text:
History Made in Twitter Moot
(Pictured above: UVIC Law TweetMooters Matthew Nefstead and Jenn Cameron work under the glare of CTV's camera. Image credit: Kim Nayyer/University of Victoria's Diana M. Priestly Law Library)
History has been made. The first Twitter Moot Court was officially brought to a close at 12:30p.m. (PST) yesterday following an hour of furious legal tweeting, hash tagging, and @mentioning. Although we might be decades away from actual cases being tried in the twittersphere, yesterday's moot provided some insight into how social media can interface with classic legal debate.
The Twitter Moot commenced with submissions from two Skunkworks sponsored tweeters, Jenn Cameron and Mathew Nefstead, representing the University of Victoria. Cameron and Nefstead argued on behalf of the Province of British Columbia in the environmental case West Moberly First Nations v. British Columbia. Cameron started her submissions by indicating that she would "briefly" state the facts of the case. This was no understatement. Limited to 140 characters or less, Cameron and all other participants were forced to find creative ways to effectively lay out the points at issue.
The tweeters, however, had clearly planned ahead. Certain tactics were adopted that allowed for the formalities of the courtroom to be brought to the world of social media. The three Twitter Moot judges, which included University of Calgary Law professor Kathleen Mahoney, lawyer-turned novelist William Deverell, and legal social media guru Omar Ha-Redeye, were content to be referred to as ML rather than My Lord. Likewise, the participants modified the formal designation of opposing counsel as "my Learned Friend" and adapted the much simpler LF.
Conversely, the informal atmosphere and peculiar affectations of twitter invariably played a part in the way the case was discussed. Judge Omar Ha-Redeye began proceedings with the tweet, "Let's get down," which is an effective and lexically economical way to begin a Twitter Moot, but unlikely to catch on in the Supreme Court of Canada. At one point, Mathew Kalkman (tweeting for Team UBC and representing the Province of Alberta in the moot), argued his side by stating that an alternative interpretation of the discussed case would constitute a "hashtag fail." Kalkman, the most comedic advocate on the day, also managed to include tweets referencing the Vic Toews/Vikileaks story, his own book on liberalism, blatant (and funny) pandering to a couple of the judges, and a great in-character rant all within his team's 10-minute time allotment.
Despite the fun that was had, the participants also effectively and seriously argued the case at hand. Nikki Peterson from Team Osgoode included a great Google Map to showcase how close the First Nation reserve lands were to various major developments impacting the area. At times, several concurrent tweets were required to convey a single argument and a veritable storm of tweets ensued. The efforts were clearly appreciated by the Twitter community as the hashtag #twtmoot became a trending topic in Canada at around 11:30a.m. PST.
Following much deliberation it was decided that the team from Osgoode School of Law, representing the West Moberly First Nations, had earned the top prize. However, Skunkworks is proud to announce that the team from University of Victoria won the People's Choice award by garnering the most online votes in a West Coast Environmental Law poll asking which Twitter Moot team most effectively argued their case.
All things considered, it was a fun day in legal education and an interesting exploration into the increasingly ubiquitous world of social media. Skunkworks congratulates and appreciates the efforts of all participants and would like to extend particular thanks to the folks at West Coast Environmental Law who conceived and organized the event. Kudos on a job well done.
Posted in: Digital Marketing / Legal Profession


text:
Ambrysus relictus är en insektsart som beskrevs av Polhemus 1994. Ambrysus relictus ingår i släktet Ambrysus och familjen vattenbin. Inga underarter finns listade i Catalogue of Life.

Källor

Vattenbin
relictus

redpajama_set_name: RedPajamaWikipedia


EIBTM will launch IBTM Knowledge Virtual Centre, a series of live sessions streamed across on the internet.
The virtual conference will stream five education sessions on 28 November from 9am (CET) as they happen live at EIBTM to an audience of 150 delegates.
The Hybrid Conference area will also feature a virtual exhibition hall, resource centre and networking lounge.
The Hybrid Event will feature speakers from The Mark of a Leader, The Right Solution, Greenwich University and My Meeting Professional (MMP).


text:
Shetler becomes a Volunteer
By MTB, 04/12/19, 10:30AM EDT
Sumner County's Josh Shetler signed to play rugby at the University of Tennessee on Wednesday at a ceremony at Beech High School.
Josh Shetler (6'1" 180 lb), from Cottontown, TN, is the son of Scott Shetler and Laurel Jordan and a senior at Beech High School in Hendersonville. Josh is currently playing center for the Sumner County All Blacks while having also spent time at flyhalf and flanker. He projects to compete at center at the collegiate level.
"Josh has been a very important part of our program for 4 years and I look forward to seeing him pull on the orange and white for Tennessee. He has been the tip of the spear for us on attack and proven to be very capable in the contact area."
Brian Silkwood, Head Coach Sumner County All Blacks
"Looking forward to getting Josh on campus. He brings high energy and a physical style of play to the field which will serve him well at Tennessee."
- Marty Bradley, Head Coach University of Tennessee
Josh will study Business at the University of Tennessee.
Tag(s): Recruiting Scholarships Volunteer News Archives

redpajama_set_name: RedPajamaCommonCrawl


The predominant causes of late graft loss after orthotopic cardiac transplantation are graft rejection, coronary artery disease, and infection.
The histopathological dianosis of acute rejection of cardiac allograft is based on cellular phenomena such as lymphocytic infultration with myocyte damage. The symptoms may be very different depending on the rejection grading scale. Usually, this form of rejection is resolved with stabdard antirejection therapy: steroid pulse therapy, increasing doses of Cyclosporine A or in the case of therapy-resistance rejection, with monoclonal antibodies.


We're finally here, at the threshold. Crimson Son has entered final revisions and is on track for the June release. My editor, Heather, bloodied things up a bit but not too badly. She rounded the manuscript out with some insightful comments which harkened back to reviews from my beta readers and had me freaking out a bit. I thought I'd fixed those issues but apparently, a couple were still lurking.
If I have a kryptonite (besides the whole its / it's thing, sheesh, going to defuse that issue right…about…now…) it is that my desire to be mysterious and clever at times translates into "where the f$%& did that come from?" for the reader. It 's a delicate balance between making the reader feel they are participating in the discoveries and not leaving them in the dark. I've shored that issue up however and it all comes together in the end in a nice little creepy family reunion.
And I have a bit of a tease as well. It involves showcasing Crimson Son in the medium the novel pays homage to. A few scenes from the novel recreated in good ol' fashion pen and ink by an incredibly talented artist are in the works.
I can't wait! Stay tuned, true believers!
Thanks! Just a few more months. Keep an eye out here and spread the word, I'll be adding some artwork, cover reveal, and sample chapters prior to release.
awesome cannot wait for the artwork.
Reblogged this on hughiegibson author.


text:
All-Star Flirtation
Maturity, sexuality, and intellectuality in Bull Durham
by Matt Hanson
in Features • 01/03/2019
At first glance, Bull Durham doesn't seem like the kind of movie that would get the Criterion Collection treatment. A cinephile's delight, Criterion is usually associated with more esoteric films: their staggeringly comprehensive editions of the works of Ingmar Bergman and Josef Von Sternberg are alluring indeed, but not what you'd call mainstream fare. Kudos to Criterion for being open-minded enough to notice how progressive, subversive, and worldly-wise Bull Durham really is. Brilliantly written by former minor leaguer Ron Shelton, the film shows authentic affection and respect for America's pastime but doesn't shy away from the deeper questions that go beyond calling balls and strikes. Bull Durham is a thinking person's sports movie, containing a deep, unapologetically intelligent and mature understanding of the world both inside and outside the ballpark.
We follow the The Durham Bulls, a very minor league baseball team based in North Carolina. Most of the players know that they aren't destined to be superstars, nor are they meant to be, which is mostly just fine by them. They're in it purely for the love of the game, enjoying the laid-back camaraderie of athletes, content to horse around beneath the bright lights on warm summer evenings. Choosing to focus on this often-ignored aspect of the sporting life is particularly pointed, since the mid '80s was a time just before baseball (and sports culture at large) got a metaphorical (and, it must be said, quite literal) shot in the arm, causing salaries and egos to run amok. The amiable Durham Bulls aren't obsessively driven to be champions, which flips the implicit triumphalism of most sports movies on its head right off the bat, so to speak.
What Bull Durham is far more interested in is exploring how a player (and, by implication, a person) must learn mental and emotional discipline in order to grow. The film is much more concerned with questions of maturity, how to train the mind equally as much as the body, than merely winning at all costs. The cocky, hotshot rookie Ebby "Nuke" LaLoosh, played with knowing ridiculousness by Tim Robbins, has a fastball that just about breaks the sound barrier but, crucially, he doesn't know the first thing about controlling it. Nuke is just as liable to strike out the side as he is to start beaning people in the stands, which might be entertaining for a little while but puts the kibosh on any hopes of helping the team, let alone his making it to the big leagues, aka "the show."
Enter Crash Davis, the worn-out veteran catcher who sardonically but accurately announces himself as "the player to be named later." Davis knows the game with a journeyman's expertise but has had to come to grips with the hard fact that he just doesn't have the stuff to make it to the show. He's reluctantly tasked with mentoring the doofus LaLoosh in the real rules of the game. Davis is clearly the star of the movie: he provides old-school gravitas as well as some of the script's best lines, from a screenplay chock full of great ones. Costner is serviceable in the role, but pretty much anybody would have been if given a script this good. I'm sorry, but Costner's cheekbones are more expressive than any of his acting choices. Dances with Wolves, which Costner produced and starred in the year after, hasn't aged very well and proves once again that winning a bunch of Oscars doesn't mean jack as far as cinematic quality is concerned. Let's not even go into the endlessly heckleable Waterworld or the four-hour insomnia cure The Postman. Some actors are able to portray stoic, world-weary gravity through accrued grit and honed talent — others were just born looking the part.
Speaking of looking the part, Susan Sarandon's sophisticated lady Annie Savoy is the most complex character in the movie, which is another subtly subversive choice. Showing the woman as the empowered one in a love triangle isn't something we see all that often. Particularly for a movie about a masculine institution like baseball, giving a woman this much agency over her sexuality and not punishing her or making her apologize for it is quite a surprisingly feminist, progressive gesture. An outspoken progressive activist, Sarandon once said that this was the reason why she lobbied so hard to land the role.
Annie has an interesting relationship to the Bulls. Every summer she's in the stands with her binoculars, expertly filling out box scores, rooting hard, and knowledgeably critiquing the ballplayer's technique. She selects one player per year to take to bed, but her involvement doesn't end in the purely carnal. Annie is unabashed about fulfilling her (occasionally rather kinky) desires, but Sarandon imbues her sensual Southern belle with a sense of class, taste, and coolly subtle dignity. Deeply literate, Annie educates and trains the young recruits in the finer things in life, reading them Walt Whitman's poetry in bed. Wittily redefining Whitman's phrase, Annie is the self-styled "teacher of athletes" and makes men out of gawky rookies by educating their minds and their bodies simultaneously. It's a very grown-up attitude towards sexuality that runs rings around most movies' (particularly sports movies) puerile, win-the-trophy approach to sexuality. Annie is a flesh and blood woman, with brains to match her earthy sex appeal, not The Natural's preternaturally supportive angel or a man-child's wet dream, as in Fever Pitch.
This is another way in which Bull Durham stands head and shoulders above most other movies of its type — it's not afraid to show that sports require brainpower to function at their best. The characters (apart from Nuke, of course) are consistently shown to be smart, funny, and conscientious, precisely because of and not despite the fact that they play sports. It's a wonderful insight that says a lot about the true nature of all sports — watching and playing them can be a very intellectually fulfilling experience. Amid all the hoots and hollers, there's a chess-like pattern of complex strategy unfolding under immense pressure.
Despite what the uninitiated might assume, baseball can be intensely cerebral. Minute calculations are of the essence, requiring athlete and audience alike to be constantly analyzing the ramifications of different issues: whether a carefully thrown ball might break two inches to either side, the angle at which a batter might be more or less likely to hit in a particular direction, where and how far out the fielders should be positioned if they do. On base percentages, earned run averages, slugging percentages, and many other factors. A great deal of the game is based in failure; it's well-known that a star hitter only succeeds about 30 percent of the time, at best. Legends can only dream of getting anywhere near 40. As Bart Giamatti, former baseball commissioner (and Yale literature scholar) once said, baseball is a game that is designed to break your heart. So much depends upon a series of instantaneous decisions, seemingly small, any or all of which can make or break a game, a series, or a championship. The problem-solving complexities of teamwork are essential, and a ball club is nothing without it. When Crash tells Nuke not to strike people out because it's "fascist" and to throw ground balls because "it's more democratic" this is part of what he's getting at.
But, charmingly, Bull Durham is about winning hearts and minds, not just ballgames. Preferably, the former through the latter. What keeps the plot moving isn't the Bulls' playoff chances but the highly amusing verbal pas de deux between Annie and Crash. Nuke's all about the hookup with Annie, but he has no concept of anything existing beyond it. Crash has been around long enough to know that it's not worth opening up for too little, and his mature refusal to let Annie play mind games with him is a genteel challenge that only intrigues Annie all the more, which speaks well for both of them. It's a Shakespearean insight about romance reminiscent of Much Ado About Nothing — watching two smart people banter who are far too self-assured and quick-witted to succumb to one another's shenanigans is always fun. The classic, endlessly quotable monologue that Crash gives as a response to Annie's manipulations is a perfect example of all-star flirtation in action.
Despite being a man's man, Crash isn't above opening up and letting Annie know that he's not afraid of being sensitive, even sensuous, or that he happens to have a curious and well-stocked mind. Crash has the expected opinions about AstroTurf, the infield fly rule, and the value of good Scotch but can also debate the dubious merits of the novels of Susan Sontag (he's right about this, by the way — after seeing the movie I just had to find out for myself, and although Sontag was a world-class intellect and a superb critic, her fiction sadly fell below her own high standards). Crash doesn't apologize for who he is, nor does he hide his intellectuality. His confidence is a result of his maturity as a person rather than his social status. After giving Annie a glance at his inner life, he walks right out her door, cracking that he isn't interested in a woman who would be interested in a "boy" like LaLoosh. He shows his own value by having standards, a form of self-respect that the showoff tendencies of our culture of mass consumption have yet to grasp.
Naturally, Annie and Crash eventually get together but their romance doesn't seem forced. Crash and Annie both resist the urge to let their pride keep them apart, but their finding love isn't treated like a consolation prize. Nuke learns the lessons Crash has to teach and advances to the big leagues with a ready line of media-friendly bullshit. We know that Crash taught him that amusing string of cliches, which we see him cockily repeating as if they were his own. Crash is too busy with Annie to envy Nuke's fame and fortune. Instead, we see how the marriage of true minds is the real victory. For all of its palpable love of the game, Bull Durham ultimately makes the winning suggestion that it's better to live happily and humbly than to be a hollow superstar, reminding a macho, winner-take-all culture that growing up and finding love means more than putting points on a scoreboard ever will. •
All illustrations by Isabella Akhtarshenas.
Matt Hanson lives in New Orleans and writes for The Arts Fuse, Boston's online independent arts and culture magazine. His work has also appeared in The Baffler, The Millions, and 3 Quarks Daily, and other places. He can usually be found in the nearest available used bookstore.
A Star is Made
2006. Just a bit more than ten years ago. Two mega blockbusters were released in…
Like a Fox
Eytan Fox, one of Israel's most acclaimed filmmakers, turns 52 today. When I interviewed him…
The Posthumous Star
We know the story. Van Gogh died having only sold one painting during his lifetime.…
Hollow Words
− 4 = two


An Olympic judge rushes into the barbershop. "You need to help me!" he pleads. "I have to judge in 10 minutes, but I've been traveling so much I look just awful." The barber looks at him carefully. "Your hair is quite long. I'll need to cut it. And you'd look silly with a beard and such short hair. You're in luck, as I've just had a cancellation. Have a seat!"
The barber does his work and goes to collect the payment. "Oh dear," said the judge. "I haven't any local currency to pay you with." Luckily, he and the barber were able to work out a deal. The judge, having fully paid the barber, leaves to go judge his match.
On his lunch break, the barber was watching the Olympic games and sure enough there was the judge, attention gazed on the performers, looking for any mistakes he could find.
Why was the judge looking for mistakes so intently?
What was the deal between the barber and the judge?
The judge is an honorable judge. There is no foul play.
The judge and the barber will never interact again. The deal is fully concluded in a mutually acceptable way.
Currency is not involved in any way.
Hmm, very open ended question.
The barber shaved his shops name onto this judges head. Judge looked intently to ensure the back of his head was always to the TV viewers camera.
He was looking for mistakes in peoples haircuts and grooming. You never specify what type of mistakes the judge is looking for.
The judge is judging a diving event. Competitive swimmers and divers shave their bodies to be more hydrodynamic. The judge lowers scores by looking more intently for mistakes, which makes contestants think they are performing poorly, and that they could do better getting shaved by the barber as a professional.
By doing this equally to all competitors, the judge feels like his is keeping the integrity of the competition.
The barber, supporting the local team, made a deal with the judge that, for each mistake by a foreign performer caught, he will deduct $1 equivalent from the debt?
It rather sounds like the judge "paid" the barber by offering to exert bias against certain athletes by looking for mistakes in their routines more intently. Perhaps the barber has a favorite they'd like to see win, or is loyal to their national team, or has bets outstanding on an event.
He wanted to minimize the total of the scores he gave.
The judge would pay the barber the total sum of the scores he gave to the participants.
Not the answer you're looking for? Browse other questions tagged lateral-thinking enigmatic-puzzle or ask your own question.
What did they kill Bob to hide?
What did Schrödinger call his cat?


Kentucky hospitals do even more that provide great, quality health care.
They also have a huge impact on the economic health of the commonwealth.
The Kentucky Hospital Association's Kentucky Hospital Statistics is a comprehensive compilation of data on Kentucky hospitals.


text:
title: "Filter API"
---

You can access and set the models for filters through the grid API, or access individual filter instances directly for more control. This page details how to do both.

## Get / Set All Filter Models

It is possible to get the state of all filters using the grid API method `getFilterModel()`, and to set the state using
`setFilterModel()`. These methods manage the filters states via the `getModel()` and `setModel()` methods of the
individual filters.

<snippet>
|// Gets filter model via the grid API
|const model = gridOptions.api.getFilterModel();
|
|// Sets the filter model via the grid API
|gridOptions.api.setFilterModel(model);
</snippet>

The filter model represents the state of filters for all columns and has the following structure:

```js
// Sample filter model via getFilterModel()
{
    athlete: {
        filterType: 'text',
        type: 'startsWith',
        filter: 'mich'
    },
    age: {
        filterType: 'number',
        type: 'lessThan',
        filter: 30
    }
}
```

This is useful if you want to save the global filter state and apply it at a later stage. It is also useful for server-side filtering, where you want to pass the filter state to the server.

### Reset All Filters

You can reset all filters by doing the following:

<snippet>
gridOptions.api.setFilterModel(null);
</snippet>

### Example: Get / Set All Filter Models

The example below shows getting and setting all the filter models in action.

- `Save Filter Model` saves the current filter state, which will then be displayed.
- `Restore Saved Filter Model` restores the saved filter state back into the grid.
- `Set Custom Filter Model` takes a custom hard-coded filter model and applies it to the grid.
- `Reset Filters` will clear all active filters.
- `Destroy Filter` destroys the filter for the **Athlete** column by calling `gridApi.destroyFilter('athlete')`. This removes any active filter from that column, and will cause the filter to be created with new initialisation values the next time it is interacted with.

(Note: the example uses the Enterprise-only [Set Filter](../filter-set/)).

<grid-example title='Filter Model' name='filter-model' type='generated' options='{ "enterprise": true, "exampleHeight": 587, "modules": ["clientside", "menu", "filterpanel", "columnpanel", "setfilter"] }'></grid-example>

## Accessing Individual Filter Component Instances

It is also possible to access the filter components directly if you want to interact with a specific filter. This also works for your own custom filters, where you can get a reference to the underlying filtering instance (i.e. what was created when AG Grid called `new` on your filter). Calling `api.getFilterInstance(colKey)` will return a reference to the filter instance for the column with key `colKey`.

<snippet>
// Get a reference to the 'name' filter instance
const filterInstance = gridOptions.api.getFilterInstance('name');
</snippet>

All of the methods of the filter are available on the instance. If using a custom filter, any other methods you have added will also be present, allowing bespoke behaviour to be added to your filter.

For filters that are created asynchronously, including React 16+ components, `getFilterInstance` will return `null` if the filter has not already been created. If your app uses asynchronous components, use the optional `callback` function which will be invoked with the filter instance when it is available.

<snippet>
// Get a reference to an asynchronously created filter instance
gridOptions.api.getFilterInstance('name', filterInstance => {
    // ... use filterInstance here
});
</snippet>

### Re-running Grid Filtering

After filters have been changed via their API, you must ensure the method `gridApi.onFilterChanged()` is called to tell the grid to filter the rows again. If `gridApi.onFilterChanged()` is not called, the grid will still show the data relevant to the filters before they were updated through the API.

<snippet>
|// Get a reference to the filter instance
|const filterInstance = gridOptions.api.getFilterInstance('name');
|
|// Set the filter model
|filterInstance.setModel({
|    filterType: 'text',
|    type: 'startsWith',
|    filter: 'abc',
|});
|
|// Tell grid to run filter operation again
|gridOptions.api.onFilterChanged();
</snippet>

### Reset Individual Filters

You can reset a filter to its original state by getting the filter instance and setting the model to `null`.

<snippet>
|// Get a reference to the filter instance
|const filterInstance = gridOptions.api.getFilterInstance('name');
|
|// Set the model to null
|filterInstance.setModel(null);
|
|// Tell grid to run filter operation again
|gridOptions.api.onFilterChanged();
</snippet>

### Example: Accessing Individual Filters

The example below shows how you can interact with an individual filter instance, using the Set Filter as an example.

- `Get Mini Filter Text` will print the text from the Set Filter's Mini Filter to the console.
- `Save Mini Filter Text` will save the Mini Filter text.
- `Restore Mini Filter Text` will restore the Mini Filter text from the saved state.
- `Reset Filter` will reset the filter.

(Note: the example uses the Enterprise-only [Set Filter](../filter-set/)).

<grid-example title='Accessing Individual Filters' name='filter-api' type='generated' options='{ "enterprise": true, "exampleHeight": 624, "modules": ["clientside", "setfilter", "menu", "columnpanel"] }'></grid-example>

redpajama_set_name: RedPajamaGithub


Discussion in 'Torrents' started by daswasser, Apr 27, 2013.
I need an invite for TemplateP2P. I can offer Torrentleech.
I Need invitation for p2p...!!!!!!!
I payed the 15$ two times and I have yet received my Invitation..
I doubt that any member can give out an invite there.
you better look for an account or wait for them to open signups. and if you have paid for it then open a dispute to get back your cash.


A civil claim is a lawsuit between individuals and/or corporations. It can address disputes about terms of contracts, or claims for injury to a person, their property or reputation.
Who can help me with my civil case?
IS there an alternative to starting a lawsuit?
WHOM do you want to sue?
WHAT information do you have to support your claim?


text:
\section*{Introduction}

This paper is a discussion of
homotopy theoretic phenomena that arise in connection with inclusions $X \subset Y \subset \mathbb{R}^{n}$ of data sets in topological data analysis.
The manuscript is not in final form, and comments are welcome.
\smallskip

Suppose that $r > 0$, and say that $X$ is $r$-dense in $Y$ if for every point $y$ in $Y$ there is an $x$ in $X$ such that the distance $d(y,x) < r$ in the ambient metric space.

The first result in this direction (Corollary \ref{cor 2x} below) implies that, under the $r$-density assumption, the induced map $V_{s}(X) \to V_{s}(Y)$ of Vietoris-Rips complexes is a homotopy equivalence if $2r < t-s$, where $t$ is the smallest number such that $V_{t}(X) \ne V_{s}(X)$.

This result can be extended to the assertion that the inclusion $L_{s,k}(X) \to L_{s,k}(Y)$ of Lesnick complexes (with fixed density parameter $k$) is a homotopy equivalence if every point $y$ in the ``configuration space'' $Y^{k+1}_{dis}$ of $k+1$ distinct elements of $Y$ has an element $x \in X^{k+1}_{dis}$ such that $d(y,x) < r$ in $\mathbb{R}^{n(k+1)}$. This result appears as Corollary \ref{cor 4x} in this paper.

Corollary \ref{cor 2x} and Corollary \ref{cor 4x} follow from Theorem \ref{th 1x} and Theorem \ref{th 3x}, respectively. Both theorems are ``interleaving'' homotopy type results (see also \cite{BlumLes}) that follow from the respective $r$-density assumptions, by methods that amount to manipulation of barycentric subdivisions. Theorem \ref{th 1x} is a special case of Theorem \ref{th 3x} (it is the case $k=0$), but Theorem \ref{th 1x} was found initially, and its proof has a certain clarity in isolation.

For a fixed $k$, the sets $\pi_{0}L_{s,k}(X)$ of path components, as $s$ varies, define a tree $\Gamma_{k}(X)$ with elements $(s,[x])$, $[x] \in \pi_{0}L_{s,k}(X)$. The inclusion $X \subset Y$ defines a poset morphism $\Gamma_{k}(X) \to \Gamma_{k}(Y)$.

The tree $\Gamma_{k}(X)$ is the object studied by the HDBSCAN clustering algorithm, while the individual sets of clusters $\pi_{0}L_{s,k}(X)$ are the objects of interest for the DBSCAN algorithm.

The poset $\Gamma_{k}(X)$ has a subobject $\operatorname{Br}_{k}(X)$ whose elements are the branch points of $\Gamma_{k}(X)$, suitably defined --- see Section 2. The branch points of $\Gamma_{k}(X)$ are in one to one correspondence with the stable components for $\Gamma_{k}(X)$ that are defined in \cite{clusters9}, in the sense that every such stable component starts at a unique branch point. Thus, we can (and do) replace the stable component discussion of \cite{clusters9} with the branch point poset $\operatorname{Br}_{k}(X)$, and make particular use of its ordering.

The tree $\Gamma_{k}(X)$ has least upper bounds, and these restrict to least upper bounds for the subobject $\operatorname{Br}_{k}(X)$ of branch points. This notion of least upper bounds is an extension of and a potential replacement for the distance function that is introduced by Carlsson and M\'emoli \cite{CM-2010B} in their description of the ultrametric structure on a data set $X$ that arises from the single linkage cluster hierarchy. The Carlsson-M\'emoli theory does not apply in general to the tree $\Gamma_{k}(X)$, because the vertex sets of the Lesnick complexes $L_{k,s}(X)$ vary with changes of the parameter $s$.

The calculus of least upper bounds and its relation with branch points is described in Lemmas \ref{lem 7x}--\ref{lem 12x} below.

The branch point tree $\operatorname{Br}_{k}(X)$ can be thought of as a highly compressed version of the hierarchy $\Gamma_{k}(X)$ that is produced by the HDBSCAN algorithm.

The inclusion $\operatorname{Br}_{k}(X) \subset \Gamma_{k}(X)$ is a homotopy equivalence of posets, where the homotopy inverse is defined by taking the maximal branch point $(s_{0},[x_{0}]) \leq (s,[x])$ below $(s,[x])$ for each object of $\Gamma_{k}(X)$. The existence of the maximal branch point below an object $(s,[x])$ is a consequence of Lemma \ref{lem 12x}.

The poset map $\Gamma_{k}(X) \to \Gamma_{k}(Y)$ defines a poset map $i_{\ast}: \operatorname{Br}_{k}(X) \to \operatorname{Br}_{k}(Y)$, via the homotopy equivalences for the data sets $X$ and $Y$ of the last paragraph.

The configuration space $r$-density assumption for Theorem \ref{th 3x} imples that there is a poset morphism $\theta_{\ast}: \operatorname{Br}_{k}(Y) \to \operatorname{Br}_{k}(X)$ that is induced by a morphism $(s,[x]) \to (s+2r,[\theta(x)])$, and that there are homotopies of poset maps $i_{\ast} \cdot \theta_{\ast} \simeq s_{\ast}$ and $\theta_{\ast} \cdot i_{\ast} \simeq s_{\ast}$, where $s_{\ast}$ is defined by the shift operator $(s,[x]) \mapsto (s+2r,[x])$ on $Y$ and $X$, respectively. These homotopies are ``bounded'' (or controlled) by the number $2r$.

In good circumstances, a branch point $(s,[x])$ is the maximal branch point below the shift $(s+2r,[x])$, and the inequalities defining the homotopies of the last paragraph become equalities in that case.
\medskip

In summary, the poset morphism $\operatorname{Br}_{k}(X) \to \operatorname{Br}_{k}(Y)$ that is induced by an inclusion of data sets $X \subset Y$ has a homotopy theoretic character, and is measurably close to a homotopy equivalence if every sufficiently large group of distinct points of $Y$ is close to a corresponding group of distinct points for the smaller data set $X$. Such a statement amounts to a stability result for hierarchies of branch points, albeit not in traditional terms.

\tableofcontents

\section{Homotopy types}

Suppose given (finite) data sets $X \subset Y \subset \mathbb{R}^{n}$. Suppose that $r > 0$.

Say that $X$ is {\bf $r$-dense} in $Y$, if for all $y \in Y$ there is an $x \in X$ such that $d(y,x) < r$.
\medskip

Suppose that $s \geq 0$. Recall that $V_{s}(X)$ is the simplicial complex with simplices $(x_{0}, \dots ,x_{n})$ with $x_{i} \in X$ and $d(x_{i},x_{j}) \leq s$.

Then we have
\begin{equation*}
  X = V_{0}(X) \subset V_{s}(X) \subset V_{t}(X) \subset \dots \subset V_{R}(X) = \Delta^{X}
\end{equation*}
for $0 \leq s < t \leq R$, and for $R$ sufficiently large, where $\Delta^{X} := \Delta^{N}$ and $N = \vert X \vert -1$.

The inclusion $i: X \subset Y$ induces a map of systems of simplicial complexes
$i: V_{s}(X) \subset V_{s}(Y)$.

The data sets $X$ and $Y$ are finite, so there is a finite string of parameter values
\begin{equation*}
  0=s_{0} < s_{1} < \dots < s_{r},
\end{equation*}
consisting of the distances between elements of $Y$. This includes the list of distances between elements of $X$. I say that the $s_{i}$ are the {\bf phase-change} numbers.

\begin{theorem}\label{th 1x}
Suppose that $X \subset Y \subset \mathbb{R}^{n}$, and that $X$ is $r$-dense in $Y$.Then there is a homotopy commutative diagram
    \begin{equation*}
      \xymatrix{
        V_{s}(X) \ar[r]^{j} \ar[d]_{i} & V_{s+2r}(X) \ar[d]^{i} \\
        V_{s}(Y) \ar[r]_{j} \ar[ur]^{\theta} & V_{s+2r}(Y)
      }
      \end{equation*}
    in which the upper triangle commutes.
\end{theorem}

\begin{proof}
            Define a function $\theta: Y \to X$ by specifying $\theta(x) = x$ for $x \in X$. For $y \in Y-X$ find $x \in X$ such that $d(x,y) < r$ and set $\theta(y) =x$.

        If $(y_{0}, \dots ,y_{n})$ is a simplex of $V_{s}(Y)$,
        \begin{equation*}
          d(\theta(y_{i}),\theta(y_{j})) \leq d(\theta(y_{i}),y_{i})
          + d(y_{i},y_{j}) + d(y_{j},\theta(y_{j})) \leq r + s + r.
          \end{equation*}
        It follows that $\theta$ induces a simplicial complex map $\theta: V_{s}(Y) \to V_{s+2r}(X)$, such that the upper triangle commutes.

        For the simplex $(y_{0}, \dots ,y_{n})$ of $V_{s}(Y)$, the string of elements
        \begin{equation*}
          (y_{0}, \dots,y_{n},\theta(y_{0}), \dots ,\theta(y_{n}))
        \end{equation*}
        defines a simplex of $V_{s+2r}(Y)$, since
        \begin{equation*}
          d(y_{i},\theta(y_{j}) \leq d(y_{i},y_{j}) + d(y_{j},\theta(y_{j}) \leq s+r.
        \end{equation*}
        Set
        \begin{equation*}
          \gamma(y_{0}, \dots ,y_{n}) = (y_{0}, \dots,y_{n},\theta(y_{0}), \dots ,\theta(y_{n})).
        \end{equation*}
        This assignment defines a morphism $\gamma: NV_{s}(Y) \to NV_{s+2r}(Y)$ of posets of non-degenerate simplices, and there are homotopies (natural transformations)
        \begin{equation*}
          j \to  \gamma \leftarrow i\cdot\theta
        \end{equation*}
        which are defined by face inclusions.
\end{proof}

        \begin{corollary}\label{cor 2x}
    Suppose that $X \subset Y \subset \mathbb{R}^{n}$, and that $X$ is $r$-dense in $Y$. Suppose that $2r < s_{i+1}-s_{i}$. Then the map
    \begin{equation*}
      i: V_{s_{i}}(X) \to V_{s_{i}}(Y)
    \end{equation*}
    is a weak homotopy equivalence.
\end{corollary}

\begin{proof}
        In the homotopy commutative diagram
\begin{equation*}
      \xymatrix{
        V_{s_{i}}(X) \ar[r]^{j} \ar[d]_{i} & V_{s_{i}+2r}(X) \ar[d]^{i} \\
        V_{s_{i}}(Y) \ar[r]_{j} \ar[ur]^{\theta} & V_{s_{i}+2r}(Y)
      }
      \end{equation*}
the horizontal morphisms $j$ are isomorphisms (identities), and so $V_{s_{i}}(X)$ is a deformation retract of $V_{s_{i}}(Y)$.
\end{proof}

Corollary \ref{cor 2x} has consequences for both persistent homology and clustering.
\medskip

Suppose that $k$ is a non-negative integer. The Lesnick subcomplex $L_{s,k}(X)$ is the full subcomplex of $V_{s}(X)$ on those vertices $x$ for which there are at least $k$ distinct vertices $x_{i} \ne x$ such that $d(x,x_{i}) \leq s$ \cite{HMc}, \cite{clusters9}, \cite{LW2}.

A simplex $\sigma = (y_{0}, \dots ,y_{n})$ of $V_{s}(X)$ is in $L_{s,k}(X)$ if and only if each vertex $y_{i}$ has at least $k$ distinct neighbours in $V_{s}(X)$ --- this is the meaning of the assertion that $L_{s,k}(X)$ is a full subcomplex of $V_{s}(X)$.

There is an array of subcomplexes
\begin{equation*}
  \xymatrix{
    V_{s}(X) \ar[r] & V_{t}(X) \\
    L_{s,k}(X) \ar[r] \ar[u] & L_{t,k}(X) \ar[u] \\
    L_{s,k+1}(X) \ar[r] \ar[u] & L_{t,k+1}(X) \ar[u]
  }
  \end{equation*}
We have the following observations:
\begin{itemize}
\item[1)] $L_{s,0}(X) = V_{s}(X)$.
\item[2)] $L_{s,k}(X)$ could be empty for small $s$ and large $k$. In general, for $s \leq t$, $L_{s,k}(X)$ and $L_{t,k}(X)$ may not have the same vertices.
  \item[3)] Every inclusion $i: X \subset Y \subset \mathbb{R}^{n}$ induces maps $i: L_{s,k}(X) \to L_{s,k}(Y)$ which are natural in $s$ and $k$.
\end{itemize}

I say that $s$ is a {\bf spatial parameter} and that $k$ is a {\bf density parameter} (also a {\bf valence}, or degree). Lesnick says \cite{LW2} that $\{ L_{s,k}(X) \}$ is the {\bf degree Rips filtration} of the system $\{ V_{s}(X) \}$.

\medskip

Write $X^{k+1}_{dis}$ for the set of $k+1$ distinct points of $X$, and think of it as a subobject of $(\mathbb{R}^{n})^{k+1}$.

\begin{theorem}\label{th 3x}
        Suppose that $X \subset Y \subset \mathbb{R}^{n}$ and that $X^{k+1}_{dis}$ is $r$-dense in $Y^{k+1}_{dis}$ and that $L_{s,k}(Y) \ne \emptyset$. Then there is a homotopy commutative diagram
        \begin{equation*}
          \xymatrix{
          L_{s,k}(X) \ar[r]^{j} \ar[d]_{i} & L_{s+2r,k}(X) \ar[d]^{i} \\
          L_{s,k}(Y) \ar[r]_{j} \ar[ur]^{\theta} & L_{s+2r,k}(Y)
          }
        \end{equation*}
        in which the upper triangle commutes in the usual sense.
\end{theorem}

\begin{proof}
            Suppose that $y \in L_{s,k}(X)_{0} - L_{s,k}(X)_{0}$. Then there are $k$ points $y_{1},\dots ,y_{k}$ of $Y$, distinct from $y$ such that $d(y,y_{i}) < s$. There is a $(k+1)$-tuple $(x_{0},x_{1}, \dots ,x_{k})$ such that
            \begin{equation*}
              d((x_{0}, \dots ,x_{k}),(y,y_{1}, \dots ,y_{k})) < r,
            \end{equation*}
            by assumption. Then $d(y,x_{0}) <r$, $d(y_{i},x_{i}) < r$, and so $d(x_{0},x_{i}) < s+2r$, so that $x_{0} \in L_{s+2r,k}(X)$.  Set $\theta(y) = x_{0}$, and observe that $d(y,\theta(y)) < r$.

            If $(y_{0}, \dots ,y_{p})$ is a simplex of $L_{s,k}(Y)$ then $(\theta(y_{0}), \dots ,\theta(y_{p})$ is a simplex of $L_{s+2r,k}(X)$, as is the string
              \begin{equation*}
                (y_{0}, \dots ,y_{p},\theta(y_{0}), \dots ,\theta(y_{p})).
              \end{equation*}
              Finish according to the method of proof for Theorem \ref{th 1x}.
\end{proof}

\begin{corollary}\label{cor 4x}
  Suppose that $X \subset Y \subset \mathbb{R}^{n}$ and that $X^{k+1}_{dis}$ is $r$-dense in $Y^{k+1}_{dis}$. Suppose that $2r < s_{i+1}-s_{i}$. Then the inclusion
$i: L_{s_{i},k}(X) \to L_{s_{i},k}(Y)$ is a weak homotopy equivalence.
\end{corollary}

\begin{lemma}
    Suppose that $X^{k+1}_{dis}$ is $r$-dense in $Y^{k+1}_{dis}$, and that $Y^{k+1}_{dis} \ne \emptyset$. Then $X^{k}_{dis}$ is $r$-dense in $Y^{k}_{dis}$.
\end{lemma}

\begin{proof}
    Suppose that $\{ y_{0}, \dots ,y_{k-1} \}$ is a set of $k$ distinct points of $Y$. Then there is a $y_{k} \in Y$ which is distinct from the $y_{i}$, so that $(y_{0},y_{1}, \dots ,y_{k})$ is a $(k+1)$-tuple of distinct points of $Y$. There is a $(k+1)$-tuple $(x_{0},\dots ,x_{k})$ of distinct points of $X$ such that
    \begin{equation*}
      d((y_{0}, \dots ,y_{k-1},y_{k}),(x_{0}, \dots ,x_{k-1},x_{k})) < r.
      \end{equation*}
        It follows that
    \begin{equation*}
      d((y_{0}, \dots ,y_{k-1}),(x_{0}, \dots ,x_{k-1})) < r.
    \end{equation*}
\end{proof}

\begin{corollary}
        Suppose that $X \subset Y \subset \mathbb{R}^{n}$ and that $X^{k+1}_{dis}$ is $r$-dense in $Y^{k+1}_{dis}$. Suppose that $2r < s_{i+1}-s_{i}$. Then the inclusion
$i: L_{s_{i},p}(X) \to L_{s_{i},p}(Y)$ is a weak homotopy equivalence for $0 \leq p \leq k$.
\end{corollary}

\section{Branch points and upper bounds}

Fix the density $k$ and suppose that $L_{s,k}(X) \ne \emptyset$ for $s$ sufficiently large. Apply the path component functor to the $L_{s,k}(X)$, to get a diagram of functions
\begin{equation*}
  \dots \to \pi_{0}L_{s,k}(X) \to \pi_{0}L_{t,k} \to \dots
\end{equation*}

There is a graph $\Gamma_{k}(X) := \Gamma(\pi_{0}L_{\ast,k}(X))$ with vertices $(s,[x])$ with $[x] \in \pi_{0}L_{s,k}(X)$, and edges $(s,[x]) \to (t,[x])$ with $s \leq t$. This graph underlies a contractible poset, and is therefore a tree (or hierarchy).

To reflect the poset structure of $\Gamma_{k}(X)$, I write the morphisms of $\Gamma_{k}(X)$ as relations $(s,[x]) \leq (t,[y])$. The existence of such a relation means that  $[x] = [y] \in \pi_{0}L_{t,k}(X)$, or that the image of $[x] \in \pi_{0}L_{s,k}(X)$ under the induced function $\pi_{0}L_{s,k}(X) \to \pi_{0}L_{t,k}(X)$ is $[y]$.
\medskip

\noindent
    {\bf Remarks}:\ 1)\ Partitions of $X$ given by the set $\pi_{0}V_{s}(X)$ are standard {\bf clusters}. The tree $\Gamma_{0}(X)=\Gamma(V_{\ast}(X))$ defines a {\bf hierarchical clustering} (similar to, but not the same as single linkage clustering).
    \smallskip

    \noindent
    2)\ The set $\pi_{0}L_{s,k}(X)$ gives a partitioning of the set of elements of $X$ having at least $k$ neighbours of distance $\leq s$, which is the subject of the {\bf DBSCAN} algorithm. The tree $\Gamma_{k}(X)=\Gamma(\pi_{0}L_{\ast,k}(X))$ is the basis of the {\bf HDBSCAN} algorithm.
    \medskip

    A {\it branch point} in the tree $\Gamma_{k}(X)$ is a vertex $(t,[x])$ such that either of following two conditions hold:
    \begin{itemize}
    \item[1)] there is an $s_{0} < t$ such that for all $s_{0} \leq s < t$ there are distinct vertices $(s,[x_{0}])$ and $(s,[x_{1}])$ with $(s,[x_{0}]) \leq (t,[x])$ and $(s,[x_{1}]) \leq (t,[x])$, or
    \item[2)] there is no relation $(s,[y]) \leq (t,[x])$ with $s < t$.
\end{itemize}
The second condition means that a representing vertex $x$ is not a vertex of $L_{s,k}(X)$ for $s < t$.
Write $\operatorname{Br}_{k}(X)$ for the set of branch points $(s,[x])$ in $\Gamma_{k}(X)$.

Every branch point $(s,[x])$ of $\Gamma_{k}(X)$ has $s=s_{i}$, where $s_{i}$ is a phase change number for $X$.

The branch point poset $\operatorname{Br}_{k}(X)$ is a tree, because the element $(s_{r},[x])$ corresponding to the highest phase change number $s_{r}$ is maximal.

The set of branch points $\operatorname{Br}_{k}(X)$ inherits a partial ordering from the poset $\Gamma_{k}(X)$, and the inclusion $\operatorname{Br}_{k}(X) \subset \Gamma_{k}(X)$ of the set of branch points defines a monomorphism of trees.

\medskip

Suppose that $(s,[x])$ and $(t,[y])$ are vertices of the graph $\Gamma_{k}(X)$. There is a vertex $(v,[w])$ such that $(s,[x]) \leq (v,[w])$ and $(t,[y]) \leq (v,[w])$. The two relations mean, among other things, that $[x]=[z]=[y]$ in $\pi_{0}L_{v,k}(X)$.

It follows that there is a unique smallest vertex $(u,[z])$ which is an upper bound for both $(s,[x])$ and $(t,[y])$. The number $u$ is the smallest parameter $v$ such that $[x]=[y]$ in $\pi_{0}L_{u,k}(X)$, and so $[z]=[x]=[y]$.

I write
\begin{equation*}
  (s,[x]) \cup (t,[y]) = (u,[z]).
  \end{equation*}
The vertex $(u,[z])$ is the {\bf least upper bound} (or join) of $(s,[x])$ and $(t,[y])$.

Every finite collection of points $(s_{1},[x_{1}]), \dots ,(s_{p},[x_{p}])$ has a least upper bound
\begin{equation*}
  (s_{1},[x_{1}]) \cup \dots \cup (s_{p},[x_{p}])
\end{equation*}
in $\Gamma_{k}(X)$.

\begin{lemma}\label{lem 7x}
  The least upper bound of branch points $(u,[z])$ of $(s,[x])$ and $(t,[y])$ is a branch point.
\end{lemma}

\begin{proof}
  For numbers $s,t<v<u$, $(v,[x])$ and $(v,[y])$ are distinct, because $(u,[z])$ is a least upper bound.

  Otherwise, $s=u$ or $t=u$, in which case $(u,[z]) = (s,[x])$ or $(u,[z])=(t,[y])$, respectively.
  \end{proof}

It follows from Lemma \ref{lem 7x} that any two branch points $(s,[x])$ and $(t,[y])$ have a least upper bound in $\operatorname{Br}_{k}(X)$, and that the poset inclusion $\alpha: \operatorname{Br}_{k}(X) \to \Gamma_{k}(X)$ preserves least upper bounds.
\medskip

\noindent
{\bf Remark}:\ The poset $\Gamma_{k}(X)$ also has greatest lower bounds (or meets). The greatest lower bound
\begin{equation*}
  (t_{1},[y_{1}]) \cap \dots \cap (t_{r},[y_{r}])
\end{equation*}
  is the least upper bound of all $(s,[x])$ such that $(s,[x]) \leq (t_{j},[y_{j}])$ for all $j$.
  \medskip

  We have the following triviality:

  \begin{lemma}\label{lem 8x}
    Suppose that $(s_{1},[x_{1}]), (s_{2},[x_{2}])$ and $(s_{3},[x_{3}])$ are vertices of $\Gamma_{k}(X)$. Then
    \begin{equation*}
      (s_{1},[x_{1}]) \cup (s_{3},[x_{3}]) \leq ((s_{1},[x_{1}]) \cup (s_{2},[x_{2}])) \cup ((s_{2},[x_{2}]) \cup (s_{3},[x_{3}])).
      \end{equation*}
  \end{lemma}

  \begin{proof}
    We have the identity
    \begin{equation*}
      ((s_{1},[x_{1}]) \cup (s_{2},[x_{2}])) \cup ((s_{2},[x_{2}]) \cup (s_{3},[x_{3}])) = (s_{1},[x_{1}]) \cup (s_{2},[x_{2}]) \cup (s_{3},[x_{3}]),
      \end{equation*}
    and then
    \begin{equation*}
      (s_{1},[x_{1}]) \cup (s_{3},[x_{3}]) \leq (s_{1},[x_{1}]) \cup (s_{2},[x_{2}]) \cup (s_{3},[x_{3}]).
      \end{equation*}
    \end{proof}

  Carlsson and M\'emoli \cite{CM-2010B} define an ultrametric $d$ on $X=V_{0}(X)$, for which they say that $d(x,y)=s$, where $s$ is the minimum parameter value such that $[x]=[y] \in
 \pi_{0}V_{s}(X)$.

 Suppose given $[x]$ and $[y]$ in $\pi_{0}L_{s,k}(X)$ (equivalently, points $(s,[x])$ and $(s,[y])$ in $\Gamma_{k}(X)$). Write $d([x],[y]) = u-s$, where $(s,[x]) \cup (s,[y]) = (u,[w])$.

 \begin{lemma}\label{lem 9x}
   Given $[x],[y]$ and $[z]$ in $\pi_{0}L_{s,k}(X)$, we have a relation
   \begin{equation*}
     d([x],[z]) \leq \max \{ d([x],[y]),d([y],[z]) \}.
\end{equation*}
   \end{lemma}

 \begin{proof}
   Suppose that $(s,[x]) \cup (s,[y]) \cup (s,[z]) = (v,[w])$. Then
   \begin{equation*}
     v -s = \max \{ d([x],[y]),d([y],[z]) \}
   \end{equation*}
   and
   \begin{equation*}
     d([x],[z]) \leq v-s
   \end{equation*}
   by Lemma \ref{lem 8x}.
 \end{proof}

 \begin{corollary}\label{cor 10x}
   The function
   \begin{equation*}
     d: \pi_{0}L_{s,k}(X) \times \pi_{0}L_{s,k}(X) \to \mathbb{R}_{\geq 0}
     \end{equation*}
of Lemma \ref{lem 9x} gives the set $\pi_{0}L_{s,k}(X)$ the structure of an ultrametric space.
   \end{corollary}

 \noindent
     {\bf Remark}:\ One could define a ``distance'' function $d$ on the full set of points of $\Gamma_{k}(X)$ by setting
     \begin{equation*}
       d((s,[x]),(t,[y])) = \max \{ u-s,u-t \},
     \end{equation*}
     where $(s,[x]) \cup (t,[y]) = (u,[z])$.

The ultrametric property of Lemma \ref{lem 9x} fails for the points $(s,[x]),(t,[x])$ and $(u,[x])$ where $s < t <u$, since it is not the case that $u-s \leq \max \{ t-s,u-t \}$

\begin{lemma}\label{lem 11x}
Every vertex $(s,[x])$ of $\Gamma_{k}(X)$ has a unique largest branch point $(s_{0},[x_{0}])$ such that $(s_{0},[x_{0}]) \leq (s,[x])$.
\end{lemma}

\begin{proof}
The least upper bound of the finite list of the branch points $(t,[y])$ such that $(t,[y]) \leq (s,[x])$ is a branch point, by Lemma \ref{lem 7x}.
\end{proof}

In the situation described by Lemma \ref{lem 11x}, I say that $(s_{0},[x_{0}])$ is the {\bf maximal branch point below} $(s,[x])$.

\begin{lemma}\label{lem 12x}
  Suppose that $(s_{0},[x_{0}])$ and $(t_{0},[y_{0}])$ are maximal branch points below the points $(s,[x])$ and $(t,[y])$, respectively.

  Then $(s_{0},[x_{0}]) \cup (t_{0},[y_{0}])$ is the maximal branch point below $(s,[x]) \cup (t,[y])$.
\end{lemma}

\begin{proof}
  Suppose that $s \leq t$.

We have
\begin{equation*}
(s_{0},[x_{0}]) \cup (t_{0},[y_{0}]) \leq (s,[x]) \cup (t,[y]).
\end{equation*}
and $(s_{0},[x_{0}]) \cup (t_{0},[y_{0}])$ is a branch point by Lemma \ref{lem 7x}.
Write
\begin{equation*}
(v,[z]) = (s_{0},[x_{0}]) \cup (t_{0},[y_{0}]).
\end{equation*}

Suppose that $v \leq t$.
Then $(t_{0},[y_{0}]) \leq (t,[y])$ and $(t_{0},[y_{0}]) \leq (v,[z])$, so that $(v,[z]) \leq (t,[y])$ since $v \leq t$. Also, $(s_{0},[x_{0}]) \leq (s,[x])$ and $(s_{0},[x_{0}]) \leq (v,[z]) \leq (t,[y])$ so that $(s,[x]) \leq (t,[y])$. Then $(s_{0},[x_{0}]) \leq (t_{0},[y_{0}])$ by maximality, and it follows that
\begin{equation*}
  (s_{0},[x_{0}]) \cup (t_{0},[y_{0}]) = (t_{0},[y_{0}])
\end{equation*}
is the maximal branch point of
\begin{equation*}
  (s,[x]) \cup (t,[y]) = (t,[y])
\end{equation*}

  Suppose that $v >t$. Then $(s,[x]) = (s,[x_{0}]) \leq (v,[z])$ and $(t,[y]) = (t,[y_{0}]) \leq (v,[z])$ because $s \leq t <v$, so that
\begin{equation*}
  (s,[x]) \cup (t,[y]) \leq (s_{0},[x_{0}]) \cup (t_{0},[y_{0}]),
\end{equation*}
Thus, $(s_{0},[x_{0}]) \cup (t_{0},[y_{0}]) = (s,[x]) \cup (t,[y])$ is a branch point,
by Lemma \ref{lem 7x}.
\end{proof}

The poset inclusion $\alpha: \operatorname{Br}_{k}(X) \to \Gamma_{k}(X)$ has an inverse
\begin{equation*}
  max: \Gamma_{k}(X) \to \operatorname{Br}_{k}(X),
\end{equation*}
  up to homotopy.

In effect, Lemma \ref{lem 11x} implies that every vertex $(s,[x])$ of $\Gamma_{k}(X)$ has a unique maximal branch point $(s_{0},[x_{0}])$ such that $(s_{0},[x_{0}]) \leq (s,[x])$. Set
\begin{equation*}
  max(s,[x]) = (s_{0},[x_{0}]).
\end{equation*}
The maximality condition implies that $max$ preserves the ordering. The composite
$max \cdot \alpha$ is the identity on $\operatorname{Br}_{k}(X)$, and the relations $(s_{0},[x_{0}]) \leq (s,x)$ define a homotopy $max \cdot \alpha \leq 1$.
\medskip

Return to the inclusion $i: X \subset Y \subset \mathbb{R}^{n}$ of finite data sets. Suppose that $X^{k+1}_{dis}$ is $r$-dense in $Y^{k+1}_{dis}$ and that $L_{s,k}(Y)$ is non-empty, as in the statement of Theorem \ref{th 3x}.

Write $i_{\ast}: \operatorname{Br}_{k}(X) \to \operatorname{Br}_{k}(Y)$ for the composite
\begin{equation*}
  \operatorname{Br}_{k}(X) \xrightarrow{\alpha} \Gamma_{k}(X) \xrightarrow{i_{\ast}} \Gamma_{k}(Y) \xrightarrow{max} \operatorname{Br}_{k}(Y)
  \end{equation*}
This map takes a branch point $(s,[x])$ to the maximal branch point below $(s,[i(x)])$. The map $i_{\ast}$ preserves least upper bounds by Lemma \ref{lem 7x}.

Poset morphisms $\theta_{\ast}: \operatorname{Br}_{k}(Y) \to \operatorname{Br}_{k}(X)$ and $s_{\ast}: \operatorname{Br}_{k}(X) \to \operatorname{Br}_{k}(X)$ are similarly defined, by the poset morphism $\theta: \Gamma_{k}(Y) \to \Gamma_{k}(X)$ with $(t,[y]) \mapsto (t+2r,[\theta(y)])$, and the shift morphism $s: \Gamma_{k}(X) \to \Gamma_{k}(X)$ with $(s,[x]) \mapsto (s+2r,[x])$.

The construction of the poset map $i_{\ast}: \operatorname{Br}_{k}(X) \to \operatorname{Br}_{k}(Y)$ is not functorial in maps of the form $X \to Y$, but it is functorial up to coherent homotopy.

Similarly, the map $i_{\ast}: \operatorname{Br}_{k}(X) \to \operatorname{Br}_{k}(Y)$ only preserves least upper bounds up to homotopy. Suppose that $(s,[x])$ and $(t,[y])$ are branch points of $X$, and let $(s_{0},[x_{0}]) \leq (s,[i(x)])$ and $(t_{0},[y_{0}]) \leq (t,[i(y)])$ be maximal branch points below the images of $(s,[x])$ and $(t,[y])$ in $\Gamma_{k}(Y)$. Then
\begin{equation*}
  (s_{0},[x_{0}]) \cup (t_{0},[y_{0}]) \leq (s,[i(x)]) \cup (t,[i(y)]),
\end{equation*}
so that
\begin{equation*}
  i_{\ast}(s,[x]) \cup i_{\ast}(t,[y]) \leq i_{\ast}((s,[x]) \cup (t,[y])).
\end{equation*}

Similar inequalities hold for least upper bounds with respect to the other maps that one encounters, namely $\theta_{\ast}: \operatorname{Br}_{k}(Y) \to \operatorname{Br}_{k}(X)$ and the shift map $s_{\ast}: \operatorname{Br}_{k}(X) \to \operatorname{Br}_{k}(X)$.
\medskip

\noindent
1)\ Consider the poset maps
\begin{equation*}
  \operatorname{Br}_{k}(X) \xrightarrow{i_{\ast}} \operatorname{Br}_{k}(Y) \xrightarrow{\theta_{\ast}} \operatorname{Br}_{k}(X).
\end{equation*}

If $(s,[x])$ is a branch point for $X$, choose maximal branch points $(s_{0},[x_{0}]) \leq (s,[i(x)]$ for $Y$, $(s_{1},[x_{1}]) \leq (s_{0}+2r,[\theta(x_{0})])$ and $(v,[y]) \leq (s+2r,[x])$ below the respective objects.

Then $\theta_{\ast}i_{\ast}(s,[x]) = (s_{1},[x_{1}])$, and there is a natural relation
\begin{equation*}
  \theta_{\ast}i_{\ast}(s,[x]) = (s_{1},[x_{1}]) \leq (v,[y]) = s_{\ast}(s,[x]) \leq (s+2r,[x]).
\end{equation*}
We therefore have a homotopy of poset maps
\begin{equation*}
  \theta_{\ast}i_{\ast} \leq s_{\ast}: \operatorname{Br}_{k}(X) \to \operatorname{Br}_{k}(X).
\end{equation*}

Note that $(s,[x]) \leq s_{\ast}(s,[x])$ since $(s,[x])$ is a branch point and $s_{\ast}(s,[x])$ is the maximal branch point below $(s+2r,[x])$. This means that the shift morphism $s_{\ast}$ is homotopic to the identity on $\operatorname{Br}_{k}(X)$.

The branch point $(s,[x])$ has a ``close'' shared upper bound $(s+2r,[x])$ with the element $(s_{0}+2r,[\theta(x_{0})])$, which is the image of the branch point $(s_{0},[x_{0}])$ under the poset map $\theta_{\ast}: \Gamma_{k}(Y) \to \Gamma_{k}(X)$.
\medskip

\noindent
2)\ Similarly, if $(t,[y])$ is a branch point of $Y$, then
\begin{equation*}
  i_{\ast}\theta_{\ast}(t,[y]) \leq s_{\ast}(t,[y]) \geq (t,[y])
\end{equation*}
while $s_{\ast}(t,[y]) \leq (t+2r,[y])$.

The element $(t+2r,[y])$ is a close shared upper bound for $(t,[y])$ and an element of the form $(t_{0},[i(y_{0})])$, where $(t_{0},[y_{0}])$ is a maximal branch point of $X$ below $(s+2r,[\theta(y)])$.
\medskip

\noindent
    {\bf Remark}:\ The subobject of $\operatorname{Br}_{k}(X)$ consisting of all branch points of the form $(s,[x])$ as $s$ varies has an obvious notion of distance on it: the distance between points $(s,[x])$ and $(t,[x])$ is $\vert t-s \vert$. The closeness referred to in constructions 1) and 2) above can be expressed in terms of such a distance.
    \medskip

Suppose that $(s_{1},[x_{1}])$ and $(s_{2},[x_{2}])$ are branch points of $X$, let
\begin{equation*}
(s,[x]) = (s_{1},[x_{1}]) \cup (s_{2},[x_{2}]),
\end{equation*}
and write
\begin{equation*}
 (t,[y]) =  (s_{1},[i(x_{1})]) \cup (s_{2},[i(x_{2})]).
\end{equation*}
Then $(s,[i(x)])$ is an upper bound for $(s_{1},[i(x_{1})])$ and $(s_{2},[i(x_{2})])$, so that $(t,[y]) \leq (s,[i(x)])$.

The element $(t+2r,[\theta(y)])$ is an upper bound for $(s_{1},[x_{1}])$ and $(s_{2},[x_{2}])$, so that
\begin{equation}\label{eq 1xx}
  (s,[x]) \leq (t+2r,[\theta(y)]) \leq (s+2r,[x]).
\end{equation}

It follows that $s-2r \leq t \leq s$, which gives a constraint on the parameter $t$ corresponding to the least upper bound $(t,[y])$ in $\Gamma_{k}(Y)$, in terms of the least upper bound $(s,[x])$ in $\Gamma_{k}(X)$, or in $\operatorname{Br}_{k}(X)$. The number $2r$ is a bound on the distances between the three points in (\ref{eq 1xx}).
\medskip

If the bound $2r$ is sufficiently small, then $(s,[x])$ is the largest branch point below $(s+2r,[x])$ and $s_{\ast}(s,[x]) = (s,[x])$ in that case.
Similarly, in $\Gamma_{k}(Y)$, $s_{\ast}(t,[y]) = (t,[y])$ if  $2r$ is sufficiently small.

Recall that if $(s,[x])$ is a branch point, then $s=s_{i}$ is one of the phase shift numbers. Then $(s_{i},[x])$ is the maximal branch point below $(s_{i}+2r,[x])$ if $2r < s_{i+1}-s_{i}$.

\vfill\eject

\nocite{BlumLes}
\nocite{clusters9}

\bibliographystyle{plain}

redpajama_set_name: RedPajamaArXiv


Do you think this should happen?
Poll closed Nov 29, 2013.
I think there should be alliances with up to 20 people and you can only be in that alliance and there are no truces. So its a alliance v a alliance.
We can try to integrate "groups" in assasinations, dont know how hard it would be to code, though.
Okay thanks? If it works it works if it doesn't it doesn't I just thought it would add rivalries and spice up the game a bit more.


text:
Elise Stefanik Speaks At 2020 RNC. Her Biography And Net Worth
Born Name Elise Marie Stefanik
Nick Name Elise Stefanik
Profession Politician
Date Of Birth July 2, 1984
Birth Place Albany, New York, United States
Age 36 Yrs Old
Parents Melanie Stefanik and Ken Stefanik
Height 5ft 4inch
Husband Matthew Manda (m. 2017)
Children Unknown
Elise Marie Stefanik is an American politician serving as the U.S. Representative for New York's 21st congressional district since 2015. She also became the youngest woman ever elected to Congress at the time. Also, she is the youngest Republican woman ever elected to Congress.
She is a married woman and is living a happy family life with her husband in Schuylerville, New York. However, the couple doesn't have any children at the moment. Wanna know more about her personal and professional life? Just continue reading until the end and all those facts will be revealed.
Early Life, Bio, Wiki Of Elise Stefanik
Elise Stefanik's Career
Elise Stefanik's Net Worth
Elise Stefanik's Personal Life
Elise Stefanik's Body Measurement
Elise Stefanik On Social Media
Early Life, Bio, Wiki Of Elise Stefanik. Age, Parents, And Childhood.
Elise Stefanik was born in Albany, New York on July 2, 1984. Born to her parents Melanie and Ken Stefanik, she is currently at the age of 36. She belongs to Czech and Italian descent.
She got her graduation from the Albany Academy for Girls and entered Harvard University again getting graduation with a degree in Government in 2006. During her study at Harvard, she received an honourable mention for the Women's Leadership Award.
Furthermore, after graduating from Harvard, she joined the administration of President George W. Bush, working as a staff to the Domestic Policy Council.
Elise Stefanik's Career. How She Achieve Her Goal? Path To Success.
Moving towards the career of Elise Stefanik, as an American Politician. She started working as a staff of the Domestic Policy Council of President George W. Bush, after completing her graduation from Harvard University. Similarly, in 2013, she appeared as the candidate for the United States House of Representatives in New York's 21st congressional district where she won the election and became the youngest Republican woman to be elected for Congress.
Furthermore, in 2015, she was appointed to be in the House Armed Services Committee. And, one month later, she became the vice-chairperson of the committees' Subcommittee on Readiness. Again in the year 2016, she won the reelection of the general election against the Democrats like Mike Derrick, Green Party, and Matt Funiciello with the majority. Also, in 2017, she won for the post of the co-chair of Tuesday Group.
In August 2020, she was invited to speak in a headline slot at the virtual GOP convention after emerging as one of Trump's most outspoken defenders last year during House impeachment hearings.
And, GOP officials initially said Stefanik would use the convention speech to offer a critique of Democratic presidential nominee Joe Biden's record during a 47-year career in politics.
Caption: Elise Stefanik talks in RNC Speech
Picture Credit: Youtube
Elise Stefanik's Net Worth. How Much She Earns? Also, Know About Her Salary.
Elise Stefanik, an American politician serving as the U.S. Representative for New York's 21st congressional district since 2015 has earned a marvellous amount of money from her career. And, as of 2020, her net worth is estimated to be $2 Million. However, the exact amount of her salary is unavailable. On the other hand, her husband, Matthew Manda works in marketing and communications and must have an excellent net worth. In this way, with all this income and net worth, the family of two is living a luxurious and healthy lifestyle.
Elise Stefanik's Personal Life. Relationship, Dating, And Affairs. Also, Know About Her Husband And Children.
Heading towards the personal life of Elise Stefanik, she is a married woman. She got married to Matthew Manda on the 19th of August 2017 in Saratoga Springs, New York. Her husband, Matthew Manda works in marketing and communications. And, as for now, the couple is living a happy family life in Schuylerville, New York. However, until the date, the couple doesn't share any children from their blissful married life.
Caption: Elise Stefanik and her husband's wedding
Picture Credit: Brides
Besides, this we don't have any information regarding her past affairs and romantic relationship.
Elise Stefanik's Body Measurement. Height, Weight, Wiki, Bio, And Many More.
Elise Stefanik is a beautiful woman with a tall and slim body figure and a fairer skin tone. She stands at a height of 5 feet 4 inches and a weight about 59 kg. She has brown coloured eyes and brunette hair, which makes her look really attractive. She holds an American nationality and holds a Polish ethnicity. She is a married woman and currently living a happy family life with her husband Matthew Manda whom she got married in 2017.
Caption: Elisa Stefanik with her husband Matthew Manda
Picture Credit: The New York Times
Elise Stefanik On Social Media. Facebook, Instagram, And Twitter.
Elise Stefanik an American politician serving as the U.S. Representative for New York's 21st congressional district since 2015 is active on various social networking sites like Facebook, Instagram and Twitter. Being a famous personality in Politics. she loves sharing personal thoughts and images on social media and has a quite large number of fans and followers over there. On her official Instagram site, she has 66.1K followers. To know more about her personal life and to be updated about her life events, you can go through her social media profile and follow her:
Follow Elise Stefanik On Instagram
Busy week of #RESULTS for #NY21 🔥🔥🔥🔥🔥
A post shared by elisestefanik (@elisestefanik) on Jul 11, 2020 at 6:13am PDT
Quick Facts Of Elise Stefanik
Where and when was Elise Stefanik born?
July 2, 1984 in Albany, New York, United States
What nationality does Elise Stefanik belong to?
What is Elise Stefanik's ethnicity?
What is Elise Stefanik's eye color?
Which color of hair does Elise Stefanik have?
How tall is Elise Stefanik?
How old is Elise Stefanik?
36 Yrs Old
We, wikiramp.com team hope you enjoy this article about Elise Stefanik. To know the latest information related to Hollywood and famous personality stay tuned with us.
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Kim Domingo's Biography
Adam Dirks Is Husband Of Famous Surfer Bethany Hamilton


text:
XXX: State of the Union
Movie of the Day for Friday, April 1, 2005
See other Movies of the Day
154/166 David Mumpower Clearly, there are limits to my fandom of Ice Cube. This is a disastrous project destined for the Bad Movie Hall of Fame.
Rising actor Vin Diesel and then-hot director Rob Cohen were so excited about creating a Generation X answer to the James Bond series that they blew off the sequel to The Fast and the Furious in order to film xXx. Even more telling about the two men's confidence in the project was the fact that they each signed up for a sequel at the same time. So, the arrival of xXx2 (apparently pronounced Triple X Squared) should indicate the return of the director and star of the first film, right?
xXx was a hit with international receipts of roughly $270 million. It was not, however, the blockbuster franchise debut many box office analysts (myself included) predicted it to be. Even worse, word-of-mouth for the movie was mediocre at best, with more people on the "Hated It" side of the ledger than the "It's better than Cats. I am going to go see it again and again" side.
In point of fact, if you ask many people what was memorable about the movie, the answer would probably be either Euro-trash goddess Asia Argento or the throwaway line of "Bitches come!" For the first film in what was hoped to be the new millennium answer to Ian Fleming, those are scary results.
Say what you will about Vin Diesel, but he has demonstrated remarkable savvy in determining projects. Testing the waters long enough to realize that no one was asking for him to do a second film, Vin and his attached-at-the-hip director showed savvy above and beyond the producers of Tomb Raider 2 and Charlie's Angels: Full Throttle. The two men chose not to do the probably unwanted Xander Cage rehash, but instead went back to a character film lovers wanted to see, Riddick.
What this leaves is a void, and we know from reading fortune cookies that nature abhors a vacuum. Rather than dump the xXx franchise altogether, a decision was made that MGM/UA can't hope to match with James Bond. Revolution Studios chose to make the Three Strikes and You're Out concept ever-renewing. The die has been cast for the lead actor to change with each iteration. Each new xXx outing will come with a new set of faces thrown in free of charge. The only continuity will come in the form of Samuel L. Jackson and his frequent entrapment of semi-thugs under the auspices of The Patriot Act.
First up under the new umbrella concept is Ice Cube. His performance as an action hero/heel in films such as Ghosts of Mars and Torque combined with his box office draw in movies such as the Friday and Barbershop franchises was more than enough for Revolution. With Cube having the keys, a second decision was made to not allow the willing Asia Argento to return. Instead, the series will include a series of xXx girls along the lines of the Bond girls (not the Vivid girls, perverts).
Effectively, after only one outing in the series, the entire concept has already been torn down and rebuilt again. Don't take that to mean that Cohen and Diesel have completely soured on the project though. To the contrary, they remain executive producers. Also, Diesel has stated a willingness to do another movie should the franchise proceed beyond two films.
Driving home the point that the series is looking to mimic Bond whenever possible, the director hired is none other than Lee Tamahori. You might remember him from his last effort behind the helm - Die Another Day. (David Mumpower/BOP)
See the latest developments for this project on the XXX: State of the Union Movie News page.
Vital statistics for XXX: State of the Union
Main Cast Ice Cube, Scott Speedman
Supporting Cast Samuel L. Jackson, Willem Dafoe, Nona Gaye, Sunny Mabrey, Michael Roof
Director Lee Tamahori
Screenwriter Rich Wilkes
Distributor Sony/Revolution Studios
Trailer Click Here for Trailer
Official Site http://www.sonypictures.com/movies/triplex2/
Rating PG-13
Screen Count 3,480
Comparison films for XXX: State of the Union
Adjusted Opening
Adj PSA
Total BO
Adjusted Total
Bourne Supremacy, The 7/23/04 52.52 52.52 3165 16594.59 16594.6 176.05 176.05 0.00
xXx 8/9/02 44.51 46.27 3374 13191.00 13191.0 141.20 146.80 3.17
Bourne Identity, The 6/14/02 27.12 28.19 2638 10281.00 10281.0 121.47 126.29 4.48
Torque 1/16/04 11.44 11.44 2463 4645.64 4645.6 21.18 21.18 0.00
Biker Boyz 1/31/03 10.11 10.11 1766 5723.00 5723.0 21.91 21.91 2.17
Return to April 2005 Release Schedule


text:
/*
 * Copyright 1999-2004 The Apache Software Foundation.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
/*
 * $Id: Quo.java,v 1.2.4.2 2005/09/14 21:31:44 jeffsuttor Exp $
 */
package com.sun.org.apache.xpath.internal.operations;

import com.sun.org.apache.xpath.internal.objects.XNumber;
import com.sun.org.apache.xpath.internal.objects.XObject;

/**
 * The 'quo' operation expression executer. (no longer supported by XPath).
 * @deprecated
 */
public class Quo extends Operation
{
    static final long serialVersionUID = 693765299196169905L;

  // Actually, this is no longer supported by xpath...

  /**
   * Apply the operation to two operands, and return the result.
   *
   *
   * @param left non-null reference to the evaluated left operand.
   * @param right non-null reference to the evaluated right operand.
   *
   * @return non-null reference to the XObject that represents the result of the operation.
   *
   * @throws javax.xml.transform.TransformerException
   */
  public XObject operate(XObject left, XObject right)
          throws javax.xml.transform.TransformerException
  {
    return new XNumber((int) (left.num() / right.num()));
  }
}


text:
The Houston Rodeo Welcomes Dierks Bentley....Again
by Shelby Grace / 838 days ago / Comments
Press Release: Dierks Bentley Announced as CRS 2018 Featured Speaker
The Houston Livestock Show and Rodeo is arguably the biggest and best rodeo in the world. Ask any native Houstonian and they will whole-heartedly back that statement up. For every country music artist, this venue is the pinnacle of their career and if they get the privilege, they know without a doubt, they have arrived. And for Dierks Bentley, well this wasn't his first Rodeo.
Dierks played his first Houston Rodeo show in 2004, making the performance on Friday, March 24th his 7th Rodeo appearance. Yes, Houston loves some Dierks Bentley, and he loves Houston back. His performance included a lot of story-telling, as any stellar country show should, leading into his hit song "I Hold On" about his favorite memory of his trip to Nashville with his dad in his 1994 Chevy pickup. While his father has since passed on, Dierks holds on to his pickup truck and like the song says, "I wouldn't trade that thing in for a rocket."
Starting off the evening with a list of ballads, his voice was pure, rugged perfection. Including "Different for Girls" in the set without his duet sidekick, the Rodeo crowd was happy to fill in for Elle King. Every cowgirl in the room sang their hearts out and it brought a big, sexy grin to Dierks' face.
Mid-set, Dierks complimented Texans for their staunch patriotism and steadfast belief in prayer, leading into a tribute to military, teachers, and other everyday heroes followed by a smashing performance of his song, "Riser". My body was fraught with chills as he sang those lyrics of strength and promise that come what may, we are all going to be alright, because as long as we keep rising, we are all survivors.
Moving into the last part of his 7th Houston Rodeo performance, Dierks continued his set with hit party songs like "Somewhere on a Beach", "What Was I Thinking", and closing with "Drunk on a Plane". All #1 singles, the crowd went wild. Men and women alike seemed to be drawn to the energy and charisma of this Arizona boy with humble roots. It's hard not to love Dierks Bentley. Always a classic entertainer, he was on point that night.
In true Houston Rodeo style, Dierks ended his set and was escorted around the NRG Arena in the back of a pickup truck to get a closer view of his buck wild fans. Dierks let Houston know he'd like to keep coming back. I have no doubt Houston will welcome him back. Mr. Bentley, we're still holding on to you.
Follow Dierks Bentley
Dierks Bentley HLSR 2017 Houston Rodeo NRG Stadium
About Shelby Grace
I'm a wife and mother of two boys, born and raised Proud Texan! I am a Graduate of the University of Houston with a Bachelor's degree in Marketing. I love music, singing, writing and spending quality time at home with my family!
Music You Need To Hear!


Stock Photo - Pomeranian redhead in nature - Wunderbare Wahl!
Our tiny white micro / teacup pomeranian puppy - YouTube. Our tiny white micro / teacup pomeranian puppy - YouTube. Pinterest. Verken deze ideeën en meer!
My cute Blue eyed blue Merle Pomeranian puppy, Peppermint. She likes to nibble fingers. My cute Blue eyed blue Merle Pomeranian puppy, Peppermint.


Since a couple of months ago there are some races on iRacing that the spotter is not working. It's just randomly. The crew chief is still telling me the lap times, differences with other, etc. but the spotter does not say a word so I have no clue when I have a car on my sides or not. Then suddenly in another race it works normally but after that maybe another 2-3 races with no spotter.
I even tried with other spotter voices but same problems.
Mine will work for a race, then mid race it would just quit. I'd hear the beep like it was going to tell me something but it never does. Very odd, was on the older version, cant get the latest version to start.
I just returned to racing after a break for a few months. Also getting this issue, just assumed it was because it was not updated in a while. Going to try a reinstall tomorrow and hope for the best.
Hello this also happens to me. Spotter seems to disappear for seemingly no reason. I did a Prac>Qual>Race this morning in iRacing and got no spotter notifications for the few times I was passed. https://pastebin.com/uZVV2M0t here is the console, the last bottom part is the race in question (25 min race) You can see me enable the spotter around the time I noticed it was silent, but it should have been enabled in the beginning. I didn't get to see if it worked after that.
EDIT: I decided not to use rolling start command anymore as I've done a few races now and spotter is working ok. I wonder if saying rolling start is causing issues because that's something I did do on the above race.
Last edited by Spooling88; 03-02-2019 at 01:59 AM.
the "rolling start" command is only intended to be used when you're running a manual rolling start. That is, when a bunch of online players have agreed to drive the first race lap as if it were a formation lap, and execute a rolling start at the end of it. This is for games that don't support a proper rolling start, and is used in some league races. In these cases the game isn't aware of the players' actions - it sends data assuming the players are actively racing.
Ahh I see, thanks for the clarification. Amazing app keep up the good work!


text:
Best Excel Tutorial
Basic Tutorial
Advanced Tutorial
Match Function: How it Works and 10 Ways to Use It
The match function is the one that search for a specific item/value in a cells' range, and then return the position that is relative to the item in the range.
Parameters and Arguments
The function has a lookup value, array and match type, and looks like this: MATCH (LOOKUP_VALUE, LOOKUP_ARRAY, [match_type]).
The descriptions of the arguments:
Lookup Value: This is an essential part of the function. It is the value that the user wishes to match in the lookup array.
Lookup Array: This is required part of the function. It is a cells' range that would be searched.
Match Type: This is optional, and can either be 0 or 1.
Example 1: Simple Match Formula
We are using a match formula to find out if the price has been set for a product.
Example 2: Where is a Product?
The business' products have been layout in a Microsoft Excel. We are now trying to find out where a product is in the list. Thanks to Match function in Excel, it is very easy to find it.
Example 3: IF and MATCH
The product has been listed. But, we are trying to find out the price of the product. But, we'd know the price of a product, and we'd want to answer if the price is right. This is why we find IF and MATCH formulas useful.
Example 4: Finding Employee with MATCH
The employees are quite many. But, the executive do not know all of them, and would like to find what row the employee has a name, and we could not find out the email. There are other functions that could be used for finding it, but we prefer using the match to find out the row. This was meant to find out what row to go to, in order to get the email of that employee.
Example 5: Double Match Formula
We'd know the name of the product, but we don't know if the price was correct or if they are on the same row. This made us worried about acknowledgement of the inputted information, which is why we find MATCH function in Excel to be very useful for verifying that the data is both completed and in the same row. We are now going to use double MATCH formula to find the answer that we are looking for.
Example 6: Did we Send Right Details and Information?
We are sending a product to a customers. The price has been set, but due to a specific deal we made with the client, we would like to make sure that the price was correct. We have determined that the client would only get to pay a specific amount of money, which is why we will use the IF and double match formula.
Example 7: Is Everything in The Same Row?
It is easy to list all the products that are being sold. But, the company has just fired one of its workers for inadequacy in their performance, and one of them was that they frequently miss one critical details that will end up costing the company money. The employee would not miss something small, but he would put 100 dollars beside a product that cost 1500. This is why we are going to use triple MATCH formulas to ensure that the expensive products have right layout. These would allow me to ensure that everything is in order.
Example 8: Complete Text
The whole data has been layout as text, and we are looking for a product. We are using the same data as previous one.
Example 9: Is Our Product in Another Spreadsheet?
We have now gone from having our data in one sheet, and would like to verify that the same data in one is matching the other.
Example 10: Information from another Document
The situation is that we have our data ready, and now we need to find the solid correspondent between both data, so we could determine if our data has been solid. We'd have the previous year in another document, and this year is in the current one, which is why we need to verify that the data is coherent. It is about acknowledging that the total is there too, so we could find it.
How to calculate variance in Excel?
How to remove green triangles from cells?
How to calculate CAGR?
How to calculate logarithms and inverse logarithms in Excel?
3 axis chart
COUNTIF function
How to calculate ROI?
How to use the integral function?
BCG Matrix
How to Break Chart's column?
Backwards Vlookup
How to remove non printable characters in Excel?
How to calculate Standard Deviation?
Two chart types in one chart
Multiple Overlay Charts
Age Population Pyramid
How to Calculate Stock Beta?
Best Excel Tutorial - complex and absolutely free tutorial of Excel. Best place to learn Excel online.
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I'm hoping to have the kits listed by Friday. Let me know if you're interested in other color options and I'll see what I can build for you!
I ordered the pattern, I'm closely watching my e-mail for it to arrive. Hope you got it. How many pages are in there?
lovely combinations, love the blue and green!


Trace Mineral B-12 - Why Should I Take It?
May 1, 2018, 7:15 a.m.
Trace Minerals-B12 was originally designed for patients with undulant fever (rising and falling fever passed from animal to human from untreated milk products). It contains a lot of manganese, which is depleted by undulant fever. This product also contains zinc, copper, iodine and vitamin B12 – all trace minerals, meaning that our bodies require low amounts of all of these minerals to help perform regulatory and structural functions.
Manganese is an enzyme activator and a ligament strengthener and has been found by doctors in the field to be useful for people with herniated discs. In the case of herniated discs, which are often times extremely painful, taking this supplement can strengthen the ligaments around the disc which will provide more support and decrease discomfort.
Breastfeeding Issues? Chiropractic Can Help!
May 1, 2018, 7:05 a.m.
We have noticed an influx of new babies in the office with latching issues and difficulty nursing. This can become extremely concerning and frustrating for the mom. In an article from Pathways magazine, Dr. Jeanne Ohm does a great job in explaining how this happens and why chiropractic care should be a consideration.
"Modern birthing procedures, even those with seemingly minimal intervention, are known to cause trauma and stress to the infant's cranium and spine.
April 1, 2018, 7:21 a.m.
Most of us realize the benefits of stretching, but how many of you actually stretch daily? I always find that the stretching routines get pushed to the side, much like the recommendations for daily veggies and fruit. In theory, it's a great idea, but many of us get "busy" or usually don't remember to stretch because they're "not in pain". We see this a lot!
Here are some great benefits to regular daily stretching. Hopefully it will make you reconsider!
Mid-day Energy Boost. Just a few minutes of stretching each afternoon can increase blood flow through your entire body, including your brain.
Improve Balance. Research shows that stretching can help with fine motor coordination skills, which definitely can help prevent tripping and falls!
Celebrating Our 9 Year Anniversary!
April 1, 2018, 7:19 a.m.
Back in January of 2009, I was an associate doctor in Johnston, IA, and Dr. Bret was finalizing plans for HIS office in Ames. We were not married yet, and although we were engaged, we thought it best to work separately.
That thought process changed just one month later and we agreed that it would be best for both of us to work together. Opening day was April 1, 2009, and I was away at training and missed it!
Throughout these past nine years many things have changed. When the office opened, we were living in Sheldahl (so that we would be in between where I was working in Johnston, to Ames). We were married in October of 2009 and then moved to Gilbert in March of 2010. We had our daughter 4 months later, and then welcomed our son 18 months after that.
What's the Deal with Lacrosse Balls?
March 1, 2018, 12:56 p.m.
We began offering lacrosse balls for sale at the office back in the fall. Many people have been curious about what exactly they are used for. Trust us, not one of us plays lacrosse! Instead, we have researched the use of these balls as a myofascial release technique and they are pretty effective.
Here are some tips on covering the main areas.


text:
package water.util;

import org.apache.log4j.Level;
import org.apache.log4j.Logger;
import org.apache.logging.log4j.core.Filter;
import org.apache.logging.log4j.core.config.Configurator;
import org.apache.logging.log4j.core.config.builder.api.*;
import org.apache.logging.log4j.core.config.builder.impl.BuiltConfiguration;

import java.io.File;
import java.net.URISyntaxException;
import java.net.URL;
import java.util.ArrayList;
import java.util.List;
import java.util.function.Function;

public class LoggerBackend {

    public static final Level[] L4J_LVLS = { Level.FATAL, Level.ERROR, Level.WARN, Level.INFO, Level.DEBUG, Level.TRACE };
    public static final org.apache.logging.log4j.Level[] L4J_LOGGING_LVLS = {
            org.apache.logging.log4j.Level.FATAL,
            org.apache.logging.log4j.Level.ERROR,
            org.apache.logging.log4j.Level.WARN,
            org.apache.logging.log4j.Level.INFO,
            org.apache.logging.log4j.Level.DEBUG,
            org.apache.logging.log4j.Level.TRACE
    };

    public int _level;
    public String _prefix;
    public String _maxLogFileSize;
    public boolean _launchedWithHadoopJar;
    public boolean _haveInheritedLog4jConfiguration;
    public Function<String, String> _getLogFilePath;

    public Logger createLog4j() {
        String h2oLog4jConfiguration = System.getProperty("h2o.log4j.configuration");

        if (h2oLog4jConfiguration != null) {
            // Try to configure via a file on local filesystem
            File file = new File(h2oLog4jConfiguration);
            if (file.exists()) {
                Configurator.reconfigure(file.toURI());
            } else {
                // Try to load file via classloader resource (e.g., from classpath)
                URL confUrl = LoggerBackend.class.getClassLoader().getResource(h2oLog4jConfiguration);
                if (confUrl != null) {
                    try {
                        Configurator.reconfigure(confUrl.toURI());
                    } catch (URISyntaxException e) {
                        System.err.println("ERROR: failed in createLog4j, exiting now.");
                        e.printStackTrace();
                        return null;
                    }
                }
            }
        } else {
            try {
                reconfigureLog4J();
            } catch (Exception e) {
                System.err.println("ERROR: failed in createLog4j, exiting now.");
                e.printStackTrace();
                return null;
            }

            // TODO: hadoop and sparkling water cases
        }
        return Logger.getLogger("water.default");
    }

    public void reconfigureLog4J() {
        ConfigurationBuilder<BuiltConfiguration> builder = ConfigurationBuilderFactory.newConfigurationBuilder();
        builder.setStatusLevel(L4J_LOGGING_LVLS[_level]);
        builder.setConfigurationName("H2OLogConfiguration");

        // configure appenders:
        String patternTail = _prefix + " %10.10t %5.5p %c: %m%n";
        String pattern = "%d{MM-dd HH:mm:ss.SSS} " + patternTail;

        LayoutComponentBuilder layoutComponentBuilder = builder.newLayout("PatternLayout").addAttribute("pattern", pattern);

        builder.add(builder.newAppender("Console", "Console")
                .addAttribute("target", "SYSTEM_OUT")
                .add(layoutComponentBuilder));

        builder.add(newRollingFileAppenderComponent(builder, "R1", "1MB", _getLogFilePath.apply("trace"), pattern, Level.TRACE));
        builder.add(newRollingFileAppenderComponent(builder, "R2", _maxLogFileSize, _getLogFilePath.apply("debug"), pattern, Level.DEBUG));
        builder.add(newRollingFileAppenderComponent(builder, "R3", _maxLogFileSize, _getLogFilePath.apply("info"), pattern, Level.INFO));
        builder.add(newRollingFileAppenderComponent(builder, "R4", "256KB", _getLogFilePath.apply("warn"), pattern, Level.WARN));
        builder.add(newRollingFileAppenderComponent(builder, "R5", "256KB", _getLogFilePath.apply("error"), pattern, Level.ERROR));
        builder.add(newRollingFileAppenderComponent(builder, "R6", "256KB", _getLogFilePath.apply("fatal"), pattern, Level.FATAL));
        builder.add(newRollingFileAppenderComponent(builder, "HTTPD", "1MB", _getLogFilePath.apply("httpd"), "%d{ISO8601} " + patternTail, Level.TRACE));

        AppenderRefComponentBuilder consoleAppenderRef = builder.newAppenderRef("Console");

        // configure loggers:
        List<AppenderRefComponentBuilder> appenderReferences = new ArrayList();
        appenderReferences.add(builder.newAppenderRef("R1"));
        appenderReferences.add(builder.newAppenderRef("R2"));
        appenderReferences.add(builder.newAppenderRef("R3"));
        appenderReferences.add(builder.newAppenderRef("R4"));
        appenderReferences.add(builder.newAppenderRef("R5"));
        appenderReferences.add(builder.newAppenderRef("R6"));
        appenderReferences.add(consoleAppenderRef);

        builder.add(newLoggerComponent(builder, "hex", appenderReferences));
        builder.add(newLoggerComponent(builder, "water", appenderReferences));
        builder.add(newLoggerComponent(builder, "ai.h2o", appenderReferences));
        builder.add(builder.newRootLogger(String.valueOf(L4J_LVLS[_level])).add(consoleAppenderRef));

        // Turn down the logging for some class hierarchies.
        builder.add(newLoggerComponent(builder, "org.apache.http", appenderReferences, "WARN"));
        builder.add(newLoggerComponent(builder, "com.amazonaws", appenderReferences, "WARN"));
        builder.add(newLoggerComponent(builder, "org.apache.hadoop", appenderReferences, "WARN"));
        builder.add(newLoggerComponent(builder, "org.jets3t.service", appenderReferences, "WARN"));
        builder.add(newLoggerComponent(builder, "org.reflections.Reflections", appenderReferences, "ERROR"));
        builder.add(newLoggerComponent(builder, "com.brsanthu.googleanalytics", appenderReferences, "ERROR"));
        // Turn down the logging for external libraries that Orc parser depends on-->
        builder.add(newLoggerComponent(builder, "org.apache.hadoop.util.NativeCodeLoader", appenderReferences, "ERROR"));

        // HTTPD logging
        appenderReferences = new ArrayList();
        appenderReferences.add(builder.newAppenderRef("HTTPD"));
        builder.add(newLoggerComponent(builder, "water.api.RequestServer", appenderReferences));

        Configurator.reconfigure(builder.build());
    }

    AppenderComponentBuilder newRollingFileAppenderComponent(ConfigurationBuilder builder, String name, String sizeBasedTriggeringPolicyValue,  String fileNameValue, String filePatternValue, Level thresholdFilterLevel) {
        ComponentBuilder triggeringPolicy = builder.newComponent("Policies")
                .addComponent(builder.newComponent("SizeBasedTriggeringPolicy").addAttribute("size", sizeBasedTriggeringPolicyValue));
        LayoutComponentBuilder layoutBuilder = builder.newLayout("PatternLayout")
                .addAttribute("pattern", filePatternValue);
        FilterComponentBuilder thresholdFilter = builder.newFilter("ThresholdFilter", Filter.Result.ACCEPT, Filter.Result.DENY)
                .addAttribute("level", thresholdFilterLevel.toString());
        ComponentBuilder rolloverStrategy = builder.newComponent("DefaultRolloverStrategy").addAttribute("max", 3);

        AppenderComponentBuilder appenderBuilder = builder.newAppender(name, "RollingFile")
                .addAttribute("fileName", fileNameValue)
                .addAttribute("filePattern", fileNameValue.concat(".%i"))
                .add(thresholdFilter)
                .addComponent(triggeringPolicy)
                .addComponent(layoutBuilder)
                .addComponent(rolloverStrategy);

        return appenderBuilder;
    }

    LoggerComponentBuilder newLoggerComponent(ConfigurationBuilder builder, String name, List<AppenderRefComponentBuilder> appenderReferences) {
        LoggerComponentBuilder loggerComponentBuilder = builder.newLogger(name);
        for (AppenderRefComponentBuilder reference : appenderReferences) {
            loggerComponentBuilder.add(reference);
        }
        loggerComponentBuilder.addAttribute("additivity", false);
        return loggerComponentBuilder;
    }

    LoggerComponentBuilder newLoggerComponent(ConfigurationBuilder builder, String name, List<AppenderRefComponentBuilder> appenderReferences, String level) {
        LoggerComponentBuilder loggerComponentBuilder = builder.newLogger(name);
        for (AppenderRefComponentBuilder reference : appenderReferences) {
            loggerComponentBuilder.add(reference);
        }
        loggerComponentBuilder.addAttribute("additivity", false);
        loggerComponentBuilder.addAttribute("level", level);
        return loggerComponentBuilder;
    }
}


text:
Pfister Award Winner Describes Brief Psychotherapy Modules for Hope in the Midst of Demoralization
Hope is a natural antidote to despair and demoralization experienced by psychiatric patients that can be encouraged and supported through brief "hope" interventions that can be employed in crisis situations, according to James L. Griffith, M.D. Griffith delivered APA's 2017 Oskar Pfister Award lecture today at IPS: The Mental Health Services Conference in New Orleans.
Griffith, the chair of psychiatry at George Washington University (GWU) School of Medicine, described his work developing brief intervention modules that help patients practice hope in demoralizing life situations and that can be taught to trainees and other mental health clinicians. His work on the subject was published in an article in Academic Psychiatry (July 2017).
"Despair from demoralization is a constant threat to patients with chronic mental illnesses, refugees fleeing persecution, elderly who are socially isolated, the medically disabled, and other marginalized or displaced people," Griffith said.
Griffith said that he and his colleagues have identified 14 discrete psychotherapeutic practices, or interventions, in the psychotherapy literature that foster hope in patients. These practices correspond to one of four types of coping (problem solving and goal seeking, activating a core identity, emotion regulation, and relational coping) that clinicians can use depending on the strengths of the specific patient. Moreover, they can be employed in a crisis situation without formal psychotherapeutic training.
He described several clinical vignettes in which the "hope" modules were employed to meet and challenge the demoralizing life situations faced by individual patients. For instance, he described a suicidal patient in despair because her house was being foreclosed, and her dog—a companion of many years—had recently died.
A second-year resident at GWU, with no formal training in psychotherapy, asked the patient, "In the past when you faced adversity, what did you do?" The patient recalled when her father, on his deathbed, told her she "was a strong fighter" and the "glue that held the family together."
These were affirmations that drew on this patient's strength, activating her core identity. The resident advised the patient to find a picture of her father and look to it whenever she felt despair. The resident also advised the patient to reach out to her children. These actions began a process of rebuilding the patient's sense of self-efficacy and control over her own fate.
Griffith said that to design psychotherapeutic interventions that help people practice hope, they must be usable in the real-life conditions in which patients find themselves.
"They must be usable under the often-chaotic conditions of refugee life, homelessness, poverty, or medical or psychiatric illness where a clinician may have only one or two conversations in settings ill-suited for psychotherapy," he said.
Look for further coverage of IPS: The Mental Health Services conference in upcoming editions of Psychiatric News.
(Image: Ellen M. Dallager)
Labels: 2017 IPS: The Mental Health Services Conference; APA, George Washington University School of Medicine., James L. Griffith, M.D., New Orleans, Oscar Pfisker Award
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John started Sal's Meat Market in Bridgeport, Connecticut, while a student at Sacred Heart University, located in Fairfield/Bridgeport, Connecticut. He was later affiliated with the ensemble group "The Downtown Cabaret." Coincidentally, he was a friend of Susan Ryan, the mother of Meg Ryan. A mutual friend, also associated with The Downtown Cabaret, was the daughter-in-law of actress Mabel Albertson, the sister of actor Jack Albertson.


Put the chicken legs in your stockpot and add 1.5 L of water. Add the garlic, carrot, celery, parsley, thyme, salt, pepper and curry powder.
Bring to a boil and, once boiling, reduce the heat. Allow to simmer for approximately 2 hours or until the water is yellow and the meat is tender. The meat should almost be falling off the bones.
Turn off the heat and let the soup cool down. Drain the vegetables and chicken from the soup. Now it is time to refrigerate the stock preferable for one night. A layer of fat will rise and harden at the top of the stock. Now you can easily skim the fat of with a spoon.
If you don't have the time to leave the soup for the night you could pour it into containers and leave them in the freezer for an hour to hasten this process.
Boil the soup again, once skimmed, and add the chicken stock cubes. Once the cubes have dissolved add the pieces of deboned chicken and fine egg noodles. Before serving you can garnish your soup with some chopped parsley leaves.