text:
Unveiling the Sandby borg massacre
Help us solve the mystery of the Iron Age massacre, at the unique archaeological site of Sandby borg in Sweden!
The Sandby borg excavation team
321 backers pledged SEK 465,619 to help bring this project to life.
Campaign Rewards FAQ Updates 27 Comments 16 Community
Kalmar, Sweden Nonfiction
SEK 465,619
pledged of SEK 400,000 goal
Pledge SEK 50 or more About US$ 6
A small step for a backer, potentially a giant leap for the Sandby borg project! At donations of 50 SEK (c. 5 €), you will have a big Thank You posted together with your name on the project homepage www.sandbyborg.se. Included in all other rewards.
Estimated delivery Jan 2015
Pledge SEK 100 or more About US$ 11
At donations of 100 SEK (c. 10 €), you will get a personal greeting sent to you on a limited edition Sandby borg postcard specifically designed for this Kickstarter campaign. Included in all rewards above this level.
Estimated delivery Feb 2015
Donations of 250 SEK (c. 25 €) will be rewarded with a personal diploma where your invaluable help is acknowledged.
At donations of 500 SEK (c. 50 €), you will recieve a really cool Sandby borg official sponsor T-shirt!
Estimated delivery Apr 2015
For backers with candy cravings, this level at 750 SEK (c. 75 €) is rewarded with an exclusive and extremely tasty box of Sandby borg chocolate, specifically developed and produced by the Sandby borg project in proud collaboration with Ölandschoklad, supplier of pralines for the Nobel Nightcap.
Pledge SEK 1,000 or more About US$ 106
Donations at this level (c. 100 €) are rewarded with a signed and individually numbered copy of the book, with texts in English and Swedish, beautifully illustrated and presenting the Sandby borg findings with special emphasis on the full excavation of House 40. Included in all rewards above this level.
At this level (c. 500 €), the reward is a beautiful and exclusive silver replica of the so called sword pendant from Sandby borg, an amazing work of art that stands as model for the project logotype and also the specially produced Sandby borg chocolate mentioned above. The silver replica is produced by the highly renowned Öland silversmith Henrik Ingemansson at Atelier Borgila, Royal Warrant of Appointment and producer of the Order of the Seraphim.
Pledge SEK 15,000 or more About US$ 1,576
The reward on this level (c. 1500 €), limited to a maximum of ten backers, is a VIP day in Kalmar and on Öland. During this unforgettable day, project and excavation leader Dr Helena Victor will take care of you and give you a personal guided tour of the fort itself on location on Öland, as well as a close encounter with the astonishing Sandby borg finds in the vaults of Kalmar County Museum.
Another reward limited to a maximum of ten backers, this level at 25 000 SEK (c. 2500 €) offers a weekend at the exclusive inn Halltorps Gästgiveri on Öland http://www.halltorpsgastgiveri.se/en/ with a fantastic three-course dinner and a VIP visit at the Sandby borg site included. Travel to and from Sweden is not included.
This reward gives a class from a local school the opportunity to visit Sandby borg for a unique learning experience. Your generosity will be rewarded with the gratitude of the children expressed in the form of a personal "Thank you"-card, together with a copy of the book.
The highest reward, at donations of 50 000 SEK (c. 5000 €), gives you an experience you will never forget. On the day of arrival, you will check in at the exclusive inn Halltorps Gästgiveri on Öland http://www.halltorpsgastgiveri.se/en/ where you stay for two nights with full board. On the first night you will get a relaxed but exciting evening introduction to the site by one of the project members. The whole next day, you will join us in the trench of the Kickstarter-funded excavations at Sandby borg, get a trowel in your hand and help us explore the secrets of the fort. With full supervision and guidance by expert archaeologists and project members, this level literally allows you to become an archaeologist for a day, and not at just any site. This reward is limited to a maximum of five backers.
Nov 27, 2014 - Dec 31, 2014 (34 days)


In this difficult and uncertain time of economic crisis, businesses across the country and in virtually every industry are confronting serious strategic and operational challenges. And, increasingly, employers must make myriad, tough decisions on an array of critical personnel matters. From downsizing and benefit reductions to protecting intellectual property, the issues facing employers in the current economic downturn are complex and fraught with legal peril.
Clearly, this is not the time to unwittingly invite potentially costly and time-consuming litigation. Indeed, it is more important than ever for employers to have the legal information and practical guidance required to make the right decisions in the right way.
In this special EBG briefing, we target the key issues ignited by today's new economic realities and provide specific suggestions for minimizing the legal risks inherent in making the hard decisions that your company currently faces or may soon confront.


text:
SAUNDERS RETAINS WBO 168LBS WORLD TITLE WITH DOMINANT POINTS WIN OVER MURRAY
FightPost: MMA & Boxing News	Boxing, Press Release	 5th Dec 2020 2 Minutes
12 x 3 mins WBO Super-Middleweight World Title
BILLY JOE SAUNDERS WUD12 (120-109, 120-109, 118-110) v MARTIN MURRAY
(Hatfield, England) (St Helens, England)
Billy Joe Saunders retained his WBO Super-Middleweight World Title with a dominant unanimous decision win over St Helens veteran Martin Murray to stay on course for a huge unification battle with the winner of Saul 'Canelo' Alvarez vs. Callum Smith next year.
The unbeaten 31-year-old dominated from the opening round with his superior ring skills as Murray fell short in his fifth World Title attempt, losing out on the judge's scorecards with scores of 120-109, 120-109 and 118-110 at The SSE Arena, Wembley.
"I wasn't really happy with that performance," Saunders told Matchroom. "I'm not taking anything away from Martin, he came with a good game plan. He got through it. He tucked up and survived well. I can only be a bit critical of myself because I had a bit of ring rust. My jab was there but there was just that bit of snap missing. I was trying to look for stuff when naturally it's there.
"When you're in a training camp getting ready for Canelo Alvarez and you're in the biggest fight of your life, you've got that fear factor and everything there, and then the pandemic came and I can only be thankful to be out this year. But then you're back in camp and it's a defence against Martin Murray, I was pencilled in to fight him twice in 2018. It was sort of like a hard kick in the teeth. But look, I've got to be thank my management team MTK that I'm even out this year.
"It is what it is, and we move on. I'm 30-0 and still unbeaten and still World Champion. I've been World Champion now since 2015. People can run my performance down but let's make the big fights, because it's certainly not me turning them away. Eddie knows that I'm always there to sign. I had the Canelo fight signed and it fell through, that's nobody's fault.
"A big well done to my lads who boxed on the show tonight. Lewie Edmondson and Donte Dixon did well. Martin was a cunning old fox, he knew what he was doing and he had the ref on his side, he had the ref eating out of his hand. Fair play to him. I learnt a lot from him to be honest. Perhaps everything happens for a reason and I learnt a hell of a lot from the fight.
"Fair play to Callum Smith and I really do wish him all of the success in that fight. I think he's got the tools to do the job. Canelo would have been training since May for this fight. He would have had Smith in his eyesight from day one. It's been sprung on him at five or six weeks. They're very clever in the way they work. If Smith has done his homework and prepared well then I give him a good chance of winning the fight. We are pushing for big fights constantly. After the Canelo fight I want to know my next date. I'm not getting any you
ypnger and I want to show my full potential."
Photo Credit: Mark Robinson/Matchroom Boxing
Published 5th Dec 2020
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redpajama_set_name: RedPajamaCommonCrawl


text:
définition - Cam_Ranh_Air_Base
Cam Ranh Air Base
For the civil use of the facility since 2004, see Cam Ranh International Airport.
Part of Vietnam People's Air Force (VPAF)
Russian Air Force (VVS)
Pacific Air Forces (USAF)
Air Force Base
11°59′53″N 109°13′10″E / 11.99806°N 109.21944°E / 11.99806; 109.21944 (Cam Ranh AB)
Joint Civil/Military Airport
IATA: none – ICAO: none
Elevation AMSL
39 ft / 12 m
02L/20R 10,000 3,048 Paved
02R/20L 10,000 3,048 Paved
Cam Ranh AB
Location of Cam Ranh Air Base, Vietnam
F-4C Serial 63-7542 of the 557th Tactical Fighter Squadron. This aircraft survived the war and eventually was retired to AMARC on July 12, 1988
McDonnell Douglas F-4C-23-MC (S/N 64-770) "Jeannie" (558th TFS) over South Vietnam in December 1968
C-7B Serial No 63-9725 of the 535th Tactical Airlift Squadron - October 1971. It is believed that this aircraft along with other C-7s from the 483d TAW was transferred to the South Vietnamese Air Force in 1972 after the 483d was deactivated.
Cam Ranh Air Base is located on Cam Ranh Bay in the province of Khanh Hoa, Vietnam. It was one of several South Vietnamese Air Force (VNAF) air bases built and used by the United States Air Force (USAF) during the Vietnam War. Between 1979 and 2002, the facility was used by the Soviet/Russian Air Force.
On May 19, 2004, after major reconstruction, Cam Ranh Airport received its first commercial flight. As Vietnam considers the facility to be important to its defense, a small garrison of troops are stationed there.
1 US military use of Cam Ranh AB
1.1 12th Tactical Fighter Wing
1.2 Airlift use
1.3 483d Tactical Airlift Wing
2 USAF withdrawal and South Vietnamese use of Cam Ranh Air Base
3 Soviet Use of Cam Ranh Air Base
4 Cam Ranh Emblem Gallery
6.1 Other sources
US military use of Cam Ranh AB
The airfield at Cam Ranh Bay was built by the U.S. Navy Civil Engineer Corps along with civilian contractors beginning in 1965. It was turned over to the USAF Pacific Air Forces on November 8.
Cam Ranh Air Base was a part of the large Cam Ranh Bay logistics facility built by the United States. It was the major military seaport used by the United States for the offloading of supplies, military equipment and as a major Naval base. Army, Navy, Marine Corps and Air Force units all had compounds and units assigned to the Cam Ranh Bay facility from its opening in 1965 until it's closure in 1972 as part of the drawdown of United states military forces in South Vietnam.
Cam Ranh Air Base served as a United States Air Force tactical fighter base, the first in South Vietnam to base the F-4C Phantom II tactical fighter-bomber. The air base also was used as a strategic and tactical airlift facility. Cargo and personnel would arrive from the United States into the logistics facilities at Cam Ranh Bau by ship and also by large Military Air Transport Service/Military Airlift Command airlifters, and then be transferred to tactical airlift for movement within South Vietnam by the 483d Tactical Airlift Wing, using C-7 Caribu and C-130 Hercules transports. Outgoing cargo and personnel would also be processed though the large aerial port facility.
12th Tactical Fighter Wing
The first USAF unit to be stationed at Cam Ranh AB was the 12th Tactical Fighter Wing, which was assigned on 8 November 1965, being deployed from MacDill Air Force Base Florida. The 12th TFW was the first permanently assigned F-4C Phantom II wing assigned to Southeast Asia. In time, the F-4C took over the bulk of the heavy tactical bombing over both North and South Vietnam. Operational squadrons of the wing at Cam Ranh were:
557th Tactical Fighter Squadron December 1, 1965 – March 31, 1970 (F-4C Tail Code: XC)
558th Tactical Fighter Squadron November 8, 1965 – March 31, 1970 (F-4C Tail Code: XT)
43d Tactical Fighter Squadron November 8, 1965 – January 4, 1966 (F-4C)(Advance party arrived October 28, 1965)
Replaced by: 559th Tactical Fighter Squadron January 1, 1966 – March 31, 1970 (Reassigned from 15th Tactical Fighter Wing, absorbed aircraft and personnel of inactivated 43d TFS; F-4C Tail Code: XN)
391st Tactical Fighter Squadron January 26, 1966 – July 22, 1968 (F-4C Tail Code: XD/XT)
Deployed from 366th TFW, Phan Rang Air Base. Aircraft transferred to 12th TFW 558th TFS July 1968 (F-4C Tail Code: XD/XT). Former 391st TFW aircraft reassigned to 475th Tactical Fighter Wing, Taegu AB, South Korea, July 1968 as Det 1., 558th Tactical Fighter Squadron
From Cam Ranh AB the wing carried out close air support, interdiction, and combat air patrol activities over both Vietnams and Laos. Following the capture of the USS Pueblo, the 558th TFS was sent TDY to augment the 475th TFW in South Korea. When that later became a permanent assignment, the 558th and 391st traded designations.
On March 30, 1970, as part of the Vietnamization process and phase out of the F-4C, fighter operations at Cam Ranh Bay AB were halted and the base turned over to Military Airlift Command control. In March 1970, as part of the Vietnamization process and phase out of the F-4C, the aircraft and personnel of the 12th were dispersed, and fighter operations at Cam Ranh Bay AB were halted, the F-4C's were transferred back to the United States and assigned to the Air National Guard.
With the transfer of jurisdiction of Cam Ranh AB to the 483d Tactical Airlift Wing, the 12th TFW was reassigned to Phu Cat AB where it replaced the 37th TFW in a name-only change.
Airlift use
Because of its close proximity to Cam Ranh Bay, Cam Ranh Airfield became an important part of the airlift system operated by 315th and 834th Air Divisions. In early 1966 C-130s from 315th Air Division squadrons based in Japan and Okinawa began "shuttle" missions out of the airfield. C-130s from Tan Son Nhut and Nha Trang made pickups at Cam Ranh, as did C-123s. In October 1966 the 483rd Troop Carrier Wing activated at Cam Ranh under the recently activated 834th Air Division to command the former Army CV-2 Caribous which were transferring to the Air Force. 834th Air Division's 2nd Aerial Port Group included the 14th Aerial Port Squadron which operated the aerial port facilities on the airfield. In 1966 a new ramp was constructed on the west side of the airfield to handle airlift operations. Cam Ranh remained as the Air Force's primary airlift base in South Vietnam until it closed. Cam Ranh-based C-130s were involved in the resupply of Khe Sanh, airdrops into A Loi Airfield in the A Shau Valley, the evacuation of Kham Duc and countless other combat airlift operations.
Military Airlift Command aircraft also operated into Cam Ranh. In July 1966, the 9th Aero Medical Evacuation Squadron was elevated to become the 9th Aeromedical Evacuation Group. It had been flying throughout Vietnam and to facilities in Japan and the Philippines. The group flew C-9 Nightingale as well as Douglas C-118 Liftmasters[1]
483d Tactical Airlift Wing
The PACAF 483d Tactical Airlift Wing was activated at Cam Ranh on October 15, 1966 under the 834th Air Division based at Tan Son Nhut AB. The mission of the wing was to manage tactical airlift operations, using air transport to haul cargo and troops, which were air-landed or air-dropped, as combat needs dictated to U.S. Army and allied ground forces throughout South Vietnam. Specifically, the 483d was assigned ex-Army CV-2B "Caribou" light transports. Upon transfer to the USAF, the aircraft was redesignated as a C-7A.
Squadrons assigned to the 483d TAW were:
457 Tactical Airlift, January 1, 1967 – April 30, 1972 (C-7A Tail Code: KA)
458 Tactical Airlift, January 1, 1967 – March 1, 1972 (C-7A Tail Code: KC)
459 Tactical Airlift, January 1, 1967 – June 1, 1970
Assigned to: Phu Cat Air Base (C-7A Tail Code: KE)
535 Tactical Airlift, January 1, 1967 – January 24, 1972
Assigned to: Vung Tau Army Airfield (C-7ATail Code: KH)
536 Tactical Airlift, January 1, 1967 – October 15, 1971
Assigned to: Vung Tau Army Airfield (C-7A Tail Code: KL)
Assigned to: Phu Cat Air Base (C-7A Tail Code: KN)
Royal Australian Air Force, Transport Flight Vietnam / 35 Tactical Airlift, January 1, 1967 – January 24, 1972 : Assigned to: Vung Tau Army Airfield
The unique capabilities of the C-7 for short landing and takeoff made Caribou transports absolutely vital to the war effort. On many occasions the C-7s flew emergency airlift missions to airstrips and combat areas that no other aircraft could reach. Most notable were those in support of special forces camps in the central highlands.
In June 1968 the wing flew a record 2,420 combat troops in three days between Dak Pek, Ben Het and Dak To. In August 1968 pinpoint night airdrops were accomplished at Duc Lap, Ha Thanh and Tonle Cham Special Forces camps. Ammunition and medical supplies were parachuted into 75-foot (23 m)-square drop zones while the camps were under attack. In June 1969 during the siege of Ben Het more than 200 tons of ammunition, POL, rations, water and medical supplies were airdropped into a 100 x 200-foot (61 m) zone with every load on target and 100 per cent recovered. In April 1970, the 483rd helped break the siege of Dak Seang. The wing flew 100 air-drop sorties under heavy hostile fire in ten days delivering some 400,000 pounds of vital supplies.
During their five years' flying for the 483rd, the C-7 Caribous carried more than 4.7 million passengers, averaging more than one million a year during 1967, 68 and 69. At the same time the wing averaged more than 100,000 tons of cargo each year.
In addition to the C-7 squadrons, the wing supported rotating C-130 Hercules squadrons rotated frequently from the 463d Tactical Airlift Wing at Clark AB. These squadrons were operated as Detachment 1. 463d Tactical Airlift Wing. These squadrons were the 29th TAS (QB); 772d TAS (QF); 773d TAS (QG); 774th TAS (QW). In addition, various C-130Es from the 374th Tactical Airlift Wing at Ching Chuan Kang Air Base, Taiwan, and the 315th Air Division from Naha AB, Okinawa performed short frequent rotating deployments to Cam Ranh.
With the deactivation of the 12th Tactical Fighter wing, the 483d became the host wing at Cam Ranh Bay on March 31, 1970. On December 1, 1971, the wing was reassigned from the 834th Air Division directly to Headquarters, Seventh Air Force at Tan Son Nhut AB. It gained a tactical electronic warfare mission in mid-1971 and a special operations mission in the autumn of 1971. These squadrons were:
20th Special Operations Squadron, September 1, 1971 – April 1, 1972 (UH–1P, No Tail Code)
Assigned to 14th Special Operations Wing, Phan Rang Air Base (squadron assigned to Cam Ranh), September 25, 1970 – September 1, 1971, reassigned to 483d TAW.
90th Special Operations, September 1, 1971 – April 15, 1972 (A-37B Tail Code: CG)
360th Tactical Electronic Warfare, August 31, 1971 – February 1, 1972 (EC-47N/P/Q Tail Code: AJ)
Reassigned from: 460th Tactical Reconnaissance Wing, Tan Son Nhut AB
361st Tactical Electronic Warfare, August 31 – December 1, 1971 (EC-47N/P/Q Tail Code: AL)
362d Tactical Electronic Warfare, August 31, 1971 – February 1, 1972 (EC-47N/P/Q C-47H Tail Code: AN)
The 90th SOS inactivated in place May 31, 1972; the 360th TEWS was reassigned to 377th Air Base Wing at Ton Son Nhut Air Base February 1, 1972; the 361st was deactivated in place December 1, 1971 and the 362d was assigned to the 366th TFW at Da Nang Air Base on February 1, 1972.
For its service in Vietnam, the 483rd was awarded two Presidential Unit Citations (January 21 – May 12, 1968; April 1 – June 30, 1970) and three Air Force Outstanding Unit Awards with combat "V" device (January 1 – April 30, 1967; May 1, 1967 – April 30, 1968; July 1, 1970 – December 31, 1971).
USAF withdrawal and South Vietnamese use of Cam Ranh Air Base
See also: Ho Chi Minh Campaign
Beginning on January 1, 1972, the 483d Tactical Airlift Wing phased down its activities, and active flying ended by March 31.[2] The unit was inactivated and Cam Ranh Air Base was turned over to the South Vietnamese government on May 15, 1972, ending USAF use of the facility.[3][4]
After the turnover to the South Vietnamese Air Force (VNAF) the base was largely abandoned. It was, quite simply, much too big for the Vietnamese to use. The base was slowly looted for its usable equipment, such as air conditioners, desks, refrigerators, and other furniture along with windows, doors and corrugated tin roofs from the buildings left by the Americans, leaving what could be categorized as a deteriorating ghost town of abandoned buildings.[5][6]
The VNAF used the airfield at Cam Ranh Bay as a storage facility for many of their propeller-driven aircraft (A-1E, T-28) while the large amount of jet F-5s and A-37s provided by the United States to the VNAF were used in operations against the North Vietnamese army from other, smaller bases.[7]
On April 3, 1975 North Vietnamese forces captured Cam Ranh Bay and all of its remaining facilities.
Soviet Use of Cam Ranh Air Base
In 1979, the Soviet Union started leasing the base rent-free from Vietnam under a 25-year leasing treaty. As part of this agreement, the Soviet Air Force stationed MiG-23 Flogger fighters, Tupolev Tu-95 long range reconnaissance aircraft, Tupolev Tu-16, Tupolev Tu-22M and occasionally, near the end of the USSR, Tupolev Tu-160 bombers at Cam Ranh Air Base.
The Russian government continued the earlier Soviet arrangement in a 1993 agreement that allowed for the continued use of the base for signal intelligence, primarily on Chinese communications in the South China Sea. By this time, Russian aircraft had been withdrawn, with only support personnel for the listening station remaining.
In 2001, the Russian government informed Vietnam that it would be withdrawing from Cam Ranh Bay completely. Russian personnel left the facility entirely in 2002.
In Tom Clancy's 1986 techno-thriller Red Storm Rising, the base at Cam Ranh Bay is described as being devoid of unusual Soviet air and naval activity, suggesting to NATO, US & Japanese analysts that the imminent Soviet offensive will be confined to Europe, limiting the scope of the war to reduce the possibility of escalation.
Cam Ranh Emblem Gallery
Pacific Air Forces (1965–1972)
834th Air Division (1966–1971)
12th Tactical Fighter Wing (1965–1970)
483d Tactical Airlift Wing (1966–1972)
Military of the United States portal
United States Air Force portal
Republic of Vietnam Air Force
Soviet Air Force
^ USAFHRA Document 01099512
^ Cam Ranh Bay American Withdrawal 1972 (Video)
^ Camh Rhan AB Ghost Town, Part 1 (Video)
^ Mikesh, Robert C. (2005) Flying Dragons: The South Vietnamese Air Force. Schiffer Publishing, Ltd. ISBN 0-7643-2158-7
Milne, Duncan (1967) Official Military Records
Endicott, Judy G. (1999) Active Air Force wings as of 1 October 1995; USAF active flying, space, and missile squadrons as of 1 October 1995. Maxwell AFB, Alabama: Office of Air Force History. CD-ROM.
Martin, Patrick (1994). Tail Code: The Complete History of USAF Tactical Aircraft Tail Code Markings. Schiffer Military Aviation History. ISBN 0-88740-513-4.
Mesco, Jim (1987) VNAF South Vietnamese Air Force 1945–1975 Squadron/Signal Publications. ISBN 0-89747-193-8
Mikesh, Robert C. (2005) Flying Dragons: The South Vietnamese Air Force. Schiffer Publishing, Ltd. ISBN 0-7643-2158-7
Ravenstein, Charles A. (1984). Air Force Combat Wings Lineage and Honors Histories 1947–1977. Maxwell AFB, Alabama: Office of Air Force History. ISBN 0-912799-12-9.
VNAF - The South Vietnamese Air Force 1951–1975
USAAS-USAAC-USAAF-USAF Aircraft Serial Numbers--1908 to present
Time Magazine:Soviet Union Pacific Overtures, Monday, November 17, 1986 By JILL SMOLOWE
Russia to complete Cam Ranh Bay naval base pullout by July. Asian Political News, April 1, 2002
US, Vietnam scratch each other's back. Asia Times Online, July 12, 2006
12th Tactical Fighter Wing Association
C-7A 63-09760 At the Air Mobility Command Museum
Cam Ranh Bay, Scenes From 1966–1968 (Video)
Cam Ranh Bay: What the Captain Means (Video)
Cam Ranh Bay Beach Party (Video)
United States Air Force Of The Vietnam War
Pacific Air Forces
2d Air Division
Seventh Air Force
Thirteenth Air Force
Bien Hoa
Binh Thuy
Phu Cat
Tan Son Nhut
3rd TFW
12th TFW
14th ACW/SOW
31st TFW
315th TAW
366th TFW
377th ABW
633d SOW
Don Muang
Takhli
Udorn
8th TFW
56th SOW
307th SW
432d TRW
Other major
Clark (Philippines)
Ching Chuan Kang (Republic of China)
Andersen (Guam)
Kadena (Japan)
Misawa (Japan)
Military of South Vietnam
Civilian Irregular Defense Group
Popular Forces
Regional Forces
Cavalry Squadron
Presidential Guard
Air bases
Coup attempts and mutinies
Notable officers
Cao Van Vien
Chung Tan Cang
Do Cao Tri
Duong Van Minh
Hoang Xuan Lam
Huynh Van Cao
Lam Van Phat
Le Minh Dao
Le Nguyen Khang
Le Van Hung
Le Van Kim
Mai Huu Xuan
Nguyen Cao Ky
Nguyen Chanh Thi
Nguyen Huu Co
Nguyen Khanh
Nguyen Van Thieu
Nguyen Viet Thanh
Ngo Quang Truong
Pham Ngoc Thao
Pham Van Phu
Ton That Dinh
Tran Thien Khiem
Tran Van Don
Retrieved from "http://en.wikipedia.org/w/index.php?title=Cam_Ranh_Air_Base&oldid=509185189"
Military of Vietnam
Soviet Air Force bases
Military installations of the Soviet Union
Closed facilities of the United States Air Force
United States military bases of the Vietnam War
Soviet Union–Vietnam relations
Toutes les traductions de Cam_Ranh_Air_Base


text:
package nl.waywayway.broodkruimels;

import android.content.*;
import android.util.*;

// Class voor tonen van notification, na ontvangen en verwerken
// van de intent die wordt verzonden na het afgaan van
// dagelijks alarm, als dat is ingesteld

public class AlarmReceiver extends BroadcastReceiver
{
    @Override
    public void onReceive(Context context, Intent intent)
	{
		MakeNotification notification = new MakeNotification(context);
		notification.showNotification();
		Log.i("HermLog", "AlarmReveiver: onReceive()");
    }
}

redpajama_set_name: RedPajamaGithub


[24/January/2017] TAIZ, Jan. 24 (Saba) - A large number of Saudi-paid mercenaries were killed and injured during their attempt to advance towards al-Tabah al-Sawdah and al-Maayer zone in Usiferah area in Taiz city.
The official added that the army and popular forces defeated groups of Saudi- paid mercenaries at the parts of al-Jadeed and al-Kadaha area towards Thubab district.
Saudi-paid mercenaries were inflicted big losses and ordnance by the army and popular forces, he said.


text:
Of Art and Volterra: Francesco Capriani (da Volterra) and Diana Mantovana
by Wladek Fuchs · April 5, 2014
Francesco Capriani (also known as Francesco da Volterra) (born in Volterra 1535, died in Rome 1594) Italian architect. Diana Scultori (also known as Diana Mantovana or Diana Volterra, born in Mantua 1547, died in Rome 1612) Italian engraver and printmaker.
Other than the record of his birth, there is nothing known about his life until 1565, when his name appears for the first time on the payroll of Count of Guastalla, Cesare I Gonzaga. From 1565 until 1570 Capriani is working on the renovation of the Gonzaga Palace in Guastalla. In 1569 da Volterra is designing also the St Peter's Cathedral in Guastalla.
Piazza Giuseppe Mazzini in Guastalla (Reggio Emila). On the left, the Concatedrale di San Pietro, at the end of the piazza the Palazzo Ducale. The facade of the Cathedral was designed in XVIII century.
It is during this time when he meets his wife, Diana (Scultori), who was a daughter of an engraver from Mantua. Diana became not only Francesco's wife but also a very important person in his future professional life.
The ceiling of the Cathedral in Volterra – by Francesco Capriani
In 1570 Francesco Capriani and Diana move to Rome. Capriani starts his career there working for Cardinal d'Este. We is working on several projects, including the elevation of the church S. Maria dell'Orto. In 1574 he receives the commission to design the ceiling in the cathedral in Volterra – a project which will take ten years to complete. During this period he must travel to Volterra often – and he is reconfirmed (together with his wife, Diana) as a citizen of Volterra (1579).
As always, the fate of the architect is connected directly to the personality, position and wealth of his patron client. A new phase of Capriani's career commences when he starts to work for Cardinal Enrico Caetani. He is working on larger projects, he is more independent and he is apparently enjoying more freedom to develop new ideas. He is working on the renovation of the Basilica Santa Pudenziana. It is a less known, but very interesting church in Rome; recognized as the oldest place of Christian worship in the city. It was built over a 2nd-century house, probably during the pontificate of Pius I in 140–155 AD, and it re-used part of a bath facility still visible in the structure of the apse. This church was the residence of the Pope in Rome until, in 313, Emperor Constantine I offered the Lateran Palace. The renovations undertaken by Cardinal Caetani significantly altered the church, replacing three naves with one, and adding a dome.
Santa Maria in Monserrato degli Spagnoli – front facade by Francesco da Volterra – completed in 1593
Francesco Capriani works on several other projects during this period: S. Silvestro in Capite, San Giacomo in Augusta and Santa Maria in Monserrato degli Spagnoli (where da Volterra designed the facade). The first two projects he did not see through completion, he died in 1594, in both cases his work was completed by by Carlo Maderno (the architect who designed the extension of the nave and the front facade of the St Peters).
The church San Giacomo in Augusta (also known as San Giacomo degli Incurabili) is probably the most interesting work by Capriani. It features an oval dome, a theme with which he experimented already in his previous projects (Santa Pudenziana), and which will be developed further by the architects of baroque in the following century.
San Giacomo in Augusta – oval dome
Francesco Capriani's life can't be understood fully without looking simultaneously at the life of his wife, Diana. She was one of the amazing female characters of XVI century, an artist, and a shrewd businesswoman. She is generally recognized as the first woman who received a Papal privilege to make, sign with her own name and market her own artwork (1575). She signed her engravings with the name Diana Mantovana or "Diana Mantuana, Civis Volaterana". (Diana from Mantua, Citizen of Volterra).
Latona Giving Birth to Apollo and Diana on the Island of Delos by Diana Mantovana
Despite the small amount of information available, Francesco and Diana come across as a married couple engaged together in the business of art and supporting each other in their efforts – maybe one of the first couples of this kind in history. Other than the work they did individually, in architecture and engraving, they apparently did some projects also together. They published jointly a Lunario (a form of a wall calendar ) for the years 1584-1586. Francesco apparently had some knowledge of astronomy, Diana knew how to mass produce graphic images. There is an evidence of the "market study analysis": the Lunario produced by our couple called upon the powers saints of Rome and Volterra, two potential buyers' markets.
Lunario for the years 1584-1586 by Francesco da Volterra and Diana Montovana
www.treccani.it (L'Enciclopedia Italiana): CAPRIANI, Francesco, detto Francesco da Volterra (Dizionario Biografico degli Italiani – Volume 19 (1976))
www.jstor.org: A Lunario for the years 1584-1586 by Francesco da Volterra and Diana Mantovana by Valeria Pagani (Print Quarterly Vol. 8, No. 2 (JUNE 1991), pp. 140-145)


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HomePosts tagged 'bernard lee'
Movie Review: YOU ONLY LIVE TWICE (1967) 5th James Bond Film
February 15, 2016 February 15, 2016 actionadventurefestival action movies, Fight Stories, Gun Stories, James Bond, Uncategorized, Violent Stories	action movies, action screenplays, akiko wakabayashi, bernard lee, donald pleasance, James bond movies, jesse ryder hughes, Lewis Gilbert, mie hama, sean connery, tetsuro tanba, You Only Live Twice
YOU ONLY LIVE TWICE, 1967
Directed by Lewis Gilbert
Starring Sean Connery, Akiko Wakabayashi, Mie Hama, Tetsuro Tanba, Donald Pleasence and Bernard Lee.
Review by Jesse Ryder Hughes
In the midst of the cold war still going on, someone is stealing Russian and American spaceships right out of space. Bond fakes his death to go undercover in Japan, to find a chemical company supplying and hiding illegal rocket fuel. A mysterious island catches Bond's eye after a young girl is found dead. On the island Bond searches a volcano that is not what it seems. Can Bond stop world War 3 and stop whoever is stealing the spaceships? I have a feeling a good predictable ending ensues.
Roald Dahl wrote the imaginative script for You Only Live Twice and it is the most imaginative script so far of the series. Abandoning Fleming's novel almost completely Dahl and the film makers make an epic Bond film dealing with the space race and the cold war. Someone is stealing ships right out of space using their own spaceship. Russia is blaming the U.S. and vice versa. Bond under the foes impression that he is now dead travels to Japan and finds that the Osato corporation is behind the crime. The themes in You Only Live Twice are great, especially for the time, before the first man hit the moon the Russians and Americans were fighting for the glory, so why not excite audiences who were all excited about the prospects of space at the time. Also this is the first film that deals with a corrupt corporation funding the money for big crime.
The first hour, You Only Live Twice is exciting and well told with great mystery woven around Japanese customs. Supposedly at the time men were put first in Japan before the women. They even say it in the movie with Bond saying I have to retire here, which doesn't help the controversy of Bond being the worlds biggest womanizer, but he is. Bond slowly figures things out and it leads him to a volcano which is in fact a secret launching pad and station for none other than SPECTRE head No.1, Ernst Stavro Blofeld petting his white cat ready to kill anyone who fails ONCE. He is ready to start World War 3 for some money.
This is the film that is truly spoofed by the Austin Powers films. Blofeld's volcano station is just crazy. Bond films were never the same grounded films after You Only Live Twice, with the exception of a couple. It pushes Bond in a direction completely away from Fleming's novels into what the studios wanted. More action, more stunts, more gadgets overriding the stories being told. And I'm not saying I don't like it. I still do, because it's fun, emotionally it becomes lost, but this is the direction the franchise takes.
There is a certain amount of convenience in most Bond films. You just have to accept as an audience member and suspend disbelief. The Americans and Russians almost seem to jump to conclusions about each other too soon for the convenience of the film. Bond gets the chance to use each one of his gadgets at a perfect time in the movie. That is the fun of these movies though. As I am watching the film I can't wait for Bond to get a chance to use a cigarette that is actually a gun.
As haywire as You only Live Twice is and fans of the novels may be disappointed. It still has its great moments, locales, action, girls and mystery to keep audiences excited. It feels like all the previous Bond films rolled into one, trying to revolutionize the genre into what it did become when Roger Moore took over.
Movie Review: THUNDERBALL (1965) 4th James Bond Movie
February 14, 2016 February 14, 2016 actionadventurefestival action movies, Fight Stories, Gun Stories, James Bond, Uncategorized	1965 james bond, action movies, adolfo celii, bernard lee, claudine auger, James bond movies, jesse ryder hughes, luciana paluzzi, m, Movie Review, sean connery, Spectre bond villain, terence young, Thunderball
THUNDERBALL, 1965
Directed by Terence Young
Starring: Sean Connery, Claudine Auger, Adolfo Celii, Luciana Paluzzi and Bernard Lee.
M sends Bond to a health spa to improve his health. SPECTRE has come up with a plan to steal two nuclear warheads and hold the world as hostage. M sends Bond to the Bahamas where Bond plays cat and mouse with SPECTRE's no. 2, Emilio Largo that climaxes in a big underwater battle.
With a bigger budget and longer running time than the last films and a great theme song by Tom Jones, Thunderball tells us that it is going to be big and exciting. Filmed in the beautiful Bahamas with a lot of underwater sequences and a lot of sharks, which appear a lot in future films after Thunderball. Supposedly Connery was almost attacked by a shark on set.
Connery is great as the 60's hero. He seems more confidant in this film. Claudine Auger as Domino is my favorite Bond girl in the series. I'm not the only one. I've had intense talks with friends where we agree that she is the best. She is, sweet, knowing, adventurous and proves she can fend for herself by the end. What can I say, she is just absolutely beautiful.
There is a lot a stake for Bond survival wise, but not as much emotional stakes as the previous two films. Though I like how matter of fact Bond is with Domino when he tells her that her brother is dead. He exploits her to get close to Largo to find out where Largo plans to detonate the warheads. He does what he has to do for the world. Does he have to sleep with Domino before he tells her? Probably not. But the movie suggests he does it because he likes her and wants to keep Domino close. It works and Domino tells Bond where Largo is going to be with his men before they go get the warheads Largo has hidden. Bond disguises himself and finds out that Largo is going to hit Miami. Bond gets the information to Felix Leiter, his good friend, and the Americans come in to intercept Largo and his men underwater in one of the only and very exciting underwater battles scenes. Sometimes it is hard to tell what's going on, but it doesn't take away from the excitement.
As the film ends, Bond and Domino strap up to a long line and send a balloon in the sky to lift the line up and a plane goes by and catches them and takes them for a ride. This is one of the James Bond stunts that is pretty ludicrous, because it takes all shred of believability out of the film and where did this plane come from. Most people I've watched this film with all give a "what the @#$%!! when they see that stunt. It goes to show that in an over the top action film some things still don't make sense.
Apart from that I still love Thunderball with the great SPECTRE meeting with all the agents around the world and No. 1, soon to be know as Ernst Stavro Blofeld, with his controls to kill anyone in their chairs that screw up. The eye-patched Largo is great, and the first real beautiful femme fatale, Fiona Volpe, is seductive and dangerous, even to watch as an audience member. Largo's pool of sharks proves an intense and exciting scene. And Bond flies a crazy jet pack.
Movie Review: FROM RUSSIA WITH LOVE, 1963. 2nd James Bond Film
February 12, 2016 actionadventurefestival action movies, Fight Stories, Gun Stories, James Bond, Uncategorized	bernard lee, bond films, daniela bianchi, From Russia with Love 1963, James bond movies, jesse ryder hughes, lotte lenya, Movie Review, Pedro Armendariz, robert shaw, sean connery, terence young
FROM RUSSIA WITH LOVE, 1962
Starring Sean Connery, Pedro Armendariz, Lotte Lenya, Robert Shaw, Daniela Bianchi and Bernard Lee.
It comes to MI6's attention that a Russian girl has defected and offered to bring a lektor decoding device to MI6 in exchange that James Bond comes and retrieves her and the device. Bond rightfully responds that it is a trap, but who is setting the trap? Is it the Russians?
Off the bat I have to say that From Russia with Love is my favorite Bond film and Bond novel. The film follows the source material relatively close, except a few minor changes, but that doesn't matter, because the film is exciting and it flows extremely well. Unlike Dr. No we know the plan of the foes right off the bat. We have to watch Bond from a distance and he thinks he's got everything figured out. He thinks the Russians are setting him up, but it is in fact SPECTRE. Bond doesn't know this until over halfway into the film and you can see on Connery's face that it is a huge blow to the ego. SPECTRE wants Bond dead for killing Dr. No and they want to steal the Lektor to sell it back to the Russians to help fund their organization. So why not kill two birds in one stone. Get MI6, who have been trying to get a lektor for ages, to send Bond to get the Lektor, SPECTRE sends an assassin to kill Bond get the Lektor into SPECTRE's hands, all the time Russia and England will be blaming each other.
The film took place during the intense cold war and the film does a good job at portraying that, which makes SPECTRE that much more diabolical is that they are taking advantage of world issues for their own gain. The film is a perfect balance. There is not too much and not too little. We aren't overwhelmed by an overabundance of set pieces and gadgets just yet and this is Connery's most vulnerable film as Bond, particularly when Red Grant, the Irish psychopath working for SPECTRE proves that bond doesn't always know what is going on, which leads into an amazing fight scene in a train car. It's not like a Jason Bourne fight, but for 1963 I can imagine it was a very similar experience at the time.
This is the first film to introduce Q and his gadgets, which become a James Bond staple. Bond gets a suitcase full of fun toys that always conveniently help him on the way.
Although the gadgetry was never in the books, it is fun, especially for young males to imagine all the cool things Bond can play with. Later films they keep topping the previous films and the gadgets get more ridiculous, but for now they are simple and fun.
The villains in From Russia with Love are very memorable. Rosa Klebb is the nasty woman who spearheads the operation under No. 1 who's face we do not see, but through her fear we know he is not to be toyed with. She hires Red Grant, a man who makes James Bond enjoyable prey to hunt. He is very strong and begins a long line of Bond foes that seem indestructible, raising the danger levels higher.
With all the new add ons that upped the ante for the series From Russia with love remains my favorite, because it is more believable than a lot of other Bond films, which is what makes the film more exciting. There's a connection with from Russia with Love that the other films don't have for me, and that is what constitutes as good story telling for this type of genre. There has to be a sense of being grounded in reality even if it is a crazy spy story and From Russia With Love achieves that the best of the early Bonds films
Movie Review: DR NO, 1962. First James Bond Film
February 11, 2016 February 11, 2016 actionadventurefestival action movies, Fight Stories, Gun Stories, James Bond, Uncategorized	bernard lee, dr no 1962, jack lord, James bond movies, jesse ryder hughes, joseph wilseman, Movie Review, sean connery, terence young, ursula andress
DR NO, 1962
Starring Sean Connery, Ursula Andress, Joseph Wiseman, Jack Lord and Bernard Lee.
James Bond is sent to investigate the murders of an operative and his secretary, stationed in Jamaica. While there he discovers there is more going on than anyone could imagine. The locals are scared out of their minds to talk, there is a huge lack of trust between anyone, a mysterious island and everyone seems to want James Bond dead.
I am a huge James Bond fan, for many reasons, like many others I love James Bond himself. A cool, ultra suave and sophisticated spy, unafraid to practically do anything dangerous. He sounds like the ultimate hero and dammit he is. The Bond films have grown with the times to suit what the audience wants (Moonraker: the Star Wars James Bond) and to even give a jolt of reality and portray Bond with real emotional feelings (On her Majesty's Secret Service, Casino Royale). The Bond girls have grown with the times as becoming more and more strong willed dependent women that don't need to fully rely on Bond and Bond to rely on them more. I just wanted to discuss where I am going to go as I do my reviews of these films I love. The first of the films Dr. No is one of my favorites and it is the film that introduced all the Bond standards you would expect from a James Bond movie.
The film starts with the signature shot looking through the gun barrel and a man turns and shoots, blood comes down the screen. It's not Connery, but we get the picture that it is James Bond and he WILL KILL YOU if you have a gun pointed at him. Pretty cool and also a little scary when you think about it. He is a dangerous man. After an arousing title sequence we start with three blind men, seemingly walking a fair distance, pretending to be blind until they meet up with Strangways, the British operative stationed in Jamaica, they use their disability cunningly and WHAT!! Yeah, they kill Strangways. They kill his secretary as well and steal a file entitled Dr. No from the office. From there we meet Bond for the first time and right off the bat we know were safe with the man where he wins the first of many hands gambling ( I actually think he can see through the backs of cards). Bond gets his first girl, which becomes a controversial subject in the Bond films, the portrayal of Women by Bond.
Bond meets M who sends him to Jamaica to investigate Strangways murder. Bond goes, and the story then unfolds almost like a Raymond Chandler novel. Dr. No more than any other Bond film is more of a mystery. That is why I like Dr. No so much. You are putting the puzzle together with Bond. A small murder case turns into a plot by Dr. No to Disrupt radio transmissions in the American space program, which would cause chaos at the cape Canaveral rocket launch sites. Like Chandler's Philip Marlowe, Bond uncovers more and more of the truth from locals, enemies and evidence pointing toward an island called crab key, that none of the locals will go near. Bond meets Honey Rider (Ursula Andress) in crab key in the most famous bond girl scene in the series. I don't blame it for being famous it is sexy and at the time probably too sexy.
So far in the film Dr. No (who belongs to a terrorist organization called SPECTRE) himself has been the ultimate mystery. For 3 quarters of the film we had only heard his voice, which was almost godlike, like a lot of future Bond villains, they appear to have complexes of all destroying the world on a global scale. Dr. No's lair is brilliantly decorated by Ken Adam who starts a trait for Bond's foes as having rich living conditions.
Overall Dr. No sets the standard for Bond films and opens us up to the world of Bond, his witty one liners and his smooth talking demeanor. Not only that it is a solid movie and definitely in my top 5 of the series. Sure it is a little outlandish and almost silly by todays standards, but it works so well and is a lot of fun. It also works to stay within the times by using the antagonist's idea to disrupt the space race which was a huge and exciting ordeal at the time. Bond is the hero we need to protect us as the world moves forward around us. He is the hero that keeps the world running smoothly.


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\section{Introduction}
\label{sec:intro}

An important approach for efficient inference in probabilistic graphical models exploits symmetries in the underlying domain. It is especially useful for statistical relational learning models such as Markov logic networks \cite{richardson&domingos06}, which exhibit repeated sub-structures -- many objects are indistinguishable from each other and their associated relations have identical probability distributions. {\em Lifted inference} algorithms (see \cite{kimmig&al15} for a survey) exploit this phenomenon by grouping symmetric states (variables) into meta-states (meta-variables) and performing inference in this reduced (lifted) graphical model.

Early approaches to lifted inference devised first order extensions of propositional inference algorithms. These include approaches for lifting exact inference algorithms such as variable elimination \cite{poole03,braz&al05}, weighted model counting \cite{gogate&domingos11}, knowledge compilation~\cite{broeck&al11}, as well as lifting approximate algorithms such as belief propagation \cite{singla&domingos08,kersting&al09,singla&al14}, Gibbs sampling~\cite{venugopal&gogate12} and importance sampling \cite{gogate&al12}. In all these approaches, the lifting technique is tied to the specific algorithm being considered. More recently, another line of work \cite{jha&al10,bui&al13,niepert&broeck14,sarkhel&al14,kopp&al15} has started looking at the notion of symmetry independent of the inference technique. In several cases, these symmetries are compactly represented using permutation groups. The computed symmetries have been used downstream for lifting existing algorithms such as variational inference \cite{bui&al13},  (integer) linear programming \cite{noessner&al13,mladenov&al14}, and Markov chain Monte Carlo (MCMC) \cite{niepert12,broeck&niepert15}, which is our focus.

A key shortcoming of existing algorithms is that they only identify and exploit sets of variables (states) that are symmetric {\em unconditionally}. Our goal is to extend the notion of symmetries to {\em contextual} symmetries, sets of states that are symmetric under a given context (variable-value assignment). Our proposal is inspired by the extension of conditional independence to context-sensitive independence \cite{boutilier&al96}, and analogously extends unconditional symmetries to contextual. As our first contribution, we develop a formal framework to define contextual symmetries. We also present an algorithm to compute contextual symmetries by reducing the problem to graph isomorphism.

Figure \ref{fig:Example-Contextual} illustrates an example of contextual symmetries. A couple A and B may like to go to a romantic movie. They are somewhat less (equally) likely to go alone compared to when they go together.
However if the movie is a thriller, A may be less interested in going by herself, but B may not change his behavior. Hence, A and B are symmetric to each other if the movie is romantic, but not symmetric if the movie is a thriller. We will call the A and B contextually symmetric conditioned on the movie being romantic.

\begin{figure}\label{fig:Example}
\subfigure[]{\includegraphics[width=0.16\textwidth]{{Figures/ContextualTable.png}}\label{fig:Example-Contextual}}
\includegraphics[width=0.15\textwidth]{{Figures/Network.png}}
\subfigure[]{\includegraphics[width=0.16\textwidth]{{Figures/OrbitalTable.png}}\label{fig:Example-Orbital}}
\caption{Illustration of (a) Contextual Symmetry (with Genre=``Romantic'')  (b) Orbital Symmetry in the Movie Network.}
\end{figure}

Finally, our paper extends the line of work on Orbital MCMC \cite{niepert12} -- a state-of-the-art approach to exploit unconditional symmetries in a generic MCMC framework.
Orbital MCMC achieved reduced mixing times compared to Gibbs sampling in domains where such symmetries exist. We design {\sc Con-MCMC}, an algorithm that uses contextual symmetries within the MCMC framework. Our experiments demonstrate that on various interesting domains (relational and propositional), where contextual symmetries may be present, {\sc Con-MCMC}\ can yield substantial gains compared to Orbital MCMC and Gibbs Sampling. We also release a reference implementation of {\sc Con-MCMC}\ sampler for wider use.\footnote{\url{https://github.com/dair-iitd/con-mcmc}}

\section{Background}

Let $\mathcal{X}= \{X_1, \ldots, X_n\}$ be a finite set of discrete
random variables. For ease of exposition, we consider Boolean random variables although our analysis extends more generally to n-ary random variables. We denote $s\in\{0,1\}^n$ to represent a {\em state}. A {\em graphical model} $\mathcal{G}$ over $\mathcal{X}$ can be
represented as the set of pairs $\{f_k,w_k\}_{k=1}^{m}$ where
$f_k$ is a formula (feature) over a subset of variables in $\mathcal{X}$
and $w_k$ is the associated weight \cite{koller&friedman09}. This is
the representation used in several existing models such as Markov
logic networks \cite{domingos&lowd09}.

\subsection{Symmetries in Graphical Models}
Some states may be symmetric; thus, they will have the same joint probability. This fact can be exploited in inference algorithms. To define symmetries, we make use of the formalism of {\em automorphism groups}, which are generic representations for symmetries between any set of objects. Automorphism groups over graphical models are defined using another algebraic structure called a {\em permutation group}.

A permutation $\theta$ is a bijection from the
set $\mathcal{X}$ onto itself. We use $\theta(X)$ to
denote the application of $\theta$ to the element $X \in \mathcal{X}$.
We also overload $\theta$ by denoting $\theta(s)$ as the permutation of a state $s$ in which
each component random variable $X$ is permuted using $\theta(X)$.

A permutation group $\Theta$ is a set of permutations
which contains the identity element, has a unique inverse for every element
in the set, and is closed under composition operator.

Following previous work \cite{niepert12} we define symmetries and automorphism groups in graphical models as follows:

\begin{defn}
A {\bf symmetry of a graphical model} $\mathcal{G}$ over the set $\cal{X}$ is
represented as the permutation $\theta$ of the variables in $\mathcal{X}$
that maps $\mathcal{G}$ back on to itself, i.e. results in the
same set of weighted formulas.
\end{defn}

\begin{defn}
An {\bf automorphism group of a graphical model} $\mathcal{G}$ is defined as the permutation group ($\Theta$) over $\mathcal{G}$ such that each $\theta \in \Theta$ is a symmetry of $\mathcal{G}$.
\end{defn}
This definition of an automorphism group of a graphical model is analogous to that of an automorphism group of an edge-colored graph, where variables in $\mathcal{G}$  act as vertices in graph, features act as edges (or hyperedges) and weights act as colors on edges. We next define  an orbit of a state.
\begin{defn}
The {\bf orbit ($\Gamma$) of a state} $s$ under the automorphism group $\Theta$ is defined as all the states that can be reached by applying a symmetry $\theta \in \Theta$ on the variables of $s$, i.e., $\Gamma_{\Theta}(s)=\{s' \in \{0,1\}^n \mid \exists
\theta \in \Theta$ s.t. $\theta(s) = s'\}$.
\end{defn}
Henceforth, we will refer to these unconditional symmetries of a graphical model as {\em orbital symmetries}. Let $P(s)$ be the probability distribution defined by model $\mathcal{G}$ over the states.
\begin{thm}
If $\Theta$ is an automorphism group of $\mathcal{G}$, then $\forall s'\in \Gamma_\Theta(s):~ P(s) = P(s')$, i.e. orbital symmetries of a graphical
model are probability preserving transformations.
\end{thm}

Therefore, the automorphism group $\Theta$ for a graphical model is also referred to as an automorphism group for the underlying probability distribution. The symmetries of a graphical models as defined above can be obtained via solving a graph automorphism problem. Though the problem is not known to be in P or NP-complete,\footnote{A quasipolynomial time algorithm \cite{babai-arxiv2015} has been proposed recently for the related graph isomorphism problem which remains to be verified.} efficient solutions
can be obtained using the software such as Saucy and Nauty
~\cite{saucy,nauty}.

\subsection{Markov chain Monte Carlo}\label{sec:background-mcmc}
Markov chain Monte Carlo (MCMC) is a popular approach for approximate inference in graphical models. A Markov chain is set up over the state space such that its stationary distribution is the same as the underlying probability distribution. An {\em Orbital Markov chain} \cite{niepert12} exploits the orbital symmetries of a model by setting up a Markov chain combining the original MCMC moves with orbital moves. Let $M_o$ denote an orbital Markov chain and $M$ be the corresponding original Markov chain. Then, given the current state $s^{(t)}$, the next state $s^{(t+1)}$ in $M_o$ is sampled as follows:
\begin{itemize}
\item {\it original move}: sample an intermediate state $s'^{(t+1)}$ from $s^{(t)}$ based on the transition probability in $M$.
\item {\it orbital move}: sample a next state $s^{(t+1)}$ uniformly at random from the orbit $\Gamma_\Theta(s'^{(t+1)})$.
\end{itemize}
Orbital MCMC converges to the same stationary distribution as the original MCMC and is shown to have significantly faster convergence properties.

\section{Contextual Symmetries}
\label{sec:framework}
Our work proposes the novel notion of contextual symmetries -- symmetries that only hold under a given context. We now extend the definitions of the previous section to their contextual counterparts. First we define a context.

\vspace{0.5ex}
\begin{defn}
A {\bf context} $C$ is a partial assignment, i.e., a set of pairs $(X_i,x_i)$, where $X_i \in \mathcal{X}$ and $x_i \in \{0,1\}$, and no $X_i$ is repeated in the set.

\end{defn}

For example, in Figure~\ref{fig:Example},
we can define a context (Genre, ``Romantic"). We refer to a context as a {\em
single variable context} if there is only one element in the context
set.

We say that a variable $X_i$ appears in a context if there
is a pair $(X_i,x_i) \in C$. Given a context $C$, we will use
$\mathcal{X}_C$ to denote the subset of variables of $\mathcal{X}$
which appear in $C$. We will use $\bar{\mathcal{X}}_{{C}}$ to denote
the complement of this set. Given a state $s$, we will use $\zeta_{X_i}(s)$ to denote
the value of $X_i$ in state $s$. We say that a state $s$ is {\em consistent}
with the context $C$ iff $\forall (X_i,x_i) \in C$ we have $x_i=\zeta_{X_i}(s)$.

In order to define contextual automorphism, we will need to define the notion of a reduced model.
\vspace{0.5ex}
\begin{defn}
Given a graphical model $\mathcal{G}= \{f_k,w_k\}_{k=1}^{m}$, and a context $C$, the {\bf reduced model} $\mathcal{G}^{r}_{C}$ is defined as the new graphical model obtained by substituting $X_i=x_i$ in each formula $f_k$ for all $(X_i,x_i)\in C$ and keeping the original weights $w_k$.
\end{defn}

Note that ${\mathcal{G}}^{r}_C$ is defined over the set
$\bar{\mathcal{X}}_{{C}}$. As an example, if the model is
represented by the formulas \{($P \vee Q$, $w_1$), ($R \vee Q
\vee S$, $w_2$)\}, the reduced model under the single variable context $\{(R,0)\}$
will be \{($P \vee Q$, $w_1$) and ($Q \vee S$, $w_2$)\}. In the
factored form representation, reduction by a context corresponds to
fixing the values of the context variables in the potential table. E.g., in
Figure~\ref{fig:Example} given the context "Romantic", we
reduce the factor to the bottom four rows of the potential
table where Genre has value "Romantic".
We are now ready to define a contextual symmetry of
a graphical model.

\vspace{0.5ex}
\begin{defn}\label{def:consym}
A {\bf contextual symmetry of a graphical model} ${\mathcal{G}}$ under context $C$ is represented as a permutation $\theta$ of variables in $\mathcal{X}$ s.t. a) $\theta(X_i) = X_i$,
$\forall X_i \in \mathcal{X}_C$ i.e. variables in the context
are mapped to themselves, and b) $\exists$ an orbital symmetry
$\theta^r$ of the reduced model ${\mathcal{G}}^{r}_{C}$
such that $\theta(X_i)=\theta^r(X_i)$ $\forall
X_i \in \bar{\mathcal{X}}_{{C}}$, i.e. mapping of the remaining
variables defines an orbital symmetry of the reduced graphical model under context $C$.
\end{defn}

For example, in Figure \ref{fig:Example}, let a permutation $\theta^*$ be: $\theta^*(G)=G, \theta^*(A)=B, \theta^*(B)=A$. $\theta^*$ is a contextual symmetry under the context (Genre, ``Romantic''), but not under the context (Genre, ``Thriller'').

\vspace{0.5ex}
\begin{defn}
A {\bf contextual automorphism group of a graphical model} ${\mathcal{G}}$ under context $C$ is defined as a permutation group ($\Theta_C$) over ${\mathcal{G}}$, such that each $\theta\in\Theta_C$ is a contextual symmetry of ${\mathcal{G}}$ under context $C$.
\end{defn}

\vspace{0.5ex}
\begin{defn}
The {\bf contextual orbit of a state} $s$ under the contextual automorphism group $\Theta_C$ (given the context $C$) is the set of those states which are consistent with $C$ and can be reached by applying $\theta \in \Theta_C$ to $s$, i.e., $\Gamma_{\Theta_C}(s)=\{s' \in \{0,1\}^n \mid \exists \theta \in \Theta_C$ s.t. $\theta(s) = s' \bigwedge \forall (X_i,x_i) \in C, \zeta_{X_i}(s')=x_i\}$.
\end{defn}
Note that $s$ must be consistent with $C$ for it to have a non-empty contextual orbit.
Analogous to orbital symmetries, contextual symmetries are also probability preserving.

\begin{thm}\label{thm:probequi}
A contextual symmetry $\theta$ of ${\mathcal{G}}$ under context $C=\{(X_i,x_i)\}$ is probability preserving $\left(P(s)=P(\theta(s))\right)$, as long as
$s$ is consistent with $C$.
\end{thm}

\subsection{Relationship with Related Concepts}
\label{sec:rel}

The set of contextual symmetries subsumes that of orbital symmetries  -- any orbital symmetry is a contextual symmetry under a null context $\emptyset$. The two notions are even more related, as the following two lemmas show. Let $\mathcal{X}_\theta^I$ be the set of variables that map onto itself in a permutation $\theta$, i.e. $\forall X\in \mathcal{X}_\theta^I: \theta(X)=X$.

\begin{lemma}
An orbital symmetry $\theta$ is a contextual symmetry under a context $C$ if ${\mathcal{X}}_C\subseteq {\mathcal{X}}_\theta^I$.
\end{lemma}

\begin{lemma}
Let $V\subseteq {\mathcal{X}}$.  If a permutation $\theta$ is a contextual symmetry of ${\mathcal{G}}$ under all possible contexts $C_i$ where ${\mathcal{X}}_{C_i}=V$, then $\theta$ is an orbital symmetry of ${\mathcal{G}}$.
\end{lemma}

We now distinguish the notions of context and contextual symmetries from two other related concepts.  First, a context is different from evidence.
External information in the form of evidence modifies the underlying
distribution represented by the graphical model. In contrast, a context  has no effect on the underlying distribution.

Second, it might be tempting to confuse contextually symmetric states with
contextually independent states \cite{boutilier&al96}. In the example of Figure \ref{fig:Example}(a) given Genre=``Thriller'', A and B are contextually independent, i.e., probability of A does not change depending on B. For this context A and B are non-symmetric. For Genre=``Romantic'' A and B are symmetric but not independent.

Finally, in Section \ref{sec:related}, we discuss the relationship between contextual symmetries and the recent notion of conditional decomposability \cite{niepert&broeck14}.

\subsection{Computing contextual symmetries}
\label{subsec:compute}

Computing contextual symmetries for $\mathcal{G}$ under a context $C$ is equivalent to computing orbital symmetries on the reduced model $\mathcal{G}_C^r=\{f_k^r, w_k^r\}_{k=1}^{m^r}$. To compute orbital symmetries we adapt the procedure from Niepert \shortcite{niepert12}. Following Niepert, we describe the construction when each $f_k^r$ is a clause, though it can be extended to the more general case.

Niepert's procedure creates a colored graph, with two nodes corresponding to every variable (one each for the positive and negative state), and one node for every formula $f_k^r$. Edges exist between the positive and negative states of every variable, and also between the formula nodes and the variable nodes (either positive or negative) appearing in the formula. Finally, colors are assigned to nodes based on the following criteria: (a) every positive variable node is assigned a common color, (b) every negative variable node is assigned a different common color, and (c) every unique formula weight $w_k^r$ is assigned a new color. The formula nodes $f_k^r$ inherit the color associated with their weight $w_k^r$.

This color graph is then passed through a graph isomorphism solver (e.g., Saucy), which
computes the automorphism group for $\mathcal{G}_C^r$. This is equivalent to computing contexual automorphism group for ${\mathcal{G}}$ under $C$:

\begin{thm}
The automorphism group for the color graph of the reduced graphical model $\mathcal{G}_C^r$ along with an identity mapping of the context variables gives a contextual automorphism group of ${\mathcal{G}}$ under $C$.
\end{thm}

Note that in case we have any evidence $E$ available, the reduced model over which we induce a colored graph corresponds to $\mathcal{G}_{C\cup E}^r$. This is in contrast with original Niepert's procedure, where evidence nodes are not removed from the color graph and instead act as additional formulas for the original graphical model with infinity weights. This elimination of evidence nodes helps discover many more symmetries in the corresponding color graph while still preserving correctness. For example, if the model is represented by formulas \{($P \vee R$, $w_1$), ($Q$, $w_1$)\}, and evidence is ($\neg{R}$), $P$ and $Q$ become symmetric only if $R$ is eliminated from the color graph, and not in Niepert's procedure.

\section{Contextual MCMC} \label{section:mcmc}
We now extend the Orbital MCMC algorithm from Section \ref{sec:background-mcmc} so that it can exploit contextual symmetries; our algorithm is named {\sc Con-MCMC}, and is parameterized by $\alpha\in[0,1)$. Orbital MCMC  reduces mixing times over original MCMC,  because it can easily transition between high probability states falling in the same orbit, which may otherwise be separated by low probability regions. Unfortunately, as Figure \ref{fig:Example} demonstrates, a domain may have little orbital symmetry, but still important contextual symmetry. {\sc Con-MCMC}($\alpha$) exploits these for inference.

We are given a set of context variables $V \subset \mathcal{X}$ (more on this later). Let $\mathcal{C}_V$ denote the set of all possible contexts involving all the variables in $V$. Overloading the notation, we will use $\mathcal{C}_V(s)$ to denote the (unique) context in $\mathcal{C}_V$ consistent with state $s$. We compute contextual symmetries $\Theta_{C}$ under each context $C \in \mathcal{C}_V$ using the algorithm from Section \ref{sec:framework}. We are also given an original regular Markov chain $M$ that converges to the desired probability distribution $\pi(s)$. {\sc Con-MCMC}($\alpha$) runs a {\em Contextual Markov Chain} $M_{con}(\alpha)$ that samples a state $s^{(t+1)}$ from $s^{(t)}$ as follows:

\begin{enumerate}
\item {\em Gibbs-orig move:} We sample an intermediate state $s'^{(t+1)}$ from the current state $s^{(t)}$ as: \\
\quad \quad (a) with probability $\alpha$ (Gibbs): flip a random context variable in $s^{(t)}$ using Gibbs transition probability. \\
\quad \quad (b) with probability $1$-$\alpha$ (original): make the move from $s^{(t)}$ based on the transition probability in $M$.
\item {\em con-orbital move: } Let $C = \mathcal{C}_V(s'^{(t+1)})$ be the context consistent with $s'^{(t+1)}$. Let $\Gamma_{\Theta_{C}}(s'^{(t+1)})$ denote the contextual orbit of $s'^{(t+1)}$ under the context $C$. Sample a state $s^{(t+1)}$ uniformly at random from $\Gamma_{\Theta_{C}}(s'^{(t+1)})$.
\end{enumerate}

When $\alpha=0$ our algorithm reduces to a direct extension of Orbital MCMC, where in second step, we sample uniformly from a contextual orbit instead of the original orbits. In the more interesting case of $\alpha > 0$, we enable the Markov chain to move more freely between different contexts using a Gibbs flip over the context variables. This Gibbs transition helps us carry over the effect of symmetries exploited under one context (via the orbital moves in step 2) to others. This can be especially useful  when symmetries are unevenly distributed across multiple contexts (as also confirmed by our experiments).

In order to sample a state uniformly at random from a contextual orbit, we use the product replacement algorithm \cite{pak00} as described and used by Niepert \shortcite{niepert12}. Recall that since we are working with contextual permutations, the context variables are mapped to themselves and we are guaranteed to not change the context. Next, we show that {\sc Con-MCMC}($\alpha$) converges to the desired stationary distribution $\pi(s)$. We need the following lemma.
\begin{lemma}\label{lem:M_go_stationary}
Let $M_1$ and $M_2$ be two Markov chains defined over a finite state space $S$ with transition probability functions $P_1$ and $P_2$, respectively, such that $\pi(s)$ is a stationary distribution for both $P_1,P_2$, i.e., $\pi(s)=\sum_{r \in S} \pi(r)*P_i(r \rightarrow s)$, $i \in \{1,2\}$. Further, let $M_2$ be regular. Then, the Markov chain $M'$ with the transition function $P'(s \rightarrow r) = \alpha*P_1(s \rightarrow r) + (1-\alpha)*P_2(s \rightarrow r)$ is also regular and has a unique stationary distribution $\pi(s)$ for $\alpha \in [0,1)$.
\end{lemma}
Let $M^{go}(\alpha)$ refer to the family of Markov chains constructed using only step 1 of our algorithm i.e. no orbital moves. $M$ is regular with the stationary distribution $\pi(s)$. Further, each individual Gibbs flip over a variable satisfies stationarity with respect to the underlying distribution $\pi(s)$ \cite{koller&friedman09}. Hence, using Lemma~\ref{lem:M_go_stationary}, $M^{go}(\alpha)$ is regular with $\pi(s)$ as a stationary distribution.
\begin{theorem}
The family of contextual Markov chains $M^{con}(\alpha)$  constructed using {\sc Con-MCMC}($\alpha$)  converges to the stationary distribution of original Markov chain $M$ for any choice of context variables $V$ and $\alpha \in [0,1)$.
\end{theorem}
\begin{proof}
Let $\pi(s)$ be the stationary distribution of $M$. Since $M^{go}(\alpha)$ is regular it is easy to see that $M^{con}(\alpha)$ is also regular (there is always a non-zero probability of coming back to the same state in an orbital move). Therefore, $M^{con}(\alpha)$ converges to a unique stationary distribution. Then, we only need to show that $\pi(s)$ is the stationary distribution of $M^{con}(\alpha)$.
Let $S=\{0,1\}^{n}$ denote the set all of all the states. For $r,s \in S$, let $P^{go}[\alpha](s\rightarrow r)$ and $P^{con}[\alpha](s\rightarrow r)$ represent the transition probability functions of $M^{go}[\alpha]$ and $M^{con}[\alpha]$, respectively. In order to show that $M^{con}[\alpha]$ also converges to $\pi(s)$, we need to show that:

\begin{equation}
\pi(s) = \sum_{r \in S} \pi(r)  P^{con}[\alpha] (r \rightarrow s)
\end{equation}
The RHS of the above equation can be written as:
\begin{eqnarray*}
  &=& \sum_{r \in S} \pi(r) \sum_{s' \in \Gamma_{\Theta_{\mathcal{C}_{V}(s)}}(s)} P^{go}[\alpha] (r \rightarrow s')  \frac{1}{|\Gamma_{\Theta_{\mathcal{C}_{V}(s)}}(s)|} \\
       &=& \sum_{r \in S} \sum_{s' \in \Gamma_{\Theta_{\mathcal{C}_{V}(s)}}(s)} \pi(r) P^{go}[\alpha] (r \rightarrow s')  \frac{1}{|\Gamma_{\Theta_{\mathcal{C}_{V}(s)}}(s)|}\\
\end{eqnarray*}
\begin{eqnarray*}
&=& \sum_{s' \in \Gamma_{\Theta_{\mathcal{C}_{V}(s)}}} \left[ \sum_{r \in S}  \pi(r)P^{go}[\alpha] (r \rightarrow s') \right]  \frac{1}{|\Gamma_{\Theta_{\mathcal{C}_{V}(s)}}(s)|}\\
&=& \sum_{s' \in \Gamma_{\Theta_{\mathcal{C}_{V}(s)}}} \pi(s')  \frac{1}{|\Gamma_{\Theta_{\mathcal{C}_{V}(s)}}(s)|}\\
&=& \sum_{s' \in \Gamma_{\Theta_{\mathcal{C}_{V}(s)}}} \pi(s)  \frac{1}{|\Gamma_{\Theta_{\mathcal{C}_{V}(s)}}(s)|}\\
       &=& \pi(s)
\end{eqnarray*}
Here, recall that $\Theta_{\mathcal{C}_{V}(s)}$ denotes the contextual automorphism group for the (unique) context $\mathcal{C}_V(s)$ consistent with the state $s$, and $\Gamma_{\Theta_{\mathcal{C}_{V}(s)}}(s)$ denotes the corresponding orbit. Step 1 above follows from the definition of contextual orbital move. Step 4 follows from the stationarity of $M^{go}[\alpha]$. Step 5 follows from the fact that all the states in the same contextual orbit have the same probability (Theorem \ref{thm:probequi}).
\end{proof}

\section{Experimental Evaluation}
\label{sec:expt}

Our experiments evaluate the use of contextual symmetries for faster inference in graphical models. We compare our approach against Orbital MCMC, which is the only available algorithm that exploits symmetries in a general MCMC framework. We also compare with vanilla Gibbs sampling, which does not exploit any symmetries. We implement {\sc Con-MCMC}($\alpha$) as an extension of the original Orbital MCMC implementation\footnote{\url{ https://code.google.com/archive/p/lifted-mcmc/}} available in the GAP language \cite{gap15}. The existing implementation uses Saucy~\cite{saucy} for graph isomorphism and Gibbs sampler as the base Markov chain.  We experiment on two versions each of two different domains, with context variables pre-specified. We next describe our domains.

\subsection{Domains and Methodology}

\begin{figure*}
\framebox{
\subfigure[]{
{\includegraphics[width=0.24\textwidth]{Figures/sports1.png}}
{\includegraphics[width=0.24\textwidth]{Figures/sports2.png}}
{\includegraphics[width=0.24\textwidth]{Figures/sports3.png}}}\label{fig:sports_size}}
\subfigure[]{
{\includegraphics[width=0.23\textwidth]{Figures/sports_single.png}}\label{fig:sports_one_sided}}

\framebox{
\subfigure[]{
{\includegraphics[width=0.24\textwidth]{Figures/yo1.png}}
{\includegraphics[width=0.24\textwidth]{Figures/yo2.png}}
{\includegraphics[width=0.24\textwidth]{Figures/yo3.png}}}\label{fig:fs_evidence}}
\subfigure[]{
{\includegraphics[width=0.23\textwidth]{Figures/yo_single.png}}\label{fig:fs_one_sided}}
\caption{{\bf (a)} {\sc Con-MCMC}\ effectiveness increases tremendously with increasing domain sizes. Note that y-axes are on different scales. {\bf (c)} New orbital symmetries are created with increasing evidence, leading to improved performance of Orbital MCMC. {\bf (b, d)} Curves for Sports Network (Single) and Y \& O (Single) respectively -- {\sc Con-MCMC}(0.01) performs the best and vastly outperforms {\sc Con-MCMC}(0).}
\label{fig:results}
\end{figure*}

\noindent{\bf Sports Network: } This Markov network models a group of students who may enter a future sport league, which could be for one of two sports, badminton or tennis (modeled as the variable $Sport$). Each student belongs to one of the dorms on campus. The league accepts both singles as well as doubles entries. For each student $X$, the domain has a variable for playing singles, $S_X$. For each pairs of students $X$, $Y$ coming from the same dorm, we have a variable indicating that they will play doubles together, $D_{XY}$. Multiple students (in the same dorm) train together in training groups, which are different for the two sports. A student's participation in the league for a given sport is (jointly) influenced by the participation of other students in her training group for that sport. Moreover, if two students decide to play singles, it increases the probability that they may also team up to play doubles independent of their training groups. In this domain, different subsets of students in a dorm (based on their training groups) are symmetrical to each other depending upon $Sport$, which becomes a natural choice for the context. In our experiments, we use training groups of $5$ students and dorms with $25$ students each.

\vspace{0.5ex}
\noindent {\bf Young and Old: } This domain is modeled as an MLN and is an extension of the Friends and Smokers (FS) \cite{singla&domingos08} network. $Y\&O$ has a propositional variable $IsYoung$ determining whether we are dealing with a population of youngsters or older folks. For every person $X$ in the domain, we have predicates $Smokes(X)$, $Cancer(X)$ and $EatsOut(X)$. We also have the predicate $Friends(X,Y)$ for every pair of persons. We have rules stating that young persons are more likely to smoke and older people are less likely to smoke. Similarly, we have rules stating that young people are more likely to eat out and old people are less likely to eat out. When the population is young, everyone has the same weight for the smoking rule and slightly different weight (sampled from a Gaussian) for eating out. When the population is old, everyone has a slightly different weight (again sampled from a Gaussian) for smoking and the same weight for eating out. As in the original FS, we have rules stating smoking causes cancer and friends have similar smoking habits. We also have rules stating that cancer and friends variables have low prior probabilities. In this domain, smoking, cancer and friends variables are symmetric to each other when population is young, whereas all eating out variables are symmetric when the population is old. Clearly, $IsYoung$ is a natural choice for context in this domain.

\vspace{0.5ex}

An important property of both these domains is that different contextual symmetries exist for {\em both} assignments of the respective context variables. To test the robustness of {\sc Con-MCMC}\ we further modify these domains so that contextual symmetries exist only on {\em one} of the two assignments of context variable. In $Y\&O$ (Single), we give (slightly) different weights to $EatsOut(X)$ variables when $IsYoung$ is false, i.e., symmetries exist only when $IsYoung$ is true. In Sports Network (Single), $S_X$ variables involved in a training group are symmetric only for tennis; for badminton, each $S_X$  in a group behaves (slightly) differently. We refer to these two variations as the {\it Single} side versions of the original domains.

For these four domains, we plot run time {\em vs.} the KL-divergence between approximate marginal probabilities computed by each algorithm and the true marginals.\footnote{computed by running a Gibbs sampler for sufficiently long time.} For both Orbital MCMC and {\sc Con-MCMC}, the time to compute symmetries is included in the run time. For each problem we run 20 iterations of each algorithm and take the mean of the marginals to reduce variance of the measurements. We also plot the 95\% confidence intervals. We show {\sc Con-MCMC}\ results for $\alpha=0$ and $0.01$, which was chosen based on performance on smaller problem sizes. We perform various control experiments by varying the size of domains, amount of available evidence, marginal posterior probability of the context variable and the value of $\alpha$ parameter. All the experiments are run on a quad-core Intel i-7 processor.

\subsection{Results}
\label{sec:results}
Figures \ref{fig:results} and \ref{fig:results_posterior} show the representative graphs across multiple domains and varying experimental conditions. We find that {\sc Con-MCMC}(0.01) almost always performs the best or at par with the best of other three algorithms. {\sc Con-MCMC}(0) usually performs better than Gibbs and Orbital MCMC, but its performance can be closer to Gibbs or {\sc Con-MCMC}($\alpha$) depending upon the experimental setting. Orbital MCMC does not usually offer much advantage over Gibbs, primarily because these domains don't have many orbital symmetries. For Sports Network, there are no orbital symmetries at all; Orbital MCMC avoids the overhead of the orbital move and performs at par with Gibbs. For $Y\&O$ Orbital MCMC finds a few symmetries, which don't particularly help in reducing mixing time. However, it still incurs the overhead of orbital moves, leading to a significantly worse performance compared to Gibbs.

\vspace{1ex}
\noindent{\bf Variation with Domain Size: } Figure \ref{fig:results}(a) compares the algorithms as we increase the domain size for the Sports network from $50$ to $200$ students. The overall trends remain similar, i.e., {\sc Con-MCMC}\ algorithms outperform Gibbs and Orbital MCMC by huge margins. A closer look reveals that the y-axes are at different scales for the three curves -- the relative edge of {\sc Con-MCMC}\ algorithms increases substantially with larger domain sizes.

\vspace{1ex}
\noindent{\bf Variation with Amount of Evidence: } Figure \ref{fig:results}(c) compares the performance of the algorithms as we vary the amount of (random) evidence available from $0\%$ to $60\%$ in the $Y\&O$ domain on predicates other than $Friends(X,Y)$ using a domain size of $50$. As earlier, {\sc Con-MCMC}\ algorithms outperform others. We observe that the relative gain of {\sc Con-MCMC}\ algorithms with Orbital MCMC decreases with increasing evidence (for 30\% evidence Orbital MCMC overlaps with Gibbs, for 60\% evidence, Orbital MCMC overlaps with {\sc Con-MCMC}). We believe that this is due the fact that more evidence tends to disconnect the network introducing additional symmetries which can be exploited by Orbital MCMC. Nevertheless, {\sc Con-MCMC}\ algorithms
perform at least as well as Orbital MCMC for all values of evidence that we tested on.

\begin{figure*}
\framebox{
\subfigure[]{
{\includegraphics[width=0.24\textwidth]{Figures/9_Sports.png}}
{\includegraphics[width=0.24\textwidth]{Figures/33_Sports.png}}
{\includegraphics[width=0.24\textwidth]{Figures/59_Sports.png}}
{\includegraphics[width=0.23\textwidth]{Figures/91_Sports.png}}}}

\caption{ {\sc Con-MCMC}\ effectiveness increases in Single Side Symmetry cases as we increase the marginal of context variable to the side having symmetry from 0.09 to 0.91. {\sc Con-MCMC}(0.01) provides significant gains even at very low posterior values. {\sc Con-MCMC}(0) performance improves with increase in the marginal.
}
\label{fig:results_posterior}
\end{figure*}

\begin{figure}
\hspace{2mm}
\includegraphics[width=0.23\textwidth]{{Figures/sports_alpha.png}}\label{fig:alpha-sports}
\includegraphics[width=0.23\textwidth]{{Figures/yo_alpha.png}}
\label{fig:alpha-fs}
\vspace{-2ex}
\caption{$\alpha$=0.01 and $\alpha$=0.1 work best across both domains. Very high as well as very low values of $\alpha$ lead to poor performance.}\label{fig:alpha}
\end{figure}

\vspace{1ex}
\noindent{\bf Variation across Versions of a Domain: }
Figure~\ref{fig:results}(b) and \ref{fig:results}(d) show the plots for the {\it Single} side versions of Sports network and $Y\&O$, respectively. We observe a significant difference in the performance of the two {\sc Con-MCMC}\ algorithms. The reason is subtle. Since symmetries exist only on one side, that side mixes quickly for {\sc Con-MCMC}(0); however, the other side does not mix as well, because of lack of symmetries. {\sc Con-MCMC}($\alpha$) for $\alpha>0$ mitigates this by upsampling the flip of the context variable. This enables the rapid mixing on symmetry side to regularly influence the non-symmetry side (via Gibbs move), which leads to a faster mixing on that side too. Nevertheless, {\sc Con-MCMC}(0) is still able to outperform both Gibbs sampling as well as Orbital MCMC by exploiting the single sided symmetry. The posterior of symmetry side is 0.33 in Sports network (Figure~\ref{fig:results}(b)) and 0.37 in $Y\&O$ (Figure~\ref{fig:results}(d)).

We also observe in the first graph of Figure \ref{fig:results}(c), that {\sc Con-MCMC}(0) performs somewhat worse than {\sc Con-MCMC}(0.01). We believe that the reason for performance in this two-sided symmetry domain is similar to the single-sided case. In $Y\&O$, when $IsYoung=$true, substantial symmetries may exist due to smoking, cancer and friends variables. However, on the other side, the symmetries are far less (only for eating out variables). This implies that {\sc Con-MCMC}(0) will have much faster mixing on one side, but not on the other. On the other hand, {\sc Con-MCMC}($0.01$) will upsample context variable flips and allow the stronger symmetry side to influence the other. In general, {\sc Con-MCMC}($\alpha$) performance is highly robust to varieties of symmetric and asymmetric domains.

\vspace{1ex}
\noindent{\textbf{Variation with Posterior of Context Variable:}}
We investigate performance on Single-sided domains further by varying the posterior marginal probability of the context variable. Figure \ref{fig:results_posterior} shows the results for Sports network (Single) with marginal probability of $Sport=$ tennis varying from $0.09$ to $0.91$. Note that $Sport=$ tennis side is the side where symmetries exist.

The graphs show an interesting trend. Even for very low marginals, {\sc Con-MCMC}(0.01) is able to benefit from one sided symmetries. Since the marginal is low we expect any MCMC algorithm to spend most of its time on the non-symmetry side. However, {\sc Con-MCMC}(0.01) will still go back and forth several times between two sides; each flip to symmetry side and back will help in potentially reaching a different region of the state space leading to better mixing on the non-symmetry side.

Not surprisingly, {\sc Con-MCMC}(0) does not perform as well for low marginals -- it does not get to switch contexts as often, and ends up mixing slowly on the important, non symmetry side. As marginal of the context variable increases, the relative performance of {\sc Con-MCMC}(0) improves substantially. As marginal becomes high ($0.91$), both {\sc Con-MCMC}\ samplers end up sampling mostly on the symmetry side, and can reap benefits of symmetries similarly. We also conduct these experiments for the $Y\&O$ domain and  observe a very similar behavior.

\vspace{1ex}
\noindent
\textbf{Variation with $\alpha$ Parameter:} Figure \ref{fig:alpha} shows the performance of {\sc Con-MCMC}($\alpha$) for different values of $\alpha$ in the range 0.001 to 0.5 for both Sports network (single) and $Y\&O$ (single) domains. Our algorithm is fairly robust for values of $\alpha$ between $0.01$ and $0.1$. Its performance starts to degrade for very low as well as very high values of $\alpha$. For very low values of $\alpha$, algorithm's behavior approaches that of {\sc Con-MCMC}(0). For very high values of $\alpha$, the algorithm spends too much time flipping the context variable and not enough time exploring the state space, resulting in poor performance.

Overall, we conclude that {\sc Con-MCMC}(0.01) is robust to various experimental settings and obtains the best results significantly outperforming Orbital MCMC and Gibbs. This underscores the importance of our contextual symmetry framework for probabilistic inference.

\section{Discussion and Future Work}
While our work extends the capability of lifted inference to a wider range of settings, it also raises important questions. In many cases, the set $V$ of context variables is known from domain knowledge or domain description especially in relational models. An open question is how to automatically compute a good set $V$, since trying all possible sets can be prohibitive. We have designed a heuristic approach that greedily chooses the most useful context variable every iteration and adds it to the context set. It uses a few initial rounds of the color passing algorithm~\cite{kersting&al09} to approximate the amount of additional symmetry obtained by making a variable part of the context. More experiments are needed to assess the effectiveness of our approach.

Another important observation is that the set of contextual symmetries may not monotonically increase with increasing context size. This may happen if additional context variables break existing symmetries, since context variables are forced to undergo identity mapping. Then, how do we design algorithms so that their effectiveness monotonically increases with larger contexts in all cases? This is an important direction for future work.

Another question concerns the robustness of performance of symmetry-based inference algorithms. Over the course of our experiments, we tested our algorithms on several domain variations. While in most cases {\sc Con-MCMC}(0.01) and {\sc Con-MCMC}(0) performed much better than Gibbs, in rare cases, the performance was worse too. Further investigations revealed two main sources of lower performance.

The first and more prominent cause is the trade-off between mixing speed and sampling time. Because all symmetry-based algorithms run an expensive product replacement algorithm \cite{pak00} to sample from an orbit, next samples for {\sc Con-MCMC}\ (and Orbital MCMC) are generated much slower than Gibbs. In domains where symmetries are prevalent, this slower sampling is mitigated by rapid mixing, but in other domains, it could result in a worse performance. An intelligent wrapper that guesses whether to exploit symmetries or not in a given domain will be crucial for developing a robust inference algorithm. The second reason for lower performance is subtle. {\sc Con-MCMC}($\alpha$) is able to exploit contextual symmetries (even single-sided)  in a wide variety of settings, but in one situation it can lose to other algorithms. This happens when the context variable has a huge Markov blanket, so much so that one Gibbs move that flips the context variable becomes overbearingly costly. Since {\sc Con-MCMC}($\alpha$) upsamples flips of context variables, this can cause significant loss to overall performance, even though the mixing is much faster with respect to number of samples.

Another observation relates to the effect of evidence in a domain. Evidence can both help and hurt symmetries in an inference problem. In some cases, evidence can break existing symmetries and reduce the relative gain of symmetry-based algorithms. In other cases, evidence can break edges and create new symmetries and help them. While in our experiments, we didn't find {\sc Con-MCMC}(0.01) to be ever worse than Gibbs due to additional evidence, such pathological cases can be constructed.

It would be interesting to see how algorithms other than MCMC can benefit from our contextual symmetry framework. In the future, we would also like to explore approximate contextual symmetries that could make our contribution applicable to several other domains, where exact contextual symmetries cannot be found. We would also like to theoretically analyze the mixing time of {\sc Con-MCMC}.

\section{Related Work}
\label{sec:related}

Some papers have discussed methods for computing symmetries under a given evidence \cite{broeck&darwiche13,venugopal&gogate14,kopp&al15}. As discussed in Section \ref{subsec:compute}, the algorithm for computing contextual symmetries is closely related to computing evidence-based symmetries. The main difference is in the way we use these symmetries for downstream inference.

While our general notion of contextual symmetries is novel it has connections to a few recent works. The RockIt system \cite{noessner&al13} identifies contextual symmetries in a very special case in which the domain theory has a set of disjunctive clauses of a specific kind $g_i \vee c$ where each $g_i$ is a single literal (or its negation). For this setting, $c$ is a natural context and symmetries among $g_i$s can be exploited. RockIt does not provide any general notion beyond this special case. It constructs a reduced ILP for MAP inference instead of marginal inference, as in our case.

There is recent work on exploring connections between the concept of exchangeability of random variables and tractability of probabilistic inference \cite{niepert&broeck14}. Our contextual symmetries can be seen as a generalization of their conditional decomposability to conditional {\em partial} decomposability where the sufficient statistics are precisely the contextual orbits. Whereas Niepert and Van den Broeck \shortcite{niepert&broeck14} primarily focus on developing the theory for conditional decomposability, we propose and additionally connect this with the symmetries present in the structure of a graphical model. Further, unlike them we develop an algorithm to compute these conditional decompositions (contextual symmetries in our case) and show how they can be used in practice for efficient probabilistic inference.

As discussed in Section \ref{sec:intro}, our work builds upon the recent literature on lifted inference that pre-computes explicit domain symmetries using automorphism groups \cite{niepert12,bui&al13,broeck&niepert15} and exploits them for efficient inference. Our work is most closely related to Orbital MCMC \cite{niepert12}. Our experimental results shows the value of {\sc Con-MCMC}\ over Orbital MCMC that does not incorporate contextual symmetries.

Our contextual symmetries are also analogous to \emph{conditional symmetries} in constraint satisfaction problems (CSPs) \cite{gent2005-cp,walsh2006-cp,gent2007-cp}. CSP symmetries are called conditional if symmetry groups exist only in a sub-problem of the original CSP, i.e., in a CSP with one or more additional constraints. The CSP problem setting and their actual manifestation in algorithms are quite different from lifted inference, but their definition and use of conditional symmetries is in the same spirit as ours.

\section{Conclusions}
We present a novel framework for contextual symmetries in probabilistic graphical models. Contextual symmetries generalize and extend previous notions of orbital symmetry. Given any context, we can efficiently compute these symmetries by reducing it to the problem of colored graph isomorphism. While our framework is independent of any inference algorithm, we illustrate its applicability by proposing {\sc Con-MCMC}, an MCMC approach that exploits contextual symmetries. Our experiments on several domains validate the efficacy of {\sc Con-MCMC}, where it outperforms existing state-of-the-art techniques for symmetry-based MCMC by wide margins. Finally, we have released a reference implementation of {\sc Con-MCMC}\ for wider use by the research community.

\section*{Acknowledgements}
We are grateful to Mathias Niepert for sharing the code implementation of Orbital MCMC and for answering our queries on the code. We would also like to thank the anonymous reviewers for their comments and feedback. We thank Ritesh Noothigattu for discussions and comments on this research.
Ankit Anand is supported by  TCS Research  Scholars Program.  Mausam and Parag Singla are supported by Visvesvaraya faculty research awards by Govt. of India. Mausam is also supported by Google and Bloomberg research awards.

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Biografia
Alexandre Antigna nasce nel comune francese di Orléans dove si avvicina all'arte sotto la guida di un pittore locale, François Salmon. Ammesso all'École nationale supérieure des beaux-arts di Parigi nel 1839, studia come allievo prima da Sébastien Norblin per un anno e poi per sette anni da Hippolyte Delaroche.

Fino al 1845, la maggior parte delle sue opere sono ritratti oppure dipinti interamente focalizzati su temi religiosi. La svolta stilistica avviene in seguito al suo soggiorno nel quartiere povero di Île Saint-Louis a Parigi, che lo avvicina al tema della povertà e della sofferenza.

Proprio per questo motivo Alexandre Antigna è spesso definito dai critici "il pittore degli umili", come dimostrano le sue opere più famose: L'Éclair (Musée des Augustins, 1848), L'Incendie (Museo di Belle Arti Orleans, tra il 1850 ed il 1851) o La Halte forcée (Musée des Augustins di Tolosa, 1855).

Nel 1850, il suo dipinto Après le bain (o Les Baigneuses, Musée des beaux-arts d'Orléans, 1849) provoca una grande scandalo nella sua città natale.

Molto rapidamente classificato tra i realisti e in particolare vicino a Gustave Courbet, Antigna si distingue nonostante tutto dal maestro di Ornans per il sentimento poetico e religioso con cui permeava le sue opere.

Dal 1860, si distingue in particolare nei ritratti di donne aragonesi, paesaggi marini e molte scene bretoni.

I suoi soggetti affrontano anche temi come la discriminazione tra abitanti delle città e poveri abitanti del villaggio nel XIX secolo.

Nel 1861, riceve la Legion d'onore e nello stesso anno sposa Hélène-Marie Pettit, anch'essa pittrice, nipote di Ambroise Rendu. Dalla loro unione nasce un figlio, André-Marc Antigna, anch'egli pittore e miniaturista.

Il cognato di Alexandre Antigna, il critico d'arte Eugène Loudun, si occupò personalmente del catalogo della vendita che si svolse dopo la morte del pittore.

Una biografia dettagliata del pittore è stata scritta nel 2007 da Christian Jamet (Éditions Demeter). Una nuova edizione, ampliata e arricchita, è stata pubblicata nel 2017 (Corsaire Éditions).

Alexndre Antigna è sepolto nella divisione 21 al cimitero di Montmartre.

Opere pittoriche
 L'Éclair, (Parigi, Musée d'Orsay, 1848)
 La Veuve (titolo originale) o La Mort du Pauvre, (museo Charles de Bruyères, Remiremont, olio su tela, 130,5x196,5 cm, 1849)
 Après le Bain, (Museo di Belle Arti di Orléans, 1849)
 L'incendie, (Museo di Belle Arti di Orléans, 262x282 cm, olio su tela, 1850)
 La Fête Dieu, (Musée des Augustins, 1855)
 La Halte forcée, (Musée des Augustins, Tolosa, 1855)
 Jeune Breton endormi, (Museo di Belle Arti di Orléans, 1857)
 Pauvre femme, (Museo di Belle Arti di Orléans, 1857)
 La Visite du docteur, intérieur breton, (Museo Archeologico e Storico di Orleans, 1861)
 Marchand d'Images, (Museo di Belle Arti di Bordeaux, 1862)
 Miroir des bois, (museo delle belle arti di Bordeaux, 1864)
 Le Roi des moutards, (Museo di Belle Arti di Orléans, 1869)
 Aragonaises d'Anso, (Museo di Belle Arti di Orléans, 1872)
 Paysanne bretonne (Musée des Beaux-Arts)
 Jeune Fille au capuchon, (Museo di Belle Arti di Orléans)
 Paysage des environs de Rochefort, (museo Cahors Henri-Martin)
 Ritratto di Hilaire Svizzera, (museo Cahors Henri-Martin)
 La fileuse endormie, (Museo d'arte e di storia di Saint-Brieuc, inv. 126)

Galleria d'immagini

Note

Bibliografia
 Emmanuel Bénézit, Dizionario di pittori, scultori, designer e incisori di tutti i tempi e di tutti i paesi, articoli su Alexandre, Marie-Hélène e Marc Antigna, edizioni Gründ, Parigi, 1976.
 Catalogo della mostra Antigna al Musée des Beaux-Arts di Orléans, prefazione di David Ojalvo, 1978.
 Marie-Christine Delacroix, "Il centenario di Jean-Pierre-Alexandre Antigna", in Journal of the love lover, 1st décembre 1978 Dicembre 1978.
 Daniel Yonnet e André Cariou, "Alexandre Antigna, Il mercante d'immagini", in Le Finistère des Peintres, p. 44, Éditions Ouest-France, 1999.
 Christophe Rameix, L'École de Crozant - I pittori di Creuse e Gargilesse 1850-1950, p. 30, Lucien Souny Publishing, 1991-2002.
 Christian Jamet, Antigna o la passione degli umili, prefazione di Isabelle Klinka-Ballesteros, curatrice principale dei musei di Orléans, Les Éditions Demeter, 2007.
 Christian Jamet, Antigna o la passione degli umili, prefazione di Isabelle Klinka-Ballesteros, capo curatore dei musei di Orléans, nuova edizione arricchita 2017 Corsaire Éditions

Altri progetti

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