title: The Works (Queen album)

text: Believed to originate from the "Works" sessions, this is an alternative piano version of "Coming on Far Too Strong". Nothing else is known about the track.


title: The Works (Queen album)

text: Written by Mercury and Giorgio Moroder, "Love Kills" was originally recorded for "The Works", but was ultimately rejected. It was then reworked as a Mercury solo track for inclusion in Moroder's 1984 restoration and edit of the 1927 silent film "Metropolis", and was also released as a single. The track was later remade into a Queen ballad and released on the 2014 album "Queen Forever".


title: The Works (Queen album)

text: This song was later re-recorded as a Mercury solo track and released on his 1985 solo album "Mr. Bad Guy".


title: The Works (Queen album)

text: "Man on Fire", written by Taylor, is believed to have been recorded in 1984 for "The Works", before it was re-recorded and then released on Taylor's second solo album "Strange Frontier" that same year. An early promo cassette for "The Works" features a very different track listing, where its title appears. Nothing else is known about the track, or even whether a complete version exists.


title: The Works (Queen album)

text: This track, written by May and Taylor, was eventually released as a Christmas single in 1984, and later appeared as the B-side to the "A Winter's Tale" single in 1995. It was also released as part of the 1999 compilation "Greatest Hits III". It was the only Christmas song Queen recorded.


title: The Works (Queen album)

text: Written by Mercury, this song was originally recorded by Mercury and Michael Jackson before being re-recorded by Queen in 1981 for their "Hot Space" album. The track was then going to be recorded to close "The Works" before Mercury and May wrote "Is This the World We Created...?". It was ultimately recorded as a solo track by Mercury and released on his 1985 solo album "Mr. Bad Guy". In 2014, a reworked Queen version with a Mercury and Jackson duet was released on the album "Queen Forever".


title: The Works (Queen album)

text: "Rolling Stone"'s Parke Puterbaugh described it as their "first real album in some time" and "a royal feast of hard rock". Sandy Robertson, in a 3-star review for "Sounds", wrote "This time around, Queen have played it safe."


title: The Works (Queen album)

text: In a retrospective review, Greg Prato of AllMusic felt that "while the songwriting had definitely improved" from its predecessor "Hot Space", he also believed "the album sonically lacked the punch of such earlier releases as "News of the World" and "The Game"".


title: The Works (Queen album)

text: For the first and only time in their career, all the songs (and one non-album track, "I Go Crazy") from a Queen album were used as either A-sides or B-sides on singles. Starting with this album, the group began issuing singles in the UK under their own catalogue numbers.


title: Kleptomania

text: Kleptomania is the inability to resist the urge to steal items, usually for reasons other than personal use or financial gain. First described in 1816, kleptomania is classified in psychiatry as an impulse control disorder. Some of the main characteristics of the disorder suggest that kleptomania could be an obsessive-compulsive spectrum disorder, but also share similarities with addictive and mood disorders.


title: Kleptomania

text: The disorder is frequently under-diagnosed and is regularly associated with other psychiatric disorders, particularly anxiety, eating disorders, alcohol and substance use. Patients with kleptomania are typically treated with therapies in other areas due to the comorbid grievances rather than issues directly related to kleptomania.


title: Kleptomania

text: Over the last 100 years, a shift from psychotherapeutic to psychopharmacological interventions for kleptomania has occurred. Pharmacological treatments using selective serotonin reuptake inhibitors (SSRIs), mood stabilizers and opioid receptor antagonists, and other antidepressants along with cognitive behavioral therapy, have yielded positive results. However, there have also been reports of kleptomania induced by selective serotonin reuptake inhibitors (SSRIs).


title: Kleptomania

text: Some of the fundamental components of kleptomania include recurring intrusive thoughts, impotence to resist the compulsion to engage in stealing, and the release of internal pressure following the act. These symptoms suggest that kleptomania could be regarded as an obsessive-compulsive type of disorder.


title: Kleptomania

text: People diagnosed with kleptomania often have other types of disorders involving mood, anxiety, eating, impulse control, and drug use. They also have great levels of stress, guilt, and remorse, and privacy issues accompanying the act of stealing. These signs are considered to either cause or intensify general comorbid disorders. The characteristics of the behaviors associated with stealing could result in other problems as well, which include social segregation and substance use. The many types of other disorders frequently occurring along with kleptomania usually make clinical diagnosis uncertain.


title: Kleptomania

text: There is a difference between ordinary theft and kleptomania: "ordinary theft (whether planned or impulsive) is deliberate and motivated by the usefulness of the object or its monetary worth," whereas with kleptomania, there "is the recurrent failure to resist impulses to steal items even though the items are not needed for personal use or for their monetary value."


title: Kleptomania

text: Many psychoanalytic theorists suggested that kleptomania is a person's attempt "to obtain symbolic compensation for an actual or anticipated loss", and feel that the key to understanding its etiology lies in the symbolic meaning of the stolen items. Drive theory was used to propose that the act of stealing is a defense mechanism which serves as to modulate or keep undesirable feelings or emotions from being expressed. Some French psychiatrists suggest that kleptomaniacs may just want the item that they steal and the feeling they get from theft itself.


title: Kleptomania

text: Cognitive-behavioral models have been replacing psychoanalytic models in describing the development of kleptomania. Cognitive-behavioral practitioners often conceptualize the disorders as being the result of operant conditioning, behavioral chaining, distorted cognitions, and poor coping mechanisms. Cognitive-behavioral models suggest that the behavior is positively reinforced after the person steals some items. If this individual experiences minimal or no negative consequences (punishment), then the likelihood that the behavior will reoccur is increased. As the behavior continues to occur, stronger antecedents or cues become contingently linked with it, in what ultimately becomes a powerful behavioral chain. According to cognitive-behavioral theory (CBT), both antecedents and consequences may either be in the environment or cognitions. For example, Kohn and Antonuccio (2002) describe a client's antecedent cognitions, which include thoughts such as "I’m smarter than others and can get away with it"; "they deserve it"; "I want to prove to myself that I can do it"; and "my family deserves to have better things". These thoughts were strong cues to stealing behaviors. All of these thoughts were precipitated by additional antecedents which were thoughts about family, financial, and work stressors or feelings of depression. "Maintaining" cognitions provided additional reinforcement for stealing behaviors and included feelings of vindication and pride, for example: "score one for the 'little guy' against the big corporations". Although those thoughts were often afterward accompanied by feelings of remorse, this came too late in the operant sequence to serve as a viable punisher. Eventually, individuals with kleptomania come to rely upon stealing as a way of coping with stressful situations and distressing feelings, which serve to further maintain the behavior and decrease the number of available alternative coping strategies.


title: Kleptomania

text: Biological models explaining the origins of kleptomania have been based mostly on pharmacotherapy treatment studies that used selective serotonin reuptake inhibitors (SSRIs), mood stabilizers, and opioid receptor antagonists.


title: Kleptomania

text: Some studies using SSRIs have observed that opioid antagonists appear to reduce the urge to steal and mute the "rush" typically experienced immediately after stealing by some subjects with kleptomania. This would suggest that poor regulation of serotonin, dopamine, and/or natural opioids within the brain are to blame for kleptomania, linking it with impulse control and affective disorders.


title: Kleptomania

text: An alternative explanation too based on opioid antagonist studies states that kleptomania is similar to the "self-medication" model, in which stealing stimulates the person's natural opioid system. "The opioid release 'soothes' the patients, treats their sadness, or reduces their anxiety. Thus, stealing is a mechanism to relieve oneself from a chronic state of hyperarousal, perhaps produced by prior stressful or traumatic events, and thereby modulate affective states."


title: Kleptomania

text: Disagreement surrounds the method by which kleptomania is considered and diagnosed. On one hand, some researchers believe that kleptomania is merely theft and dispute the suggestion that there are psychological mechanisms involved, while others observe kleptomania as part of a substance-related addiction. Yet others categorize kleptomania as a variation of an impulse control disorder, such as obsessive-compulsive disorder or eating disorders.


title: Kleptomania

text: According to the "Diagnostic and Statistical Manual of Mental Disorders" fourth edition (DSM IV-TR), a frequent and widely used guide for the diagnosis of mental disorders, the following symptoms and characteristics are the diagnostic criteria for kleptomania:


title: Kleptomania

text: Skeptics have decried kleptomania as an invalid psychiatric concept exploited in legal defenses of wealthy female shoplifters. During the twentieth century, kleptomania was strongly linked with the increased prevalence of department stores, and "department store kleptomaniacs" were a widely held social stereotype that had political implications.


title: Kleptomania

text: Kleptomania seems to be linked with other psychiatric disorders, especially mood swings, anxiety, eating disorders, and alcohol and substance use. The occurrence of stealing as a behavior in conjunction with eating disorders, particularly bulimia nervosa, is frequently taken as a sign of the harshness of the eating disorder.


title: Kleptomania

text: A likely connection between depression and kleptomania was reported as early as 1911. It has since been extensively established in clinical observations and available case reports. The mood disorder could come first or co-occur with the beginning of kleptomania. In advanced cases, depression may result in self-inflicted injury and could even lead to suicide. Some people have reported relief from depression or manic symptoms after theft.


title: Kleptomania

text: It has been suggested that because kleptomania is linked to strong compulsive and impulsive qualities, it can be viewed as a variation of obsessive-compulsive spectrum disorders, together with pathological gambling, compulsive buying, pyromania, nailbiting and trichotillomania. This point achieves support from the unusually higher cases of obsessive-compulsive disorder (OCD; see below) in close relatives of patients with kleptomania.


title: Kleptomania

text: Data from epidemiological studies additionally propose that there is an affiliation between kleptomania and substance use disorders along with high rates in a unidirectional manner. Phenomenological data maintain that there is a relationship between kleptomania and drug addictions. A higher percentage of cases of kleptomania has been noted in adolescents and young adults, and a lesser number of cases among older adults, which imply an analogous natural history to that seen in substance use disorders. Family history data also propose a probable common genetic input to alcohol use and kleptomania. Substance use disorders are more common in kin of persons with kleptomania than in the general population. Furthermore, pharmacological data (e.g., the probable efficacy of the opioid antagonist, naltrexone, in the treatment of both kleptomania and substance use disorders) could present additional support for a joint relationship between kleptomania and substance use disorders. Based on the idea that kleptomania and substance use disorders may share some etiological features, it could be concluded that kleptomania would react optimistically to the same treatments. As a matter of fact, certain non-medical treatment methods that are successful in treating substance use are also accommodating in treating kleptomania.


title: Kleptomania

text: Kleptomania is frequently thought of as being a part of obsessive-compulsive disorder (OCD), since the irresistible and uncontrollable actions are similar to the frequently excessive, unnecessary, and unwanted rituals of OCD. Some individuals with kleptomania demonstrate hoarding symptoms that resemble those with OCD.


title: Kleptomania

text: Prevalence rates between the two disorders do not demonstrate a strong relationship. Studies examining the comorbidity of OCD in subjects with kleptomania have inconsistent results, with some showing a relatively high co-occurrence (45%-60%) while others demonstrate low rates (0%-6.5%). Similarly, when rates of kleptomania have been examined in subjects with OCD, a relatively low co-occurrence was found (2.2%-5.9%).


title: Kleptomania

text: Pyromania, another impulse disorder, has many ties to kleptomania. Many pyromaniacs begin fires alongside petty stealing which often appears similar to kleptomania.


title: Kleptomania

text: Although the disorder has been known to psychologists for a long time, the cause of kleptomania is still ambiguous. Therefore, a diverse range of therapeutic approaches have been introduced for its treatment. These treatments include: psychoanalytic oriented psychotherapy, behavioral therapy, and pharmacotherapy.


title: Kleptomania

text: Several explanations of the mechanics of kleptomania have been presented. A contemporary social approach proposes that kleptomania is an outcome of consumerism and the large quantity of commodities in society. Psychodynamic theories depend on a variety of points of view in defining the disorder. Psychoanalysts define the condition as an indication of a defense mechanism deriving in the unconscious ego against anxiety, prohibited intuition or desires, unsettled struggle or forbidden sexual drives, dread of castration, sexual excitement, and sexual fulfillment and orgasm throughout the act of stealing. The psychoanalytic and psycho-dynamic approach to kleptomania granted the basis for prolonged psychoanalytic or psycho-dynamic psychotherapy as the core treatment method for a number of years. Like most psychiatric conditions, kleptomania was observed within the psycho-dynamic lens instead of being viewed as a bio-medical disorder. However, the prevalence of psychoanalytic approach contributed to the growth of other approaches, particularly in the biological domain.


title: Kleptomania

text: Cognitive-behavioural therapy (CBT) has primarily substituted the psychoanalytic and dynamic approach in the treatment of kleptomania. Numerous behavioural approaches have been recommended as helpful according to several cases stated in the literature. They include: hidden sensitisation by unpleasant images of nausea and vomiting, aversion therapy (for example, aversive holding of breath to achieve a slightly painful feeling every time a desire to steal or the act is imagined), and systematic desensitisation. In certain instances, the use of combining several methods such as hidden sensitisation along with exposure and response prevention were applied. Even though the approaches used in CBT need more research and investigation in kleptomania, success in combining these methods with medication was illustrated over the use of drug treatment as the single method of treatment.


title: Kleptomania

text: The phenomenological similarity and the suggested common basic biological dynamics of kleptomania and OCD, pathological gambling and trichotillomania gave rise to the theory that the similar groups of medications could be used in all these conditions. Consequently, the primary use of selective serotonin reuptake inhibitor (SSRI) group, which is a form of antidepressant, has been used in kleptomania and other impulse control disorders such as binge eating and OCD. Electroconvulsive therapy (ECT), lithium and valproic acid (sodium valproate) have been used as well.


title: Kleptomania

text: The SSRI's usage is due to the assumption that the biological dynamics of these conditions derives from low levels of serotonin in brain synapses, and that the efficacy of this type of therapy will be relevant to kleptomania and to other comorbid conditions.


title: Kleptomania

text: Opioid receptor antagonists are regarded as practical in lessening urge-related symptoms, which is a central part of impulse control disorders; for this reason, they are used in treatment of substance use. This quality makes them helpful in treating kleptomania and impulse control disorders in general. The most frequently used drug is naltrexone, a long-acting competitive antagonist. Naltrexone acts mainly at μ-receptors, but also antagonises κ- and λ-receptors.


title: Kleptomania

text: There have been no controlled studies of the psycho-pharmacological treatment of kleptomania. This could be as a consequence of kleptomania being a rare phenomenon and the difficulty in achieving a large enough sample. Facts about this issue come largely from case reports or from bits and pieces gathered from a comparatively small number of cases enclosed in a group series.


title: Kleptomania

text: In the nineteenth century, French psychiatrists began to observe kleptomaniacal behavior, but were constrained by their approach. By 1890, a large body of case material on kleptomania had been developed. Hysteria, imbecility, cerebral defect, and menopause were advanced as theories to explain these seemingly nonsensical behaviors, and many linked kleptomania to immaturity, given the inclination of young children to take whatever they want. These French and German observations later became central to psychoanalytic explanations of kleptomania.


title: Kleptomania

text: The term "kleptomania" was derived from the Greek words "κλέπτω" (klepto) "to steal" and "μανία" (mania) "mad desire, compulsion". Its meaning roughly corresponds to "compulsion to steal" or "compulsive stealing".


title: Kleptomania

text: In the early twentieth century, kleptomania was viewed more as a legal excuse for self-indulgent haut bourgeois ladies than a valid psychiatric ailment by French psychiatrists.


title: Kleptomania

text: Sigmund Freud, the creator of controversial psychoanalytic theory, believed that the underlying dynamics of human behaviours associated with uncivilized savages—impulses were curbed by inhibitions for social life. He did not believe human behaviour to be rational. He created a large theoretical corpus which his disciples applied to such psychological problems as kleptomania. In 1924, one of his followers, Wilhelm Stekel, read the case of a female kleptomaniac who was driven by suppressed sexual urges to take hold of "something forbidden, secretly". Stekel concluded that kleptomania was "suppressed and superseded sexual desire carried out through medium of a symbol or symbolic action. Every compulsion in psychic life is brought about by suppression".


title: Kleptomania

text: Fritz Wittels argued that kleptomaniacs were sexually underdeveloped people who felt deprived of love and had little experience with human sexual relationships; stealing was their sex life, giving them thrills so powerful that they did not want to be cured. Male kleptomaniacs, in his view, were homosexual or invariably effeminate.


title: Kleptomania

text: A famous large-scale analysis of shoplifters in the United Kingdom ridiculed Stekel's notion of sexual symbolism and claimed that one out of five apprehended shoplifters was a "psychiatric".


title: Kleptomania

text: Empirically based conceptual articles have argued that kleptomania is becoming more common than previously thought, and occurs more frequently among women than men. These ideas are new in recent history but echo those current in the mid to late nineteenth century.


title: Gimbal

text: A gimbal is a pivoted support that permits rotation of an object about an axis. A set of three gimbals, one mounted on the other with orthogonal pivot axes, may be used to allow an object mounted on the innermost gimbal to remain independent of the rotation of its support (e.g. vertical in the first animation). For example, on a ship, the gyroscopes, shipboard compasses, stoves, and even drink holders typically use gimbals to keep them upright with respect to the horizon despite the ship's pitching and rolling.


title: Gimbal

text: The gimbal suspension used for mounting compasses and the like is sometimes called a Cardan suspension after Italian mathematician and physicist Gerolamo Cardano (1501–1576) who described it in detail. However, Cardano did not invent the gimbal, nor did he claim to. The device has been known since antiquity, first described in the 3rd c. BC by Philo of Byzantium, although some modern authors support the view that it may not have a single identifiable inventor.


title: Gimbal

text: The gimbal was first described by the Greek inventor Philo of Byzantium (280–220 BC). Philo described an eight-sided ink pot with an opening on each side, which can be turned so that while any face is on top, a pen can be dipped and inked — yet the ink never runs out through the holes of the other sides. This was done by the suspension of the inkwell at the center, which was mounted on a series of concentric metal rings so that it remained stationary no matter which way the pot is turned.


title: Gimbal

text: In Ancient China, the Han Dynasty (202 BC – 220 AD) inventor and mechanical engineer Ding Huan created a gimbal incense burner around 180 AD. There is a hint in the writing of the earlier Sima Xiangru (179–117 BC) that the gimbal existed in China since the 2nd century BC. There is mention during the Liang Dynasty (502–557) that gimbals were used for hinges of doors and windows, while an artisan once presented a portable warming stove to Empress Wu Zetian (r. 690–705) which employed gimbals. Extant specimens of Chinese gimbals used for incense burners date to the early Tang Dynasty (618–907), and were part of the silver-smithing tradition in China.


title: Gimbal

text: The authenticity of Philo's description of a cardan suspension has been doubted by some authors on the ground that the part of Philo's "Pneumatica" which describes the use of the gimbal survived only in an Arabic translation of the early 9th century. Thus, as late as 1965, the sinologist Joseph Needham suspected Arab interpolation. However, Carra de Vaux, author of the French translation which still provides the basis for modern scholars, regards the "Pneumatics" as essentially genuine. The historian of technology George Sarton (1959) also asserts that it is safe to assume the Arabic version is a faithful copying of Philo's original, and credits Philon explicitly with the invention. So does his colleague Michael Lewis (2001). In fact, research by the latter scholar (1997) demonstrates that the Arab copy contains sequences of Greek letters which fell out of use after the 1st century, thereby strengthening the case that it is a faithful copy of the Hellenistic original, a view recently also shared by the classicist Andrew Wilson (2002).


title: Gimbal

text: The ancient Roman author Athenaeus Mechanicus, writing during the reign of Augustus (30 BC–14 AD), described the military use of a gimbal-like mechanism, calling it "little ape" ("pithêkion"). When preparing to attack coastal towns from the sea-side, military engineers used to yoke merchant-ships together to take the siege machines up to the walls. But to prevent the shipborne machinery from rolling around the deck in heavy seas, Athenaeus advises that "you must fix the "pithêkion" on the platform attached to the merchant-ships in the middle, so that the machine stays upright in any angle".


title: Gimbal

text: After antiquity, gimbals remained widely known in the Near East. In the Latin West, reference to the device appeared again in the 9th century recipe book called the "Little Key of Painting"' ("mappae clavicula"). The French inventor Villard de Honnecourt depicts a set of gimbals in his sketchbook (see right). In the early modern period, dry compasses were suspended in gimbals.


title: Gimbal

text: The word "gimbal" began as a noun. Most modern dictionaries continue to list it as such. Lacking a convenient term to describe the swinging movement of a rocket engine, engineers began also using the word "gimbal" as a verb. When a thrust chamber is swung by an attached actuator, the movement is referred to as "gimballed" or "gimballing". Official rocket documentation reflects this usage.


title: Gimbal

text: In inertial navigation, as applied to ships and submarines, a minimum of three gimbals are needed to allow an inertial navigation system (stable table) to remain fixed in inertial space, compensating for changes in the ship's yaw, pitch, and roll. In this application, the inertial measurement unit (IMU) is equipped with three orthogonally mounted gyros to sense rotation about all axes in three-dimensional space. The gyro outputs are kept to a null through drive motors on each gimbal axis, to maintain the orientation of the IMU. To accomplish this, the gyro error signals are passed through "resolvers" mounted on the three gimbals, roll, pitch and yaw. These resolvers perform an automatic matrix transformation according to each gimbal angle, so that the required torques are delivered to the appropriate gimbal axis. The yaw torques must be resolved by roll and pitch transformations. The gimbal angle is never measured.


title: Gimbal

text: In inertial navigation systems, gimbal lock may occur when vehicle rotation causes two of the three gimbal rings to align with their pivot axes in a single plane. When this occurs, it is no longer possible to maintain the sensing platform's orientation.


title: Gimbal

text: In spacecraft propulsion, rocket engines are generally mounted on a pair of gimbals to allow a single engine to vector thrust about both the pitch and yaw axes; or sometimes just one axis is provided per engine. To control roll, twin engines with differential pitch or yaw control signals are used to provide torque about the vehicle's roll axis.


title: Gimbal

text: In portable photography equipment, single-axis gimbal heads are used in order to allow a balanced movement for camera and lenses. This proves useful in wildlife photography as well as in any other case where very long and heavy telephoto lenses are adopted: a gimbal head rotates a lens around its center of gravity, thus allowing for easy and smooth manipulation while tracking moving subjects.


title: Gimbal

text: Very large gimbal mounts in the form 2 or 3 axis altitude-altitude mounts are used in satellite photography for tracking purposes.


title: Gimbal

text: Gyrostabilized gimbals which house multiple sensors are also used for airborne surveillance applications including airborne law enforcement, pipe and power line inspection, mapping, and ISR (intelligence, surveillance, and reconnaissance). Sensors include thermal imaging, daylight, low light cameras as well as laser range finder, and illuminators.


title: Gimbal

text: Gimbal systems are also used in scientific optics equipment. For example, they are used to rotate a material sample along an axis to study their angular dependence of optical properties.


title: Gimbal

text: Handheld 3-axis gimbals are used in stabilization systems designed to give the camera operator the independence of handheld shooting without camera vibration or shake. There are two versions of such stabilization systems: mechanical and motorized.


title: Gimbal

text: Mechanical gimbals have the sled, which includes the top "stage" where the camera is attached, the "post" which in most models can be extended, with the monitor and batteries at the bottom to counterbalance the camera weight. This is how the Steadicam stays upright, by simply making the bottom slightly heavier than the top, pivoting at the gimbal. This leaves the center of gravity of the whole rig, however heavy it may be, exactly at the operator's fingertip, allowing deft and finite control of the whole system with the lightest of touches on the gimbal.


title: Gimbal

text: Powered by three brushless motors, motorized gimbals have the ability to keep the camera level on all axes as the camera operator moves the camera. An inertial measurement unit (IMU) responds to movement and utilizes its three separate motors to stabilize the camera. With the guidance of algorithms, the stabilizer is able to notice the difference between deliberate movement such as pans and tracking shots from unwanted shake. This allows the camera to seem as if it is floating through the air, an effect achieved by a Steadicam in the past. Gimbals can be mounted to cars and other vehicles such as drones, where vibrations or other unexpected movements would make tripods or other camera mounts unacceptable. An example which is popular in the live TV broadcast industry, is the Newton 3-axis camera gimbal.


title: Gimbal

text: The rate of a mechanical marine chronometer is sensitive to its orientation. Because of this, chronometers were normally mounted on gimbals, in order to isolate them from the rocking motions of a ship at sea.


title: Gimbal

text: Gimbal lock is the loss of one degree of freedom in a three-dimensional, three-gimbal mechanism that occurs when the axes of two of the three gimbals are driven into a parallel configuration, "locking" the system into rotation in a degenerate two-dimensional space.


title: Gimbal

text: The word lock is misleading: no gimbal is restrained. All three gimbals can still rotate freely about their respective axes of suspension. Nevertheless, because of the parallel orientation of two of the gimbals' axes there is no gimbal available to accommodate rotation about one axis.


title: Partially ordered set

text: In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set. A poset consists of a set together with a binary relation indicating that, for certain pairs of elements in the set, one of the elements precedes the other in the ordering. The relation itself is called a "partial order."


title: Partially ordered set

text: The word "partial" in the names "partial order" and "partially ordered set" is used as an indication that not every pair of elements needs to be comparable. That is, there may be pairs of elements for which neither element precedes the other in the poset. Partial orders thus generalize total orders, in which every pair is comparable.


title: Partially ordered set

text: A partial order defines a notion of comparison. Two elements "x" and "y" may stand in any of four mutually exclusive relationships to each other: either "x" < "y", or "x" = "y", or "x" > "y", or "x" and "y" are "incomparable".


title: Partially ordered set

text: A set with a partial order is called a partially ordered set (also called a poset). The term "ordered set" is sometimes also used, as long as it is clear from the context that no other kind of order is meant. In particular, totally ordered sets can also be referred to as "ordered sets", especially in areas where these structures are more common than posets.


title: Partially ordered set

text: A partial order relation is a homogeneous relation that is transitive and antisymmetric. There are two common sub-definitions for a partial order relation, for reflexive and irreflexive partial order relations, also called "non-strict" and "strict" respectively. The two definitions can be put into a one-to-one correspondence, so for every strict partial order there is a unique corresponding non-strict partial order, and vice versa. The term partial order typically refers to a non-strict partial order relation.


title: Partially ordered set

text: A reflexive, weak, or is a homogeneous relation ≤ on a set formula_1 that is reflexive, antisymmetric, and transitive. That is, for all formula_2 it must satisfy:


title: Partially ordered set

text: An irreflexive, strong, or is a homogeneous relation < on a set formula_1 that is irreflexive, asymmetric, and transitive; that is, it satisfies the following conditions for all formula_11


title: Partially ordered set

text: Irreflexivity and transitivity together imply asymmetry. Also, asymmetry implies irreflexivity. In other words, a transitive relation is asymmetric if and only if it is irreflexive. So the definition is the same if it omits either irreflexivity or asymmetry (but not both).


title: Partially ordered set

text: Strict and non-strict partial orders on a set formula_1 are closely related. A non-strict partial order formula_19 may be converted to a strict partial order by removing all relationships of the form formula_20 that is, the strict partial order is the set formula_21 where formula_22 is the identity relation on formula_23 and formula_24 denotes set subtraction. Conversely, a strict partial order < on formula_1 may be converted to a non-strict partial order by adjoining all relationships of that form; that is, formula_26 is a non-strict partial order. Thus, if formula_19 is a non-strict partial order, then the corresponding strict partial order < is the irreflexive kernel given by


title: Partially ordered set

text: Conversely, if < is a strict partial order, then the corresponding non-strict partial order formula_19 is the reflexive closure given by:


title: Partially ordered set

text: The "dual" (or "opposite") formula_31 of a partial order relation formula_32 is defined by letting formula_31 be the converse relation of formula_32, i.e. formula_35 if and only if formula_36. The dual of a non-strict partial order is a non-strict partial order, and the dual of a strict partial order is a strict partial order. The dual of a dual of a relation is the original relation.


title: Partially ordered set

text: We can consider a poset as a 3-tuple formula_37, where formula_19 is a non-strict partial order relation on formula_1, formula_40 is the associated strict partial order relation on formula_1 (the irreflexive kernel of formula_19), formula_43 is the dual of formula_19, and formula_45 is the dual of formula_40.


title: Partially ordered set

text: Any one of the four partial order relations formula_47 on a given set uniquely determines the other three. Hence, as a matter of notation, one may write formula_48 or formula_49, and assume that the other relations are defined appropriately. Defining via a non-strict partial order formula_19 is most common. Some authors use different symbols than formula_19 such as formula_52 or formula_53 to distinguish partial orders from total orders.


title: Partially ordered set

text: When referring to partial orders, formula_19 should not be taken as the complement of formula_45. The relation formula_45 is the converse of the irreflexive kernel of formula_19, which is always a subset of the complement of formula_19, but formula_45 is equal to the complement of formula_19 if, and only if, formula_19 is a total order.


title: Partially ordered set

text: One familiar example of a partially ordered set is a collection of people ordered by genealogical descendancy. Some pairs of people bear the descendant-ancestor relationship, but other pairs of people are incomparable, with neither being a descendant of the other.


title: Partially ordered set

text: In order of increasing strength, i.e., decreasing sets of pairs, three of the possible partial orders on the Cartesian product of two partially ordered sets are (see Fig.4):


title: Partially ordered set

text: Applied to ordered vector spaces over the same field, the result is in each case also an ordered vector space.


title: Partially ordered set

text: Another way to combine two (disjoint) posets is the ordinal sum (or linear sum), "Z" = "X" ⊕ "Y", defined on the union of the underlying sets "X" and "Y" by the order "a" ≤ "b" if and only if:


title: Partially ordered set

text: Series-parallel partial orders are formed from the ordinal sum operation (in this context called series composition) and another operation called parallel composition. Parallel composition is the disjoint union of two partially ordered sets, with no order relation between elements of one set and elements of the other set.


title: Partially ordered set

text: The examples use the poset formula_68 consisting of the set of all subsets of a three-element set formula_69 ordered by set inclusion (see Fig.1).


title: Partially ordered set

text: As another example, consider the positive integers, ordered by divisibility: 1 is a least element, as it divides all other elements; on the other hand this poset does not have a greatest element (although if one would include 0 in the poset, which is a multiple of any integer, that would be a greatest element; see Fig.6). This partially ordered set does not even have any maximal elements, since any "g" divides for instance 2"g", which is distinct from it, so "g" is not maximal. If the number 1 is excluded, while keeping divisibility as ordering on the elements greater than 1, then the resulting poset does not have a least element, but any prime number is a minimal element for it. In this poset, 60 is an upper bound (though not a least upper bound) of the subset formula_103 which does not have any lower bound (since 1 is not in the poset); on the other hand 2 is a lower bound of the subset of powers of 2, which does not have any upper bound.


title: Partially ordered set

text: Given two partially ordered sets ("S", ≤) and ("T", ≼), a function formula_104 is called order-preserving, or monotone, or isotone, if for all formula_105 formula_106 implies "f"("x") ≼ "f"("y").


title: Partially ordered set

text: If ("U", ≲) is also a partially ordered set, and both formula_104 and formula_108 are order-preserving, their composition formula_109 is order-preserving, too.


title: Partially ordered set

text: A function formula_104 is called order-reflecting if for all formula_105 "f"("x") ≼ "f"("y") implies formula_112


title: Partially ordered set

text: If formula_113 is both order-preserving and order-reflecting, then it is called an order-embedding of ("S", ≤) into ("T", ≼).


title: Partially ordered set

text: In the latter case, formula_113 is necessarily injective, since formula_115 implies formula_116 and in turn formula_117 according to the antisymmetry of formula_118 If an order-embedding between two posets "S" and "T" exists, one says that "S" can be embedded into "T". If an order-embedding formula_104 is bijective, it is called an order isomorphism, and the partial orders ("S", ≤) and ("T", ≼) are said to be isomorphic. Isomorphic orders have structurally similar Hasse diagrams (see Fig.7a). It can be shown that if order-preserving maps formula_104 and formula_108 exist such that formula_122 and formula_123 yields the identity function on "S" and "T", respectively, then "S" and "T" are order-isomorphic.


title: Partially ordered set

text: For example, a mapping formula_124 from the set of natural numbers (ordered by divisibility) to the power set of natural numbers (ordered by set inclusion) can be defined by taking each number to the set of its prime divisors. It is order-preserving: if formula_125 divides formula_126 then each prime divisor of formula_125 is also a prime divisor of formula_128 However, it is neither injective (since it maps both 12 and 6 to formula_129) nor order-reflecting (since 12 does not divide 6). Taking instead each number to the set of its prime power divisors defines a map formula_130 that is order-preserving, order-reflecting, and hence an order-embedding. It is not an order-isomorphism (since it, for instance, does not map any number to the set formula_131), but it can be made one by restricting its codomain to formula_132 Fig.7b shows a subset of formula_133 and its isomorphic image under formula_134 The construction of such an order-isomorphism into a power set can be generalized to a wide class of partial orders, called distributive lattices, see "Birkhoff's representation theorem".


title: Partially ordered set

text: A partial order formula_135 on a set formula_136 is an extension of another partial order formula_19 on formula_136 provided that for all elements formula_139 whenever formula_140 it is also the case that formula_141 A linear extension is an extension that is also a linear (that is, total) order. As a classic example, the lexicographic order of totally ordered sets is a linear extension of their product order. Every partial order can be extended to a total order (order-extension principle).


title: Partially ordered set

text: In computer science, algorithms for finding linear extensions of partial orders (represented as the reachability orders of directed acyclic graphs) are called topological sorting.


title: Partially ordered set

text: Strict partial orders correspond directly to directed acyclic graphs (DAGs). If a graph is constructed by taking each element of formula_1 to be a node and each element of formula_19 to be an edge, then every strict partial order is a DAG, and the transitive closure of a DAG is both a strict partial order and also a DAG itself. In contrast a non-strict partial order would have self loops at every node and therefore not be a DAG.


title: Partially ordered set

text: Every poset (and every preordered set) may be considered as a category where, for objects formula_125 and formula_126 there is at most one morphism from formula_125 to formula_128 More explicitly, let hom("x", "y") = {("x", "y")} if "x" ≤ "y" (and otherwise the empty set) and formula_148 Such categories are sometimes called "posetal".


title: Partially ordered set

text: Posets are equivalent to one another if and only if they are isomorphic. In a poset, the smallest element, if it exists, is an initial object, and the largest element, if it exists, is a terminal object. Also, every preordered set is equivalent to a poset. Finally, every subcategory of a poset is isomorphism-closed.


title: Partially ordered set

text: If formula_1 is a partially ordered set that has also been given the structure of a topological space, then it is customary to assume that formula_150 is a closed subset of the topological product space formula_151 Under this assumption partial order relations are well behaved at limits in the sense that if formula_152 and formula_153 and for all formula_154 formula_155 then formula_156


title: Partially ordered set

text: An "interval" in a poset "P" is a subset of "P" with the property that, for any "x" and "y" in and any "z" in "P", if "x" ≤ "z" ≤ "y", then "z" is also in . (This definition generalizes the "interval" definition for real numbers.)


title: Partially ordered set

text: For "a" ≤ "b", the "closed interval" is the set of elements "x" satisfying "a" ≤ "x" ≤ "b" (that is, "a" ≤ "x" and "x" ≤ "b"). It contains at least the elements "a" and "b".


title: Partially ordered set

text: Using the corresponding strict relation "<", the "open interval" is the set of elements "x" satisfying "a" < "x" < "b" (i.e. "a" < "x" and "x" < "b"). An open interval may be empty even if "a" < "b". For example, the open interval on the integers is empty since there are no integers such that .


title: Partially ordered set

text: An interval is bounded if there exist elements formula_157 such that . Every interval that can be represented in interval notation is obviously bounded, but the converse is not true. For example, let as a subposet of the real numbers. The subset is a bounded interval, but it has no infimum or supremum in "P", so it cannot be written in interval notation using elements of "P".


title: Partially ordered set

text: A poset is called locally finite if every bounded interval is finite. For example, the integers are locally finite under their natural ordering. The lexicographical order on the cartesian product formula_158 is not locally finite, since .


title: Partially ordered set

text: Using the interval notation, the property ""a" is covered by "b"" can be rephrased equivalently as formula_159


title: Partially ordered set

text: This concept of an interval in a partial order should not be confused with the particular class of partial orders known as the interval orders.


title: Nuclear weapon yield

text: The explosive yield of a nuclear weapon is the amount of energy released when that particular nuclear weapon is detonated, usually expressed as a TNT equivalent (the standardized equivalent mass of trinitrotoluene which, if detonated, would produce the same energy discharge), either in kilotonnes (kt—thousands of tonnes of TNT), in megatonnes (Mt—millions of tonnes of TNT), or sometimes in terajoules (TJ). An explosive yield of one terajoule is equal to . Because the accuracy of any measurement of the energy released by TNT has always been problematic, the conventional definition is that one kilotonne of TNT is held simply to be equivalent to 10 calories.


title: Nuclear weapon yield

text: The yield-to-weight ratio is the amount of weapon yield compared to the mass of the weapon. The practical maximum yield-to-weight ratio for fusion weapons (thermonuclear weapons) has been estimated to six megatonnes of TNT per tonne of bomb mass (25 TJ/kg). Yields of 5.2 megatonnes/tonne and higher have been reported for large weapons constructed for single-warhead use in the early 1960s. Since then, the smaller warheads needed to achieve the increased net damage efficiency (bomb damage/bomb mass) of multiple warhead systems have resulted in increases in the yield/mass ratio for single modern warheads.


title: Nuclear weapon yield

text: In comparison, the blast yield of the GBU-43 Massive Ordnance Air Blast bomb is 0.011 kt, and that of the Oklahoma City bombing, using a truck-based fertilizer bomb, was 0.002 kt. The estimated strength of the explosion at the Port of Beirut is 0.3-0.5 kt. Most artificial non-nuclear explosions are considerably smaller than even what are considered to be very small nuclear weapons.


title: Nuclear weapon yield

text: The yield-to-mass ratio is the amount of weapon yield compared to the mass of the weapon. According to nuclear-weapons designer Ted Taylor, the practical maximum yield-to-mass ratio for fusion weapons is about 6 megatonnes of TNT per tonne (25 TJ/kg). The "Taylor limit" is not derived from first principles, and weapons with yields as high as 9.5 megatonnes per tonne have been theorized. The highest achieved values are somewhat lower, and the value tends to be lower for smaller, lighter weapons, of the sort that are emphasized in today's arsenals, designed for efficient MIRV use or delivery by cruise missile systems.


title: Nuclear weapon yield

text: Large single warheads are seldom a part of today's arsenals, since smaller MIRV warheads, spread out over a pancake-shaped destructive area, are far more destructive for a given total yield, or unit of payload mass. This effect results from the fact that destructive power of a single warhead on land scales approximately only as the cube root of its yield, due to blast "wasted" over a roughly hemispherical blast volume, while the strategic target is distributed over a circular land area with limited height and depth. This effect more than makes up for the lessened yield/mass efficiency encountered if ballistic missile warheads are individually scaled down from the maximal size that could be carried by a single-warhead missile.


title: Nuclear weapon yield

text: The following list is of milestone nuclear explosions. In addition to the atomic bombings of Hiroshima and Nagasaki, the first nuclear test of a given weapon type for a country is included, as well as tests that were otherwise notable (such as the largest test ever). All yields (explosive power) are given in their estimated energy equivalents in kilotons of TNT (see TNT equivalent). Putative tests (like Vela Incident) have not been included.


title: Nuclear weapon yield

text: Yields of nuclear explosions can be very hard to calculate, even using numbers as rough as in the kilotonne or megatonne range (much less down to the resolution of individual terajoules). Even under very controlled conditions, precise yields can be very hard to determine, and for less controlled conditions the margins of error can be quite large. For fission devices, the most precise yield value is found from "radiochemical/Fallout analysis"; that is, measuring the quantity of fission products generated, in much the same way as the chemical yield in chemical reaction products can be measured after a chemical reaction. The radiochemical analysis method was pioneered by Herbert L. Anderson.


title: Nuclear weapon yield

text: For nuclear explosive devices where the fallout is not attainable or would be misleading, neutron activation analysis is often employed as the second most accurate method, with it having been used to determine the yield of both Little Boy and thermonuclear Ivy Mike's respective yields.


title: Nuclear weapon yield

text: Yields can also be inferred in a number of other remote sensing ways, including scaling law calculations based on blast size, infrasound, fireball brightness (Bhangmeter), seismographic data (CTBTO), and the strength of the shock wave.


title: Nuclear weapon yield

text: Enrico Fermi famously made a (very) rough calculation of the yield of the Trinity test by dropping small pieces of paper in the air and measuring how far they were moved by the blast wave of the explosion; that is, he found the blast pressure at his distance from the detonation in pounds per square inch, using the deviation of the papers' fall away from the vertical as a crude blast gauge/barograph, and then with pressure "X" in psi, at distance "Y", in miles figures, he extrapolated backwards to estimate the yield of the Trinity device, which he found was about 10 kilotonnes of blast energy.


title: Nuclear weapon yield

text: The blast wave, however, was likely assumed to grow out as the surface area of the approximately hemispheric near surface burst blast wave of the Trinity gadget.


title: Nuclear weapon yield

text: The paper is moved 2.5 meters by the wave, so the effect of the Trinity device is to displace a hemispherical shell of air of volume 2.5 m × 2π(16 km). Multiply by 1 atm to get an energy of ~ 100 kT TNT.


title: Nuclear weapon yield

text: A good approximation of the yield of the Trinity test device was obtained in 1950 by the British physicist G. I. Taylor from simple dimensional analysis and an estimation of the heat capacity for very hot air. Taylor had initially done this highly classified work in mid-1941 and published an article with an analysis of the Trinity data fireball when the Trinity photograph data was declassified in 1950 (after the USSR had exploded its own version of this bomb).


title: Nuclear weapon yield

text: Taylor noted that the radius "R" of the blast should initially depend only on the energy "E" of the explosion, the time "t" after the detonation, and the density ρ of the air. The only equation having compatible dimensions that can be constructed from these quantities is


title: Nuclear weapon yield

text: Here "S" is a dimensionless constant having a value approximately equal to 1, since it is low-order function of the heat capacity ratio or adiabatic index


title: Nuclear weapon yield

text: Using the picture of the Trinity test shown here (which had been publicly released by the U.S. government and published in "Life" magazine), using successive frames of the explosion, Taylor found that "R"/"t" is a constant in a given nuclear blast (especially between 0.38 ms, after the shock wave has formed, and 1.93 ms, before significant energy is lost by thermal radiation). Furthermore, he estimated a value for "S" numerically at 1.


title: Nuclear weapon yield

text: Thus, with "t" = 0.025 s and the blast radius being 140 metres, and taking "ρ" to be 1 kg/m (the measured value at Trinity on the day of the test, as opposed to sea-level values of approximately 1.3 kg/m) and solving for "E", Taylor obtained that the yield was about 22 kilotonnes of TNT (90 TJ). This does not take into account the fact that the energy should only be about half this value for a hemispherical blast, but this very simple argument did agree to within 10% with the official value of the bomb's yield in 1950, which was (see G. I. Taylor, "Proc. Roy. Soc. London A" 200, pp. 235–247 (1950)).


title: Nuclear weapon yield

text: The value of the heat capacity ratio here is between the 1.67 of fully dissociated air molecules and the lower value for very hot diatomic air (1.2), and under conditions of an atomic fireball is (coincidentally) close to the STP (standard) gamma for room-temperature air, which is 1.4. This gives the value of Taylor's S constant to be 1.036 for the adiabatic hypershock region where the constant "R"/"t" condition holds.


title: Nuclear weapon yield

text: As it relates to fundamental dimensional analysis, if one expresses all the variables in terms of mass "M", length "L", and time "T":


title: Nuclear weapon yield

text: and then derive an expression for, say, "E", in terms of the other variables, by finding values of formula_12, formula_13, and formula_5 in the general relation


title: Nuclear weapon yield

text: such that the left and right sides are dimensionally balanced in terms of "M", "L", and "T" (i.e., each dimension has the same exponent on both sides).


title: Nuclear weapon yield

text: Where these data are not available, as in a number of cases, precise yields have been in dispute, especially when they are tied to questions of politics. The weapons used in the atomic bombings of Hiroshima and Nagasaki, for example, were highly individual and very idiosyncratic designs, and gauging their yield retrospectively has been quite difficult. The Hiroshima bomb, "Little Boy", is estimated to have been between (a 20% margin of error), while the Nagasaki bomb, "Fat Man", is estimated to be between (a 10% margin of error).


title: Nuclear weapon yield

text: Such apparently small changes in values can be important when trying to use the data from these bombings as reflective of how other bombs would behave in combat, and also result in differing assessments of how many "Hiroshima bombs" other weapons are equivalent to (for example, the Ivy Mike hydrogen bomb was equivalent to either 867 or 578 Hiroshima weapons — a rhetorically quite substantial difference — depending on whether one uses the high or low figure for the calculation).


title: Nuclear weapon yield

text: Other disputed yields have included the massive Tsar Bomba, whose yield was claimed between being "only" or at a maximum of by differing political figures, either as a way for hyping the power of the bomb or as an attempt to undercut it.


title: Andy Bernard

text: Andrew Baines Bernard is a fictional character from the NBC comedy television series "The Office", portrayed by Ed Helms. He is introduced in Season 3 as the Regional Director in Charge of Sales at the Stamford branch of paper distribution company, Dunder Mifflin when Jim Halpert transfers there. Ultimately, the Stamford branch merges with the Scranton branch later in the season. He became Regional Manager at the Scranton branch, courtesy of Robert California, in the eighth season following the departure of Michael Scott, although he is temporarily fired and replaced by Nellie Bertram before his reinstatement by new CEO David Wallace. Throughout the ninth season, Andy's relationship with Wallace deteriorates from Andy's lack of focus and professionalism, eventually culminating in Andy being fired by Wallace.


title: Andy Bernard

text: Andy has no counterpart in the original British version of the series. However, from season eight onwards, some of his traits (such as his position as the Regional Manager, his ineptitude in management, his increasingly deteriorating relationships with his now-subordinates, and his failed attempt at a career in entertainment after being fired) are reminiscent of David Brent, the British counterpart of Michael Scott.


title: Andy Bernard

text: Although Helms received praise for his performance, the character received a mixed reception. Andy was named one of the most annoying TV characters of 2011 by "Vulture." In contrast, "Nerve" ranked him the second funniest character on the series, behind only Michael Scott. Andy's characterization in the show's final season was subject to poor critical reception; Alan Sepinwall of Uproxx described Andy's personality as a "malevolent version of Michael Scott", while Erik Adams of "The A.V. Club" wrote "no amount of last-minute humanizing can win the audience back to [Andy's] side."


title: Andy Bernard

text: Andy is introduced in the season 3 premiere as the Regional Director in Charge of Sales at the Stamford branch, where Jim had transferred to. Following the closure of the Stamford branch and the merger with Scranton, Andy attempts to gain favor with the manager Michael Scott, and has a brief rivalry with co-worker Dwight Schrute. Though Michael initially takes a liking to Andy, he soon becomes agitated at Andy's sycophantic attitude and poor salesmanship. When Andy's behavior begins to irritate the office staff, Jim plays a prank on Andy by hiding his mobile phone in the ceiling and repeatedly calling it; the phone's ringtone is Andy's rendition of "Rockin' Robin". Andy becomes increasingly agitated each time the phone rings, and eventually punches a hole in the office wall out of frustration. Andy is subsequently sent to anger management by corporate.


title: Andy Bernard

text: Andy returns from anger management a few months later and accompanies Jim to meet with clients from a local high school; Andy unexpectedly runs into his girlfriend at the school and is horrified to discover she is a high school student. At the Beach Games, Andy captains a team alongside Jim, Dwight and Stanley Hudson in a competition for Michael's selection of the next Regional Manager of the Scranton branch, as Michael believes he is a shoo-in for a position at corporate. However, he falls plight to the sabotage of Angela Martin, who favors Dwight. When Dwight is pre-emptively named Regional Manager by Michael (who is confident that he will receive the promotion), Andy is named Assistant Regional Manager. However, this never comes to fruition, as Michael does not receive the corporate promotion.


title: Andy Bernard

text: With the departure of Karen Filippelli, Andy becomes the only salesman from Stamford aside from Jim to stay at the Scranton branch. He develops a friendship with Dwight and also develops a relationship with Angela, unaware of Dwight and Angela's previous romantic interludes. He steals an elaborate ice sculpture for Angela's launch party and serenades her with a rendition of the ABBA song "Take a Chance on Me", receiving a rare, yet quickly suppressed smile in return. He finally wins Angela over by gifting her a cat and a sentimental note. Angela and Andy's relationship sends Dwight spiraling into crushing depression, and rekindles his dislike for Andy.


title: Andy Bernard

text: In "Goodbye, Toby", Andy proposes to Angela (unbeknownst to him, at the same moment Jim had been preparing to propose to Pam) with a ring that he has carried in his wallet for six years. Angela accepts his proposal with an irritated "Okay". Shortly after the proposal, however, Angela has sex with Dwight in the office, which is witnessed by Phyllis and the camera crew.


title: Andy Bernard

text: Unaware of Angela and Dwight's affair, Andy plans his wedding with Angela although his ideas are often rejected by her. Angela eventually manipulates Andy into having the wedding take place at Dwight's farm. During the office Christmas party, Phyllis reveals Angela and Dwight's affair to the staff; however, the office staff neglect to inform Andy, which leads Michael to tell Andy the truth. Angela reluctantly confirms the affair occurred, though she tells Andy that she loves him. Andy later confronts Dwight and challenges him to a duel. They meet out in the parking lot, where Dwight realizes that Angela has had sex with Andy as well, despite telling Dwight that she had only been sleeping with him. Realizing that they have both been lied to, Andy cancels his wedding cake, and Dwight throws out the bobblehead in his likeness, implying the men's relationships with Angela are now over.


title: Andy Bernard

text: Despite ending his relationship with Angela, her affair with Dwight and the broken engagement affects Andy's perspective on relationships. When Kevin seeks dating advice from others in the office, Andy gives him romantic advice that appears to reflect his own experiences with Angela, telling him to never give compliments, push for physical contact, or be assertive to the point of rudeness. In "Heavy Competition", Andy offers bargain deals for Jim and Pam's wedding. However, he mistakes Pam's rejection of Jim's ideas as Pam controlling him. Andy assumes the role of Jim's emotional rock, which Jim goes along with as a prank. After realizing Jim is messing with him, Andy confronts him; Jim tells Andy that he is very happy with Pam, and while Andy's breakup with Angela was "a bummer", he assures Andy that he will find someone else in the future.


title: Andy Bernard

text: Andy develops a friendship and an attraction to Erin, who is the new office secretary. However, the pair are both too timid to reveal their feelings for one another. In "Secret Santa", Andy requests to be Erin's Secret Santa and proceeds to give Erin gifts resembling the Twelve Days of Christmas. To complete his Secret Santa gift, Andy hires 12 professional drummers to perform for Erin and the rest of the staff in the parking lot; Erin is visibly pleased by the gesture. In "The Delivery," Michael arranges a date between Erin and Kevin; this incites Andy to finally ask Erin out, which she accepts.


title: Andy Bernard

text: In "Secretary's Day", Andy wants to ensure that Erin has a memorable Secretary's Day, and asks a reluctant Michael to treat Erin out to lunch. During lunch, Michael reveals that Andy was engaged to Angela, a fact that Andy had concealed from Erin to Michael's surprise. Returning to the office, Erin enters the main party, throws cake in Andy's face, and reveals her knowledge about his previous engagement with Angela. Deciding she cannot trust Andy, Erin breaks up with him, which leaves Andy distraught.


title: Andy Bernard

text: During "The Cover-Up", Andy receives a call from a client claiming that their Sabre printer caught fire during a routine operation. In order to confirm his suspicions, Andy investigates and discovers that the Sabre printer indeed catches fire; he manages to record the incident on video. When the press gets word of the Sabre printers catching fire, the company's CEO Jo Bennett (Kathy Bates) goes out of her way to find the culprit. Andy initially denies sending the video, but eventually comes clean, admitting to submitting a letter and the video to a news editor. Though Andy is harassed by the sales staff over the report, he is commended by Erin for his bravery, leaving him pleased.


title: Andy Bernard

text: In Season 7, Erin begins a romantic relationship with Gabe, devastating Andy. However, as the season continues, Erin gradually begins to lose interest in Gabe, eventually confiding in Michael that she may be in love with Andy again. After Erin publicly breaks up with Gabe in front of the staff, Gabe becomes venomously angry toward Andy, wrongly believing Andy had triggered Erin's brutal public breakup with him. In "Dwight K. Schrute, (Acting) Manager", Gabe breaks down and, crying, makes Andy promise not to date Erin, to which an uncomfortable Andy agrees. However, when Gabe tells Erin what Andy said about them not dating, Andy shuts Gabe up by pointing out Gabe's crying fit to Erin.


title: Andy Bernard

text: In "Search Committee", Andy interviews to replace Michael's initial replacement, Deangelo, as the regional manager, which Gabe tries to sabotage. However, Andy remains a managerial candidate once Gabe's behavior gets him transferred out of Scranton. Erin asks Andy out on a date, and he eventually refuses, claiming that he has gotten over her. However, Andy later tells the camera that he thinks Erin is great.


title: Andy Bernard

text: Robert California, selected by the search committee, declines to become Branch Manager and convinces Jo Bennett to give him her position as CEO, thus giving Robert the authority to appoint Andy as the new manager. Upon discovering a list that divides the office into winners and losers, and being moved into the loser section after questioning Robert about it, he retaliates by hosting a pizza party for the losers and publicly confronts Robert about the positive attributes of the losers. This act earns the respect of Robert and the office. Robert eventually reveals that Andy's selection as the Regional Manager was done because he's a "simple underdog whom people will rally behind."


title: Andy Bernard

text: In "The Incentive", Robert California urges the doubling of sales growth, which Andy attempts to fulfill with an incentive program. This program spirals out of control when Andy offers a tattoo on his posterior as one of the prizes, worth 5,000 points. In comedic fashion, the office pools their points and succeeds in winning this prize. Andy bravely steps up, only for the office to change the originally more-raunchy tattoo design to one that honors Andy's nickname of "The Nard Dog."


title: Andy Bernard

text: During "Garden Party", Andy throws a garden party to impress Robert with his parents Walter Sr. (Stephen Collins), Ellen (Dee Wallace), and younger brother Walter, Jr. (Josh Groban) in attendance. However, Andy is also trying to prove himself to his parents, who were under the impression that he was the CEO of the company. Andy goes to great lengths to try and impress his parents, which leads Walter, Sr. to later speak with Andy. He insults Andy's job and states Andy needs to stop seeking his approval like a little kid. This conversation is overheard by some of the office staff, prompting everyone to understand why Andy feels the need to get everyone to like him. Following the garden party, a dejected Andy plans to head home himself, but Darryl and Oscar decide to cheer him up with an impromptu barbecue.


title: Andy Bernard

text: In "Christmas Wishes", Andy introduces his new girlfriend Jessica to the office staff, much to the chagrin of Erin. During the office Christmas party, Erin drunkenly tells Andy that her Christmas wish is for Jessica to die, offending and angering Andy. He tells Erin to get over the fact that he turned her down for a date and storms off. Later, during the party, Andy becomes concerned when Erin gets a ride home from Robert. While driving Meredith home, Andy follows Robert to Erin's apartment, but to his relief, he sees Robert hug Erin goodbye with comforting words and instructs her to take care of her hangover.


title: Andy Bernard

text: Seemingly despondent over his impending divorce, Robert hosts an impromptu "Pool Party" at his soon-to-be-sold mansion. The staff attends with Andy and Jessica, much to Erin's consternation. Andy carries around his parents' engagement ring, claiming that his parents fell in love with Jessica. Desperate for Andy's attention, Erin and Dwight engage in a series of competitive pool games with Andy and Jessica. Later on, Andy accidentally loses the ring and frantically searches for it; Erin recovers the ring in the pool and gives it to Andy, knowing the history behind the ring. Andy confides to Erin that he's confused about his relationship with Jessica, which gives Erin hope.


title: Andy Bernard

text: In "Last Day in Florida", Andy learns that Erin isn't coming back to Scranton and realizes he still loves her. He decides to go to Florida to win her back. The two get back together, and Andy breaks up with Jessica. Returning to Scranton, Andy discovers that Nellie Bertram, one of the initial interviewees for Regional Manager, has claimed Andy's manager position at Scranton, with Andy subsequently demoted to a salesman. In a deliberate callback to his outburst in Season 3, Andy punches a hole in the office wall and gets fired from Dunder Mifflin.


title: Andy Bernard

text: In "Turf War", Andy manages to win a major client and uses it as leverage to get David Wallace to purchase Dunder Mifflin. He also calls Robert and threatens to get him fired if David buys the company. Wallace ultimately buys back Dunder Mifflin, fires Nellie and Robert, and reinstates Andy as manager. While Andy is reinstated, Robert swindles his way into getting a million dollars from David, while Andy hires Nellie out of guilt and sorrow.


title: Andy Bernard

text: In the season premiere, it is revealed that Andy was sent to Outward Bound manager training by David Wallace, which caused him to revert to his previous cockier and meaner persona. Wanting revenge on Nellie, he continues to torment her. When she needs an employer's signature to verify her employment at an adoption agency, he refuses in front of the entire office, upsetting her and Erin. Andy later finds Erin crying after this, which prompts him to sign Nellie's papers.


title: Andy Bernard

text: Andy discovers his father has abandoned their family, leaving them nearly penniless. He consults with Oscar and Darryl to sell enough family assets for his mother to live. They urge Andy to sell their family boat, which Andy had always wanted to drive; Andy relents and sells it to a dealer in the Bahamas. After he and Erin drive to Connecticut to see off the boat themselves, Andy discovers Walter Jr. disheveled and hung over in one of the cabins. Andy decides to sail the boat to the Bahamas himself with Walter Jr., leaving Erin behind. Though grateful to Erin for cheering him up, he doesn't notice how hurt she is at being left behind. Upon arriving in the Bahamas, Andy decides to stay for several more weeks. This upsets Erin greatly and causes her to become closer to her friend and co-worker Pete Miller.


title: Andy Bernard

text: After three months, Andy returns from the Bahamas and immediately alienates the staff with his behavior: ignorantly expecting the staff to take him seriously as if he never left, voiding a major sale that Dwight had with Jan Levinson, and shamelessly collecting his paychecks plus the "merit bonus" he acquired for the staff excelling their sales quota. He holds a meeting with the staff to catch up on what he missed, so as to meet with David Wallace, who has been under the impression that Andy has been at the office the entire time via phone calls and e-mails. Andy ultimately manages to get through the meeting without repercussions. Erin, feeling neglected by Andy, dumps Andy for mistreating her and for leaving her alone for three months; the conversation is heard by David Wallace on speakerphone.


title: Andy Bernard

text: Distraught over their breakup, Andy's professional relationship with Erin and the rest of the staff worsens. Wallace chastises Andy but allows him to keep his job. After discovering that Pete is dating Erin, Andy impulsively fires Pete, but Toby tells Andy that he can't fire Pete over a personal grudge. When Erin and Pete lecture Andy, telling him that he needs to move on, Andy decides to hire their exes at the branch, in a bid to make Erin and Pete uncomfortable. The ploy works, and Erin and Pete's past relationship issues surface. Andy smugly states that seeing Erin and Pete unhappy has made him feel better.


title: Andy Bernard

text: As promos start to circulate for the documentary series about the branch, Andy comes to realize that he's disillusioned about his job, and meets with real estate/talent agent Carla Fern (Roseanne Barr), who takes Andy on as a client. Andy pays her $5,000 to sign with her agency, and he books his first job in an industrial film about a chemical lab. Inspired to finally follow his dreams, Andy takes drastic measures to get fired, including initiating an ugly argument with David Wallace. Irritated by Andy's actions, David becomes enraged and fires Andy; Andy returns to the office to say goodbye, and performs a moving rendition of Sarah McLachlan's song "I Will Remember You". Surprised by Andy's performance, the staff embrace Andy and say goodbye, convinced that he may have some talent after all. In "A.A.R.M.", Andy auditions for a singing reality TV show, but is asked to leave before his audition due to overcrowding. Enraged, Andy bursts into the audition room, demands the judges let him audition, and throws a crying tantrum.


title: Andy Bernard

text: In the series finale, Andy found a job at Cornell University's Admissions Office. The video of Andy's tantrum has become viral on YouTube, inspiring a parody on "Saturday Night Live". Andy's confidence and ease around everyone increase when he stunningly realizes that most of the crowd at the documentary reunion panel are not only there to see him, but are genuine fans of his portrayal on the show. Returning to the office after Dwight and Angela's wedding, Andy's former co-workers watch his Cornell speech and are unanimously impressed by it; Andy nearly breaks into tears as he tells the camera, "I wish there was a way to know you're in the good old days before you've actually left them".


title: Andy Bernard

text: In season 6, Andy takes an interest in receptionist Erin Hannon, who has mutual affection, but due to miscommunication, there was a long period where the two waited for each other to make a move. However, Andy eventually asks Erin out on a date, and she graciously accepts. Three weeks later, after Erin discovers, through Michael Scott, of Andy's former engagement to accountant Angela Martin, she throws cake in Andy's face and decides that they need to take a break from one another. Over a year later, Erin, after breaking up with Gabe Lewis, asks Andy out on a date, but he dismisses her advances, because of his lingering issues with her leaving him for Gabe. When Andy introduces his girlfriend Jessica to the Office at a Christmas party, Erin becomes drunk and confesses to Andy that she wishes Jessica was dead. Greatly offended, Andy informs Erin that she needs to get over their break-up, and briskly leaves. Upon learning that Erin wishes to live in Tallahassee, Florida, Andy drives to Tallahassee to get back together with Erin. At first, he is unsuccessful, but ultimately gets her back; they make up and kiss in the middle of the street. During season 9, their relationship starts to show cracks as Andy comes back from a training seminar that has made him more confident, but seemingly more selfish to Erin. When Andy takes his parents' boat to the Bahamas for three weeks, he leaves Erin behind, who looks on disappointed. Erin later goes out with Pete, a new co-worker for drinks. When Andy decides to stay in the Bahamas for three more months, Erin becomes increasingly unhappy, and finally breaks up with Andy upon his return. Later in the season, Andy's distraught behavior affects his professional relationship with Erin and the staff. When Andy learns of Erin's relationship with Pete, he acts irrationally to where Erin and Pete lecture him that he needs to move on. In the episode Livin' the Dream, Andy and Erin are seen speaking pleasantly to each other; Erin admits her concern for Andy's well-being, saying she's worried he'll "be homeless or even starve." During Andy's goodbye song, Erin stares at Andy with a serious look of affection, making it unclear whether or not the two still have romantic feelings for each other. In the series finale, Andy, Erin, and Pete are all shown to be getting along well at the after-party, indicating the tensions from earlier have eased.


title: Andy Bernard

text: In the fourth season, Andy begins a relationship with accountant Angela Martin, who half-heartedly began dating him on the rebound, after she had broken up with Dwight Schrute (whose relationship with her had been unknown to the majority of the staff). After dating for about seven months, Andy proposes to Angela during Toby Flenderson's farewell party, and she begrudgingly accepts. However, during their engagement, she resumes her affair with Dwight. Andy endures tremendous effort in order to prepare for Angela's dream wedding. Upon learning about the affair, both he and Dwight break up with her, and Andy is initially crushed. When Andy is leaving the office for good after he quits to seek fame, Angela tries to talk him out of it. Andy wrongly assumes she regrets ending their relationship, and says he does think about her often, but Angela is able to choke back her disgust and they part ways with a hug.


title: Andy Bernard

text: After transferring to the Scranton branch, Andy has a strategy to become the number two of the branch by name repetition, personality mirroring, and never breaking off a handshake first; Michael immediately likes him. In "Traveling Salesmen", Andy picks Michael as his traveling salesman partner, and during the car ride, Michael tells Andy about Dwight going behind his back and talking to Jan. When they do their joint sale pitch, Andy ruins the pitch, infuriating Michael. Andy finds the toll booth receipt that shows Dwight went to New York, and suggests that he wanted to talk with Jan again, resulting in Michael confronting Dwight; Dwight quits Dunder Muffin. In "The Return", Michael talks to Jim about Andy; Jim tells Michael that Andy is a yes man, and did the same thing with his old boss, Josh, at the Stamford branch. After Angela tells Michael why Dwight went to New York, Michael decides to leave the office to get Dwight back. Andy tries to come with him and begins telling Michael about his weekend plans for the two of them. Finally, Michael tells him to stop, realizing he made a mistake trying to replace Dwight with Andy. Following Andy's return from anger management, Michael gives him a second chance, naming him a team captain for the beach games competition and considering him as a potential replacement. For the remainder of the series, Michael is on good terms with Andy, and when Michael leaves Dunder Mifflin for Colorado, he gifts Andy all of his clients as a way of motivating him. Although he initially loses one of those clients, Andy's ability to maintain a relationship with the others greatly boosts his confidence.


title: Andy Bernard

text: Since Andy's arrival, he and Dwight had a competitive professional relationship, and the two eventually duel over Angela when it is found she is cheating on Andy with Dwight. After the fight, both relationships end, and Angela is left heartbroken and alone. A few months later, the two soon begin competing for Erin's attention, but Dwight ultimately decides to cease pursuing her in order to maintain a good relationship with Andy. However, after Andy is hired as Regional Manager, Andy makes Dwight his "Enforcer" in order to stay on good terms, but Dwight later states in an interview that he will "wait for Andy's inevitable demise". During "Couples Discount", Dwight is unable to get Andy's sign-off on prices with a major sale that Dwight landed, although when Andy suddenly reappears, he chastises Dwight for not having his approval on the prices. When Dwight informs him that Andy was on a boat and unreachable, Andy tries again to maintain his authority. This backfires when Andy decides to renege on the prices with Dwight's client, thus voiding a major sale for the company and wrecking Dwight's sales record. Dwight later tells false stories to Andy when Andy asks for an update on the branch, in hopes of sabotaging Andy. When Dwight learns he's in line to become the permanent branch manager and Andy asks if his plan to quit and seek stardom is a good idea, Dwight kindly but firmly tells Andy that he should not quit, even if this denies Dwight his dream job. In the series finale, Andy returns to Scranton to attend Dwight and Angela's wedding.


title: Andy Bernard

text: Andy was the subject of many pranks by Jim and Pam, some of which have caused his anger issues to unfold. Andy also had a romantic interest in Pam, but due to intentionally misleading advice given to him by Jim, it did not develop into a relationship. Although the two will, at times, act considerably mean to Andy, Jim and Pam are often pleasant to him, and even give him advice when he needs it. When Andy goes through a rough breakup, he gives Jim wildly bad advice when he suspects Pam of controlling him. However, Jim uses it as an opportunity to prank Andy throughout the day before he sees through the ruse, prompting Jim to comfort him about finding someone else.


title: Andy Bernard

text: Initially, Darryl and Andy were foes. Darryl states that Andy once used him as a scapegoat, nearly getting him fired from his job, for a mistake that Andy had made. Andy also attempts to order Darryl around when Sabre's "Sales is King" policy greatly affects the sales staffs' egos. However, over time, the two develop a strong friendship. When Darryl confides in Andy that he wished he had remained a member of the warehouse staff, Andy convinces him to make the most of his position and continue rising in the company. When Darryl is depressed over not winning a lottery that the warehouse staff won and shared, he demands that Andy either terminate him or give him the Manager position. Andy is blunt, but kind, as he informs Darryl the truth about his shortcomings, and Darryl subsequently rededicates himself to his job. When he meets Andy's family, Darryl overhears Andy's father berate him over his status in life, and finally understands why Andy needs to please others, and later participates in cheering Andy up, along with the rest of the staff. Darryl is also one of the few people in the office, along with Jim, Pam and Erin, who did not accept Nellie Bertram's attempt at usurping Andy's job. Darryl is not impressed with Andy's acting ability, to the point of bluntly saying Andy needs to have a job that will tolerate his inevitable and chronic mistakes. In the series finale, Darryl initially avoids Andy, but impressed with Andy's speech at Cornell, he gives Andy a hug.


title: Andy Bernard

text: While initially having a neutral relationship with Gabe, Andy develops a dislike for Gabe when he begins dating Erin. After Erin breaks up with Gabe, a heartbroken and jealous Gabe begins to heavily resent Andy, and threatens him not to make any advances on Erin. When Andy interviews for the Regional Manager position, Gabe displays a negative, biased opinion of him. Later, he unsuccessfully attempts to convince the CEO of Sabre, Jo Bennett, not to hire Andy as Manager. For the next year (until Gabe is written out), Andy and Gabe are generally rivals, often making snide remarks to one another. After Erin breaks up with Andy, Andy briefly hires Gabe to make Erin feel uncomfortable.


title: Andy Bernard

text: After becoming the new CEO of Sabre, Robert California appointed Andy as Regional Manager of the Scranton branch. Since then, Andy has developed an awkward relationship with Robert, who he is eager to impress, and highly intimidated by. Robert states that the reason he chose Andy for the Manager position is because he is "All surface... Uncomplicated, what you see is what you get". Andy and Robert's contentious relationship climaxes when Robert allows Nellie Bertram to usurp Andy's Regional Manager position, and Andy is fired for refusing to accept Nellie as manager, only able to reclaim his managerial role by convincing David Wallace to purchase Dunder Mifflin away from Sabre and Robert.


title: Andy Bernard

text: The character is named after American economist Andrew Bernard, professor of international economics at the Tuck School of Business at Dartmouth College. While Andy was initially meant as a temporary character in season 3 of "The Office", the character "grew" on Greg Daniels and the writers, and they decided to have Andy return to the office from anger management and become a permanent character.


title: Andy Bernard

text: Initially considered an abrasive addition to the show, Andy Bernard later became a fan favorite due to his character development throughout the series. Fans did not enjoy his arc in the final season, which saw Andy revert to his worst tendencies in his early seasons and treat his coworkers poorly, with some commentators wondering if the show's writers "did not know what to do" with the character.


title: Special drawing rights

text: Special drawing rights (SDRs, code ) are supplementary foreign exchange reserve assets defined and maintained by the International Monetary Fund (IMF). SDRs are units of account for the IMF, and not a currency "per se". They represent a claim to currency held by IMF member countries for which they may be exchanged. SDRs were created in 1969 to supplement a shortfall of preferred foreign exchange reserve assets, namely gold and U.S. dollars. The ISO 4217 currency code for special drawing rights is and the numeric code is "960".


title: Special drawing rights

text: SDRs are allocated by the IMF to countries, and cannot be held or used by private parties. The number of SDRs in existence was around XDR 21.4 billion in August 2009. During the global financial crisis of 2009, an additional XDR 182.6 billion was allocated to "provide liquidity to the global economic system and supplement member countries' official reserves". By October 2014, the number of SDRs in existence was XDR 204 billion. Due to economic stress caused by the COVID-19 pandemic some economists and several finance ministers of poorer countries have called for a new allocation of $4T to support member economies as they seek ways to recover. In March 2021 the G24 and others proposed an allocation of $500B for this purpose. In response, XDR 456.5 billion (about US$650B) was allocated on August 23, 2021.


title: Special drawing rights

text: The value of a SDR is based on a basket of key international currencies reviewed by IMF every five years. The weights assigned to each currency in the XDR basket are adjusted to take into account their current prominence in terms of international trade and national foreign exchange reserves. Currently, the XDR basket consists of the following five currencies: U.S. dollar 43.38%, euro 29.31%, renminbi (Chinese yuan) 12.28%, Japanese yen 7.59%, British pound sterling 7.44%.


title: Special drawing rights

text: While the ISO 4217 currency code for special drawing rights is XDR, they are often referred to by their acronym SDR. Both refer to the name "special drawing rights".


title: Special drawing rights

text: Intentionally innocuous and free of connotations because of disagreements over the nature of this new reserve asset during its creation, the name derives from a debate about its primary function—money or credit. While the name would offend neither side, it can be argued that prior to 1981 the XDR was a debt security and so a form of credit. Member countries receiving XDR allocations were required by the reconstitution provision of the XDR articles to hold a prescribed number of XDRs. If a state used any of its allotment, it was expected to rebuild its XDR holdings. As the reconstitution provisions were abrogated in 1981, the XDR now functions less like credit than previously. Countries are still expected to maintain their XDR holdings at a certain level, but penalties for holding fewer than the allocated amount are now less onerous.


title: Special drawing rights

text: The name may actually derive from an early proposal for IMF "reserve drawing rights". The word "reserve" was later replaced with "special" because the idea that the IMF was creating a foreign exchange reserve asset was contentious.


title: Special drawing rights

text: Special drawing rights were created by the IMF in 1969 and were intended to be an asset held in foreign exchange reserves under the Bretton Woods system of fixed exchange rates. After the collapse of that system in the early 1970s, the XDR has taken on a less important role. Acting as the unit of account for the IMF has been its primary purpose since 1972.


title: Special drawing rights

text: The IMF itself calls the current role of the XDR "insignificant". Developed countries, who hold the greatest number of XDRs, are unlikely to use them for any purpose. The only actual users of XDRs may be those developing countries that see them as "a rather cheap line of credit".


title: Special drawing rights

text: One reason XDRs may not see much use as foreign exchange reserve assets is that they must be exchanged into a currency before use. This is due in part to the fact private parties do not hold XDRs: they are only used and held by IMF member countries, the IMF itself, and a select few organizations licensed to do so by the IMF. Basic functions of foreign exchange reserves, such as market intervention and liquidity provision, as well as some less prosaic ones, such as maintaining export competitiveness via favorable exchange rates, cannot be accomplished directly using XDRs. This fact has led the IMF to label the XDR as an "imperfect reserve asset".


title: Special drawing rights

text: Another reason they may see little use is that the number of XDRs in existence is relatively few. As of January 2011, XDRs represented less than 4% of global foreign exchange reserve assets. To function well a foreign exchange reserve asset must have sufficient liquidity, but XDRs, because of their small number, may be perceived to be an illiquid asset. The IMF says, "expanding the volume of official XDRs is a prerequisite for them to play a more meaningful role as a substitute reserve asset."


title: Special drawing rights

text: The XDR comes to prominence when the U.S. dollar is weak or otherwise unsuitable to be a foreign exchange reserve asset. This usually manifests itself as an allocation of XDRs to IMF member countries. Distrust of the U.S. dollar is not the only stated reason allocations have been made, however. One of its first roles was to alleviate an expected shortfall of U.S. dollars . At this time, the United States had a conservative monetary policy and did not want to increase the total amount of U.S. dollars in existence. If the United States had continued down this path, the dollar would have become a less attractive foreign exchange reserve asset: it would not have had the necessary liquidity to serve this function. Soon after XDR allocations began, the United States reversed its former policy and provided sufficient liquidity. In the process a potential role for the XDR was removed. During this first round of allocations, 9.3 billion XDRs were distributed to IMF member countries.


title: Special drawing rights

text: The XDR resurfaced in 1978 when many countries were wary of taking on more foreign exchange reserve assets denominated in U.S. dollars. This suspicion of the dollar precipitated an allocation of 12 billion XDRs over a period of four years.


title: Special drawing rights

text: Concomitant with the financial crisis of 2007–08, the third round of XDR allocations occurred in the years 2009 and 2011. The IMF recognized the financial crisis as the cause for distributing the large majority of these third-round allotments, but some allocations were couched as distributing XDRs to countries that had never received any and others as a re-balancing of IMF quotas, which determine how many XDRs a country is allotted, to better represent the economic strength of emerging markets.


title: Special drawing rights

text: During this time China, a country with large holdings of U.S. dollar foreign exchange reserves, voiced its displeasure at the current international monetary system, and promoted measures that would allow the XDR to "fully satisfy the member countries' demand for a reserve currency." These comments, made by a chairman of the People's Bank of China, Zhou Xiaochuan, drew media attention, and the IMF showed some support for China's stance. It produced a paper exploring ways the substance and function of the XDR could be increased. China has also suggested the creation of a substitution account to allow exchange of U.S. dollars into XDRs. When substitution was proposed before, in 1978, the United States appeared reluctant to allow such a mechanism to become operational.


title: Special drawing rights

text: In 2001, the UN suggested allocating XDRs to developing countries for use by them as cost-free alternatives to building foreign exchange reserves through borrowing or running current account surpluses. In 2009, an XDR allocation was made to countries that had joined the IMF after the 1979–1981 round of allocations was complete (and so had never been allocated any). First proposed in 1997, many of the beneficiaries of this 2009 allocation were developing countries.


title: Special drawing rights

text: On August 23, 2021, the IMF allocated $650 billion worth of XDRs to all 190 members of the IMF in proportion to member quotas in response to COVID-19 related balance of payments concerns. This allocation of XDRs represents roughly 2/3rds of all XDRs currently in circulation, and was by far the largest ever single allocation of XDRs.


title: Special drawing rights

text: To determine the composition of the XDR, the IMF takes into account several currencies important to the world's trading and financial systems. A currency's importance is currently measured by two factors: the amount of exports sold in that currency, and whether that currency is considered "freely usable" (determined by its use as a foreign exchange reserve asset and how widely it is used in international transactions).


title: Special drawing rights

text: An XDR basket definition remains valid for five years. Approximately one to two months before the end of this time period, the IMF Executive Board will re-evaluate the XDR basket; the currencies included as well as their weights can then change. Changing the XDR's value definition requires at least 70% of the votes among the IMF members. The changes take effect at the end of the five-year period (one to two months after the board review). One business day before taking effect, the newly defined weights are converted to currency amounts based on an average of the exchange rate over the past three months, such that the value of the XDR in U.S. dollars remains the same before and after the change. The currency amounts then remain fixed throughout the five-year period.


title: Special drawing rights

text: The IMF reserves the right to perform a re-evaluation after less than five years if it decides that the current basket no longer reflects "the relative importance of currencies in the world’s trading and financial systems"; it also reserves the right to postpone re-evaluations. If either occurs (causing the old definition to be valid for less or more than five years), the new definition will still be valid for a full five years.


title: Special drawing rights

text: At the time of the XDR's creation in 1969, the United States dollar was backed by the gold standard and the XDR was fixed at 1/35 troy ounce of gold or exactly 1 US dollar. After the Nixon Shock of 1971 and during the collapse of the Bretton Woods system between 1971 and 1973, the XDR initially remained at 1 US dollar (even as its value relative to gold dropped to 1/38 troy ounce in 1972 and 1/42.22 troy ounce in 1973). On July 1, 1974, the XDR instead became defined by a currency basket of 16 currencies.


title: Special drawing rights

text: On January 1, 1981, the five-year schedule was introduced and the XDR basket was reduced to five currencies: the United States dollar, the Deutsche mark, the French franc, the British pound, and the Japanese yen. When the euro was introduced in January 1999, it replaced the German mark and French franc and the basket consisted of four currencies.


title: Special drawing rights

text: In November 2010, the IMF determined that the Chinese yuan met the export requirement but failed to meet the "freely usable" requirement and thus was not included in the XDR basket taking effect on January 1, 2011. In November 2015, the IMF announced that the Chinese yuan now met the "freely usable" requirement and would be included in the next basket definition, changing its size back to five currencies. The effective date of the re-evaluation was postponed to October 1, 2016, in order to "allow users sufficient lead time to adjust".


title: Special drawing rights

text: In March 2021, the IMF announced that the next re-evaluation, normally scheduled for October 1, 2021, would be postponed to August 1, 2022, in order to prevent the basket's definition from changing during the COVID-19 pandemic.


title: Special drawing rights

text: Because of fluctuating exchange rates, the relative value of each currency varies continuously, as does the value of the XDR. The IMF sets the value of the XDR in terms of U.S. dollars every day. The latest U.S. dollar valuation of the XDR is published on the IMF website. For example, on January 31, 2021, the value was US$1.44080, and on June 22, 2021, the value was US$1.426480.


title: Special drawing rights

text: SDRs are allocated to member countries by the IMF. A country's IMF quota, the maximum amount of financial resources that it is obligated to contribute to the fund, determines its allotment of XDRs. Any new allocations must be voted on in the XDR Department of the IMF and pass with an 85% majority. All IMF member countries are represented in the XDR Department, but this is not a one country, one vote system; voting power is determined by a member country's IMF quota. For example, the United States has 16.7% of the vote as of March 2, 2011.