title: Vanessa Bell

text: "Street Corner Conversation" (also created in 1913) features four individuals in conversation amidst massive geometrical forms.


title: Vanessa Bell

text: "Summer Camp" (1913), oil on board, illustrates a summer camp organized at Brandon on the Norfolk-Suffolk border near Thetford.


title: Vanessa Bell

text: "By the Estuary" (1915), oil on canvas, is a modestly scaled landscape showing her fondness for clarity of design in which segments of contrasting color harmonize.


title: Vanessa Bell

text: "Nude with Poppies" (1916), oil on canvas, is a preliminary design for a headboard which Bell painted for Mary Hutchinson.


title: Vanessa Bell

text: In 2021, Bell was one of four featured women artists at an exhibition at the Laing Gallery, Newcastle.


title: Vanessa Bell

text: Bell was portrayed by Janet McTeer in the Dora Carrington biopic "Carrington" (1995), and by Miranda Richardson in the film "The Hours" (2002).


title: Vanessa Bell

text: Bell is the subject of the Susan Sellers novel "Vanessa and Virginia" (2010) and of the Priya Parmar novel "Vanessa and Her Sister" (2014). She was portrayed by Phoebe Fox and Eve Best in the BBC mini-series "Life in Squares" (2015).


title: Waterbed

text: A waterbed, water mattress, or flotation mattress is a bed or mattress filled with water. Waterbeds intended for medical therapies appear in various reports through the 19th century. The modern version, invented in San Francisco and patented in 1971, became a popular consumer item in the United States through the 1980s with up to 20% of the market in 1986 and 22% in 1987. By 2013, they accounted for less than 5% of new bed sales.


title: Waterbed

text: A hard-sided waterbed consists of a water-containing mattress inside a rectangular frame of wood resting on a plywood deck that sits on a platform.


title: Waterbed

text: A soft-sided waterbed consists of a water-containing mattress inside of a rectangular frame of sturdy foam, zippered inside a fabric casing, which sits on a platform. It looks like a conventional bed and is designed to fit existing bedroom furniture. The platform usually looks like a conventional foundation or box spring, and sits atop a reinforced metal frame.


title: Waterbed

text: Early waterbed mattresses, and many inexpensive modern mattresses, have a single water chamber. When the water mass in these "free flow" mattresses is disturbed, significant wave motion can be felt, and they need time to stabilize after a disturbance. Later models employed wave-reducing methods, including fiber batting. Some models only partially reduce wave motion, while more expensive models almost eliminate wave motion.


title: Waterbed

text: Water beds are normally heated. If no heater is used, the water will equalize with the room air temperature (around 70 °F).


title: Waterbed

text: In models with no heater, there are at least several inches of insulation above the water chamber. This partially eliminates the body-contouring benefit of a waterbed, and the ability to control the bed temperature. For these reasons, most waterbeds have temperature control systems. Temperature is controlled via a thermostat and set to personal preference, most commonly around average skin temperature, . A typical heating pad consumes 150–400 watts of power. Depending on insulation, bedding, temperature, use, and other factors, electricity usage may vary significantly.


title: Waterbed

text: Waterbeds are usually constructed from soft polyvinyl chloride (PVC) or similar material. They can be repaired with practically any vinyl repair kit.


title: Waterbed

text: A form of waterbed was invented in 1833 by the Scottish physician Neil Arnott. "Dr. Arnott's Hydrostatic Bed" was devised to prevent bedsores in patients, and comprised a bath of water with a covering of rubber-impregnated canvas, on which lighter bedding was placed. Arnott didn't patent it, permitting anyone to construct a bed to this design.


title: Waterbed

text: The use of a waterbed (for the ailing Mrs. Hale) is mentioned in Elizabeth Gaskell's 1855 novel "North and South".


title: Waterbed

text: On May 18, 1863, a proposal for waterbed supplies was posted to newspapers by the USA Medical and Hospital Department, Medical Purveyor's Office, Washington D.C. The proposal requested a supplier for "water-beds, India Rubber Rubber Cushions, for air or water".


title: Waterbed

text: In 1871, a waterbed was in use in Elmira, New York, for "invalids". It was briefly mentioned by Mark Twain in his article "A New Beecher Church", which was published in "The New York Times" on 23 July 1871. Twain wrote: "In the infirmary will be kept one or two water-beds (for invalids whose pains will not allow them to be on a less yielding substance) and half a dozen reclining invalid-chairs on wheels. The water-beds and invalid-chairs at present belonging to the church are always in demand, and never out of service".


title: Waterbed

text: A newspaper classified want ad in 1877 requested "AN INDIA RUBBER Water-bed. 3 feet by 2 feet, new or second hand. Call immediately at 1,222 Broadway."


title: Waterbed

text: The protagonist Graham is placed on a waterbed in a glass case during his coma of 203 years in the 1898 H. G. Wells novel "The Sleeper Awakes".


title: Waterbed

text: Science fiction writer Robert A. Heinlein described therapeutic waterbeds in his novels "Beyond This Horizon" (1942), "Double Star" (1956), and "Stranger in a Strange Land" (1961). In 1980 Heinlein recalled in "Expanded Universe":


title: Waterbed

text: Heinlein made no attempt to build his invention, but its first builder, Charles Hall, was denied a patent claim based on Heinlein's "prior works".


title: Waterbed

text: Apparently, the initial patent application by Charles Hall for the waterbed was denied as being too broad, as the device itself had been described by Heinlein in several of his novels that had been published more than 25 years prior to Hall trying to make one. Hall was later granted a patent when he modified and specified his design.


title: Waterbed

text: The modern waterbed was created by Charles Prior Hall in 1968, while he was a design student at San Francisco State University in California. Hall originally wanted to make an innovative chair. His first prototype was a vinyl bag with 300 pounds (136 kg) of cornstarch. Ultimately, he abandoned working on a chair, and settled on perfecting a bed.


title: Waterbed

text: Hall was granted a patent (#3,585,356) on his waterbed in 1971, which he originally called "liquid support for human bodies." The same year, he founded Innerspace Environments, a manufacturing and sales company which became the leading retailer of waterbeds in the United States, with 30 owned-and-operated stores. The patent came to trial in 1991 in "Intex v. Hall /wbx". The patent was upheld in court, and Hall received a $4.8 million judgment for infringement. Hall /wbx received additional royalties from licensing. Some later lawsuits were dismissed because of laches.


title: Waterbed

text: In 1987, sales peaked at 22% of the domestic mattress industry. Although the waterbed was initially advertised as offering "undisturbed sleep", Hall admitted that customers "bought it for the sensual or the sexual part of it", and the sexually associated advertising was highly effective in the 1970s and early 1980s. Henry Petroski of Duke University said of the waterbed: "Not only was it the cool new gadget, but it emerged during a time when the culture embraced anything different, especially a product that embodied sexual liberation".


title: Waterbed

text: The waterbed can be useful and comfortable for some and dangerous for others. The main feature of the waterbed found attractive is its form-fitting, pressure-minimizing nature. Not only is this beneficial to those seeking mere comfort, but the removal of pressure from the spine can provide relief to those with back pain. In addition, the distribution of weight can prevent bedsores among the paralytic and the comatose. However, the National Institute of Child Health and Human Development warns that the form-fitting nature of the water-bed poses a danger to infants, providing a possibility of asphyxiation.


title: Waterbed

text: Another advantage of a waterbed is its easy cleaning. It is impossible for dirt and dead skin particles to penetrate the water mattress, which can then be wiped away periodically with a cloth and vinyl cleaner. The cover over the mattress can be regularly washed—thus virtually eliminating house dust mites in the bed. Dust mites can trigger asthma, eczema, and allergies in people sensitive to them.


title: Waterbed

text: First, since some hard-sided waterbeds are of different sizes from other mattresses, bed sheets are harder to find and come in fewer varieties. Second, moving a waterbed is more difficult than moving a normal bed; the water must be drained and the frame disassembled, then the frame must be reassembled, the mattress refilled with water, and the water heated for a potentially long period to get the new water to the correct temperature. Heating the bed can be costly; a waterbed consumes between 300 and 1,500 kWh/year ($36–180 USD at 12c/kWh, the US national average cost for residential energy), depending on the climate, bed size, and other factors. The energy usage can be decreased by about 60% with the use of a soft-sided waterbed. The ability to heat the bed is lost if there is a power outage, and this can make the bed too cold to sleep on, particularly if the power outage occurs during winter, and/or the room cannot be heated. The water itself can pose challenges when water mattresses occasionally leak. Plastic liners will reduce damage, but emptying, patching, refilling, and reheating the bed (and sleeping elsewhere until all this is completed) can be an inconvenience. Another factor is the weight of a waterbed. Waterbed mattresses, depending on the size, hold about of water, which could bring the weight of the entire bed to over . This weight could pose a risk to the floor the bed is on. Some landlords may not allow a tenant to have a waterbed due to this, especially if it is on a higher floor.


title: Ignacio Serricchio

text: Ignacio Ariel Serricchio (born April 19, 1982) is an Argentine actor. He is known for his role as Diego Alcazar on "General Hospital" and as Alejandro "Alex" Chavez on "The Young and the Restless". Other roles include Lifetime's "Witches of East End", seasons 9-12 of "Bones", and the Netflix reboot of "Lost in Space".


title: Ignacio Serricchio

text: Serricchio was born in Lanús, Argentina, and is a graduate of Syracuse University's drama department. In October 2004, Serricchio joined the cast of the ABC daytime soap "General Hospital" as troubled youth Diego Alcazar. He left the soap in November 2006. He returned as Diego on February 22, 2008, until his character was killed off on March 5, 2008. In 2005, Serricchio portrayed a streetwise Mormon missionary in the critically acclaimed film "States of Grace". In 2007, he appeared in 6 episodes of "Ghost Whisperer", where he played the character Gabriel Lawrence. In 2008, he portrayed Luis in the CW's "Privileged". The show stopped filming on February 24, 2009, and was cancelled on May 19, 2009. From December 2012 to January 2014, he played the recurring role of police detective Alex Chavez on the CBS daytime soap "The Young and the Restless". In 2014, he played the recurring role of medic Tommy Cole during the second and final season of the Lifetime drama series "Witches of East End". In the summer of 2015, Serrichio was cast in the role of Miguel on the BET sitcom, "Zoe Ever After" starring Brandy Norwood. He played Dr. Rodolfo Fuentes on "Bones", seasons 9-12. Starting in 2018, he appeared as Don West in "Lost in Space", the Netflix remake of the 1965 TV series.


title: Pregnancy test

text: A pregnancy test is used to determine whether a female is pregnant or not. The two primary methods are testing for the female pregnancy hormone (human chorionic gonadotropin (hCG)) in blood or urine using a pregnancy test kit, and scanning with ultrasonography. Testing blood for hCG results in the earliest detection of pregnancy. Almost all pregnant women will have a positive urine pregnancy test one week after the first day of a missed menstrual period.


title: Pregnancy test

text: Identified in the early 20th century, human chorionic gonadotropin (hCG) is a glycoprotein hormone that rises quickly in the first few weeks of pregnancy, typically reaching a peak at 8- to 10-weeks gestational age. hCG is produced by what will become the placenta. hCG testing can be performed with a blood (serum) sample (typically done in a medical facility) or with urine (which can be performed in a medical facility or at home). The assays used to detect the presence of hCG in blood or urine are generally reliable and inexpensive. Secretion of hCG can occur as soon as 6 days following ovulation and on average 8–10 days following ovulation; this is the earliest hCG can be detected in a blood sample. The hCG concentration in blood is higher than in urine. Therefore, a blood test can be positive while the urine test is still negative.


title: Pregnancy test

text: Qualitative tests (yes/no or positive/negative results) look for the presence of the beta subunit of human chorionic gonadotropin (hCG) in blood or urine. For a qualitative test the thresholds for a positive test are generally determined by an hCG cut-off where at least 95% of pregnant women would get a positive result on the day of their first missed period. Qualitative urine pregnancy tests vary in sensitivity. High-sensitivity tests are more common and typically detect hCG levels between 20 and 50 milli-international units/mL (mIU/mL). Low-sensitivity tests detect hCG levels between 1500 and 2000 mIU/mL and have unique clinical applications, including confirmation of medication abortion success. Qualitative urine tests available for home use are typically designed as lateral flow tests.


title: Pregnancy test

text: Quantitative tests measure the exact amount of hCG in the sample. Blood tests can detect hCG levels as low as 1 mIU/mL, and typically clinicians will diagnose a positive pregnancy test at 5mIU/mL.


title: Pregnancy test

text: There is a multilevel urine pregnancy test (MLPT) that measures hCG levels semiquantitatively. The hCG levels are measured at <25, 25 to 99, 100 to 499, 500 to 1999, 2000 to 9999, and >10,000 mIU/mL. This test has utility for determining the success of medication abortion.


title: Pregnancy test

text: Obstetric ultrasonography may also be used to detect and diagnose pregnancy. It is very common to have a positive at home urine pregnancy test before an ultrasound. Both abdominal and vaginal ultrasound may be used, but vaginal ultrasound allows for earlier visualization of the pregnancy. With obstetric ultrasonography the gestational sac (intrauterine fluid collection) can be visualized at 4.5 to 5 weeks gestation, the yolk sac at 5 to 6 weeks gestation, and fetal pole at 5.5 to 6 weeks gestation. Ultrasound is used to diagnose multiple gestation.


title: Pregnancy test

text: A systematic review published in 1998 showed that home pregnancy test kits, when used by experienced technicians, are almost as accurate as professional laboratory testing (97.4%). When used by consumers, however, the accuracy fell to 75%: the review authors noted that many users misunderstood or failed to follow the instructions included in the kits.


title: Pregnancy test

text: Spurious "evaporation lines" may appear on many home pregnancy tests if read after the suggested 3–5 minute window or reaction time, independent of an actual pregnancy. False positives may also appear on tests used past their expiration date.


title: Pregnancy test

text: False positive pregnancy test can happen due to 'phantom hCG' which is due to people having human antianimal or heterophilic antibodies.


title: Pregnancy test

text: False positives can also be caused by (in order of incidence) quiescent pregnancy, pituitary sulfated hCG, heterophilic antibody, familial hCG syndrome and cancer.


title: Pregnancy test

text: Urine tests can be falsely positive in those that are taking the medications: chlorpromazine, promethazine, phenothiazines, methadone, aspirin, carbamazepine and drugs that cause high urinary pH.


title: Pregnancy test

text: False negative readings can occur when testing is done too early. hCG levels rise rapidly in early pregnancy and the chances of false negative test results diminish with time (increasing gestational age). Less sensitive urine tests and qualitative blood tests may not detect pregnancy until three or four days after implantation. Menstruation occurs on average 14 days after ovulation, so the likelihood of a false negative is low once a menstrual period is late. Ovulation may not occur at a predictable time in the menstrual cycle. A number of factors may cause an unexpectedly early or late ovulation, even for people with a history of regular menstrual cycles.


title: Pregnancy test

text: More rare, false negative results can also occur due to a "hook effect", where a sample with a very high level of hCG is tested without dilution, causing an invalid result.


title: Pregnancy test

text: Pregnancy tests may be used to predict if a pregnancy is likely to continue or is abnormal. Miscarriage, or spontaneous abortion or pregnancy loss, is common in early pregnancy. Serial quantitative blood tests may be done, usually 48 hours apart, and interpreted based on the knowledge that hCG in a viable normal pregnancy rises rapidly in early pregnancy. For example, for a starting hCG level of 1,500 mIU/ml or less, the hCG of continuing, normal pregnancy will increase at least 49% in 48 hours. However, for pregnancies with a higher starting hCG, between 1,500 and 3,000 mIU/ml, the hCG should rise at least 40%; for a starting hCG greater than 3,000 mIU/ml, the hCG should increase at least 33%. Failure to rise by these minimums may indicate that the pregnancy is not normal, either as a failed intrauterine pregnancy or a possible ectopic pregnancy.


title: Pregnancy test

text: Ultrasound is also a common tool for determining viability and location of a pregnancy. Serial ultrasound may be used to identify non-viable pregnancies, as pregnancies that do not grow in size or develop expected structural findings on repeated ultrasounds over a 1-2 week interval may be identified as abnormal. Occasionally, a single ultrasound may be used to identify a pregnancy as non-viable; for example, an embryo that is greater than a certain size but that lacks a visible heart beat may be confidently determined to be not viable without the need for follow up ultrasound for confirmation.


title: Pregnancy test

text: Research has identified at least one other possible marker that may appear earlier and exclusively during pregnancy. For example, early pregnancy factor (EPF) can be detected in blood within 48 hours of fertilization, rather than after implantation. However, its reliable use as a pregnancy test remains unclear as studies have shown its presence in physiological situations besides pregnancy, and its application to humans remains limited.


title: Pregnancy test

text: Records of attempts at pregnancy testing have been found as far back as the ancient Greek and ancient Egyptian cultures. The ancient Egyptians watered bags of wheat and barley with the urine of a possibly pregnant woman. Germination indicated pregnancy. The type of grain that sprouted was taken as an indicator of the fetus's sex. Hippocrates suggested that a woman who had missed her period should drink a solution of honey in water at bedtime: resulting abdominal distention and cramps would indicate the presence of a pregnancy. Avicenna and many physicians after him in the Middle Ages performed "uroscopy", a nonscientific method to evaluate urine.


title: Pregnancy test

text: Selmar Aschheim and Bernhard Zondek introduced testing based on the presence of human chorionic gonadotropin (hCG) in 1928. Early studies of hCG had concluded that it was produced by the pituitary gland. In the 1930s, Doctor Georgeanna Jones discovered that hCG was produced not by the pituitary gland, but by the placenta. This discovery was important in relying on hCG as an early marker of pregnancy. In the Aschheim and Zondek test, an infantile female mouse was injected subcutaneously with urine of the woman to be tested, and the mouse later was killed and dissected. Presence of ovulation indicated that the urine contained hCG and meant that the subject was pregnant. A similar test was developed using immature rabbits. Here, too, killing the animal to check her ovaries was necessary.


title: Pregnancy test

text: At the beginning of the 1930s, Hillel Shapiro and Harry Zwarenstein, who were researchers at the University of Cape Town, discovered that if urine from a pregnant woman was injected into the South African Xenopus frog and the frog ovulated, this indicated that the subject was pregnant. This test, known as the frog test, was used throughout the world from the 1930s to 1960s, with Xenopus frogs being exported in great numbers. Shapiro's advisor, Lancelot Hogben, claimed to have developed the pregnancy test himself, but refuted by both Shapiro and Zwarenstein in a letter to the "British Medical Journal". A later article, independently authored, granted Hogben credit for the principle of using Xenopus to determine gonadotropin levels in a pregnant woman's urine, but not for its usage as a functional pregnancy test.


title: Pregnancy test

text: Hormonal pregnancy tests such as Primodos and Duogynon were used in the 1960s and 1970s in the UK and Germany. These tests involved taking a dosed amount of hormones, and observing the response a few days later. A pregnant woman does not react, as she is producing the hormones in pregnancy; a subject who is not pregnant responds to the absence of the hormone by beginning a new menstrual cycle. While the test was (is) generally considered accurate, research advancements have replaced it with simpler techniques.


title: Pregnancy test

text: Immunologic pregnancy tests were introduced in 1960 when Wide and Gemzell presented a test based on in-vitro hemagglutination inhibition. This was a first step away from in-vivo pregnancy testing and initiated a series of improvements in pregnancy testing leading to the contemporary at-home testing. Direct measurement of antigens, such as hCG, was made possible after the invention of the radioimmunoassay in 1959. Radioimmunoassays require sophisticated apparatus and special radiation precautions and are expensive.


title: Pregnancy test

text: Organon International obtained the first patent on a home pregnancy test in 1969, two years after product designer Margaret Crane noticed that the laboratory testing procedure was relatively simple and made a prototype. The product became available in Canada in 1971, and the United States in 1977, after delays caused by concerns over sexual morality and the ability of potentially pregnant women to perform the test and cope with the results without a doctor.


title: Pregnancy test

text: Another home pregnancy testing kit was based on the work of Judith Vaitukaitis and Glenn Braunstein, who developed a sensitive hCG assay at the National Institutes of Health. That test went onto the market in 1978.


title: Pregnancy test

text: In the 1970s, the discovery of monoclonal antibodies led to the development of the relatively simple and cheap immunoassays, such as agglutination-inhibition-based assays and sandwich ELISA, used in modern home pregnancy tests. Tests are now so cheap that they can be mass-produced in a general publication and used for advertising.


title: Hungarian algorithm

text: The Hungarian method is a combinatorial optimization algorithm that solves the assignment problem in polynomial time and which anticipated later primal–dual methods. It was developed and published in 1955 by Harold Kuhn, who gave the name "Hungarian method" because the algorithm was largely based on the earlier works of two Hungarian mathematicians: Dénes Kőnig and Jenő Egerváry.


title: Hungarian algorithm

text: James Munkres reviewed the algorithm in 1957 and observed that it is (strongly) polynomial. Since then the algorithm has been known also as the Kuhn–Munkres algorithm or Munkres assignment algorithm. The time complexity of the original algorithm was formula_1, however Edmonds and Karp, and independently Tomizawa noticed that it can be modified to achieve an formula_2 running time. One of the most popular formula_2 variants is the Jonker–Volgenant algorithm. Ford and Fulkerson extended the method to general maximum flow problems in form of the Ford–Fulkerson algorithm. In 2006, it was discovered that Carl Gustav Jacobi had solved the assignment problem in the 19th century, and the solution had been published posthumously in 1890 in Latin.


title: Hungarian algorithm

text: In this simple example there are three workers: Paul, Dave, and Chris. One of them has to clean the bathroom, another sweep the floors and the third washes the windows, but they each demand different pay for the various tasks. The problem is to find the lowest-cost way to assign the jobs. The problem can be represented in a matrix of the costs of the workers doing the jobs. For example:


title: Hungarian algorithm

text: The Hungarian method, when applied to the above table, would give the minimum cost: this is $6, achieved by having Paul clean the bathroom, Dave sweep the floors, and Chris wash the windows.


title: Hungarian algorithm

text: In the matrix formulation, we are given a nonnegative "n"×"n" matrix, where the element in the "i"-th row and "j"-th column represents the cost of assigning the "j"-th job to the "i"-th worker. We have to find an assignment of the jobs to the workers, such that each job is assigned to one worker and each worker is assigned one job, such that the total cost of assignment is minimum.


title: Hungarian algorithm

text: This can be expressed as permuting the rows and columns of a cost matrix "C" to minimize the trace of a matrix:


title: Hungarian algorithm

text: If the goal is to find the assignment that yields the "maximum" cost, the problem can be solved by negating the cost matrix "C".


title: Hungarian algorithm

text: The algorithm can equivalently be described by formulating the problem using a bipartite graph. We have a complete bipartite graph formula_5 with worker vertices () and job vertices (), and each edge has a nonnegative cost formula_6. We want to find a perfect matching with a minimum total cost.


title: Hungarian algorithm

text: Let us call a function formula_7 a potential if formula_8 for each formula_9. The "value" of potential is the sum of the potential over all vertices: formula_10.


title: Hungarian algorithm

text: The cost of each perfect matching is at least the value of each potential: the total cost of the matching is the sum of costs of all edges; the cost of each edge is at least the sum of potentials of its endpoints; since the matching is perfect, each vertex is an endpoint of exactly one edge; hence the total cost is at least the total potential.


title: Hungarian algorithm

text: The Hungarian method finds a perfect matching and a potential such that the matching cost equals the potential value. This proves that both of them are optimal. In fact, the Hungarian method finds a perfect matching of tight edges: an edge formula_11 is called tight for a potential if formula_12. Let us denote the subgraph of tight edges by formula_13. The cost of a perfect matching in formula_13 (if there is one) equals the value of .


title: Hungarian algorithm

text: During the algorithm we maintain a potential and an orientation of formula_13 (denoted by formula_16) which has the property that the edges oriented from to form a matching . Initially, is 0 everywhere, and all edges are oriented from to (so is empty). In each step, either we modify so that its value increases, or modify the orientation to obtain a matching with more edges. We maintain the invariant that all the edges of are tight. We are done if is a perfect matching.


title: Hungarian algorithm

text: In a general step, let formula_17 and formula_18 be the vertices not covered by (so formula_19 consists of the vertices in with no incoming edge and formula_20 consists of the vertices in with no outgoing edge). Let be the set of vertices reachable in formula_16 from formula_19 by a directed path only following edges that are tight. This can be computed by breadth-first search.


title: Hungarian algorithm

text: If formula_23 is nonempty, then reverse the orientation of a directed path in formula_16 from formula_19 to formula_20. Thus the size of the corresponding matching increases by 1.


title: Hungarian algorithm

text: We repeat these steps until is a perfect matching, in which case it gives a minimum cost assignment. The running time of this version of the method is formula_1: is augmented times, and in a phase where is unchanged, there are at most potential changes (since increases every time). The time sufficient for a potential change is formula_37.


title: Hungarian algorithm

text: We must show that as long as the matching is not of maximum possible size, the algorithm is always able to make progress — that is, to either increase the number of matched edges, or tighten at least one edge. It suffices to show that at least one of the following holds at every step:


title: Hungarian algorithm

text: If is of maximum possible size, we are of course finished. Otherwise, by Berge's lemma, there must exist an augmenting path with respect to in the underlying graph . However, this path may not exist in formula_13: Although every even-numbered edge in is tight by the definition of , odd-numbered edges may be loose and thus absent from formula_13. One endpoint of is in formula_19, the other in formula_20; w.l.o.g., suppose it begins in formula_19. If every edge on is tight, then it remains an augmenting path in formula_13 and we are done. Otherwise, let formula_48 be the first loose edge on . If formula_49 then we have found a loose-tailed path and we are done. Otherwise, is reachable from some other path of tight edges from a vertex in formula_19. Let formula_51 be the subpath of beginning at and continuing to the end, and let formula_52 be the path formed by travelling along until a vertex on formula_51 is reached, and then continuing to the end of formula_51. Observe that formula_52 is an augmenting path in with at least one fewer loose edge than . can be replaced with formula_52 and this reasoning process iterated (formally, using induction on the number of loose edges) until either an augmenting path in formula_13 or a loose-tailed path in is found.


title: Hungarian algorithm

text: To show that every edge in remains after adjusting , it suffices to show that for an arbitrary edge in , either both of its endpoints, or neither of them, are in . To this end let formula_58 be an edge in from to . It is easy to see that if is in then must be too, since every edge in is tight. Now suppose, toward contradiction, that formula_59 but formula_49. itself cannot be in formula_19 because it is the endpoint of a matched edge, so there must be some directed path of tight edges from a vertex in formula_19 to . This path must avoid , since that is by assumption not in , so the vertex immediately preceding in this path is some other vertex formula_63. formula_64 is a tight edge from to and is thus in . But then contains two edges that share the vertex , contradicting the fact that is a matching. Thus every edge in has either both endpoints or neither endpoint in .


title: Hungarian algorithm

text: To show that remains a potential after being adjusted, it suffices to show that no edge has its total potential increased beyond its cost. This is already established for edges in by the preceding paragraph, so consider an arbitrary edge from to . If formula_65 is increased by , then either formula_66, in which case formula_67 is decreased by , leaving the total potential of the edge unchanged, or formula_68, in which case the definition of guarantees that formula_69. Thus remains a potential.


title: Hungarian algorithm

text: Given workers and tasks, and an × matrix containing the cost of assigning each worker to a task, find the cost minimizing assignment.


title: Hungarian algorithm

text: where a, b, c and d are the workers who have to perform tasks 1, 2, 3 and 4. a1, a2, a3, a4 denote the penalties incurred when worker "a" does task 1, 2, 3, 4 respectively. The same holds true for the other symbols as well. The matrix is square, so each worker can perform only one task.


title: Hungarian algorithm

text: Then we perform row operations on the matrix. To do this, the lowest of all "a" (i belonging to 1-4) is taken and is subtracted from each element in that row. "This will lead to at least one zero in that row" (We get multiple zeros when there are two equal elements which also happen to be the lowest in that row). This procedure is repeated for all rows. "We now have a matrix with at least one zero per row."


title: Hungarian algorithm

text: As there are workers and tasks, adding or subtracting a fixed number to each item in a row or a column will only change the cost of the assignment by that amount; but the minimum cost assignment under old weights will remain a minimum cost assignment under new weights.


title: Hungarian algorithm

text: Now we try to assign tasks to agents such that each agent is doing only one task and the penalty incurred in each case is zero. As all weights are non-negative, the assignment will be of minimum cost. This is illustrated below.


title: Hungarian algorithm

text: Sometimes it may turn out that the matrix at this stage cannot be used for assigning, as is the case for the matrix below.


title: Hungarian algorithm

text: In the above case, no assignment can be made. Note that task 1 is done efficiently by both agents c and d. Both can't be assigned the same task. Also note that no one does task 3 efficiently.


title: Hungarian algorithm

text: To overcome this, we repeat the above procedure for all columns (i.e. the minimum element in each column is subtracted from all the elements in that column) and then check if an assignment is possible.


title: Hungarian algorithm

text: In most situations this will give the result, but if it is still not possible then we need to keep going.


title: Hungarian algorithm

text: All zeros in the matrix must be covered by marking as few rows and/or columns as possible. The following procedure is "one way" to accomplish this:


title: Hungarian algorithm

text: The zero on Row 3 is uncovered. We find on the path the first zero of Row 1, then the second zero of Row 1, then we are done.


title: Hungarian algorithm

text: The aforementioned detailed description is "just one way" to draw the minimum number of lines to cover all the 0s. Other methods work as well.


title: Hungarian algorithm

text: From the elements that are left, find the lowest value. Subtract this from every unmarked element and add it to every element covered by two lines.


title: Hungarian algorithm

text: This is equivalent to subtracting a number from all rows which are not covered and adding the same number to all columns which are covered. These operations do not change optimal assignments.


title: Hungarian algorithm

text: Repeat steps 3–4 until an assignment is possible; this is when the minimum number of lines used to cover all the 0s is equal to min(number of people, number of assignments), assuming dummy variables (usually the max cost) are used to fill in when the number of people is greater than the number of assignments.


title: Hungarian algorithm

text: From Kőnig's theorem, the minimum number of lines (minimum Vertex cover) will be (the size of maximum matching). Thus, when lines are required, minimum cost assignment can be found by looking at only zeroes in the matrix.


title: Hungarian algorithm

text: Note that not all of these satisfy the formula_2 time complexity, even if they claim so. Some may contain errors, implement the slower formula_1 algorithm, or have other inefficiencies. In the worst case, a code example linked from Wikipedia could later be modified to include exploit code. Verification and benchmarking is necessary when using such code examples from unknown authors.


title: Dilip Vengsarkar

text: Dilip Balwant Vengsarkar (born 6 April 1956) is a former Indian cricketer and a cricket administrator. He was known as one of the foremost exponents of the drive. Along with Sunil Gavaskar and Gundappa Viswanath, he was a key player in the Indian batting line up in the late 70s and early 80s. He went on to play until 1992.


title: Dilip Vengsarkar

text: At the pinnacle of his career, Vengsarkar was rated as the best batsman in the Coopers and Lybrand rating (a predecessor of the PWC ratings) and he held the number one slot for 21 months until 2 March 1989.


title: Dilip Vengsarkar

text: Vengsarkar made his international cricket debut against New Zealand at Auckland in 1975–76 as an opening batsman. India won this Test convincingly, but he did not have much success. Later on he usually batted in the No.3 or No.4 position.


title: Dilip Vengsarkar

text: He played a memorable inning in 1979 against Asif Iqbal's Pakistan team in the 2nd Test at Feroz Shah Kotla, Delhi. Requiring 390 to win on the final day, he led India's chase getting the team very close to a victory. India ended up with 364 for 6, just 26 runs short of what would have been a remarkable win. With Yashpal Sharma, Kapil Dev and Roger Binny back to the pavilion after the Tea break, Vengsarkar saw himself running out of partners and decided to play the last few overs for a draw. He remained unbeaten on 146.


title: Dilip Vengsarkar

text: During the 1978–79 Test Series in India against the West Indies, he was involved in a partnership of over 300 runs with Sunil Gavaskar at Calcutta, with both batsman scoring centuries.


title: Dilip Vengsarkar

text: He was a member of the 1983 World Champion's team. He had a productive run of scores between 1985 and 1987, where he scored centuries against Pakistan, Australia, England, West Indies and Sri Lanka, many of them in successive games.


title: Dilip Vengsarkar

text: While the West Indies pacemen dominated the cricket world, Dilip Vengsarkar was one of the few batsmen who was successful against them, and scored 6 centuries against the likes of Malcolm Marshall, Michael Holding and Andy Roberts.


title: Dilip Vengsarkar

text: He is currently team mentor and coach for Telugu Warrior team in the Celebrity Cricket League Season 5.


title: Dilip Vengsarkar

text: He also scored a century at Lord's in 1986, thus scoring consecutive Test match centuries at Lord's in three matches.


title: Dilip Vengsarkar

text: Vengsarkar took over the captaincy from Kapil Dev after the 1987 Cricket World Cup, despite criticism that he missed the semi-final match due to a stomach disorder resulting from a seafood allergy. Although he started with two centuries in his first series as captain, his captaincy period was turbulent and he lost the job following a disastrous tour of the West Indies in early 1989 and a stand-off with the Board of Control for Cricket in India).


title: Dilip Vengsarkar

text: After retiring, Vengsarkar started the Elf-Vengsarkar Academy in 1995. He became the vice-president of the Mumbai Cricket Association in 2003. Although, he was the front runner for the post of the Chairman, Selection Committee, Dilip opted out because of his policy against zonal representation. He was appointed the Chairman of the Talent Resource Development Wing when it was created in 2002 to develop cricket talent within the country.


title: Dilip Vengsarkar

text: In March 2006, the BCCI proposed Vengsarkar as a match referee, but the proposal did not move forward as Vengsarkar accepted the job as chairman of selectors of the BCCI later in the year.


title: Dilip Vengsarkar

text: He runs three cricket academies, two in Mumbai and one in Pune. These academies give training free of charge to players selected on their skill level.


title: Dilip Vengsarkar

text: A Bollywood film "83" released in 2021 about the events around India's first World Cup win, at Lords in 1983, features Adinath Kothare as Vengsarkar.


title: Julian Clary

text: Julian Peter McDonald Clary (born 25 May 1959) is an English actor, comedian, novelist and presenter. He began appearing on television in the mid-1980s. Since then he has also acted in films, television and stage productions, numerous pantomimes and was the winner of "Celebrity Big Brother 10" in 2012.


title: Julian Clary

text: Clary was born on 25 May 1959 in Surbiton, Surrey, to Brenda ( McDonald) Clary, a probation officer, and Peter J. Clary, a police officer. He was brought up in Teddington, Middlesex, with two older sisters. By his own account, he was conceived "in broad daylight" in Clacton-on-Sea in 1958. Two of his great-grandparents were Germans who emigrated to Britain at the end of the nineteenth century. He and his siblings were raised as Roman Catholics. He attended St Benedict's School, Ealing and, later, he studied English and Drama at Goldsmiths' College, University of London.


title: Julian Clary

text: Clary is an openly gay comedian who refers to himself as a "renowned homosexual" and is known for his outrageous and flamboyant costumes and make-up, and interactions with his audience such as looking in their bags, comments on their attire and flirting with straight men in the audience. For those who get too close he is quick to respond "Don't touch me". He has been assisted by Hugh Jelly and others in audience participation segments.


title: Julian Clary

text: Clary began his career under the name Leo Hurll, a fake keyboardist for pop band Thinkman (a recording project conceived by Rupert Hine). He entered the alternative comedy scene in the early 1980s, first under the alias Gillian Pieface and later as The Joan Collins Fan Club. He wore heavy glam make-up and dressed in outrageous clothes, often involving leather/PVC and hinting at bondage. His pet dog Fanny the Wonderdog, a whippet mongrel, also featured in performances.


title: Julian Clary

text: Since then, Clary has undertaken several successful tours of his stage act, some of which have been released on home video, including:


title: Julian Clary

text: He was named Ambassador for the 2016 Adelaide Fringe, responsible for promoting the festival internationally.


title: Julian Clary

text: After a number of appearances on "Friday Night Live" in the mid- to late 1980s, Clary co-hosted the short-lived ITV game show "Trick or Treat" in 1989 with Mike Smith, before achieving greater success later that year with his own high-camp Channel 4 game show, "Sticky Moments with Julian Clary". More a vehicle for his brand of humour than a genuine gameshow, "Sticky Moments" was a light-hearted "non-quiz" satire, with him often awarding points because he liked the contestants, rather than because they possessed a particular skill or aptitude. He later starred in the 1992 audience participation sitcom "Terry and Julian" with Lee Simpson, again for Channel 4.


title: Julian Clary

text: Also in 1992, he played a cameo guest star part in the BBC drama "Virtual Murder". In the episode "A Dream of Dracula", he played an undertaker, alongside other guest stars including Alfred Marks, Jill Gascoine, Ronald Fraser and Peggy Mount. In the same year, while visiting Australia, he made a controversial appearance alongside Rex Mossop on "Tonight Live with Steve Vizard", during which Mossop espoused homophobic opinions. He also appeared in an episode of the improvisational comedy show "Whose Line Is It Anyway?" in 1991.


title: Julian Clary

text: On 12 December 1993, he made an infamous appearance at the British Comedy Awards, where he made a joke comparing the set to Hampstead Heath (some of which is known as a cruising area for gay men) and stated he had just been fisting the former Chancellor of the Exchequer Norman Lamont, who had presented an award earlier in the ceremony. Due to the instant audience reaction, the punchline ("Talk about a red box!") was widely overlooked. Although the joke was met with uproarious laughter from the audience and Lamont himself did not complain over it, he was criticised in some newspapers, particularly by the "Daily Mail" and "The Sun", who both launched a campaign to have him banned from television. Despite these attempts, Clary's next series was the BBC's studio-based "All Rise for Julian Clary" in 1996, in which he played a judge in a mock courtroom setting.


title: Julian Clary

text: From 1998 to 2001, he hosted three series of the Sky TV show "Prickly Heat", the first two series with Davina McCall, the last one with Denise van Outen. Additionally, from 1999 to 2002 he was the face of Daz laundry detergent, taking over from Shane Richie, Michael Barrymore and Danny Baker. He is a recurring performer and one of the most popular performers in the ITV Pantos. He played "First Henchman" and "Tim" in 1998's "Jack and The Beanstalk"; "The Good Fairy" in 2000's "Cinderella"; "The Genie of the Lamp" in 2000's "Aladdin"; and, possibly his favourite character, "Chris the Cat" in 2002's "Dick Whittington". In 1999, he became a team captain on the quiz show "It's Only TV...but I Like It", alongside Phill Jupitus and Jonathan Ross. In 2003, he presented the first series of the Japanese TV clip show, "Sushi TV" for Challenge. In 2004, he took part in the BBC series "Strictly Come Dancing", finishing third with his partner Erin Boag. In 2005, he hosted "Come and Have A Go" for the National Lottery.


title: Julian Clary

text: He was the subject of "This Is Your Life" in 2001 when he was surprised by Michael Aspel during the curtain call of the pantomime Cinderella at the Richmond Theatre.


title: Julian Clary

text: On 1 February 2006, he appeared on the BBC programme "Who Do You Think You Are?", a genealogy series which traced his ancestors to a World War I flight engineer and German immigrants among both his mother's and father's forebears. In May 2006, and again in April 2008, he hosted an episode of the topical quiz show "Have I Got News for You".


title: Julian Clary

text: In September 2006, he returned to primetime TV as presenter and judge on Channel 5's brand new celebrity performance programme "The All Star Talent Show". He was joined by two guest judges every week to assess celebrity performances and co-presented with Myleene Klass and Andi Peters. He also narrated the Channel 5 children's series "The Little Princess" with Jane Horrocks.


title: Julian Clary

text: In November 2006, he appeared on "QI", a panel game/comedy show hosted by Stephen Fry and also appeared on an episode of "The New Paul O'Grady Show".


title: Julian Clary

text: In 2007, he made a cameo appearance in the Australian soap opera, "Neighbours", in scenes filmed in London with Natalie Bassingthwaighte.


title: Julian Clary

text: From 20 March 2007, Clary presented a brand-new show for the BBC called "The Underdog Show". Celebrities and children were paired up with rescue dogs. They then commenced training and competed against each other in obedience and agility trials in a live arena. The show ran until 26 April 2007.


title: Julian Clary

text: He also appeared on television regularly in 2008, starting in January when he was drafted in as a relief presenter for "This Morning", co-presenting alongside Fern Britton and Ruth Langsford during Phillip Schofield's absence. In April, he once again fronted the BBC One series "Have I Got News for You", and he filmed an episode of "Celebrity Bargain Hunt" in May. He was also a short-notice guest on "The Paul O'Grady Show" in October 2008, after Peter Andre and Katie Price could not appear (Clary and O'Grady are friends and neighbours).


title: Julian Clary

text: In 2012, Clary was one of the contestants in "Celebrity Big Brother 10" and went on to win the series. In 2013, he was a judge on the ITV entertainment series "Your Face Sounds Familiar", alongside Emma Bunton.


title: Julian Clary

text: In March 2015, it was announced that Clary would take part in ITV's "Give a Pet a Home" show which works alongside the RSPCA in Birmingham. The series began airing on 15 April 2015 for six episodes.


title: Julian Clary

text: From 1 August 2015, Clary presented "Nature Nuts with Julian Clary", a new three-part nature show for ITV.


title: Julian Clary

text: Clary played Leigh Bowery in the West End of London musical "Taboo" in 2002. He also took part in the touring production in 2004.


title: Julian Clary

text: In Spring 2007, Clary did a theatre tour of the UK with his show "An Evening with... Julian Clary". From 2 October 2007, he played the much coveted role of 'Emcee', in Rufus Norris's Olivier Award-winning production of "Cabaret", which was in its second year in the West End. Clary was with the show until 19 April 2008. The following year he took part in the "Strictly Come Dancing" Tour in January and February 2009. He was partnered with Lilia Kopylova.


title: Julian Clary

text: Clary starred as Michael in "Le Grand Mort", a play written specifically for him by playwright Stephen Clark (prior to his death in 2016), opposite James Nelson-Joyce as Tim from 20 September to 28 October 2017 at Trafalgar Studios 2 in London's West End.


title: Julian Clary

text: Clary was due to appear as Norman in a UK tour of "The Dresser" by Ronald Harwood, alongside Matthew Kelly as 'Sir' in September 2020, however due to the ongoing COVID-19 pandemic, the production has been postponed to 2021.


title: Julian Clary

text: Clary has appeared in numerous Christmas pantomimes and has recently become a regular star of the London Palladium pantomimes. In December 2019, Clary was inducted in a ceremony held by Andrew Lloyd Webber onto the Wall of Fame, joining the many stars that have appeared at the Palladium.


title: Julian Clary

text: Clary appeared in the film "Carry On Columbus" (1992), an unsuccessful attempt to revive the "Carry On" series of films. It was widely panned by critics, but was more financially profitable than the two other Columbus films released the same year: "" and "".


title: Julian Clary

text: Clary returned to film in 2001 in the film "The Baby Juice Express" which starred Lisa Faulkner, Samantha Womack, Ruth Jones and David Seaman, about a prisoner who is desperate to find some way of conceiving with his wife whilst he is in prison, but the sperm ends up getting hijacked. It was released on DVD in 2004.


title: Julian Clary

text: In 1992 Clary hosted a radio show for the BBC called "Intimate Contact", the premise of which was for him to act as a genial 'Mr Fix-it' for a wide range of 'punter' problems. Clary attempted to solve these issues over the telephone, with the assistance of roving reporter "Hugh Jelly" (actor Philip Herbert). It originally aired on BBC Radio 1 for two series; the pilot and 6-part first series have since been repeated on BBC Radio 4 Extra a number of times.


title: Julian Clary

text: Clary has released two large format comedy books: "My Life With Fanny The Wonder Dog" (1989) and "How To Be A Man" (1992). Between 2005 and 2008, Clary wrote a fortnightly column for the "New Statesman" magazine.


title: Julian Clary

text: He published an autobiography, "A Young Man's Passage", which covers his life and career up to the 1993 "Norman Lamont incident" at the British Comedy Awards (see above). Then in 2021 "The Lick of Love: How Dogs Changed My Life" telling his life through his pets to more recent times.


title: Julian Clary

text: In 2007, Clary released his first novel, "Murder Most Fab", published by Ebury Press. His second novel, "Devil in Disguise", was published in 2009.


title: Julian Clary

text: Clary often performs comical renditions of musical numbers in his stage and television appearances, ranging from old classics to original material. He released a music single in 1988 (credited as the Joan Collins Fan Club), a humorous rendition of "Leader of the Pack", which he often performed in his stage and television appearances at the time. The single was produced by Rupert Hine and reached no. 60 in the UK Singles Chart.


title: Julian Clary

text: Another single, "Wandrin' Star", was released in 1990. The single was backed with the self-penned track "Uncanny and Unnatural".


title: Julian Clary

text: Clary’s boyfriend Christopher died of AIDS in 1991. Clary has been in a relationship with Ian Mackley since 2005, and the couple were married on 19 November 2016. They lived at Goldenhurst Farm, a seventeenth-century manor house once owned by Noël Coward, in Aldington, Kent until 2018. Clary also has a house in Camden, North London.


title: Julian Clary

text: On 7 September 2005, the University of London's Goldsmiths College made Clary an Honorary Fellow. In July 2014, the University of East Anglia awarded Clary an honorary Doctorate of Civil Law.


title: Brandon Mychal Smith

text: Brandon Mychal Smith (born May 29, 1989) is an American actor, singer, dancer, and rapper. He is best known for playing Bug Wendal in "Gridiron Gang", Li'l Danny Dawkins in "Phil of the Future", Nico Harris in "Sonny with a Chance" and "So Random!", Stubby in "Starstruck", Lord of da Bling in "Let It Shine", and Marcus in "One Big Happy". He received critical acclaim for his portrayal of Tayshawn Mitchell in "The Ron Clark Story" (2006) and Little Richard in the 2014 James Brown biopic "Get on Up". He voices Michelangelo in the Nickelodeon animated series "Rise of the Teenage Mutant Ninja Turtles".


title: Brandon Mychal Smith

text: Smith won a Family Television Award and Young Artist Award in 2007 for his performance as Tayshawn in "The Ron Clark Story". His other credits include the 2006 production of "Gridiron Gang" as Bug Wendal, and a recurring role as Mario in "Unfabulous". He starred in the 2010 Disney Channel Original Movie "Starstruck". He also performs the song and music video "Party Up" for "Starstruck". He was a competitor on the "Dancing with the Stars" sequel "Skating with the Stars" but had to withdraw due to illness. He produced Maxrank's track "Winna Girl".


title: Killer Frost

text: Killer Frost is a name used by several female supervillains and superheroes appearing in comic books published by DC Comics: Crystal Frost, Louise Lincoln, and Caitlin Snow. Each different individual in the DC Universe assuming the Killer Frost persona usually has some connection to the superhero Firestorm.


title: Killer Frost

text: Various iterations of Killer Frost, primarily Crystal Frost and Louise Lincoln, have appeared in various animated projects and video games, with a majority of them voiced by Jennifer Hale. Additionally, Danielle Panabaker portrays Caitlin Snow and her Killer Frost persona in The CW's Arrowverse franchise, such as the television series "The Flash".


title: Killer Frost

text: Crystal Frost was the first incarnation, first appearing in "Firestorm" #3 (June 1978). While Frost was studying to be a scientist in Hudson University, she fell in love with her teacher Martin Stein. While working on a project in the Arctic, Frost was upset to learn that Stein did not reciprocate her feelings; Stein told a fellow researcher that Frost was a withdrawn student and that Stein had merely tried to draw her out of her shell, which Crystal completely misinterpreted. Frost accidentally locked herself in a thermafrost chamber but survived, being transformed in a way in which she was able to absorb heat from a living being and project cold and ice. Calling herself "Killer Frost", she began her murderous crusade against men and clashed with Firestorm on many occasions. Killer Frost eventually died after she absorbed too much energy from Firestorm. She has been identified as one of the deceased villains entombed below the Hall of Justice. Her body was reanimated as a Black Lantern.


title: Killer Frost

text: Dr. Louise Lincoln is the second incarnation; she first appeared in "Firestorm" (vol. 2) #21 (March 1984) and used the "Killer Frost" name in "Firestorm" (vol. 2) #34 (April 1985). Lincoln was a colleague and friend to Crystal Frost. After her friend's death, Lincoln decided to repeat the experiment as a last respect to her friend, with Lincoln herself as the second Killer Frost. Just as ruthless as her predecessor, she began her own personal vendetta against Firestorm whom she blamed for her friend's death. She briefly served as a member of the Suicide Squad and sold her soul to Neron for more power.


title: Killer Frost

text: During the "Underworld Unleashed" event, Killer Frost attacked Hawaii, freezing part of the islands before being stopped by Superboy and Knockout.


title: Killer Frost

text: After a group of mobsters put out a hit on Lois Lane, Killer Frost rescued Lois from Solomon Grundy, only to then leave the reporter bound and gagged on a set of train tracks, hoping to take the credit and reward for Lane's death. Her plan was foiled by Superman who rescued Lois before the train could hit.


title: Killer Frost

text: Killer Frost was later freed when the DEO refrigeration truck transporting her crashed. Effigy happened upon the crash and she discovered the heat from Effigy's pyrokinetic abilities enabled her to kiss Effigy without him freezing over. The two had a brief flirtatious partnership that dissolved when Effigy lost patience with her lecturing on how to defeat Green Lantern. After Green Lantern buried them both under a mountain of snow, Effigy escaped and abandoned her to be apprehended again.


title: Killer Frost

text: In the "Superman/Batman" "Public Enemies" arc, Killer Frost was one of many supervillains seeking to earn a $1 billion reward offered by President Lex Luthor to sanction Superman and Batman. She teamed with Mister Freeze, Icicle (Cameron Mahkent) and Captain Cold in an attempt to ambush the two heroes in Washington D.C., but all four were defeated. They attacked in a second wave, along with more villains such as Giganta and Gorilla Grodd, but a similar backup of superheroes battered them all into submission. It was later discovered that this ice-themed team of villains was being mind controlled by Grodd.


title: Killer Frost

text: Dr. Light hired Killer Frost and Mirror Master to attack Green Arrow and Black Lightning at a hospital in Chicago, Illinois, where Kimiyo Hoshi was being held. Green Arrow stopped Killer Frost by firing an arrow filled with Greek fire into her thigh. Unable to absorb the heat from the arrow, she was defeated.


title: Killer Frost

text: Around this time, Lincoln discovered that she had contracted cancer, and tricked Jason Rusch, the new Firestorm, into curing her. With her health and powers restored, Killer Frost went on a rampage, only to be defeated when Jason's abilities reversed the alterations to Lincoln's body, returning her cancer.


title: Killer Frost

text: Killer Frost returned during the events of "One Year Later", where she had apparently entered into a relationship with Mr. Freeze. Together, the two villains went on a killing spree in Manhattan, hoping to draw Firestorm into an elaborate trap. Once the hero arrived, Killer Frost used a device to send both of them into space, where she sought to absorb the heat energy of the sun. Firestorm narrowly managed to stop her plan, and both Killer Frost and Mister Freeze were taken into custody by Batman. As they were being sent away, Killer Frost angrily revealed to Mister Freeze that she had only been using her lover as a pawn, and had no romantic interest.


title: Killer Frost

text: Killer Frost was later seen battling Firestorm in the "Justice League of America Wedding Special" until Lex Luthor, the Joker and Cheetah arrived, subdued Firestorm, and invited Killer Frost to join the new Injustice League. She then appeared in "Salvation Run", where she was sent to the Prison Planet after having been defeated and captured by the Suicide Squad.


title: Killer Frost

text: In "DC Universe" #0, she was seen as a member of Libra's Secret Society of Super Villains. She is later seen as one of the villains sent to retrieve the Get Out of Hell Free card from the Secret Six, and ultimately helped deal the killing blow to the crazed supervillain Junior and the troubled vigilante Tarantula. A short time after this encounter with the Secret Six, Killer Frost appeared as one of the participants in a metahuman fighting tournament in Tokyo. She was defeated by Wonder Woman and Black Canary who had disguised themselves as villains to take down the tournament from the inside.


title: Killer Frost

text: The "DC Rebirth" version of Louise Lincoln debuts in the "Watchmen" sequel "Doomsday Clock". While Firestorm considers "The Superman Theory" as a hoax, Killer Frost claims that Captain Atom, Firehawk, Moonbow, and Typhoon are the government's creations. Killer Frost later accompanied Black Adam's attack on the White House.


title: Killer Frost

text: In September 2011, The New 52 rebooted DC's continuity; Killer Frost is reintroduced in September 2013, as the "Villains Month" part of the "Forever Evil" – she was featured in the one-shot "Justice League of America" (vol. 3) #7.2, also titled "Killer Frost" #1. She can also be seen on the cover of "Forever Evil" #1, which hints at her involvement in that series where she's revealed to be Dr. Caitlin Snow, a scientist sent to S.T.A.R. Labs Outpost #72 in the Arctic to work on a thermodynamic engine whose creator had committed suicide. Snow soon discovered the place had been infiltrated by H.I.V.E. agents. When they tried to kill her inside the engine, Snow frantically ripped off the coolant system, merging her body with ice. Transformed into a heat vampire, she killed the H.I.V.E. agents out of revenge. She then wandered out into the cold until she came across a Norwegian camp and took their heat too. Hijacking a helicopter, she made it back to her hometown Pittsburgh. She even created a suit that helped her retain heat for longer. She later encountered the superhero Firestorm and discovered that his powers could temporarily heal her mutation. She tried recreating the Firestorm Nuclear Matrix several times, only to fail with each attempt. When Firestorm and the Justice League were declared dead by the Crime Syndicate, she lost hope for a cure to her condition.


title: Killer Frost

text: Killer Frost later has the scientist Byte track down Martin Stein, the original creator of the Firestorm Matrix, to a secluded cabin while he had gone into hiding during the Crime Syndicate's takeover of Earth. She encountered Steve Trevor who was sent there on a mission to try to find the Justice League who were imprisoned inside Firestorm. Learning Stein was alive, Snow allied herself with the two men to find them. Soon they were attacked by supervillains Multiplex, Black Bison, Hyena, Tempest and Plastique for betraying the Crime Syndicate. While fighting them off, Frost, Stein, and Trevor teleported to another A.R.G.U.S. base, where they learned that to free the Justice League, they needed Wonder Woman's Lasso of Truth. Discovering Cheetah was keeping it as a trophy, they found her and her Menagerie, but were subdued. Doctor Light (Arthur Light) suddenly appeared and blasted everyone except Frost and Trevor unconscious. After defeating him, they managed to deliver the Lasso of Truth to Cyborg who successfully used it to free his teammates.


title: Killer Frost

text: In DC Rebirth, Caitlin Snow is taken to Belle Reve Penitentiary, where she is introduced to the Suicide Squad and offered a place on the team by Amanda Waller. She accepts and joins the team. She helps the Suicide Squad in their fight against the Justice League, but subsequently assists them against Maxwell Lord when he is possessed by Eclipso, whose attempt to tap into her "darkest desire" only unlocks her desire to make a difference. She then has to save all the Suicide Squad and the Justice League by absorbing the energy out of Superman and using it against Lord. Afterwards, Waller is forced to release Snow into Batman's custody. She then joined the new Justice League of America made up of Batman, the Atom, Lobo, Black Canary, Vixen and the Ray.


title: Killer Frost

text: All versions have shown the ability to absorb heat from external sources and transmute it into waves of cold. Using these powers, Killer Frost can create an ice-sheen across her entire body that grants her increased durability, cause intense blizzards that can instantly freeze the target and generate objects composed completely of ice, such as projectiles in the form of ice shards and defensive walls or shields. She can also instantly freeze animate matter through physical contact and is unable to touch a normal person without freezing them. Although she is able to kiss people who can can cool her down and negate her cryo-kinetic abilities like Firestorm.


title: Killer Frost

text: Her weakness is the need to absorb external heat sources to generate ice: although heat-based weapons such as flamethrowers only make her stronger, she can be imprisoned in cold surroundings such as being locked in a refrigeration truck or buried under a mountain of snow. The Caitlin Snow version of Killer Frost is constantly plagued by a hunger for heat, which can only be sated by absorbing the heat from a living being, a process which inevitably kills the victim. However, in recent stories she seems to have finally gotten it under control by only absorbing a tiny amount of heat from every person she touches, sparing them and leaving them otherwise unharmed. The Caitlin Snow and Louise Lincoln versions of the character have, albeit inconsistently, demonstrated the ability to fly, either by riding Arctic winds or through an unknown manner of self-propulsion.


title: Killer Frost

text: While the exact limits of her abilities have yet to be established, how much power Frost can channel at once seems to depend on how much heat she has absorbed and stored in her body. For example, when she absorbed all the heat from Superman (whose body is supercharged by yellow solar energy) during a stand-off between the Justice League and the Suicide Squad, she was able to flash-freeze the entire League in a single blast.


title: Killer Frost

text: It also seems that using up all the heat energy she has stored can put Frost's life in danger. If she does not feed in time, she even risks dying of "starvation".


title: Killer Frost

text: The Caitlin Snow version also boasts a genius-level intellect, being S.T.A.R. Labs' youngest and brightest scientist prior to her transformation. She could solve complex equations easily, operate heavy energy generating machinery and appeared particularly skilled in the field of physics and research about energy. She once managed to create an ice prism with her powers that converted Superman's heat vision into a bright burst of sunlight to defeat Eclipso.


title: Killer Frost

text: Several adaptations of the villain have also depicted the Crystal Frost and Louise Lincoln incarnations as having basic skills in melee combat which they use in conjunction with their powers as well as impressive agility, being able to perform maneuvers such as leaps or cartwheels with ease.


title: Killer Frost

text: Killer Frost appeared in the "DC Super Friends" comic as part of a group of ice-themed villains called the "Ice Pack" that encased a city in ice and snow.


title: Killer Frost

text: The Crystal Frost version appeared along with Mr. Freeze, Captain Cold, Minister Blizzard, Cryonic Man, Icicle, Polar Lord and Snowman in the "Justice League Adventures" comic.


title: Killer Frost

text: Killer Frost appears in the "DC Bombshells" continuity, which takes place during World War II. She serves Hugo Strange of the Nazi Regime alongside Penguin and a brainwashed Harvey Dent (who is eventually rescued by the Batgirls). While Penguin is in love with her, it's unknown if she truly reciprocates the same feeling. This version is Louise L'inconnue, who is of French and German descent. In 1870, her mother is killed by angry villagers for conceiving a child with a German man and was thrown into an ice-cold well to die with her child. Louise emerges from the well with blue skin and freezes all the villagers to death. She is later adopted by the Joker's Daughter, who trained her in magic and controlling her powers (while also giving her the chance to kill her father). After clashing with Baroness Paula Von Gunther, she expresses her desire to have the world filled with superhumans like her.


title: Killer Frost

text: Killer Frost appeared in the "DC Super Hero Girls" by the name of "Frost". In the series, she is shown to be a superhero, instead of a supervillain. She has her own separate bio with her powers and personality listed. She is shown to be very smart too. There she lives with Lady Shiva, Miss Martian and Star Sapphire. She has her own bedroom with: a nightstand, a king sized bed, a desk and other decorations. Her appearance is also different: she has long hair made into a ponytail. She has blue eyes, white skin and all of her outfits have something to do with ice and snow.


title: Killer Frost

text: Danielle Panabaker portrays Dr. Caitlin Snow / Killer Frost, a series regular on "The Flash", which is set in The CW's Arrowverse family of related shows. Her character also makes occasional guest appearances on "Arrow" (in which she debuted), "Legends of Tomorrow", and "Supergirl". This version is a member of the Central City-based S.T.A.R. Labs team alongside Cisco Ramon / Vibe and Harrison Wells, which supports Barry Allen / Flash.


title: Killer Frost

text: In season one, she struggles with her fiancé Ronnie Raymond's apparent death following S.T.A.R. Labs particle accelerator exploding and creating various metahumans before later discovering Raymond survived as part of Firestorm. Caitlin and Raymond later marry, but shortly thereafter, he gives his life to help the Flash close a singularity that opened over Central City. During season two, Caitlin grieves for Raymond, but grows closer to Hunter Zolomon while he was disguised as Jay Garrick. When Zolomon reveals he has a disease that limits the use of his super-speed, Caitlin develops the Velocity serum to save his life. However, she and Team Flash soon discover Zolomon's true identity before he kidnaps her and takes her to Earth-2, where she meets her evil Earth-2 doppelganger, Killer Frost. Following this encounter, Caitlin begins to fear whether she has a capacity for evil as well.


title: Killer Frost

text: Due to Allen altering the timeline while creating and undoing the "Flashpoint" timeline in season three, Caitlin has developed cryokinetic abilities and an alternate, villainous personality, both of which she attempts to hide from her friends. She also develops a relationship with Julian Albert. Caitlin is advised by her mother, Dr. Carla Tannhauser, to not use her powers or her transformations will become irreversible. However, Catlin's abilities fully manifest when Albert removes her power-suppressing necklace so she can use her healing abilities to save herself, triggering her transformation into Killer Frost. Joining Savitar as his enforcer, Killer Frost battles Team Flash. Following a fight with Ramon, she turns against Savitar after being given a cure developed by Albert. She defends her former teammates from Savitar and assists in defeating him before leaving to rediscover herself.


title: Killer Frost

text: In season four, Caitlin and Killer Frost develop a "Jekyll and Hyde"-esque relationship. The former works in a criminal underworld bar until Ramon convinces her to return to Team Flash. Caitlin also comes to terms with her dual personalities, giving herself the ability to switch between her two personas at will. Furthermore, Killer Frost begins to show a more heroic side and agrees to use her powers to help Team Flash. Later in the season, Caitlin discovers her powers and Killer Frost originated during her childhood and that she suppressed the memories.


title: Killer Frost

text: In season five, she discovers further that her father, Thomas Snow, experimented on her and himself in an attempt to cure their ALS genes, resulting in them both developing alternate personalities with cryokinetic powers. After he becomes Icicle, Caitlin and Killer Frost work together to save Thomas from his evil persona.


title: Killer Frost

text: In season six, Caitlin experiments with giving Frost more time with their shared body and allowing her to live her own life. In season seven, they become exposed to Eva McCulloch / Mirror Monarch's rays, which severs their telepathic connection and causes Frost's cells to replicate to the point where she acquires her own body. As such, Caitlin and Frost decide to live separate lives as twin sisters.


title: Killer Frost

text: In season eight, Killer Frost transforms into "Hellfrost" and gives her life to defeat Deathstorm. Having secretly taken a hair sample from Frost, Caitlin plans to restore her with Chillblaine's help and the Consciousness Resurrection Chamber.


title: Kawasaki P-1

text: The Kawasaki P-1 (previously P-X, XP-1) is a Japanese maritime patrol aircraft developed and manufactured by Kawasaki Aerospace Company. Unlike many maritime patrol aircraft, which are typically conversions of civilian designs, the P-1 is a purpose-built maritime aircraft with no civil counterpart and was designed from the onset for the role. It has the distinction of being the first operational aircraft in the world to make use of a fly-by-optics control system.


title: Kawasaki P-1

text: The P-1 has entered service with the Japan Maritime Self-Defense Force (JMSDF) as a replacement for the P-3C Orion. On 26 March 2013, the JMSDF took delivery of the first two operational P-1 aircraft. Export customers are also being sought for the type as part of a general loosening of Japanese military export restrictions.


title: Kawasaki P-1

text: Observing that its fleet of P-3C aircraft had been in service for some time, the JMSDF began searching for a replacement maritime patrol aircraft. Since other similar aircraft produced abroad did not meet the JMSDF's requirements, the development of a purpose-built indigenous aircraft became necessary. The Japanese Defense Agency (JDA) submitted the domestic development of a P-X maritime patrol aircraft as part of its April 2001 – March 2006 Five-Year Defense Plan. In 2001, following its earlier proposal, the Kawasaki Aerospace Company received prime contractor status for the P-X program, as well as the adjacent C-X program for a next generation cargo aircraft; this selection process occurred almost 30 years since the previous large-scale domestic development of an aircraft in Japan.


title: Kawasaki P-1

text: The P-X shares some components with the C-X, later designated as the twin-engined Kawasaki C-2, another indigenously developed aircraft to replace the Kawasaki C-1 and C-130H Hercules cargo aircraft. Although the P-X and C-X designs were originally independent, it was decided that having common components to both designs would be useful. The JDA mandated that the two aircraft share identical body components; common components include the cockpit windows, outer wings, horizontal stabilizer, and other systems. Internal shared parts include the auxiliary power unit, cockpit panel, flight control system computer, anti-collision lights, and gear control unit. Due to the different roles of the two aircraft, they remain distinctly separate. The sharing of development resources had allowed for a large reduction in overall development costs which, when including the C-2, were reported in 2007 as being .


title: Kawasaki P-1

text: In addition to a level of commonality with the C-2, one proposed derivative of the P-1 is a civilian airliner, the proposed project has typically been referred to as the Kawasaki YPX. If development is pursued, the YPX would make extensive use of technology and components of the P-1, such as the wingbox, empennage, and fuselage.


title: Kawasaki P-1

text: An indigenously produced turbofan engine, the IHI Corporation F7, was also developed to power the P-X. By April 2004, the JDA had completed a successful evaluation of five XF7 research engines, by which point it was viewed as being the sole candidate powerplant for the P-X program. In May 2005, the IHI Corporation received a contract for an additional seven XF-7 test engines from the JDA following the completion of initial tests in December 2004, four of these engines were to equip the first flight test aircraft. The Full Authority Digital Engine Control (FADEC)-equipped F7 engine had a bypass ratio of 8:1, which was reported as being substantially higher than rivals such as the General Electric CF34-8E.


title: Kawasaki P-1

text: In April 2004, Japan and US extended discussions on potential cooperative efforts on the P-X and US Navy's Multi-mission Maritime Aircraft (MMA) programmes; options ranged from terminating the P-X program to participate in the US-led MMA program to incorporating some of the MMA's technology onto the P-X to reduce costs. The Japanese Defence Ministry ultimately opted to persist with the P-X program, stating that: "there was a possibility that foreign aircraft would not satisfy the required capability and there was a possibility that foreign aircraft would not meet the required period of introduction...it is necessary to domestically develop the aircraft". In addition to the P-1, studies were also conducted into the use of ship-based UAVs to support maritime aviation activities.


title: Kawasaki P-1

text: Since 2014, Japan has been making approaches to other nations for prospective export sales of the P-1. New Zealand was the first country to which the P-1 had been offered in what had been referred to by a Japanese official as a "one on one fight with Boeing's P-8 patrol plane." The P-1 was offered in conjunction with the C-2 to give New Zealand the advantage of commonality for their patrol and transport aircraft. On 9 July 2018 New Zealand selected the P-8 Poseidon instead.


title: Kawasaki P-1

text: Japanese officials have claimed that the P-1 is a more capable, albeit more expensive, aircraft than the Boeing P-8 Poseidon; in comparison to the P-8, the P-1 has a greater range, a larger bomb bay, and has been purpose-built for the maritime patrol mission. Prior to 2015, the P-1 was being procured at a typical rate of one or two aircraft deliveries per year; in 2015, this changed to a bulk order for 20 P-1s as part of a measure to cut the aircraft's unit costs. By October 2016, 10 P-1s had been delivered to the JMSDF, with 60 or more aircraft needed to replace Japan's P-3C fleet; production will rise to about five annually.


title: Kawasaki P-1

text: The Kawasaki P-1 is a purpose-built maritime patrol aircraft equipped with four engines. The P-1 is powered by four podded IHI F7-10 turbofan engines underneath the low-set wings. The four-engine low-wing loading design adopted for the P-1 results in a flight profile with better maneuverability and stability at low-speed, low-altitude flight and allows the aircraft to continue its mission in the event of a single engine failure. As well as greater operational survivability, the high-bypass engines provide for quiet, fuel-efficient operation. The P-1 has reduced transit times in comparison to turboprop-powered competitors, and the turbofans are quieter, making it more difficult for submerged submarines to detect it acoustically.


title: Kawasaki P-1

text: The P-1 is equipped with many newly developed technologies and features, particularly in terms of its avionics and missions systems. One such key feature is the use of a fly-by-optics flight control system, which essentially replaces standard metal wiring with optical fiber cables. This has the effect of decreasing electro-magnetic disturbances to the sensors in comparison to more common fly-by-wire control systems. The P-1 is the first production aircraft in the world to be equipped with such a flight control system. Various onboard systems are provided by Honeywell, which is the largest non-Japanese supplier to the project, such as the auxiliary power unit, environmental and pressurization control systems, ram air turbine, sonobuoy dispensers and elements of the avionics.


title: Kawasaki P-1

text: The P-1 is equipped with various sensors to enable the aircraft to perform its primary purpose of detecting submarines and surface vessels; these include the Toshiba HPS-106 active electronically scanned array (AESA) radar which uses a total of three antennas to provide 240 degree coverage, and Fujitsu HAQ-2 Infrared/Light detection systems for surface detection. The P-1 is also furnished with a CAE Inc.-built magnetic anomaly detector (MAD) embedded into the aircraft's tail, along with deployable sonobuoys, which is used for the detection of submerged submarines. Sophisticated acoustic systems are also used for this purpose. The P-1 has an artificial intelligence (AI) system to assist TACCO operations; similar to the SH-60K, this advanced combat direction system directs the TACCO operator to the optimal flight course to attack a submarine.


title: Kawasaki P-1

text: A large bomb bay housed within the main fuselage, similar in size to that of the Hawker Siddeley Nimrod's, contains the bulk of the aircraft's munitions. The bomb bay is supplemented by a total of eight external hardpoints mounted on the wings. Weapons available on the P-1 include torpedoes, mines, depth charges, air-to-surface missiles (ASMs) (such as the US-built Harpoon), or bombs. Armaments are managed by a Smith Aerospace-built stores management system, which includes a newly developed Universal Stores Control Unit (USCU) capable of accommodating hundreds of different munitions, including future ones and precision weapons. Multiple radar warning receivers provide all-round awareness of missile threats, which is combined with a defensive countermeasures suite.


title: Kawasaki P-1

text: On 31 August 2007, the Japanese Ministry of Defense revealed that they would procure four production airframes. The request in the FY2008 budget was , the unit price for each aircraft at US$141.5 million. In 2013, the ministry ordered two units for ¥44.5 billion. These P-1s were reported to possess increased detection/discrimination capability, flight performance, information processing capability, and strike capabilities as a successor to the existing P-3C fixed-wing patrol aircraft.


title: Kawasaki P-1

text: In June 2007, Kawasaki rolled out the XP-1, a prototype for the P-X program. The rollout had been delayed for three months due to the discovery of defective rivets provided by a US supplier which required remedial repairs to be performed. On 28 September 2007, the XP-1 conducted its maiden flight from Gifu Air Field, Kakamigahara, Gifu, Japan; this flight lasted about one hour and ended successfully. The P-X was redesignated XP-1 at this time. By March 2010, Kawasaki Heavy Industries had delivered four XP-1 maritime patrol test aircraft to Japanese Ministry of Defense; the company also stated its aim for type certification to be achieved in time for the formal delivery of the first two aircraft by the end of March 2012.


title: Kawasaki P-1

text: On 8 August 2011, the Japanese Ministry of Defense announced that two aircraft used for ground testing had developed tears in various parts of the craft, including the fuel tank and central part of the fuselage. In response, modifications to reinforce the affected areas were planned. By October 2012, the problems had been reportedly resolved. On 26 March 2013, Japan's Maritime Self-Defense Force took delivery of its first pair of P-1s, ahead of a planned two years of test flights. On 14 May 2013, these aircraft were grounded after one developed an unstable combustion condition in some of its engines during mid-flight.


title: Kawasaki P-1

text: During efforts to sell the aircraft to the UK, a pair of P-1s (one of Air Development Squadron 51 and one of Air Patrol Squadron 3 were present for the 2015 Royal International Air Tattoo, one aircraft performing a flying display while the other was on static display; this was the first time that any Japanese military aircraft had performed in a European flight display. After its UK appearance, the P-1s proceeded to the Japan Self-Defense Force Base Djibouti at Ambouli International Airport, Djibouti, to continue with operational trials within tropical and desert climates.


title: Kawasaki P-1

text: In November 2016, two P-1s in New Zealand to celebrate the Royal New Zealand Navy's 75th anniversary took part in damage surveys after the 2016 Kaikoura earthquake along with P-3 Orions of the Royal New Zealand Air Force and the United States Navy.


title: Kawasaki P-1

text: In December 2018, the Japanese Ministry of Defense alleged that a Gwanggaeto the Great-class destroyer of the South Korean Navy locked its separate target illumination radar onto a P-1 belonging to Air Patrol Squadron 3. The South Korean Navy stated that it had used the radar of an optical camera system and not a fire control system. The incident led to a diplomatic row between Japan and South Korea.


title: Kawasaki P-1

text: In 2018 it was reported that Kawasaki was offering the P-1 to France to replace its Breguet Atlantic aircraft.


title: Kawasaki P-1

text: There have been reports that Vietnam is considering buying used P-3 Orions from either the JMSDF or the US Navy or the Kawasaki P-1.


title: Kawasaki P-1

text: The P-1 was reportedly offered to Germany as a replacement for its P-3C Orion aircraft in 2018. However, in September 2020, Germany was no longer considering the P-1 due to concerns the aircraft would not be able to achieve military type certification within a required five years time frame.


title: Kawasaki P-1

text: In January 2015, it was reported that Tokyo was holding a series of defence talks with the United Kingdom to ascertain a possible sale of P-1s to the Royal Air Force to replace their recently retired fleet of Hawker Siddeley Nimrod patrol aircraft. The proposal was part of a wider initiative to lower restrictions on Japanese military exports. It was claimed that Britain may consider jointly manufacturing the type, and that the nation could retain rights over related radar and sensor technologies. On November 23, 2015 the UK announced it would buy the Boeing P-8 Poseidon instead of the Kawasaki P-1.


title: Kawasaki P-1

text: New Zealand requested information on the P-1 and Kawasaki C-2 to meet the country's patrol and transport aircraft needs. This request was met with unclassified information in September 2016 and a more detailed proposal including purchase price, manufacturing arrangements, and maintenance complete by mid-2017. This put the P-1 in direct competition with the P-8. On July 9, 2018 it was announced that New Zealand had selected the P-8.


title: Gospel of James

text: The Gospel of James (or the Protoevangelium of James) is a second-century infancy gospel telling of the miraculous conception of the Virgin Mary, her upbringing and marriage to Joseph, the journey of the couple to Bethlehem, the birth of Jesus, and events immediately following. It is the earliest surviving assertion of the perpetual virginity of Mary, meaning her virginity not just prior to the birth of Jesus, but during and afterwards, and despite being condemned by Pope Innocent I in 405 and rejected by the Gelasian Decree around 500, became a widely influential source for Mariology.


title: Gospel of James

text: The Gospel of James was well known to Origen in the early third century and probably to Clement of Alexandria at the end of the second, so is assumed to have been in circulation soon after "circa" 150 AD. The author claims to be James the half-brother of Jesus by an earlier marriage of Joseph, but in fact his identity is unknown. Early studies assumed a Jewish milieu, largely because of its frequent use and knowledge of the Septuagint (a Greek translation of the Jewish scriptures); further investigation demonstrated that it misunderstands and/or misrepresents many Jewish practices, but Judaism at this time was highly diverse, and recent trends in scholarship do not entirely dismiss a Jewish connection. Its origin is probably Syrian, and it possibly derives from a sect called the Encratites, whose founder, Tatian, taught that sex and marriage were symptoms of original sin.


title: Gospel of James

text: The gospel is a "midrash" (an elaboration) on the birth narratives found in the gospels of Matthew and Luke, and many of its elements, notably its very physical description of Mary's pregnancy and the examination of her hymen by the midwife Salome, suggest strongly that it was attempting to deny the arguments of docetists and Marcionites, unorthodox Christians who held that Jesus was entirely supernatural. It also draws heavily on the Septuagint for historical analogies, turns of phrase, and details of Jewish life. Ronald Hock and Mary F. Foskett have drawn attention to the influence of Greco-Roman literature on its themes of virginity and purity.


title: Gospel of James

text: Scholars generally accept that the Gospel of James was originally composed in Greek. Over 100 Greek manuscripts have survived, and translations were made into Syriac, Ethiopian, Coptic, Georgian, Old Church Slavonic, Armenian, Arabic, and presumably Vulgar Latin, given that it was apparently known to the compiler of the Gelasian Decree. The oldest is Papyrus Bodmer 5 from the fourth or possibly third century, discovered in 1952 and now in the Bodmer Library, Geneva, while the fullest is a 10th-century Greek codex in the Bibliothèque Nationale, Paris. The first widely printed edition (as opposed to hand-copied manuscripts) was a 1552 edition printed in Basel, Switzerland, by Guillaume Postel, who printed his Latin translation of a Greek version of the work. Postel also gave the work the Latin name (Proto-Gospel of James) because he believed (incorrectly) that the work antedated the main gospels of the New Testament (proto- for first, evangelion for gospel). Emile de Stryker published the standard modern critical edition in 1961, and in 1995 Ronald Hock published an English translation based on de Stryker.


title: Gospel of James

text: Mary is presented as an extraordinary child destined for great things from the moment of her conception. Her parents, the wealthy Joachim and his wife Anna (or Anne), are distressed that they have no children, and Joachim goes into the wilderness to pray, leaving Anna to lament her childless state. God hears Anna's prayer, angels announce the coming child, and in the seventh month of Anna's pregnancy (underlining the exceptional nature of Mary's future life), she is born. Anna dedicates the child to God and vows that she shall be raised in the Temple. Joachim and Anna name the child Mary, and when she is three years old, they send her to the Temple, where she is fed each day by an angel.


title: Gospel of James

text: When Mary approaches her 12th year, the priests decide that she can no longer stay in the Temple lest her menstrual blood render it unclean, and God finds a widower, Joseph, to act as her guardian: Joseph is depicted as elderly and the father of grown sons; he has no desire for sexual relations with Mary. He leaves on business, and Mary is called to the Temple to help weave the temple curtain, where one day an angel appears and tells her that she has been chosen to conceive Jesus the Saviour, but that she will not give birth as other women do. Joseph returns and finds Mary six months pregnant, and rebukes her, fearing that the priests will assume that he is the guilty party. They do, but the chastity of both is proven through the "test of bitter waters".


title: Gospel of James

text: The Roman census forces the holy couple to travel to Bethlehem, but Mary's time comes before they can reach the village. Joseph settles Mary in a cave, where she is guarded by his sons, while he goes in search of a midwife, and for an apocalyptic moment as he searches all creation stands still. He returns with a midwife, and as they stand at the mouth of the cave, a cloud overshadows it, an intense light fills it, and suddenly a baby is at Mary's breast. Joseph and the midwife marvel at the miracle, but a second midwife named Salome (the first is not given a name) insists on examining Mary, upon which her hand withers as a sign of her lack of faith; Salome prays to God for forgiveness and an angel appears and tells her to touch the Christ Child, upon which her hand is healed.


title: Gospel of James

text: The gospel concludes with the visit of the Three Magi, the massacre of the innocents in Bethlehem, the martyrdom of the High Priest Zechariah (father of John the Baptist), and the election of his successor Simeon, and an epilogue, telling the circumstances under which the work was supposedly composed.


title: Gospel of James

text: The Gospel of James was a widely influential source for Christian doctrine regarding Mary. According to Bernhard Lohse, it is the earliest assertion of her perpetual virginity, meaning her virginity not just prior to the birth of Jesus, but during the birth and afterwards. Its explanation of the gospels' "brothers of Jesus" (the "adelphoi") as the offspring of Joseph by an earlier marriage remains the position of the Eastern church, but in the West, influential theologian Jerome asserted that Joseph himself had been a perpetual virgin, and that the" adelphoi "were cousins of the Lord. Due to Jerome, the Protoevangelium was condemned by Pope Innocent I in 405 and rejected by the Gelasian Decree around 500, but despite being officially condemned, it was taken over almost "in toto" by another apocryphal work, the Gospel of Pseudo-Matthew, which popularised most of its stories.


title: Gospel of James

text: The Gospel of James was the first to give the name Anne to the mother of Mary, taking it probably from Hannah, the mother of the prophet Samuel, and Mary, like Samuel, is taken to spend her childhood in the temple. Some manuscripts say of Anne's pregnancy that it was the result of normal intercourse with her husband, but current scholars prefer the oldest texts, which say that Mary was conceived in Joachim's absence through divine intervention; nevertheless, the Gospel of James does not advance the idea of Mary's Immaculate Conception.


title: Gospel of James

text: Various manuscripts place the birth of Mary in the sixth, seventh, eighth, or ninth month, with the oldest having the seventh; this was in keeping with both the Judaism of the period, which had similar seventh-month births for significant individuals such as Samuel, Isaac, and Moses, as the sign of a miraculous or divine conception. Further signs of Mary's supremely holy nature follow, including Anne's vow that the infant would never walk on the earth (her bedroom is made a "sanctuary" where she is attended by "undefiled daughters of the Hebrews"), her blessing "with the ultimate blessing" by the priests on her first birthday with the declaration that because of her God will bring redemption to Israel, and the angels who bring her food in the Temple, where she is attended by the priests and engages herself in weaving the temple curtain.


title: Gospel of James

text: The ordeal of the bitter water serves to defend Jesus against accusation of illegitimacy levied in the second century by pagan and Jewish opponents of Christianity. Christian sensitivity to these charges made them eager to defend both the virgin birth of Jesus and the immaculate conception of Mary (i.e., her freedom from sin at the moment of her conception).


title: Gospel of James

text: The Quranic stories of the Virgin Mary and the birth of Jesus are similar to those of the Protoevangelium, which was widely known in the Near East. These include its mention of Mary fed by angels, the choice of her guardian (Joseph) through the casting of lots, and her occupation making a curtain for the Temple immediately before the Annunciation. Nevertheless, while the Quran holds Mary in high esteem and modern Muslims agree with Christians that she was a virgin when she conceived Jesus, they would see the idea of her perpetual virginity (which is the central idea of James) as contrary to the Islamic ideal of women as wives and mothers.


title: Discounted cash flow

text: The discounted cash flow (DCF) analysis is a method in finance of valuing a security, project, company, or asset using the concepts of the time value of money.


title: Discounted cash flow

text: Discounted cash flow analysis is widely used in investment finance, real estate development, corporate financial management and patent valuation. It was used in industry as early as the 1700s or 1800s, widely discussed in financial economics in the 1960s, and became widely used in U.S. courts in the 1980s and 1990s.


title: Discounted cash flow

text: To apply the method, all future cash flows are estimated and discounted by using cost of capital to give their present values (PVs). The sum of all future cash flows, both incoming and outgoing, is the net present value (NPV), which is taken as the value of the cash flows in question;


title: Discounted cash flow

text: and for the mechanics see valuation using discounted cash flows, which includes modifications typical for startups, private equity and venture capital, corporate finance "projects", and mergers and acquisitions.


title: Discounted cash flow

text: Using DCF analysis to compute the NPV takes as input cash flows and a discount rate and gives as output a present value. The opposite process takes cash flows and a price (present value) as inputs, and provides as output the discount rate; this is used in bond markets to obtain the yield.


title: Discounted cash flow

text: Discounted cash flow calculations have been used in some form since money was first lent at interest in ancient times. Studies of ancient Egyptian and Babylonian mathematics suggest that they used techniques similar to discounting future cash flows. Modern discounted cash flow analysis has been used since at least the early 1700s in the UK coal industry.


title: Discounted cash flow

text: Discounted cash flow valuation is differentiated from the accounting book value, which is based on the amount paid for the asset. Following the stock market crash of 1929, discounted cash flow analysis gained popularity as a valuation method for stocks. Irving Fisher in his 1930 book "The Theory of Interest" and John Burr Williams's 1938 text "The Theory of Investment Value" first formally expressed the DCF method in modern economic terms.


title: Discounted cash flow

text: The discounted cash flow formula is derived from the present value formula for calculating the time value of money


title: Discounted cash flow

text: Where multiple cash flows in multiple time periods are discounted, it is necessary to sum them as follows: