text:
Women's Writing Before Woolf: A Social Reference/Anne Cary (1615-1671)

Anne Cary (born 1614), more commonly known as Dame Clementina, was a British Benedictine Nun and author from London, England. She served as a Benedictine nun in Paris, establishing the “Our Lady of Good Hope” monastery in 1651 after spending time training as a nun in Cambrai. During her service as a nun, Anne authored over eight Collection Books, Spiritual songs and Psalms Translations. Till today, it is still debated of her participation in the mystery of the written work, “Life”. Anne remained in Paris at the monastery up to her death in 1671 due to illness.

Early Life Anne was born in 1614 in London, England, and baptised at Berkhamsted the same year. She was the eldest daughter of mother, Elizabeth Cary and father, Henry Cary. Elizabeth was a well-known figure in the author community, being one of the first women to publish an original play in English, while Henry served as the first Viscount of Falkland, working as the Jewel house master. Anne was considered “very zealous” at a young age and grew up in Aldenham in London amongst her ten siblings. In 1622, the family moved to Dublin following Henry’s promotion to Lord Deputy of Ireland. Three years after arriving in Ireland, Anne returned to England for some time, travelling between Ireland and England. There she developed a lifelong friendship with Queen Henriette Maria.

Religious Conversion and Cambrai In November 1626, Elizabeth Cary discreetly converted to Catholicism under the eye of Father John Fursdon. During this time, the relationship between Anne’s parents had become strained, and the announcement of Elizabeth’s conversions caused the two to split and live separately with the children assumedly living with their father. When Anne’s father died in 1633, Elizabeth attempted to regain custody of the children with the intention to convert them to Catholicism however, King Charles 1 received news of her plans, and instead sent Anne, alongside her sisters, Lucy, Mary and Elizabeth to the Great Tew estate which was governed by their brother Lucius Cary. The irony of this plan, however, lies in the fact that Anne, alongside her sisters had previously converted to Catholicism in 1634 discreetly, and not informing their mother. However, in 1636, Elizabeth ‘kidnapped’ the children, alongside two of Anne’s brothers, Patrick and Henry, and took them to the convent of Our Lady of Consolation in Cambrai. There, Anne took on the religious name of Clementia and began to take their vows which lasted 8 months from 1638 to 1639. On the 8th of March 1639, Anne officially joined the Benedictines as a choir nun, at the age of 24. According to writings from the Class of 1640 form the convent, Anne, amongst her sisters were described as “more prolific than any other group of nuns educated and professed together at Cambrai.” During her time at Cambrai, Anne began intensely devoting her time and energy to the promotion of Catholicism. Like her mother, she took great pride in her servitude to God. An obituary notice claimed that Clementina often shunned “frequent visits and longe discources”, instead utilising the time to promote prayer and working towards religious perfection. Similarly, when it was announced that a prominent figure in the convent, Father Baker was asked to teach some of the novices, Anne was excited, indicated by her disappointment when the event was cancelled. But his teachings still influenced Anne, emphasised by her death notice which outlined the instructions and mental exercises she adapted from Baker, stating that “she found non more easie and plean to be understood then those of Reverend Father Bakers.” Anne’s time at the convent would end in October 1651, after a downturn in the economic struggle the convent began to experience. To alleviate these difficulties, Anne, alongside her sister Mary, and Sister Scholastica Hodson and Father Serenus Cressy were sent to Paris to establish a new convent, the convent of Our Lady of Good Hope.

“Our Lady of Good Hope Convent” The journey to Paris took them around 1 month, of which Anne was suffering from an illness throughout and they arrived on the 1st of November where they lodged with a commune of Augustinian nuns. With her arrival in Paris, Anne tuned to her friendship with Queen Henrietta Maria to aid in the nun’s goal of establishing a new convent in the city. They were offered an ongoing pension to support them, which remained intact until the Queen died in 1669 and Anne rented a house on Rue St. Dominique for the group, and for the potential to get more sisters for the convent. Similarly, Anne was able to procure funds and support for the development of the convent from Maria and Abbot Walter Montagu. Anne’s skills and such connections made her the key element in the convent being established. Her ability to speak French, and her scholarship made establishing constitutions for the convent significantly easier, a necessary component of the development. And while offered for her significant contributions to the development of the covenant, Anne turned down the position of Abbess.

“Life” Authorship One of the largest mysteries that surround Anne and her family, is the authorship of the written work, Life, which explores the life of their mother, Elizabeth Cary. Over the years there has been extensive research and debate over which of the family wrote the work, but there has been no conclusive evidence for any. It is widely accepted that the work was composed at Cambrai, indicating that author was one of the four sisters, Mary, Anne, Lucy or Elizabeth and was also annotated by some of the other sisters and brother, Patrick. The text is composed of its main text and four editorial commentaries which aim at correcting misinformation in the original text. One belief debates that Anne authored one of these editorial commentaries. However, another belief debates that Anne was the author of the original text and is consistently cited as such in papers. Donald Foster states that that ‘it is clear from a collation of the internal and external evidence that the biography cannot have been written by anyone but Anne Cary.’ And elaborates that she may have preserved many of her mother’s writing as well.

Works Anne’s talents as an author were already recognisable. Her skills as a linguist, and her influence from her mother saw her excel in the literary field. During her time as a nun in Paris, Anne developed over eight collection books, wrote several spiritual songs and translated several Psalms from their Latin Vulgate editions, and has also been titled as one of significant contributors to the Blosius manuscript. Of all her translations, three quires survived and are currently stored at the Archives Departementales du Nord in Lille. The first of these quires contains translations of the Psalms 69 to 78. The second quire contains the end of Psalm 120 to 139, and the final quire covers Psalm 139 to 149. Anne, through her work as a nun, also contributed to the translations of other monastery works. Anne’s written style relies heavily on her usage of the dramatic voice which established a direct communication between God and the speaker. This also establishes Anne’s recognition of the stylised written format, including her familiarity of tone and meter.

Death Anne died on the 26th of April 1671 at the “Our Lady of Good Hope Convent” in Paris due to illness. Her obituary stated that Anne “embraced her illness as a gift from God “and died peacefully on her deathbed.

Legacy After her death, Anne left behind a legacy in both Catholicism and the literary world. Her contributions to the translation of the Psalms, and her original works all altered both the Cambrai and Paris Catholic communities. However, her most significant contribution rests in the development of the “Our Lady of Good Hope covenant” which remains as lasting evidence of the legacy that Anne left behind in her death. During her life, she was praised for both her wisdom, and her devotion to the Catholic faith, and this remained until after her death.

Further Reading “Cambrai & The Life of Lady Falkland.” By Heather Wolfe “Sisters and Brothers: Divided Sibling Identity in the Cary Family.” Essay. In Women Writers and Familial Discourse in the English Renaissance: Relative Values. By Marion Wynne-Davies

References Bowden, Caroline. “Collecting the Lives of Early Modern Women Religious: Obituary Writing and the Development of Collective Memory and Corporate Identity.” Women's History Review 19, no. 1 (2010): 7–20. https://doi.org/10.1080/09612020903444619. LISA, JARDINE A FOREWORD BY. Literatures of Exile in the English Revolution and Its Aftermath, 1640-1690. Edited by Philip Major. ROUTLEDGE, 2018. Rhodes, Jan. “The Library Catalogue of the English Benedictine Nuns of Our Lady of Good Hope in Paris.” The Downside Review 130, no. 459 (2012): 54–86. https://doi.org/10.1177/001258061213045904. Wolfe, Heather, ed. Literary Career and Legacy of Elizabeth Cary 1613 1680. Palgrave Macmillan, 2007. Wolfe, Heather. “CAMBRAI & THE LIFE OF LADY FALKLAND.” Monlib.org, n.d. http://www.monlib.org.uk/papers/ebch/1998wolfe.pdf. Wynne-Davies, Marion. “Sisters and Brothers: Divided Sibling Identity in the Cary Family.” Essay. In Women Writers and Familial Discourse in the English Renaissance: Relative Values. Basingstoke England: Palgrave Macmillan, 2007.


text:
Women's Writing Before Woolf: A Social Reference/Anne Cary (1615-1971)

Anne Cary (born 1614), more commonly known as Dame Clementina, was a British Benedictine Nun and author from London, England. She served as a Benedictine nun in Paris, establishing the “Our Lady of Good Hope” monastery in 1651 after spending time training as a nun in Cambrai. During her service as a nun, Anne authored over eight Collection Books, Spiritual songs and Psalms Translations. Till today, it is still debated of her participation in the mystery of the written work, “Life”. Anne remained in Paris at the monastery up to her death in 1671 due to illness.

Early Life
Anne was born in 1614 in London, England, and baptised at Berkhamsted the same year. She was the eldest daughter of mother, Elizabeth Cary and father, Henry Cary. Elizabeth was a well-known figure in the author community, being one of the first women to publish an original play in English, while Henry served as the first Viscount of Falkland, working as the Jewel house master. Anne was considered “very zealous” at a young age and grew up in Aldenham in London amongst her ten siblings. In 1622, the family moved to Dublin following Henry’s promotion to Lord Deputy of Ireland. Three years after arriving in Ireland, Anne returned to England for some time, travelling between Ireland and England. There she developed a lifelong friendship with Queen Henriette Maria.

Religious Conversion and Cambrai
In November 1626, Elizabeth Cary discreetly converted to Catholicism under the eye of Father John Fursdon. During this time, the relationship between Anne’s parents had become strained, and the announcement of Elizabeth’s conversions caused the two to split and live separately with the children assumedly living with their father. When Anne’s father died in 1633, Elizabeth attempted to regain custody of the children with the intention to convert them to Catholicism however, King Charles 1 received news of her plans, and instead sent Anne, alongside her sisters, Lucy, Mary and Elizabeth to the Great Tew estate which was governed by their brother Lucius Cary. The irony of this plan, however, lies in the fact that Anne, alongside her sisters had previously converted to Catholicism in 1634 discreetly, and not informing their mother. However, in 1636, Elizabeth ‘kidnapped’ the children, alongside two of Anne’s brothers, Patrick and Henry, and took them to the convent of Our Lady of Consolation in Cambrai. There, Anne took on the religious name of Clementia and began to take their vows which lasted 8 months from 1638 to 1639. On the 8th of March 1639, Anne officially joined the Benedictines as a choir nun, at the age of 24. According to writings from the Class of 1640 form the convent, Anne, amongst her sisters were described as “more prolific than any other group of nuns educated and professed together at Cambrai.”

During her time at Cambrai, Anne began intensely devoting her time and energy to the promotion of Catholicism. Like her mother, she took great pride in her servitude to God. An obituary notice claimed that Clementina often shunned “frequent visits and longe discources”, instead utilising the time to promote prayer and working towards religious perfection. Similarly, when it was announced that a prominent figure in the convent, Father Baker was asked to teach some of the novices, Anne was excited, indicated by her disappointment when the event was cancelled. But his teachings still influenced Anne, emphasised by her death notice which outlined the instructions and mental exercises she adapted from Baker, stating that “she found non more easie and plean to be understood then those of Reverend Father Bakers.”

Anne’s time at the convent would end in October 1651, after a downturn in the economic struggle the convent began to experience. To alleviate these difficulties, Anne, alongside her sister Mary, and Sister Scholastica Hodson and Father Serenus Cressy were sent to Paris to establish a new convent, the convent of Our Lady of Good Hope.

“Our Lady of Good Hope Convent”
The journey to Paris took them around one month, of which Anne was suffering from an illness throughout and they arrived on the 1st of November where they lodged with a commune of Augustinian nuns. With her arrival in Paris, Anne tuned to her friendship with Queen Henrietta Maria to aid in the nun’s goal of establishing a new convent in the city. They were offered an ongoing pension to support them, which remained intact until the Queen died in 1669 and Anne rented a house on Rue St. Dominique for the group, and for the potential to get more sisters for the convent. Similarly, Anne was able to procure funds and support for the development of the convent from Maria and Abbot Walter Montagu. Anne’s skills and such connections made her the key element in the convent being established. Her ability to speak French, and her scholarship made establishing constitutions for the convent significantly easier, a necessary component of the development. And while offered for her significant contributions to the development of the covenant, Anne turned down the position of Abbess.

“Life” Authorship
One of the largest mysteries that surround Anne and her family, is the authorship of the written work, Life, which explores the life of their mother, Elizabeth Cary. Over the years there has been extensive research and debate over which of the family wrote the work, but there has been no conclusive evidence for any. It is widely accepted that the work was composed at Cambrai, indicating that author was one of the four sisters, Mary, Anne, Lucy or Elizabeth and was also annotated by some of the other sisters and brother, Patrick. The text is composed of its main text and four editorial commentaries which aim at correcting misinformation in the original text. One belief debates that Anne authored one of these editorial commentaries. However, another belief debates that Anne was the author of the original text and is consistently cited as such in papers. Donald Foster states that that ‘it is clear from a collation of the internal and external evidence that the biography cannot have been written by anyone but Anne Cary.’  And elaborates that she may have preserved many of her mother’s writing as well.

Works
Anne’s talents as an author were already recognisable. Her skills as a linguist, and her influence from her mother saw her excel in the literary field. During her time as a nun in Paris, Anne developed over eight collection books, wrote several spiritual songs and translated several Psalms from their Latin Vulgate editions, and has also been titled as one of significant contributors to the Blosius manuscript. Of all her translations, three quires survived and are currently stored at the Archives Departementales du Nord in Lille. The first of these quires contains translations of the Psalms 69 to 78. The second quire contains the end of Psalm 120 to 139, and the final quire covers Psalm 139 to 149. Anne, through her work as a nun, also contributed to the translations of other monastery works.

Anne’s written style relies heavily on her usage of the dramatic voice which established a direct communication between God and the speaker. This also establishes Anne’s recognition of the stylised written format, including her familiarity of tone and meter.

Death
Anne died on the 26th of April 1671 at the “Our Lady of Good Hope Convent” in Paris due to illness. Her obituary stated that Anne “embraced her illness as a gift from God “and died peacefully on her deathbed.

Legacy
After her death, Anne left behind a legacy in both Catholicism and the literary world. Her contributions to the translation of the Psalms, and her original works all altered both the Cambrai and Paris Catholic communities. However, her most significant contribution rests in the development of the “Our Lady of Good Hope covenant” which remains as lasting evidence of the legacy that Anne left behind in her death. During her life, she was praised for both her wisdom, and her devotion to the Catholic faith, and this remained until after her death.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
User:AuthorsAndContributorsBot/blacklist

ArchiverBot Flow talk page manager JackBot Maintenance script MaintenanceBot MediaWiki default MediaWiki message delivery QUBot SteinsplitterBot AuthorsAndContributorsBot Elliot Harkness Is Stupid Jifzzunt InternetArchiveBot ClueBot SmackBot DumZiBoT OrphanBot GreenC bot ZéroBot Yobot SwiftBot DrilBot ClueBot NG BG19bot CitationCleanerBot Citation bot Bender the Bot RussBot Rei-bot JackieBot KolbertBot Magic links bot


text:
User:Aaron Liu/sandbox

| Mexico

Pan de Muerto, Spanish for "Bread of the Dead", is a sweet traditional Mexican bread that is commonly made during Day of the Dead. It is traditionally used as an offering for a dead relative. The family will eat the bread, and thus nourish the dead relative's spirit with its "essence". It is a regular bun with a cross at the top and sugar sprinkled on it.

Ingredients

 * 5 eggs
 * 80 grams (⅓ cup) unsalted margarine
 * 1 teaspoon (5 mL) salt
 * 100 grams (½ cup) sugar
 * 500 grams (4 cups) all-purpose flour
 * 60 ml (¼ cup) warm water about 110°F (43°C)
 * 2 tablespoons (30 mL) active-dry yeast
 * 80 grams (approx. ⅓ cup) butter + rest of the bar for brushing
 * Zest from 2 oranges.
 * 1 teaspoon (5 mL) orange blossom water or orange essence.
 * 2

Equipment

 * 1 mixing bowl
 * 1 mixer with paddle attachment
 * Work surface
 * Plastic wrap
 * 2 greased baking sheets
 * Oven

Procedure

 * 1) Place 4 eggs, the margarine, the salt, and half of the sugar into the mixing bowl. Work the dough with the paddle attachment for about 2 minutes.
 * 2) Add the flour in small amounts alternating with the warm water.
 * 3) Add the yeast and mix until well combined.
 * 4) Add the butter, the zest, the rest of the sugar and the orange blossom water one at a time. Mix well each time until soft dough forms.
 * 5) Transfer the dough onto a work surface and knead until smooth.
 * 6) Transfer the dough into a container and wrap in plastic wrap. Set aside in a warm place until dough doubles in size; usually takes 45 mins ~ 1 hour.
 * 7) Transfer the dough onto a work surface. Reserve 300g of dough which will be used to form the cross and separate the rest into 70g pieces.

*/ Photos of the procedures as they are completed should be in |thumb| format, so a caption identifying what step is being performed can be included in the pic. /*

Notes, tips, and variations

 * Cut the margarine and butter into smaller pieces before adding them into the mixing bowl.
 * If the dough sticks to the working surface, coat the working surface with some flour.
 * If you want two large buns instead of 16 small ones, separate the dough into two equal pieces after reserving 300g instead.

Warnings

 * Pay attention to the amount of water and flour that should be added. The correct amount is 60 ml of water and 64 tablespoons of flour.
 * Warning 2
 * etc.

title: User:Aaron Liu/sandbox


text:
Talk:English-Hanzi/Electric current

$=50%/>user-1

title: Talk:English-Hanzi/Electric current


text:
Minecraft/Enchanted Book

Enchanted books are items that hold enchantments for later.

Obtaining
There are many ways to get enchanted books. They can be bought off librarian villagers, fished up, found in chests in almost every naturally generated structure with a chest, and can even be made. To make one, just make a book and enchant it on an enchantment table.

Use
To use one, combine it with the item you want to enchant on an anvil.

title: Minecraft/Enchanted Book


text:
Minecraft/Anvil

Anvils are versatile and useful, with several uses to players with enough iron to make one.

Obtaining
They also can be found in villages.

Use
They can do three main things:
 * 1) Combine two items of the same type and material together to repair them.
 * 2) Combined a damaged iktem with the mineral used to craft them to repair them. This repairs a quarter of the durability, so you could potentially use more materials than was used to craft it. Sometimes it may be better to just craft a new item, unless it is enchanted or only slightly damaged.
 * 3) Combine two items together to combine its enchantments. This is the most expensive operation, costing the most experience points. Try swapping the two items to see which way is cheeper.

Each of the above costs experience points. On each use, the anvil is slowly damaged, eventually breaking.

title: Minecraft/Anvil


text:
Visual Basic .NET/Objects

OBJECTS The world is full of objects,such as motor cars,dogs,cities,people,customers,cash registers and so on.We can also consider an object to be a container for data,with attributes,and the operations needed to manipulate that data.Objects function well as software modules because they can be created, used and maintained independently of one another.

title: Visual Basic .NET/Objects


text:
User:Benjamin.kutschan/sandbox

test

title: User:Benjamin.kutschan/sandbox


text:
Emerging Technologies in Transportation Casebook/Parking Management

Introduction
Searching for parking costs American drivers $73 billion a year, or an average of $345 per person [1]. Parking, an inevitable action taken when owning a vehicle, can cause significant stress for drivers. While demand is an important factor to consider when allotting spaces and their rates, emerging technologies are at the forefront of management applications, both for the supplier and consumer. Technologies support parking management in three main ways: finding parking, enforcing parking, and paying for parking. Consequently, these are the most significant problems in public parking facilities that can easily deter users. This chapter focuses on how existing and emerging technologies are providing parking management solutions for individuals, cities, and private lots.

This chapter was written by Patrick Morrison, Katy Nicholson and Iqbal Safi for Dr. Jonathan Gifford's Emerging Technologies, Transportation and Public Policy class at the George Mason University Schar School of Policy and Government.

Finding Parking
Every large city has a parking issue. For instance, daily, roughly 6 million cars in New York City alone require a parking space. Many more people do not have the luxury of renting an apartment with assigned parking; however, some do. Parking insufficiency causes long meter lines or causes people to drive around in circles until a space opens close to where they're going. It's understandable why so many drivers give up, park illegally, or choose to take public transportation [2].

The problem of struggling to find a parking space has been defined in terms of supply or management; we are narrowing this chapter to parking management, i.e., policies and initiatives that improve the efficiency of using parking spaces. One area in parking management is the provision of information to residents, employees, and or those who visit a commercial, residential, or mixed-use building in urban or suburban areas.[3] There is a wide range of emerging technology solutions that are designed to assist in finding a parking space.

Smart Sensors
Smart sensors are one of the emerging technology solutions that spot open parking spaces and simplify the parking process. Smart sensors use GPS to determine the location of the drivers and guide them toward empty parking spaces near them. With smart sensors, drivers receive real-time notifications and traffic information along with directions to the closest available parking space [2].

Driverless Parking
Driverless parking is another emerging technology solution; with the use of driverless parking technology, vehicles may find and occupy parking places by themselves. This technology saves time as drivers no longer will need to be concerned about finding a parking space or “getting lost” in a big parking lot [2].

Parking Apps
Parking apps are other emerging technology solutions that drivers use to find parking spaces rapidly and in a stress-free manner. The development of numerous automobile parking innovation technologies around the world bodes well for the future of parking. Numerous parking app technologies are already available and in use. Parking apps have helped some well-known urban centers' inefficient parking management.

Case Study: Rosslyn, Arlington, Virginia
The Rosslyn Coordinated Redevelopment District was established in May 1996 by the Arlington County Board. The establishment of Rosslyn district was intended to increase Rosslyn’s potential for a densely populated urban area. The County has planned to achieve this goal through economic and physical expansion of the area; particularly, mixed-use, i.e., commercial, and residential building structures are developed in the area. As the downtown of Arlington, Rosslyn has concentrated housing and jobs within a densely populated urban center. Rosslyn also puts a premium on sustainable development. The vision for Rosslyn district is that the district will have a refined transportation network that connects people and takes them to places that are accessible through multi-modal transportation connections. The district is going to be a walkable neighborhood that has complete streets and off-street parking facilities [4]. Rosslyn, as an urban gateway from Washington, D.C. to Arlington, provides its residents and visitors with tremendous opportunities and provides the best view of the Washington, D.C. area’s monuments and landmarks. The natural beauty of Washington, D.C. can be best viewed from the views that Rosslyn offers. However, the parking options in Rosslyn do not meet the requirements of Rosslyn’s residents and visitors. Rosslyn is one of the cities that uses parking apps in informing and guiding drivers to better fulfill their parking needs. Three parking apps that are used in Rosslyn are:

Parkmobile
With Parkmobile, one can reserve a parking spot before they leave for their destination; the technology solution has a feature that can add time without the need for the driver to run back to the meter. The process is simple and has the following four major steps: Enter the zone number, set the duration, select the vehicle, and pay [5].

SpotHero
With Spothero one can search and reserve parking in thousands of lots and garages across the country. The app allows customers to search for and compare prices at different parking facilities, make a secure payment, and receive an online parking pass [6].

ParkWhiz
ParkWhiz is one consumer app that is powered by “Arrive,” which provides technology solutions for improved mobility. ParkWhiz is famous for its economical parking, allowing users to locate parking and pay to reserve a space [7].

Policy
Despite Rosslyn district’s tremendous efforts to improve parking management, residents, and visitors have expressed that they need more parking options. Rosslyn district maintains that the parking spaces in Rosslyn are abundant; this implies that the problem remains in parking management. Technology solutions can assist in improving the parking process; however, continuous improvement of the transport policy combined with emerging technology solutions could be a more effective and practical solution to the parking problem in Rosslyn. We furthermore recommend enhanced research into and development of Rosslyn’s transportation and land development policies [8].

Paying for Parking
Surface parking spaces cost an estimated $5,000 to $10,000 to construct, including land value. Parking structures cost approximately $25,000 to $50,000 per space. Despite these high costs, users often are not charged to occupy the spaces. Parking is most commonly priced in city centers by private owners and municipalities due to high demand. Because parking systems are locally controlled, there is a dearth of aggregated data on parking prices and policies throughout the United States [9].

Mechanical parking meters were introduced in the 1920s and charged a nickel per hour. In recent years, new technologies have changed the parking payment landscape as the world moves toward cashless payments [10]. A recent survey by the American Parking Association found that more than two thirds of drivers were interested in paying by app for parking at airports and on-street spaces, and an International Parking and Mobility Institute survey showed that 80 percent of drivers in the United States have used their phones to pay for parking [11]. Various technologies have been developed during the 21st century to address parking payment, and ultimately many municipalities end up using combinations of these technologies to support public policy and improve the customer experience.

Single-Space Meters
Unlike the mechanical meters of old, smart meters allow the user to conduct a cashless transaction with credit cards or e-wallets. In some cases, these meters also can collect license plate information and data such as usage patterns to help cities predict occupancy levels and streamline parking enforcement [12]. In early 2022, the City of Fayetteville, Arkansas installed smart meters that offer the option to pay with a credit card or the ParkMobile app, in addition to coins. The new meters also have sensors that record when a car pulls into the space. This allows for parking fee grace periods for short durations and provides parking availability data [13]. Smart meters also allow for dynamic pricing, which can help localities increase revenue and/or optimize parking utilization. Single-space meters have the benefit of being visually present at each parking space as a reminder to customers, but they also contribute to visual clutter on the sidewalk. New York, Boston, Seattle and Los Angeles are some additional examples of cities that use these types of meters [14]. Solar-powered smart meters typically cost around $500.00 each, though the cost varies by brand and features.

Multi-Space Meters
Multi-space meters can handle parking payments for entire blocks of parking spaces. They can be configured as pay-and-display, pay-by-plate, or pay-by-space systems. In the mid 1990s, Aspen, Colorado became the first U.S. city to adopt a pay-and-display system for on-street parking. At the time, local merchants were upset about the city’s transition from free, timed parking to a paid system, but they quickly realized that the increased parking turnover was good for business. Additionally, the paid parking encouraged employees to park in the city garage instead of occupying on-street spaces all day. During the next 10 years, many other cities and towns followed suit. Customers park, pay at the kiosk and go back to their cars to display the ticket on their dashboard [15].

.Pittsburgh, Pennsylvania became the first city to adopt pay-by-plate technology in 2012. As with the pay-and-display system, users walk down the block to a kiosk, but they are able to enter their license plate number in the system and pay, negating the need for a ticket (and a walk back to the vehicle to display said ticket). The downside is that the customer needs to remember their license plate number [15].

Pay-by-space systems allow users to enter their parking space number into a payment machine or app, allowing for a contactless, cashless experience [11]. Washington, D.C., implemented this payment system in 2015 in certain areas of the city. Users park in spaces designated by numbered posts. They then enter the space number into a curbside payment kiosk or mobile app to pay for parking [16]. Multi-space meters typically cost more than $5,000.00 each, though this varies by brand and features.

Mobile Payment
When it was introduced in Canada in 2001, PayByPhone became North America’s first mobile payment service for parking. It is now the largest parking payment provider in the world with more than 12.5 million users worldwide. Users can call the phone number on the sign or meter near the parking space and follow the prompts to pay. Parking can be extended with another phone call [17].

Mobile apps also have become a popular method of paying for parking. Companies like ParkMobile have developed apps that allow drivers to locate, reserve and pay for their parking spaces. A website is available for users who do not want to download the app [18]. ParkMobile works with municipalities, airports, college campuses, event venues and other parking providers [19]. In December 2021, ParkMobile reported that it had a total of 30 million customers and had added 200 new locations in the previous year [18].

Pay-by-text allows customers to pay with their mobile phones without downloading an app. The customer sends a text message to the phone number displayed on a sign or decal near the parking space or scans a QR code. They receive a secure link that takes them to a website where they can enter their parking information and payment method. The system can be used in either a pay-by-plate or pay-by-space configuration and can be used on its own or with other types of systems. This technology has been released by Flowbird, which already offers a mobile app [20]. Text2Park is another provider that claims this technology is easier on the customer than downloading an app and creating an account [21].

Pay-in-Car
In-Car meters are small, programmable devices hang from the vehicle’s rearview mirror or grab bar, or are mounted on the dashboard. They are pre-loaded with funds, and deduct the cost after the driver selects the parking zone and activates the timer. Some of these devices contain GPS systems that allow them to automatically deduct the correct amount. In-car meters typically are used as a payment option along with single- or multi-space meters. They allow the customer to pay for parking without visiting the meter, but can be subject to theft [14].

Parkopedia has developed an in-car “infotainment” screen, which can manage payments for parking, tolls, electric vehicle charging, and fueling. The company announced early in 2022 that it has partnered with Passport, a U.S.-based digital transportation payment company, to expand its in-vehicle payment services to 800 towns in the United States. Parkopedia emphasizes the convenience of paying for most vehicle-related expenses through a single platform [22].

AI Parking Recognition
Metropolis Technologies Inc. recently received $167 million in venture capital to continue the development of a system that uses artificial intelligence to charge for parking. Customers sign up for the system through an app or QR code, and computer vision artificial intelligence recognizes the customer’s vehicle when it enters and exits a set parking zone. The customer is then billed through the system [23].

Case Study: San Francisco, California
Prior to the SFpark program, San Francisco’s parking system was not particularly sophisticated and was not designed to meet the city’s evolving needs. Parking meter rates charged the same price all day, every day, and on-street parking was less expensive than garage parking, which incentivized drivers to circle the block looking for an on-street space. The city found that its flat meter rates and short time limits were somewhat effective in achieving parking turnover and budgetary goals, but it wanted to work toward a system that was more convenient for drivers and focused on parking availability [24].

The San Francisco Municipal Transportation Agency (SFMTA) launched the SFpark pilot project in 2010-2011. The SFMTA had approved the legislation for the project in 2008, and the Port of San Francisco, which owns more than 1,400 parking spaces along the waterfront, also signed on to the project. The pilot focused on 6,000 parking spaces (approximately 25 percent of the city’s parking inventory) and 12,250 SFMTA-managed garage spaces (approximately 75 percent of city-operated off-street parking) to study the relationship between pricing and parking choices [24]. The project cost $24.75 million, $20 million of which was federally funded [25].

SFMTA used several new technologies, including smart meters, parking sensors, and a data management tool to optimize parking availability[24] with the following objectives in mind:

 * Safety: When drivers circle the block looking for parking, they are distracted while making left- and right-hand turns, creating a hazard for pedestrians and bicyclists. When they double-park due to a lack of available parking, other drivers must go around their vehicles, which also is a safety issue [24].
 * Transit and traffic efficiency: These drivers, whether they are double-parking or circling the block, add to traffic congestion and reduce the reliability of the Muni bus system [24].
 * Economy: A lack of parking, or even a perceived lack of parking, in San Francisco’s commercial districts can discourage residents and visitors from spending time – and money – in those neighborhoods [24].
 * Environment: Vehicles that are idling or circling the block also waste gas and contribute to greenhouse gas emissions [24].

SFMTA used demand-responsive pricing, periodically adjusting rates to ensure that there were always some spaces available on each block and in each garage, while preventing spaces from sitting unused for long. The city’s target occupancy rate for on-street parking was 60-80 percent. When occupancy was 80-100 percent, rates increased by 25 cents per hour. When the occupancy rate was 60-80 percent, rates did not change. When the occupancy rate was 30-60 percent, the rates decreased by 25 cents per hour. And at less than 30 percent occupancy, the rates decreased by 50 cents per hour. Hourly rates were not to go above $6.00 per hour or below 25 cents per hour. During the two-year pilot program, rates were adjusted every eight weeks – 10 times in total [24]

For garage parking, the city decreased its commuter discounts and changed its payment system to match that of the on-street system, with different occupancy thresholds. In addition to demand, the garage rates also were adjusted to reduce entries and exits during the heaviest traffic times by providing off-peak discounts. Previous early-bird discounts had incentivized drivers to enter and exit the garages during rush hour [24].

At the end of the program in 2013, on-street parking rates increased on half of the blocks included in the program, and decreased on the other half. Overall, on-street and garage rates decreased during the course of the program. Availability increased by 16 percent in the areas included in the program, while decreasing by 50 percent in excluded areas. In the program area, the target occupancy rate was met by an additional 31 percent, compared to 6 percent in excluded areas. SFpark also helped to increase the utilization of city parking garages (11 percent increase), particularly during off-peak times (14 percent increase). Finally, the program reduced the number of commuters parking in SFMTA-operated garages, providing increased parking availability for visitors (an economic win) and a reduction in commuters driving into the commercial district (an environmental win). During the pilot period of 2011-2013, the city’s population, employment, travel and economic activity increased [24].

SFMTA conducted the pilot program not only for its own benefit, but to provide valuable data to the U.S. Department of Transportation, other jurisdictions for consideration in developing their own parking programs, and the transportation research community.[25]

The SFpark pilot program demonstrated that new technologies can allow communities to meet their changing parking needs, and that parking pricing can help to control demand. There are many new parking payment technologies available. They add convenience and increase compliance, but perhaps their most compelling advantage is the ability to support public policy. While paid parking has been used in the past to generally help limit the duration of occupancy and to fill budget gaps, today’s technologies – smart meters and occupancy sensors – allow cities to more precisely control occupancy rates by adjusting prices based on demand.

License Plate Recognition
License Plate Recognition, or LPR, is at the forefront of recent technology applications for parking management and enforcement. LPR was first implemented in a bulky and costly attempt in the United Kingdom to combat terrorism in 1981, but advancements in camera quality and software design have made the technology a more efficient and cost-friendly enforcement mechanism for private and public parking management [26]. LPR uses fixed, mounted, or handheld cameras to take images of license plates, which are then fed through a software program, characterizing, and identifying the read licenses in an electronic format, feeding into the selected local database to determine the legality of the vehicle in real-time [27].

LPR itself is not a new technology, but many stakeholders are finding innovative solutions to parking problems with the technology. LPR is an attractive solution as higher quality cameras are available for relatively cheap costs and can reliably identify infractions. LPR allows public and private entities to monitor and penalize infractions in real-time. However, like all technologies, LPR has its limitations. It does not work well in inclement weather such as sleet, fog, or rain, and raises some privacy concerns. Improvements have certainly been made to address these disadvantages, but LPR remains an imperfect enforcement tool.

Autonomy and Automation
As vehicles become more connected with their surroundings on the road, the capabilities of autonomous technologies can also remedy parking management problems. Modern cars also come with park-assist and other sensor technologies that can maneuver vehicles autonomously into tight spaces. While these features are tailored to assist individual vehicle operators in proximity, garages in urban centers are investing in automated technology more like that found in manufacturing or warehouse facilities to save space in land-spent cities [28]. Vehicles simply drive onto a platform upon checking in, and the vehicle is stored automatically, often on racks or some other vertical storage space, and retrieved automatically when the owner returns.

While automation offers a unique solution to crowded urban areas, there are other benefits as well. More efficient car storage means less land area and building volume, as well as fewer emissions from drivers searching for a spot [29]. Vendors often promise scratch-free parking and timely delivery of one’s vehicle, but a quick google search of automated lots in the United States will reveal online ratings that system failures are critical, leaving customers without their cars for over 12 hours in some cases.

Automated parking provides a promising solution to crammed cities searching for space for residents, commuters, and other visitors to park their cars. While expensive, at up to $50,000 per space, there are land-use, economic, and environmental incentives to continue investment into bettering the technology implementation [30].

Parkmatic
Parkmatic provides automated and attended mechanical parking solutions for private buildings and lots. While their attended solutions do make more efficient use of space, their automated solutions can double the number of spaces as a ground lot or typical garage. Four different automated designs (carousel, puzzle, rack & rail, and tower) each best suited for a specific environment, move cars into the garage after owners drive onto the platform, and vehicles are then automatically stored and retrieved [28].

Parkmatic offers the most promise for parking garages and lots that have little space, but plenty demand for car storage. Car dealerships, universities, and other larger operations with little space, both horizontally and vertically, are best suited to seek Parkmatic parking management solutions. Parkmatic, like other automated parking companies, also boasts increased security and minimal theft.

Genetec
Genetec leverages license plate recognition software to offer better management for private garages and lots. Integrating existing cameras and data from their customers, Genetec provides a breadth of services, including mobile parking enforcement, security solutions, infrastructure analysis and more. The AutoVu system manages the enforcement and data privacy of Genetec projects. Genetec claims to have the most sophisticated cameras and integration software in the industry, allowing for their wide range of quality services.

Genetec’s primary market is large, publicly used lots, meant to serve lots of people. Richmond, VA, the Montreal-Trudeau airport, the University of Wisconsin-La Crosse, the Danish police force, and many others use Genetec for parking management and security solutions [31].

Klaus Multiparking
Klaus Multiparking is a German parking assist product and service provider, with an international reach in over 80 countries. Klaus believes movement is the essential design element in intelligent parking systems, so many of their goods provide flexible options, such as parking pallets, fully automated parking systems, semi-automated parking systems, and other space-maximizing alternatives to manual parking.

Klaus is more active in private parking management, as their international projects focus on multi-family residential and single-family homes or commercial offices. Their smaller-scale designs can increase storage space in urban neighborhoods with limited space for car storage [32].

City Scanner
City Scanner offers automated tools best suited for on-street parking enforcement for municipalities. A vehicle with a mounted camera simply patrols the area, and while driving around, multiple images are taken to detect parking infractions and unpaid parking fees. City Scanner runs a flexible operation, with the capacity to add additional sensors tailored to shifting demands. The German start-up also offers parking and infrastructure analysis leveraging their high-quality cameras. The technology can be suited to any vehicle, offering a low-cost asset-lite solution to parking enforcement. Most of their clients are city municipalities patrolling on-street parking [33].

PayBySky
PayBySky is a Canadian cloud-based parking and connected vehicle service provider. Their smartphone application, Kerbeze, leverages connected vehicle information to inform restaurants and other merchants of pick-up and drop off arrival times with pinpoint accuracy to streamline delivery, pick-up and other services for consumers and merchants.

Continuing leveraging of car-based data, Skymeter is the firm’s autonomous payment system that identifies unique vehicles entering lots with PayBySky spaces, and the system automatically bills the selected credit card, completely removing the need to think about paying for parking.

While many newer car models with inherent technology only need to pay the subscription ($15/month), most vehicles produced after 1996 can purchase an adapter for $250. However, as an exclusive network, PayBySky is limited in its potential to have far reaching effects, until competitors disrupt the market to leave room for interoperability or purge the firm from the market if it fails to evolve [34].

Greeley, CO
A small suburban city, Greeley, Colorado issues automated traffic citations to illegally parked cars from vehicle-mounted cameras and integrated LPR to detect infractions and scofflaws. The technology allows public officials to quickly identify abandoned or inoperable vehicles. Passport Inc. was contracted as the service provider to solve the parking crisis in the city’s internal operations and physical environment. Their services also include curb management geared towards micromobility, and parking management software to expedite locating available spots via smart phone app [35].

Washington, D.C.
As one of the most congested American cities with an under-performing and slow public transportation service, Washington, D.C. launched a pilot in the winter of 21-22 to determine the feasibility of automated bus lane enforcement. The District Department of Transportation and stakeholders equipped buses traveling through transit priority lanes and corridors with mounted cameras to detect infractions with LPR and enforce tickets, including illegal parking, picking up and dropping off, travelling through the lane, and other infractions.

Results from the short pilot may have been unconvincing as the pilot duration coincided with sever snowstorms and low visibility. Mounted cameras on moving vehicles are less reliable than fixed cameras, like those at intersections. The final report included recommendations to install more reliable, but less flexible, more common cameras mounted to intersection poles [36].

Stuttgart, Germany Airport
In late 2020 at the Stuttgart Airport, Mercedes with their new S-class of vehicles combined with German group Bosch to pilot new applications of autonomous parking and management. Regular and thorough mapping of the garage and leveraging cameras and connected vehicles enables the German duo to map pre-determined routes for cars in the garage to their spot, maximizing space and limiting customer idling. Unlike most autonomous technology, Bosch is not relying on more-expensive LiDAR.

The project does not rely on any automated storage mechanics to further maximize space, as this is achieved fractionally through parking the cars closer to each other without space required for drivers and passengers to open doors and remove their luggage (37).

Role of Policy
Local private parking management does not interact too much with public policy on a micro level, as automated garages can easily comply with local noise ordinances and land-use contracts. However, land acquisition in a market meant to capture externalities in crammed urban areas is certainly an obstacle to implementing new construction projects.

Municipal parking enforcement leveraging innovative technologies must prepare at the front end to create policy frameworks and legislative and regulatory authority. License plate recognition software ticketing automatically can only issue tickets to the owner of the vehicle according to the registration information. With stolen vehicles and other reasons for petitions, additional support and appeal processes must be established to account for the limitations of automated enforcement. Municipalities must also consider how they will signify to the public that they are in an automated enforcement zone

Some cities have disincentivized driving or parking in congested downtown areas through a variety of different methods. Washington D.C. implemented a demand-based pricing model in a pilot in 2019, cities in India have odd-even policies in which only vehicle plates ending in an odd or even number are allowed entry on alternating days [38,39].

Other policy efforts from cities battling congestion, pollution, and safety problems have removed parking minimums from high-density areas, increased tolls and parking rates to disincentivize driving in those areas. This is a future of urban policy decision-making that must be considered in a discussion of the future of parking management. Will solutions tailored to smaller, local challenges, like those offered by Klaus prevail as the least obtrusive and smallest scale solutions outlast the rest of the market? Or will cities continue to discourage cars, making it difficult for large vertical storage solution providers, like Parkmatic, to find new projects to sustain innovation and growth?

Conclusion
Parking is a public policy issue that has safety, economic, environmental and quality-of-life implications. Existing and emerging technologies can help to improve the customer experience and manage behavior to support public and private sector parking objectives. In particular, mobile apps help drivers locate and pay for parking, vehicle recognition technology has been revolutionary for parking enforcement, and data collection provides insight into demand. Not all of these technologies are brand new, but parking management leaders continue to identify innovative ways to use them. As artificial intelligence continues to develop, it is likely to play a growing role in parking management, which could lead to privacy issues. Cities and towns, as well as private businesses, have numerous options for parking management technologies, and they can choose the combination of these tools that best fits their budget, customer base, and goals. The technology must be paired with smart, data-driven policies to achieve these objectives and truly optimize parking management.


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User:Smartpig101

Hello!

title: User:Smartpig101


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Statistics/Interval Estimation

Introduction
Previously, we have discussed, which gives us an estimator $$\hat\theta$$ for the value of an unknown parameter $$\theta$$. Now, suppose we want to know the size of of the point estimator $$\hat\theta$$, i.e. the difference between $$\hat\theta$$ and the unknown parameter $$\theta$$. Of course, we can make use of the value of the of $$\hat\theta$$, $$\mathbb E[(\hat\theta-\theta)^2]$$, or other things.

However, what if we only know about one specific ? We cannot calculate the mean squared error of its corresponding point estimator with this point estimates, right? So, how do we know the possible size of error of this ? Indeed, it is impossible to tell, since we are only given a particular estimated value of parameter $$\theta$$, but of course we do know the value of the unknown parameter $$\theta$$, thus the difference between this point estimate and $$\theta$$ is also unknown.

To illustrate this, consider the following example: suppose we take a random sample of 10 students from one particular course in university to estimate the mean score of the students in the final exam in that course, denoted by $$\mu$$, (assume the score is normally distributed), and the observed value of the sample mean is $$\overline x=60$$. Then, what is the difference between this point estimate and the true unknown parameter $$\mu$$? Can we be "confident" that this sample mean is close to $$\mu$$, say $$\mu\in[\overline x-5,\overline x+5]=[55,65]$$?

It is possible that $$\mu$$ is, say 90, and somehow the students in the sample are the one with very poor performance. On the other hand, it is also possible that $$\mu$$ is, say 30, and somehow the students in the sample are the one who perform well (relatively). Of course, it is also possible that the $$\mu$$ is quite close to 60, say 59. From this example, we can see that a particular value $$\overline x=60$$ does not tell us the possible size of error: the error can be very large, and also can be very small.

In this chapter, we will introduce where we use  that can describe the size of error through providing the probability for the random interval (i.e. interval with at least one of its bounds to be a random variable) given by the interval estimator to contain the unknown parameter $$\theta$$, which measures the "accuracy" of the interval estimator of $$\theta$$, and hence the size of error.

As suggested by the name, the estimator involves some sort of. Also, as one may expect, is also based on :

Of course, we would like the probability for the unknown parameter $$\theta$$ to lie in the interval to be close to 1, so that the interval estimator is very accurate. However, a very accurate interval estimator may have a very bad "precision", i.e. the interval covers "too many" plausible values of an unknown parameter, and therefore even if we know that $$\theta$$ is very likely to be one of such values, there are too many different possibilities. Hence, such interval estimator is not very "useful". To illustrate this, suppose the interval concerned is $$\mathbb R$$, which is the parameter space of $$\theta$$. Then, of course $$\mathbb P(\theta\in \mathbb R)=1$$ (so the "confidence" is high) since $$\theta$$ must lie in its parameter space. However, such interval has basically "zero precision", and is quite "useless", since the "plausible values" of $$\theta$$ in the intervals are essentially all possible values of $$\theta$$.

From this, we can observe the need of the "precision" of the interval, that is, we also want the of the interval to be small, so that we can have some ideas about the "location" of $$\theta$$. However, as the interval becomes smaller, it is more likely that such interval misses $$\theta$$, i.e. does not cover the actual value of $$\theta$$, and therefore the probability for $$\theta$$ to lie in that interval becomes smaller, i.e. the interval becomes less "accurate". To illustrate this, let us consider the extreme case: the interval is so small that it becomes an interval containing a single point (the two end-points of the interval coincide). Then, the "interval estimator" basically becomes a "point estimator" in some sense, and we know that it is very unlikely that the true value of $$\theta$$ equals the value of the point estimator $$\hat\theta$$ ($$\theta$$ lies in that "interval" is equivalent to $$\theta=\hat\theta$$ in this case). Indeed, if the distribution of $$\hat\theta$$ is, then $$\mathbb P(\hat\theta=\theta)=0$$.

As we can see from above, although we want the interval to have a very high "confidence" and also "very precise" (i.e. the interval is very narrow), we cannot have both of them, since an increase in confidence causes a decrease in "precision", and an increase in "precision" causes a decrease in confidence. Therefore, we need to make some compromises between them, and pick an interval that gives a sufficiently high confidence, and also is quite precise. In other words, we would like to have a interval that will cover $$\theta$$ with a.

Terminologies
Now, let us formally define some terminologies related to.

Construction of confidence intervals
After understanding what confidence interval is, we would like to know how to construct one naturally. A main way for such construction is using the, which is defined below.

After having such pivotal quantity $$Q(\mathbf X,\theta)$$, we can construct a $$1-\alpha$$ confidence interval for $$\theta$$ by the following steps:
 * 1) For that value of $$\alpha$$, find $$a,b$$ such that $$\mathbb P(a\le Q(\mathbf X,\theta)\le b)=1-\alpha$$ ($$a,b$$ does not involve $$\theta$$ since $$Q(\mathbf X,\theta)$$ is a pivotal quantity).
 * 2) After that, we can transform $$a\le Q(\mathbf X,\theta)\le b$$ to $$L(\mathbf X)\le \theta\le U(\mathbf X)$$ since the expression of $$Q(\mathbf X,\theta)$$ involves $$\theta$$, as we have assumed (the resulting inequalities should be  to the original inequalities, that is, $$a\le Q(\mathbf X,\theta)\le b{\color{darkgreen}\iff} L(\mathbf X)\le \theta\le U(\mathbf X)$$, so that $$\mathbb P(L(\mathbf X)\le\theta\le U(\mathbf X)){\color{darkgreen}=}\mathbb P(a\le Q(\mathbf X,\theta)\le b)$$).

Confidence intervals for means of normal distributions
In the following, we will use the concept of pivotal quantity to construct confidence intervals for means and variances of distributions. After that, because of the central limit theorem, we can construct confidence intervals for means and variances of other types of distributions that are not normal.

Mean of a normal distribution
Before discussing this confidence interval, let us first introduce a notation: We can find (or calculate) the values of $$z_{\alpha}$$ for different $$\alpha$$ from.
 * $$z_{\alpha}$$ is the upper percentile of $$\mathcal N(0,1)$$ at level $$\alpha$$, i.e. it satisfies $$\mathbb P(Z\ge z_{\alpha})=\alpha$$ where $$Z\sim\mathcal N(0,1)$$.

The following graph illustrates $$\mathbb P(-z_{\alpha/2}\le Z\le z_{\alpha/2})=1-\alpha$$: |                 *-|-*                 /##|##\                   /###|###\  <- area 1-a /####|####\             /#####|#####\             /######|######\            /|######|######|\ area    --*.|######|######|.*-- a/2 --> ....|######|######|.... <--- area a/2 *---          -z_{a/2}       z_{a/2}

We have previously discussed a way to construct confidence interval for the mean when the variance is. However, this is not always the case in practice. We may not know the variance, right? Then, we cannot use the $$\sigma$$ in the confidence interval from the previous theorem.

Intuitively, one may think that we can use the $$S^2$$ to "replace" the $$\sigma^2$$, according to the weak law of large number. Then, we can simply replace the unknown $$\sigma$$ in the confidence interval by the known $$S$$ (or its realization $$s$$ for interval estimate). However, the flaw in this argument is that the sample size may not be large enough to apply the weak law of large number for approximation.

So, you may now ask that when the sample size is large enough, can we do such "replacement" for approximation. The answer is, and we will discuss in the last section about approximated confidence intervals.

Before that section, the confidence intervals discussed is in the sense that no approximation is used to construct them. Therefore, the confidence intervals constructed "work" for sample size, no matter how large or how small it is (it works even if the sample size is 1, although such confidence interval constructed may not be very "nice", in the sense that the width of the interval may be quite large).

Before discussing how to construct an confidence interval for the mean when the variance is unknown, we first give some results that are useful for deriving such confidence interval.

Using this proposition, we can prove the following theorem. Again, before discussing this confidence interval, let us introduce a notation:
 * $$t_{\alpha,\nu}$$ is the upper percentile of $$t_{\nu}$$ at level $$\alpha$$, i.e. it satisfies $$\mathbb P(T\ge t_{\alpha,\nu})=\alpha$$ where $$T\sim t_{\nu}$$.

Difference in means of two normal distributions
Sometimes, apart from estimating mean of a normal distribution, we would like to estimate the  in means of  normal distributions for making comparison. For example, apart from estimating the mean amount of time (lifetime) for a bulb until it burns out, we are often interested in estimating the between life of two different bulbs, so that we know which of the bulbs will last longer in average, and then we know that bulb has a higher "quality".

First, let us discuss the case where the two normal distributions are.

Now, the problem is that how should we construct a confidence interval for the in two means. It seems that we can just construct two $$1-\alpha$$ confidence intervals $$[L(\mathbf X),U(\mathbf X)],[L(\mathbf Y),U(\mathbf Y)]$$ for each of the two means $$\mu_X,\mu_Y$$ respectively. Then, the $$1-\alpha$$ confidence interval for $$\mu_X-\mu_Y$$ is $$[L(\mathbf X)-L(\mathbf Y),U(\mathbf X)-U(\mathbf Y)]$$. However, this is indeed incorrect since when we have $$\mathbb P(L(\mathbf X)\le \mu_X\le U(\mathbf X))=1-\alpha$$ and $$\mathbb P(L(\mathbf Y)\le \mu_Y\le U(\mathbf Y))=1-\alpha$$, it does mean that $$\mathbb P(L(\mathbf X)-L(\mathbf Y)\le \mu_X-\mu_Y\le U(\mathbf X)-U(\mathbf Y))$$ (there are no results in probability that justify this).

On the other hand, it seems that since $$\{L(\mathbf X)\le \mu_X\le U(\mathbf X)\}$$ and $$\{L(\mathbf Y)\le\mu_Y\le U(\mathbf Y)\}$$ are independent (since the normal distributions we are considering are independent), then we have $$\mathbb P(L(\mathbf X)\le \mu_X\le U(\mathbf X)\text{ and }L(\mathbf Y)\le \mu_Y\le U(\mathbf Y))=(1-\alpha)^2.$$ Then, when $$L(\mathbf X)\le \mu_X\le U(\mathbf X)$$ and $$L(\mathbf Y)\le \mu_Y\le U(\mathbf Y)$$, we have $$L(\mathbf X)-U(\mathbf Y)\le\mu_X-\mu_Y\le U(\mathbf X)-L(\mathbf Y),$$ so $$\mathbb P(L(\mathbf X)-U(\mathbf Y)\le\mu_X-\mu_Y\le U(\mathbf X)-L(\mathbf Y))=(1-\alpha)^2,$$ which means $$[L(\mathbf X)-U(\mathbf Y),U(\mathbf X)-L(\mathbf Y)]$$ is a $$(1-\alpha)^2$$ confidence interval.

However, this is actually also incorrect. The flaw is that "when $$L(\mathbf X)\le \mu_X\le U(\mathbf X)$$ and $$L(\mathbf Y)\le \mu_Y\le U(\mathbf Y)$$, we have $$L(\mathbf X)-U(\mathbf Y)\le\mu_X-\mu_Y\le U(\mathbf X)-L(\mathbf Y)$$" only means $$\{L(\mathbf X)\le \mu_X\le U(\mathbf X)\text{ and }L(\mathbf Y)\le\mu_Y\le U(\mathbf Y)\}\subseteq \{L(\mathbf X)-U(\mathbf Y)\le \mu_X-\mu_Y\le U(\mathbf X)-L(\mathbf Y)\}$$ (we do not have the reverse subset inclusion in general). This in turn means $$(1-\alpha)^2=\mathbb P(L(\mathbf X)\le \mu_X\le U(\mathbf X)\text{ and }L(\mathbf Y)\le\mu_Y\le U(\mathbf Y)){\color{darkgreen}\le}\mathbb P(L(\mathbf X)-U(\mathbf Y)\le \mu_X-\mu_Y\le U(\mathbf X)-L(\mathbf Y)).$$ So, $$[L(\mathbf X)-U(\mathbf Y),U(\mathbf X)-L(\mathbf Y)]$$ is actually a $$(1-\alpha)^2$$ confidence interval (in general).

So, the above two "methods" to construct confidence intervals for difference in means of two independent normal distributions actually do not work. Indeed, we do use the confidence interval for each of the two means, which is constructed previously, to construct a confidence interval for difference in the two means. Instead, we consider a of the difference in the two means, which is a standard way for constructing confidence intervals.

Now, we will prove the above theorem based on the result shown in the previous exercise:

Now, we will consider the case where the variances are. In this case, the construction of the confidence interval for the difference in means is more complicated, and even more complicated when $$\sigma_X^2\ne \sigma_Y^2$$. Thus, we will only discuss the case where $$\sigma_X^2=\sigma_Y^2$$ is unknown. As you may expect, we will also use some results mentioned previously for constructing confidence interval for $$\mu$$ when $$\sigma^2$$ is unknown in this case.

Now, what if the two normal distributions concerned are ? Clearly, we cannot use the above results anymore, and we need to develop a new method to construct a confidence interval for the difference of means in this case. In this case, we need to consider the notion of.

Variance of a normal distribution
After discussing the confidence intervals for means of normal distributions, let us consider the confidence intervals for of normal distributions. Similarly, we need to consider a pivotal quantity of $$\sigma^2$$. Can you suggest a pivotal quantity of $$\sigma^2$$, based on a previous result discussed?

Recall that we have $$\frac{nS^2}{\sigma^2}\sim\chi^2_{n-1}$$, and $$\chi^2_{n-1}$$ is independent from $$\sigma^2$$ with some suitable assumptions. Thus, this result gives us a pivotal quantity of $$\sigma^2$$, namely $$\frac{nS^2}{\sigma^2}$$. Before discussing the theorem for constructing a confidence interval for $$\sigma^2$$. Let us introduce a notation: Some values of $$\chi^2_{\alpha,\nu}$$ can be found in the chi-squared table.
 * $$\chi^2_{\alpha,\nu}$$ is the upper percentile of $$\chi^2_{\nu}$$ at level $$\alpha$$, i.e. it satisfies $$\mathbb P(X\ge \chi^2_{\alpha,\nu})=\alpha$$ where $$X\sim\chi^2_{\nu}$$.
 * To find the value of $$\chi^2_{\alpha,\nu}$$, locate the row for $$\nu$$ degrees of freedom and the column for "probability content" $$\alpha$$.

Ratio of variances of two independent normal distributions
Similar to the case for means, we would also sometimes like to compare the variances of two normal distributions. One may naturally expect that we should construct a confidence interval for in variances, similar to the case for means. However, there are simple ways to do this, since we do not have some results that help with this construction. Therefore, we need to consider an alternative way to the variances, without using the  in variances. Can you suggest a way?

Recall the definition of in point estimation. gives us a nice way to compare two variances without considering their difference, where the of two variances is considered. Fortunately, we have some results that help us to construct a confidence interval for the of two variances.

Recall that the definition of $$F$$-distribution: if $$U\sim\chi^2_$$ and $$V\sim\chi^2_$$ are independent, then $$\frac{U/{\color{red}\nu_1}}{V/{\color{blue}\nu_2}}$$ follows the $$F$$-distribution with $${\color{red}\nu_1}$$ and $${\color{blue}\nu_2}$$ degrees of freedom, denoted by $$F_{{\color{red}\nu_1},{\color{blue}\nu_2}}$$. From the definition of $$F$$-distribution, we can see that it involves a ratio of two independent chi-squared random variables. How can it be linked to the ratio of two variances?

Recall that we have $$\frac{nS^2}{\sigma^2}\sim\chi^2_{n-1}$$ with some suitable assumptions. This connects the variance with the chi-squared random variable, and thus we can use this property together with the definition of $$F$$-distribution to construct a pivotal quantity, and hence a confidence interval.

Let us introduce a notation before discussing the construction of confidence interval: Some values of $$F_{\alpha,\nu_1,\nu_2}$$ can be found in $F$-tables (there is different $$F$$-tables for different values of $$\alpha$$, and the row and column of each table indicates the first and second degrees of freedom respectively). Also, using the property that $$F_{\alpha,\nu_1,\nu_2}=\frac{1}{F_{1-\alpha,\nu_2,\nu_1}}$$, we can obtain some more values of $$F_{\alpha,\nu_1,\nu_2}$$ which are not included in the $$F$$-tables.
 * $$F_{\alpha,\nu_1,\nu_2}$$ is the upper percentile of $$F_{\nu_1,\nu_2}$$ at level $$\alpha$$, i.e. it satisfies $$\mathbb P(X\ge F_{\alpha,\nu_1,\nu_2})=\alpha$$.

Apart from using this confidence interval to variances (or standard deviations), it can also be useful to  some assumptions about variances. Let us illustrate these two usages in the following examples.

Approximated confidence intervals for means
Previously, the distributions for the population are assumed to be normal, but the distributions are often normal in reality. So, does it mean our previous discussions are meaningless in reality? No. The discussions are indeed still quite meaningful in reality, since we can use the to "connect" the distributions in reality (which are usually not normal) to normal distribution. Through this, we can construct confidence intervals, since we use central limit theorem for approximation.

To be more precise, recall that the suggests that $$\frac{\overline X-\mu}{\sigma/\sqrt n}\;\overset{d}\to\;Z\sim\mathcal N(0,1)$$ with some suitable assumptions. Therefore, if the sample size $$n$$ is large enough (a rule of thumb: at least 30), then $$\frac{\overline X-\mu}{\sigma/\sqrt n}$$ follows standard normal distribution. Hence, $$\frac{\overline X-\mu}{\sigma/\sqrt n}$$ is a pivotal quantity (approximately). Recall from the property of normal distribution that if $$X_1,\dotsc,X_n$$ is a random sample from $$\mathcal N(\mu,\sigma^2)$$, then we have $$\frac{\overline X-\mu}{\sigma/\sqrt n}\sim\mathcal N(0,1)$$ (not approximately), and we have used this for the pivotal quantity for the confidence interval for mean when variance is known, and also the confidence interval for $$\mu_X-\mu_Y$$ when $$\sigma_D^2$$ is known. Therefore, we can just use basically the same confidence interval in these cases, but we need to notice that such confidence intervals are approximated, but not exact since we have used the central limit theorem for constructing the pivot quantity.

Now, how about the other confidence intervals where the pivotal quantity is "not in this form"? In the confidence interval for difference in means when variance is unknown, the pivotal quantity is similar in some sense: $$\frac{(\overline X-\overline Y)-(\mu_X-\mu_Y)}{\sqrt{\sigma_X^2/n+\sigma^2_Y/m}}\sim\mathcal N(0,1)$$ (see the corresponding theorem for the meaning of the notations involved). Can we use the central limit theorem to conclude that when the distributions involved are not normal (but are still independent), and the sample sizes $$n$$ and $$m$$ are both large enough, then $$\frac{(\overline X-\overline Y)-(\mu_X-\mu_Y)}{\sqrt{\sigma_X^2/n+\sigma^2_Y/m}}\sim\mathcal N(0,1)$$ ? The answer is yes. For the proof, see the following exercise.

As a result, we know that we can again just use basically the same confidence interval in this case, but of course such confidence interval is approximated.

There are still some confidence intervals that are not considered yet. Let us first consider the confidence interval for mean when the variance is.

Recall that we have mentioned that we can simply replace the "$$\sigma$$" by "$$S$$" according to the weak law of large number, which is quite intuitive. But why can we do this? Consider the following theorem.

So far, we have not discussed how to construct an approximated confidence interval for $$\mu_X-\mu_Y$$ when $$\sigma_X^2=\sigma_Y^2=\sigma^2$$ is unknown, as well as approximated confidence intervals of variances. Since the pivotal quantities used are constructed according to some results that are exclusive to normal distributions, they all do work when the distributions involved are not normal. Therefore, there are no simple ways to perform such constructions.

The following table summarizes the approximated $$1-\alpha$$ confidence intervals in different cases: $$ \begin{array}{c|c|c} \big(\text{approximated }(1-\alpha)\text{ confidence intervals}\big)&\text{mean}&\text{difference in means}\\ \hline \text{known variance}&\left[\overline X-z_{\alpha/2}\frac{\sigma}{\sqrt n},\overline X+z_{\alpha/2}\frac{\sigma}{\sqrt n}\right]&\left[(\overline X-\overline Y)-z_{\alpha/2}\sqrt{\frac{\sigma_X^2}{n}+\frac{\sigma_Y^2}{m}},(\overline X-\overline Y)+z_{\alpha/2}\sqrt{\frac{\sigma_X^2}{n}+\frac{\sigma_Y^2}{m}}\right]\text{ OR }\left[\overline D-z_{\alpha/2}\frac{\sigma_D}{\sqrt n},\overline D+z_{\alpha/2}\frac{\sigma_D}{\sqrt n}\right](\text{paired samples})\\ \hline \text{unknown variance}&\left[\overline X-z_{\alpha/2}\frac{S}{\sqrt n},\overline X+z_{\alpha/2}\frac{S}{\sqrt n}\right]&\left[\overline D-z_{\alpha/2}\frac{S_D}{\sqrt n},\overline D+z_{\alpha/2}\frac{S_D}{\sqrt n}\right](\text{paired samples})\\ \end{array} $$

Let us consider an application of the approximated confidence intervals.

title: Statistics/Interval Estimation


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Chess Opening Theory/1. d4/1...d5/2. c4/2...c6/3. Nc3/3...e5

= Winawer Countergambit =

3...e5
Black offers a gambit pawn in order to develop more quickly, as well as displacing White's knight. If the gambit is accepted, Black usually regains the pawn but more than returns the time: after 4. dxe5 d4 5. Ne4 Qa5+ 6. Bd2 Qxe5 7. Ng3, Black has his pawn back, but Nf3 is coming with tempo, and it is white who has the greater development. An alternative is 6. Nd2, after which Black is best not capturing on e5 immediately, but instead playing 6...Nd7, preparing something like 7. Ngf3 Nxe5 8. Nxe5 Qxe5. The old line 6. Nd2 f6!?, making the gambit sincere, has been analyzed by Schiller, building on work by Silman and Donaldson, but has never been played at the highest level.

Of course, White can also capture on d5 before considering the gambit: 4. cxd5 cxd5 and now any of 5. dxe5, 5. Nf3, 5. e3, and even 5. e4 are playable. 5. dxe5 gives Black an isolated queen's pawn, but after 5...d4 6. Ne4 Qa5+ 7. Nd2 Nc6 8. Nf3 Bg4 he will regain his gambit pawn at the cost of the bishop pair, with the d pawn potentially becoming passed after e.g. 9. g3 Bxf3 10. exf3 Qxe5 11. Qe2 Qxe2. 5. Nf3 gets kicked around twice by 5...e4 6. Ne5 f6 7. Qa4+ Nd7, with complex, unclear positions after either 8. Nxd7 Bxd7 9. Qb3 Bc6 or 8. Ng4 Kf7. 5. e3 allows Black to equalize with either the space-gaining 5...e4 or simply 5...exd4. 5. e4 is perhaps the strongest of White's fifth-move choices, and is always followed with 5...dxe4. Then the main continuation is 6. Bb4+ Bd7 7. dxe5 Bb4 8. Bd2 Bxc3 9. Bxd7+ (9. Bxc3 would be a losing mistake) Nxd7 10. Bxc3 Nc5, offering a queen trade while threatening ...Nd3+. 6. d5 bears mention mainly for the historic game Marshall-Winawer, 1901 rather than any great strength.

Finally, White can decline the gambit immediately with either 4. Nf3 or 4. e3. After 4. Nf3, Black equalizes with 4...exd4, or can try for more with 4...e4, where after 5. Nd2 Nf6 6. e3 a reversed French results. 4. e3 is best met with 4...exd4 5. exd4 Nf6. 4. e3 e4 results in a reversed French, but unlike the previous example, White can put the extra tempo to immediate use with 5. Qb3 etc.

Theory table
'''1. d4 d5 2. c4 c6 3.Nc3 e5'''


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Template:Minecraft resource gathering/crafting

Crafting recepie: This makes.


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User talk:Safuan12616

Welcome
Welcome, Safuan12616!

If you have any questions, you can ask in the assistance reading room or possibly contact me personally. - 🇺🇦 Слава🇺🇦Україні 🇺🇦 Героям🇺🇦Слава🇺🇦 (talk)🇺🇦 10:43, 5 November 2022 (UTC)

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title: User talk:Safuan12616


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Complete Guide to Essential Oils/A to Z of essential oils/Agarwood

Derived from the agarwood tree, agarwood essential oil has a unique and intense fragrance. It's been used for centuries in Asia for religious ceremonies and traditional medicine. Agarwood oil has some impressive properties, including antibacterial and anti-inflammatory effects. Read on to learn more about the benefits of this oil and how to use it safely. Agarwood essential oil is one of the rarest and most expensive oils in the world. Emotionally, it inspires strength and can deepen a sense of personal awareness. This highly coveted essential oil is not commonly found in most oilers' collections. Find out agarwood essential oil benefits and uses, plus a few DIY recipes to try. This precious oil is often used as a base ingredient in commercial fragrances but what is really wonderful is that agarwood essential oil, also called oud essential oil, can be used as a natural cologne all on its own. This essential oil is extracted from the fungus-infected wood of the agarwood tree, commonly called the “wood of the gods”. The process to make essential oil is very special. The wood is naturally pale in color and nearly odorless but when the wood is threatened by mold, it produces a dark, aromatic oleoresin to get rid of the fungus. This creates a dark, fragrant, resin-rich heartwood. The heartwood is then harvested and steam distilled to make the rare oil. Agarwood has a very unique aroma but you can try rich wood oils like Buddha wood, Sandalwood, Rosewood, or Ho wood. When using essential oils topically, it is best practice to dilute them in carrier oil first before applying them to the skin. Jojoba and fractionated coconut oil are popular choices. When using agarwood oil for aromatherapy, patience is needed. This rare oil is very thick and it can be slow to get a drop to come out of the bottle. Good thing is that one drop can really go a long way. It is frequently used as a base when making natural perfume/cologne. Many also like to enjoy adding this calming oil to their meditation routine. Just inhale the aroma to help you to enter a deeply spiritual state. Agarwood Essential Oil Benefits and Uses: Strengthens concentration; Promotes inner peace and balance; Supports healthy digestion; Enhances meditation; Powerful natural aphrodisiac; Soothes ongoing stress; Inspires strength and clarity; Supports greater personal awareness; Eases muscle spasms.

Source: Jennifer Lane - Certified Aromatherapist


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Chess Opening Theory/1. d4/1...d5/2. c4/2...c6/3. Nf3/3...Nf6/4. Nc3/4...a6

= a6 Slav = The move 4...a6 introduces the a6 (or Chebanenko or Chameleon) Slav. Though it seems a small move, it prepares ideas of ...b5 (either to attack White's c4 pawn or to shore up Black's after ...dxc4) and eases the problems of developing Black's light-squared bishop, as now Qb3 can be met with ...Ra7. The weakening of the b6 square, however, invites White to simply push - 5. c5 is the most common response, but White can also play 5. e3, solidifying his d pawn and adding his light-squared bishop to the fight, while accepting 5...b5. Less common are 5. a4, preventing ...b5, and 5. cxd5, releasing the central tension but leaving Black to show what purpose ...a6 now serves.

Theory table
1.d4 d5 2.c4 c6 3.Nf3 Nf6 4.Nc3 a6


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Cookbook:Ramen Noodle

Ramen noodles are a variety of wheat noodles used primarily in ramen.

History
Ramen noodles are a derivative of Chinese lamian, which were pulled noodles brought to Japan sometime between the 18th and early 20th centuries. They were initially sometimes called shina soba, meaning "Chinese wheat noodles". They became widely popular after World War II, when the American occupation imported large amounts of wheat.

Characteristics
Ramen are long and thin, made from wheat flour and containing an alkaline solution called kansui that gives them a springy texture and yellow color. They can be straight or curly, and they tend to be approximately 1.5 mm thick. The noodles are available in fresh, dried, and instant varieties. Instant ramen noodles are par-cooked and then dehydrated either by drying or deep-frying.

Procurement and storage
Instant ramen noodles have become widespread, and they are common at standard grocery stores outside of Japan. Dried and fresh ramen noodles are more limited to specialty Asian grocers in the Western world, and they will have a larger selection.

Fresh noodles can be kept in the refrigerator or freezer, while dried and instant varieties have a very long shelf-life at room temperature.

Uses
Ramen noodles are primarily used in ramen soup, of which there are many varieties. The noodles are briefly boiled and drained before adding to the soup along with various toppings. The longer the noodles sit in the broth, the mushier they will get—as a result, the noodles should be eaten relatively quickly after the soup is assembled.

Different types of ramen noodle are sometimes used for specific types of ramen. For example, straight noodles are often served with heartier, richer broths, while wavy noodles may be served with miso ramen.

title: Cookbook:Ramen Noodle


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User talk:189.188.92.230

You cannot edit for 1 week due to disruptive editing. You are welcome to contribute constructively when editing privileges are restored. You may appeal this action with a reasonable argument by adding the text below.

--Xania   talk 06:54, 6 November 2022 (UTC)

title: User talk:189.188.92.230


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User:Kelti/sandbox/Test2/Exercises

Topic: ...

title: User:Kelti/sandbox/Test2/Exercises


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Chess Opening Theory/1. d4/1...d5/2. c4/2...c6/3. Nf3/3...Nf6/4. Nc3/4...a6/5. c5

= a6 Slav = White plays 5. c5 (the Advance System) to control the weak b6 square and forestall any ...dxc4 or ...b5 ideas. If he can make this space advantage permanent, he will have a very comfortable game, so Black needs to start planning a pawn break on either b6 or e5. To support this, the main move is 5...Nbd7, developing the queen's knight to its best available square and preparing whichever break Black chooses. The main alternatives are 5...Bf5, developing the bishop before it gets blocked in by ...Nbd7, and 5...g6, preparing a fianchetto. 5...Bg4 is also played occasionally, with the idea of pressuring the e5 square indirectly, but there is no reason White cannot simply occupy it at once with 6. Ne5.

Theory table
'''1.d4 d5 2.c4 c6 3.Nf3 Nf6 4.Nc3 a6 5. c5'''


text: User:GoodLineBadLine

title: User:GoodLineBadLine


text:
MATLAB Programming/Authors & Contributors

This list is updated automatically by AuthorsAndContributorsBot. Please do not update it manually.

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Chess Opening Theory/1. d4/1...Nf6/2. c4/2...e6/3. Nc3/3...Bb4/4. e3

= Nimzo-Indian Defence, Rubinstein Variation =

4. e3
White assesses that an immediate 4...Bxc3 is not a threat, but also that 4. a3, provoking the capture, is not necessary (yet). Instead, 4. e3 simply clears the way for White's light-squared bishop to develop, usually to d3, where it helps control the all-important e4 square. Black has three main responses:

 * 4...O-O is the most common. Since Black will never castle queenside in a Nimzo-Indian, castling kingside now is a useful but still highly flexible move.
 * 4...c5 puts pressure on White's center immediately. Taking on c5 and accepting tripled isolated pawns (after ...Bxc3 bxc3) is right out of the question, and pushing d5 now simply creates a target, so White instead continues his development and leaves the tension.
 * 4...b6 is the St. Petersburg Variation (not to be confused with the Leningrad Variation). This move prepares to strengthen Black's control of e4 yet further by fianchettoing a bishop to b7, though ...Ba6 is not yet out of the question.

In all three cases White has a choice between 5. Nge2 and 5. Bd3.

Theory table
.

'''1. d4 Nf6 2. c4 e6 3. Nc3 Bb4 4. e3'''