text:
The rich? They're all animals
Uncanny parallels between jungle creatures and human high society have been found by naturalist Richard Conniff, writes Sarah Baxter
October 20 2002, 1:00am, The Sunday Times
The dominant magnate is Ronald Perelman, the Revlon cosmetics billionaire, who sports a trophy fourth wife on his arm, the Hollywood actress Ellen Barkin. The scene is unfolding at the Four Seasons restaurant in Manhattan, the "in" place for a showy power lunch, where Perelman is conversing with Barry Diller, head of Vivendi Universal Entertainment, no small fry himself.
Observing their behaviour patterns from a table in the corner is Richard Conniff, a naturalist and writer of what has become Manhattan's new buzz book, The Natural History of the Rich: A Field Guide, which tracks the similarities between the filthy rich and the animal world. Perelman is "sending a signal of dominance", Conniff whispers, translating his body language. "Wow, he looks really good." Perelman, he…


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text:
St. Joseph's Primary School
Dungarvan, Co. Waterford
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St. Joseph's Primary School is a Catholic school under the patronage of the Bishop of Waterford and Lismore. The school caters for boys from 2nd to 6th classes. It is located on Mitchell Street in Dungarvan, Co. Waterford, a bustling seaside town at the mouth of the River Colligan set against the backdrop of the Comeragh Mountains.
Dungarvan harbour
The school has 133 boys on the roll for the school year 2019-2020 and our pupils are from Ireland, England, Poland, Hungary, Lithuania, China, Thailand and Syria, with family links to Wales, Malaysia, the Czech Republic and the USA. Our motto is "Ní neart go cur le chéile", which means there is no strength without unity. Our ethos is one of inclusion and we welcome pupils from all races and faiths. In 2008 we created a Garden of Inclusion that welcomes visitors as they enter the school building.
National flags in our Garden of Inclusion
Principal Maeve Saunderson leads a team of ten teachers, four special needs assistants, a secretary, a caretaker and two cleaners. The school is also served by a Home School Community Liaison Co-ordinator. There is a very active Parents' Council and there are links to the local community through the Board of Management. Facilities in the school include five mainstream classrooms, a shared learning resource classroom, three resource teaching rooms, a parents' room, a library, and an assembly hall which is also used for indoor PE activities and performances. Each classroom is equipped with a digital overhead projector, an interactive whiteboard and a teaching computer, as well as three computers and a printer for use by pupils. All our computers are networked and protected with an NCTE firewall for Internet access.The school also has twenty iPads for class, group and and individual work.
Phone/fax: 058-42873 Email: info@stjosephsprimary.ie St Josephs Primary School , Mitchell Street , Dungarvan , Co Waterford - click for map
website by Crondesign Award winning Irish website design and development Copyright St. Josephs Primary School ©2011. All rights reserved

redpajama_set_name: RedPajamaCommonCrawl


text:
Small grocer has big impact; Civic leader's devotion to Shady Side is strong
By Kirsten Scharnberg
In a cramped food market, behind a counter overflowing with cigarettes, breath mints and cheap liquor, the mayor of Shady Side peddles steaks and toilet paper, good news and philosophy to his loyal townsfolk.
"I once heard a story," begins Mohan Grover, the self-appointed civic leader of this Anne Arundel County peninsula village and the proprietor of a five-aisle food mart in the heart of town.
"There was this man who wanted to change the world. But it did not work. So he said, 'Then I will change just my country instead.' But it did not work. So he said, 'Then I will change just my state instead.' But it did not work. So he said, 'Then I will change just my town.'
"A man must start small," the dignified, gray-templed grocer concludes.
And some men, by staying small, become very big.
Mohan Grover's empire is modest. The paint on the outside of his little store is peeling, and the sign announcing "Renno's Food Market" sags on one side.
Grover, his wife and three daughters have made their home not in one of the lush new subdivisions near town, but in a sparse apartment above their store.
His living room furniture is out of style, and the left-hand cuff of his starched dress shirt is missing a button and is held together with a bright red twist-tie.
But everything they have is bought and paid for, thanks to the grocery store he has opened 14 hours a day, seven days a week since 1974.
Now he could lose it all.
With the possibility of three supermarket giants building in the area, Grover -- and other small-time, well-liked business owners struggling to keep current on their car payments and to send their kids through private college -- worry that even their most loyal customers will be lured away by the 24-hour convenience of the one-stop grocery store.
"I wish I could look into a crystal ball and see how these stores will affect the quality of my life and the character of my town," he says. "But I cannot."
Environmentalists can protest, county officials can debate zoning and anti-growth activists can raise a big stink, but it's people like Mohan Grover who put a face on what fast-encroaching commercial development means in quiet little places like southern Anne Arundel County.
Grover watches over the comings and goings of this sleepy town while he rings up sales of lottery tickets and lunch meat. He knows most of his 3,500 constituents personally.
"Hello, sweetie," he says to the teen-age girl stopping by for a Coke after school.
"How have you been feeling? Any better?" he asks an elderly woman purchasing eggs.
And although Shady Side is unincorporated and the title isn't formal, virtually everyone waves and says, "See you around, mayor," on their way out.
Grover, still boyish at 54, looks bashful when people call him that.
"That's just their way of honoring me," he explains.
And why not? Grover has given plenty to this little town.
He attends every local funeral. Next to his store's cash register -- always -- there is a jar filled with nickels and quarters and pennies that he is collecting for one local cause or another.
Whenever there is a fatal accident on Shady Side Road, Grover places a wreath at the site to memorialize the victims.
Once, when firefighters spent all night fighting a terrible blaze, Grover opened his store at 2 a.m. and handed out sandwiches to soot-covered men.
And people notice.
One local pastor, Rev. Roberta Matthews, refers to Grover as the "man behind the town."
"He lives for this town," she said. "Do you think people can't see that? He's the kind of guy who makes you want to give back."
About seven years ago, when Grover suffered a bleeding ulcer and was rushed to the hospital, a handful of Shady Side residents showed up in the Annapolis emergency room offering to donate blood.
"For weeks after that, people would come into the store to buy something, and after they left, my wife would look at me and say, 'They were there that night,'" Grover says.
"Can you imagine what that means to a man?"
Shady Side is a provincial place with a rich history.
Situated in the southern portion of a waterfront county, the little town is one big environmentally sensitive wetland.
Residents are renowned for being loudly anti-development and tirelessly pro-environment. And as more and more people move in -- especially well-to-do folks looking to live the quiet life and make the easy commute to Washington -- longtime locals have grown increasingly annoyed by outsiders.
Yet somehow Grover, a man who is neither a Shady Side lifer nor even an American-born citizen, became de facto overseer of this place.
Born near New Delhi, India, Grover moved to the United States to attend Howard University. Trained as an engineer, he couldn't find a job after graduation, so he bought Renno's Food Market.
"I worked hard," he said. "Long days. Long hours. You could say I put all my eggs in one basket with this store."
Even after more than two decades as Renno's owner, Grover still balks at changing the name of the store.
"My customers tell me I've earned my name and should change it to Grover's," he says. "They say, 'Grover, you are a pillar of this community.' But I say, 'No, we'll just keep it Renno's."
Grover earned his customers' loyalty by going out on a financial limb.
In a dog-eared accounting ledger, the grocer recorded the bread and ketchup, hot dogs and butter that left his market bound for the homes of people who couldn't afford them.
"We can even up later," Grover became known for saying to faithful customers who were a paycheck behind or a mortgage payment short. "I trust you."
The three proposed stores -- a Food Lion, a Safeway and a Shoppers' Food Warehouse -- would all sit within about two miles of Renno's Food Mart and several other mom-and-pop variety groceries.
The Safeway complex, which would sit on nearly 15 acres at Bay Front and Deale Churchton roads in Deale, is proposed as a 55,000-square-foot store, 13 times the size of Grover's store.
The Food Lion, which would be at Deale Churchton and Shady Side roads near Deale, would be a 37,000-square-foot store, eight times bigger.
The Shoppers' Food Warehouse, in such a preliminary stage that no formal building plan has been drawn up, would sit so close to Grover's shop that he could walk there in a couple of minutes.
"How do you compete with that?" Grover asks. "I think it would be very hard to say those stores would not hurt my business and that scares me, no doubt.
"But even more than that, I worry about what that will do to Shady Side. If we had wanted to live in a metropolitan area, we would have. Instead, we chose a village."
Twenty-five years of seven-day work weeks will tire a man out. And some days, Grover would give anything for a nap or a vacation.
"But then I say, 'Hey, you're supposed to be tired at the end of a hard day's work, right?' " he asks, laughing.
Retirement sounds good sometimes, he admits. Not so that he could take up golfing or fishing, but so that he could have time to get involved in more community activities.
"I love this place," Grover says. "I'd like to do more."
Instead, he works.
He owes thousands for his oldest daughter's college education. His middle daughter attends Mount Holyoke College in Massachusetts at a cost of $30,000 a year. And his youngest daughter, a high school sophomore, is leaning toward choosing an expensive private college as well.
"Sometimes you look around and think, 'I don't have much to show for all this work,' " he said. "But then you look at your kids -- good kids with good educations who are honest and kind and don't use drugs -- and you think, 'I am a rich man.' "
So while the building plans for the sprawling, brightly lighted, grocery stores sit in the county's Planning and Code Enforcement files, Grover continues to pull 14-hour days to keep his little shop profitable.
And as townspeople stop in to chat and buy milk and drop their extra change in the store's big glass charity jar, Grover knows that like the man who wanted to change the world but settled for a town, he has altered the face of Shady Side.
Pub Date: 2/21/99


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The very first time I booted StarRay, I got the strangest feeling I'd played this game before.
In StarRay, you pilot the ship that provides the game's name. Your mission is pretty simple: Blast all the invaders to atoms before they kill you or destroy all the vital installations on the planet you are defending. The planet is many screens wide and wraps around horizontally so you can fly continuously in one direction and circle the world. Fortunately, you have a long-range radar screen that shows the entire planet's surface so you can locate enemies and installations that are under attack.
The StarRay can thrust left or right, move up and down the full height of the screen and is vulnerable to collisions with its enemies and the shots they fire. The types of attackers vary from wave to wave because there are actually seven different "worlds" to defend (you must survive three waves on each one), each with its own dangers.
For example, on the first planet, called Gorbaxa, there are Landers (gee, this sounds awfully familiar), Krellian Mother Ships that shatter into a bunch of tiny attack ships when you hit them and so forth. On the second planet, called Sirion, you'll encounter Landers and weird little beehives that split into a bunch of fragments that shortly turn into batlike creatures...sounds kinda like those Krellian Mother Ships, eh? If you spend too much time completing a wave, vicious Blue Hunters will start zipping around and try to kill you.
Okay, maybe the bard didn't put it quite that way. But the quote fits because StarRay, by any other name, seems to be a graphically souped-up and modified version of the classic arcade game Defender.
There are differences between this game and Defender, but mostly they are of the cosmetic variety. For example, on each planet there will be a different kind of installation for you to defend, ranging from energy cells to forest robots and antigravity generators, but their basic function is identical to that of the humanoids in Defender. You must defend them, else the Landers will land on them (hence the name) and convert them into something nasty, like gun employments.
Unlike Defender, the Landers do not have to lift the target to the top of the screen in order to carry out their nefarious schemes. They merely have to park their buns on the target installation for a short time and the dreadful transformation will occur. If an installation is so corrupted, it is considered lost, and you should destroy it. If all the installations are corrupted and/or destroyed rather than being blown into deep space, as Defender would do, the screen slowly fades to black, and the game ends. No second chance.
The StarRay fighter is equipped with a rapid-fire forward-shooting laser and a limited supply of "vaporizers," which will destroy all opponents on the screen (but not their shots!). You should be careful of the installations when shooting at ground level. Fortunately, the installations are unaffected by your smart bombs...oops! I mean vaporizers! This is all very much like Defender, however, unlike its inspiration, StarRay does not feature any sort of hyperspace option.
Okay, okay, I've jumped on the Defender parallel more than enough. But just because it's a Defender-type game, does that make it bad?
StarRay is a solid piece of programming. The graphics move quickly and smoothly. The sound is good, but not outstanding. The thing that makes this game fun is that it's a well-balanced blend of smooth play action and good graphics.
And speaking of graphics, in this department StarRay leaves Defender in the interstellar dust. No mere outline of a planet's surface in front of twinkling stars in this game. The scenery is loaded with detail. Zooming through the jungle of Sirion, you'll see no less than six levels of background detail scrolling by on the jungle floor, in addition to the tall trees is the background and the sky beyond. The sensation of movement and depth is very good.
Each planet appears for three waves, then it's off to the next one. There are a total of seven planets, each with its own unique look and its own pitfalls. The third planet, Sharlon, is covered in ice and snow. Ice floes fill the oceans. Landers are there, as always, as are the expected pod-type ships (that split into many ships when you hit them). But there's a new danger here: Shoot one of the funny-looking satellites floating halfway up the screen and it starts spinning wildly, generating interference that screws up your radar! Higher up in the game are collapsing cave passages, guided missiles and so on.
There's one drawback to these super-detailed graphics, and that's a cluttered screen. It's easy to crash into something you didn't see when you're zooming along at maximum speed. The smaller aliens can get lost in the background blur.
As far as the screen display goes, the radar scan, your shield level, score and number of vaporizers appear at the bottom of the screen rather than the top. I found that as I tried to keep the invaders from getting too low, my eyes tended to be fixed more toward the top of the screen than the bottom, and thus checking the status of my shields and so forth forced me to continuously look away from what I was doing, sometimes with disastrous results.
There are other aspects of StarRay that differentiate it from Defender. First, you have only one ship and do not get extras. When you die, it's all over. The way Star-Ray makes up for what would otherwise be a fatal flaw is that the ship is equipped with a shield that can withstand a number of hits before it collapses. Your single ship can actually survive more hits than the total number of ships you start with in Defender.
When you blast a Lander, it doesn't always just vanish without a trace. Sometimes a Bonus Ball will appear in its wake. Picking these up (by touching them with your ship) will enhance the StarRay fighter in various ways. Bonus Balls are labeled with a letter that describes their function. "A" stands for improved acceleration, "C" gives you continuous fire for 100 shots and "I" provides ten seconds of invulnerability (great for ramming through a bunch of invaders). They can be destroyed by laser fire and disappear after a short time if you don't collect them.
Bonus Air Buses will appear if you are doing well. If you shoot these, they will drop a bonus object, which you must touch to collect.
Control can be either by keyboard or joystick, though I found the joystick to be more intuitive. The lasers are fired with the joystick fire button, but the vaporizers/smart bombs must be triggered with the keyboard. Which key? The space bar would be the obvious candidate, but did the programmers use it? Nope. They used the CapsLock key. Imagine trying to find the CapsLock key during that desperate moment when you need a vaporizer. Good luck!
The space bar pauses the game and brings up a menu of options allowing you to do such things as enable/disable the music and sound effects, restart the game at any of the first four planets and even enables a "Last Game Option," which will stop StarRay dead in its tracks at the end of the current game, preventing you from playing "just one more game!"
The game features background music that, while not bad, I found distracting. With it on I couldn't hear the sound effects well and found it easy to miss the sound that warns you when an installation is under attack. Fortunately, you can disable the music. You can also disable the sound effects (which makes the game play faster and harder), but I prefer the sound.
If you have one megabyte or more RAM, the title screen will be accompanied by digitized music, which can be output through an ST Replay cartridge (if you have one) and played through your stereo. Great, except that I don't particularly like the title music, and the other sounds in the game (including the background music) can't be output in this manner. The most annoying thing about the title music is that every time the game ends, the program reloads the title screen and music and plays it again. Fortunately, one button press kills it, but it's annoying nonetheless.
The "manual", which consists of instructions printed on the back of a small StarRay poster is written for the Amiga version. A small card featuring notes for the ST version accompanies this. The instructions are brief...too brief. There's a lot of glib writing, but not much useful information. For example, there is no mention of whether it is possible to recharge your shields or how to gain extra vaporizers. Neither is there even a hint that the destruction of all your installations will cause the end of the game.
But, all in all, StarRay is a fun and playable game. It adds enough twists to keep it from being a blow-by-blow rerun of Defender, and the graphics add a lot to its appeal. If you liked Defender, you'll probably love StarRay.
I just wish there was a #% §@# hyperspace button!


text:
\section{Introduction}
\label{sec:introduction}
\emph{Graph clustering}, i.e., the partitioning of the entities of a network into densely connected groups, has received growing attention in the literature of the last decade, with applications ranging from the analysis of social networks to recommendation systems and bioinformatics~\cite{f-c-09}.
Mathematical formulations thereof abound; for an extensive overview on different approaches see for example the reviews of Fortunato~\cite{f-c-09} and Schaeffer~\cite{s-gc-07}.

One line of research that recently gained a lot of popularity is based on \emph{null models}, the most prominent objective function in this context being the \emph{modularity} of a clustering~\cite{ng-fecsn-04}.
Roughly speaking, the idea behind this approach is to compare the number of edges within the same cluster to its expected value in a random graph that inherits some properties of the graph given as input.

In a wider sense, the measure called~\emph{surprise} that has recently been suggested as an alternative to modularity is also based on a null model, although, compared to modularity and its modifications~\cite{f-c-09}, it uses a different tradeoff between the observed and expected number of edges within clusters.
Surprise is used as a quality function in the tools UVCLUSTER and Jerarca to analyze protein interaction data~\cite{amm-icapi-05,am-jeacn-10}.
The authors' main arguments for using surprise instead of modularity is that it exhibits better behavior with respect to synthetic benchmarks and, empirically, it does not suffer to the same extent from the \emph{resolution limit} of modularity~\cite{bf-rlcd-07}, i.e.~the tendency to merge small natural communities into larger ones~\cite{am-dncss-11,am-e-13,am-s-13}.
However,  these results are hard to assess, since a metaheuristic is used instead of directly optimizing the measure.
It chooses among a set of clusterings produced by general clustering algorithms the one that is best with respect to surprise.

In this work, we take first steps towards a theoretical analysis of surprise.
We show that the problem of finding a clustering with optimal surprise is $\mathcal{NP}$-hard in general and polynomially solvable on trees.
Moreover, we formulate surprise as a bicriterial problem, which allows to find provably optimal solutions for small instances by solving a small number of integer linear programs.

\vspace{2ex}
\noindent
\textbf{Notation.}
All graphs considered are
unweighted, undirected and simple, i.e.~they do not contain loops or parallel edges.
A clustering $\ensuremath{\zeta}$ of a graph $G=(V,E)$ is a partitioning of $V$.
Let $n:=|V|$ and $m:=|E|$ denote the number of vertices and edges of $G$, respectively.
If $C$ is a cluster in $\ensuremath{\zeta}$, $i_e(C)$ denotes the number of \emph{intracluster edges} in $C$, i.e., the number of edges having both endpoints in $C$.
Similarly, $i_p(C) := \binom{|C|}{2}$ is the number of vertex pairs in $C$.
Furthermore, let $p := \binom{n}{2}$ be the number of vertex pairs in $G$, $i_p(\ensuremath{\zeta}) := \sum_{C \in \ensuremath{\zeta}} i_p(C)$ be the total number of intracluster vertex pairs and $i_e(\ensuremath{\zeta}) := \sum_{C \in \ensuremath{\zeta}} i_e(C)$ the total number of intracluster edges.
If the clustering is clear from the context, we will sometimes omit $\ensuremath{\zeta}$ and just write $i_p$ and $i_e$.
To ease notation, we will allow binomial coefficients $\binom{n}{k}$ for all $n$ and $k \in \mathbb{N}$.
If $k > n$, $\binom{n}{k} = 0$ by definition.

\section{Definition and Basic Properties}
Let $\ensuremath{\zeta}$ be a clustering of a graph $G=(V,E)$ with $i_e$ intracluster edges.
Among all graphs labeled with vertex set $V$ and exactly $m$ edges, we draw a graph $\mathcal{G}$ uniformly at random.
The surprise $S(\ensuremath{\zeta})$ of this clustering is then the probability that $\mathcal{G}$ has at least $i_e$ intracluster edges with respect to $\ensuremath{\zeta}$.
The lower this probability, the more \emph{surprising} it is to observe that many intracluster edges within $G$, and hence, the better the clustering.
The above process corresponds to an urn model with $i_p(\ensuremath{\zeta})$ white and $p-i_p(\ensuremath{\zeta})$ black balls from which we draw $m$ balls without replacement.
The probability to draw at least $i_e$ white balls then follows a hypergeometric distribution, which leads to the following definition\footnote{This is the definition used in the original version~\cite{amm-icapi-05}; later on, it was replaced by maximizing $-\log_{10} S(\ensuremath{\zeta})$, which is equivalent with respect to optimum solutions.}; the lower $S(\ensuremath{\zeta})$, the better the clustering
$$S(\ensuremath{\zeta}) := \sum_{i=i_e}^{m} \frac{\binom{i_p}{i} \cdot \binom{p - i_p}{m-i}}{\binom{p}{m}}$$

\noindent
\textbf{Basic Properties.}
For a fixed graph, the value of $S$ only depends on two variables, $i_p$ and $i_e$.
To ease notation, we will use the term $S(i_p, i_e)$ for the value of a clustering with $i_p$ intracluster pairs and $i_e$ intracluster edges.
The urn model view
yields some simple properties
that lead to a better understanding of how surprise behaves, and that are heavily used in the $\mathcal{NP}$-hardness proof.

\begin{lemma}
Let $i_e$, $i_p$, $p$ and $m$ be given by a clustering, i.e.~$0\leq i_e \leq i_p \leq p$, $i_e \leq m$ and $m-i_e \leq p-i_p$.
Then, the following statements hold:
\begin{enumerate}
 \item[(i)] $S(i_p, i_e+1) < S(i_p, i_e).$
 \item[(ii)] If $i_e > 0$, then $S(i_p-1, i_e) < S(i_p, i_e)$
 \item[(iii)] If $p - i_p > m - i_e$, then $S(i_p+1, i_e+1) < S(i_p, i_e).$
\end{enumerate}
  \label{lem:basic_props}
\end{lemma}
\begin{proof}
 Statement (i) is obvious.
 Similarly, statement (ii) is not hard to see if we recall that $S(i_p-1, i_e)$ corresponds to the probability to draw at least $i_e$ white balls after replacing one white ball with a black one.

 For statement (iii), we show that the number $k_1$ of $m$-element subsets of the set of all balls containing at least $i_e$ white balls is larger than the number $k_2$ of $m$-element subsets containing at least $i_e+1$ white balls after painting one black ball $b$ white.
 Any subset $A$ that contributes to $k_2$ also contributes to $k_1$, as at most one ball in $A$ got painted white.
 On the other hand, every $m$-element subset not containing $b$ that contains exactly $i_e$ white balls contributes to $k_1$, but not to $k_2$.
 As there are at least $i_e$ white balls, and $p-i_p > m-i_e$ implies that there are at least $m-i_e+1$ black balls, there is at least one subset with these properties.
 Hence $k_1 > k_2$, which is equivalent to $S(i_p+1, i_e+1) < S(i_p, i_e)$.\qed
\end{proof}

In other words, the value of surprise improves the more edges and the less vertex pairs within clusters exist.
Moreover, part (iii) shows that if we increase the number of intracluster edges such that the number of \emph{intracluster non-edges}, i.e., vertex pairs within clusters that are not linked by an edge, does not increase, this leads to a clustering with strictly smaller surprise.
This immediately yields some basic properties of optimal clusterings with respect to surprise.
Part (i) of the following proposition is interesting as it shows that optimal clusterings always fulfill the assumptions of Lemma~\ref{lem:basic_props}(ii)-(iii).
\begin{proposition}
 Let $G=(V,E)$ be a graph that has at least one edge and that is not a clique and $\ensuremath{\zeta}$ be an optimal clustering of $G$ with respect to surprise. Then,
 \begin{enumerate}
  \item[(i)] $i_e(\ensuremath{\zeta}) > 0$ and $p-i_p(\ensuremath{\zeta}) > m-i_e(\ensuremath{\zeta})$
  \item[(ii)] $1 < |\ensuremath{\zeta}| < |V|$
  \item[(iii)] $\ensuremath{\zeta}$ contains at least as many intracluster edges as any clustering $\ensuremath{\zeta}'$ of $G$ into cliques.
  \item[(iv)] Any cluster in $\ensuremath{\zeta}$ induces a connected subgraph.
 \end{enumerate}
 \label{lem:props_opt_sol}
\end{proposition}
\begin{proof}
(i): If $i_e(\ensuremath{\zeta}) = 0$ or $p - i_p(\ensuremath{\zeta}) = m - i_e(\ensuremath{\zeta})$, it can be easily seen that $S(\ensuremath{\zeta})=1$.
On the other hand, let us consider a clustering $\ensuremath{\zeta}'$ where each cluster contains one vertex, except for one cluster that contains two vertices linked by an edge $e$.
As $m<p$, there is at least one labeled graph on $V$ with $m$ edges that does not contain $e$.

(ii):
If $|\ensuremath{\zeta}|=1$, $p-i_p(\ensuremath{\zeta}) = 0 = m-i_e(\ensuremath{\zeta})$ and if $|\ensuremath{\zeta}|=|V|$, $i_e(\ensuremath{\zeta})=0$.
The statement now follows from (i).

(iii): Let us assume that $i_e(\ensuremath{\zeta}) < i_e(\ensuremath{\zeta}')$.
Lemma~\ref{lem:basic_props}(ii) can be used to show that $S(\ensuremath{\zeta}) = S\bigl(i_p(\ensuremath{\zeta}), i_e(\ensuremath{\zeta})\bigr) \geq S\bigl(i_e(\ensuremath{\zeta}), i_e(\ensuremath{\zeta})\bigr)$ and from Lemma~\ref{lem:basic_props}(iii), it follows that $S\bigl(i_e(\ensuremath{\zeta}), i_e(\ensuremath{\zeta})\bigr) > S\bigl(i_e(\ensuremath{\zeta}'), i_e(\ensuremath{\zeta}')\bigr) = S(\ensuremath{\zeta}')$.

(iv): Follows from Lemma~\ref{lem:basic_props}(ii) and the fact that splitting a disconnected cluster into its connected components decreases the number of intracluster pairs and does not affect the number of intracluster edges. \qed
\end{proof}

\vspace{2ex}
\noindent
\textbf{Bicriterial View.}
\label{sec:connection}
From Lemma~\ref{lem:basic_props}, it follows that an optimal solution with respect to surprise is \emph{pareto optimal} with respect to (maximizing) $i_e$ and (minimizing) $i_p$.
Interestingly, this also holds for a simplification of modularity whose null model does not take vertex degrees into account and that was briefly considered by Reichardt and Bornholdt~\cite{rb-smcd-06,rb-dfcsc-04}, although the tradeoff between the two objectives is different.
Hence, an optimal clustering
can be found by solving the following optimization problem for all $0 \leq k \leq m$ and choosing the solution that optimizes surprise.
\begin{problem}[minIP]
 Given a graph $G$ and an integer $k>0$, find a clustering $\ensuremath{\zeta}$ with $i_e(\ensuremath{\zeta}) = k$, if there exists one, such that $i_p(\ensuremath{\zeta})$ is minimal.
\end{problem}
Unfortunately, the decision variant of minIP~is $\mathcal{NP}$-complete even on bipartite graphs, as it is equivalent to the unweighted Minimum Average Contamination problem~\cite{lt-tcamc-11}.
However, the formulation of minIP~does not involve binomial coefficients and is thus in some aspects easier to handle.
For example, in contrast to surprise, it can be easily cast into an integer linear program.
We will use this in Sect.~\ref{sec:algorithms} to compute optimal solutions for small instances.

One might guess from the $\mathcal{NP}$-completeness of minIP~that surprise minimization is also $\mathcal{NP}$-complete.
However, there is no immediate reduction from minIP~to the decision variant of surprise optimization, as the number of intracluster edges in an optimal clustering with respect to surprise is not fixed.
In the following section, we will therefore give a proof for the hardness of finding a clustering with optimal surprise.

\section{Complexity}\label{sec:complexity}
We show $\mathcal{NP}$-completeness of the corresponding decision problem:
\begin{problem}[\textsc{Surprise Decision (SD)}]
 Given a graph $G$ and a parameter $k>0$, decide whether there exists a clustering $\ensuremath{\zeta}$ of $G$ with $S(\ensuremath{\zeta}) \leq k$.
\end{problem}
As $S$ can be clearly evaluated in polynomial time, \textsc{SD}~is in $\mathcal{NP}$.
To show $\mathcal{NP}$-completeness, we use a reduction from \textsc{Exact Cover by 3-Sets}~\cite{gj-ci-79}:
\begin{problem}[\textsc{Exact Cover by 3Sets (X3S)}]
 Given a set $\ensuremath{\mathcal{X}}$ of elements and a collection $\ensuremath{\mathcal{M}}$ of 3-element subsets of $\ensuremath{\mathcal{X}}$,
 decide whether there is a subcollection $\ensuremath{\mathcal{R}}$ of $\ensuremath{\mathcal{M}}$ such that each element in $\ensuremath{\mathcal{X}}$ is contained in exactly one member of $\ensuremath{\mathcal{R}}$.
\end{problem}

\begin{wrapfigure}[10]{r}{.4\textwidth}
\vspace{-8ex}
 \begin{center}
   \includegraphics[scale = 0.7]{reduction_small}
 \end{center}
 \vspace{-2ex}
 \caption{Illustration for reduction.}
 \label{fig:reduction}
\end{wrapfigure}
Let $I = (\ensuremath{\mathcal{X}}, \ensuremath{\mathcal{M}})$ be an instance of \textsc{X3S}.
The reduction is based on the idea of implanting large disjoint cliques in the transformed instance that correspond to the subsets in $\ensuremath{\mathcal{M}}$. The size of these cliques is polynomial in $|\ensuremath{\mathcal{M}}|$, but large enough to ensure that they can neither be split nor merged in a clustering with low surprise.
Hence, each of these cliques induces a cluster.
The transformed instance further contains a vertex for each element in $\ensuremath{\mathcal{X}}$ that is linked with the cliques corresponding to the subsets it is contained in.
The idea is to show that in a clustering $\ensuremath{\zeta}$ with low surprise, each of these vertices is contained in a cluster induced by exactly one subset, and each cluster contains either three ``element vertices'' or none, which induces an exact cover of $\ensuremath{\mathcal{X}}$.

In the following, we will assume without loss of generality\footnote{Otherwise, the instance is trivially non-solvable.} that each element of $\ensuremath{\mathcal{X}}$ belongs to at least one set in $\ensuremath{\mathcal{M}}$, hence $|\ensuremath{\mathcal{X}}| \leq 3|\ensuremath{\mathcal{M}}|$.
We construct an instance $I' = (G,k)$ of \textsc{SD} in the following way.
Let $r := 3|\ensuremath{\mathcal{M}}|$.
First, we map each set $M$ in $\ensuremath{\mathcal{M}}$ to an $r^2$-clique $C(M)$ in $G$.
Furthermore, we introduce an $|\ensuremath{\mathcal{X}}|$-clique to $G$, where each of the vertices $v(x)$ in it is associated with an element $x$ in $\ensuremath{\mathcal{X}}$.
We link $v(x)$ with each vertex in $C(M)$, if and only if $x$ is contained in $M$.
Let $V_\ensuremath{\mathcal{X}}$ be the set containing all vertices corresponding to elements in $\ensuremath{\mathcal{X}}$, and $V_\ensuremath{\mathcal{M}}$ the set of vertices corresponding to subsets.
Fig.~\ref{fig:reduction}~illustrates the reduction, clearly, it is polynomial.
In the proof, we will frequently use the notion \emph{for large $r$, statement $A(r)$ holds}.
Formally, this is an abbreviation for the statement that there exists a constant $c>0$ such that for all $r \geq c$, $A(r)$ is true.
Consequently, the reduction only works for instances that are larger than the maximum of all these constants, which suffices to show that \textsc{SD} is $\mathcal{NP}$-complete\footnote{Smaller instances have constant size and can therefore be trivially solved by a brute-force algorithm.}.

\begin{lemma}
 \label{lem:os_many_ie}
Let $\ensuremath{\zeta}$ be an optimal clustering of $G$ with respect to $S$. Then, $i_e(\ensuremath{\zeta}) \geq |\ensuremath{\mathcal{M}}| \cdot \binom{r^2}{2}$.
\end{lemma}
\begin{proof}
Follows from Proposition~\ref{lem:props_opt_sol}(iii) and the fact that the clustering whose clusters are the cliques in $V_\ensuremath{\mathcal{M}}$ and the singletons in $V_\ensuremath{\mathcal{X}}$ is a clustering into cliques with $|\ensuremath{\mathcal{M}}| \cdot \binom{r^2}{2}$ intracluster edges. \qed
\end{proof}
Next, we give an upper bound on the number of \emph{intracluster non edges}, i.e., vertex pairs within clusters that are not linked by an edge, in an optimal clustering of $G$.
Its (rather technical) proof makes use of the asymptotic behavior of binomial coefficients and can be found in App.~\ref{app:asymptotics}.

\begin{lemma}
 Let $\ensuremath{\zeta}$ be an optimal clustering of $G$ with respect to surprise. Then, for large $r$, $i_p(\ensuremath{\zeta}) - i_e(\ensuremath{\zeta}) \leq \frac{r^4}{2}.$
 \label{lem:os_few_intra_non}
\end{lemma}

This can now be used to show that an optimal clustering of $G$ is a clustering into cliques.
We start by showing that the cliques in $V_\ensuremath{\mathcal{M}}$ cannot be split by an optimal clustering.
\begin{figure}[tbp]
  \begin{center}
   \includegraphics[scale = 1]{./Illu_Proof}
 \end{center}
 \caption{Illustration for proof of Lemma~\ref{lem:clique_not_split}}
 \label{fig:Illu_Proof}
\end{figure}

  \begin{lemma}
 \label{lem:clique_not_split}
Let $r$ be large and $\ensuremath{\zeta}$ be an optimal clustering of $G$ with respect to $S$.
Then, the cliques $C(M)$ in $V_\ensuremath{\mathcal{M}}$ are not split by $\ensuremath{\zeta}$.
\end{lemma}
\begin{proof}
Assume that there is at least one clique that is split by $\ensuremath{\zeta}$.
$\ensuremath{\zeta}$ induces a partition of each clique that it splits.
We call the subsets of this partition the \emph{parts} of the clique.

\emph{Claim 1: Every clique $C(M)$ contains a part with at least $r^2-6$ vertices.}

\emph{Proof of Claim 1:}
Assume that there is a clique $K$ where each part has at most $r^2-7$ vertices.
We can now greedily group the parts in two roughly equal sized regions, such that the smaller region contains at least $7$ vertices and the larger region at least $r^2/2$ vertices.
Let us look at the clustering we get by removing the vertices in $K$ from their clusters and cluster them together.
The vertices in $K$ have in total $3r^2$ edges to vertices outside $K$ and we gain at least $7/2 \cdot r^2$ new intracluster edges between the regions.
Hence, the number of intracluster edges increases and the number of intracluster non-edges can only decrease.
By Lemma~\ref{lem:basic_props}(iii) and Lemma~\ref{lem:basic_props}(i), it can be seen that this operation leads to a clustering with better surprise, which contradicts the optimality of $\ensuremath{\zeta}$.

Let us now call the parts with size at least $r^2-6$ \emph{large parts} and the other parts \emph{small parts}.

\emph{Claim 2: No two large parts are clustered together.}

\emph{Proof of Claim 2:}
Assume that there is a cluster that contains more than one large part.
This cluster induces at least $(r^2-6)^2$ intracluster non-edges.
For large $r$, this is larger than $r^4/2$ and Lemma~\ref{lem:os_few_intra_non} tells us that $\ensuremath{\zeta}$ was not optimal.

A simple counting argument now yields the following corollary.

\emph{Corollary: There must exist a large part $B$ contained in a split clique whose cluster contains at most $|B|+6$ vertices in $V_\ensuremath{\mathcal{M}}$}.

Let $B$ as in the corollary and $A$ be the set of the vertices that are in the same clique as $B$ but not in $B$ and $C$ be the set of vertices that are in the same cluster as $B$ but not in $B$.
Fig.~\ref{fig:Illu_Proof} illustrates this case.
We consider the clustering that we get by removing the vertices in $A$ and $B$ from their cluster and cluster them together.
The number of vertices in $A$ and $C$, respectively, is at most $6$, and each of these vertices has at most $3$ neighbors in $V_\ensuremath{\mathcal{X}}$.
Hence, we lose at most $36$ intracluster edges by this operation.
On the other hand, we gain at least $r^2-6$ intracluster edges between $A$ and $B$, thus, for large $r$, the number of intracluster edges increases.
Again, the number of intracluster non-edges can only decrease and by Lemma~\ref{lem:basic_props}(iii) and Lemma~\ref{lem:basic_props}(i), we get that this operation leads to a clustering with better surprise, which contradicts the optimality of $\ensuremath{\zeta}$. \qed
\end{proof}

\begin{lemma}
\label{lem:cliques_apart}
 Let $r$ be large and $\ensuremath{\zeta}$ be an optimal clustering of $G$ with respect to $S$.
 Then, no two of the cliques in $V_\ensuremath{\mathcal{M}}$ are contained in the same cluster.
\end{lemma}
\begin{proof}
 A cluster that contains two cliques in $V_\ensuremath{\mathcal{M}}$ induces at least $r^4$ intracluster non-edges.
 The statement now follows from Lemma~\ref{lem:os_few_intra_non}. \qed
\end{proof}

\begin{lemma}
 \label{lem:vertices_assigned}
Let $r$ be large and $\ensuremath{\zeta}$ an optimal clustering of $G$ with respect to $S$.
Then, each $v(x)$ in $V_\ensuremath{\mathcal{X}}$ shares a cluster with a clique $C(M)$ such that $x \in M$.
\end{lemma}
\begin{proof}From Lemma~\ref{lem:clique_not_split} and Lemma~\ref{lem:cliques_apart} we know that $\ensuremath{\zeta}$ clusters the vertices in $V_\ensuremath{\mathcal{M}}$ according to the cliques we constructed.
 Assume that there is a vertex $v(x)$ in $V_\ensuremath{\mathcal{X}}$ that is not contained in any of the clusters induced by the sets containing $x$.
  Since each element in $\ensuremath{\mathcal{X}}$ is contained in at least one set in $\ensuremath{\mathcal{M}}$,  there exists a clique $K$ in $V_\ensuremath{\mathcal{M}}$ that contains $r^2$ neighbors of $v(x)$.
  As $v(x)$ has at most $|\ensuremath{\mathcal{X}}| -1$ neighbors in its own cluster, removing it from its cluster and moving it to the cluster of $K$ increases the number of intracluster edges.
  On the other hand, $x$ is linked with all vertices in its new cluster and thus, the number of intracluster non-edges cannot increase.
  Hence, this operation leads to a clustering with better surprise, which contradicts the optimality of $\ensuremath{\zeta}$. \qed
\end{proof}

\begin{theorem}
 For large $r$, $I=(\ensuremath{\mathcal{X}},\ensuremath{\mathcal{M}})$ has a solution if and only if there exists a clustering $\ensuremath{\zeta}$ of $G$ with $S(\ensuremath{\zeta}) \leq k := {\binom{p}{m}}^{-1} \cdot \left({\binom{|\ensuremath{\mathcal{M}}| \cdot r^2 + |\ensuremath{\mathcal{X}}|}{2} - |\ensuremath{\mathcal{M}}| \cdot \binom{r^2}{2} - |\ensuremath{\mathcal{X}}| \cdot r^2 - |\ensuremath{\mathcal{X}}| \atop  (3|\ensuremath{\mathcal{M}}| - |\ensuremath{\mathcal{X}}|) \cdot r^2 + \binom{|\ensuremath{\mathcal{X}}|}{2} - |\ensuremath{\mathcal{X}}|} \right)$.
\end{theorem}
\begin{proof}
  $\Rightarrow$: Let $R$ be a solution of $I$.
  $R$ induces a clustering of $G$ in the following way: For each $M \in \ensuremath{\mathcal{M}} \setminus R$ we introduce a cluster $C_M=C(M)$ and for each $M' \in R$ a cluster $C_{M'} = C(M') \cup \{v(x) \mid x \in M'\}$.
  As $R$ is an exact cover, this is a partition $\ensuremath{\zeta}$ of the vertex set.
  It is $p=\binom{|\ensuremath{\mathcal{M}}| \cdot r^2 + |\ensuremath{\mathcal{X}}|}{2}$, $m=|\ensuremath{\mathcal{M}}| \cdot \binom{r^2}{2} + 3 \cdot |\ensuremath{\mathcal{M}}| \cdot r^2 + \binom{|\ensuremath{\mathcal{X}}}{2}$ and $i_p(\ensuremath{\zeta})=i_e(\ensuremath{\zeta})=|\ensuremath{\mathcal{M}}| \cdot \binom{r^2}{2}  + |\ensuremath{\mathcal{X}}| \cdot r^2 + |\ensuremath{\mathcal{X}}|$.
  It can be easily verified that $S(\ensuremath{\zeta}) = k$.

  $\Leftarrow$: Let $\ensuremath{\zeta}$ be an optimal clustering of $G$ with respect to surprise and assume that $S(\ensuremath{\zeta}) \leq k$.
  From Lemma~\ref{lem:clique_not_split}, Lemma~\ref{lem:cliques_apart} and Lemma~\ref{lem:vertices_assigned}, we know that, for large $r$, we have one cluster for each set $M$ in $\ensuremath{\mathcal{M}}$ that contains $C(M)$ and each vertex $v(x)$ in $V_\ensuremath{\mathcal{X}}$ shares a cluster with a clique $C(M)$ such that $x \in M$.
  In particular, all clusters in $\ensuremath{\zeta}$ are cliques and hence $\binom{i_p(\ensuremath{\zeta})}{i_e(\ensuremath{\zeta})} = 1$.
  It follows that $\binom{p}{m} \cdot k \geq \binom{p}{m} \cdot S(\ensuremath{\zeta}) =  \binom{p - i_e(\ensuremath{\zeta})}{m - i_e(\ensuremath{\zeta})}$.
  This term is strictly decreasing with $i_e(\ensuremath{\zeta})$ and the above bound is tight for $i_e(\ensuremath{\zeta}) = |\ensuremath{\mathcal{M}}| \cdot \binom{ \cdot r^2}{2} + |\ensuremath{\mathcal{X}}| \cdot r^2 + |\ensuremath{\mathcal{X}}|:= t$.
  Hence, $\ensuremath{\zeta}$ contains at least $t$ intracluster edges.
  The number of intracluster edges within $V_\ensuremath{\mathcal{M}}$ is exactly $|\ensuremath{\mathcal{M}}| \cdot \binom{r^2}{2}$ and the number of intracluster edges linking $V_\ensuremath{\mathcal{M}}$ with $V_\ensuremath{\mathcal{X}}$ is exactly $|\ensuremath{\mathcal{X}}| \cdot r^2$.
  The only quantity we do not know is the number of intracluster edges within $V_\ensuremath{\mathcal{X}}$, which we denote by $i_e(V_\ensuremath{\mathcal{X}})$.
  As $i_e(\ensuremath{\zeta}) \geq t$, it follows that $i_e(V_\ensuremath{\mathcal{X}}) \geq |\ensuremath{\mathcal{X}}|$.
  Thus, every vertex in $V_\ensuremath{\mathcal{X}}$ has in average two neighbors in $V_\ensuremath{\mathcal{X}}$ that are in the same cluster.
  On the other hand, vertices in $V_\ensuremath{\mathcal{X}}$ can only share a cluster if they are ``assigned'' to the same clique $C(M)$.
  As the sets in $\ensuremath{\mathcal{M}}$ only contain three elements, vertices in $V_\ensuremath{\mathcal{X}}$ can only have at most two neighbors in $V_\ensuremath{\mathcal{X}}$ in their cluster.
  It follows that $\ensuremath{\zeta}$ partitions $V_\ensuremath{\mathcal{X}}$ into triangles.
  Hence, the set of subsets $R$ corresponding to cliques $C(M)$ whose clusters contain vertices in $V_\ensuremath{\mathcal{X}}$ form an exact cover of $\ensuremath{\mathcal{X}}$. \qed
\end{proof}

We now have a reduction from \textsc{X3S} to \textsc{SD} that works for all instances that are larger than a constant $c > 0$.
Hence, we get the following corollary.
\begin{corollary}
 \textsc{Surprise Decision} is $\mathcal{NP}$-complete.
\end{corollary}

To show that an optimal clustering with respect to surprise can be found in polynomial time if $G$ is a tree, we consider the following problem MACP~\cite{lt-tcamc-11}:
\begin{problem}[MACP]
Given a graph $G=(V,E)$ together with a weight function $w:V\rightarrow \mathbb{Q}_{\geq 0}$ on $V$ and a parameter $k$.
Find a clustering $\ensuremath{\zeta}$ of $G$ such that $m - i_e(\ensuremath{\zeta})=k$ and $\sum_{C \in \ensuremath{\zeta}} {\bigl(\sum_{v \in C} w(v)\bigr)}^2$ is minimal.
\end{problem}
For the special case that $w(v)$ equals the degree of $v$ and $G$ is a tree, Dinh and Thai give a dynamic program that solves MACP for all $0 \leq k\leq m$ simultaneously~\cite{dt-tocdf-}.
This yields an $O(n^5)$ algorithm for modularity maximization in (unweighted) trees.
In the context of surprise, we are interested in the special case that $w(v)=1$ for all $v \in V$.
 The following conversion shows that this is equivalent to minIP~with respect to optimal solutions:
\begin{equation} \label{minIP_MACP}
i_p(\mathcal{C})
= \sum_{C \in \mathcal{C}} {\frac{\left|C\right|(\left|C\right| - 1)}{2}}
= \frac{1}{2} \sum_{C \in \mathcal{C}} {\left|C\right|^2} -
\underbrace{\frac{1}{2} \left|V\right|}_{=\mathrm{const.}}
\end{equation}

The dynamic program of Dinh and Thai has a straightforward generalization to general vertex weights, which is polynomial in the case that each vertex has weight $1$.
For completeness, App.~\ref{app:trees} contains a description of the dynamic program in this special case, together with a runtime analysis.
\begin{theorem}\label{theoremTrees}
Let $T = (V,E)$ with $n:=\left| V \right|$ be an unweighted tree. Then, a surprise optimal clustering of $T$ can be calculated in $O(n^5)$ time.
\end{theorem}
\section{Exact Solutions}
\label{sec:algorithms}
  In this section, we give an integer linear program for minIP~and discuss some variants of how to use this to get optimal clusterings with respect to surprise.

  \vspace{2ex}
  \noindent
  \textbf{Linear Program for minIP.}
  The following ILP is very similar to a number of linear programs used for other objectives in the context of graph clustering and partitioning, in particular, to one used for modularity maximization~\cite{dt-tocdf-}.
  It uses a set of $\binom{n}{2}$ binary variables $\Xer{u}{v}$ corresponding to vertex pairs, with the interpretation that $\Xer{u}{v}=1$ iff $u$ and $v$ are in the same cluster.
  Let $\mathrm{Sep}(u,v)$ be a minimum $u$-$v$ vertex separator in $G$ if $\{u,v\} \notin E$ or in $G'=(V, E\setminus{\{u,v\}})$, otherwise.
  The objective is to
  \begin{align}
    \text{minimize }\sum_{\{u,v\} \in \binom{V}{2}} \Xer{u}{v} & \label{eq:basic_objective}
 \end{align}
 such that
 \begin{align}
 \renewcommand{\baselinestretch}{1.7}\normalsize
    \Xer{u}{v} \in \{0,1\}, &\quad \{u,v\} \in \binom{V}{2} \\
      \Xer{u}{w} + \Xer{w}{v} - \Xer{u}{v} \leq 1,  &\quad \{u,v\} \in \binom{V}{2}, w \in \mathrm{Sep}(u,v) \label{con:transitivity}\\
    \sum_{\{u,v\} \in E} \Xer{u}{v} = k &\quad \label{con:exactly_k}
 \end{align}
 Dinh and Thai consider the symmetric and reflexive relation induced by $\mathcal{X}$ and show that Constraint~(\ref{con:transitivity}) suffices to enforce transitivity in the context of modularity maximization~\cite{dt-tocdf-}.
 Their proof solely relies on the following argument.
 For an assignment of the variables $\Xer{u}{v}$ that does not violate any constraints, let us consider the graph $G'$ induced by the vertex pairs $\{u,v\}$ with $\Xer{u}{v}=1$.
 Now assume that there exists a connected component in $G'$ that can be partitioned into two subsets $A$ and $B$ such that there are no edges in the original graph $G$ between them.
 Setting $\Xer{a}{b} := 0$ for all $a \in A$, $b \in B$ never violates any constraints and strictly improves the objective function.
 It can be verified that this argument also works in our scenario.
 Hence, a solution of the above ILP induces an equivalence relation and therefore a partition of the vertex set.
 As $\mathrm{Sep}(u,v)$ is not larger than the minimum of the degrees of $u$ and $v$, we have $O(nm)$ constraints over $O(n^2)$ variables.

  \vspace{2ex}
  \noindent
  \textbf{Variants.}
  We tested several variants of the approach described in Sect.~\ref{sec:introduction} to decrease the number of ILPs we have to solve.
  \begin{itemize}
   \item \emph{Exact(E)}: Solve $m$ times the above ILP and choose among the resulting clusterings the one optimizing surprise.
   \item \emph{Relaxed(R)}:   We relax Constraint~(\ref{con:exactly_k}), more specifically we replace it by
    \begin{equation}
    \sum_{\{u,v\} \in E} \Xer{u}{v} \geq k
    \label{con:at_least_k}
  \end{equation}
  Lemma~\ref{lem:basic_props}(i) tells us that the surprise of the resulting clustering is at least as good as the surprise of any clustering with exactly $k$ intracluster edges.
  Moreover, by Lemma~\ref{lem:basic_props}(ii), if $i_p$ is the value of a solution to the modified ILP, $S(i_p, k')$ is a valid lower bound for the surprise of any clustering with $k'\geq k$ intracluster edges.
  In order to profit from this, we consider all possible values for the number of intracluster edges in increasing order and only solve an ILP if the lower bound is better than the best solution found so far.
    \item \emph{Gap(G)}:    Similarly to the relaxed variant, we replace Constraint~(\ref{con:exactly_k}) by~(\ref{con:at_least_k}) and modify~(\ref{eq:basic_objective}) to
    \begin{equation}
    \text{minimize }\sum_{\{u,v\} \in \binom{V}{2}} \Xer{u}{v} - \sum_{\{u,v\} \in E} \Xer{u}{v}
    \label{eq:gap_objective}
    \end{equation}
    By Lemma~\ref{lem:basic_props}(ii), if $g$ is the objective value and $i_e$ the number of intracluster edges in a solution to the modified ILP, $S(k'+g, k')$ is a valid lower bound for the surprise of any clustering with $k'\geq k$ intracluster edges.
    Moreover, by Lemma~\ref{lem:basic_props}(iii), we know that $S(i_e+g, i_e)$ is not larger than the surprise of any clustering with exactly $k$ intracluster edges.
    Again, we consider all $k$ in increasing order and try to prune ILP computations with the lower bound.
  \end{itemize}

\vspace{2ex}
\noindent
\textbf{Case Study.}
     \begin{table}[btp]
   \caption{Number of linear programs solved and running times in seconds of successive ILP approach, different strategies.}
   \label{tab:running_times}
   \begin{center}
   \begin{footnotesize}
\begin{tabular}{|l|cc|cc|cc|cc|}
\hline \multicolumn{1}{|c|}{} & \multicolumn{2}{c|}{\texttt{karate}} & \multicolumn{2}{c|}{\texttt{lesmis}} & \multicolumn{2}{c|}{\texttt{grid6}} & \multicolumn{2}{c|}{\texttt{dolphins}} \\
variant & ILP & t(s) & ILP & t(s) & ILP & t(s) & ILP & t(s) \\
\hline Exact & 79 & 51 & 255 & 1192 & 61 & 470 & 160 & 494 \\
Relaxed & 49 & 21 & 176 & 282 & 42 & 449 & 107 & 163 \\
Gap & 39 & \textbf{15} & 112 & \textbf{205} & 37 & \textbf{401} & 91 & \textbf{147} \\
\hline \end{tabular}
  \end{footnotesize}
  \end{center}
  \end{table}
  Table~\ref{tab:running_times}~shows an overview of running times and the number of solved ILPs of the different strategies on some small instances.
  \texttt{karate}($n=34, m=78$), \texttt{dolphins}($n=62,m=159$) and \texttt{lesmis}($n=77,m=254$) are real world networks from the website of the 10th DIMACS implementation Challenge\footnote{\url{http://www.cc.gatech.edu/dimacs10/}} that have been previously used to evaluate and compare clusterings, whereas
  \texttt{grid6}($n=36, m=60$) is a 2 dimensional grid graph.
  We used the C++-interface of \texttt{gurobi5.1}~\cite{gurobi} and computed the surprise of the resulting clusterings with the help of the GNU Multiple Precision Arithmetic Library, in order to guarantee optimality.
  The tests were executed on one core of an AMD Opteron Processor 2218.
  The machine is clocked at 2.1 GHz and has 16 GB of RAM.
  Running times are averaged over $5$ runs.

It can be seen that the gap variant, and, to a smaller extent, the relaxed variant, are able to prune a large percentage of ILP computations and thus lead to less overall running time.
These running times can be slightly improved by using some heuristic modifications described and evaluated in App.~\ref{app:heuristics}.

\vspace{2ex}
\noindent
\textbf{Properties of optimal clusterings.}
\begin{figure}[tbp]
 \begin{center}
  \subfigure[\texttt{karate}]{\includegraphics[scale=0.2]{karate}}
  \subfigure[\texttt{dolphins}]{\includegraphics[scale=0.2]{dolphins}}
  \subfigure[\texttt{grid6}]{\includegraphics[scale=0.2]{grid6}}
  \subfigure[\texttt{lesmis}]{\includegraphics[scale=0.35]{lesmis}}
    \subfigure[\texttt{football}]{\includegraphics[scale=0.75]{football_nicer}}
  \caption{Optimal clusterings with respect to surprise(colors) and, for (a) to (d), modularity(grouping). The grouping in (e) represents the \emph{ground-truth clustering}, i.e.~the mapping of teams to conferences.}
  \label{fig:opt_sol}
 \end{center}
\end{figure}
\begin{table}[p]
\caption{Properties of optimal clusterings with respect to surprise. $S'$ denotes the surprise as defined by Aldecoa and Mar{\'\i}n~\cite{am-dncss-11}, i.e. $S'(\ensuremath{\zeta}) = -\log_{10} S(\ensuremath{\zeta})$. $S_o$ denotes the clustering with optimum surprise, $S_h$ the heuristically found clusterings from~\cite{am-dncss-11}, if this information was available, and $M_o$ the modularity optimal clustering.}
\label{tab:prop_opt}
\nprounddigits{2}
\begin{center}
\begin{tabular}{|l|r|r|l|r|r|r|r|r|}
\hline instance & $i_e$ & $i_p$ & $S(S_o)$ & $S'(S_o)$ &$S'(S_h)$  & $|S_o|$ & $|S_h|$ & $|M_o|$\\
\hline
\texttt{karate} & $29$ & $30$ & $\numprint{2.02474e-26}$ & $25.69$ & $25.69$ & $19$ & $19$ & $4$\\
\texttt{grid6} & $36$ & $54$ & $\numprint{2.89981e-29}$ & $28.54$ & - & $9$ & - & $4$ \\
\texttt{dolphins} & $87$ & $121$ & $\numprint{9.93152e-77}$ & $76.00$ & - & $22$ & - & $5$\\
\texttt{lesmis} & $165$ & $179$ & $\numprint{1.5385e-184}$ & $183.81$ & -  &$33$ & - & $6$\\
\texttt{football} &  $399$ & $458$ & $\numprint{5.64724e-407}$ &  $\numprint{406.248}$& -& $15$ & $15$ & $10$ \\ \hline
\end{tabular}
\end{center}
\end{table}
Fig.~\ref{fig:opt_sol} illustrates optimal clusterings with respect to surprise and modularity on the test instances, Table~\ref{tab:prop_opt} summarizes some of their properties.
We also included one slightly larger graph, \texttt{football}($n=115,m=613$), as it has a known, well-motivated \emph{ground truth clustering} and has been evaluated in~\cite{am-dncss-11}.
The surprise based clusterings contain significantly more and smaller clusters than the modularity based ones, being \emph{refinements} of the latter in the case of \texttt{karate} and \texttt{lesmis}.
Another striking observation is that the surprise based clusterings contain far more \emph{singletons}, i.e. clusters containing only one vertex with usually low degree; this can be explained by the fact that surprise does not take vertex degrees into account and hence, merging low degree vertices into larger clusters causes larger penalties.
It reconstructs the ground-truth clustering of the \texttt{football} graph quite well.
This confirms the observations of Aldecoa and Mar{\'\i}n based on heuristically found clusterings~\cite{am-dncss-11}; in fact, we can show that for \texttt{karate}, this clustering was already optimal.
\section{Conclusion}
\label{sec:conclusion}
We showed that the problem of finding a clustering of a graph that is optimal with respect to the measure surprise is $\mathcal{NP}$-hard.
The observation that surprise is pareto optimal with respect to (maximizing) the number of edges and (minimizing) the number of vertex pairs within clusters yields a (polynomial time) dynamic program on trees.
Furthermore, it helps to find exact solutions in small, general graphs via a sequence of ILP computations.
The latter can be used to gain insights into the behavior of surprise, independent of any artifacts stemming from a particular heuristic.
Moreover, optimal solutions are helpful to assess and validate the outcome of heuristics.

\bibliographystyle{abbrv}

redpajama_set_name: RedPajamaArXiv


5/27 – We enjoyed our short stay in Siem Reap. The heat of the day was broken by a short afternoon rain (we are in the beginning of monsoon or wet season) so we were able to walk around and see some of the city. When we were in Thailand, there were three seasons; the hot, the wet and the dry. Here in Cambodia there are only two seasons; the wet and the dry. It is always HOT. There are lots of restaurants and bars on Pub Street.
It's a wonder that the electricity works at all in Asia. Every town has a similar challenge with wires.
Although drugs are illegal here, marijuana is exempt because it is an herb used in cooking. It is an ingredient in Happy Pizza and other Happy dishes. I wonder what they put in Ecstatic Pizza?
Isn't this a good name for a laundry? Someone has a sense of humor.
Lots of markets. Anyone need a crocodile?
5/28 – Today we hopped on the bus for the six hour ride to Cambodia's capital, Phnom Penh. This bus had a hostess with a microphone who announced our itinerary in both Khmer and English, and played an endless loop DVD of Cambodian crooners singing love songs to adoring girls in long dresses and beehive hairdos.
About two hours into the trip, the paved road became a dirt road. We understand that as the wet season progresses, many roads become impassable.
We stopped for a break midway through, and Jim wanted a snack. The roadside snack shack specialized in fried bugs (grasshoppers?), so he bought a bagful.
For the record, he said they were crunchy and very tasty, sort of like Fritos. I will take his word on that!
The rest of the ride was uneventful, but the sky was awesome, so here are some cloud pix. As we neared the city, the road became paved once again.
And now we are in our cozy guesthouse with another awesome pool!
The three temples we visited yesterday is called the small circuit. Today we took the grand tour of lesser known temples that show a variety of building styles. Sorry, I don't know the names of all these temples.
There were many fewer tourists on today's tour, so it was much more relaxing for us, and we could really poke around without waiting in lines. Here are some highlights.
Lots of intricate carving – some look like pieces from different carvings have been mashed together.
5/25 – Half an hour north of Siem Reap is a collection of ancient temples known as Angkor. They are actually different cities, built in different centuries (between the sixth and the twelfth) by different kings. When rediscovered by the French in the late 1800s, it was thought that the temples were so intricate and advanced that they must have been built by the Romans. They were built as Hindu temples, and some of the later ones were converted to Buddhist. They are in the process of being restored.
We hired a tuk-tuk at our hotel to drive us out to see them. The road to the temples is well paved – Siem Reap hosts over two million tourists a year who come to visit the temples. Here is our view from the tuk-tuk. Our driver asked right away how old we were. When we told him, he expressed surprise. "Old people in my country could not walk at the temples." He pantomimed a bent old person hobbling with a cane. "You say you are old, but you do not act old." He drove very carefully over the bumps in the road, and drove us right up to the entrance. What a nice young man.
The main attraction, Angkor Wat, lies across a protective moat. The weather was swelteringly hot, and the paths were brimming with tourists.
This temple complex is huge, with many corridors. The rooms are empty and unlit except for where the roof has fallen and the sun shines in. The corridors reminded me of some of the monasteries we visited in Europe.
The walls are decorated with intricate bas relief.
After an hour, we got back in our tuk-tuk and drove to the next temple, at Angkor Thom. The entrance road has a row of figures on either side, holding onto a naga like a tug-o-war. Some of the faces have been restored, others washed away by time.
This temple is known for its towers, which have faces carved on all four sides. There are differences of opinion on what the faces are meant to represent. You have to look hard to see some of the faces.
Amazing. My favorite so far.
Our last temple of the day was Ta Phrohm. In great disrepair, it is best known for the huge spung trees that have reclaimed the buildings for the jungle. The trees were huge and looked like they could walk.
An exhausting and amazing day.
5/22 – Our stay in Japan was too short. Today we took the train back to Osaka, where we met Jim's friend Carl for breakfast. Then it was on to the Kansai Osaka Airport where we arrived at noon. What to do until our flight at midnight? We went back to the posh airport hotel. They have a huge lobby with couches, easy chairs, strong wifi, and a piano that plays by itself 24/7. We settled in for a long afternoon and evening. I got a whole book read!
Midnight flight back to Bangkok, Thailand, then a layover from 4am until our Siem Riep flight at 10am. We got to see the sun rise from the Bangkok observation deck.
It was nice to fly during daylight. Pretty clouds and blue sky.
Getting off the plane in Siem Reap, the heat and humidity smacked us right in the face. Couldn't wait to get back into shorts and sandals. The airport is very Asian.
We got our visas at the airport, where the $30.00 payment was requested in U.S. dollars. As we only had Thai baht, we paid the equivalent of $35.00 each. Bring dollars if you travel here – the Cambodians use their own money as change only. 1000 riel is worth 25 cents. All prices are given in dollars, and the ATMs dispense dollars too. It's been a while since we've seen Andrew Jackson on a $20!
We got a tuk-tuk ride into town, and passed several luxurious resort hotels, which look out of place next to the little shops and shacks on the dusty street. Due to its proximity to the Angkor Wat temples, Siem Reap hosts over two million tourists a year, and accommodates all comfort levels.
Now we are settled in at the Banyan Leaf Hotel, with its lovely pool and sumptuous breakfast buffet, all for $20.00 a night. We had a lovely supper for $1.50, and a beer for 50 cents. You could live here forever!


text:
HOME NEWS TRIBUNE
Parents ordered to pay B-R $38,329 tuition
On 35 occasions, court papers say, the child and his mother were seen at a South Bound Brook address, and each time, the child was taken directly to school.
Parents ordered to pay B-R $38,329 tuition On 35 occasions, court papers say, the child and his mother were seen at a South Bound Brook address, and each time, the child was taken directly to school. Check out this story on mycentraljersey.com: http://mycj.co/2uzWst0
Mike Deak, @MikeDeakMyCJ Published 3:17 p.m. ET July 7, 2017 | Updated 3:39 p.m. ET July 7, 2017
Bridgewater-Raritan High School(Photo: ~File)
BRIDGEWATER - The state has ordered the parents of a second-grader to reimburse the Bridgewater-Raritan School District for a year's tuition because the student did not live in the district.
The state Department of Education has agreed with an administrative law judge's finding in April that the Milltown Road School student lived in South Bound Brook during the 2015-16 school year. The state ordered the parents, identified only by initials to protect the child's identity, to pay the school district $38,329.20 in tuition costs based on a daily rate of $212.94.
According to court records, Walter Kalicki, the school district's attendance officer, received an anonymous email in September 2015 that the child was living in South Bound Brook.
READ: Parents must pay $54,966 to Branchburg schools
PHOTOS: Bridgewater-Raritan High School graduation
READ: Bridgewater-Raritan High School Class of 2017
Kalicki then began an investigation, which consisted of 60 occasions of surveillance.
Kalicki also discovered that the family's two vehicles were registered at the South Bound Brook address.
Kalicki testified that once when he was conducting surveillance, the child's mother quickly changed lanes on the highway, got behind him, tailgated him, then honked her horn and waved at him.
The child's mother testified that she and her husband have lived in the basement of a house owned by her in-laws since they started dating in 1995. The father said he did not live in the house between June and December 2015 because he was undergoing court-ordered rehabilitation for addiction issues.
The mother testified that she stayed at her mother's house in South Bound Brook, because she had pulmonary edema, while her son stays in Bridgewater with her in-laws.
But she said her son wakes at 3 a.m. or 4 a.m. screaming and wanting his mother, a manifestation of separation anxiety. She then drives to Bridgewater, picks him up and returns to South Bound Brook and then, in the morning, drives him back to school in Bridgewater.
That happens four to five times a week, she testified.
However, in an interrogatory before the hearing, the mother said that it happened only about 10 times in two months.
The grandmother confirmed her daughter-in-law's story, saying the child would wake up screaming, "I need mommy," 14 to 15 times a month. .
Administrative Law Judge Dean Buono found that the testimony given by the parents and grandmother "was not credible" because they did not agree on the number of days that they boy experienced separation anxiety.That inconsistency made their testimony "suspect," he ruled.
However, the judge found Kalicki's testimony to be "especially credible and persuasive."
Buono concluded that the mother would keep the son with her in South Bound Brook because of his father's substance abuse.
The judge ruled that it was "obvious" that the parents were attempting to "sell" their version of the facts.
Staff Writer Mike Deak: 908-243-6607; mdeak@mycentraljersey.com
Read or Share this story: http://mycj.co/2uzWst0
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Fans at home enjoyed the street dancer's dramatic facial expressions in response to the acts.
The Greatest Dancer host Jordan Banjo scolded the studio audience after they failed to vote through an act which he deemed "dope".
Street dancer Banjo, part of the group Diversity, reprimanded the crowd after Mindtrick failed to secure 75% of their vote to move through to the next round of the BBC One programme.
At least three quarters must switch on their light to open the mirror-wall separating the act and the studio.
Tweeting after, Banjo admitted he was still thinking about Mindtrick's missed chance.
He wrote: "I can't lie, I'm still stressed about Mindtrick not going through.
Fans at home, however, appeared more interested in Banjo's overly dramatic reactions to the evening's acts.
One claimed the reason they loved the show was because of the presenter's varied and emotive range of facial expressions.
Others celebrated Banjo's positive attitude, suggesting it made a change to see such optimism on TV.
#GreatestDancer It's so nice to see positivity on #TGD @Jordan_Banjo always keeps it upbeat and he's always 100% with all the dancers. Keep up the good work fella!
A third focused on both Banjo and judge Matthew Morrison, noting that they had both pulled amusing faces throughout the show.


YEKATERINBURG: Substitute Keisuke Honda equalised with 12 minutes left as Japan twice pegged back Senegal in a thrilling 2-2 draw on Sunday that leaves World Cup Group H wide open.
All eyes will now be on the other group match later in the evening between Poland and Colombia following this stalemate at the Yekaterinburg Arena.
As it stands, Japan and Senegal have four points after two games, with Colombia and Poland on zero, though they have played a game less.
Midfielder Honda was the hero for Japan, scoring the deserved leveller after goalkeeper Khadim N'Diaye flapped at a cross.
Senegal, who reached the quarter-finals in the country's previous World Cup appearance in 2002, needed just over 10 minutes to go in front.
Japan failed to deal with a right-wing cross with Genki Haraguchi nodding the ball straight to Senegal defender Youssouf Sabaly in the box.
He fired at Eiji Kawashima and the goalkeeper made a mess of it, punching the ball into the lurking Liverpool star Sadio Mane.
The ball bounced off the striker and into the net for his first goal at this tournament — cue raucous Senegal celebrations with Khadim N'Diaye racing the length of the pitch to join in.
This match was billed as the pace and power of Senegal against the tactical and technical nous of Japan, who took a gamble and replaced Vahid Halilhodzic with Akira Nishino as coach just weeks before the World Cup.
Backed by a vocal Japanese following who never stopped singing and with the locals also on their side, Japan were now the better side after a nervous start.
Mane found himself at left-back at one point as the Blue Samurai threatened to slice their way through, in what was growing to be an absorbing contest in the warm Yekaterinburg evening.
Aliou Cisse, Senegal's likeable coach and their skipper in that World Cup run in 2002, sent his substitutes to warm up five minutes into the second period as Japan began the half the better.
Working down the Africans' left side, the 26-year-old talisman Mane was only a sporadic danger.
Japan should have taken the lead on the hour but Yuya Osako, the match-winner against Colombia, somehow missed the ball when unmarked inside Senegal's six-yard box.
Inui then struck the bar from distance after the Senegal defence went AWOL.
On 71 minutes, Japan allowed a scuffed cross to go right across their goal and defender Moussa Wague arrived all alone at the far post to grab what looked like being an unlikely winner.
But Honda, the former AC Milan midfielder who had only been on the pitch six minutes, hit the late equaliser to leave Group H up for grabs.


Is your home starting to look tired, worn, or outdated? Then maybe it's time for a total overall. If that's the case, a seasoned Interior Design Toronto team should be called upon to transform your home to create a stylish, sophisticated, up-to-date abode that you can be proud of.
Of course, Interior Design has a lot to do with improving the aesthetics of your home. But it's not just reserved to that. Interior design is a lot more than about how your home looks. It's also about finding ideal design solutions for your home while enhancing the flow and functionality of the space. At its very crux, Interior Design is meant to appeal to your visual senses and enhance your overall quality of life.
Many homeowners may try to tackle the Interior Design process on their own, but often find it tedious, cumbersome, and utterly confusing. Without thorough training or a keen eye for creativity, coming up with a cohesive look in an interior can be nearly impossible for someone with little to no experience in the world of interior designing.
That's when it's time to call in the experts. Interior designers and decorators are fully trained and educated in their respective fields and have all the tools and tactics needed to create the perfect look for your home. They're also a creative and imaginative bunch and have the ability to visualize how a space can work for each client they work with.
Everyone has their own unique tastes, and interior decorators and designers are among them. Of course, they may have their own ideas of what they would want in their own spaces, but that doesn't mean they'll push these ideas on to you. Everyone is different, and Interior Design professionals totally understand that.
That's why they take the time to get to know you and develop an understanding of your tastes and needs. They'll get to know you and your family's lifestyle, and will take the time to meander through your home to get a feel of what needs updating and what can be left alone.
The consultation phase of the Interior Design and Decorating process is a critical one. It's at this point that the professional will ask all the pertinent questions, and allow you to do the same. This is the time that you'll have a chance to communicate your needs and tastes so that the design strategy encompasses it all and takes it into consideration. Without a consultation, designers and decorators will not have a chance to fully grasp exactly what it is that you're looking for.
When it comes time to revamp your home, every detail and component is considered. Whether you need new floors, new wall paint, new furniture, new cabinets, new light fixtures, and beyond, Interior Design is the way to go. No detail will be left untouched. Every component of a space needs to be carefully considered in order to make sure that space is pulled together evenly and appropriately from every angle.
Interior Design is a critical component to transforming a space properly and appropriately. With a proper plan and strategy in place, an interior can look unbalanced and disheveled. That's why a trained eye from a professional in the world of Interior Design and decor is critical to making sure that proper cohesion exists in the final product.
At Hope Designs, we help homeowners create the perfect interior that goes well beyond their wildest dreams. We take the time to carefully examine each client's home and ask the right questions to ensure we extract all the information needed to create the perfect product.
If you're considering changing things up in your home, be sure to get in touch with the professional interior decorators at Hope Designs today!


text:
Resolution Opposing Sensenbrenner Bill (H.R. 4437)
REFORMA Legislative Committee
Updated 4/12/06 1:30 PM
Whereas, REFORMA's main and ongoing mission is to promote library and information services to Latinos and the Spanish-speaking,
Whereas, REFORMA is on record in support of immigrants' rights,
Whereas, anti-immigrant measures, such as Sensenbrenner Bill H.R. 4437 deleteriously affects the entire Latino community, regardless of legal status or citizenship status,
Whereas, the Sensenbrenner Bill - H.R. 4437 is totally punitive in trying to make felons out of undocumented immigrants, denying them any human, civil, working, or due process rights; seeks to make criminals out of people who aid undocumented immigrants, including clergy, health care workers, teachers, and possibly librarians; gives no recognition of the significant contributions immigrants make to our local and national economies and to our communities; and was passed by the United States House of Representatives on December 16, 2005 by a vote of 239-182 http://www.nclr.org/content/policy/detail/35618/ and has been sent to the Senate, Whereas, Senate Judiciary Committee Chair Specter (R. Pennsylvania) has drawn upon existing bills and the Sensenbrenner bill into a draft bill, the Comprehensive Immigration Reform Act of 2006, which is currently being debated in the Senate,
Therefore be it resolved that, REFORMA is against Senator Specter's bill, the Comprehensive Immigration Reform Act of 2006
Be it further resolved that, REFORMA will take immediate action to alert the Senate about their position on this legislation
Be it further resolved that, REFORMA will alert and encourage their members to contact the Senate in opposition of this and any future similar anti-immigrant legislation
Be it further resolved that, REFORMA will alert and encourage their allied ethnic library associations and ALA to oppose anti-immigration legislation,
Be it further resolved that, REFORMA will alert their members to take an active part in educating their communities about immigration and social justice for all immigrant communities,
Be it further resolved that, REFORMA will promote libraries as safe sites and venues for citizen education about immigration issues,
Be it further resolved that, REFORMA will encourage library workers to act as advocates for the education of undocumented immigrants about their human rights.


text:
United Nations Declares Invest India the winner of the Investment Promotion Award 2020. Click here for Live Updates >>
The Genome India Project
Taking inspiration from the Human Genome Project, this year, the Department of Biotechnology (DBT) initiated the ambitious "Genome India Project" (GIP) on 3rd January 2020. The GIP aims to collect 10,000 genetic samples from citizens across India, to build a reference genome. This is no mean feat, given that the genome contains all the genetic matter in an organism, i.e., the complete set of DNAs.
Whole-genome sequencing and subsequent data analysis of the genetic data of these 10,000 individuals would be carried out. This would aid our understanding of the nature of diseases affecting the Indian population, and then ultimately support the development of predictive diagnostic markers. This is a landmark initiative, particularly because it would bring valuable addition to existing genome research, which has so far been limited to the Western context. It allows India to draw upon its tremendous genetic diversity, given the series of large migrations historically, and thus, add greatly to the current information about the human species.
Through whole-genome sequencing, the plan is to build an exhaustive catalogue of genetic variations for the Indian population. This would aid in the designing of genome-wide association chips which will facilitate further large-scale genetic studies in a cost-effective manner. Furthermore, it would also open new vistas for advancing next-generation personalized medicine in the country, paving the way for predicting health and disease outcomes and modulating treatment protocols based on the genome sequences. The initiative would also support the development of targeted preventive care, as it has the potential to help identify those population groups which are more susceptible to various risk factors for certain diseases. For instance, if a region shows a tendency towards a specific disease, customized interventions can be made in the region, accordingly, leading to more effective treatment overall.
This project is led by the Centre for Brain Research at Bengaluru-based Indian Institute of Science, which acts as the central coordinator between a collaboration of 20 leading institutions, each collecting samples and conducting its own research. Institutes involved include the Indian Institute of Science (IISc) in Bengaluru as well as several Indian Institutes of Technology (IITs). For conducting the project, investigators in hospitals will lead the data collection through a simple blood test from participants and the information will be added to biobanks.
Some of the priority areas are Precision health, Rare genetic disorders, Mutation spectrum of genetic and complex diseases in the Indian population, Genetic Epidemiology of Multifactorial Lifestyle Diseases, and Translational Research.
This initiative reflects India's progress in gene therapies and precision medicine, and its movement towards emerging next-generation medicine which yields the possibilities for greater customization, safety, and earlier detection. This initiative would help lay the foundation of personalized healthcare for a very large group of persons on the planet.
https://sites.google.com/site/wealthprojects/genomevally-biotechhubofindia
https://www.drishtiias.com/daily-updates/daily-news-editorials/genome-india-project-1#:~:text=What%20is%20the%20Genome%20India,agriculture%20and%20the%20life%20sciences.
https://ghr.nlm.nih.gov/primer/hgp/genome#:~:text=A%20genome%20is%20an%20organism's,cells%20that%20have%20a%20nucleus.
http://dbtindia.gov.in/schemes-programmes/research-development/medical-biotechnology/human-genetics-genome-analysis
https://pib.gov.in/newsite/mainpage.aspx
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At Rozenhart Family Chiropractic, we address the cause of your pain, not just the symptom. Call today!
Welcome to Rozenhart Family Chiropractic located in San Jose California. At Rozenhart Family Chiropractic we take care of every person with a whole body approach, finding the most efficient way to get rid of your problem and making sure it doesn't return! We love taking care of people with headaches, neck pain, shoulder pain, sciatica, irritability and fatigue.
We chose San Jose, California as our place to practice because we both attended Palmer College Of Chiropractic -West here in San Jose. Growing up in Canada, we endured endless winters with tons of snow! Upon graduating and falling in love with the weather here in the south bay, we made the decision to stay here and start our practice. We love the pace of life here in San Jose and love the ability to escape the craziness into the mountains or the beach if we need to!
We are located at the corner of Branham and Meridian in the Cambrian neighborhood of San Jose. We are located in Meridian Park Plaza with Lunardi's and CVS, kiddy corner from Branham High School.
If you have been reading this far, it's likely that you have something we can help you with. Our promise to you is that we will give you the most comprehensive evaluation and let you know exactly what we will be doing before we do it. Take advantage of our new patient offer on this page and get scheduled in our San Jose office today. Get back to doing what you love, get back to your life! Relief, better sleep and more happiness are just a phone call away!
One common misconception we hear in our San Jose office is "once you go you have to go forever!". This couldn't be further from the truth. Exercise? You can stop anytime! Brushing your teeth? You can stop anytime! Your body is not physically addicted to chiropractic, but it sure helps everything work better- most people choose not to stop! Another misconception we hear in our San Jose office is that adjusting is painful and scary! In fact, it's the opposite! We take care of infants and have many many techniques that are gentle and not painful at all. The technique we choose for you will be designed to give you the best results in the shortest amount of time.
What sets us our office apart from other offices in San Jose is that we are a true family practice, we are sisters and you get the benefit of both of our expertise. We also have advanced training in pediatric care,maternity care, personal injury work and have over 35 years of practice experience combined.
Whether your needs are related to injuries from a car accident, have poor posture, or have chronic issues from sitting all day in front of a computer….we can help.
We take care of people who have headaches and neck pain. San Jose is known for people spending incredible amounts of time on computers and electronic devices. This unfortunately leads to many issues in your head, neck , shoulders and upper back. Because your lifestyle is unlikely to change, we have developed strategies to help you adapt as best as you possibly can to these types of chronic stresses. Low back pain is another common, but not normal, condition that we see in our office. Again, too much sitting, and a sedentary lifestyle can be triggers to this debilitating problem. We have also seen extremely active people with the same issue. Stress on the body whether it's a one-time accident or consistent lifestyle stress can cause problems and we can help.


That Lance Armstrong is a naughty chap aye? I wonder what Lord Lance could do on a weighty touring bike… for that matter I wonder what any of the peloton riders could do to Mike Halls around the world record or Scott Napiers 125 day Deadhorse to Ushuaia record. Mark Beaumont is nothing compared to those athletes, they're the real deal, not just TV personalities. Although what could Beaumont do if he was EPOed up to his eyeballs? Maybe he was, maybe his camera crew were giving him blood transfusions… everyone in TV is on something.. right???
When I'm not excited and totally engaged with my riding my mind often decides to go on its own journey. Leaving Santiago I continued my great southerly surge, cycling robotically and branching out on wild mental tangents in the process. Trying my darndest to avoid the Pan American highway, which down here is busy and really ugly, whilst aiming for nothing other than distance towards my next object of exploration, the Chilean Lake District, I sped away from Santiago. Hot blue sky summer days punctuated by overpriced nights in irrelevant towns and the push to progress accompanied by the sting of lactic acid. Riding hard and fast I knocked off some distance and didn't have a half bad time doing it.
Life can't be a continuous string of prestige routes, sometimes those bricks need some mortar pasting between them. The bulk of this latest stretch of riding from Santiago to Ralco was just that, mortar; grey, dull, hardly noticed but vital to the bigger picture. Although not strictly my cup to tea, riding like this can still be a lot of fun. I love to ride my bike, wherever or however. Sometimes I lose this passion to attitude but I always know it is good to be made to appreciate what we have rather than obsess over what we may want. As I made my way down the Chilean map the ride evolved towards what I usually crave; pavement gave way to ripio, dense woodland sprung up around me and snow-capped volcanoes appeared on the horizon. It is to experience this evolution that I insist on riding the more mundane stretches… how many times do I hear myself proclaim 'context is king'?
Leaving Santiago on a Sunday is no accident, discovering large parts of my exit route closed off to motorised traffic is a very fortunate coincidence.
About 15 km short of Ralco I find a friendly restaurant owner who lets me camp behind her house, feeds me and talks about the other touring cyclist she had come through… an English guy on a bike like mine who stopped the year before.
There really aren't too many options for a direct route south from Santiago. With a local road option often bordering the Pan American highway it's seldom that you're forced onto the dreaded Ruta 5 itself. This is a darn good thing as it is a much busier and more threatening road than the one I encountered north of Santiago. If you want to stay in the fruit-growing Colchagua and Maule valley areas and not deviate down to the coast then route finding can be a frustrating task. There are usually a plethora of smaller roads each side of Ruta 5 but they seldom link up in a way that works. If you really want to avoid the pavement then you probably can in many instances but I don't honestly believe there is any value in prolonging the tedium of riding through what is essentially a flat and featureless land.
Buy a cold Coke at every opportunity… there has to be some upsides to civilization!
hope u are fine mate.
how is the south ?!?
everything good in santiago – super hot !!!


Named for the three small islands off Punta Mita's coast, Las Marietas is a casual spot for authentic Mexican and international cuisines. Regional specialties are served beneath the three open palapas—little beach houses.
Allowing breathtaking Pacific views, its inviting alfresco atmosphere is conveniently located next to the resort's family pool.


We have a little vegan boy smashing his way around our apartment. At 17-months, he can pretty much pick up any piece of furniture and toss it across the room. He runs into things full-speed and eats an entire tray of food by the fistful. He is 100% vegan.
We are expecting another vegan baby at the end of next month so, hopefully, that will give Little Hulk enough of a distraction that he'll settle down. Meanwhile, the only thing he sits still for (besides food), is a good book.
Recently, friends of ours (one of which has a vegan blog here), gave us a copy of Lois Ehltert's wonderful board book, "Eating the Alphabet." Lois Ehlert's Caldecott-winning children's books are alive with vibrant colors and her collages are just beautiful. Hailing from Wisconsin, so many of her books are a natural part of every infant's library that they traditionally share a shelf with Eric Carle's "Very Hungry Caterpillar." The big, noticeable difference between Carle's gastronomic tome and Lois' "Eating the Alphabet" is that one book is vegan and the other … well, sorry caterpillar fans, is not.
As vegan parents, we are always prepared to replace un-vegan passages with vegan phrases: "This Little Piggy went to market … this Little Piggy stayed home … this Little Piggy had kale salad …" You get the idea.
The interesting thing about "Eating the Alphabet" that I think is worth pointing out is that it doesn't have to be edited. Lois Ehlert takes us from A to Z without once stopping at "C' is for chicken, or "P" is for pork, or "W" for water buffalo. And to be even more specific, the author didn't use cheese or eggs (which also shouldn't be consumed).
To some, this might be overlooked but to me there is a very powerful message in this book that resonates with me every time I read it: animals are not food.
There is no valid reason or argument to eat animals and anyone who continues to do so, is not clearly not making the connection. Animals are our friends and we don't eat our friends. At least I don't.
Questions About Being Vegan? Here Are the Answers.
What's Your Favorite Vegan Blog? This One, Of Course! Let @VegNews Know!
I didn't know you already had a little one and congratulations about the new one on the way! Thanks for sharing this book. I would love to get a copy for our house. I'm sending your wife good vibes. I hope y'all have an amazing birth!
Thank you, Celeste. We are very much looking forward to a newborn so we can sleep even less.
I love that book, so glad you are getting good use out of it!
It's a great book to read to your energetic toddler when you're near-comatose with new-infant-sleep-deprivation. Cheers. I hope all is well up there in Ithaca!
Thank you! Yes, vegan baby #2 is due any day! Better buy stock in Gimme! Coffee.
Jealous that you (may?) have a baby and I don't! I've noticed your absence, but thankful that you throw a few crumbs out for us anyway.
Yes, another little vegan entered the world on September 29. Little Paisley is just 6 lbs. but the most beautiful baby ever.
So glad your dite found me!