Dr. Jeffrey T. Brodie specializes in the treatment of foot and ankle conditions with a special interest in foot and ankle arthritis and ankle replacement. Dr. Brodie was recognized among Baltimore Magazine's Top Doc list of 2018 for his excellence in orthopedic surgery.
In addition to foot and ankle arthritis, Dr. Brodie provides treatment for a variety of conditions including disorders of the Achilles tendon, flat foot deformities, ankle instability, and nerve compression of the lower extremity. He sees athletes of all levels from recreational teams to the pros.
Dr. Brodie will also see patients seeking a second opinion. Please contact his office for more information.
Dr. Brodie graduated from Emory University with a B.A. He received his M.S. and M.D. degrees from Georgetown University and completed his post-graduate training at Monmouth Medical Center and the Mayo Clinic, Scottsdale. Dr. Brodie is fellowship trained in surgery of the foot and ankle.
Foot and Ankle Orthopaedic Surgeon Dr. Jeffrey Brodie named to annual Top Doctors' List by Baltimore Magazine.
UMMS and University of Maryland St. Joseph Medical Center Physicians including orthopaedic surgeon Jeffrey Brodie, M.D., were recently named to 2016 Top Doctors list by Baltimore Magazine.
Dr. Brodie, a multi-year recipient of the annual honor, is fellowship trained in surgery of the foot and ankle. He joined Towson Orthopaedic Associates in 1997.
Top Doctor results are based on a Baltimore magazine survey of nearly 10,000 physicians in the Baltimore area, including Baltimore City and the surrounding seven counties, asking where they would send a member of their family in dozens of specialties. Also, recently, the Baltimore Sun featured an inspirational story of an athlete treated by Dr. Brodie.
Dr. Brodie was also named Top Doc in 2008, 2010, 2013, 2014, 2015 and 2016.
Please tell us about YOUR experience with Dr. Brodie!
Dear Dr. Jeff Brodie & Staff: Bob & I would like to "Thank You!" for all the patience and kindness you had during his ordeal. He was not always the ideal patient. I do apologize for him. Dr. Brodie, thank you for your expertise and the wonderful job that you were able to perform on that leg. We will always be thankful we found you. Tony, I know you must really love what you do. A patient like Bob puts you to the test. Bless you for hanging in there... (Read more below) -- Diane & Robert S.
Dear Dr. Brodie: I wanted to express a sincere thanks to you for fixing my ankle. I am leaving you this photo of my visit to Egypt as a sign that you have done a fantastic job. Thank you. Sincerely, -- Maxine Y.
Dr. Brodie: Thank You for helping me to walk again., -- Rosanna P.
Hi Dr. (Brodie): Wishing you all the joy and happiness that Christmas brings! Merry Christmas. Happy New Year. Hope you are doing well, and there is lots of knee business! I am A-ok, and never cease to be amazed at the new life I enjoy, each day, with my knees, thanks to you. -- Angela P.
With many thanks to you for your kindness & professionalism. Hey Doc (Dr. Brodie), Just wanted to express my thanks for fixing me up. So far, so good! The soreness gets less each day & it's great to run with my 9-10 girls B-Ball team. Have a great week. -- Tim T.
Dear Dr. Brodie: I wanted to take a few moments to write and let you know how right you were with your assessment of my problem and how well you did with the procedure. I am still amazed. I went two years with the problem you worked on and was in considerable pain a good part of the time. I saw no less than 5 doctors who really didn't have a clue and seemed to pass it off as part of the pain you may feel with aging. You took the time to listen and probe and felt you knew what was wrong... (Read more below) -- Ron G.
Dear Dr. Brodie and Staff: Thank you ever so much for everything you have done for me over the past six weeks! Everyone has been great and has given me a lot of TLC! I know right where to come the next time I fall off the sliding board and break an arm (ONLY TEASING!!) Thanks Again. -- Nicole M.
Dr. Jeffrey T. Brodie: Just a note to express my deep appreciation for you going to bat so I could receive a Roll-A-Bout. Trying on my own didn't help but your help did. I truly appreciate your help. If all doctors were more like you, all patients would care more about their recovery, and want to get better and well. Thank you again. -- Bill G.
Hello Doc (Dr. Brodie): Just a note to tell you that I'm doing well so far. Thanks for all that you have done for me. Please tell your staff "thanks" also. I hope to see you all when I return. -- Charles D.
Dr. Brodie: Thought I would send you a getting well picture of my foot. Healing well, pain more down to 1-2, yea! I'm glad your my doctor, have a peaceful day! -- Miss P.
Here's a photo of me dancing at my 70th birthday celebration!! Thanks for all you did to make this possible. Sincerely, -- Donna H.
I would like to take a moment to thank you for the great job you did repairing the nerve damage. My drop foot is gone and I am doing really well working. I walk over 6 miles a day at my job, so not wearing a foot brace is wonderful. You did a great job. People are amazed about how well I'm doing. Thanks again -- Bill B.
Dr. Jeffrey Brodie, I want to say thank you for the care you provided for me during my stay in February 2017. You were very attentive to my care and concerns. The food was very delicious, hot and prepared and delivered well. My stay was brief and I am doing well after my total ankle replacement. I look forward to seeing you for my appointment and x-rays to see how I am doing so far with the surgery. I could not have asked for better doctors, hospital, staff and care. Thanks again. --Sincerely, Sandra S.


Here's a classic one: Two ladies argue with one another every day from their windows, across an intervening lane. They never agreed, which was to be expected of course, for they argued from different premises!
2019, February 22 .Reading time 1 minute.


Actually, I've been creating a few dramatic watercolor flowers for my upcoming "Expressive Flower Painting in Watercolor" workshop. A fun introductory workshop to free style watercolor painting that I am teaching at the end of the month.
This summer was pretty wild, I taught quite a variety of workshops to people of just about every age!
So I am off to paint!
This entry was posted in Art and tagged art workshop, daisy, painting, watercolor. Bookmark the permalink.
Thanks, Amy. Wish I could write. It's so challenging for me.
(smile) We all have our strong points, yes?
I love watercolor botanicals! Beautiful!
How beautiful, Janell! I love that color combination!
Hi Janell, the way you use colours in your painting is unique and amazing.


good Word of Yahweh, and the works of power of a coming age, and having fallen away, it is impossible for them again to renew to repentance, crucifying again for themselves the Son of Yahweh, and putting Him to open shame.... good Word of Yahweh, and the works of power of a coming age, and having fallen away, it is impossible for them again to renew to repentance, crucifying again for themselves the Son of Yahweh, and putting Him to open shame.
About Tribes of Yahweh. A twentieth-anniversary reprint of the landmark book that launched the current explosion of social-scientific studies in the biblical field.
Norman Gottwald's monumental The Tribes of Yahweh caused an immediate sensation when first published in 1979, and its influence has continued to be felt, both in the area of biblical politics and in the application of sociological methods to the Hebrew Bible.


text:
www.USPages.com - the best of US business
Accident & Health Insurance
The Fortune 500
USPages
USPages > Business Directory > Accident & Health Insurance > AFLAC Incorporated
AFLAC Incorporated
Industry: Accident & Health Insurance
Fortune Rank: 130
AFLAC, Incorporated operates in the insurance industry and primarily sells supplemental health insurance in Japan and the U.S. For the 6 months ended 6/30/05, total revenues increased 9% to $7.13B. Net income increased 18% to $664M. Revenues reflect growth in Aflac Japan's new annualized premium sales, and favorable foreign currency translation. Net income also reflects improved gross margins.
AFLAC Incorporated is a general business holding company and acts as a management company, overseeing the operations of its subsidiaries by providing management services and making capital available. Its principal business is supplemental health and life insurance, which is marketed and administered through American Family Life Assurance Company of Columbus (AFLAC), which operates in the United States (AFLAC U.S.) and as a branch in Japan (AFLAC Japan). AFLAC Japan sells cancer plans, care plans, general medical expense plans, medical/sickness riders to the Company's cancer plan, a living benefit life plan, ordinary life insurance plans and annuities. AFLAC U.S. sells cancer plans and various types of health insurance, including accident and disability, fixed-benefit dental, personal sickness and hospital indemnity, hospital intensive care, long-term care, ordinary life and short-term disability plans.
AFLAC Incorporated is a Fortune 500 company. In 2010 AFLAC Incorporated was ranked number 130 on the Fortune 500 list, making it the 130th largest company in the United States when judged by revenue.
AFLAC Incorporated achieved revenue of $18,254.40 million in 2010 and earned a profit of $1,497.00 million.
AFLAC Incorporated' rank improves
The company ranking improved in 2010, moving up the Fortune 500 list to 130th compared to 152nd in 2009. This was based on its 2009 revenue of $16,554 million (a change of 2 million compared to 2010) and profits of $1,254 million (a change of $0 million compared to 2009).
Another point of view
To many investors, profits are more important than the revenue a company earns. If the Fortune 500 was ranked by profits instead of revenue then AFLAC Incorporated would be ranked 87th rather than 130th due to its profits of $1,497 in 2010.
Profit*
Fortune Ranking
18,254 1,497 130
* US$ Million
1932 Wynnton Road
Website: www.aflac.com
Stock Symbol: AFL
More health insurance companies in Georgia
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text:
Q: If logistic regression is a linear classifier why does it fail on linearly separable data? Logistic regression is a linear model, decision boundary generated is linear.
If the data points are linearly separable, then why does Logistic regression fail? Shouldn't it perform better on data that is actually linearly separable?

A: If the data are linearly separable with a positive margin, so that it can be separated by a plane in more than two (so infinitely many ways), then all those ways will maximize the probability, so the model maximizing the likelihood is not unique. So what the iterative method used to maximize the likelihood converges to is not unique. In that sense the logistic regression is unstable.
But a well implemented algorithm will find one of those solutions, and that might be good enough. And if what you want is the estimated probabilities, they will be the same for all those solutions.
So if your goal really is to find a separating plane with maximum margin, then logistic regression is the wrong method. If your goal is to estimate risk probabilities, the problem is another one: estimated risks of zero or one might be very unrealistic. So the answer to your question really depends on your goal, and you didn't tell us that.
About this question Brian Ripley in "Pattern Recognition and Neural Networks" says

We feel to much have been made of this. The difficulty is in
  inappropriate parameterization and the limits for infinite $\|\beta\|$
   of the fitted posterior probabilities remain perfectly suitable
  fits, albeit sometimes predicting probability zero or one.

See Why does logistic regression become unstable when classes are well-separated?  where all this is discussed with much more detail.

redpajama_set_name: RedPajamaStackExchange


A beautiful crisp autumn's day, a full field of golfers, and fun at the sponsored holes at Clovelly Golf Club, ensured that The Sunflower Fund's annual Golf Day was a pleasurable success.
The golf was of the highest quality with a winning Alliance score of 110 points. Sauce-ing, Puma and AB technologies were the key line sponsors of the day and together with many corporates and companies, made the day and prize giving a great success. The guest speakers were Corne Krige and an amazing survival story from Brett Archibald. Renowned auctioneer Phillip Powell auctioned off a Springbok Blazer donated by Percy Montgomery, who was also present at the prize giving.
MC Gawie Marx , a leukaemia survivor and Ambassador of The Sunflower Fund spoke to the guests about The Sunflower Funds mission to raise funds and create awareness around Leukaemia and other blood related diseases in order to recruit new donors to the SA Bone Marrow Registry (SABMR).


Lil Wayne Releases New Music Featuring Post Malone & Gucci Mane - Get Yours Daily | All Things News, Music, & Entertainment!
Lil Wayne, and his highly anticipated album The Carter V, finally released back in September. There's no secret that Weezy was going through a tough legal battle wit Birdman which resulted in the delay of his album.
With the on going success of his much anticipated album, Weezy has now added two new tracks to his album, "Hasta La Vista" and "In This House" featuring Gucci Mane. He also gave us an updated version of "What About Me" featuring Post Malone.
Check out the new songs below.


text:
\section{Problems Involving Negator Relationships}
\label{sec:CompComp}

In this section, we will examine problems involving negator relationships.
The problems \NegPath/ and \NegSat/ have been analyzed in previous work while \NegStab/ is a novel problem.

\subsection{Recapitulation of previous problems}
We will first recapitulate the previously analyzed problems.

\subsubsection{\NegPath/}
In \cite{HutterISORC2020}, we considered the following problem:
\begin{definition}[\NegPath/]\label{def:NegPath}
Let $\T/$ be a finite set of tasks, $\mathcal{N} \subseteq \T/ \times \T/$ a set of negator relationships among those tasks and
$\mathcal{C} \subseteq \T/ \times \T/$ a set of communication relationships between those tasks
(with $(S,T)\in \mathcal{C}$ iff task $S$ is allowed to send a message to task $T$).

The decision problem \NegPath/ is now stated as follows:
Given two assigned tasks $A, B \in \T/$, does a set of assigned tasks $\mathcal{V}\subseteq \T/$ exist
(with $T \in \mathcal{V}$ iff task $T\in \T/$ is assigned to a PE) so that the following
conditions are all satisfied:
\begin{enumerate}[label=(\arabic*)]
\item There is no task $T \in (\T/ \setminus \mathcal{V})$ that could be assigned to a PE even if all PEs had infinite computational resources,\label{item:NegPath:Def:1}
\item $\mathcal{V}$ is a stable task assignment, i.e. all negator relationships among tasks from $\mathcal{V}$ are respected,\label{item:NegPath:Def:2}
\item $A$ can send a message to $B$ (possibly via multiple hops), i.e. there exists a path from $A$ to $B$ using only edges from $\mathcal{C}$ with
$A$, $B$ and all intermediate tasks contained in $\mathcal{V}$.\label{item:NegPath:Def:3}
\end{enumerate}
\end{definition}
Put in simple terms, \NegPath/ asks whether a stable task assignment exists so that a message sent by task $A$ can be received by task $B$, possibly transformed by other tasks along the way.
Condition~\ref{item:NegPath:Def:1} prevents the system's computational capacities from imposing any limits on such task assignment.

\subsubsection{\NegSat/}
In \cite{HutterSENSYBLE2020}, we looked at a similar problem:
\begin{definition}[\NegSat/]\label{def:NegSat}
Let $\T/$ be a finite set of tasks and $\mathcal{N} \subseteq \T/ \times \T/$ a set of negator relationships among those tasks.

The decision problem \NegSat/ is now stated as follows:
Given a task $A \in \T/$, does a set of assigned tasks $\mathcal{V}\subseteq \T/$ exist
(with $T \in \mathcal{V}$ iff $T$ is assigned to a PE) so that the following
conditions are all satisfied:
\begin{enumerate}[label=(\arabic*)]
\item There is no task $T \in (\T/ \setminus \mathcal{V})$ that could be assigned to a PE even if all PEs had infinite computational resources,\label{item:NegSat:Def:1}
\item $\mathcal{V}$ is a stable task assignment, i.e. all negator relationships among tasks from $\mathcal{V}$ are respected,\label{item:NegSat:Def:2}
\item $A\in \mathcal{V}$, i.e. task $A$ is assigned to some PE.\label{item:NegSat:Def:3}
\end{enumerate}
\end{definition}

In simple terms, \NegSat/ asks whether a stable task assignment exists so that $A$ can be assigned to a PE.
Similarly to \NegPath/, condition~\ref{item:NegSat:Def:1} prevents the system's computational capacities from imposing any limits on such task assignment.

\subsubsection{Computational Complexity}
While both problems seem to be simple at a first glance, they turn out to be quite hard in terms of computational complexity:
\begin{theorem}\label{thm:NegPathNPComplete}
	\NegPath/ is NP-complete.
\end{theorem}
\begin{proof}
	See \cite{HutterISORC2020}.
\end{proof}

\NegPath/ asks for the existence of a communication path and may thus require multiple tasks to be assigned.
Intuitively, asking whether a given \emph{single} task can be assigned at all, seems to be a simpler problem.
However, this is not the case:
\begin{theorem}\label{thm:NegSatNPComplete}
	\NegSat/ is NP-complete.
\end{theorem}
\begin{proof}
	See \cite{HutterSENSYBLE2020}.
\end{proof}

Thus, in terms of computational complexity, both problems are equally hard.
This shows the power introduced by negators:
Unless $\text{P}=\text{NP}$ holds, it is not possible to decide either problem in deterministic polynomial time.

\subsubsection{Alternative Proof for NP-hardness of \NegPath/}
The proof of \NegPath/'s NP-hardness from \cite{HutterISORC2020} used a polynomial-time reduction of \dreisat/ to \NegPath/.
However, when utilizing the NP-completeness of \NegSat/, an elegant and short alternative proof is possible:
\begin{lemma}
	\label{lemma:NegPathNPHard}
	\NegPath/ is NP-hard.
\end{lemma}

The following alternative proof is based on the idea that if an algorithm were known that could decide \NegPath/ in polynomial time, one could use it to also decide \NegSat/ in polynomial time:

\begin{proof}
By reduction of \NegSat/ to \NegPath/:

\begin{figure}
\centering
\includegraphics[max width=\linewidth]{pics/NegPath/NEGATOR-SAT_to_NEGATOR-PATH}
\caption{Transformation of \NegSat/ to \NegPath/}
\label{fig:NegSatToNegPath}
\end{figure}

Let $(\T/, \mathcal{N}, A)$ be a \NegSat/ instance.
We will transform this input into a \NegPath/ instance as follows:
\begin{itemize}
	\item We introduce two additional tasks $X$ and $Y$ and
	\item introduce the communication relationships $(X, A)$ and $(A, Y)$.
\end{itemize}
It is easy to see that there exists a task assignment of the transformed input so that a path from $X$ to $Y$ exists
iff a task assignment of the original input exists so that task $A$ is assigned (with both assignments satisfying conditions~\ref{item:NegPath:Def:1} and \ref{item:NegPath:Def:2}),
cf. Figure~\ref{fig:NegSatToNegPath}.
Thus, the transformed input is an instance of \NegPath/ iff the original input is an instance of \NegSat/.

The corresponding transformation can be computed in polynomial time w.r.t. the input length:
Only two tasks and two communication relationships have to be added.

Thus, $\NegSat/ \leq_p \NegPath/$ holds.
Since $\NegSat/$ is NP-complete, the NP-hardness of \NegPath/ follows.
\end{proof}

\subsection{\NegStab/}
Informally, both \NegPath/ and \NegSat/ ask whether a stable task assignment exists so that some condition is satisfied simultaneously.

Yet, it turns out that only asking for the existence of a stable task assignment is an NP-complete problem on its own.
Consider the following problem:
\begin{definition}[\NegStab/]
	\label{def:NegStab}
	Let $\T/$ be a finite set of tasks and $\mathcal{N} \subseteq \T/ \times \T/$ a set of negator relationships among those tasks.

	The decision problem \NegStab/ is now stated as follows:
	Does a set of assigned tasks $\mathcal{V}\subseteq \T/$ exist (with $T \in \mathcal{V}$ iff $T$ is assigned to a PE) so that the following
	conditions are both satisfied:
	\begin{enumerate}[label=(\arabic*)]
	\item There is no task $T \in (\T/ \setminus \mathcal{V})$ that could be assigned to a PE even if all PEs had infinite computational resources,\label{item:NegStab:Def:1}
	\item $\mathcal{V}$ is a stable task assignment, i.e. all negator relationships among tasks from $\mathcal{V}$ are respected.\label{item:NegStab:Def:2}
	\end{enumerate}
\end{definition}

As with the previous problems, condition~\ref{item:NegStab:Def:1} prevents the system's computational capacities from imposing any limits on the task assignment.

We will now prove that \NegStab/ is NP-hard:
\begin{theorem}
	\label{thm:NegStabNPHard}
	\NegStab/ is NP-hard.
\end{theorem}
\begin{proof}
	By reduction of \NegSat/ to \NegStab/:

	Let $I\coloneqq (\T/', \mathcal{N}, A)$ be a \NegSat/ instance.
	We will transform this input into a \NegStab/ instance as follows:
	\begin{itemize}
		\item We introduce three additional tasks $X$, $Y$, $Z$ (so that the resulting task set is $\T/ \coloneqq \T/' \cup \{X,Y,Z\}$) and
		\item introduce the negator relationships $(A,X)$, $(A,Y)$, $(A,Z)$ as well as
		$(X,Z)$, $(Z,Y)$ and $(Y,X)$.
	\end{itemize}

	This transformation $\tau$ is sketched in Figure~\ref{fig:NegStabConstruction}.
	It is easy to see that $\tau$ can be computed in polynomial time w.r.t. the input length:
	Only a constant number of tasks and negator relationships have to be added.

	\begin{figure}
		\centering
		\includegraphics[max width=\linewidth]{pics/NegStab/NEGATOR-SAT_to_NEGATOR-STAB}
		\caption{Transformation of \NegSat/ to \NegStab/}
		\label{fig:NegStabConstruction}
	\end{figure}

	Thus, it remains to be shown that
	\begin{gather*}
		I \in \NegPath/ \\
		\Updownarrow \\
		\tau(I) \in \NegStab/
	\end{gather*}
	holds.

	Before proving this assertion, we will first consider the ``task triangle'' given by tasks $X$, $Y$ and $Z$ as well as their negator relationships:
	It is easy to see that these tasks will never allow a stable system state.
	Instead, these tasks force the assignment to oscillate in some way:
	\begin{enumerate}[label=\arabic*),ref=\arabic*]
		\item Figure~\ref{fig:NegStabOscillationTriangle} shows the oscillation sequence that starts when one task is assigned ($X$ was arbitrarily chosen as the first task here).
			Afterwards, a second task can be assigned since it has no inbound negator
			(per condition~\ref{item:NegStab:Def:1}, this second task will be assigned).
			However, this second task will now send a negator forcing the first task to be stopped, leading to the oscillating sequence shown in the figure.\label{item:NegStabOscVariant1}
		\item Figure~\ref{fig:NegStabOscillationTriangleVariant2} shows a corner case:
			If at least three PEs exist, all three tasks might simultaneously be assigned on three different PEs, leading to the oscillation sequence shown in the figure.\footnote{This oscillation sequence can only occur if all three tasks are assigned simultaneously.
			This requires a very specific AHS constellation to be in effect;
			if less than three tasks are assigned simultaneously, oscillation variant \ref{item:NegStabOscVariant1} occurs instead.}
			\label{item:NegStabOscVariant2}
	\end{enumerate}

	\begin{figure*}
		\centering
		\begin{subfigure}{0.25\linewidth}
			\centering
			\includegraphics[page=1]{pics/NegStab/Oscillation}\\
			\textbf{\footnotesize(1)}
		\end{subfigure}%
		\begin{subfigure}{0.25\linewidth}
			\centering
			\includegraphics[page=2]{pics/NegStab/Oscillation}\\
			\textbf{\footnotesize(2)}
		\end{subfigure}%
		\begin{subfigure}{0.25\linewidth}
			\centering
			\includegraphics[page=3]{pics/NegStab/Oscillation}\\
			\textbf{\footnotesize(3)}
		\end{subfigure}%
		\begin{subfigure}{0.25\linewidth}
			\centering
			\includegraphics[page=4]{pics/NegStab/Oscillation}\\
			\textbf{\footnotesize(4)}
		\end{subfigure}\\[2\floatsep]
		\begin{subfigure}{0.25\linewidth}
			\centering
			\includegraphics[page=5]{pics/NegStab/Oscillation}\\
			\textbf{\footnotesize(5)}
		\end{subfigure}%
		\begin{subfigure}{0.25\linewidth}
			\centering
			\includegraphics[page=6]{pics/NegStab/Oscillation}\\
			\textbf{\footnotesize(6)}
		\end{subfigure}%
		\begin{subfigure}{0.25\linewidth}
			\centering
			\includegraphics[page=7]{pics/NegStab/Oscillation}\\
			\textbf{\footnotesize(7)}
		\end{subfigure}%
		\begin{subfigure}{0.25\linewidth}
			\centering
			\includegraphics[page=2]{pics/NegStab/Oscillation}\\
			\textbf{\footnotesize(8)}
		\end{subfigure}
		\caption{Oscillating task assignment, oscillation variant \ref{item:NegStabOscVariant1}}
		\label{fig:NegStabOscillationTriangle}
	\end{figure*}

	\begin{figure*}
		\centering
		\begin{subfigure}{0.25\linewidth}
			\centering
			\includegraphics[page=1]{pics/NegStab/Oscillation}\\
			\textbf{\footnotesize(1)}
		\end{subfigure}%
		\begin{subfigure}{0.25\linewidth}
			\centering
			\includegraphics[page=8]{pics/NegStab/Oscillation}\\
			\textbf{\footnotesize(2)}
		\end{subfigure}%
		\begin{subfigure}{0.25\linewidth}
			\centering
			\includegraphics[page=1]{pics/NegStab/Oscillation}\\
			\textbf{\footnotesize(3)}
		\end{subfigure}%
		\begin{subfigure}{0.25\linewidth}
			\centering
			\includegraphics[page=8]{pics/NegStab/Oscillation}\\
			\textbf{\footnotesize(4)}
		\end{subfigure}%
		\caption{Oscillating task assignment, oscillation variant \ref{item:NegStabOscVariant2}}
		\label{fig:NegStabOscillationTriangleVariant2}
	\end{figure*}

	As a result, the transformed input's task assignment $\mathcal{V}$ will only satisfy condition~\ref{item:NegStab:Def:2}
	if task $A$ is assigned and thus prevents $X$, $Y$ and $Z$ from being assigned (and thus from oscillating).

	Therefore, we need to distinguish two cases:
	\begin{enumerate}[label=\alph*)]
		\item $I \in \NegSat/$:
			In this case, there exists some set of assigned tasks $\mathcal{V}'\subseteq \T/'$ that satisfies
			conditions~\ref{item:NegSat:Def:1} and \ref{item:NegSat:Def:2} from \NegSat/'s definition (which are identical
			to conditions~\ref{item:NegStab:Def:1} and \ref{item:NegStab:Def:2} from \NegStab/'s definition) and
			includes task $A$.

			However, since $A$ is assigned, its negator relationships prevent $X$, $Y$ and $Z$ from being instantiated.
			Thus, $\mathcal{V}'$ is a set of assigned tasks for $\tau(I)$ that satisfies conditions~\ref{item:NegStab:Def:1} and \ref{item:NegStab:Def:2} from \NegStab/:
			No further task can be assigned due to inbound negator relationships and no negator relationship is violated.
			Therefore, $\tau(I)\in \NegStab/$ must hold.

			As a result, $I \in \NegSat/ \Rightarrow \tau(I) \in \NegStab/$ holds.
		\item $I \not\in \NegSat/$:
			No set of assigned tasks $\mathcal{V}'\subseteq \T/'$ exists that satisfies
			conditions~\ref{item:NegSat:Def:1} and \ref{item:NegSat:Def:2} from \NegSat/'s definition
			and includes task $A$.

			Thus, consider any set of assigned tasks $\mathcal{V}''\subseteq \T/=\T/' \cup \{X,Y,Z\}$.

			There are two possibilities for task $A$'s assignment:
			\begin{enumerate}[label=b.\arabic*)]
				\item $A \in \mathcal{V}''$.
					If $A$ is assigned, condition~\ref{item:NegStab:Def:1} and/or \ref{item:NegStab:Def:2} must be violated
					since $I$ is no \NegSat/ instance and thus cannot be assigned without violating at least one of those conditions.
				\item $A \not\in \mathcal{V}''$.
					If $A$ is not assigned, the tasks $X$, $Y$ and $Z$ receive no inbound negator from task $A$ and may thus be assigned.
					However, every possible task assignment of a subset of these three tasks violates condition~\ref{item:NegStab:Def:1} and/or \ref{item:NegStab:Def:2} (cf. Figure~\ref{fig:NegStabOscillationTriangle}):
					If a task receives no inbound negator but is not assigned, condition~\ref{item:NegStab:Def:1} is violated.
					If a task receives an inbound negator and is assigned, condition~\ref{item:NegStab:Def:2} is violated.
			\end{enumerate}
			Thus, no set $\mathcal{V}''\subseteq \T/' \cup \{X,Y,Z\}$ can satisfy both conditions simultaneously.
			Therefore, $\tau(I)$ is no \NegStab/ instance.

			Generally, this shows that
			$I \not\in \NegSat/ \Rightarrow \tau(I) \not\in \NegStab/$, which is equivalent to
			$\tau(I) \in \NegStab/ \Rightarrow I \in \NegSat/$.
	\end{enumerate}
	Combining both cases, $I \in \NegSat/ \iff \tau(I) \in \NegStab/$ holds.

	As we have already argued that $\tau$ can be computed in polynomial time w.r.t. the input $I$'s length,
	$\tau$ is a polynomial-time reduction from \NegSat/ to \NegStab/.

	Thus, \NegStab/ must be at least as hard as \NegSat/.
	Since \NegSat/ is NP-complete (Theorem~\ref{thm:NegSatNPComplete}), the NP-hardness of \NegStab/ follows.
\end{proof}

As \NegPath/ and \NegSat/, \NegStab/ is also NP-complete:
\begin{theorem}
	\NegStab/ is NP-complete.
\end{theorem}
\begin{proof}
	Let $(\T/, \mathcal{N})$ be an input consisting of a set of tasks \T/
	and a set of negator relationships $\mathcal{N}$.

	A nondeterministic Turing machine can now nondeterministically select
	a subset $\mathcal{V}\subseteq \T/$ of assigned tasks and then
	deterministically check that conditions~\ref{item:NegStab:Def:1} and \ref{item:NegStab:Def:2}
	from Definition~\ref{def:NegStab} are both satisfied:
	\begin{enumerate}[label=(\arabic*)]
		\item This condition is satisfied if, for each $T \in (\T/ \setminus \mathcal{V})$, there is a negator relationship $(T', T) \in \mathcal{N}$ so that $T' \in \mathcal{V}$.
		This can be checked in $\GrossO(\poly(|\T/|,|\mathcal{N}|))$ time.
		\item This condition is satisfied if, for each $T \in \mathcal{V}$, there is \emph{no} negator relationship $(T', T) \in \mathcal{N}$ so that $T' \in \mathcal{V}$.
		This can also be checked in $\GrossO(\poly(|\T/|,|\mathcal{N}|))$ time.
	\end{enumerate}
	The Turing machine shall accept the input iff all three conditions are satisfied.

	Since, after nondeterministically guessing $\mathcal{V}$, the verification can be performed in polynomial time w.r.t. the input length,
	it follows that $\NegStab/ \in \textrm{NP}$.
	Together with Theorem~\ref{thm:NegStabNPHard}, it follows that \NegStab/ is NP-complete.
\end{proof}

As a result, all three problems are equally hard in terms of computational complexity, although this result might appear counter-intuitive:
\NegPath/ asked whether a stable task assignment exists that contains a communication path from $A$ to $B$ (and thus required at least two tasks to be assigned).
\NegSat/ relaxed this problem and only asks whether a stable task assignment exists so that a single distinguished task is assigned.
\NegStab/ further relaxes these conditions and only asks whether a stable task assignment exists at all.
Yet, in terms of computational complexity, all three problems are equally hard and cannot be decided efficiently by a deterministic computer unless $\textrm{P}=\textrm{NP}$ holds.

\section{Conclusion}
\label{sec:Conclusion}
In this report, we revisited the \NegPath/ and \NegSat/ problems originally introduced in \cite{HutterISORC2020} and \cite{HutterSENSYBLE2020}.
First, we presented an alternative proof for \NegPath/'s NP-hardness by utilizing \NegSat/'s NP-completeness.
Then, the new problem \NegStab/ was introduced and also proved to be NP-complete.

In addition, we presented examples of \NegPath/, \NegSat/ and \NegStab/ instances in an AHS simulator.
This proved that the theoretical results are applicable to real-world implementations of the negator concept and thus highly relevant when designing systems using negator relationships.

Moreover, we have shown building blocks composed from tasks and negator relationships that behave like NOR gates and flip-flops and even ring oscillators.
In theory, combining these building blocks allows the construction of sequential logic circuits using tasks and negator relationships.
Of course, the practical relevance of constructing arbitrary logic circuits with negators is questionable to say the least:
Using tasks and negators to build a circuit and evaluating it by (ab-)using the AHS implies a \emph{massive} resource and performance overhead while an equivalent function could simply be realized as a single task computing the result.

Nevertheless, this is an interesting theoretical result as it again shows the power introduced by negators and especially answers \emph{why} seemingly simple questions such as
\begin{itemize}
	\item ``Does a stable task assignment exist so that task $A$ may send a message to $B$ (via multiple hops)?'' (\NegPath/),
	\item ``Does a stable task assignment exist that includes task $A$?'' (\NegSat/) or even
	\item ``Does a stable task assignment exist?'' (\NegStab/)
\end{itemize}
are hard to answer when dealing with negator relationships:
Negators can be used to represent arbitrary logic circuits, thus explaining why the reduction of \dreisat/ to the mentioned problems was successful.

In future work, we plan to conduct research on additional aspects of negators.
Since even checking whether a stable task assignment exists for a given task set at all, it is an interesting question if the use of negators can be restricted in a way that still allows to express sufficiently powerful task relationships while lowering the complexity of various decision problems.

This is also a prerequisite for investigating the timing aspects of negators.
Since the original AHS (without negators) guarantees tight bounds for the duration of its self-configuration and self-healing after PE failures, it is an interesting question which timing guarantees can be given when negators are present.
Of course, this requires a stable system or its self-configuration's duration cannot be bounded at all.

\section{Examples}
\label{sec:Examples}
In this section, we want to give short examples for the transformation from \dreisat/ to \NegPath/ resp. \NegSat/.
However, we only give the results of the transformations and not their theoretical construction.\footnote{
	Note that, for \NegPath/, we use the transformation shown in \cite{HutterISORC2020} and \emph{not} the one used in the alternative proof of Lemma~\ref{lemma:NegPathNPHard}.
}
For more information on this matter, please refer to \cite{HutterISORC2020} and \cite{HutterSENSYBLE2020}.

\subsection{Theoretical Transformation}
In the following, we will use the formula
\begin{equation*}
f\coloneqq (\overline{x_1}\lor \overline{x_2}\lor \overline{x_3})\land (x_1 \lor x_2 \lor x_3).
\end{equation*}
It is easy to see that $f$ is satisfiable and hence $f \in \dreisat/$.

\subsubsection{\NegPath/}
\label{sec:Examples:Theoretical:NegPath}
\begin{figure}
\centering
\includegraphics[max width=\linewidth,page=3]{pics/NegPath/Construction}
\caption{\NegPath/ instance constructed from \dreisat/ instance $f=\textcolor{blue!50!black}{(\overline{x_1}\lor\overline{x_2}\lor\overline{x_3})}\land \textcolor{green!50!black}{(x_1\lor x_2\lor x_3)}$}
\label{fig:NegPathExampleConstruction}
\end{figure}

Figure~\ref{fig:NegPathExampleConstruction} shows the construction of a \NegPath/ instance from formula $f$.

\begin{figure*}
\begin{subfigure}{0.48\linewidth}
\centering
\includegraphics[max width=\linewidth,page=5]{pics/NegPath/Construction}
\caption{Task assignment corresponds to unsatisfying interpretation:\\$\mathcal{I}(x_1)=\mathcal{I}(x_2)=\mathcal{I}(x_3)=1$}
\label{fig:NegPathExampleInterpretedUnsatisfied}
\end{subfigure}
\hfill
\begin{subfigure}{0.48\linewidth}
\centering
\includegraphics[max width=\linewidth,page=4]{pics/NegPath/Construction}
\caption{Task assignment corresponds to satisfying interpretation:\\$\mathcal{I}(x_1)=\mathcal{I}(x_2)=0$ and $\mathcal{I}(x_3)=1$}
\label{fig:NegPathExampleInterpretedSatisfied}
\end{subfigure}
\caption{\NegPath/ instance from Figure~\ref{fig:NegPathExampleConstruction} with two task assignments. Inactive tasks as well as negator and communication relationships are shown in gray.}
\label{fig:NegPathExampleInterpreted}
\end{figure*}

Figure~\ref{fig:NegPathExampleInterpreted} shows two possible task assignments which are subsets of the task set \T/:
Figure~\ref{fig:NegPathExampleInterpretedUnsatisfied}'s task assignment corresponds to an unsatisfying interpretation of $f$ while
the one corresponding to Figure~\ref{fig:NegPathExampleInterpretedSatisfied} satisfies $f$.

It can easily be checked that the second task assignment $\mathcal{V}$ is consistent with the three conditions stated in Definition~\ref{def:NegPath}:\footnote{
	In fact, the first task assignment satisfies conditions~\ref{item:NegPath:Def:1} and \ref{item:NegPath:Def:2}, but not condition~\ref{item:NegPath:Def:3}.}
\begin{enumerate}[label=(\arabic*)]
	\item For every non-assigned task $T$, there exists a negator relationship $(T',T)\in \mathcal{C}$ with $T' \in \mathcal{V}$
	that prevents $T$ from being assigned,
	\item for each negator relationship $(T,T')\in \mathcal{N}$, $T$ and $T'$ are not simultaneously assigned,
	\item there exists a path from $A$ to $B$ using only tasks in $\mathcal{V}$.
\end{enumerate}
Therefore, $\tau(f)\in\NegPath/$ holds.
Put in simple terms, there exists at least one stable task assignment so that task $A$ can send a message to task $B$ (via task $J_1$ as an intermediary hop).

\subsubsection{\NegSat/}
\label{sec:Examples:Theoretical:NegSat}
\begin{figure}
\centering
\includegraphics[max width=\linewidth,page=3]{pics/NegSat/Construction_NEGATOR-SAT}
\caption{\NegSat/ instance constructed from \dreisat/ instance $f=\textcolor{blue!50!black}{(\overline{x_1}\lor\overline{x_2}\lor\overline{x_3})}\land \textcolor{green!50!black}{(x_1\lor x_2\lor x_3)}$}
\label{fig:NegSatExampleConstruction}
\end{figure}

Figure~\ref{fig:NegSatExampleConstruction} shows the construction of a \NegSat/ instance from formula $f$.

\begin{figure*}
\begin{subfigure}{0.48\linewidth}
\centering
\includegraphics[max width=\linewidth,page=4]{pics/NegSat/Construction_NEGATOR-SAT}
\caption{Task assignment corresponds to unsatisfying interpretation:\\$\mathcal{I}(x_1)=\mathcal{I}(x_2)=\mathcal{I}(x_3)=1$}
\label{fig:NegSatExampleInterpretedUnsatisfied}
\end{subfigure}
\hfill
\begin{subfigure}{0.48\linewidth}
\centering
\includegraphics[max width=\linewidth,page=5]{pics/NegSat/Construction_NEGATOR-SAT}
\caption{Task assignment corresponds to satisfying interpretation:\\$\mathcal{I}(x_1)=\mathcal{I}(x_2)=0$ and $\mathcal{I}(x_3)=1$}
\label{fig:NegSatExampleInterpretedSatisfied}
\end{subfigure}
\caption{\NegSat/ instance from Figure~\ref{fig:NegSatExampleConstruction} with two task assignments. Inactive tasks as well as negator and communication relationships are shown in gray.}
\label{fig:NegSatExampleInterpreted}
\end{figure*}

Two task assignments corresponding to an unsatisfying resp. satisfying interpretation of $f$ are shown in Figure~\ref{fig:NegSatExampleInterpreted}.

It can easily be checked that the task assignment from Figure~\ref{fig:NegSatExampleInterpretedSatisfied} $\mathcal{V}$ is consistent with the three conditions stated in Definition~\ref{def:NegSat}:\footnote{
	In fact, the first task assignment satisfies conditions~\ref{item:NegSat:Def:1} and \ref{item:NegSat:Def:2}, but not condition~\ref{item:NegSat:Def:3}.}
\begin{enumerate}
	\item For every non-assigned task $T$, there exists a negator relationship $(T',T)\in \mathcal{C}$ with $T' \in \mathcal{V}$
	that prevents $T$ from being assigned,
	\item for each negator relationship $(T,T')\in \mathcal{N}$, $T$ and $T'$ are not simultaneously assigned,
	\item $A\in\mathcal{V}$ holds.
\end{enumerate}
Therefore, $\tau(f)\in\NegSat/$ holds.
Put in simple terms, there exists at least one stable task assignment so that task $A$ is assigned.

\subsubsection{\NegStab/}
Since the transformation used for \NegStab/ only involves the addition of three additional tasks and six negator relationships to an \NegSat/ instance, we omitted giving a complete example for brevity.
Please refer to Figure~\ref{fig:NegStabConstruction} instead.

\subsection{In an AHS Simulator}
In order to show that the theoretical constructions used for proving the NP-completeness of \NegPath/ and \NegSat/ can also be realized in practice, we implemented our negator extension in an AHS simulator~\cite{rentelnExaminatingTaskDistribution2008,brinkschulteOrganicRealTimeMiddleware2013}.
This simulator performs an accurate simulation of the AHS' inner workings by exchanging hormones the same way the AHS middleware does.

We then translated the constructions from sections~\ref{sec:Examples:Theoretical:NegPath} and \ref{sec:Examples:Theoretical:NegSat} into appropriate simulator configuration files.
There were two reasons we chose a simulator instead of the real AHS middleware for these scenarios:
\begin{enumerate}
	\item The simulator allows to force an initial task assignment, which is not possible in the AHS middleware.
	This allowed us to easily instantiate one specific assignment task for each variable $x_k$.
	The AHS middleware would have given us no direct control over which assignment tasks would have been instantiated.
	It shall be noted that only the assignment tasks were initially fixed, all other tasks were automatically
	instantiated by the simulator respecting all negator relationships.
	\item Using the simulator, it is easy to restrict the assignment of certain tasks to specific PEs.
	We made use of this feature in two ways:
	\begin{enumerate}
		\item For each assignment task $X_k$ resp. $\overline{X_k}$, we created one PE that can only instantiate this single task.
		This allowed us to easily switch the corresponding interpretation of the formula by temporarily suspending the PE.
		As a result, the assignment task $X_k$ resp. $\overline{X_k}$ could not be allocated on any other PE and the now missing negator hormone would cause the inverse
		assignment task $\overline{X_k}$ resp. $X_k$ to be allocated on its PE instead.
		\item We created one PE each for tasks $A$, $B$ and all join tasks that can only instantiate this specific task.
		Similarly, for each clause $c_i$ in $f$, there is exactly one PE that can only instantiate the literal tasks created from $c_i$'s literals.
		In consequence, a path from $A$ to $B$ exists iff each of those PEs is executing at least one task.
		This allows to check the existence of such path at a glance, especially since the AHS identifies tasks by an integer
		which would otherwise make this check rather complex for the human eye.
	\end{enumerate}
\end{enumerate}

\subsubsection{\NegPath/}
\begin{figure*}
\begin{subfigure}{0.48\linewidth}
\centering
\includegraphics[max width=\linewidth]{pics/NegPath/HorSimExampleUNSAT.png}
\caption{Task assignment corresponds to unsatisfying interpretation: $\mathcal{I}(x_1)=\mathcal{I}(x_2)=\mathcal{I}(x_3)=1$}
\label{fig:NegPathExampleSimulatorUnsatisfied}
\end{subfigure}
\hfill
\begin{subfigure}{0.48\linewidth}
\centering
\includegraphics[max width=\linewidth]{pics/NegPath/HorSimExampleSAT.png}
\caption{Task assignment corresponds to satisfying interpretation: $\mathcal{I}(x_1)=\mathcal{I}(x_2)=0$ and $\mathcal{I}(x_3)=1$}
\label{fig:NegPathExampleSimulatorSatisfied}
\end{subfigure}
\caption{\NegPath/ instance from Figure~\ref{fig:NegSatExampleInterpreted} in AHS simulator. A path from task $A=7$ to $B=15$ exists iff at least one task is running on PE in the second row.}
\label{fig:NegPathExampleSimulator}
\end{figure*}

Figure~\ref{fig:NegPathExampleSimulator} shows the \NegPath/ construction from Figure~\ref{fig:NegPathExampleConstruction} in the simulator for the task assignments from Figure~\ref{fig:NegPathExampleInterpreted}.
Each colored box represents a PE while an integer $i$ denotes that task $i$ is running on the corresponding PE.
The top row of PEs is responsible for instantiating the assignment tasks $1$ to $6$
while the PEs on the bottom row are responsible for instantiating the tasks $A=7$, $B=15$, the join task $11$
as well as all literal tasks.
Thus, a path from $A$ to $B$ exists iff there is at least one task running per bottom-row-PE:
This is false for the unsatisfying interpretation in Figure~\ref{fig:NegPathExampleSimulatorUnsatisfied}, but true for the satisfying one
in Figure~\ref{fig:NegPathExampleSimulatorSatisfied}.

As a consequence, only the second task assignment allows task $A$ to send a message (via multiple hops that might transform it along the way) to task $B$.

\subsubsection{\NegSat/}
\begin{figure*}
\begin{subfigure}{0.48\linewidth}
\centering
\includegraphics[max width=\linewidth]{pics/NegSat/HorSimExampleUNSAT.png}
\caption{Task assignment corresponds to unsatisfying interpretation: $\mathcal{I}(x_1)=\mathcal{I}(x_2)=\mathcal{I}(x_3)=1$}
\label{fig:NegSatExampleSimulatorUnsatisfied}
\end{subfigure}
\hfill
\begin{subfigure}{0.48\linewidth}
\centering
\includegraphics[max width=\linewidth]{pics/NegSat/HorSimExampleSAT.png}
\caption{Task assignment corresponds to satisfying interpretation: $\mathcal{I}(x_1)=\mathcal{I}(x_2)=0$ and $\mathcal{I}(x_3)=1$}
\label{fig:NegSatExampleSimulatorSatisfied}
\end{subfigure}
\caption{\NegSat/ instance from Figure~\ref{fig:NegSatExampleInterpreted} in AHS simulator}
\label{fig:NegSatExampleSimulator}
\end{figure*}

Figure~\ref{fig:NegSatExampleSimulator} shows the \NegSat/ construction from Figure~\ref{fig:NegSatExampleConstruction} in the simulator for the same task assignments as shown in Figure~\ref{fig:NegSatExampleInterpreted}.

The first row of PEs is again responsible for instantiating the assignment tasks $1$ to $6$ while the blue PEs on the second row are responsible
for instantiating the inverted clause tasks $7$ and $8$.
Finally, the yellow PE in the third row is responsible for instantiating task $A=9$.
As a result, the interpretation corresponding to the task assignment satisfies the formula $f$ iff task $9$ is running on the yellow PE:
This is false for the unsatisfying interpretation in Figure~\ref{fig:NegSatExampleSimulatorUnsatisfied}, but true for the satisfying one
in Figure~\ref{fig:NegSatExampleSimulatorSatisfied}.
It can also easily be seen from example that the inverted clause tasks are assigned iff none of the assignment tasks corresponding to their clause's literals are assigned
and task $A$ is assigned iff none of the inverted clause tasks are assigned.

\subsubsection{\NegStab/}
\begin{figure*}
\begin{subfigure}{0.48\linewidth}
\centering
\includegraphics[max width=\linewidth]{pics/NegStab/HorSimExampleUNSAT.png}
\caption{Task assignment corresponds to unsatisfying interpretation: $\mathcal{I}(x_1)=\mathcal{I}(x_2)=\mathcal{I}(x_3)=1$}
\label{fig:NegStabExampleSimulatorUnsatisfied}
\end{subfigure}
\hfill
\begin{subfigure}{0.48\linewidth}
\centering
\includegraphics[max width=\linewidth]{pics/NegStab/HorSimExampleSAT.png}
\caption{Task assignment corresponds to satisfying interpretation: $\mathcal{I}(x_1)=\mathcal{I}(x_2)=0$ and $\mathcal{I}(x_3)=1$}
\label{fig:NegStabExampleSimulatorSatisfied}
\end{subfigure}
\caption{\NegStab/ instance for $f=(\overline{x_1}\lor\overline{x_2}\lor\overline{x_3})\land (x_1\lor x_2\lor x_3)$ in AHS simulator}
\label{fig:NegStabExampleSimulator}
\end{figure*}

Figure~\ref{fig:NegStabExampleSimulator} shows a \NegStab/ instance constructed from formula $f$ in the simulator.
The first three rows of PEs are identical to the \NegSat/ instance from Figure~\ref{fig:NegSatExampleSimulator},
the PE in the fourth row is responsible for instantiating the three oscillating tasks $X=10$, $Y=11$ and $Z=12$ (cf. Figure~\ref{fig:NegStabConstruction}).

In case of the unsatisfying interpretation shown in Figure~\ref{fig:NegStabExampleSimulatorUnsatisfied}, task $A$ is not assigned and thus tasks $10$, $11$ and $12$ cause the assignment to oscillate.
In fact, the snapshot shows both $11$ and $10$ assigned, corresponding to Figure~\ref{fig:NegStabOscillationTriangle}, sequence~(3).

In contrast, Figure~\ref{fig:NegStabExampleSimulatorSatisfied} shows a satisfying interpretation of $f$.
Here, task $A=9$ can be assigned and no task can be instantiated on the PE in the fourth row, causing the task assignment to be stable.

\subsubsection{Summary}
These examples show that the theoretical considerations regarding the problems \NegPath/, \NegSat/ and \NegStab/ can also be applied to a real implementation of our negator concept.
Thus, these problems are highly relevant when designing systems using negator relationships:
If a message can never reach its destination (no \NegPath/ instance), some task cannot be instantiated in a stable system at all (no \NegSat/ instance) or the system is not stable (no \NegStab/ instance), the resulting system most probably contains some design mistake.

The next section will deal with another aspect of negators that explains \emph{why} problems involving negator relationships are computationally hard.

\section{Introduction}
The \emph{Artificial Hormone System} (AHS) \cite{brinkschulteOrganicRealTimeMiddleware2013} is a middleware based on Organic Computing principles to allocate tasks in distributed systems.
The task allocation is performed by realizing closed control loops based on exchange of short digital messages, called \emph{hormones}.

The AHS is self-configuring (meaning it automatically finds a working initial task distribution based on the processing elements (PEs) suitability for the different tasks) and self-healing (in case a PE fails, its tasks are automatically re-assigned to healthy PEs).
Furthermore, by being completely decentralized, it has no single point of failure.

However, it assumes all tasks to be independent.
Thus, in previous works, we introduced the concept of \emph{negator hormones} into the AHS to enable modeling task dependencies.

This allows to e.g. realize the dependency shown in Figure~\ref{fig:ConceptionNegator}: Here, task $T_i$ may only be assigned to a processing element (PE) if task $T_j$ is \emph{not} assigned.
Such dependency can be represented by the tuple $(T_j, T_i)$.

\begin{figure}
	\centering
	\includegraphics[page=1, scale=2]{pics/ConceptionNegator}
	\caption{Negator relationship between tasks $T_j$ and $T_i$: If $T_j$ is assigned, $T_i$ must not be assigned}
	\label{fig:ConceptionNegator}
\end{figure}

This report's contribution is four-fold:
\begin{enumerate}
	\item We revisit two decision problems involving negators and present an alternative proof for one problem's NP-hardness.
	\item We introduce an additional decision problem involving negators and prove its NP-completeness.
	\item We simulate instances of these problems in an AHS simulator.
	\item We describe concepts of realizing arbitrary logic circuits using negator relationships, giving an explanation \emph{why} the mentioned problems are NP-complete.
\end{enumerate}

The report is structured as follows:
Section~\ref{sec:CompComp} recaps the problems \NegPath/ and \NegSat/, presents an alternative proof of \NegPath/'s NP-hardness, introduces the novel decision problem \NegStab/ and proves its NP-completeness.
Section~\ref{sec:Examples} shows examples for these problems as well as simulations within an AHS simulator.
Section~\ref{sec:boolLogicWithNegators} shows ways to construct arbitrary logic circuits using negator relationships.
Finally, Section~\ref{sec:Conclusion} concludes this report.

\section{Constructing Logic Circuits using Negators}
\label{sec:boolLogicWithNegators}
In the previous sections, we have seen that various negator-related problems are computationally hard.
In order to explain \emph{why} this is the case, we will now look at these problems from a different perspective.
To do so, we will primarily generalize the concepts used for the reduction from \dreisat/ to \NegSat/ as shown in \cite{HutterSENSYBLE2020} (cf. Figure~\ref{fig:NegSatExampleConstruction}).
Nevertheless, the results are also applicable to \NegPath/ and \NegStab/.

\subsection{Interpreting Negator Hormones as Logic Levels}
In the following, we will interpret negator hormones and the tasks sending them as boolean logic levels.
Specifically, the following convention will be used:
\begin{itemize}
	\item HIGH $\iff$ negator hormone is sent\newline
		\phantom{HIGH} $\iff$ sending task is assigned,
	\item \phantomas[l]{HIGH}{LOW} $\iff$ negator hormone is \emph{not} sent\newline
		\phantom{HIGH} $\iff$ sending task is \emph{not} assigned.
\end{itemize}
This interpretation allows to construct arbitrary logic gates using negators.

\begin{figure}
\centering
\includegraphics[page=1]{pics/Logic/NegatorGates}
\caption{Task set with negators behaving like a NOR gate}
\label{fig:NORWithNegators}
\end{figure}

\begin{table}
	\begin{subtable}[t]{0.48\linewidth}
		\centering
		\begin{tabular}{cc|c}
			\toprule
			$A$ & $B$ & \boldmath$C$\unboldmath \\
			\midrule
			0 & 0 & \textbf{1} \\
			0 & 1 & \textbf{0} \\
			1 & 0 & \textbf{0} \\
			1 & 1 & \textbf{0} \\
			\bottomrule
		\end{tabular}
		\caption{Assignment of task $C$ in dependence of $A$ and $B$'s assignment (1 $\iff$ task is assigned)}
		\label{tbl:Assignment}
	\end{subtable}\hfill%
	\begin{subtable}[t]{0.48\linewidth}
		\centering
		\begin{tabular}{cc|c}
			\toprule
			$a$ & $b$ & \boldmath$a \overline{\lor} b$\unboldmath \\
			\midrule
			0 & 0 & \textbf{1} \\
			0 & 1 & \textbf{0} \\
			1 & 0 & \textbf{0} \\
			1 & 1 & \textbf{0} \\
			\bottomrule
		\end{tabular}
		\caption{Truth table of NOR gate}
		\label{tbl:NORGate}
	\end{subtable}
	\caption{Assignment of task $C$ compared to truth table of NOR gate}
\end{table}

Consider the task set with negator relationships shown in Figure~\ref{fig:NORWithNegators}.
The negator hormone from task $C$ to $D$ will be sent iff $C$ is assigned to some PE.
However, $C$ will only be assigned if no negator hormone is sent to $C$.
Thus, the negator hormone from $C$ to $D$ will only be sent if neither $A$ nor $B$ send a negator hormone to $C$.
Equivalently, $C$ will only be assigned if neither $A$ nor $B$ are assigned.
$C$'s assignment status in dependence of $A$ and $B$'s assignment states is shown in Table~\ref{tbl:Assignment}.
However, when compared to Table~\ref{tbl:NORGate}, it can be seen that $C$'s assignment matches the formula $c=a\, \overline{\lor}\, b$ and thus a NOR gate's behavior.

Since NOR on its own forms a functionally complete operator set, arbitrary logic gates can be constructed using the NOR gate as a building block.

\subsection{CNF to Task Set with Negators}
A formula $f$ in conjunctive normal form (CNF) can easily be represented as a task set with negator relationships
by realizing it as a two-stage NOR circuit.
This can be achieved by double negation and application of De Morgan's laws:
\begin{align*}
	f &= (\overline{x_1}\lor \overline{x_2} \lor \overline{x_3}) \land (x_1 \lor x_2 \lor x_3) \\
	&\equiv \overline{\overline{(\overline{x_1}\lor \overline{x_2} \lor \overline{x_3}) \land (x_1 \lor x_2 \lor x_3)}} \\
	&\equiv \overline{\overline{(\overline{x_1}\lor \overline{x_2} \lor \overline{x_3})} \lor \overline{(x_1 \lor x_2 \lor x_3)}}
\end{align*}
Figure~\ref{fig:CnfNorExample} shows the graphical construction of $f$ as a two-stage NOR circuit and the conversion to a task set with negators using Figure~\ref{fig:NORWithNegators} as a building block:
Task $\overline{C_1}$ and $\overline{C_2}$ can only be assigned if \emph{none} of their respective literal tasks are assigned;
task $A$ can only be assigned if neither $\overline{C_1}$ nor $\overline{C_2}$ are assigned.

\begin{figure*}
	\centering
	\begin{subfigure}[t]{0.3\linewidth}
	\centering
	\includegraphics[max width=\linewidth,page=2]{pics/Logic/NegatorGates}
	\caption{Two-stage OR/AND realization}
	\end{subfigure}
	\hfill
	\begin{subfigure}[t]{0.3\linewidth}
	\centering
	\includegraphics[max width=\linewidth,page=3]{pics/Logic/NegatorGates}
	\caption{After double negation and De Morgan's laws: Two-stage NOR realization}
	\end{subfigure}
	\hfill
	\begin{subfigure}[t]{0.3\linewidth}
	\centering
	\includegraphics[max width=\linewidth,page=4]{pics/Logic/NegatorGates}
	\caption{Converted to task set with negators}
	\label{fig:CnfNorExample:Negators}
	\end{subfigure}
	\caption{Construction of two-stage NOR circuit from CNF formula and conversion to task set with negators}
	\label{fig:CnfNorExample}
\end{figure*}

In fact, this construction has already been used implicitly for transforming \dreisat/ to \NegSat/ in Theorem~\ref{thm:NegSatNPComplete}'s proof (cf. \cite{HutterSENSYBLE2020} and Figure~\ref{fig:NegSatExampleConstruction}), albeit the transformation used
an additional building block to ensure that exactly one of the tasks $x_k$ and $\overline{x_k}$ is assigned at any time, thus forcing a consistent formula interpretation by means of mutual exclusion.
As this building block is missing from the construction shown in Figure~\ref{fig:CnfNorExample:Negators}, the assignment tasks could be assigned in a conflicting way.

\subsection{Flip-Flops with Negators}
In fact, the mentioned mutual exclusion building block (as shown in Figure~\ref{fig:AssignmentTasks}) behaves like a SR latch built from NOR gates.
Figure~\ref{fig:SRlatchNOR} shows such a SR latch while Figure~\ref{fig:SRlatchNegators} depicts a task set with negators behaving identically.
This is achieved by using the mutual exclusion building block from Figure~\ref{fig:AssignmentTasks} resp. the NOR building block from Figure~\ref{fig:NORWithNegators}:
In a stable system, either task $Q$ or task $\overline{Q}$ may be assigned while the other task is blocked by the sent negator.
By temporarily sending a negator ($R$ resp. $S$) to the assigned task, the latch's current value can be flipped.

\begin{figure*}
	\centering
	\begin{subfigure}[t]{0.3\linewidth}
	\centering
	\includegraphics[max width=\linewidth,page=5]{pics/Logic/NegatorGates}
	\caption{Building block: Assignment tasks realizing mutual exclusion of tasks $x_k$ and $\overline{x_k}$}
	\label{fig:AssignmentTasks}
	\end{subfigure}
	\hfill
	\begin{subfigure}[t]{0.3\linewidth}
	\centering
	\includegraphics[max width=\linewidth,page=6]{pics/Logic/NegatorGates}
	\caption{SR latch built from NOR gates}
	\label{fig:SRlatchNOR}
	\end{subfigure}
	\hfill
	\begin{subfigure}[t]{0.3\linewidth}
	\centering
	\includegraphics[max width=\linewidth,page=7]{pics/Logic/NegatorGates}
	\caption{Task set with negators behaving like a SR latch}
	\label{fig:SRlatchNegators}
	\end{subfigure}
	\caption{Construction of flip-flops using task sets with negators}
\end{figure*}

In theory, this allows to construct more complex flip-flops (e.g. gated D latches) or even whole sequential circuits by appropriately combining different building blocks although the practical relevance of their \emph{intentional} construction seems questionable at best.

\subsection{Oscillating Task Assignments}
\label{sec:boolLogicWithNegators:Oscillation}
Figure~\ref{fig:Oscillation:Inverter} shows a ring oscillator circuit built from three inverter gates.
Since an inverter can also be considered as a NOR gate with a single input, it is easy to adapt this circuit to negator logic as shown in Figure~\ref{fig:Oscillation:Negator}.

\begin{figure*}
	\centering
	\begin{subfigure}[t]{0.45\linewidth}
	\centering
	\includegraphics[max width=\linewidth,page=9]{pics/Logic/NegatorGates}
	\caption{Ring oscillator circuit constructed from an odd number of inverters}
	\label{fig:Oscillation:Inverter}
	\end{subfigure}
	\hfill
	\begin{subfigure}[t]{0.45\linewidth}
	\centering
	\includegraphics[max width=\linewidth,page=8]{pics/Logic/NegatorGates}
	\caption{Equivalent realization using a task set with negator relationships}
	\label{fig:Oscillation:Negator}
	\end{subfigure}
	\caption{Construction of a ring oscillator circuit}
	\label{fig:Oscillation}
\end{figure*}

In fact, we have already encountered this gadget in the reduction from \NegSat/ to \NegStab/ (cf. Theorem~\ref{thm:NegStabNPHard}).
The negators' oscillation pattern known from Figure~\ref{fig:NegStabOscillationTriangle} corresponds to the one realized by the three inverters while the pattern from Figure~\ref{fig:NegStabOscillationTriangleVariant2} is a peculiarity of the AHS and its implementation.

As oscillating task sets obviously prevent a system from ever reaching a stable task assignment,
they are yet another pitfall to avoid while employing negator relationships for designing systems.

\subsection{Sequential Logic}
\label{sec:boolLogicWithNegators:Sequential}
In theory, it should even be possible to realize sequential logic circuits with negators using the flip-flop and ring oscillator building blocks.
As an example, consider a \dreisat/ formula $f$ transformed to a \NegSat/ instance (cf. section~\ref{sec:Examples:Theoretical:NegSat}).
\NegSat/ only asks whether a task assignment exists so that the system is stable and some distinguished task $A$ is assigned, but does not require the AHS to find such task assignment on its own.

\begin{figure*}
	\centering
	\includegraphics[width=\linewidth]{pics/Logic/SequentialAutomaton}
	\caption{Example of a sequential logic circuit that could be implemented using tasks and negator relationships}
	\label{fig:SequentialSatSolver}
\end{figure*}

Using sequential logic, one could actually realize a brute force SAT solver like the example shown in Figure~\ref{fig:SequentialSatSolver} inside the AHS using tasks and negator relationships.
This circuit uses one flip-flop per variable $x_i$ that is triggered on a rising clock edge.
Starting with $x_1=x_2=\dots=x_n=0$, the circuit sequentially evaluates $f$ for each of the $2^n$ input combinations.
Once either all combinations were tested ($x1=x_2=\dots=x_n=1$) or $f$ evaluates to $1$, the clock is disabled by pulling it to $0$.
One of the lines SAT resp. UNSAT rises to $1$ once the clock is stopped and gives the final result regarding $f$'s satisfiability.

\section*{Note}
This is a supplementary report to \cite{HutterISORC2020} and \cite{HutterSENSYBLE2020}, extending the results of both papers.

Although this report includes the most relevant information required for understanding, we nevertheless expect the reader to be familiar with at least one of the aforementioned papers.

\input{Introduction}
\input{ComputationalComplexity}
\input{Examples}
\input{LogicGates}
\input{Conclusion}

redpajama_set_name: RedPajamaArXiv


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Filming will begin in mid-July after the casting calls for men wrap up, and the first episode will air after "Oh My Ghostess" finishes its run in late August.


text:
AT&T and Twitch Scout the Next Generation of Streamers
DALLAS, November 18, 2021
TWITCH AND AT&T SCOUT THE NEXT GENERATION OF STREAMERS FOR THE FIRST AT&T "CLASS OF" PROGRAM
Follow 12 Streamers on Their Journey to Become Career Creators on Twitch
Introducing the AT&T Class of 2021, a collaboration between Twitch, the interactive livestreaming service, and AT&T to provide 12 promising Twitch streamers with a unique opportunity to elevate their careers to the next level.
As part of the Class of 2021, each streamer will receive:
Mentorship: An established Twitch creator will be connected with a cohort of six to provide on- and off-camera guidance on how to turn their passion for streaming into a sustainable career, grow their community and reach new heights on Twitch. Additionally, these established streamers will co-stream their cohorts' broadcasts and direct their viewers to mentees'channels. Mentors for the AT&T Class of 2021 are Alexandra and Andrea Botez, of BotezLive, and SypherPK.
Equipment: An AT&T expert will help explore upgrades to the up-and-coming streaming equipment and studio setups, which may include AT&T Fiber or 5G wireless services with AT&T's Right to YouSM where available. Each streamer will be paired with an AT&T expert to hand deliver and set up their wireless devices at home or the office at no additional cost – as early as the same day the order is placed9, where available. That way, each creator can stay connected to their audience anywhere they go.
Sponsored Stream by AT&T: AT&T will support sponsored streams for each emerging creator — unlocking additional pathways for creators to financially support themselves as streamers.
Career Amplifications: Each creator will be featured on Twitch's homepage and periodically featured on AT&T's Twitch channel. In addition, Twitch and AT&T will feature a select number of Class of 2021 emerging creators in custom AT&T commercials on Twitch that will further build their presence across the service.
"This custom sponsorship program is about finding the next generation of up-and-coming streamers, celebrating them, and providing the resources and guidance to grow their communities," said Lou Garate, Head of Global Sponsorship Sales at Twitch. "Creators are the heart of Twitch, and we're proud to build a program with AT&T that directly connects with our community's values around creator support."
On November 19 at 9:30am PT, tune in to www.twitch.tv/att for the live Class of 2021 selection show, featuring appearances from all participating creators.
"Collaborating with Twitch on the AT&T Class of 2021 is a unique opportunity for us to elevate up-and-coming voices in the content creation space," said Sabina Ahmed, assistant vice president of sponsorships and experiential marketing at AT&T. "So many compelling and innovative streamers are just beginning their journey as creator, and it's an honor for us to help connect them with new audiences, build a community, and provide the right resources to grow their careers."
About AT&T's Gaming & Esports Sponsorships:
AT&T has built powerful connections with key gaming organizations since entering the space and is committed to keeping the gaming fan at the center. Most recently, AT&T and top-tier streamer and content creator Tim "TimTheTatman" Betar entered a strategic agreement collaborating on content, events and innovation to showcase AT&T's 5G capabilities.
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text:
Welcome to the ArtInfo-MusInfo Site
Exhibition of works by the GAIV at the Centre Pompidou in Paris,
from July 2022 to June 2023, on the 4th floor of the Centre, room 29.
Over fifty years ago, a group of painters, musicians, psychologists, educators, linguists, mathematicians, poets, architects and computer scientists gathered within the Computer Science Department of the University of Vincennes (*) to form what became known as the "Group of Art and Informatique of Vincennes".
This site is dedicated to these bright people.
During the first ten years of existence of the Group, a newsletter was published, the famous "ARTINFO-MUSINFO" which gave its name to this site. It serves as a repository to all that has been written, seen or heard during this fertile period which began in 1969, the year of creation of the University of Vincennes and ended in 1980, the year of its transfer to Saint Denis.
If you have articles, texts, pictures, sounds, programms, plans, ... or any other materials related to the GAIV activites from this period and if you want to share it, please contact us.
The Artinfo-Musinfo Site features today:
53 issues, reports or manuals,
from 99 authors,
representing 221 articles
and totalizing 3238 scanned pages.
60 events,
totalizing 518 scanned images or photos.
18 magazine articles,
totalizing 60 press clippings.
Displayed on 1647 pages in Polyglot HTML5.
(*) Vincennes is a city, close to Paris, France, not related to the Vincennes University (VU), a public University whose main campus is located in Vincennes, Indiana, United States of America.


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text:
Vancouver, Can We Talk About Housing Without Getting So Angry?
It's supply! It's demand! It's offshore buyers! Instead of winning arguments, let's chill and talk about the future.
By Christopher Cheung 9 Jul 2018 | TheTyee.ca
Christopher Cheung reports on urban issues for The Tyee. Follow him on Twitter at @bychrischeung.
How can we move towards more helpful housing conversations? Collage by Christopher Cheung. The School of Athens by Raphael, public domain.
They say you should never discuss politics or religion at the dinner table. In Vancouver, housing is just as divisive, and a harder topic to avoid.
Unaffordability in Vancouver — from the increasingly large chunk of income eaten up by the average rent or the increasing number of years a local wage earner must work to buy an average home — has made conversations about housing polarizing and emotional. Media cover housing news play-by-play like hockey games.
Sometimes an event or chat room can be helpful; other times, these forums can be harmful. There's the fiery volleying you'll find online in places like Twitter, with data and quotes by local experts used like ammo, name-calling, trolling and even snarky poetry. "It's less digital agora and more cyber cesspool," said Andy Yan, the director of Simon Fraser University's City Program, a Twitter user himself. Politicians and professors are often pulled into the fray.
But it's not just online. There's also the intimidating mobs you'll find at events like the protests in the Marpole neighbourhood against social housing in modular buildings and a recent homeowners' rally on Vancouver's west side against a surtax on high-value properties.
Depending on what one is advocating for, actors in Vancouver's housing drama are cast in different roles. If you're against property taxes, you might view homeowners as hardworking, average people who don't deserve to be punished. But if you support property taxes, you might view homeowners as entitled and think they should pay a portion of their massive gains to help fund public investments. Governments could be brave or predatory for pushing policy. Foreign buyers could be disasters or healthy contributors to our economy. Experts might be labelled as socialist or development shills for sharing their opinions. Renters might be rowdy invaders or neglected residents. These Jungian archetypes appear and reappear consistently in coverage, but who's a hero and who's a villain depends on who's speaking.
Struggles of unaffordability and displacement have plagued Vancouver's low-income renters for decades. But now, these struggles have crept up the income ladder.
"It illustrates the parallel Vancouvers that exist right now and the lack of leadership trying to break those parallels," said Yan. "It's a city that is emerging as a series of factions of identity politics as opposed to one that comes together in understanding the civic virtues of creating an inclusive metropolis."
Why have these discussions become so heated?
Justin Fung, a founder of Housing Action for Local Taxpayers, a group that mostly advocates for reducing housing speculation, points to a famous psychological theory. "Think about Maslow's hierarchy of needs," he said. "Shelter is a key need. The absence of it can be incredibly stressful." On Maslow's pyramid, shelter is a basic physiological need that comes before others like safety, belonging and self-actualization.
Nathanael Lauster, a sociologist at the University of British Columbia and author of The Death and Life of the Single-Family House, says housing emotions are fuelled by the inability of those who grew up in homes owned by their parents to follow the cultural "script" of being able to purchase a home of their own, often imagined as a detached house, as part of the "package deal of adulthood" as they start careers and families.
"But in Vancouver, that script just doesn't work," said Lauster.
For people who already own property, Lauster says change gets emotional because they might think: "I have my dream home. Why are you trying to take it away from me?"
And then there's the emotion of seeing one's neighbourhood change, like seeing a local coffee shop or grocery store vanish. "Challenges to people's sense of home extend beyond housing units and legal lot lines."
A lone counter-protester crashes a protest by Vancouver homeowners bitterly opposed to the provincial government's new school property tax. Source: KyleBryan via Twitter.
The suggested solutions to Vancouver's housing crisis are as varied as the many causes to blame for unaffordability. But often, people are stubborn and don't like to listen to what others have to say. Jens von Bergmann, the local data analyst who created the public CensusMapper tool, once said, "Don't bring data to a culture war." If you survey Twitter or Facebook, you'll see people, organizations and companies choosing to highlight voices and research that advance their arguments.
Suggested housing affordability solutions fall largely into the two camps of supply and demand, though there are variations within those camps too. Some supply-siders might welcome more of any kind of housing; others might like to see more supply that isn't market condos because the new units are unaffordable for many locals. Demand-siders want to see more regulation on development and transactions, such as speculative investment.
A peek into #vanre, a hub for Vancouver housing discussions on Twitter, reveals the clash between supporters of supply and demand solutions.
Some supply-siders have used hashtags like #ItsSupplyStupid to accompany arguments that say we need to reduce red tape and build more housing to solve the housing crisis.
But they have been mocked by demand-siders who say this is real estate industry messaging. They've fired back with their own hashtags: #DensityForWhom; #MOAR, an Internet spelling of "more" which the Urban Dictionary calls "a cry of lust," to poke at the obsession with building new supply, and the ironically-used #AdjustYourExpectations, which one Twitter user has said is industry rhetoric for trying to convince first-time buyers to pay more for less space. The industry has also been called the #RECartel online.
Fung of HALT also believes it is easy for those who work in real estate to hog the media spotlight to share their views.
"The media would naturally go to the Bob Rennie, the UDIs and the spokesperson from the BC Real Estate Association to talk about these issues," said Fung. "It's pretty one-sided. There's a lot of money to be made in this. It's been a bit of struggle for advocacy groups who put personal time and effort into it when they are other folks being paid to toe a certain message."
But Anne McMullin, president and CEO of the Urban Development Institute, doesn't believe blaming development is useful in trying to solve housing unaffordability.
"We're just building homes and trying to follow the rules," she said. "There are lots of reasons why prices escalate; it's got very little to do with the developer. A lot of the policies that we see create limited supply while there's huge demand.
"We're a large industry with a large footprint. I recognize the fear — there's change. People generally don't like change... it's easier to blame somebody else than say, 'What role do we have to play in this?'"
McMullin recently wrote an op-ed in Westcoast Homes & Design on "putting the civility back into civic politics."
"As our city and communities continue to grow in both size and complexity, how do we positively elevate the level of engagement in planning future neighbourhoods?" she wrote.
McMullin hopes "NIMBYs" (people with a "Not In My Backyard" mentality) shed their fear of change and consider how the region might accommodate growth, especially since much of the region is zoned for detached houses.
"How do we get to YES or YIMBY (Yes in My Backyard)?" she continued. "How can we ensure city councils and other elected officials can make informed decisions without fear of ballot box retribution? Plenty of best practices exist, particularly if you integrate digital public participation, such as short online or video presentations.... "
A two-year-old Vancouver advocacy group called Abundant Housing has also challenged people to think about the future of the region and encouraged them to consider new solutions. The group supports additional housing of all types. Their voices are a recent addition to a conversation about neighbourhood change historically dominated by homeowners, but because of their pro-growth views critics have called them friends of the development industry.
Stuart Smith, one of the group's directors, says this argument is "silly and reductive."
"That criticism about zoning reform as some sort of gift to developers? I find that problematic because not building anything is a gift to landlords," said Smith. "If you're a landlord, you really like things to be scarce. We should talk about that."
Abundant Housing has said that "when housing choices are limited, the wealthy always win."
The group has been advocating for building more housing in low-density areas of Vancouver that have remained unchanged for many years.
"It's about asking neighbours to welcome more people in their neighbourhoods," said Smith.
The group has led tours of Vancouver neighbourhoods, such as Mount Pleasant, that it believes has a diversity of housing options — not just detached houses — to try and share a vision of how monolithically-zoned parts of the city could evolve.
"For example, we all agree we like this neighbourhood. We all agree that it works great and all agree it has a mix of housing for all people. So why is it not legal anywhere else?"
For example, small apartment buildings (#4floorsandcornerstores) are one building type the group would like to see more commonly and evenly spread around the city.
Smith says another way to encourage dialogue is to talk about the city's future.
"Talk about people's kids," he said. "Do you want your children and grandkids to be able to live near you? If you would, it means we have to allow changes in our neighbourhoods. We can have many debates about those changes, but we have to at least talk about it."
Going beyond 'I'm right!'
While advocates often have a supply or demand leaning, many acknowledge that solving affordability will require different types of solutions.
1) Supply matters. Constantly denying/minimizing this does not help us out of the crisis.
2)Money laundering and corruption matters. Constantly denying/minimizing this does not help us out of this crisis.
It's not binary. #vanre #bcpoli #vanpoli
— Mike Lang (@invancouber) July 4, 2018
"It's the thoughtful toolkit, not the silver bullet, that wins the day," said Yan of SFU.
Vancouver Housing Advocates Rise Up to Tackle Unaffordability
Yan is known for his data analyses, such as reports on foreign ownership and Vancouver's million-dollar property line. But he says locals using data simply to prove a point are doing harm.
"Data starts a conversation; it never ends it," he said. "What we've seen is some parties using data just to say, 'Oh, this ends the conversation!' as opposed to using them to inform the consequences of action and inaction. That actually wasn't how I was taught to use data. The conversation continues. The city continues beyond a study."
The topic of how foreign participation in real estate affects affordability is one conversation that politicians and real industry players have tried to shut down with data and cries of racism. Yan calls this a "social hack" or "shutdown code" aimed at blocking a dialogue on globalization and housing affordability.
Lauster, the UBC sociologist, also encourages people to keep conversations on housing going. Talk to actors involved and hear how they see things, "not leave people as faceless, dehumanized villains," he suggests. Find common ground on a vision of how Vancouver should be, "versus picking fights or taking a left opposed to a right on the road map to get there."
"Housing is complicated stuff," said Lauster. "To really understand what's going on, you should be motivated more by curiosity rather than, 'I'm right! I'm going to show you I'm right!' Interrogate the ambiguity. Embrace the complexity."
Read more: Housing, Municipal Politics


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text:
New Zealand|Education
Turtle-bot heads into battle
22 Sep, 2014 05:00 PM 2 minutes to read
The University of Auckland team (from left) Michael Li, Matthew Boyes, Brook Dyer, Kirsten Johnston, Briony Forsberg and Simon Gray have high hopes for their robot, nicknamed Turtle-bot. Photo / Dean Purcell
Nicholas Jones
Political Reporter
New Zealand university students are about to battle international competition to decide who has built and programmed the best robot.
A team from the University of Auckland will today fly to Sydney - with their hopes pinned on a creation nicknamed "Turtle-bot".
Thirty teams will battle it out for the title and $3000 first prize at the Australasian National Instruments Autonomous Robotics Competition.
Thursday's competition focuses on agriculture, which is experiencing increasing demand for robotics.
Each team's creation will need to complete tasks such as collect and deposit seeds, and navigate a farm area littered with obstacles.
Michael Li, one of six students who make up the University of Auckland team, undertook the challenge as part of a final-year project in his mechatronics engineering degree.
The 21-year-old and one other were tasked with the mechanical design of the robot, and built it from scratch. The other members focused on the coding and intelligence of the machine.
It took about six months to set up the robot, which has been nicknamed "Turtle-bot" because of its round shape.
Mr Li said: "Building this robot taught us a lot of mechanical design, electrical design, and a little bit of programming."
Ready, set, robot
• University teams to take part in a competition in which they design and build robots, and then have them complete certain tasks.
• The University of Auckland machine took about six months to build.
• Final is held in Sydney on Thursday.
• Other New Zealand universities competing are the Manukau Institute of • Technology, Massey University and Victoria University of Wellington.
Star Wars Batman mashup
'I've never had to reboot my dog'
Bigger iPhones debut - to long lines
Actor's C3PO demands


As fate has it, this year Little Santa gets his chance when Santa takes a tumble and sprains his ankle, and his son must be the one to don the red suit and deliver the gifts. And, with his dad's surprise help, he delivers even more to one special child. This is a beautifully original, heartwarming picture book for Christmas lovers of all ages.


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#TakeYourSeat - 2019/20 Season Tickets on sale
Season Tickets now available to buy or renew...
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It's time to #TakeYourSeat as MK Dons Season Tickets are now on sale for the 2019/20 campaign, with best prices available before 13th April 2019.
MK Dons have enjoyed plenty of success at Stadium MK under manger Paul Tisdale and currently boast a 63% win record in Milton Keynes since his arrival last summer. There have been last-minute winners, come-from-behind turnarounds and, of course, 6-0 thrashings!
You can be a part of the action next season, by signing up for a 2019/20 MK Dons Season Ticket.
Your Season Ticket will ensure your seat at all 23 of their home league fixtures during the 2019/20 campaign on top of a number of other benefits that come with being a Season Ticket holder including regular special offers and discounts from MK Dons, Stadium MK and Club Partners - click HERE for a full list of benefits!
Season Ticket prices have been frozen for a fourth consecutive campaign, with best prices available before 13th April 2019. Prices will increase after this time but won't thereafter, even in the event of promotion to Sky Bet League One.
Adult Season Tickets are priced from £26 a month; over-65s from £15.50 a month and under-25s from £10.50 a month while under-18s are able to enjoy the full 2019/20 campaign from just £2.50 a month - click HERE for a full list of prices!
The Under-12s go FREE offer remains too, meaning the Club's youngest supporters can watch all 23 home league matches in the 2019/20 season for FREE. Three Under-12s can sign up for FREE Season Tickets when accompanied by one Adult Season Ticket holder. This season, there is no need to purchase a Young Dons membership to receive a FREE Under-12 Season Ticket, outside of clubRed (£50), clubGold and clubPlatinum. The Young Dons Club remains open for those who wish to still receive a goodie bag, birthday card and much more. The 12-month membership is priced at just £10 - click HERE for more information!
Under-25 and unable to make every game? MK Dons provide two packages for young supporters that can't commit to a Season Ticket due to University, starting a new job or living away from home. The Super Six package is priced at just £5 per month and allows you to choose any six league games to attend in the 2019/20 season while the Terrific Ten package is priced at £8 per month and allows you attend 10 league games of your choice - click HERE for more information!
Click HERE to view the full 2018/19 Season Ticket prices
There are a number of ways you can pay for your Season Ticket, including the Club's in-house Direct-Debit scheme.
Our Direct-Debit scheme remains the most popular and easiest method of payment, allowing you to spread the cost of your Season Ticket - and those of family members or friends - over 12 months - click HERE for more information!
When you choose to pay by Direct Debit, you will automatically be entered into the Academy Supporters Draw at an additional cost of £1 per month. At the first home game of every month, one supporter will be chosen to win back the price they paid for their Season Ticket. To opt-out, inform the Box Office at the time of purchase or before 13th April 2019 if renewing. Terms and conditions apply - click HERE for more information!
Don't wish to pay by Direct Debit? Not to worry, you can pay the full amount of your Season Ticket over the phone or in person at the Box Office. Credit/debit card, cheque, gift voucher and cash payments accepted.
How to buy (current Season Ticket holders)
If you currently pay by Direct Debit your Season Ticket(s) will be automatically renewed and you do not need to take any further action.
Should you wish to change the location of your Season Ticket(s), purchase additional tickets or remove/join the 'Young Dons club' call the Box Office or visit us in person before 13th April 2019 and we will talk you through your options.
If you are renewing your Season Ticket(s) and not paying by Direct Debit, you can do so by completing the Application Form, which can be found at the bottom of the page, and drop it in at the Box Office. Alternatively, you can complete the form in person at the Box Office or over the phone by calling 0333 200 5343.
How to buy (new Season Ticket holders)
If you want to pay for your Season Ticket by Direct Debit, download and complete the online Direct-Debit form, as well as the Season Ticket Application Form, and hand it in at the Box Office. Both forms can be found at the bottom of the page. Alternatively, you can complete the forms in person at the Box Office or over the phone by calling 0333 200 5343.
If you want to pay for your Season Ticket in one go, you can do so by completing the Application Form, which can be found at the bottom of the page, and drop it in at the Box Office. Alternatively, you can complete the form in person at the Box Office or over the phone by calling 0333 200 5343.
Undecided where to sit? Take a look at the stadium plan and pricing grid, which can be found at the bottom of the page, and then give the Box Office a call - we will talk you through your options. The Club also run regular tours for you to choose your seat in person - for more information on those, get in touch with the Box Office.
Click HERE to view the full 2019/20 Season Ticket pricing chart!
Click HERE to download the 2019/20 Season Ticket Application Form!
Click HERE to download the 2019/20 Direct-Debit form!
Direct debits resume for Option 1 and 2 Season Ticket holders
Direct-debit payments for Season Ticket holders resumed this week, in line with the Club's 2020/21 Compensation policy.
Season Ticket holder compensation policy - deadline to select options this Saturday!
Season Ticket holders still have the opportuntiy to select their compensation options, following the Government's decision to pause the return of supporters to stadiums.
Interview: Andrew Cullen on 2020/21 Season Ticket compensation policy
Season Tickets - sign up for the 20/21 campaign!
Sign up for an MK Dons Season Ticket today and watch Russell Martin's men in action during the 2020/21 campaign.
Season Ticket Holders – how to watch on iFollow MK Dons!
While matches continue to take place behind closed doors at Stadium MK, Season Ticket holders will have access to watch all home league matches LIVE on iFollow MK Dons!
Burton Albion tickets - capacity reached for Saturday's League One clash!
MK Dons can confirm that capacity has been reached for the Sky Bet League One fixture with Burton Albion, following applications from Priority 1 Season Ticket holders.


Is it possible to "relocalize" energy? This is a critical question that must be addressed if we are to achieve true global resilience.
In our brand new book (September 4, 2012), Power From the People, energy expert Greg Pahl decisively argues that the answer is YES.
Power From the People is the second book in our Community Resilience Guides series, The book illustrates how communities across the country are already generating their own energy at the local level. From citizen-owned wind turbines to co-op biofuel producers to community-wide initiatives combining multiple resources and technologies, Pahl outlines the steps necessary and plan, organize, finance and launch community energy projects.
The book showcases over 25 real-life examples of local energy projects, offering a range of challenges and solutions that can be adapted and reapplied.
It's been said that we must leave fossil fuels before they leave us. Power From the People shows how that might be done.?? We're very excited about this, our latest publication. Take advantage of the special Friends of Post Carbon discount: Buy the book today directly from Chelsea Green Publishing with discount code PFTP.
Thanks again for supporting and being a part of our work!