text:
Gaza Strip Israeli attacks News Report
PCHR: 47 Israeli airstrikes in past 24 hours killed 13, wounded 117 and destroyed 40 homes
From 10:00 on Tuesday, 15 July 2014 to 10:00 on Wednesday, 16 July 2014, 13 Palestinians, including 10 civilians, were killed. Additionally, 117 Palestinians, mostly civilians, were wounded – this number includes 33 children and 20 women. Israeli warplanes also targeted and destroyed 40 houses.The latest developments since the press release issued by PCHR yesterday noon have been as follows:
The Northern Gaza Strip:
Israeli warplanes launched 47 airstrikes targeting houses, agricultural plots and open areas. As a result of these attacks, 71 Palestinians, including 16 children and 16 women, were wounded. Israeli warplanes also attacked 13 houses, destroying 8 of them.
The most significant attacks were as follows:
– At approximately 19:30 on Tuesday, 15 July 2014, an Israeli drones fired a missile at the garden of a 3-storey house belonging to 'Omar Khalil 'Omar in al-Shaimaa' area in Beit Lahia. Twenty minutes later, an Israeli warplane lunched a missile at the garden, heavily damaging it.
– At approximately 20:35, Israeli warplanes bombarded and destroyed a 3-storey house belonging to Salah 'Awadh Rajab in Beit Lahia.
– At approximately 21:50, an Israeli drone fired a missile at a house belonging to 'Emad Dawas in al-Shaimaa' Street in Beit Lahia. Ten minutes later, an Israeli warplane launched a missile at the house and destroyed it.
– At approximately 00:20 on Wednesday, 16 July 2014, Israeli warplanes bombarded and destroyed a 4-storey house belonging to Ismail al-Ashqar, Member of the Palestinian Legislative Council, in Jabalya.
– At approximately 00:35, Israeli warplanes bombarded and destroyed a 4-storey house belonging to Mousa al-Hajj 'Ali in Jabalya.
– At approximately 00:45, Israeli warplanes bombarded and destroyed a 2-storey house belonging to Zaher Rajab Abu Nasser in Jabalya. A nearby meeting hall belonging to the Rawagh family was also destroyed.
– At approximately 01:00, an Israeli drone fired a missile at a 2-storey house belonging to Dawod Hammouda in Beit Lahia. As a result, the house was destroyed.
– At approximately 01:40, an Israeli drone fired a missile at a 5-storey house belonging to Fathi Hammad, former Interior Minister, in Beit Lahia.
– At approximately 02:10, an Israeli drone fired a missile at a house belonging to the Matar family in Jabalya.
– At approximately 03:45, Israeli warplanes bombarded and destroyed a house belonging to Jameela al-Shanti, Member of the Palestinian Legislative Council, in Jabalya.
– At approximately 04:20, Israeli warplanes bombarded and destroyed a 5-storey house belonging to sons of Ibrahim 'Abdul Fattah Kutkut in Jabalya.
– At approximately 09:30, Israeli warplanes bombarded and destroyed a house belonging to Khaled 'Ataya al-Kilani in al-Shaimaa' area in Beit Lahia.
Gaza City:
Israeli warplanes launched 23 airstrikes targeting houses of political and field leaders, governmental buildings, a mosque and a hospital. As a result of these attacks, a Palestinian civilian was killed and 12 others, including 4 children and 2 women, were wounded. Additionally, Israeli warplanes bombarded 18 houses, destroying 14 of them.
– At approximately 15:30 on Tuesday, 15 July 2014, Israeli drones fired 2 missiles at a 3-storey house belonging to Suleiman Mohammed al-Dahdouh, in which 30 people live, in al-Zaytoun neighborhood in the southeast of Gaza City. Soon after, an Israeli warplane launched a missile at the house destroying it.
– At approximately 16:10, Israeli warplanes launched 2 missiles at a house belonging to Ahmed Ahmed al-Ghoul, 28, in al-Shati refugee camp, west of Gaza City. The house was destroyed. Before the attack, Israeli forces phoned the family to evacuate the house.
– At approximately 18:15, Israeli drones fired 2 missiles at 4-storey house belonging to the heirs of Ghanem Hajjaj, in which 40 people live, in al-Shuja'iya neighborhood in the east of Gaza City.
– At approximately 18:20, an Israeli drone fired a missile at a 4-storey house belonging to Musbah Swailem Abu Ghanima in al-Shuja'iya neighborhood in the east of Gaza City. As a result, the third floor of the house was damaged.
– At approximately 18:30, an Israeli warplane fired a missile at Ismail Fattouh Ismail Fatouh, 24, while he was irrigating crops in his land in Al-Zaytoun neighborhood, southeast of Gaza City. He was seriously wounded. He died of his wound a few minutes following his evacuation to the hospital.
– Also at approximately 18:30, an Israeli drone fired a missile at 4-storey house belonging to Jamal Deeb Bakroun, in which 50 people live, in al-Shuja'iya neighborhood in the east of Gaza City. The fourth floor of the house was damaged.
– At approximately 20:00, Israeli drones fired 2 missiles at 4-storey house belonging to 'Atiya Ibrahim Abu Shari'a, in which 45 people live, in al-Sabra neighborhood in the south of Gaza City.
– At approximately 21:10, Israeli drones fired 2 missiles at a 5-storey house belonging to Yousef 'Abed al-Banna in al-Sabra neighborhood in the south of Gaza City. A few minutes later, an Israeli warplane launched a missile at the house destroying it.
– At approximately 21:30, Israeli warplanes launched 3 missiles at a 4-storey house belonging to Hani Ya'qob Halasa, in which 35 people live, in al-Shuja'iya neighborhood in the east of Gaza City. The house was destroyed.
– Between 22:00 on Tuesday until 08:15 on Wednesday, 16 July 2014, Israeli warplanes bombarded and destroyed 7 houses in Gaza City: a house belonging to Sami Hashem in Tal al-Hawa neighborhood; a house belonging to the heirs of Nabeel Shabet in al-Tuffah neighborhood; a house belonging to Mahmoud 'Atallah in al-Ghefari area; a house belonging to Mahmoud al-Zahhr, a leader of Hamas, in al-Sabra neighborhood; a house belonging to Na'im al-Harazinin al-Zaytoun neighborhood; a house belonging to Tayseer al-'Ashi in al-Remal neighborhood; and a house belonging to 'Adnan Killab in al-Shati refugee camp. Israeli warplanes bombarded also 2 flats in Tal al-Hawa neighborhood, a minaret of a mosque in al-Shati refugee camp, a building of the Ministry of Interior and al-Wafaa' Hospital, which Israeli forces ordered its evacuation.
On Friday evening and Saturday morning, Israeli gunboats and tanks fired dozens of shells at various areas in Gaza City, especially at the fishing harbor. A number of fishing boats were extensively damaged, one of which was totally burnt.
The Central Gaza Strip:
Israeli warplanes launched 10 airstrikes targeting houses, agricultural lands and open area. As a result of these attacks, a member of a Palestinian armed group was killed, and 17 Palestinians, including 4 children and a woman, were wounded. Five houses were also destroyed.
– At approximately 22:10 on Tuesday, 15 July 2014, an Israeli drone fired a missile at Khalil Ibrahim al-Sha'afi, 41, a member of a Palestinian armed group, when he was going to a mosque in Juhor al-Dik village.
– At approximately 02:00 on Wednesday, 16 July 2014, an Israeli drone fired a missile a 2-storey house belonging to Mohammed Deeeb Abu Nasser, in which 4 families live, in al-Zawaida village. A few minutes later, an Israeli warplane launched a missile at the house and destroyed it.
– At approximately 02:10, an Israeli drone fired a missile at a house belonging to Ahmed 'Abdullah Mishmesh in al-Zawaida village. A few minutes later, an Israeli warplane launched a missile at the house and destroyed it.
– At approximately 04:10, an Israeli drone fired a missile a house belonging to 'Ali 'Obaid Abu Gharqoud, in which 15 people live, in al-Zawaida village. A few minutes later, an Israeli warplane launched a missile at the house and destroyed it.
– At approximately 06:30, an Israeli drone fired a missile a 2-storey house belonging to Jamal Ahmed al-Asmar, in which 6 people live, in al-Nussairat refugee camp. A few minutes later, an Israeli warplane launched a missile at the house and destroyed it.
– At approximately 07:00, an Israeli drone fired a missile a 2-storey house belonging to Fathi Ibrahim 'Aabed, in which 18 people live, in Deir al-Balah. A few minutes later, an Israeli warplane launched a missile at the house and destroyed it.
Khan Yunis:
Israeli warplanes launched 19 airstrikes targeting houses, agricultural plots, open areas and security and police sites in the southern Gaza Strip town of Khan Yunis. Israeli tanks and gunboats also fired dozens of shells at agricultural and open areas. As a result, 4 Palestinian civilians were killed, and 9 others including 4 children, were wounded. Additionally, Israeli warplanes targeted 3 houses. A mosque was also damaged by an Israeli attack.
– At approximately 15:00 on Tuesday, 15 July 2014, an Israeli warplane launched a missile at a shed on an agricultural plot in the northwest of Khan Yunis. The shed was destroyed and Subhi 'Abdul Hamid Hussein Mousa, 78, was killed.
– Also at approximately 15:00, Israeli warplanes launched 5 airstrikes on agricultural plots and open areas in al-Qarara village and al-Satar al-Gharbi area in the northwest of Khan Yunis. No casualties were reported.
– At approximately 20:00, an Israeli drone fired 2 missiles at a uninhabited house belonging to Mohammed Nidal Abu Shab in Bani Suhaila village, east of Khan Yunis. Half an hour later, an Israeli warplane launched a missile at the house. At approximately 22:00, an Israeli warplane launched a missile at the house and destroyed it. A nearby mosque and 2 houses were damaged and 3 Palestinian civilians were wounded.
– At approximately 01:00 on Wednesday, 16 July 2014, an Israeli drone fired a missile at the vicinity of 'Asqalan School in al-Fakhari area in the southeast of Khan Yunis. As a result, Fareed Mahmoud Abu Daqqa, 33, was killed when he was near his house in the area. His body was found at approximately 07:00.
– At approximately 03:00, an Israeli drone fired a missile at Mohammed Tayseer Yousef Shurrab, 23, when he was on his way back home in Gizan Abu Rashwan area in the southeast of Khan Yunis. He was instantly killed.
– At approximately 03:10, an Israeli drone fired a missile at a house belonging to Mohammed 'Abdullah Salam al-'Arjani, in which 20 people live, in Gizan Abu Rashwan area in the southwest of Khan Yunis, without a prior warning. As a result, al-'Arjani's son, 19-year-old 'Abdullah, was killed, and his father, his 4 children and his grandchild were wounded.
– At approximately 06:40, Israeli drones fired 2 missiles at a house belonging to Muneer Abu Hatab in Khan Yunis refugee camp. The house was damaged.
Israeli warplanes launched 26 airstrikes targeting houses, agricultural lands, open areas and members of Palestinian armed groups. As a result, 7 Palestinians, including 5 civilians, were killed, and 8 others, including 5 children, were wounded. Two houses were also destroyed.
– At approximately 22:50 on Tuesday, 15 July 2014, an Israeli drones fired a missile at a taxi in which 6 Palestinians were traveling near Martyr Abu Yousef al-Najjar Hospital in al-Junaina neighborhood in Rafah. As a result, two of thes Palestinians were instantly killed: Mousa Sa'id Dahliz, 30; and Yasser 'Ali al-Mahmoum, 18. The other 4 ones were wounded, one of whom, Ahmed 'Aadel al-Nawajha, 23, the taxi driver, died of his wound 4 hours later.
– At approximately 02:20 on Wednesday, 16 July 2014, an Israeli drone fired a missile at members of a Palestinian armed group in the Swedish Village in the southwest of Rafah. Two members were instantly killed: Mohammed 'Abdullah al-Zahouq, 25; and Mohammed Ismail Abu Ouda, 28. A third one was also wounded.
– At approximately 02:35, an Israeli drone fired a missile at Mohammed Sabri al-Dibari, 21, when he was near his house in al-Shouka village, southeast of Rafah. He was instantly killed.
– At approximately 06:40, an Israeli drone fired a missile at Ashraf Fares Abu Shanab, 26, when he was working on an agricultural plot in the east of Rafah. He was instantly killed.
– At approximately 07:10, Israeli drones fired 3 missiles at a house belonging to Mohammed Mahmoud al-Qadhi, in which 12 people live, in al-Siamat area in the north of Rafah. Soon after, an Israeli warplane launched a missile at the house and destroyed it.
– At approximately 08:05, Israeli drones fired 3 missiles at a 2-storey house belonging to Subhi Dawod Abu Sha'ar, in which 30 people live, in al-Shaboura refugee camp in Rafah. A few minutes later, an Israeli warplane launched 2 missiles at the house and destroyed it.
PCHR reiterates condemnation, expresses utmost concern for these crimes, and:
1. Warns of deterioration of the humanitarian situation in the Gaza Strip in light of this continuous Israeli military escalation, threats to expand military operations, and the continued tightened closure of the Gaza Strip;
2. Calls upon the international community to act immediately to stop these crimes, and renews the call to the High Contracting Parties of the Fourth Geneva Convention to fulfill their obligation under Article 1 of the Convention to ensure that it is respected at all times, and their responsibilities under Article 146 to pursue perpetrators of serious violations of the Convention, which are determined in Article 147, which lists violations of the Convention amounting to war crimes; and
3. Calls for establishing a UN fact-finding mission to investigate suspected war crimes committed by Israeli forces against Palestinian civilians in the Gaza Strip, and take necessary steps to prosecute responsible for them.
Israeli Drone Kills Three Family Members In Khan Younis, Five Injured
Israeli Naval Ships Attack Children on Gaza Beach, Killing Four


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Leuggelbach railway station is a railway station in the municipality of Glarus Süd in the Swiss canton of Glarus. It takes its name from the nearby village of Leuggelbach. The station is situated on the Weesen to Linthal railway line, and served by the hourly Zürich S-Bahn service S25 between Zurich and Linthal.

References

Railway stations in the canton of Glarus
Swiss Federal Railways stations

redpajama_set_name: RedPajamaWikipedia


text:
Laos Dam Collapse Blamed on Substandard Construction
Poor construction methods, with soil used in place of concrete, are now being blamed for a fatal hydropower dam collapse last year in Laos in what has been called the country's worst flooding in decades.
The disaster occurred on July 23, 2018 when a saddle dam at the Xe Pian Xe Namnoy (PNPC) hydropower project collapsed following heavy rains, inundating 12 villages and killing at least 40 people in Champassak and Attapeu provinces, leaving many more missing.
A report sent to the Lao government in March, but still not released to the public, reveals that "construction of the saddle dam was substandard," a PNPC official told RFA's Lao Service this week.
"It was built with soil," the official said, speaking on condition of anonymity. "That was the cause of the collapse. It couldn't handle that massive amount of water."
A new saddle dam, saddle dam D, is now under construction at a location a little more than a kilometer away from the dam that failed, the official said, adding that the new 400-meter-long structure will be built with concrete and anchored at a depth of at least 10 meters into the ground.
The team investigating the cause of the July 2018 disaster has recommended that all other saddle dams at the hydropower site also be built with concrete, he said.
Talks with South Korea
Also speaking to RFA, Singphet Bounsavattiphanh-vice chairman of the Lao government inspection agency-confirmed that the government had received the report and its recommendations in March.
"But they cannot publish it right now because they are in the process of negotiating with the South Korean government about what information should or should not be released to the public," he said.
PNPC is a consortium formed by a local Lao company and South Korea's SK Engineering & Construction, and Korean involvement in the project had earlier prompted Seoul to send relief teams to Laos to help mitigate the effects of the disaster.
The Lao government is expected to officially publish the investigation's results when talks with South Korea are concluded, Singphet said.
All findings of the report should be released as quickly as possible, though, Premredee Daohuang of the Thailand-based NGO Laos Dam Investigation Monitor said, also speaking to RFA.
"This is so the public can verify the information and raise questions," he said, adding, "This information shouldn't be known only to the Lao and South Korean governments."
In the wake of the Xe Pian Xe Namnoy disaster, Laos has stepped up scrutiny of an ambitious hydropower dam building program under which it aims to serve as the "battery of Asia" and sell hydropower to its more industrialized neighbors China, Thailand and others.
Reported and translated by Max Avary for RFA's Lao Service. Written in English by Richard Finney.
Copyright © 1998-2018, RFA. Published with the permission of Radio Free Asia, 2025 M St. NW, Suite 300, Washington DC 20036

redpajama_set_name: RedPajamaCommonCrawl


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Elise Vehicles
Elise Menu
Elise SC Hertz (2010-)
2010 Lotus Elise SC Hertz
Elise Club Racer (2010-)
2010 Lotus Elise Club Racer
Supercharged Elise SC (2008-)
2008 Lotus Supercharged Elise SC
Elise S2 S (2006-2006)
2006 Lotus Elise S
Elise S2 Sportsracer (2005-2005)
2005 Lotus Elise Sports Racer
Original Price: $31,995
Elise S2 111R (2004-2004)
2004 Lotus Elise S2 111R
Motorsport Elise (2001-2001)
2001 Lotus Motorsport Elise
Elise S1 111S (1999-2000)
2000 Lotus Elise 111S
Elise S1 (1996-2000)
Average Auction Sale: $21,188
Median Auction Sale: $21,188
Elise (1995-)
2020 Lotus Elise Cup 250 Bathurst Edition
2020 Lotus Elise Classic Heritage Edition
Produced: 100
2017 Lotus Elise Sprint 220
2017 Lotus Elise Cup 250
Produced: 30
2016 Lotus Elise Race 250
2016 Lotus Elise 250 Special Edition
2014 Lotus Elise S Cup R
2008 Lotus Elise SC Clark Type 25
2008 Lotus Eco Elise
2007 Lotus Elise Type 72D
Lotus, manufacturer of some of the world's greatest sports cars, has unveiled its highest-performance Elise model yet, the 1.8 litre 111R, equipped with a high-tech engine that allows it to sprint 0-60mph in a supercar-thrashing 4.9 seconds. Top speed is a certified 150mph.
The hand-assembled Elise 111R is the latest result of Lotus' work to offer a combination of award-winning design, power and accessibility for those looking to own a higher performance Lotus Elise as their everyday car.
In town, the new 111R is compact and powerful enough to dart in and out of traffic, whilst the soft-top and Blaupunkt sound system make it perfect for those hood down, music up cruises through the city. Out of town the 111R's race-bred pedigree comes into its own, with a steering and suspension set up that allows the driver to hug corners before punching out on to the straight.
To balance out the extra power under the bonnet, Lotus has developed an improved braking system. For the first time, track-tuned servo-assisted ABS brakes come as standard on a Lotus Elise, to make stopping the 111R as easy as accelerating.
Ansar Ali, general manager, Lotus Cars Ltd, said: 'The 111R is a car for those who demand the style and innovation of the Elise but want increased performance. Without doubt, the new engine and set-up deliver unrivalled handling and power in its class. With the 111R we hope we've delivered our most exciting, truest and addictive drive yet.'
As standard, the 111R comes with eight spoke alloys, half leather interior and central locking. Buyers can opt for the Touring Pack that includes a sound and thermal insulated soft-top, full leather trim and a DAB radio. Other options include air conditioning and hard top.
The 111R will go on sale on 26 January 2004 at an RSP of £27,995.
The Lotus Elise is a true sportscar that has taken the world by storm, winning countless awards for handling, innovation and just pure fun. The Elise was first unveiled at the Frankfurt Motorshow in 1995 before entering production with first deliveries in August 1996. Since then, over 17,000 Elises have been built – some achievement for a car that was originally designed to be built in volumes of only 700 a year! The Elise was designed as a sportscar to be appreciated by real driving enthusiasts, fashion leaders and those who really appreciate technology and innovation.
The Lotus Elise introduced a range of technologies that revolutionised the automotive industry; such as a chassis made from extruded and bonded aluminium, a composite energy absorbing front crash structure and light weight composite body panels. The whole car weighed in at half the weight of an average family saloon. This light weight bestowed the car with phenomenal acceleration and handling. In 1996 the Lotus Elise was easily pulling 1g in steady state cornering with standard production tyres and a 0-100km/h (0-62mph) in 5.9 seconds.
In 2000 Lotus introduced the second generation Elise. This evolutionary car, arguably one of the most important cars in Lotus' fifty-two year history, added to the technology introduced on the Elise in 1996. It was a big stride forward, achieving the quality standards expected of a world leading sportscar manufacturer and globally respected engineering consultancy. This Elise introduced industry standard quality, much of it based upon the learning gained from working with Lotus' global motor industry partners.
All Lotus Elises are hand assembled by skilled craftsmen at Lotus' headquarters in Hethel, England. Each Elise takes about 100 man-hours to build and the final product is fine testament to the skills of Lotus.
As soon as a driver sits behind the wheel of a Lotus, they instantly know that they are in something special. From the composite sports seats that hug the driver under the g-forces that are experienced on cornering, acceleration and braking, to the race designed steering wheel and the extruded aluminium pedals perfectly suited to both cruising as well as hard driving - the Elise is a car that invites to be driven.
The twin instrumentation dials show road speed and engine speed (for the 111R, now showing to 10,000rpm) and are updated for 2004 across the whole of the Elise range, with clearer graphics and orange back lighting which is proven to be easier on the eye. Links between the Elise and the track have always been strong, and the ambience of the facia and trim with the chassis tub sides provoke a strong sense of being seated in a racing derived but comfortable cockpit.
A four speaker Blaupunkt stereo system with CD player is provided as standard along with a radio receiver wiring loom including dipole aerial kit located in the front of the Elise 111R.
The legendary chassis…
During the early days of the original Elise development programme, Lotus searched for an appropriate and available chassis technology for its new lightweight sportscar. Unable to find a suitable technology, and unwilling to compromise, Lotus set out to change the rules. Lotus engineers looked outside the automotive industry and brought together aluminium extrusions and modern aerospace bonding techniques to produce a lightweight and exceptionally rigid structure.
The ground-breaking epoxy-bonded aluminium tub chassis, unveiled in September 1995 represented a breakthrough in sportscar technology.
The structure is an assembly of individually extruded lengths bonded together by epoxy resin adhesive, a world first in automobile manufacture. The adhesive used to bond the Lotus chassis achieves exceptional strength with the ability to absorb the most extreme loads, pressures and forces that it may encounter. Never before had a modern vehicle's chassis been bonded together.
The bonding of lap joints provides a superior joint to traditionally welded butted joints (with bonded joints, there is no distortion of the material's integrity at the join). Self-pierce rivets further increase the structural integrity through reducing material 'peel' in the most severe of impacts.
The chassis received modifications in 2000, including lower, reinforced longitudinal sills to improve the access into the cockpit.
Now with the introduction of the VVTL-i power unit, further enhancements have been made to the rear of the chassis structure. Utilising experience gained from the development of advanced lightweight steel, a new highly efficient rear subframe offers increased strength. In keeping with Lotus' philosophy, this structure is an elegant integrated single solution for the engine cradle and improved suspension and exhaust silencer mounting points.
Ride and handling that sets the benchmark…
The aluminium chassis allows vehicle dynamics engineers at Lotus to continue to set standards by which all other sportscars are judged. Indeed, the Elise continues to build on the multi-award winning ride and handling for which it has become renowned the world over.
Lotus has taken a no-compromise approach in carrying over these philosophies to the Elise 111R. The development team has succeeded in creating a car that leaves the driver craving more time in the cockpit and more road on which to enjoy the thrill and engagement of each journey.
Run in parallel to Lotus' USA (Federal) Elise programme, the 111R faced a gruelling development programme exceeding 500,000 miles throughout 2003 that took the car across Europe and the USA. This has resulted in an exciting and progressive ride and handling package that integrates the constituents that make up the dynamics characteristics, tuning them to work in harmony with each other, the driver and the road.
For the Elise 111R, the Eibach coaxial coil springs and Bilstein high pressure monotube gas dampers have been retuned and optimised to maintain the Elise's trademark agility, body control and poise while improving the isolation of both smaller and larger impacts.
The unique Bridgestone Potenza RE040 tyres (175/55R16 front and 225/45R17 rear) have been carried over from the Lotus Elise and the Elise 111S. The Lotus Ride and Handling team have maximised the ability to hone the chassis and tyre characteristics to ensure that this latest and highest performing version of the Elise holds true to Lotus' values of peerless ride and handling and pure driving fun.
An ABS system like no other…
The servo-assisted four-channel system individually monitors and distributes braking force to each wheel as required, enhancing braking performance and minimising stopping distance.
However, Lotus has specifically tuned the initiation point to allow a skilled driver to maximise the potential of the braking system through the utilisation of forward weight transfer. In the event of the driver demanding more braking performance than is possible, only then does the system intervene to optimise the force generated at the wheel.
Power-to-weight in abundance…
Lotus undertook a thorough and exhaustive evaluation of a wide range of state-of-the-art engines. Toyota's 2ZZ-GE 1.8 litre 4 cylinder 16-valve VVTL-i engine and C64 six-speed gearbox was chosen as an outstanding package, excellently suited to the Elise.
This engine has breath taking power and torque characteristics, and critically for a Lotus, is lightweight, featuring a compact metal matrix composite alloy cylinder block.
A bespoke exhaust system has been developed for the Elise 111R with the twin exhaust pipes exiting through the rear diffuser.
Lotus subjected the 2ZZ-GE to a rigorous testing and development programme covering a wide range of extreme climate conditions from the Arctic Circle to the Arizona and Nevada deserts, and at altitude in Colorado. Furthermore, the engine management system, bifurcated exhaust downpipe, and bespoke gearshift mechanism are designed and developed by Lotus, resulting in a power unit perfectly integrated with the Elise's chassis and dynamics.
Lotus has tuned the engine to suit the very essence of the Elise by employing a brand new, custom-engineered Lotus T4 engine management system (EMS). The software for the EMS was designed and developed by Lotus specifically for the Elise 111R. All calibration and validation work was undertaken solely by Lotus engineers, ensuring that the Elise performs as a true Lotus should.
Toyota's world-renowned VVTL-i system allows the engine management system the flexibility to select the optimum camshaft profile, lift and timing across the full range of engine operating conditions. This interaction between the Lotus T4 EMS and the VVTL-i system gives the Elise its optimum linear torque characteristics, peaking at 181Nm (133.5 lb.ft) @ 6800rpm coupled with the peak power of 192 PS (189hp, 141kW) at 7800rpm.
The all-aluminium lightweight Toyota C64 six-speed gearbox is fitted with an all-new Lotus designed and developed shift operating mechanism. With the closest ratios and gearset afforded by the transmission, the gearbox offers a fast, precise and light gearshift, ensuring drivers have total control and flexibility to apply the power exactly as and when required.
True to Colin Chapman's philosophy of performance through lightweight, the power density available from the Toyota power unit gives the Elise a staggering 223PS/tonne (220hp/tonne, 164kW/tonne) and a 0-100km/h sprint in 5.2 seconds (0-60mph in 4.9 seconds)!
Proof, if needed, that there actually is a substitute for 'cubic inches'!
Standard equipment for the Elise 111R includes: half leather interior, sun visors, central door locking, Blaupunkt Lausanne radio CD-R/W player and Blaupunkt high performance front and rear speakers
Optional equipment includes a Touring Pack, which provides a combination of options designed to increase comfort and convenience, while still maintaining the essence of a Lotus sports car. This pack includes:
Auxiliary front driving lights, a choice of either full leather or Alcantara trim, a soft-top with sound and thermal insulation, electric windows, an upgraded Blaupunkt Woodstock DAB radio, CD-R/W and MP3 player, interior stowage net, sound insulation, and full carpet with a lightweight aluminium passenger footrest.
Other options also include metallic paint, air-conditioning and a body coloured hard top.
Source - Lotus
Model Production *
* Please note, dates are approximate
Related Articles and History
Lotus Models
18 FJ
51 and 51A
Elite Type 14 Coupé
Elite Types 75 and 83
Mark VI


Size: 84cm main chain; 41cm side chain; 7.5cm tassels; 9cm by 5.5cm extended textured bars. Textured designed metal bars separated by gold colored beads. two long side chains with detailed metal tassels. Lobster claw clasp makes chain adjustable.


text:
open standards
Dell EMC to Join Open Source OpenSDS Project to Advance Storage Interoperability, Contribute Code
Press Release | The Linux Foundation | December 19, 2016
The Linux Foundation, the nonprofit advancing professional open source management for mass collaboration, today welcomed Dell EMC to the OpenSDS Project. The OpenSDS community is forming to address software-defined storage integration challenges with the goal of driving enterprise adoption of open standards. As part of its support for the open source project, Dell EMC is also contributing its first project to OpenSDS, the CoprHD SouthBound SDK (SB SDK), to help promote storage interoperability and compatibility...
Dutch Parliament: Vendor Dependence Too High a Cost
By Gijs Hillenius | April 25, 2015
The Dutch government's lack of vendor independence is too high a cost for society, the Dutch Parliament concludes. The government should enforce its policy on open standards in ICT procurement and should also devise exit strategies - to reduce its dependence on ICT suppliers. This week Tuesday, the parliament adopted a resolution criticizing the government for having no open source ambition. The resolution was adopted with 136 votes in favour and 14 against. The parliament calls upon the government to make sure that in any new ICT project, the specifications give open source a fair chance. When proprietary software is selected, this needs to be explained, the parliament stipulates. "(the) dependence on a limited number of large software vendors (is) too strong", the resolutions says, adding that this can lead to software costs that are too high for society.
Eclipse Backs Open Source For Internet Of Things
Darryl K. Taft | TechWeek Europe | January 23, 2014
The Eclipse Foundation is seeking to create a strong open-source developer community that is focused on the Internet of Things. Read More »
Eclipse Updates Four Key IoT Projects, Launches a New One
Darryl K. Taft | eWeek | June 16, 2016
The Eclipse Foundation announced new releases of four open-source IoT projects to accelerate IoT solution development. The Eclipse Foundation, which has been leading an effort to develop open-source technologies for Internet of things application development, announced that the Eclipse Internet of Things (IoT) Working Group has delivered new releases of four open-source IoT projects the group initiated over a year ago. The four projects, hosted at the Eclipse Foundation, are Eclipse Kura 2.0, Eclipse Paho 1.2, Eclipse SmartHome 0.8 and Eclipse OM2M 1.0. These projects are helping developers rapidly create new IoT solutions based on open source and open standards...
EHI Live Interview: Liam Maxwell
Rebecca Todd | eHealth Insider | October 26, 2012
Deputy government chief information officer Liam Maxwell wants to see large IT contracts disaggregated so more small and medium-sized enterprises can compete in the NHS IT market. Rebecca Todd reports. Read More »
EHI Live UK Conference Hosts State–of-the-Art Open Source Health IT Solutions
Press Release | EHI Live | October 20, 2015
EHI live, now in its 8th year, is the UK's leading exhibition for digital health, hospital information and healthcare innovation. The event attracts visitors and delegates from around the UK and beyond who are keen to learn from industry leaders and examine new technologies. The EHI Live exhibition gives visitors the chance to see the best that NHS IT suppliers have to offer. EHI Live will take place in Birmingham, UK, Nov 3-4, in Hall 1 at the National Exhibition Centre, Birmingham. The event will host more than 250 exhibitors showcasing the latest advances in IT healthcare solutions. It will also feature free-to-attend conferences that will address the major healthcare IT industry issues such...[including] the annual HANDI Health Apps conference which features its own specialist app zone, a feature dedicated to the use of open source technology.
European Parliament To Weigh Open Source Pilots
Gijs Hillenius | JoinUp | June 18, 2014
Next Monday, the European Parliament's budget committee will consider a proposal from the Green/EFA group to pilot the use of open source encryption software, to be used by parliament members and their staff. The Green/EFA group is also asking to trial the use of open standards and open source to make available the EP's data available in machine-readable format...
European Union's 5-year Roadmap for IT and Open Source
By Paul Brownell | June 16, 2015
After months of preparation, the European Commission (EC) released its broad 5-year roadmap in early May for information and communications technology (ICT) policy, the Digital Single Market Strategy, or DSM. The plan is structured around three main pillars or goals, which include...
Free as in Bach: Open Goldberg Variations Released
Robert Douglass | OpenSource.com | June 11, 2012
The Kickstarter funded collaboration between Kimiko Ishizaka and MuseScore has released their new recording and score of Bach's Goldberg Variations into the public domain using the Creative Commons Zero (CC0) licensing tool. This is just one of the ways in which Kickstarter...is revolutionizing the business of music.
Govt Takes Forward Open Standards Plans
Lyn Whitfield | E-Health Insider | February 14, 2012
The Cabinet Office has launched a consultation on open standards for government IT. Read More »
Grahame Grieve on What Project Argonaut Means for the HL7/FHIR Community
By Grahame Grieve | December 11, 2014
Project Argonaut was announced last week. You can see the announcement here. That press release was intended for an external community, and didn't address lots of important questions for the HL7 community itself. So here's an outline of what project Argonaut means in practice for HL7.
Grahame Grieve's FHIR report from Baltimore HL7 Meeting
By Grahame Grieve | October 4, 2016
Last week, HL7 held it's annual plenary meeting in Baltimore at the Hyatt Regency...For the FHIR project, our main attention was the ballot. Across the core standard, and multiple implementation guides, we received >800 detailed comments as part of the ballot. This represents a slight increase over the last ballot, but there was a clear change in the focus of the comments – there was a significant drop in the number of comments relating to the infrastructure, and much more focus on the domain content, and it's applicability to real world problems. This is a clear marker of the growing maturity of the standard. We continue to expect that we'll publish FHIR release 3 at the end of this year.
Grand Opening: Federal Cloud Innovation Center
Anthony Brino | Government Health IT | October 23, 2013
As more state and federal government agencies try to catch up with the private sector in using cloud-based IT, IBM is giving them a lift. Read More »
Greek Government Moving to Open Source, Open Data
By Gijs Hillenius | August 18, 2015
The Greek government wants the country's public administrations to transition to free and open source software, open standards and open data. The Ministry of Economy, Infrastructure, Marine and Tourism has asked the Greek free and open source software society (Gfoss) to help organize workshops and conferences, train public administrations and propose research and development projects. The objective of the transition to open technologies is to strengthen Greece's economy.
Growth Of SMART Health Care Apps May Be Slow, But Inevitable
Andy Oram | O'Reilly Radar | September 13, 2012
This week has been teaming with health care conferences, particularly in Boston, and was declared by President Obama to be National Health IT Week as well. I chose to spend my time at the second ITdotHealth conference, where I enjoyed many intense conversations with some of the leaders in the health care field [...]. Read More »


While it is always wise to first seek out local organizations that can inform your congregation about environmental injustices that are near or far away, there are a host of websites that provide information that could be relevant to your community and state. When it comes to matters such as air and water pollution or access to affordable, healthy food, always seek to keep track of who suffers the most in terms of race and class. For example, studies show that black people are more likely to breathe in higher levels of air pollution than whites. They are also more likely to live within 30 miles of a coal plant, the high exposure zone for the pollutants that cause afflictions ranging from birth defects to heart disease.
You can insert your address or zip code into this map and learn about both dirty and clean facilities in your area. Facilities categorized as coal, nuclear, biomass, trash, hydro, geothermal, wind, solar, and more can all be found here. Moreover, you can add layers to the map that show you the racial demographics and income levels of your community and the surrounding areas.
The US Environmental Protection Agency provides this interactive program that allows you to enter your geographical location to access data about toxic releases, air quality, water quality, state energy sources, cancer risk, and more.
The US National Library of Medicine provides this research tool for locating "superfund" sites of hazardous waste cleanup, reported toxic chemical releases, and various waste management activities.
This map program can tell you about oil and gas drilling in your state along with related earthquake activities.
Earth Justice created this interactive map that details reports of poisoned drinking water, polluted air, industrial disasters, and more that are related to oil and gas drilling.
Food and Water Watch created this map which shows where factor farms are located. These are farms that confine thousands of cows, hogs, and chickens in tightly packed facilities. These farms generate air and water pollutants that pose health hazards to workers and neighboring communities.
While this article reports on the lack of data on lead poisoning and the problems with much of the data that exists, it also provides maps and information about the data that does exist.


text:
class SunspearClient(object):
    """
    The class is used to create, delete, remove and update activity stream items.
    This is the main class you use to interact with ``sunspear``
    """
    def __init__(self, backend, **kwargs):
        self._backend = backend

    def clear_all(self):
        """
        Deletes all activity stream data
        """
        self._backend.clear_all()

    def clear_all_objects(self):
        """
        Deletes all objects data
        """
        self._backend.clear_all_objects()

    def clear_all_activities(self):
        """
        Deletes all activities data
        """
        self._backend.clear_all_activities()

    def create_object(self, object_dict):
        """
        Creates an object that can be used as part of an activity. If you specific and object with an id
        that already exists, that object is overidden.

        :type object_dict: dict
        :param object_dict: a dictionary representing the object we want to store in the backend.
        """

        return self._backend.create_obj(object_dict)

    def create_activity(self, actstream_dict):
        """
        Creates an activity. You can provide objects for activities as dictionaries or as ids for already
        existing objects.

        If you provide a dictionary for an object, it is saved as a new object. If you provide
        an object id and the object does not exist, it is saved anyway, and returned as an empty dictionary when
        retriving the activity.

        :type actstream_dict: dict
        :param actstream_dict: a dictionary representing the ``activity`` we want to store in the backend.
        """

        return self._backend.create_activity(actstream_dict)

    def create_reply(self, activity, actor, content, extra={}, **kwargs):
        """
        Creates a ``reply`` for an activity.

        :type activity: a string or dict
        :param activity: the activity we want to create the sub-item for
        :type actor: a string or dict
        :param actor: the ``object`` creating the sub-activity
        :type content: a string or dict
        :param content: a string or an ``object`` representing the content of the sub-activity
        :type extra: dict
        :param extra: additional data the is to be included as part of the ``sub-activity`` activity
        """
        return self._backend.create_sub_activity(activity, actor, content,\
            extra=extra, sub_activity_verb="reply", **kwargs)

    def create_like(self, activity, actor, content="", extra={}, **kwargs):
        """
        Creates a ``like`` for an activity.

        :type activity: a string or dict
        :param activity: the activity we want to create the sub-item for
        :type actor: a string or dict
        :param actor: the ``object`` creating the sub-activity
        :type content: a string or dict
        :param content: a string or an ``object`` representing the content of the sub-activity
        :type extra: dict
        :param extra: additional data the is to be included as part of the ``sub-activity`` activity
        """
        return self._backend.create_sub_activity(activity, actor, content,\
            extra=extra, sub_activity_verb="like", **kwargs)

    def delete_activity(self, activity_id, **kwargs):
        """
        Deletes an activity item and all associated sub items

        :type activity_id: string
        :param activity_id: The id of the activity we want to create a reply for
        """
        return self._backend.delete_activity(activity_id, **kwargs)

    def delete_reply(self, activity_id, **kwargs):
        """
        Deletes a ``reply`` made on an activity. This will also update the corresponding activity.

        :type activity_id: string
        :param activity_id: the id of the reply activity to delete.
        """
        return self._backend.delete_sub_activity(activity_id, "reply", **kwargs)

    def delete_like(self, activity_id, **kwargs):
        """
        Deletes a ``like`` made on an activity. This will also update the corresponding activity.

        :type activity_id: string
        :param activity_id: the id of the like activity to delete.
        """
        return self._backend.delete_sub_activity(activity_id, "like", **kwargs)

    def get_objects(self, object_ids=[]):
        """
        Gets a list of objects by object_ids.

        :type object_ids: list
        :param object_ids: a list of objects
        """
        return self._backend.get_obj(object_ids)

    def get_activities(self, activity_ids=[], **kwargs):
        """
        Gets a list of activities. Specific backends may support other arguments. Please
        see reference of the specific backends to see all ``kwargs`` supported.

        :type activity_ids: list
        :param activity_ids: The list of activities you want to retrieve
        """
        return self._backend.get_activity(activity_ids=activity_ids, **kwargs)

    def get_backend(self):
        """
        The backend the client was initialized with.

        :return: reference to the backend the client was initialized with.
        """
        return self._backend

redpajama_set_name: RedPajamaGithub


text:
\section{Introduction}

Electricity is different from other commodities in at least three important respects: it cannot currently be stored efficiently, it flows through the electricity grid according to the laws of electromagnetism rather than directly from a producer to a consumer, and at any moment supply and demand must match almost exactly to avoid blackouts or other issues.
The capacity of the transmission network also limits the amounts of power that can be injected or withdrawn at certain locations. Therefore, in order for an electricity grid to function safely and efficiently, the configuration and physical limits of the grid and the locations of generation and consumption must be taken into account when making decisions about consumption and production.  To this end, many grid operators around the world have adopted a spatial and temporal pricing mechanism known as Locational Marginal Pricing (LMP) \cite{Bohn}.  This mechanism sets potentially different prices at hundreds or thousands of important locations (nodes) throughout an electricity grid.  These prices are part of the solution to an Optimal Power Flow (OPF) problem \cite{OPF}, and represent the increase in optimized total system costs as a result of a small increase in the amount of power consumed at a location at a specific time.

In this paper we study the properties of LMPs in two North American wholesale electricity markets: Pennsylvania-New Jersey-Maryland (PJM) \cite{PJM}, and Midcontinent Independent System Operator (MISO) \cite{MISO}.  In particular, in both of these markets there are two types of LMPs: day-ahead (forward) LMPs, and real-time (spot) LMPs \cite{ferc1}.  The day-ahead prices are outputs of what can be thought of as a planning exercise by the system operator, in which OPF problems are run every day for each hour of the next (target day).  The real-time LMPs are then the outputs of the OPF problems that are solved in real time (usually every 5 or 15 minutes) to adjust the schedules output from the day-ahead runs.

Our main goal is to understand what information can be inferred from day-ahead and real-time LMPs.  Specifically, we are interested in whether any underlying structure can be inferred from the correlations between prices. As discussed above, LMPs result from a highly structured and constrained optimization problem \cite{Zimmerman}, which induces non-local correlations between prices. It is therefore interesting to understand how prices are correlated according to various measures, how clusters of nodes emerge, and whether these can be understood in terms of the spatial distribution of nodes in the grid.

We will use a combination of methods introduced in the machine learning and statistical physics literatures.
One interesting approach begins by first \textit{filtering} the relevant information from covariance and correlation matrices.  This approach has mainly been used in the financial literature, in order to remove possible noise and to focus only on the most important structures.  We will have to introduce a few caveats and differences which are due to the underlying physical structure of power grids \cite{potters1, aste1, Caravelli}. Given the specific spiky nature of the time series, as an alternative to the Pearson correlation, we also introduce a method commonly used for neural networks, \textit{event synchronization}, to measure the synchronization between spikes at various locations.
We will also test another correlation measure introduced in machine learning: the graphical lasso method. This is then used to cluster the time series.  For this purpose, we use both the Minimal Spanning Tree method, the Planar Maximally Filtered Graph algorithms approach and Spectral Clustering. We then compare the results to clustering based on the node names as a proxy for node location.

\section{Data structure}\label{sec:data}

The dataset we will analyse has been collected by Invenia TCC. A subset of the data was used in \cite{Caravelli}, where a description of the data is also provided \cite{Data}.  The time series we consider is available for each node in the PJM and MISO grids for a period of 3 years (January 1, 2012 to December 31, 2015) at hourly resolution. We focus on a subset of 1287 nodes for PJM and 2568 nodes in MISO (these are nodes which virtual participants can transact on).

The full (day-ahead or real-time) price of electricity at node $n$ and  time $t$ is given by:
\begin{equation}
LMP(n,t) = MEC(t) + MCC(n,t) + MLC(n,t),
\end{equation}
where MEC stands for \textit{Marginal Energy Cost}, MCC stands for \textit{Marginal Congestion Cost} and MLC stands for \textit{Marginal Loss Cost}.
The $MCC(n,t)$ component is the price due to transmission congestion, i.e., it is the marginal cost of supplying the next increment of load at a location, taking into account the transmission constraints of the grid.  This can be positive or negative, and is often $0$.  For example, when a power line at some location is at its limit for carrying power, the load at that location must be serviced through another line, which can be more costly.
$MLC(n,t)$ is the price due transmission losses on the grid.  This is generally small compared to $MEC$.
$MEC(t)$ can roughly be thought of as the price of electricity at any given node if there is no congestion and loss to that node.
The $MEC$ component is independent of node, and thus represents a price shift for the whole market.
The $MLC$ and $MCC$ components are instead time and node dependent, but we observe that in general $MCC\gg MLC$.
Thus, for the present paper we study only the MCC component of the prices in the day ahead market, which directly address the inefficiency of power transmission and is the main source of volatility in the $LMP$ time series.  An important quantity for many market participants and for the grid operator is the difference between day-ahead and real-time prices:
\begin{equation}
\Delta(n,t)=DA(n,t)-RT(n,t).
\end{equation}
This is the time series we will focus on.

One important detail which will be important for our analysis is the fact that each nodal price has a string associated to it, which is of the form ``NODENAME\_CODE". The text ``NODENAME" can be loosely associated with the location of the node. We can in fact run a clustering algorithm based on the name and compare to the results based on price correlations only. This will allow us to compare correlation matrices obtained from independent methods and identify the best price correlation technique to pair nodes and associated clusters.

\section{Correlations, synchronization measures, and filtering processes}
We begin by introducing several measures of interdependence between time series which will be relevant in our analysis.

\subsection{Pearson Correlation}
The Pearson correlation is one of the most commonly used and simplest measures.  It assumes stationarity and a linear relationship between the time series. The correlation matrix is defined as:
\begin{equation}
C_{ij}=Corr[X_i,X_j]= \frac{Cov[X_i,X_j]}{\sqrt{Var[X_i] Var[X_j]}},
\end{equation}
where
\begin{equation}
Cov[X_i,X_j]= \langle X_i X_j\rangle - \langle X_i\rangle \langle X_j\rangle,
\end{equation}
and $Var[X_i]=\sigma_i^2=\langle X_i^2\rangle-\langle X_i\rangle^2$. The averages are defined as temporal ones, e.g. $\langle X_i\rangle=T^{-1} \sum_{t=1}^T x_i(t)$.

The limitations of the Pearson correlation are well know, but we will nevertheless use it as a benchmark in what follows. The Pearson correlation matrix is shown in the first row of Fig. \ref{fig:Pearson, exp, es} for MISO (left) and  PJM (right).

\begin{figure}
	\includegraphics[scale=0.45]{corrMISO.jpg}
	\includegraphics[scale=0.45]{corrPJM.jpg}\\
	\includegraphics[scale=0.45]{EXPCorrMISO.jpg}
	\includegraphics[scale=0.45]{EXPCorrPJM.jpg}\\
	\includegraphics[scale=0.45]{ESCorrMISO.jpg}
	\includegraphics[scale=0.45]{ESCorrPJM.jpg}
	\caption{\textbf{Pearson correlation, exponential smoothing Pearson and event synchronization} for MISO (left) and PJM (right) market.}
	\label{fig:Pearson, exp, es}
\end{figure}

\subsection{Exponential smoothing for Pearson correlation}
Assigning the same weight to each time point (standard Pearson correlation) assumes that recent events and remote past events have the same importance, which is often not a realistic assumption for many purposes \cite{pozzi2012exponential,musmeci2016multiplex}.
In order to take this idea into account, we need to assign different weights for different time points, and the weights should satisfy the following three requirements: $(i)$ $\mathbf{w}\geq0$, $(ii)$ $\forall u > v, w_{u} > w_{v}$, and $(iii)$ $\sum_{t=1}^{T}w_{t}=1$.  The weighted Pearson correlation is then defined as
	\begin{equation}
	\varrho_{ij}^{w} = \frac{\sigma_{ij}^{w}}{\sigma_{i}^{w}\sigma_{j}^{w}},
	\end{equation}
	where $\sigma_{k}^{w}=\sqrt{\sum_{t=1}^{T}w_{t}(X_{kt} - \hat{X_{k}})^{2}}$, $\sigma_{ij}^{w} = \sum_{t = 1}^{T}w_{t}(X_{it} - \hat{X_{i}})(X_{jt} - \hat{X_{j}})$, and $\hat{X_{k}} = \sum_{t = 1}^{T}w_{t}X_{kt}$.

A common way to construct the weights vector is by using an exponential function which leads to the  \textit{exponentially smoothed Pearson correlation}, where
\begin{equation}
w_{t} = w_{0}\exp\left(\frac{t - T}{\theta}\right),
\label{exponential smoothing}
\end{equation}
where $t\in{1, 2, 3,\ldots,T}$ and $\theta > 0$ is the weights decay factor. We can control the smoothness of the weights by varying $\theta$. If $\theta \rightarrow 0$, only the most recent data point is relevant, and if $\theta \rightarrow \infty$, the smoothed correlation converges to the Pearson correlation.
The experimental results for $\theta=3$ are shown in the second row of Fig. \ref{fig:Pearson, exp, es} for MISO (left) and  PJM (right).

\subsection{Event Synchronization}

\begin{figure}
\centering
\includegraphics[scale=0.43]{Synchronization.jpg}
\caption{\textbf{Illustration of event synchronization.} \textit{(top)} Filtering the MCC time series with extremely spiky behavior according to its positive and negative median value.  \textit{(bottom)} Filtered time series obtained by thresholding.}
\label{fig:filt}
\end{figure}

Given the spiky nature of electricity prices, we consider another distance between time series which is a variation of event synchronization, which is inspired by other studies of spiky time series, such EEG time series \cite{Kreuz}. A spike in the MCC time series can be intuitively associated to the failure of efficient dispatch and congestion in the power grid (prices are related to Lagrange multipliers of constraints that are imposed on the system \cite{Tesfatsion}).
We introduce the quantity $c^{\tau}(x|y)$, which is the number of times an event appears in $x$ shortly after it appears in $y$,
\begin{equation}
c^\tau(x|y)=\sum_i \sum_j J^\tau_{ij},
\end{equation}
where $J^\tau_{ij}=1$ if the spikes occur within the interval $\tau$, i.e. $0<|t_i^x-t_i^y|\le \tau$, $J_{ij}=1/2$ if $t_i^x=t_i^y$ and zero otherwise.
We then define
$Q_{\tau}=\frac{c^\tau(y|x)+c^\tau(x|y)}{\sqrt{m_x m_y}}$
which is a symmetrized matrix based on the counting above.
$Q_\tau$ is not a measure of correlation yet, as it has to be normalized. Further note that this measure does not consider the fact that two spikes can be anti-correlated.

Here we generalize the above by first introducing a notion of ``event".
Given a time series $x(t)$ with values which can be positive or negative, we introduce the positive and negative thresholds $mp_{x}$ as the median of the positive values, and $mn_{x}$ as the median of the negative values of $x$ respectively, calculated in a time window of length $T$.
We consider a positive event as a particular time where $x(t)$ is above the threshold $mp_{x}$, and a negative event as one where $x(t)$ below $mn_{x}$.
When the time series is between $mp_{x}$ and $mn_{x}$ the filtered signal is set to zero.
This results in a transformed time series $\epsilon_x(t) \in \{-1, 0, 1\}$.
This filtering is depicted in Fig. \ref{fig:filt}.

We can then construct the matrix $J^{\tau}_{ij}$ as follows:
\begin{equation}
J_{ij}^\tau=\sum_{t} \epsilon_{x_i}(t) \sum_{t^\prime, |t-t^\prime|\leq \tau} \epsilon_{x_j}(t^\prime).
\end{equation}
We then consider the matrix $D_{ij}=\delta_{ij} \sum_{j^\prime}J_{ij^\prime}$, and normalize the synchronization matrix $J_{ij}^\tau$, obtaining an alternative correlation matrix:
\begin{equation}
C^\prime=\sqrt{D^{-1}} J \sqrt{D^{-1}},
\end{equation}
which is symmetric by construction. This measure for $\tau=3$ h is shown in the last row of Fig. \ref{fig:Pearson, exp, es} for MISO (left) and PJM (right). The difference between the Event Synchronization correlation and the Pearson correlation is shown in Fig. \ref{fig:escorr}.  Note how the two methods obtain different results for MISO (left) and PJM (right), and that this difference is in particular visibly stronger in the case of PJM. Note that two time series can be positively correlated according to the Pearson correlation, and yet have negative correlation in terms of spikes.

\begin{figure}
	\includegraphics[scale=0.45]{DiffCorrMISO.jpg}
	\includegraphics[scale=0.45]{DiffCorrPJM.jpg}\\
	\caption{\textbf{Absolute value of the difference between standard Pearson correlation and Modified Event Synchronization}, for MISO (left) and PJM (right).}
	\label{fig:escorr}
\end{figure}

\subsection{Filtered correlations using random matrix theory}

In this section we discuss and apply a technique based on Random Matrix Theory (RMT) which is widely
used to identify the non-random components of empirical Pearson correlation matrices \cite{Potters}.
The eigenvalue of a correlation matrix based on $N$ completely random time series of
duration $T$ follows the Marchenko-Pastur (or Sengupta-Mitra) distribution:
\begin{equation}
\rho(\lambda) =\frac{1}{\rho} \frac{\sqrt{(\lambda_{+}-\lambda)(\lambda-\lambda_{-})}}{2\pi\lambda},
\end{equation}
and
\begin{equation}
\lambda_{\pm}=(1 \pm \sqrt{\rho})^2,
\end{equation}
where $\rho=\frac{T}{N}$, and $1 < \frac{T}{N} < \infty$, when $N\rightarrow \infty$ and $T\rightarrow \infty$.

In general the correlation matrix can be decomposed into two parts, $C=C^r+C^s$, where $C^r$ is the ``random" component and $C^s$ is the matrix containing information.
Due to the information contained in the time series, the distribution of the spectrum of empirical correlation matrices is different from the corresponding Marchenko-Pastur distribution. This suggests filtering Gaussian noise efficiently by removing the random component given by RMT.
For instance,
in Fig. \ref{fig:correlationmp} we show the eigenvalue density of the empirical correlation matrix obtained for MISO and PJM. In the inset figure, we give the Marchenko-Pastur distribution
with the same values of N and T.
It has been shown in many studies that a typical feature
of the spectrum of empirical correlation matrices is that the largest observed eigenvalue $M$ (denoted the market mode in Fig. \ref{fig:correlationmp} for PJM and MISO) is much larger than all other eigenvalues.
And the corresponding eigenvector has all positive elements and one can therefore
identify this eigencomponent of the correlation matrix as the so-called market mode \cite{Dong2005,MacMahon}, which is a common factor in all of the time series.

If we also consider the market component, we have the splitting
\begin{equation}
C=C^r+C^g+C^m.
\end{equation}
where $C^g$ represents correlations at the level of sub-groups of time series, which is often referred to as the ``group" mode \cite{MacMahon}, and $C^m$ represents the ``market'' component.
The result of the filtering procedure is shown in Fig. \ref{fig:filteredRMT}. In MISO we observe that most of the anti-correlation between the upper and lower block disappears, and that the lower block correlation is more pronounced. For PJM, we observe that most of the information is indeed filtered, leaving only a few strong correlation blocks.

\begin{figure}[h]
\includegraphics[scale=0.45]{Spectrum_MISO.jpg}
\includegraphics[scale=0.45]{Spectrum_PJM.jpg}
\caption{\textbf{Pearson Correlation matrix spectrum distributions} and their corresponding \textbf{Marchenko-Pastur distributions} (inset) for MISO (left) and PJM (right). }
\label{fig:correlationmp}
\end{figure}

\begin{figure*}[h]
	\includegraphics[scale=0.45]{CorrMISORMTFiltered.jpg} \includegraphics[scale=0.45]{CorrPJMRMTFiltered.jpg}\\
	\caption{\textbf{Filtered correlations evaluated using RMT} for MISO (left) and PJM (right).}
	\label{fig:filteredRMT}
\end{figure*}

\subsection{Graphical lasso}
The next measure of correlation we consider is Graphical Lasso, which has been introduced in statistical learning \cite{Friedman2008gl}.
This measure has several advantages over the standard Pearson correlation, especially for high dimensional time-series which live in a relatively smaller dimensional subspace. The statistical uncertainty of the Pearson correlation for such data is extremely high. This method can also be thought of as learning a pairwise Gaussian Markov Random Field (GMRF) \cite{Rue2005GMRF}, where each vertex stands for a variable and each edge exists if the corresponding variables are correlated. For empirical data, the GMRF should be a fully connected graph, because it is unlikely for two time series to have zero empirical correlation.
The goal is then to reveal the inherent sparse graph structure from empirical data by eliminating ``weak'' edges.
An intuitive way to solve the problem above is minimizing the reconstruction error between the Pearson correlation and the desired correlation, and shrinking the insignificant correlations to zero. This can be done  by introducing an $L_{1}$ penalty, and minimizing the functional:
\begin{equation}
\tilde{\Sigma}=\arg\min_{\Sigma}|\Sigma-\Sigma_{n}|_{F}^{2}+\rho|\Sigma|_{1},
\end{equation}
where $\Sigma_{n}$ is the empirical correlation matrix, $|\cdot|_F$ is the Frobenius norm which measures the reconstruction error, and $|\cdot|_1$ is an $L_1$ norm regularizer, with the constraint that $\Sigma$ is positive definite. Ying \cite{cui2016sparse} proposed a method to solve this optimization problem efficiently and the related algorithm can be found in references.

In Fig. \ref{fig:sparse} we can see that the graphical lasso has a similar structure to the Pearson correlation shown in Fig. \ref{fig:Pearson, exp, es}.
In a sense however this correlation matrix is more significant than Pearson (especially the lower block for MISO), because it removed many negligible elements.
\begin{figure*}[h]
	\includegraphics[scale=0.45]{Sparse_MISO.jpg} \includegraphics[scale=0.45]{Sparse_PJM.jpg}\\
	\caption{\textbf{Sparse Correlations evaluated using  graphical lasso optimization} for MISO (left) and PJM (right). }
	\label{fig:sparse}
\end{figure*}

\subsection{String Correlation}\label{sec: string}
Next we introduce a correlation measure which is based on the names of the LMP time series. We will use this as an independent method to test the validity of the preceding correlations measures. In the two electricity grids we are studying each LMP time series is assigned an identifier which is given by a string of the form `place-name code-number'. This allows us to use the \textit{string kernel} \cite{kernel3, stringkernel} method to calculate the similarity between identifier strings. In the statistical learning community there are several kernel methods which are used to  estimate relationships between various types of datasets. For example, it is  possible to construct kernels for estimating the correlation between images and sentences \cite{kernel1,kernel2,kernel3}. Intuitively, a higher string kernel similarity suggests that the two time series locations are more likely to be near each other geographically.

\section{Clustering methods}

\subsection{Spectral clustering}
A standard approach for inferring structure in high dimensional time series data is to \textit{cluster} the data \cite{aste1}.
As a first example, consider the Girvan-Newman algorithm \cite{Girvan}, which infers structure by progressively removing edges from an original graph (inferred from the correlations between the time series for example), with the final remaining connected components representing `communities' in the data.
One drawback of the Girvan-Newman algorithm is its inefficiency for large graphs, which results from the need to calculate the eigenvectors of the corresponding graph Laplacian at each iteration. Also, as noted in \cite{MacMahon}, the Girvan-Newman algorithm is not well suited for correlation matrices and requires a slight modification.

In the following we will instead use \textit{spectral clustering} which is based on the same intuition as the Girvan-Newman algorithm \cite{Von2007tutorialonSL}, but we only need to find the spectrum of the original graph Laplacian and then use the k-means algorithm to find the underlying communities.
In Fig. \ref{fig: Spectral clustering result} we show a selected sample of the original clustering results in the case of a small set of MISO nodes. The matrix elements lower than median correlation have been neglected.  A total of $200$ clusters were used in original result (see Section 5 for further discussion).

\subsection{Community detection algorithms}
Another approach to clustering is to use community detection algorithms. In order to improve the efficiency of these algorithms and filter out any noise that may be present, we will use various filtering algorithms before we cluster.
The first approach to filtering empirical correlation matrices is based on Minimal Spanning Trees (MST) which are tree structure graphs which only contain the largest correlations \cite{aste1,MacMahon,Tumminello,Gomez}.
For a system with $N$ elements, a tree structure graph with only $N-1$ links are retained by the MST filtering algorithm. This approach is closely related to the Single Linkage hierarchical clustering algorithm \cite{musmeci2015relation}, which automatically produces an agglomerative algorithm that ends up with a dendrogram that arranges the elements into a hierarchical structure
from the original correlation matrix \cite{MacMahon, musmeci2015relation}. Previous research \cite{MacMahon} also shows that MST is more reliable when first using the strongest correlations to determine the low-level structure of the taxonomic tree, while it is progressively less reliable when using the weaker correlations to determine a high-level taxonomic tree.
A generalization of MST which releases the topological constraint to contain a larger number of links is called Planar Maximally Filtered Graph (PMFG). This retains the MST as well as a number of additional links, provided that the resulting graph is still a planar graph\footnote{The graph can be drawn on a plane without any crossing of links} \cite{MacMahon}. Since MST is associated with hierarchical clustering algorithms, PMFG has been shown to be related to Directed Bubble Hierarchical Tree (DBHT), which contain more information \cite{musmeci2015relation}.

\begin{figure*}

	\includegraphics[scale=0.125]{SP_Pearson}
	\includegraphics[scale=0.125]{SP_EXP}\\
	\includegraphics[scale=0.125]{SP_ES}
	\includegraphics[scale=0.125]{SP_Group}\\
	\includegraphics[scale=0.125]{SP_Sparse}
	\includegraphics[scale=0.125]{SP_String}\\
	\caption{\textbf{Network reconstruction} for a small set of nodes of MISO. The location string of each node is shown in the figure. Nodes with the same color belong to the same cluster, which has been calculated by \textbf{spectral clustering}. Black nodes are those misclassified with respect to location proxy partition.  }
	\label{fig: Spectral clustering result}
\end{figure*}

\begin{figure*}

	\includegraphics[scale=0.125]{MSTMM_Pearson}
	\includegraphics[scale=0.125]{MSTMM_EXP}\\
	\includegraphics[scale=0.125]{MSTMM_ES}
	\includegraphics[scale=0.125]{MSTMM_Group}\\
	\includegraphics[scale=0.125]{MSTMM_Sparse}
	\includegraphics[scale=0.125]{MSTMM_String}\\
	\caption{\textbf{Network reconstruction} for a small set of nodes of MISO using \textbf{MST filtering}.The location string of each node is shown in the figure. Nodes with same color belong to same cluster, which has been calculated by means \textbf{modularity maximization}. Black nodes are those misclassified with respect to location proxy partition. }
	\label{fig:MST result}
\end{figure*}

\begin{figure*}

	\includegraphics[scale=0.125]{PMFGMM_Pearson}
	\includegraphics[scale=0.125]{PMFGMM_EXP}\\
	\includegraphics[scale=0.125]{PMFGMM_ES}
	\includegraphics[scale=0.125]{PMFGMM_Group}\\
	\includegraphics[scale=0.125]{PMFGMM_Sparse}
	\includegraphics[scale=0.125]{PMFGMM_String}\\
	\caption{\textbf{Network reconstruction} for a small set of nodes of MISO with \textbf{PMFG filtering}. The location string of each node is shown in the figure. Nodes with same color belong to same cluster, which has been calculated by means of \textbf{modularity maximization}. Black nodes are those misclassified with respect to location proxy partition. }
	\label{fig:PMFG result}
\end{figure*}

As with the MST, the goal of this method to find the postulated approximating structure, rather than searching for groups of time series that are more correlated internally than with each other. Therefore we also need a graph community detection method, so we will use a modularity maximization algorithm to detect graph communities.
The modularity of a partition is a scalar value between $-1$ and $1$ that measures the density of links inside communities as compared to links between communities \cite{mm2}. In the case of weighted networks (weighted networks are networks that have weights on their links), it is defined as
\begin{equation}
Q=\frac{1}{m}\sum_{i,j}[A_{i,j}-\frac{k_{i}k_{j}}{2m}]\delta(c_{i},c_{j}),
\end{equation}
where $A_{i,j}$ represents the weight of the edge between $i$ and $j$, $k_{i} =  \sum_{j} A_{i,j}$ is the sum of
the weights of the edges attached to vertex $i$, and $c_{i}$ is the community to which vertex $i$ is assigned.
We use the algorithm proposed in \cite{mm}, which is fast and stable. See Fig. \ref{fig:MST result} for a small set of nodes of the clustering results based on the MST method, and Fig. \ref{fig:PMFG result} for PMFG.

In our toy example, we have two groups, CIN and AMMO, according to their locations. For AMMO, we have $3$ subgroups: MERAMEC, KEOKUK, and RCCKETG, which contains $4$, $8$, and $3$ elements respectively. For CIN, there are $3$ subgroups which contain more than $1$ elements, which are MIAMWEB ($5$ elements), VERMN ($5$ elements), and SUCRKGT ($2$ elements), and $5$ subgroups only contain $1$ element (we call them \textit{'single element'}): GIBSON, WR1CT, HE, CONNERV, and NOBLEVL.

Ideally, a good partition should cluster elements from the same subgroup together, and if an element is single, it should be assigned to the similar subgroup. Thus, our location proxy is shown to provide a good benchmark (last figure in Fig.\ref{fig: Spectral clustering result}-\ref{fig:PMFG result}). By counting the black nodes, we find nearly all the methods can detect large subgroups (such as AMMO\_ KEOKUK and CIN\_ VERMN) correctly, and mistakes often occur when it comes to small subgroups. In our examples, the RMT filtered Correlation and Sparse Correlation perform better than others. We believe this to be due to the fact that these methods are more sensitive to smaller subgroups, where we find the other methods to provide less accurate results. As for clustering, we find that MST and PMFG are significantly better than spectral clustering, because they learn a sparse network structure which contains as much information as possible while filtering noise.

\section{Spectral clustering analysis}
In applying the spectral clustering method we must choose the number of clusters.  We will use the disparity (the heterogeneity measure) and Adjusted Rand Index (the similarity measure).

\subsection{Clustering heterogeneity measure: disparity}
Disparity is used to measure the heterogeneity of cluster sizes. Some clustering methods might prefer many clusters with balanced size, while others might provide a subdivision into a few very large clusters and many small clusters \cite{musmeci2015relation}. In order to characterize the distribution of the cluster size with a single quantity, we can use the disparity measure \cite{musmeci2015relation}:
\begin{equation}
d = \frac{\sigma_{S}}{\bar{S}},
\label{disparity}
\end{equation}
where $\sigma_{S}$ is the standard deviation
\begin{equation}
\sigma_{S} = \sqrt{\frac{1}{N_{c}-1}\sum_{a}(S_{a}-\bar{S})^{2}}.
\label{cluster standard deviation}
\end{equation}
The normalization factor $\bar{S}$ is the average
\begin{equation}
\bar{S} = \frac{1}{N_{c}}\sum_{a}S_{a},
\label{average}
\end{equation}
where $S_{a}$ is the cardinality of cluster $a$ and $N_{c}$ is the number of clusters. The case where $d=0$ corresponds to all clusters being the same size, and large $d$ means that cluster sizes are more heterogeneous.

\subsection{Clustering similarity measure: Adjusted Rand Index}
The Adjusted Rand Index ($R_{ARI}$) is typically used to measure the similarity between the results of two clustering methods. In the case where we have the ground truth of the data partition, we can use $R_{ARI}$ as an accuracy measure for clustering algorithms.  If we assume that location provides a good partition for the LMP data, we can compare our clustering results by using $R_{ARI}$ with respect to the location proxy calculated from the string kernel correlation.
This method calculates the number of pairs of objects that are in the same cluster in both partitions, and then compares this with the one expected under the hypothesis of independent partitions \cite{musmeci2015relation}.
$R_{ARI}$ takes values in $[-1, 1]$, with $1$ corresponding to the case of identical clusters, and $0$ to two completely uncorrelated clusters \cite{musmeci2015relation}.
Negative values show anti-correlation between two partitions, which means the number of overlapping pairs of these two partitions is less than the expected overlap between two random partitions \cite{musmeci2015relation}.

We calculate the ``contingency table'' $M$ between two partitions $Y$ and $Y'$ with coefficients \cite{musmeci2015relation}:
\begin{equation}
m_{ij} = |Y_{i}\cap Y'_{j}|.
\end{equation}
This is the number of objects in the intersection of clusters $Y_{i}$ and $Y'_{j}$. $M$ is a $k\times l$ matrix, where $k$ and $l$ are the number of clusters for $Y$ and $Y'$ respectively. Let us call $a$ the number of pairs of objects that are in the same cluster both in $Y$ and in $Y′$, and $b$ the number of pairs that are in two different clusters in both $Y$ and $Y′$ \cite{wagner2007comparing}. Then the Rand Index is defined as the sum of $a$ and $b$, normalized by the total number of pairs \cite{wagner2007comparing}:
\begin{equation}
R(Y, Y')=\frac{2(a+b)}{N(N-1)}=\sum_{i=1}^{k}\sum_{j=1}^{l}{m_{ij} \choose 2}.
\end{equation}
We then use as null hypothesis associated to two independent clusters the generalized hypergeometric distribution, and define the Adjusted Rand Index as the difference between the Rand Index and its mean value under the null hypothesis, normalized by the maximum that this difference can reach \cite{musmeci2015relation}:
\begin{equation}
R_{ARI} = \frac{R - t_{3}}{\frac{t_{1}+t_{2}}{2}-t_{3}},
\label{ARI}
\end{equation}
where $t_{1} = \sum_{i = 1}^{k}{|Y_{i}| \choose 2}$, $t_{2} = \sum_{j = 1}^{l}{|Y'_{j}| \choose 2}$, $t_{3} = \frac{2t_{1}t_{2}}{N(N - 1)}$.

We will use these two measures to tune the parameter in spectral clustering.

\subsection{Choice of the number of clusters}
In order to tune the number of clusters $n$ in spectral clustering we compare the clustering results with the location proxy partition for each type of correlation. The location proxy is the spectral clustering result based on the string correlation, which means we need to determine the number of clusters $n_{s}$ for the location proxy. This can be achieved by constructing a relation between $n$ and $n_{s}$:
\begin{eqnarray}
n_{s} =
\begin{cases}
144       & n \leq 144 \\
 n  & n > 144
\end{cases},
\label{string information}
\end{eqnarray}
where $144$ is the number of different `name codes' in MISO (see section \ref{sec: string}). If $n_{s}=144$, we use exactly the same information as if we use the `code' partition. If $n_{s} > 144$, we use more information than the codes provide because some codes will be divided into several parts.
If the clustering evaluation requires more information, it will grows as the number of clusters $n$ increases. We calculate $R_{ARI}$ with respect to the location proxy for each type of correlation measure with $n$ from $1$ to $300$. A good cluster number $n$ should make the clustering result stable, so we want to adjust the number of clusters until ARI is insensitive.
\begin{figure*}[h]
	\centering
	\includegraphics[scale=0.32]{tunning.jpg}
	\caption{\textbf{Disparity and ARI as a function of the number of clusters based on five correlation measures.} Here we use the last $5000$ hours of LMP data for MISO. }
	\label{Tuning number of clusters}
\end{figure*}

Fig. \ref{Tuning number of clusters} shows how disparity and ARI change with respect to the number of clusters. As we can see, disparity and ARI converge when the number of clusters increasing. We can find, all of the ARIs increase at first, then decrease, and converge when the number of clusters are larger than (approximately) $200$. For RMT filtered correlations, the ARI converges to around $0.3$, while the others converge to $0.15$. As for disparity, these six correlations increase as the number of clusters grows, and converge to a value when the number of clusters reach about $200$.
Based on these result, we use $200$ as the number of clusters for spectral clustering.

\section{Dynamical analysis of the market structure}
In this section we analyze changes in the market structure as a function of time. We first analyze the behavior of the mean and the largest eigenvalues of each correlation matrix, then we analyze how the clustering results change through time.

The methodology we use has been introduced in \cite{musmeci2016multiplex} to estimate when structural changes (e.g. which span across the market) occur.

\subsection{Dynamical analysis of correlation matrices}
The mean of a correlation matrix represents the internal correlation strength of a set of time series, and the largest eigenvalue of an adjacency matrix provides information on the average degree of the graph\footnote{In fact, the largest eigenvalue $\lambda_{A}$ of the adjacency matrix $A$ of a general graph satisfies the inequality:
$\max(d_{avg},\sqrt{d_{max}})\leq \lambda_{A}\leq d_{max}$, where $d_{avg}$ is the average degree of nodes in the graph and $d_{max}$ is the largest degree.}. Also, it provides a sense of how each correlation is changing over time.
\begin{figure*}[h]
	\includegraphics[scale=0.32]{correlation_result.jpg}
	\caption{\textbf{Mean correlation and largest eigenvalue} of six different correlation measures for each week.}
	\label{mean and largest eigenvalue correlations}
\end{figure*}
\begin{table}[]
	\footnotesize
	\centering

	\label{averaged mean and norm}
	\begin{tabular}{|c|c|c|}
		\hline
		& Mean   & Norm   \\ \hline
		Pearson 			             & 0.5703 & 905.46 \\ \hline
		smoothed Pearson & 0.8656 & 1329.5 \\ \hline
		Event synchronization            & 0.44   & 697.04 \\ \hline

		RMT filtered correlation         & 0.12   & 203.6  \\ \hline
		Sparse correlation               & 0.3323 & 539.84 \\ \hline
	\end{tabular}
		\caption{\textbf{Averaged mean and norm} for each correlation matrix}
\end{table}

Table \ref{averaged mean and norm} and Fig. \ref{mean and largest eigenvalue correlations} show the change of the mean and largest eigenvalue for different correlation matrices as a function of time. The RMT filtered correlation has the lowest correlation strength and highest sparsity, meanwhile the smoothed Pearson correlation has the highest strength and lowest sparsity.  We observe that Smoothed Pearson does change abruptly over time (both in mean and in the highest eigenvalue), but as we will see below, it is one of the two methods (together with Event Synchronization) which provides fairly stable ARI over time.

\subsection{Dynamical analysis of clustering results}
In this section we analyze the dynamical properties of the partitions using spectral clustering and Minimum Spanning Tree modularity. We consider $5$ different correlation measures\footnote{PMFG is not included because it is similar to MST but requires much more computational resources.}.
We employed ARIs to measure the difference between two clustering results and disparity to measure the heterogeneity of cluster sizes.
We considered two ARI measures: ``ARI location", which is based on the location proxy partition from the same clustering method, and ``ARI benchmark", which is based on the clustering from the corresponding correlation matrix of the last week (the $209$th week).

\subsubsection{Spectral clustering results analysis}
For each correlation method we calculate the correlation matrix of the LMPs for each week in the data, and use spectral clustering with a cluster number equal to $200$.
\begin{table}[]
	\footnotesize
	\centering

	\label{clustering dynamic table}
	\begin{tabular}{|c|c|c|c|}
		\hline
		& Disparity & ARI\_benchmark & ARI\_location
		\\ \hline
		Pearson correlation              & 3.3031, 5.7603 (104)    & 0.1633, 0.3254 (97)         & 0.1303, 0.2256 (54)        \\ \hline
		Smoothed Pearson 			 & 3.8523, 9.426 (73)    & 0.0581, 0.1857 (76)         & 0.0595, 0.2255(108)         \\\hline
		Event synchronization            & 2.9588, 5.7923 (99)    & 0.1379, 0.3224 (3)         & 0.1203, 0.2355 (184)        \\ \hline

		RMT filtered correlation         & 8.6147, 12.2508 (118)    & 0.0716, 0.3633 (69)         & 0.0659, 0.386 (106)        \\ \hline
		Sparse correlation               & 6.866, 10.8894 (62)     & 0.1161, 0.5735 (69)         & 0.0411, 0.1709 (176)        \\ \hline
	\end{tabular}
		\caption{\textbf{Average and Maximum} disparity, ARI benchmark and ARI location of spectral clustering results for each correlation matrix. The number in parenthesis stands for the week when the maximum is reached.}
\end{table}
\begin{figure*}[h]
	\includegraphics[scale=0.32]{Dynamic.jpg}
	\caption{\textbf{The dynamics of disparities and AIRs of spectral clustering} results for $5$  correlation measures.}
	\label{spectral dynamics}
\end{figure*}

Figure \ref{spectral dynamics} shows the behavior in time of the spectral clustering results based on three different correlation measures. Table \ref{clustering dynamic table} shows the average and maximum\footnote{The number in brackets is the week that the measure reached its maximum.} of each spectral clustering.
We can see that disparity, in the case of RMT filtered correlations and the sparse correlation method are high with respect to the average (around $8.6$ and $6.8$ respectively). This means that the RMT filtered correlations and sparse correlation method prefer high heterogeneity of cluster sizes and less stable partitions in the spectral clustering setting.

The values attained by ARI with respect to the location proxy, smoothed correlation, RMT filtered correlation, and sparse correlation are respectively around $0.07$, while the latter are \textit{circa} $0.13$.  The reason is that these three methods remove a significant portion of the original correlation matrix, but the ARIs for both groups are quite small:  the difference is not significant in this case. The RMT filtered correlations have the highest maximum ARIs: this tells us it may have potential to out-perform other correlation methods. As for fluctuations, we see that all correlation measures have a similar behavior.

\subsubsection{MST modularity maximization clustering analysis}
Similar with the analysis using spectral clustering, we construct a Minimum Spanning Tree for each correlation matrix, and find clusters based on the modularity maximization algorithms.
\begin{table}[]
	\footnotesize
	\centering

	\label{MST clustering dynamic table}
	\begin{tabular}{|c|c|c|c|}
		\hline
		& Disparity & ARI\_benchmark & ARI\_location
		\\ \hline
		Pearson correlation              & 0.3598, 0.4977 (144)    & 0.1114, 0.1941 (207)         & 0.0885, 0.1132 (24)        \\ \hline
		Smoothed correlation			 & 0.3758, 0.5221 (114)    & 0.0672, 0.1928 (208)         & 0.0697, 0.0952 (133)        \\ \hline
		Event synchronization            & 0.4236, 0.5736 (164)    & 0.1578, 0.3437 (208)         & 0.1413, 0.1847 (113)        \\ \hline

		RMT filtered correlation         & 1.0171, 2.5354 (56)     & 0.0772, 0.1223 (199)         & 0.2262, 0.3526 (117)        \\ \hline
		Sparse correlation               & 0.6527, 3.5332 (36)     & 0.1299, 0.3912 (207)         & 0.1576, 0.2988 (131)        \\ \hline
	\end{tabular}
\caption{\textbf{Average and Maximum} disparity, ARI benchmark and ARI location of \textbf{MST modularity maximization} results for each correlation matrix. The number in parenthesis stands for the week when the maximum is reached.}
\end{table}

Figure \ref{MST dynamics} shows three measurements for the MST modularity maximization based on different correlation measures. Table \ref{MST clustering dynamic table} shows the average and maximum of each measurement.
\begin{figure*}[h]
	\includegraphics[scale=0.32]{Dynamic_MM.jpg}
	\caption{\textbf{The dynamics of disparities and AIRs of MST modularity maximization} for $5$ correlation measures. }
	\label{MST dynamics}
\end{figure*}

The behaviour of dynamic disparity for MST clustering is similar to spectral clustering, while the RMT filtered correlations and sparse correlation measures have a higher average (around $1$ and $0.65$ respectively) and fluctuations of disparity, and the others have a similar average (around $0.38$) and fluctuations.
For ARI with respect to the location proxy, event synchronization measure, RMT filtered correlations and sparse correlation measure are around $0.2$, while the others are about $0.07$. It can be concluded that using the MST modularity maximization method applied to these three correlations performance is significantly better than the Pearson and smoothed Pearson measures.

From Figure \ref{spectral dynamics} and Figure \ref{MST dynamics} we further see that the disparity from MST is significantly lower than spectral clustering. The averaged ARI with respect to the location proxy is also higher than spectral clustering. Moreover, we find that the maximum ARI based on the benchmark is reached at around the $207$th week, which is very close to the benchmark ($209$th week), but the spectral clustering result in Table \ref{clustering dynamic table} does not show a similar behaviour. One possible explanation is that the spectral clustering method has more difficulty revealing patterns than MST modularity maximization in a large and dense network.

\begin{figure*}[h]
	\includegraphics[scale=0.33]{MSTD2.jpg}\\
	\includegraphics[scale=0.33]{MSTD1.jpg}
	\caption{The moving standard deviation of ARI location for spectral clustering and MST modularity maximization with rolling window size equals to $50$. We find that MST provides more stable results than spectral clustering. RMT filtered correlation and sparse correlation are unstable in both situation.}
	\label{MSTD1}
\end{figure*}
From the moving standard deviation of ARI for spectral clustering and MST modularity maximization across time (Fig.\ref{MSTD1}), we observe that MST is significantly stable compared with spectral clustering. And RMT filtered correlation and Sparse Correlation are found to be unstable over time, while the other correlation methods can be considered stable.
This suggests that the electricity market structure revealed by RMT and MST modularity maximization changes frequently in time and is thus seems not reliable for these markets. Of course, here a note of warning should be made: this depends on our proxy measure, which is the string correlation method. In general, we believe this to be due to the properties of the market itself, and the strong non-stationarity, on which these methods strongly rely upon. However, methods based on Pearson and Event Synchronization, in particular MST, were found to be rather stable. It should be said, however, that even in the case of financial market time series, previous findings \cite{Dong2005} show that there are only a few clusters in stock markets which are stable over time (using RMT filtered correlation and modularity maximization). This suggests that electricity markets are far more unstable than other financial markets. One possible explanation of the non-stationarity is that electricity markets are based on a strongly non-local optimization problem which spreads disturbances and creates correlations across the entire footprint of the grid. Nonetheless, the method based on Event Synchronization (which focuses only on rare and strong events) and (Smoothed and non) Pearson are less sensitive to fluctuations.

\section{Conclusions}
In this paper we discussed various correlation, filtering, and clustering methods with the purpose of analyzing the underlying structure of wholesale electricity market data. Specifically, we have analyzed the nodal price difference between day-ahead and real-time, which are relevant for understanding the inefficiencies in the planning process that outputs the day-ahead prices.
We also introduced an alternative measure of correlation based on a modification of Event Synchronization, which focuses on more rare and strong events (spikes) in time series. We have argued that most of the correlations observed in our dataset are due to random fluctuations and that these should be filtered, or a nonlinear measure of correlation should be used instead.
In addition to this, we explored various methods for inferring the correlation structure for MISO, identifying various clusters. These methods are robust as they use only the strongest correlation links.

Finally and most importantly, we provided a framework to choose and filter correlation matrices of electricity price data by using the string kernel correlation proxy, which we believe can be used to test the validity of our methodology.

We also extended our results to the time domain and analyzed how the market structure changes from week to week. This analysis provides a quantitative method to infer non-stationarity as well as to test the clustering methods. We concluded that the MST modularity maximization method is more suitable than spectral clustering.
Furthermore, even after filtering multiple types of noise, the clustering results for RMT filtered correlation matrices were found to be, in some cases, unstable over time (with respect to the proxy), although it has achieved the best performance. Of all the methods, we have found Pearson based and the Event Synchronization methods to be the most stable overtime. Overall, we have found Event Synchronization in conjunction with MST to be the most appropriate clustering method for its stability and remarkable performance.
An interesting avenue for future work is to try to reconstruct the network using methods of graph inference based on entropy maximization \cite{tiziano}.\ \\\ \\

\begin{centering}
\textbf{Acknowledgements}\\
\end{centering}
FC and TC would like to thank Invenia Labs for previous funding and support respectively. We would like to thank L. Roald at LANL for comments on an earlier version of this paper. FC acknowledges the support of NNSA for the U.S. DoE at LANL under Contract No. DE-AC52-06NA25396. TC acknoledges the support of National scientific and Technological Innovation Zone (No. 17-H863-01-ZT-005-005-01) and State's Key Project of Research and Development Plan (No. 2016QY03D0505). \ \\\ \\

\begin{centering}
\textbf{Bibliography}\ \\\ \\
\end{centering}

redpajama_set_name: RedPajamaArXiv


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Gardening specialists provide lawn care advice to existing and prospective clients at no extra cost. A common lawn care advice solicited would be what grass species will thrive in a particular locality. Having had previous experience with other customers, these experts in lawn care advice can very well take care of your needs to create that fine-looking garden and preserve its lush greenery.
An attractive lawn does not happen overnight. It takes utmost care coupled with particular skills to maintain one.
Your familiarity with the environment is another aspect to consider. For instance, you come across a very eye-catching lawn. Naturally, you would conclude that the owner is a gardening wizard and therefore a reliable source of lawn care advice. Given a particular type of soil and weather situation in the locality, this person would be able to specifically point out the plus factors needed to achieve the perfect lawn and those that do not.
He would also be equipped with the latest technology and expertise in lawn care that you can adopt in cultivating your very own dream lawn. This is a realistic example of lawn care advice put to action.
You can also refer to newspapers and other publications for lawn care advice. Your town or city might even have local subscriptions on the same subject matter with writers who are local expert gardeners themselves and hence authorities in giving sound lawn care advice. For more info see http://www.lawncare-help.com/ on Lawn Care.
Their articles would include insights and highlights of their own experiences with their beautiful gardens. A lawn care advice segment may be provided by them. Such publications would also have a directory of the best garden centers in town that offer all the lawn products and supplies you can imagine.
Hence, it is highly recommended that you subscribe to these newspapers or magazines which regularly come out. Definitely, lawn care advice and information that you will find here are fresh and up-to-date.
You can also find more info on Lawn Care Services and Lawn Maintenance. Lawncare-help.com is a comprehensive resource to know about Lawn Care.