Brimming with eco-messages, Greenpeace's flagship Rainbow Warrior visited Puerto Vallarta the second week of January. As part of a Latin American tour aimed at raising environmental consciousness and exposing specific instances of pollution, Greenpeace members and activists from other groups spoke to the press, released a new report on toxic contamination of Mexican rivers and gave the public guided tours of a nearly 160-foot ship often powered by the wind.
Unseasonably rainy weather coincided with the Rainbow Warrior's port-of-call to Banderas Bay.
In response to a question from FNS, Lara assessed the new energy reform promulgated by the administration of President Enrique Pena Nieto and approved by the Mexican Congress last month as a policy that will privilege "dirty energy," further Mexico's dependence on oil, leave renewable energy in the back seat, and deny social justice.
In a similar vein, Sinai Guevara, Greenpeace Mexico toxics campaign coordinator, criticized the reform as paving the way for the hydraulic fracturing of shale gas and oil, or fracking, especially in arid, northern states like Coahuila beset by drought and water shortages.
"This worries us," Guevara said. "A lot of water and chemicals are used to extract (energy resources), Guevara said of the process used in the fracking technique. "(Fracking) will take away water from communities." Greenpeace Mexico is working with other organizations in the Mexican Alliance against Fracking, she added.
At a press conference, Guevara presented Greenpeace Mexico's report on toxic contamination of two important river basins-the Lerma in west-central Mexico and the Atoyac in the south-central part of the nation. Situated in and around Mexico's most densely populated corridors of Mexico City and Guadalajara, both ecosystems provide a source of water for millions of people.
According to the Mexican environmentalist, the report documents that the Mexican government's strategy of relying on primary and secondary wastewater treatment to keep rivers clean fails to remove heavy metals and chemicals, dozens of which were detected in the Lerma and Atoyac river basins by researchers.
The report notes the presence of substances linked to cancers, reproductive and immunological disorders and hormonal disruptions.
Cancer-causing cadmium and chromium were among the heavy metals found in the Rio Lerma, while 51 volatile organic compounds were discovered in the sediments of both the Rio Lerma and Rio Atoyac during a 2013 Greenpeace investigation.
Some of the substances discussed in the report have been banned in the European Union, Guevara said. "It's only one case," Guevara said of the report. "But it's a very worrisome case of what's happening to rivers in Mexico," she said.
Greenpeace demands that the Mexican federal government update its wastewater discharge regulations to take toxic substances into account, make the registration of toxic discharges obligatory and require reporting of accidental toxic discharges into rivers.
Omar Arellano, member of the Mexican Union of Concerned Scientists, said a "lack of planning and scientific knowledge about protecting aquatic ecosystems" combines with official omission in the ecological crisis of Mexican rivers.
Other Mexican rivers in similarly bad ecological shape include the Colorado and Rio Grande in the northern border region, Guevara said.
Representatives of two Guadalajara-area organizations, Un Salto de Vida and the Mexican Institute for Community Development (IMDEC), joined Guevara in denouncing the condition of Mexican rivers like the Rio Santiago, where residents have waged a long anti-pollution campaign that's reached the Montreal-based Commission for Environmental Cooperation and other international institutions.
Sofia Enciso, Un Salto de Vida spokesperson, contended that cancers and other health maladies are becoming more pronounced in the Rio Santiago zone, where hundreds of foreign and national industries discharge wastewater.
Maria Gonzalez, IMDEC director, described the Rio Santiago pollution as a massive human rights violation of the type that is under increased consideration in the United Nations.
Private industry as well as government should be held accountable, Gonzalez demanded. Overall, the Rio Santiago contamination represented a "grave problem of public health," she contended.
Greenpeace's Puerto Vallarta visit was the second stop in a winter voyage to Mexico and Colombia.
Prior to Puerto Vallarta, the Rainbow Warrior docked in Mazatlan, Sinaloa, after departing from San Diego. Upwards of three or four thousand people turned out for the Mazatlan visit, estimated Edith Martinez, Greenpeace press liaison. Keen public interest was also evident in Puerto Vallarta, where crowds began forming to board a ship that is akin to a floating eco-village.
According to crew members, the Dutch-designed Rainbow Warrior was built in Poland and Germany with recycled materials, and relies on five big sails to traverse the oceans whenever possible.
"We're trying to show everyone that wind has a place not only on land, but also on the sea," said Joel Stewart, the Rainbow Warrior's captain.
Constructed for a 32-member crew, the ship boasts a heliport and state-of-the-art navigational technology. For garbage recycling, the Rainbow Warrior has separate trash bins and a compost container. Crew members enjoy meals prepared by a chef who uses food purchased from cooperatives and organic producers at ports the Rainbow Warrior visits.
Greenpeace's sleek ship is the third one to bear the Rainbow Warrior name. In an effort to squash Greenpeace anti-nuclear protests in the South Pacific, French intelligence agents blew up the first vessel in New Zealand back in 1985, killing photographer Fernando Pereira in the attack.
"It's incredible that a strong government like France would feel threatened by such a (smaller) organization like Greenpeace was at the time," Stewart reflected.
The second Rainbow Warrior was retired a couple of years ago and transformed into a ship for climate refugees in Bangladesh, Stewart said.
A survivor of the 1985 French attack on the Rainbow Warrior, the wooden Dave the Dolphin, sits high on the deck of the new ship gazing forward into the sea. Appropriately enough, leaping dolphins and lumbering humpback whales were visible not far from the pier where the Dave the Dolphin and the Rainbow Warrior rested on Banderas Bay.
The Rainbow Warrior is part of Greenpeace's three-ship fleet, which also includes the Esperanza and Artic Sunrise. The Russian government's seizure of the Artic Sunrise and its 30-member crew in international waters last September prompted an international uproar. All of the anti-oil drilling activists accused of piracy were released from jail by the end of last month, but the Artic Sunrise remains in Russian custody.
After Puerto Vallarta, the Rainbow Warrior headed to Acapulco before continuing on to Colombia, where the group is increasingly active. The eco-ship plans on returning to Mexico in February, with visits programmed for Cozumel and Veracruz.


Apple iPhone 8 Plus has an internal memory of 64GB. The redesigned stereo speakers of this 64GB iPhone 8 Plus deliver a powerful sound.The Apple iPhone 8 Plus packs class-leading processing powers in a durable all-glass body. The phone is reinforced with an aerospace?grade aluminum band and laser?welded steel foundation for enhanced durability. Furthermore, it provides excellent resistance from water, splashes, and dust, thanks to its precision-engineered make. The phone has support for wireless charging, so it can easily be charged with Qi wireless chargers that are commonly found in cafes, hotels, airports, and cars. The 5.5inch Retina HD display, with True Tone technology and a wide color gamut, makes every visual crisp and captivating. Furthermore, the wide?angle and telephoto lenses on this Apple mobile enable digital zoom, as well as the optical zoom of up to 10x for breathtaking photos and videos. The 7MP front camera delivers superior video calls on FaceTime so that you can be in touch with your long distant family and friends. Also, it clicks awe-inspiring selfies in low light, thanks to the retina flash. This silver iPhone 8 Plus is fueled by an A11 Bionic CPU that can take on high-graphics games and heavy-duty apps with less drain on the battery. The phone packs an internal memory of 64GB, which means you store all your data such as, videos, audio files, documents, and pictures under one roof. The advanced apps of iOS 11 are engineered to be incredibly intuitive and intelligent, thereby giving you a mind-blowing smartphone experience.


text:
#include "network.h"
#include <event2/listener.h>
#include <event2/event.h>

class TCPLinkImpl;
typedef SharedPtr<TCPLinkImpl> TCPLinkImplPtr;
typedef std::vector<TCPLinkImplPtr> TCPLinkImplPtrs;
class ServerHandleImpl;
typedef SharedPtr<ServerHandleImpl> ServerHandleImplPtr;
typedef std::vector<ServerHandleImplPtr> ServerHandleImplPtrs;

class ServerHandleImpl : public ServerHandle
{
	friend class TCPLinkImpl;
public:
	~ServerHandleImpl();

	static ServerHandleImplPtr Listen(
		struct event_base* ev_base,
		uint16_t port,
		const Network::ListenCallbacksPtr& listen_cbs
	);

	virtual void Close() override;
	virtual bool IsListening() const override { return listening_; }

protected:
	struct event_base* ev_base_;
	Network::ListenCallbacksPtr listen_cbs_;

	evconnlistener * conn_listener_;

	bool listening_;

	TCPLinkImplPtrs conns_;

	int m_ErrorCode;

	std::string m_ErrorMsg;
	ServerHandleImplPtr self_ptr_;

	ServerHandleImpl(struct event_base* ev_base, Network::ListenCallbacksPtr listen_cbs);

	bool Listen(uint16_t port);

	static void ListenCallback(evconnlistener* listener, evutil_socket_t sock_fd, sockaddr * addr, int len, void * ctx);

	void RemoveLink(const TCPLinkImpl* link);
};

redpajama_set_name: RedPajamaGithub


This is a list of U.S. states by date of statehood, that is, the date when each U.S. state joined the Union. Although the first 13 states can be considered to have been members of the United States from the date of the Declaration of Independence – Thursday, July 4, 1776 – they are presented here as being "admitted" on the date each ratified the present United States Constitution; most other such lists, including the 50 State Quarters program, do the same. The admission dates for later states were set by either the act of admission or a later resolution issued under that act, except for Ohio, whose date of admission was determined by act of Congress in 1953 (see note below).
This list does not account for the secession during the American Civil War of 13 states, 11 of which formed the Confederate States of America, and the subsequent restoration of those states to representation in Congress (sometimes called "readmission") between 1866 and 1870, or the end of Reconstruction in those states. Nor do the dates on the list reflect ratification of the Articles of Confederation, which is the original document naming the United States as such.
* Congress recognized the state of Ohio on February 19, 1803 [ [http://rs6.loc.gov/cgi-bin/ampage?collId=llsl&fileName=002/llsl002.db&recNum=238 "An act to provide for the due execution of the laws of the United States, within the state of Ohio"] , Seventh Congress, Session II, Chapter VII] , but no formal date of statehood was set by the act of admission or a later resolution, as occurred with all other new states. On August 7, 1953, Congress passed a law retroactively setting the date of Ohio's statehood at March 1, 1803, the date when Ohio's first legislature convened.
† The actual statehood proclamations for North and South Dakota were intentionally shuffled so that no one actually knows which was admitted first; President Benjamin Harrison always refused to tell the order in which he signed the two statehood bills. However, North Dakota's proclamation was published first in the "Statutes at Large" (since it is first alphabetically).


text:
eLibraries Manitoba
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Promise and Peril
An inside, in-depth look at the leadership of Justin Trudeau, by a veteran political journalist
A must-read for all Canadians before the next federal election
Justin Trudeau came to power on the promise of "hope and hard work" and a pledge to seek a common good for all Canadians. From the outset, his critics called him naive, inexperienced and a danger to the economy. His proponents have touted his intentions for the middle class, the environment and refugees, which they argue have moved forward real change despite challenges and criticism. Veteran political journalist Aaron Wherry has extensively interviewed decision-makers, influencers and political insiders, from the prime minister's closest advisors to cabinet ministers to the prime minister himself, to provide the most in-depth, inside examination—beyond the headlines and the tweets—of how Justin Trudeau has performed on his promises for Canada.
Promise and Peril: Justin Trudeau in Power explores how the Trudeau government has succeeded or failed in its biggest commitments—resource development, immigration, climate change, trade, reconciliation—against a backdrop of economic uncertainty, global political tumult and the roar of populist revolt. It reveals what was happening behind the scenes during the government's most crucial and public moments, including:
the NAFTA negotiations
the infamous Trump tweets at the G7 summit
that island vacation
the SNC-Lavalin affair
Promise and Peril is a must-read for all voters before the next election. It examines whether a politician who came to office with immense potential has measured up to expectations—and what is at stake for Canada's future at home and abroad.
Publisher: HarperCollins Canada
Biography & Autobiography Politics Nonfiction
Aaron Wherry - Author
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redpajama_set_name: RedPajamaCommonCrawl


Designing a dating or greeting card website with an interactive platform can be a monumental task without factoring in the time you invest to produce graphics. Our free large love icons help to reduce the time it takes to implement graphics into your project. The icons are available in a variety of sizes and formats and provide professional quality in two versions including with shadows and without shadows and a transparent background.


text:
MISSION OF THE PRESIDENT OF UKRAINE
IN THE AUTONOMOUS REPUBLIC OF CRIMEA
Strategies, Programs and Plans
Educational and Scientific Materials
Citizens Requests
Partners' Structures
Expert Board
Work Priorities
History of the Mission
Purification of Government
Anti-Corruption Activities
New Resolution of Parliamentary Assembly OSCE on Russia's aggression in Crimea
In July 11 2018 without any regard for the dirty provocation of the state- aggressor's delegation at the 27th Annual Session of the OSCE Parliamentary Assembly in Berlin, the Resolution "Continuing Violations of Human Rights and Fundamental Freedoms in the Autonomous Republic of Crimea and the City of Sevastopol" was adopted by the majority of members.
The OSCE Parliamentary Assembly strongly condemns the illegal occupation by the Russian Federation of the Autonomous Republic of Crimea and the city of Sevastopol, Ukraine, and reiterates its call on the Russian Federation to stop aggression against Ukraine and to fully comply with its obligations under the UN Charter, the Helsinki Final Act and other norms and principles of international law, and the OSCE principles and commitments.
The Resolution condemns violations, abuses, measures and practices of discrimination against the residents of temporarily occupied Crimea, including Crimean Tatars, as well as Ukrainians and persons belonging to other ethnic and religious groups, by the Russian occupation authorities.
The OSCE Parliamentary Assembly condemns the unlawful imposition of laws, jurisdiction and administration in occupied Crimea by the Russian Federation, and demands that the Russian Federation respect obligations under international law with regard to respecting the laws in force in Crimea prior to occupation, reads the statement.
In the Resolution, the OSCE PA "calls upon the Russian Federation to uphold all of its obligations under applicable international law as an occupying power in effective control of Crimea" and "restore enjoyment of the rights of all individuals, without any discrimination based on origin, religion or belief, and to revoke the decisions that banned cultural and religious institutions, NGOs, human rights organizations, media outlets, and to restore enjoyment of the rights of individuals belonging to ethnic communities in Crimea, in particular Ukrainians and Crimean Tatars, including to engage in cultural gatherings".
The OSCE PA calls by the Resolution, upon the Russia Federation to halt the eradication of education in and of the Ukrainian language, restriction and suppression of cultural, religious and other manifestations of the Ukrainian identity and to ensure the availability of education I Ukrainian and Crimean Tatar Languages.
The Resolution calls on to revoke immediately the decision declaring the Mejlis of the Crimean Tatar People an extremist organization and banning its activists, repeal the decision banning leaders of the Mejlis from entering Crimea and refrain from maintaining or imposing limitations on the ability of the Crimean Tatar community to conserve its representative institutions, including Mejlis and Kurultay.
Russia is called on by the resolution to create and maintain a safe and enabling environment for journalists, human rights defenders and defense lawyers to perform their work independently and without undue interference in Crimea; to end the practice of compelling Crimean residents to serve in the armed auxiliary forces of the Russian Federation, including through pressure and propaganda; to stop persecution and illegal detention of all those residents of Crimea who oppose the illegal occupation of the peninsula.
The OSCE PA calls by the Resolution upon to conduct prompt, impartial investigations into all cases of human rights violations in Crimea, including the cases of torture, abductions and enforced disappearances and to stop imposing the application of the Russia federation's laws in occupied Crimea, as well as forced conferral of Russian citizenship to residents of Crimea in violation of international law as well as forcible deportation of Ukrainian citizens without Russian passports from Crimea.
In the Resolution Russia is called on to refrain from transferring persons in detention or social care institutions, including children, to the Russian Federation and other territories under its control. As well as it calls on to release immediately and uncondititonally Crimean activists Oleg Sentsov, Olexander Kolchenko, Mislim Aliev, Emir Usein Kuku, Vadim Siruk, Arsen Dzhepparov, Refat Alimov and other Ukrainian citizens, who have been unlawfully detained or imprisoned under the fabricated charges by the de facto authorities in occupied Crimea.
Про проведення оцінки корупційних ризиків
Порядок відшкодування фактичних витрат на копіювання або друк документів, що надаються за запитом на публічну інформацію, розпорядником якої є Представництво Президента України в Автономній Республіці Крим
MISSION OF THE PRESIDENT OF UKRAINE IN THE AUTONOMOUS REPUBLIC OF CRIMEA
8, Petro Bolbochan Street, Kyiv 01014. E - mail: ark@ppu.gov.ua
42 Ushakov Avenue, Kherson, 73003, tel/faх: +38(0552)49-59-39, E - mail: zvernennia@ppu.gov.ua, Skype: ark predstavnictvo
VERKHOVNA RADA OF UKRAINE
CABINET OF MINISTERS OF UKRAINE
MINISTRY OF REINTEGRATION OF THE TEMPORARILY OCCUPIED TERRITORIES OF UKRAINE
MINISTRY OF FOREIGN AFFAIRS OF UKRAINE
COMMISSIONER OF THE VERKHOVNA RADA OF UKRAINE ON HUMAN RIGHTS
OFFICE OF THE PROSECUTOR GENERAL
PROSECUTORS OFFICE OF THE AUTONOMOUS REPUBLIC OF CRIMEA AND CITIES OF SEVASTOPOL
MAIN DEPARTMENT OF THE NATIONAL POLICE IN THE AUTONOMOUS REPUBLIC OF CRIMEA AND THE CITY OF SEVASTOPOL
KHERSON REGIONAL STATE ADMINISTRATION
MEJLIS OF THE CRIMEAN TATAR PEOPLE


text:
What I learned in my research of the "Involuntary Adjunct"
Article October 14, 2019 part-time faculty
By Bobbi-Lee Smart, Cerritos Faculty Federation
My dissertation research focused on the perceptions of the impact of adjuncts on community college campuses in Southern California. I specifically wanted to understand the reality of involuntary adjuncts — those whose who want full-time tenure track jobs, couldn't get a position, so worked as "full-time" adjuncts (those whose adjunct work is the majority or entirety of their income).
The key findings of my research and interviews follow.
"Adjunct" is not a dirty word, but it's treated like one, and this stigma masks the truth.
While some have balked at my use of the term "adjunct" in my research, it was intentional. I wanted to draw attention to adjuncts' original role in higher education. The term adjunct, literally means something which is a non-essential or temporary "attachment," or" appendage." Adjuncts were never meant to be majority of faculty, and yet they are, and just as the word "adjunct" denotes, the state and most community college districts treat them as if they are auxiliary to the campus and not vital to the institutions in which they work.
Due to the negative stigma of the word adjunct, quite a few people prefer to use alternative language, such as "contingent," "part-time," "lecturer," "non-tenure track lecturer," and "instructor." All of these names mask the work conditions of adjuncts, as each implies something different, generally something more stable and positive. Changing our job title may make these instructors feel better, and it may make others feel more comfortable to use these terms. None of this however of this changes the way we are treated.
The structure of higher education faculty has changed, yet the work condition of adjuncts has been slow to keep pace with the new reality.
Full-time equal opportunity hiring is equal opportunity in name only.
While the numbers of adjunct positions are constantly on the rise, the number of full-time tenure-track faculty positions has stagnated, making adjunct positions highly desirable and competitive.
In California, Title V stipulates that when a tenure-line position opens, the job is to be publicly announced, and that, in the name of equal opportunity, even adjuncts at the campus where the position is open are not supposed to be given any sort of favoritism or conversely, be discriminated against.
However, the exact opposite was found multiple times during my dissertation interviews and from faculty applicant observations. One former college president, along with several deans and department chairs, and both full-time and adjunct faculty observed that the way job ads were written either favored a specific adjunct they currently employed and wanted to hire, or conversely, so that none of the current adjuncts would rank very high, thus allowing for an outside candidate to rank higher than the current adjuncts and thus secure the full-time position.
With regard to whether on-campus adjuncts were being effectively catered to or excluded, one interviewee succinctly stated that, for better or worse, current adjuncts are a "known quantity." This suggests loopholes in current hiring policies that are intended to create equity are being exploited.
To be seen as adjunct is to be seen as less than.
In multiple spaces I heard that just because someone is a good adjunct does not mean they deserve to be full-time, or that just because someone has been on a campus for years, doing the work doesn't mean they deserve to be full-time.
This is demeaning to the work adjuncts do and dismisses their potential to be successful and impactful full-time tenured faculty. This logic also gives districts a reason not to invest in their adjuncts, and it also gives the adjuncts reasons not to invest in the campuses beyond teaching. This impacts a college's campus culture and its ability to perform vital duties such as curriculum development and student mentoring activities. There are typically not enough full-time faculty to perform these tasks.
Time for an internal promotion system?
Most interviewees felt that the hiring process should become more of a promotion system, like in most other industries. This would incentivize the districts to invest in their adjuncts through professional development and integrate them into the campus. It would also motivate and incentivize adjuncts to invest in their campuses and become more involved in campus life.
No more excuses. The time for change is now.
The treatment of adjuncts and the hiring process are systemic problems that must be addressed on a systemic level. We cannot continue to point to hiring laws as the reason that things cannot be changed. Laws can be changed and updated, and the current laws do not reflect the new reality of higher education faculty, which suggests they are in need of an update.
There is a need for a massive overhaul laws governing supposed equal opportunity hiring practices. The work conditions and treatment of adjuncts impacts not only the adjuncts, but the campus as a whole. Campuses who better value adjuncts will have better campus cultures, and better student outcomes.
Bobbi-Lee Smart is Vice President for Part-Time Faculty with the Cerritos College Faculty Federation
Topic: Education Issues
Topic: Standing Together
part-time faculty


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Representatives of Belarusian opposition movements have adopted a declaration to set up a joint coordination council.
The new body is created with the aim of pressing for the release of detained activists and to inform the international community about the current state of the country's politics.
According to Belarusian media, the council will also work for Belarus to return to law and democracy as well as create conditions for organizing free and democratic elections. The council unites such movements as the Congress of Democratic Trade Unions, two Belarusian Social-Democratic Parties, the Leftist party Just World, the civil initiative Speak the Truth, as well as the movements For Freedom, Young Front, European Belarus, and others.
One of the organizers, the head of the Just World party, Sergey Kalyakin, told the press that the council will not have any leaders as it is made up of independent movements with their own positions on each issue. "We are not creating an over-party structure," the politician said.
The move to set up the opposition coordination council came after a massive crackdown on opposition last month. Back then, several political parties and movements organized a massive rally in the center of Minsk in protest against what they call an "unlawful" result in the presidential election, in which Alexander Lukashenko won his fourth term in office. Police dissolved the rally and detained many of its participants, including five of eleven presidential candidates. The move caused an outcry in Europe and prompted the possible introduction of sanctions against Belarusian leaders by the European Union. On Monday, Russian agency RIA Novosti quoted a diplomatic source as saying that Germany, Great Britain, Sweden and Poland support sanctions against Belarus over the post-election crackdown on the opposition.


Among Christian people there are many varying opinions about what holidays to celebrate, how to celebrate, and such. "One man esteemeth one day above another: another esteemeth every day alike. Let every man be fully persuaded in his own mind. He that regardeth the day, regardeth it unto the Lord; and he that regardeth not the day, to the Lord he doth not regard it…"(Rom 14:5-6a) Many consider Halloween, Christmas, and Easter to be just a holiday in which to celebrate. It is true that they are all pagan holidays. Therefore as Christians, in raising our children we do not celebrate the pagan holidays. The rule is simple in our home. Only observe that which points us and others to Christ.
Therefore, as the world celebrates Santa Clause, reindeer, and elves, as believers we celebrate the birth of Christ. As the world celebrates Easter bunnies and the pagan goddess of fertility, we celebrate the resurrection of Jesus Christ. As the world celebrates Cupid and arrows on Valentine's Day, we celebrate God's great love. Each day being a special reminder of God, His Son, and the great love for mankind. Which brings us to the celebration of Halloween. Can the celebration of Halloween point us and other's to Christ? No. In fact, it does just the opposite.
The world celebrating Halloween is not the issue of discussion. After all, one would expect the world to do worldly things. But, Christian people are peculiar people, set apart from the world. True believers in Christ do not love the world or the things of the world (I John 2:15). Why, then if over 80% of Americans claim to be "Christian" are we celebrating this holiday? Why is Halloween the second most decorated holiday in our country? Is this a holiday that can point us and others to Jesus Christ?
There are three reasons that I believe Christians celebrate Halloween. The first reason is simply that they do not know the truth. That have never been taught the origins of Halloween. You see, like most people when my first child was born I went along with the flow of the tide. When Halloween came around I found a costume for my baby like everyone else did and took him to get candy. No harm in that! No bothered conscience. But the second year, I remember taking him to the mall on Halloween. The absolute evil and oppression present was astonishing. It was then that I questioned why I was doing this. I started my research in the place that all Christian people should – the Bible. It didn't take long to know the will of God in this matter. The question then came. What was I going to do with this knowledge?
Which brings us to the second reason Christian people celebrate Halloween. They know the truth and do not care. Did you know that a person can justify anything? They can read in scripture to abhor evil and to abstain from even the appearance of evil and yet somehow justify in their mind and heart that what they are doing is not evil. Unfortunately, the average person's mind is full of the world (Mark 4:18-19) and their heart is deceitfully wicked (Jer. 17:9). But amazingly, we will trust our hearts and minds over the very Words of God. A person will read in scripture that we are to be separate from the world but yet they will justify in their hearts their love for the things of this world. Did you know that we are called to be the light of the world? A city that is set on a hill cannot be hid. Do you know why a city on a hill cannot be hid? It is because the light is separated. A person wondering around with the masses trying to shine their lighted jack-o-lanterns with the rest of the world will not give off much light, but take a person who is called out, a peculiar person, a holy person, a chosen person (I Peter 2:9) and set this person up on a hill for all the world to see.
The third reason and saddest of all is that those who claim Christianity are not true believers. Therefore, they cannot help but be workers of darkness. Without Christ there is not capability of righteousness. Can we judge someone's salvation? NO. But they can and should before it's too late. Examine yourselves, whether ye be in the faith; prove your own selves. (2Co 13:5a) We are called to be fruit inspectors who look at the fruits of those who claim Christianity. And an apple tree that produces figs is not an apple tree no matter how much it claims to be one.
As professing Christians, we teach our children that every word, every action and every deed should be done for the glory of God. To celebrate (observe, show happiness, mark an occasion) Halloween can in no way bring glory to God. Churches often participate in this holiday. There are those who have Halloween parties to "bring in the world" and witness to them. It is due to a damaging pragmatic thinking of "we must be like the world in order to win the world.". When a person tells me that they will use this evil day to witness to the world my question for them is, "Are you witnessing for the Lord on all the other days? Do you hand out tracts and talk to people about their salvation the rest of the year?" A person trying to get another person saved while participating in Halloween seems to be equivalent to a doctor taking his dying heart patient to Krispy Kreme Donuts to discuss the importance of eating healthy foods. The message would be looked at in disgust. This might explain why the world looks at the message of the church in utter disdain.
So, my question for Christians who celebrate this holiday is why? Are you truly a child of God, do you just not care about God's Word, or have you never searched out the truth? For those who truly want to know the truth and who are willing to search out God's will I encourage them to open the Word of God. Open His precious Word, not with intents to trample on it but in a humble spirit. For in reality, God's ways to a true believer are not grievous. His ways are light, His ways are worthy, His ways are above all others.
My husband found this article several years ago while working with the youth in our church. We are not sure where it came from but is very good. For those who are seeking the truth continue reading….
Halloween – Can it be an entirely innocent practice?
What is the origin of Halloween? It is generally agreed that in the church history Halloween took the place of a special day celebrated by the ancient Druids who was the priestly class of the Celtic religion. Our modern Halloween appears to initially be traced to their winter festival on October 31. The Celts and their Druid priest began their New Year on November 1, which marked the beginning of winter. They apparently believed that on October 31 the Lord of Death gathered the souls of the evil dead who had been condemned to enter into the bodies of animals. Thus they believed that on their New Years Eve (October 31) ghost, evil spirits and some say witches roamed about. On this night evil or frustrated ghost were also supposed to play tricks on humans.
Halloween is the most sacred day of witchcraft and other occults. It remains a special day for Satanists. It was and is believed by Satanists to be the only day of the year in which the devil's help could be invoked for a variety of things.
Human sacrifice was and is offered on this day.
It has and will continue to encourage occult activity on the part of children and adults. It is common for children to pull out an Ouija board and attempt to contact the ghost and spirits that are believed to be roaming about.
It helps support pagan philosophies and practices by encouraging people's interest in things like ghost.
Probably no Halloween activity or symbol can be found that does not go back to pagan occultism. For example: Jack-O-Lantern – This comes from a legend of a drunk man named Jack who tricked the devil into agreeing to never come after his soul. As Jack is leaving hell the devil throws a hot piece of coal at Jack. So Jack wanders the earth carrying the coal in a pumpkin. Halloween costumes – Halloween was a night where evil spirits roamed freely and played tricks on the living. So it was to the advantage of people to hide from them or scare them away by wearing costumes. Trick or Treat – This is related to the idea that ghost and witches created mischief on this night. For example, if the living did not provide food (or "treats") for the spirits than they would "trick" them. When a child goes door to door in the ritual of "trick or treat" he is re-enacting the ancient superstition.
Christians participating in Halloween may be a ploy of the devil to mock God. How does God feel when He looks down on Halloween night (in full awareness of the events that have happened on this night) and views Christian children dressed up as ghosts, devils, witches, and goblins? Or, even innocent characters but going out, as those in the world, on the very night that Satan is most honored. Satan, of course, knows the meanings of all of these symbols and so does God.
The Bible has many references condemning the practices of witchcraft, sorcery, spiritism, contacting the dead and so forth.
Is it possible to glorify God by imitating what occultists do on their special day, however innocently? Historically, this is the very day that evil powers have chosen above all others. Most people think that imitating these things on Halloween is innocent enough since they are not engaging in the original practices or intents.
But, what does the Bible say? Christian, is the Word of God going to be your only source for Truth? Are you going to base your life on it? Will it determine how you live?
This is a heavy one! I have always done Halloween-with the stipulation that our family will only dress up as funny/silly things or princesses,etc. I did think that in some way our kids were showing the world they could have fun w/o being scary,etc. We do have pumpkins but no other Halloween items. Lately, though, I noticed how many horrible decorations places like target are carrying. While we have avoided all that, I do see the point of understanding what Halloween really is. I'll be reading yr post with my husband tonight. Thanks for all the details-some of this I did not know.
Heather, I know it is heavy. I'm very careful to share my thoughts because I realize how offensive it can be at times. That is the last thing I ever want to do. But the truth is that we are living in the last days and there is a whole world of people who are dying in their sins. They need Christians to shine with the light of truth. If we look, act, dress, and talk like they do and if we participate in the same worldly things, we loose our influence.
By the way, my youngest loves to dress up. He has a suitcase full of play clothes that he plays with all year long. I have never felt like my children miss out and I don't think they do either. We completely ignore Halloween. We keep our porch light off and stay inside. We usually have a fun family evening. I'll make pizza or something everyone loves and we'll play a game or watch a movie as a family. I also decorate my house in beautiful fall colors, with leaves and pumpkins. It gets our hearts ready for Thanksgiving.
Thanks so much for your boldness and the truth on this subject. Too many people are afraid to go there. We don't celebrate this holiday and I am so excited to have in words now to explain to others why.
I don't find that hiding under a bushell helps my light to shine, either…I turn on our porch light and hand out the tracks and goodies…we've passed more gospel tracts out b/c the kids were asking..now if they read it~who knows. But they got it…that's my job as a believer.
I've been in christmas parades and loads of stuff including attending festivals just to hand someone the gospel…yup~count me as one who has done it and will as much as I can.
You are soo right, Kimberly. We are to share His light!


If you love heading to your local sports bar to watch the big game, read on! We've rounded up the best sports bars in DC for you. Whether you like to watch early morning Premier League or Monday Night Football, there's a sports bar in DC for you. Also, find out where you can cheer for your hometown or college teams!
This Dupont Circle favorite is always hosting NFL and college football watch parties (it's Tarheel territory). Happy Hour runs every weekday from 4-7 p.m., with drink specials and selected appetizers for just $6.50. Saturdays and Sundays, Buffalo Billiards offers specials on all forms of beer – cans, buckets, drafts, and pitchers! Of course, there are plenty of pool tables, along with skeeball, foosball, ping pong, and more.
Redskins fans flock to this Georgetown beer hall. Church Hall carries the SEC Network, Big Ten Network, ESPN, ABC, and CBS on eight 70″ screens. You can count on this bar to always have the biggest games on throughout the day. Check out its Monday through Friday Happy Hour from 4 – 7 p.m. with $5 rail cocktails and select pints and $6 select food items. Definitely try the Shandy slushie! Church Hall has an impressive lineup of 28 draft beers, plus draft cocktails like Cherry Blossom Gin & Tonic and the Hibiscus John Daly (made with vodka, hibiscus-infused black tea, and homemade lemonade). Save room for the Funnel cakes for dessert!
If you're a Boston sports lover, head to Dirty Water to watch all of your teams' games: Bruins, Patriots, Red Sox and Celtics! You'll also enjoy beer from Massachusetts' Cisco Brewers, and daily specials on draft beers during Happy Hour.
Three big screens TVs and 22 TVs make Lucky Bar, located just south of Dupont Circle, the perfect place to watch multiple games. It's also great for DC soccer fans, as it opens early on the weekends for breakfast so you can watch those Premier league games. Check out the schedule here. Lucky Bar runs a generous five-hour Happy Hour (from 3 – 8 p.m.!), on every weeknight, except Thursdays, with $3.50 pints, $5 local craft beers, and $4 rail drinks. Check out Lucky Bar on an upcoming Taco Tuesday, when you'll enjoy $1 tacos and $5 Tecates all night.
Chicago and Detroit natives can get a taste of home at Ivy and Coney near Logan Circle. You can count on watching teams from these two cities here, plus University of Michigan games. Enjoy the best of midwestern fare here, like Chicago and Detroit style hot dogs, Chicago Italian beefs, and beers including Strohs, Old Style, Goose Island 312 and Bell's Two Hearted. Stop by for Happy Hour every weekday from 4 – 7 p.m. or for Dollar Wings during NFL games. Note: Ivy and Coney only accepts cash.
Located near Capital One Arena, this two-level bar welcomes fans of the University of Oklahoma and UCLA. It is also the home base of the DC Chapter of the American Outlaws. Mackey's offers a fabulous variety of local brews and classic pub fare. Check out one of its chicken sandwiches served on the Savory Doughnut Bun!
Located in the U Street Corridor in what was once the historic Addison Scurlock Photography Studio, Nellies Sports Bar offers far more than just sports (Ping Pong Madness on Mondays, Karaoke on Tuesdays, etc). You can bring your sports league team on Thursday nights. Nellies offers a great lineup of very creative cocktails such as its Key-lime Pie cocktail.
Home base for fans of DC-based fans of the University of Colorado, Penn Social offers three bars, serving 30 draft beers! Stop by for daily happy hour from 4-7 p.m. for $2 off draft beer, $5 rail drinks and $6 glasses of wine. The menu features classic pub grub including sliders, nachos, pizza, wings, and soft pretzels. When there's a break in the action, check out Penn Social's super fun selection of games like shuffleboard, corn hole, foosball, and Rock 'Em Sock 'Em Robots, arcade games and much more.
Located in the Dupont Circle neighborhood, Public Bar is home to a whopping 48 TVs throughout its three levels (including a rooftop bar). You can catch just about any sporting event here – NFL, UFC, NBA, UEFA, NHL, boxing, golf, college football, and NASCAR. Happy hour at Public Bar runs Tuesday through Friday from 4 – 8 p.m. and all day on Thursday! Enjoy burgers, salads, sandwiches, and more while watching the big game.
Billing itself as a "high end sports bar serving All American classics with a gourmet twist," this sports bar near Metro Center welcomes both Washington Redskins and New England Patriots fans. Proper 21 offers Margarita Mondays, half-price bottles of rose on Tuesdays, all-day Happy Hour on Thursdays (11:30 a.m. – 6:30 p.m.), and live music every Friday night. Be sure to try the Thai Chili Mussels and Truffle Fries as your appetizers!
If you love the Caps and the Nats (and Wisconsin cheese curds!), you'll love The Big Stick, near Nats Park. Happy Hour runs from 3 – 7 p.m. every weekday (except Nats game days) with $4 drafts, rail drinks, and house wines. Check out the "Big Sticks" menu, with an impressive variety of sausages (Cajun, Polish, Italian, and more).
Love to bowl? Head to The Eleanor and show off your skills on its two-lane bowling alley. This Eckington bar and grille prides itself on "fresh, local, seasonal and handmade food, local beers, craft cocktails, and approachable wines." The menu offers sandwiches, salads, and entrees (with lots of good vegetarian options). The Eleanor offers beer (20 on tap!), wine, creative cocktails, and a variety of "slushies and swizzles!" The Eleanor is open for brunch.
Convenient to Nats Park, this Navy Yard bar boasts a variety of weekend and sports specials, including $4 Miller Lite Pints/$30 Towers and $5 Blue Moon Pints/$35 Towers. The Ugly Mug serves 24 beers on tap in all! You can also enjoy live music at the Ugly Mug. Monday night is Trivia Night or visit on a Tuesday to take advantage of the "Affordable Meal Act," with $7 meals and drink specials starting at 4 p.m.
Florida State and Chicago Bears fans, head to Capitol Hill's Union Pub for the next big game and enjoy $15 buckets of Bud or Bud Light (or $14 pitchers). Be sure to try the Chicago Style Hot Dog Special or sample from its "Drunk Food" menu, which includes cheese curds, fried pickles, mini corns dogs, and Old Bar Crab Dip. Tuesday Night is Trivia Night at Union Pub and it is open for brunch as well.
As you can see, DC is a great place for sports fans from all across the country. Did we miss your favorite place to watch the big game or cheer for your hometown team? Let us know so we can add it to our list of the best sports bars in DC!
For more local insight, make sure you're getting our monthly blog round-up!


text:
Did Jabhat al-Nusra leave Qaidat al-Jihad or it is Qaidat al-Jihad that is part of Nusra now?
Analysis of Abu Mohammed Joulani new front: From Nusra to Fath al-Sham
Key words: Nusra, Jabhat al-Nusra, Al-Qaida, Qaidat al-Jihad, Syria.
By Elijah J. Magnier : @EjmAlrai
Original article published alrai.li/fjxg39r via @AlraiMediaGroup
The leader and Emir of Jabhat al-Nusra (JaN) Abu Mohammed al-Joulani introduced a new front with a new name "Jabhat Fath al-Sham" (JFS) – as published by this author on the 26th of this month – and the abolishment of the old JaN title. But did Joulani and his Mujahedeen break with Qaidat al-Jihad (AQ) in Khorasan, or is it the AQ core leadership and Mujahedeen (in Syria since the war began), who have merged into this new group JFS?
Just before Joulani's video message showing his portrait for the first time, Al-Manara al-Bayda' official outlet released an audio of Ahmed Hassan Abul-Khair, first deputy Emir of AQ Central (Sheikh Ayman al-Zawahiri) speaking about JaN, saying that it had become "a force to be reckoned with, excellently managing the liberated territories (Idlib/Syria) with legitimate courts that rule with the Law of Allah, and organising service institutions that guard and take care of what matters to people – a new generation brought up on the jurisprudence of honour, and on the Jihad as the means for protecting the region. The stage which the Ummah (Islamic nation) has now reached in terms of the spread of the Jihad and its penetration into the Muslim community (shifting from the understanding of an elitist jihad to the Jihad of a nation) should not be driven by group mentality or by a single organisation".
Within the same audio of Abul-Kheir, from Ayman al-Zawahiri, a short message will be found: "The organisational links are transient-metamorphic (…) Your union and your association and the unity of your groups rises above any organisational affiliation (…)." Zawaheri was clearly blessing JaN's widely coordinated and thoughtful move towards the other groups operating in the Levant.
It is clear that neither JaN nor its Emir Abu Mohammed al Joulani have regressed by a single step on their Jihadist operational line, their ideology and their creed. These include the objectives and concept of the Islamic nation as understood by the Mujahedeen. Not only that, but JFS have raised, above AQ level, an organisation capable of providing moral and knowledge support, with its Emir acting as a father, but without the necessity to offer financial support or weapons.
Khorasan, the base of Qaidat al-Jihad, looks from afar toward its sons in Yemen, Somalia, Syria and other countries that host the same ideology but also have enough men fighting for their objectives. JaN's move is not new to Qaidat al-Jihad. What used to be known as Al-Qaida in the Arabian Peninsula (AQAP) had also changed name. Today it is known as "Ansar al-Sharia", "Sons of Hadramout" or "sons of Abyan". Therefore, the question arises, what is the need and the motivation for making so much fuss around a name changed from JaN to JFS: especially when the objectives and the ideology are both stable and robust?
Abu Mohammed al-Joulani was being honest when he said "Jabhat Fath al-Sham has no affiliation to any external entity". The new JFS has all the right elements to receive and host the Mujahideen – Mujahideen from all over the world – because it is already, as Ahmed Hassan Abul-Khair said, established in "a liberated territory", running an Islamic administration and courts, raising the banner of "there is only one God" and is promoting jihad "for God's sake".
Therefore, it cannot be overstated that the exit of JaN from under the mantle of AQ is not a change of creed but a step already requested, in fact, and promoted by the head of AQ Legal Council, the late Sheikh Atiyah Allah al-Libi. He said: "The declaration of the Mujahideen that they are al-Qaeda and that they have link to al Qaeda, even this link existed, should not be expressed now, since it lacks any operational interest. The only people to gain are the Americans, who wish it because it serves their political ends. Because in word public opinion the name of AQ is now distorted, it is appropriate to keep away from it and not manifest any link to it (AQ). Perhaps, through this new stage, God is expressing his will otherwise".
Joulani did not come out with his announcement (breaking ties with AQ, or stating that Jabhat Fath al-Sham has no affiliation to any external entity) to please the United States of America and Russia. His brief message with Abu Faraj al Masri on his right (real name Ahmad Salama Mabruk, who accompanied al-Zawahiri for many years until he reached the Levant and became a member of JaN Shura Council) is no coincidence. Joulani is relatively carefree about the attitude of stand of Russia and the US. His message in the first place is to the Mujahedeen of Nusra to say that the creed hasn't changed, is sound and is well guarded. This is seen as a purely internal move directed towards the Syrian groups. Joulani is responding to insistent demands by all the local Syrian organisations expressing a readiness for unity, provided that Nusra disengage with the base of Qaidat al-Jihad ("the motherland").
Al-Zawahri and his deputy therefore agreed on any step that would lead to the connection of all groups in al-Sham, moving away from any narrow organisational link. All they want from Nusra is to expand towards a much larger global jihad to including al-Sham (the Levant). This must spread and consolidate the ideology and doctrine on the ground, to unite jihadi and non jihadi groups, and integrating the rest of the Syrian and other Muhajereen (foreign fighters). That way they all become one strong front prepared for when President Barack Obama leaves.
However, there is a difference between aiming at consolidation and managing to achieve real unification. There are secular groups and others related to and directly financed by the various countries of the region, including some supported by the US. A unification of all these groups seems far from reality. Joulani and the leadership around him are aware of the Syrian theatre and the multi-diversity of its conditions for belonging. Joualni, by announcing a new front, disarms all excuses previously presented as obstacles to the unification. This was a necessity, because if these were to remain active but hidden, faced with this very public move, it cannot be ruled out that JFS might in the future adopt a more aggressive and confrontational attitude against anyone who stands in the way of the jihad.
Joulani has appeared publicly with a warm smile stretching out his hand not to America or Russia to avoid being hit, but to the Sham theatre. Will the base respond to him? Achieving unity among different factions is a daunting, near impossible task weighing not only on Joulani, but also on al-Zawahiri himself. Even Osama bin Laden was struggling with the group Joulani was belonging to previously (Islamic State in Iraq) up to the day of the divorce: then followed the rivalry and animosity between Zawaheri and the Caliph of the "Islamic State" group, Abu Bakr al Baghdadi.
So far, Ahrar al-Sham (another Salafi jihadi group considered the largest in numbers in the north of Syria), Tajam'mo Ahl al-Elm Fil-sham , Ansar al-Din, Hizb al-Islami al-Turkistani, Fajr al-Sham and Ajnad al-Sham have welcomed Nusra's step. The communiqué of Jund al-Aqsa, a salafi jihadist close to both al-Qaida and the "Islamic State" group (ISIS), is quite revealing, unwittingly stating that nothing has changed but the name. More groups may follow, but the overall enthusiasm to embrace a unity of all groups under one command is still shy. If Ahrar accepts to merge into one group with Nusra in its new group JFS, this step will create confusion, forcing the US and Russia to rethink their attitude toward rebel groups. If not the change of name will have been tactical, merely mythical.
There is no doubt that the Mujahideen of al-Qaeda had been absorbed in the Levant within JaN, and now today, within the new organisation JFS. Every step Joulani made was accurate, calibrated and indicates the presence of an entire team with broad experience in the jihad arena. These moves measure the consequences of every decision taken, seeking to minimise collateral and internal damage. Despite being core AQ, these moves have showed pragmatism in dealing with the various groups involved, and this includes secular ones and others connected, trained and paid for by the CIA.
There is therefore now little doubt that Qaidat al-Jihad has became part of Nusra, title "Jabhat Fatah al-Sham".
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Akira K says:
Reblogged this on The Fourth Revolutionary War.
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text:
\section{Introduction}\label{sec_Intro}

Let $K$ be a full-dimensional convex subset of $\mathbb{R}^n$
containing a ball of finite radius centered at $c_0$ and contained
in a ball of finite radius $R$. The \emph{separation problem} for
$K$ is that of finding a hyperplane that separates a given point
$p$ from $K$, or concluding that $p\in K$. The separation problem
is quite general in that it has been shown to be polynomial-time
equivalent to other natural convex programming problems
\cite{GLS88}.  One of these problems is the \emph{optimization
problem}, which is the problem of maximizing a linear functional
$c^Tx$ over all $x\in K$ for a given $c\in\mathbb{R}^n$.

It may arise in some applications that solving the optimization
problem for $K$ is more practically feasible than solving the
separation problem directly, for example, if the extreme points of
$K$ are parameterized by a number of parameters that is
significantly smaller than $n$.\footnote{Clearly this condition by
no means guarantees that the optimization problem is easier.
However, even if this is not the case, the optimization problem
may still be more ``feasible'' than the separation problem if only
because the former is better studied and thus software for it more
readily available.} In such a case, it might make sense to solve
an instance of the separation problem by solving polynomially many
instances of the optimization problem, using a Turing reduction
\cite{GJ79} from separation to optimization. Despite this
practical philosophy, which the authors have adopted with some
success to the (NP-hard \cite{Gur03}) quantum separability
problem\footnote{The quantum separability problem is related to
the problem of entanglement detection.  Entanglement is a
fundamental physical resource which plays a central role in
quantum computing and quantum cryptography \cite{NC00}.}
\cite{ITCE04,qphIoa05}, the main purpose of research into
polynomial-time reductions among convex body problems is
theoretical -- to uncover the intrinsic beauty of the subject of
convex programming algorithms, which historically marries physical
intuition and mathematical rigor in a unique way. Our
heuristics-based reduction is a fine example of this marriage.

\section{Convex Body Problems and Cutting-plane Feasibility Algorithms}\label{sec_DefinitionsAndBackground}

Let $S(K,\delta)$ denote the union of all balls of radius $\delta$
with centers belonging to $K$, and let $S(K,-\delta)$ denote the
union of all centers of all balls of radius $\delta$ contained in
$K$, where the balls are defined with respect to the Euclidean
norm. We now give the formal definitions of the basic convex body
problems that will concern us, taken from
\cite{GLS88}.\footnote{As a reminder, because computers use finite
representation of numbers, the problems are suitably weakened with
small accuracy parameters. As well, the rational field
$\mathbb{Q}$ is used instead of the real field $\mathbb{R}$, and
the $l_\infty$-norm (maximum norm) appears instead of the
$l_2$-norm (Euclidean norm); however, these technicalities will
not be carried through the paper.}

\begin{definition}[Weak Optimization Problem for $K$ (WOPT($K$))]\label{def_WOPT}
Given a rational vector $c\in\mathbb{R}^n$ and rational
$\epsilon>0$, either
\begin{itemize}
\item find a rational vector $y\in\mathbb{R}^n$ such that $y\in
S(K,\epsilon)$ and  $c^Tx\leq c^Ty +\epsilon$ for every $x\in K$;
or

\item assert that $S(K,-\epsilon)$ is
empty.\label{eqn_WSEPEntAssertion}
\end{itemize}
\end{definition}

\begin{definition}[Weak Separation Problem for $K$ ($\textrm{WSEP($K$)}$)]\label{def_WSEP}
Given a rational vector $p\in\mathbb{R}^n$ and rational
$\delta>0$, either
\begin{itemize}
\item assert $p\in S(K,\delta)$,
\hspace{2mm}\textrm{or}\label{eqn_WSEPSepAssertion}

\item find a rational vector $c\in\mathbb{R}^n$ with
$||c||_\infty= 1$ such that $c^Tx < c^Tp$ for every $x\in
K$.\label{eqn_WSEPEntAssertion}
\end{itemize}
\end{definition}

\noindent Let $K'$ be a full-dimensional bounded convex subset of
$\mathbb{R}^n$.

\begin{definition}[Weak Violation Problem for $K'$ (WVIOL($K'$))]\label{def_WVIOL}
Given a rational vector $c\in\mathbb{R}^n$ and rationals $\gamma$
and $\epsilon'>0$, either
\begin{itemize}
\item assert that $c^Tx\leq\gamma+\epsilon'$ for all $x\in
S(K',-\epsilon')$, or

\item find a vector $y\in S(K',\epsilon')$ with
$c^Ty\geq\gamma-\epsilon'$.
\end{itemize}
\end{definition}

\noindent If $\gamma=-1$ and $c$ is the origin
$\bar{0}\in\mathbb{R}^n$, then WVIOL($K'$) reduces to the
\emph{weak feasibility problem for} $K'$, denoted WFEAS($K'$).  By
taking $\delta$, $\epsilon$, and $\epsilon'$ to be zero, we
implicitly define the corresponding \emph{strong} problems,
denoted SSEP, SOPT, SVIOL, and SFEAS.  Note that SFEAS($K'$) is
the problem of deciding whether $K'$ is empty or finding a point
in $K'$.

Central to our reduction are cutting-plane algorithms for
WFEAS($K'$), relative to a WSEP($K'$) oracle $\mathcal{O}_{\text{\begin{tiny}\textsc{SSEP}($K'$)\end{tiny}}}$.  All
such algorithms have the same basic structure:

\begin{enumerate}
\item Define a (possibly very large) regular bounded convex set
$P_0$ which is guaranteed to contain $K'$, such that, for some
reasonable definition of ``center'', the center $\omega_0$ of
$P_0$ is easily computed.  The set $P_0$ is called an \emph{outer
approximation} to $K'$.  Common choices for $P_0$ are the
origin-centered hyperbox, $\{x\in\mathbb{R}^n: -2^L \leq x_i \leq
2^L, \hspace{2mm}1\leq i\leq n \}$ and the origin-centered
hyperball, $\{x: x^Tx \leq 2^L\}$ (where $2^L$ is a trivially
large bound).

\item Give the center $\omega$ of the current outer approximation
$P$ to $\mathcal{O}_{\text{\begin{tiny}\textsc{SSEP}($K'$)\end{tiny}}}$.

\item If $\mathcal{O}_{\text{\begin{tiny}\textsc{SSEP}($K'$)\end{tiny}}}$ asserts ``$\omega\in K'$'', then HALT.

\item Otherwise, say $\mathcal{O}_{\text{\begin{tiny}\textsc{SSEP}($K'$)\end{tiny}}}$ returns the hyperplane
$\pi_{c,b}$ such that $K'\subset \{x: c^Tx \leq b\}$.  Update
(shrink) the outer approximation $P:=P\cap \{x: c^Tx \leq b'\}$
for some $b'\geq b$. Possibly perform other computations to
further update $P$. Check stopping conditions; if they are met,
then HALT. Otherwise, go to step (ii).
\end{enumerate}
\noindent  The difficulty with such algorithms is knowing when to
halt in step (iv).  Generally, the stopping conditions are related
to the size of the current outer approximation.  Because it is
always an approximate (weak) feasibility problem that is solved,
the associated accuracy parameter $\epsilon'$ can be exploited to
get a ``lower bound'' $V$ on the ``size'' of $K'$, with the
understanding that if $K'$ is smaller than this bound, then the
algorithm can correctly assert that $S(K',-\epsilon')$ is empty.
Thus the algorithm stops in step (iv) when the current outer
approximation is smaller than $V$.

The cutting-plane algorithm is called \emph{(oracle-)
polynomial-time} if it runs in time
$O(\textrm{poly}(n,\log(R'/\epsilon')))$ with unit cost for the oracle,
where $R'$ is the outer radius of $K'$. It is called
\emph{(oracle-) fully polynomial} if it runs in time
$O(\textrm{poly}(n,R'/\epsilon'))$.

There are a number of such polynomial-time convex feasibility
algorithms (see \cite{AV95} for a discussion of all of them).  The
three most important are the \emph{ellipsoid method}, the
\emph{volumetric center method}, and the \emph{analytic center
method}.  The ellipsoid method has $P_0=\{x:x^Tx\leq 2^L\}$ and is
the only one which requires ``further update'' of the outer
approximation $P$ in step (iv) after a cut has been made -- a new
minimal-volume ellipse is drawn around $P:=P\cap \{x: c^Tx \leq
b'\}$.  The ellipsoid method, unfortunately, suffers badly from
gigantic precision requirements, making it practically unusable.
The volumetric center and analytic center algorithms are more
efficient than the ellipsoid algorithm and are very similar to
each other in complexity and precision requirements, with the
analytic center algorithm having some supposed practical
advantages.\footnote{To date, no one has implemented a
polynomial-time cutting plane algorithm. For an implementation of
a fully polynomial algorithm, see
http://ecolu-info.unige.ch/logilab.}

The cutting plane $\{x: c^Tx = b'\}$ requires further definition:
\begin{equation}
\textrm{If } \left\{ \begin{array}{rcl}  b'&<& c^T\omega\\
b'&=& c^T\omega
\\  b'&>& c^T\omega\end{array}\right\} \textrm{ then the above is a } \left\{ \begin{array}{c} \textrm{\emph{deep-cut}} \\
\textrm{\emph{central-cut}}
\\ \textrm{\emph{shallow-cut}} \end{array}\right\}\textrm{ algorithm.}
\end{equation}
\noindent Intuitively, deep-cut algorithms should be fastest.
Ironically, though, except for the case of ellipsoidal algorithms
(which are practically inefficient), the algorithms that are
provably polynomial-time are central- or even shallow-cut
algorithms.

\section{Reduction via Heuristics}\label{sec_SearchHeuristic}

Assume without loss that $c_0=\bar{0}$. Our goal is to develop a
new oracle-polynomial-time algorithm for WSEP($K$) with respect to
an oracle for WOPT($K$) (running in time
$O(\textrm{poly}(n,\log(R/\delta)))$).  We do this via a geometric
approach, which differs from the standard approach covered in the
next section.  In this section, we ignore the weakness of the
separation and optimization problems, as it obfuscates the main
ideas; that is, we assume we are solving SSEP($K$) with an oracle
for SOPT($K$).

Suppose we have an oracle $\mathcal{O}_{\text{\begin{tiny}\textsc{SOPT}($K$)\end{tiny}}}$ for the optimization problem
over $K$ such that, given a nonzero input vector $c$, $\mathcal{O}_{\text{\begin{tiny}\textsc{SOPT}($K$)\end{tiny}}}$
outputs a point  $\mathcal{O}_{\text{\begin{tiny}\textsc{SOPT}($K$)\end{tiny}}}(c)\\ \equiv k_c\in K$ that maximizes
$c^Tx$ for all $x\in K$. An important step in developing the
algorithm is noting that, given $\mathcal{O}_{\text{\begin{tiny}\textsc{SOPT}($K$)\end{tiny}}}$, the search for a
separating hyperplane reduces to the search for a region on the
$(n-1)$-dimensional surface of the unit hypersphere $S_n$
(embedded in $\mathbb{R}^n$) centered at the origin. For $p\notin
K$, this region $M_p$ is simply $\{c\in S_n:\hspace{2mm} c^T
k_c<c^T p\}$ (see Figure \ref{K_p}).

\begin{figure}[ht]
\centering \resizebox{150mm}{!}{\includegraphics{K_p.eps}}
\caption[The sets $M_p$ and $K_p$ in $\mathbb{R}^2$]{The sets
$M_p$ and $K_p$ in $\mathbb{R}^2$.  Pictured in heavy outline is a
set $K$ in $\mathbb{R}^2$, where $K:=\mathrm{conv}\{(0,1), (-1,1), (-1,0),
(1,-2)\}$.  A point $p=(-7/8,-3/4)$ is shown as a heavy dot.  The
unit circle is drawn in a dashed line.  The set $M_p$ is the arc
of the unit circle that the shaded pie-slice subtends; the set
$K_p$ is the shaded pie-slice.  In two dimensions, the set $M_p$
($K_p$) is easy to construct.  This construction has been
illustrated: draw the two distinct lines through $p$ that are
tangent to $K$; the lines that determine the pie-slice are the two
straight lines that are perpendicular to the lines through $p$.}
\label{K_p}
\end{figure}

The first observation is that, since $K$ properly contains the
origin, $M_p$ is contained in the hemisphere defined by $\{x: p^T
x\geq 0\}$:
\begin{fact}\label{Fact_InitialCut} For all $m\in M_p$, $m^Tp>0$.
\end{fact}
\begin{proof}
Let $m\in M_p$.  Then $m^Tp>m^Tk$ for all $k\in K$.  But the fact
that the 0-vector is properly contained in $K$ implies that there
exists $k\in K$ such that $m^Tk>0$.\end{proof}

The second observation, Lemma \ref{lem_Donny}, is based on the
following heuristic, which can be pictured in $\mathbb{R}^2$ and
$\mathbb{R}^3$. Suppose $c$, $||c||=1$, is not in $M_p$ (but is
reasonably close to $M_p$) and that the oracle returns $k_c$. What
is a natural way to modify the vector $c$, so that it gets closer
to $M_p$? Intuition dictates moving $c$ \emph{away from} $k_c$ and
\emph{towards} $p$, that is, add a small component of the vector
$(p-k_c)$ to $c$, in order to generate a new guess
$c'=c+\lambda(p-k_c)/||p-k_c||$, for some $\lambda>0$, which we
could then give to the oracle again (see Figure \ref{DonnyLemma}).
Incidentally, we have found that the following little program,
which embodies this heuristic, actually performs well:\footnote{We
tested the program in $\mathbb{R}^{15}$, where $K$ is the convex
hull of $\{\alpha\alpha^*\otimes\beta\beta^*:
\alpha,\beta\in\mathbb{C}^2, ||\alpha||_2=||\beta||_2=1\}$ (which
is viewed as full-dimensional in $\mathbb{R}^{15}$), where $*$
denotes complex-conjugate transpose, and $\otimes$ denotes
Kronecker product.  This corresponds to the quantum separability
problem for two qubits \cite{qphIoa05}.}

\vspace{2mm} \fbox{\begin{minipage}{11cm}
\begin{description} \item
$c:=p/||p||;\hspace{2mm}d:=1;\hspace{2mm}i:=0;$ \item
\textsc{while}\hspace{2mm}$(d>0$\hspace{2mm}\textsc{and}\hspace{2mm}$i<N)$\hspace{2mm}\textsc{do}\hspace{2mm}$\lbrace$
\item\hspace{5mm}$k_c:=\mathcal{O}_{\text{\begin{tiny}\textsc{SOPT}($K$)\end{tiny}}}(c);$
\item\hspace{5mm}$d:=c^Tk_c-c^Tp;$
\item\hspace{5mm}\textsc{if}$\hspace{2mm}(d<0)$\hspace{2mm}\textsc{then}\hspace{2mm}$\lbrace$
\textsc{return} $c$ $\rbrace$
\item\hspace{10mm}\textrm{\textsc{else}\hspace{2mm}$\lbrace$ $c:=
c+d(p-k_c)/||p-k_c||$};\hspace{2mm}$c:=c/||c||$;\hspace{2mm}$i:=i+1\rbrace\rbrace;$
\item\textrm{\textsc{return} ``INCONCLUSIVE''}
\end{description}
\end{minipage}}
\vspace{2mm}

\noindent This program can be regarded as an extremely simple
heuristic for the separation problem when given an optimization
subroutine (of course, it may give inconclusive results; in
practice, one should set $N$ as large as is practically feasible).

Interestingly, the above heuristic can be formalized as follows.
If $c$ is not in $M_p$ but is sufficiently close to $M_p$, then
$c$, $p$, and $k_c$ can be used to define a hemisphere which
contains $M_p$ and whose great circle cuts through $c$. More
precisely:
\begin{lemma}\label{lem_Donny} Suppose $m\in M_p$,
$c\notin M_p$, and let $\bar{a}:=(p-k_c)-\mathrm{Proj}_c(p-k_c)$.
If $m^Tc\geq 0$ then $m^T\bar{a}> 0$.
\end{lemma}
\begin{proof}
Note that $m^T\bar{a} = m^T(p-k_c)-[c^T(p-k_c)](m^Tc)$.  The
hypotheses of the lemma immediately imply that $m^T(p-k_c)>0$ and
$c^T(p-k_c)\leq 0$.  Thus, if $m^Tc\geq 0$, then $m^T\bar{a}> 0$.
\end{proof}
\noindent The lemma gives a method for reducing the search space
after each query to $\mathcal{O}_{\text{\begin{tiny}\textsc{SOPT}($K$)\end{tiny}}}$ by giving a cutting plane
$\{x:\bar{a}^Tx=0\}$ that slices off a portion of the search
space.
\begin{figure}[ht]
\centering \resizebox{150mm}{!}{\includegraphics{DonnyLemma.eps}}
\caption[Illustration of heuristic behind Lemma
\ref{lem_Donny}]{Illustration of heuristic behind Lemma
\ref{lem_Donny}. Continuing from Figure \ref{K_p}, the unit vector
$c$ is a test vector that is close to $M_p$ but not in $M_p$.
Evidently, adding a component of $(p-k_c)$ to $c$ moves it closer
to $M_p$.  This intuition also holds in $\mathbb{R}^3$.}
\label{DonnyLemma}
\end{figure}
Our search problem can easily be reduced to an instance of
SFEAS($K'$), where
$K'$ is
\begin{eqnarray}\label{def_K_p}
K_p:=\left[\mathrm{ConvexHull}\left( M_p\cup \{\bar{0}\}\right)
\right] \setminus \{\bar{0}\}.
\end{eqnarray}
The set $K_p$, if not empty, can be viewed as a cone-like object,
emanating from the origin and cut off by the unit hypersphere (see
Figure \ref{K_p}).
The oracle $\mathcal{O}_{\text{\begin{tiny}\textsc{SOPT}($K$)\end{tiny}}}$, along with Lemma \ref{lem_Donny},
essentially gives a separation oracle for $K_p$, as long as the
test vectors $c$ given to $\mathcal{O}_{\text{\begin{tiny}\textsc{SOPT}($K$)\end{tiny}}}$ satisfy
\begin{eqnarray}\label{HypothesisOfDonnyLemma}
\text{$m^T c\geq 0$ for all $m\in M_p$}.
\end{eqnarray}

How could we ensure that all our test vectors $c$ satisfy
(\ref{HypothesisOfDonnyLemma})?  Recall Fact
\ref{Fact_InitialCut}, which says that the set $K_p$ is contained
in the halfspace $\lbrace x:p^T x\geq 0\rbrace$. Let $B_n$ be the
origin-centered unit hyperball in $\mathbb{R}^n$ and let
$a_1:=p/||p||$. Thus, straight away, the search space is reduced
to the hemisphere $B_n\cap\lbrace x:a_1^T x\geq 0\rbrace$. The
first test vector to give to the oracle $\mathcal{O}_{\text{\begin{tiny}\textsc{SOPT}($K$)\end{tiny}}}$ is $p/||p||$,
which clearly has nonnegative dot-product with all points in $K_p$
and hence all $m\in M_p$.  By way of induction, assume that, at
some later stage in the algorithm, the current search space has
been reduced to $P:=B_n\bigcap \cap_{i=1}^{h}\lbrace x:a_i^T x\geq
b_i \rbrace$ by the generation of cutting planes $\lbrace x: a_i^T
x=b_i \rbrace$, where the $a_i$, for $i=2,3,\ldots, h$, are the
normalized $\bar{a}$ from $h-1$ invocations of Lemma
\ref{lem_Donny}.  Let $\omega$ be the ``center'' of $P$, and
\emph{suppose} that this ``center'' is a positive linear (conic)
combination of the normal vectors $a_i$, that is,
\begin{eqnarray}\label{eqn_CenterIsConicCombinationOfNormals}
\omega = \sum_{i=1}^h \lambda_i a_i,\hspace{2mm}\textrm{where
$\lambda_i\geq 0$ for all $i=1,2,\ldots, h$.}
\end{eqnarray}
Then, by inductive hypothesis, this implies that $m^T \omega\geq
0$ for all $m\in M_p$. Thus, $c:=\omega/||\omega||$ is a suitable
vector to give to the oracle $\mathcal{O}_{\text{\begin{tiny}\textsc{SOPT}($K$)\end{tiny}}}$ and use in Lemma
\ref{lem_Donny}. Therefore, it suffices to find a definition of
``center $\omega$ of $P$'' that satisfies
(\ref{eqn_CenterIsConicCombinationOfNormals}), in order that all
our test vectors $c$ satisfy (\ref{HypothesisOfDonnyLemma}).
 Because we require (\ref{HypothesisOfDonnyLemma}), none of the
feasibility algorithms mentioned in Section
\ref{sec_DefinitionsAndBackground} can be applied directly.
However, the analytic-center algorithm due to Atkinson and Vaidya
\cite{AV95} beautifully lends itself to
a modification that allows (\ref{HypothesisOfDonnyLemma}) to be satisfied.

Reducing the separation problem for $K$ to the convex feasibility
problem for some $K'$, while using the optimization oracle for $K$
as a separation oracle for $K'$, is not a new concept in convex
analysis.  But the precise way that Lemma \ref{lem_Donny}
generates each new cutting plane, incorporating the
correction-heuristic, does not appear in the literature.  This is
likely because there is a more general way to carry out such a
reduction, covered in the next section, which does not require
(\ref{eqn_CenterIsConicCombinationOfNormals}).\footnote{The more
general reduction was established by the early 1980s. Our
reduction seems to require the result in \cite{AV95}, which was
not known prior to 1992.}

\section{Comparison to Standard Reduction}\label{sec_ConnToOtherKnownMethods}

Note that our reduction requires knowledge of $c_0$ and $R$. A
polynomial-time Turing reduction from WSEP($K$) to WOPT($K$) is
well known -- even when $c_0$ and $R$ are unknown. One such
(ellipsoidal) reduction is given in Theorem 4.4.7 in \cite{GLS88};
however, it may be more general than is necessary. If $R$ is
known, then the standard way to perform the reduction of the
previous section may be found in the synthesis of Lemma 4.4.2 and
Theorem 4.2.2 in \cite{GLS88}; we outline it in the following
paragraph.

\begin{definition}[Polar of $K$] The \emph{polar} $K^\star$ of a full-dimensional convex set
$K\subset \mathbb{R}^n$ that contains the origin is defined as
\begin{eqnarray}
K^\star := \{c\in\mathbb{R}^n: c^Tx\leq 1 \hspace{2mm}\forall x
\in K\}.
\end{eqnarray}
\end{definition}

If $c\in K^\star$, then the plane $\pi_{c,1}\equiv\{x: c^Tx=1\}$
separates $p\in\mathbb{R}^n$ from $K$ when $c^Tp >1$. Thus, the
separation problem for $p$ is equivalent to the feasibility
problem for $Q_p$, defined as\footnote{Note that $Q_p$ is
guaranteed not to be empty when $p\notin K$.  For, then, there
certainly exists some plane $\pi_{c',b'}$ separating $p$ from $K$.
But since $K$ contains the origin, $b'$ may be taken to be
positive. Thus $\pi_{c'/b', 1}$ separates $p$ from $K$.}
\begin{eqnarray}
Q_p := K^\star \cap \{c: p^Tc \geq 1\}.
\end{eqnarray}
As mentioned in the previous section (and elaborated on in the
next section), to solve the feasibility problem for any $K'$, it
suffices to have a separation routine for $K'$.  Because we can
easily build a separation routine $\mathcal{O}_{\text{\begin{tiny}\textsc{SSEP}($Q_p$)\end{tiny}}}$ for $Q_p$ out of
$\mathcal{O}_{\text{\begin{tiny}\textsc{SSEP}($K^\star$)\end{tiny}}}$, it suffices to have a separation routine
$\mathcal{O}_{\text{\begin{tiny}\textsc{SSEP}($K^\star$)\end{tiny}}}$ for $K^\star$ in order to solve the feasibility
problem for $Q_p$.\footnote{We slightly abuse the oracular
``$\mathcal{O}$'' notation by using it for both truly oracular
(black-boxed) routines and for other (possibly not completely
black-boxed) routines.}  Building $\mathcal{O}_{\text{\begin{tiny}\textsc{SSEP}($Q_p$)\end{tiny}}}$ out of
$\mathcal{O}_{\text{\begin{tiny}\textsc{SSEP}($K^\star$)\end{tiny}}}$ is done as follows:\\

\indent\indent\indent\indent\indent\indent\indent Routine $\mathcal{O}_{\text{\begin{tiny}\textsc{SSEP}($Q_p$)\end{tiny}}}(y)$:\\
\indent\indent\indent\indent\indent\indent\indent \textsc{case:} $p^Ty < 1$\\
\indent\indent\indent\indent\indent\indent\indent\indent \textsc{return} $-p$\\
\indent\indent\indent\indent\indent\indent\indent \textsc{else:} $p^Ty \geq 1$\\
\indent\indent\indent\indent\indent\indent\indent\indent \textsc{call} $\mathcal{O}_{\text{\begin{tiny}\textsc{SSEP}($K^\star$)\end{tiny}}}(y)$\\
\indent\indent\indent\indent\indent\indent\indent\indent \textsc{case:} $\mathcal{O}_{\text{\begin{tiny}\textsc{SSEP}($K^\star$)\end{tiny}}}(y)$ returns separating vector $q$\\
\indent\indent\indent\indent\indent\indent\indent\indent\indent \textsc{return} $q$\\
\indent\indent\indent\indent\indent\indent\indent\indent \textsc{else:} $\mathcal{O}_{\text{\begin{tiny}\textsc{SSEP}($K^\star$)\end{tiny}}}(y)$ asserts $y\in K^\star$\\
\indent\indent\indent\indent\indent\indent\indent\indent\indent \textsc{return} ``$y\in Q$''\\

\noindent It remains to show that the optimization routine
$\mathcal{O}_{\text{\begin{tiny}\textsc{SOPT}($K$)\end{tiny}}}$ for $K$ gives a separation routine $\mathcal{O}_{\text{\begin{tiny}\textsc{SSEP}($K^\star$)\end{tiny}}}$ for
$K^\star$. Suppose $y$ is given to $\mathcal{O}_{\text{\begin{tiny}\textsc{SOPT}($K$)\end{tiny}}}$, which returns $k\in
K$ such that $y^Tx \leq y^Tk =:b$ for all $x\in K$. If $b\leq 1$,
then $\mathcal{O}_{\text{\begin{tiny}\textsc{SSEP}($K^\star$)\end{tiny}}}$ may assert $y\in K^\star$. Otherwise,
$\mathcal{O}_{\text{\begin{tiny}\textsc{SSEP}($K^\star$)\end{tiny}}}$ may return $k$, because $\pi_{k,1}$ (and hence
$\pi_{k,b}$) separates $y$ from $K^\star$: since $k^Ty=b > 1$, it
suffices to note that $k^Tc=c^Tk\leq 1$ for all $c\in K^\star$ by
the definition of $K^\star$ and the fact that $k\in K$.

\begin{figure}[ht]
\centering \resizebox{150mm}{!}{\includegraphics{Connection.eps}}
\caption[Relationship between convex separation methods]{The upper
picture is a set $K$ in $\mathbb{R}^2$, where  $K:=\mathrm{conv}\{(0,1),
(-1,1), (-1,0), (1,-2)\}$.  A point $p=(-7/8,-3/4)$ is shown.  The
polar $K^\star$ of $K$ is shown in heavy outline in the lower
picture; $K^\star = \mathrm{conv} \{(0,1),(-1,0),(-1,-1),(3,1)\}$.  The
set $Q_p$ is the shaded polytope, bounded by the long-dashed plane
$\{c: p^Tc =1\}$. The set $K_p$ is the shaded pie-slice and is the
radial projection of $Q_p$ onto $B_n$ (whose boundary is shown as
a short-dashed circle).  The particular $K$ and $K^\star$ are
taken from \cite{NW88}.} \label{Connection}
\end{figure}

Figure \ref{Connection} shows the relationship between the method
of Section \ref{sec_SearchHeuristic} and the above method, by
illustrating that the set $K_p$ (defined in (\ref{def_K_p})) is
just the radial projection of $Q_p$ onto $B_n$.  Using ``$A
\longrightarrow B$'' to mean ``$B$ Turing-reduces to $A$'', the
standard reduction chain is
\begin{eqnarray}
\textrm{WOPT}(K) \longrightarrow \textrm{WSEP}(K^\star)
\overset{R}{\longrightarrow} \textrm{WSEP}(Q_p) \longrightarrow
\textrm{WFEAS}(Q_p),
\end{eqnarray}
where we indicate that the middle reduction requires knowledge of
outer radius $R$.  Our reduction, which is substantially less
general, may be written
\begin{eqnarray}\label{OurTuringReductionChain}
\textrm{WOPT}(K) \longrightarrow
\textrm{WSEP}(K_p)\Bigl.\Bigr|_{(\ref{HypothesisOfDonnyLemma})}
\overset{R,
c_0}{\underset{(\ref{eqn_CenterIsConicCombinationOfNormals})}{\longrightarrow}}
\textrm{WFEAS}(K_p),
\end{eqnarray}
where the weak separation problem has been restricted (queries
must satisfy the condition (\ref{HypothesisOfDonnyLemma}) of Lemma
\ref{lem_Donny}) and we note that the rightmost link requires, in
addition to knowledge of $R$ and $c_0$, a WFEAS algorithm whose
centers satisfy (\ref{eqn_CenterIsConicCombinationOfNormals}) (see
Section \ref{sec_AnalyticCenters}).

The two reductions have similar structure; the novelty of our
reduction lies in the \emph{way} the cutting planes are generated,
which is based on the heuristic:  if the center $\omega$ satisfies
(\ref{eqn_CenterIsConicCombinationOfNormals}), then cutting near
$\omega$ pushes the new center in the direction of the normal of
the new cutting plane; but this direction is essentially $(p-k_c)$
(except with the projection onto $c$ removed).  Note that the
normal of every new cutting plane depends on the given point $p$,
whereas in the standard reduction it does not.  These attributes
tempt us to conjecture that our reduction performs ``better'' in
practice when $p\notin K$ (though not in any significant
asymptotic sense).

Note that, even though $\mathcal{O}_{\text{\begin{tiny}\textsc{SSEP}($K^\star$)\end{tiny}}}$, built on $\mathcal{O}_{\text{\begin{tiny}\textsc{SOPT}($K$)\end{tiny}}}$, gives
deep cuts $\pi_{k,1}$, it is not known how to utilize the deep
cuts to get a polynomial-time algorithm using analytic or
volumetric centers. Our cut-generation method in Section
\ref{sec_SearchHeuristic} is capable only of giving central cuts;
but this does not, \emph{a priori}, put it at any disadvantage
(relative to the standard cut-generation method) with regard to
polynomial-time analytic or volumetric center algorithms.  In the
next section, we briefly outline how our heuristic indeed yields a
polynomial-time algorithm (justifying the Turing reduction in
(\ref{OurTuringReductionChain})).

\section{Analytic Centers}\label{sec_AnalyticCenters}

Let $P$ be the current outer approximation $P:=B_n\bigcap
\cap_{i=1}^{h}\lbrace x:a_i^T x\geq b_i \rbrace$, as described in
the second-last paragraph of Section \ref{sec_SearchHeuristic}.
Recall that we need a definition of ``center $\omega$ of $P$''
that satisfies (\ref{eqn_CenterIsConicCombinationOfNormals}).
Define the \emph{analytic center} $\omega$ of $P$ as the unique
minimizer of the real convex function
\begin{eqnarray}\label{def_F}
F(x):= -\sum_{i=1}^{h}\log(a_i^T x-b_i) - \log(1-x^T x).
\end{eqnarray}
The relation $\nabla F(\omega)=0$ gives
\begin{eqnarray}\label{eqn_defw}
\omega=\frac{1-\omega^T\omega}{2}\sum_{i=1}^{h}\frac{a_i}{a_i^T
\omega - b_i},
\end{eqnarray}
which shows that $\omega$, defined as the analytic center of $P$,
indeed satisfies (\ref{eqn_CenterIsConicCombinationOfNormals}).

Our algorithm is a modification of the one in \cite{AV95}: we use
a hypersphere for $P_0$ instead of a hyperbox (i.e. we adapt the
analysis to handle a convex quadratic constraint). We refer to
\cite{qphIoa05} for details (which rely on results in
\cite{NN94,Ren01}), but remind the reader of some of the
algorithm's characteristics. The algorithm stops when the current
outer approximation becomes either too small (volume-wise) or too
thin to contain $K_p$. For this, a lower bound $r>0$ on the radius
of the largest ball contained in $K_p$ is needed. By exploiting
the accuracy parameter $\delta$ of the weak separation problem,
such an $r$ exists (and is derived in \cite{qphIoa05}). The actual
algorithm is not as straightforward. For instance, it is a
shallow-cut algorithm ($b_i<0$) so as to keep the analytic center
of the old $P$ in the new $P$ and the new center close to the old
center. As well, cutting planes are occasionally discarded so that
$h$ does not exceed some prespecified number.

Incidentally, it is an open problem whether there exists a
polynomial-time, analytic center algorithm for the convex
feasibility problem that does not require shallow cutting. It has
been suggested by Mitchell \cite{Mit03,Mit05} that central cutting
can be used in the Atkinson-Vaidya algorithm, if certain
techniques from \cite{MT92} are employed to compute the new
analytic center. However, from correspondence with Mitchell and Ye
\cite{Ye05}, it is unclear whether modifying the Atkinson-Vaidya
algorithm in this way retains the polynomial-time convergence:
while it is clear that a new analytic center can be efficiently
computed when central cuts are used, it is not clear that all the
other delicate machinery in the convergence argument emerges
unscathed.  If central cuts may indeed be used, then the
worst-case precision requirements of our algorithm are
significantly reduced \cite{qphIoa05}.

\section{Acknowledgements}

We gratefully acknowledge an anonymous referee who pointed out the
relationship between our reduction and the standard reduction,
allowing us to streamline this paper and correctly identify its
novel contribution.  We also thank Tom Stace and Coralia Cartis
for assistance.  LMI acknowledges the support of GCHQ and ORS
(UK), and NSERC (Canada); BCT acknowledges CMI (UK); DC
acknowledges NSERC and the University of Waterloo.

\bibliographystyle{unsrt}

redpajama_set_name: RedPajamaArXiv


text:
Frank Grey may refer to:
 Frank Grey (umpire), South African cricket umpire
 Frank R. Grey, English illustrator

See also
 Frank Gray (disambiguation)

redpajama_set_name: RedPajamaWikipedia


ErhvervsPhD-projekt med Fyns Amt under den kommunale strukturreform som case og e-learning-leverandøren MOCH A/S som samarbejdspartner.
The industrial PhD-project work title is: Digital mediated learning and knowledge processes in periods of radical organizational transitions. Field studies and technology development projects in social institutions for mentally handicapped individuals during the Danish Municipality reform.
The Municipality Reform in Denmark seems to enhance the ongoing transition from a job based to a competency based public sector. The reform is also characterized by the ideas of new public management and radical changes within the field of professionals. At this very moment; there is a strong need for internal and external clarity about policies, strategies, resources, competencies, jobs i.e. among politicians, managers and administrative staffs. In this situation, the employees and organizations need to develop, reflect on, exploit and brand its competencies. This situation results in new needs for routines and (digital) systems that fasten knowledge creation and distribution.
A competency management system (cms) at the institution Minibo. A cms provides a systematic work process for clarify individual and organizational skills, aptitudes and competencies. Minibo seeks to describe its competencies for branding and planning purposes. The institution will be divided into two organizations after January 2007 and goes to two new established communes.
A workflow management system (wms) at Strandvænget. A wms provides a systematic way of handling procedures and documents. Strandvænget seeks to do its client plan processes more efficient and standardized. At this moment, the processes varies in length and quality because of the existence of many local cultures/practices, lack of experience and common standards, i.e.
A knowledge management system (kms) at Østruplund. A kms provides a platform for registrate and distribute data/information and learning objects. In this study, we introduce a wiki which is a type of website that allows users to add, remove as well as edit all content, quickly and easily. Østruplund seeks to describe its competencies (for profiling and prepare a competence based strategy) when it goes to the new established county (Region Syddanmark).
A learning management system (lms) at the institution Lindebjerg. A lms provides a systematic way of handling short and long term educationally courses. Lindebjerg seeks to send all its social educators on a 10 weeks course at Odense Pædagogiske Seminarium (regional institute for social educations). The goal is to train and prepare the employees to a new kind of group of clients in the future, because the institution's status changes from regional (county) to local institution (commune).
The research process is based upon the ideas of action based research and critical realism, whereas the technology development projects are based upon participatory design principles. Finally, the project combines several theory categories; social learning theories (individual and organizational level), political sociology, neo-institutional organization and strategy theory and participatory design theory.
The core participants are University of Southern Denmark/Knowledge Lab, Copenhagen Business School, Fyns Amt (county) and MOCH A/S. A selected it-vendor sponsors the Minibo-project with tailor-made competency registration software.


text:
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His personality fills a room, his laughter lifting its occupants, his excitement contagious. There is nothing small about him, other than his name. Everything Mark Small does is big. Forty years ago he assumed the financial leadership of a Mentor, Ohio, construction company founded by his father. Along with his four brothers, they grew Cleveland Construction Inc. into a national firm employing hundreds, with multiple offices in several states
Relying on hard work, on-the-job training, and his natural business acumen, Mark successfully oversaw all phases of Cleveland Construction's accounting, insurance, bonding, self-insured programs, banking, and financial risk management while actively participating in business development and project administration. And, as he has been quoted saying, "I'm also the person who put out fires!"
In 1996, Mark served as president of the Northern Ohio Chapter of the Associated Builders and Contractors, a national U.S. trade association of 69 chapters with more than 22,000 commercial contractors and construction-related firms among its members representing the construction industry. He later served as the national executive vice president for the ABC, winning the group's Contractor of the Year award in 2003. Mark also served on the following boards, including acting as the Chairman to: Construction Legal Rights Foundation; Trimmer Education Scholarship Foundation; National Center for Construction Education and Research and participated is a board member of Lake Hospital; Richard G. Small Foundation. At age 36, Mark was listed by Cleveland Crain's as a 40-Under-40 recipient.
Lauded for his leadership in several educational foundations, and philanthropy for youth-oriented concerns, Mark also pursues his avid interest in offshore racing as owner of the Cleveland Construction offshore racing team.
Mark brings his larger-than-life approach to A Cut Above, employing his years of financial experience and business leadership to assemble a top-notch team offering top-quality meat and provisions in a top-of-the-line facility.