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Basics of fine-art photography/Creating works in experimental photography

Experimental photography is a genre of photographic art based on an artistic representation of an object or action consciously modified through figurative thinking.

General information
Experimental photography is a subclass of conceptual photography, the subgenres of this direction are surrealism and subjective photography.

The goal is to explore the possibilities of photography through trial and error.

Viewers may ambiguously evaluate experimental works: many are accustomed to the classic, documentary reflection of reality, which will lead to a subconscious rejection of "incomprehensible", sometimes abstract topics.

Ways of implementation
In order to create a more or less interesting photo work related to the described genre, you need to be able to see world around us outside the box, sometimes with a certain degree of philosophical understanding.

Technically, you should use such techniques as pseudo-solarization, double (or multiple) exposure (see photo 2 in the gallery), photogram, blurry image effect. In addition, a wide range of digital post-processing software is at your disposal. In other words, you should experiment, as indicated by the root of the word displayed in the title of this chapter.

The reaction of an ordinary viewer can not always serve as an indicator. If your creation was not appreciated by a neighbor or a colleague, it does not mean that it is not aesthetic enough, but in the case of a negative assessment by a specialist, it is worth changing the direction of creativity.

It is difficult to imagine a ready-made recipe for creating images of this kind. Carefully look at the author's photographs as examples, try to come up with an original theme that is not like anything you have seen before.

If this genre does not appeal to you, close the page and choose another chapter of the textbook for yourself, for example, documentary photography.

Description of the image processing methods presented in this chapter of the textbook

 * 1) "Coming from the past" (in the upper right corner of the page); "Delusion" (photo No. 2 in the gallery) — double exposure on the same frame, plus post-processing with a graphic editor.
 * 2) "Lunar Landscape", "Path of the Dead", "Unearthly Flowers" (photos No. 1, 4, 5 in the gallery) — post-processing by graphic editors.
 * 3) "Happy NU year!"  (photo No. 3 in the gallery) — long exposure (approx. 30-60 seconds), as a result of which employed sparklers (3 pcs.) visually merged into one.


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User:Ashley Ramjattan/sandbox

Waiting for the Barbarians is a novel written by J.M Coetzee. Under the strict regulations of the dominant culture of The Empire, people known as the barbarians must follow the laws and abide by the people who make up The Empire. The Barbarians are often seen as a lower class of people. In comparison The Empire is much more high class of people whose distinct way of life suggests a greater degree of “civilization”  than the barbarians. According to Bill Ashcroft’s  Key Concepts the meaning of colonialism is, “employed to create the idea of the inferiority of the colonial subject” (“Colonialism”). The barbarians are the subjects while The Empire imposes its ideology and proves those subjects to be inferior. In Waiting for the Barbarians the real barbarians are not the inferior race of people but the The Empire. It is the Empire because its leaders impose torture on the barbarians while they themselves do nothing to Empire. The conspiracy in the novel that the Barbarians are such bad people is often disguised because The Empire are making most of the judgments and create most of the conspiracies against the Barbarians.

In the novel, the barbarians are seen as people who cause disruption and The Empire believes it must impose order and protect itself from danger, however, with news being released from the capital it is hard to decipher what is really true and what is really false. The novel’s description of the barbarians stems from the capital. The magistrate states of the account,“ last year stories began to reach us from the capital of unrest among the barbarians…The barbarian tribes were arming the rumor went; the Empire should take precautionary measures”( Coetzee 8). The novel describes the horrible way the Empire plays the victim. The magistrate identifies that it is a rumor that comes from the Capital. Barbarians may not even exist yet the capital describes them as tribal people who are going against the Empire. The news they receive is most likely propaganda. There is no real evidence that so called barbarian tribes want war. The distinction between the two groups of people is constructed to show that the Empire must remain powerful. They must seem powerful in order to continue implementing the laws and regulating the society.

There is no relation or proof that barbarians are actually in the novel itself. We never see this deception. In fact, the Magistrate often questions the word barbarians. He doesn’t believe that these people are really barbarians. The Magistrate says, “we speak of the barbarians…Are you sure they were barbarians?”(Coetzee 49). The novel often talks about tribal people. He questions whether these people are even real barbarians because the lack of communication the Empire has with the people is fantasy, rumor and evident in these lines. We often see that this concept of barbarians is often a mix up between reality. If the people are not barbarians, then they must be normal people living in this place as the Magistrate.

However, we see this concept of the barbarian arises when the Magistrate is with the barbarian girl. She is a barbarian and we can see that there is a difference between gender roles in the novel. Most importantly we see that being a barbarian girl is significant to the Magistrate. She was the one who initiates sex. The Magistrate states, “ I feel her hand groping under my clothes, her tongue licking my ear…With a heave I am upon her she is warm, swollen, ready for me” (Coetzee 63). The Magistrate notices details of the Barbarian girl. She is the one he loves the most in the novel. Her attitude towards him is open even though she is a prisoner of the Empire. The girl is passionate towards him in this scene. There are no rules between the Barbarian girl and the Magistrate. It is almost as if there love for each other unites both people. One example of torture the Empire inflicts on the barbarians is in the novel the barbarian girl has scars on her face. The Magistrate notices these scars and asks the girl if they have done this to her and she replies yes. The Magistrate says, “It has been growing more and more clear to me that until the marks on this girl’s body are deciphered and understood I cannot let go of her” (Coetzee 31). The significance of the quote is that the Magistrate is the only person that is sympathetic towards the barbarian girl; who has been inflicted with torture.

Maria Boletsi’s article Barbaric Encounters: Rethinking Barbarism in C.R Cavafy’s and J.M Coetzee’s Waiting for the Barbarians explains the meaning of the word barbarian. “The term ‘barbarian’ is used to designate members of the underclass of the newly urbanized European peasants, but it is also employed for other marginal figures” ( 69). Barbarians throughout history were never thought of as important people. Lunatics actually describes the Empire because they are so fascinated with the barbarians themselves that they become angry and crazy in believing in them. Boletsi also explains how the term sets up opposition: “reading them today cannot bypass their striking pertinence to the contemporary world in which strict oppositional thinking in terms of ‘us’ and ‘them,’ ‘civilization’ and ‘barbarism’ is staging a comeback in political rhetoric and everyday discourse” (Boletsi 94). If civilization has to include barbarians then they must be of some significance in Waiting for the Barbarians. Civilization has been using the term “us” and “them” and the distinction as we see in the novel, is a thin line.

Post-Colonial Studies: The Key Concepts gives a definition of race that, “intersects in important ways with the cultural implications of colonial domination”(“Race”). It shows that race often separates people. As long there is race in society, the dominant race rules the cultural norms and the lower race often has to submit to the dominant culture. In other words the Magistrate is dominant but when it comes to love the Barbarian girl is the most dominant character. In Waiting for the Barbarians race is often challenged as we see that the Magistrate can be with the Barbarian girl and she is allowed to be with him. So race identifies both individuals because they are two people with different backgrounds yet their society and culture has brought them together because of love.

The article, Into the Dark Chamber: The Ovelist and South Africa, gives an insightful definition of torture. According to Coetzee, “in the torture room unlimited force is exerted upon the physical being of an individual…destroying the kernel of resistance within him”( 61). When much of the torture is being done by the Empire. Their acts of crime hurts not only the barbarians but the Magistrate as well. While physical pain is being done to the Barbarian girl, the Magistrate  feels emotional pain. Torture not only causes physical pain but also impacts both the Empire and the so called barbarians. Most of all, the one under the most emotional pain is the Magistrate because he observes the indecency of the Empire. While he is not the one to be held responsible for the actions of the Empire, he still notices that he is trapped because he has feelings for the barbarian girl.

The so called barbarians and the people of the Empire create a great deal of conflict. While there is no proof of an actual fight between the two races of people, the Empire still manages to inflict their power over the barbarians by physical force.What causes the most pain to the Magistrate is not the physical abuse but emotional abuse. The Magistrate is tortured by the emotional shame the Empire has caused him. The Magistrate says, “ I wanted to live outside the history that Empire imposes on its subjects…I never wished it for the barbarians that they should have the history of Empire laid upon them. How can I believe that that is cause for shame?” (Coetzee 154). It shows how much the Magistrate hates the Empire for inflicting so much pain onto these people who are innocent people. He feels ashamed of the Empire. It is possible that the Empire is just a symbol of the barbarians because without the barbarians there would be no Empire.

So called Barbarians are discussed throughout of the novel. They are often talked about aside from The Empire. Is is just faith or a coincidence that the Magistrate has feelings for the Barbarian girl. She in many ways represents what it means to be a Barbarian as colonial powers define them. Likewise the Magistrate represents what it  means to be under the law of the Empire. While Barbarians were never seen as civilized people throughout history, Waiting for the Barbarians, they are an important group of people whose story is one of endurance, pain, and love.

Waiting for the Barbarians is a novel that depicts the essence of what it means to be the Magistrate. The book deals with a lot of interesting concepts of barbarians. The significance of the Barbarian girl is the love between her and the Magistrate. The Empire symbolizes order, law, and colonialism. The Empire’s downfall is not the lack of structure but too much structure. In the end of the book we can understand the Magistrate’s oblivious outlook.

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User:LodestarChariot2/Collections/Open Scholarship Press Collections: Connection

 * Open Scholarship Press Collections: Connection
 * Open Scholarship Press Collections: Connection/Introduction
 * Open Scholarship Press Collections: Connection/Knowledge Commons as Sites of Connection
 * Open Scholarship Press Collections: Connection/Forms of Connection and Collaboration in Digital Knowledge Commons
 * Open Scholarship Press Collections: Connection/Maintaining Connections and Fostering Care in Digital Knowledge Commons
 * Open Scholarship Press Collections: Connection/Complete Alphabetical List of References


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User:LodestarChariot2/Collections/Open Scholarship Press Collections: Policy

 * Open Scholarship Press Collections: Policy
 * Open Scholarship Press Collections: Policy/Introduction
 * Open Scholarship Press Collections: Policy/Foundational Policies and Policy Frameworks
 * Open Scholarship Press Collections: Policy/Open Scholarship and the Open Scholarship Movement
 * Open Scholarship Press Collections: Policy/Scholarly Communication
 * Open Scholarship Press Collections: Policy/Infrastructure
 * Open Scholarship Press Collections: Policy/Collaboration and Community Engagement
 * Open Scholarship Press Collections: Policy/Policy Development, Implementation, and Analysis
 * Open Scholarship Press Collections: Policy/Complete Alphabetical List of References


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User:LodestarChariot2/Collections/Open Scholarship Press Collections: Training

 * Open Scholarship Press Collections: Training
 * Open Scholarship Press Collections: Training/Introduction
 * Open Scholarship Press Collections: Training/Digital Humanities Pedagogy and Training
 * Open Scholarship Press Collections: Training/Open Resources
 * Open Scholarship Press Collections: Training/Complete Alphabetical List of References


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Lentis/Carpooling

Introduction
Ridesharing is the connection of privately-owned vehicle drivers to ride-needing passengers. Carpooling is a form of rideshare that occurs on a regular basis; subsets includes coworker carpooling and casual carpooling—also known as “slugging". Carpooling groups eliminate the need for individuals to drive independently or find public transportation.

Carpooling should not be confused with terms like "carsharing" or "car sharing" (AU, NZ, CA, TH, US) or "car clubs" (UK), which is a form of car rental where rented vehicles are privately-owned rather than owned by companies.

History
Ridesharing began during World War II as a rationing tactic to conserve rubber for the war effort. In 1942, the U.S. government required ridesharing arrangements to the workplace called, "car clubs" or "car-sharing clubs," whenever alternative transportation was not available. The U.S. Office of Civilian Defense, launched during WWII, asked neighborhood councils to encourage four workers to travel in one vehicle. It also created a ridesharing program called the Car Sharing Club Exchange and Self-Dispatching System, which grouped travelers from a workplace bulletin board.

After WWII, the use of carpooling rose in the late 1960s. A decade later, the 1973 oil crisis, caused by an Arab oil embargo imposed on several countries including the U.S., sparked further increase in carpooling.

Incentives have remained useful in encouraging carpooling: employer-sponsored commuter programs, vanpooling, HOV lanes, and park-and-ride facilities are prime examples.

Employer-sponsored programs
Many companies developed commuter ridematching programs to limit congestion and preserve office parking supply. During the 1970s, ridematching programs were primarily used for energy conservation rather than managing parking logistics.. The Federal Highway Administration (FHWA) looked at successful employer ridematching programs and published the Carpool & Buspool Matching Guide, which looked at companies like Hallmark Cards, who collected data from employees, hand-matching neighborhood employees and distributing a personalized list to participants. Jantzen, Inc. General Dynamics, NASA, McDonnell Doulas Corporation, Hewlett Packard, Burroughs Corporation, and more used similar methods which were later computerized.

Slugging
Casual carpooling—also known as “slugging"—began in the 1970s. Today, commuters use slugging to travel in High Occupancy Vehicle (HOV) lanes to and from US metropolitan areas: Houston, Texas; Washington, D.C., and Northern Virginia; the San Francisco Bay Area, and Pittsburgh, Pennsylvania.

Benefits/Incentives
Carpooling can reduce road congestion causing widespread travel-time reductions and, if efficiently employed, reduce the global fuel consumption and the need for additional parking infrastructure. If only 1 additional person is added 1 in every 10 vehicles, 7.54 to 7.74 billion gallons of fuel could be saved per year in the U.S. This decrease in automobile emissions would result in a decrease of 68.0 million tons of GHG emissions annually in the U.S..

On an individual level, carpooling participants experience cost savings due to shared travel costs of fuel, tolls, and parking; reduced travel time by way of High Occupancy Vehicle (HOV) lanes; and reduced commuter stress. They can also benefit from parking incentives including parking permits in areas of limited parking.

Georgia's Commuter Rewards
In eligible counties in the state of Georgia, there are several reward programs that enters participants with a Georgia Commute Options account into drawings for cash prizes, gas cards, or direct cash awards. Individuals earn $5 a day up to $150 for switching from driving alone to a clean commute such as public transportation, biking, walking, carpooling, teleworking, etc. by enrolling in the Gimme Five program and logging clean commutes. Once a commuter has reached the $150 limit for logging there clean commutes, they can continue tracking to enter a drawing for a monthly $25 gift card. Carpools of 3 or more people can earn a $40 gas card each month for up to 12 months within a 3-year period. There is also a vanpool referral program granting $50 to users who refer a driver who completes three consecutive months in a vanpool.

Barriers and Problems
Despite the benefits and incentives of carpooling, there are barriers that deter its widespread adoption. Because ridesharing requires drivers and riders, ridematching must be based not only on pickup location to destination but also on individual schedules. Carpooling is best suited for commuters with similar, regular schedules, and lacks the flexibility of dynamic schedules. This can discourage commuters from carpooling if they believe they cannot find a ride home in the event of a schedule-change.

Companies, communities, and even state programs have been made to encourage carpooling. However, carpooling lacks a widely-accepted platform with clear standards with which to create ride groups. These programs are often limited to more urban locations which may already have more transportation options than rural areas. Outside of the incentives added by programs like Gimme Five, there is also a lack of widespread incentives. HOV lanes are exclusive to major cities and often exploited by single occupancy vehicles due to the challenges of occupancy requirement enforcement.

The "first and last mile" is the distance from your destination from where a rider is dropped off. This is a large deterrent for users of public transportation without a transit stop within a reasonable distance to their secondary method of travel. This problem can also carry over to carpooling where commuters must find a method to travel the remaining distance to and from the pick-up and drop-off locations. Carpools that directly pick-up and drop-off their commuters to and from their destination are more attainable. However, the time it takes for the carpool to travel the "first and last mile" for every commuter adds up. In this way, the "first and last mile" can also disincentivize drivers and riders if the incentive to carpool does not outweigh the cost of the added commute.

Charlottesville, Virginia
Rideshare programs and incentives are implemented in many ways across the world, and those cases illustrate the costs and benefits of adoption. Charlottesville, Virginia is one such case, with multiple organizations attempting to promote rideshare.

2017 University of Virginia Transportation Survey
The University of Virginia (UVA), located in Charlottesville, employs over 25,000 people from the greater Charlottesville area. In a 2017 survey of 621 employees, UVA collected personal transportation data that reflected how and why their employees commuted. Employees who drove single occupancy vehicles to work were asked why they haven't tried a rideshare instead. The survey stated that 51% haven't tried because of their work schedule and need for flexibility, and 27% were uncomfortable with the prospect.
 * 82% of UVA employees primarily drive alone to work
 * 10,000 tons of carbon dioxide emissions annually
 * 8000 filled parking spots
 * 20,000 car seats without passengers

Thomas Jefferson Planning District Commission (TJPDC)
Locally appointed commissions in the Charlottesville area such as the TJPDC support carpooling through partnerships with programs like RideShare. RideShare provides information, group matching, and support to Charlottesville area carpool/vanpool commuters. The program offers members a voucher for a taxi or rental car in case of an emergency through their "guaranteed ride home" initiative.

Sara Pennington, RideShare Program Manager spoke about that system to the TJPDC: "That is a great comfort and always what we hear as the first deterrent that keeps folks from taking that alternative transportation.” Pennington describes the how the lack of flexibility is a barrier to rideshare adoption, and how the vouchers assuage many member concerns.

Conclusion
Carpooling reduces road congestion, emissions, fossil fuel dependency, and parking infrastructure demand. Carpoolers can also benefit from reduced travel times, commuter stress, and reduced travel costs or reward programs that their community many provide. Direct subsidies and other incentives have also increased carpooling adoption.

The 2017 University of Virginia Transportation Survey data supports that claim that more people would prefer to carpool over driving personal vehicles. However, barriers such as safety, availability, and flexibility prevent them from trying. Carpooling options are limited and often complicated to set up. Widespread adoption requires significant incentives, accommodations, and availability. Guaranteed ride home options need to be available to address commuters hesitancy to carpool due to a dynamic work schedule. Federal or state policy could standardize the various programs across the country and lead to a widespread platform being used.

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Lentis/Office Productivity in the Changing Workplace

Introduction
The early 20th century concept that working more strenuous hours increased overall productivity has been challenged by employees and employers alike. Today, many companies in the United States, and around the world are looking to use alternative approaches to increase workplace output without increasing the burden on workers. These new trends promote employee freedom, flexibility and comfort. Many employers are enticing workers with options such as remote work, fewer working hours and incentive programs. Research has shown that these techniques can be effective. However, the implementation has varied significantly across American workplaces.

Overview
Working from home, or “telecommuting”, entered the modern American workplace in the 1970’s. Despite initial pushbacks, telecommuting continued to steadily rise through the turn of the century with support from the National Telecommuting Initiative. In the past decade, the percentage of people working from home has increased dramatically. And more so in light of the COVID-19 pandemic. In 2020, CDC guidelines encouraged companies to pursue telecommuting to lessen the risk of infection. As a result of public health concerns, companies enabled their employees to work from home resulting in a 35% increase in telecommuting. But even as the pandemic subsided, people still preferred to work from home.

Positive Impact
Remote work has many benefits including saving employees hundreds of dollars per month on commuting and food. It also reduces carbon emissions directly, with fewer cars on the road. Remote work has proven effective for many, with 57% of employees claiming they are more productive and 49% claiming concentration improves when working from home. Sixty-four percent of Americans cited a better work-life balance. Psychologically, an imbalance in this regard can lead to exhaustion and Occupational Burnout Syndrome which decreases productivity. Employers are recognizing this; 82% of management leaders will permit remote work at least one day a week. Some will go further. Industry leaders such as Airbnb, Lyft , and 3M allow completely remote and hybrid work for nearly all employees.

Negative Effects
Although telecommuting is appealing to many, there are drawbacks to be considered. Elon Musk, CEO of SpaceX, Tesla, and Twitter, believes that remote employees can "pretend to work", or not work as hard without supervision. The companies have given ultimatums: return to in person work for at least 40 hours a week or leave. Furthermore, remote work can increase inequalities among economic classes. During COVID-19, 73% of those making greater than $200,000/year were able to telecommute, while only 12.7% of those making less than $25,000/year were able to telecommute. And, while some workers have seen an increase in mental health, others have reported a blurring of work-life balance, leading to a decrease in mental health.

Background
During the Industrial Revolution in the early 19th century, workers were often required to work upwards of 80 hours a week. The majority of work was physically demanding, leading to high amounts of fatigue among employees. This led to labor unions, such as the American Federation of Labor , advocating for a decrease in working hours. Throughout the early 20th century, working standards fluctuated, but a general downward trend in required hours was seen. By the early to mid 1900s, the progress of labor unions along with the influence of Henry Ford's assembly line, popularized the 40 hour work week. In 1940, the United States government amended the Fair Labor Standards Act solidifying the 40 hour work week. Since 1940, standards have generally remained the same: 9am to 5pm, 5 days a week. It is only recently that the status quo has started to be questioned by scientists and companies looking to increase efficiency and adapt to the changing work environment.

The Role of Technology
On the subject of productivity, technology is naturally at the forefront of the conversation. Both long standing progress and recent developments have led to the reckoning that workplace expectations are currently facing. Twentieth century technology has shifted the focus of employees away from algorithmic processes, which have become increasingly automated, and more towards a heuristic-based approach. With critical thinking, which is more mentally engaging and taxing, as the new emphasis, scientists and employers have begun to reevaluate the efficiency of a system popularized in a different technological era. More recently, the dawning of smartphones, email, and social media has only strengthened corporate urgency to reassess worker efficiency. A 2018 study found that between distractions and fatigue, less than three hours of a typical eight hour workday were spent on relevant tasks.

COVID-19 Effects
The COVID-19 pandemic upended the status quo in all areas of life, creating an environment ripe for post-pandemic change. Two factors of working from home in particular affected how people viewed the 40 hour work week. The first factor was isolation. In being confined to their homes away from coworkers, employees were starved of social and professional interaction, creating less work-life balance and greater fatigue. From a management perspective, the second important factor was a clean slate that was presented. As mentioned earlier, questioning of workplace standards had slowly come to a head. The transition to working from home, along with rising scientific approval, gave employers the opportunity to make drastic changes when bringing employees back to the office. The largest example of large scale change is a 2022 study, where more than 70 companies transitioned to a four day, 32 hour workweek. Results were positive, with most companies stating they would make the policy permanent after the study concluded. This study will almost certainly influence other companies to do the same.

Incentives and distractions
Modern companies have been trying new methods to increase productivity, this includes providing incentives and reducing distractions.

Providing incentives has been proven to increase efficiency in the workplace. An incentive for a specific task will help the employee focus on a specific task and increase productivity by twenty seven percent. Incentives also increase the morale of the staff, companies that have implemented incentive or reward programs have increased productivity by forty four percent. The employees' lifestyle also affects the type of incentive they should receive. Companies that are familiar with the hobbies and the type of family that their employees have makes the incentive selection easier, therefore, the productivity is increased.

Providing amenities in the workplace is an excellent example of a physical incentive. Another way to provide incentives is to give employees the option to work remotely from home. The workplace in modern society is always changing, in the last couple of years the percentage of people working remotely has increased exponentially. As of now, there are 5.7 million people working completely in the United Kingdom alone. The government can also provide incentives to increase the state's productivity. In California there is a law that has mandated the reimbursement of all the employees’ expenses that are working remotely, this includes the monthly wifi expenses.

The distractions are one of the main reasons companies lose productive time on a daily basis. The most significant distraction in the modern workplace is technological distraction, known as cyberslacking. The millennials and Gen Z-ers spend about twenty five percent of their workday on their smartphones for non-work purposes. Facebook alone takes eighty six percent of this non-productive time. The physical distractions are also a factor that reduces productivity. Working in cubicles in highly dense offices creates an environment of monotony and robot-like scenarios where the employees can get frustrated or overwhelmed. Another issue with the cubicles is the weak division of working space, the noise of fellow employees can create distractions. If the cubicles are not tall enough, visual distractions can also affect productivity. Not having enough breaks is also a major cause of unproductive work time. Overworking can cause dizziness, headaches, irritability, and even weaken the immune system. In the regular modern company, seventy percent of questioned employees admitted to be distracted at some point of the day, and sixteen percent admitted to be distracted almost all the time.

Companies usually provide work phones and emails to their employees in order to avoid technological distractions from the employees’ personal life. In addition, some companies still provide the option for their collaborators to work from home, even after the pandemic. This type of arrangement usually helps companies with crowded offices or employees that have to live far from the company facilities.

Implications
In an analysis of office productivity trends, it can be generalized that employees are pushing for more comfortable working conditions. Most workers desire options such as hybrid remote work, 32 hour work weeks and incentive programs. Employers are providing these options so as to increase productivity. However, while the data shows that productivity is generally improved by these sociotechnical transitions, some areas, such as mental health, show mixed results. On average, social norms are changing from a stricter workplace towards a more flexible environment. This change is also apparent in other areas of professional life such as the rise of casual dress in the workplace.

While the research suggests that these changes may provide a net positive to the workforce, companies must also be aware of comfort zone biases. These biases promote behavior that is comfortable rather than reasonable and may factor into the American public's general acceptance of relaxing traditional workplace standards. As the science becomes more clear and new generations enter the workforce, standards will continue to fluctuate until a new status quo is formed. The data suggests that as society evolves, so will the working environment. Companies will keep looking for ways to increase productivity, and employees will look for a better working standards.


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Lentis/Caffeine Addiction

Introduction
Caffeine, chemically known as 1,3,7 trimethylxanthine, is a bitter substance that occurs naturally in plants, including coffee beans and tea leaves, and also synthetically, made for use in medicines, foods, and drinks. Caffeine is a central nervous system stimulant, giving humans a boost of energy and a feeling of awakeness. Caffeine is also a diuretic, causing the body to dispose of extra salt and water by increasing urination. It can also increase the release of acid in the stomach, causing heartburn and an upset stomach, often causing an increase in blood pressure. Caffeine peaks in the blood 15 minutes to 2 hours after consumption, dissolving in the body’s water and fat molecules after entrance into the gut and crossing into the brain.

The U.S. Food and Drug Administration considers 400 milligrams, or around 4 cups of coffee, a safe maximum amount of caffeine for healthy adults to drink in a day. Drinking coffee, in addition to giving an energy boost, can positively impact the health of adults by decreasing chances of heart disease, stroke, and diabetes, specifically in women, and also help prevent heart failure. Caffeine has also been seen to reduce weight gain and promote weight loss. Studies have suggested that caffeine may also enhance some thinking skills and promote brain function.

History of Caffeine
While the exact origins of caffeine are currently unknown, an ancient Chinese legend proposes that the first use of caffeine was by Emperor Shen Nung in 2437 BCE when the wind accidentally blew leaves into his boiling water. The concoction’s pleasant taste and restorative properties established the drink as the first cup of tea. Coffee dates back to another legend from the native tribes of the Ethiopian Peninsula in the 9th century CE. When a herder noticed how jumpy and alert his goats were after consuming the berries of an arabica plant, he gave the berries to a local monk. The monk used them to create a drink for long prayer hours, thus creating the first cup of coffee. Coffee was widely popular across the Middle East and Europe by the 17th century, where it was consumed in coffee houses that quickly became hubs of social activity, entertainment, and information exchange. The energizing and stimulating effects of caffeine transformed civilizations and changed the course of history. Caffeine has contributed to times of golden ages and enlightenment, the industrial revolution, capitalism, and even democracy. Before caffeine in hot coffee and tea, individuals turned to fermented drinks like beer and hard cider to avoid the risk of microbial infection from contaminated water. Alcohol was drunk daily, fogging the minds of workers and contributing to hazardous workplaces. The introduction of caffeine provided an energizing alternative to unsafe water, which promoted productivity and a more focused way of thinking.

Caffeine’s considerable impact on the rise of capitalism was initially due to the expansion of global trade. When caffeine in coffee, tea, and chocolate became beloved in 17th century Europe, the market for these products exploded, and countries flocked to become superpowers in their production and sale. Caffeine’s stimulatory effects meant that workers could work at all times of the day despite the body’s natural rhythms. The coffee houses that quickly rose in popularity became sites of shared interest in topics such as science, politics, and literature. They were spaces where men of all classes could mix, spreading democratic and liberal ideals. As a hub of people and ideas, they eventually brought forth important capitalist institutions like the London Stock Exchange.

Caffeine is the most used psychoactive drug in the world today, with nearly 90% of adults regularly consuming caffeine in any form. Its consumption is a fixture in most people’s lives, but there is a common lack of awareness surrounding its safety.

Culture of Drinking Coffee
Originating in Ethiopia and expanding towards religious ritual use in Yemen, the culture of drinking coffee has spread all over the world, influencing traditional tea drinking countries to become obsessed as well. Besides the chemical effects of drinking coffee on the body, coffee houses have grown in popularity due to their use of meeting places for businessmen in European countries in the 18th century and beyond. Cafes became popular in Europe due to their significance in the social sphere and ease of convenience. The small selections of coffee and affordable price allowed for people of all social classes to enjoy the sanctuary of coffeehouses. The working class was able to enjoy the community and exchange ideas and philosophy with one another with comfort.

Beyond allowing working class men to exchange ideas, coffeehouses also provided the public with unification of the community. As the shift from drinking regular coffee to specialty coffee drinks increased, chains like Starbucks and Tim Hortons became popular. The public enjoyed both the convenience and affordability of these fancy drinks, leading businessmen, students, and the general public to find appeal in these coffeehouses. The culture of drinking coffee has become more than enjoying the alertness that comes from it– it has become a social phenomenon.

Caffeine Addiction
Caffeine addiction is clinically known as Caffeine Use Disorder is the Diagnostic and Statistical Manual of Mental Disorders. It is currently a Condition for Further Study because there is a lack of data on the prevalence and clinical significance of caffeine use disorder among the general population. Like other addictions, caffeine addiction is characterized by the continued use of caffeine and failure to control use despite negative physical and psychological consequences. Regular consumption of caffeine causes physical and psychological dependence. Dependence requires increasing dosing to achieve the same effects, which leads to caffeine intoxication, restlessness, nervousness, insomnia, irregular heartbeat, and gastrointestinal distress. Many regular caffeine consumers are unaware of the risks of consuming large amounts of caffeine.

Currently, there is no criteria for the amount of caffeine that must be consumed to be considered an addiction. Instead, it is dependent on the subjective symptoms and psychological effect caffeine has on the user. Caffeine addiction is connected to brain interactions, genetic disposition, environment, and individual life experiences. For example, in an academic setting, many college age students tend to increase their caffeine intake as academic demands grow. The tendency to drink coffee is increased on college campuses with the social aspect of coffee shops being used as study spots. This behavior becomes a habit and is continued into adulthood, which can further develop into addiction if the user becomes dependent upon the substance.

People consume caffeine in the morning to increase alertness and boost mood in order to find motivation to work. Over 90% of adults regularly drink caffeine in the US, consuming an average of 200 mg of caffeine per day. Consumption of these beverages everyday causes chemical changes in the brain, leading to a dependency on caffeine. Caffeine tolerance develops similarly to tolerance of other drugs and alcohol. Increased consumption is often required to produce the same effects of alertness that was once produced during the start of the dependency. Abruptly halting consumption will lead to withdrawal symptoms and potentially causing users to relapse and continue drinking caffeinated beverages.

Caffeine’s effect on the brain is the main cause of becoming an addictive substance. Caffeine is absorbed through the small intestine and soon dissolved into the bloodstream, crossing the blood-brain barrier and entering the brain. Caffeine’s structure resembles adenosine, which is naturally present in the brain, which allows it to fit neatly into the brain cells’ adenosine receptors, blocking them off. Caffeine molecules blocking off these receptors allows for the sense of alertness and energy that replace the normal feeling of tiredness that comes from the adenosine receptors.

Withdrawal
In people with this caffeine dependency, their brain’s chemistry and physical characteristics change over time. The brain will begin to grow more adenosine receptors to maintain equilibrium, developing caffeine tolerance and requiring more chemicals to block the receptors. Caffeine withdrawal can cause headache, irritability, fatigue, anxiety, tremors, and depression. To overcome addiction, individuals with caffeine addiction often go through withdrawal. After discontinuing regular consumption of caffeine, some individuals experience withdrawal symptoms. These include headache, fatigue, irritability, depressed mood, difficulty concentrating, and flu-like symptoms. Symptoms of withdrawal begin 12 to 24 hours after stopping caffeine consumption. Withdrawal symptoms peak between 20 to 51 hours after stopping consumption, and last for 2 to 9 days.

Economic Effect
The United States is the top coffee consumer by total thousands of 60-pound bags of dry coffee beans. Economically, the average American worker spends $14.40 on coffee per week, or $1100 annually. This is $2 per day on coffee, when calculated for home-brewing. In Washington state, the average cost of a cup of coffee from a coffee shop is $3.46, with 23.8 coffee shops per 100,000 people. Drinking coffee is a mixture of both a social experience and physical need/dependency supported by society and its culture. Caffeine consumption is not isolated to just the United States. From a global perspective, many European countries consume large amounts of coffee. Finland is the top coffee consumer per person per year in the world. The average Finn consumes 4 cups of coffee per day, which equates to 12 kilograms per year. Coffee is so popular that 2-10 minute coffee breaks are legally mandated for Finnish workers.

Conclusion
Caffeine addiction is a disorder that develops from a physical, emotional, and psychological dependence on the substance that is perpetuated by the cultural and societal norms of caffeine consumption. Future work in the study of caffeine can include the effects of caffeine addiction on the culture of drinking coffee and the expansion of how the history of caffeine shaped the world today.

title: Lentis/Caffeine Addiction


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LMIs in Control/Click here to continue/Applications of Linear systems/Mixed H2-H∞ Optimal Voltage Control Design for Smart Transformer Low-Voltage Inverter

Smart transformers are often used in situations with variable loads such as the integration of renewable energy sources. This section examines a system of Linear Matrix Inequalities as analyzed by Wei Hu, Yu Shen, Zhichun Yang, and Huaidong Min in their paper for Mixed $$H_2$$/$$H_{\infty}$$ Optimal Voltage Control Design for Smart Transformer Low-Voltage Inverter.

The System
State space modelling is used in order to develop a system that describes the inverter behavior.

\begin{align} \dot{x_p} &= A_px + B_{p1}v_c+B_{p2}w_p \\ y &= C_px_p \\ \end{align}$$

The system formulation for a simple inverter system draws directly from electric circuit theory. $$A_p = \begin{bmatrix} -R/L & -1/L \\ 1/C & 0 \end{bmatrix} $$ $$ B_{p1} = \begin{bmatrix} 1/L \\ 0 \end{bmatrix}$$ $$ B_{p2} = \begin{bmatrix} 0 \\ 1/C \end{bmatrix}$$ $$C_p = \begin{bmatrix} 0 & 1 \end{bmatrix}$$ where the above variables are defined as follows:

 * $$R$$ is the resistance
 * $$L$$ is the inductance
 * $$C$$ is the capacitance

This system is further augmented by adding multiple resonant controllers to ensure the system can reach zero steady-state error when tracking sinusoidal target outputs. The augmented system is then derived as follows:

\begin{align} \dot{x_p} &= Ax + B_1v_c+B_2w_p+Ry^* \\ y &= Cx \\ \end{align}$$

where

$$A=\begin{bmatrix} A_p & 0 & 0 & & 0 & 0 \\ -C_p & j\omega & 0 & ... & 0 &0 \\ -C_p & 0 & -j\omega &  & 0 &0\\ &...&&...&&...\\-C_p & 0 & 0 &  & j_n\omega &0\\ -C_p & 0 & 0 & ... & 0 &-j_n\omega \end{bmatrix}$$

$$B_1=\begin{bmatrix} B_{p1} & 0 &0&\cdots&0&0 \end{bmatrix}^T$$

$$B_2=\begin{bmatrix} B_{p2} & 0 &0&\cdots&0&0 \end{bmatrix}^T$$

$$C=\begin{bmatrix} C_{p} & 0 &0&\cdots&0&0 \end{bmatrix}$$

$$R=\begin{bmatrix} 0 & 1 & 1 &\cdots&1&1 \end{bmatrix}$$

The Data
The data required to solve this problem includes the values of resistance, inductance, capacitance, switch frequency, output peak voltage, and the DC link voltage.

The Optimization Problem
The optimization problem aims to minimize a combined $$H_2$$/$$H_{\infty}$$ norm of the system as defined above. In order to accomplish this task, constraints and the objective must first be defined.

 * Objective: Combined $$H_2$$/$$H_{\infty}$$ norm
 * Constraints: Closed-loop poles are restricted to a desired section of the complex plane,

The LMI: Mixed H2-H∞ Optimal Voltage Control
$$\begin{align} \begin{cases} &\text{min} \quad a\gamma + bTrace(M) \\ &\text{s.t.} \quad \begin{bmatrix} M & I \\ I & W_1 \end{bmatrix} > 0 \\ \\ &\quad \quad \begin{bmatrix} (AW_1 - B_1V_1) + (AW_1 - B_1V_1)^T & W_1 & V_1^T \\ W_1 & -Q_{inv} & 0 \\ V_1 & 0 & -R^{-1} \end{bmatrix} < 0 \\ \\ &\quad \quad AX+B_1W + (AX+B_1W)^T + BB^T< 0 \\ \\ &\quad \quad L_j \otimes W_3 + M_j\otimes (AW_3+B_1V_3) + M_j^T \otimes (AW_3+B_1V_3)^T < 0, j=1,2,3 \\ \\ &\quad \quad \begin{bmatrix} (AW_2 - B_1V_2) + (AW_2 - B_1V_2)^T & B_2 & W_2C^T \\ B_2^T & -\gamma I & 0 \\ CW_2 & 0 & -\gamma I \end{bmatrix} < 0 \\ \\ \end{cases} \\ \end{align}$$

In the above LMIs, the coefficients a and b represent the weighting factor applied to the $$H_2$$ and $$H_{\infty}$$ norms respectively. R is some given positive-definite matrix.

Conclusion
Mixed $$H_2$$/$$H_{\infty}$$ optimal control can be effectively used to design efficient and useful smart transformers.

Implementation
This LMI can be implemented using MATLAB when combined with YALMIP and an LMI solver such as SeDuMi.

Related LMIs

 * Mixed H2-H∞ Satellite Attitude Control


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LMIs in Control/Click here to continue/Applications of Linear systems/LMI-based State Feedback Design for mass varying Quadcopter Optimal path control and Tracking

Introduction
An LMI-based  state  feedback  approach  that  ensures optimum  path  tracking  and  improved  steady  state performance  of  a  quadrotor  in  both  translational  and rotational movements.

Quadcopter Dynamics
The motion of Quad Copter in 6DOF is controlled by varying the rpm of four rotors individually, thereby changing the vertical, horizontal and rotational forces.

 * ASSUMPTIONS:
 * 1) The structure is symmetric, thus the inertia matrices are diagonal.
 * 2) The center of mass corresponds to the origin of the physical coordinate system.
 * 3) A quadcopter is a rigid body.

State Space Representation

\begin{align} \dot x(t)&=Ax(t)+Bu(t)\\ y(t)&=Cx(t)+Du(t)\\ \end{align}$$

where x(t) is state vector, y(t) is output vector and u(t) is Input or control vector.

$$ \dot x(t)=\frac{d}{dt} x(t) $$
 * A is the system matrix
 * B is the input matrix
 * C is the output matrix
 * D is the feed forward matrix

Quadcopter modelling with 6 degree of freedom

 * REQUIRED 12 STATES:

The state vector x is $$ x^T= $$ $$ \begin{bmatrix} x & y  & z  & x' & y' & z' & \phi & \theta & \psi & \phi' & \theta' & \psi' \end{bmatrix} $$

The Input matrix u is, $$ u^T=$$$$ \begin{bmatrix} U1 & U2 & U3  & U4 \end{bmatrix} $$, where

 * U1 is the Total Upward Force on the quadrotor along z-axis ( T-mg)
 * U2 is the Pitch Torque (about x-axis)
 * U3 is the Roll Torque (about y-axis)
 * U4 is the Yaw Torque (about z-axis)

The Output matrix y is $$ y^T=$$$$ \begin{bmatrix} x & y & z & \phi & \theta & \psi \end{bmatrix} $$

The State differential equations written in matrix form as,

$$ \begin{bmatrix} x'\\ y'\\ z' \\ x''\\ y''\\ z''\\ \phi'\\ \theta'\\ \psi'\\ \phi''\\ \theta''\\ \psi''\\

\end{bmatrix}$$     = $$ \begin{bmatrix} 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\               0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & -g & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & g & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\               0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ \end{bmatrix} $$ $$ \begin{bmatrix} x\\ y\\ z \\ x'\\ y'\\ z'\\ \phi\\ \theta\\ \psi\\ \phi'\\ \theta'\\ \psi'\\

\end{bmatrix}$$ + $$ \begin{bmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ \frac{1}{m} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & \frac{1}{l_{x}} & 0 & 0 \\ 0 & 0 & \frac{1}{l_{y}} & 0 \\ 0 & 0 & 0 & \frac{1}{l_{z}} \\ \end{bmatrix} $$$$ \begin{bmatrix} U1\\ U2 \\ U3 \\ U4 \end{bmatrix} $$

The above martices represents the equation $$ x'=Ax+Bu$$

$$ \begin{bmatrix} x\\ y\\ z \\ \phi\\ \theta\\ \psi\\\end{bmatrix} $$=$$ \begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\               0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\ \end{bmatrix} $$$$ \begin{bmatrix} x\\ y\\ z \\ x'\\ y'\\ z'\\ \phi\\ \theta\\ \psi\\ \phi'\\ \theta'\\ \psi'\\

\end{bmatrix}$$+$$ \begin{bmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ \end{bmatrix}$$$$ \begin{bmatrix} U1\\ U2 \\ U3 \\ U4 \end{bmatrix} $$

The above martices represents the equation $$ y=Cx+Du$$

LMI for stability Analysis
$$ \begin{bmatrix} PA^T-W^TB^T+AP-BW+\mu^2\delta & -PA^T+W^TB^T-DP & I \\ PD^T-AP+BW & D^TP+PD & -P \\ I & -P & -\delta I \\ \end{bmatrix} <0 $$

 * $$K=WP^-1$$

Solving the above LMI yields the unknown coefficients of the feedback control. The system will be then asymptotically stable and path track will be achieved.

LPV Attitude State Feedback Controller Design
To design a $$ H\infty $$ LPV feedback control scheme for the altitude/attitude stabilization of the quadrotor aircraft,

 * Output $$y=\begin{bmatrix} \phi & \theta& \psi&  \Z \end{bmatrix}^T$$ of the system must track r =$$\begin{bmatrix} \phi_{ref} & \theta_{ref}&  \psi_{ref}&  \Z_{ref} \end{bmatrix}^T$$, a reference trajectory.

 * To achieve the objective outputs of the integrator are considered as extra state variables $$x_{e}=\begin{bmatrix}x_{\phi} & x_{\theta}& x_{\psi}&  x_{Z} \end{bmatrix}^T$$ as

$$x_{\phi}=\int_{0}^{t} e_{\phi} (\delta) d\delta \,dx ,e_{\phi}=\phi_{ref}-\phi$$

$$x_{\theta}=\int_{0}^{t} e_{\theta} (\delta) d\delta \,dx ,e_{\theta}=\theta_{ref}-\theta$$

$$x_{\psi}=\int_{0}^{t} e_{\psi} (\delta) d\delta \,dx ,e_{\psi}=\psi_{ref}-\psi$$

$$x_{z}=\int_{0}^{t} e_{z} (\delta) d\delta \,dx ,e_{z}=z_{ref}-z$$

In this case the error signal e=y-r ,for the outputs $$ U_{1},U_{2},U_{3},U_{4}$$,the weight functions $$ W_{ui},i=1,2,3,4 $$are added to the system. The system matrices of weight functions are $$A_{ui},B_{ui},C_{ui}and D_{ui}.$$

The dynamic of all the weight functions $$ W_{u1},W_{u2},W_{u3},W_{u4}$$ can be constituted as,

\begin{align} \dot{x}_{u}=A_{u}x_{u}+B_{u}u\\ y_{u}=C_{u}x_{u}+D_{u}u \end{align}$$

where $$x_{u}=\begin{bmatrix} x_{u1}&x_{u2}&x_{u3}&x_{u4}\end{bmatrix}^T$$ is the state,$$u=\begin{bmatrix}U_{1} & U_{2}&U_{3}&U_{4}\end{bmatrix}^T$$ represents the input $$y_{u}=\begin{bmatrix} Z_{1}&Z_{2}&Z_{3}&Z_{4}\end{bmatrix}^T$$

$$\Delta_{u}=\begin{bmatrix} \Delta_{u1}&0&0&0\\0&\Delta_{u2}&0&0\\0&0&\Delta_{u3}\\0&0&0&\Delta_{u4}\end{bmatrix}$$,$$\Delta\in{A,B,C,D}$$
 * The system matrices of the weight function can be deducted as,

$$w=\begin{bmatrix} r&d\end{bmatrix}^T$$,$$z=\begin{bmatrix} y_{u}&e\end{bmatrix}^T$$,and $$\bar{x}=\begin{bmatrix} x&x_{e}&x_{u}\end{bmatrix}^T$$ are the exogenous input and exogenous output respectively.

 * The system differential equations with augumented ststes and weight functions are,

\begin{align} \dot{\bar x}=\sum_{i=1}^{16} \mu_{i} (\bar A_{i}\bar x+\bar B1_{i}w+\bar B_{2}u)\\ z=C_{\bar x}+D11 w+D12 u \end{align}$$

where,

$$\bar A_{i}=\begin{bmatrix} \bar A_{i} &0&0&0\\ -C&0 &0\\0 &0&A_{u} \end{bmatrix}$$;

$$ \bar B_{1}=\begin{bmatrix} 0 & \bar E_{i}\\ -I_{4} & 0\\0 &0 \end{bmatrix}$$

$$ \bar B_{2}=\begin{bmatrix} \bar B_{i}\\ 0\\ B_{u}\end{bmatrix}$$

$$ C_{1}=\begin{bmatrix} 0& 0& C_{u}\\ C &0&0\end{bmatrix}$$

$$ D_{11}=\begin{bmatrix} 0 &0\\-I_{4}&0\end{bmatrix}$$

$$ D_{12}=\begin{bmatrix} D_{u}\\0\end{bmatrix}$$

Making the closed loop system,

$$dot{\bar x}=\sum_{i=1}^{16} \mu_{i} ((\bar A_{i}+\bar B_{2}ki)\bar x(t)+\bar B_{1}w)$$

LMI for H∞ optimal state-feedback
$$ X=X^T>0$$

$$\begin{bmatrix} He(\bar A_{i}X+\bar B_{2}Y_{i} &(*)^T &(*)^T\\ \bar B_{1i} ^T & -\gamma I&(*)^T \\ \bar C_{1i}X+D_{12}Y_{i}& \bar D_{11} &-\gamma I \end{bmatrix}<0 $$

$$He(\bar A_{i}X+\bar B_{2}Y_{i}+2\alpha X <0$$ ; i=1 to 16

By solving the LMI,the optimal H\inf state feed-back controller with the smallest attenuation level \gamma >0 for the attitude/altitude subsystem of the mass-varying quadcopter is $$K(\rho)=\sum_{i=1}^{16} \mu_{i} Y_{i} X^-1$$

Conclusion
This LMI can be used to analyze the state feedback control and path tracking of a quadcopter.

Implementation
This LMI can be used in a problem and can be solved using the solvers like Yalmip,sedumi,gurobi etc,.


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LMIs in Control/Click here to continue/Applications of Linear systems/LPV state-feedback controller for Attitude and Altitude stabilization of a mass-varying quadcopter

Introduction
An LMI-based  state  feedback  approach  that  ensures optimum  path  tracking  and  improved  steady  state performance  of  a  quadrotor  in  both  translational  and rotational movements.

Quadcopter Dynamics
The motion of Quad Copter in 6DOF is controlled by varying the rpm of four rotors individually, thereby changing the vertical, horizontal and rotational forces.

 * ASSUMPTIONS:
 * 1) The structure is symmetric, thus the inertia matrices are diagonal.
 * 2) The center of mass corresponds to the origin of the physical coordinate system.
 * 3) A quadcopter is a rigid body.

Derivations

 * Roll motion

The torque about x-axis is modeled as $$\tau _{x} $$i.e. rolling moment. Now r (moment arm) is distance of individual forces from x-axis

$$\tau _{x} =\sum_{i=1}^{4} r_{i}f_{i} $$

$$\tau _{x}= r_{1} f_{1}+r_{2} f_{2}+r_{3} f_{3}+r_{4} f_{4}$$

As the rotors 1 and 3 are placed along with body x-axis so their moment arm is zero and they do not contribute in rolling moment

$$ r_{2}=d;r_{4}=-d$$

so $$ \tau_{x}=d_{f2}-d_{f4}$$

Thus, when rotor 4 applies force it tends to rotate the system about x-axis opposite to curl of fingers so using the right hand rule (RHR) its torque contribution in x-axis is negative.

Similarly the rotor 2 produces positive torque about x-axis according to Right Hand Rule.

 * Pitch motion

The torque about y-axis is modeled as i.e. pitching moment. Now r(moment arm) is distance of individual forces

$$\tau _{}= r_{1} f_{1}+r_{2} f_{2}+r_{3} f_{3}+r_{4} f_{4}$$

where r is the distance of individual force form vertical axis

$$r_{2}=r_{4}=0; r_{1}=-r_{3}=d$$

so \tau_{y}=d_{f1}-d_{f3}

when rotor 3 applies force it tends to rotate the system about y-axis opposite to curl of fingers.so using Right Hand rule its torque contribution in y-axis is negative. Similarly the rotor 1 produces positive torque about x-axis according to Right Hand Rule.

 * Yaw motion

Finally the yawing moment is modeled as $$\tau_{z}$$ and its torque about Z axis.As the motors rotate the rotors encounter a reactive torque due to air drag on rotor blade, this reactive torque is modeled as Q.The yaw is accomplished by rotor rpm imbalance between clockwise and counter-clockwise rotating propellers. The reactive torque as a convention is taken positive for counter clockwise rotating motors/rotors and negative for clockwise rotating ones. All the four rotors contribute in yawing moment.

$$\tau _{z} =\sum_{i=1}^{4} Q_{i}f_{i} $$

Whereas $$Q=cF_{i}$$ if rotation of the ith rotor is counterclockwise and $$-cF_{i}$$, if clockwise. So opening the summation becomes:

$$ \tau_{z}=c(-F_{1}+F_{2}-F_{3}+F_{4})$$

 * Vertical motion

The vertical motion is governed by the total thrust produced

$$T =\sum_{i=1}^{4} F_{i} $$

$$Z=\frac{T-mg}{m}$$

 * Horizontal motion

The horizontal motion in the x & y-axes is accomplished by decreasing the rpm of the rotor in whose direction it is intended to move, and subsequently increasing the rpm of the rotor on the opposite side of the same arm.

The force imbalance will cause the quad copter to tilt to one side and the horizontal component of the thrust force will impart horizontal linear motion to the quadcopter.

If the mass of the quad copter is ‘m’, then referring to (figure 4), the linear acceleration in the horizontal x-direction can be written as:

$$ x=-\frac{\tau cos\theta}{m}$$

using small angle approximation $$sin\theta \approx. 0 $$ and as 0 is small $$T \approx. mg$$, $$x=-g\theta,y=g\theta$$

State Space Representation

\begin{align} \dot x(t)&=Ax(t)+Bu(t)\\ y(t)&=Cx(t)+Du(t)\\ \end{align}$$

where x(t) is state vector, y(t) is output vector and u(t) is Input or control vector.

$$ \dot x(t)=\frac{d}{dt} x(t) $$
 * A is the system matrix
 * B is the input matrix
 * C is the output matrix
 * D is the feed forward matrix

Quadcopter modelling with 6 degree of freedom

 * REQUIRED 12 STATES:

The state vector x is $$ x^T= $$ $$ \begin{bmatrix} x & y  & z  & x' & y' & z' & \phi & \theta & \psi & \phi' & \theta' & \psi' \end{bmatrix} $$

The Input matrix u is, $$ u^T=$$$$ \begin{bmatrix} U1 & U2 & U3  & U4 \end{bmatrix} $$, where

 * U1 is the Total Upward Force on the quadrotor along z-axis ( T-mg)
 * U2 is the Pitch Torque (about x-axis)
 * U3 is the Roll Torque (about y-axis)
 * U4 is the Yaw Torque (about z-axis)

The Output matrix y is $$ y^T=$$$$ \begin{bmatrix} x & y & z & \phi & \theta & \psi \end{bmatrix} $$

The State differential equations written in matrix form as,

$$ \begin{bmatrix} x'\\ y'\\ z' \\ x''\\ y''\\ z''\\ \phi'\\ \theta'\\ \psi'\\ \phi''\\ \theta''\\ \psi''\\

\end{bmatrix}$$     = $$ \begin{bmatrix} 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0\\               0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & -g & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & g & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\               0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ \end{bmatrix} $$ $$ \begin{bmatrix} x\\ y\\ z \\ x'\\ y'\\ z'\\ \phi\\ \theta\\ \psi\\ \phi'\\ \theta'\\ \psi'\\

\end{bmatrix}$$ + $$ \begin{bmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ \frac{1}{m} & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & \frac{1}{l_{x}} & 0 & 0 \\ 0 & 0 & \frac{1}{l_{y}} & 0 \\ 0 & 0 & 0 & \frac{1}{l_{z}} \\ \end{bmatrix} $$$$ \begin{bmatrix} U1\\ U2 \\ U3 \\ U4 \end{bmatrix} $$

The above martices represents the equation $$ x'=Ax+Bu$$

$$ \begin{bmatrix} x\\ y\\ z \\ \phi\\ \theta\\ \psi\\\end{bmatrix} $$=$$ \begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\               0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0\\                0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0\\ \end{bmatrix} $$$$ \begin{bmatrix} x\\ y\\ z \\ x'\\ y'\\ z'\\ \phi\\ \theta\\ \psi\\ \phi'\\ \theta'\\ \psi'\\

\end{bmatrix}$$+$$ \begin{bmatrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ \end{bmatrix}$$$$ \begin{bmatrix} U1\\ U2 \\ U3 \\ U4 \end{bmatrix} $$

The above martices represents the equation $$ y=Cx+Du$$

LMI for stability Analysis
$$ \begin{bmatrix} PA^T-W^TB^T+AP-BW+\mu^2\delta & -PA^T+W^TB^T-DP & I \\ PD^T-AP+BW & D^TP+PD & -P \\ I & -P & -\delta I \\ \end{bmatrix} <0 $$

 * $$K=WP^-1$$

Solving the above LMI yields the unknown coefficients of the feedback control. The system will be then asymptotically stable and path track will be achieved.

LPV Attitude State Feedback Controller Design
To design a $$ H\infty $$ LPV feedback control scheme for the altitude/attitude stabilization of the quadrotor aircraft,

 * Output $$y=\begin{bmatrix} \phi & \theta& \psi&  \Z \end{bmatrix}^T$$ of the system must track r =$$\begin{bmatrix} \phi_{ref} & \theta_{ref}&  \psi_{ref}&  \Z_{ref} \end{bmatrix}^T$$, a reference trajectory.

 * To achieve the objective outputs of the integrator are considered as extra state variables $$x_{e}=\begin{bmatrix}x_{\phi} & x_{\theta}& x_{\psi}&  x_{Z} \end{bmatrix}^T$$ as

$$x_{\phi}=\int_{0}^{t} e_{\phi} (\delta) d\delta \,dx ,e_{\phi}=\phi_{ref}-\phi$$

$$x_{\theta}=\int_{0}^{t} e_{\theta} (\delta) d\delta \,dx ,e_{\theta}=\theta_{ref}-\theta$$

$$x_{\psi}=\int_{0}^{t} e_{\psi} (\delta) d\delta \,dx ,e_{\psi}=\psi_{ref}-\psi$$

$$x_{z}=\int_{0}^{t} e_{z} (\delta) d\delta \,dx ,e_{z}=z_{ref}-z$$

In this case the error signal e=y-r ,for the outputs $$ U_{1},U_{2},U_{3},U_{4}$$,the weight functions $$ W_{ui},i=1,2,3,4 $$are added to the system. The system matrices of weight functions are $$A_{ui},B_{ui},C_{ui}and D_{ui}.$$

The dynamic of all the weight functions $$ W_{u1},W_{u2},W_{u3},W_{u4}$$ can be constituted as,

\begin{align} \dot{x}_{u}=A_{u}x_{u}+B_{u}u\\ y_{u}=C_{u}x_{u}+D_{u}u \end{align}$$

where $$x_{u}=\begin{bmatrix} x_{u1}&x_{u2}&x_{u3}&x_{u4}\end{bmatrix}^T$$ is the state,$$u=\begin{bmatrix}U_{1} & U_{2}&U_{3}&U_{4}\end{bmatrix}^T$$ represents the input $$y_{u}=\begin{bmatrix} Z_{1}&Z_{2}&Z_{3}&Z_{4}\end{bmatrix}^T$$

$$\Delta_{u}=\begin{bmatrix} \Delta_{u1}&0&0&0\\0&\Delta_{u2}&0&0\\0&0&\Delta_{u3}\\0&0&0&\Delta_{u4}\end{bmatrix}$$,$$\Delta\in{A,B,C,D}$$
 * The system matrices of the weight function can be deducted as,

$$w=\begin{bmatrix} r&d\end{bmatrix}^T$$,$$z=\begin{bmatrix} y_{u}&e\end{bmatrix}^T$$,and $$\bar{x}=\begin{bmatrix} x&x_{e}&x_{u}\end{bmatrix}^T$$ are the exogenous input and exogenous output respectively.

 * The system differential equations with augumented ststes and weight functions are,

\begin{align} \dot{\bar x}=\sum_{i=1}^{16} \mu_{i} (\bar A_{i}\bar x+\bar B1_{i}w+\bar B_{2}u)\\ z=C_{\bar x}+D11 w+D12 u \end{align}$$

where,

$$\bar A_{i}=\begin{bmatrix} \bar A_{i} &0&0&0\\ -C&0 &0\\0 &0&A_{u} \end{bmatrix}$$;

$$ \bar B_{1}=\begin{bmatrix} 0 & \bar E_{i}\\ -I_{4} & 0\\0 &0 \end{bmatrix}$$

$$ \bar B_{2}=\begin{bmatrix} \bar B_{i}\\ 0\\ B_{u}\end{bmatrix}$$

$$ C_{1}=\begin{bmatrix} 0& 0& C_{u}\\ C &0&0\end{bmatrix}$$

$$ D_{11}=\begin{bmatrix} 0 &0\\-I_{4}&0\end{bmatrix}$$

$$ D_{12}=\begin{bmatrix} D_{u}\\0\end{bmatrix}$$

Making the closed loop system,

$$dot{\bar x}=\sum_{i=1}^{16} \mu_{i} ((\bar A_{i}+\bar B_{2}ki)\bar x(t)+\bar B_{1}w)$$

LMI for H∞ optimal state-feedback
$$ X=X^T>0$$

$$\begin{bmatrix} He(\bar A_{i}X+\bar B_{2}Y_{i} &(*)^T &(*)^T\\ \bar B_{1i} ^T & -\gamma I&(*)^T \\ \bar C_{1i}X+D_{12}Y_{i}& \bar D_{11} &-\gamma I \end{bmatrix}<0 $$

$$He(\bar A_{i}X+\bar B_{2}Y_{i}+2\alpha X <0$$ ; i=1 to 16

By solving the LMI,the optimal H\inf state feed-back controller with the smallest attenuation level \gamma >0 for the attitude/altitude subsystem of the mass-varying quadcopter is $$K(\rho)=\sum_{i=1}^{16} \mu_{i} Y_{i} X^-1$$

Conclusion
This LMIs can be used model the state-feedback controller for attitude/altitude stabilization of a mass-varying quadcopter

Implementation
This LMI can be used in a problem and can be solved using the solvers like Yalmip,sedumi,gurobi etc,.


text:
User:Megarurp

Hey!

I'm megarurp and I like: You can find me on a multitude of platforms!
 * Math
 * Reading Reference books for fun
 * 3rd Strike

title: User:Megarurp


text: Template:OpenRewi/Author

title: Template:OpenRewi/Author


text:
JavaScript/Async

Without particular keywords and techniques, the JavaScript engine executes statements one after the next in the sequence of the written code. In most cases, this is necessary because the result of a line is used in the following line.

Lines 1 and 2 must be finished entirely before line 3 can be executed. This is the usual sequential behavior.

But there are situations where it is not necessary for the following statements to wait for the end of the current one. Or, you expect that an activity will run for a long time, and you want to do something else in the meanwhile. Such parallel execution has the potential to reduce the overall response time dramatically. That becomes possible because modern computers have multiple CPUs and are able to perform multiple tasks at the same time. In the above example, lines 1 and 2 may run in parallel. Moreover, the client/server architecture delegates activities across multiple servers.

Typical situations are long-running database updates, handling of huge files, or CPU-intensive computations. But even for simple-looking things like the rendering of an HTML page, a browser typically runs multiple tasks.

Single-threaded
Natively, "JavaScript is single-threaded and all the JavaScript code executes in a single thread. This includes your program source code and third-party libraries that you include in your program. When a program makes an I/O operation to read a file or a network request, this blocks the main thread".

To reach the goal of simultaneous activities anyway, browsers, service workers, libraries, and servers offer additional appropriate interfaces. Their primary use case is the unblocking execution of HTTP and database requests; a smaller proportion focuses on CPU-intensive computations.

At the level of the JavaScript language, there are three techniques to achieve asynchronism - what 'feels' like simultaneity.
 * Callback function
 * Promise
 * Keywords  and

The basic technique is the use of callback functions. This term is used for functions that are passed as an argument to another function, especially - but not only - for functions that implement an asynchronous behavior.

A Promise represents the final completion or failure of an asynchronous operation, including its result. It steers further processing after the end of such asynchronous running operations.

Because the evaluation of Promises with  and   may lead to hard-to-read code - especially if they are nested -, JavaScript offers the keywords   and. Their usage generates well-arranged code comparable with  of traditional JavaScript. But they don't implement additional features. Instead, under the hood they are based on Promises.

Strictly sequential? No.
To demonstrate that code is not always executed in strict sequential order, we use a script that contains a CPU-intensive computation within a more or less huge loop. Depending on your computer, it runs for several seconds.

Expected output:

 * The core of the asynchronous function  is a loop where a mathematical computation is done [(3) line 14]. The loop needs more or less time depending on the given parameter.
 * The return value of  is not a simple value but a Promise. [(2) line 6]
 * is invoked by  once per element of the given array. [(4) line 24]
 * Because of the asynchronous nature of  the function   is executed totally before   runs! This can be observed by the program output.
 * The  [(1) line 5] is a dummy call. It suspends the execution of , giving   the chance to continue. If you delete this statement, the output will be different. Conclusion: To make the function really asynchronous you need both keywords,   in the function signature and   in the function body.
 * If you have a tool to observe your computer in detail, you can recognize that the three invocations of  doesn't run at the same time on different CPUs but run one after the next (on the same or on different CPUs).

Callback
Passing a function as a parameter to an (asynchronous) function is the original technique in JavaScript. We demonstrate its purpose and advantage with the predefined  function. It takes two parameters. The first one is the callback function we are speaking about. The second is a number specifying the milliseconds after which the callback function is called.

If  is invocated, it runs instantly. If  is invocated, it passes   as a callback function to , which executes it after a delay of 3 seconds.

Promise
A Promise keeps track of whether an (asynchronous) function has been executed successfully or has terminated with an error, and it determines what happens next, invoking either  or.

The Promise is in one of three states:
 * Pending: Initial state, before 'resolved' or 'rejected'
 * Resolved: After successful completion of the function:  was called
 * Rejected: After completion of the function with an error:  was called

Expected output:

When  is invoked, it creates a new Promise and returns it. Then, it performs the time-consuming action, and depending on the result, it invokes  or.

Next (in the meanwhile, the calling script has done other things), either the  or the   functions behind the call to   are executed. The two functions accept an (anonymous) function as their parameter. The parameter given to the anonymous function is the value of the Promise.

Please notice that the last statement of the script has been executed previously.

Many interfaces to libraries, APIs, and server functions are defined and implemented as functions returning a Promise, similar to the above. As long as it's not necessary that you create your own asynchronous functions, it's not necessary that you create Promises. Often it's sufficient to call an external interface and work only with  or   (or the   or   of next chapter).

async / await
The keyword  forces the JavaScript engine to run the script named behind   entirely - including the   part - before executing the following statement. Hence, - from the standpoint of the calling script - the asynchronous behavior is removed. Functions with  must be flagged in their signature with the keyword.

The use of  allows you to work with the traditional   statement instead of   and.

A realistic example
We use the freely available demo API. It offers a small amount of test data in JSON format.

The steps of the example are:
 * : Get the data behind the URL. The  part guarantees that the script will not continue before the   has delivered all data.
 * reads the stream which contains the resulting data.
 * The resulting data is an array of 10 elements. Each element is in JSON format, e.g.:

 * As an example, the script shows the complete data and some of its parts in the console.

Note: It's likely that you will run into a CORS error when you use an arbitrary URL.

Exercises

 * ... are available on another page (click here).

title: JavaScript/Async


text:
JavaScript/Async/Exercises

Topic: Asynchronous functions

1. Define a function that
 * reads the users via the jsonplaceholderapi of the previous page
 * shows all ten usernames together with their hometown
 * include log-messages to observe the program flow

title: JavaScript/Async/Exercises


text:
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Examples

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An overview of the templates used in the project can be found at Template:OpenRewi.

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Template:OpenRewi/Authors/doc

Purpose
This template will be included in the OpenRewi - Open Legal Science project at the beginning of each chapter started. The purpose of the infobox is to point out the following:
 * Who is behind OpenRewi + logo.
 * a comment field, with which individual parts of the chapter can be commented directly
 * hints and requests for further use of the materials

Examples

 * Public International Law

Further notes
A contact option by mail has just been omitted to encourage the use of the comment function.

An overview of the templates used in the project can be found at Template:OpenRewi.

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text:
Lentis/The Geopolitics of Asymmetric War: The Case of Ukraine

Introduction
Asymmetric warfare describes a form of conflict in which the relative military power of the engaged parties differs significantly. Many cases of asymmetric warfare have existed, and throughout most of history have been won by strong actors, however, since 1950 weak actors have won a majority of all asymmetric conflicts. This has led to a question among academics: if power is what wins wars, then what reasons exist as to why significantly weaker actors are able to resist much stronger actors. In this chapter, we will be looking at a modern case of asymmetric warfare: the Ukraine-Russia case.

Disclaimer: This article is written as of December 2022. As the conflict unfolds, the information in this article will need to be updated.

Strategic Interaction
Victory in war comes from breaking the opposition's will or means to fight. This can come from displaying overwhelming military superiority, inflicting mass suffering or loss of life on the enemy, or capturing the enemy’s center of power. The aggressor must prove to the defender that resistance is futile.

The defender in asymmetric warfare relies on maintaining the will to fight, the will to endure suffering, being capable of producing meaningful resistance, and oftentimes will rely on foreign powers for aid.

A strong national identity helps both the aggressor and the defender.

Willingness of the Weak to Suffer More or Bear Higher Costs

In many cases, the national identity of the defender is at stake. The ideas and values that define the defender are under direct attack. For this reason, the defender is often willing to result in a more total form of warfare than the aggressor.

In the case of Ukraine, Ukraine has continued to resist despite lacking electricity, consistent food and water, losing their homes, and enduring a significant loss of life. U.S. General Mark Milley released estimates that 100,000 Ukrainian soldiers and 40,000 civilians had been killed in the conflict. President Zelenskyy’s office claims that over 1.4 million Ukrainian households are without electricity. The temperature in Ukraine is below freezing. Ukrainian citizens live in fear of airstrikes.

Despite widespread suffering, loss of life, and battling a stronger opponent, Ukraine resists longer than any external estimates had predicted.

Ukrainian soldiers have presented more willingness to die for their cause than Russian soldiers. At the beginning of the conflict, multiple Ukrainian soldiers were reported killed in a rocket strike on Snake Island after telling a Russian warship to “Go f***k yourself”. The Ukrainian response to Russian demands to surrender became a rallying cry for Ukrainian civilians and foreign actors. Throughout the conflict, videos of Ukrainian soldiers and civilians willfully risking their lives have demonstrated Ukraine’s continued will to fight.

On Russia’s side, numerous events have come to light showing Russian soldiers and citizens lacking the same desire to fight. A number of Russian soldiers have said that they were lied to about the intent of the invasion and that they do not believe that they should be there. U.S. intelligence agencies claim that Russian soldiers have refused to fight and have even sabotaged their own vehicles.

Additionally, thousands have been arrested at home for holding mass protests in opposition to the war. Russia has begun conscripting soldiers and relying on mercenary groups such as the Wagner group to keep the war effort continued.

The defending nation, whose ideas and values are at stake, is often willing to sacrifice more than the aggressor.

External Support of Weak Actors
External support towards weak actors have played a critical role in many instances of asymmetric warfare. Whether through the support of troops, arms, or other aid, external interference has played a large war in many prior instances of asymmetric warfare. In the case of Russia and Ukraine, the effect of external support has made a significant impact on the war outcome. Throughout the past 9 month, the Kremlin has spent more than $82 billion on the war effort; $29 billion to the support of its army, $16 billion to pay its soldiers salaries, another $16 billion on the families of killed or injured servicemen, and $21 billion in damages due to the massive losses of military equipment as the Russian military still services many soviet era armaments. Meanwhile, the Ukrainian government has received over $99 billion dollars in aid, over half of which comes directly in the form of newly produced weapons and equipment far superior to the Russian arsenal. Though Russia has attempted strategies to reduce the external support being sent to Ukraine through threatening to cut oil exports, NATO allies have instead decided to continue supporting Ukraine while suffering the energy shortage.

Reluctance of Strong Actors to Escalate Violence
Ukraine also relies on mutually-assured destruction from other global nuclear superpowers, such as the United States, who stated in September 2020 that Russia would face “catastrophic consequences” should they use nuclear weapons **. Despite this, nuclear weapons remain one of Russia’s strongest weapons, mainly for its defensive threat to other superpowers. If the US were to directly engage or give too much unjustified support to Ukraine, Russia can rely on the threat of nuclear backlash. For instance, on Nov 29, 2022, the US increased Ukraine aid to help recover from continued air attacks, bringing the total contributions since the initial invasion to more than $19 billion. This along with other US contributions draws the pattern of a positive correlation between the strength of Russia’s attacks and US support.

Internal Group Dynamics
Both Russia and many Western officials predicted a fractured Ukrainian leadership. However, Zelenskyy swiftly supported his people since the start of the war, taking selfies with his fellow Ukrainians in Kyiv, sending daily support videos, repairing political feuds, supporting local businesses with reduced taxes, and presenting a strong head for the underdog, defying expectations.

It seems plausible that Russia was relying on a combination of surprise and Western/Ukrainian incoordination for a successful invasion. Part of Putin’s rhetoric after initial invasion failures was of the West’s inferiority, pointing to political instability. However, the people of Ukraine have rallied together out of necessity, partially due to Zelenskyy’s government.

Inflated Strong Actor War Aims
Inflated strong actor war aims, which is the overestimation in the ability of a strong actor to advance their war agenda, is commonly believed to be a contributing reason to weaker actors being able to overcome stronger actors. This can be seen in the case of the Russian Ukrainian war. Initially, Russia intended to completely cripple Ukraine with only 30% of the military force gathered along the border, a show of force to NATO and the EU, and it was expected by the ISW that the capital of Ukraine, Kyiv, would fall in 96 hours. These ambitions, however, were not met as Russian troops met far more resistance than anticipated and suffered due to poor logistics and other factors, which according to the ISW, “Russian forces in northeast Ukraine face growing morale and supply issues, likely due to poor planning and ad hoc command structures”. The ISW continued to claim “Russian forces remain much larger and more capable than Ukraine’s conventional military”, demonstrating that it was due not to lack of Russian military strength but overestimation in the ease with which the Russian military could take Ukraine. Because of this, Russian troops were forced to withdraw from Northern Ukraine, whereas if they had acted with the entirety of the Russian might the war may have ended nearly as soon as it had begun.

Evolution of Asymmetric Rivals' Attitudes Towards Time
As time progresses, objectives and ideals of actors shift in asymmetric conflict. This often can be seen in a reduction of war aims or loss in morale in strong actors engaged in forestalled combat. Initially, when Russia began its invasion on February 24th, it had intended to swiftly capture the capital Kyiv to “demilitarize and de-Nazify Ukraine” Ukraine. In mid-March, however, after the operation to swiftly take Kyiv and topple the Ukrainian government had failed, it shifted focus to the Luhansk and Donetsk regions. Due to the insufficiencies of military hardware and contract soldiers, Russia was unable to expand beyond the regions that they had initially captured in February and March. However, in September, due to the Ukrainian counteroffensive, the Russian army changed from a stance of actively attacking Ukraine to defending the territories initially captured. In October, the Kremlin introduced state-of-emergency laws, shifting the focus of the Russian strategy from all-out warfare to strategic defense, surrendering attempts to hold cities such as Kherson, and modified talks on the realistic goal of the “special operation” to hold a land corridor to Crimea. Ukraine, however, has not seen a change in attitude, as they are still resisting Russian control over Ukrainian territory bitterly. The success of Ukrainian resistance can be attributed to the reshaping of Russian military goals as the attitude towards its war capabilities has changed over time, for if the Kremlin had continued its assault on Kyiv, disregarding the costs, the defenses of Ukraine may not have lasted.

Conclusion
Advances in technology have turned the tide in asymmetric warfare. The use of the internet and social media has allowed ordinary civilians, with no military experience, to significantly contribute to the war effort. In the future, we will see if continued advances in technology contribute to this trend.


text:
Themes in Literature/Isolation and Community/Langston Hughes

Langston Hughes was an African-American poet, social activist, novelist, playwright, and columnist who examined life in United States during the first part of the 20th Century, exposing oppression, discrimination, and inequality. Hughes was born on February 1, 1902 in Joplin, Missouri. After Hughes' parents divorced, he began living with his grandmother, Mary Langston, who encouraged him to understand the importance of racial issues in America, so he dedicated much of his work to celebrating African American culture. The difficult experiences that he went through at a young age like growing up during a time of segregation motivated him to write poems while he was at grammar school. Later, while Hughes attended Central High School in Ohio, his Latin teacher taught him the importance of writing literature so he began writing for the newspaper and yearbook. He began writing short stories because books helped him escape from the hardships that he experienced. At the age of seventeen, he wrote his first poem called “When Sue Wears Red."

In the 1920s, Hughes became one of the leaders of the Harlem Renaissance, a congregation of African American artistic, intellectual, and political talent centered in the neighborhood of Harlem, New York. He became famous for defending racial integration around the world, especially with younger generations of Black writers, who considered Hughes as a defender of minorities’ rights. One case in point was his encouragement of Black Americans to join World War II because he believed it would help them obtain civil rights at a time of racial segregation in the United States. Hughes died on May 22, 1967 in Stuyvesant Polyclinic in New York City.


text:
Themes in Literature/Isolation and Community/Emily Dickinson

Emily Dickinson was a 19th-century American poet whose distinctive writing style made her stand out from the other poets in her era. She is known for her notably unconventional writing style that was unique at the time, where she often made use of dashes and unusual capitalization, and frequently used slant rhyme, which is a type of rhyme with words that have similar but not identical sounds. She ignored the typical rules of versification and grammar, making her work brave and completely original. Dickinson was highly educated and was raised in a Calvinist household, which emphasized the sovereignty of God and the authority of the Bible. This religious influence permeates throughout her work. She had a complicated relationship with her religious beliefs and God; while her friends and family proclaimed their love of Christ, she was reluctant to join the church and ultimately stopped attending services altogether.

Dickinson’s family was well known in the Massachusetts community where they lived. Her grandfather was a trustee of Amherst College, while her father had served in both state and federal Congresses. Although Dickinson herself was more socially active at a younger age, she became more reclusive later in the later years of her life. Scholars believe she was troubled from a young age by the "deepening menace" of death; throughout her lifetime she would suffer tremendous loss of friends and family, while later living through the time of the American Civil war that began in 1861 and ended in 1865. She began to isolate herself in her room in her family’s homestead and did not leave unless it was absolutely necessary. She began to talk to her visitors from the other side of her door instead of speaking to them face to face. Only the few people who knew her personally and had exchanged written correspondence with her during the last years of her life had ever seen her in person. Her writing was said to be an outlet for her to express herself verbally rather than socially. Her works reflect this, as they are full of religious imagery and nuance, conversations about death, the ironies of life, her love of nature, and criticisms of societal behaviors.

Dickinson died of heart failure at her home on May 15th, 1886. Only a handful of poems and a single letter were published during her life. After her death, her younger sister discovered Dickinson’s vast collection of nearly 1,800 poems and letters, and she had Dickinson's first volume published almost four years after her death. Literary scholar Thomas H. Johnson would eventually publish Dickinson's Complete Poems in 1955, and her poems have been in print continuously since.


text:
Themes in Literature/Isolation and Community/Octavia E. Butler

Born in Pasadena in 1947, Octavia E. Butler was a prolific female black American science fiction author who heavily featured afro-futurism and feminism in her writing. She was raised by her mother and grandmother, after her father’s death, and took on jobs that would allow her enough free time to write. Despite many rejections early on in her career, her literature has received some of the most prestigious literary awards, including the prestigious Hugo Award for her novelette Bloodchild and her short story “Speech Sounds”, an acknowledgement for best in science fiction of the year preceding the award. She also received Nebula Awards, which also recognizes exceptional work in the science fiction genre, for her aforementioned novelette, Bloodchild and her novel, Parable of The Talents. Butler was also the first writer to obtain a MacArthur Fellowship. A complete list of her awards and literature can be found on her website. Butler died in February 2006. It was only near the end of her life when her stories—focused as they were on feminism, global warming, racial and other social injustice—became more widely known and loved, as present society’s focus tilted towards these concerns. Today, her books, poems and essays are taught in schools.


text:
Fractals/Computer graphic techniques/2D/plane inversion

In Mathematics and logic inversion may refer to ( Disambiguation )
 * Involution, a function that is its own inverse (when applied twice, the starting value is obtained)
 * Inversion in discrete mathematics, any item that is out of order in a sequence
 * Inverse element
 * Inversive geometry, like circle inversion, a transformation of the Euclidean plane that maps generalized circles to generalized circles
 * Inversion in a point, or point reflection, a kind of isometric (distance-preserving) transformation in a Euclidean space
 * Inversion transformation, a conformal transformation (one which preserves angles of intersection)
 * Method of inversion, the image of a harmonic function in a sphere (or plane); see [ethod of image charges
 * Multiplicative inverse] the reciprocal of a number (or any other type of element for which a multiplication function is defined)
 * Matrix inversion, an operation on a matrix that results in its multiplicative inverse
 * Model inversion
 * Set inversion

=inversion of curves and surfaces= In inversive geometry ibversion is a transformation of the Euclidean plane, like:
 * circle inversion
 * Parabola inversion

=plane inversion = Plane inversion is an example of plane transformation. Inversion transformation, is a conformal transformation (one which preserves angles of intersection). Inversion can be composite with another transformation, like translation.

parameter plane (with Mandelbrot set) inversion
Inversions by plane types
 * inversion of standard Mandelbrot set ( c-plane ) $$ f_c(z) = z^2 + c $$
 * inversion of lambda mandelbrot set ( lambda plane) $$z = \lambda z(1- z)$$

c-plane
Description by Nikola Ubavić: Žulijev i Mandelbrotov skup ( in serbian)
 * composition of the inversion with respect to the unit circle centered at zero, and the conjugation (axial symmetry with respect to the real line). The cardioid from the boundary of the Mandelbrot set in the "standard" parameterization corresponds to the tear-shaped curve in the 1/c parameterization.
 * Inverted c-plane : "Geometrically, the ... relationship between the parameters represents the composition of the inversion with respect to the unit circle centered at zero, and the conjugation (axial symmetry with respect to the real line). Due to this connection, the cardioid from the boundary of the Mandelbrot set in the "standard" parameterization corresponds to the tear-shaped curve in the alpha parameterization."
 * "if translation is performed for before the inversion 1/4, then the cardioid is imaged in a parabola" $$z = z^2 + \frac{1}{c+ 1/4}$$

Description by [https://mathcs.clarku.edu/~djoyce/julia/altplane.html David E. Joyce: Julia and Mandelbrot Sets. Alternate Parameter Planes]
 * The inverse of the cardioid is the exterior of a teardrop shape. The circles on the outside of the cardioid are inverted to circles on the inside of the teardrop. The cusp of the cardioid becomes the cusp of the teardrop.

Continous inversion methods by Arneauxtje

 * Mandelbrot set inversion, 4 different methods in one image
 * Mandelbrot set inversion revisited

Description by Arneauxtje: the transformation from the cardioid of the body of the set to a circle. This is done in c-space (a+ib) as follows:

rho=sqrt(a*a+b*b)-1/4 phi=arctan(b/a) a-new=rho*(2*cos(phi)-cos(2*phi))/3 b-new=rho*(2*sin(phi)-sin(2*phi))/3

Then, there's the 4 different ways on how to get from c to 1/c, that group in 3 families:
 * addition: c -> c-c*t+t/c and t=0..1
 * multiplication: c -> c/(t*(c*c-1)+1) and t=0..1
 * exponentiation: c -> c^t and t=1..-1

The first 2 are pretty elementary to work out. The 3rd makes use of the fact that:
 * c = a+ib = r*exp(i*phi) where r=sqrt(a*a+b*b) and phi=arctan(b/a)
 * then c^t = r^t*exp(t*i*phi) = r^t*[cos(t*phi)+i*sin(t*phi)]

lambda plane
lambda mandelbrot set : $$z = \lambda z(1- z)$$

Description by Nikola Ubavić: Žulijev i Mandelbrotov skup ( in serbian)
 * "By inverting a complex plane around a unit circle with center at zero, one of these circles remains invariant, while the other image is inside it." $$z = \frac{z(1-z)}{\lambda}$$
 * "If ... translation is performed before the inversion1, then the two circles are mapped into two parallel lines. In this way the second of the next two figures was obtained." $$z = \frac{z(1-z)}{\lambda +1}$$

Videos
 * Cat Eye Revisited by denis archambaud

Dynamic plane ( with Julia set) inversion

 * f(z) = z^2+c convert to f(z) = z^2 + 1/c
 * inverting the polynomial formula Ax(1-x) in the circle of radius 1, resulting in the formula f(x)= x^2/A(1-x).

basilica

 * normal basilica f(z) = z^2 - 1
 * inverted basilica
 * rational with degree = 2 : reversed basilica : f(z) = z^2/(z^2 -1)

Videos
 * The Inverted Julia Sets by The Donut Man

=References=
 * Mandelbrot-Sets-Alternate-Parameter-Planes
 * Imploded cauliflower - is a Julia set for c=1/4+epsilon with epsilon >0. How many different ways are there to show such set ?


text:
Cookbook:Scrambled Eggs with Herbs

Ingredients

 * 2–4 eggs
 * Salt
 * Black pepper, crushed
 * Dried parsley flakes
 * Basil, fresh or dried, crushed or torn into pieces
 * Rosemary
 * ~½ tablespoon water

Equipment

 * Small pan
 * Small bowl
 * Whisk (a fork is an adequate substitute)
 * Corner spoon (any small spatula will suffice)

Procedure

 * 1) Spray pan with non-stick cooking spray—this is optional but recommended.
 * 2) Put pan on stovetop at medium heat.
 * 3) Determine number of eggs to use—2 will serve one, 3 if especially hungry, and 4 will feed two.
 * 4) Get a small bowl. Crack eggs on countertop, then split them so the whites and yolks fall into the bowl. Make sure no shell fragments get in; if they do, remove them.
 * 5) Sprinkle salt, crushed black pepper, parsley flakes, and crushed basil onto the eggs.
 * 6) Add a small number (<7) of flakes of rosemary.
 * 7) Add a small amount (~½ tablespoon) of water.
 * 8) Holding the bowl at an angle, quickly but carefully whisk the ingredients in the bowl, moving the whisk in a rapid circular motion. Continue until ingredients appear blended, with the eggs being a homogeneous yellow.
 * 9) Pour mixture into pan, which should at this point have heated up.
 * 10) Stir gently with corner spoon for several minutes until mixture begins to congeal into lumps.
 * 11) Let the lumps sizzle briefly, then flip over to allow the other side to cook. Continue this until the entire surface area of all the scrambled eggs is no longer visibly wet.
 * 12) Serve.

title: Cookbook:Scrambled Eggs with Herbs