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Rural Hospitals Theorem
The rural hospitals theorem (RHT) is a fundamental theorem in the theory of stable matching. It considers the problem of matching doctors to hospitals for residency, where each doctor is matched to a single hospital but each hospital has several positions for doctors. The total number of positions is larger than the total number of doctors, so some hospitals inevitably remain with unfilled positions. Usually, ''rural hospitals'' are less wanted than urban hospitals, so they often remain with many empty positions. This raised the question of whether the mechanism used to match doctors to hospitals can be changed in order to help these rural hospitals. The ''rural hospitals theorem'' answers this question negatively assuming all preferences are strict (i.e., no doctor is indifferent between two hospitals and no hospital is indifferent between two doctors). The theorem has two parts: # The set of assigned doctors, and the number of filled positions in each hospital, are the same in a ...
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Stable Matching
In mathematics, economics, and computer science, the stable matching problem is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. A matching is a bijection from the elements of one set to the elements of the other set. A matching is ''not'' stable if: In other words, a matching is stable when there does not exist any pair (''A'', ''B'') which both prefer each other to their current partner under the matching. The stable marriage problem has been stated as follows: The existence of two classes that need to be paired with each other (heterosexual men and women in this example) distinguishes this problem from the stable roommates problem. Applications Algorithms for finding solutions to the stable marriage problem have applications in a variety of real-world situations, perhaps the best known of these being in the assignment of graduating medical students to their first hospital appointments. ...
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Medical Doctor
A physician, medical practitioner (British English), medical doctor, or simply doctor is a health professional who practices medicine, which is concerned with promoting, maintaining or restoring health through the study, diagnosis, prognosis and treatment of disease, injury, and other physical and mental impairments. Physicians may focus their practice on certain disease categories, types of patients, and methods of treatment—known as specialities—or they may assume responsibility for the provision of continuing and comprehensive medical care to individuals, families, and communities—known as general practice. Medical practice properly requires both a detailed knowledge of the academic disciplines, such as anatomy and physiology, underlying diseases, and their treatment, which is the science of medicine, and a decent competence in its applied practice, which is the art or craft of the profession. Both the role of the physician and the meaning of the word itself vary ...
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Hospitals
A hospital is a healthcare institution providing patient treatment with specialized health science and auxiliary healthcare staff and medical equipment. The best-known type of hospital is the general hospital, which typically has an emergency department to treat urgent health problems ranging from fire and accident victims to a sudden illness. A district hospital typically is the major health care facility in its region, with many beds for intensive care and additional beds for patients who need long-term care. Specialized hospitals include trauma centers, rehabilitation hospitals, children's hospitals, geriatric hospitals, and hospitals for specific medical needs, such as psychiatric hospitals for psychiatric treatment and other disease-specific categories. Specialized hospitals can help reduce health care costs compared to general hospitals. Hospitals are classified as general, specialty, or government depending on the sources of income received. A teaching hospital cam ...
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Medical Residency
Residency or postgraduate training is a stage of graduate medical education. It refers to a qualified physician (one who holds the degree of MD, DO, MBBS/MBChB), veterinarian ( DVM/VMD, BVSc/BVMS), dentist ( DDS or DMD), podiatrist ( DPM), optometrist ( OD), pharmacist ( PharmD), or Medical Laboratory Scientist ( Doctor of Medical Laboratory Science) who practices medicine or surgery, veterinary medicine, dentistry, optometry, podiatry, clinical pharmacy, or Clinical Laboratory Science, respectively, usually in a hospital or clinic, under the direct or indirect supervision of a senior medical clinician registered in that specialty such as an attending physician or consultant. The term ''residency'' is named as such due to resident physicians (resident doctors) of the 19th century residing at the dormitories of the hospital in which they received training. In many jurisdictions, successful completion of such training is a requirement in order to obtain an unrestricted l ...
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Alvin E
''Alvin'' (DSV-2) is a crewed deep-ocean research submersible owned by the United States Navy and operated by the Woods Hole Oceanographic Institution (WHOI) of Woods Hole, Massachusetts. The original vehicle was built by General Mills' Electronics Group in Minneapolis, Minnesota. Named to honor the prime mover and creative inspiration for the vehicle, Allyn Vine, ''Alvin'' was commissioned on June 5, 1964. The submersible is launched from the deep submergence support vessel , which is also owned by the U.S. Navy and operated by WHOI. The submersible has made more than 5,200 dives, carrying two scientists and a pilot, observing the lifeforms that must cope with super-pressures and move about in total darkness, as well as exploring the wreck of ''Titanic''. Research conducted by ''Alvin'' has been featured in nearly 2,000 scientific papers. Design ''Alvin'' was designed as a replacement for bathyscaphes and other less maneuverable oceanographic vehicles. Its more nimble des ...
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Different Stable Matchings
Different may refer to: Music * "Different", a song by Cass Elliot from the soundtrack of the 1970 film '' Pufnstuf'' * '' Different'', a 1989 album by Thomas Anders * '' Different'', a 2002 album by Kate Ryan * "Different", a song by Egypt Central from their eponymous 2005 album * "Different", a song by Acceptance from the 2005 album '' Phantoms'' * "Different", a 2006 song by Jamie Shaw * "Different", a song by Dreamscape from the 2007 album '' 5th Season'' * "Different", a song by Pendulum from the 2008 album ''In Silico'' * "Different", a song by Ximena Sariñana from the 2011 album Ximena Sariñana * " Different", a 2012 song by Robbie Williams * "Different", a song by No Malice from the 2013 album ''Hear Ye Him'' * "Different", a song by Winner from the 2014 album ''2014 S/S'' * "Different", a 2017 song by Micah Tyler * "Different", a song by Future and Juice Wrld from the 2018 mixtape ''Wrld on Drugs'' * "Different", a song by Burna Boy from the 2019 album ''African Giant'' ...
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National Resident Matching Program
The National Resident Matching Program (NRMP), also called The Match, is a United States–based private non-profit non-governmental organization created in 1952 to place U.S. Medical education in the United States, medical school students into residency (medicine), residency training programs located in United States teaching hospitals. Its mission has since expanded to include the placement of U.S. citizen and non-U.S. citizen international medical school students and graduates into residency and fellowship training programs. In addition to the annual Main Residency Match that in 2021 encompassed more than 48,000 applicants and 38,000 positions, the NRMP conducts Fellowship Matches for more than 60 subspecialties through its Specialties Matching Service (SMS). The NRMP is sponsored by a board of directors that includes medical school deans, teaching hospital executives, graduate medical education program directors, medical students and residents, and one public member. NRMP Inte ...
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Envy-free Matching
In economics and social choice theory, an envy-free matching (EFM) is a matching between people to "things", which is envy-free in the sense that no person would like to switch their "thing" with that of another person. This term has been used in several different contexts. In unweighted bipartite graphs In an unweighted bipartite graph G = (''X''+''Y'', ''E''), an envy-free matching is a matching in which no unmatched vertex in ''X'' is adjacent to a matched vertex in ''Y''. Suppose the vertices of ''X'' represent people, the vertices of ''Y'' represent houses, and an edge between a person ''x'' and a house ''y'' represents the fact that ''x'' is willing to live in ''y''. Then, an EFM is a partial allocation of houses to people such that each house-less person does not envy any person with a house, since they do not like any allocated house anyway. Every matching that saturates ''X'' is envy-free, and every empty matching is envy-free. Moreover, if , ''NG''(''X''), ≥ , X, ...
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Stable Matching
In mathematics, economics, and computer science, the stable matching problem is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. A matching is a bijection from the elements of one set to the elements of the other set. A matching is ''not'' stable if: In other words, a matching is stable when there does not exist any pair (''A'', ''B'') which both prefer each other to their current partner under the matching. The stable marriage problem has been stated as follows: The existence of two classes that need to be paired with each other (heterosexual men and women in this example) distinguishes this problem from the stable roommates problem. Applications Algorithms for finding solutions to the stable marriage problem have applications in a variety of real-world situations, perhaps the best known of these being in the assignment of graduating medical students to their first hospital appointments. ...
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