title: Summary execution

text: Under military law, summary execution is illegal in almost all circumstances, as a military tribunal would be the competent judge needed to determine guilt and declare a sentence of death. However, there are certain exceptions to this rule in emergencies and warfare where summary execution is legal.


title: Summary execution

text: Major treaties such as the Geneva Conventions and Hague Conventions, and customary international law from history, protect the rights of captured regular and irregular enemy soldiers, along with civilians of enemy states. Prisoners-of-war (POWs) must be treated in carefully defined ways which definitively ban summary execution, as the Second Additional Protocol of the Geneva Conventions (1977) states:


title: Summary execution

text: However, some classes of combatants may not be accorded POW status, but that definition has broadened to cover more classes of combatants over time. In the past, summary execution of pirates, spies, and francs-tireurs have been performed and considered legal under existing international law. Francs-tireurs (a term originating in the Franco-Prussian War) are enemy civilians or militia who continue to fight in territory occupied by a warring party and do not wear military uniforms, and may otherwise be known as guerrillas, partisans, insurgents, etc. Though they could be legally jailed or executed by most armies a century ago, the experience of World War II influenced nations occupied by foreign forces to change the law to protect this group. Many of the post-war victors, such as France, Poland, and the USSR, had the experience of resistance fighters being summarily executed by the Axis if they were captured. The war also influenced them to make sure that commandos and other special forces who were caught deep behind enemy lines would be protected as POWs, rather than summarily executed as Hitler decreed through his 1942 Commando Order.


title: Summary execution

text: The Commando Order was issued by Adolf Hitler on October 18, 1942, stating that all Allied commandos encountered by German forces in Europe and Africa should be killed immediately without trial, even in proper uniforms or if they attempted to surrender. Any commando or small group of commandos or a similar unit, agents and saboteurs not in proper uniforms who fell into the hands of the German military forces by some means other than direct combat (through the police in occupied territories, for instance) were to be handed over immediately to the Sicherheitsdienst (SD, Security Service). The order, which was issued in secret, made it clear that failure to carry out such orders by any commander or officer would be considered to be an act of negligence punishable under German military law. This was in fact the second "Commando Order", the first being issued by Generalfeldmarschall Gerd von Rundstedt on July 21, 1942, stipulating that parachutists should be handed over to the Gestapo. Shortly after World War II, at the Nuremberg Trials, the Commando Order was found to be a direct breach of the laws of war, and German officers who carried out illegal executions under the Commando Order were found guilty of war crimes.


title: Summary execution

text: According to Article 4 of the Third Geneva Convention of 1949, irregular forces are entitled to prisoner of war status if they are commanded by a person responsible for the subordinates, have a fixed distinctive sign recognizable at a distance, carry arms openly, and conduct their operations in accordance with the laws and customs of war. If they do not meet all of those conditions, they may be considered "francs-tireurs" (in the original sense of "illegal combatant") and punished as criminals in a military jurisdiction, which may include summary execution.


title: Summary execution

text: Soldiers who are wearing uniforms of the opposing army "after the start of combat" may be considered illegal combatants and subject to summary execution. Many armies have performed that kind of false flag ruse in the past, including both German and US special forces during World War II. However, if soldiers remove their disguises and put on proper insignia "before the start of combat" in such an operation, they are considered legal combatants and must be treated as prisoners-of-war if captured. That distinction was settled by a military tribunal in the postwar trial of Otto Skorzeny, who led Operation Greif, an infiltration mission in which German commandos wore US uniforms to infiltrate US lines during the Battle of the Bulge.


title: Summary execution

text: Within a state's policy, martial law may be declared in emergencies such as invasions or insurrections, and in such a case constitutionally protected rights would be suspended. Depending on a state's interpretation of martial law, this may allow police or military forces to decide and carry out punishments that include death on its own citizens, in order to restore lawful authority or for other vital reasons.


title: Summary execution

text: That would not include killing a suspect who is directly endangering another's life, which is always legal for police, but executing a suspect under one's control as a punishment. Proving that a summary execution fell under the legal exception would be exceptionally difficult, as one would have to show why a judgment and sentence of death absolutely needed to be meted out on the spot. Hence, such extraordinary acts are almost always seen as illegal violations of human rights.


title: DJI

text: SZ DJI Technology Co., Ltd. or Shenzhen DJI Sciences and Technologies Ltd. () in full, more popularly known as its trade name DJI, which stands for Da-Jiang Innovations (), is a Chinese technology company headquartered in Shenzhen, Guangdong, backed by several state-owned entities. DJI manufactures commercial unmanned aerial vehicles (drones) for aerial photography and videography. It also designs and manufactures camera gimbals, action cameras, camera stabilizers, flight platforms, propulsion systems and flight control systems.


title: DJI

text: DJI accounts for around 76% of the world's consumer drone market as of March 2021. Its camera drone technology is widely used in the music, television and film industries. The company's products have also been used by militaries and police forces, as well as terrorist groups, with the company taking steps to limit access to the latter.


title: DJI

text: US government institutions have prohibited the internal use of DJI products, but as of 2020, various agencies at the local and federal level continued to use DJI products. In December 2021, the United States Department of the Treasury prohibited investment in DJI by U.S. individuals and entities, accusing the company of complicity in aiding the Uyghur genocide.


title: DJI

text: The company was founded in 2006 by Frank Wang (Wāng Tāo, ). Born in Hangzhou, Zhejiang, he enrolled as a college student in the Hong Kong University of Science and Technology (HKUST) in 2003. He was part of the HKUST team participating in ABU Robocon and won third prize.


title: DJI

text: Wang built the first prototypes of DJI's projects in his dorm room, selling the flight control components to universities and Chinese electric companies. He used the proceeds to move to the industrial hub of Shenzhen and hired a small staff in 2006. The company struggled at first with a high degree of churn among employees attributed to Wang's abrasive personality and perfectionist expectations. The company sold a modest number of components during this period, relying on financial support from Wang's family friend, Lu Di, who provided US$90,000 and managed the company's finances. In 2009, DJI's components enabled a team to successfully pilot a drone around the peak of Mt. Everest.


title: DJI

text: In 2010, Wang hired a high school friend, Swift Xie Jia, to run the company's marketing. DJI began to cater more to drone hobbyists in markets outside of China. In 2011, Wang met Colin Guinn at a trade show, and the two of them founded DJI North America, a subsidiary company focusing on mass market drone sales. In 2013, DJI released the first model of the Phantom drone, an entry-level drone which was more user-friendly than other drones on the market at the time.


title: DJI

text: The Phantom was commercially successful but led to conflict between Guinn and Wang. Midway through the year, Wang made an offer to buy out Guinn, which was refused. By the end of the year, DJI had locked employees of the North American subsidiary out of their email accounts in the process shutting down the subsidiary's operations. Guinn sued DJI, with the case being settled out of court.


title: DJI

text: In 2015, DJI eclipsed the success of the Phantom with the Phantom 3, whose even greater popularity was in part due to the addition of a built in live-streaming camera. DJI was now the largest consumer drone company in the world, driving many of its competitors out of the market. 2015 also marked the beginning of DJI's RoboMaster Robotics Competition (), an annual international collegiate robot combat tournament held at the Shenzhen Bay Sports Centre.


title: DJI

text: In November 2015, DJI announced the establishment of a strategic partnership with Hasselblad. In January 2019, DJI acquired a majority stake in Hasselblad.


title: DJI

text: In 2017, DJI won a Technology & Engineering Emmy Award for its camera drone technology, which was used in the filming of various television shows including "The Amazing Race", "American Ninja Warrior", "Better Call Saul" and "Game of Thrones". That same year, Wang became Asia's youngest tech billionaire, and world's first drone billionaire.


title: DJI

text: Also in 2017, signed a strategic cooperation agreement to provide surveillance drones for use by the Chinese police in Xinjiang.


title: DJI

text: On 5 June 2018, police body cam and Taser maker Axon announced a partnership with DJI to sell surveillance drones to U.S. police departments. As of 2020, DJI products are also widely used by U.S. police and fire departments.


title: DJI

text: On 21 January 2019, DJI announced that an internal probe had uncovered "extensive" fraud by some employees who "inflated the costs of parts and materials for certain products for personal financial gain." DJI estimated the cost of the fraud at "up to CN¥1 billion" (US$147 million), but maintained that the company "did not incur a full year loss in 2018."


title: DJI

text: In January 2020, the United States Department of the Interior announced that it would be grounding around 800 drones which it had been using for wildlife conservation and infrastructure monitoring purposes. By March 2020, DJI retained 77% of the US market share for consumer drones with no other company holding more than 4%.


title: DJI

text: In 2020, DJI drones are being used by many countries around the world to combat the Coronavirus. In China, DJI drones are used by the police force to remind people to wear masks. In other countries, such as Morocco and Saudi Arabia, their drones are used to disinfect urban areas and monitor human temperatures in order to contain the spread of Coronavirus.


title: DJI

text: In 2018, DJI raised roughly $1 billion in funds in preparation for an envisioned IPO at the Hong Kong Stock Exchange. As of July 2020, these rumors persisted with no indication that an IPO is forthcoming. The company had previously raised $500 million in a 2015 funding round from investors including state-owned New China Life Insurance, GIC, and New Horizon Capital, the latter being co-founded by the son of China's former premier minister Wen Jiabao.


title: DJI

text: DJI has also received investment from Shanghai Venture Capital Co., SDIC Unity Capital, owned by the State Development & Investment Corporation, and the China Chengtong Holdings Group, owned by the State-owned Assets Supervision and Administration Commission of the State Council.


title: DJI

text: DJI counts roughly 14,000 employees and has 17 offices internationally. The company is known for having a very difficult hiring process, as well as an extremely competitive internal culture, where teams are often pitted against each other to design better products.


title: DJI

text: DJI's factories in Shenzhen include highly sophisticated automated assembly lines. Many of the components for these assembly lines are built in-house.


title: DJI

text: DJI develops flight controllers intended for multi-rotor stabilization control of various platforms or heavy payloads in aerial photography. Their most prominent controller, the A2 controller, includes orientation, landing, and home return features. Some of their products include GPS-compass receivers, LED indicators and Bluetooth connectivity.


title: DJI

text: The Flame Wheel (风火轮) series are multirotor platforms for aerial photography. As of 2016, there is the hexacopter F550, and quadcopters F330 and F450. The most recent is the ARF KIT.


title: DJI

text: The Phantom (精灵) series has evolved to integrated flight programming with a camera, Wi-Fi or Lightbridge connectivity, and the pilot's mobile device. Phantoms are made for aerial cinematography and photography applications, but are also used in recreational use.


title: DJI

text: There have now been four generations of the product line, the most recent one is the Phantom 4 RTK, announced on October 15, 2018.


title: DJI

text: The Mavic (御) series currently includes Mavic Pro, Mavic Pro Platinum, Mavic Air, Mavic Air 2, DJI Air 2S, Mavic 2 Pro, Mavic 2 Zoom, Mavic 2 Enterprise, Mavic 2 Enterprise Advanced, Mavic 3, Mavic 3 Cine, Mavic Mini, DJI Mini SE, and DJI Mini 2 and Dji Mini 3 Pro. The release of the Mavic Air 2 was not without controversy, however, as DJI announced that a key safety feature, AirSense (ADS-B), would not be available on models outside the USA. Shortages on components and complexities of production owing to the ongoing COVID-19 crisis at the time were blamed.


title: DJI

text: Starting with the Mini 2, the Mavic name was dropped from most of the new models such as the Air 2S and the Mini SE.


title: DJI

text: The DJI Mavic 3 and the Mavic 3 Cine was released on November 4, 2021, at 10PM EDT. The Mavic 3 superseded the Mavic 2 Pro and the Mavic 2 Zoom and was priced for prosumers and professionals more than hobbyists. The Mavic 3 Enterprise and Mavic 3 Thermal were released on September 27, 2022, and superseded Phantom 4 RTK and Mavic 2 Enterprise Advanced drones in surveying, inspection, safety, and rescue tasks.


title: DJI

text: The Inspire (悟) series is a professional series of camera quadcopters similar to the Phantom line, but with an aluminum-magnesium body with carbon fibre arms, as well as detachable props on the Inspire 2. It was presented in 2017.


title: DJI

text: Released in May 2017, the Spark (晓) features a 12-megapixel camera stabilized mechanically by a 2-axis gimbal. The Spark also carries an advanced infrared 3D camera that helps the drone to detect obstacles in front of it, as well as facilitating hand-gesture control. In addition to a smartphone app with virtual controller, a physical controller can also be bought.


title: DJI

text: There have been multiple complaints that the drone switches off and fall while flying. DJI responded to this by releasing a mandatory battery firmware update in August 2017.


title: DJI

text: On March 2, 2021, DJI announced the launch of the DJI FPV, an entirely new type of hybrid drone combining the first-person view (FPV) and high-speed performance of racing drones, the cinematic camera and reliability of traditional consumer drones, and an optional innovative motion controller that allows pilots to control the drone with just single-handed movements. Based on DJI's earlier Digital FPV system, the drone features high-performance motors for a maximum air speed of and a 0-100 km acceleration of just 2 seconds under manual mode, an intuitive user interface and the latest safety features for greater flight control. The new FPV system lets pilots see from the drone's perspective in low-latency high-definition video thanks to "O3", the third iteration of DJI's proprietary OcuSync technology. It allows pilots to capture ultra-smooth and stable 4K video at 60 fps with the stabilization of RockSteady electronic image stabilization.


title: DJI

text: The Spreading Wings (筋斗云) series are mainly industrial UAVs for professional aerial photography, high definition 3D mapping, ultra-light search and rescue, and surveillance etc. based on camera gear on board. In 2013, two models were released: S800 regular and EVO.


title: DJI

text: The Matrice (经纬) series is designed for industrial applications, including surveying, inspection, search and rescue and firefighting.


title: DJI

text: The Matrice 100 is a fully programmable and customizable drone, launched on July 6, 2015. It has expansion bay and communication ports, which allows developers to add additional components for different purposes.


title: DJI

text: Agras is DJI's agricultural drone series with a takeoff weight of 25 - 80kg. Drones are used for spraying crops. Agras models have environmental protection and have IP67 rating for core parts and IP54 rating for batteries.


title: DJI

text: The Ronin (如影) is a standalone ground-based camera platform developed for cinematography and aerial filmmaking in professional environments. It is built for professional videography and photography and targets the film industry. By using three individual motors, Ronin stabilizes when moving vigorously. Later models of the Ronin include the Ronin-M, Ronin 2, Ronin-S, Ronin-SC, and the Ronin 4D.


title: DJI

text: The Osmo (灵眸) is a camcorder developed by DJI. The camera uses a smartphone to view camera footage and can record 4K and take either 12–16 MP stills. Later models include the Osmo Pocket and the Osmo Action.


title: DJI

text: The Osmo mobile relies on the user's smartphone as the camera. Most smartphones are accepted into the gimbal with a width range of 2.31–3.34 inch (58.6-84.8 mm). The original Osmo Mobile has reached its end-of-life and has been replaced with a second generation, called Mobile Osmo 2. Osmo Mobile 3 was announced in August 2019, and is designed for the social media crowd.


title: DJI

text: The DJI FPV series are head-mounted displays designed for FPV drone flying. There are two different product lines in the FPV series, the DJI Goggles (DJI) and the Digital FPV System (FPV). The DJI Goggles are designed to interface with DJI-branded drones, using dual LC display screens, wireless connectivity and direct photo and video capture control. In November 2017, DJI also released DJI Goggles RE ("Racing Edition"), which featured compatibility with racing quadcopters. The DJI Digital FPV System is a standalone system designed for non-DJI brand or custom-built drones.


title: DJI

text: On 11 June 2019, DJI unveiled the RoboMaster S1 ( S1), its first consumer ground drone, named after DJI's annual RoboMaster robot combat competition, of which it is now an unofficial mascot. The S1 is a tank-like rover remotely controlled in first-person view via Wi-Fi and an app on Microsoft Windows, Apple iOS or Google Android mobile devices. Designed to be an "advanced educational robot", the user has to assemble the S1 out of the box from loose parts and learn to program its AI functionality. Both Scratch and Python are programming languages employed by DJI along with app learning modules to teach the end user how to code.


title: DJI

text: The DJI RoboMaster EP ( EP) was officially released on March 9, 2020, although it was first teased in a YouTube RoboMaster S1 commercial on November 25, 2019.


title: DJI

text: The EP supports more than 20 third-party sensors and open-source hardware such as Micro Bit, Arduino and Raspberry Pi.


title: DJI

text: The United States Department of the Interior's Office of Aviation Services said in their analysis in July 2017 that DJI's software they did not meet requirement ""to decline and lock out any device information sharing including telemetry through aircraft, software or applications preventing any automated uploads or downloads."" As response DJI published the offline mode that allows its drones to fly without transferring data over the internet.


title: DJI

text: "The Register" reported in August 2017 that the DJI's Go app contained JSPatch framework which allowed DJI to hot-patch the app without triggering a review by Apple, or without first seeking user consent. This was against Apple's rules and 45,000 apps were blocked from the AppStore because of "hot patching concerns". In August the United States Army also changed its internal guidance on disallowing the use of DJI products, especially in battlefield scenarios. Guidance was based on an Army Research Laboratory report from May 2017 which found cyber-vulnerabilities. The US Army's decision launched public research where it was speculated that the decision was because the data link between the controller and the drone was vulnerable.


title: DJI

text: As a result, DJI released a bug bounty program for finding flaws. Security researcher Kevin Finisterre reported a security breach of private customer data at DJI to the bug bounty program. In the breach, developers had pushed the private keys for SSL, Cloud storage and firmware AES keys to a GitHub repository. As per Finisterre's description in Ars Technica, he was "able to access flight log data and images uploaded by DJI customers, including photos of government IDs, drivers licenses, and passports. Some of the data included flight logs from accounts associated with government and military domains." However, the after the long discussion with DJI's legal team, he decided to turn down the $30,000 bounty and publish the information.


title: DJI

text: In 2018, in response to the allegations of mishandling user data, DJI commissioned Kivu Consulting to make larger analysis. Kivu found that only DJI GO 4 app was connected to the Internet, it worked without Internet connection and only uploaded data after user confirmation. It also used servers which were located in the US except the crash reporting app called Bugly which uploaded crash reports to the server located in China.


title: DJI

text: In January 2020, the United States Department of the Interior announced that it would be grounding around 800 DJI drones over security concerns, which it had been using for wildlife conservation and infrastructure monitoring purposes.


title: DJI

text: In a May 2020 report analyzing the data use of DJI's Mimo app, which is used to control the Osmo gimbles from a smartphone, security research company River Loop Security made several discoveries "of concern" for users and policy-makers. According to the researchers, the social media app sends a variety of data, including sensitive personal information, through insecure means to servers located in China without user consent, raising suspicions that personal user data could be freely accessible to the Chinese authorities. User information was also sent to third-party servers, "where the Terms of Use Agreement supports cooperation with the Chinese Government."


title: DJI

text: In July 2020, the reports by Synacktiv and GRIMM on the security of the DJI GO 4 mobile app found that it collected user information (IMSI, IMEI, the serial number of the SIM card) from phones and was able to force the installation of updates. The app also prompted the user to grant permission to "Install Unknown Apps" for installing update from DJI site. The app also integrated to social media site Weibo's SDK similar way and allowed to install Weibo related third-party apps also. Synacktiv wrote "Given the wide permissions required by DJI GO 4 — contacts, microphone, camera, location, storage, change network connectivity — the DJI or Weibo Chinese servers have almost full control over the user's phone."


title: DJI

text: DJI responded that "system detects if a DJI app is not the official version – for example, if it has been modified to remove critical flight safety features like geofencing or altitude restrictions – we notify the user and require them to download the most recent official version of the app from our website. In future versions, users will also be able to download the official version from Google Play if it is available in their country" In the statement release DJI said that to use Weibo SDK user's need proactively turn it on. DJI also responded that “DJI GO 4 is not able to restart itself without input from the user, and we are investigating why these researchers claim (that it will stay running after it is closed) ”. In August 2020, Synacktiv alleged that DJI's Pilot app shares many of the same issues present in DJI GO 4, which DJI denied.


title: DJI

text: A 2020 analysis by Booz Allen Hamilton reported that they did not find evidence of unauthorized data transfers to China. The apps used the backend servers located in US. The only exception was the crash analytics which connected to Chinese servers.


title: DJI

text: In November 2020, senators Chris Coons, Rick Scott, and others criticized a decision by the United States Air Force to purchase DJI drones on security grounds.


title: DJI

text: In December 2020, the United States Department of Commerce added DJI to the Bureau of Industry and Security's Entity List. In January 2021, then President Trump signed an executive order mandating the removal of Chinese-made drones from U.S. government fleets. In December 2021, the United States Department of the Treasury prohibited investment in DJI by U.S. individuals and entities, accusing the company of assisting the People's Liberation Army and complicity in aiding the Uyghur genocide. In October 2022, the United States Department of Defense added DJI to a list of "Chinese military companies" operating in the U.S.


title: DJI

text: In May 2021, United States Department of Defense issued an analysis on DJI products. The unclassified portion of the report concluded that two types of drone in the DJI "Government Edition" line-up shows "no malicious code or intent and are recommended for use by government entities and forces working with US services." This is according to a summary obtained by "The Hill" though the Defense Department did not respond to an inquiry asking for elaboration.


title: DJI

text: In January 2015, a Phantom 3 drone crashed into the White House's south lawn, in Washington, D.C., US. DJI later set up a no-fly Geo-system according to prohibited airspace, and forced all drones to update the firmware. The system introduced will prevent flights from getting closer to, or take off in restricted zones, based on GPS location.


title: DJI

text: A DJI Phantom 2 drone carrying radioactive material was landed on the Prime Minister's Official Residence in Tokyo, Japan—the 2015 Tokyo drone incident. Subsequently, the National Diet passed a law restricting drone flights near government buildings and nuclear sites.


title: DJI

text: In 2016, ISIS used DJI drones as exploding devices in Iraq. DJI later created a broad no-fly zone over nearly all of Iraq and Syria. That year, a DJI drone was nearly involved in a midair collision with a Chinese fighter jet. The Chinese government subsequently insisted that DJI develop an air traffic registry to track its drones within China.


title: DJI

text: On 4 August 2018, two Matrice 600 drones detonated explosives near Avenida Bolívar, Caracas in an apparent attempt to assassinate Venezuelan president Nicolás Maduro.


title: DJI

text: Ukraine has used DJI drones extensively after being invaded by Russia, while battlefield footage suggests their usage by Russia as well. After German retailer Media Markt stopped selling DJI drones, DJI said that its products were for civilian use and inappropriate for the military. Following criticism of the company's operation in Russia, DJI suspended its business in both Russia and Ukraine to prevent its products from being used in combat.


title: DJI

text: Ukrainian troops have used DJI drones to conduct reconnaissance and direct strikes on Russian forces. Ukrainian troops have also used modified DJI drones to drop improvised explosives on opposing forces.


title: DJI

text: A Ukrainian soldier told CNN that Russian forces were able to use the drones' AeroScope function to track Ukrainian operators. Ukrainian Vice Prime Minister Mykhailo Fedorov said that without no-fly zones imposed by DJI, its drones were being used by Russia against Ukrainian forces and that Russian forces were able to track Ukrainian drones using the AeroScope detection platform. DJI replied to him on Twitter saying that its drones are designed for civilians and that requirements such as AeroScope and Remote ID make them inappropriate for military use. DJI can set up geofencing in Ukraine if its government were to make a formal request, but doing so could affect all parties' drones unless individual units are prevented from downloading the geofencing update. "The Verge" did not find any confirmed reports on Russian AeroScope usage and interviewed a DJI spokesperson to clarify the issue.


title: Paradise, Nevada

text: Paradise is an unincorporated town and census-designated place (CDP) in Clark County, Nevada, United States, adjacent to the city of Las Vegas. It was formed on December 8, 1950. Its population was 191,238 at the 2020 census, making it the fifth most populous CDP in the United States; if it were an incorporated city, it would be the fifth largest in Nevada. As an unincorporated town, it is governed by the Clark County Commission with input from the Paradise Town Advisory Board.


title: Paradise, Nevada

text: Paradise contains Harry Reid International Airport, the University of Nevada, Las Vegas (UNLV), most of the Las Vegas Strip, and most of the tourist attractions in the Las Vegas area (excluding downtown).


title: Paradise, Nevada

text: The southern part of the Las Vegas Valley was referred to as Paradise Valley as early as 1910, owing to a high water table that made the land particularly fertile for farming. County commissioners established a Paradise school district in 1914.


title: Paradise, Nevada

text: In 1950, mayor Ernie Cragin of Las Vegas sought to annex the Las Vegas Strip, which was unincorporated territory, in order to expand the city's tax base to fund his ambitious building agenda and pay down the city's rising debt. A group of casino executives, led by Gus Greenbaum of the Flamingo, lobbied the county commissioners for town status, which would prevent the city from annexing the land without the commission's approval. The commission voted to create the unincorporated town of Paradise on December 8, 1950. The town encompassed a strip wide and long, from the southern city limits of Las Vegas to just south of the Flamingo. The town board initially consisted of five casino managers, chaired by Greenbaum.


title: Paradise, Nevada

text: A month after its establishment, the town was expanded to include the residential areas of Paradise Valley, giving it a total area of . Months later, however, it was reported that county officials had determined that the town had not been properly established, because the petition for the town's formation had an insufficient number of signatures and because it had violated a state law forbidding formation of a town spanning multiple school districts. On August 20, 1951, county commissioners accepted petitions to create two new towns covering the area of the putative town. Town "A" of Paradise included the areas that lay within a Las Vegas school district, extending from the city limits to a point one mile south, while Town "B" included the areas within the Paradise school district.


title: Paradise, Nevada

text: In 1975, Nevada enacted a law that would have incorporated Paradise (along with Sunrise Manor and Winchester) into the City of Las Vegas. Before it could take effect, however, the bill was struck down as unconstitutional by the Nevada Supreme Court.


title: Paradise, Nevada

text: According to the United States Census Bureau, the census-designated place (CDP) of Paradise (which may not coincide exactly with the town boundaries) has a total area of , all of it land.


title: Paradise, Nevada

text: The official town boundaries are bordered by Desert Inn Road to the north, Nellis Boulevard to the east, Sunset Road to the south and Decatur Boulevard to the west. There is a southern finger between Bermuda Road and Eastern Avenue south to Silverado Ranch Boulevard. South of Russell Road, the eastern border stair steps on a rough 45-degree angle toward the corner of Eastern and Robindale Road, and there is an additional finger surrounding Interstate 215 east to St. Rose Parkway.


title: Paradise, Nevada

text: At the census of 2010, there were 223,167 people residing in Paradise. The racial makeup was 59.8% White, 8.9% African American, 0.8% Native American, 9.5% Asian, 1.0% Pacific Islander, and 5.5% from two or more races. Hispanic or Latino residents made up 31.2% of the population, and 46.3% of the population was non-Hispanic White.


title: Paradise, Nevada

text: As of the census of 2000, there were 186,070 people, 77,209 households, and 43,314 families residing in the CDP. The population density was . There were 85,398 housing units at an average density of . The racial makeup of the CDP was 72.51% White, 6.59% African American, 0.77% Native American, 6.52% Asian, 0.59% Pacific Islander, 8.37% from other races, and 4.65% from two or more races. Hispanic or Latino of any race were 23.47% of the population.


title: Paradise, Nevada

text: There were 77,209 households, out of which 24.6% had children under the age of 18 living with them, 39.7% were married couples living together, 10.5% had a female householder with no husband present, and 43.9% were non-families. 31.9% of all households were made up of individuals, and 7.5% had someone living alone who was 65 years of age or older. The average household size was 2.39 and the average family size was 3.04.


title: Paradise, Nevada

text: In the CDP, the population was spread out, with 21.2% under the age of 18, 10.8% from 18 to 24, 33.3% from 25 to 44, 23.6% from 45 to 64, and 11.1% who were 65 years of age or older. The median age was 35 years. For every 100 females, there were 109.1 males. For every 100 females age 18 and over, there were 110.0 males.


title: Paradise, Nevada

text: The median income for a household in the CDP was $39,376, and the median income for a family was $46,578. Males had a median income of $31,412 versus $25,898 for females. The per capita income for the CDP was $21,258. 11.8% of the population and 8.1% of families were below the poverty line. 15.3% of those under the age of 18 and 7.6% of those 65 and older were living below the poverty line.


title: Paradise, Nevada

text: The Clark County School District serves Paradise, as well as the rest of Clark County. The township is home to the University of Nevada, Las Vegas.


title: Paradise, Nevada

text: Paradise is home to Las Vegas's three major league sports teams: the Vegas Golden Knights of the National Hockey League (NHL), which play at T-Mobile Arena, the Las Vegas Raiders of the National Football League (NFL) which play at Allegiant Stadium, and the Las Vegas Aces of the WNBA which play at Michelob Ultra Arena. Super Bowl LVIII in 2024 will be played at Allegiant Stadium.


title: Paradise, Nevada

text: As UNLV is located in Paradise, most of its various teams play in the township. The UNLV Rebels football program plays at Allegiant Stadium, and the Runnin' Rebels and Lady Rebels play at Thomas & Mack Center and in the Cox Pavilion respectively.


title: Paradise, Nevada

text: Also, since 2004, the Las Vegas Summer League, organized by the National Basketball Association (NBA), is played in the Thomas & Mack Center and in the Cox Pavilion.


title: Paradise, Nevada

text: Paradise will also become the home of the upcoming Las Vegas Grand Prix where the circuit will take place around the Las Vegas Strip. The grand prix will become take place in November 2023 as part of the 2023 Formula One World Championship.


title: Environmental issues

text: Environmental issues are effects of human activity on the biophysical environment, most often of which are harmful effects that cause environmental degradation. Environmental protection is the practice of protecting the natural environment on the individual, organizational or governmental levels, for the benefit of both the environment and humans. Environmentalism is a social and environmental movement that addresses environmental issues through advocacy, legislation education, and activism.


title: Environmental issues

text: Environment destruction caused by humans is a global, ongoing problem. Water pollution also cause problems to marine life. Most scholars think that the project peak global world population of between 9-10 billion people, could live sustainably within the earth's ecosystems if human society worked to live sustainably within planetary boundaries. The bulk of environmental impacts are caused by the most wealthy populations in the globe consuming too much industrial goods. The UN Environmental Program, in its "Making Peace With Nature" Report in 2021, found addressing key planetary crises, like pollution, climate change and biodiversity loss, was achievable if parties work to address the Sustainable Development Goals.


title: Environmental issues

text: Major current environmental issues may include climate change, pollution, environmental degradation, and resource depletion. The conservation movement lobbies for protection of endangered species and protection of any ecologically valuable natural areas, genetically modified foods and global warming. International frameworks for environmental issues focus on three key issues as the "triple planetary crises": climate change, pollution, and biodiversity loss.


title: Environmental issues

text: Environmental issues are addressed at a regional, national or international level by government organizations.


title: Environmental issues

text: The largest international agency, set up in 1972, is the United Nations Environment Programme. The International Union for Conservation of Nature brings together 83 states, 108 government agencies, 766 Non-governmental organizations and 81 international organizations and about 10,000 experts, scientists from countries around the world. International non-governmental organizations include Greenpeace, Friends of the Earth and World Wide Fund for Nature. Governments enact environmental policy and enforce environmental law and this is done to differing degrees around the world.


title: Environmental issues

text: There are an increasing number of films being produced on environmental issues, especially on climate change and global warming. Al Gore's 2006 film "An Inconvenient Truth" gained commercial success and a high media profile.


Metal Gear Solid 4: Guns of the Patriots is a 2008 stealth game developed by Kojima Productions and published by Konami for the PlayStation 3. It is the sixth "Metal Gear" game directed by Hideo Kojima.


title: Metal Gear Solid 4: Guns of the Patriots

text: Set five years after the events of "", the story centers around a prematurely aged Solid Snake, now known as Old Snake, as he goes on one last mission to assassinate his nemesis Liquid Snake, who now inhabits the body of his former henchman Revolver Ocelot under the guise of Liquid Ocelot, before he takes control of the Sons of the Patriots, an A.I. system that controls the activities of PMCs worldwide. It was released worldwide on June 12, 2008.


text: "Guns of the Patriots" received universal acclaim, with praise for its gameplay, graphics, story, characters, and emotional weight, although a few criticized its plot as convoluted and the emphasis on cutscenes. The game garnered Game of the Year awards from several major gaming publications. It is considered one of the seventh generation's console gaming's most significant titles, as its release caused a boost in sales of the PlayStation 3, and had sold over six million copies worldwide by 2014.


text: In "MGS4", players assume the role of an aged Solid Snake (colloquially referred to as Old Snake), using stealth, close quarters combat, and traditional "Metal Gear" combat. The overhead third-person camera of earlier games has been replaced by a streamlined view and over-the-shoulder camera for aiming a weapon, with an optional first-person view at the toggle of a button.


text: A further addition to gameplay mechanics is the Psyche Meter. Psyche is decreased by non-lethal attacks and is influenced by battlefield psychology. Stressors (including temperature extremes, foul smells, and being hunted by the enemy) increase Snake's stress gauge, eventually depleting his Psyche. Adverse effects include difficulty in aiming, more frequent back pain and the possibility of Snake passing out upon receiving damage. If Snake kills too many enemies in a short amount of time, he will have a vision of Liquid and vomit, greatly reducing his Psyche. Among the available methods of restoring Psyche are eating, drinking, smoking, and reading an adult magazine.


text: Snake has a few gadgets to aid him in battle. The OctoCamo suit mimics the appearance and texture of any surface in a similar fashion to an octopus, decreasing the probability of Snake being noticed. Additionally, FaceCamo is made available to players after they defeat Laughing Octopus. FaceCamo can be worn by Solid Snake on his face and it can be set to either work in tandem with the Octocamo or instead mimic the face of other in-game characters. However, to get access to these unique FaceCamos, players have to complete certain in-game requirements first. When the FaceCamo is worn with OctoCamo, under ideal conditions, Snake's stealth quotient can reach 100%. The Solid Eye device highlights items and enemies and can operate in a night vision and a binocular mode. It also offers a baseline map, which indicates the location of nearby units. The latter function is also performed by the Threat Ring, a visualization of Snake's senses that deforms based on nearby unit proximity and relays them to the player.


text: Metal Gear Mk.II (later replaced with Mk.III), a small support robot that always tags along with Snake, offers codec functionality and a means to the in-game menu for a large part of Snake's mission. It can be remotely controlled to stun enemies, provide reconnaissance and interact with the environment. Its design is based on the namesake robot from "Snatcher", a game designed by Hideo Kojima. It is also controlled during the beginning of each separate "Act", although the player is not able to utilize its capabilities during this time.


text: Whenever the Drebin menu is available, weapons, attachments, and ammunition can be purchased via Drebin Points (DPs), awarded for on-site procurement of weapons already in the inventory and by initiating specific scripted events or destroying Unmanned Vehicles. The conversion rate between weapons and DPs depends on current battlefield conditions, with more-intense fighting yielding higher prices. Also, Drebin would purchase items from the player at a discounted price, especially at certain points in the story and certain days in real life. The game may also be finished without killing anyone, using non-lethal weapons.


text: The Virtual Range, similar to the training of previous titles, functions as a test facility for weapon performance and gameplay controls.


text: "Guns of the Patriots" is set within an alternate history timeline in which the Cold War continued into the 1990s before ending before the turn of the century. The events themselves take place in 2014, five years after "Sons of Liberty", and form the final chapter in the storyline covering the character of Solid Snake, providing conclusions to the events that led up to "Guns of the Patriots".


text: The world's economy relies on continuous civil wars fought by PMCs, which outnumber government military forces. Soldiers are equipped with nanomachines that monitor and enhance their performance on the battlefield, controlled by a vast network known as the Sons of the Patriots (SOP) system. Revolver Ocelot, missing since the events of "Sons of Liberty", is possessed by the will of Liquid Snake and re-emerges from hiding to launch an insurrection against the Patriots, a secret cabal which manipulates global affairs from the shadows.


text: Solid Snake, meanwhile, is experiencing accelerated aging and has about a year left to live. He is living on board the airplane "Nomad" with Dr. Hal "Otacon" Emmerich and Olga Gurlukovich's daughter Sunny, a child prodigy in computer programming. Since the aftermath of the , Raiden has drifted away from Rose, who had apparently suffered a miscarriage with their child and gone to live with his former commander Colonel Roy Campbell, and has become a cyborg ninja fighting against the Patriots. Meryl Silverburgh commands a PMC inspection unit in the U.S. military, which includes Johnny Sasaki.


text: After learning of his year-long lifespan from Werner syndrome-like symptoms, Snake is tasked by Campbell, now working with the UNSC, to assassinate Liquid Ocelot. In a Middle-Eastern war zone occupied by one of Liquid's PMCs, Snake meets Drebin, an arms dealer who injects Snake with nanomachines to use the latest weaponry, and Meryl. Snake reaches Liquid, but the latter transmits a signal that incapacitates those nearby with nanomachines. Snake sees Dr. Naomi Hunter, who departs with Liquid.


text: In South America, Snake locates Naomi, herself a captive of Liquid. She explains that Liquid plans to use Big Boss' biometrics to access and take command of the Patriots' firearms control system. Snake learns his accelerated aging is due to intentional genetic mutations as a clone. The FOXDIE virus inside him will also mutate within months, spreading to the general populace and causing a deadly pandemic. Liquid's PMC soldiers kidnap Naomi, but Snake rescues her, assisted by Drebin and Raiden, and they escape, though Raiden is injured by Vamp.


text: Snake locates an Eastern-European resistance group to heal Raiden and which possesses the comatose body of Big Boss. Its leader EVA reveals she was the surrogate mother to Snake and Liquid through the cloning process. They move Big Boss' body by boat while Liquid's PMC soldiers attack decoys. Liquid captures the body and obtains the biometrics, intending to infiltrate the Patriots' system by using the , as a trojan. US soldiers arrive to arrest Liquid, but he kills them after disabling their firearms. Big Boss' body is set alight, and Snake saves EVA from the fire when she tries to save the body, but in the process, he gets badly injured and his left cheek is permanently burned. Naomi leaves with Liquid, but Otacon tracks them. EVA dies from her injuries.


text: Snake and Otacon learn that Liquid aims to destroy the Patriots' master AI with a nuclear strike, allowing GW to take control. A non-ID-tagged warhead is required from Metal Gear REX at Shadow Moses in Alaska. There, Snake is ambushed by Vamp, accompanied by Naomi. Vamp is killed when his self-healing nanomachines are disabled via injection. Naomi reveals she has terminal cancer; overcome with guilt for her mistakes, she also disables the nanomachines keeping her alive and dies. Snake and Raiden use REX to escape and fend off Liquid piloting a Metal Gear RAY. Liquid reveals "Outer Haven", a modified Arsenal Gear. Raiden saves Snake from being crushed before the USS "Missouri", captained by Mei Ling, arrives and forces Haven to retreat.


text: Snake, Meryl, and Johnny board Haven when it surfaces to launch the nuke. At the core, Snake installs a virus coded by Naomi and Sunny into Liquid's trojan; it destroys not only the core AI but the entire Patriot network controlling global affairs, leaving the necessities for civilization to survive. Atop Haven, Liquid explains to Snake that he allowed the virus' installation to destroy the Patriots. The two fight, with Snake victorious. Liquid becomes Ocelot again before dying.


text: Meryl reconciles with her father, Campbell, and marries Johnny. Raiden reunites with Rose after learning their child was not miscarried and that her marriage to Campbell was a ruse to protect them from the Patriots. Snake visits Gray Fox’s grave at a cemetery. Having no further purpose, and to prevent an epidemic from his FOXDIE, Snake attempts suicide but relents.


text: Snake is then met by Big Boss with a vegetative Zero; the body burned in Europe was Solidus Snake. Big Boss reveals that the Patriots were founded by himself, Zero, EVA, Ocelot, Sigint, and Para-Medic to realize the will of the Boss, Big Boss' mentor. Differing interpretations split the group into two factions: Zero's, which stood for government control of society to prevent conflict, and Big Boss', where soldiers fought for personal beliefs, unrestrained by governments. Zero consigned control to artificial intelligence networks, the Patriots. After Big Boss' downfall in Zanzibar, the Patriots placed him in an induced coma, and later initiated the war economy, a vision far from the Boss' will. Ocelot and EVA planned to restore Big Boss by destroying the Patriots. The "possession" of Ocelot through Liquid was a ruse to draw the Patriots' attention. Big Boss then kills Zero by cutting off his life support.


text: He informs Snake that the nanomachines from Drebin contained FOXDIE, engineered by the Patriots to kill EVA, Ocelot, and Big Boss. With the new strain supplanting the mutated strain, Snake poses no risk of becoming a biological weapon unless he lives long enough for it to mutate. After understanding his mentor's will and telling Snake to find a new reason to keep living, Big Boss dies beside the Boss' grave. Snake decides to live the time he has left peacefully with Otacon and Sunny.


text: "Metal Gear Solid 4" started development due to fan demand. Series creator Hideo Kojima had previously directed the prequel "" which was meant to end the series. However, people's demand to have a sequel to "" and clear the mysteries Kojima wanted to leave to the players' interpretations resulted in the making of "Metal Gear Solid 4". Kojima announced that he would be retiring as director of the "Metal Gear" series after "", and would leave his position open to another person for "Metal Gear Solid 4". As a joke, the new director was announced as "Alan Smithee", but in "R", a 400-page book bundled with "Metal Gear Solid 3"s Japanese "Premium Package", the director was revealed to be Shuyo Murata, co-writer of "MGS3" and director of "". He also contributed easter eggs to "Metal Gear Solid 2: Sons of Liberty" and "Metal Gear: Ghost Babel". However, it was announced that Kojima would be co-directing the game with Murata after substantial negative fan reaction, including death threats.


text: Hideo Kojima wished to implement a new style of gameplay which was set in a full-scale war zone. Kojima wanted to also retain the stealth elements from previous entries in the series, which made the team abandon the original "No Place to Hide" concept. The only announced war zone before release was the Middle East. Using several locations emphasized Kojima's original intention to present the world in full-scale armed conflict. Solid Snake was physically aged to portray to the player the games' overarching theme, "SENSE", and to assign them to a character whose task was to pass moral values to future generations. Kojima's initial ending for the "MGS4" would entail Snake and Otacon turning themselves in for breaking the law, and subsequently convicted and executed. This was avoided after negative feedback from the development team. Snake's experience across the series made the creation of new enemies challenging and encouraged staff to create groups of non-human enemies to rival Snake.


text: During development, the game's exclusivity was continuously questioned, even after Kojima officially confirmed the exclusivity several times. The exclusivity of the game was still in doubt from non-PlayStation 3 owners for a long period after the initial release, with the company confirming that the 25th Anniversary edition of the game released in late 2012 was still a PS3 exclusive. Upon the release of "", Kojima had once again firmly denied chances of "MGS4"s release on any other console, stating that an "Xbox 360 version [will not be] released, because an Xbox 360 version of "MGS4" hasn't gone on sale." and that "the amount of data in "MGS4" is just too enormous".


text: The game was publicly announced first at E3 2005, by means of a humorous and slightly abstract gag machinima using characters from "Metal Gear Solid 3", under the slogan of "No Place to Hide". The title was described as "essentially finished" by January 2008 and went through extensive beta testing. At Destination PlayStation on February 26, 2008, Sony announced that "MGS4" would be released worldwide on June 12, 2008, along with the special "MGS4" PlayStation 3 bundle. It was announced that "Guns of the Patriots" is the first PlayStation 3 game that uses a 50GB dual layer Blu-ray Disc even with the use of file compression.


text: The budget for the game has been estimated to be between US$ 50-70 million. However, Kenichiro Imaizumi from Kojima Productions denied this stating if it had cost this much, the game would have been for multiple platforms. One of the main objectives of the budget was research of environments the game would feature.


text: The score to "Metal Gear Solid 4" was led by Harry Gregson-Williams, his third "Metal Gear Solid" soundtrack, and Nobuko Toda, who provided music for "Metal Gear Acid" and "Metal Gear Acid 2". Other contributors are Konami employees Shuichi Kobori, Kazuma Jinnouchi, Akihiro Honda, and Sota Fujimori. Directed by Norihiko Hibino, GEM Impact employees Yoshitaka Suzuki and Takahiro Izutani also made compositions late in the game's production. It was revealed in an interview with Norihiko Hibino that the team, in fact, wrote 90 minutes of music for the game's cutscenes, only 15 minutes of which made its way onto the official soundtrack.


text: There are two vocal themes for the game. The opening theme, "Love Theme", is sung by Jackie Presti and composed by Nobuko Toda. The ending theme, "Here's to You", is sung by Lisbeth Scott. Before the release of the game, "MGS4 - Theme of Love - Smash Bros. Brawl Version" was provided for "Super Smash Bros. Brawl" in the Shadow Moses Island level. The "Metal Gear Solid Main Theme", composed by Tappi "Tappy" Iwase, was notably omitted from the soundtrack, and the soundtrack of "". In an interview with "Electronic Gaming Monthly", Norihiko Hibino stated that the company had difficulties with "Russian composers who said we stole their music", referring to an occasion when a group of Russian games journalists presented Hideo Kojima with a composition by Georgy Sviridov and claimed this had been plagiarised to create the theme. Hibino states that "they didn't actually", however, the company was "too sensitive about the situation" and elected to drop the theme.


text: The official soundtrack was released on May 28, 2008, by Konami Digital Entertainment under the catalog number GFCA-98/9. It consists of two discs of music and 47 tracks. A soundtrack album was also packaged with "Metal Gear Solid 4: Guns of the Patriots Limited Edition".


text: In August 2009, when asked if there would be a patch to add Trophies to the game, Kojima Productions' Sean Eyestone asked people to "stay patient". This led to speculation that an updated version of the game in the vein of "Substance" or "Subsistence" would be released alongside a Trophy patch. In November 2010, an updated Greatest Hits box art of the game was released, which in the top right-hand corner boasted the addition of "Trophies" to the game. This was later reported as a "typo", and removed from later printings. False reports of an "incoming Trophy Patch" often appeared, usually on internet forums and on April Fools' Day, some even going to the extent of a mock-up Trophy listing. In July 2012, a patch was announced which would include Trophies for the game, which would later be released on August 6, 2012. In addition to the support for Trophies, the patch also allowed a full install of the game onto the hard drive to remove the installs between acts.


text: The game received new content through PlayStation Network (in-game downloads) between 2008 and 2009. A total of 49 free add-ons have been released, which include 25 additional OctoCamo patterns, 12 podcasts and 12 iPod songs (a thirteenth song, named "Chair Race" was removed for copyright reasons in 2011). On July 16, 2014, it was announced on the Japanese site that all DLC downloads would terminate on July 31. However, a workaround was made in January 2015. As of today, this is the only way to obtain the content, as it was never made available on PlayStation Store.


text: "Metal Gear Solid 4" includes the Starter Pack for "Metal Gear Online" ("MGO"). "MGO" features up to 16 player online tactical battles and incorporates several gameplay elements from "Metal Gear Solid 4", including the SOP system that allows players to have a visual confirmation of their teammates' position and battle status. "MGO" also allows fully customizable characters. The Starter Pack allows players to engage in sneaking missions, where Old Snake and Metal Gear Mk.II acquire dog tags from other human contestants, along with standard Deathmatch, Team Deathmatch, and several special modes. Expansions packs, offering more maps and playable special characters (Mei Ling, Meryl, Akiba, Liquid Ocelot, Raiden, and Vamp), can be purchased via the "MGO" menu item "MGO Shop (PlayStation Network)", or via MGO or Konami's shop. The PlayStation Wallet is used for the first option and a credit card for the latter two. "Metal Gear Online" was completely shut down on June 13, 2012.


text: On June 19, 2008, Konami released the "Metal Gear Solid 4 Database" onto the PlayStation Store in North America and Japan, and one week later on the European store. The Database is a downloadable application for PlayStation 3 that catalogs every piece of "Metal Gear" lore from all the canonical entries in the series released up to "Metal Gear Solid 4" in the form of an encyclopedia (browsable by alphabet and category), a timeline, and character relationship diagrams. Highlighted words in each article link to related articles, and it keeps track of which ones the user has already read. The Database automatically locks any items related to "MGS4", in order to prevent the leaking of spoilers to players who have not completed the game yet. In order to reveal these articles, the user must have a completed "MGS4" game save that was created on the same console and with a version of the game from the same region as their account.


text: At a press conference on May 13, 2008, Hideo Kojima announced a marketing campaign and agreements with several companies to promote the game. Apple computers and monitors feature in the game and an Apple iPod is an in-game item that Snake can use to change the background music, listen to in-game podcasts and collect hidden songs scattered throughout the game. ReGain Energy Drinks are used in the game as a Psyche gauge booster, and Sony Ericsson mobile phones are used, specifically by Naomi and Vamp. In addition, the motorcycles featured in the game are a Triumph Bonneville and Speed Triple. Konami and Ubisoft put an unlockable costume in the game for Snake, Altaïr from the Ubisoft stealth game "Assassin's Creed". Initially revealed on April Fool's Day 2008, Kojima later announced that it would actually be in the game, unlockable by doing "something special". To obtain the attire, the player must acquire the "Assassin Emblem", a nod to the game's title (or input a password in the Extras section).


text: Konami had originally planned to organize grand launch events in Tokyo, but some of them were canceled with the "safety of participants in mind" in light of the Akihabara massacre on June 8, 2008. On June 15, 2009, a year after its release, Konami re-released "MGS4" as a part of Sony's Greatest Hits collection.


text: "Metal Gear Solid Touch" for the iPhone, iPod Touch and iPad is a "touch shooting" game that revisits "MGS4"s plot and action through the touch interface. Developers of the game "LittleBigPlanet", Media Molecule, released an expansion pack based on "Metal Gear Solid 4" on December 23, 2008. It includes character skins for Old Snake, Raiden, Meryl, and Screaming Mantis, as well as a "Metal Gear"-themed set of levels.


text: In October 2011, Konami and Hasbro produced a special "MGS4"-themed version of "Risk", which had playing pieces based on the game's various characters, plus a battle map based on Outer Haven. The game's characters can also be used as special allies. A novelization of "Guns of the Patriots" written by Project Itoh was published by Kadokawa Shoten in Japan on the day of the game's release. An English-language translation of the novel was published in North America in June 2012.


text: A Limited Edition was released simultaneously with the game's standard edition, as an enhanced counterpart. The limited edition contains "Guns of the Patriots", a box with artwork by Yoji Shinkawa, a Blu-ray Disc containing two "making of" documentaries, and partial game soundtrack containing only songs written by Harry Gregson-Williams. The Limited Edition was available exclusively at GameStop in the United States and EB Games in Canada, while a similar bundle with an additional 6-inch 'Olive Drab' Old Snake Figurine was made available at Play.com in the United Kingdom. It is also included in the 40GB Limited Edition PlayStation 3 "Metal Gear Solid 4" bundle.


text: In North America, a bundle containing an 80GB PlayStation 3, a DualShock 3 wireless controller, a downloadable game coupon for "Pain", and a copy of "Metal Gear Solid 4: Guns of the Patriots" was released for US$499 on June 12, 2008, to coincide with the release of the standalone edition. Japan saw the release of the "Guns of the Patriots Welcome Box" that contains the game itself, a DualShock 3 controller, a Sixaxis controller, and a 40GB PlayStation 3 in either black, white or silver.


text: Sony also announced a limited edition pre-order bundle containing "Guns of the Patriots Limited Edition" and a matte grey (officially titled Gunmetal Grey) 40GB PlayStation 3. First announced in Japan on March 18, 2008, at a cost of ¥51,800, the bundle sold out by March 25, 2008. An identical bundle was available in North America for pre-order on May 19, 2008, in "very limited" supply for US$600 at Konami's official website. David Reeves has announced a similar bundle for Europe which includes a 40GB PlayStation 3, the game itself and a DualShock 3 controller.


text: A downloadable version of the game was released on PlayStation Store at the end of 2014. It was also briefly available as a PlayStation Now rental title in North America, before being delisted by Konami due to undisclosed reasons. It was added again to the service in March 2019.


text: "Metal Gear Solid 4" received universal acclaim, according to review aggregator website Metacritic. The first review was a 10/10 from "PlayStation Official Magazine" (UK), commenting ""MGS4" shifts gears constantly, innovating again and again". The game has been awarded 10/10 from "Game Informer" and a 5/5 in all categories (graphics, control, sound, and fun factor) from "GamePro". Japanese magazine "Famitsu" (40/40) and "Empire". The game received a 9.9/10 from IGN United Kingdom, a 9.5/10 from IGN Australia, and a 10/10 from IGN USA. IGN was quoted in a video review, saying "MGS4" is "one of the best games ever made". "Edge" and "Eurogamer" both gave the game 8/10. GameSpot gave it a 10/10 saying ""Metal Gear Solid 4: Guns of the Patriots" is the most technically stunning video game ever made", making "MGS4" one of only five games ever to receive a perfect "10" from both IGN and GameSpot, and the sixth of only nine games to receive a perfect ten from GameSpot overall.


text: Reviewers acclaimed the manner in which the title concludes the series. Eurogamer stated that "You could not ask for a funnier, cleverer, more ambitious or inspired or over-the-top conclusion", and IGN found that the result "refines the "MGS" formula and introduces just enough new (or respectfully influenced) ideas to ensure that it stands on its own as a game". "Edge" concluded that "it is faithful to its fans, its premise and its heart, delivering an experience that is, in so many ways, without equal", while IGN UK described it simply as "the ultimate "Metal Gear" game" and "a dazzling, heart-lifting, voyage of discovery". The game was also described as being unusually sad and depressing for a video game. Kotaku said, ""Metal Gear Solid 4" is so unusual in that it's the rare game that asks them to be interested in something else: a march toward defeat, an interactive tragedy."


text: The new control scheme ("the ideal balance of intuitiveness and range"), camouflage system and shift to more free-form, "replayable" gameplay (in particular the Drebin Points system and alternatives to "stealthy" play) were particularly highly praised with a few minor annoyances. The variety of set-piece events, details such as the "psyche" meter, and healthy provision of secrets were also remarked upon. Eurogamer tempered their overall praise with concern that one of the chapters may induce "ennui", but noted that the game quickly recovered, while "Edge" expressed mild disappointment that the "Beauty and the Beast" unit compare poorly to the previous title's main foes, the "Cobra Unit".


text: The game was also lauded for its technological and artistic achievements, with "Edge" describing the "Otacon" character as "the real star", and "a gaming revolution" while they found the game's score to be superior to that of many Hollywood offerings. The magazine felt that the few visual shortfalls (such as texture detail) did nothing to detract from the game's overall quality. IGN UK commented that the attention to detail in both visuals and audio represented "sublime brilliance", and remarked upon innovations such as the use of split-screen.


text: Criticism of the game was largely leveled at the storyline, which reviewers found at times to be confusing or poorly executed and with IGN UK advising players to revisit the earlier titles for clarity. However, the overall result was praised as emotionally engaging and topical, and characters such as Liquid Ocelot were singled out for the quality of their depiction. It was generally conceded that although the use of cutscenes were more intrusive than they needed to be (comprising "about half of the content of the game" by one estimate, and which "might make you crave action, or wonder why they couldn't have been turned into interactive sequences"), the style was somewhat appropriate given the rest of the series ("in many ways it's a vindication of Kojima's unique interpretation of the videogame medium") and unlikely to trouble fans. The addition of a pause function for these story sequences was universally welcomed.


text: "Edge" and "Eurogamer" alike concluded that although the game represents an apotheosis of the series style, it ultimately fails to revitalize it, and would not win over new fans. IGN UK was concerned that the game's hype and widespread praise may lead to disappointment, but felt that the game was a "masterpiece".


text: According to Konami, the game shipped over 3 million units worldwide on the day of its release. According to Enterbrain, "Guns of the Patriots" sold 476,334 copies in its first four days on sale in Japan, which includes copies bundled with the PlayStation 3, and caused a boost in PlayStation 3 sales. The PS3, which at the time sold about 10,000 units in a given week, went on to sell 77,208 units in the games debut week. It was the 11th best-selling game of Japan in 2008, selling 686,254 copies. According to Chart-Track, the game is the second fastest-selling PlayStation 3 title in the United Kingdom after "Grand Theft Auto IV" and was below ""'s opening weekend figure by 14,000 copies recorded in 2002; the sales of the PlayStation 3 increased by a "minimal" seven percent over the opening weekend. Konami has reported that "MGS4" sold over one million copies across Europe in its first week, with 25,000 limited-edition copies "snapped up almost immediately". The game received a "Platinum" sales award from the Entertainment and Leisure Software Publishers Association (ELSPA), indicating sales of at least 300,000 copies in the United Kingdom. In the United States, "MGS4" was the best-selling game in June 2008 selling 774,600 copies (nearly one million if the number of copies bundled with the PlayStation 3 console was included), causing PS3 sales to double over the previous month, according to the NPD Group. As of December 2009, the game had sold over 5 million copies worldwide, as stated on page 5 of Konami's 3rd Quarter Financial Results. This milestone labeled it as the best-selling PlayStation 3 exclusive until the release of "Gran Turismo 5". Metal Gear Solid 4: Guns of the Patriots is now one of the Platinum range of bestselling games. However, these figures were widely misreported as it also included other games in the franchise. On May 21, 2014, Ryan Payton, a former employee of Kojima Productions who worked on "Metal Gear Solid 4", stated that the game has sold 6 million copies.


text: Following the critical acclaim it received upon its release, "Metal Gear Solid 4" won many Game of the Year awards from many international outlets, these including GameSpot, Gamezine, and "PALGN", along with a significant number of Readers' Choice awards, and awards directed towards its story-telling, graphical, and voice-acting aspects. GameSpot praised the game significantly, and awarded it "Game of the Year", "Best PS3 Game", "Best Graphics (Technical)", "Best Boss Battles", "Best Story", "Best Voice Acting", "Most Memorable Moment", and "Best Action/Adventure Game". IGN awarded the game "Best PS3 Game of 2008", "Best Graphics Technology", "Best Original Score", and "Best Action Game". "PALGN" awarded it "Game of the Year", "PS3 Game of the Year", and "Best Visuals". "PC World" also heralded "MGS4" with "Game of the Year". Playfire awarded the game "Game of the Year", "Best Action/Adventure Game", and "Best Graphics". "MGS4" also won "Game of the Year" from the Portuguese Eurogamer. On NeoGAF, MGS4 was also awarded "Game of the Year". The German site 4PLAYER.de gave "MGS4" "Game of the Year" also. GamePro awarded the game "Best PS3 Game of 2008" and "Best Action/Adventure Game". 1UP.com gave "MGS4" "Game of the Year", "Best PS3 Game", "Best Action Game", and "Best Audiovisual Experience". Fox News Channel awarded the game "Best PS3 Game of 2008" and "Best Game of 2008". GameSpy awarded it "Best PS3 Action Game". From "Gamezine", "MGS4" won "Game of the Year", and "Best PS3 Game". Giant Bomb gave it "Best PS3-Only Game", "Best Graphics", and "Most Satisfying Sequel". In the Golden Joystick 2008 awards, "MGS4" was awarded "Best PS3 Game". At Tokyo Game Show 2009, "Metal Gear Solid 4" received the Grand Award (alongside "Mario Kart Wii") and the Award of Excellence. The readers of "PlayStation Official Magazine" voted it the 5th best PlayStation title released.


text: At the 12th Annual AIAS Interactive Achievement Awards (now known as the D.I.C.E. Awards), "Metal Gear Solid 4: Guns of the Patriots" won "Outstanding Achievement in Original Music Composition", and was also nominated for "Overall Game of the Year", "Console Game of the Year", "Outstanding Achievement in Animation", "Outstanding Achievement in Character Performance" for David Hayter's vocal portrayal of Old Snake, "Outstanding Achievement in Game Direction", and "Outstanding Achievement in Visual Engineering".


text: Several publications have commented on limitations given to pre-release reviewers by Konami, including discussion on the length of cutscenes and size of the PS3 installation. These limitations resulted in "Electronic Gaming Monthly" delaying its review. In lieu of a review, the magazine printed a roundtable discussion about the game. Kojima Productions spokesperson Ryan Payton has since explained more specifically what the NDA restricts, and has amended "some items [that] are outdated and require more explanation." He also listed the length of install times, noting that the restrictions were intended to prevent spoilers regarding what occurs "during" the installations.


text: Following this statement, gaming site GameSpot published a blog entry in which it claims it will be unable to review the game either, claiming Konami have withheld review code because of non-compliance with the limitations. The article originally implied that the absence of a review was due to GameSpot's refusal to attend the "Boot Camp" event at Kojima Productions' offices. However, it has revised it to state that the Boot Camp was a mid-development feedback and PR exercise, and would not have led to a review in any case.


text: The day before Konami's restrictions were to be lifted, "Electronic Gaming Monthly" ("EGM") reviewer Jeremy Parish clarified the reasons for the self-imposed review embargo, dispelling rumors of a disagreement between Konami and "EGM" on the review conditions in a lengthy blog commentary. His review of the game appeared on the website shortly after.


title: Mahima Chaudhry

text: Mahima Chaudhry is an Indian actress and model who worked in Hindi films. During the 1990s, Chaudhry did a few modelling assignments and appeared in several television commercials before venturing into films. She made her acting debut in the 1997 film "Pardes", for which she won the Filmfare Award for Best Female Debut. She established a career with several roles in films including "Daag" (1999), "Dhadkan" (2000), "Kurukshetra" (2000), "Dil Hai Tumhaara" (2002), and received critical recognition for her performances in "Dil Kya Kare" (1999) and "Lajja" (2001).


title: Mahima Chaudhry

text: Mahima Chaudhry was born in Darjeeling, West Bengal, India. She attended Dow Hill in Kurseong until class 10 and later moved to Loreto College, Darjeeling.


title: Mahima Chaudhry

text: Chaudhry has played a variety of roles, starting with a village girl in "Pardes" (1997). Her other roles were in "" (1999), where she played a dual role; in "Pyaar Koi Khel Nahin" (1999) she played a widow forced to marry her brother-in-law; in "Dhadkan" (2000) she is a loving friend of a man who is madly in love with another woman: in "Deewane" she plays a singer in love with a thief: in "Kurukshetra" she plays the stubborn wife of a police officer: in "Lajja" she plays a young bride forced to fight dowry; in "Yeh Teraa Ghar Yeh Meraa Ghar" (2001) she plays a stubborn tenant who will not give up her home at any cost; in "Om Jai Jagadish" she is the loving homemaker; in "Dil Hai Tumhaara" (2002) she is the sister who would do anything for her sister's happiness; in "Dobara" she is the frustrated housewife; in "The Film" she is a desperate struggling screenwriter; in "" she's a paralytic dancer, in "Film Star" she is an uptight arrogant fading actress; in "Home Delivery" (2005) she's a South Indian superstar; and in "" (2006) she plays a desperate housewife who has an affair with her stepdaughter's boyfriend.


title: Mahima Chaudhry

text: In 2010, Chaudhry starred in a Knightsbridge Media Production film, "Pusher", directed by Assad Raja. She also worked in the thriller "Mumbhaii - The Gangster", co-starring Om Puri and Sanjay Kapoor.


title: Stochastic process

text: In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, cryptography and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance.


title: Stochastic process

text: Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion process, used by Louis Bachelier to study price changes on the Paris Bourse, and the Poisson process, used by A. K. Erlang to study the number of phone calls occurring in a certain period of time. These two stochastic processes are considered the most important and central in the theory of stochastic processes, and were discovered repeatedly and independently, both before and after Bachelier and Erlang, in different settings and countries.


title: Stochastic process

text: The term random function is also used to refer to a stochastic or random process, because a stochastic process can also be interpreted as a random element in a function space. The terms "stochastic process" and "random process" are used interchangeably, often with no specific mathematical space for the set that indexes the random variables. But often these two terms are used when the random variables are indexed by the integers or an interval of the real line. If the random variables are indexed by the Cartesian plane or some higher-dimensional Euclidean space, then the collection of random variables is usually called a random field instead. The values of a stochastic process are not always numbers and can be vectors or other mathematical objects.


title: Stochastic process

text: Based on their mathematical properties, stochastic processes can be grouped into various categories, which include random walks, martingales, Markov processes, Lévy processes, Gaussian processes, random fields, renewal processes, and branching processes. The study of stochastic processes uses mathematical knowledge and techniques from probability, calculus, linear algebra, set theory, and topology as well as branches of mathematical analysis such as real analysis, measure theory, Fourier analysis, and functional analysis. The theory of stochastic processes is considered to be an important contribution to mathematics and it continues to be an active topic of research for both theoretical reasons and applications.


title: Stochastic process

text: A stochastic or random process can be defined as a collection of random variables that is indexed by some mathematical set, meaning that each random variable of the stochastic process is uniquely associated with an element in the set. The set used to index the random variables is called the index set. Historically, the index set was some subset of the real line, such as the natural numbers, giving the index set the interpretation of time. Each random variable in the collection takes values from the same mathematical space known as the state space. This state space can be, for example, the integers, the real line or formula_1-dimensional Euclidean space. An increment is the amount that a stochastic process changes between two index values, often interpreted as two points in time. A stochastic process can have many outcomes, due to its randomness, and a single outcome of a stochastic process is called, among other names, a sample function or realization.


title: Stochastic process

text: A stochastic process can be classified in different ways, for example, by its state space, its index set, or the dependence among the random variables. One common way of classification is by the cardinality of the index set and the state space.


title: Stochastic process

text: When interpreted as time, if the index set of a stochastic process has a finite or countable number of elements, such as a finite set of numbers, the set of integers, or the natural numbers, then the stochastic process is said to be in discrete time. If the index set is some interval of the real line, then time is said to be continuous. The two types of stochastic processes are respectively referred to as discrete-time and continuous-time stochastic processes. Discrete-time stochastic processes are considered easier to study because continuous-time processes require more advanced mathematical techniques and knowledge, particularly due to the index set being uncountable. If the index set is the integers, or some subset of them, then the stochastic process can also be called a random sequence.


title: Stochastic process

text: If the state space is the integers or natural numbers, then the stochastic process is called a discrete or integer-valued stochastic process. If the state space is the real line, then the stochastic process is referred to as a real-valued stochastic process or a process with continuous state space. If the state space is formula_1-dimensional Euclidean space, then the stochastic process is called a formula_1-dimensional vector process or formula_1-vector process.


title: Stochastic process

text: The word "stochastic" in English was originally used as an adjective with the definition "pertaining to conjecturing", and stemming from a Greek word meaning "to aim at a mark, guess", and the Oxford English Dictionary gives the year 1662 as its earliest occurrence. In his work on probability "Ars Conjectandi", originally published in Latin in 1713, Jakob Bernoulli used the phrase "Ars Conjectandi sive Stochastice", which has been translated to "the art of conjecturing or stochastics". This phrase was used, with reference to Bernoulli, by Ladislaus Bortkiewicz who in 1917 wrote in German the word "stochastik" with a sense meaning random. The term "stochastic process" first appeared in English in a 1934 paper by Joseph Doob. For the term and a specific mathematical definition, Doob cited another 1934 paper, where the term "stochastischer Prozeß" was used in German by Aleksandr Khinchin, though the German term had been used earlier, for example, by Andrei Kolmogorov in 1931.


title: Stochastic process

text: According to the Oxford English Dictionary, early occurrences of the word "random" in English with its current meaning, which relates to chance or luck, date back to the 16th century, while earlier recorded usages started in the 14th century as a noun meaning "impetuosity, great speed, force, or violence (in riding, running, striking, etc.)". The word itself comes from a Middle French word meaning "speed, haste", and it is probably derived from a French verb meaning "to run" or "to gallop". The first written appearance of the term "random process" pre-dates "stochastic process", which the Oxford English Dictionary also gives as a synonym, and was used in an article by Francis Edgeworth published in 1888.


title: Stochastic process

text: The definition of a stochastic process varies, but a stochastic process is traditionally defined as a collection of random variables indexed by some set. The terms "random process" and "stochastic process" are considered synonyms and are used interchangeably, without the index set being precisely specified. Both "collection", or "family" are used while instead of "index set", sometimes the terms "parameter set" or "parameter space" are used.


title: Stochastic process

text: The term "random function" is also used to refer to a stochastic or random process, though sometimes it is only used when the stochastic process takes real values. This term is also used when the index sets are mathematical spaces other than the real line, while the terms "stochastic process" and "random process" are usually used when the index set is interpreted as time, and other terms are used such as "random field" when the index set is formula_1-dimensional Euclidean space formula_6 or a manifold.


title: Stochastic process

text: A stochastic process can be denoted, among other ways, by formula_7, formula_8, formula_9 formula_10 or simply as formula_11 or formula_12, although formula_12 is regarded as an abuse of function notation. For example, formula_12 or formula_15 are used to refer to the random variable with the index formula_16, and not the entire stochastic process. If the index set is formula_17, then one can write, for example, formula_18 to denote the stochastic process.


title: Stochastic process

text: One of the simplest stochastic processes is the Bernoulli process, which is a sequence of independent and identically distributed (iid) random variables, where each random variable takes either the value one or zero, say one with probability formula_19 and zero with probability formula_20. This process can be linked to repeatedly flipping a coin, where the probability of obtaining a head is formula_19 and its value is one, while the value of a tail is zero. In other words, a Bernoulli process is a sequence of iid Bernoulli random variables, where each coin flip is an example of a Bernoulli trial.


title: Stochastic process

text: Random walks are stochastic processes that are usually defined as sums of iid random variables or random vectors in Euclidean space, so they are processes that change in discrete time. But some also use the term to refer to processes that change in continuous time, particularly the Wiener process used in finance, which has led to some confusion, resulting in its criticism. There are other various types of random walks, defined so their state spaces can be other mathematical objects, such as lattices and groups, and in general they are highly studied and have many applications in different disciplines.


title: Stochastic process

text: A classic example of a random walk is known as the "simple random walk", which is a stochastic process in discrete time with the integers as the state space, and is based on a Bernoulli process, where each Bernoulli variable takes either the value positive one or negative one. In other words, the simple random walk takes place on the integers, and its value increases by one with probability, say, formula_19, or decreases by one with probability formula_20, so the index set of this random walk is the natural numbers, while its state space is the integers. If the formula_24, this random walk is called a symmetric random walk.


title: Stochastic process

text: The Wiener process is a stochastic process with stationary and independent increments that are normally distributed based on the size of the increments. The Wiener process is named after Norbert Wiener, who proved its mathematical existence, but the process is also called the Brownian motion process or just Brownian motion due to its historical connection as a model for Brownian movement in liquids.


title: Stochastic process

text: Playing a central role in the theory of probability, the Wiener process is often considered the most important and studied stochastic process, with connections to other stochastic processes. Its index set and state space are the non-negative numbers and real numbers, respectively, so it has both continuous index set and states space. But the process can be defined more generally so its state space can be formula_1-dimensional Euclidean space. If the mean of any increment is zero, then the resulting Wiener or Brownian motion process is said to have zero drift. If the mean of the increment for any two points in time is equal to the time difference multiplied by some constant formula_26, which is a real number, then the resulting stochastic process is said to have drift formula_26.


title: Stochastic process

text: Almost surely, a sample path of a Wiener process is continuous everywhere but nowhere differentiable. It can be considered as a continuous version of the simple random walk. The process arises as the mathematical limit of other stochastic processes such as certain random walks rescaled, which is the subject of Donsker's theorem or invariance principle, also known as the functional central limit theorem.


title: Stochastic process

text: The Wiener process is a member of some important families of stochastic processes, including Markov processes, Lévy processes and Gaussian processes. The process also has many applications and is the main stochastic process used in stochastic calculus. It plays a central role in quantitative finance, where it is used, for example, in the Black–Scholes–Merton model. The process is also used in different fields, including the majority of natural sciences as well as some branches of social sciences, as a mathematical model for various random phenomena.


title: Stochastic process

text: The Poisson process is a stochastic process that has different forms and definitions. It can be defined as a counting process, which is a stochastic process that represents the random number of points or events up to some time. The number of points of the process that are located in the interval from zero to some given time is a Poisson random variable that depends on that time and some parameter. This process has the natural numbers as its state space and the non-negative numbers as its index set. This process is also called the Poisson counting process, since it can be interpreted as an example of a counting process.


title: Stochastic process

text: If a Poisson process is defined with a single positive constant, then the process is called a homogeneous Poisson process. The homogeneous Poisson process is a member of important classes of stochastic processes such as Markov processes and Lévy processes.


title: Stochastic process

text: The homogeneous Poisson process can be defined and generalized in different ways. It can be defined such that its index set is the real line, and this stochastic process is also called the stationary Poisson process. If the parameter constant of the Poisson process is replaced with some non-negative integrable function of formula_16, the resulting process is called an inhomogeneous or nonhomogeneous Poisson process, where the average density of points of the process is no longer constant. Serving as a fundamental process in queueing theory, the Poisson process is an important process for mathematical models, where it finds applications for models of events randomly occurring in certain time windows.


title: Stochastic process

text: Defined on the real line, the Poisson process can be interpreted as a stochastic process, among other random objects. But then it can be defined on the formula_1-dimensional Euclidean space or other mathematical spaces, where it is often interpreted as a random set or a random counting measure, instead of a stochastic process. In this setting, the Poisson process, also called the Poisson point process, is one of the most important objects in probability theory, both for applications and theoretical reasons. But it has been remarked that the Poisson process does not receive as much attention as it should, partly due to it often being considered just on the real line, and not on other mathematical spaces.


title: Stochastic process

text: A stochastic process is defined as a collection of random variables defined on a common probability space formula_30, where formula_31 is a sample space, formula_32 is a formula_33-algebra, and formula_34 is a probability measure; and the random variables, indexed by some set formula_35, all take values in the same mathematical space formula_36, which must be measurable with respect to some formula_33-algebra formula_38.


title: Stochastic process

text: In other words, for a given probability space formula_30 and a measurable space formula_40, a stochastic process is a collection of formula_36-valued random variables, which can be written as:


title: Stochastic process

text: Historically, in many problems from the natural sciences a point formula_42 had the meaning of time, so formula_12 is a random variable representing a value observed at time formula_16. A stochastic process can also be written as formula_45 to reflect that it is actually a function of two variables, formula_42 and formula_47.


title: Stochastic process

text: There are other ways to consider a stochastic process, with the above definition being considered the traditional one. For example, a stochastic process can be interpreted or defined as a formula_48-valued random variable, where formula_48 is the space of all the possible functions from the set formula_35 into the space formula_36. However this alternative definition as a "function-valued random variable" in general requires additional regularity assumptions to be well-defined.


title: Stochastic process

text: The set formula_35 is called the index set or parameter set of the stochastic process. Often this set is some subset of the real line, such as the natural numbers or an interval, giving the set formula_35 the interpretation of time. In addition to these sets, the index set formula_35 can be another set with a total order or a more general set, such as the Cartesian plane formula_55 or formula_1-dimensional Euclidean space, where an element formula_42 can represent a point in space. That said, many results and theorems are only possible for stochastic processes with a totally ordered index set.


title: Stochastic process

text: The mathematical space formula_36 of a stochastic process is called its "state space". This mathematical space can be defined using integers, real lines, formula_1-dimensional Euclidean spaces, complex planes, or more abstract mathematical spaces. The state space is defined using elements that reflect the different values that the stochastic process can take.


title: Stochastic process

text: A sample function is a single outcome of a stochastic process, so it is formed by taking a single possible value of each random variable of the stochastic process. More precisely, if formula_60 is a stochastic process, then for any point formula_61, the mapping


title: Stochastic process

text: is called a sample function, a realization, or, particularly when formula_35 is interpreted as time, a sample path of the stochastic process formula_60. This means that for a fixed formula_61, there exists a sample function that maps the index set formula_35 to the state space formula_36. Other names for a sample function of a stochastic process include trajectory, path function or path.


title: Stochastic process

text: An increment of a stochastic process is the difference between two random variables of the same stochastic process. For a stochastic process with an index set that can be interpreted as time, an increment is how much the stochastic process changes over a certain time period. For example, if formula_67 is a stochastic process with state space formula_36 and index set formula_17, then for any two non-negative numbers formula_70 and formula_71 such that formula_72, the difference formula_73 is a formula_36-valued random variable known as an increment. When interested in the increments, often the state space formula_36 is the real line or the natural numbers, but it can be formula_1-dimensional Euclidean space or more abstract spaces such as Banach spaces.


title: Stochastic process

text: For a stochastic process formula_77 defined on the probability space formula_30, the law of stochastic process formula_11 is defined as the image measure:


title: Stochastic process

text: where formula_34 is a probability measure, the symbol formula_81 denotes function composition and formula_82 is the pre-image of the measurable function or, equivalently, the formula_48-valued random variable formula_11, where formula_48 is the space of all the possible formula_36-valued functions of formula_42, so the law of a stochastic process is a probability measure.


title: Stochastic process

text: The law of a stochastic process or a random variable is also called the probability law, probability distribution, or the distribution.


title: Stochastic process

text: For a stochastic process formula_11 with law formula_93, its finite-dimensional distribution for formula_94 is defined as:


title: Stochastic process

text: This measure formula_95is the joint distribution of the random vector formula_96; it can be viewed as a "projection" of the law formula_93 onto a finite subset of formula_35.


title: Stochastic process

text: For any measurable subset formula_99 of the formula_1-fold Cartesian power formula_101, the finite-dimensional distributions of a stochastic process formula_11 can be written as:


title: Stochastic process

text: The finite-dimensional distributions of a stochastic process satisfy two mathematical conditions known as consistency conditions.


title: Stochastic process

text: Stationarity is a mathematical property that a stochastic process has when all the random variables of that stochastic process are identically distributed. In other words, if formula_11 is a stationary stochastic process, then for any formula_42 the random variable formula_15 has the same distribution, which means that for any set of formula_1 index set values formula_107, the corresponding formula_1 random variables


title: Stochastic process

text: all have the same probability distribution. The index set of a stationary stochastic process is usually interpreted as time, so it can be the integers or the real line. But the concept of stationarity also exists for point processes and random fields, where the index set is not interpreted as time.


title: Stochastic process

text: When the index set formula_35 can be interpreted as time, a stochastic process is said to be stationary if its finite-dimensional distributions are invariant under translations of time. This type of stochastic process can be used to describe a physical system that is in steady state, but still experiences random fluctuations. The intuition behind stationarity is that as time passes the distribution of the stationary stochastic process remains the same. A sequence of random variables forms a stationary stochastic process only if the random variables are identically distributed.


title: Stochastic process

text: A stochastic process with the above definition of stationarity is sometimes said to be strictly stationary, but there are other forms of stationarity. One example is when a discrete-time or continuous-time stochastic process formula_11 is said to be stationary in the wide sense, then the process formula_11 has a finite second moment for all formula_42 and the covariance of the two random variables formula_15 and formula_114 depends only on the number formula_115 for all formula_42. Khinchin introduced the related concept of stationarity in the wide sense, which has other names including covariance stationarity or stationarity in the broad sense.