title: Holy water

text: Although "Holy water" is not a term used in official rites of the Church of England, font water is sanctified in the Church of England baptism rite. In contrast, the Episcopal Church (United States) does expressly mention the optional use of holy water in some recent liturgies of blessing. More generally, the use of water within High Church Anglicanism or Anglo-Catholicism adheres closely to Roman Catholic practice. In many Anglican churches baptismal water is used for the asperges. A widely-used Anglo-Catholic manual, "Ritual Notes", first published by A. R. Mowbray in 1894, discusses the blessing and use of holy water. In addition to "the pious custom" of blessing oneself on entering and leaving a church "in memory of our baptism and in token of the purity of heart with which we should worship Almighty God", the book commends that "Holy water should be obtained from the parish priest, may be (and indeed should be) taken away and kept for use privately by the faithful in their homes." An English translation of the traditional rite for the blessing of water and salt, including the exorcisms, was included in the Anglican Missal. Shorter forms are found in "A Priest's Handbook" by Dennis G. Michno, and "Ceremonies of the Eucharist" by Howard E. Galley. Some parishes use a stoup, basin, or font to make holy water available for the faithful to use in blessing themselves, making the sign of the cross upon entering the church.


title: Holy water

text: In the "Book of Occasional Services" of the Episcopal Church (United States), in the rite for Restoring of Things Profaned, the bishop or priest while processing around the church or chapel recites Psalm 118 with the antiphon :


title: Holy water

text: A rubric directs that as each profaned object is addressed, "it may be symbolically cleansed by the use of signs of purification, such as water or incense."


title: Holy water

text: Holy water is important to the Ethiopian Orthodox Tewahedo Church and regarded as healing from demonic possession and for treating sick people, particularly in cases of mental illness. It can be consumed or poured over someone supposed to be afflicted by harmful things. A majority of studies show that many Ethiopians prefer holy water for biomedical purposes, especially for treatment of HIV AIDS. Pilgrims visit different monasteries such as Tsadkane Mariam and Entoto Kidane Mehret to acquire holy water.


title: Holy water

text: Besides, holy water also used for Ethiopian Orthodox holidays such as Timkat (Epiphany) where Christians gather at notable squares and churches and priests bless holy water and spatter them. In Gondar, the Fasilides Bath is used to bathe and represents the Jordan River.


title: Holy water

text: The use of holy water in some synods of Lutheranism is for the baptism of infants and new members of the church. The water is believed to be blessed by God, as it is used in a sacrament. The water is applied to the forehead of the laity being baptised and the minister performs the sign of the cross. Lutherans tend to have baptismal water fonts near the entrance of the church.


title: Holy water

text: Other synods do not use holy water, however they do typically treat the water used for baptisms in a respectful manner.


title: Holy water

text: In the Methodist tradition, Holy Baptism is often administered by sprinkling or pouring holy water over the candidate. The official Baptismal Liturgy, as well as the liturgy for Reaffirmation of Baptism commonly done through asperges, has a prayer for the blessing of this water:


title: Holy water

text: One of the holiest sites in Sikhism, Harmandir Sahib, is surrounded by a pool of water called "amritsar" or "amritsarovar". For those who wish to take a dip in the pool, the Temple provides a half hexagonal shelter and holy steps to "Har ki Pauri". Bathing in the pool is believed by many Sikhs to have restorative powers, purifying one's karma. Some carry bottles of the pool water home particularly for sick friends and relatives. The pool is maintained by volunteers who perform "kar seva" (community service) by draining and desilting it periodically.


title: Holy water

text: Sikhs use the Punjabi term "amrita" (ਅੰਮ੍ਰਿਤ) for the holy water used in the baptism ceremony known as "Amrit Sanskar" or "Amrit Chhakhna".


title: Holy water

text: In Hinduism, water represents God in a spiritual sense which is the central theme in Mantra Pushpam from Taithreeya Aranyakam of Yajur Veda. Bathing in holy water is, thus, a key element in Hinduism, and the Ganges is considered the holiest Hindu river. Holy water in Hinduism is thought to purify the soul and combat evil. Some Hindus use holy water to wash hands before ringing a bell.


title: Holy water

text: The idea of "blessed water" is used in virtually all Buddhist traditions. In the Theravada tradition, water is put into a new pot and kept near a "Paritrana" ceremony, a blessing for protection. This "lustral water" can be created in a ceremony in which the burning and extinction of a candle above the water represents the elements of earth, fire, and air. This water is later given to the people to be kept in their home. Not only water but also oil and strings are blessed in this ceremony. Most Mahayana Buddhists typically recite sutras or various mantras (typically that of the bodhisattva Avalokitesvara for example) numerous times over the water, which is then either consumed or is used to bless homes afterwards. In Vajrayana Buddhism, a "Bumpa", a ritual object, is one of the "Ashtamangala", used for storing sacred water sometimes, symbolizing wisdom and long life.


title: Holy water

text: The Muslim variety of holy water is the Zamzam water that comes from a spring near the Kaaba in Mecca.


title: Holy water

text: The drinking of "healing water" ("āb-i shifā") is a practice in various denominations of Shia Islam. In the tradition of the Twelver Shi’a, many dissolve the dust of sacred locations such as Karbala ("khāk-i shifa") and Najaf and drink the water ("āb-i shifā") as a cure for illness, both spiritual and physical.


title: Holy water

text: The Ismaili tradition involves the practice of drinking water blessed by the Imam of the time. This water is taken in the name of the Imam and has a deep spiritual significance. This is evident from the names used to designate the water, including light ("nūr") and ambrosia ("amṛt, amī, amīras, amījal"). This practice is recorded from the 13th and 14th centuries and continues to the present day. The ceremony is known as "ghat-pat" in South Asia.


title: Holy water

text: In Mandaeism, mambuha (), sometimes spelled "mambuga", is sacramental drinking water used in rituals such as the masbuta (baptism), while halalta () is sacramental rinsing water used in rituals such as the masiqta (death mass).


title: Holy water

text: In Ancient Greek religion, holy water called "chernips" () was created when a torch from a religious shrine was extinguished in it. In Greek religion, purifying people and locations with water was part of the process of distinguishing the sacred from the profane.


title: Holy water

text: In Wicca and other ceremonial magic traditions, a bowl of salt is blessed and a small amount is stirred into a bowl of water that has been ritually purified. In some traditions of Wicca, this mixture of water and salt symbolizes the brine of the sea, which is regarded as the womb of the Goddess, and the source of all life on Earth. The mixture is consecrated and used in many religious ceremonies and magical rituals.


title: Holy water

text: Holy water has also been believed to ward off or act as a weapon against mythical evil creatures, such as vampires. In eastern Europe, one might sprinkle holy water onto the corpse of a suspected vampire in order to destroy it or render it inert. Thereafter, the concept proliferated into fiction about such creatures.


title: Black caiman

text: The black caiman (Melanosuchus niger) is a species of large crocodilian and is the largest species of the family Alligatoridae. It is a carnivorous reptile that lives along slow-moving rivers, lakes, seasonally flooded savannas of the Amazon basin, and in other freshwater habitats of South America. It is a large species, growing to at least and possibly up to in length, which makes it the third largest reptile in the Neotropical realm, behind the American crocodile, and the Orinoco crocodile. As its common and scientific names imply, the black caiman has a dark coloration as an adult. In some individuals, the dark coloration can appear almost black. It has grey to brown banding on the lower jaw. Juveniles have a more vibrant coloration compared to adults with prominent white to pale yellow banding on the flanks that remains present well into adulthood, at least more when compared to other species. The morphology is quite different from other caimans but the bony ridge that occurs in other caimans is present. The head is large and heavy, an advantage in catching larger prey. Like all crocodile-like animals, caimans are long, squat creatures, with big jaws, long tails and short legs. They have thick, scaled skin, and their eyes and noses are located on the tops of their heads. This enables them to see and breathe while the rest of their bodies are underwater.


title: Black caiman

text: The black caiman is the second largest known predator in the Amazon ecosystem, after the Orinoco crocodile, preying on a variety of fish, reptiles, birds, and mammals. It is a generalist and apex predator, potentially capable of taking any animal within its range, including other predators. Few ecological studies have been carried out on the species, but the black caiman has its own ecological niche that enables coexistence without too much competition. As the largest predator in the ecosystem, it may also be a keystone species, playing an important role of maintaining the structure of the ecosystem. Reproduction takes place in the dry season. Females build a nest mound with an egg chamber, protecting the eggs from predators. Hatchlings form groups called pods, guarded by the presence of the female. These pods may contain individuals from other nests. Once common, it was hunted to near extinction primarily for its commercially valuable hide. It is now making a comeback, listed as Conservation Dependent. Overall a little-known species, it was not researched in any detail until the 1980s, when the leather-trade had already taken its toll. It is a dangerous species to humans, and attacks have occurred in the past.


title: Black caiman

text: The black caiman has dark-coloured, scaly skin. The skin coloration helps with camouflage during its nocturnal hunts, but may also help absorb heat (see "thermoregulation"). The lower jaw has grey banding (brown in older animals), and pale yellow or white bands are present across the flanks of the body, although these are much more prominent in juveniles. This banding fades only gradually as the animal matures. The bony ridge extending from above the eyes down the snout, as seen in other caiman, is present. The eyes are large, as befits its largely nocturnal activity, and brown in colour. Mothers on guard near their nests are tormented by blood-sucking flies that gather around their vulnerable eyes, leaving them bloodshot.


title: Black caiman

text: The black caiman is structurally dissimilar to other caiman species, particularly in the shape of the skull. Compared to other caimans, it has distinctly larger eyes. Although the snout is relatively narrow, the skull (given the species' considerably larger size) is much larger overall than other caimans. Black caimans are relatively more robust than other crocodilians of comparable length. There appears to be varying skull morphology in this species depending on the age and particular individual animal, which is not uncommon in other modern crocodilians, and by gender, with adult males typically having much more massive skulls relative to their size than like-age females. Due to the differences, males have a stronger bite force and likely exploit a different, and larger, prey base than females. Young black caiman can be distinguished from large spectacled caimans by their proportionately larger head, as well as by the colour of the jaw, which is light coloured in the spectacled caiman and dark with three black spots in the black caiman.


title: Black caiman

text: The black caiman is one of the largest extant reptiles. It is the largest predator in the Amazon basin, and also potentially the largest member of the family Alligatoridae. It is also significantly larger than other caiman species. Most adult black caimans are in length, with a few old males exceeding . Sub-adult male specimens of around will weigh roughly , around the same size as a mature female, but will quickly increase in bulk and weight. The average size of adult females at their nests was found to be . Mid-sized mature males of weigh approximately , while larger male specimens reach weights of more than , possibly up to , being relatively bulky crocodilians. A relatively small adult male of a total length of weighed while an adult male considered fairly large at a length of weighed approximately . Another sampling of subadult males found them to range in length from , averaging , and that they weighed from , averaging . In some areas (such as the Araguaia River) this species is consistently reported at in length, although specimens this size are uncommon. Several widely reported but unconfirmed (and probably largely anecdotal) reports claim that the black caiman can grow to over in length and weigh up to . While it is unclear what the sources for this maximum size are, many scientific papers accept that this species can attain extreme sizes as such. In South America, two other crocodilians reportedly reach similar sizes: the American crocodile ("Crocodylus acutus") and the Orinoco crocodile ("C. intermedius").


title: Black caiman

text: Black caimans are apex predators with a generalist diet, and can take virtually any terrestrial and riparian animal found throughout their range. Similar to other large crocodilians, black caimans have even been observed catching and eating smaller species, such as the spectacled caiman and sometimes cannibalizing smaller individuals of their own kind. Hatchlings mostly eat small fish, frogs, and invertebrates such as crustaceans and insects, but with time and size graduate to eating larger fish, including piranhas, catfish, and perch, which remain a significant food source for all black caimans. Dietary studies have focused on young caimans (due both to their often being more common than large adults and to their being easier to handle), the largest specimen examined for stomach contents in one study being only notably under sexually mature size, which is at a minimum in smaller females. Although diverse prey is known to be captured by young black caimans, dietary studies have shown snails often dominate the diet of young caiman, followed by quite small fish. Fish were the main prey of black caimans of over subadult size in Manú National Park, Peru. Various prey will be taken by availability, includes snakes, turtles, birds and mammals, the latter two mainly when they come to drink at the river banks. Mammalian prey mostly include common Amazonian species such as various monkeys, sloths, armadillos, pacas, agoutis, coatis, and capybaras. Large prey can include other species of caiman, deer, peccaries, tapirs, anacondas, giant otters,Amazon river dolphins and domestic animals including pigs, cattle, horses, and dogs. Although rare predations on cougars or even jaguars have been reported, very little evidence exists of such predation, and cats are likely to avoid ponds with large adult black caimans, suggesting that adults of this species are higher in the food chain than even the jaguar. Where capybara and white-lipped peccary herds are common, they are reportedly among the most common prey item for large adults. Evidence has suggested fairly large river turtles can be counted among the prey of adult black caimans, the bite force of which is apparently sufficient to shatter a turtle shell. Large males have even been observed to cannibalize other Black Caimans. Compared to the smaller caiman species, the black caiman more often hunts terrestrially at night, using its acute hearing and sight. As with all crocodilian species, their teeth are designed to grab but not chew, so they generally try to swallow their food whole after drowning or crushing it. Large prey that cannot be swallowed whole are often stored so that the flesh will rot enough to allow the caiman to take bites out of the flesh.


title: Black caiman

text: At the end of the dry season, females build a nest of soil and vegetation, which is about across and wide. They lay up to 65 eggs (though usually somewhere between 30 and 60), which hatch in about six weeks, at the beginning of the wet season, when newly flooded marshes provide ideal habitat for the juveniles once hatched. The eggs are quite large, averaging in weight. Unguarded clutches (when the mother goes off to hunt) are readily devoured by a wide array of animals, regularly including mammals such as South American coatis ("Nasua nasua") or large rodents, egg-preying snakes and birds such as herons and vultures. Occasionally predators are caught and killed by the mother caiman. Hatching is said to occur between 42 and 90 days after the eggs are laid. It is well documented that, as with other crocodilians, caimans frequently move their young from the nest in their mouths after hatching (whence the erroneous belief that they eat their young), and transport them to a safe pool. The mother will assist chirping, unhatched young to break out of the leathery eggs, by delicately breaking the eggs between her teeth. She will try to look after her young for several months but the baby caimans are largely independent and most do not survive to maturity. Baby black caimans are subject to predation even more regularly after they hatch, facing many of the same mesopredators, as well any other crocodilian (including those of their own species), large snake or large, carnivorous fish that they encounter. Predation is so common that black caimans count on their young to survive via safety in numbers. The female black caiman only breeds once every 2 to 3 years.


title: Black caiman

text: Many predators, including various fish, mammal, reptile and even amphibian species, feed on caiman eggs and hatchlings. The black caiman shares its habitat with at least 3 other semi-amphibious animals considered apex predators and is usually able to co-exist with them by focusing on different prey and micro-habitats. These are giant otters which are social and are obligate aquatic foragers and piscivorans, green anacondas which are slow, infrequent feeders mostly on medium-sized mammals and reptiles, and jaguars, which are the most terrestrial of these and focus their diet mainly on relatively larger mammals and reptiles. Black caimans eat more or less all the same prey as the other species. They are possibly the most opportunistic but, despite being the largest predator of the area, can metabolically live off of their food longer and thus may not need to hunt as frequently. Usually, each predator avoids encounters with adults of the others but battles, which can be lost by nearly any side, may rarely occur. More so than even otters and anaconda, jaguars and black caiman arguably sit atop this food chain. Once the black caiman attains a length of a few feet, it has few natural predators. Large anacondas may take an occasional young caiman of this species. The jaguar ("Panthera onca"), being a known predator of all other caiman species, is the only primary predatory threat to juvenile and subadult black caimans, with several records of predation on young black caimans and eggs. Adult black caimans have no natural predators, as is true of other similarly-sized crocodilian species given the size, weight, bite force, thick hide, and immense strength; in rare instances, they even may themselves prey upon jaguars.


title: Black caiman

text: Humans hunt black caimans for leather or meat. This species was classified as Endangered in the 1970s due to the high demand for its well-marked skin. The trade in black caiman leather peaked from the 1950s to 1970s, when the smaller but much more common spectacled caiman ("Caiman crocodilus") became the more commonly hunted species. Local people still trade black caiman skins and meat today at a small scale but the species has rebounded overall from the overhunting in the past. That black caimans lay, on average, around 40 eggs has helped them recover to some degree. Perhaps an equal continuing threat is habitat destruction, since development and clear-cutting is now epidemic in South America. Spectacled caimans have now filled the niche of crocodilian predator of fish in many areas. Due to their greater numbers and faster reproductive abilities, the Spectacled populations are locally outcompeting black caimans, although the larger species dominates in a one-on-one basis. Persistent management is needed to control caiman-hunting and is quite difficult to enforce effectively. After the depletion of the black caiman population, piranhas and capybaras, having lost perhaps their primary predator, reached unnaturally high numbers. This has, in turn, led to increased agricultural and livestock losses.


title: Black caiman

text: Compounding the conservation issues it faces, this species occasionally preys on humans. Most tales are poorly documented and unconfirmed but, given this species' formidable size and strength, attacks on humans are quite often fatal.


title: Black caiman

text: The species is uncommon in captivity and breeding it has proven to be a challenge. The first captive breeding outside its native range was at Aalborg Zoo in 2013.


title: Ami Dolenz

text: Dolenz was born in Burbank, California, into a show business family. She is the daughter of Micky Dolenz of the 1960s group the Monkees, and British television presenter Samantha Juste. Her paternal grandparents were the film actors George Dolenz and Janelle Johnson.


title: Ami Dolenz

text: At age 15, Dolenz won a junior talent contest and decided to become an actress. She dropped out of high school and began appearing in roles on various television series. One of her first acting roles was in the television movie "The Children of Times Square", followed by a two-episode stint on "Growing Pains". In 1987, she had a small role in the comedy "Can't Buy Me Love". Later that year, she landed the role of Melissa McKee in the long-running soap opera "General Hospital"; the role garnered critical attention for Dolenz and she earned two nominations (in 1988 and 1989, respectively) for a Young Artist Award.


title: Ami Dolenz

text: After leaving "General Hospital" in 1989, Dolenz landed a co-starring role opposite Tony Danza in "She's Out of Control". The following year, she portrayed Sloane Peterson in "Ferris Bueller", a television sitcom based on "Ferris Bueller's Day Off", which lasted only thirteen episodes and was cancelled in 1991. After its demise, Dolenz starred in "Children of the Night" and then had the lead role in 1992's "Miracle Beach".


title: Ami Dolenz

text: Throughout the 1990s, Dolenz continued to appear in films and television, including ""; ""; "Murder, She Wrote"; "Wake, Rattle and Roll"; ""; "Demolition University"; "Pacific Blue"; and "Teen Angel". In 1998, she voiced a character for the children's show "The Secret Files of the Spy Dogs". After a four-year hiatus from acting, Dolenz returned in the independent film "Mr. Id", in a co-starring role with Steve Parlavecchio. In 2007, she appeared in the film "Even If", which she also produced.


title: Ami Dolenz

text: In addition to acting, Dolenz and her husband manage KidPix Productions, a company that stages movie shoots as birthday parties for children. She also performs with the Write Act Repertory Theatre, and owns Bluebell Boutique, an online custom jewelry shop that she previously co-owned and operated with her late mother.


title: Riemannian manifold

text: In differential geometry, a Riemannian manifold or Riemannian space , so called after the German mathematician Bernhard Riemann, is a real, smooth manifold "M" equipped with a positive-definite inner product "g" on the tangent space "T""M" at each point "p".


title: Riemannian manifold

text: The family "g" of inner products is called a Riemannian metric (or Riemannian metric tensor). Riemannian geometry is the study of Riemannian manifolds.


title: Riemannian manifold

text: A common convention is to take "g" to be smooth, which means that for any smooth coordinate chart on "M", the "n" functions


title: Riemannian manifold

text: With further restrictions on the formula_2, one could also consider Lipschitz Riemannian metrics or measurable Riemannian metrics, among many other possibilities.


title: Riemannian manifold

text: A Riemannian metric (tensor) makes it possible to define several geometric notions on a Riemannian manifold, such as angle at an intersection, length of a curve, area of a surface and higher-dimensional analogues (volume, etc.), extrinsic curvature of submanifolds, and intrinsic curvature of the manifold itself.


title: Riemannian manifold

text: In 1828, Carl Friedrich Gauss proved his "Theorema Egregium" ("remarkable theorem" in Latin), establishing an important property of surfaces. Informally, the theorem says that the curvature of a surface can be determined entirely by measuring distances along paths on the surface. That is, curvature does not depend on how the surface might be embedded in 3-dimensional space. See "Differential geometry of surfaces". Bernhard Riemann extended Gauss's theory to higher-dimensional spaces called manifolds in a way that also allows distances and angles to be measured and the notion of curvature to be defined, again in a way that is intrinsic to the manifold and not dependent upon its embedding in higher-dimensional spaces. Albert Einstein used the theory of pseudo-Riemannian manifolds (a generalization of Riemannian manifolds) to develop his general theory of relativity. In particular, his equations for gravitation are constraints on the curvature of spacetime.


title: Riemannian manifold

text: The tangent bundle of a smooth manifold formula_4 assigns to each point formula_5 of formula_4 a vector space formula_7 called the tangent space of formula_4 at formula_9 A Riemannian metric (by its definition) assigns to each formula_5 a positive-definite inner product formula_11 along with which comes a norm formula_12 defined by formula_13 The smooth manifold formula_4 endowed with this metric formula_15 is a Riemannian manifold, denoted formula_16.


title: Riemannian manifold

text: When given a system of smooth local coordinates on formula_17 given by formula_18 real-valued functions formula_19 the vectors


title: Riemannian manifold

text: form a basis of the vector space formula_21 for any formula_22 Relative to this basis, one can define metric tensor "components" at each point formula_5 by


title: Riemannian manifold

text: One could consider these as formula_25 individual functions formula_26 or as a single formula_27 matrix-valued function on formula_28 note that the "Riemannian" assumption says that it is valued in the subset consisting of symmetric positive-definite matrices.


title: Riemannian manifold

text: In terms of tensor algebra, the metric tensor can be written in terms of the dual basis of the cotangent bundle as


title: Riemannian manifold

text: If formula_16 and formula_31 are two Riemannian manifolds, with formula_32 a diffeomorphism, then formula_33 is called an isometry if formula_34 i.e. if


title: Riemannian manifold

text: One says that a map formula_38 not assumed to be a diffeomorphism, is a local isometry if every formula_36 has an open neighborhood formula_40 such that formula_41 is an isometry (and thus a diffeomorphism).


title: Riemannian manifold

text: One says that the Riemannian metric formula_15 is continuous if formula_26 are continuous when given any smooth coordinate chart formula_44 One says that formula_15 is smooth if these functions are smooth when given any smooth coordinate chart. One could also consider many other types of Riemannian metrics in this spirit.


title: Riemannian manifold

text: In most expository accounts of Riemannian geometry, the metrics are always taken to be smooth. However, there can be important reasons to consider metrics which are less smooth. Riemannian metrics produced by methods of geometric analysis, in particular, can be less than smooth. See for instance (Gromov 1999) and (Shi and Tam 2002).


title: Riemannian manifold

text: Examples of Riemannian manifolds will be discussed below. A famous theorem of John Nash states that, given any smooth Riemannian manifold formula_46 there is a (usually large) number formula_47 and an embedding formula_48 such that the pullback by formula_49 of the standard Riemannian metric on formula_50 is formula_51 Informally, the entire structure of a smooth Riemannian manifold can be encoded by a diffeomorphism to a certain embedded submanifold of some Euclidean space. In this sense, it is arguable that nothing can be gained from the consideration of abstract smooth manifolds and their Riemannian metrics. However, there are many natural smooth Riemannian manifolds, such as the set of rotations of three-dimensional space and the hyperbolic space, of which any representation as a submanifold of Euclidean space will fail to represent their remarkable symmetries and properties as clearly as their abstract presentations do.


title: Riemannian manifold

text: Phrased differently: relative to the standard coordinates, the local representation formula_26 is given by the constant value formula_57


title: Riemannian manifold

text: This is clearly a Riemannian metric, and is called the standard Riemannian structure on formula_53 It is also referred to as Euclidean space of dimension "n" and "g" is also called the (canonical) Euclidean metric.


title: Riemannian manifold

text: Let formula_16 be a Riemannian manifold and let formula_60 be an embedded submanifold of formula_17 which is at least formula_62 Then the restriction of "g" to vectors tangent along "N" defines a Riemannian metric over "N".


title: Riemannian manifold

text: Let formula_16 be a Riemannian manifold and let formula_69 be a differentiable map. Then one may consider the pullback of formula_15 via formula_33, which is a symmetric 2-tensor on formula_72 defined by


title: Riemannian manifold

text: In this setting, generally formula_77 will not be a Riemannian metric on formula_78 since it is not positive-definite. For instance, if formula_33 is constant, then formula_77 is zero. In fact, formula_77 is a Riemannian metric if and only if formula_33 is an immersion, meaning that the linear map formula_83 is injective for each formula_84


title: Riemannian manifold

text: Let formula_16 and formula_31 be two Riemannian manifolds, and consider the cartesian product formula_89 with the usual product smooth structure. The Riemannian metrics formula_15 and formula_91 naturally put a Riemannian metric formula_92 on formula_93 which can be described in a few ways.


title: Riemannian manifold

text: A standard example is to consider the "n"-torus formula_114 define as the "n"-fold product formula_115 If one gives each copy of formula_116 its standard Riemannian metric, considering formula_117 as an embedded submanifold (as above), then one can consider the product Riemannian metric on formula_118 It is called a flat torus.


title: Riemannian manifold

text: Let formula_119 and formula_120 be two Riemannian metrics on formula_121 Then, for any number formula_122


title: Riemannian manifold

text: is also a Riemannian metric on formula_121 More generally, if formula_125 and formula_126 are any two positive numbers, then formula_127 is another Riemannian metric.


title: Riemannian manifold

text: This is a fundamental result. Although much of the basic theory of Riemannian metrics can be developed by only using that a smooth manifold is locally Euclidean, for this result it is necessary to include in the definition of "smooth manifold" that it is Hausdorff and paracompact. The reason is that the proof makes use of a partition of unity.


title: Riemannian manifold

text: where formula_128 is the Euclidean metric on formula_129 and formula_130 is its pullback along formula_131.


title: Riemannian manifold

text: If formula_133 is differentiable, then it assigns to each formula_134 a vector formula_135 in the vector space formula_136 the size of which can be measured by the norm formula_137 So formula_138 defines a nonnegative function on the interval formula_139 The length is defined as the integral of this function; however, as presented here, there is no reason to expect this function to be integrable. It is typical to suppose "g" to be continuous and formula_140 to be continuously differentiable, so that the function to be integrated is nonnegative and continuous, and hence the length of formula_141


title: Riemannian manifold

text: is well-defined. This definition can easily be extended to define the length of any piecewise-continuously differentiable curve.


title: Riemannian manifold

text: In many instances, such as in defining the Riemann curvature tensor, it is necessary to require that "g" has more regularity than mere continuity; this will be discussed elsewhere. For now, continuity of "g" will be enough to use the length defined above in order to endow "M" with the structure of a metric space, provided that it is connected.


title: Riemannian manifold

text: It is mostly straightforward to check the well-definedness of the function formula_145 its symmetry property formula_146 its reflexivity property formula_147 and the triangle inequality formula_148 although there are some minor technical complications (such as verifying that any two points can be connected by a piecewise-differentiable path). It is more fundamental to understand that formula_149 ensures formula_150 and hence that formula_151 satisfies all of the axioms of a metric.


title: Riemannian manifold

text: The observation that underlies the above proof, about comparison between lengths measured by "g" and Euclidean lengths measured in a smooth coordinate chart, also verifies that the metric space topology of formula_152 coincides with the original topological space structure of formula_121


title: Riemannian manifold

text: Although the length of a curve is given by an explicit formula, it is generally impossible to write out the distance function formula_151 by any explicit means. In fact, if formula_4 is compact then, even when "g" is smooth, there always exist points where formula_156 is non-differentiable, and it can be remarkably difficult to even determine the location or nature of these points, even in seemingly simple cases such as when formula_16 is an ellipsoid.


title: Riemannian manifold

text: As in the previous section, let formula_16 be a connected and continuous Riemannian manifold; consider the associated metric space formula_159 Relative to this metric space structure, one says that a path formula_160 is a unit-speed geodesic if for every formula_161 there exists an interval formula_162 which contains formula_163 and such that


title: Riemannian manifold

text: Informally, one may say that one is asking for formula_165 to locally 'stretch itself out' as much as it can, subject to the (informally considered) unit-speed constraint. The idea is that if formula_160 is (piecewise) continuously differentiable and formula_167 for all formula_168 then one automatically has formula_169 by applying the triangle inequality to a Riemann sum approximation of the integral defining the length of formula_170 So the unit-speed geodesic condition as given above is requiring formula_171 and formula_172 to be as far from one another as possible. The fact that we are only looking for curves to "locally" stretch themselves out is reflected by the first two examples given below; the global shape of formula_16 may force even the most innocuous geodesics to bend back and intersect themselves.


title: Riemannian manifold

text: Note that unit-speed geodesics, as defined here, are by necessity continuous, and in fact Lipschitz, but they are not necessarily differentiable or piecewise differentiable.


title: Riemannian manifold

text: As above, let formula_16 be a connected and continuous Riemannian manifold. The Hopf–Rinow theorem, in this setting, says that (Gromov 1999)


title: Riemannian manifold

text: The essence of the proof is that once the first half is established, one may directly apply the Arzelà–Ascoli theorem, in the context of the compact metric space formula_198 to a sequence of piecewise continuously-differentiable unit-speed curves from formula_5 to formula_195 whose lengths approximate formula_201 The resulting subsequential limit is the desired geodesic.


title: Riemannian manifold

text: The assumed completeness of formula_152 is important. For example, consider the case that formula_16 is the punctured plane formula_204 with its standard Riemannian metric, and one takes formula_205 and formula_206 There is no unit-speed geodesic from one to the other.


title: Riemannian manifold

text: Let formula_16 be a connected and continuous Riemannian manifold. As with any metric space, one can define the diameter of formula_152 to be


title: Riemannian manifold

text: The Hopf–Rinow theorem shows that if formula_152 is complete and has finite diameter, then it is compact. Conversely, if formula_152 is compact, then the function formula_156 has a maximum, since it is a continuous function on a compact metric space. This proves the following statement:


title: Riemannian manifold

text: This is not the case without the completeness assumption; for counterexamples one could consider any open bounded subset of a Euclidean space with the standard Riemannian metric.


title: Riemannian manifold

text: Note that, more generally, and with the same one-line proof, every compact metric space has finite diameter. However the following statement is "false": "If a metric space is complete and has finite diameter, then it is compact." For an example of a complete and non-compact metric space of finite diameter, consider


title: Riemannian manifold

text: So, although all of the terms in the above corollary of the Hopf–Rinow theorem involve only the metric space structure of formula_46 it is important that the metric is induced from a Riemannian structure.


title: Riemannian manifold

text: A Riemannian manifold "M" is geodesically complete if for all , the exponential map exp is defined for all , i.e. if any geodesic "γ"("t") starting from "p" is defined for all values of the parameter . The Hopf–Rinow theorem asserts that "M" is geodesically complete if and only if it is complete as a metric space.


title: Riemannian manifold

text: If "M" is complete, then "M" is non-extendable in the sense that it is not isometric to an open proper submanifold of any other Riemannian manifold. The converse is not true, however: there exist non-extendable manifolds that are not complete.


title: Riemannian manifold

text: The statements and theorems above are for finite-dimensional manifolds—manifolds whose charts map to open subsets of formula_217 These can be extended, to a certain degree, to infinite-dimensional manifolds; that is, manifolds that are modeled after a topological vector space; for example, Fréchet, Banach and Hilbert manifolds.


title: Riemannian manifold

text: Riemannian metrics are defined in a way similar to the finite-dimensional case. However there is a distinction between two types of Riemannian metrics:


title: Riemannian manifold

text: Length of curves is defined in a way similar to the finite-dimensional case. The function formula_248 is defined in the same manner and is called the geodesic distance. In the finite-dimensional case, the proof that this function is a metric uses the existence of a pre-compact open set around any point. In the infinite case, open sets are no longer pre-compact and so this statement may fail.


title: Riemannian manifold

text: Theorem: Let formula_234 be a strong Riemannian manifold. Then metric completeness (in the metric formula_151) implies geodesic completeness (geodesics exist for all time). Proof can be found in (Lang 1999, Chapter VII, Section 6). The other statements of the finite-dimensional case may fail.


title: Riemannian manifold

text: If formula_15 is a weak Riemannian metric, then no notion of completeness implies the other in general.


title: Lady Shiva

text: Lady Shiva (real name Sandra San or more recently Sandra Wu-San) is a fictional character appearing in American comic books published by DC Comics. The character was co-created by Dennis O'Neil and Ric Estrada, and first appeared in "Richard Dragon, Kung Fu Fighter" #5. Over time, she has become more closely associated with Batman and related characters, both as an enemy and an ally. She is a martial arts grandmaster and one of the most skilled combatants in the DC Universe. She is an assassin-for-hire who specializes in killing her targets with her bare hands, and is the mother of Cassandra Cain, a.k.a. Cassandra Wu-San, Batgirl.


title: Lady Shiva

text: Shiva's first introduced as an antagonist to martial artist Richard Dragon, believing him to be a spy responsible for the murder of her sister, Carolyn. In reality, Carolyn's murder was orchestrated by Guano Cravat, a corrupt businessman whose criminal ambitions had been foiled by Dragon. Cravat convinced Woosan that Dragon killed Carolyn, deliberately pitting her against Dragon in an act of revenge.


title: Lady Shiva

text: In order to avenge her sister, Woosan becomes a master combatant. During the course of her training, she discovers that she is a prodigy, rapidly mastering several martial arts and eventually dubbing herself "Lady" Shiva.


title: Lady Shiva

text: When Shiva tracks Dragon down and lures him to Cravat's hideout, Dragon reveals Cravat's deception. The Swiss, Carolyn's real murderer and Cravat's underling, had already died in battle with Dragon, rendering Shiva's vendetta moot.


title: Lady Shiva

text: Afterward, she briefly takes up crimefighting with Dragon and fellow martial artist Ben Turner, to allay her feelings of purposelessness, saying "I tolerate Dragon because danger seems to cling to him like flies to honey... and without danger my life is empty!" Dragon, in hopes that she might follow his example and use her skills for good, coaxes her to explore the spiritual side of martial arts, to no apparent success. When the three eventually part ways, Shiva begins a wandering existence, training herself further, and eventually parlaying her skills into a career as a master assassin.


title: Lady Shiva

text: Shiva was born in a shanty town, in an unknown country, and raised to be a warrior and protector of the village. Eventually, Shiva fled the village with her sister. Years later, when the heroine Black Canary visits the village to experience Shiva's training, a village child named Sin is held hostage by the villagers, with the promise that if Canary fails to become the warrior-protector of the village, Sin is to take her place, suggesting that Shiva's sister was once used in a similar manner. Speaking about her childhood, Sin says that Ra's al Ghul's League of Assassins ran the village where she and Shiva were born and raised.


title: Lady Shiva

text: The sisters moved to Detroit, Michigan, using the names Sandra and Carolyn Wu-San. There, they devoted their time to practicing the martial arts. Because of the girls' young ages, talent, and unique bond as sisters, their practice evolved into a secret, perfected language that only they could share. Out of love for her sister, Sandra held back in her spars with Carolyn. The assassin David Cain saw this restraint in Sandra one day when he visited Detroit to see the siblings perform. Considering Sandra a kindred spirit, Cain murdered Carolyn, in order to remove the obstruction that blunted Sandra's true potential.


title: Lady Shiva

text: Discovering that David Cain had murdered her sister, Sandra hunted him down, only to be lured into an ambush by Ra's al Ghul's League of Assassins, of which Cain was a member. In the heat of a losing battle, Sandra realized how Carolyn had held her back, and how much undeveloped potential she had. Cain spared her life, and in exchange, Sandra agreed to bear Cain a child, and leave it for him to raise. The child, Cassandra Cain, was to be Ra's al Ghul's "One Who is All", a perfected bodyguard, whose only form of communication was literacy in body language, and whose sole instinct was for hand-to-hand combat. With Carolyn gone, Cassandra and Sandra were the only two humans known to share this gift. The day of Cassandra's birth, Sandra set out to become reborn as the Lady Shiva: creator and destroyer.


title: Lady Shiva

text: During her time with Richard Dragon, Shiva becomes addicted to combat and life-or-death situations. Already a very accomplished martial artist, Shiva hires herself out as a mercenary both to recapture the thrill and to finance further training. Her considerable skills allow her to ask a high price for her services, and she soon becomes highly sought after.


title: Lady Shiva

text: Shiva is eventually hired by Reverend Hatch, the corrupt adjunct to the mayor of Hub City, to fight troublesome masked crimefighter the Question. She defeats him with ease, but rather than have Shiva kill him, Hatch instead has his men beat the Question further, shoot him in the head with an air gun, and dump him into the river. Seeing "a passion for combat" in the hero, Shiva rescues a near-death Question, and brings him to Richard Dragon's mountain hideaway, to give him a chance to fulfill his potential. In his civilian identity as Victor Sage, the Question enters Dragon's tutelage, training in combat and undergoing a spiritual awakening.


title: Lady Shiva

text: On leaving Dragon, Sage meets Shiva, who orders him to fight her. She ends the fight after only a few moves, and confirms her own suspicions of a "warrior's passion" in him, because he was willing to fight her even after his previous, crushing defeat. However, influenced by Dragon's philosophy, Sage proposes that he was simply "curious" what would happen if they fought again. Shiva leaves without telling Sage why she saved him, and Sage readopts the identity of the Question, returning to Hub City.


title: Lady Shiva

text: Shiva eventually travels to Manchuria to visit with her godfather, the O-Sensei, former instructor of Richard Dragon and Bronze Tiger. After living over 150 years, he has finally decided to die. He intends to keep a promise to his wife, and be buried alongside her, but his wife's family had hidden her remains to punish him for abandoning her. The O-Sensei has Shiva select three warriors to aid him in the search for her remains: the Question, Green Arrow, and Batman. Reluctant to acknowledge the O-Sensei's death wish, Shiva expresses her ambivalence both verbally and physically, unnecessarily applying deadly force in battles with O-Sensei's assailants.


title: Lady Shiva

text: Shiva and the O-Sensei then travel to Hub City, meeting with the Question, who, in turn, brokered Shiva's first meeting with Batman. Compelled to test his skill, Shiva immediately fights the vigilante only to be stopped by the O-Sensei. They do, however, convince Batman to aid them.


title: Lady Shiva

text: In their search for Green Arrow, Shiva encounters slave traders, killing all except one, who successfully cuts her; she rewards him with a kiss on the forehead. After locating Green Arrow, she meets Black Canary for the first time, and spars with the hero. Although Canary does not know it at the time, the two had both studied under Sensei Otomo, though non-concurrently.


title: Lady Shiva

text: After recruiting Green Arrow, Shiva returns to Hub City, and saves the Question from an attack by former employees of the now-dead Reverend Hatch. Shiva kills the men, who had been after a fortune in embezzled funds stored in Hatch's abandoned home, and sets fire to the money. Later, she nurses the Question's elderly friend Tot back to health. While the Question puzzles over her inscrutable and violent nature, she confesses that the O-Sensei was "the one man I am certain I would not harm if he kissed me".


title: Lady Shiva

text: When Batman discovers that the remains of the O-Sensei's wife had been moved to a small island, Shiva, the O-Sensei, Green Arrow, and the Question set out for the island, only to be caught in a storm. The O-Sensei is lost overboard, but the group discovers that his wife's remains had likewise been mislaid, years earlier, while in transport, leaving O-Sensei's promise fulfilled.


title: Lady Shiva

text: When Hub City falls victim to rapid, systemic urban decay, Shiva returns to offer her services to one of the ruling gangs, but instead kills the members for sending "unskilled" men to kill her. On meeting the Question, she is dismayed to find that staying in Hub City has atrophied his fighting skills. Nevertheless, she repeatedly saves both him and his lover, Mayor Myra Fermin, from assassins.


title: Lady Shiva

text: She vanishes sometime later, only to reappear stepping out of a helicopter meant to rescue the Question and his companions, who have decided to flee the city. Shiva explains that though the Question and his friends wished to leave, it is now a fit place for her to go toward. The Question and Shiva have a final exchange before he leaves.


title: Lady Shiva

text: Shiva continues to work as a mercenary for money, challenge, and perfection of her skills. Eventually, she crosses paths with the League of Assassins, and its leader, Ra's al Ghul, and begins an on-and-off association with them. Though she has kept close ties with the League, she sometimes works against their interests, as seen during "".


title: Lady Shiva

text: While training prospective assassins, mercenaries, and terrorists in war-torn country, she is approached by Jason Todd, the second Robin, and his guardian Batman, acting on evidence that she had associated with Todd's father, and speculating that she might be his mother.


title: Lady Shiva

text: Eager to finally face Batman uninterrupted, Shiva knocks Robin unconscious and challenges the Dark Knight. Initially underestimating Shiva, Batman soon learns that her skills are such that she could kill him, and begins to fight in earnest. It takes intervention from Robin to knock Shiva unconscious and subdue her for interrogation. When asked if she was Jason's mother, Shiva laughs, sarcastically claiming to have littered dozens of babies across the globe. When Batman doses her with sodium pentothal, Shiva claims to have no children, confirming that Jason is not her son. Batman leaves her in the desert, reasoning that she would soon free herself from her bonds. Shiva warns him that they would meet again, to which Batman simply replies "Too bad".


title: Lady Shiva

text: Later, Shiva begins to track down those who referred to themselves as Shihan, "Master", or any other title proclaiming mastery of a martial arts form. She would learn what she could from them and, depending on their skill and personal whim, kill them when they were of no further use to her.


title: Lady Shiva

text: In further pursuit of her art, Shiva tracks the defeats of martial arts masters, in order to discover new techniques. In this way, she develops an interest in the defeat of Koroshi, master of the art of empty-handed fighting. Gaining no information from Koroshi himself, she begins to search for King Snake, the man rumored to have defeated him. During her search, she meets Tim Drake, who is fighting King Snake's criminal organization, the Ghost Dragons, as part of his training to become the third Robin.


title: Lady Shiva

text: Shiva sees potential in Drake, and takes him on as a student for a few weeks. As a bonus, she offers to train him in one weapon, and he chooses the bo staff. Shiva derisively mentions that it is not a lethal weapon, and Drake explains that was the reason he had chosen it. At the end of his training, he defeats Shiva in a sparring match with the bo by using a whistle to distract her, and she gives him a collapsible bo staff.


title: Lady Shiva

text: Eventually, they discover that the Ghost Dragons are creating a virulent plague. Robin, Shiva, and ally Clyde Rawlins attempt to stop them from releasing it, but the Dragons escape with a few canisters. After tracking them to Hong Kong, they eventually defeat King Snake, though Rawlins dies in the attempt and Shiva mostly witnesses the proceedings. While King Snake hangs precariously on the ledge of a building, Shiva orders Robin to kill him to signify his "graduation" and become her "weapon". Robin refuses and leaves. Shiva then throws King Snake off the ledge herself, though he survives the fall.


title: Lady Shiva

text: After Bane breaks Batman's back, Batman seeks training from Shiva to help him regain his skills and fighting spirit (see ""). Though she deems him unworthy of her efforts, she devises a training regimen, out of respect for what he had been before his injuries. As part of this training, Shiva kills the Armless Master, a sensei notable for training Catwoman, while wearing a tengu mask, making sure that his death was both witnessed and relayed to his best students. Shiva then makes Batman wear the mask while performing training missions. He is then ambushed by the master's students, who mistake him for the "Tengu Mask warrior". He defeats all of them in turn, but Shiva attempts to complete Batman's training by manipulating him into killing an opponent using her fatal Leopard Blow. Batman simply feigns using the maneuver on an assailant to trick her into believing he used lethal force. Shiva later discovers the truth, but does not seek vengeance.


title: Lady Shiva

text: Later, she helps Batman fight Ra's al Ghul and his League of Assassins, including Bane, when Ghul attempts to release a deadly virus called Ebola Gulf A that would have killed half the world's population (see ""). The trail leads Batman to Calcutta, India. Since their knowledge of the city is limited, Oracle contacts Shiva, who agrees to help Batman. Together they defeat Ghul's men and prevent the virus from being released.


title: Lady Shiva

text: Shiva later travels to an army base in Transbelvia to fight a young political rebel and martial artist named Dava Sbörsc, who specializes in undefeatable "single-blow techniques" and wishes to learn Shiva's Leopard Blow. Instead, Dava's friend, her former pupil Tim Drake, in his identity as Robin, jumps into the fray in her place. Granted superspeed by a drug Dava gave him, and unused to its effects, Robin unwittingly uses lethal force, killing Shiva in battle. He quickly administers CPR, both reviving Shiva and dosing her with the drug. Thus enhanced, she kills attacking soldiers while Robin and Dava make their escape, vanishing immediately after.


title: Lady Shiva

text: During the "No Man's Land" story arc, Shiva fights in the Brotherhood of the Monkey Fist's martial arts tournament under the alias "Paper Monkey". In a final, close battle, she fights and defeats Connor Hawke, the Green Arrow. As repayment for saving her life, Robin asks her to spare Connor. She relents, warning Robin that this use of her favor means she would challenge and kill him when he grew older.


title: Lady Shiva

text: Over the years, Shiva amasses groups of followers who worship her as an incarnation of Shiva, the Hindu representation of the lord of destruction. She pays them little attention, occasionally using them as lackeys or killing them when it suits her whims. Some of her followers have even created temples to honor her victories, one of which is in Gotham, which she later destroys.


title: Lady Shiva

text: At age 8, Shiva's daughter Cassandra flees from David Cain, horrified after killing a man with her bare hands on her first assassination. She then wanders the world as a mute, and, seeking redemption, finds herself in Gotham City during the events of No Man's Land. Seeing promise in Cassandra, Batman and former Batgirl, Barbara Gordon, give Cassandra their blessings to take up the mantle of Batgirl.


title: Lady Shiva

text: Eventually, Batgirl's skills attract Shiva's attention. Without telling her of their relationship, Shiva challenges Batgirl to a battle to the death. To Shiva's disappointment, she defeats Batgirl soundly. Batgirl's body language fluency is newly impaired by a telepath's forcible inculcation of the ability to speak. Wanting to fight Batgirl at her peak, Shiva spares her life, and promises to retrain her on the condition that they have a rematch in one year. The secret to being undefeatable, Shiva explains, is to not fear death, even to seek it. Under Shiva's care, Batgirl soon regains her abilities.


title: Lady Shiva

text: Shiva reappears to fight Batgirl at the Forum of The Twelve Caesars, and kills her in combat. Realizing that Batgirl had not given her all, Shiva revives her. Batgirl admits to harboring a death wish ever since Cain first forced her to kill; her ability to perfectly read the agony of her victim had deeply traumatized her. Having overcome her death wish, Batgirl fights Shiva again, shattering her sword. In the midst of battle, Batgirl accuses Shiva of having a death wish herself, really only traveling and fighting in search of her own death. Batgirl thus defeats Shiva.


title: Lady Shiva

text: In Gail Simone's ""Birds of Prey"" series, during a joint hunt with Black Canary for the murderer of a shared, beloved sensei, a sensei Shiva so respected that she has vowed to never use anything he taught her in a fight where her goal was the death of her opponent, Shiva is beaten and kidnapped by supervillain Cheshire. Cheshire ties up, gags and locks Shiva in the trunk of a car wired with explosives, so as to use a charred corpse in a plan to fake her death and flee the country after murdering a senator. Shiva is saved when Catwoman discovers her. After Cheshire confesses to murdering their sensei, Black Canary punches her out of a helicopter (using Ted Grant's Haymaker) to prevent Shiva from killing her in a vengeful rage. Shiva subsequently offers to share her knowledge with Black Canary, who takes her offer under consideration.


title: Lady Shiva

text: Cassandra begins to suspect that Shiva is her mother, but cannot provoke Cain into an admission. She embarks on a search for Shiva, eventually finding her as the new sensei of the League of Assassins under the leadership of Nyssa Raatko, Ra's al Ghul's eldest daughter. In battle, Cassandra sacrifices her life to save former League member Tigris from an attack by her own unsuccessful experimental predecessor, Mad Dog. Shiva decides to resurrect Cassandra in a Lazarus Pit to reveal the truth of her heritage, and fight her once more.


title: Lady Shiva

text: On reviving her, Shiva admits that the reason she agreed to give birth was that she hoped her child would be the one to kill her. In an evenly matched battle, Cassandra breaks Shiva's neck, paralyzing her. She appears ready to place Shiva in the Lazarus Pit, but Shiva pleads with her not to do so. In response, Cassandra impales Shiva on a hook hanging over the pit, apparently killing her. Although Cassandra's intent regarding this action is left ambiguous, whether to kill her or let her fall into the pit and be revived, it has been confirmed that Shiva is alive in "One Year Later". Cassandra then abandons the identity of Batgirl and returns to her life as a wanderer.


title: Lady Shiva

text: During the "Infinite Crisis" storyline, Shiva later appears as a member of Alexander Luthor, Jr.'s Secret Society of Super Villains.


title: Lady Shiva

text: In the 2006 "One Year Later" storyline, having switched places with Black Canary in order to allow them both to experience each other's life experiences, Shiva joins Oracle's covert team of female operatives known as the Birds of Prey (with Canary hoping that spending time with them would soften Shiva), using the name "Jade Canary". Shiva remains unchanged, however. Oracle semiseriously refers to Shiva as a sociopath, and refuses to call Shiva by the Jade Canary title, even though Shiva (as part of the deal with Canary) has taken to wearing Black Canary's boots and trademark fishnet stockings (though she hates wearing them).


title: Lady Shiva

text: Shiva continues to perform solo work, and visits Robin to assist him (much to Robin's chagrin) in discovering the truth behind Batgirl's recent disappearance and recent upheaval within the League of Assassins. She refuses to allow herself or Oracle's team to be involved, and instead trusts her former pupil to handle the situation. It appears that she holds no ill-will towards Cassandra as she informs Tim that she hopes that her daughter is well.


title: Lady Shiva

text: During a recent mission, Oracle's team confronts the villain Prometheus, whose helmet allows him to copy the skills of 30 of the world's greatest martial artists, including Shiva herself. This had allowed him a victory against Batman in the past. Shiva believes that his files on her would be out of date, and that she would be able to defeat her "old self". She seems unconcerned about the skills of the other 29 fighters, and apparently decides to attack Prometheus head-on. Prometheus, however, has more up-to-date files than Shiva suspected, and in three seconds knocks her to the ground. After this defeat, Shiva vanishes, leaving a message for Black Canary: "Tell the Canary, I release her".


title: Lady Shiva

text: Stripped of her chance to mold Black Canary in her own image, and stripped of Sin, the young girl who was next in line as her successor, Shiva is last seen talking to Bethany Thorne, daughter of the late Crime Doctor. It appears that she is yet again hoping to train a new heir in the art of her lethal form of martial arts.


title: Lady Shiva

text: Still, although Shiva is no longer an active member of the Birds of Prey, she continues to be protective of her former teammates. Such is the case when the Birds of Prey are being threatened by Spy Smasher, who attempts to steal control away from Oracle. After a mission in Russia, Oracle and Spy Smasher fight against one another for control of the team. Although Oracle is unable to use her legs, she is victorious, although Spy Smasher attempts to go back on their deal. Unfortunately, she is confronted outside by every single living Birds of Prey Agent Oracle has ever recruited, who warn her against ever going after Oracle again; Lady Shiva is among them. When Barbara later asks the others who called Shiva, no one responds.


title: Lady Shiva

text: During the events of the "Blackest Night", Shiva tracks down Renee Montoya, the new Question, and tells her she intends to test her in battle. The two women begin their duel, only to be interrupted when Victor Sage, now a reanimated Black Lantern, arrives on the scene and attacks them. Using his new supernatural abilities, Sage effortlessly defeats Shiva and tries to kill her by tearing out her heart. However, Shiva realizes that the Black Lanterns feed on human emotion, and cuts herself off from all feeling through the use of meditation, rendering her invisible to Sage. After the others on the scene do the same, Victor angrily departs.


title: Lady Shiva

text: During the events of the "Brightest Day" crossover, a new martial artist known as the White Canary comes to Gotham and sets a plan into motion to ruin Black Canary's life by framing her for the murder of a European terrorist. When Black Canary first encounters the White Canary, she muses that the villain may be Shiva in disguise. but later White Canary pits Black Canary against Lady Shiva in an honor bound match to the death after breaking Black Canary's wrist, thereby making sure she would be killed. Both parties accept because White Canary dangles the life of Sin, Black Canary's adopted daughter, as her bait. However, the Huntress challenges Shiva instead and even manages to knock her down, to everyone's surprise, even after receiving many blows. The death match is stopped when Black Canary rescues Sin herself and points out a technicality, they need not continue the battle to the death immediately and can pick it up at any time in the future.


title: Lady Shiva

text: In The New 52 (a 2011 reboot of the DC Comics universe), Lady Shiva appears in "Nightwing" (vol. 3) #0. While initially meant only to provide information, Dick Grayson enters the field against orders when Batman is wounded. He fights her in his debut as Robin with a costume composed of spare Bat costume parts. Lady Shiva easily defeats him but praises his fighting skills and tells him he has too much potential to stay in Batman's shadow. Before leaving, Shiva tells Dick Grayson to come find her once he's ready to unlock his full potential.


title: Lady Shiva

text: In issue #13, she returns to Gotham City several years later to kill another target and Dick Grayson, now Nightwing, sets out to stop her. He's surprised to see that she remembers him from their first encounter and even more so when she praises his progress since their last meeting. She repeats that he's squandering his natural talent by not learning from her. Shiva completes her mission by throwing an axe at the S.E.C building door (to intimidate into initiating lockdown) but quickly realises that Nightwing was already injured before their fight. To Dick Grayson's surprise she says that him fighting at a disadvantage shows more than he knows and that he has too much skill to kill without a concrete reason. It is later revealed that Penguin hired her AND told Nightwing about her mission in the hopes that either he'd be saved from paying Shiva's high fees, or that she would kill Nightwing.


title: Lady Shiva

text: She is later revealed to be a League of Assassins member who taught Red Hood along with Bronze Tiger. She fights alongside Bronze Tiger, Cheshire, December Graystone, Rictus, and Red Hood as the Untitled infiltrated the League of Assassin's secret city.


title: Lady Shiva

text: Instead of her traditional black coat, the New 52 version of Shiva has appeared in a teal kabuki-like garb and mask, and is shown to be a master of weapons and martial arts, going to battle with throwing knives, swords, and usually a pair of kusarigama. In full gear she appears to have an extremely long, auburn braid with blades embedded in the hair that can be used offensively, but this is merely a wig connected to her mask. With the hooded mask off, her hair is shown to be black, and while it appears cropped in one issue, it is medium length in following issues. The character December Greystone is extremely similar in appearance to Lady Shiva's pre-New 52 look, but is a male and spell caster.


title: Lady Shiva

text: In all of her appearances so far, she has soundly defeated nearly every opponent, including Batman, Nightwing, and Arsenal. But when she engages Red Hood, her own arrogance gets the better of her, as he is able to defeat her with a simple chop to the neck that she taught him long ago, as a way of balancing their sparring lessons because she believed he could never actually beat her without using "shortcuts".


title: Lady Shiva

text: She appears in the flesh at the end of "Detective Comics" #950, observing Cassandra Cain from a rooftop. Batman later finds out from both Shiva herself and Ra's that she has separated from him & the League of Assassins, believing him to be too complacent with the wealthy and aiming for peace rather than destruction. She had taken Ra's' secret League of Shadows with her, and was responsible for multiple attacks across the city and attacks on the anti-League military squad, the Colony. After a duel with her daughter Cassandra, Ra's Al Ghul appears and shoots Shiva with a rifle. Ra's takes her body with the intent of resurrecting her for questioning.


title: Lady Shiva

text: Lady Shiva has no superpowers, but she is regarded as one of the best assassins and martial artists on the planet. She is known to have mastered numerous martial arts, including kung fu, judo, jujutsu, wing chun, capoeira, savate, karate, aikido, kobudō, taekwondo and eskrima. She is able to read people's movements through their body language, predicting their movements beforehand. She taught this trick to her daughter Cassandra Cain. She is able to hold her own against multiple opponents. She is commonly seen as the world's foremost martial artist, as powerful as Richard Dragon and Batman. Batman, who is also considered to be one of the greatest martial artists, stated that "she may well be the best fighter alive".


title: Lady Shiva

text: Although she is willing to kill, and on one occasion attempted to manipulate Batman into a position where he would have to kill in order to make a worthy opponent in the future, Shiva has shown a certain sense of honor, helping to train the third Robin in combat while working with him during an investigation, and assisting Batman in regaining his skills after he was injured by Bane and lost his fighting instinct even after his back was healed. She has also been noted as having some respect for her old teachers; when she and Black Canary learned that they had each studied under Sensei Otomo, Shiva noted that, out of respect for Otomo's preference not to kill his opponents, she never uses the skills he taught her in fights where her goal is the death of her enemies.


title: Lady Shiva

text: In 2011, UGO Networks featured Lady Shiva on their list of 25 Hot Ninja Girls: "She's the type of woman who makes it obvious why Bruce Wayne never really found love - his type is all too capable of kicking his ass". She was ranked #8 on the list of Top 10 Fictional Ninjas by Fandomania for being "one of the deadliest martial artists in the DC Comics universe".


High-bandwidth Digital Content Protection (HDCP) is a form of digital copy protection developed by Intel Corporation to prevent copying of digital audio and video content as it travels across connections. Types of connections include DisplayPort (DP), Digital Visual Interface (DVI), and High-Definition Multimedia Interface (HDMI), as well as less popular or now deprecated protocols like Gigabit Video Interface (GVIF) and Unified Display Interface (UDI).


title: High-bandwidth Digital Content Protection

text: The system is meant to stop HDCP-encrypted content from being played on unauthorized devices or devices which have been modified to copy HDCP content. Before sending data, a transmitting device checks that the receiver is authorized to receive it. If so, the transmitter encrypts the data to prevent eavesdropping as it flows to the receiver.


text: In order to make a device that plays HDCP-enabled content, the manufacturer must obtain a license for the patent from Intel subsidiary Digital Content Protection LLC, pay an annual fee, and submit to various conditions. For example, the device cannot be designed to copy; it must "frustrate attempts to defeat the content protection requirements"; it must not transmit high definition protected video to non-HDCP receivers; and DVD-Audio works can be played only at CD-audio quality by non-HDCP digital audio outputs (analog audio outputs have no quality limits).


text: Cryptanalysis researchers demonstrated flaws in HDCP as early as 2001. In September 2010, an HDCP master key that allows for the generation of valid device keys was released to the public, rendering the key revocation feature of HDCP useless. Intel has confirmed that the crack is real, and believes the master key was reverse engineered rather than leaked. In practical terms, the impact of the crack has been described as "the digital equivalent of pointing a video camera at the TV", and of limited importance for consumers because the encryption of high-definition discs has been attacked directly, with the loss of interactive features like menus. Intel threatened to sue anyone producing an unlicensed device.


text: Each HDCP-capable device has a unique set of 40 56-bit keys. Failure to keep them secret violates the license agreement. For each set of values, a special private key called a KSV (Key Selection Vector) is created. Each KSV consists of 40 bits (one bit for each HDCP key), with 20 bits set to 0 and 20 bits set to 1.


text: During authentication, the parties exchange their KSVs under a procedure called Blom's scheme. Each device adds its own secret keys together (using unsigned addition modulo 2) according to a KSV received from another device. Depending on the order of the bits set to 1 in the KSV, a corresponding secret key is used or ignored in the addition. The generation of keys and KSVs gives both devices the same 56-bit number, which is later used to encrypt data.


text: Encryption is done by a stream cipher. Each decoded pixel is encrypted by applying an XOR operation with a 24-bit number produced by a generator. The HDCP specifications ensure constant updating of keys after each encoded frame.


text: If a particular set of keys is compromised, their corresponding KSV is added to a revocation list burned onto new discs in the DVD and Blu-ray formats. (The lists are signed with a DSA digital signature, which is meant to keep malicious users from revoking legitimate devices.) During authentication, the transmitting device looks for the receiver's KSV on the list, and if it is there, will not send the decrypted work to the revoked device.


text: Each device may contain one or more HDCP transmitters and/or receivers. (A single transmitter or receiver chip may combine HDCP and HDMI functionality.)


text: In the United States, the Federal Communications Commission (FCC) approved HDCP as a "Digital Output Protection Technology" on 4 August 2004. The FCC's Broadcast flag regulations, which were struck down by the United States Court of Appeals for the District of Columbia Circuit, would have required DRM technologies on all digital outputs from HDTV signal demodulators. Congress is still considering legislation that would implement something similar to the Broadcast Flag. The HDCP standard is more restrictive than the FCC's Digital Output Protection Technology requirement. HDCP bans compliant products from converting HDCP-restricted content to full-resolution analog form, presumably in an attempt to reduce the size of the analog hole.


text: On 19 January 2005, the European Information, Communications, and Consumer Electronics Technology Industry Associations (EICTA) announced that HDCP is a required component of the European "HD ready" label.


text: HDCP strippers decrypt the HDCP stream and transmit an unencrypted HDMI video signal so it will work in a non-HDCP display. It is currently unclear whether such devices would remain working if the HDCP licensing body issued key-revocation lists, which may be installed via new media (e.g. newer Blu-ray Discs) played-back by another device (e.g. a Blu-ray Disc player) connected to it.


text: In 2001, Scott Crosby of Carnegie Mellon University wrote a paper with Ian Goldberg, Robert Johnson, Dawn Song, and David Wagner called "A Cryptanalysis of the High-bandwidth Digital Content Protection System", and presented it at ACM-CCS8 DRM Workshop on 5 November.


text: The authors concluded that HDCP's linear key exchange is a fundamental weakness, and discussed ways to:


text: They also said the Blom's scheme key swap could be broken by a so-called "conspiracy attack": obtaining the keys of at least 40 devices and reconstructing the secret symmetrical master matrix that was used to compute them.


text: Around the same time, Niels Ferguson independently claimed to have broken the HDCP scheme, but he did not publish his research, citing legal concerns arising from the controversial Digital Millennium Copyright Act.


text: In November 2011 Professor Tim Güneysu of Ruhr-Universität Bochum revealed he had broken the HDCP 1.3 encryption standard.


text: On 14 September 2010, Engadget reported the release of a possible genuine HDCP master key which can create device keys that can authenticate with other HDCP compliant devices without obtaining valid keys from The Digital Content Protection LLC. This master key would neutralize the key revocation feature of HDCP, because new keys can be created when old ones are revoked. Since the master key is known, it follows that an unlicensed HDCP decoding device could simply use the master key to dynamically generate new keys on the fly, making revocation impossible. It was not immediately clear who discovered the key or how they discovered it, though the discovery was announced via a Twitter update which linked to a Pastebin snippet containing the key and instructions on how to use it. Engadget said the attacker may have used the method proposed by Crosby in 2001 to retrieve the master key, although they cited a different researcher. On 16 September, Intel confirmed that the code had been cracked. Intel has threatened legal action against anyone producing hardware to circumvent the HDCP, possibly under the Digital Millennium Copyright Act.


text: In August 2012 version 2.1 was proved to be broken. The attack used the fact that the pairing process sends the "Km" key obfuscated with an XOR. That makes the encryptor (receiver) unaware of whether it encrypts or decrypts the key. Further, the input parameters for the XOR and the AES above it are fixed from the receiver side, meaning the transmitter can enforce repeating the same operation. Such a setting allows an attacker to monitor the pairing protocol, repeat it with a small change and extract the "Km" key. The small change is to pick the "random" key to be the encrypted key from the previous flow. Now, the attacker runs the protocol and in its pairing message it gets "E(E(Km))". Since "E()" is based on XOR it undoes itself, thus exposing the "Km" of the legitimate device.


text: V2.2 was released to fix that weakness by adding randomness provided by the receiver side. However the transmitter in V2.2 must not support receivers of V2.1 or V2.0 in order to avoid this attack. Hence a new erratum was released to redefine the field called "Type" to prevent backward compatibility with versions below 2.2. The "Type" flag should be requested by the content's usage rules (i.e. via the DRM or CAS that opened the content).


text: In August 2015, version 2.2 was rumored to be broken. An episode of AMC's series "Breaking Bad" was leaked to the Internet in UHD format; its metadata indicated it was an "HDMI cap", meaning it was captured through HDMI interface that removed HDCP 2.2 protection.


text: On 4 November 2015, Chinese company LegendSky Tech Co., already known for their other HDCP rippers/splitters under the HDFury brand, released the HDFury Integral, a device that can remove HDCP 2.2 from HDCP-enabled UHD works. On 31 December 2015, Warner Bros and Digital Content Protection, LLC (DCP, the owners of HDCP) filed a lawsuit against LegendSky. Nevertheless, the lawsuit was ultimately dropped after LegendSky argued that the device did not "strip" HDCP content protection but rather downgraded it to an older version, a measure which is explicitly permitted in DCP's licensing manual.


text: HDCP can cause problems for users who want to connect multiple screens to a device; for example, a bar with several televisions connected to one satellite receiver or when a user has a closed laptop and uses an external display as the only monitor. HDCP devices can create multiple keys, allowing each screen to operate, but the number varies from device to device; e.g., a Dish or Sky satellite receiver can generate 16 keys. The technology sometimes causes handshaking problems where devices cannot establish a connection, especially with older high-definition displays.


text: Edward Felten wrote "the main practical effect of HDCP has been to create one more way in which your electronics could fail to work properly with your TV," and concluded in the aftermath of the master key fiasco that HDCP has been "less a security system than a tool for shaping the consumer electronics market."


text: Additional issues arise when interactive media (i.e. video games) suffer from control latency, because it requires additional processing for encoding/decoding. Various everyday usage situations, such as live streaming or capture of game play, are also adversely affected.


text: There is also the problem that all Apple laptop products, presumably in order to reduce switching time, when confronted with an HDCP-compliant sink device, automatically enable HDCP encryption from the HDMI / Mini DisplayPort / USB-C connector port. This is a problem if the user wishes to use recording or videoconferencing facilities further down the chain, because these devices most often do not decrypt HDCP-enabled content (since HDCP is meant to avoid direct copying of content, and such devices could conceivably do exactly that). This applies even if the output is not HDCP-requiring content, like a PowerPoint presentation or merely the device's UI. Some sink devices have the ability to disable their HDCP reporting entirely, however, preventing this issue from blocking content to videoconferencing or recording. However, HDCP content will then refuse to play on many source devices if this is disabled while the sink device is connected.


text: When connecting a HDCP 2.2 source device through compatible distribution to a video wall made of multiple legacy displays the ability to display an image can not be guaranteed.


text: The 2.x version of HDCP is not a continuation of HDCPv1, and is rather a completely different link protection. Version 2.x employs industry-standard encryption algorithms, such as 128-bit AES with 3072 or 1024-bit RSA public key and 256-bit HMAC-SHA256 hash function. While all of the HDCP v1.x specifications support backward compatibility to previous versions of the specification, HDCPv2 devices may interface with HDCPv1 hardware only by natively supporting HDCPv1, or by using a dedicated converter device. This means that HDCPv2 is only applicable to new technologies. It has been selected for the WirelessHD and Miracast (formerly WiFi Display) standards.


text: HDCP 2.x features a new authentication protocol, and a locality check to ensure the receiver is relatively close (it must respond to the locality check within 7 ms on a normal DVI/HDMI link). Version 2.1 of the specification was cryptanalyzed and found to have several flaws, including the ability to recover the session key.


title: Hypervigilance

text: Hypervigilance (more accurately understood as Hyper-awareness) is a condition in which the nervous system is filtering sensory information and the individual is in an enhanced state of sensory sensitivity or sensory domination. The name itself is misleading as vigilance is not an interest in violence, but more likely a self defense. These symptoms are unique to the individual's encounters and youth experience. This appears to be linked to a different nervous system which can often be caused by traumatic events or PTSD. Normally, the nervous system releases stress signals in certain situations as a defense mechanism to protect one from perceived dangers. In some cases, the nervous system becomes intermittently or chronically unbalanced, causing a release of stress signals that are unique to the situation. Hyper-awareness may bring about a state of increased anxiety which can cause exhaustion.


title: Hypervigilance

text: All humans experience a perpetual scanning of the environment to search for sights, sounds, people, behaviors, smells, or anything else that is reminiscent of activity, threat or trauma. In this case the individual is avoiding danger. Hypervigilance (hyper-awareness) can lead to a variety of trust issues. The stress created by this lifestyle is not psychosis but a normal human emotion.


title: Hypervigilance

text: Hyper-awareness is differentiated from dysphoric hyperarousal in that the person remains cogent and aware of their surroundings. In dysphoric hyperarousal, a person with PTSD may lose contact with reality and re-experience the traumatic event verbatim. The name itself is misleading as vigilance is not an interest in violence, but more likely a self defense. Many people connect the word to violence by default. Hyper-awareness is more accurate for those seeking to understand the condition.


title: Hypervigilance

text: Hyper-awareness is likely a symptom of post-traumatic stress disorder (PTSD) and various types of anxiety disorders. It is distinguished from paranoia. Paranoid diagnoses, such as can occur in schizophrenia, can seem superficially similar, but are characteristically different.


title: Hypervigilance

text: People suffering from Hyper-awareness may become preoccupied with scanning their environment for possible threats. They might 'overreact' to loud and unexpected noises, exhibit an overactive startle response or become agitated in highly crowded or noisy environments. They will often have a difficult time getting to sleep or staying asleep. These symptoms are unique to their individual encounters and youth experience. Sustained states of hyper-awareness, lasting for a decade or more, will require an immersive positive reinforcement treatment plan in a balanced environment with healthy people. After resolution of the situation demanding their attention, people exhibiting hyper-awareness may be exhausted and will require exposure therapy before returning to normal activities.


title: Camila (album)

text: Camila is the debut studio album by Cuban-American singer and songwriter Camila Cabello. It was released on January 12, 2018, through Epic Records and Syco. Work on the album began in January 2017, following Cabello's departure from the girl group Fifth Harmony. The project was originally titled "The Hurting. The Healing. The Loving.", with Cabello's debut solo single "Crying in the Club" intended as the lead single. The album was later retitled "Camila" with "Havana" serving as its official lead single due to the rising success of the song, and "Crying in the Club" was cut from the final track listing. "Havana" became an international success, topping the charts of multiple countries including Australia, Brazil, Canada, France, the UK, and the US, and reaching the top 10 of several others. Primarily a pop record, it also incorporates elements of R&B, Latin, reggaeton, dancehall and hip hop. "Camila" was produced by Frank Dukes, Skrillex and T-Minus, among others.


title: Camila (album)

text: "Camila" was met with generally positive reviews from contemporary music critics, many of whom commended the Latin influences and ballads. The album debuted at number one on the US "Billboard" 200 chart, earning 119,000 album-equivalent units, of which 65,000 came from pure album sales. The album sold 5 million copies as of 2019. "Never Be the Same" was released as a single on December 7, 2017, reaching the top 10 in several countries. "Consequences" was released to contemporary hit radio as the album's final single on October 9, 2018, and an orchestra version was serviced to adult contemporary radio in October 22. Cabello promoted the album through televised performances, her Never Be the Same Tour (2018–19), and as an opening act on Taylor Swift's Reputation Stadium Tour (2018). "Camila" was nominated for Best Pop Vocal Album at the 61st Annual Grammy Awards.


title: Camila (album)

text: Cabello first rose to fame as a member of girl group Fifth Harmony, formed during the second season of "The X Factor" in 2012. The group came in third place in the competition, and subsequently signed a recording contract with Syco Music and Epic Records. The group rose to prominence with their breakthrough single "Worth It" (2015), and achieved further success with the US top-ten single "Work from Home" (2016). Fifth Harmony released two studio albums with Cabello in the group, both of which earned gold certifications in the United States. Cabello appeared as a lead artist with Canadian singer Shawn Mendes on his single "I Know What You Did Last Summer" (2015), serving as her first release outside of the group. She next collaborated with Machine Gun Kelly on the song "Bad Things" (2016), which went on to become her first top-ten single as a solo artist. Cabello's solo work led to months of media speculation that she would be leaving Fifth Harmony to focus on a solo music career.


title: Camila (album)

text: In December 2016, it was officially confirmed that Cabello had parted ways with Fifth Harmony. During an interview with "Latina" magazine, she commented about her choice and future plans, stating "I needed to follow my heart and my artistic vision. I'm grateful for everything we had in Fifth Harmony and for [this new] opportunity, I am less focused on success and more on doing my best and pursuing my artistic vision to the fullest, wherever that takes me." Her departure from the group was likened to Beyoncé and Justin Timberlake, both of whom rose to fame as part of a group before earning highly successful solo careers.


title: Camila (album)

text: During the recording of "Camila", Cabello was featured in several collaborations. She was featured on the Cashmere Cat single "Love Incredible", as well as the Spanglish "Hey Ma"; the latter was featured on the soundtrack to "The Fate of the Furious" (2017). She further collaborated with Major Lazer, Travis Scott, and Quavo on the song "Know No Better". The song was a hit in several European territories, most notably the United Kingdom and France. She served as the opening act for Bruno Mars on his 24K Magic World Tour on select dates, performing several songs from her then-unfinished debut effort.


title: Camila (album)

text: Work on the album officially began in January 2017. Initial recording sessions saw Camila working with a number of well known producers and writers, including Diplo and Pharrell Williams. While none of her collaborations with the former were featured on "Camila", the latter is credited as a writer for "Havana". She further collaborated with Andrew "Pop" Wansel on unreleased songs; Wansel said of Cabello "I never underestimated her talent, but I was not expecting her to have such a powerful vision." Cabello wanted the album to tell "the story of my journey from darkness into light, from a time when I was lost to a time when I found myself again." Songs on the album were meant to lyrically deal with the emotions of hurting, healing, and loving. She recorded the song "Crying in the Club" for the album, written by Sia. Cabello wrote additional lyrics for the song, which lyrically deals with the topic of "healing through the power of music." It was produced by Benny Blanco, Cashmere Cat, and Happy Perez. She worked with writer and producer Jesse Shatkin on the song "I Have Questions".


title: Camila (album)

text: British singer and songwriter Ed Sheeran wrote a demo for a song titled "The Boy" and sent it to Cabello, with Sheeran stating Cabello changed "90%" of the song's lyrics to her liking. He likened the song to "Crazy in Love" by Beyoncé, describing it as "funk-influenced". Cabello also worked on multiple songs with Ryan Tedder. Tedder praised Cabello's songwriting abilities, claiming to be "blown away" by the songs. He told ABC News "The stuff that we've done and that I've heard, they're gonna get stuff that is very, very contemporary and cutting edge but it feels like her. It's got that kind of Cuban spirit to it." The song "Into It", co-written by Tedder, is the only song from the pair to make the album's track list. Cabello additionally confirmed a song titled "Sangria Wine". Production duo Stargate produced "OMG", a hip-hop-influenced song that features rapper Quavo. The song was co-written by Cabello, Quavo, Stargate, Noonie Bao, Alexandra Yatchenko, and pop singer Charli XCX. The latter went on to praise Camila's writing as well, commenting "Such an incredible writer, she just came with everything, I was like 'Why am I here? She is crushing it, she was so next level, like I am so honoured to work with her. I was so stoked." Bao and Yatchenko additionally co-wrote the song "Never Be the Same" for "Camila".


title: Camila (album)

text: Prior to the release of "Crying in the Club", rumors began to circulate of a song titled "A Good Reason to Go", which was set to be released as her lead single. There was speculation that the song would be about her departure from Fifth Harmony, though the rumors were halted when Cabello announced her official first single. The song appears on the album under the title "Something's Gotta Give". That May, Cabello confirmed another song titled "It's Only Natural" for the album. While on the 24K Magic World Tour, she premiered the then-unreleased songs "Havana", "OMG", "Inside Out", and "Never Be the Same". Cabello confirmed the songs would be featured on her debut album. She later announced the songs "Scar Tissue" and "In the Dark" would be featured on the album.


title: Camila (album)

text: Following the surprise commercial success of "Havana", Cabello confirmed that she had chosen to push back the album's release date in order to record further material. She later confirmed that a lot of the material previously recorded had been scrapped from the final product. She recorded more songs with the album's executive producer Frank Dukes that were influenced by Latin music and contemporary reggaeton, inspired by acts such as Calle 13 and J Balvin. As a result, the album's original concept of hurting, healing, and love was scrapped in favor of the newly recorded material. She later told MTV, "You know, you only have one chance to make a debut album and at this point, I have so many songs I'm passionate about. You know those albums where they are songs that aren't as good as the singles. I want every song to be single-worthy." Cabello worked with Dukes' management company Electric Feel, with Dukes executively producing the album. Work on the album was completed in November 2017.


title: Camila (album)

text: Primarily a pop record, "Camila" also incorporates elements of R&B, Latin, reggaeton, dancehall and hip hop music, AllMusic said that "Camila" is a "warmly produced set of romantic pop" with "several rhythmically infectious Latin-influenced tracks informed by her Cuban heritage."


title: Camila (album)

text: "Never Be the Same" was described by "Billboard" as a dark pop ballad. A "NME" writer described it as "bombastic" electro. Lyrically, it incorporates themes of a pain-is-pleasure type of love. In one part of the song Cabello reaches to a high G falsetto in the pre-chorus. "All These Years" is a "R&B-tinged" song, Lyrically, it is about an encounter with her ex. "She Loves Control" is an "electronica-tinged, dancehall-ready" track.


title: Camila (album)

text: "Havana" is a mid-tempo track, containing a mix of "Latin fusion" and pop. It is the only song on the album that features another artist, with a guest appearance by Young Thug. "Rolling Stone"s Brittany Spanos said it is "clubby, smooth" track, where Cabello sings about falling in love with "a mysterious suitor from East Atlanta", though she has left her heart in her hometown. "Inside Out" is a reggaeton tune that features buoyantly percussive, steel drums. "Consequences" is a piano-led ballad. Lyrically, it's about the impact of a partner that was in her life. It was the album's third and final single on October 9, 2018.


title: Camila (album)

text: "Real Friends" is a pop ballad that features an acoustic guitar and handclap as percussion. Lyrically, she talks about being surrounded by negative things and people, while asking for an honest friendship. Sam Lansky of "Time" cited the song and the "heartfelt" track "Consequences" as "pretty" ballads which showcased Cabello's voice. "Somethings Gotta Give" is a ballad. "In the Dark" is a trap-pop song. Lyrically, it is about an unnamed famous boy Camila met at an after-party. "Into It" is a R&B song with a fast tempo. AllMusic called the track "contagious".


title: Camila (album)

text: Having signed with Epic Records and Syco Music as a member of Fifth Harmony, it was announced merely days after her departure from the group that Cabello had re-signed with both parties to release her solo work. She announced the album's title as "The Hurting. The Healing. The Loving." in May 2017, slated for release that September. She described the project as "the story of my journey from darkness into light, from a time when I was lost to a time when I found myself again." She wrote, "It was a kind of chapter you never want to read out loud", and explained the "whole album-making process" helped her deal with her emotions. When Cabello announced she had pushed back the album's release date to record new material, it was rumored that the album's title would be changed as well. She confirmed in November that the original name and concept of the album had been scrapped and that the project would be released "early next year." Cabello announced on December 5 that the project would be titled "Camila", and was set to be released on January 12, 2018. "Camila" became available for pre-order through digital music providers on December 7.


title: Camila (album)

text: She revealed the album artwork on her personal Instagram account, and explained the name change stating "I decided to call it by my name, because this is where this chapter in my life ended. It started with somebody else's story, it ended with me finding my way back to myself." The cover for the project sees Camila sitting in a dress and flip flops, with the album's title in bold letters in the center of the cover. "Billboard" described the album's cover art as "gorgeous". The album's cover art and booklet were shot at Little Havana in Miami, Florida. Retail chain Target sold a deluxe edition of the album, featuring a remix of "Havana" that included Daddy Yankee. The album was also released in a limited Japanese edition, featuring the aforementioned remix and the song "I Have Questions", released alongside "Crying in the Club" in May. The album's booklet contains several shots similar to the cover, as well as pictures of Cabello recording the album and childhood photos. The album's artwork was shot by Amber Park. It additionally features a message to Cabello's fans, stating "This album saw me enter the room shattered, and nervous, and insecure, and it's seen me come to life, bright-eyed, and ready for anything. So, in other words... you have my heart in your hands."


title: Camila (album)

text: Originally, "Crying in the Club" was released as the album's lead single on May 19, 2017. The song reached number 47 on the "Billboard" Hot 100. The song was accompanied by the promotional single "I Have Questions", released on May 22. The songs were performed together in several promotional appearances.