An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming, in which the objective function and the constraints are linear. Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems. If some decision variables are not discrete the problem is known as a mixed-integer programming problem. An integer linear program in canonical form is expressed as: maximize c T x subject to A x ≤ b, x ≥ 0, x ∈ Z n, an ILP in standard form is expressed as maximize c T x subject to A x + s = b, s ≥ 0, x ≥ 0, x ∈ Z n, where c, b are vectors and A is a matrix, where all entries are integers; as with linear programs, ILPs not in standard form can be converted to standard form by eliminating inequalities, introducing slack variables and replacing variables that are not sign-constrained with the difference of two sign-constrained variables The plot on the right shows the following problem.
Max y − x + y ≤ 1 3 x + 2 y ≤ 12 2 x + 3 y ≤ 12 x, y ≥ 0 x, y ∈ Z The feasible integer points are shown in red, the red dashed lines indicate their convex hull, the smallest polyhedron that contains all of these points. The blue lines together with the coordinate axes define the polyhedron of the LP relaxation, given by the inequalities without the integrality constraint; the goal of the optimization is to move the black dotted line as far upward while still touching the polyhedron. The optimal solutions of the integer problem are the points and which both have an objective value of 2; the unique optimum of the relaxation is with objective value of 2.8. Note that if the solution of the relaxation is rounded to the nearest integers, it is not feasible for the ILP; the following is a reduction from minimum vertex cover to integer programming that will serve as the proof of NP-hardness. Let G = be an undirected graph. Define a linear program as follows: min ∑ v ∈ V y v y v + y u ≥ 1 ∀ u v ∈ E y v ≥ 0 ∀ v ∈ V y v ∈ Z ∀ v ∈ V Given that the constraints limit y v to either 0 or 1, any feasible solution to the integer program is a subset of vertices.
The first constraint implies. Therefore, the solution describes a vertex cover. Additionally given some verte
Americans are nationals and citizens of the United States of America. Although nationals and citizens make up the majority of Americans, some dual citizens and permanent residents may claim American nationality; the United States is home to people of many different ethnic origins. As a result, American culture and law does not equate nationality with race or ethnicity, but with citizenship and permanent allegiance. English-speakers, speakers of many other languages use the term "American" to mean people of the United States; the word "American" can refer to people from the Americas in general. The majority of Americans or their ancestors immigrated to America or are descended from people who were brought as slaves within the past five centuries, with the exception of the Native American population and people from Hawaii, Puerto Rico and the Philippine Islands, who became American through expansion of the country in the 19th century, additionally America expanded into American Samoa, the U. S. Virgin Islands and Northern Mariana Islands in the 20th century.
Despite its multi-ethnic composition, the culture of the United States held in common by most Americans can be referred to as mainstream American culture, a Western culture derived from the traditions of Northern and Western European colonists and immigrants. It includes influences of African-American culture. Westward expansion integrated the Creoles and Cajuns of Louisiana and the Hispanos of the Southwest and brought close contact with the culture of Mexico. Large-scale immigration in the late 19th and early 20th centuries from Southern and Eastern Europe introduced a variety of elements. Immigration from Asia and Latin America has had impact. A cultural melting pot, or pluralistic salad bowl, describes the way in which generations of Americans have celebrated and exchanged distinctive cultural characteristics. In addition to the United States and people of American descent can be found internationally; as many as seven million Americans are estimated to be living abroad, make up the American diaspora.
The United States of America is a diverse country and ethnically. Six races are recognized by the U. S. Census Bureau for statistical purposes: White, American Indian and Alaska Native, Black or African American, Native Hawaiian and Other Pacific Islander, people of two or more races. "Some other race" is an option in the census and other surveys. The United States Census Bureau classifies Americans as "Hispanic or Latino" and "Not Hispanic or Latino", which identifies Hispanic and Latino Americans as a racially diverse ethnicity that comprises the largest minority group in the nation. People of European descent, or White Americans, constitute the majority of the 308 million people living in the United States, with 72.4% of the population in the 2010 United States Census. They are considered people who trace their ancestry to the original peoples of Europe, the Middle East, North Africa. Of those reporting to be White American, 7,487,133 reported to be Multiracial. Additionally, there are Latinos.
Non-Hispanic Whites are the majority in 46 states. There are four minority-majority states: California, New Mexico, Hawaii. In addition, the District of Columbia has a non-white majority; the state with the highest percentage of non-Hispanic White Americans is Maine. The largest continental ancestral group of Americans are that of Europeans who have origins in any of the original peoples of Europe; this includes people via African, North American, Central American or South American and Oceanian nations that have a large European descended population. The Spanish were some of the first Europeans to establish a continuous presence in what is now the United States in 1565. Martín de Argüelles born 1566, San Agustín, La Florida a part of New Spain, was the first person of European descent born in what is now the United States. Twenty-one years Virginia Dare born 1587 Roanoke Island in present-day North Carolina, was the first child born in the original Thirteen Colonies to English parents. In the 2017 American Community Survey, German Americans, Irish Americans, English Americans and Italian Americans were the four largest self-reported European ancestry groups in the United States forming 35.1% of the total population.
However, the English Americans and British Americans demography is considered a serious under-count as they tend to self-report and identify as "Americans" due to the length of time they have inhabited America. This is over-represented in the Upland South, a region, settled by the British. Overall, as the largest group, European Americans have the lowest poverty rate and the second highest educational attainment levels, median household income, median personal income of any racial demographic in the nation. According to the American Jewish Archives and the Arab American National Museum, some of the first Middle Easterners and North Africans arrived in the Americas between the late 15th and mid-16th centuries. Many were fleeing ethnic or ethnoreligious persecution during the Spanish Inquisition, a few were taken to the Americas as slaves. In 2014, The United States Census Bureau began finalizing the ethnic classification of MENA populations. According to the Arab American Institute, Arab
Hyde Park Academy High School
Hyde Park Academy High School is a public 4–year high school located in the Woodlawn neighborhood on the south side of Chicago, United States. Opened in 1863, Hyde Park is located in the Woodlawn neighborhood south of the University of Chicago. Hyde Park is operated by the Chicago Public Schools district. In 2012, Hyde Park became the fourth Chicago public high school to become an International Baccalaureate school; the school was established by the Chicago Board of Education as Hyde Park High School in 1863. The school was housed in several locations from its opening until 1886 when the board of education dedicated a three-floor school building located at Kimbark Avenue and 56th Streets in Hyde Park neighborhood. Hyde Park remained at the location from 1889 until it was decided that a new location was needed to house the school's growing population in 1910. Chicago officials decided on a site bordered by Stony Island Avenue to the east, Harper Avenue to the west, 62nd street to the north and 63rd street to the south.
Hyde Park moved to its present site at 6220 South Stony Island Avenue in July 1914. The school underwent several major renovations during the 20th century. From the school's beginning, Hyde Park's student body was predominantly White. Whites were the highest populated in the area; the school's demographics began to change during the mid–1940s after the government pushed for integration of schools and neighborhoods. Over a span of twenty years beginning in 1947, the white population at the school began to decline due to whites being opposed to accepting low income African–Americans to attend the school. In January 1966, The Chicago board of education was charged with violation federal and state laws when they approved a plan to modernize Hyde Park and build a new high school that would serve Hyde Park's current white student body attracting other white students located next to the school; the plan was in violation of the United States Civil Rights Act of 1964, the plan was never carried out. By 1967, the school was predominantly African–American by a total of 97%.
Although the demographics among students had changed, the teaching staff remained the same. The opening of Kenwood High School in 1969 resulted in white enrollment at the school becoming negligible to non-existent. In April 1973, the school became a magnet school and its named changed to Hyde Park Career Academy, establishing the school as a "career academy"; the push to change the school's name and curriculum was made by principal Weldon Beverly Jr.. Hyde Park began to offer International Baccalaureate classes to its students during the 2000–2001 school year. In 2004, Chicago Public Schools CEO Arne Duncan and Chicago mayor Richard M. Daley introduced the Renaissance 2010 program. Under this program, Hyde Park was forced to accept more than 300 more area–students than any other high school in the city during a two–year period; the school name changed to Hyde Park Academy High School in 2012 when the school became International Baccalaureate. On November 26, 1957, Shortly after 2:00 p.m.. At the time, this had been the school's fourth time receiving a bomb threat within a one-month period.
On December 8, 1988, three teenage males were caught trespassing in the school at around 2:15 p.m.. On February 15, 2013, President Barack Obama delivered a televised speech in the school's gymnasium addressing the issue of gun violence in Chicago. Hyde Park competes in the Chicago Public League and is a member of the Illinois High School Association. Hyde Park sport teams are known as Thunderbirds. Hyde Park boys' basketball team have been regional champions four times; the boys' track and field placed first in the state in 1903 and 1929. The girls' basketball team won regional titles three consecutive seasons. Hyde Park Career Academy School Website
Belgium the Kingdom of Belgium, is a country in Western Europe. It is bordered by the Netherlands to the north, Germany to the east, Luxembourg to the southeast, France to the southwest, the North Sea to the northwest, it has a population of more than 11.4 million. The capital and largest city is Brussels; the sovereign state is a federal constitutional monarchy with a parliamentary system. Its institutional organisation is structured on both regional and linguistic grounds, it is divided into three autonomous regions: Flanders in the north, Wallonia in the south, the Brussels-Capital Region. Brussels is the smallest and most densely populated region, as well as the richest region in terms of GDP per capita. Belgium is home to two main linguistic groups or Communities: the Dutch-speaking Flemish Community, which constitutes about 59 percent of the population, the French-speaking Community, which comprises about 40 percent of all Belgians. A small German-speaking Community, numbering around one percent, exists in the East Cantons.
The Brussels-Capital Region is bilingual, although French is the dominant language. Belgium's linguistic diversity and related political conflicts are reflected in its political history and complex system of governance, made up of six different governments. Belgium was part of an area known as the Low Countries, a somewhat larger region than the current Benelux group of states that included parts of northern France and western Germany, its name is derived after the Roman province of Gallia Belgica. From the end of the Middle Ages until the 17th century, the area of Belgium was a prosperous and cosmopolitan centre of commerce and culture. Between the 16th and early 19th centuries, Belgium served as the battleground between many European powers, earning the moniker the "Battlefield of Europe", a reputation strengthened by both world wars; the country emerged in 1830 following the Belgian Revolution. Belgium participated in the Industrial Revolution and, during the course of the 20th century, possessed a number of colonies in Africa.
The second half of the 20th century was marked by rising tensions between the Dutch-speaking and the French-speaking citizens fueled by differences in language and culture and the unequal economic development of Flanders and Wallonia. This continuing antagonism has led to several far-reaching reforms, resulting in a transition from a unitary to a federal arrangement during the period from 1970 to 1993. Despite the reforms, tensions between the groups have remained, if not increased. Unemployment in Wallonia is more than double that of Flanders. Belgium is one of the six founding countries of the European Union and hosts the official seats of the European Commission, the Council of the European Union, the European Council, as well as a seat of the European Parliament in the country's capital, Brussels. Belgium is a founding member of the Eurozone, NATO, OECD, WTO, a part of the trilateral Benelux Union and the Schengen Area. Brussels hosts several of the EU's official seats as well as the headquarters of many major international organizations such as NATO.
Belgium is a developed country, with an advanced high-income economy. It has high standards of living, quality of life, education, is categorized as "very high" in the Human Development Index, it ranks as one of the safest or most peaceful countries in the world. The name "Belgium" is derived from Gallia Belgica, a Roman province in the northernmost part of Gaul that before Roman invasion in 100 BC, was inhabited by the Belgae, a mix of Celtic and Germanic peoples. A gradual immigration by Germanic Frankish tribes during the 5th century brought the area under the rule of the Merovingian kings. A gradual shift of power during the 8th century led the kingdom of the Franks to evolve into the Carolingian Empire; the Treaty of Verdun in 843 divided the region into Middle and West Francia and therefore into a set of more or less independent fiefdoms which, during the Middle Ages, were vassals either of the King of France or of the Holy Roman Emperor. Many of these fiefdoms were united in the Burgundian Netherlands of the 15th centuries.
Emperor Charles V extended the personal union of the Seventeen Provinces in the 1540s, making it far more than a personal union by the Pragmatic Sanction of 1549 and increased his influence over the Prince-Bishopric of Liège. The Eighty Years' War divided the Low Countries into the northern United Provinces and the Southern Netherlands; the latter were ruled successively by the Spanish and the Austrian Habsburgs and comprised most of modern Belgium. This was the theatre of most Franco-Spanish and Franco-Austrian wars during the 17th and 18th centuries. Following the campaigns of 1794 in the French Revolutionary Wars, the Low Countries—including territories that were never nominally under Habsburg rule, such as the Prince-Bishopric of Liège—were annexed by the French First Republic, ending Austrian rule in the region; the reunification of the Low Countries as the United Kingdom of the Netherlands occurred at the dissolution of the First French Empire in 1815, after the defeat of Napo
An economist is a practitioner in the social science discipline of economics. The individual may study and apply theories and concepts from economics and write about economic policy. Within this field there are many sub-fields, ranging from the broad philosophical theories to the focused study of minutiae within specific markets, macroeconomic analysis, microeconomic analysis or financial statement analysis, involving analytical methods and tools such as econometrics, economics computational models, financial economics, mathematical finance and mathematical economics; the professionalization of economics, reflected in academia, has been described as "the main change in economics since around 1900." Economists debate the path. It is a debate between a scholastic orientation, focused on mathematical techniques, a public discourse orientation, more focused on communicating to lay people pertinent economic principles as they relate to public policy. Surveys among economists indicate a preference for a shift toward the latter.
Most major universities have an economics faculty, school or department, where academic degrees are awarded in economics. Getting a PhD in economics takes six years, on average, with a median of 5.3 years. The Nobel Memorial Prize in Economics, established by Sveriges Riksbank in 1968, is a prize awarded to economists each year for outstanding intellectual contributions in the field of economics; the prize winners are announced in October every year. They receive their awards on the anniversary of Alfred Nobel's death. Economists work in many fields including academia, government and in the private sector, where they may "...study data and statistics in order to spot trends in economic activity, economic confidence levels, consumer attitudes. They assess this information using advanced methods in statistical analysis, computer programming they make recommendations about ways to improve the efficiency of a system or take advantage of trends as they begin."In contrast to regulated professions such as engineering, law or medicine, there is not a required educational requirement or license for economists.
In academia, to be called an economist requires a Ph. D. degree in Economics. In the US government, on the other hand, a person can be hired as an economist provided that they have a degree that included or was supplemented by 21 semester hours in economics and three hours in statistics, accounting, or calculus. A professional working inside of one of many fields of economics or having an academic degree in this subject is considered to be an economist. In addition to government and academia, economists are employed in banking, accountancy, marketing, business administration and non- or not-for profit organizations. Politicians consult economists before enacting economic policy. Many statesmen have academic degrees in economics. Economics graduates are employable in varying degrees depending on the regional economic scenario and labour market conditions at the time for a given country. Apart from the specific understanding of the subject, employers value the skills of numeracy and analysis, the ability to communicate and the capacity to grasp broad issues which the graduates acquire at the university or college.
Whilst only a few economics graduates may be expected to become professional economists, many find it a base for entry into a career in finance – including accounting, insurance and banking, or management. A number of economics graduates from around the world have been successful in obtaining employment in a variety of major national and international firms in the financial and commercial sectors, in manufacturing, retailing and IT, as well as in the public sector – for example, in the health and education sectors, or in government and politics. Small numbers go on to undertake postgraduate studies, either in economics, teacher training or further qualifications in specialist areas. In Brazil, unlike most countries in the world where the profession is not regulated, the profession of Economist is regulated by Law. 1411 of August 13, 1951. The professional designation of economist, according to the said law, is exclusive to the bachelors in economics graduates in Brazil. According to the United States Department of Labor, there were about 15,000 non-academic economists in the United States in 2008, with a median salary of $83,000 the top ten percent earning more than $147,040 annually.
Nearly 135 colleges and universities grant around 900 new Ph. D.s every year. Incomes are highest for those in the private sector, followed by the federal government, with academia paying the lowest incomes; as of January 2013, PayScale.com showed Ph. D. economists' salary ranges as follows: all Ph. D. economists, $61,000 to $160,000. D. corporate economists, $71,000 to $207,000. The largest single professional grouping of economists in the UK are the more than 1000 members of the Government Economic Service, who work in 30 government departments and agencies. Analysis of destination surveys for economics graduates from a number of selected top schools of economics in the United Kingdom, shows nearly 80 percent in employment six months after graduation – with a wide range of roles and employers, including regional and international organisations, across many sectors; this figure compares favourably with the national picture, with 64 percent of economics graduates in employment. Some current we
Yale University is a private Ivy League research university in New Haven, Connecticut. Founded in 1701, it is the third-oldest institution of higher education in the United States and one of the nine Colonial Colleges chartered before the American Revolution. Chartered by Connecticut Colony, the "Collegiate School" was established by clergy to educate Congregational ministers, it moved to New Haven in 1716 and shortly after was renamed Yale College in recognition of a gift from British East India Company governor Elihu Yale. Restricted to theology and sacred languages, the curriculum began to incorporate humanities and sciences by the time of the American Revolution. In the 19th century, the college expanded into graduate and professional instruction, awarding the first Ph. D. in the United States in 1861 and organizing as a university in 1887. Its faculty and student populations grew after 1890 with rapid expansion of the physical campus and scientific research. Yale is organized into fourteen constituent schools: the original undergraduate college, the Yale Graduate School of Arts and Sciences and twelve professional schools.
While the university is governed by the Yale Corporation, each school's faculty oversees its curriculum and degree programs. In addition to a central campus in downtown New Haven, the university owns athletic facilities in western New Haven, a campus in West Haven and forest and nature preserves throughout New England; the university's assets include an endowment valued at $29.4 billion as of October 2018, the second largest endowment of any educational institution in the world. The Yale University Library, serving all constituent schools, holds more than 15 million volumes and is the third-largest academic library in the United States. Yale College undergraduates follow a liberal arts curriculum with departmental majors and are organized into a social system of residential colleges. All members of the Faculty of Arts and Sciences—and some members of other faculties—teach undergraduate courses, more than 2,000 of which are offered annually. Students compete intercollegiately as the Yale Bulldogs in the NCAA Division I – Ivy League.
As of October 2018, 61 Nobel laureates, 5 Fields Medalists and 3 Turing award winners have been affiliated with Yale University. In addition, Yale has graduated many notable alumni, including five U. S. Presidents, 19 U. S. Supreme Court Justices, 31 living billionaires and many heads of state. Hundreds of members of Congress and many U. S. diplomats, 78 MacArthur Fellows, 247 Rhodes Scholars and 119 Marshall Scholars have been affiliated with the university. Its wealth and influence have led to Yale being reported as amoungst the most prestigious universities in the United States. Yale traces its beginnings to "An Act for Liberty to Erect a Collegiate School", passed by the General Court of the Colony of Connecticut on October 9, 1701, while meeting in New Haven; the Act was an effort to create an institution to train ministers and lay leadership for Connecticut. Soon thereafter, a group of ten Congregational ministers, Samuel Andrew, Thomas Buckingham, Israel Chauncy, Samuel Mather, Rev. James Noyes II, James Pierpont, Abraham Pierson, Noadiah Russell, Joseph Webb, Timothy Woodbridge, all alumni of Harvard, met in the study of Reverend Samuel Russell in Branford, Connecticut, to pool their books to form the school's library.
The group, led by James Pierpont, is now known as "The Founders". Known as the "Collegiate School", the institution opened in the home of its first rector, Abraham Pierson, today considered the first president of Yale. Pierson lived in Killingworth; the school moved to Saybrook and Wethersfield. In 1716, it moved to Connecticut. Meanwhile, there was a rift forming at Harvard between its sixth president, Increase Mather, the rest of the Harvard clergy, whom Mather viewed as liberal, ecclesiastically lax, overly broad in Church polity; the feud caused the Mathers to champion the success of the Collegiate School in the hope that it would maintain the Puritan religious orthodoxy in a way that Harvard had not. In 1718, at the behest of either Rector Samuel Andrew or the colony's Governor Gurdon Saltonstall, Cotton Mather contacted the successful Boston born businessman Elihu Yale to ask him for financial help in constructing a new building for the college. Through the persuasion of Jeremiah Dummer, Elihu "Eli" Yale, who had made a fortune through trade while living in Madras as a representative of the East India Company, donated nine bales of goods, which were sold for more than £560, a substantial sum at the time.
Cotton Mather suggested that the school change its name to "Yale College".. Meanwhile, a Harvard graduate working in England convinced some 180 prominent intellectuals that they should donate books to Yale; the 1714 shipment of 500 books represented the best of modern English literature, science and theology. It had a profound effect on intellectuals at Yale. Undergraduate Jonathan Edwards discovered John Locke's works and developed his original theology known as the "new divinity". In 1722 the Rector and six of his friends, who had a study group to discuss the new ideas, announced that they had given up Calvinism, become Arminians and joined the Church of England, they were returned to the colonies as missionaries for the Anglican faith. Thomas Clapp became president in 1745 and struggled to return the college to Calvinist orthodoxy, but he did not close the library. Other students found Deist books in the library. Yale was swept up by the great intellectual movements of the peri
Leuven or Louvain is the capital of the province of Flemish Brabant in Belgium. It is located about 25 kilometres east of Brussels; the municipality itself comprises the historic city and the former neighbouring municipalities of Heverlee, Kessel-Lo, a part of Korbeek-Lo, Wilsele and Wijgmaal. It is the eighth largest city in Belgium and the fourth in Flanders with more than 100,244 inhabitants. Leuven is home to the KU Leuven, the largest and oldest university of the Low Countries and the oldest Catholic university still in existence; the related university hospital of UZ Leuven is one of the largest hospitals in Europe. The city is known for being the headquarters of Anheuser-Busch InBev, the world's largest brewer and one of the five largest consumer-goods companies in the world; the earliest mention of Leuven dates from 891, when a Viking army was defeated by the Frankish king Arnulf of Carinthia. According to a legend, the city's red and white arms depict the blood-stained shores of the river Dyle after this battle to Austria’s Flag.
Situated beside this river, near to the stronghold of the Dukes of Brabant, Leuven became the most important centre of trade in the duchy between the 11th and 14th centuries. A token of its former importance as a centre of cloth manufacture is shown in that ordinary linen cloth was known, in late-14th-century and 15th-century texts, as lewyn. In the 15th century, a new golden era began with the founding of what is now the largest and oldest university in the Low Countries, the Catholic University of Leuven, in 1425. In the 18th century, the brewery Den Horen flourished. In 1708, Sebastien Artois became the master brewer at Den Horen, gave his name to the brewery in 1717, now part of AB InBev, whose flagship beer, Stella Artois, is brewed in Leuven and sold in many countries. Leuven occupied by foreign armies. In the 20th century, both world wars inflicted major damage upon the city. Upon Germany's entry into World War I, the town was damaged by rampaging soldiers. In all, about 300 civilians lost their lives.
The university library was destroyed on 25 August 1914, using petrol and incendiary pastilles. 230,000 volumes were lost in the destruction, including Gothic and Renaissance manuscripts, a collection of 750 medieval manuscripts, more than 1,000 incunabula. The destruction of the library shocked the world, with the Daily Chronicle describing it as war not only against civilians but against "posterity to the utmost generation." It was rebuilt after the war, much of the collection was replaced. Great Britain and the United States were major providers of material for the replenishment of the collection; the new library building was financed by the National Committee of the United States for the Restoration of the University of Louvain and built to the design of architect Whitney Warren. Richard Harding Davis, a war correspondent for the New York Tribune, was in Leuven and wrote a column titled "The Germans Were Like Men After an Orgy" in which he described the organized civilian murders and vandalism committed by the occupying troops.
In World War II, after the start of the German offensive, Leuven formed part of the British Expeditionary Force's front line and was defended by units of the 3rd Division and Belgian troops. From 14 to 16 May 1940, the German Army Group B assaulted the city with heavy air and artillery support; the British withdrew their forces to the River Senne on the night of 16 May and the town was occupied the next day. The new university library building was set on fire by shelling, on 16 May, nearly a million books were lost. Given the presence of the KU Leuven, Europe's most innovative university according to Reuters, much of the local economy is concentrated on spin-offs from academic research. In addition, the Leuven-based research centre, IMEC, is a world class research centre in the field of nano-electronics and digital technologies; as a result, dozens of companies in high technological fields such as biotech, additive manufacturing and IT, are located near these research institutes on the Arenberg Science Park and Haasrode Research-Park.
Quite a few international companies such as Siemens, Nitto Denko, JSR Corporation or Commscope have important research oriented branches, in Leuven. The academic hospital Gasthuisberg is another advanced research institute, it is one of Europe's most advanced hospitals. As a result, large numbers of private service providers are active in the medical and legal fields; because it is the capital of the region of Flemish Brabant, many governmental institutions are located in Leuven, as well as the regional headquarters of transport corporations such as De Lijn. As one of Flanders Art-Cities, with a large range of cafés, cultural institutions and shopping neighbourhoods, Leuven attracts a fair share of tourists. Leuven is the worldwide headquarters of Anheuser-Busch InBev, the largest beer company in the world and is considered one of the largest fast-moving consumer goods companies in the world. InBev's Stella Artois brewery and main offices dominate the entire north-eastern part of the town, between the railway station and the canal to Mechelen.
As of 1 November 2016, the population of Leuven was 100,244. The arrondissement of Leuven