This year, I have thrown down the proverbial gauntlet and am taking no prisoners when it comes to my health. Now that I am 36, I look back and realize I have done my body no favors by the choices I've made so far. Although I've always remained somewhat active, there have been times that I've let that slide for too long. My main focus this year though, centers around my diet. Gone are the days of poor nutritional choices, for in 2013, this girl is turning over a new leaf.
To stay healthy, it's recommended that 30 minutes of moderate exercise be performed each and every day. My goal this year is to make exercise a top priority, as soon as I've completely reformulated my junk-filled diet. Somehow someway, I will create a regular space to exercise in and that will be my time alone. Just like I always find the time to bathe and brush my teeth, no matter how hectic life becomes, I must now carve out this daily time allotment for fitness.
Now I LOVE bread and pasta, but what I need to do here is tweak what type of bread and pasta I'm consuming. Enriched white flour, white pasta, white potatoes, etc. are actually very bad for your body, because they are processed by your body in much the same way as swallowing a spoonful of sugar. These processed carbs overload your body with a quick spike of sugar, wreaking havoc on your insulin levels and spiking your blood sugar temporarily, only to leave you crashing hard later. For optimum health, it's best to keep your blood sugar level steady throughout the day and eating whole grains is a great way to do just that.
Fiber-filled snacks are terrific at curbing your appetite until mealtime and they keep you feeling full and satisfied for hours. Unfortunately, finding snacks made from whole grains is easier said than done. Thankfully, the Quaker Oats Company has designed an entire line of healthy snacks just right for your entire family called Quaker® PoppedTM, which are available at your local Walmart. They're tasty, low in calories and extremely portable. The best thing is, these bite-sized snacks are actually made from whole grain brown rice and corn, and they're popped, not fried.
This year, I am getting back to my roots and doing my best to ditch all of those highly processed foods from my diet. In my opinion, eating whole foods is the most healthy route to go, so I'm spending longer in the store reading labels in order to make the best choices. Basically, I'm looking for items containing a minimum number of ingredients, especially those devoid of preservatives, artificial sweeteners, or unrecognizable additives.
The thing I try to remember is that all five of these goals are to be conquered one at a time. Major changes like these take up to 66 days to incorporate into my daily schedule and eventually they will become automatic. When that time comes, I'll move on to the next and work on making that goal a "no-brainer". By the end of 2013, I will hopefully have all five living healthy goals under my belt. "The journey of a thousand miles begins with a single step..." What will you be journeying toward this year?
"The journey of a thousand miles begins with a single step..." What will you be journeying toward this year?


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UKIP MEP Tim Aker slams Theresa May's speech in Florence
UKIP MEP and Aveley councillor Tim Aker has slammed Prime Minister Theresa May over her Brexit speech in Florence on Friday afternoon.
PM Theresa May has said there should be a transition period of "about" two years after Brexit, during which trade should continue on current terms.
EU migrants will still be able to live and work in the UK but they will have register with the authorities, under her proposals.
And the UK will pay into the EU budget so member states are not left out of pocket.
Cllr Tim Aker MEP said: "Chief Remainer Theresa May has yet again sold out the 17m people that voted for Brexit.
"The people that voted Tory at the last General Election gave Mrs May the power to yet again U-Turn on her promises.
"If people keep on voting for the Tories, then Brexit will truly be at risk."
UKIP MEP Tim Aker slams Theresa May's speech in Florence added by Staff Reporter on September 22, 2017

redpajama_set_name: RedPajamaCommonCrawl


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Simeone: Griezmann's history and numbers speak for themselves
December 1, 2019 admin FOOTBALL 0
Atletico Madrid head into the clash with Barcelona in the knowledge that a victory puts them right back into the Spanish title race, however without Antoine Griezmann's return threatening to overshadow the match itself, Diego Simeone has made clear that the Frenchman's history speaks for itself.
It's expected that the former Atletico forward will receive a harsh welcome from home supporters on his first visit back to the Estadio Wanda Metropolitano.
"Griezmann's history and numbers speak for themselves, I don't need to add anything," Simeone explained in his pre-match press conference.
"I won't talk about Griezmann because he plays for another team.
"What people do is their decision, I was always clear about what I thought of him when I worked with him."
Joao Felix was on the receiving end of a Simeone tirade last weekend, with the Portuguese forward seemingly unaware he was supposed to be on the left, yet the former River Plate coach will start him against Los Cules.
"He is getting better," he added.
"The progression we were talking about before the Granada match came as a result of it.
"He will surely start from the beginning, and we shall see if that's on the wing or alongside Alvaro."
It's been noted that Simeone's record against the Blaugrana is far better in the Champions League than in LaLiga Santander, but he believes whatever the competition a visit from the Catalan giants is always a tough test.
"I always see it as a difficult match, they are a strong rival," he intimated.
"We have two players out, and last year we also had injuries.
"We have different responses to see what scenarios they create for us."
Zidane: Real Madrid wil count on him
Valverde: I would vote for the best to win Ballon d'Or, we all know who he is


The Outer Banks hotels on the northern end of the island tend to be concentrated in Kill Devil Hills and Nags Head. We have linked up with Hotel Combined. This is exciting because wherever you see the name of the hotel as a link (blue text), click on it and it will provide you with more details of the hotel, how previous guest have rated the hotel, pictures of the hotel and you can book your stay right on Outer Banks Revealed. No need to do massive hunting on the Internet. All the information is provided right here!
We have included an "average price" amount for each Outer Banks hotel. This is an average across the entire year, which means the rates are likely to be higher during the summer months and cheaper during the off-season periods (November through April). Again, use this more to compare on a relative basis than as an absolute indicator of costs.
Also indicated are those Outer Banks hotels that advertise as an "Outer Banks pet friendly hotel", meaning you are able to have your pet stay with you in the room. It is likely that more than those indicated allow pets, so you may want to ask. A separate pet fee is likely to apply.


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Iran Says Arrests Made Over Downing Of Ukrainian Passenger Plane
TEHRAN, Iran — Iran's judiciary said Tuesday arrests have been made for the accidental shootdown of a Ukrainian passenger plane that killed all 176 people on board just after takeoff from Tehran last week.The announcement came amid an upswell of anger and protests by Iranians in recent days over the downing of the jetliner last Wednesday and apparent attempts by senior officials in Iran to coverup the cause of the crash.Iran, which initially dismissed allegations that a missile had brought down the plane, acknowledged only on Saturday — three days after and in the face of mounting evidence — that its Revolutionary Guard had shot down the plane by mistake as the force braced for a possible military confrontation with the United States.Judiciary spokesman Gholamhossein Esmaili said "extensive investigations have taken place and some individuals are arrested." His statement on the judiciary's website did not say how many individuals had been detained or name them.RELATED
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Iran's president on Tuesday also called for a special court to be set up to probe the incident."The judiciary should form a special court with a ranking judge and dozens of experts," President Hassan Rouhani said in a speech televised in Iran. "This is not an ordinary case. The entire the world will be watching this court."Rouhani called the incident "a painful and unforgivable" mistake and promised that his administration would pursue the case "by all means.""The responsibility falls on more than just one person," he said, adding that those found culpable "should be punished.""There are others, too, and I want that this issue is expressed honestly," he said, without elaborating.Iran shot down the plane as its forces were on alert for possible U.S. retaliation after Iran launched ballistic missiles on two military bases housing U.S. troops in Iraq. No one was hurt in that attack, which was carried out in response to the stunning killing of Revolutionary Guard Gen. Qassem Soleimani in an American airstrike in Baghdad.While Rouhani pointed to mistakes and negligence, he also repeated the government's line that the tragedy was ultimately rooted in U.S. aggression."It was the U.S. that made for an agitated environment. It was the U.S. that created an unusual situation. It was the U.S. that threatened and took our beloved (Soleimani)," he said.Rouhani called the government's admission that Iranian forces shot down the plane a "first good step."He added that Iranian experts who retrieved the Ukrainian plane's flight recorder, the so-called black box, have sent it to France for analysis.The plane, en route to the Ukrainian capital of Kyiv, was carrying 167 passengers and nine crew members from several countries, including 82 Iranians, 57 Canadians — including many Iranians with dual citizenship — and 11 Ukrainians, according to officials. There were several children among the passengers, including an infant.Gen. Amir Ali Hajizadeh, the head of the Guard's aerospace division, said over the weekend his unit accepts full responsibility for the shootdown. He said when he learned about the downing of the plane, "I wished I was dead."Dozens detained in protests The incident raised questions about why Iran did not shut down its international airport or airspace the day it was on alert for U.S. military retaliation.The shootdown and the lack of transparency around it has reignited anger in Iran at the country's leadership. Online videos appeared to show security forces firing live ammunition and tear gas to disperse protests in the streets.Also Tuesday, Iran's judiciary said that 30 people had been detained in the protests, and that some were released, without elaborating further. An Iranian film director who'd called for protests in Tehran's Azadi, or Freedom Square, is among those released.Iranian authorities briefly arrested British Ambassador Rob Macaire on Saturday evening. He has said he went to a candlelight vigil to pay his respects for the victims of the Ukrainian plane shootdown and left as soon as the chanting began and it turned into a protest.Iran's Foreign Ministry summoned the British ambassador on Sunday to protest what it said was his presence at an illegal protest. Britain, in turn, summoned Iran's ambassador on Monday "to convey our strong objections" over the weekend arrest.
Read more: https://www.huffingtonpost.ca/entry/iran...
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Rita Katz Hunts Terrorists
In her excellent book, Terrorist Hunter: The Extraordinary Story of a Woman Who Went Undercover to Infiltrate the Radical Islamic Groups Operating in America, Rita Katz (who published it anonymously, but has since been exposed because of lawsuits) describes what she found out about front groups in the United States. She explains how they work, where the money comes from, and where the money goes (to Jihadis who kill kafirs).
There is a LOT of money behind these front groups (wealthy Saudi oil-barons), and they want to make a show of innocence (using the Islamic principle of taqiyya) so they are suing Katz. She has helped expel Jihadis from America, and her work helps prevent known terrorists (and promoters of jihad) from coming freely to the USA as they used to be able to do. She is a hero, and I recommend her book, Terrorist Hunter.
Read an interview with Katz: The Terrorist Hunter Speaks.
Video Makers, the White Roses
A group calling themselves "White Roses" has created a video to inform non-Muslims about Islam. It's called Three Things About Islam. You can view it on YouTube or click here to see it on Citizen Warrior.
White Roses is based in Sweden. Their first version is in English, and they're now working on two more versions in German and Swedish.
The name "White Roses" is based on a student resistance group "Die weiße Rose" in Nazi Germany. The group became known for an anonymous leaflet campaign, from June 1942 until February 1943, which called for active opposition to Adolf Hitler's regime.
A spokeswoman for White Roses said, "We see a parallel here concerning the protection of free speech. As you posted today, freedom of speech is getting more and more limited. The intention in choosing this name is to make a point that there will be groups opposing the doctrine of the state and speaking their mind."
We're honored to say the video was inspired, in part, by three Citizen Warrior articles:
The Least You Need to Know About Islam
What "Religion of Peace" Really Means
What is the Root Cause of Islamic Terrorism?
We've given White Roses the Citizen Warrior Hero Award because they are doing exactly what needs to be done — what we should all be doing: Sharing with non-Muslims key information about Islam, making it interesting and easy to hear, keeping it non-partisan, focusing on Sharia and not on Muslims, keeping it clean and not staining it with racism or hatred, and in this case, putting it in a form that is easily shareable by others.
I've posted the video on a new site I'm building. The purpose of the new site is to help us reach people who might be put off by anything that smacks of Islam-bashing. I suggest you use that site to share the video with your uninformed friends: Three Things About Islam Video.
One last thing: The video presents information you probably already know, but its "target market" is people who don't know much, so it's a good tool we can use to share with less-informed people. I hope you use it.
Labels: Sweden
I tried to read the Quran many times, but I couldn't stay awake, and it was confusing because the traditional way to arrange the chapters is from the longest chapter to the shortest, rather than arranging them in the order they were written. Since many of the passages are events in Mohammad's life, reading the Quran start to finish is disorienting. It jumps around.
And many of the passages have no context. They seem to start in the middle, or assume the reader already knows things about Mohammad's life.
Not only that but most English translations are written in Olde English, which makes it even harder to read. And the original Quran is full of tedious repetitions of the same stories.
But Bill Warner, a former professor of physics, created a readable Quran. This is a vital key to defeating the third jihad. We non-Muslims need to know what is in that book since 61% of it is about us. Reading the Quran is the single most important thing a non-Muslim can do to educate themselves about Islam. Warner's book makes this a lot easier.
The book is entitled An Abridged Koran. It is written in chronological order in plain modern English, it removes the repetition, and it includes biographical information where needed so you actually know what it the passages refer to. It it excellent.
Bill also has several great weekly newsletters. Sign up here: Political Islam (in the left-hand column).
Trencherbone the Great
A blogger who calls himself "Trencherbone" has done us a great service. On a single page, he has compiled an enormous collection of resources entitled, Everything You Need to Know About Islam, arranged in alphabetical order.
Each category has several, sometimes very many, links to articles on that topic.
When we're talking to our fellow non-Muslims about Islam, they want proof. They want facts, statistics, examples. Their minds are not blank when it comes to Islam. They have already been told by seeming experts that Islam is a religion of peace, that it has been hijacked by extremists, and that people like you are racist, bigoted Islamophobes. So you had better make a good case if you want to get through.
Trencherbone has made it much easier to make a good case. And for that, and all the effort he has put into this excellent resource, he has justly earned the Citizen Warrior Hero Award. Check out his page: Everything You Need to Know About Islam.
Al Dajjal: Dangerous to Islamic Supremacists
I first read about Al Dajjal in an article about Pakistan. The article mentioned that Pakistan had blocked certain web sites and blogs that criticized Islamic doctrine, preventing their citizens from seeing them. It specifically mentioned the blog, Islam Exposed. And I thought, "If it's good enough to be blocked by Pakistan, it must be worth reading."
I was surprised to discover my petition to stop Muslim immigration in the Islam Exposed sidebar. I introduced myself to him. I was immediately impressed with his ability to document everything he said using core Islamic texts.
When White Roses posted their video, Three Things About Islam, Al Dajjal created a supporting post, showing the validity of the points made in the video. And he just did the same with Citizen Warrior's most famous article, The Terrifying Brilliance of Islam.
In the comments on the White Roses video, Muslims often make comments, producing confusion (sometimes deliberately, I think) and it was interfering with the purpose of the video, which was to educate people who don't know much about Islam. For people who know little about Islam, it's confusing when Muslims say "none of this is true." So Al Dajjal's doctrinal reference post is important. The post shows clearly the voluminous support in core Islamic doctrines for the message in the video. And since the video has already been viewed by well over a million people (and it's still relatively new) this support has made a big difference.
And many people had urged us to provide proof for each point in The Terrifying Brilliance of Islam. We assumed people would be motivated to learn on their own, but many people asked for proof and were sometimes looking for a reason to dismiss the information, but Al Dajjal again provided the support, allowing that article to have greater influence.
In addition to allying with others in the Resistance, Al Dajjal is a formidable warrior on his own, running both Islam Exposed and the Crusader's Armory.
For the work he does doing the one thing that needs to be done — educating non-Muslims about Islam's prime directive — he has definitely earned the Citizen Warrior Hero Award.
Risking Their Lives For Freedom
A group of Muslims have openly renounced their faith, exposing themselves to the wrath of Islam. It is a sin punishable by death to leave Islam. But these people are doing it, they're doing it in public, and they're saying why they're doing it.
They are opposed to Britain's culture of accepting and appeasing the intolerant religion of Islam. They believe in freedom of speech, freedom of sexuality, and freedom of religion.
Read more at their web site: Council of Ex-Muslims.


Here is the email address if anyone is unable to attend. planning@co.slo.ca.us Email it no later than Tuesday.
ATTENTION: HEARING OCT 22 AGENDA ITEM #14 FREEPORT MCMORAN.
The points we need to make is that in fact the 10-year-old FEIR is NOT ADEQUATE. Personal experiences are always good too. Covers all the bases.
Some talking points. 1) We have them dead to rights on a flawed FEIR 10 years ago. 2) There was not a emergency drought mandate in effect 10 years ago 3) Earthquakes were not considered 4) subsidence not mentioned. 5) Injecting billions of gallons of toxic waste into a protected aquifer is an ongoing illegal and unlawful activity in violation of the Safe Drinking Water Act.
1) The United States EPA called DOGGR's handling of the Underground Injection Program 'Shocking." Translation. There wasn't one. No Underground Injection Control program in place at the time of the FEIR 10 years ago. It would appear this whole operation is in violation of the Safe Drinking Water and an illegal operation. Deny it.
Wells must meet standards and spec for re injection of waste water set by the yet to be implemented UIC program. DOGGR screwed up but that does not diminish the fact that it is still illegal and unlawful.
Underground Injection Control program was not addressed in the 2004 FEIR and predates the Energy Policy of 2005 which means the FEIR for PXP was in violation of the Safe Drinking Water Act in 2004 and still is. http://www.latimes.com/…/la-me-lawmakers-grill-oil-regulato… Deny it.
All the wells currently in production are doing so in violation of the law. What should really be happening here is a cease and desist order. An immediate moratorium on all illegal drilling operations at the AGOF.
The 2004 FEIR predates the Energy Policy Act of 2005 and violates all the laws on Clean Air, Clean Water, Safe Drinking Water Act, Resources Conservation and Recovery Act, The National Environmental Policy Act and the Community Right to Know Act that were exempted by the unlawful "Halliburton Loophole". So NO the old FEIR is not adequate. Yes it should be denied.
2) Earthquakes are a big deal and not addressed in the original EIR. Here are a couple of articles that could help educate the commissioners and Board members.
The California Council on Science and Technology's EIR mandated by SB4 reported that the technology needed to accurately track, monitor, measure, subsurface activity to include earthquakes and re injected toxic waste water is at least 3 years down the road. Anything submitted about underground activity at this point in time is only a guessamation and does not qualify as accurate valid scientific data.
DOGGR is understaffed and underfunded solely at the discretion of Governor Brown and he has made sure they cannot adequately perform their duties and prevent pollution and protect the environment. He just appointed an oiloyalists as the new executive director of DOGGR.
3) EIR report requires findings on subsistence. PXP's FEIR does not address that issue. However, San Luis Obispo has a history of subsidence. Article below of 1987 case of subsidence in SLO.
4) New DOGGR rules regulating and upgrading cement casings specs and waste disposal of toxic walnut shells and filters also absent from the outdated and outmoded EIR. Cement casings fail on average of 50% within the first year. New specs need to be enforced.
And, this way of hiding toxic waste and avoiding scrutiny has worked for them for over 50 years. Time we wise up. It wasn't safe then, it isn't safe now and it will never be safe no matter how many exemptions they get.
5) California emergency drought mandates 25% cutback on non-essential water use. NASA reports California has 5 months of stored water left, that includes groundwater. San Luis Obispo County is under D4 restrictions. It is the highest Federal rating. We are hurting.
Freeport McMoRan's non-essential water use will increase by 300% or over 1.5 billion gallons a year which also means an increase in their toxic waste disposal production which is going directly into a protected aquifer that is totally vulnerable to earthquakes and subsistence and any disturbance of the sub surface terrain could send billions of gallons of toxic waste water to undisclosed, unpredictable locations in an instant. Order the fields shut down.
The right to first refusal is still in our hands. We can refuse to allow the fossil fuel industry to force their exemptions and will on us by refusing to let them harvest our resources and use our precious water.
We have a different set of values and what is important to us is not important to them. So, No we will not waive our rights to clean air and water so they can dominate and capture our natural resources purely for their own personal enrichment.
NO is the new yes. At least 16 other countries, 3 other states, 5 counties and 13 municipalities in California have just said NO to fracking and won their freedom from all the deadly entrapment's that are the Hallmark of the fossil fuel industry. YES.
This is the first in a series of hearings before the planning commission makes their final recommendation to deny or approve the whole, sorted, stinky, ugly, smelly, putrefied expansion to the Board of Supervisors.
Email response today. Please do it today or you will forget.
This entry was posted in Call to Action, Events, Newsletter, San Luis Obispo County, Updates and tagged newsletter. Bookmark the permalink.


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Despite Predictability, Small-Town Murder Mystery Is an Unputdownable Read
Like the seedy, 1-star motel where she works, Juliet Townsend is "halfway to anywhere that mattered, stuck" (15). Although she had grand dreams of leaving her hometown of Midway, Indiana, she's still there ten years after graduating high school. Working as a hotel housekeeper, living with her mother, and seeing the same faces every day makes for a dreary, banal existence.
Then, Madeline Bell walks into the Mid-Night Inn. Wearing beautifully tailored clothes and a gleaming diamond on her finger, Juliet's old friend and rival looks like a movie star. What she's doing at a rundown hotel like the Mid-Night, Juliet can't fathom. She doesn't get a chance to find out, either, as Madeline's dead body is found the next morning hanging from a railing. Why would a beautiful, wealthy woman like that commit suicide? When evidence of murder comes to light, Juliet finds herself a suspect in the killing of the woman to whom she's always played second fiddle. In order to clear her name, the housekeeper will have to find out who really killed Madeline Bell before her own body is found swinging from the rafters.
Little Pretty Things, a murder mystery by Lori Rader-Day, tells a taut, unputdownable story about two very different women tied to the same dead-end town. While the tale is depressing as all get-out, it's also an engrossing mystery that I couldn't stop reading. That's saying something since I saw where the plot was heading almost from the start. Even though it's predictable, the novel is a fast-paced page turner that will resonate with anyone who, like Juliet, feels stuck in a life she never saw herself living. Despite some disturbing subject matter, I enjoyed this one.
(Readalikes: Reminds me of other novels by Lori Rader-Day, including Under a Dark Sky and The Day I Died)
for language (no F-bombs), violence, and disturbing subject matter
To the FTC, with love: Another fine find
Labels:B Grade Books,Lori Rader-Day,Murder Mysteries,Mystery/Suspense,R-rated Books,U.S. Settings: Indiana
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Many HVAC systems have an indoor unit and an outdoor unit, but packaged systems combine both parts in one unit. They're more efficient than conventional heaters and air conditioners, and they can help you save money on your utility bills. Packaged HVAC systems offer many heating and cooling options. They're easy to install and maintain, and they can increase the value of your Tarpon Springs, Florida, home.
You can have a packaged HVAC system installed on your roof or on the ground — similar to a conventional system. With this arrangement, you can set different temperatures in various areas or zones in your home.
Zoned heating and cooling can keep all your family members comfortable. It also helps you save energy by not heating or cooling unoccupied rooms. You can choose a packaged heat pump, an electric unit, or a gas unit in many sizes. Ductless packaged systems are available, and you can easily have a packaged system installed for a new addition to your home.
Since packaged HVAC systems come in only one casing, they're easier to install and maintain than conventional heaters and air conditioners. The compressor, cooling coil, air handling unit, and air filter are assembled at the factory, not at your home. When an HVAC professional performs maintenance on a packaged system, the individual needs to look at only one unit.
A home with a packaged HVAC unit can utilize more free space than a house with a conventional system. You won't have to use a part of your home to store an indoor unit. When you're ready to sell your home, the high efficiency and quiet operation of a packaged system can help you attract potential homebuyers.
Advanced Cooling Systems is a Trane Comfort Specialist with decades of heating and cooling experience. We can help you install, repair, and maintain your HVAC system, including packaged units. Call us at 866-827-7662 for outstanding service.


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El Distrito de Pacucha es uno de los 19 distritos de la Provincia de Andahuaylas  ubicada en el departamento de Apurímac, bajo la administración del Gobierno regional de Apurímac, en el sur del Perú.

Desde el punto de vista jerárquico de la Iglesia católica forma parte de la Diócesis de Abancay la cual, a su vez, pertenece a la Arquidiócesis de Cusco.

En este distrito se encuentra la laguna Pacucha y el sitio arqueológico de Sóndor.

Historia
El distrito fue creado mediante Ley N.º 14629 del 21 de agosto de 1963, durante el gobierno de Fernando Belaúnde.

Población
De acuerdo al último censo nacional, el distrito de Pacucha tiene una población de 9 841 habitantes.

Superficie
El distrito tiene un área de 170,39 km².

Autoridades

Municipales
 2015-2018
 Alcalde: Claudio Máximo Velasque Oscco.
 Regidores: Eugenio Vargas Rivas, Mauro Huamán Naveros, Bertha Aydeé Huamán Mondalgo, Erson Orosco Olivera, Karen Vilma Cruz Huamán.

 2019-2022
 Alcalde: Hainor Luis Navarro Huamán
 Regidores: Gaudencio Víctor Rivas Pedraz, Rubén Franco Herhuay, Rodolfo Morel Sánchez, Hermelinda Rodríguez Ramos, Raúl Quispe Juárez.

Festividades
 Junio:
 19 Sóndor Raymi.
 29 San Pedro.
 Agosto: Virgen de las Nieves.

Galería

Véase también
 Organización territorial del Perú
 Departamento de Apurímac

Referencias

Enlaces externos
 INEI Perú.

Pacucha

redpajama_set_name: RedPajamaWikipedia


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\section{Setting}

Computational Real Algebraic Geometry really began with the Cylindrical Algebraic Decomposition (CAD) work of Collins \cite{Collins1975}, and independently W\"uthrich \cite{Wuthrich1976}: previous results such as \cite{Seidenberg1954,Tarski1951} having been effective in name only.

\begin{definition}
An {\em algebraic proposition\/} is one built up from expressions of the form $p_i(x_1,\ldots,x_n)=0$ (where the $p_i$ are polynomials with integer coefficients) joined together by the logical connectives $\lnot$ (not), $\land$ (and) and $\lor$ (or). A {\em semi-algebraic proposition\/} is the same, except that the building blocks are expressions of the form $p_i(x_1,\ldots,x_n)\sigma0$ where $\sigma \in \{=,\ne,>,\ge,<,\le\}$. The language of semi-algebraic propositions is also called the \emph{Tarski language} ${\cal L}$.
\end{definition}

\begin{notation}
\label{N1}
Although not strictly in the Tarski language, we will find it convenient to describe ``the $i$-th root of $p$'' by ${\strut}_i\sqrt[n]{p}$ (or more generally ${\strut}_i\mathop{\rm RootOf}\nolimits(p,y)$) to mean the $i$th real root (counting from $-\infty$) of $p$, as a polynomial in $y$ ($\strut_ip$ when the variable is clear).
\end{notation}
Thom's Lemma \cite{CosteRoy1988} means that these can be converted into statements in ${\cal L}$, at the cost of adding additional polynomials --- the derivatives of the ones we have.

\begin{notation}
We let ${\bf R}^*$ be ${\bf R}$ to which we add $\epsilon$ to make the ordered ring ${\bf R}[\epsilon]$ with $0<\epsilon<$ any positive real, and then add $\pm\infty$ to the underlying ordered set.
\end{notation}
See \cite{Kosta2016a} for the rationale behind these symbols in Virtual Term Substitution.

\begin{problem}[Quantifier Elimination]\label{Pr:1}
Consider a quantified proposition\footnote{Any proposition with quantified variables can be converted into one in this so-called
{\em prenex normal form\/}
 --- see any standard logic text.}
\begin{equation}\label{eq:QE}
Q_1 y_1\ldots Q_m y_m F(y_1,\ldots,y_m,x_1,\ldots,x_n),
\end{equation}
where $F\in{\cal L}$ and $Q_i \in \{\exists,\forall\}$.  Does there exist a quantifier-free equivalent semi-algebraic proposition $G(x_1,\ldots,x_n)$ and if so, can we compute it?
\end{problem}

\begin{notation}
The structure of (\ref{eq:QE}) forces an order onto the variables, which we take from first to last as $x_1,\ldots,\allowbreak x_n,y_1,\ldots,y_m$.
\end{notation}
The most used complete method to solve Problem \ref{Pr:1} is Cylindrical Algebraic Decomposition (CAD) \cite[and much subsequent work]{Collins1975}, although Virtual Term Substitution (VTS) \cite[and much subsequent work]{Weispfenning1988} is very useful when it is applicable: see, for example, \cite{Tonks2020a}.
Problem \ref{Pr:1} is known to be doubly-exponential (in $n+m$) in the worst case \cite{BrownDavenport2007,DavenportHeintz1988}, but more accurately it is doubly-exponential in the number of times the sequence of $Q_i$ changes from $\exists$ to $\forall$ or \emph{vice versa} \cite{Basu1999}.

An important special case of Problem \ref{Pr:2} is the following.
\begin{problem}[Satisfiability]\label{Pr:2}
Given a fully existentially quantified proposition
\begin{equation}\label{eq:P2}
\exists x_1\exists x_2\cdots\exists x_n F(x_1,\ldots,x_n),
\end{equation}
where $F\in{\cal L}$, does there exist a solution?  I.e. is this {\bf true} or {\bf false} (also known as the problem being {\bf SAT} or {\bf UNSAT})?
\end{problem}
Despite the fact that (\ref{eq:P2}) is a quantified piece of algebra, the problem is known as ``Quantifier-Free Non-linear Real Arithmetic'' (\verb!QF_NRA!) in the Satisfiability Modulo Theories (SMT) community \cite{Barrettetal2017a}, since all variables in SMT are assumed to be existentially quantified anyway. Traditionally Problem \ref{Pr:1} was the focus of the symbolic computation community and Problem \ref{Pr:2} the focus of the Satisfiability Checking community, but recently there has been a joint effort \cite{SC2}.

By \cite{Basu1999} it is soluble in time singly-exponential in $n$, but the authors know of no implementation of this.
A fundamental difference between Problem \ref{Pr:2} and the famous Boolean version of Satisfiability Checking is that there are an infinite number of possible values for the $x_i$, so direct `brute force' is not an option.

A subtle variant of Problem \ref{Pr:2} is the following.
\begin{problem}[Proven Satisfiability]\label{Pr:3}
Given a fully existentially quantified proposition (\ref{eq:P2}),
where $F\in{\cal L}$, produce a computer-verifiable proof of {\bf SAT} or {\bf UNSAT}.
\end{problem}
If the answer is {\bf SAT}, all the major algorithms (at least VTS and CAD, as well as hybrids of these methods) will actually compute the witnesses $x_i$, so the computer-verifiable proof of {\bf SAT} is relatively easy (we say relatively easy as we must bear in mind that these $x_i$ might be algebraic numbers). The challenge is the {\bf UNSAT} case.  The main body of work on this problem is by Cohen and Mahboubi \cite{Mahboubi2006}, \cite{Mahboubi2007}, \cite{CM10}, \cite{CohenMahboubi2012a}.  In the former works an attempt was made to formalise CAD but to the best of our knowledge this was not completed. In those latter papers QE is verified but not via CAD but with an algorithm described in \cite{Hormander1983}, which falls in the ``effective in name only'' category.

\subsection*{Thesis and plan of this article}

The authors of the present paper have recently developed a new algorithm for tackling Problem \ref{Pr:2} in \cite{Abrahametal2020a} which offers computational advantages over CAD.  The algorithm is based around the new idea of Cylindrical Algebraic Coverings and so we refer to it here as CAC.  The present article is essentially a position paper where we present our thesis that the UNSAT results produced by CAC may be far more susceptible to formal proof than those of the traditional tools. We present examples which show that CAC produced proofs that are much closer to those of a human.  The aim of the paper is to present this thesis to the formal proof community to garner interest and insight into whether it may be followed.

The paper continues by introducing the two leading technologies for tackling our problems in Section \ref{SEC:Background}.  Then in Section \ref{SEC:CAC} we summarise our recent CAC algorithm.  In Section \ref{SEC:Examples} we present some examples that illustrate our thesis.

\section{Traditional algorithms for these problems}
\label{SEC:Background}

\subsection{Cylindrical Algebraic Decomposition}

This was first introduced by Collins in \cite{Collins1975}. The key idea is to partition ${\bf R}^n$ into connected subsets called cells with the following properties:
\begin{enumerate}
\item Each cell is sign-invariant for all the polynomials in $F$.
\item Each cell $C$ has a sample point $s_C$ identified within it.
\item The cells and sample points are arranged cylindrically.  This means that for all $k<m+n$, the projections onto the first $k$ variables of two cells are either equal or disjoint, and if equal their sample points will have the same values for the first $k$ coordinates.
\item The cells have semi-algebraic descriptions.
\end{enumerate}
Then the truth of $\exists y F(y,x_1,\ldots,x_n),$ at a sample point $s=(s_1,\ldots,s_n)$ follows from the truth of \emph{any} of the sample points $s'=(s_1,\ldots,s_n,s_{n+1})$ above it (and if they are all false, then $\exists y F$ is false). Similarly, the truth of $\forall y F(y,x_1,\ldots,x_n),$ at $s$ follows from the truth of \emph{all} of the sample points $s'$ above it (and if any of them are false, then $\forall y F$ is false).
The truth of $\exists y$ from the truth at any sample point (and the falsity of $\forall y$ from the falsity at any sample point) are obvious: the converses follow from the completeness of the decomposition, i.e. that there is no behaviour not captured by a sample point.

There are improvements to the original \cite{Collins1975} by many authors: in particular \cite{McCallum1984} has a more efficient computation, but may \emph{explicitly} state that the decomposition is not complete (``nullification'' or ``not well ordered''), and \cite{Lazard1994} (justified only recently in \cite{McCallumetal2019a}), is more efficient still but always complete. Further efficiencies can be found when $F$ has certain structure, for example, \cite{McCallum1999a} considered the case where $F$ has the form $p(y_1,\ldots,y_m,x_1,\ldots,x_n)=0 \land F'(y_1,\ldots,y_m,x_1,\ldots,x_n)$ where $p$ is referred to as an \emph{equational constraint}; \cite{McCallum2001}, \cite{Englandetal2019a} considered the case of several equational constraints; and \cite{Bradfordetal2016a} considered more complicated combinations, re-defining (1) in the construction to:
\begin{enumerate}
\item[1$'$] Each cell is truth-invariant for $F$, but not necessarily sign-invariant for all the polynomials in $F$.
\end{enumerate}
See for example the introduction of \cite{Englandetal2019a} for a more detailed review.  The key point is that however the decomposition is constructed, the fundamental requirement is \emph{completeness}, i.e. that all cases, however defined, are captured as a cell (sample point) in the decomposition.

\subsection{Virtual Term Substitution}

Virtual term Substitution (VTS) was introduced in \cite{Weispfenning1988}, and many developments are gathered in \cite{Kosta2016a,Kostaetal2016a}. Here the key idea for $Q y F(y,x_1,\ldots,x_n)$ is to consider a $y$-value from every interval of the real line according to those intervals formed by the real roots of all polynomials contained in $F$, regarded as elements of ${\bf Q}[x_1,\ldots,x_n][y]$. Unlike CAD, it is limited to elimination of quantified variables appearing as low degree - currently the methodology is described for up to degree 3 in \cite{Kosta2016a}. Action of elimination by VTS may even increase the degree of intermediate formulae, and as such all $x_1,\dots,x_n$ appearing at most cubically is not a guarantee VTS can complete QE alone.

If $n=0$, these would truly be values $v_i$ in ${\bf R}^*$, the truth of $\exists y F(y)$ would be that of $\bigvee_i F(v_i)$, and the truth of $\forall y F(y)$ would be that of $\bigwedge_i F(v_i)$.
In general, of course, $n>0$, so we have terms rather than values, which are the roots in $y$ of these polynomials in ${\bf Q}[x_1,\ldots,x_n][y]$, and the substitution into $F$ is ``virtual''.  We write  $F[y/\hskip-2pt/v_i]$ for ``the virtual substitution of $v_i$ for $y$ in $F$'', which is especially relevant if the $v_i\in{\bf R}^*\setminus{\bf R}$.

Again, if a $F(y/\hskip-2pt/v_i)$ is true, then $\exists y F(y)$ is true, and if a $F(y/\hskip-2pt/v_i)$ is false, then $\forall y F(y)$ is false.  Deducing the converse again requires that the set of $v_i$ be ``complete''. If $v_i\in{\bf R}^*\setminus{\bf R}$ is a witness to truth/falsity, then it is possible, with the hindsight of knowing the expressions in which it occurs, to replace $\infty$ by a large enough number, and $\epsilon$ by a small enough one - see Algorithm 1 from \cite{Tonks2020a}.

\section{Cylindrical Algebraic Coverings}
\label{SEC:CAC}

We recently presented a new algorithm for determining the satisfiability of conjunctions of non-linear polynomial constraints over the reals \cite{Abrahametal2020a}, which can be used to solve Problem \ref{Pr:2}. The algorithm is based around the technology of CAD but does not build a decomposition of ${\bf R}^n$. Instead, overlapping cells are generated, until we have a covering of the sample space.  Sample points are constructed incrementally, either until a satisfying sample is found or sufficient samples have been sampled to conclude unsatisfiability.  The choice of samples is guided by both the input constraints and previous conflicts (combinations of constraints and samples found to be unsatisfiable).  The key idea behind our new approach is to start with a partial sample; demonstrate that it cannot be extended to a full sample; and from the reasons for that rule out a larger space around the partial sample, which build up incrementally into a covering of the space.  The cells are still arranged in cylinders and have semi-algebraic descriptions and thus we call the data structure produced a Cylindrical Algebraic Covering (CAC).

Unlike CAD, which starts with projection to generate algebraic information, the algorithm described in \cite{Abrahametal2020a} starts with ``guessing'' a sample point dimension-wise, starting in the lowest dimension and iteratively extending it to higher dimensions. Either we ``guessed'' right and find a satisfying sample or we face a partial sample that cannot be extended to a full solution and use it to guide the projection (and thus the cell construction). To do so, we recursively execute the following:
\begin{itemize}

\item Given an $i$-dimensional sample $s=(s_1,\ldots,s_{i})$, we try to extend it to a sample $(s_1,\ldots,s_i,s_{i{+}1})$  that does not evaluate any input constraint to false.

\item If this works out then either the sample is full dimensional and we report consistency (and this witness), or we continue with extending the sample in the next dimension.

\item Otherwise we take note of the reason the sample cannot be extended, and exclude from further search not just this particular sample $s$, but all extensions of $(s_1,\ldots,s_{i{-}1})$ into the $i$th dimension with any value from a (hopefully large) interval around $s_i$ which is non-extensible for the same reason.

\item We continue and check further extensions of $(s_1,\ldots,s_{i{-}1})$ until either we find a solution or the $i$th dimension is fully covered by excluding intervals.

\item In the latter case, we analyse the collection of intervals to try and rule out not just the original sample in $\mathbb{R}^{i{-}1}$ but an interval around it within dimension $(i{-}1)$, i.e. the same procedure we benefited from in the recursive call.

\end{itemize}
The generalisation of the unsatisfying sample to a wider interval is based upon CAD technology, i.e. we know the truth of a constraint can only change when we cross the real roots of certain projection polynomials calculated with tools such as coefficients, discriminants and resultants.  Intuitively, each sample $s\times s_i$ violating a constraint with polynomial $p$ can be generalised to a cell in a $p$-sign-invariant CAD. So when all extensions of  $s$ have been excluded (the $i$th dimension is fully covered by excluding intervals) then we project all the covering cells to dimension $i{-}1$ and exclude their intersection from further search.

The conflict generalisation guides the algorithm to sample away from the reasons of previous conflicts, which should allow for a satisfying sample to be found quicker if one exists.  In the case of UNSAT, a covering in which every cell is UNSAT could use less cells than an entire decomposition.

See  \cite{Abrahametal2020a} for full details of the algorithm including worked examples and details of experimental results.
The CAC based algorithm has similarities with the incremental variant of CAD, the NLSAT method of Jovanovi\'{c} and de~Moura \cite{JdM12}, and the NuCAD algorithm of Brown \cite{Brown2015} but the examples in \cite{Abrahametal2020a} demonstrate its unique advantages.

In the present paper we hope to demonstrate another potential advantage:  the increased susceptibility to formal verification of its output.

\section{Examples}
\label{SEC:Examples}

We demonstrate our thesis with some simple UNSAT examples.

\begin{figure}
\centering
\includegraphics[width=0.45\textwidth]{Ex1} \qquad
\includegraphics[width=0.45\textwidth]{Ex2}
\caption{Graphs of polynomials involved in the worked examples.}
\label{pic}
\end{figure}

\subsection{Example 1}
\label{Ex:1}

Consider $F:=(x^2+y^2<1)\land((x-4)^2+y^2<1)$. The circles are graphed on the left of Figure \ref{pic} and we see they do not intersect and thus $F$ must be UNSAT.

\subsubsection{CAD:}

To solve Problem \ref{Pr:2}, the CAD algorithm would do the following:
\begin{itemize}
\item[(a)] partitions the $x$-axis at\footnote{$x=\pm1$ are the extremal points of the first circle, and $x=3,5$ of the second. One could ask why $x=2$. The answer is that both circles (boundaries of the discs) in $F$ have common zeros at $x-2,y=\pm\sqrt{-3}$: of course these zeros are not real, but have a real $x$-component.} $-1,1,2,3,5$;
\item[(b)] constructs 27 cells and associated sample points in $R^2$ (see Table \ref{T:Ex1});
\item[(c)] deduces that no sample points have both $x^2+y^2<1$ and $(x-4)^2+y^2<1$ true at once;
\item[(d)] and therefore (since the polynomials are sign-invariant in the cells) concludes that no cells have both true anywhere over them;
\item[(e)] and because the union of cells is ${\bf R}^2$, the statement must be nowhere true.
\end{itemize}

Step (c) is analogous to verifying {\bf SAT}, and, due to the cylindrical nature of the decomposition, (e) is relatively easy. The problem is verifying (d). Its truth depends on the fine details of the CAD algorithm used (for example \cite{McCallum1984} is distinctly different from \cite{Collins1975}, and the Lazard method \cite{McCallumetal2019a} is based on entirely different mathematics again).

\subsubsection{VTS:}

Virtual Term Substitution would consider a variety of possible values $v_i$ for $y$. In the implementation of \cite{Tonks2020a}, the set of $v_i$ starts with $-\infty$, then various other trivial (in the sense of immediately yielding false) values, and the first non-trivial one is ${\strut}_1\sqrt{1-x^2}+\epsilon$. Virtually substituting this into $F$ yields
\begin{equation}
\underbrace{x^2<1}_{\hbox{guard}}\land \underbrace{\hbox{true}}_{x^2+y^2<1}\land \underbrace{\left(-x<-2\lor\left(x=2\land x^2<1\right)\right)}_{(x-4)^2+y^2<1},
\end{equation}
where the guard is there to make sure that the substitution makes sense, and ``$-x<-2$'' is the simplification of $(x-4)^2+\left({\strut}_1\sqrt{1-x^2}+\epsilon\right)^2<1$. In all there are 41 VTS test points, of which 21 are initial ones used in $y$, and of the remaining 20 on $x$, there are 7 distinct ones (used on similar intermediate formulae). They are characterised in a manner intelligible as semi-algebraic sets (to compare with CAD) in Table \ref{T:Ex1VTS}. It is important to note that this is only a characterisation, considering VTS does not in itself operate geometrically.  We have fewer substitutions of exact values for $x$ (what would be analogous to computing ``sections'' in CAD).

Speaking generally, VTS is an algebraic approach on formulae as opposed to geometry.  Amongst the formulae produced in $x$, $x=2$ appears, but other atomic formulae are all strong relations, such that this is the only substitution of an ``exact'' value. All of the generated test points are substituted in order to deduce {\bf UNSAT}, as we form a disjunction of formulae all equivalent to false.

\begin{table}
\caption{Structural Test Points for VTS (as semi-algebraic sets) for the example in Section \ref{Ex:1}\label{T:Ex1VTS}}
\center \begin{tabular}{c|c|c|c|c|c|c}
$x<-1$ \,&\, $-1<x<1$ \,&\, $1<x<2$ \,&\, $x=2$ \,&\, $2<x<3$ \,&\, $3<x<5$ \,&\, $x>5$
\end{tabular}
\end{table}

\subsubsection{Human:}

Of course no human prover would proceed in either of these ways. A human produced argument would be along the lines of
\begin{align*}
x^2+y^2<1 &\Rightarrow x^2<1 \Rightarrow x<1\\
(x-4)^2+y^2<1 &\Rightarrow (x-4)^2<1 \Rightarrow x-4 \in (-1,1) \Rightarrow x-4>-1 \Rightarrow x>3
\end{align*}
with the two right most statements clearly incompatible.

\subsubsection{CAC:}

Cylindrical Algebraic Covering proceeds by choosing a variety of sample $x$ values, then recursing on $y$ (and any subsequent variables if there were any. In this example it it proceeds as follows, but we note that the theoretical algorithm allows a great deal of choice in computation path.
\begin{description}
\item[$x=-1$:] This would require $y^2<0$ which is unsatisfiable. However, we can deduce nothing about the neighbouring values of $x$, as $-1$ is a root of the discriminant of $x^2+y^2-1$.
\item[$x<-1$:] We sample $x=-2$ and find this is also impossible for the same reason.  The nearest root of this resultant is $-1$, so $(-\infty,-1)$ is ruled out along with $x=-2$.
\item[$x>-1$:] We sample $x=0$.  Here $y\in(-1,1)$ can not be ruled out by $x^2+y^2<1$ (obviously), but $(x-4)^2+y^2<1$ rules out this value of $x$ immediately, and the generalisation rules out with it the whole of $(-\infty,3)$.
\item[$x\ge3$:] We sample $x=4$.  This trivially conflicts with $x^2+y^2<1$, which rules out $(1,\infty)$.
\item[\rm{Hence}] the whole of ${\bf R}$ is ruled out for $x$, and we may conclude UNSAT.
\end{description}
While this is not quite as simple as the human proof above, it is much closer to it. If we pruned the reasoning, it would be that $x\in(-\infty,3)$ is infeasible because of $(x-4)^2+y^2<1$, and $x\in(1,\infty)$ because of $x^2+y^2<1$.  Most importantly, the argument of unsatisfiability can be reconstructed from the algorithm flow and output.

\subsection{Example 2}
\label{Ex:2}

Consider $F:=(x^2+y^2<1)\land\left(\left(x-\frac32\right)^2+\left(y-\frac32\right)^2<1\right)$.    The circles are graphed on the right of Figure \ref{pic} and we see they again do not intersect and thus $F$ must be UNSAT.

\subsubsection{CAD:}

To solve Problem \ref{Pr:2}, the CAD algorithm behaves similarly to Example 1: the two circles have critical points (roots of the discriminant) at $x=-1,x=1$ and $x=\frac12,x=\frac52$ respectively. This time the resultant of the two circles is $18x^2-27x+\frac{45}4$, whose roots are not real numbers and so do not contribute to the set of critical points.  However, because the circles overlap the cylinders above the $x$-axis are more decomposed and we have 41 cells as in Table \ref{T:Ex2}.

\subsubsection{VTS:}

VTS this time receives non-false formulae owing to substitutions of test points in $y$ from both circles. Virtual substitution can substitute roots directly from multivariate polynomials (which, in fact, is some of the cadence behind the terminology ``virtual''). An example is the virtual substitution of $\strut_1\mathop{\rm RootOf}\nolimits{}\left( \left(x-\frac32\right)^2+\left(y-\frac32\right)^2-1 \right) + \epsilon$ for $y$ into $F$, leading to (after some minor simplification):
\begin{align*}
4x^2 - 12x + 5 < 0 \land \Bigl( & x<0  \land -8x^2 + 12x - 5<0 \,\lor\, \\ & 8x^2 - 12x + 5 < 0 \,\lor\, \\ & x \geq 0 \land 8x^2 - 12x + 5 = 0 \land 2x^2 - 6x + 7 < 0 \Bigr)
\end{align*}
Now, $4x^2 - 12x + 5 = (2x-1)(2x-5)$, but $8x^2 - 12x + 5$ and $2x^2 - 6x + 7$ are irreducible. As a result of the irreducible polynomials, in contrast to Problem \ref{Pr:1}, VTS must then use test points from quadratic polynomials in $x$ rather than using purely linear test points. In fact, $8x^2 - 12x + 5$ has no real roots, and the negative discriminant manifests in a guard evaluating as false to prevent substitution from this. In total, in the same manner as Table \ref{T:Ex1VTS} we have Table \ref{T:Ex2VTS} as the characterisation of the geometry in $x$ that VTS finds relevant.

\begin{table}
\caption{Structural Test Points for VTS (as semi-algebraic sets) for the example in Section \ref{Ex:2}\label{T:Ex2VTS}}
\begin{tabular}{lc|cl}
$x<\strut_1\mathop{\rm RootOf}\nolimits{}(2x^2 + 6x - 7)$
& \hspace{0.2in} & \hspace{0.2in} &$x=\strut_1\mathop{\rm RootOf}\nolimits{}(2x^2 - 6x + 7)$
\\ \\
$\strut_1\mathop{\rm RootOf}\nolimits{}(2x^2 - 6x + 7)<x<0$
& \qquad && $x=0$
\\ \\
$0<x<\frac12$
& \qquad && $\frac12<x<\strut_2\mathop{\rm RootOf}\nolimits{}(2x^2 - 6x + 7)$
\\  \\
$x=\strut_2\mathop{\rm RootOf}\nolimits{}(2x^2 + 6x - 7)$
& \qquad && $\strut_2\mathop{\rm RootOf}\nolimits{}(2x^2 - 6x + 7)<x<\frac52$
\\ \\
$x>\frac52$ & \qquad &&
\end{tabular}
\end{table}

\noindent The only other non trivial formula VTS must traverse in $x$ is: $$x^2 < 1 \land \left( ( 3 < 2x \land -8x^2 + 12x < 5 ) \lor ( 3 \leq 2x \land -8x^2 + 12x - 5 = 0 ) \right)$$ with significant overlap in terms of test points, but also additionally identifying $x = \pm 1 + \epsilon$, making for a total of 11 unique non-degenerate test points in $x$. Again, there are fewer substitutions owing to exact roots than CAD, with VTS not identifying $x=\frac12$ or $x=\frac52$ as meaningful to substitute. Yet again all test points are substituted to receive \textbf{UNSAT}.

\subsubsection{CAC:}

Our implementation of the Cylindrical Algebraic Covering algorithm operates on this example as follows.

\begin{description}
	\item[$x=-1$:] Similarly yo the previous example, this would require $y^2 < 0$ and again we can not deduce anything around this value, as $-1$ is a root of the discriminant of $x^2+y^2-1$.
	\item[$x<-1$:] As in the first example we sample $x = -2$ and again find it to be unsatisfiable due to $y^2 < -3$, excluding the whole interval $(-\infty,-1)$.
	\item[$-1 < x$:] We have now excluded $(-\infty,-1]$ and sample $x=0$. While $y^2<1$ is still satisfiable, the second constraint evaluates to $(y-3/2)^2 < - \frac{5}{4}$ which is directly conflicting. The characterisation ends up excluding the interval $(-\infty, \frac{1}{2})$, essentially superseding all previous intervals.
	\item[$\frac{1}{2} < x$:] We sample $x=1$ and obtain a direct conflict with $y^2 < 0$. As with the first sample ($x=-1$) we only exclude the point interval $[1,1]$.
	\item[$\frac{1}{2} < x < 1$:] To take care of this interval we sample $x = \frac{3}{4}$ which finally needs both constraints to realize that no value for $y$ is feasible. The characterisation excludes exactly the interval $(\frac{1}{2},1)$. Note that the point $\frac{1}{2}$ remains uncovered.
	\item[$x=\frac{1}{2}$:] We now check the remaining point $x=\frac{1}{2}$ which directly conflicts with the second constraint. As $\frac{1}{2}$ is a root of the discriminant of the second constraints polynomial, only this point interval is excluded.
	\item[$1 < x$:] We continue with $x=2$, which is a direct conflict with the first constraint due to $y^2 < -3$, excluding $(1,\infty)$ and thereby completing the covering of the $x$-axis.
\end{description}
We have ascertained that no value for $x \in {\bf R}$ can satisfy the constraints and so may conclude UNSAT.

Note that, after pruning, the reasoning consists of the following components:
\begin{description}
	\item[1: $x \not\in (-\infty,\frac{1}{2})$] because of the second constraint,
	\item[2: $x \neq \frac{1}{2}$] because of the second constraint,
	\item[3: $x \not\in (\frac{1}{2},1)$] because of both constraints,
	\item[4: $x \neq 1$] because of the first constraint and
	\item[5: $x \not\in (1,\infty)$] because of the first constraint.
\end{description}

\subsubsection{Human:}
\font\manual=manfnt at 6pt
\def\raise 4pt\hbox{{\manual\char127}}{\raise 4pt\hbox{{\manual\char127}}}

There is no trivial human proof this time like in Example 1.  If we proceed as there we find conditions on $x$ which are compatible and can only conclude that $x \in (\frac{1}{2}, 1)$.  Manipulation of these restrictions into the constraints would find a small range of potential $y$-axis over that $x$-interval where both constraints could possibly be satisfied. In other words there is no ``quick win''.
There are two obvious proof approaches. Both require to know that at one point, say $x=1$, the two constraints are not simultaneously satisfied. We use {\raise 4pt\hbox{{\manual\char127}}} to indicate points where geometric reasoning would seem to be necessary.
\begin{enumerate}
\item The resultant of the two circles {\raise 4pt\hbox{{\manual\char127}}} is $18x^2-27x+\frac{45}4$, whose roots are not real, and \emph{a fortiori} not in $[\frac32,1]$, so the two curves do not cross over $[\frac32,1]$, and hence there are no solutions here.
\item Let $\xi$ be a value in $[\frac32,1]$. Then we  need {\raise 4pt\hbox{{\manual\char127}}} to have
\begin{equation}\label{eq:1}
y<\strut_2\sqrt{1-\xi^2}.
\end{equation}
Similarly we need {\raise 4pt\hbox{{\manual\char127}}} to have
\begin{equation}\label{eq:2}
y>\frac32+\strut_1\sqrt{1-(\xi-\frac32)^2}\ge0.
\end{equation}
We can square (\ref{eq:2}):
\[
y^2>\frac94 +3\strut_1\sqrt{1-(\xi-\frac32)^2}+\left(1-(\xi-\frac32)^2\right)
\]
since it is an inequality of positive numbers, which also implies we can square (\ref{eq:1}): $y^2<1-\xi^2$. So
\[
1-\xi^2>\frac94 +3\strut_1\sqrt{1-(\xi-\frac32)^2}+\left(1-(\xi-\frac32)^2\right).
\]
Hence
\[
0>\frac94 +3\strut_1\sqrt{1-(\xi-\frac32)^2}+3\xi-\frac94=3\left(\xi+\strut_1\sqrt{1-(\xi-\frac32)^2}\right).
\]
Then we have
\[
-\strut_1\sqrt{1-(\xi-\frac32)^2}>\xi,
\]
again an inequality of positive numbers, and so either  $1-(\xi-\frac32)^2>\xi^2$, or $1-2\xi^2+3\xi-\frac94>0$. This is not true when $\xi=1$, and the roots of this quadratic (which is essentially the resultant) are not in $[\frac12,1]$ (in fact they are not real). Hence the inequality is nowhere true.
\end{enumerate}
The first approach requires less geometric reasoning, and furthermore that reasoning is essentially uniform --- ``curves can only cross at roots of the resultant''.  It is in fact very similar to line 3 of the CAC proof. Hence, at least in this case, CAC has essentially produced one of the possible proofs that a human would.

\section{Conclusion}

For general quantifier elimination (Problem \ref{Pr:1}), we have two standard implemented methods in the literature: CAD and VTS. Both require a completeness result to accept their results, which is currently beyond the reach of formal proof.

For the purely existential version (Problem \ref{Pr:2}), where SAT is easy to verify, but UNSAT is hard, we have a third method: CAC. At least in easy cases, its execution induces proofs much closer to the human proof.  The trace of the algorithm and its output seem to often allow for verifiable results without reliance on a verified completeness result for the entire algorithm.   We acknowledge that no verification has yet been conducted --- we publish this paper to highlight the opportunity to the verification community and encourage their input. Is it possible to regard CAC as a tactic that can guide an automatic theorem prover?

\input{CICM2020.bbl}

\begin{landscape}

\begin{table}[p]
\caption{CAD cells constructed for the example in Section \ref{Ex:1}\label{T:Ex1}}
\centering
\begin{tabular}{l||c|c|c|c|c|c|c|c|c|c|c}
\footnotesize
$x$:&$<-1$&$=-1$&$-1<x<1$&$=1$&$1<x<2$&$=2$&$2<x<3$&$=3$&$3<x<5$&$=5$&$>5$
\\ \hline
	$y$:&---&$<f_1$&$<\strut_1f_1$&$<f_1$&---&---&---&$<f_2$&$<\strut_1f_2$&$<f_2$&---
	\\
	$y$:&&$=f_1$&$=\strut_1f_1$&$=f_1$&&&&$=f_2$&$=\strut_1f_2$&$=f_2$
	\\
	$y$:&&$>f_1$&$\strut_1f_1<y<\strut_2f_1$&$>f_1$&&&&$>f_2$&$\strut_1f_2<y<\strut_2f_2$&$>f_2$
	\\
	$y$:&&&$=\strut_1f_1$&&&&&&$=\strut_2f_2$&
	\\
	$y$:&&&$>\strut_2f_1$&&&&&&$>\strut_2f_2$&
\\ \hline
\#&1&3&5&3&1&1&1&3&5&3&1
\end{tabular}
\\where $f_1=\mathop{\rm RootOf}\nolimits(x^2+y^2-1,y)$, $f_2=\mathop{\rm RootOf}\nolimits((x-4)^2+y^2-1,y)$,\\and $\strut_1f_i$ refers to an ordered root of the polynomials (Notation \ref{N1}).
\end{table}

\begin{table}[p]
\caption{Cells for the example in Section \ref{Ex:2}\label{T:Ex2}}
\centering
\begin{tabular}{l||c|c|c|c|c|c|c|c|c|}
$x$:&$<-1$&$=-1$&$-1<x<\frac12$				&$=\frac12$					&$\frac12<x<1$				&=1							&$1<x<\frac52$				&$=\frac52$	&$>\frac52$
\\ \hline
$y$:&---&$<f_1$	&$<\strut_1f_1$				&$<\strut_1f_1$				&$<\strut_1f_1$				&$<f_1$						&$<\strut_1f_2$				&$<f_2$ & ---\\
$y$:&	&$=f_1$	&$=\strut_1f_1$				&$=\strut_1f_1$				&$=\strut_1f_1$				&$=f_1$						&$=\strut_1f_2$ 			&$=f_2$ & \\
$y$:&	&$>f_1$	&$\strut_1f_1<y<\strut_2f_1$&$\strut_1f_1<y<\strut_2f_1$&$\strut_1f_1<y<\strut_2f_1$&$>f_1$						&$\strut_1f_2<y<\strut_2f_2$&$>f_2$ & \\
$y$:&	&		&$=\strut_2f_1$				&$=\strut_2f_1$				&$=\strut_2f_1$				&$f_1<y<\strut_1f_2$		&$\strut_1f_2<y<\strut_2f_2$&		& \\
$y$:&	&		&$>\strut_2f_1$				&$\strut_2f_1<y<f_2$		&$\strut_2f_1<y<\strut_1f_2$&$\strut_1f_2<y<\strut_2f_2$&$>\strut_2f_2$				&		& \\
$y$:&	&		&							&$=f_2$						&$=\strut_1f_2$				&$=\strut_2f_2$				&							&		& \\
$y$:&	&		&							&$>f_2$						&$\strut_1f_2<y<\strut_2f_2$&$>\strut_2f_2$				&							&		& \\
$y$:&	&		&							&							&$=\strut_2f_2$				&							&							&		& \\
$y$:&	&		&							&							&$>\strut_2f_2$				&							&							&		&
\\ \hline
\#	&1	&3		&5							&7							&9							&7							&5							&3		&1
\end{tabular}
\\where $f_1=\mathop{\rm RootOf}\nolimits(x^2+y^2-1,y)$, $f_2=\mathop{\rm RootOf}\nolimits\left((x-\frac32)^2+(y-\frac32)^2-1,y\right)$.
\end{table}

\end{landscape}

\end{document}

redpajama_set_name: RedPajamaArXiv


It is very easy to suggest a new ILIAS feature or the improvement of an existing one. Read this page to learn how to do this. You can also consult our German-language screencasts.
On this page you find all necessary information on how to contribute your ideas to the ILIAS software development process. You make your and our live easier if you respect these guidelines because it will ease our communication and the ILIAS development.
You need to have an account on ilias.de to be able to create new pages in this wiki and modify existing ones. You find the registration button on the top of the screen at the right side.
If you want to suggest a new feature you have to describe the feature on a wiki page. If you want to suggest several features please create one page for every feature. But before you add a new page, please have a look if a similar request has been made already to avoid duplicates. Just go to the Overview page of this wiki and open the category page of the module / component to which your request belongs to.
To create a new feature wiki page you go to the feature category to which your feature request belongs to, e.g. a new feature for the ILIAS wiki has to be created in category 'Wiki'.
Change on the page to Edit mode and add the title for the new feature within the first section 'Suggested features...'. Please consider that page titles should be short (because they are used as links too) and that all list items are sorted alphabetically.
Add wiki brackets (in this format: []) around your feature title or simply highlight the text with your mouse and click on the Wiki bracket button in the editor bar.
Save the page and click on the red link of the new page title to create the new wiki page.
ILIAS will ask you to select a template for this new page. Please select 'Creating A New Feature Page' in any case! ILIAS creates the new page with a predefined structure that you can fill out.
Now describe your suggestions and requirements in the predefined chapters. Please write in English in order to enable a broad discussion with all users worldwide. Describe the problem you want to solve and how this could be done as clearly as possible. If feasible, add a mock-up to the page to get an impression what you want to change in ILIAS and how it might look like.
Please add your name and contact in chapter 5. In case you have interest in funding this feature, please indicate this in chapter 6.
If you can offer funding, please let us know. Add the name of the funding institution / company to chapter 6 "Funding". Several institutions or companies can show their interest in funding in this list.
Add your name and e-mail to the feature request so we can contact you. If you activated your public profile on this installation, use the user name link in the page editor, see following screenshot.
There are already a lot of suggested features that haven't it made into ILIAS until now. Often the reason is missing funding. Sometimes a feature has been postponed due to open conceptual issues or missing ressources to implement the feature before the scheduled ILIAS version.
If you see a feature request in the section Already Suggested of a module page and you want to suggest it for the next upcoming ILIAS version, just copy the feature title and add it to the first list in chap 1. Suggested Features.
If you want to add your idea or comment to an existing feature request, you can add a posting in the Discussion block of the related feature wiki page.
Please add your name (see hint above) and the date of your posting, then describe your ideas or add your comment.
Please select the paragraph format "DiscussionPosting" for your entry. You can do so by using the drop-down menu Paragraph in the editor's top bar.
Feel free to add a mock-up to illustrate your idea / requirement.
Activate the notificiation for the wiki to get an e-mail when a reply or another change has been made to this page. You can do so by clicking on the small bell icon on the top of the page.
At least when the Jour Fixe has decided upon your suggestion and scheduled it for the next ILIAS version, you should start to get into contact with the responsible maintainer to discuss the next steps.
The responsible maintainer is mentioned on the page of the feature request and also on the module page to which your feature request belongs (link to this page in block Status of Feature in the right column of the wiki page, section Related Component/Module).
Contact the maintainer to clarify the necessary funding and to get a tender.
If you need assistance in this process, contact the ILIAS product manager (Kunkel, Matthias [mkunkel]).


The following are guidelines for formatting your creative thesis.
Follow the guidelines in the Graduate Thesis Handbook for page margins and numbering. Use Times or Times New Roman, 12 point font throughout. In the actual creative text, other fonts and sizes may be used as appropriate for effect.
Times or Times New Roman font, 12 point; not bold, not italic, left aligned; spacing as noted. Use Title Case (first letter of words capitalized except for articles and prepositions, unless they are the first word) or use the font formatting as it occurs in the piece (for example, a poem title that is all lower case). See sample for examples.
* Due to the nature of the creative thesis, in the text this page will contain only the words Chapter II (line break) Title of Collection. The creative work will begin on the subsequent page. If a title page is used for Chapter I it would read Chapter I (line break) Artist's Statement.
Chapter headings and section headings in the text shall be unranked, i.e., all will be in the same font as the text (Times or Times New Roman, 12 point, no bold, no Italics) unless other formatting is necessary for the creative work. Prose is double-spaced with a five-space indent for new paragraphs. No double-double spacing between paragraphs.
Titles of the individual pieces, chapters or sections may be presented as appropriate to the piece. Consistency throughout the document is appreciated. If the piece, chapter or section has no title, it should be listed in the Table of Contents as "Untitled" and the title line may be left blank in the text itself.
Each essay, story or chapter can begin on a new page or can continue on the same page as the previous piece. The title between the sections may be formatted as desired, but consistency should prevail throughout the thesis. Poems embedded in prose text may be formatted as appropriate to the creative work.
If a poem is embedded in prose text, the author may format it any way he or she chooses. However, the formatting should be consistent throughout the text, when that is appropriate.
In general, each poem is identified with its title in Title Case (first letter of words capitalized except for articles and prepositions, unless they are the first word) unless other formatting is particular to the creative piece (such as a poem that uses no capital letters). Each poem should start on a new page, unless embedded in prose text.
If the piece has no title the heading "Untitled" may be used or the title line may be left blank.
The text itself may be formatted as desired by the writer, but the formatting should be consistent, and page margins should follow the Thesis Handbook. In general, prose is aligned left. A five-space indent is used between paragraphs rather than a double space, as in this example.
In general, poems should be centered on the page, although the individual lines should only be "aligned center" when appropriate for the poem.
The small rain does rain.


text:
Hosted Systems
Alpha3Cloud
Colocation Services
Specialized Data Centers
Colocation Packages
Providence Data Centers
Network Design & NOC Services
Wide Area Networking
Scalable Point to Point Solutions
By Ron Sacks
Prov.net News
02/22/12 – Anetics Selects...
Anetics selects prov.net as data center – colocation services provider
SSAE16 SOC II and Flexibility Were Key Factors
Providence, R.I., February 22, 2012 – Provdotnet, LLC. A leading provider of data center solutions, today announced that it has begun providing colocation services to Anetics, LLC.
Anetics is an application service provider based in Western Massachusetts, supporting financial services customers world-wide. "We selected prov.net because their proposal demonstrated that they were both flexible and capable of providing all of the services to support the design and operating requirements needed by Anetics," said Rob Sammons, Partner at Anetics.
Ron Sacks, Provdotnet's Managing Partner, noted that Anetics required a "SAS70" provider to host their platform and also said, "that prov.net had completed the SSAE16 SOC2 which replaced the SAS70 Type II AICPA standards".
About Anetics.net
Anetics develops and hosts a suite of tools that streamline workflow, provide in-depth reporting, and allow for easy information exchange within the global Securities Finance industry. Tasked to do more with less, with headcount at a premium, Anetics tools make it easy to discover supply and demand. To open, maintain, then return, new borrows and loans- hundreds, if not thousands, at a time. Anetics has tools to automate the Short Sale Locate process (Affirmative Determination). With robust exception reporting, and a rebate/ fee allocation engine that allows you to recover, share and profit from the distribution of borrow costs and rewards.
Anetics clients include:
Broker/ dealers acting as principal intermediary, borrowing and lending, customer facilitation, financing, in support of proprietary trading.
Custodial bank and trust companies, agents, and others representing beneficial owners with securities lending services.
Hedge funds, funds and investors as they locate and arrange to borrow securities, or seek to finance positions and portfolios.
About Provdotnet LLC
Provdotnet, LLC is a colocation, cloud services and managed data center services provider located in Providence, RI. Provdotnet opened its initial 2000 square foot facility at 1155 Westminster Street in July 2009 for customers requiring disaster recovery, cloud services, managed services and colocation facilities. Currently, Provdotnet has over 6000 square feet and can house up to 200 full data cabinets and associated computing equipment. Provdotnet also has the ability to expand the existing facility up to 10,000 square feet, significantly expanding overall capacity if and when needed.
More information is available at http://www.prov.net
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text:
News » Family
Gay Man Skips Sister's Wedding for Gay Club... Find Out Why
by Emell Adolphus
EDGE Media Network Contributor
Originally published on September 30, 2022
(Source:EDGE composite image)
Social media commentators are getting behind a gay man who skipped his sister's wedding to a homophobe to go to the gay bar with his boyfriend.
As reported by Newsweek, the man, who posted anonymously on Reddit as u/throwaway363738839, was praised by many commenters for choosing his mental health and taking a stand against silently suffering at his sister's wedding.
In the post titled "AITA for skipping my homophobic sister's wedding to go to a gay club?" the 23-year-old man said he and his older sister were close growing up. After he came out, she and his family were supportive until she met her fiancé.
"He grew up in a very traditional Christian household," the post read. "They met at a frat mixer at Bama (she was in a sorority, he was in a frat)."
Soon after, his sister reportedly began to become visibly uncomfortable with discussions of guys and dating. Her fiancé began to change her views.
"One time when her fiancé was on Facetime with us, I mentioned a Tinder date with a guy, and she told him I was joking," the post read. "We sort of grew apart as we got older."
The poster said the two kept in touch after he moved to California to go to college but he began to hide more of himself from her.
The post has raved more than 9,700 upvotes and 1,200 comments since.
After months of an increasingly strained relationship, including a conversation about how him bringing a date to the wedding would make families uncomfortable, his sister's wedding day arrived on the same day as his boyfriend's birthday. He chose his boyfriend.
He told his sister the morning of the wedding that he would no longer be a groomsman, and they haven't spoken since.
"I felt guilty for missing my sister's wedding, and I know I'm not blameless here: we were close for so long that it hurts regardless of what she said to me," the post read. "But I felt so invalidated during that rehearsal dinner, and I made a decision, and I can't undo that."
To the situation, he questioned: "Is it time to cut her off for a while, or should I be the one to apologize?"
Commentators felt he did the right thing.
"Your sister & her husband do not accept you and your partner for who you are," one commenter noted. "Instead, they want you to fit into their picture of what the wedding should look like. They are pretty intolerant and obviously homophobic."
Another commenter added, "Her comment about you 'forcing it on everyone else' is bonkers. I find it heartbreaking that she allowed this bigoted homophobe and his family to change her views and ruin her relationship with you...a gay club sounds much more fun than a wedding with guests who judge you for whom you love."
Others theorized that his sister chose a homophobic man because she is indeed homophobic.
"Her 'don't rub it in peoples faces' is rich since you're going to a wedding where they're rubbing their hetero relationship on everyone there," said the commentator.
What's your take? Did he do the right thing?


text:
Long Islanders Urged to Prepare for Hurricane Joaquin
By Rashed Mian and Timothy Bolger Posted on October 1, 2015
Hurricane Joaquin is expected to slam central Bahamas overnight. (Photo: NOAA)
With Hurricane Joaquin threatening the East Coast, Long Island officials began urging the public to prepare for the worst despite the storm's uncertain path as it reached major hurricane status Thursday.
The National Hurricane Center upgraded Joaquin to a Category 4 hurricane with 130 mph sustained winds, terming it "extremely dangerous." It was expected to batter the central Bahamas overnight. As for where Joaquin will hit next, meteorologists are grappling with major unknowns due to the myriad atmospheric conditions in play. The intensifying storm could make landfall in the Northeast or veer further into the Atlantic, sparing significant coastal damage.
"Right now we're essentially in a 'prepare and pray' mode," Suffolk County Executive Steve Bellone told reporters during a press conference at police headquarters in Yaphank. "We're gonna prepare for a worst-case scenario; we're gonna pray that it does not unfold."
Although the National Hurricane Center said a hurricane watch may not be issued for the East Coast until Friday at the earliest, the National Weather Service issued a coastal flood watch and high surf advisory through 6 a.m. Friday to start. Astronomically higher than usual tides are forecast to cause barrier beach erosion and flood coastal homes.
The message from officials in both Nassau and Suffolk counties is to stay informed, have go-kits ready for residents in low-lying areas, stock up on enough food and water that would last at least three days, gas up vehicles and generators, and heed evacuation warnings, if any are issued, so as not to put first responders unnecessarily in harm's way.
"The county is prepared to respond," Nassau County Executive Ed Mangano said Thursday morning during a press conference at the Nassau County Office of Emergency Management in Bethpage.
The county executive expressed confidence in a rapid and efficient reaction if the storm strikes, noting that Nassau learned from Superstorm Sandy, which hit LI three years ago this month. He added that residents also have to play their part, because early preparation prior to Sandy "saved lives."
Both Mangano and Bellone said their counties have more assets to help tackle the storm than they did during Sandy, touting dozens of high-axle vehicles used for flood rescues, portable traffic lights for blackouts and a slew of new emergency generators. One of the major issues in the early days following Sandy were the power outages that knocked out traffic lights, making roads very dangerous. An increase in portable traffic lights should help alleviate that problem, Mangano noted.
Local municipalities are also calling residents to be vigilant. Town of Hempstead said it's preparing equipment for a potential storm and urged boaters to begin removing their vessels from marinas.
"It is critical for each and every one of us to formulate a hurricane preparedness plan, and to be ready when and if the storm arrives," said Town of Hempstead Supervisor Kate Murray.
In Brookhaven Town, supervisor Ed Romaine informed residents that they should visit the town's website for news and weather updates, and also to access its "Hurricane Survival Guide."
Calling for the public to be proactive, Islip town officials not only cited Sandy's aftermath, but also invoked the "unprecedented and unpredicted" storm in August 2014 that flooded neighborhoods with a record-setting 13 inches of rainfall, the most ever measured in a 24-hour period statewide.
If a major tropical storm does hit LI, it would be the first true test for PSEG Long Island since it took over for the Long Island Power Authority in January 2014 amid outrage over LIPA's inadequate response to Sandy. The utility said it's monitoring Hurricane Joaquin and is preparing for a potential deluge of rain and powerful wind gusts. Resources will be in place over the weekend to initiate electric service restoration "as soon as the storm passes," PSEG LI said in a statement.
Officials remain concerned about LI's Sandy-battered infrastructure. For example, construction is ongoing at Bay Park Sewage Treatment Plant, which suffered a catastrophic failure during Sandy. Mangano said the county will use sandbags as an added layer of protection around the plant because a planned storm wall is still being built. Pumps have also been installed to keep pumping sewage away from people's homes, the county executive said.
On the other side of the county line, Bellone expressed concern that the dunes on Fire Island have yet to be restored since they were flattened by Sandy, which puts coastal communities on the Great South Bay at risk of flooding. Fire Island Ferries, the largest boat service to the mostly car-free barrier island, said it plans to suspend service Sunday.
Meanwhile, without knowing where Joaquin will go next, Gov. Andrew Cuomo told all New Yorkers to get ready for the hurricane.
"Since we don't know if the storm is downstate or upstate, you have to prepare statewide," Gov. Andrew Cuomo reporters on a conference call Thursday.After Sandy,many upstate communities were devastated by severe flooding that left bridges impassable for days, if not weeks.
The governor said it's too early to tell what major roads, if any, will be closed or whether mass transit will be shut down in New York City and on Long Island as it was during Irene and Sandy.
He added that maintenance crews are clearing problem areas in streams and conduits that have proven problematic in past storms, as emergency management offices are being activated statewide and are coordinating with utility agencies, "especially on Long Island."
Cuomo said that experience with prior hurricanes have helped the state better prepare for tropical cyclones. But he cautioned that Mother Nature always finds a blind spot.
"You can't be prepared for everything," he warned.
One thing's for sure, more rain is definitely heading toward LI, with heavy downfall expected Friday morning and possibly through the weekend along with strong winds.
Rashed Mian
Rashed Mian has been covering local news for the Long Island Press since 2011. He graduated from Hofstra University in 2010 where he studied print journalism. Rashed, the staff's multimedia reporter, covers daily news for the web, shoots/edits feature videos and writes about civil liberties. He loves Afghan food and sports. Rashed is also a caffeine freak. Email: [email protected] Twitter: rashedmian
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FINALLY! Grand Central Madison station opens after decades of planning and construction
Blakeman Doesn't See Current Nassau Coliseum as 'Viable' Option for Las Vegas Sands Redevelopment
Hochul Lays Out Big Plans for Housing Production, Public Safety in State of the State Address


text:
Browse the biggest quotes making the news for the last week.
Recent News Headlines : Gulf Of Oman -
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CHINA AND INDIA SAIL INTO CHOPPY WATERS IN NEW GREAT GAME
Strategically, Gwadar represents China's presence in the Indian Ocean near the Strait of Hormuz, making it a two-ocean power... READ MORE›
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For every major celebrity there's an assistant who sees it all - and that means everything. From extreme diva moments to flat-out weird habits, check out this list of celebrity personal assistant stories.
The running joke might be that celebs are just like us - but we all know that is so not true. For example, would you be able to rip out and reinstall all the toilets at a concert hall just because you hate the idea of all the germs? Madonna can! Or maybe you just can't be bothered to wash your own hair. And why would you if you could pay someone else to do it like Mariah Carey does?
Lucky for us, those behind the scenes are spilling all their celebrity assistant stories. These are the celebrity assistant horror stories that only those on the very very inside would know - like Jamie Dornan's obsession with needlepoint. But let's not spill all the beans just yet - check out these tales as celebrity assistants spill embarrassing personal stories about their famous former bosses.
As an assistant to Khloe Kardashian told Radar Online, "Khloe doesn't lift a finger at her house! She just barks orders at her assistant and housekeepers to have the cookies and other goodies displayed so that they will look good on camera."
"1. The only plants allowed in his house are cacti.
5. He can only eat off of plates made out of abalone shells."
According to source for InTouch Weekly, Madonna "had all of the commodes, showers and sinks removed, scrubbed down and then reinstalled" before her concert at the Palais Nakaia concert hall in France.


text:
Suðuroyar sýsla (danska Suderø, Sydö syssel) är en av Färöarnas 6 sýslur (Färöarnas regioner).

Geografi
Suðuroyar sýsla ligger i landets södra del och har en area av cirka 167 km².

Regionen omfattar hela ön Suðuroy och småön Lítla Dímun.

Befolkningen uppgår till cirka 5 000 invånare och huvudorten är Tvøroyri.

Färöarnas sydligaste punkt ligger i Suðuroyar sýsla med Akraberg nära Sumba (se även Färöarnas ytterpunkter).

Indelning
Regionen är indelad i 7 kommuner (kommunur).
 Fámjins kommuna
 Hovs kommuna
 Hvalbiar kommuna
 Porkeris kommuna
 Sumbiar kommuna
 Tvøroyrar kommuna
 Vágs kommuna

Historia
Färöarnas regioner har använts som administrativ indelning sedan lång tid och bygger på de historiska områdena på Färöarna. Varje syssel styrdes traditionellt av en Sýslumaður (sysselmannen) och ett Várting (Vårting).

Under den danska reformationen år 1536 avskaffades den danska sysselindelningen helt medan de kvarstår på Färöarna.

Före 1957 utgjorde regionerna även landets valkretsar innan man ändrade valkretsarnas gränser för att öka balansen vid val  varpå Suðuroyar sýsla delades i Suðuroyar Norðra (norra) och Suðuroyar Sunnara (södra).

Källor

Externa länkar
 Om Suðuroyar sýsla
 Färöarnas statistiska centralbyrå

Färöarnas regioner


The Japanese word for autumn is aki. You pronounce it "ah-kee".
You'll notice that the kanji for aki has two parts. Each part of a kanji has a meaning and is called a "radical". In this case, the left one means "grain" and the right one means "fire".
In Japan, the number four is an unlucky number. Because of its pronunciation, it means "death".


text:
Council clean-up continues
At Tuesday's Cabinet meeting additional funding of £100,000 was allocated for the Council's city-wide clean-up plans.
More estates have been added to plans for deep cleans over the next year, with Stantonbury, Bradville, Fullers Slade and Beanhill all set to receive work to tackle problem areas in the estates.
Labour councillor for Stantonbury ward, Cllr Martin Petchey, told us: "After hearing from local residents in my ward I donated half of my 2019/20 councillor budget to a Bradville clean-up"
He continued: "I'm glad to see that our Labour-led Council has listened to local people's concerns and gone one step further by allocating more funding to include Stantonbury & Bradville in the city-wide clean up."
Labour councillor for Stantonbury ward, Cllr Martin Petchey
Clean up activities will include clearing overgrown landscaping, tackling weed infested footpaths, litter picking and action on the rat population.
Labour councillor for Woughton & Fishermead, Cllr Hannah O'Neill, added: "Labour-led MK Council are committed to getting the basics right and this additional funding will help us to continue to meet this commitment."
She concluded: "I'm delighted to see Beanhill has been added to the list of estates and that it will receive a clean-up alongside neighbouring Netherfield & Coffee Hall. I know this will be very welcomed by residents there"


text:
Airport Dining
Bush Intercontinental is tops in North America for airport dining
Get Your Passport Ready
Grand Cayman getaway: Beautiful beaches, great diving in the Caribbean
Minute Suites DFW Airport
New sleep-by-the-minute suites usher in nap time at Dallas-Fort Worth AIrport
New sleep-by-the-minute suites usher in nap time at DFW Airport
Mar 21, 2017, 9:00 am
It's nap time at Minute Suites. Photo courtesy of Minute Suites
Dallas-Fort Worth International Airport travelers looking to grab a little shut-eye have another place to roost. Today (March 21), Minute Suites opens a location in Terminal A, next to gate A38.
This is the second location at DFW. The new Terminal A location will have seven suites, consisting of four regular and three "premium" window suites, which have more room than standard suites, including a connecting suite for groups and families.
The original location opened in Terminal D in 2013. It has 10 suites, plus two showers. With the new location, that makes a total of 17 suites.
Suites require a one-hour minimum reservation. You can also book an eight-hour day rate and a flat overnight rate, too.
A one-hour rental is $42, with $10.50 for every 15 minutes after. The day rate is $160, and the overnight rate (11 pm-7 am) is $140. A 30-minute shower is $30, or $20 with room rental.
Minute Suites was founded in 2008 as a healthier way for people to travel. They're the first company in North America to provide private suites inside security at airports, where travelers can nap, relax, or work. Similar accommodations exist at airports in other countries such as Japan, but they're usually just a simple bed.
Each suite comes with a daybed sofa with a sliding trundle bed, plus pillows, blankets, desk, and office chair. A sound-masking system helps neutralize noise, and a unique Nap26 audio program is available to help deliver a refreshing power nap.
Each room has a computer with a 32-inch screen equipped with high-speed internet, flight-tracking information, and DirecTV. Laptop users can connect with the internet using airport Wi-Fi or a direct connection port. Guests can use the alarm clock in the suite or request a wake-up call.
According to Minute Suites co-founder Daniel Solomon, about 50 percent of users take a nap, 30 percent relax, and 20 percent work.
This opening marks the fourth airport location. The first Minute Suites opened in Atlanta in 2009, and there's also a facility in Philadelphia, with plans to open more in 2017, says Solomon in a release.
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The Legend is a high-end RDTA with a diameter of 22mm. It can also be used as a RDA by unscrewing two parts and reassembling it with a dedicated kit (click here for instructions).
Its revolutionary spring-loaded deck is made plated with 24K gold. This rebuildable stainless steel sprayer offers a 2-pole mounting plate with spring clamps. These run over the whole deck and allow for either MTL vaping (using micro coil) or targeted vape clouds (using Clapton assembly). This wonderful system allows not to move the legs of the coils during its installation.
Machined housings on the deck allow for an axis to be positioned up to a diameter of 4mm in order to place the coil. One must then simply clamp the two legs of the coil using the spring clamps. This system has never been used on this type of atomizer before.
The chamber is very compact, which gives it a dense vapour and reveals the aromas to the fullest.
Two top caps are delivered with the E-Phoenix The Legend: one for an air draft with large air flow and drip tip 810, and a second for directed flavor with a drip tip and a drip tip adapter 510.
This high-end atomizer is made of noble materials: 24k gold brass for the electrical connectors, peek (which is the best plastic insulator), and high quality stainless steel. The black color treatments are high quality PVD.
Filling: by bottom feeder and filling by deck for the 2ml tank.
Materials: stainless steel, peek, ultem, gold brass.


text:
System.register(['angular2/core', './voter.component'], function(exports_1, context_1) {
    "use strict";
    var __moduleName = context_1 && context_1.id;
    var __decorate = (this && this.__decorate) || function (decorators, target, key, desc) {
        var c = arguments.length, r = c < 3 ? target : desc === null ? desc = Object.getOwnPropertyDescriptor(target, key) : desc, d;
        if (typeof Reflect === "object" && typeof Reflect.decorate === "function") r = Reflect.decorate(decorators, target, key, desc);
        else for (var i = decorators.length - 1; i >= 0; i--) if (d = decorators[i]) r = (c < 3 ? d(r) : c > 3 ? d(target, key, r) : d(target, key)) || r;
        return c > 3 && r && Object.defineProperty(target, key, r), r;
    };
    var __metadata = (this && this.__metadata) || function (k, v) {
        if (typeof Reflect === "object" && typeof Reflect.metadata === "function") return Reflect.metadata(k, v);
    };
    var core_1, voter_component_1;
    var VoteTakerComponent;
    return {
        setters:[
            function (core_1_1) {
                core_1 = core_1_1;
            },
            function (voter_component_1_1) {
                voter_component_1 = voter_component_1_1;
            }],
        execute: function() {
            VoteTakerComponent = (function () {
                function VoteTakerComponent() {
                    this.agreed = 0;
                    this.disagreed = 0;
                    this.voters = ['Mr. IQ', 'Ms. Universe', 'Bombasto'];
                }
                VoteTakerComponent.prototype.onVoted = function (agreed) {
                    agreed ? this.agreed++ : this.disagreed++;
                };
                VoteTakerComponent = __decorate([
                    core_1.Component({
                        selector: 'vote-taker',
                        template: "\n
Should mankind colonize the Universe?
\n
Agree: {{agreed}}, Disagree: {{disagreed}}
\n    <my-voter *ngFor=\"#voter of voters\"\n      [name]=\"voter\"\n      (onVoted)=\"onVoted($event)\">\n    </my-voter>\n  ",
                        directives: [voter_component_1.VoterComponent]
                    }),
                    __metadata('design:paramtypes', [])
                ], VoteTakerComponent);
                return VoteTakerComponent;
            }());
            exports_1("VoteTakerComponent", VoteTakerComponent);
        }
    }
});
//# sourceMappingURL=voter-taker.component.js.map

redpajama_set_name: RedPajamaGithub


Burch and Vertue staff, who did the lights at the 1937 Aldershot Tattoo. Maurice is in row 3, 4th in.
Met Maria Josephina when on service in Belgium during WW2. Named after Augustus Wilson. Buried in Redan Hill cemetery, Aldershot.