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Algebraic closure

In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. It is one of many closures in mathematics.

Using Zorn's lemma or the weaker ultrafilter lemma,   it can be shown that every field has an algebraic closure, and that the algebraic closure of a field K is unique up to an isomorphism that fixes every member of K. Because of this essential uniqueness, we often speak of the algebraic closure of K, rather than an algebraic closure of K.

The algebraic closure of a field K can be thought of as the largest algebraic extension of K. To see this, note that if L is any algebraic extension of K, then the algebraic closure of L is also an algebraic closure of K, and so L is contained within the algebraic closure of K. The algebraic closure of K is also the smallest algebraically closed field containing K, because if M is any algebraically closed field containing K, then the elements of M that are algebraic over K form an algebraic closure of K.

The algebraic closure of a field K has the same cardinality as K if K is infinite, and is countably infinite if K is finite.

Examples

 * The fundamental theorem of algebra states that the algebraic closure of the field of real numbers is the field of complex numbers.
 * The algebraic closure of the field of rational numbers is the field of algebraic numbers.
 * There are many countable algebraically closed fields within the complex numbers, and strictly containing the field of algebraic numbers; these are the algebraic closures of transcendental extensions of the rational numbers, e.g. the algebraic closure of Q(π).
 * For a finite field of prime power order q, the algebraic closure is a countably infinite field that contains a copy of the field of order qn for each positive integer n (and is in fact the union of these copies).

Existence of an algebraic closure and splitting fields
Let $$S = \{ f_{\lambda} | \lambda \in \Lambda\}$$ be the set of all monic irreducible polynomials in K[x]. For each $$f_{\lambda} \in S$$, introduce new variables $$u_{\lambda,1},\ldots,u_{\lambda,d}$$ where $$d = {\rm degree}(f_{\lambda})$$. Let R be the polynomial ring over K generated by $$u_{\lambda,i}$$ for all $$\lambda \in \Lambda$$ and all $$i \leq {\rm degree}(f_{\lambda})$$. Write
 * $$f_{\lambda} - \prod_{i=1}^d (x-u_{\lambda,i}) = \sum_{j=0}^{d-1} r_{\lambda,j} \cdot x^j \in R[x]$$

with $$r_{\lambda,j} \in R$$. Let I be the ideal in R generated by the $$r_{\lambda,j}$$. Since I is strictly smaller than R, Zorn's lemma implies that there exists a maximal ideal M in R that contains I. The field K1=R/M has the property that every polynomial $$f_{\lambda}$$ with coefficients in K splits as the product of $$x-(u_{\lambda,i} + M),$$ and hence has all roots in K1. In the same way, an extension K2 of K1 can be constructed, etc. The union of all these extensions is the algebraic closure of K, because any polynomial with coefficients in this new field has its coefficients in some Kn with sufficiently large n, and then its roots are in Kn+1, and hence in the union itself.

It can be shown along the same lines that for any subset S of K[x], there exists a splitting field of S over K.

Separable closure
An algebraic closure Kalg of K contains a unique separable extension Ksep of K containing all (algebraic) separable extensions of K within Kalg. This subextension is called a separable closure of K. Since a separable extension of a separable extension is again separable, there are no finite separable extensions of Ksep, of degree > 1. Saying this another way, K is contained in a separably-closed algebraic extension field. It is unique (up to isomorphism).

The separable closure is the full algebraic closure if and only if K is a perfect field. For example, if K is a field of characteristic p and if X is transcendental over K, $$K(X)(\sqrt[p]{X}) \supset K(X)$$ is a non-separable algebraic field extension.

In general, the absolute Galois group of K is the Galois group of Ksep over K.

title: Algebraic closure


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Advanced Power Management

Advanced power management (APM) is a technical standard for power management developed by Intel and Microsoft and released in 1992 which enables an operating system running an IBM-compatible personal computer to work with the BIOS (part of the computer's firmware) to achieve power management.

Revision 1.2 was the last version of the APM specification, released in 1996. ACPI is the successor to APM. Microsoft dropped support for APM in Windows Vista. The Linux kernel still mostly supports APM, though support for APM CPU idle was dropped in version 3.0.

Overview
APM uses a layered approach to manage devices. APM-aware applications (which include device drivers) talk to an OS-specific APM driver. This driver communicates to the APM-aware BIOS, which controls the hardware. There is the ability to opt out of APM control on a device-by-device basis, which can be used if a driver wants to communicate directly with a hardware device.

Communication occurs both ways; power management events are sent from the BIOS to the APM driver, and the APM driver sends information and requests to the BIOS via function calls. In this way the APM driver is an intermediary between the BIOS and the operating system.

Power management happens in two ways; through the above-mentioned function calls from the APM driver to the BIOS requesting power state changes, and automatically based on device activity.

In APM 1.0 and APM 1.1, power management is almost fully controlled by the BIOS. In APM 1.2, the operating system can control PM time (e.g. suspend timeout).

Power management events
There are 12 power events (such as standby, suspend and resume requests, and low battery notifications), plus OEM-defined events, that can be sent from the APM BIOS to the operating system. The APM driver regularly polls for event change notifications.

Power Management Events:

APM functions
There are 21 APM function calls defined that the APM driver can use to query power management statuses, or request power state transitions. Example function calls include letting the BIOS know about current CPU usage (the BIOS may respond to such a call by placing the CPU in a low-power state, or returning it to its full-power state), retrieving the current power state of a device, or requesting a power state change.

Power states
The APM specification defines system power states and device power states.

System power states
APM defines five power states for the computer system:
 * Full On: The computer is powered on, and no devices are in a power saving mode.
 * APM Enabled: The computer is powered on, and APM is controlling device power management as needed.
 * APM Standby: Most devices are in their low-power state, the CPU is slowed or stopped, and the system state is saved. The computer can be returned to its former state quickly (in response to activity such as the user pressing a key on the keyboard).
 * APM Suspend: Most devices are powered off, but the system state is saved. The computer can be returned to its former state, but takes a relatively long time. (Hibernation is a special form of the APM Suspend state).
 * Off: The computer is turned off.

Device power states
APM also defines power states that APM-aware hardware can implement. There is no requirement that an APM-aware device implement all states.

The four states are:
 * Device On: The device is in full power mode.
 * Device Power Managed: The device is still powered on, but some functions may not be available, or may have reduced performance.
 * Device Low Power: The device is not working. Power is maintained so that the device may be 'woken up'.
 * Device Off: The device is powered off.

CPU
The CPU core (defined in APM as the CPU clock, cache, system bus and system timers) is treated specially in APM, as it is the last device to be powered down, and the first device to be powered back up. The CPU core is always controlled through the APM BIOS (there is no option to control it through a driver). Drivers can use APM function calls to notify the BIOS about CPU usage, but it is up to the BIOS to act on this information; a driver cannot directly tell the CPU to go into a power saving state.

ATA drives
The ATA specification and SATA specification defines APM provisions for hard drives, which specifies a trade-off between spin-down frequency and always-on performance. Unlike the BIOS-side APM, the ATA APM and SATA APM has never been deprecated.

Aggressive spin-down frequencies may reduce drive lifespan by unnecessarily accumulating load cycles; most modern drives are specified to sustain 300,000 cycles and usually last at least 600,000. On the other hand, not spinning down the drive will cause extra power draw and heat generation; high temperatures also reduce the lifespan of hard drives.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Advanced Power Management


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Adolphe Sax

Antoine-Joseph "Adolphe" Sax (6 November 1814 – 7 February 1894) was a Belgian inventor and musician who invented the saxophone in the early 1840s, patenting it in 1846. He also invented the saxotromba, saxhorn and saxtuba, and redesigned the bass clarinet in a fashion still used to the present day. He played the flute and clarinet.

Early life
Antoine-Joseph Sax was born on 6 November 1814 in Dinant, in what is now Belgium, to Charles-Joseph Sax and his wife Marie-Joseph (Masson). While his given name was Antoine-Joseph, he was referred to as Adolphe from childhood. His father and mother were instrument designers themselves, who made several changes to the design of the French horn. Adolphe began to make his own instruments at an early age, entering two of his flutes and a clarinet into a competition at the age of 15. He subsequently studied performance on those two instruments as well as voice at the Royal Conservatory of Brussels.

Sax faced many brushes with death. As a child, he once fell from a height of three floors, hit his head on a stone and was believed dead. At the age of three, he drank a bowl full of acidic water, mistaking it for milk, and later swallowed a pin. He received serious burns from a gunpowder explosion and once fell onto a hot cast-iron frying pan, burning his side. Several times he avoided accidental poisoning and asphyxiation from sleeping in a room where varnished furniture was drying. Another time young Sax was struck on the head by a cobblestone and fell into a river, almost dying.

His mother once said that "he's a child condemned to misfortune; he won't live". His neighbors called him "little Sax, the ghost".

Career and later life
After leaving the Royal Conservatory of Brussels, Sax began to experiment with new instrument designs, while his parents continued their business of making conventional instruments. Sax's first important invention was an improvement in bass clarinet design, which he patented at the age of 24. He relocated permanently to Paris in 1842 and began working on a new set of valved bugles. While he did not invent this instrument, his examples were much more successful than those of his rivals and became known as saxhorns. Hector Berlioz was so enamoured of these that he arranged in February 1844 for one of his pieces to be played entirely on saxhorns. They were made in seven different sizes and paved the way for the creation of the flugelhorn. Today saxhorns are sometimes used in concert bands, marching bands, and orchestras. The saxhorn also laid the groundwork for the modern euphonium.

Sax also developed the saxotromba family, valved brass instruments with narrower bore than the saxhorns, in 1845, though they survived only briefly.

The use of saxhorns spread rapidly. The saxhorn valves were accepted as state-of-the-art in their time and remain largely unchanged today. The advances made by Adolphe Sax were soon followed by the British brass band movement, which exclusively adopted the saxhorn family of instruments. A decade after saxhorns became available, the Jedforest Instrumental Band (1854) and The Hawick Saxhorn Band (1855) were formed in the Scottish Borders.

The period around 1840 saw Sax inventing the clarinette-bourdon, an early unsuccessful design of contrabass clarinet. On 28 June 1846 he patented the saxophone, intended for use in orchestras and military bands. By 1846 Sax had designed saxophones ranging from sopranino to subcontrabass, although not all were built. Composer Hector Berlioz wrote approvingly of the new instrument in 1842, but despite his support, saxophones did not become a standard part of the orchestra. Their ability to play technical passages easily like woodwinds yet project loudly like brass instruments led to their inclusion in military bands in France and elsewhere. Sax's reputation helped secure him a job teaching at the Paris Conservatory in 1857.

He continued to make instruments later in life and presided over the new saxophone course at the Paris Conservatory. Legal troubles involving patents continued for over 20 years, with rival instrument makers attacking the legitimacy of his patents and Sax suing them for patent infringement. He was driven into bankruptcy three times: in 1852, 1873 and 1877.

Sax suffered from lip cancer between 1853 and 1858 but made a full recovery. In 1894 he died of pneumonia in Paris, in poverty, and was interred in section 5 (Avenue de Montebello) at the Cimetière de Montmartre in Paris.

Honors and awards
In his birthplace Dinant in Belgium the Mr Sax's House is dedicated to his life and saxophones.
 * 1849: Awarded the Chevalier rank of the Legion of Honour.
 * 1867: 1e Grand Prix de la Facture Instrumentale at the 1867 Paris International Exposition.
 * 1995: In 1995, his likeness was featured on the front of Belgium's 200 Belgian francs banknote.
 * 2015: Google Doodle commemorated his 201st birthday.

title: Adolphe Sax


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Aspirated consonant

In phonetics, aspiration is the strong burst of breath that accompanies either the release or, in the case of preaspiration, the closure of some obstruents. In English, aspirated consonants are allophones in complementary distribution with their unaspirated counterparts, but in some other languages, notably most South Asian languages (including Indian ones) and East Asian languages, the difference is contrastive.

In dialects with aspiration, to feel or see the difference between aspirated and unaspirated sounds, one can put a hand or a lit candle in front of one's mouth, and say spin and then pin. One should either feel a puff of air or see a flicker of the candle flame with pin that one does not get with spin.

Transcription
In the International Phonetic Alphabet (IPA), aspirated consonants are written using the symbols for voiceless consonants followed by the aspiration modifier letter ⟨◌ʰ⟩, a superscript form of the symbol for the voiceless glottal fricative ⟨h⟩. For instance, ⟨p⟩ represents the voiceless bilabial stop, and ⟨pʰ⟩ represents the aspirated bilabial stop.

Voiced consonants are seldom actually aspirated. Symbols for voiced consonants followed by ⟨◌ʰ⟩, such as ⟨bʰ⟩, typically represent consonants with murmured voiced release (see below). In the grammatical tradition of Sanskrit, aspirated consonants are called voiceless aspirated, and breathy-voiced consonants are called voiced aspirated.

There are no dedicated IPA symbols for degrees of aspiration and typically only two degrees are marked: unaspirated ⟨k⟩ and aspirated ⟨kʰ⟩. An old symbol for light aspiration was ⟨ʻ⟩, but this is now obsolete. The aspiration modifier letter may be doubled to indicate especially strong or long aspiration. Hence, the two degrees of aspiration in Korean stops are sometimes transcribed ⟨kʰ kʰʰ⟩ or ⟨kʻ⟩ and ⟨kʰ⟩, but they are usually transcribed and, with the details of voice onset time given numerically.

Preaspirated consonants are marked by placing the aspiration modifier letter before the consonant symbol: ⟨ʰp⟩ represents the preaspirated bilabial stop.

Unaspirated or tenuis consonants are occasionally marked with the modifier letter for unaspiration ⟨◌˭⟩, a superscript equals sign: ⟨t˭⟩. Usually, however, unaspirated consonants are left unmarked: ⟨t⟩.

Phonetics
Voiceless consonants are produced with the vocal folds open (spread) and not vibrating, and voiced consonants are produced when the vocal folds are fractionally closed and vibrating (modal voice). Voiceless aspiration occurs when the vocal folds remain open after a consonant is released. An easy way to measure this is by noting the consonant's voice onset time, as the voicing of a following vowel cannot begin until the vocal folds close.

In some languages, such as Navajo, aspiration of stops tends to be phonetically realised as voiceless velar airflow; aspiration of affricates is realised as an extended length of the frication.

Aspirated consonants are not always followed by vowels or other voiced sounds. For example, in Eastern Armenian, aspiration is contrastive even word-finally, and aspirated consonants occur in consonant clusters. In Wahgi, consonants are aspirated only when they are in final position.

Degree
The degree of aspiration varies: the voice onset time of aspirated stops is longer or shorter depending on the language or the place of articulation.

Armenian and Cantonese have aspiration that lasts about as long as English aspirated stops, in addition to unaspirated stops. Korean has lightly-aspirated stops that fall between the Armenian and Cantonese unaspirated and aspirated stops as well as strongly-aspirated stops whose aspiration lasts longer than that of Armenian or Cantonese. (See voice onset time.)

Aspiration varies with place of articulation. The Spanish voiceless stops have voice onset times (VOTs) of about 5, 10, and 30 milliseconds, and English aspirated  have VOTs of about 60, 70, and 80 ms. Voice onset time in Korean has been measured at 20, 25, and 50 ms for  and 90, 95, and 125 for.

Doubling
When aspirated consonants are doubled or geminated, the stop is held longer and then has an aspirated release. An aspirated affricate consists of a stop, fricative, and aspirated release. A doubled aspirated affricate has a longer hold in the stop portion and then has a release consisting of the fricative and aspiration.

Preaspiration
Icelandic and Faroese have consonants with preaspiration, and some scholars interpret them as consonant clusters as well. In Icelandic, preaspirated stops contrast with double stops and single stops: Preaspiration is also a feature of Scottish Gaelic: Preaspirated stops also occur in most Sami languages. For example, in Northern Sami, the unvoiced stop and affricate phonemes, , , , are pronounced preaspirated  in medial or final position.

Fricatives and sonorants
Although most aspirated obstruents in the world's languages are stops and affricates, aspirated fricatives such as, or  have been documented in Korean, though these are allophones of other phonemes. Similarly, aspirated fricatives and even aspirated nasals, approximants, and trills occur in a few Tibeto-Burman languages, some Oto-Manguean languages, the Hmongic language Hmu, the Siouan language Ofo, and the Chumashan languages Barbareño and Ventureño. Some languages, such as Choni Tibetan, have as many as four contrastive aspirated fricatives,  and.

Voiced consonants with voiceless aspiration
True aspirated voiced consonants, as opposed to murmured (breathy-voice) consonants such as the that are common among the languages of India, are extremely rare. They have been documented in Kelabit.

Phonology
Aspiration has varying significance in different languages. It is either allophonic or phonemic, and may be analyzed as an underlying consonant cluster.

Allophonic
In some languages, stops are distinguished primarily by voicing, and voiceless stops are sometimes aspirated, while voiced stops are usually unaspirated.

English voiceless stops are aspirated for most native speakers when they are word-initial or begin a stressed syllable. Pronouncing them as unaspirated in these positions, as is done by many Indian English speakers, may make them get confused with the corresponding voiced stop by other English-speakers. Conversely, this confusion does not happen with the native speakers of languages which have aspirated and unaspirated but not voiced stops, such as Mandarin Chinese.

S+consonant clusters may vary between aspirated and nonaspirated depending upon if the cluster crosses a morpheme boundary or not. For instance, distend has unaspirated since it is not analyzed as two morphemes, but distaste has an aspirated middle  because it is analyzed as dis- + taste and the word taste has an aspirated initial t.

Word-final voiceless stops are sometimes aspirated.

Voiceless stops in Pashto are slightly aspirated prevocalically in a stressed syllable.

Phonemic
In many languages, such as Hindi, tenuis and aspirated consonants are phonemic. Unaspirated consonants like and aspirated consonants like  are separate phonemes, and words are distinguished by whether they have one or the other.

Consonant cluster
Alemannic German dialects have unaspirated as well as aspirated ; the latter series are usually viewed as consonant clusters.

Absence
French, Standard Dutch, Afrikaans, Tamil, Finnish, Portuguese, Italian, Spanish, Russian, Polish, Latvian and Modern Greek are languages that do not have phonetic aspirated consonants.

Chinese
Standard Chinese (Mandarin) has stops and affricates distinguished by aspiration: for instance,,. In pinyin, tenuis stops are written with letters that represent voiced consonants in English, and aspirated stops with letters that represent voiceless consonants. Thus d represents, and t represents.

Wu Chinese and Southern Min has a three-way distinction in stops and affricates:. In addition to aspirated and unaspirated consonants, there is a series of muddy consonants, like. These are pronounced with slack or breathy voice: that is, they are weakly voiced. Muddy consonants as initial cause a syllable to be pronounced with low pitch or light (陽 yáng) tone.

Indian languages
Many Indo-Aryan languages have aspirated stops. Sanskrit, Hindustani, Bengali, Marathi, and Gujarati have a four-way distinction in stops: voiceless, aspirated, voiced, and voiced aspirated, such as. Punjabi has lost voiced aspirated consonants, which resulted in a tone system, and therefore has a distinction between voiceless, aspirated, and voiced:.

Other languages such as Telugu, Malayalam, and Kannada, have a distinction between voiced and voiceless, aspirated and unaspirated.

Armenian
Most dialects of Armenian have aspirated stops, and some have breathy-voiced stops.

Classical and Eastern Armenian have a three-way distinction between voiceless, aspirated, and voiced, such as.

Western Armenian has a two-way distinction between aspirated and voiced:. Western Armenian aspirated corresponds to Eastern Armenian aspirated  and voiced, and Western voiced  corresponds to Eastern voiceless.

Greek
Ancient Greek, including the Classical Attic and Koine Greek dialects, had a three-way distinction in stops like Eastern Armenian:. These series were called, , (psilá, daséa, mésa) "smooth, rough, intermediate", respectively, by Koine Greek grammarians.

There were aspirated stops at three places of articulation: labial, coronal, and velar. Earlier Greek, represented by Mycenaean Greek, likely had a labialized velar aspirated stop, which later became labial, coronal, or velar depending on dialect and phonetic environment.

The other Ancient Greek dialects, Ionic, Doric, Aeolic, and Arcadocypriot, likely had the same three-way distinction at one point, but Doric seems to have had a fricative in place of in the Classical period.

Later, during the Koine and Medieval Greek periods, the aspirated and voiced stops of Attic Greek lenited to voiceless and voiced fricatives, yielding  in Medieval and Modern Greek. Cypriot Greek is notable for aspirating its inherited (and developed across word-boundaries) voiceless geminate stops, yielding the series /pʰː tʰː cʰː kʰː/.

Debuccalization
The term aspiration sometimes refers to the sound change of debuccalization, in which a consonant is lenited (weakened) to become a glottal stop or fricative.

Breathy-voiced release
So-called voiced aspirated consonants are nearly always pronounced instead with breathy voice, a type of phonation or vibration of the vocal folds. The modifier letter ⟨◌ʰ⟩ after a voiced consonant actually represents a breathy-voiced or murmured consonant, as with the "voiced aspirated" bilabial stop ⟨bʰ⟩ in the Indo-Aryan languages. This consonant is therefore more accurately transcribed as ⟨b̤⟩, with the diacritic for breathy voice, or with the modifier letter ⟨bʱ⟩, a superscript form of the symbol for the voiced glottal fricative ⟨ɦ⟩.

Some linguists restrict the double-dot subscript ⟨◌̤⟩ to murmured sonorants, such as vowels and nasals, which are murmured throughout their duration, and use the superscript hook-aitch ⟨◌ʱ⟩ for the breathy-voiced release of obstruents.

title: Aspirated consonant


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Arteriovenous malformation

An arteriovenous malformation (AVM) is an abnormal connection between arteries and veins, bypassing the capillary system. Usually congenital, this vascular anomaly is widely known because of its occurrence in the central nervous system (usually as a cerebral AVM), but can appear anywhere in the body. The symptoms of AVMs can range from none at all to intense pain or bleeding, and they can lead to other serious medical problems.

Signs and symptoms
Symptoms of AVMs vary according to their location. Most neurological AVMs produce few to no symptoms. Often the malformation is discovered as part of an autopsy or during treatment of an unrelated disorder (an "incidental finding"); in rare cases, its expansion or a micro-bleed from an AVM in the brain can cause epilepsy, neurological deficit, or pain.

The most general symptoms of a cerebral AVM include headaches and epileptic seizures, with more specific symptoms that normally depend on its location and the individual, including:
 * Difficulties with movement coordination, including muscle weakness and even paralysis;
 * Vertigo (dizziness);
 * Difficulties of speech (dysarthria) and communication, such as aphasia;
 * Difficulties with everyday activities, such as apraxia;
 * Abnormal sensations (numbness, tingling, or spontaneous pain);
 * Memory and thought-related problems, such as confusion, dementia, or hallucinations.

Cerebral AVMs may present themselves in a number of different ways:
 * Bleeding (45% of cases)
 * "parkinsonism" 4 symptoms in Parkinson's disease.
 * Acute onset of severe headache. May be described as the worst headache of the patient's life. Depending on the location of bleeding, may be associated with new fixed neurologic deficit. In unruptured brain AVMs, the risk of spontaneous bleeding may be as low as 1% per year. After a first rupture, the annual bleeding risk may increase to more than 5%.
 * Seizure or brain seizure (46%). Depending on the place of the AVM, it can contribute to loss of vision.
 * Headache (34%)
 * Progressive neurologic deficit (21%)
 * May be caused by mass effect or venous dilatations. Presence and nature of the deficit depend on location of lesion and the draining veins.
 * Pediatric patients
 * Heart failure
 * Macrocephaly
 * Prominent scalp veins

Pulmonary arteriovenous malformations
Pulmonary arteriovenous malformations are abnormal communications between the veins and arteries of the pulmonary circulation, leading to a right-to-left blood shunt. They have no symptoms in up to 29% of all cases, however they can give rise to serious complications including hemorrhage, and infection. They are most commonly associated with hereditary hemorrhagic telangiectasia.

Genetics
AVMs are usually congenital and are part of the RASopathy family of developmental syndromes. The understanding of the anomaly's genetic transmission patterns are incomplete, but there are known genetic mutations (for instance in the epithelial line, tumor suppressor PTEN gene) which can lead to an increased occurrence throughout the body.

The anomaly can occur due to autosomal dominant diseases, such as hereditary hemorrhagic telangiectasia.

Pathophysiology
In the circulatory system, arteries carry blood away from the heart to the lungs and the rest of the body, where the blood normally passes through capillaries—where oxygen is released and waste products like carbon dioxide absorbed—before veins return blood to the heart. An AVM interferes with this process by forming a direct connection of the arteries and veins, bypassing the capillary bed. AVMs can cause intense pain and lead to serious medical problems. Although AVMs are often associated with the brain and spinal cord, they can develop in other parts of the body.

As an AVM lacks the dampening effect of capillaries on the blood flow, the AVM can get progressively larger over time as the amount of blood flowing through it increases, forcing the heart to work harder to keep up with the extra blood flow. It also causes the surrounding area to be deprived of the functions of the capillaries. The resulting tangle of blood vessels, often called a nidus (Latin for 'nest'), has no capillaries. It can be extremely fragile and prone to bleeding because of the abnormally direct connections between high-pressure arteries and low-pressure veins. One indicator is a pulsing 'whoosh' sound caused by rapid blood flow through arteries and veins, which has been given the term bruit (French for 'noise'). If the AVM is severe, this may produce an audible symptom which can interfere with hearing and sleep as well as cause psychological distress.

Diagnosis

AVMs are diagnosed primarily by the following imaging methods:
 * Computerized tomography (CT) scan is a noninvasive X-ray to view the anatomical structures within the brain to detect blood in or around the brain. A newer technology called CT angiography involves the injection of contrast into the blood stream to view the arteries of the brain. This type of test provides the best pictures of blood vessels through angiography and soft tissues through CT.
 * Magnetic resonance imaging (MRI) scan is a noninvasive test, which uses a magnetic field and radio-frequency waves to give a detailed view of the soft tissues of the brain.
 * Magnetic resonance angiography (MRA) – scans created using magnetic resonance imaging to specifically image the blood vessels and structures of the brain. A magnetic resonance angiogram can be an invasive procedure, involving the introduction of contrast dyes (e.g., gadolinium MR contrast agents) into the vasculature (circulatory system) of a patient using a catheter inserted into an artery and passed through the blood vessels to the brain. Once the catheter is in place, the contrast dye is injected into the bloodstream and the MR images are taken. Additionally or alternatively, flow-dependent or other contrast-free magnetic resonance imaging techniques can be used to determine the location and other properties of the vasculature.

AVMs can occur in various parts of the body:
 * brain (cerebral AV malformation)
 * spleen
 * lung
 * kidney
 * spinal cord
 * liver
 * intercostal space
 * iris
 * spermatic cord
 * extremities – arm, shoulder, etc.

AVMs may occur in isolation or as a part of another disease (for example, Sturge-Weber syndrome or hereditary hemorrhagic telangiectasia).

AVMs have been shown to be associated with aortic stenosis.

Bleeding from an AVM can be relatively mild or devastating. It can cause severe and less often fatal strokes.

Treatment
Treatment for AVMs in the brain can be symptomatic, and patients should be followed by a neurologist for any seizures, headaches, or focal neurologic deficits. AVM-specific treatment may also involve endovascular embolization, neurosurgery or radiosurgery. Embolization, that is, cutting off the blood supply to the AVM with coils, particles, acrylates, or polymers introduced by a radiographically guided catheter, may be used in addition to neurosurgery or radiosurgery, but is rarely successful in isolation except in smaller AVMs. A gamma knife may also be used.

If a cerebral AVM is detected before a stroke occurs, usually the arteries feeding blood into the nidus can be closed off to avert the danger. Interventional therapy may be relatively risky in the short term.

Treatment of lung AVMs is typically performed with endovascular embolization alone, which is considered the standard of care.

Epidemiology
The estimated detection rate of AVM in the US general population is 1.4/100,000 per year. This is approximately one-fifth to one-seventh the incidence of intracranial aneurysms. An estimated 300,000 Americans have AVMs, of whom 12% (approximately 36,000) will exhibit symptoms of greatly varying severity.

History
Hubert von Luschka (1820–1875) and Rudolf Virchow (1821–1902) first described arteriovenous malformations in the mid-1800s. Herbert Olivecrona (1891–1980) performed the first surgical excision of an intracranial AVM in 1932.

Notable cases

 * Actor Ricardo Montalbán was born with spinal AVM. During the filming of the 1951 film Across the Wide Missouri, Montalbán was thrown from his horse, knocked unconscious, and trampled by another horse which aggravated his AVM and resulted in a painful back injury that never healed. The pain increased as he aged, and in 1993, Montalbán underwent $9 1/2$ hours of spinal surgery which left him paralyzed below the waist and using a wheelchair.
 * Composer and lyricist William Finn was diagnosed with AVM and underwent gamma knife surgery in September 1992, soon after he won the 1992 Tony Award for best musical, awarded to "Falsettos". Finn wrote the 1998 Off-Broadway musical A New Brain about the experience.
 * Phoenix Suns point guard AJ Price nearly died from AVM in 2004 while a student at the University of Connecticut.
 * On December 13, 2006, Senator Tim Johnson of South Dakota was diagnosed with AVM and treated at George Washington University Hospital.
 * Actor/comedian T. J. Miller was diagnosed with AVM in 2010; Miller had a seizure and was unable to sleep for a period. He successfully underwent surgery that had a mortality rate of 10%.
 * On August 3, 2011, Mike Patterson of the Philadelphia Eagles collapsed on the field and had a seizure during a practice, leading to him being diagnosed with AVM.
 * Former Florida Gators and Oakland Raiders linebacker Neiron Ball was diagnosed with AVM in 2011 while playing for Florida, but recovered and was cleared to play. On September 16, 2018, Ball was placed in a medically induced coma due to complications of the disease, which lasted until his death on September 10, 2019.
 * Indonesian actress died from complications of AVM on November 29, 2013.
 * Jazz guitarist Pat Martino experienced an AVM and subsequently developed amnesia and manic depression. He eventually re-learned to play the guitar by listening to his own recordings from before the aneurysm.
 * YouTube vlogger Nikki Lilly (Nikki Christou), winner of the 2016 season of Junior Bake Off was born with AVM, which has resulted in some facial disfigurement.
 * Country music singer Drake White was diagnosed with AVM in January 2019, and is undergoing treatment.

Cultural depictions

 * In the HBO series Six Feet Under (2001), main character Nate Fisher discovers he has an AVM after being in a car accident and getting a precautionary cat scan at the hospital during Season 1. His AVM becomes a key focus during Season 2 and again in Season 5.
 * In season 1 episode 9 of House (2004), titled "DNR", a jazz musician has an AVM and is misdiagnosed with ALS. Two season three episodes also involve AVM - "Top Secret" (episode 16), in which a veteran who believes himself to be suffering from Gulf War syndrome is found to have spinal and pulmonary AVM from hereditary hemorrhagic telangiectasia; and "Resignation" (episode 22), where the patient developed AVM in her intestines after drinking pipe cleaner fluid in a suicide attempt.
 * In the 2005 Lifetime film Dawn Anna, the titular character learns she has AVM, and undergoes a serious operation and subsequent rehabilitation, which she recovers from.

title: Arteriovenous malformation