text:
Human capital

Human capital or human assets is a concept used by economists to designate personal attributes considered useful in the production process. It encompasses employee knowledge, skills, know-how, good health, and education. Human capital has a substantial impact on individual earnings. Research indicates that human capital investments have high economic returns throughout childhood and young adulthood.

Companies can invest in human capital; for example, through education and training, improving levels of quality and production.

History
Adam Smith included in his definition of capital "the acquired and useful abilities of all the inhabitants or members of the society". The first use of the term "human capital" may be by Irving Fisher. An early discussion with the phrase "human capital" was from Arthur Cecil Pigou:

"There is such a thing as investment in human capital as well as investment in material capital. So soon as this is recognised, the distinction between economy in consumption and economy in investment becomes blurred. For, up to a point, consumption is investment in personal productive capacity. This is especially important in connection with children: reducing unduly expenditure on their consumption may greatly lower their efficiency in after-life. Even for adults, after we have descended a certain distance along the scale of wealth, so that we are beyond the region of luxuries and 'unnecessary' comforts, a check to personal consumption is also a check to investment."

But the term only found widespread use in economics after its popularization by economists of the Chicago School, in particular Gary Becker, Jacob Mincer, and Theodore Schultz.

The early 20th century Austrian sociologist Rudolf Goldscheid's theory of organic capital and the human economy also served as a precedent for later concepts of human capital.

The use of the term in the modern neoclassical economic literature dates back to Jacob Mincer's article "Investment in Human Capital and Personal Income Distribution" in the Journal of Political Economy in 1958. Then Theodore Schultz also contributed to the development of the subject matter. The best-known application of the idea of "human capital" in economics is that of Mincer and Gary Becker. Becker's book entitled Human Capital, published in 1964, became a standard reference for many years. In this view, human capital is similar to "physical means of production", e.g., factories and machines: one can invest in human capital (via education, training, medical treatment) and one's outputs depend partly on the rate of return on the human capital one owns. Thus, human capital is a means of production, into which additional investment yields additional output. Human capital is substitutable, but not transferable like land, labor, or fixed capital.

Some contemporary growth theories see human capital as an important economic growth factor. Further research shows the relevance of education for the economic welfare of people.

Adam Smith defined four types of fixed capital (which is characterized as that which affords a revenue or profit without circulating or changing masters). The four types were: Smith defined human capital as follows:
 * 1) useful machines, instruments of the trade;
 * 2) buildings as the means of procuring revenue;
 * 3) improvements of land;
 * 4) the acquired and useful abilities of all the inhabitants or members of the society.

Fourthly, of the acquired and useful abilities of all the inhabitants or members of the society. The acquisition of such talents, by the maintenance of the acquirer during his education, study, or apprenticeship, always costs a real expense, which is a capital fixed and realized, as it were, in his person. Those talents, as they make a part of his fortune, so do they likewise that of the society to which he belongs. The improved dexterity of a workman may be considered in the same light as a machine or instrument of trade which facilitates and abridges labor, and which, though it costs a certain expense, repays that expense with a profit.

Therefore, Smith argued, the productive power of labor are both dependent on the division of labor:

"The greatest improvement in the productive powers of labor, and the greater part of the skill, dexterity, and judgement with which it is anywhere directed, or applied, seem to have been the effects of the division of labor."

There is a complex relationship between the division of labor and human capital.

In the 1990s, the concept of human capital was extended to include natural abilities, physical fitness and healthiness, which are crucial for an individual's success in acquiring knowledge and skills.

As a result of his conceptualization and modeling work using Human Capital as a key factor, the 2018 Nobel Prize for Economics was jointly awarded to Paul Romer, who founded the modern innovation-driven approach to understanding economic growth.

In the recent literature, the new concept of task-specific human capital was coined in 2004 by Robert Gibbons, an economist at MIT, and Michael Waldman, an economist at Cornell University. The concept emphasizes that in many cases, human capital is accumulated specific to the nature of the task (or, skills required for the task), and the human capital accumulated for the task are valuable to many firms requiring the transferable skills. This concept can be applied to job-assignment, wage dynamics, tournament, promotion dynamics inside firms, etc.

Background
Human capital in a broad sense is a collection of activities: all the knowledge, skills, abilities, experience, intelligence, training and competences possessed individually and collectively by individuals in a population. These resources are the total capacity of the people that represents a form of wealth that can be directed to accomplish the goals of the nation or state or a portion thereof. The human capital is further distributed into three kinds;
 * 1) Knowledge capital
 * 2) Social capital
 * 3) Emotional capital.

Many theories explicitly connect investment in human capital development to education, and the role of human capital in economic development, productivity growth, and innovation has frequently been cited as a justification for government subsidies for education and job skills training.

It was assumed in early economic theories, reflecting the context – i.e., the secondary sector of the economy was producing much more than the tertiary sector was able to produce at the time in most countries – to be a fungible resource, homogeneous, and easily interchangeable, and it was referred to simply as workforce or labor, one of three factors of production (the others being land, and assumed-interchangeable assets of money and physical equipment). Just as land became recognized as natural capital and an asset in itself, human factors of production were raised from this simple mechanistic analysis to human capital. In modern technical financial analysis, the term "balanced growth" refers to the goal of equal growth of both aggregate human capabilities and physical assets that produce goods and services.

The assumption that labor or workforces could be easily modelled in aggregate began to be challenged in 1950s when the tertiary sector, which demanded creativity, begun to produce more than the secondary sector was producing at the time in the most developed countries in the world. Accordingly, much more attention was paid to factors that led to success versus failure where human management was concerned. The role of leadership, talent, even celebrity was explored.

Today, most theories attempt to break down human capital into one or more components for analysis. Most commonly, Emotional capital is the set of resources (the personal and social emotional competencies) that is inherent to the person, useful for personal, professional and organizational development, and participates to social cohesion and has personal, economic and social returns (Gendron, 2004, 2008). Social capital, the sum of social bonds and relationships, has come to be recognized, along with many synonyms such as goodwill or brand value or social cohesion or social resilience and related concepts like celebrity or fame, as distinct from the talent that an individual (such as an athlete has uniquely) has developed that cannot be passed on to others regardless of effort, and those aspects that can be transferred or taught: instructional capital. Less commonly, some analyses conflate good instructions for health with health itself, or good knowledge management habits or systems with the instructions they compile and manage, or the "intellectual capital" of teams – a reflection of their social and instructional capacities, with some assumptions about their individual uniqueness in the context in which they work. In general, these analyses acknowledge that individual trained bodies, teachable ideas or skills, and social influence or persuasion power, are different.

Management accounting is often concerned with questions of how to model human beings as a capital asset. However it is broken down or defined, human capital is vitally important for an organization's success (Crook et al., 2011); human capital increases through education and experience. Human capital is also important for the success of cities and regions: a 2012 study examined how the production of university degrees and R&D activities of educational institutions are related to the human capital of metropolitan areas in which they are located.

In 2010, the OECD encouraged the governments of advanced economies to embrace policies to increase innovation and knowledge in products and services as an economical path to continued prosperity. International policies also often address human capital flight, which is the loss of talented or trained persons from a country that invested in them, to another country which benefits from their arrival without investing in them.

World Economic Forum Global Human Capital Index
Since 2012 the World Economic Forum has annually published its Global Human Capital Report, which includes the Global Human Capital Index (GHCI). In the 2017 edition, 130 countries are ranked from 0 (worst) to 100 (best) according to the quality of their investments in human capital. Norway is at the top, with 77.12.

World Bank Human Capital Index
In October 2018, the World Bank published the Human Capital Index (HCI) as a measurement of economic success. The Index ranks countries according to how much is invested in education and health care for young people. The World Bank's 2019 World Development Report on The Changing Nature of Work showcases the Index and explains its importance given the impact of technology on labor markets and the future of work. One of the central innovations of the World Bank Human Capital Index was the inclusion and harmonization of learning data across 164 countries. This introduced a measure of human capital which directly accounts for the knowledge and skills acquired from schooling, rather than using schooling alone, now widely recognized to be an incomplete proxy. The learning outcomes data, methodology, and applications to the human capital literature underlying this effort were published in Nature.

• # 🇸🇬 singapore 0.88
 * Human Capital Index ranking (top 50 countries)

• # 🇰🇷 south korea 0.84

• # 🇯🇵 japan 0.84

• # 🇭🇰 hong kong, SAR of China 0.82

• # 🇫🇮 finland 0.81

• # 🇮🇪 ireland 0.81

• # 🇦🇺 australia 0.80

• # 🇸🇪 sweden 0.80

• # 🇳🇱 netherlands 0.80

• # 🇨🇦 canada 0.80

• # 🇩🇪 germany 0.79

• # 🇦🇹 austria 0.79

• # 🇸🇮 slovenia 0.79

• # 🇨🇿 czech republic 0.78

• # 🇬🇧 united kingdom 0.78

• # 🇵🇹 portugal 0.78

• # 🇩🇰 denmark 0.77

• # 🇳🇴 norway 0.77

• # 🇮🇹 italy 0.77

• # 🇨🇭 switzerland 0.77

• # 🇳🇿 new zealand 0.77

• # 🇫🇷 france 0.76

• # 🇮🇱 israel 0.76

• # 🇺🇸 united states 0.76

• # undefined, SAR of China 0.76

• # 🇧🇪 belgium 0.76

• # 🇷🇸 serbia 0.76

• # 🇨🇾 cyprus 0.75

• # 🇪🇪 estonia 0.75

• # 🇵🇱 poland 0.75

• # 🇰🇿 kazakhstan 0.75

• # 🇪🇸 spain 0.74

• # 🇮🇸 iceland 0.74

• # undefined 0.73

• # 🇱🇻 latvia 0.72

• # 🇭🇷 croatia 0.72

• # 🇱🇹 lithuania 0.71

• # 🇭🇺 hungary 0.70

• # 🇲🇹 malta 0.70

• # undefined 0.69

• # 🇱🇺 luxembourg 0.69

• # 🇬🇷 greece 0.68

• # 🇸🇨 seychelles 0.68

• # 🇧🇬 bulgaria 0.68

• # 🇨🇱 chile 0.67

• # 🇨🇳 china 0.67

• # 🇧🇭 bahrain 0.67

• # undefined 0.67

• # 🇦🇪 united arab emirates 0.66

• # 🇺🇦 ukraine 0.65

Other methods
A new measure of expected human capital calculated for 195 countries from 1990 to 2016 and defined for each birth cohort as the expected years lived from age 20 to 64 years and adjusted for educational attainment, learning or education quality, and functional health status was published by The Lancet in September 2018. Finland had the highest level of expected human capital: 28·4 health, education, and learning-adjusted expected years lived between age 20 and 64 years. Niger had the lowest at less than 1·6 years.

Measuring the human capital index of individual firms is also possible: a survey is made on issues like training or compensation, and a value between 0 (worst) and 100 (best) is obtained. Enterprises which rank high are shown to add value to shareholders.

Human capital management
Human capital management (HCM) is the term used to describe workforce practices and resources that focus on maximizing needed skills through the recruitment, training, and development of employees. Departments and software applications responsible for HCM often manage tasks that include administrative support, reporting and analytics, education and training, and hiring and recruitment.

Cumulative growth
Human capital is distinctly different from the tangible monetary capital due to the extraordinary characteristic of human capital to grow cumulatively over a long period of time. The growth of tangible monetary capital is not always linear due to the shocks of business cycles. During the period of prosperity, monetary capital grows at relatively higher rate while during the period of recession and depression, there is deceleration of monetary capital. On the other hand, human capital has uniformly rising rate of growth over a long period of time because the foundation of this human capital is laid down by the educational and health inputs. The current generation is qualitatively developed by the effective inputs of education and health. The future generation is more benefited by the advanced research in the field of education and health, undertaken by the current generation. Therefore, the educational and health inputs create more productive impacts upon the future generation and the future generation becomes superior to the current generation. In other words, the productive capacity of future generation increases more than that of current generation. Therefore, rate of human capital formation in the future generation happens to be more than the rate of human capital formation in the current generation. This is the cumulative growth of human capital formation generated by superior quality of manpower in the succeeding generation as compared to the preceding generation.

Intangibility and portability
Human capital is an intangible asset, and it is not owned by the firm that employs it and is generally not fungible. Specifically, individuals arrive at 9am and leave at 5pm (in the conventional office model) taking most of their knowledge and relationships with them.

Human capital when viewed from a time perspective consumes time in one of these key activities:

 * 1) Knowledge (activities involving one employee),
 * 2) Collaboration (activities involving more than 1 employee),
 * 3) Processes (activities specifically focused on the knowledge and collaborative activities generated by organizational structure – such as silo impacts, internal politics, etc.) and
 * 4) Absence (annual leave, sick leave, holidays, etc.).

Despite the lack of formal ownership, firms can and do gain from high levels of training, in part because it creates a corporate culture or vocabulary teams use to create cohesion.

In recent economic writings the concept of firm-specific human capital, which includes those social relationships, individual instincts, and instructional details that are of value within one firm (but not in general), appears by way of explaining some labour mobility issues and such phenomena as golden handcuffs. Workers can be more valuable where they are simply for having acquired this knowledge, these skills and these instincts. Accordingly, the firm gains for their unwillingness to leave and market talents elsewhere.

Marxist analysis
In some way, the idea of "human capital" is similar to Karl Marx's concept of labor power: he thought in capitalism workers sold their labor power in order to receive income (wages and salaries). But long before Mincer or Becker wrote, Marx pointed to "two disagreeably frustrating facts" with theories that equate wages or salaries with the interest on human capital.

 * 1) The worker must actually work, exert their mind and body, to earn this "interest." Marx strongly distinguished between one's capacity to work, labor power, and the activity of working.
 * 2) A free worker cannot sell his human capital in one go; it is far from being a liquid asset, even more illiquid than shares and land. He does not sell his skills, but contracts to utilize those skills, in the same way that an industrialist sells his produce, not his machinery. The exception here are slaves, whose human capital can be sold, though the slave does not earn an income himself.

An employer must be receiving a profit from his operations, so that workers must be producing what Marx (under the labor theory of value) perceived as surplus-value, i.e., doing work beyond that necessary to maintain their labor power. Though having "human capital" gives workers some benefits, they are still dependent on the owners of non-human wealth for their livelihood.

The term appears in Marx's article in the New-York Daily Tribune "The Emancipation Question," January 17 and 22, 1859, although there the term is used to describe humans who act like a capital to the producers, rather than in the modern sense of "knowledge capital" endowed to or acquired by humans.

Neo-Marxist economists have argued that education leads to higher wages not by increasing human capital, but rather by making workers more compliant and reliable in a corporate environment. The reasoning of which being that higher education creates the illusion of a meritocracy, thus justifying economic inequality to the benefit of capitalists, regardless of whether the educated human capital actually provides additional labor value.

Risk
When human capital is assessed by activity-based costing via time allocations it becomes possible to assess human capital risk. Human capital risks can be identified if HR processes in organizations are studied in detail. Human capital risk occurs when the organization operates below attainable operational excellence levels. For example, if a firm could reasonably reduce errors and rework (the process component of human capital) from 10,000 hours per annum to 2,000 hours with attainable technology, the difference of 8,000 hours is human capital risk. When wage costs are applied to this difference (the 8,000 hours) it becomes possible to financially value human capital risk within an organizational perspective.

Risk accumulates in four primary categories:
 * 1) Absence activities (activities related to employees not showing up for work such as sick leave, industrial action, etc.).  Unavoidable absence is referred to as Statutory Absence.  All other categories of absence are termed "Controllable Absence";
 * 2) Collaborative activities are related to the expenditure of time between more than one employee within an organizational context.  Examples include: meetings, phone calls, instructor led training, etc.;
 * 3) Knowledge Activities are related to time expenditures by a single person and include finding/retrieving information, research, email, messaging, blogging, information analysis, etc.; and
 * 4) Process activities are knowledge and collaborative activities that result due to organizational context such as errors/rework, manual data transformation, stress, politics, etc.

Corporate management
In corporate management, human capital is one of the three primary components of intellectual capital (which, in addition to tangible assets, comprise the entire value of a company). Human capital is the value that the employees of a business provide through the application of skills, know-how and expertise. It is an organization's combined human capability for solving business problems. Human capital is inherent in people and cannot be owned by an organization. Therefore, human capital leaves an organization when people leave. Human capital also encompasses how effectively an organization uses its people resources as measured by creativity and innovation. A company's reputation as an employer affects the human capital it draws.

Criticism
Some labor economists have criticized the Chicago-school theory, claiming that it tries to explain all differences in wages and salaries in terms of human capital. One of the leading alternatives, advanced by Michael Spence and Joseph Stiglitz, is "signaling theory". According to signaling theory, education does not lead to increased human capital, but rather acts as a mechanism by which workers with superior innate abilities can signal those abilities to prospective employers and so gain above average wages.

The concept of human capital can be infinitely elastic, including unmeasurable variables such as personal character or connections with insiders (via family or fraternity). This theory has had a significant share of study in the field proving that wages can be higher for employees on aspects other than human capital. Some variables that have been identified in the literature of the past few decades include, gender and nativity wage differentials, discrimination in the work place, and socioeconomic status.

The prestige of a credential may be as important as the knowledge gained in determining the value of an education. This points to the existence of market imperfections such as non-competing groups and labor-market segmentation. In segmented labor markets, the "return on human capital" differs between comparably skilled labor-market groups or segments. An example of this is discrimination against minority or female employees.

Following Becker, the human capital literature often distinguishes between "specific" and "general" human capital. Specific human capital refers to skills or knowledge that is useful only to a single employer or industry, whereas general human capital (such as literacy) is useful to all employers. Economists view firm-specific human capital as risky, since firm closure or industry decline leads to skills that cannot be transferred (the evidence on the quantitative importance of firm specific capital is unresolved).

Human capital is central to debates about welfare, education, health care, and retirement.

In 2004, "human capital" (Humankapital) was named the German Un-Word of the Year by a jury of linguistic scholars, who considered the term inappropriate and inhumane, as individuals would be degraded and their abilities classified according to economically relevant quantities.

"Human capital" is often confused with human development. The UN suggests "Human development denotes both the process of widening people's choices and improving their well-being". The UN Human Development indices suggest that human capital is merely a means to the end of human development: "Theories of human capital formation and human resource development view human beings as means to increased income and wealth rather than as ends. These theories are concerned with human beings as inputs to increasing production".

title: Human capital


text:
Garuda

Garuda (गरुड; गरुळ; Vedic Sanskrit: गरुळ, ) is a Hindu deity who is primarily depicted as the mount (vahana) of the Hindu god Vishnu. This divine creature is mentioned in the Hindu, Buddhist and Jain faiths. Garuda is also the half-brother of the Devas, Gandharvas, Daityas, Danavas, Nāgas, Vanara and Yakshas. He is the son of the sage Kashyapa and Vinata. He is the younger brother of Aruna, the charioteer of the Sun. Garuda is mentioned in several other texts such as the Puranas and the Vedas.

Garuda is described as the king of the birds and a kite-like figure. He is shown either in a zoomorphic form (a giant bird with partially open wings) or an anthropomorphic form (a man with wings and some ornithic features). Garuda is generally portrayed as a protector with the power to swiftly travel anywhere, ever vigilant and an enemy of every serpent. He is also known as Tarkshya and  Vainateya.

Garuda is a part of state insignia of India, Indonesia and Thailand. Both Indonesia and Thailand has Garuda as their coat of arms, the Indian Army uses the Garuda on their Guards Brigade Regimental Insignia. The Indian Air Force named their special operations unit after him as the Garud Commando Force. It is often associated with the Greater adjutant stork (Leptoptilos dubius).

Hinduism
In Hinduism, is a divine eagle-like sun bird and the king of birds. A Garutman is mentioned in the Rigveda who is described as celestial deva with wings. The Shatapatha Brahmana embedded inside the Yajurveda text mentions Garuda as the personification of courage. In the Mahabharata, Garutman is stated to be same as Garuda, then described as the one who is fast, who can shapeshift into any form and enter anywhere. He is a powerful creature in the epics, whose wing flapping can stop the spinning of heaven, earth and hell. He is described to be the vehicle mount of the Hindu god Vishnu, and typically they are shown together. He is the younger brother of Aruna, who is a charioteer of the sun god, Surya.

According to George Williams, Garuda has roots in the verb gri, or speak. He is a metaphor in the Vedic literature for Rik (rhythms), Saman (sounds), Yajna (sacrifices), and the atman (Self, deepest level of consciousness). In the Puranas, states Williams, Garuda becomes a literal embodiment of the idea, and the Self who attached to and inseparable from the Supreme Self (Vishnu). Though Garuda is an essential part of the Vaishnavism, he also features prominently in Shaivism, Shaiva texts such as the Garuda Tantra and Kirana Tantra, and Shiva temples as a bird and as a metaphor of atman.

Iconography
The Hindu texts on Garuda iconography vary in their details. If in the bird form, he is eagle-like, typically with the wings slightly open as if ready and willing to fly wherever he needs to. In part human-form, he may have an eagle-like nose, beak or legs, his eyes are open and big, his body is the color of emerald, and his wings are golden-yellow. He may be shown with either two or four hands. If he is not carrying Vishnu, he holds a jar of amrita (immortality nectar) in one hand in the rear and an umbrella in the other, while the front pair of hands are in anjali (namaste) posture. If he is carrying Vishnu, the rear hands provide the support for Vishnu's feet.

According to the text Silparatna, states Rao, Garuda is best depicted with only two hands and with four bands of colours: "golden yellow colour from feet to knees, white from knees to the navel, scarlet from navel to neck, and black above the neck". His hands, recommends the text, should be in abhaya (nothing to fear) posture. In Sritatvanidhi text, the recommended iconography for Garuda is a kneeling figure, who wears one or more serpents, pointed bird-beak like nose, his two hands in namaste posture. This style is commonly found in Hindu temples dedicated to Vishnu.

In some iconography, Garuda carries Vishnu and his two consorts by his side: Lakshmi and Bhumi.

Garuda iconography is found in early temples of India, such as on the underside of the eave at Cave 3 entrance of the Badami cave temples (6th-century).

Mythology
Garuda's mythology is linked to that of Aruna – the charioteer of Surya (The Hindu Sun god). Both Aruna and Garuda developed from an egg. According to one version related by George Williams, Kashyapa Prajapati's two wives Vinata and Kadru wanted to have children, and Kashyapa granted each of them a boon. Kadru asked for one thousand Nāga sons, while Vinata asked for just two, but each an equal to all of Kadru's thousand sons. Kashyapa blessed them, and then retreated to a forest to meditate. Later, Kadru gave birth to one thousand eggs, while Vinata gave birth to two eggs. After incubating them for five hundred years, Kadru's eggs hatched and out came her 1,000 sons. Vinata, eager for her own sons, impatiently broke one of her eggs. From this egg emerged the partially formed Aruna, looking radiant and reddish as the morning sun - but not as bright as the midday sun as he was promised to be. Aruna chided his mother Vinata for her impatience, and warned her to not break open the second egg, cursing her to be a slave until his brother rescued her. Aruna then left to become the charioteer of Surya, the sun god.

Vinata waited, and after many years the second egg hatched, and Garuda was born. After losing a bet to Kadru through trickery, Vinata was forced to become her slave. Garuda later on asked his brothers to free his mother from her slavery, to which they demanded Amrita from heaven. Garuda waged a war against gods with his extraordinary might and abilities beyond thinking, and defeated all of them, including Indra. He then took Indra's nectar vessel and flew back to earth. Vishnu then came to Garuda, and asked him to be his ride, to which he agreed. Indra requested that Garuda not give the Amrita to the Nagas though, as it would bring great trouble later, so they forged a plan. Upon reaching his brothers Garuda placed the vessel before them, and asked them to first purify themselves before drinking. Meanwhile, Jayanta (the son of Indra) stole the vessel back. On returning, the nagas were all devoured by Garuda.

Some myths present Garuda as so massive that he can block out the sun. The text Garuda Purana is named after him.

Garuda is presented in the Mahabharata as one who eats snake meat, such as the story about him planning to kill and eat Sumukha snake, where Indra intervenes. Garuda in anger, vaunt about his feats and compares himself to Indra's equal. Vishnu teaches a lesson to Garuda and cured his pride on might. Garudas are also a race of birds who devour snakes in the epic.

The Suparṇākhyāna, a late Vedic period poem considered to be among the "earliest traces of epic poetry in India," relates the legend of Garuda, and provides the basis for a later, expanded version which appears within the Mahābhārata.

Symbolism
Garuda's links to Vishnu – the Hindu god who fights injustice and destroys evil in his various avatars to preserve dharma – have made him an iconic symbol of kings' duty and power, an insignia of royalty or dharma. His eagle-like form is shown either alone or with Vishnu, signifying divine approval of the power of the state. He is found on the faces of many early Hindu kingdom coins with this symbolism, either as a single-headed bird or a three-headed bird that watches all sides.

Throughout the Mahabharata, Garuda is invoked as a symbol of impetuous violent force, speed, and martial prowess. Powerful warriors advancing rapidly on doomed foes are likened to Garuda swooping down on a serpent. Defeated warriors are like snakes beaten down by Garuda. The Mahabharata character Drona uses a military formation named after Garuda. Krishna carries the image of Garuda on his banner.

Temples
Though Garuda stautues and iconography can be seen in many Vishnu temples, there are very few temples dedicated to Garuda as a deity in India. Some of them are:

 * Vellamassery Garuda Temple, Triprangode, Tirur, Malappuram, Kerala

A 1800 year old ancient kavu dedicated to Garuda, it is famous in the state for the alleviation of 'sarpa dosham'. Nearby the main temple is a rare subsidiary shrine dedicated to the Kurma avatar of Lord Vishnu.

 * Chemmanadu Sri Krishna Garuda Mahavishnu Temple, Tiruvaniyoor, Ernakulam, Kerala

This temple was believed to have been constructed after Garuda himself manifested in eagle form in front of the devotees during the consecration ceremony. Lord Vishnu is present in his Mohini swaroopam in this temple, adding to its rarity.

 * Garuda Swamy Temple, Koladevi, Mulbagal, Kolar, Karnataka

Buddhism
Garuda, also referred to as Garula, are golden-winged birds in Buddhist texts. Under the Buddhist concept of saṃsāra, they are one of the Aṣṭagatyaḥ, the eight classes of inhuman beings. In Buddhist art, they are shown as sitting and listening to the sermons of the Buddha. They are enemies of the Nāgas (snakes) and are sometimes depicted with a serpent held between their claws. Like the Hindu art, both zoomorphic (giant eagle-like bird) and partially anthropomorphic (part bird, part human) iconography is common across Buddhist traditions.

In Buddhism, the Garuda (Sanskrit; Pāli: ) are enormous predatory birds with a wingspan of 330 yojanas. They are described as beings with intelligence and social organisation. They are also sometimes known as (Sanskrit; Pāli: ), meaning "well-winged, having good wings". Like the Nāgas, they combine the characteristics of animals and divine beings, and may be considered to be among the lowest of the devas. The Garudas have kings and cities, and at least some of them have the magical power of changing into human form when they wish to have dealings with people. On some occasions Garuda kings have had romances with human women in this form. Their dwellings are in groves of the simbalī, or silk-cotton tree.

Jataka stories describe them to be residents of Nagadipa or Seruma.

The Garuda are enemies to the nāga, a race of intelligent serpent- or dragon-like beings, whom they hunt. The Garudas at one time caught the nāgas by seizing them by their heads; but the nāgas learned that by swallowing large stones, they could make themselves too heavy to be carried by the Garudas, wearing them out and killing them from exhaustion. This secret was divulged to one of the Garudas by the ascetic Karambiya, who taught him how to seize a nāga by the tail and force him to vomit up his stone (Pandara Jātaka, J.518).

The Garudas were among the beings appointed by Śakra to guard Mount Sumeru and the Trayastrimsa heaven from the attacks of the asuras.

In the Maha-samaya Sutta (Digha Nikaya 20), the Buddha is shown making temporary peace between the Nagas and the Garudas.

In the Qing dynasty fiction The Story of Yue Fei (1684), Garuda sits at the head of the Buddha's throne. But when a celestial bat (an embodiment of the Aquarius constellation) flatulates during the Buddha's expounding of the Lotus Sutra, Garuda kills her and is exiled from paradise. He is later reborn as Song dynasty General Yue Fei. The bat is reborn as Lady Wang, wife of the traitor Prime Minister Qin Hui, and is instrumental in formulating the "Eastern Window" plot that leads to Yue's eventual political execution. The Story of Yue Fei plays on the legendary animosity between Garuda and the Nagas when the celestial bird-born Yue Fei defeats a magic serpent who transforms into the unearthly spear he uses throughout his military career. Literary critic C. T. Hsia explains the reason why Qian Cai, the book's author, linked Yue with Garuda is because of the homology in their Chinese names. Yue Fei's courtesy name is Pengju (鵬舉). A Peng (鵬) is a giant mythological bird likened to the Middle Eastern roc. Garuda's Chinese name is Great Peng, the Golden-Winged Illumination King (大鵬金翅明王).

Jainism
The Garuda is a yaksha or guardian for Shantinatha in Jain iconography and mythology. Jain iconography shows Garuda as a human figure with wings and a strand-circle.

As a cultural and national symbol
In India and the rest of Southeast Asia the eagle symbolism is represented by Garuda, a large bird with eagle-like features that appears in both Hindu and Buddhist epic as the vahana (vehicle) of the god Vishnu. Garuda became the national emblem of Thailand and Indonesia; Thailand's Garuda is rendered in a more traditional anthropomorphic style, while that of Indonesia is rendered in heraldic style with traits similar to the real Javan hawk-eagle.

Cambodia
The word Garuda (គ្រុឌ – " Krud ") is literally derived from Sanskrit.

 * In Cambodia, Khmer architects have used the Garuda sculptures as the exquisite ornate to equip on temples, Viharas of wat and many elite houses since ancient time, especially from Khmer empire era until nowadays.
 * Garuda is also mentioned in many legendary tales as the vehicle of Vishnu and its main rival is Naga.

China

 * In China, Garuda (Chinese: 迦楼羅 Jiālóuluó) is considered one of the Eight Legions of Devas and Nāgas. Another Chinese name for Garuda is Great Peng, the Golden-Winged Illumination King (大鵬金翅明王)
 * In some temples in the Central Plains, Garuda is also considered to be a manifestation of Avalokitesvara, the Bodhisattva Guanyin.

India
India primarily uses Garuda as a martial motif:

 * Garud Commando Force is a Special Forces unit of the Indian Air Force, specialising in operations deep behind enemy lines.
 * Brigade of the Guards of the Indian Army uses Garuda as their symbol
 * Elite bodyguards of the medieval Hoysala kings were called Garudas
 * Kerala and Andhra pradesh state road transport corporations use Garuda as the name for a/c mofussil buses
 * Garuda rock, a rocky cliff in Tirumala in Andhra pradesh
 * The insignia of the 13th century Aragalur chief, Magadesan, included Rishabha the sacred bull and the Garud
 * Indian Hindi-language TV serial Dharm Yoddha Garud, based on the life of Garuda
 * ICAI (The Institute of Chartered Accountants of India) uses Garuda as their logo.

As an art form
 * Garudan Thookam, a temple dance primarily found in Central Kerala districts, where dancers dress as Garuda, and dance in praise of Goddess Kali.

Indonesia
Indonesia uses the Garuda in a form called the Garuda Pancasila as its national symbol. The Garuda Pancasila is coloured black or gilded, symbolising both the greatness of the nation and the elang Jawa (Javan hawk-eagle Nisaetus bartelsi). The black color represents nature. There are 17 feathers on each wing, 8 on the lower tail, 19 on the upper tail and 45 on the neck, which together make up the date 17 August 1945, when Indonesia proclaimed its independence. The shield it carries bears the motto Panca Sila, which symbolises self-defense and protection in struggle.

 * Garuda Indonesia - national airline of Indonesia
 * Garuda Contingent - peacekeeping force of the Indonesian National Armed Forces
 * Airlangga University, one of the oldest and leading university in Indonesia uses Garuda on its emblem. The emblem, containing a Garuda in a blue and yellow circle, is called "Garudamukha", and depicts Garuda as the bearer of knowledge, carrying a jug of Amrita, the water of eternity, symbolising eternal knowledge.
 * In Bali and Java, the Garuda has become a cultural symbol. The wooden statue and mask of Garuda is a popular feature in artworks and souvenirs.
 * The tallest Garuda statue, made of copper and brass standing 75 m tall (or 122 metres tall including the pedestal), is located in Garuda Wisnu Kencana complex in Bali.
 * The stylised brush stroke that resembles Garuda appears in the logo of 2011 Southeast Asian Games, held in Palembang and Jakarta, Indonesia.
 * The stylised curves that took the form of Garuda Pancasila appears in the logo of Wonderful Indonesia tourism campaign.

Japan

 * The Karura (迦楼羅) is a divine creature with human torso and birdlike head in Japanese Hindu-Buddhist epics.
 * Kannon Avatar Garuda.jpg name is a transliteration of Garuda (Sanskrit: Garuḍa गरुड; Pāli: Garuḷa) a race of enormously gigantic birds in Hinduism, upon which the Japanese Buddhist version is based. The same creature may go by the name of konjichō (金翅鳥, lit. "gold-winged bird", Skr. suparṇa).

Mongolia

 * The Garuda, known as Khangarid, is the symbol of the capital city of Mongolia, Ulan Bator. According to popular Mongolian belief, Khangarid is the mountain spirit of the Bogd Khan Uul range who became a follower of Buddhist faith. Today he is considered the guardian of that mountain range and a symbol of courage and honesty.
 * Khangarid (Хангарьд), a football (soccer) team in the Mongolia Premier League also named after Garuda.
 * State Garuda (Улсын Гарьд) is a title given to the debut runner up in wrestling tournament during Mongolian National Festival Naadam.

Myanmar

 * In Burmese epics, which was influenced by Hindu-Buddhist beliefs, Garuda is known as Galone, the nemesis of the Nāgas.
 * The Garuda symbolises Sunday in the Burmese zodiac, which is based on the days of the week.

Nepal

 * Garuda is found in Nepalese traditions of Hinduism and Buddhism.
 * The first sounding rocket of Nepal is named Garuda.
 * The central bank, Nepal Rastra Bank uses Garuda in their official logo.
 * Ancient palaces in Kathmandu Valley use statue of Garuda at their gates.

Philippines

 * in Luzon Mythology, Garuda or Galurâ (in Kapampangan) is a winged assistant of Apúng Sinukuan (Mariang Sinukuan), he is represented by a giant eagle and believed to be the bringer of storms.
 * The Maranao people of southern Philippines believe in a race of creatures called garuda who dwell beneath the sea. These beings are winged, have big teeth, and huge talons that can carry six men. They look like eagles when flying in the sky but transform into humans when in their lairs.
 * Artifacts from the Tabon Caves in the island of Palawan ,is an image of Garuda, the bird who is the mount of Vishnu. The discovery of sophisticated Hindu imagery in gold

Suriname

 * In Suriname, there is a radio and TV station called Radio en Televisie Garuda, which broadcasts programming from Indonesia, particularly Java, aimed at the Javanese Surinamese population.

Thailand
Thailand uses the Garuda (ครุฑ, khrut) as its national symbol, known as the Phra Khrut Pha, meaning "Garuda, the vehicle (of Vishnu)," also used as the symbol of royalty. It adorns the banknote of their currency - the Baht - as well.
 * The Kingdom of Siam has had an image of Garuda in its coins at least since the Ayutthaya era.
 * Statues and images of Garuda adorn many Buddhist temples in Thailand. It also has become a cultural symbol of Thailand.
 * The figure of Garuda is also installed as the figurehead or masthead of Thai royal barges.

United States
The Electronic Attack Squadron 134 (VAQ-134) of the United States Navy is named after and uses the Garuda Insignia.

Gallery

 * Insignia

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

title: Garuda


text:
Financial capital

Financial capital (also simply known as capital or equity in finance, accounting and economics) is any economic resource measured in terms of money used by entrepreneurs and businesses to buy what they need to make their products or to provide their services to the sector of the economy upon which their operation is based (e.g. retail, corporate, investment banking). In other words, financial capital is internal retained earnings generated by the entity or funds provided by lenders (and investors) to businesses in order to purchase real capital equipment or services for producing new goods or services.

In contrast, real capital (or economic capital) comprises physical goods that assist in the production of other goods and services (e.g. shovels for gravediggers, sewing machines for tailors, or machinery and tooling for factories).

IFRS concepts of capital maintenance
Financial capital generally refers to saved-up financial wealth, especially that used in order to start or maintain a business. A financial concept of capital is adopted by most entities in preparing their financial reports. Under a financial concept of capital, such as invested money or invested purchasing power, capital is synonymous with the net assets or equity of the entity. Under a physical concept of capital, such as operating capability, capital is regarded as the productive capacity of the entity based on, for example, units of output per day.

Financial capital maintenance can be measured in either nominal monetary units or units of constant purchasing power. Accordingly, there are three concepts of capital maintenance in terms of International Financial Reporting Standards (IFRS):

 * 1) Physical capital maintenance;
 * 2) Financial capital maintenance in nominal monetary units; and
 * 3) Financial capital maintenance in units of constant purchasing power.

Financial capital is provided by lenders for a price: interest. Also see time value of money for a more detailed description of how financial capital may be analyzed. Furthermore, financial capital, is any liquid medium or mechanism that represents wealth, or other styles of capital. It is, however, usually purchasing power in the form of money available for the production or purchasing of goods, etcetera. Capital can also be obtained by producing more than what is immediately required and saving the surplus.

Financial capital can also be in the form of purchasable items such as computers or books that can contribute directly or indirectly to obtaining various other types of capital. Financial capital has been subcategorized by some academics as economic or "productive capital" necessary for operations, signaling capital which signals a company's financial strength to shareholders, and regulatory capital which fulfills capital requirements.

Sources of capital

 * Long term – usually above 7 years
 * Share Capital
 * Mortgage loan
 * Retained Profit
 * Venture capital
 * Debenture
 * Project finance
 * Medium term – usually between 2 and 7 years
 * Term Loans
 * Revenue-based financing
 * Leasing
 * Hire Purchase
 * Short term – usually under 2 years
 * Bank Overdraft
 * Trade credit
 * Deferred Expenses
 * Factoring

Capital market

 * Long-term funds are bought and sold:
 * Shares
 * Debenture
 * Long-term loans, often with a mortgage bond as security
 * Reserve funds
 * Euro Bonds

Money market

 * Financial institutions can use short-term savings to lend out in the form of short-term loans:
 * Commercial paper
 * Credit on open account
 * Bank overdraft
 * Short-term loans
 * Bills of exchange
 * Factoring of debtors

Differences between shares and debentures

 * Shareholders are effectively owners; debenture-holders are creditors.
 * Shareholders may vote at AGMs (Annual General Meetings, alternatively Annual Shareholder Meetings) and be elected as directors; debenture-holders may not vote at AGMs or be elected as directors.
 * Shareholders receive profit in the form of dividends; debenture-holders receive a fixed rate of interest.
 * If there is no profit, the shareholder does not receive a dividend; interest is paid to debenture-holders regardless of whether or not a profit has been made.
 * In case of dissolution the firm's debenture holders are paid first, before shareholders.

Fixed capital
Fixed capital is money firms use to purchase assets that will remain permanently in the business and help it make a profit. Factors determining fixed capital requirements:
 * Nature of business
 * Size of business
 * Stage of development
 * Capital invested by the owners
 * location of that area

Working capital
Firms use working capital to run their business. For example, money that they use to buy stock, pay expenses and finance credit. Factors determining working capital requirements:
 * Size of business
 * Stage of development
 * Time of production
 * Rate of stock turnover ratio
 * Buying and selling terms
 * Seasonal consumption
 * Seasonal product
 * profit level
 * growth and expansion
 * production cycle
 * general nature of business
 * business cycle
 * business policies
 * Debt ratio

Own and borrowed capital
Capital contributed by the owner or entrepreneur of a business, and obtained, for example, by means of savings or inheritance, is known as own capital or equity, whereas that which is granted by another person or institution via debt instruments is called borrowed capital, and this must usually be paid back with interest. The ratio between debt and equity is named leverage. It has to be optimized as a high leverage can bring a higher profit but create solvency risk.

Borrowed capital is capital that the business borrows from institutions or people, and includes debentures:
 * Redeemable debentures
 * Irredeemable debentures
 * Debentures to bearer
 * Ordinary debentures
 * bonds
 * deposits
 * loans

Own capital is private capital that owners of a business (shareholders and partners, for example) provide, sometimes called owners equity. The ownership interest is typically represented in preferred shares, and may be of various types, for example:
 * Preference shares/hybrid source of finance
 * Ordinary preference shares
 * Cumulative preference shares
 * Participating preference shares
 * Ordinary shares
 * Bonus shares
 * Founders' shares

These typically have preference over the common shares. This means the payments made to the shareholders are first paid to the preference shareholder(s) and then to the equity shareholders.

Instruments
A contract regarding any combination of capital assets is called a financial instrument, and may serve as a
 * medium of exchange,
 * standard of deferred payment,
 * unit of account, or
 * store of value.

Most indigenous forms of money (wampum, shells, tally sticks and such) and the modern fiat money are only a "symbolic" storage of value and not a real storage of value like commodity money.

Valuation
Normally, a financial instrument is priced accordingly to the perception by capital market players of its expected return and risk. Unit of account functions may come into question if valuations of complex financial instruments vary drastically based on timing. The "book value", "mark-to-market" and "mark-to-future" conventions are three different approaches to reconciling financial capital value units of account.

Issuing and trading
Like money, financial instruments may be "backed" by state military fiat, credit (i.e. social capital held by banks and their depositors), or precious metals resources. Governments generally closely control the supply of it and usually require some "reserve" be held by institutions granting credit. Trading between various national currency instruments is conducted on a money market. Such trading reveals differences in probability of debt collection or store of value function of that currency, as assigned by traders.

When in forms other than money, financial capital may be traded on bond markets or reinsurance markets with varying degrees of trust in the social capital (not just credits) of bond-issuers, insurers, and others who issue and trade in financial instruments. When payment is deferred on any such instrument, typically an interest rate is higher than the standard interest rates paid by banks, or charged by the central bank on its money. Often such instruments are called fixed-income instruments if they have reliable payment schedules associated with the uniform rate of interest. A variable-rate instrument, such as many consumer mortgages, will reflect the standard rate for deferred payment set by the central bank prime rate, increasing it by some fixed percentage. Other instruments, such as citizen entitlements, e.g. "U.S. Social Security", or other pensions, may be indexed to the rate of inflation, to provide a reliable value stream.

Typically commodity markets depend on politics that affect international trade, e.g. boycotts and embargoes, or factors that influence natural capital, e.g. weather that affects food crops. Meanwhile, stock markets are more influenced by trust in corporate leaders, i.e. individual capital, by consumers, i.e. social capital or "brand capital" (in some analyses), and internal organizational efficiency, i.e. instructional capital and infrastructural capital. Some enterprises issue instruments to specifically track one limited division or brand. "Financial futures", "Short selling" and "financial options" apply to these markets, and are typically pure financial bets on outcomes, rather than being a direct representation of any underlying asset.

Broadening the notion
The relationship between financial capital, money, and all other styles of capital, especially human capital or labor, is assumed in central bank policy and regulations regarding instruments as above. Such relationships and policies are characterized by a political economy – feudalist, socialist, capitalist, green, anarchist or otherwise. In effect, the means of money supply and other regulations on financial capital represent the economic sense of the value system of the society itself, as they determine the allocation of labor in that society.

So, for instance, rules for increasing or reducing the money supply based on perceived inflation, or on measuring well-being, reflect some such values, reflect the importance of using (all forms of) financial capital as a stable store of value. If this is very important, inflation control is key - any amount of money inflation reduces the value of financial capital with respect to all other types.

If, however, the medium of exchange function is more critical, new money may be more freely issued regardless of impact on either inflation or well-being.

Economic role
Socialism, capitalism, feudalism, anarchism, and other civic theories take markedly different views of the role of financial capital in social life, and propose various political restrictions to deal with that.

Financial capitalism is the production of profit from the manipulation of financial capital. It is held in contrast to industrial capitalism, where profit is made from the manufacture of goods.

Marxist perspectives
It is common in Marxist theory to refer to the role of finance capital as the determining and ruling class interest in capitalist society, particularly in the latter stages.

title: Financial capital


text:
Dijkstra's algorithm

Dijkstra's algorithm is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, road networks. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later.

Dijkstra's algorithm finds the shortest path from a given source node to every other node. It can also be used to find the shortest path to a specific destination node, by terminating the algorithm once the shortest path to the destination node is known. For example, if the nodes of the graph represent cities, and the costs of edges represent the average distances between pairs of cities connected by a direct road, then Dijkstra's algorithm can be used to find the shortest route between one city and all other cities. A common application of shortest path algorithms is network routing protocols, most notably IS-IS (Intermediate System to Intermediate System) and OSPF (Open Shortest Path First). It is also employed as a subroutine in other algorithms such as Johnson's algorithm.

The algorithm uses a min-priority queue data structure for selecting the shortest paths known so far. Before more advanced priority queue structures were discovered, Dijkstra's original algorithm ran in $$\Theta(|V|^2)$$ time, where $$|V|$$ is the number of nodes. The idea of this algorithm is also given in. proposed using a Fibonacci heap priority queue to optimize the running time complexity to $$\Theta(|E|+|V|\log|V|)$$. This is asymptotically the fastest known single-source shortest-path algorithm for arbitrary directed graphs with unbounded non-negative weights. However, specialized cases (such as bounded/integer weights, directed acyclic graphs etc.) can indeed be improved further, as detailed in Specialized variants. Additionally, if preprocessing is allowed, algorithms such as contraction hierarchies can be up to seven orders of magnitude faster.

Dijkstra's algorithm is commonly used on graphs where the edge weights are positive integers or real numbers. It can be generalized to any graph where the edge weights are partially ordered, provided the subsequent labels (a subsequent label is produced when traversing an edge) are monotonically non-decreasing.

In many fields, particularly artificial intelligence, Dijkstra's algorithm or a variant of it is known as uniform cost search and formulated as an instance of the more general idea of best-first search.

History
"What is the shortest way to travel from Rotterdam to Groningen, in general: from given city to given city. It is the algorithm for the shortest path, which I designed in about twenty minutes. One morning I was shopping in Amsterdam with my young fiancée, and tired, we sat down on the café terrace to drink a cup of coffee and I was just thinking about whether I could do this, and I then designed the algorithm for the shortest path. As I said, it was a twenty-minute invention. In fact, it was published in '59, three years later. The publication is still readable, it is, in fact, quite nice. One of the reasons that it is so nice was that I designed it without pencil and paper. I learned later that one of the advantages of designing without pencil and paper is that you are almost forced to avoid all avoidable complexities. Eventually, that algorithm became to my great amazement, one of the cornerstones of my fame." Dijkstra thought about the shortest path problem when working at the Mathematical Center in Amsterdam in 1956 as a programmer to demonstrate the capabilities of a new computer called ARMAC. His objective was to choose both a problem and a solution (that would be produced by computer) that non-computing people could understand. He designed the shortest path algorithm and later implemented it for ARMAC for a slightly simplified transportation map of 64 cities in the Netherlands (64, so that 6 bits would be sufficient to encode the city number). A year later, he came across another problem from hardware engineers working on the institute's next computer: minimize the amount of wire needed to connect the pins on the back panel of the machine. As a solution, he re-discovered the algorithm known as Prim's minimal spanning tree algorithm (known earlier to Jarník, and also rediscovered by Prim). Dijkstra published the algorithm in 1959, two years after Prim and 29 years after Jarník.

Algorithm

Let us choose a starting node, and let the distance of node N be the distance from the starting node to N. Dijkstra's algorithm will initially start with infinite distances and will try to improve them step by step.

 * 1) Mark all nodes as unvisited. Create a set of all the unvisited nodes called the unvisited set.
 * 2) Assign to every node a distance from start value: for the starting node, it is zero, and for all other nodes, it is infinity, since initially no path is known to these nodes. During execution of the algorithm, the distance of a node N is the length of the shortest path discovered so far between the starting node and N.
 * 3) From the unvisited set, select the current node to be the one with the smallest finite distance; initially, this will be the starting node, which has distance zero. If the unvisited set is empty, or contains only nodes with infinite distance (which are unreachable), then the algorithm terminates by going to step 6. If we are only concerned about the path to a target node, we may terminate here if the current node is the target node. Otherwise, we can continue to find the shortest paths to all reachable nodes.
 * 4) For the current node, consider all of its unvisited neighbors and update their distances through the current node; compare the newly calculated distance to the one currently assigned to the neighbor and assign it the smaller one. For example, if the current node A is marked with a distance of 6, and the edge connecting it with its neighbor B has length 2, then the distance to B through A is 6 + 2 = 8. If B was previously marked with a distance greater than 8, then update it to 8 (the path to B through A is shorter). Otherwise, keep its current distance (the path to B through A is not the shortest).
 * 5) When we are done considering all of the unvisited neighbors of the current node, mark the current node as visited and remove it from the unvisited set. This is so that a visited node is never checked again, which is correct because the distance recorded on the current node is minimal (as ensured in step 3), and thus final. Go back to step 3.
 * 6)  Once the loop exits (steps 3–5), every visited node will contain its shortest distance from the starting node.

Description
Suppose you would like to find the shortest path between two intersections on a city map: a starting point and a destination. Dijkstra's algorithm initially marks the distance (from the starting point) to every other intersection on the map with infinity. This is done not to imply that there is an infinite distance, but to note that those intersections have not been visited yet. Some variants of this method leave the intersections' distances unlabeled. Now select the current intersection at each iteration. For the first iteration, the current intersection will be the starting point, and the distance to it (the intersection's label) will be zero. For subsequent iterations (after the first), the current intersection will be a closest unvisited intersection to the starting point (this will be easy to find).

From the current intersection, update the distance to every unvisited intersection that is directly connected to it. This is done by determining the sum of the distance between an unvisited intersection and the value of the current intersection and then relabeling the unvisited intersection with this value (the sum) if it is less than the unvisited intersection's current value. In effect, the intersection is relabeled if the path to it through the current intersection is shorter than the previously known paths. To facilitate shortest path identification, in pencil, mark the road with an arrow pointing to the relabeled intersection if you label/relabel it, and erase all others pointing to it. After you have updated the distances to each neighboring intersection, mark the current intersection as visited and select an unvisited intersection with minimal distance (from the starting point) – or the lowest label—as the current intersection. Intersections marked as visited are labeled with the shortest path from the starting point to it and will not be revisited or returned to.

Continue this process of updating the neighboring intersections with the shortest distances, marking the current intersection as visited, and moving onto a closest unvisited intersection until you have marked the destination as visited. Once you have marked the destination as visited (as is the case with any visited intersection), you have determined the shortest path to it from the starting point and can trace your way back following the arrows in reverse. In the algorithm's implementations, this is usually done (after the algorithm has reached the destination node) by following the nodes' parents from the destination node up to the starting node; that's why we also keep track of each node's parent.

This algorithm makes no attempt of direct "exploration" towards the destination as one might expect. Rather, the sole consideration in determining the next "current" intersection is its distance from the starting point. This algorithm therefore expands outward from the starting point, interactively considering every node that is closer in terms of shortest path distance until it reaches the destination. When understood in this way, it is clear how the algorithm necessarily finds the shortest path. However, it may also reveal one of the algorithm's weaknesses: its relative slowness in some topologies.

Pseudocode
In the following pseudocode, dist is an array that contains the current distances from the source to other vertices, i.e. dist[ u ] is the current distance from the source to the vertex u. The prev array contains pointers to previous-hop nodes on the shortest path from source to the given vertex (equivalently, it is the next-hop on the path from the given vertex to the source). The code u ← vertex in Q with min dist[u], searches for the vertex u in the vertex set Q that has the least dist[ u ] value. Graph.Edges( u, v ) returns the length of the edge joining (i.e. the distance between) the two neighbor-nodes u and v. The variable alt on line 14 is the length of the path from the source node to the neighbor node v if it were to go through u. If this path is shorter than the current shortest path recorded for v, then the distance of v is updated to alt.

1 function Dijkstra(Graph, source): 2      3      for each vertex v in Graph.Vertices: 4         dist[v] ← INFINITY 5         prev[v] ← UNDEFINED 6         add v to Q 7     dist[source] ← 0 8      9      while Q is not empty: 10         u ← vertex in Q with minimum dist[u] 11         remove u from Q 12         13          for each neighbor v of u still in Q: 14             alt ← dist[u] + Graph.Edges(u, v) 15             if alt < dist[v]: 16                 dist[v] ← alt 17                 prev[v] ← u 18 19     return dist[], prev[]

If we are only interested in a shortest path between vertices source and target, we can terminate the search after line 10 if. Now we can read the shortest path from source to target by reverse iteration:

1 S ← empty sequence 2 u ← target 3 if prev[u] is defined or u = source:          // Do something only if the vertex is reachable 4     while u is defined:                       // Construct the shortest path with a stack S 5         insert u at the beginning of S        // Push the vertex onto the stack 6         u ← prev[u]                           // Traverse from target to source

Now sequence S is the list of vertices constituting one of the shortest paths from source to target, or the empty sequence if no path exists.

A more general problem would be to find all the shortest paths between source and target (there might be several different ones of the same length). Then instead of storing only a single node in each entry of prev[] we would store all nodes satisfying the relaxation condition. For example, if both r and source connect to target and both of them lie on different shortest paths through target (because the edge cost is the same in both cases), then we would add both r and source to prev[ target ]. When the algorithm completes, prev[] data structure will actually describe a graph that is a subset of the original graph with some edges removed. Its key property will be that if the algorithm was run with some starting node, then every path from that node to any other node in the new graph will be the shortest path between those nodes in the original graph, and all paths of that length from the original graph will be present in the new graph. Then to actually find all these shortest paths between two given nodes we would use a path finding algorithm on the new graph, such as depth-first search.

Using a priority queue
A min-priority queue is an abstract data type that provides 3 basic operations: add_with_priority, decrease_priority and extract_min. As mentioned earlier, using such a data structure can lead to faster computing times than using a basic queue. Notably, Fibonacci heap or Brodal queue offer optimal implementations for those 3 operations. As the algorithm is slightly different in appearance, it is mentioned here, in pseudocode as well:

1  function Dijkstra(Graph, source): 2      create vertex priority queue Q 3 4      dist[source] ← 0                          // Initialization 5      Q.add_with_priority(source, 0)            // associated priority equals dist[·] 6 7      for each vertex v in Graph.Vertices: 8          if v ≠ source 9              prev[v] ← UNDEFINED               // Predecessor of v 10             dist[v] ← INFINITY                // Unknown distance from source to v 11             Q.add_with_priority(v, INFINITY) 12 13 14     while Q is not empty:                     // The main loop 15         u ← Q.extract_min                   // Remove and return best vertex 16         for each neighbor v of u:             // Go through all v neighbors of u 17             alt ← dist[u] + Graph.Edges(u, v) 18             if alt < dist[v]: 19                 prev[v] ← u 20                 dist[v] ← alt 21                 Q.decrease_priority(v, alt) 22 23     return dist, prev

Instead of filling the priority queue with all nodes in the initialization phase, it is also possible to initialize it to contain only source; then, inside the  block, the decrease_priority becomes an add_with_priority operation if the node is not already in the queue.

Yet another alternative is to add nodes unconditionally to the priority queue and to instead check after extraction that it isn't revisiting, or that no shorter connection was found yet in the   block. This can be done by additionally extracting the associated priority  from the queue and only processing further   inside the   loop.

These alternatives can use entirely array-based priority queues without decrease-key functionality, which have been found to achieve even faster computing times in practice. However, the difference in performance was found to be narrower for denser graphs.

Proof of correctness
To prove the correctness of Dijkstra's algorithm, we proceed by mathematical induction on the number of visited nodes.

Invariant hypothesis: For each visited node v, dist[v] is the shortest distance from source to v, and for each unvisited node u, dist[u] is the shortest distance from source to u when traveling via visited nodes only, or infinity if no such path exists. (Note: we do not assume dist[u] is the actual shortest distance for unvisited nodes, while dist[v] is the actual shortest distance)

Base case:

The base case is when there is just one visited node, source. Its distance is defined to be zero, which is the shortest distance, since negative weights are not allowed. Hence, the hypothesis holds.

Inductive step:

Assume the hypothesis holds for $$k$$ visited nodes. We wish to show it holds for $$k+1$$ nodes. Let u be the next visited node according to the algorithm, i.e. the node with minimum dist[u]. We claim that dist[u] is the shortest distance from source to u.

To prove this claim, we proceed by contradiction. If there were a shorter path, then this shorter path either contains another unvisited node or not.

 * In the former case, let w be the first unvisited node on this shorter path. By the induction hypothesis, the shortest paths from source to u and w through visited nodes only have costs dist[u] and dist[w] respectively. This means the cost of going from source to u via w has the cost of at least dist[w] + the minimal cost of going from w to u. As the edge costs are positive, the minimal cost of going from w to u is a positive number. However, dist[u] is at most dist[w] because otherwise w would have been picked by the priority queue instead of v. This is a contradiction, since it has already been established that dist[w] + a positive number < dist[u].

 * In the latter case, let w be the last but one node on the shortest path. That means dist[w] + Graph.Edges[w,u] < dist[u]. That is a contradiction because by the time w is visited, it should have set dist[u] to at most dist[w] + Graph.Edges[w,u].

For all other visited nodes v, the dist[v] is already known to be the shortest distance from source already, because of the inductive hypothesis, and these values are unchanged.

After processing u, it will still be true that for each unvisited node w, dist[w] will be the shortest distance from source to w using visited nodes only. If there were a shorter path that did not use u, we would have found it previously, and if there were a shorter path using u we would have updated it when processing u.

After all nodes are visited, the shortest path from source to any node v consists only of visited nodes. Therefore, dist[v] is the shortest distance.

Running time
Bounds of the running time of Dijkstra's algorithm on a graph with edges $E$ and vertices $V$ can be expressed as a function of the number of edges, denoted $$|E|$$, and the number of vertices, denoted $$|V|$$, using big-O notation. The complexity bound depends mainly on the data structure used to represent the set $Q$. In the following, upper bounds can be simplified because $$|E|$$ is $$O(|V|^2)$$ for any simple graph, but that simplification disregards the fact that in some problems, other upper bounds on $$|E|$$ may hold.

For any data structure for the vertex set $Q$, the running time is in
 * $$\Theta(|E| \cdot T_\mathrm{dk} + |V| \cdot T_\mathrm{em}),$$

where $$T_\mathrm{dk}$$ and $$T_\mathrm{em}$$ are the complexities of the decrease-key and extract-minimum operations in $Q$, respectively.

The simplest version of Dijkstra's algorithm stores the vertex set $Q$ as a linked list or array, and edges as an adjacency list or matrix. In this case, extract-minimum is simply a linear search through all vertices in $Q$, so the running time is $$\Theta(|E| + |V|^2) = \Theta(|V|^2)$$.

For sparse graphs, that is, graphs with far fewer than $$|V|^2$$ edges, Dijkstra's algorithm can be implemented more efficiently by storing the graph in the form of adjacency lists and using a self-balancing binary search tree, binary heap, pairing heap, or Fibonacci heap as a priority queue to implement extracting minimum efficiently. To perform decrease-key steps in a binary heap efficiently, it is necessary to use an auxiliary data structure that maps each vertex to its position in the heap, and to keep this structure up to date as the priority queue $Q$ changes. With a self-balancing binary search tree or binary heap, the algorithm requires
 * $$\Theta((|E| + |V|) \log |V|)$$

time in the worst case; for connected graphs this time bound can be simplified to $$\Theta( | E | \log | V | )$$. The Fibonacci heap improves this to
 * $$\Theta(|E| + |V| \log|V|).$$

When using binary heaps, the average case time complexity is lower than the worst-case: assuming edge costs are drawn independently from a common probability distribution, the expected number of decrease-key operations is bounded by $$\Theta(|V| \log (|E|/|V|))$$, giving a total running time of
 * $$O\left(|E| + |V| \log \frac{|E|}{|V|} \log |V|\right).$$

Practical optimizations and infinite graphs
In common presentations of Dijkstra's algorithm, initially all nodes are entered into the priority queue. This is, however, not necessary: the algorithm can start with a priority queue that contains only one item, and insert new items as they are discovered (instead of doing a decrease-key, check whether the key is in the queue; if it is, decrease its key, otherwise insert it). This variant has the same worst-case bounds as the common variant, but maintains a smaller priority queue in practice, speeding up the queue operations.

Moreover, not inserting all nodes in a graph makes it possible to extend the algorithm to find the shortest path from a single source to the closest of a set of target nodes on infinite graphs or those too large to represent in memory. The resulting algorithm is called uniform-cost search (UCS) in the artificial intelligence literature and can be expressed in pseudocode as

procedure uniform_cost_search(start) is node ← start frontier ← priority queue containing node only expanded ← empty set do if frontier is empty then return failure node ← frontier.pop if node is a goal state then return solution(node) expanded.add(node) for each of node's neighbors n do if n is not in expanded and not in frontier then frontier.add(n) else if n is in frontier with higher cost replace existing node with n

The complexity of this algorithm can be expressed in an alternative way for very large graphs: when $C^{*}$ is the length of the shortest path from the start node to any node satisfying the "goal" predicate, each edge has cost at least $ε$, and the number of neighbors per node is bounded by $b$, then the algorithm's worst-case time and space complexity are both in $O(b^{1+⌊C^{*} 1/undefined ε⌋})$.

Further optimizations of Dijkstra's algorithm for the single-target case include bidirectional variants, goal-directed variants such as the A* algorithm (see ), graph pruning to determine which nodes are likely to form the middle segment of shortest paths (reach-based routing), and hierarchical decompositions of the input graph that reduce $s–t$ routing to connecting $s$ and $t$ to their respective "transit nodes" followed by shortest-path computation between these transit nodes using a "highway". Combinations of such techniques may be needed for optimal practical performance on specific problems.

Specialized variants
When arc weights are small integers (bounded by a parameter $$C$$), specialized queues which take advantage of this fact can be used to speed up Dijkstra's algorithm. The first algorithm of this type was Dial's algorithm for graphs with positive integer edge weights, which uses a bucket queue to obtain a running time $$O(|E|+|V|C)$$. The use of a Van Emde Boas tree as the priority queue brings the complexity to $$O(|E|\log\log C)$$. Another interesting variant based on a combination of a new radix heap and the well-known Fibonacci heap runs in time $$O(|E|+|V|\sqrt{\log C})$$. Finally, the best algorithms in this special case are as follows. The algorithm given by runs in $$O(|E|\log\log|V|)$$ time and the algorithm given by  runs in $$O(|E| + |V|\min\{(\log|V|)^{1/3+\varepsilon}, (\log C)^{1/4+\varepsilon}\})$$ time.

Related problems and algorithms
The functionality of Dijkstra's original algorithm can be extended with a variety of modifications. For example, sometimes it is desirable to present solutions which are less than mathematically optimal. To obtain a ranked list of less-than-optimal solutions, the optimal solution is first calculated. A single edge appearing in the optimal solution is removed from the graph, and the optimum solution to this new graph is calculated. Each edge of the original solution is suppressed in turn and a new shortest-path calculated. The secondary solutions are then ranked and presented after the first optimal solution.

Dijkstra's algorithm is usually the working principle behind link-state routing protocols, OSPF and IS-IS being the most common ones.

Unlike Dijkstra's algorithm, the Bellman–Ford algorithm can be used on graphs with negative edge weights, as long as the graph contains no negative cycle reachable from the source vertex s. The presence of such cycles means there is no shortest path, since the total weight becomes lower each time the cycle is traversed. (This statement assumes that a "path" is allowed to repeat vertices. In graph theory that is normally not allowed. In theoretical computer science it often is allowed.) It is possible to adapt Dijkstra's algorithm to handle negative weight edges by combining it with the Bellman-Ford algorithm (to remove negative edges and detect negative cycles); such an algorithm is called Johnson's algorithm.

The A* algorithm is a generalization of Dijkstra's algorithm that cuts down on the size of the subgraph that must be explored, if additional information is available that provides a lower bound on the "distance" to the target.

The process that underlies Dijkstra's algorithm is similar to the greedy process used in Prim's algorithm. Prim's purpose is to find a minimum spanning tree that connects all nodes in the graph; Dijkstra is concerned with only two nodes. Prim's does not evaluate the total weight of the path from the starting node, only the individual edges.

Breadth-first search can be viewed as a special-case of Dijkstra's algorithm on unweighted graphs, where the priority queue degenerates into a FIFO queue.

The fast marching method can be viewed as a continuous version of Dijkstra's algorithm which computes the geodesic distance on a triangle mesh.

Dynamic programming perspective
From a dynamic programming point of view, Dijkstra's algorithm is a successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by the Reaching method.

In fact, Dijkstra's explanation of the logic behind the algorithm, namely "Problem 2. Find the path of minimum total length between two given nodes $P$ and $Q$.

We use the fact that, if $R$ is a node on the minimal path from $P$ to $Q$, knowledge of the latter implies the knowledge of the minimal path from $P$ to $R$."

is a paraphrasing of Bellman's Principle of Optimality in the context of the shortest path problem.

title: Dijkstra's algorithm