title: Prison–industrial complex

text: More expansive definitions often include as elements of the system tough-on-crime politicians and district attorneys seeking office, conservative political lobbies and legislatures passing punitive laws, and investment banks and rural economic developers leveraging public debt into private profit through prison construction and employment contracts. The widest definitions of the prison-industrial complex include even larger and more abstract institutions and processes, such as the news media sensationalizing crime and influencing public perception, gentrification disrupting urban environments and displacing precarious residents, and public schools increasingly subjecting students to police oversight and legal punishment since the 1980s. In the U.S., the specific relationships between the criminal justice system and the private businesses that interact with it vary significantly from state to state.


title: Prison–industrial complex

text: Critics and scholars argue that mass incarceration is an emergent property of the prison-industrial complex. Because mass incarceration has exacerbated the economic and racial inequality in the United States, contemporary social critics like Ruth Wilson Gilmore refer to the prison-industrial complex as an infrastructure of racial capitalism.


title: Prison–industrial complex

text: Marc Mauer, executive director of the criminal justice reform group The Sentencing Project, has argued that the growth and expansion of the prison-industrial complex since the 1970s has its roots in the War on Drugs, which, rather than suppressing the illegal drug trade, has produced a perpetual cycle of drug dealing and imprisonment. This he attributes to a structural feature of the drug trade, a market with perpetually high demand and lucrative potential profits. Mauer describes the "replacement effect", in which no matter how many drug suppliers are incarcerated, other sellers simply take their place; since there is a constant supply of new drug sellers, there is thus a constant supply of potential prison inmates. According to this view, the prison-industrial complex depends on this guarantee of future inmates to ensure its growth and profitability, making prison construction, operation, services, and technology all safe investments.


title: Prison–industrial complex

text: The U.S. criminal justice system has a high rate of recidivism. A 2021 Bureau of Justice Statistics investigation reported that about 66% of prisoners released across 24 states in 2008 were rearrested within 3 years, and 82% were rearrested within 10 years.


title: Prison–industrial complex

text: Statistics show that incarceration and unemployment are correlated, although unevenly. Nevertheless, such a high rate of recidivism can be attributed in part to the difficulty formerly incarcerated people encounter in finding stable employment. The Evidence-Based Professionals Society suggests two reasons for this difficulty: "First, most of the offenders may simply lack the necessary job skills for specific positions, keeping them from those usually higher paid and more stable jobs. Second, many employers are reluctant to hire these people due to the stigma imposed by their previous criminal records."


title: Prison–industrial complex

text: Scholars and critics describe the existence of a "school-to-prison pipeline", a system in which public school policies contribute to funneling urban students of color into the prison-industrial complex. Students at urban schools and other schools with high percentages of minority students are more likely to experience out-of-school suspensions and academic failure, which have been correlated to a higher likelihood of incarceration after leaving school. Moreover, since the 1970s, urban public school districts have dramatically increased police presence in their schools, and students have been increasingly subject to "arrests for minor noncriminal violations of school rules." This trend has both disrupted urban learning environments and decreased the average age of the incarcerated population of the United States' major cities.


title: Prison–industrial complex

text: The War on Drugs has disproportionately impacted African Americans. Although African Americans use drugs at similar rates to Americans from other demographic groups, they are prosecuted at much higher rates.


title: Prison–industrial complex

text: Many commentators point to the racial disproportionality of the US prison population as evidence of structural racism. For further information, see .


title: Prison–industrial complex

text: In the decades following World War II, the American domestic economy was characterized by growth, but also by deindustrialization, the decline of the labor movement, austerity and the privatization of government services, the transformation of welfare to workfare policies, and suburbanization, including white flight from city centers. These large-scale transformations had particularly damaging effects on the economic activity of large American cities, generally increasing urban unemployment and exacerbating income and racial inequality.


title: Prison–industrial complex

text: Statistics have shown that the unemployment rate is correlated to the incarceration rate, and American historians such as Heather Ann Thompson and Alex Lichtenstein have argued that mass incarceration has accompanied the public-sector abandonment of former urban-industrial cores, and contributed to the rise of the Sun Belt as an important economic region. In this view, the prison-industrial complex is not simply the cumulative effect of decades of increasingly punitive legislation, but is an integral sector in the neoliberal national economy, with the largest and fastest-growing states—like Florida, California, and Texas ("Flocatex")—also leading the country in number of inmates and prison privatization.


title: Prison–industrial complex

text: As large-scale human holding facilities, prisons contain enormous reserves of labor power. Since the establishment of the Federal Prison Industries in 1930, these capacities have been put to work for the public sector, and since the 1979 Prison Industry Enhancement Certification Program, for the private sector too. Sociologist Erin Hatton defines four types of prison labor:


title: Prison–industrial complex

text: Advocates of prison labor argue that rehabilitation is promoted through discipline, a strong work ethic, and providing inmates with valuable skills to be used upon release. Gina Honeycutt, executive director of the National Correctional Industries Association, stated in 2015 that moreover, "in recent years, the focus of many work programs has shifted to concentrate even more on effective rehabilitation of inmates. The transition in the last five years has been away from producing a product to producing a successful offender as our product." Indeed, studies have shown that participants in prison labor programs often have a lower risk of recidivism; these studies may be misleading, however, as it is often only obedient and industrious inmates who are allowed to participate in prison labor in the first place.


title: Prison–industrial complex

text: Anti-prison activists have argued that corporations that contract or subcontract prison labor have a vested interest in the expansion of the prison system, since its expansion provides more inmates available for cheap labor. Activists Eve Goldberg and Linda Evans (writing while incarcerated in California) explain that For private business, prison labor is like a pot of gold. No strikes. No union organizing. No health benefits, unemployment insurance, or workers' compensation to pay. No language barriers, as in foreign countries. New leviathan prisons are being built on thousands of eerie acres of factories inside the walls. Prisoners do data entry for Chevron, make telephone reservations for TWA, raise hogs, shovel manure, make circuit boards, limousines, waterbeds, and lingerie for Victoria's Secret—all at a fraction of the cost of 'free labor.'"Several scholars argue that the practice of "hiring out prisoners", from the Reconstruction-era convict lease system to the contemporary prison-industrial complex, is a continuation of the U.S. history of slavery. These scholars all cite the Thirteenth Amendment to the Constitution of the United States, abolishing the institution of slavery "except as a punishment for crime whereof the party shall have been duly convicted."


title: Prison–industrial complex

text: In a Bureau of Prisons (BOP)–funded study, privatized prisons were compared side-to-side with the public prisons on economic performance, and quality of life. The study found that in a trade-off for allowing prisons to be more cheaply run and operated, the degree to which prisoners are reformed goes down. Because the privatized prisons are so much larger than the public-run prisons, they were subject to economies of scale, allowing for a more efficient, lower-cost alternative to government spending on incarceration.


title: Prison–industrial complex

text: In 2016, GEO Group and CoreCivic each commanded $900 million in open credit from six banks: Bank of America, JPMorgan Chase, BNP Paribas, SunTrust, U.S. Bancorp, and Wells Fargo.


title: Prison–industrial complex

text: In 2011, The Vera Institute of Justice surveyed 40 state correction departments to gather data on what the true cost of prisons were. Their reports showed that most states had additional costs ranging from one percent to thirty-four percent outside of what their original budget was for that year.


title: Prison–industrial complex

text: John W. Whitehead, constitutional attorney and founder of the Rutherford Institute asserts that "Prison privatization simply encourages incarceration for the sake of profits, while causing millions of Americans, most of them minor, nonviolent criminals, to be handed over to corporations for lengthy prison sentences which do nothing to protect society or prevent recidivism." Whitehead argues that it characterizes an increasingly inverted justice system dependent upon an advancement in power and wealth of the corporate state.


title: Prison–industrial complex

text: Hadar Aviram, Professor of Law at UC Hastings, suggests that critics of the prison-industrial complex focus too much on private prisons. While Aviram shares their concerns that "private enterprises designed to directly benefit from human confinement and misery is profoundly unethical and problematic," she contends that "the profit incentives that brought private incarceration into existence, rather than private incarceration itself, are to blame for the PIC and its evils". In the neoliberal era, she argues, "private and public actors alike respond to market pressures and conduct their business, including correctional business, through a cost/benefit prism".


title: Prison–industrial complex

text: Funding of the Immigration and Naturalization Service (INS) is increasing as about a total of $4.27 billion was allotted to the INS in the 2000 fiscal budget. This is 8% more than in the 1999 fiscal budget. This expansion, experts claim, has been too rapid and thus has led to an increased chance on the part of faculty for negligence and abuse. Lucas Guttengag, director of the ACLU Immigrants' Rights Project stated that, "immigrants awaiting administrative hearings are being detained in conditions that would be unacceptable at prisons for criminal offenders." Such examples include "travelers without visas" (TWOVs) being held in motels near airports nicknamed "Motel Kafkas" that are under the jurisdiction of private security officers who have no affiliation to the government, often denying them telephones or fresh air, and there are some cases where detainees have been shackled and sexually abused according to Guttengag. Similar conditions arose in the ESMOR detention center at Elizabeth, New Jersey where complaints arose in less than a year, despite having a "state-of-the-art" facility.


title: Prison–industrial complex

text: The number of unauthorized immigrants in the U.S. is 11.3 million. Those that argue against the PIC claim that effective immigration policy has failed to pass since private detention centers profit from keeping undocumented immigrants detained. They also claim that despite having the incarceration rate grow "10 times what it was prior to 1970... it has not made this country any safer." Since the September 11 attacks in 2001, the budget for Customs and Border Protection (CBP), and U.S. Immigration and Customs Enforcement (ICE), have nearly doubled from 2003 to 2008, with CBP's budget increasing from $5.8 billion to $10.1 billion and ICE from $3.2 billion to $5 billion and even so there has been no significant decrease in immigrant population. Professor Wayne Cornelius, professor Emeritus of Political Science at UC San Diego, even argued that it is so ineffective that "92–97%" of immigrants who attempt to cross in illegally "keep trying until they succeed", and that such measures actually increase the risk and cost of travel, leading to longer stays and settlement in the US.


title: Prison–industrial complex

text: There are around 400,000 immigrant detainees per year, and 50% are housed in private facilities. In 2011, CCA's net worth was $1.4 billion and net income was $162 million. In this same year, The GEO Group had a net worth of $1.2 billion and net income of $78 million. As of 2012, CCA has over 75,000 inmates within 60 facilities and the GEO Group owns over 114 facilities. Over half of the prison industry's yearly revenue comes from immigrant detention centers. For some small communities in the Southwestern United States, these facilities serve as an integral part of the economy. According to Chris Kirkham, this constitutes part of a growing immigration industrial complex: "Companies dependent upon continued growth in the numbers of undocumented immigrants detained have exerted themselves in the nation's capital and in small, rural communities to create incentives that reinforce that growth." A study by the ACLU says that many are housed in inhumane conditions as many facilities operated by private companies are exempt from government oversight, and studies are made difficult as such facilities may not be covered by a Freedom of Information Act.


title: Prison–industrial complex

text: In 2009, University of Kansas professor Tanya Golash-Boza coined the term, "Immigration Industrial Complex", defining it as "the confluence of public and private sector interests in the criminalization of undocumented migration, immigration law enforcement, and the promotion of 'anti-illegal' rhetoric," in her paper "The Immigration Industrial Complex: Why We Enforce Immigration Policies Destined to Fail".


title: Prison–industrial complex

text: In 2009, congressional immigration detention policies requires that ICE maintain 34,000 immigration detention beds daily. This immigration bed quota has steadily increased with each passing year, costing ICE around $159 to detain one individual for one day.


title: Prison–industrial complex

text: In 2010, immigration detention policies implemented by ICE benefited the two major private prison corporations CCA and GeoGroup, increasing their share of immigrant detention beds by 13%. Compared to data from 2009, the percentage of ICE immigrant detention beds in the United States are owned and operated by private for-profit prison corporations has increased by 49%, with CCA and GeoGroup operating 8 out of 10 of the largest facilities. Although the combined revenues of CCA and GEO Group were about $4 billion in 2017 from private prison contracts, their number one customer was ICE.


title: Prison–industrial complex

text: In 1994, the UN Special Rapporteur on Violence Against Women was released which stated that "Among many other abuses women prisoners have identified, are pat searches (male guards pat searching and groping women), illegal strip searches (male guards observing strip searches of women), constant lewd comments and gestures, violations of their right to privacy (male guards watching women in showers and toilets), and in some instances, sexual assault and rape." International human rights standards reinforce this by stating "the rape of a woman in custody is an act of torture." In addition, some prisons fail to meet women's needs with providing basic hygiene and reproductive health products.


title: Prison–industrial complex

text: In regards to women and the prison-industrial complex, Angela Davis stated that "State-sanctioned punishment is informed by patriarchal structures and ideologies that have tended to produce historical assumptions of female criminality linked to ideas about the violation of social norms defining a 'woman’s place'. Considering the fact that as many as half of all women are assaulted by their husbands or partners combined with dramatically rising numbers of women sentenced to prison, it may be argued that women in general are subjected to a far greater magnitude of punishment than men." She also suggested that the "historical and philosophical connections between domestic violence and imprisonment [comprise] two modes of gendered punishment – one located in the private realm, the other in the public realm."


title: Prison–industrial complex

text: Davis continues:the sexual abuse of women in prison is one of the most heinous state-sanctioned human rights violations within the United States today. Women prisoners represent one of the most disenfranchised and invisible adult populations in our society. The absolute power and control the state exercises over their lives both stems from and perpetuates the patriarchal and racist structures that, for centuries, have resulted in the social domination of women.According to Davis and Cassandra Shaylor in their research entitled "Race, Gender, and the Prison-Industrial Complex", most women in prison experience some degree of depression or post-traumatic stress disorder. Very often they are neither diagnosed nor treated, with injurious consequences for their mental health in and out of prison. Many women report that when requesting counseling, they are offered psychotropic medications instead. As technologies of imprisonment become increasingly repressive and practices of isolation become increasingly routine, mentally ill women often are placed in solitary confinement, which can only exacerbate their condition.


title: Prison–industrial complex

text: Davis further explains why there is such an increase in female incarceration in the book, "Are Prisons Obsolete?", in which Davis investigates the structures which the current prison system has formed around:


title: Prison–industrial complex

text: 70 percent of the United States prison population is composed of racial minorities. Due to a variety of factors, different ethnic groups have different rates of offending, arrest, prosecution, conviction and incarceration. In terms of percentage of ethnic populations, in descending order, the U.S. incarcerates more Native Americans, African Americans, followed by Hispanics, Whites, and finally Asians. Native Americans are the largest group incarcerated per capita. It is worth noting that Black women are the fastest growing population of incarcerated people.


title: Prison–industrial complex

text: A 2014 report by the American Friends Service Committee, Grassroots Leadership, and the Southern Center for Human Rights claims that recent reductions in the number of people incarcerated has pushed the prison industry into areas previously served by non-profit behavioral health and treatment-oriented agencies, referring to it as the "Treatment Industrial Complex", which "has the potential to ensnare more individuals, under increased levels of supervision and surveillance, for increasing lengths of time – in some cases, for the rest of a person's life." Sociologist Nancy A. Heitzeg and activist Kay Whitlock claim that contemporary bipartisan reforms being proposed "are predicated on privatization schemes, dominated by the anti-government right and neoliberal interests that more completely merge for-profit medical treatment and other human needs supports with the prison-industrial complex."


title: Prison–industrial complex

text: Sociologist Loïc Wacquant of UC Berkeley is also dismissive of the term for sounding too conspiratorial and for overstating its scope and effect. However Bernard Harcourt, Professor of Law at Columbia University, considers the term useful insofar as "it highlights the profitability of prison building and the employment boom associated with prison guard labor. There is no question that the prison expansion served the financial interests of large sectors of the economy."


title: Prison–industrial complex

text: Another writer of the era who covered the expanding prison population and attacked "the prison industrial complex" was Christian Parenti, who later disavowed the term before the publication of his book, "Lockdown America" (2000). "How, then, should the left critique the prison buildup?" asked "The Nation" in 1999:


title: Prison–industrial complex

text: Prisons in the U.S. are becoming the primary response to mental illness among poor people. The institutionalization of mentally ill people, historically, has been used more often against women than against men.


title: Prison–industrial complex

text: Other scholars, such as Nils Christie and Mechthild Nagel, have proposed alternative terms such as "criminal industrial complex" and "criminal (justice) industrial complex". Nagel argues the latter in particular "encompasses tentacles of punitive measures of which "prison" is only one—albeit a severe one—of many forms of social control" and has justice in brackets as it "hides the permanent element of repression that is endemic in a system geared to overempower those who exert power and domination."


title: Prison–industrial complex

text: A response to the prison industrial complex is the prison abolition movement. The goal of prison abolition is to end the prison industrial complex by eliminating prisons. Prison abolitionists aim to do this by changing the socioeconomic conditions of the communities that are affected the most by the prison-industrial complex. Abolitionists propose reallocating funds to social programs such as education, mental healthcare, housing, and non-armed dispute forces. The purpose of abolition is not necessarily to dismantle, but to revise. Angela Davis, a known political activist and co-founder of Critical Resistance describes the purpose of abolition, "All of these things help to create security and safety. It’s about learning that safety, safeguarded by violence, is not really safety."


title: Prison–industrial complex

text: Due to the overcrowding in prisons and detention centers by for-profit corporations, organizations such as Amnesty International, propose using alternatives such as reporting requirements, bonds, or the use of monitoring technologies. The questions often brought up with alternatives include whether they are effective or efficient. A study published by the Vera Institute attempts to answer this question by stating that when alternatives such as monitoring technologies were used, they found that 91% of the individuals appeared at their court date. The Institute recorded that the relative cost of using such alternatives has been estimated at $12 per day a relatively low price in comparison to the reported average cost of incarceration in the U.S., which has been priced at roughly $87.61 per day.


title: Prison–industrial complex

text: Despite the relative efficiency and effectiveness of alternative to detention, there is still much debate that these alternatives will not change the dynamics of incarceration. This argument lies in the fact that major corporations such as the GEO Group and Corrections Corporations of America will still be profiting by simply re-branding and moving towards rehabilitation services and monitoring technologies. Rather than effectively ending and finding a solution to the PIC, more people will simply find themselves imprisoned by another system. Other opposition to alternatives comes from the public. According to Ezzat Fattah, opposition towards prison alternatives and correctional facilities is due to the public fearing having that having these facilities in their neighborhoods will threaten the security and integrity of their communities and children.


title: Prison–industrial complex

text: The movement gained momentum in 1997, when a group of prison abolition activists, scholars, and former prisoners collaborated to organize a three-day conference to examine the prison-industrial complex in the U.S. The founders of Critical Resistance include Angela Davis, Ruth Wilson Gilmore, and Rose Braz. The conference, Critical Resistance to the prison-industrial complex, was held in September 1998 at the University of California, Berkeley and was attended by over 3,500 people of diverse academic, socioeconomic and ethnic backgrounds. Two years after the conference, a political grassroots organization was founded bearing the same name with the mission to challenge and dismantle the prison-industrial complex.


title: Prison–industrial complex

text: In 2001, the organization adopted a national structure with local chapters in Portland, Los Angeles, Oakland, and New York City to develop campaigns and projects working towards abolishing the prison industrial complex. Currently, the cause has shifted towards supporting efforts towards resisting state repression and developing tools to re-imagine life without the prison industrial complex.


title: Prison–industrial complex

text: In 2010, at the U.S. Social Forum, committed activists joined together to discuss prison justice and stated that "Because we share a vision of justice and solidarity against confinement, control, and all forms of political repression, the prison industrial complex must be abolished." Following the forum, the rise of Formerly Incarcerated, Convicted People's Movement helped to incorporate abolition into other movements such as Occupy Wall Street, Black Lives Matter, and the Movement for Black Lives.


title: Prison–industrial complex

text: A competing explanation for the disproportionate arrest and incarceration of people of color and persons with lower socioeconomic status is the school-to-prison pipeline, which generally proposes that practices in public schools (such as zero-tolerance policies, police in schools, and high-stakes testing) are direct causes of students dropping out of school and, subsequently, committing crimes that lead to their being arrested. 68% of state prisoners had not completed high school in 1997, including 70 percent of women state prisoners. Suspension, expulsion, and being held back during middle school years are the largest predictors of arrest for adolescent women. The school-to-prison pipeline disproportionately affects young black men with an overall incarceration risk that is six to eight times higher than young whites. Black male high school dropouts experienced a 60% risk of imprisonment as of 1999. There is a recent trend of authors describing the school-to-prison pipeline as feeding into the prison-industrial complex.


title: Prison–industrial complex

text: Since the shortcomings of zero-tolerance discipline have grown very clear, there has been a widespread movement to support reform across school districts and states. Growing research that shows suspensions, especially for minor infractions and misbehavior, are a flawed disciplinary response has encouraged many districts to adopt new disciplinary alternatives. In 2015, mayor of New York City Bill de Blasio joined with the Department of Education to address school discipline in a campaign to tweak the old policies. De Blasio also spearheaded a leadership team on school climate and discipline to take recommendations and craft the foundations for more substantive policy. The team released recommendations that work towards reducing the racial disparity in suspension and discussing the underlying root cause of disciplinary infractions through restorative justice.


title: Orthopnea

text: Orthopnea or orthopnoea is shortness of breath (dyspnea) that occurs when lying flat, causing the person to have to sleep propped up in bed or sitting in a chair. It is commonly seen as a late manifestation of heart failure, resulting from fluid redistribution into the central circulation, causing an increase in pulmonary capillary pressure and causing difficulty in breathing. It is also seen in cases of abdominal obesity or pulmonary disease. Orthopnea is the opposite of platypnea, shortness of breath that worsens when sitting or standing upright.


title: Orthopnea

text: Orthopnea is often a symptom of left ventricular heart failure and/or cardiogenic pulmonary edema. It can also occur in those with asthma and chronic bronchitis, as well as those with sleep apnea or panic disorder. It is also as associated with polycystic liver disease. From a neuromuscular perspective, orthopnea is potentially a sign of severe diaphragmatic weakness. Under such circumstances, patients may describe shortness of breath when they bend over (e.g. when tying shoelaces), called bendopnea.


title: Orthopnea

text: Orthopnea is due to increased distribution of blood to the pulmonary circulation when a person lies flat or closer to a horizontal position. Lying flat decreases the inhibitory effect that the gravity usually has on the blood when coming back to the heart from the lower extremities of the body. This increases the right sided venous return. In a normal person, this redistribution of blood has little effect on respiratory function as the left ventricle has the adequate capacity to suddenly increase its stroke volume (as a result of the Frank-Starling mechanism). In a person with heart failure, the left ventricle has an inadequate capacity to respond to increased arrival of blood from the pulmonary circulation. This leads to the pooling up of blood in the pulmonary circulation and doesn't change its volume enough. The increased intra-parenchymal pulmonary intravascular pressure can also result in hydrostatic pressure related fluid transudation into the alveoli, thus causing cardiogenic pulmonary edema and further worsening shortness of breath. Thus, shortness of breath is commonly experienced after a reasonably short time lying near to flat for a person with left ventricular failure. This is different from the dyspnea experienced by someone with lung parenchymal pathology (both restrictive and obstructive) when lying down, which is sudden and instead related to an acute change in diaphragmatic/accessory respiratory muscle mechanical advantage lost when moving the body into a more horizontal position.


title: Orthopnea

text: Diagnosis is based mostly on the clinical features and symptoms, as well as finding causes like heart failure.


title: Orthopnea

text: Based on the cause, Orthopnea can be treated with respiratory support devices such as CPAP or biPAP while the disease causing it is addressed.


title: Orthopnea

text: The word "orthopnea" uses combining forms of "ortho-" + "-pnea", from Greek "ortho", straight, regular, + "pnoia", breath. See pronunciation information at "dyspnea".


title: Edward F. Cox

text: Edward Ridley Finch Cox (born October 2, 1946) is an American corporate and finance lawyer and the former chairman of the New York Republican State Committee. He is the son-in-law of President Richard M. Nixon and First Lady Pat Nixon, and the brother-in-law of Julie Nixon.


title: Edward F. Cox

text: Cox was born to Howard Ellis Cox and Anne Crane Delafield (Finch) Cox in Stony Brook Southampton Hospital in Southampton, New York. He attended Westhampton Beach Elementary School and Allen-Stevenson School in New York City. Cox is named for his grandfather, Judge Edward R. Finch, a prominent New York jurist who served as a Justice of the New York State Supreme Court (1915–43), Presiding Justice of the New York Supreme Court Appellate Division, First Department, and Associate Judge on the New York Court of Appeals. His father, Howard Ellis Cox, was a decorated World War II aviator, New York lawyer, and Long Island real estate developer.


title: Edward F. Cox

text: Cox graduated from the Princeton University Woodrow Wilson School of Public and International Affairs (1968) and Harvard Law School (1972). Cox was battalion commander of his Army ROTC unit at Princeton where he put together and accredited a seminar on war, he completed officer and airborne training at Fort Benning, Georgia and subsequently served as a reserve officer with the 11th Special Forces Group.


title: Edward F. Cox

text: In 1971, Cox married Tricia Nixon, the daughter of President Richard Nixon, in a White House Rose Garden ceremony. The wedding was described in "Life Magazine" as "a union 'akin to American royalty'". Edward and Tricia Cox have a son, Christopher Nixon Cox. The Coxes reside on Long Island, New York.


title: Edward F. Cox

text: Cox started his legal career at Cravath Swaine & Moore, and after serving as a general counsel in the Reagan Administration, was a corporate partner in the Donovan Leisure firm and subsequently a member of the management committee and the chairman of the corporate department at Patterson Belknap Webb & Tyler LLP.


title: Edward F. Cox

text: His law practice has covered a wide variety of transactions and representations including securities litigations, project financings, M&A, startups, IPOs, municipal financings, securitizations, private placements and bankruptcies.


title: Edward F. Cox

text: Cox served as a director for 35 years of Noble Energy which is an upstream independent oil and natural gas company.


title: Edward F. Cox

text: To attempt to stay in shape, Cox participates in an Olympic-distance triathlon each year, and he swims, bikes and runs whenever possible in preparation. He ran and finished the New York City Marathon in 2017.


title: Edward F. Cox

text: From 1981 to 1983 Cox served in the Reagan Administration as the Senior Vice President and General Counsel of a government corporation, The United States Synthetic Fuels Corporation.


title: Edward F. Cox

text: He has served Presidents Richard Nixon and George H.W. Bush in the international arena. He has visited with numerous officials, including heads of state or government, in more than 30 countries including China, Russia, Israel, Cuba, England, Japan, Korea, Singapore, Taiwan, Italy, Greece, Hungary, Bulgaria, Romania, Turkey, Pakistan, Egypt, Jordan, Lebanon and Saudi Arabia.


title: Edward F. Cox

text: He was commissioner of the Commission on Judicial Nomination (nominating candidates for New York's highest court, 1991 to 2009) and Chairman of the New York Council of Parks, Recreation and Historic Preservation (1995 to 2008).


title: Edward F. Cox

text: He was a Trustee of the State University of New York (SUNY) from 1995 to 2009. From 1999 to 2009 as Co-Chairman and Chairman of SUNY's Charter School Committee, Cox founded SUNY's Charter School Institute and led the authorization of fifty charter schools.


title: Edward F. Cox

text: In 2006, Cox served as the chairman of newly elected Attorney General Andrew Cuomo's environmental and energy transition team.


title: Edward F. Cox

text: In K-12 education, Cox has served as a director of Student Sponsor Partnership, which supports and mentors parochial high school students, since its founding in 1985. He is also a director of the New York Institute for Special Education which has been a leading school for the blind since 1831.


title: Edward F. Cox

text: Cox has served for more than 15 years as Chairman of the New York League of Conservation Voters Education Fund.


title: Edward F. Cox

text: He has led an American delegation to, and presented at, Ditchley conferences, and is a director of Ditchley's American Advisory Board.


title: Edward F. Cox

text: His work has appeared in The Wall Street Journal, The New Republic, the Antitrust Law Journal and the New York Post, and in 1968 and 1969 he researched and co-authored The Nader Report on the Federal Trade Commission (FTC) which spawned “Nader’s Raiders” and the rejuvenation of the FTC as a consumer advocate.


title: Edward F. Cox

text: Cox has assisted Republican candidates in New York at all levels in numerous election cycles. In the 1994 state election, Cox played a key role in electing George Pataki Governor and Dennis Vacco Attorney General.


title: Edward F. Cox

text: Cox was rumored to be considering a run for Governor of New York in 2006 if then-Gov. George Pataki opted not to seek re-election. Pataki did not run again, but Cox later chose instead to seek the seat held by incumbent U.S. Senator Hillary Clinton (D) in the 2006 New York U.S. Senate election. However, after Pataki endorsed a rival Republican--Westchester County District Attorney Jeanine Pirro—for Senate, Cox announced on October 14, 2005 that he was no longer running.


title: Edward F. Cox

text: Cox was elected chairman of the New York State Republican Committee at the committee's meeting on September 30, 2009. Cox had a seven-point "agenda for the future" when elected chairman:


title: Edward F. Cox

text: Cox announced on May 20, 2019 that he was joining President Donald Trump's re-election campaign and that he would not run for re-election as Chairman of the New York Republican State Committee stating, "Serving as Chairman of the NYGOP over the last ten years has been one of the most rewarding chapters of my life, and I will continue to actively help elect more Republicans here in New York'". On July 1, 2019, Nick Langworthy, the Erie County Chairman succeeded Ed Cox as Chairman the New York State Republican Committee.


title: Interactive whiteboard

text: An interactive whiteboard (IWB), also known as interactive board or smart board, is a large interactive display board in the form factor of a whiteboard. It can either be a standalone touchscreen computer used independently to perform tasks and operations, or a connectable apparatus used as a touchpad to control computers from a projector. They are used in a variety of settings, including classrooms at all levels of education, in corporate board rooms and work groups, in training rooms for professional sports coaching, in broadcasting studios, and others.


title: Interactive whiteboard

text: The first interactive whiteboards were designed and manufactured for use in the office. They were developed by PARC around 1990. This board was used in small group meetings and round-tables.


title: Interactive whiteboard

text: The interactive whiteboard industry was expected to reach sales of US$1 billion worldwide by 2008; one of every seven classrooms in the world was expected to feature an interactive whiteboard by 2011 according to market research by Futuresource Consulting. In 2004, 26% of British primary classrooms had interactive whiteboards. The Becta Harnessing Technology Schools Survey 2007 indicated that 98% of secondary and 100% of primary schools had IWBs. By 2008, the average numbers of interactive whiteboards rose in both primary schools (18 compared with just over six in 2005, and eight in the 2007 survey) and secondary schools (38, compared with 18 in 2005 and 22 in 2007).


title: Interactive whiteboard

text: An interactive whiteboard (IWB) device can either be a standalone computer or a large, functioning touchpad for computers to use.


title: Interactive whiteboard

text: A device driver is usually installed on the attached computer so that the interactive whiteboard can act as a Human Input Device (HID), like a mouse. The computer's video output is connected to a digital projector so that images may be projected on the interactive whiteboard surface.


title: Interactive whiteboard

text: The user then calibrates the whiteboard image by matching the position of the projected image in reference to the whiteboard using a pointer as necessary. After this, the pointer or other device may be used to activate programs, buttons and menus from the whiteboard itself, just as one would ordinarily do with a mouse. If text input is required, user can invoke an on-screen keyboard or, if the whiteboard software provides for this, utilize handwriting recognition. This makes it unnecessary to go to the computer keyboard to enter text.


title: Interactive whiteboard

text: Thus, an IWB emulates both a mouse and a keyboard. The user can conduct a presentation or a class almost exclusively from the whiteboard.


title: Interactive whiteboard

text: In addition, most IWBs are supplied with software that provides tools and features specifically designed to maximize interaction opportunities. These generally include the ability to create virtual versions of paper flipcharts, pen and highlighter options, and possibly even virtual rulers, protractors, and compasses—instruments that would be used in traditional classroom teaching.


title: Interactive whiteboard

text: The majority of IWBs sold globally involve one of four forms of interaction between the user and the content projected on the whiteboard. These are an infrared scan technology; a resistive, touch-based board; an electromagnetic pen and associated software; and an ultrasonic pen.


title: Interactive whiteboard

text: An infrared interactive whiteboard is a large interactive display that connects to a computer and projector. The board is typically mounted to a wall or floor stand. Movement of the user's finger, pen, or other pointer over the image projected on the whiteboard is captured by its interference with infrared light at the surface of the whiteboard.


title: Interactive whiteboard

text: When the whiteboard surface is pressed, software triangulates the location of the marker or stylus. Infrared IWBs may be made of any material, no dry-erase markers are involved, and may be found in many settings, including various levels of classroom education, corporate boardrooms, training or activity rooms for organizations, professional sports coaching facilities, and broadcasting studios.


title: Interactive whiteboard

text: A touch-based IWB also involves a simple pointing device. In this case, the material of the board is important. In the most common resistive system, a membrane stretched over the surface deforms under pressure to make contact with a conducting backplate. The touch point location can then be determined electronically and registered as a mouse event. For example, when a finger is pressed on the surface, it is registered as the equivalent of the left mouse click. Again, such a board requires no special instruments. This leads to the claim of resistive systems manufacturers that such a whiteboard is easy and natural to use. It is, however, heavily dependent on the construction of the board itself.


title: Interactive whiteboard

text: An electromagnetic pen-based interactive whiteboard involves an array of wires embedded behind the solid board surface that interacts with a coil in the stylus tip to determine the horizontal and vertical coordinates of the stylus. The pen itself usually is passive, i.e., it contains no batteries or other power source; it alters the electrical signals produced by the board. For instance, when close to the surface of the board, the mouse pointer can be sensed, giving the board "mouse-over" capabilities. When it is pressed in against the board in one way, the board activates a switch in the pen to signal a mouse click to the computer; pressed in another way, contact with the board signals a click of the right mouse-button. Like a scaled-up version of a graphics tablet used by professional digital artists and designers, an electromagnetic IWB can emulate mouse actions accurately, will not malfunction if a user leans on the board, and can potentially handle multiple inputs.


title: Interactive whiteboard

text: This technology uses infrared light and ultrasound positioning technology. The technology works in a similar way to lightning in a thunderstorm by computing the time difference between the speed of light and the speed of sound. An infrared IWB is also available in a portable format. After moving the set-up to a new location, the system acquires connection to the computer with a simple re-calibration of the projected image — again using the electronic pen. The device or bar scans a bracketed area (usually 3m by 1.5m, giving a whiteboard that is 110" wide). Typically, multiple brackets can be added, providing for users at different sites to share the same virtual whiteboard.


title: Interactive whiteboard

text: A portable IR pen-based whiteboard works on a variety of surfaces — an existing whiteboard, a flat wall, even a chalkboard with dry-erase paint, transforms those surface into an interactive whiteboard. No battery is required for USB signal receiver and the unit can be mounted to the ceiling if a permanent solution is required. Made of a tiny and lightweight material, the PIWB is easy to transport.


title: Interactive whiteboard

text: A Wii-based IR system was invented by Johnny Chung Lee, PhD. in 2007. Lee claimed that the system "Makes a technology available to a much wider percentage of the population" (Speaking at TED, April 2008) by using an ordinary Wii remote control as a pointer and the IR camera on the front of the remote control as tracking device sensing light from an IR light pen. Lee produced several videos on YouTube about this system to demonstrate its operability, flexibility, and ease of use, and pointing out its modest price — the most inexpensive part is the infrared LED of the pen. This is an approach with a shallow learning curve since the gaming system is already familiar to many. A large programming support community may be available, both in opensource and commercial offerings.) However, the system cannot be used near direct sunlight, nor can it share the software of manufacturers of the IWB-types already mentioned. Certain considerations about the Bluetooth connection of the light pen also apply. Two lines of sight are involved (the controller and the pen) in the case of rear-projection case. unlike many others)


title: Interactive whiteboard

text: An interactive projector IWB involves a CMOS camera built into the projector, so that the projector produces the IWB image, but also detects the position of an active IR light pen when it contacts the surface where the image is projected. This solution, developed in 2007 and patented in 2010 by U.S. manufacturer Boxlight, like the other IR whiteboard systems, can suffer from potential problems caused by 'line of sight' between the pen and the projector/receiver and, like them also, does not provide mouse-over capability found in other solutions.


title: Interactive whiteboard

text: In some classrooms, interactive whiteboards have replaced traditional whiteboards or flipcharts, or video/media systems such as a DVD player and TV combination. Even where traditional boards are used, the IWB often supplements them by connecting to a school network digital video distribution system. In other cases, IWBs interact with online shared annotation and drawing environments such as interactive vector based graphical websites.


title: Interactive whiteboard

text: Brief instructional blocks can be recorded for review by students — they will see the exact presentation that occurred in the classroom with the teacher's audio input. This can help transform learning and instruction.


title: Interactive whiteboard

text: Many companies and projects now focus on creating supplemental instructional materials specifically designed for interactive whiteboards. One recent use of the IWB is in shared reading lessons. Mimic books, for instance, allow teachers to project children's books onto the interactive whiteboard with book-like interactivity.


title: Interactive whiteboard

text: Some manufacturers also provide classroom response systems as an integrated part of their interactive whiteboard products. Handheld 'clickers' operating via Infrared or Radio signals, for example, offer basic multiple choice and polling options. More sophisticated clickers offer text and numeric responses and can export an analysis of student performance for subsequent review.


title: Interactive whiteboard

text: By combining classroom response with an interactive whiteboard system, teachers can present material and receive feedback from students in order to direct instruction more effectively or else to carry out formal assessments. For example, a student may both solve a puzzle involving math concepts on the interactive whiteboard and later demonstrate his or her knowledge on a test delivered via the classroom response system. Some classroom response software can organize and develop activities and tests aligned with State standards.


title: Interactive whiteboard

text: There are now several studies revealing contradictory conclusions about the effect of the use of IWBs is effective on student learning. A compilation of this research is available.


title: Interactive whiteboard

text: According to the findings of a study conducted by the London Institute of Education with the funding of the DfES evaluated the educational and operational effectiveness of the London Challenge element of the adoption of the use of interactive whiteboards in the London area under a program called "the Schools Whiteboard Expansion project." At Key Stage 3, interactive whiteboards here associated with little significant impact on student performance in Mathematics and English and only a slight improvement in Science. In the same schools, at Key Stage 4, use of interactive whiteboards was found to have negative effects for Mathematics and Science, but positive effects for English. The authors cite several possible causes for the Key Stage 4 findings, including: a Type II statistical error, disruption to teaching methods leading to reduced pupil performance when IWBs were installed, or a non-random deployment decision of IWB installation resulting in a skew of the data.


title: Interactive whiteboard

text: At the same time, there is evidence of improved performance gains with the use of interactive whiteboards. The BECTA (UK) commissioned a study into the impact of Interactive Whiteboards over a two-year period. This study showed a very significant learning gains, particularly with second cohorts of students, where they benefited from the teacher's experience with the device.


title: Interactive whiteboard

text: Between 2003 and 2004, The DfES Primary Schools Whiteboard Expansion project (PSWE) provided substantial funding to 21 local authorities for the acquisition and use of interactive whiteboards in UK primary schools. The BECTA-sponsored study investigated the impact of this investment with 20 local authorities, using data for 7272 learners in 97 schools.


title: Interactive whiteboard

text: Variables considered in the research included length of exposure to interactive whiteboard technology, the age of pupils (down to individual birthdays), gender, special needs, entitlement to free schools meals and other socio-economic groupings. The implementation and impacts of the project were evaluated by a team at Manchester Metropolitan University, led by Professor Bridget Somekh. To date it is the largest and longest study conducted into the impact of interactive whiteboards.


title: Interactive whiteboard

text: The principal finding of this large-scale study was that, "[w]hen teachers have used an interactive whiteboard for a considerable period of time (by the autumn of 2006 for at least two years) its use becomes embedded in their pedagogy as a mediating artefact for their interactions with their pupils, and pupils' interactions with one another." The authors of the study argued that "mediating interactivity" is a sound concept, offering "a ... theoretical explanation for the way in which the multi-level modelling (MLM) analyses link the length of time pupils have been taught with interactive whiteboards to greater progress in national test scores year on year."


title: Interactive whiteboard

text: The research showed that interactive whiteboard technology led to consistent gains across all key stages and subjects with increasingly significant impact on the second cohorts, indicating that embedding of the technology into the classroom and teacher experience with the technology are key factors.


title: Interactive whiteboard

text: Gains were measured in 'months progress' against standard measures of attainment over the two-year study period.


title: Interactive whiteboard

text: Glover & Miller conducted a study on the pedagogic impact of interactive whiteboards in a secondary school. They found that although interactive whiteboards are theoretically more than a computer if it is only being used as an adjunct to teaching its potential remains unrealized. The authors' research was primarily to ascertain the extent and type of use in the classroom.


title: Interactive whiteboard

text: In order to determine if any change in pedagogy or teaching strategies was taking place the researchers conducted a detailed questionnaire. The authors found that the teachers used the IWBs in one of three ways; as an aid to efficiency, as an extension device, and as a transformative device. They noted that teachers' use of the technology was not primarily affected by training, access, or software availability. When used as a transformative device (approximately 10% of teachers taking part in the study) the impact on pedagogy was transformative.


title: Interactive whiteboard

text: In recent times, manufacturers of IWB technology have been setting up various online support communities for teachers and educational institutions deploying the use of the interactive whiteboards in learning environments. Such websites regularly contribute research findings and administer free whiteboard lessons to promote widespread use of interactive whiteboards in classrooms.


title: Interactive whiteboard

text: An article posted on the National Association of Secondary School Principals web site details pros & cons of interactive whiteboards.


title: Interactive whiteboard

text: There are a number of literature reviews, findings and papers on the use of interactive whiteboards in the classroom:


title: Interactive whiteboard

text: Interactive whiteboards may use one of several types of sensing technology to track interaction on the screen surface: resistive, electromagnetic, infrared optical, laser, ultra-sonic, and camera-based (optical).


title: Interactive whiteboard

text: An interactive display board may be made by attaching an electronic multimedia device such as a tablet to a display board. Methods for attaching tablets to display boards include cutting a window into a display board and fixing a pocket behind the window to insert and hold the tablet, pushing pins into the face of a display board with the tablet resting on the pins, attaching a lanyard to the tablet in order to hang it on the display board, or using dual sided adhesive tape to attach the tablet to the display board. Projex Boards manufactures a display board for tablets, with a pocket, easel and header board. The purpose of tablet display boards is to hold the tablet at eye level on the display board to facilitate better communication between audience and presenter. Some tablet interactive display boards have apertures for electrical cords in the form of openings at the bottom of the display board.


title: Interactive whiteboard

text: Permanent markers and use of regular dry erase markers can create problems on some interactive whiteboard surfaces because interactive whiteboard surfaces are most often melamine, which is a porous, painted surface that can absorb marker ink. Punctures, dents and other damage to surfaces are also a risk.


title: Interactive whiteboard

text: Some educators have found that the use of interactive whiteboards reinforces an age-old teaching method: the teacher speaks, and students listen. This teaching model is contrary to many modern instructional models.


title: Interactive whiteboard

text: Some manufacturers also provide an option to raise and lower the display to accommodate users of different heights.


title: Interactive whiteboard

text: Some manufacturers offer short-throw projection systems in which a projector with a special wide angle lens is mounted much closer to the interactive whiteboard surface and projects down at an angle of around 45 degrees. These vastly reduce the shadow effects of traditional front-projection systems and eliminate any chance for a user to see the projector beam. The risk of projector theft, which is problematic for some school districts, is reduced by integrating the projector with the interactive whiteboard.


title: Interactive whiteboard

text: Some manufacturers have provided a unified system where the whiteboards, short throw projection system and audio system are all combined into a single unit which can be set at different heights and enable young children and those in wheelchairs to access all areas of the board. Reduced installation costs make these short-throw projection systems cost effective.


title: Interactive whiteboard

text: In most cases, the touch surface must be initially calibrated with the display image. This process involves displaying a sequence of dots or crosses on the touch surface and having the user select these dots either with a stylus or their finger. This process is called alignment, calibration, or orientation. Fixed installations with projectors and boards bolted to roof and wall greatly reduce or eliminate the need to calibrate.


title: Interactive whiteboard

text: A few interactive whiteboards can automatically detect projected images during a different type of calibration. The technology was developed by Mitsubishi Electric Research Laboratories Inc and is disclosed in patent 7,001,023. The computer projects a Gray Code sequence of white and black bars on the touch surface and light sensitive sensors behind the touch surface detect the light passing through the touch surface. This sequence allows the computer to align the touch surface with the display; however, it has the disadvantage of having tiny fiber-sized "dead spots" in the resistive touch surface where the light sensors are present. The "dead spots" are so small that touches in that area are still presented to the computer properly.


title: Interactive whiteboard

text: Another system involves having a light sensor built into the projector and facing the screen. As the projector generates its calibration image (a process called "training"), it detects the change in light reflected from the black border and the white surface. In this manner it can uniquely compute all the linear matrix transform coefficients.


title: Interactive whiteboard

text: Yet another system includes a camera built into the handheld pen, with human imperceptible targets injected into the image stream sent to the projector or display, containing positioning information, where the camera detects that information and calculates position accordingly, requiring no calibration at all. Such a technology and system is integrated into penveu, and is further disclosed in patent 8,217,997


title: Chinna Thambi

text: Chinna Thambi () is a 1991 Indian Tamil-language romantic drama film written and directed by P. Vasu. The film stars Prabhu as the titular character, an uneducated village simpleton and Khushbu as Nandini, a homeschooled wealthy girl. Manorama, Radha Ravi, Uday Prakash, Rajeshkumar, and Goundamani play supporting roles. The music was composed by Ilaiyaraaja, and the film released on 12 April 1991.


title: Chinna Thambi

text: The film was remade in Kannada as "Ramachaari" (1991), Telugu as "Chanti" (1992) and Hindi as "Anari" (1993). The film was one of Prabhu's biggest blockbusters and completed a 356-day run in 9 screens and 100-day run in 47 screens.


title: Chinna Thambi

text: The film starts with the birth of a baby girl, Nandini, in a rich family. Her three elder brothers throw a feast in honour of her. The young son of the local singer (who had died) is brought in to sing for the event. The three brothers raise Nandini like their own child as their parents had died. At the age of five, an astrologer predicts that Nandini will bring much happiness to the family, but she will marry a person of her choice and not of her brothers' choosing. This angers the brothers, and to prevent this from happening, they raise Nandhini within the confines of the house. She is homeschooled, and when she does go out, all the men are warned to hide from Nandini and that seeing her will be met with dire consequences.


title: Chinna Thambi

text: Nandini soon reaches puberty. The few males allowed around her are the service staff and her bodyguards. Meanwhile, the boy who sang, Chinna Thambi, grows up to be a naïve and gullible simpleton with a heart of gold. He is raised by his widowed mother Kannamma. He does not go to school and spends his time singing and entertaining the people of the village.


title: Chinna Thambi

text: One day the bodyguards get into a fight with Chinna Thambi, who defeats them. Impressed with Chinna Thambi's naivete and fighting skills, the brothers hire Chinna Thambi to be Nandini's bodyguard and butler. Nandini meanwhile starts to resent her lack of freedom. She coerces Chinna Thambi to show her the village without her brothers' knowledge. Chinna Thambi complies with her wishes and shows her the village, which results in Nandini falling ill. Chinna Thambi is blamed for Nandini getting sick and is beaten up by the brothers. Nandini, who has just started to like Chinna Thambi, feels guilty for being the reason for him getting thrashed. She shares her medicine with Chinna Thambi, who inadvertently equates Nandini to his mother, as being the few people who truly care for him. This incident brings them closer together emotionally.


title: Chinna Thambi

text: One day, a factory worker is punished for leering at Nandini. He plots to kill her at the inauguration of the new factory owned by her brothers. Chinna Thambi overhears the plot, and in a desperate attempt to save Nandini, lunges at her and inadvertently feels her up in public. Nandini does not mind and defends Chinna Thambi by arguing that he would not do something like that in public without good reason. But her brothers are enraged and beat Chinna Thambi to the point that they almost kill him. Nandini stops them and gives him a chance to explain. When Chinna Thambi explains the situation, they hang their heads in shame. Chinna Thambi quits his job on the spot, despite Nandini's silent apology.


title: Chinna Thambi

text: At night, Nandini meets Chinna Thambi and apologise and perhaps convince him to come back to the job. Chinna Thambi refuses to come back as he does not want to put up with the violent nature of her brothers. She thinks if Chinna Thambi marries her, they will not be able to manhandle Chinna Thambi. She convinces Chinna Thambi to tie a mangalsutra around her neck, which will protect him from her brothers. Chinna Thambi, without realising the sanctity of the act, does as told and does not realise that he is now married to her.


title: Chinna Thambi

text: Chinna Thambi comes back to work and is given a higher level of respect by the brothers for saving Nandini's life. Nandini too starts emulating her sisters-in-law in taking care of her husband. This makes Chinna Thambi nervous, but he still remains clueless. Her change in behaviour is noticed by her sisters-in-law, who urge the brothers to get Nandini married off before she brings shame to the family. Nandini, realising that they are trying to get her married off, tries to make Chinna Thambi understand that they are already married. Chinna Thambi refuses to understand and runs away to his mother, who upon learning what has happened, pulls him out of denial. She sends him away in an attempt to protect him.


title: Chinna Thambi

text: The brothers come to know what has happened and torture Kannamma to get her to reveal where her son is hiding. She is saved in time by her son, who almost kills the brothers. The wives of the brothers stop him from killing them and ask him to save Nandini, who has now resorted to self-destruction upon hearing the torturous acts of her brothers. Chinna Thambi rushes back to save his wife and revives her with his singing. Nandini runs towards him and they embrace, with her brothers finally supporting their relationship.


title: Chinna Thambi

text: P. Vasu's son Sakthi made his screen debut as a child artist at the age of seven with this film; he appeared as young Prabhu in the film. Khushbu joined the film at Vasu's insistence. Vasu was initially sceptical about casting Manorama as Prabhu's mother as he believed people would compare it to her vastly different role in Vasu's previous film "Nadigan" (1990), but Manorama remained confident it would not happen. The filming was held at Gobichettipalayam.


title: Chinna Thambi

text: The soundtrack was composed by Ilaiyaraaja and lyrics were written by Vaali, Ilaiyaraaja and Gangai Amaran. The song "Nee Engey En Anbe" is set to the Carnatic raga Keeravani, as is "Poovoma Oorgolam". Ilaiyaraaja composed all the songs within 35 minutes. All of them were chartbusters. The film proved to be a breakthrough for playback singer Swarnalatha.


title: Chinna Thambi

text: "The Indian Express" wrote, "The conflicts are generated in such a way as to excite the sentiments of lay audiences".


title: Chinna Thambi

text: "Chinna Thambi" became a major breakthrough for Prabhu and Khushbu. They became one of the successful lead pairs in Tamil cinema of the 1990s through this film. The success of the film also led the director, actor and actress to collaborate in another project "Kizhakku Karai" (1991) the following year. After the release, Vasu was conferred "Navarasa Director" award by Amudha Surabhi Kalai Mandram, Madurai.


title: Chinna Thambi

text: Khushbu said in 2006, "I am still around only because of "Chinna Thambi". None of us imagined it would become the kind of cult film it did. I remember director P. Vasu, hero Prabhu and I were very skeptical about the film while shooting. It was a bold subject at the time, and we thought it would either be a huge flop or a huge hit". Prabhu recalled, "People still talk about "Chinna Thambi" [...] I still remember my father’s words after the show. "Just as I got a Bhimbsingh, you've got Vasu", he said".


title: Chinna Thambi

text: Vasu alluded to his film's success in a scene in his later film "Mannan" (1992), in which Krishnan (Rajinikanth) and Muthu (Goundamani) would be seen rushing in the crowd to buy tickets to watch "Chinna Thambi". After the film's success, Gobichettipalayam became a shooting hub for many films.


title: UFC 248

text: UFC 248: Adesanya vs. Romero was a mixed martial arts event produced by the Ultimate Fighting Championship that took place on March 7, 2020 at the T-Mobile Arena in Paradise, Nevada, part of the Las Vegas Metropolitan Area, United States.


title: UFC 248

text: A UFC Middleweight Championship bout between the current champion Israel Adesanya and former interim title challenger (as well as 2000 Olympic silver medalist and former world champion in freestyle wrestling) Yoel Romero headlined the event.


title: UFC 248

text: A UFC Women's Strawweight Championship bout between the current champion Zhang Weili and former champion Joanna Jędrzejczyk took place as the co-main event.


title: UFC 248

text: A middleweight bout between former champion Robert Whittaker (also welterweight winner) and Jared Cannonier was expected to take place at this event. However, it was announced on January 15 that Whittaker pulled out of the bout. Subsequently, promotion officials announced that Cannonier would be on standby in the event that one of the main event participants were to pull out of that contest. In turn, Cannonier indicated in mid-February that he had suffered a torn pectoral injury while training and would be sidelined for several months.


title: UFC 248

text: A bantamweight bout between Sean O'Malley and bantamweight winner José Alberto Quiñónez was originally scheduled to take place at UFC 229. However, it was scrapped after O'Malley failed a United States Anti-Doping Agency (USADA) drug test. The bout was then expected to take place at UFC 247, but it was eventually moved to this event for unknown reasons.<ref name="O'Mally/Quiñónez"></ref>


title: UFC 248

text: While not officially announced by the organization, a featherweight bout between Calvin Kattar and Jeremy Stephens was expected to take place at the event. However, Stephens was removed from the card in mid-January with an injury. The pairing was left intact and rescheduled for UFC 249.


title: UFC 248

text: A featherweight bout between Douglas Silva de Andrade and Movsar Evloev was scheduled to take place at the event. However, de Andrade withdrew from the bout due to injury and was replaced by promotional newcomer Jamall Emmers. Subsequently, Evloev pulled out of the fight in late February citing injuries sustained in a road accident. He was replaced by Giga Chikadze.


title: UFC 248

text: A middleweight bout between Derek Brunson and Edmen Shahbazyan was scheduled to take place at the event. However, it was announced on February 20 that the bout had moved to .


title: UFC 248

text: At the weigh-ins, Emily Whitmire weighed in at 117.5 pounds, 1.5 pounds over the strawweight non-title fight limit of 116 pounds. She was fined 20% of her purse and her bout with Polyana Viana was expected to proceed as scheduled at a catchweight. However, Whitmire was hospitalized the day of the event and the fight was cancelled.


title: UFC 248

text: The following is the reported payout to the fighters as reported to the Nevada State Athletic Commission (NSAC). It does not include sponsor money and also does not include the UFC's traditional "fight night" bonuses. The total disclosed payout for the event was $2,086,000.


title: UFC 248

text: On September 3, it was announced that the Nevada State Athletic Commission (NAC) suspended Deron Winn for nine months and fined him fined $1,800 after he tested positive for amphetamines in relation to this event. The suspension is retroactive to the date of the positive test.


title: Engel v. Vitale

text: Engel v. Vitale, 370 U.S. 421 (1962), was a landmark United States Supreme Court case in which the Court ruled that it is unconstitutional for state officials to compose an official school prayer and encourage its recitation in public schools, due to violation of the First Amendment. The ruling has been the subject of intense debate.


title: Engel v. Vitale

text: In 1962 the Board of Regents of New York approved a nondenominational prayer for their morning procedures.  Students would be given the choice to be excused for the morning prayer if they chose to.  The prayer was twenty-two words that went as followed:


title: Engel v. Vitale

text: The case was brought by a group of families of public school students in New Hyde Park from the Herricks Union Free School District who sued the school board president William J. Vitale, Jr. The families argued that the voluntary prayer written by the state board of regents to "Almighty God" contradicted their religious beliefs. Led by Steven I. Engel, a Jewish man, the plaintiffs sought to challenge the constitutionality of the state's prayer in school policy. They were supported by groups opposed to the school prayer including rabbinical organizations, Ethical Culture, and Jewish organizations.


title: Engel v. Vitale

text: The acting parties were not members of one particular religious persuasion, or all atheists. Their religious identities were legally identified in court paperwork as two Jews, an atheist, a Unitarian church member, and a member of the New York Society for Ethical Culture. However, despite being listed in the court papers as an atheist, plaintiff Lawrence Roth, who was raised Jewish, later denied that he was an atheist and described himself as religious and a participant of prayer. When religious affiliation was discussed during preparations for the case, Roth claimed he was "a very religious person, but not a churchgoer" and that he said prayers but was unsure of what prayer could accomplish. This resulted in the group's lawyer telling him "You're the atheist." Roth later stated "apparently, you have to have an atheist in the crowd, so we started from there."


title: Engel v. Vitale

text: The plaintiffs argued that opening the school day with such a prayer violates the Establishment Clause of the First Amendment to the United States Constitution (as applied to the states through the Fourteenth Amendment), which states, in part, "Congress shall make no law respecting an establishment of religion". The governments of twenty-two states submitted an "amicus curiae" brief to the Supreme Court urging affirmance of the New York Court of Appeals decision that upheld the constitutionality of the prayer. The American Jewish Committee, the Synagogue Council of America, and the American Ethical Union each submitted briefs urging the Court to instead reverse and rule that the prayer was unconstitutional.


title: Engel v. Vitale

text: In a 6–1 decision, the Supreme Court held that reciting government-written prayers in public schools was unconstitutional, violating the Establishment Clause of the First Amendment.


title: Engel v. Vitale

text: In his opinion for the Court, Justice Black explained the importance of separation between church and state by giving a lengthy history of the issue, beginning with the 16th century in England. He noted that prayer is a religious activity by its very nature, and that prescribing such a religious activity for school children violates the Establishment Clause.


title: Engel v. Vitale

text: The Court rejected the defendant's arguments that students were not asked to observe any specific established religion, that the traditional heritage of the nation was religious, and that the prayer was voluntary. The Court held that the mere promotion of a religion is sufficient to establish a violation, even if that promotion is not coercive. The Court further held that the fact that the prayer is vaguely-enough worded not to promote any particular religion is not a sufficient defense, as it still promotes a family of religions (those that recognize "Almighty God"), which still violates the Establishment Clause.


title: Engel v. Vitale

text: In a concurring opinion, Justice Douglas argued that the Establishment Clause is also violated when the government grants financial aid to religious schools.


title: Engel v. Vitale

text: In his dissenting opinion, Justice Stewart contended that the Establishment Clause was originally written to abolish the idea of a state-sponsored church, and not to stop a non-mandatory "brief non-denominational prayer".


title: Engel v. Vitale

text: Since its decision, "Engel" has been the subject of intense debate. It has become considered one of the Court's "liberal" decisions alongside decisions such as its sequel, "Abington School District v. Schempp", "Griswold v. Connecticut", "Miranda v. Arizona" and its sequel, "in re Gault", "Eisenstadt v. Baird", "Roe v. Wade", "Obergefell v. Hodges", "Miller v. California" and "Mapp v. Ohio", and has been criticized for its broadness in holding that a showing of coercion is not required to demonstrate an Establishment Clause violation.


title: Engel v. Vitale

text: "Engel" has been the basis for several subsequent decisions limiting government-directed prayer in school. In "Wallace v. Jaffree" (1985), the Supreme Court ruled Alabama's law permitting one minute for prayer or meditation was unconstitutional. In "Lee v. Weisman" (1992), the court prohibited clergy-led prayer at middle school graduation ceremonies. "Lee v. Weisman", in turn, was a basis for "Santa Fe ISD v. Doe" (2000), in which the Court extended the ban to school-organized "student"-led prayer at high school football games in which a majority of students voted in favor of the prayer.


title: Engel v. Vitale

text: One myth of the "Engel v. Vitale" case was that an atheist leader Madalyn Murray O'Hair was responsible for the landmark ruling of the case. A year after the 1962 ruling there were two separate suits challenging Bible-reading; one by Ed Schempp in Philadelphia and the other by Mrs. O'Hair in Maryland. The court combined the two cases and subsequently ruled consistent with "Engel".


title: Luke Combs discography

text: American country music singer and songwriter Luke Combs has released three studio albums, four extended plays and fifteen singles.


title: Valerie Curtin

text: Curtin was born in Jackson Heights, New York, the daughter of radio actor Joseph Curtin. She attended Lake Erie College.


title: Valerie Curtin

text: She is a cousin of TV comedian/actress Jane Curtin. She was married to writer and director Barry Levinson from 1975–1982.


title: Valerie Curtin

text: Curtin performed with comedy groups and acted in theatrical productions in New York before going to Los Angeles in 1971. There, she was a member of The Committee, a comedy group.


title: Valerie Curtin

text: Curtin began her writing career in the 1970s working on episodes of the television sitcom "The Mary Tyler Moore Show". Curtin and her then husband Barry Levinson were nominated for an Academy Award (in the category of Best Writing, Screenplay Written Directly for the Screen) for "...And Justice for All" (1979) starring Al Pacino. They also co-wrote the semi-autobiographical "Best Friends" (1982), which starred Burt Reynolds and Goldie Hawn.


title: Valerie Curtin

text: Curtin's acting career has run concurrently with her writing career. During the 1970s, she made various guest appearances on television in shows such as "Happy Days", "Welcome Back, Kotter", "Rhoda", "The Rockford Files", and "Barney Miller". In March 1976, ABC shot the pilot episode for "Three's Company", in which Curtin appeared alongside John Ritter and Susanne Zenor. Curtin played a character named Jenny, who eventually became Janet Wood, played by Joyce DeWitt.


title: Valerie Curtin

text: Her movie appearances include "Alice Doesn't Live Here Anymore" (her first movie appearance, 1974), "All the President's Men", "Silver Streak", and "Silent Movie" (all 1976), "Why Would I Lie?" (1980), as well as "Maxie" (1985) and John Cassavetes' final film, the 1986 comedy "Big Trouble", plus a small, uncredited role in "Best Friends."


title: Valerie Curtin

text: In 1982, Curtin was given the role of Judy Bernly in the television sitcom "9 to 5" based on the 1980 movie of the same name. Her TV role was portrayed by Jane Fonda in the film version. Curtin was dropped from the show after two seasons, when James Komack came on as the new executive producer, replacing the team led by Jane Fonda. However, Curtin returned for a syndicated version of "9 to 5" (1986–1988), reprising her earlier role; the new version was successful. In the 1980s and 1990s, her writing credits included mainstream films such as "Inside Moves" (1980), the 1984 remake of "Unfaithfully Yours", and "Toys" (1992).


title: Valerie Curtin

text: Curtin has also guest-starred in shows such as "Frasier", "Party of Five", "Becker", "The District", "Just Shoot Me", and "ER".


title: Worcester County, Massachusetts

text: Worcester County is a county located in the U.S. state of Massachusetts. At the 2020 census, the population was 862,111, making it the second-most populous county in Massachusetts while also being the largest in area. The largest city and traditional shire town is the city of Worcester. Worcester County is included in the Worcester, MA-CT Metropolitan Statistical Area as well as the Boston-Worcester-Providence, MA-RI-NH-CT Combined Statistical Area.


title: Worcester County, Massachusetts

text: Worcester County was formed from the eastern portion of colonial Hampshire County, the western portion of the original Middlesex County and the extreme western portion of the original Suffolk County. When the government of Worcester County was established on April 2, 1731, Worcester was chosen as its shire town (later known as a county seat). From that date until the dissolution of the county government, it was the only county seat. Because of the size of the county, there were fifteen attempts over 140 years to split the county into two counties, but without success.


title: Worcester County, Massachusetts

text: Initially, Lancaster was proposed as the seat of the northern county; later, Petersham was proposed once and Fitchburg was proposed repeatedly, most recently in 1903. Perhaps as a concession, in August 1884 the Worcester County Registry of Deeds was split in two, with the Worcester Northern registry placed in Fitchburg.


title: Worcester County, Massachusetts

text: According to the U.S. Census Bureau, the county has a total area of , of which is land and (4.3%) is water.


title: Worcester County, Massachusetts

text: It is the largest county in Massachusetts by area. The county is larger geographically than the entire state of Rhode Island even including Rhode Island's water ocean limit boundaries. The county constitutes Central Massachusetts, separating the Greater Springfield area from the Greater Boston area. It stretches from the northern to the southern border of the state. The geographic center of Massachusetts is in Rutland.


title: Worcester County, Massachusetts

text: Worcester County is one of two Massachusetts counties that borders three different neighboring states; the other being Berkshire County. They are also the only two counties to touch both the northern and southern state lines.


title: Worcester County, Massachusetts

text: At the 2000 census there were 750,963 people, 283,927 households, and 192,502 families in the county. The population density was 496 people per square mile (192/km). There were 298,159 housing units at an average density of 197 per square mile (76/km). The racial makeup of the county was 89.61% White, 2.73% Black or African American, 0.25% Native American, 2.62% Asian, 0.04% Pacific Islander, 2.93% from other races, and 1.82% from two or more races. 6.77%. were Hispanic or Latino of any race. 15.9% were of Irish, 12.3% Italian, 11.7% French, 8.0% French Canadian, 8.0% English, 5.6% Polish and 5.0% American ancestry according to Census 2000. 85.1% spoke English, 6.1% Spanish and 1.9% French as their first language.


title: Worcester County, Massachusetts

text: Of the 283,927 households 33.60% had children under the age of 18 living with them, 52.50% were married couples living together, 11.40% had a female householder with no husband present, and 32.20% were non-families. 26.20% of households were one person and 10.40% were one person aged 65 or older. The average household size was 2.56 and the average family size was 3.11.


title: Worcester County, Massachusetts

text: The age distribution was 25.60% under the age of 18, 8.40% from 18 to 24, 31.10% from 25 to 44, 21.80% from 45 to 64, and 13.00% 65 or older. The median age was 36 years. For every 100 females, there were 95.50 males. For every 100 females age 18 and over, there were 92.10 males.


title: Worcester County, Massachusetts

text: The median household income was $47,874 and the median family income was $58,394. Males had a median income of $42,261 versus $30,516 for females. The per capita income for the county was $22,983. About 6.80% of families and 9.20% of the population were below the poverty line, including 11.30% of those under age 18 and 9.50% of those age 65 or over.


title: Worcester County, Massachusetts

text: At the 2010 census, there were 798,552 people, 303,080 households, and 202,602 families in the county. The population density was . There were 326,788 housing units at an average density of . The racial makeup of the county was 85.6% white, 4.2% black or African American, 4.0% Asian, 0.2% American Indian, 3.6% from other races, and 2.3% from two or more races. Those of Hispanic or Latino origin made up 9.4% of the population. In terms of ancestry, 22.2% were Irish, 15.1% were French as well as 6.7% French Canadians, 14.4% were Italian, 11.7% were English, 7.0% were Polish, 6.9% were German, and 3.2% were American.


title: Worcester County, Massachusetts

text: Of the 303,080 households, 33.7% had children under the age of 18 living with them, 50.0% were married couples living together, 12.2% had a female householder with no husband present, 33.2% were non-families, and 26.2% of households were made up of individuals. The average household size was 2.55 and the average family size was 3.09. The median age was 39.2 years.


title: Worcester County, Massachusetts

text: The median household income was $64,152 and the median family income was $79,121. Males had a median income of $56,880 versus $42,223 for females. The per capita income for the county was $30,557. About 6.9% of families and 9.5% of the population were below the poverty line, including 12.1% of those under age 18 and 9.0% of those age 65 or over.


title: Worcester County, Massachusetts

text: The ranking of unincorporated communities that are included on the list are reflective of the census designated locations and villages were included as cities or towns. Data is from the 2007-2011 American Community Survey 5-Year Estimates.


title: Worcester County, Massachusetts

text: Worcester County is one of the 8 (of the total of 14) Massachusetts counties that have had no county government or county commissioners since July 1, 1998, when county functions were assumed by state agencies at local option following a change in state law. The county has an elected county sheriff, county prosecutor, and court officials, administered under the state department of public safety. The state correctional system in the county is known as the Worcester County Jail or "House of Corrections" at West Boylston, and the Worcester County District courts (state administered) are housed at Worcester, Fitchburg and other district courts within county boundaries. The Worcester County district attorney is a county-wide position even though the district includes one town from a neighboring county. In Massachusetts, Sheriffs have more limited roles than most states and are responsible for corrections, court service and bailiffs and jail release programs. County Sheriffs in Massachusetts are elected to six-year terms. The Worcester County Sheriff is Lewis Evangelidis, (R), and the Worcester County District Attorney is Joseph Early Jr. (D).(see the info-box for elected officials at county level). The Worcester County Conservation District has countywide boundaries. The county has a regional planning commission.


title: Worcester County, Massachusetts

text: Massachusetts law allows regional compacts, traditional counties and other governmental entities. Traditional County governments in the state include: Norfolk, Bristol, Dukes, Nantucket, and Plymouth Counties. Barnstable County, which is Cape Cod, functions as a modern regional county government. Suffolk County which is mainly Boston is under the Boston City Council. The Massachusetts General Laws describe this relationship of county government and the options for abolishing county governments and/or chartering regional governmental compacts in subchapter 34 B. Four other new county compacts have been created by the state legislature and these are in Hampshire, Franklin, Barnstable Counties, and a regional planning council level for Berkshire County. Thus 9 of 14 Counties have some form of county regional governments. Worcester County could exercise that option if it chooses for example, for public safety and, or preparedness due to its rather large geography, by a request to and a special act of the legislature, by local referendum or by one of three mechanisms. See the references for the state statute, and the League of Women Voters link.


title: Hypergraph

text: In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two vertices.


title: Hypergraph

text: Formally, an undirected hypergraph formula_1 is a pair formula_2 where formula_3 is a set of elements called "nodes" or "vertices", and formula_4 is a set of non-empty subsets of formula_3 called "hyperedges" or "edges". Therefore, formula_4 is a subset of formula_7, where formula_8 is the power set of formula_3. The size of the vertex set is called the "order of the hypergraph", and the size of edges set is the "size of the hypergraph".


title: Hypergraph

text: A directed hypergraph differs in that its hyperedges are not sets, but ordered pairs of subsets of formula_3, with each pair's first and second entries constituting the tail and head of the hyperedge respectively.


title: Hypergraph

text: While graph edges connect only 2 nodes, hyperedges connect an arbitrary number of nodes. However, it is often desirable to study hypergraphs where all hyperedges have the same cardinality; a "k-uniform hypergraph" is a hypergraph such that all its hyperedges have size "k". (In other words, one such hypergraph is a collection of sets, each such set a hyperedge connecting "k" nodes.) So a 2-uniform hypergraph is a graph, a 3-uniform hypergraph is a collection of unordered triples, and so on. An undirected hypergraph is also called a "set system" or a "family of sets" drawn from the universal set.


title: Hypergraph

text: Hypergraphs can be viewed as incidence structures. In particular, there is a bipartite "incidence graph" or "Levi graph" corresponding to every hypergraph, and conversely, most, but not all, bipartite graphs can be regarded as incidence graphs of hypergraphs.


title: Hypergraph

text: Hypergraphs have many other names. In computational geometry, an undirected hypergraph may sometimes be called a range space and then the hyperedges are called "ranges".


title: Hypergraph

text: In cooperative game theory, hypergraphs are called simple games (voting games); this notion is applied to solve problems in social choice theory. In some literature edges are referred to as "hyperlinks" or "connectors".


title: Hypergraph

text: Undirected hypergraphs are useful in modelling such things as satisfiability problems, databases, machine learning, and Steiner tree problems. They have been extensively used in machine learning tasks as the data model and classifier regularization (mathematics). The applications include recommender system (communities as hyperedges), image retrieval (correlations as hyperedges), and bioinformatics (biochemical interactions as hyperedges). Representative hypergraph learning techniques include hypergraph spectral clustering that extends the spectral graph theory with hypergraph Laplacian, and hypergraph semi-supervised learning that introduces extra hypergraph structural cost to restrict the learning results. For large scale hypergraphs, a distributed framework built using Apache Spark is also available.


title: Hypergraph

text: Directed hypergraphs can be used to model things including telephony applications, detecting money laundering, operations research, and transportation planning. They can also be used to model Horn-satisfiability.


title: Hypergraph

text: Although hypergraphs are more difficult to draw on paper than graphs, several researchers have studied methods for the visualization of hypergraphs.


title: Hypergraph

text: In one possible visual representation for hypergraphs, similar to the standard graph drawing style in which curves in the plane are used to depict graph edges, a hypergraph's vertices are depicted as points, disks, or boxes, and its hyperedges are depicted as trees that have the vertices as their leaves. If the vertices are represented as points, the hyperedges may also be shown as smooth curves that connect sets of points, or as simple closed curves that enclose sets of points.


title: Hypergraph

text: In another style of hypergraph visualization, the subdivision model of hypergraph drawing, the plane is subdivided into regions, each of which represents a single vertex of the hypergraph. The hyperedges of the hypergraph are represented by contiguous subsets of these regions, which may be indicated by coloring, by drawing outlines around them, or both. An order-"n" Venn diagram, for instance, may be viewed as a subdivision drawing of a hypergraph with "n" hyperedges (the curves defining the diagram) and 2 − 1 vertices (represented by the regions into which these curves subdivide the plane). In contrast with the polynomial-time recognition of planar graphs, it is NP-complete to determine whether a hypergraph has a planar subdivision drawing, but the existence of a drawing of this type may be tested efficiently when the adjacency pattern of the regions is constrained to be a path, cycle, or tree.


title: Hypergraph

text: An alternative representation of the hypergraph called PAOH is shown in the figure on top of this article. Edges are vertical lines connecting vertices. Vertices are aligned on the left. The legend on the right shows the names of the edges. It has been designed for dynamic hypergraphs but can be used for simple hypergraphs as well.


title: Hypergraph

text: Classic hypergraph coloring is assigning one of the colors from set formula_11 to every vertex of a hypergraph in such a way that each hyperedge contains at least two vertices of distinct colors. In other words, there must be no monochromatic hyperedge with cardinality at least 2. In this sense it is a direct generalization of graph coloring. Minimum number of used distinct colors over all colorings is called the chromatic number of a hypergraph.


title: Hypergraph

text: Hypergraphs for which there exists a coloring using up to "k" colors are referred to as "k-colorable". The 2-colorable hypergraphs are exactly the bipartite ones.


title: Hypergraph

text: There are many generalizations of classic hypergraph coloring. One of them is the so-called mixed hypergraph coloring, when monochromatic edges are allowed. Some mixed hypergraphs are uncolorable for any number of colors. A general criterion for uncolorability is unknown. When a mixed hypergraph is colorable, then the minimum and maximum number of used colors are called the lower and upper chromatic numbers respectively.


title: Hypergraph

text: Because hypergraph links can have any cardinality, there are several notions of the concept of a subgraph, called "subhypergraphs", "partial hypergraphs" and "section hypergraphs".


title: Hypergraph

text: A subhypergraph is a hypergraph with some vertices removed. Formally, the subhypergraph formula_27 induced by formula_28 is defined as


title: Hypergraph

text: An extension of a subhypergraph is a hypergraph where each hyperedge of formula_1 which is partially contained in the subhypergraph formula_27 is fully contained in the extension formula_32. Formally


title: Hypergraph

text: The partial hypergraph is a hypergraph with some edges removed. Given a subset formula_36 of the edge index set, the partial hypergraph generated by formula_37 is the hypergraph


title: Hypergraph

text: The dual formula_41 of formula_1 is a hypergraph whose vertices and edges are interchanged, so that the vertices are given by formula_43 and whose edges are given by formula_44 where


title: Hypergraph

text: When a notion of equality is properly defined, as done below, the operation of taking the dual of a hypergraph is an involution, i.e.,


title: Hypergraph

text: A connected graph "G" with the same vertex set as a connected hypergraph "H" is a host graph for "H" if every hyperedge of "H" induces a connected subgraph in "G". For a disconnected hypergraph "H", "G" is a host graph if there is a bijection between the connected components of "G" and of "H", such that each connected component "G<nowiki>'</nowiki>" of "G" is a host of the corresponding "H<nowiki>'</nowiki>".


title: Hypergraph

text: The 2-section (or clique graph, representing graph, primal graph, Gaifman graph) of a hypergraph is the graph with the same vertices of the hypergraph, and edges between all pairs of vertices contained in the same hyperedge.


title: Hypergraph

text: The transpose formula_52 of the incidence matrix defines a hypergraph formula_53 called the dual of formula_1, where formula_55 is an "m"-element set and formula_56 is an "n"-element set of subsets of formula_55. For formula_58 and formula_59 if and only if formula_60.


title: Hypergraph

text: For a directed hypergraph, the heads and tails of each hyperedge formula_61 are denoted by formula_62 and formula_63 respectively. formula_50 where


title: Hypergraph

text: A hypergraph "H" may be represented by a bipartite graph "BG" as follows: the sets "X" and "E" are the parts of "BG", and ("x", "e") are connected with an edge if and only if vertex "x" is contained in edge "e" in "H".


title: Hypergraph

text: Conversely, any bipartite graph with fixed parts and no unconnected nodes in the second part represents some hypergraph in the manner described above. This bipartite graph is also called incidence graph.


title: Hypergraph

text: A parallel for the adjacency matrix of a hypergraph can be drawn from the adjacency matrix of a graph. In the case of a graph, the adjacency matrix is a square matrix which indicates whether pairs of vertices are adjacent. Likewise, we can define the adjacency matrix formula_66 for a hypergraph in general where the hyperedges formula_67have real weights formula_68 with


title: Hypergraph

text: In contrast with ordinary undirected graphs for which there is a single natural notion of cycles and acyclic graphs, there are multiple natural non-equivalent definitions of acyclicity for hypergraphs which collapse to ordinary graph acyclicity for the special case of ordinary graphs.


title: Hypergraph

text: A first definition of acyclicity for hypergraphs was given by Claude Berge: a hypergraph is Berge-acyclic if its incidence graph (the bipartite graph defined above) is acyclic. This definition is very restrictive: for instance, if a hypergraph has some pair formula_70 of vertices and some pair formula_71 of hyperedges such that formula_72 and formula_73, then it is Berge-cyclic. Berge-cyclicity can obviously be tested in linear time by an exploration of the incidence graph.


title: Hypergraph

text: We can define a weaker notion of hypergraph acyclicity, later termed α-acyclicity. This notion of acyclicity is equivalent to the hypergraph being conformal (every clique of the primal graph is covered by some hyperedge) and its primal graph being chordal; it is also equivalent to reducibility to the empty graph through the GYO algorithm (also known as Graham's algorithm), a confluent iterative process which removes hyperedges using a generalized definition of ears. In the domain of database theory, it is known that a database schema enjoys certain desirable properties if its underlying hypergraph is α-acyclic. Besides, α-acyclicity is also related to the expressiveness of the guarded fragment of first-order logic.