanted to stay another year at Weymouth but I got told I wasn't going anywhere. I was staying at Bournemouth. They were saying I wasn't doing as well as I should have been.
Calum Ward of Bournemouth during a first team training session at the Vitality Stadium (Image: Photo by Robin Jones - AFC Bournemouth/AFC Bournemouth via Getty Images)
"I was getting fed up because I wasn't playing so needed to get a loan. In fairness, the club did bring me into train back with the first team, so I wasn't quite sure what was going on. I began training well and Mossy (Neil Moss) at the time told me I was doing well.
"But after four months, I hadn't played any games so I asked for another loan and was allowed to go. Then I went to Finland."
Headed to Northern Europe at the height of a pandemic wasn't quite the traditional loan of a young player at a Championship club. Ward's frustration at being denied a return to Weymouth saw him and his agent actively seek a loan elsewhere. But progress was only made when two team mates in particular heard of Ward's intentions.
"Asmir Begovic was here and he's honestly such a nice guy," smiles Ward. "He decided to help me out and spoke to my agent. He set the wheels in motion. Asmir spoke to Jack Stacey who knew the old assistant coach at Luton, Joaquín Gómez. Joaquín also coached at other clubs in England like Brighton and Stoke, but had moved to Finland to become the manager at a club called HIFK.
"It was a coincidence that Stace knew Gomez and Asmir knew HIFK's goalkeeper coach. You will know him... Antti Niemi, the old Southampton keeper. And he was very good. He was a good laugh. He knew Asmir and it kind of went from there."
HIFK compete in the Veikkausliiga, the highest tier in Finnish football. They are based in Helsinki and in the 1960s, twice played in the European Cup, now known as the Champions League. Initially, Ward would join on a four-month loan deal until June 2021.
Once the green light was given by Neil Moss, Bournemouth's goalkeeping coach and the club, Ward was handed his travel arrangements by his new side. But COVID and post-Brexit issues meant, unsurprisingly, things didn't go quite to plan.
Gavin Bazunu, left, and Calum Ward during a Republic of Ireland U21 training session in November 2020 (Image: Photo By Seb Daly/Sportsfile via Getty Images)
"My parents dropped me off at Heathrow and I had to get a COVID test straight away. I had to get two flights, the first being to Frankfurt. I got to Germany but realised I had eight hours to wait for my connecting flight. There was no hotel nearby so I slept on little metal chairs!
"Anyway, I got there at 8 pm and was going through passport control. The German officers said to me 'why are you coming here?' They then told me that due to some rules regarding Brexit they would not let me through and I needed a Visa. Bournemouth had already said they would get me one once I'd been in Finland for 90 days.
"I just remembered thinking this is something I don't need. They asked for a reason as to why I was going into the country and I said I'd been invited to play football. I went to phone the CEO of HIFK and he told me he'd sort everything out. So it should have been fine...
"I then walked back to the ticket desk and the German officers had booked me a flight back to Heathrow for 7.30 am the next morning. At this point, I was sh**ing my pants. I just thought 'what am I doing here?' I took the ticket to get back to Heathrow and went for a walk to to clear my head. But I got lost!
"It turns out I ended up walking myself to a different passport control and there was a lady who let me straight through. It was only about 9 pm and my flight was not till 10 am the next morning. I had my coat and my beanie on and in my hand luggage I had my PlayStation, so it was pretty difficult to sleep, knowing I couldn't leave it. It was horrendous.
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"I got to Helsinki and had to immediately isolate for five days. They put me in a hotel where there was no beds or mattresses so we had to get it all sorted out. It was freezing and for some reason, I only brought one coat and a body warmer. There was snow everywhere. The first few days were a struggle because I realised I was alone in Finland, like what am I doing? It was a big shock."
Having overcome early teething issues at his new club and in his new country, the next challenge the loanee faced was accruing the thing he desired most; game-time.
"I went out there thinking I was just going to go straight to the team," admits Ward. "I trained well the first session, and then the other goalkeeper at the time was a very good trainer. I wasn't as good in training but I was better in games. Hee smashed it every day, which you're meant to do. He played in the first few games then I came in.
Ward signing an autograph for a young HIJK supporter (Image: Photo: HIJK/Calum Ward)
While the awakening Ward received proved harsh lessons, both in Finland's natural elements conditions and the battle for the number one spot, the deepest cut was yet to come. Having made the trip to Helsinki alone, where temperatures in January and February ranged from -2° to -7°, the goalkeeper was informed of his release from Bournemouth.
"Gaz (Gareth Stewart, Development Squad GK coach) called me up and I knew it was coming," Ward, who has previously been called up to the Republic of Ireland's under-21 squad, says. "He just said 'you haven't played enough games for us, the time has come.' He told me I could either come back for the rest of the season and they'll happily let me train and put clips together of me to send out to other clubs.
"But I just thought 'screw it, I'll stay out here'. I was enjoying living in Helsinki and ended up playing a decent amount of games and did well. I was staying in an apartment with a team mate who was English, so it worked."
Rather than serve as a roadblock, news of his release acted as a catalyst. While Ward received opportunities from Bournemouth to access support and advice in planning the next steps in his career, the goalkeeper wanted to remain where he was.
News came of a further fourth-month loan extension, taking his deal until the end of the Finnish season coincided with Ward's form and confidence going from strength to strength. Finland's emergence out of inhibiting COVID restrictions also helped to smooth over Ward's difficult start in the country.
"The derby against HJK was amazing. At the start, it was behind closed doors but when the derbies came around there were people in the stadiums. We were rivals and yet we trained at the same place! Our home stadium was their home stadium.
"Whenever we wanted to train in the stadium we had to pay them because they owned it and because they had more money. We played them three times in the season. I played two of them. We lost the first 1-0 and I just remember it being so cold and pouring with rain. But in the second game... we won 2-0. It was just incredible."
Ward signing for AC Oulu (Image: Photo: AC Oulu/Calum Ward)
Indeed, Ward enjoyed Finland so much he decided to do it all over again for the following 2021/22 campaign. This time though, at a different club.
"The season finished and I was coming back to England. But I got a WhatsApp from AC Oulu's sporting director. I didn't know how he got my number.
"I didn't reply, I just forwarded it on to my agent and then they talked. By this point, I had already been offered a new contract at HIJK but I wasn't keen on it because Joaquin had gone and the backroom situation had changed. There was going to be more change and no money.
"A few days later, my agent messaged me and he said they sorted it out. It was for more money, they paid for a better apartment and they paid for lunch after training, which wasn't there at the other club. So I've signed a one-year deal and I'm going back to Finland. I've got to thank Asmir and Stace for that!"
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