title: A Clash of Kings

text: As with its predecessor, "A Clash of Kings" was positively received by critics. Dorman Shindler of "The Dallas Morning News" described it as "one of the best [works] in this particular subgenre", praising "the richness of this invented world and its cultures ... [that] lends Mr. Martin's novels the feeling of medieval history rather than fiction." Writing in "The San Diego Union-Tribune", Jim Hopper called "A Clash of Kings" "High Fantasy with a vengeance" and commented: "I'll admit to staying up too late one night last week to finish off this big book, and I hope it's not too terribly long until the next one comes out." Danielle Pilon wrote in the "Winnipeg Free Press" that the book "shows no signs of the usual 'middle book' aimlessness". Although she found the constantly switching viewpoints "momentarily confusing", she felt that it "draws the reader deep into the labyrinthine political and military intrigues and evokes sympathy for characters on all sides of the conflict." Bradley H. Sinor of the "Tulsa World" praised Martin for "keep[ing] readers balanced on a sword's edge" and managing to do "three important things" with "A Clash of Kings": "It grips the reader whether or not they read the earlier book, tells a satisfying story and leaves the reader wanting the next book as soon as possible." "The Oregonian's" Steve Perry called the book "easily as good as the first novel" and commented that the "Song of Ice and Fire" books were "so complex, fascinating and well-rendered that readers will almost certainly be hooked into the whole series." However, he cautioned that "if it were a movie, it would be rated "R" for sex and violence, so don't pick the book up for your 10-year-old nephew who likes Conan."


title: Mariette Hartley

text: Mary Loretta "Mariette" Hartley (born June 21, 1940) is an American film and television actress. She is best known for work with Bill Bixby on "The Incredible Hulk" (1978) and "Goodnight, Beantown" (1983–1984), an original "" episode (1969), Sam Peckinpah's "Ride the High Country" (1962) with Randolph Scott and Joel McCrea, and a series of commercials with James Garner in the 1970s and 1980s.


title: Mariette Hartley

text: Hartley was born in Weston, Connecticut on June 21, 1940, the daughter of Mary "Polly" Ickes (née Watson), a manager and saleswoman, and Paul Hembree Hartley, an account executive. Her maternal grandfather was John B. Watson, an American psychologist who established the psychological school of behaviorism. She grew up in Weston, Connecticut, an affluent Fairfield County suburb within commuting distance to Manhattan.


title: Mariette Hartley

text: Hartley began her career as a 13-year-old in the White Barn Theatre in Norwalk, Connecticut. In her teens as a stage actress, she was coached and mentored by Eva Le Gallienne. She graduated in 1957 from Staples High School in Westport, Connecticut, where she was an active member of the school's theater group, Staples Players. Hartley also worked at the American Shakespeare Festival.


title: Mariette Hartley

text: Her film career began with an uncredited cameo appearance in "From Hell to Texas" (1958), a Western with Dennis Hopper. In the early 1960s, she moved to Los Angeles and joined the UCLA Theater Group.


title: Mariette Hartley

text: Hartley's first credited film appearance was alongside Randolph Scott and Joel McCrea in the 1962 Sam Peckinpah Western "Ride the High Country"; the role earned her a BAFTA award nomination. She continued to appear in film during the 1960s, including the lead role in the adventure "Drums of Africa" (1963), and prominent supporting roles in Alfred Hitchcock's psychological thriller "Marnie" (1964) — alongside Tippi Hedren and Sean Connery — and the John Sturges drama "Marooned" (1969).


title: Mariette Hartley

text: Hartley also guest-starred in numerous TV series during the decade, with appearances in "Gunsmoke", "The Twilight Zone" (the episode "The Long Morrow"), "The Travels of Jaimie McPheeters" (starring a young Kurt Russell), the syndicated "Death Valley Days" (then hosted by Ronald Reagan), "Judd, for the Defense", "Bonanza", and "" (as Zarabeth in the 3rd season episode "", 1969) among others. In 1965, she had a significant role as Dr. Claire Morton in 32 episodes of "Peyton Place".


title: Mariette Hartley

text: Hartley continued to perform in film and TV during the 1970s, including two Westerns alongside Lee Van Cleef, "Barquero" (1970) and "The Magnificent Seven Ride!" (1972), and TV series including "The Love Boat", "The Streets of San Francisco", "Emergency!", "McCloud", "Little House on the Prairie", "Love American Style", "Police Woman", and "Columbo" — starring in two editions of the latter alongside Peter Falk; "Publish or Perish" co-starring Jack Cassidy (1974) and "Try and Catch Me" with Ruth Gordon (1977). Hartley portrays similar characters as a publisher's assistant in both episodes.


title: Mariette Hartley

text: In 1977, Hartley appeared in the TV movie "The Last Hurrah", a political drama based on the Edwin O'Connor novel of the same name; and earned her first Emmy Award nomination.


title: Mariette Hartley

text: Her role as psychologist Dr. Carolyn Fields in "Married", a 1978 episode of the TV series "The Incredible Hulk" in which she marries Bill Bixby's character, the alter ego of the Hulk, won Hartley the Primetime Emmy Award for Outstanding Lead Actress in a Drama Series. She was nominated for the same award for her performance in an episode of "The Rockford Files" the following year.


title: Mariette Hartley

text: In 1983, Hartley reunited with Bixby in the sitcom "Goodnight, Beantown", which ran for two seasons and brought her another Emmy Award nomination. (She worked with Bixby again in the 1992 TV movie "", the first of three TV movies that launched the series "").


title: Mariette Hartley

text: In 1987, she co-hosted CBS's "The Morning Program" weekday morning news show alongside Rolland Smith, for ten months.


title: Mariette Hartley

text: In the 1990s, Hartley toured with Elliott Gould and Doug Wert in the revival of the mystery play "Deathtrap".


title: Mariette Hartley

text: Numerous roles in TV movies and guest appearances in TV series during the 1990s and 2000s followed, including "Murder, She Wrote" (1992), "Courthouse" (1995), "Nash Bridges" (2000), and "NCIS" (2005). She had recurring roles as Sister Mary Daniel in the soap opera "One Life to Live" (1999–2001; 10 episodes), and as Lorna Scarry in six episodes of "" (2003–2011).


title: Mariette Hartley

text: From 1995 to 2015, she hosted the long-running television documentary series "Wild About Animals", an educational program.


title: Mariette Hartley

text: In 2006, Hartley starred in her own one-woman show, "If You Get to Bethlehem, You've Gone Too Far", which ran in Los Angeles. She returned to the stage in 2014 as Eleanor of Aquitaine with Ian Buchanan's Henry in the Colony Theater Company production of James Goldman's "The Lion in Winter".


title: Mariette Hartley

text: In January 2018, Hartley began a recurring role on the Fox first-responder drama "9-1-1" as Patricia Clark, the Alzheimer's-afflicted mother of dispatcher Abby Clark (Connie Britton).


title: Mariette Hartley

text: In the late 1970s and early 1980s, Hartley appeared with James Garner in a popular series of television commercials advertising Polaroid cameras. The two actors had such amazing on-screen chemistry that many viewers erroneously believed that they were married in real life. Hartley's 1990 biography, "Breaking the Silence", indicates that she began to wear a T-shirt printed with the phrase "I am not Mrs. James Garner." (Hartley went as far to have a shirt made for her infant son, reading "I am not James Garner's Child" and even one for her then-husband: "I am not James Garner!" James Garner's actual wife then jokingly had a T-shirt printed with "I am Mrs. James Garner.") Hartley guest-starred in an episode of Garner's television series "The Rockford Files" in 1979. The script required the two to kiss at one point and unbeknownst to them, a paparazzo was photographing the scene from a distance. The photos were run in a tabloid trying to provoke a scandal. An article that ran in "TV Guide" was titled: "That woman is "not" James Garner's wife!"


title: Mariette Hartley

text: Between 2001 and 2006, Hartley endorsed the See Clearly Method, a commercial eye exercise program, whose sales were halted by an Iowa court after a finding of fraudulent business practices and advertising.


title: Mariette Hartley

text: Hartley has been married three times. Her first marriage was to John Seventa (1960–1962). She married Patrick Boyriven on August 13, 1978, with whom she had two children, Sean (born 1975) and Justine (born 1978). The couple divorced in 1996. In 2005, Hartley married Jerry Sroka.


title: Mariette Hartley

text: In her 1990 autobiography "Breaking the Silence", written with Anne Commire, Hartley talked about her struggles with psychological problems, pointing directly to her grandfather's (Dr. Watson) practical application of his theories as the source of the dysfunction in his family. She has also spoken in public about her experience with bipolar disorder and was a founder of the American Foundation for Suicide Prevention. She currently serves as the foundation's national spokesperson.


title: Mariette Hartley

text: In 2003, Hartley was hired by pharmaceutical company GlaxoSmithKline to increase awareness of bipolar medications and treatments. She frequently promotes awareness of bipolar disorder and suicide prevention.


title: Mariette Hartley

text: Her brother, Paul Hartley, has a PhD in research philosophy and is the author of the book "The Seventh Tool: a novel in 3 volumes" (2013)"."


title: Face

text: The face is the front of an animal's head that features the eyes, nose and mouth, and through which animals express many of their emotions. The face is crucial for human identity, and damage such as scarring or developmental deformities may affect the psyche adversely.


title: Face

text: The front of the human head is called the face. It includes several distinct areas, of which the main features are:


title: Face

text: Facial appearance is vital for human recognition and communication. Facial muscles in humans allow expression of emotions.


title: Face

text: The face is itself a highly sensitive region of the human body and its expression may change when the brain is stimulated by any of the many human senses, such as touch, temperature, smell, taste, hearing, movement, hunger, or visual stimuli.


title: Face

text: The face is the feature which best distinguishes a person. Specialized regions of the human brain, such as the fusiform face area (FFA), enable facial recognition; when these are damaged, it may be impossible to recognize faces even of intimate family members. The pattern of specific organs, such as the eyes, or of parts of them, is used in biometric identification to uniquely identify individuals.


title: Face

text: The shape of the face is influenced by the bone-structure of the skull, and each face is unique through the anatomical variation present in the bones of the viscerocranium (and neurocranium). The bones involved in shaping the face are mainly the maxilla, mandible, nasal bone and zygomatic bone. Also important are various soft tissues, such as fat, hair and skin (of which color may vary).


title: Face

text: The face changes over time, and features common in children or babies, such as prominent buccal fat-pads disappear over time, their role in the infant being to stabilize the cheeks during suckling.


title: Face

text: While the buccal fat-pads often diminish in size, the prominence of bones increase with age as they grow and develop.


title: Face

text: Visible variable features of the face other than shapes and proportions include color (paleness, sun tan and genetic default pigmentation), hair (length, color, loss, graying), wrinkles, facial hair (e.g. beards), skin sagging, discolorations (dark spots, freckles and eye circles), pore-variabilities, skin blemishes (pimples, scars, burn marks). Many of these features can also vary over time due to aging,<ref name="10.1111/ics.12128"></ref><ref name="10.1186/s13104-019-4404-z"></ref> skin care, nutrition,<ref name="10.1111/jdv.16614"></ref><ref name="10.3892/etm.2019.8342"></ref> the exposome<ref name="10.1016/j.jdermsci.2016.09.015"></ref> (such as harmful substances of the general environment, workplace and cosmetics), psychological factors, and behavior (such as smoking, sleep, physical activity and sun damage).


title: Face

text: Mechanisms underlying these include changes related to peptides (notably collagen), inflammation, production of various proteins (notably elastin and other ECM proteins), the structure of subcutaneous tissue,<ref name="10.1371/journal.pone.0008021"></ref> hormones, fibers (such as elastic fibers or elasticity) and the skin barrier.


title: Face

text: The desire of many to look young for their age and/or attractive has led to the establishment of a large cosmetics industry, which is largely concerned with make-up that is applied on top of the skin (topically) to temporarily change appearance but it or dermatology also develop anti-aging products (and related products and procedures) that in some cases affect underlying biology and are partly applied preventively. Facial traits are also used in biometrics and there have been attempts at reproducible quantifications.<ref name="10.1117/12.975404"></ref> Skin health is considered a major factor in human well-being and the perception of health in humans.<ref name="10.1016/j.clindermatol.2019.04.002"></ref>


title: Face

text: Genes are a major factor in the particular appearance of a person's face with the high similarity of faces of indicating that most of facial variability is determined genetically.


title: Face

text: Studies have identified genes and gene regions determining face shape and differences in various facial features. A 2021 study found that a version of a gene associated with lip thickness – possibly selected for due to adaption to cold climate via fat distribution – introgressed from ancient humans – Denisovans – into the modern humans Native Americans. Another study found look-alike humans (Doppelgängers) have genetic similarities, sharing genes affecting not only the face but also some phenotypes of physique and behavior. A study identified genes controlling the shape of the nose and chin. Biological databases may be used to aggregate and discover associations between facial phenotypes and genes.


title: Face

text: Faces are essential to expressing emotion, consciously or unconsciously. A frown denotes disapproval; a smile usually means someone is pleased. Being able to read emotion in another's face is "the fundamental basis for empathy and the ability to interpret a person’s reactions and predict the probability of ensuing behaviors". One study used the Multimodal Emotion Recognition Test to attempt to determine how to measure emotion. This research aimed at using a measuring device to accomplish what many people do every day: read emotion in a face.


title: Face

text: The muscles of the face play a prominent role in the expression of emotion, and vary among different individuals, giving rise to additional diversity in expression and facial features.


title: Face

text: People are also relatively good at determining if a smile is real or fake. A recent study looked at individuals judging forced and genuine smiles. While young and elderly participants equally could tell the difference for smiling young people, the "older adult participants outperformed young adult participants in distinguishing between posed and spontaneous smiles". This suggests that with experience and age, we become more accurate at perceiving true emotions across various age groups.


title: Face

text: Gestalt psychologists theorize that a face is not merely a set of facial features, but is rather something meaningful in its form. This is consistent with the Gestalt theory that an image is seen in its entirety, not by its individual parts. According to Gary L. Allen, people adapted to respond more to faces during evolution as the natural result of being a social species. Allen suggests that the purpose of recognizing faces has its roots in the "parent-infant attraction, a quick and low-effort means by which parents and infants form an internal representation of each other, reducing the likelihood that the parent will abandon his or her offspring because of recognition failure". Allen's work takes a psychological perspective that combines evolutionary theories with Gestalt psychology.


title: Face

text: Research has indicated that certain areas of the brain respond particularly well to faces. The fusiform face area, within the fusiform gyrus, is activated by faces, and it is activated differently for shy and social people. A study confirmed that "when viewing images of strangers, shy adults exhibited significantly less activation in the fusiform gyri than did social adults". Furthermore, particular areas respond more to a face that is considered attractive, as seen in another study: "Facial beauty evokes a widely distributed neural network involving perceptual, decision-making and reward circuits. In those experiments, the perceptual response across FFA and LOC remained present even when subjects were not attending explicitly to facial beauty".


title: Face

text: Cosmetic surgery can be used to alter the appearance of the facial features. Maxillofacial surgery may also be used in cases of facial trauma, injury to the face and skin diseases. Severely disfigured individuals have recently received full face transplants and partial transplants of skin and muscle tissue.


title: Face

text: Caricatures often exaggerate facial features to make a face more easily recognized in association with a pronounced portion of the face of the individual in question—for example, a caricature of Osama bin Laden might focus on his facial hair and nose; a caricature of George W. Bush might enlarge his ears to the size of an elephant's; a caricature of Jay Leno may pronounce his head and chin; and a caricature of Mick Jagger might enlarge his lips. Exaggeration of memorable features helps people to recognize others when presented in a caricature form.


title: Face

text: By extension, anything which is the forward or world-facing part of a system which has internal structure is considered its "face", like the façade of a building. For example, a public relations or press officer might be called the "face" of the organization he or she represents. "Face" is also used metaphorically in a sociological context to refer to reputation or standing in society, particularly Chinese society, and is spoken of as a resource which can be won or lost. Because of the association with individuality, the anonymous person is sometimes referred to as "faceless".


title: Area

text: Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or "plane area" refers to the area of a shape or planar lamina, while "surface area" refers to the area of an open surface or the boundary of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analogue of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept).


title: Area

text: The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (written as m), which is the area of a square whose sides are one metre long. A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.


title: Area

text: There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. For shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus.


title: Area

text: For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area. Formulas for the surface areas of simple shapes were computed by the ancient Greeks, but computing the surface area of a more complicated shape usually requires multivariable calculus.


title: Area

text: Area plays an important role in modern mathematics. In addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry. In analysis, the area of a subset of the plane is defined using Lebesgue measure, though not every subset is measurable. In general, area in higher mathematics is seen as a special case of volume for two-dimensional regions.


title: Area

text: Area can be defined through the use of axioms, defining it as a function of a collection of certain plane figures to the set of real numbers. It can be proved that such a function exists.


title: Area

text: An approach to defining what is meant by "area" is through axioms. "Area" can be defined as a function from a collection M of a special kinds of plane figures (termed measurable sets) to the set of real numbers, which satisfies the following properties:


title: Area

text: Every unit of length has a corresponding unit of area, namely the area of a square with the given side length. Thus areas can be measured in square metres (m), square centimetres (cm), square millimetres (mm), square kilometres (km), square feet (ft), square yards (yd), square miles (mi), and so forth. Algebraically, these units can be thought of as the squares of the corresponding length units.


title: Area

text: and so, a rectangle with different sides (say length of 3 metres and width of 2 metres) would have an area in square units that can be calculated as:


title: Area

text: 3 metres × 2 metres = 6 m. This is equivalent to 6 million square millimetres. Other useful conversions are:


title: Area

text: In non-metric units, the conversion between two square units is the square of the conversion between the corresponding length units.


title: Area

text: There are several other common units for area. The are was the original unit of area in the metric system, with:


title: Area

text: In the 5th century BCE, Hippocrates of Chios was the first to show that the area of a disk (the region enclosed by a circle) is proportional to the square of its diameter, as part of his quadrature of the lune of Hippocrates, but did not identify the constant of proportionality. Eudoxus of Cnidus, also in the 5th century BCE, also found that the area of a disk is proportional to its radius squared.


title: Area

text: Subsequently, Book I of Euclid's "Elements" dealt with equality of areas between two-dimensional figures. The mathematician Archimedes used the tools of Euclidean geometry to show that the area inside a circle is equal to that of a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius, in his book "Measurement of a Circle". (The circumference is 2"r", and the area of a triangle is half the base times the height, yielding the area "r" for the disk.) Archimedes approximated the value of π (and hence the area of a unit-radius circle) with his doubling method, in which he inscribed a regular triangle in a circle and noted its area, then doubled the number of sides to give a regular hexagon, then repeatedly doubled the number of sides as the polygon's area got closer and closer to that of the circle (and did the same with circumscribed polygons).


title: Area

text: Swiss scientist Johann Heinrich Lambert in 1761 proved that π, the ratio of a circle's area to its squared radius, is irrational, meaning it is not equal to the quotient of any two whole numbers. In 1794, French mathematician Adrien-Marie Legendre proved that π is irrational; this also proves that π is irrational. In 1882, German mathematician Ferdinand von Lindemann proved that π is transcendental (not the solution of any polynomial equation with rational coefficients), confirming a conjecture made by both Legendre and Euler.


title: Area

text: Heron (or Hero) of Alexandria found what is known as Heron's formula for the area of a triangle in terms of its sides, and a proof can be found in his book, "Metrica", written around 60 CE. It has been suggested that Archimedes knew the formula over two centuries earlier, and since "Metrica" is a collection of the mathematical knowledge available in the ancient world, it is possible that the formula predates the reference given in that work.


title: Area

text: In 499 Aryabhata, a great mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy, expressed the area of a triangle as one-half the base times the height in the "Aryabhatiya" (section 2.6).


title: Area

text: A formula equivalent to Heron's was discovered by the Chinese independently of the Greeks. It was published in 1247 in "Shushu Jiuzhang" ("Mathematical Treatise in Nine Sections"), written by Qin Jiushao.


title: Area

text: In the 7th century CE, Brahmagupta developed a formula, now known as Brahmagupta's formula, for the area of a cyclic quadrilateral (a quadrilateral inscribed in a circle) in terms of its sides. In 1842, the German mathematicians Carl Anton Bretschneider and Karl Georg Christian von Staudt independently found a formula, known as Bretschneider's formula, for the area of any quadrilateral.


title: Area

text: The development of Cartesian coordinates by René Descartes in the 17th century allowed the development of the surveyor's formula for the area of any polygon with known vertex locations by Gauss in the 19th century.


title: Area

text: The development of integral calculus in the late 17th century provided tools that could subsequently be used for computing more complicated areas, such as the area of an ellipse and the surface areas of various curved three-dimensional objects.


title: Area

text: For a non-self-intersecting (simple) polygon, the Cartesian coordinates formula_1 ("i"=0, 1, ..., "n"-1) of whose "n" vertices are known, the area is given by the surveyor's formula:


title: Area

text: The most basic area formula is the formula for the area of a rectangle. Given a rectangle with length and width , the formula for the area is:


title: Area

text: That is, the area of the rectangle is the length multiplied by the width. As a special case, as in the case of a square, the area of a square with side length is given by the formula:


title: Area

text: The formula for the area of a rectangle follows directly from the basic properties of area, and is sometimes taken as a definition or axiom. On the other hand, if geometry is developed before arithmetic, this formula can be used to define multiplication of real numbers.


title: Area

text: For an example, any parallelogram can be subdivided into a trapezoid and a right triangle, as shown in figure to the left. If the triangle is moved to the other side of the trapezoid, then the resulting figure is a rectangle. It follows that the area of the parallelogram is the same as the area of the rectangle:


title: Area

text: However, the same parallelogram can also be cut along a diagonal into two congruent triangles, as shown in the figure to the right. It follows that the area of each triangle is half the area of the parallelogram:


title: Area

text: Similar arguments can be used to find area formulas for the trapezoid as well as more complicated polygons.


title: Area

text: The formula for the area of a circle (more properly called the area enclosed by a circle or the area of a disk) is based on a similar method. Given a circle of radius , it is possible to partition the circle into sectors, as shown in the figure to the right. Each sector is approximately triangular in shape, and the sectors can be rearranged to form an approximate parallelogram. The height of this parallelogram is , and the width is half the circumference of the circle, or . Thus, the total area of the circle is :


title: Area

text: Though the dissection used in this formula is only approximate, the error becomes smaller and smaller as the circle is partitioned into more and more sectors. The limit of the areas of the approximate parallelograms is exactly , which is the area of the circle.


title: Area

text: This argument is actually a simple application of the ideas of calculus. In ancient times, the method of exhaustion was used in a similar way to find the area of the circle, and this method is now recognized as a precursor to integral calculus. Using modern methods, the area of a circle can be computed using a definite integral:


title: Area

text: The formula for the area enclosed by an ellipse is related to the formula of a circle; for an ellipse with semi-major and semi-minor axes and the formula is:


title: Area

text: Most basic formulas for surface area can be obtained by cutting surfaces and flattening them out (see: developable surfaces). For example, if the side surface of a cylinder (or any prism) is cut lengthwise, the surface can be flattened out into a rectangle. Similarly, if a cut is made along the side of a cone, the side surface can be flattened out into a sector of a circle, and the resulting area computed.


title: Area

text: The formula for the surface area of a sphere is more difficult to derive: because a sphere has nonzero Gaussian curvature, it cannot be flattened out. The formula for the surface area of a sphere was first obtained by Archimedes in his work "On the Sphere and Cylinder". The formula is:


title: Area

text: where is the radius of the sphere. As with the formula for the area of a circle, any derivation of this formula inherently uses methods similar to calculus.


title: Area

text: To find the bounded area between two quadratic functions, we subtract one from the other to write the difference as


title: Area

text: where "f"("x") is the quadratic upper bound and "g"("x") is the quadratic lower bound. Define the discriminant of "f"("x")-"g"("x") as


title: Area

text: By simplifying the integral formula between the graphs of two functions (as given in the section above) and using Vieta's formula, we can obtain


title: Area

text: The general formula for the surface area of the graph of a continuously differentiable function formula_37 where formula_38 and formula_39 is a region in the xy-plane with the smooth boundary:


title: Area

text: An even more general formula for the area of the graph of a parametric surface in the vector form formula_41 where formula_42 is a continuously differentiable vector function of formula_43 is:


title: Area

text: The areas of irregular (and thus arbitrary) polygons can be calculated using the "Surveyor's formula" (shoelace formula).


title: Area

text: The isoperimetric inequality states that, for a closed curve of length "L" (so the region it encloses has perimeter "L") and for area "A" of the region that it encloses,


title: Area

text: and equality holds if and only if the curve is a circle. Thus a circle has the largest area of any closed figure with a given perimeter.


title: Area

text: At the other extreme, a figure with given perimeter "L" could have an arbitrarily small area, as illustrated by a rhombus that is "tipped over" arbitrarily far so that two of its angles are arbitrarily close to 0° and the other two are arbitrarily close to 180°.


title: Area

text: For a circle, the ratio of the area to the circumference (the term for the perimeter of a circle) equals half the radius "r". This can be seen from the area formula "πr" and the circumference formula 2"πr".


title: Area

text: The area of a regular polygon is half its perimeter times the apothem (where the apothem is the distance from the center to the nearest point on any side).


title: Area

text: Doubling the edge lengths of a polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the dimension of the space the polygon resides in). But if the one-dimensional lengths of a fractal drawn in two dimensions are all doubled, the spatial content of the fractal scales by a power of two that is not necessarily an integer. This power is called the fractal dimension of the fractal.


title: Area

text: There are an infinitude of lines that bisect the area of a triangle. Three of them are the medians of the triangle (which connect the sides' midpoints with the opposite vertices), and these are concurrent at the triangle's centroid; indeed, they are the only area bisectors that go through the centroid. Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter (the center of its incircle). There are either one, two, or three of these for any given triangle.


title: Area

text: All area bisectors of a circle or other ellipse go through the center, and any chords through the center bisect the area. In the case of a circle they are the diameters of the circle.


title: Area

text: Given a wire contour, the surface of least area spanning ("filling") it is a minimal surface. Familiar examples include soap bubbles.


title: Area

text: A cyclic polygon (one inscribed in a circle) has the largest area of any polygon with a given number of sides of the same lengths.


title: Area

text: A version of the isoperimetric inequality for triangles states that the triangle of greatest area among all those with a given perimeter is equilateral.


title: Area

text: The triangle of largest area of all those inscribed in a given circle is equilateral; and the triangle of smallest area of all those circumscribed around a given circle is equilateral.


title: Area

text: The ratio of the area of the incircle to the area of an equilateral triangle, formula_46, is larger than that of any non-equilateral triangle.


title: Area

text: The ratio of the area to the square of the perimeter of an equilateral triangle, formula_47 is larger than that for any other triangle.


title: Alex Caruso

text: Alex Michael Caruso (born February 28, 1994) is an American professional basketball player for the Chicago Bulls of the National Basketball Association (NBA). Nicknamed "Bald Mamba" or "Carushow", he played college basketball for the Texas A&M Aggies, earning second-team all-Southeastern Conference (SEC) honors as a senior in 2016. He won an NBA championship with the Los Angeles Lakers in 2020.


title: Alex Caruso

text: Caruso attended A&M Consolidated High School in his native College Station, Texas, where he played basketball under head coaches Rusty Segler and Rick German. As a senior, he averaged 18 points and nine rebounds and was named TABC All-Regional, All-State as well as TABC All-Star and district MVP after leading his team to the postseason.


title: Alex Caruso

text: After graduating from high school, Caruso joined the Texas A&M Aggies. In 137 games over his four-year career, he averaged 8.0 points, 4.7 assists and 2.02 steals per game, finishing as the school's all-time leader in assists with 649 and steals with 276, surpassing David Edwards in those categories. As a senior he led the Aggies to the Sweet 16 of the NCAA Tournament; he also earned SEC All-Defensive Team and second-team All-SEC honors.


title: Alex Caruso

text: After going undrafted in the 2016 NBA draft, Caruso joined the Philadelphia 76ers for the 2016 NBA Summer League. On September 23, 2016, he signed with the Oklahoma City Thunder, but was later waived on October 17. On November 3, he was acquired by the Oklahoma City Blue of the NBA Development League.


title: Alex Caruso

text: Caruso joined the Lakers for the 2017 NBA Summer League. After several productive games, including one in which Caruso started in place of the injured Lonzo Ball and led the Lakers to a victory, he was signed to the Lakers' first two-way contract on July 13, 2017. He became the first player to go directly from the D-League (now G League) to the NBA via two-way contract. He also helped lead the Lakers win the 2017 NBA Summer League Championship in Las Vegas. Caruso made his NBA debut on October 19, 2017, against the Los Angeles Clippers. He played 12 minutes and recorded two points, two assists, and one rebound in a 108–92 loss. He had a career-high 15 points and seven rebounds in a victory in the final game of the season against the Clippers.


title: Alex Caruso

text: Caruso signed another two-way contract with the Los Angeles Lakers after a successful showing in the 2018 NBA Summer League. On March 6, 2019, he recorded a season-high 15 points, six rebounds, and three assists in a 99–115 loss to the Denver Nuggets. He scored a new career-high 32 points in a 122–117 victory over the Clippers on April 5. He also became the only Laker that season other than LeBron James to record a 30+ point, 10+ rebound, 5+ assist game. On April 7, 2019, with the Lakers missing James for the remaining six games, Caruso scored 18 points with a career-high 11 assists in a 113–109 home win over the Utah Jazz.


title: Alex Caruso

text: On July 6, 2019, Caruso signed a two-year contract with the Lakers worth $5.5 million. He won his first NBA championship with them on October 11, 2020, when the Lakers defeated the Miami Heat in six games. Caruso started the clinching game of the NBA Finals. He became an unrestricted free agent after the 2020–21 season.


title: Alex Caruso

text: On January 21, 2022, during a 90–94 loss to the Milwaukee Bucks, Caruso was fouled by opposing guard Grayson Allen. Allen was ejected from the game. The next day, the Bulls announced that Caruso had a fractured right wrist and would undergo surgery, keeping him out for at least 6-to-8 weeks.


title: Alex Caruso

text: Caruso has two sisters. His father played four years at Creighton and was an associate athletic director at Texas A&M.


title: Alex Caruso

text: Caruso grew up around the A&M program, spending many seasons as a ball boy for the Aggies. While studying at Texas A&M he majored in sports management.


title: Alex Caruso

text: On June 22, 2021, he was arrested at Easterwood Airport in College Station, Texas, for residual marijuana left on a grinder.


title: Mark Lee (singer)

text: Mark Lee (born August 2, 1999), professionally known as Mark, is a Canadian rapper, singer, and dancer based in South Korea. He is a member of the South Korean boy band NCT and its fixed sub-units NCT 127 and NCT Dream, as well as the South Korean supergroup SuperM.


title: Mark Lee (singer)

text: In 2012, Mark joined SM Entertainment as a trainee after passing the SM Global Audition in Vancouver, Canada.


title: Mark Lee (singer)

text: On December 16, 2013, he was introduced as a member of SM Rookies, a pre-debut team of trainees under SM Entertainment. As a part of the SM Rookies program, in October 2014, he and several his co-members appeared on the Mnet-produced "", a show starring labelmates Exo, where they perform dances to K-pop songs from the 1990s.


title: Mark Lee (singer)

text: In 2015, Mark and other SM Rookies members starred as Mouseketeers in a Korean revival of "", which aired on Disney Channel Korea. The show included musical performances, games, and skits, similar to the original American show. It aired from July 23 to December 17, 2015, hosted by Leeteuk of Super Junior.


title: Mark Lee (singer)

text: In April 2016, SM Entertainment confirmed that Mark and four other members of SM Rookies—Taeyong, Doyoung, Ten and Jaehyun—would debut as members of NCT's first sub-unit, NCT U. They released their first digital single on April 9, titled "The 7th Sense", in which he and Taeyong participated in songwriting. Three months later, SM Entertainment announced that Mark would become a member of NCT's second sub-unit, NCT 127, along with Taeyong, Taeil, Yuta, Jaehyun, Winwin and Haechan. NCT 127 made their official debut with the extended play "NCT #127" and title track "Fire Truck" on July 10, 2016.


title: Mark Lee (singer)

text: Mark joined NCT's third sub-unit, NCT Dream, which consisted of members Renjun, Jeno, Haechan, Jaemin, Chenle and Jisung. The group officially debuted on August 24, 2016, with the single "Chewing Gum". The following month, Mark featured on Henry Lau's "Going Through Your Heart", an original soundtrack for the KBS drama, "Sweet Stranger and Me". This marked his first solo endeavour since his debut in NCT.


title: Mark Lee (singer)

text: In January 2017, Mark joined "High School Rapper", a survival hip hop reality TV show that aired on Mnet. He advanced to the finals and performed an original song, "Drop" featuring labelmate Seulgi of Red Velvet, and placed seventh overall. In July 2017, Mark collaborated with Exo's Xiumin on single "Young & Free". It was released through Season 2 of SM Entertainment's digital music project SM Station. The same month, Mark appeared in the first season of the music variety show "Snowball Project". He teamed up with Park Jae-jung to release "Lemonade Love" on July 21, also through SM Station, which was produced by former labelmate Henry Lau and Yoon Jong-shin.


title: Mark Lee (singer)

text: Beginning in February 2018, Mark served as one of the main hosts of the music program "Show! Music Core", leaving in January 2019 to focus on activities with NCT 127. In May 2018, he became a regular cast member on the MBC reality TV show "It's Dangerous Beyond The Blankets". In October 2018, Mark released the song "Dream Me" with Red Velvet's Joy for the soundtrack of the KBS drama "The Ghost Detective." Mark was the first member to officially graduate from NCT Dream on December 31, 2018.


title: Mark Lee (singer)

text: On August 7, 2019, Mark was confirmed as a member of SuperM, a supergroup created by SM Entertainment in collaboration with Capitol Records. The group began promoting in October of that year in the American music market. SuperM's self-titled debut EP was released on October 4, 2019, led by the single "Jopping". Mark continued to promote with SuperM throughout 2020, through the release the group's first studio album, "Super One". On April 14, SM Entertainment announced through an official statement that Mark would be rejoining NCT Dream, thus abolishing their original age-based graduation system. His return was affirmed through his participation in the NCT Dream song "Déjà Vu" on the group-wide studio album "NCT 2020 Resonance".


title: Mark Lee (singer)

text: On January 28, 2022, it was announced that Mark would release his first single, "Child", on February 4, as part of "NCT Lab". "Child", described as an emotional hip-hop track, was commended for its lyrics.


title: Michael Schenker

text: Michael Schenker (born 10 January 1955) is a German guitarist. He played in the rock band UFO and leads the Michael Schenker Group. He was an early member of the hard rock band Scorpions, a band co-founded by his elder brother Rudolf Schenker. In the mid-1970s, Schenker joined UFO, playing lead and rhythm guitar. He left the band in 1978 to found the Michael Schenker Group. He has rejoined UFO three times, producing an album each time. Schenker continues to perform and record. He has been called "a legendary figure in the history of metal guitar."


title: Michael Schenker

text: Schenker started playing guitar at an early age, after his brother Rudolf got a Gibson Flying V guitar for his birthday, which captured his imagination. His main influences were Jimmy Page, Jeff Beck, Eric Clapton, Leslie West, Johnny Winter and Rory Gallagher. He played his first gig when he was 11, with Rudolf and the Scorpions in a nightclub. Schenker debuted with Scorpions on their debut album "Lonesome Crow" at age 16.


title: Michael Schenker

text: The Scorpions went on tour after recording their first album as the opening act for up-and-coming UK band UFO in Germany. Schenker was offered the position of lead guitar player for UFO (taking over for Bernie Marsden, himself a temporary replacement for Mick Bolton) and, with the blessing of his brother, accepted (Scorpions replaced him with Uli Roth), even though he didn't speak English.


title: Michael Schenker

text: Schenker co-wrote most of the songs on UFO's major label (Chrysalis Records) debut album "Phenomenon". His career with UFO was turbulent, sometimes walking off mid-song causing shows to be cancelled. Despite having a series of successful albums and tours, Schenker unequivocally quit UFO after their show in Palo Alto, California, on 29 October 1978. During this tour the band had recorded six concerts whose selected tracks would make up their live album "Strangers in the Night", which was released after he left the band.


title: Michael Schenker

text: Schenker briefly re-joined Scorpions in late 1978, when they were recording the album "Lovedrive". He composed and played lead guitar on three songs, "Another Piece of Meat", "Coast To Coast" and "Lovedrive". Although it had been widely believed for decades that the three songs were Schenker's only contribution to the record, during an interview with satellite radio host Eddie Trunk, Schenker vehemently maintained that he contributed to the whole album. In 1979, Schenker briefly toured with the band in support of the album. He blamed his very short stay on finding out he did not enjoy playing other people's songs. He was permanently replaced by Matthias Jabs, who had originally joined Scorpions before Schenker's return.


title: Michael Schenker

text: Schenker auditioned for Aerosmith in 1979 after Joe Perry left. According to Martin Huxley, Schenker stormed out of the room after producer Gary Lyons made several jokes about Nazis. After the death of Randy Rhoads, Ozzy Osbourne's first call was to Schenker to replace Rhoads, as the German guitarist and his iconic Flying V were a huge influence on Rhoads. But, Osbourne claims, Schenker made too many outlandish demands (including a private jet). Schenker himself, in an interview with KNAC radio, claims he was the one to say "no" to Osbourne: "If I would have joined Ozzy Osbourne, I would have screwed up my life. I was almost about to do it, and something told me: DON'T!!" Schenker has also claimed that at some point he was offered, but turned down joining the likes of Deep Purple, Thin Lizzy, Ian Hunter and Motörhead in order to focus on his solo career.


title: Michael Schenker

text: In 1979, Schenker started a solo career by founding the Michael Schenker Group (MSG). The history of MSG is strewn with personality conflicts and incidents. In 1982, original singer Gary Barden, who sang on the first two studio albums and a live album, was fired in favour of Graham Bonnet. Bonnet lasted one album ("Assault Attack") and a single gig, at Sheffield University, where he drunkenly exposed himself and was subsequently fired from the band. Barden rejoined MSG for the rest of the tour. He also appeared on the 1983 studio album ("Built to Destroy") and the band's second live album ("Rock Will Never Die").


title: Michael Schenker

text: After Barden's second departure, Schenker reorganized the band around himself and new singer Robin McAuley and renamed it the McAuley Schenker Group. The new incarnation of MSG was steered toward a more commercial hard rock sound. After three albums, Schenker and McAuley parted company. In the meantime, he briefly replaced Robbin Crosby in Ratt, appearing on their 1990 MTV Unplugged performance.


title: Michael Schenker

text: In 1993, Schenker rejoined UFO. He co-wrote (with Phil Mogg) nearly the whole of their reunion album, "Walk on Water" (1995), and toured with them briefly.


title: Michael Schenker

text: He then resurrected the Michael Schenker Group with all new members and recorded three more albums, "Written in the Sand", "The Unforgiven", and "Be Aware of Scorpions" before rejoining UFO for two further releases, "Covenant" and "Sharks".


title: Michael Schenker

text: Schenker fell on hard times in the early 2000s, despite his rejoining UFO that year. He later recorded the album "Arachnophobiac" and supported it with two years of touring. In 2004, recognition came from Dean Guitars, which began producing a Schenker signature Dean V (with subtle differences from the Gibson, but with the split black and white trademark Schenker finish).


title: Michael Schenker

text: 2005 was the 25th anniversary of the Michael Schenker Group. Schenker put together a new album of songs called "Tales of Rock'n'Roll" to celebrate the anniversary and enlisted singers from each iteration of the band to sing on the album. However, in that same year the collection "Heavy Hitters", a set of covers featuring Schenker and a revolving group of heavy metal all-stars, was marketed as a Michael Schenker Group album, with the result that Schenker only received a flat fee.


title: Michael Schenker

text: After nearly-disastrous North American and European tours in 2007, which included cancelled shows and less-than-stellar performances caused by heavy drinking, Schenker regained his composure and toured in the UK as Michael Schenker & Friends in 2008. Early 2008, Schenker worked with Gary Barden, Don Airey, Simon Phillips, and Neil Murray on a new MSG album "In the Midst of Beauty", which was released in May 2008, followed by touring.


title: Michael Schenker

text: In 2009 Schenker toured extensively including Russia, UK and the US with MSG including original members Gary Barden and Chris Glenn.


title: Michael Schenker

text: In November 2010, Schenker was given the Marshall "11" award in London along with other rock legends including Ron Wood and Slash. The award was presented to Schenker by Alice Cooper, with Jimmy Page, Tony Iommi and John Paul Jones also in attendance. The award is given to "those artists and musicians who represent rock 'n' roll excess and livin' on the edge."


title: Michael Schenker

text: In 2011 Schenker released a new album, "Temple of Rock". It was supported with a tour of Europe, Japan and the USA. In Europe the line up included Herman Rarebell on drums and Francis Buchholz on bass, both former members of Scorpions (Rarebell also joined the band for the Japanese dates) and Doogie White, formerly singer for Rainbow and Yngwie Malmsteen. With this line-up he recorded the album "Bridge the Gap" which was released in 2013.


title: Michael Schenker

text: In August 2012 Schenker received a Lifetime Achievement in Rock and Roll Award from "Vegas Rocks! Magazine." The award was presented by David Coverdale of Whitesnake. During the award ceremony Schenker performed with Sammy Hagar of Chickenfoot, Montrose and Van Halen.


title: Michael Schenker

text: Schenker's main guitar for most of his career was a Gibson Flying V, which he typically played through a "cocked" wah-wah pedal (switched on but left in a single position, around halfway through the travel of the foot pedal, and used as an equaliser to strengthen the midrange "sweet spot") and Marshall amplifiers. Schenker's "unmistakable midrange tone" was emphasised by the partially engaged wah pedal, as exemplified on the song "Rock Bottom" from the live UFO album "Strangers in the Night", was listed among the 50 greatest tones of all time by "Guitar Player" magazine. Since 2004, Schenker has switched to using a signature model Dean V.


title: Michael Schenker

text: In 2007 Dean Guitars, after producing Schenker's signature Dean V, also made two acoustic models with the familiar black and white "V" design.


title: Michael Schenker

text: Schenker has been on the covers of many guitar magazines and has influenced many notable guitar players, including Kirk Hammett and James Hetfield (Metallica), Dave Mustaine and Marty Friedman (Megadeth), Dimebag Darrell (Pantera), Alex Skolnick and Eric Peterson (Testament), Mike McCready (Pearl Jam), Gary Holt (Exodus), Rob Cavestany (Death Angel), Adrian Smith (Iron Maiden), Slash, John Norum (Europe), Paul Gilbert, Randy Rhoads, George Lynch (Dokken), Warren DeMartini (Ratt), John Petrucci (Dream Theater), Michael Amott (Arch Enemy), Dan Spitz (Anthrax), Criss Oliva (Savatage), Jeff Waters (Annihilator), Phil Campbell (Motörhead), Kerry King (Slayer), and Syu (Galneryus).


title: The Dawn of the Black Hearts

text: The Dawn of the Black Hearts (subtitled Live in Sarpsborg, Norway 28/2, 1990) is a bootleg live album by the Norwegian black metal band Mayhem. The title originates from a line of lyrics Fenriz of Darkthrone wrote for the band.


title: The Dawn of the Black Hearts

text: Despite being a bootleg, the album is sometimes listed as one of the band's main albums, mainly due to the notoriety regarding the cover art, which is an image of the late Mayhem vocalist Per "Dead" Ohlin shortly after he committed suicide.


title: The Dawn of the Black Hearts

text: The bootleg is a recording of a live show that took place on 28 February 1990 in Sarpsborg, Norway. Metalion, an early figure in the scene who helped to organise this show, claimed that there were around 300 people in attendance and the members of Darkthrone and Immortal were present as well.


title: The Dawn of the Black Hearts

text: The album is infamous and controversial for bearing a photograph of vocalist Dead (Per Yngve Ohlin), shortly after his suicide on 8 April 1991. The photograph was taken by guitarist Euronymous (Øystein Aarseth), shortly after he entered the house the band shared and discovered the body.


title: The Dawn of the Black Hearts

text: Bullmetal, a penpal of Euronymous and owner of Warmaster Records, was sent a copy of one of the photos Euronymous had taken of Dead's body. Euronymous had taken additional pictures of Dead's body in different positions (one of them with Dead "sitting half up, with the shotgun on his knee"), but these photos were later found and destroyed by Euronymous' father after he was killed in 1993, two years before the album bootleg was released.


title: The Dawn of the Black Hearts

text: According to Metalion, the bootleg was made and released by an individual from South America. This individual has been identified as Mauricio “Bull Metal” Montoya from the Colombian metal scene, who was apparently a pen-pal of Euronymous. The latter is said to have given Bull Metal the photographs, which were used for the first printings of the bootleg in South America. However, some of these details are considered more mythical than substantiated.


title: The Dawn of the Black Hearts

text: Dayal Patterson, a historian of metal, has referred to the live record as "perhaps the most bootlegged black metal release of all time." The bootleg was the gateway to discovering Dead-era Mayhem for a number of later black metal musicians, such as Black Emperor of Spain's Supremacía Satánica, D of Indonesia's , and Semjaza of Greece's Thy Darkened Shade.


title: The Dawn of the Black Hearts

text: "The Dawn of the Black Hearts" was officially reissued in 2017 on vinyl under the name "Live in Sarpsborg", using a photo of Necrobutcher as a new cover. This 2017 release uses improved audio from a master source.


title: The Dawn of the Black Hearts

text: Extra songs included on many reissues (recorded in 1985 with Messiah as vocalist and Manheim as drummer):


title: Scrapple

text: Scrapple, also known by the Pennsylvania Dutch name "Pannhaas" ("pan tenderloin" in English), is traditionally a mush of pork scraps and trimmings combined with cornmeal and wheat flour, often buckwheat flour, and spices. The mush is formed into a semi-solid congealed loaf, and slices of the scrapple are then pan-fried before serving. Scraps of meat left over from butchering, not used or sold elsewhere, were made into scrapple to avoid waste. Scrapple is best known as an American food of the southern Mid-Atlantic region (Delaware, Maryland, South Jersey, Pennsylvania, Virginia, and Washington, D.C.).


title: Scrapple

text: Scrapple and "panhaas" are commonly considered an ethnic food of the Pennsylvania Dutch, including the Mennonites and Amish. Scrapple is found in supermarkets throughout the region in both fresh and frozen refrigerated cases.


title: Scrapple

text: Scrapple is typically made of hog offal, such as the head, heart, liver, and other trimmings, which are boiled with any bones attached (often the entire head), to make a broth. Once cooked, bones and fat are removed, the meat is reserved, and (dry) cornmeal is boiled in the broth to make a mush. The meat, finely minced, is returned to the pot and seasonings, typically sage, thyme, savory, black pepper, and others are added. The mush is formed into loaves and allowed to cool thoroughly until set. The proportions and seasoning are very much a matter of the region and the cook's taste.


title: Scrapple

text: A few manufacturers have introduced beef and turkey varieties and color the loaf to retain the traditional coloration derived from the original pork liver base.


title: Scrapple

text: Scrapple is typically cut into slices and pan-fried until brown to form a crust. It is sometimes first coated with flour. It may be fried in butter or oil and is sometimes deep-fried. Scrapple can also be broiled, which gives the scrapple a crisp exterior.


title: Scrapple

text: Scrapple is usually eaten as a breakfast side dish. It can be served plain or with either sweet or savory condiments: apple butter, ketchup, jelly, maple syrup, honey, or mustard.


title: Scrapple

text: The roots of the culinary traditions that led to the development of scrapple in America have been traced back to pre-Roman Europe. The more immediate culinary ancestor of scrapple was the Low German dish called "panhas", which was adapted to make use of locally available ingredients, and it is still called "Pannhaas", "panhoss", "ponhoss", or "pannhas" in parts of Pennsylvania. The first recipes were created by German colonists who settled near Philadelphia and Chester County, Pennsylvania in the 17th and 18th centuries. As a result, scrapple is strongly associated with areas surrounding Philadelphia, Pittsburgh, Baltimore, Washington, D.C.; Eastern Pennsylvania, New Jersey, Maryland, Delaware, Southern New York, and the Delmarva Peninsula. Its popularity on the Delmarva Peninsula is celebrated the second weekend of October during the annual "Apple Scrapple Festival" in Bridgeville, Delaware.


title: Scrapple

text: The two largest brands of scrapple in Philadelphia are Habbersett and Rapa, controlling approximately half and one-quarter of the market respectively. Rapa accounts for about three-quarters of the Baltimore market.


title: Scrapple

text: The title of jazz artist Charlie Parker's 1947 composition "Scrapple from the Apple" is inspired by the food scrapple, in the Big Apple (New York City).


title: Calcite

text: Calcite is a carbonate mineral and the most stable polymorph of calcium carbonate (CaCO). It is a very common mineral, particularly as a component of limestone. Calcite defines hardness 3 on the Mohs scale of mineral hardness, based on scratch hardness comparison. Large calcite crystals are used in optical equipment, and limestone composed mostly of calcite has numerous uses.


title: Calcite

text: Other polymorphs of calcium carbonate are the minerals aragonite and vaterite. Aragonite will change to calcite over timescales of days or less at temperatures exceeding 300 °C, and vaterite is even less stable.


title: Calcite

text: Calcite is derived from the German "Calcit", a term from the 19th century that came from the Latin word for lime, "calx" (genitive calcis) with the suffix "-ite" used to name minerals. It is thus etymologically related to chalk.


title: Calcite

text: When applied by archaeologists and stone trade professionals, the term alabaster is used not just as in geology and mineralogy, where it is reserved for a variety of gypsum; but also for a similar-looking, translucent variety of fine-grained banded deposit of calcite.


title: Calcite

text: In publications, two different sets of Miller indices are used to describe directions in hexagonal and rhombohedral crystals, including calcite crystals: three Miller indices in the formula_1 directions, or four Bravais-Miller indices in the formula_2 directions, where formula_3 is redundant but useful in visualizing permutation symmetries.


title: Calcite

text: To add to the complications, there are also two definitions of unit cell for calcite. One, an older "morphological" unit cell, was inferred by measuring angles between faces of crystals, typically with a goniometer, and looking for the smallest numbers that fit. Later, a "structural" unit cell was determined using X-ray crystallography. The morphological unit cell is rhombohedral, having approximate dimensions and , while the structural unit cell is hexagonal (i.e. a rhombic prism), having approximate dimensions and . For the same orientation, must be multiplied by 4 to convert from morphological to structural units. As an example, calcite cleavage is given as "perfect on {1 0 1}" in morphological coordinates and "perfect on {1 0 4}" in structural units. In formula_4 indices, these are {1 0 1} and {1 0 4}, respectively. Twinning, cleavage and crystal forms are often given in morphological units.


title: Calcite

text: The diagnostic properties of calcite include a defining Mohs hardness of 3, a specific gravity of 2.71 and, in crystalline varieties, a vitreous luster. Color is white or none, though shades of gray, red, orange, yellow, green, blue, violet, brown, or even black can occur when the mineral is charged with impurities.


title: Calcite

text: Calcite has numerous habits, representing combinations of over 1000 crystallographic forms. Most common are scalenohedra, with faces in the hexagonal {2 1 1} directions (morphological unit cell) or {2 1 4} directions (structural unit cell); and rhombohedral, with faces in the {1 0 1} or {1 0 4} directions (the most common cleavage plane). Habits include acute to obtuse rhombohedra, tabular habits, prisms, or various scalenohedra. Calcite exhibits several twinning types adding to the variety of observed habits. It may occur as fibrous, granular, lamellar, or compact. A fibrous, efflorescent habit is known as "lublinite". Cleavage is usually in three directions parallel to the rhombohedron form. Its fracture is conchoidal, but difficult to obtain.


title: Calcite

text: Scalenohedral faces are chiral and come in pairs with mirror-image symmetry; their growth can be influenced by interaction with chiral biomolecules such as L- and D-amino acids. Rhombohedral faces are not chiral.


title: Calcite

text: Calcite is transparent to opaque and may occasionally show phosphorescence or fluorescence. A transparent variety called "Iceland spar" is used for optical purposes. Acute scalenohedral crystals are sometimes referred to as "dogtooth spar" while the rhombohedral form is sometimes referred to as "nailhead spar". The rhombohedral form may also have been the "sunstone" whose use by Viking navigators is mentioned in the Icelandic Sagas.


title: Calcite

text: Single calcite crystals display an optical property called birefringence (double refraction). This strong birefringence causes objects viewed through a clear piece of calcite to appear doubled. The birefringent effect (using calcite) was first described by the Danish scientist Rasmus Bartholin in 1669. At a wavelength of about 590 nm, calcite has ordinary and extraordinary refractive indices of 1.658 and 1.486, respectively. Between 190 and 1700 nm, the ordinary refractive index varies roughly between 1.9 and 1.5, while the extraordinary refractive index varies between 1.6 and 1.4.


title: Calcite

text: The carbon dioxide released by this reaction produces a characteristic effervescence when dilute hydrochloric acid is dropped on a calcite sample.


title: Calcite

text: Ambient carbon dioxide, due to its acidity, has a slight solubilizing effect on calcite. The overall reaction is


title: Calcite

text: If the amount of dissolved carbon dioxide drops, the reaction reverses to precipitate calcite. As a result, calcite can be either dissolved by groundwater or precipitated by groundwater, depending on such factors as the water temperature, pH, and dissolved ion concentrations. When conditions are right for precipitation, calcite forms mineral coatings that cement rock grains together and can fill fractures. When conditions are right for dissolution, the removal of calcite can dramatically increase the porosity and permeability of the rock, and if it continues for a long period of time, may result in the formation of caves. Continued dissolution of calcium carbonate-rich formations can lead to the expansion and eventual collapse of cave systems, resulting in various forms of karst topography.


title: Calcite

text: Calcite exhibits an unusual characteristic called retrograde solubility in which it becomes less soluble in water as the temperature increases. Calcite is also more soluble at higher pressures.


title: Calcite

text: Pure calcite has the composition . However, the calcite in limestone often contains a few percent of magnesium. Calcite in limestone is divided into low-magnesium and high-magnesium calcite, with the dividing line placed at a composition of 4% magnesium. High-magnesium calcite retains the calcite mineral structure, which is distinct from that of dolomite, . Calcite can also contain small quantities of iron and manganese. Manganese may be responsible for the fluorescence of impure calcite, as may traces of organic compounds.


title: Calcite

text: Ancient Egyptians carved many items out of calcite, relating it to their goddess Bast, whose name contributed to the term alabaster because of the close association. Many other cultures have used the material for similar carved objects and applications.


title: Calcite

text: A transparent variety of calcite known as Iceland spar may have been used by Vikings for navigating on cloudy days.


title: Calcite

text: High-grade optical calcite was used in World War II for gun sights, specifically in bomb sights and anti-aircraft weaponry. It was used as a polarizer (in Nicol prisms) prior to the invention of Polaroid plates and still finds use in optical instruments. Also, experiments have been conducted to use calcite for a cloak of invisibility.


title: Calcite

text: Microbiologically precipitated calcite has a wide range of applications, such as soil remediation, soil stabilization and concrete repair.


title: Calcite

text: Calcite, obtained from an 80 kg sample of Carrara marble, is used as the IAEA-603 isotopic standard in mass spectrometry for the calibration of δO and δC.


title: Calcite

text: Calcite is a common constituent of sedimentary rocks, limestone in particular, much of which is formed from the shells of dead marine organisms. Approximately 10% of sedimentary rock is limestone. It is the primary mineral in metamorphic marble. It also occurs in deposits from hot springs as a vein mineral; in caverns as stalactites and stalagmites; and in volcanic or mantle-derived rocks such as carbonatites, kimberlites, or rarely in peridotites.


title: Calcite

text: Calcite is often the primary constituent of the shells of marine organisms, such as plankton (such as coccoliths and planktic foraminifera), the hard parts of red algae, some sponges, brachiopods, echinoderms, some serpulids, most bryozoa, and parts of the shells of some bivalves (such as oysters and rudists). Calcite is found in spectacular form in the Snowy River Cave of New Mexico as mentioned above, where microorganisms are credited with natural formations. Trilobites, which became extinct a quarter billion years ago, had unique compound eyes that used clear calcite crystals to form the lenses. It also forms a substantial part of birds' eggshells, and the δC of the diet is reflected in the δC of the calcite of the shell.


title: Calcite

text: The largest documented single crystal of calcite originated from Iceland, measured and and weighed about 250 tons. Classic samples have been produced at Madawaska Mine, near Bancroft, Ontario.


title: Calcite

text: Bedding parallel veins of fibrous calcite, often referred to in quarrying parlance as "beef", occur in dark organic rich mudstones and shales, these veins are formed by increasing fluid pressure during diagenesis.


title: Calcite

text: Calcite formation can proceed by several pathways, from the classical terrace ledge kink model to the crystallization of poorly ordered precursor phases like amorphous calcium carbonate (ACC) via an Ostwald ripening process, or via the agglomeration of nanocrystals.


title: Calcite

text: The crystallization of ACC can occur in two stages. First, the ACC nanoparticles rapidly dehydrate and crystallize to form individual particles of vaterite. Second, the vaterite transforms to calcite via a dissolution and reprecipitation mechanism, with the reaction rate controlled by the surface area of a calcite crystal. The second stage of the reaction is approximately 10 times slower.


title: Calcite

text: However, crystallization of calcite has been observed to be dependent on the starting pH and concentration of magnesium in solution. A neutral starting pH during mixing promotes the direct transformation of ACC into calcite without a vaterite intermediate. But when ACC forms in a solution with a basic initial pH, the transformation to calcite occurs via metastable vaterite, following the pathway outlined above. Magnesium has a noteworthy effect on both the stability of ACC and its transformation to crystalline CaCO, resulting in the formation of calcite directly from ACC, as this ion destabilizes the structure of vaterite.


title: Calcite

text: Calcite may form in the subsurface in response to microorganism activity, such as sulfate-dependent anaerobic oxidation of methane, where methane is oxidized and sulfate is reduced, leading to precipitation of calcite and pyrite from the produced bicarbonate and sulfide. These processes can be traced by the specific carbon isotope composition of the calcites, which are extremely depleted in the C isotope, by as much as −125 per mil PDB (δC).


title: Calcite

text: Calcite seas existed in Earth's history when the primary inorganic precipitate of calcium carbonate in marine waters was low-magnesium calcite (lmc), as opposed to the aragonite and high-magnesium calcite (hmc) precipitated today. Calcite seas alternated with aragonite seas over the Phanerozoic, being most prominent in the Ordovician and Jurassic periods. Lineages evolved to use whichever morph of calcium carbonate was favourable in the ocean at the time they became mineralised, and retained this mineralogy for the remainder of their evolutionary history. Petrographic evidence for these calcite sea conditions consists of calcitic ooids, lmc cements, hardgrounds, and rapid early seafloor aragonite dissolution. The evolution of marine organisms with calcium carbonate shells may have been affected by the calcite and aragonite sea cycle.


title: Calcite

text: Calcite is one of the minerals that has been shown to catalyze an important biological reaction, the formose reaction, and may have had a role in the origin of life. Interaction of its chiral surfaces (see Form) with aspartic acid molecules results in a slight bias in chirality; this is one possible mechanism for the origin of homochirality in living cells.


title: Genetic algorithm

text: In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems by relying on biologically inspired operators such as mutation, crossover and selection. Some examples of GA applications include optimizing decision trees for better performance, solving sudoku puzzles, hyperparameter optimization, etc.


title: Genetic algorithm

text: In a genetic algorithm, a population of candidate solutions (called individuals, creatures, organisms, or phenotypes) to an optimization problem is evolved toward better solutions. Each candidate solution has a set of properties (its chromosomes or genotype) which can be mutated and altered; traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodings are also possible.


title: Genetic algorithm

text: The evolution usually starts from a population of randomly generated individuals, and is an iterative process, with the population in each iteration called a "generation". In each generation, the fitness of every individual in the population is evaluated; the fitness is usually the value of the objective function in the optimization problem being solved. The more fit individuals are stochastically selected from the current population, and each individual's genome is modified (recombined and possibly randomly mutated) to form a new generation. The new generation of candidate solutions is then used in the next iteration of the algorithm. Commonly, the algorithm terminates when either a maximum number of generations has been produced, or a satisfactory fitness level has been reached for the population.


title: Genetic algorithm

text: A standard representation of each candidate solution is as an array of bits (also called "bit set" or "bit string"). Arrays of other types and structures can be used in essentially the same way. The main property that makes these genetic representations convenient is that their parts are easily aligned due to their fixed size, which facilitates simple crossover operations. Variable length representations may also be used, but crossover implementation is more complex in this case. Tree-like representations are explored in genetic programming and graph-form representations are explored in evolutionary programming; a mix of both linear chromosomes and trees is explored in gene expression programming.


title: Genetic algorithm

text: Once the genetic representation and the fitness function are defined, a GA proceeds to initialize a population of solutions and then to improve it through repetitive application of the mutation, crossover, inversion and selection operators.


title: Genetic algorithm

text: The population size depends on the nature of the problem, but typically contains several hundreds or thousands of possible solutions. Often, the initial population is generated randomly, allowing the entire range of possible solutions (the search space). Occasionally, the solutions may be "seeded" in areas where optimal solutions are likely to be found.


title: Genetic algorithm

text: During each successive generation, a portion of the existing population is selected to breed a new generation. Individual solutions are selected through a "fitness-based" process, where fitter solutions (as measured by a fitness function) are typically more likely to be selected. Certain selection methods rate the fitness of each solution and preferentially select the best solutions. Other methods rate only a random sample of the population, as the former process may be very time-consuming.


title: Genetic algorithm

text: The fitness function is defined over the genetic representation and measures the "quality" of the represented solution. The fitness function is always problem dependent. For instance, in the knapsack problem one wants to maximize the total value of objects that can be put in a knapsack of some fixed capacity. A representation of a solution might be an array of bits, where each bit represents a different object, and the value of the bit (0 or 1) represents whether or not the object is in the knapsack. Not every such representation is valid, as the size of objects may exceed the capacity of the knapsack. The "fitness" of the solution is the sum of values of all objects in the knapsack if the representation is valid, or 0 otherwise.


title: Genetic algorithm

text: In some problems, it is hard or even impossible to define the fitness expression; in these cases, a simulation may be used to determine the fitness function value of a phenotype (e.g. computational fluid dynamics is used to determine the air resistance of a vehicle whose shape is encoded as the phenotype), or even interactive genetic algorithms are used.


title: Genetic algorithm

text: The next step is to generate a second generation population of solutions from those selected, through a combination of genetic operators: crossover (also called recombination), and mutation.


title: Genetic algorithm

text: For each new solution to be produced, a pair of "parent" solutions is selected for breeding from the pool selected previously. By producing a "child" solution using the above methods of crossover and mutation, a new solution is created which typically shares many of the characteristics of its "parents". New parents are selected for each new child, and the process continues until a new population of solutions of appropriate size is generated.


title: Genetic algorithm

text: Although reproduction methods that are based on the use of two parents are more "biology inspired", some research suggests that more than two "parents" generate higher quality chromosomes.


title: Genetic algorithm

text: These processes ultimately result in the next generation population of chromosomes that is different from the initial generation. Generally, the average fitness will have increased by this procedure for the population, since only the best organisms from the first generation are selected for breeding, along with a small proportion of less fit solutions. These less fit solutions ensure genetic diversity within the genetic pool of the parents and therefore ensure the genetic diversity of the subsequent generation of children.


title: Genetic algorithm

text: Opinion is divided over the importance of crossover versus mutation. There are many references in Fogel (2006) that support the importance of mutation-based search.


title: Genetic algorithm

text: Although crossover and mutation are known as the main genetic operators, it is possible to use other operators such as regrouping, colonization-extinction, or migration in genetic algorithms.


title: Genetic algorithm

text: It is worth tuning parameters such as the mutation probability, crossover probability and population size to find reasonable settings for the problem class being worked on. A very small mutation rate may lead to genetic drift (which is non-ergodic in nature). A recombination rate that is too high may lead to premature convergence of the genetic algorithm. A mutation rate that is too high may lead to loss of good solutions, unless elitist selection is employed. An adequate population size ensures sufficient genetic diversity for the problem at hand, but can lead to a waste of computational resources if set to a value larger than required.


title: Genetic algorithm

text: In addition to the main operators above, other heuristics may be employed to make the calculation faster or more robust. The "speciation" heuristic penalizes crossover between candidate solutions that are too similar; this encourages population diversity and helps prevent premature convergence to a less optimal solution.


title: Genetic algorithm

text: This generational process is repeated until a termination condition has been reached. Common terminating conditions are:


title: Genetic algorithm

text: Genetic algorithms are simple to implement, but their behavior is difficult to understand. In particular, it is difficult to understand why these algorithms frequently succeed at generating solutions of high fitness when applied to practical problems. The building block hypothesis (BBH) consists of:


title: Genetic algorithm

text: Despite the lack of consensus regarding the validity of the building-block hypothesis, it has been consistently evaluated and used as reference throughout the years. Many estimation of distribution algorithms, for example, have been proposed in an attempt to provide an environment in which the hypothesis would hold. Although good results have been reported for some classes of problems, skepticism concerning the generality and/or practicality of the building-block hypothesis as an explanation for GAs efficiency still remains. Indeed, there is a reasonable amount of work that attempts to understand its limitations from the perspective of estimation of distribution algorithms.


title: Genetic algorithm

text: There are limitations of the use of a genetic algorithm compared to alternative optimization algorithms:


title: Genetic algorithm

text: The simplest algorithm represents each chromosome as a bit string. Typically, numeric parameters can be represented by integers, though it is possible to use floating point representations. The floating point representation is natural to evolution strategies and evolutionary programming. The notion of real-valued genetic algorithms has been offered but is really a misnomer because it does not really represent the building block theory that was proposed by John Henry Holland in the 1970s. This theory is not without support though, based on theoretical and experimental results (see below). The basic algorithm performs crossover and mutation at the bit level. Other variants treat the chromosome as a list of numbers which are indexes into an instruction table, nodes in a linked list, hashes, objects, or any other imaginable data structure. Crossover and mutation are performed so as to respect data element boundaries. For most data types, specific variation operators can be designed. Different chromosomal data types seem to work better or worse for different specific problem domains.


title: Genetic algorithm

text: When bit-string representations of integers are used, Gray coding is often employed. In this way, small changes in the integer can be readily affected through mutations or crossovers. This has been found to help prevent premature convergence at so-called "Hamming walls", in which too many simultaneous mutations (or crossover events) must occur in order to change the chromosome to a better solution.


title: Genetic algorithm

text: Other approaches involve using arrays of real-valued numbers instead of bit strings to represent chromosomes. Results from the theory of schemata suggest that in general the smaller the alphabet, the better the performance, but it was initially surprising to researchers that good results were obtained from using real-valued chromosomes. This was explained as the set of real values in a finite population of chromosomes as forming a "virtual alphabet" (when selection and recombination are dominant) with a much lower cardinality than would be expected from a floating point representation.


title: Genetic algorithm

text: An expansion of the Genetic Algorithm accessible problem domain can be obtained through more complex encoding of the solution pools by concatenating several types of heterogenously encoded genes into one chromosome. This particular approach allows for solving optimization problems that require vastly disparate definition domains for the problem parameters. For instance, in problems of cascaded controller tuning, the internal loop controller structure can belong to a conventional regulator of three parameters, whereas the external loop could implement a linguistic controller (such as a fuzzy system) which has an inherently different description. This particular form of encoding requires a specialized crossover mechanism that recombines the chromosome by section, and it is a useful tool for the modelling and simulation of complex adaptive systems, especially evolution processes.


title: Genetic algorithm

text: A practical variant of the general process of constructing a new population is to allow the best organism(s) from the current generation to carry over to the next, unaltered. This strategy is known as "elitist selection" and guarantees that the solution quality obtained by the GA will not decrease from one generation to the next.


title: Genetic algorithm

text: Parallel implementations of genetic algorithms come in two flavors. Coarse-grained parallel genetic algorithms assume a population on each of the computer nodes and migration of individuals among the nodes. Fine-grained parallel genetic algorithms assume an individual on each processor node which acts with neighboring individuals for selection and reproduction.


title: Genetic algorithm

text: Other variants, like genetic algorithms for online optimization problems, introduce time-dependence or noise in the fitness function.


title: Genetic algorithm

text: Genetic algorithms with adaptive parameters (adaptive genetic algorithms, AGAs) is another significant and promising variant of genetic algorithms. The probabilities of crossover (pc) and mutation (pm) greatly determine the degree of solution accuracy and the convergence speed that genetic algorithms can obtain. Instead of using fixed values of "pc" and "pm", AGAs utilize the population information in each generation and adaptively adjust the "pc" and "pm" in order to maintain the population diversity as well as to sustain the convergence capacity. In AGA (adaptive genetic algorithm), the adjustment of "pc" and "pm" depends on the fitness values of the solutions. In "CAGA" (clustering-based adaptive genetic algorithm), through the use of clustering analysis to judge the optimization states of the population, the adjustment of "pc" and "pm" depends on these optimization states.


title: Genetic algorithm

text: It can be quite effective to combine GA with other optimization methods. A GA tends to be quite good at finding generally good global solutions, but quite inefficient at finding the last few mutations to find the absolute optimum. Other techniques (such as simple hill climbing) are quite efficient at finding absolute optimum in a limited region. Alternating GA and hill climbing can improve the efficiency of GA while overcoming the lack of robustness of hill climbing.


title: Genetic algorithm

text: This means that the rules of genetic variation may have a different meaning in the natural case. For instance – provided that steps are stored in consecutive order – crossing over may sum a number of steps from maternal DNA adding a number of steps from paternal DNA and so on. This is like adding vectors that more probably may follow a ridge in the phenotypic landscape. Thus, the efficiency of the process may be increased by many orders of magnitude. Moreover, the inversion operator has the opportunity to place steps in consecutive order or any other suitable order in favour of survival or efficiency.


title: Genetic algorithm

text: A variation, where the population as a whole is evolved rather than its individual members, is known as gene pool recombination.


title: Genetic algorithm

text: A number of variations have been developed to attempt to improve performance of GAs on problems with a high degree of fitness epistasis, i.e. where the fitness of a solution consists of interacting subsets of its variables. Such algorithms aim to learn (before exploiting) these beneficial phenotypic interactions. As such, they are aligned with the Building Block Hypothesis in adaptively reducing disruptive recombination. Prominent examples of this approach include the mGA, GEMGA and LLGA.


title: Genetic algorithm

text: Problems which appear to be particularly appropriate for solution by genetic algorithms include timetabling and scheduling problems, and many scheduling software packages are based on GAs. GAs have also been applied to engineering. Genetic algorithms are often applied as an approach to solve global optimization problems.


title: Genetic algorithm

text: As a general rule of thumb genetic algorithms might be useful in problem domains that have a complex fitness landscape as mixing, i.e., mutation in combination with crossover, is designed to move the population away from local optima that a traditional hill climbing algorithm might get stuck in. Observe that commonly used crossover operators cannot change any uniform population. Mutation alone can provide ergodicity of the overall genetic algorithm process (seen as a Markov chain).


title: Genetic algorithm

text: Examples of problems solved by genetic algorithms include: mirrors designed to funnel sunlight to a solar collector, antennae designed to pick up radio signals in space, walking methods for computer figures, optimal design of aerodynamic bodies in complex flowfields


title: Genetic algorithm

text: In 1950, Alan Turing proposed a "learning machine" which would parallel the principles of evolution. Computer simulation of evolution started as early as in 1954 with the work of Nils Aall Barricelli, who was using the computer at the Institute for Advanced Study in Princeton, New Jersey. His 1954 publication was not widely noticed. Starting in 1957, the Australian quantitative geneticist Alex Fraser published a series of papers on simulation of artificial selection of organisms with multiple loci controlling a measurable trait. From these beginnings, computer simulation of evolution by biologists became more common in the early 1960s, and the methods were described in books by Fraser and Burnell (1970) and Crosby (1973). Fraser's simulations included all of the essential elements of modern genetic algorithms. In addition, Hans-Joachim Bremermann published a series of papers in the 1960s that also adopted a population of solution to optimization problems, undergoing recombination, mutation, and selection. Bremermann's research also included the elements of modern genetic algorithms. Other noteworthy early pioneers include Richard Friedberg, George Friedman, and Michael Conrad. Many early papers are reprinted by Fogel (1998).


title: Genetic algorithm

text: Although Barricelli, in work he reported in 1963, had simulated the evolution of ability to play a simple game, artificial evolution only became a widely recognized optimization method as a result of the work of Ingo Rechenberg and Hans-Paul Schwefel in the 1960s and early 1970s – Rechenberg's group was able to solve complex engineering problems through evolution strategies. Another approach was the evolutionary programming technique of Lawrence J. Fogel, which was proposed for generating artificial intelligence. Evolutionary programming originally used finite state machines for predicting environments, and used variation and selection to optimize the predictive logics. Genetic algorithms in particular became popular through the work of John Holland in the early 1970s, and particularly his book "Adaptation in Natural and Artificial Systems" (1975). His work originated with studies of cellular automata, conducted by Holland and his students at the University of Michigan. Holland introduced a formalized framework for predicting the quality of the next generation, known as Holland's Schema Theorem. Research in GAs remained largely theoretical until the mid-1980s, when The First International Conference on Genetic Algorithms was held in Pittsburgh, Pennsylvania.


title: Genetic algorithm

text: In the late 1980s, General Electric started selling the world's first genetic algorithm product, a mainframe-based toolkit designed for industrial processes.


title: Genetic algorithm

text: In 1989, Axcelis, Inc. released Evolver, the world's first commercial GA product for desktop computers. The New York Times technology writer John Markoff wrote about Evolver in 1990, and it remained the only interactive commercial genetic algorithm until 1995. Evolver was sold to Palisade in 1997, translated into several languages, and is currently in its 6th version. Since the 1990s, MATLAB has built in three derivative-free optimization heuristic algorithms (simulated annealing, particle swarm optimization, genetic algorithm) and two direct search algorithms (simplex search, pattern search).


title: Tokaimura nuclear accidents

text: There have been two noteworthy nuclear accidents at the Tōkai village nuclear campus, Ibaraki Prefecture, Japan. The first accident occurred on 11 March 1997, producing an explosion after an experimental batch of solidified nuclear waste caught fire at the Power Reactor and Nuclear Fuel Development Corporation (PNC) radioactive waste bituminisation facility. Over twenty people were exposed to radiation. The second was a criticality accident at a separate fuel reprocessing facility belonging to Japan Nuclear Fuel Conversion Co. (JCO) on 30 September 1999 due to improper handling of liquid uranium fuel. The incident spanned approximately 20 hours and resulted in radiation exposure for 667 people and the death of two workers.


title: Tokaimura nuclear accidents

text: Nuclear power was an important energy alternative for natural-resource-poor Japan to limit dependence on imported energy, providing approximately 30% of Japan’s electricity up until the Fukushima nuclear disaster of 2011, after which nuclear electricity production fell into sharp decline.


title: Tokaimura nuclear accidents

text: The village of Tōkai's location (approximately seventy miles from Tokyo) and available land space made it ideal for nuclear power production, so a series of experimental nuclear reactors and then the Tōkai Nuclear Power Plantthe country's first commercial nuclear power stationwere built here. Over time, dozens of companies and government institutes were established nearby to provide nuclear research, experimentation, manufacturing, and fuel fabrication, enrichment and disposal facilities. Nearly one-third of Tokai’s population rely upon nuclear industry-related employment.


title: Tokaimura nuclear accidents

text: On 11 March 1997, the village of Tokai's first serious nuclear-related incident occurred at PNC's bituminisation facility. It is sometimes referred to as the Dōnen accident (動燃事故, "Dōnen jiko"), 'Dōnen' being an abbreviation of PNC's full Japanese name "Dōryokuro Kakunenryō Kaihatsu Jigyōdan". The site encased and solidified low-level liquid waste in molten asphalt (bitumen) for storage, and that day was trialling a new asphalt-waste mix, using 20% less asphalt than normal. A gradual chemical reaction inside one fresh barrel ignited the already-hot contents at 10:00 a.m. and quickly spread to several others nearby. Workers failed to properly extinguish the fire, and smoke and radiation alarms forced all personnel to evacuate the building. At 8 p.m., just as people were preparing to reenter the building, built up flammable gases ignited and exploded, breaking windows and doors, which allowed smoke and radiation to escape into the surrounding area.


title: Tokaimura nuclear accidents

text: The incident exposed 37 nearby personnel to trace amounts of radiation in what the government's Science and Technology Agency declared the country’s worst-yet nuclear accident, which was rated a 3 on the International Nuclear Event Scale. A week after the event, meteorological officials detected unusually high levels of caesium 40 kilometers (25 miles) south-west of the plant. Aerial views over the nuclear processing plant building showed a damaged roof from the fire and explosion allowing continued external radiation exposure.


title: Tokaimura nuclear accidents

text: PNC management mandated two workers to falsely report the chronological events leading to the facility evacuation in order to cover-up lack of proper supervision. Dōnen leadership failed to immediately report the fire to the Science and Technology Agency (STA). This delay was due to their own internal investigation of the fire causing hampered immediate emergency response teams and prolonged radioactivity exposure. Dōnen facility officials initially reported a 20 percent increase of radiation levels in the area surrounding the reprocessing plant but later revealed the true percent was ten times higher than initially published. Tokai residents demanded criminal prosecution of PNC officials, reorganization of company leadership and closure of the plant itself. Following public outcry, the facility closed until reopening in November 2000 when it was reinstated as a nuclear fuel reprocessing plant.


title: Tokaimura nuclear accidents

text: Later, Prime Minister Ryutaro Hashimoto criticized the delay that allowed radiation to continue to impact local areas.


title: Tokaimura nuclear accidents

text: The second, more serious Tokai nuclear accident (Japanese: 東海村JCO臨界事故 "Tōkai-mura JCO-rinkai-jiko") occurred approximately four miles away from the PNC facility on 30 September 1999, at a fuel enrichment plant operated by JCO, a subsidiary of Sumitomo Metal Mining Company. It was the worst civilian nuclear radiation accident in Japan prior to the Fukushima Daiichi nuclear disaster of 2011. The incident exposed the surrounding population to hazardous nuclear radiation after the uranium mixture reached criticality. Two of the three technicians mixing fuel lost their lives. The incident was caused by lack of regulatory supervision, inadequate safety culture and improper technician training and education.


title: Tokaimura nuclear accidents

text: The JCO facility converted uranium hexafluoride into enriched uranium dioxide fuel. This served as the first step in producing nuclear reactor fuel rods for Japan's power plants and research reactors. Enriching nuclear fuel requires precision and has the potential to impose extreme risks to technicians. If done improperly, the process of combining nuclear products can produce a fission reaction which, in turn, produces radiation. In order to enrich the uranium fuel, a specific chemical purification procedure is required. The steps included feeding small batches of uranium oxide powder into a designated dissolving tank in order to produce uranyl nitrate using nitric acid. Next, the mixture is carefully transported to a specially-crafted buffer tank. The buffer tank containing the combined ingredients is specially designed to prevent fission activity from reaching criticality. In a precipitation tank, ammonia is added forming a solid product. This tank is meant to capture any remaining nuclear waste contaminants. In the final process, uranium oxide is placed in the dissolving tanks until purified, without enriching the isotopes, in a wet-process technology specialized by Japan.