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Because the phenotype of a cell or individual is affected by which of its genes are transcribed, heritable transcription states can give rise to epigenetic effects. There are several layers of regulation of gene expression. One way that genes are regulated is through the remodeling of chromatin. Chromatin is the complex of DNA and the histone proteins with which it associates. If the way that DNA is wrapped around the histones changes, gene expression can change as well. Chromatin remodeling is accomplished through two main mechanisms:
The first way is post translational modification of the amino acids that make up histone proteins. Histone proteins are made up of long chains of amino acids. If the amino acids that are in the chain are changed, the shape of the histone might be modified. DNA is not completely unwound during replication. It is possible, then, that the modified histones may be carried into each new copy of the DNA. Once there, these histones may act as templates, initiating the surrounding new histones to be shaped in the new manner. By altering the shape of the histones around them, these modified histones would ensure that a lineage-specific transcription program is maintained after cell division. | Epigenetics | Wikipedia | 256 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
The second way is the addition of methyl groups to the DNA, mostly at CpG sites, to convert cytosine to 5-methylcytosine. 5-Methylcytosine performs much like a regular cytosine, pairing with a guanine in double-stranded DNA. However, when methylated cytosines are present in CpG sites in the promoter and enhancer regions of genes, the genes are often repressed. When methylated cytosines are present in CpG sites in the gene body (in the coding region excluding the transcription start site) expression of the gene is often enhanced. Transcription of a gene usually depends on a transcription factor binding to a (10 base or less) recognition sequence at the enhancer that interacts with the promoter region of that gene (Gene expression#Enhancers, transcription factors, mediator complex and DNA loops in mammalian transcription). About 22% of transcription factors are inhibited from binding when the recognition sequence has a methylated cytosine. In addition, presence of methylated cytosines at a promoter region can attract methyl-CpG-binding domain (MBD) proteins. All MBDs interact with nucleosome remodeling and histone deacetylase complexes, which leads to gene silencing. In addition, another covalent modification involving methylated cytosine is its demethylation by TET enzymes. Hundreds of such demethylations occur, for instance, during learning and memory forming events in neurons. | Epigenetics | Wikipedia | 308 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
There is frequently a reciprocal relationship between DNA methylation and histone lysine methylation. For instance, the methyl binding domain protein MBD1, attracted to and associating with methylated cytosine in a DNA CpG site, can also associate with H3K9 methyltransferase activity to methylate histone 3 at lysine 9. On the other hand, DNA maintenance methylation by DNMT1 appears to partly rely on recognition of histone methylation on the nucleosome present at the DNA site to carry out cytosine methylation on newly synthesized DNA. There is further crosstalk between DNA methylation carried out by DNMT3A and DNMT3B and histone methylation so that there is a correlation between the genome-wide distribution of DNA methylation and histone methylation.
Mechanisms of heritability of histone state are not well understood; however, much is known about the mechanism of heritability of DNA methylation state during cell division and differentiation. Heritability of methylation state depends on certain enzymes (such as DNMT1) that have a higher affinity for 5-methylcytosine than for cytosine. If this enzyme reaches a "hemimethylated" portion of DNA (where 5-methylcytosine is in only one of the two DNA strands) the enzyme will methylate the other half. However, it is now known that DNMT1 physically interacts with the protein UHRF1. UHRF1 has been recently recognized as essential for DNMT1-mediated maintenance of DNA methylation. UHRF1 is the protein that specifically recognizes hemi-methylated DNA, therefore bringing DNMT1 to its substrate to maintain DNA methylation.
Although histone modifications occur throughout the entire sequence, the unstructured N-termini of histones (called histone tails) are particularly highly modified. These modifications include acetylation, methylation, ubiquitylation, phosphorylation, sumoylation, ribosylation and citrullination. Acetylation is the most highly studied of these modifications. For example, acetylation of the K14 and K9 lysines of the tail of histone H3 by histone acetyltransferase enzymes (HATs) is generally related to transcriptional competence (see Figure). | Epigenetics | Wikipedia | 494 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
One mode of thinking is that this tendency of acetylation to be associated with "active" transcription is biophysical in nature. Because it normally has a positively charged nitrogen at its end, lysine can bind the negatively charged phosphates of the DNA backbone. The acetylation event converts the positively charged amine group on the side chain into a neutral amide linkage. This removes the positive charge, thus loosening the DNA from the histone. When this occurs, complexes like SWI/SNF and other transcriptional factors can bind to the DNA and allow transcription to occur. This is the "cis" model of the epigenetic function. In other words, changes to the histone tails have a direct effect on the DNA itself.
Another model of epigenetic function is the "trans" model. In this model, changes to the histone tails act indirectly on the DNA. For example, lysine acetylation may create a binding site for chromatin-modifying enzymes (or transcription machinery as well). This chromatin remodeler can then cause changes to the state of the chromatin. Indeed, a bromodomain – a protein domain that specifically binds acetyl-lysine – is found in many enzymes that help activate transcription, including the SWI/SNF complex. It may be that acetylation acts in this and the previous way to aid in transcriptional activation.
The idea that modifications act as docking modules for related factors is borne out by histone methylation as well. Methylation of lysine 9 of histone H3 has long been associated with constitutively transcriptionally silent chromatin (constitutive heterochromatin) (see bottom Figure). It has been determined that a chromodomain (a domain that specifically binds methyl-lysine) in the transcriptionally repressive protein HP1 recruits HP1 to K9 methylated regions. One example that seems to refute this biophysical model for methylation is that tri-methylation of histone H3 at lysine 4 is strongly associated with (and required for full) transcriptional activation (see top Figure). Tri-methylation, in this case, would introduce a fixed positive charge on the tail. | Epigenetics | Wikipedia | 474 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
It has been shown that the histone lysine methyltransferase (KMT) is responsible for this methylation activity in the pattern of histones H3 & H4. This enzyme utilizes a catalytically active site called the SET domain (Suppressor of variegation, Enhancer of Zeste, Trithorax). The SET domain is a 130-amino acid sequence involved in modulating gene activities. This domain has been demonstrated to bind to the histone tail and causes the methylation of the histone.
Differing histone modifications are likely to function in differing ways; acetylation at one position is likely to function differently from acetylation at another position. Also, multiple modifications may occur at the same time, and these modifications may work together to change the behavior of the nucleosome. The idea that multiple dynamic modifications regulate gene transcription in a systematic and reproducible way is called the histone code, although the idea that histone state can be read linearly as a digital information carrier has been largely debunked. One of the best-understood systems that orchestrate chromatin-based silencing is the SIR protein based silencing of the yeast hidden mating-type loci HML and HMR.
DNA methylation
DNA methylation frequently occurs in repeated sequences, and helps to suppress the expression and mobility of 'transposable elements': Because 5-methylcytosine can be spontaneously deaminated (replacing nitrogen by oxygen) to thymidine, CpG sites are frequently mutated and become rare in the genome, except at CpG islands where they remain unmethylated. Epigenetic changes of this type thus have the potential to direct increased frequencies of permanent genetic mutation. DNA methylation patterns are known to be established and modified in response to environmental factors by a complex interplay of at least three independent DNA methyltransferases, DNMT1, DNMT3A, and DNMT3B, the loss of any of which is lethal in mice. DNMT1 is the most abundant methyltransferase in somatic cells, localizes to replication foci, has a 10–40-fold preference for hemimethylated DNA and interacts with the proliferating cell nuclear antigen (PCNA). | Epigenetics | Wikipedia | 474 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
By preferentially modifying hemimethylated DNA, DNMT1 transfers patterns of methylation to a newly synthesized strand after DNA replication, and therefore is often referred to as the 'maintenance' methyltransferase. DNMT1 is essential for proper embryonic development, imprinting and X-inactivation. To emphasize the difference of this molecular mechanism of inheritance from the canonical Watson-Crick base-pairing mechanism of transmission of genetic information, the term 'Epigenetic templating' was introduced. Furthermore, in addition to the maintenance and transmission of methylated DNA states, the same principle could work in the maintenance and transmission of histone modifications and even cytoplasmic (structural) heritable states.
RNA methylation
RNA methylation of N6-methyladenosine (m6A) as the most abundant eukaryotic RNA modification has recently been recognized as an important gene regulatory mechanism.
Histone modifications
Histones H3 and H4 can also be manipulated through demethylation using histone lysine demethylase (KDM). This recently identified enzyme has a catalytically active site called the Jumonji domain (JmjC). The demethylation occurs when JmjC utilizes multiple cofactors to hydroxylate the methyl group, thereby removing it. JmjC is capable of demethylating mono-, di-, and tri-methylated substrates.
Chromosomal regions can adopt stable and heritable alternative states resulting in bistable gene expression without changes to the DNA sequence. Epigenetic control is often associated with alternative covalent modifications of histones. The stability and heritability of states of larger chromosomal regions are suggested to involve positive feedback where modified nucleosomes recruit enzymes that similarly modify nearby nucleosomes. A simplified stochastic model for this type of epigenetics is found here.
It has been suggested that chromatin-based transcriptional regulation could be mediated by the effect of small RNAs. Small interfering RNAs can modulate transcriptional gene expression via epigenetic modulation of targeted promoters. | Epigenetics | Wikipedia | 440 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
RNA transcripts
Sometimes a gene, after being turned on, transcribes a product that (directly or indirectly) maintains the activity of that gene. For example, Hnf4 and MyoD enhance the transcription of many liver-specific and muscle-specific genes, respectively, including their own, through the transcription factor activity of the proteins they encode. RNA signalling includes differential recruitment of a hierarchy of generic chromatin modifying complexes and DNA methyltransferases to specific loci by RNAs during differentiation and development. Other epigenetic changes are mediated by the production of different splice forms of RNA, or by formation of double-stranded RNA (RNAi). Descendants of the cell in which the gene was turned on will inherit this activity, even if the original stimulus for gene-activation is no longer present. These genes are often turned on or off by signal transduction, although in some systems where syncytia or gap junctions are important, RNA may spread directly to other cells or nuclei by diffusion. A large amount of RNA and protein is contributed to the zygote by the mother during oogenesis or via nurse cells, resulting in maternal effect phenotypes. A smaller quantity of sperm RNA is transmitted from the father, but there is recent evidence that this epigenetic information can lead to visible changes in several generations of offspring.
MicroRNAs
MicroRNAs (miRNAs) are members of non-coding RNAs that range in size from 17 to 25 nucleotides. miRNAs regulate a large variety of biological functions in plants and animals. So far, in 2013, about 2000 miRNAs have been discovered in humans and these can be found online in a miRNA database. Each miRNA expressed in a cell may target about 100 to 200 messenger RNAs(mRNAs) that it downregulates. Most of the downregulation of mRNAs occurs by causing the decay of the targeted mRNA, while some downregulation occurs at the level of translation into protein.
It appears that about 60% of human protein coding genes are regulated by miRNAs. Many miRNAs are epigenetically regulated. About 50% of miRNA genes are associated with CpG islands, that may be repressed by epigenetic methylation. Transcription from methylated CpG islands is strongly and heritably repressed. Other miRNAs are epigenetically regulated by either histone modifications or by combined DNA methylation and histone modification. | Epigenetics | Wikipedia | 505 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
mRNA
In 2011, it was demonstrated that the methylation of mRNA plays a critical role in human energy homeostasis. The obesity-associated FTO gene is shown to be able to demethylate N6-methyladenosine in RNA.
sRNAs
sRNAs are small (50–250 nucleotides), highly structured, non-coding RNA fragments found in bacteria. They control gene expression including virulence genes in pathogens and are viewed as new targets in the fight against drug-resistant bacteria. They play an important role in many biological processes, binding to mRNA and protein targets in prokaryotes. Their phylogenetic analyses, for example through sRNA–mRNA target interactions or protein binding properties, are used to build comprehensive databases. sRNA-gene maps based on their targets in microbial genomes are also constructed.
Long non-coding RNAs
Numerous investigations have demonstrated the pivotal involvement of long non-coding RNAs (lncRNAs) in the regulation of gene expression and chromosomal modifications, thereby exerting significant control over cellular differentiation. These long non-coding RNAs also contribute to genomic imprinting and the inactivation of the X chromosome.
In invertebrates such as social insects of honey bees, long non-coding RNAs are detected as a possible epigenetic mechanism via allele-specific genes underlying aggression via reciprocal crosses.
Prions
Prions are infectious forms of proteins. In general, proteins fold into discrete units that perform distinct cellular functions, but some proteins are also capable of forming an infectious conformational state known as a prion. Although often viewed in the context of infectious disease, prions are more loosely defined by their ability to catalytically convert other native state versions of the same protein to an infectious conformational state. It is in this latter sense that they can be viewed as epigenetic agents capable of inducing a phenotypic change without a modification of the genome. | Epigenetics | Wikipedia | 394 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
Fungal prions are considered by some to be epigenetic because the infectious phenotype caused by the prion can be inherited without modification of the genome. PSI+ and URE3, discovered in yeast in 1965 and 1971, are the two best studied of this type of prion. Prions can have a phenotypic effect through the sequestration of protein in aggregates, thereby reducing that protein's activity. In PSI+ cells, the loss of the Sup35 protein (which is involved in termination of translation) causes ribosomes to have a higher rate of read-through of stop codons, an effect that results in suppression of nonsense mutations in other genes. The ability of Sup35 to form prions may be a conserved trait. It could confer an adaptive advantage by giving cells the ability to switch into a PSI+ state and express dormant genetic features normally terminated by stop codon mutations.
Prion-based epigenetics has also been observed in Saccharomyces cerevisiae.
Molecular basis
Epigenetic changes modify the activation of certain genes, but not the genetic code sequence of DNA. The microstructure (not code) of DNA itself or the associated chromatin proteins may be modified, causing activation or silencing. This mechanism enables differentiated cells in a multicellular organism to express only the genes that are necessary for their own activity. Epigenetic changes are preserved when cells divide. Most epigenetic changes only occur within the course of one individual organism's lifetime; however, these epigenetic changes can be transmitted to the organism's offspring through a process called transgenerational epigenetic inheritance. Moreover, if gene inactivation occurs in a sperm or egg cell that results in fertilization, this epigenetic modification may also be transferred to the next generation.
Specific epigenetic processes include paramutation, bookmarking, imprinting, gene silencing, X chromosome inactivation, position effect, DNA methylation reprogramming, transvection, maternal effects, the progress of carcinogenesis, many effects of teratogens, regulation of histone modifications and heterochromatin, and technical limitations affecting parthenogenesis and cloning. | Epigenetics | Wikipedia | 462 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
DNA damage
DNA damage can also cause epigenetic changes. DNA damage is very frequent, occurring on average about 60,000 times a day per cell of the human body (see DNA damage (naturally occurring)). These damages are largely repaired, however, epigenetic changes can still remain at the site of DNA repair. In particular, a double strand break in DNA can initiate unprogrammed epigenetic gene silencing both by causing DNA methylation as well as by promoting silencing types of histone modifications (chromatin remodeling - see next section). In addition, the enzyme Parp1 (poly(ADP)-ribose polymerase) and its product poly(ADP)-ribose (PAR) accumulate at sites of DNA damage as part of the repair process. This accumulation, in turn, directs recruitment and activation of the chromatin remodeling protein, ALC1, that can cause nucleosome remodeling. Nucleosome remodeling has been found to cause, for instance, epigenetic silencing of DNA repair gene MLH1. DNA damaging chemicals, such as benzene, hydroquinone, styrene, carbon tetrachloride and trichloroethylene, cause considerable hypomethylation of DNA, some through the activation of oxidative stress pathways.
Foods are known to alter the epigenetics of rats on different diets. Some food components epigenetically increase the levels of DNA repair enzymes such as MGMT and MLH1 and p53. Other food components can reduce DNA damage, such as soy isoflavones. In one study, markers for oxidative stress, such as modified nucleotides that can result from DNA damage, were decreased by a 3-week diet supplemented with soy. A decrease in oxidative DNA damage was also observed 2 h after consumption of anthocyanin-rich bilberry (Vaccinium myrtillius L.) pomace extract.
DNA repair | Epigenetics | Wikipedia | 428 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
Damage to DNA is very common and is constantly being repaired. Epigenetic alterations can accompany DNA repair of oxidative damage or double-strand breaks. In human cells, oxidative DNA damage occurs about 10,000 times a day and DNA double-strand breaks occur about 10 to 50 times a cell cycle in somatic replicating cells (see DNA damage (naturally occurring)). The selective advantage of DNA repair is to allow the cell to survive in the face of DNA damage. The selective advantage of epigenetic alterations that occur with DNA repair is not clear.
Repair of oxidative DNA damage can alter epigenetic markers
In the steady state (with endogenous damages occurring and being repaired), there are about 2,400 oxidatively damaged guanines that form 8-oxo-2'-deoxyguanosine (8-OHdG) in the average mammalian cell DNA. 8-OHdG constitutes about 5% of the oxidative damages commonly present in DNA. The oxidized guanines do not occur randomly among all guanines in DNA. There is a sequence preference for the guanine at a methylated CpG site (a cytosine followed by guanine along its 5' → 3' direction and where the cytosine is methylated (5-mCpG)). A 5-mCpG site has the lowest ionization potential for guanine oxidation.
Oxidized guanine has mispairing potential and is mutagenic. Oxoguanine glycosylase (OGG1) is the primary enzyme responsible for the excision of the oxidized guanine during DNA repair. OGG1 finds and binds to an 8-OHdG within a few seconds. However, OGG1 does not immediately excise 8-OHdG. In HeLa cells half maximum removal of 8-OHdG occurs in 30 minutes, and in irradiated mice, the 8-OHdGs induced in the mouse liver are removed with a half-life of 11 minutes.
When OGG1 is present at an oxidized guanine within a methylated CpG site it recruits TET1 to the 8-OHdG lesion (see Figure). This allows TET1 to demethylate an adjacent methylated cytosine. Demethylation of cytosine is an epigenetic alteration. | Epigenetics | Wikipedia | 503 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
As an example, when human mammary epithelial cells were treated with H2O2 for six hours, 8-OHdG increased about 3.5-fold in DNA and this caused about 80% demethylation of the 5-methylcytosines in the genome. Demethylation of CpGs in a gene promoter by TET enzyme activity increases transcription of the gene into messenger RNA. In cells treated with H2O2, one particular gene was examined, BACE1. The methylation level of the BACE1 CpG island was reduced (an epigenetic alteration) and this allowed about 6.5 fold increase of expression of BACE1 messenger RNA.
While six-hour incubation with H2O2 causes considerable demethylation of 5-mCpG sites, shorter times of H2O2 incubation appear to promote other epigenetic alterations. Treatment of cells with H2O2 for 30 minutes causes the mismatch repair protein heterodimer MSH2-MSH6 to recruit DNA methyltransferase 1 (DNMT1) to sites of some kinds of oxidative DNA damage. This could cause increased methylation of cytosines (epigenetic alterations) at these locations. | Epigenetics | Wikipedia | 263 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
Jiang et al. treated HEK 293 cells with agents causing oxidative DNA damage, (potassium bromate (KBrO3) or potassium chromate (K2CrO4)). Base excision repair (BER) of oxidative damage occurred with the DNA repair enzyme polymerase beta localizing to oxidized guanines. Polymerase beta is the main human polymerase in short-patch BER of oxidative DNA damage. Jiang et al. also found that polymerase beta recruited the DNA methyltransferase protein DNMT3b to BER repair sites. They then evaluated the methylation pattern at the single nucleotide level in a small region of DNA including the promoter region and the early transcription region of the BRCA1 gene. Oxidative DNA damage from bromate modulated the DNA methylation pattern (caused epigenetic alterations) at CpG sites within the region of DNA studied. In untreated cells, CpGs located at −189, −134, −29, −19, +16, and +19 of the BRCA1 gene had methylated cytosines (where numbering is from the messenger RNA transcription start site, and negative numbers indicate nucleotides in the upstream promoter region). Bromate treatment-induced oxidation resulted in the loss of cytosine methylation at −189, −134, +16 and +19 while also leading to the formation of new methylation at the CpGs located at −80, −55, −21 and +8 after DNA repair was allowed. | Epigenetics | Wikipedia | 326 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
Homologous recombinational repair alters epigenetic markers
At least four articles report the recruitment of DNA methyltransferase 1 (DNMT1) to sites of DNA double-strand breaks. During homologous recombinational repair (HR) of the double-strand break, the involvement of DNMT1 causes the two repaired strands of DNA to have different levels of methylated cytosines. One strand becomes frequently methylated at about 21 CpG sites downstream of the repaired double-strand break. The other DNA strand loses methylation at about six CpG sites that were previously methylated downstream of the double-strand break, as well as losing methylation at about five CpG sites that were previously methylated upstream of the double-strand break. When the chromosome is replicated, this gives rise to one daughter chromosome that is heavily methylated downstream of the previous break site and one that is unmethylated in the region both upstream and downstream of the previous break site. With respect to the gene that was broken by the double-strand break, half of the progeny cells express that gene at a high level and in the other half of the progeny cells expression of that gene is repressed. When clones of these cells were maintained for three years, the new methylation patterns were maintained over that time period.
In mice with a CRISPR-mediated homology-directed recombination insertion in their genome there were a large number of increased methylations of CpG sites within the double-strand break-associated insertion.
Non-homologous end joining can cause some epigenetic marker alterations
Non-homologous end joining (NHEJ) repair of a double-strand break can cause a small number of demethylations of pre-existing cytosine DNA methylations downstream of the repaired double-strand break. Further work by Allen et al. showed that NHEJ of a DNA double-strand break in a cell could give rise to some progeny cells having repressed expression of the gene harboring the initial double-strand break and some progeny having high expression of that gene due to epigenetic alterations associated with NHEJ repair. The frequency of epigenetic alterations causing repression of a gene after an NHEJ repair of a DNA double-strand break in that gene may be about 0.9%. | Epigenetics | Wikipedia | 483 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
Techniques used to study epigenetics
Epigenetic research uses a wide range of molecular biological techniques to further understanding of epigenetic phenomena. These techniques include chromatin immunoprecipitation (together with its large-scale variants ChIP-on-chip and ChIP-Seq), fluorescent in situ hybridization, methylation-sensitive restriction enzymes, DNA adenine methyltransferase identification (DamID) and bisulfite sequencing. Furthermore, the use of bioinformatics methods has a role in computational epigenetics.
Chromatin Immunoprecipitation
Chromatin Immunoprecipitation (ChIP) has helped bridge the gap between DNA and epigenetic interactions. With the use of ChIP, researchers are able to make findings in regards to gene regulation, transcription mechanisms, and chromatin structure.
Fluorescent in situ hybridization
Fluorescent in situ hybridization (FISH) is very important to understand epigenetic mechanisms. FISH can be used to find the location of genes on chromosomes, as well as finding noncoding RNAs. FISH is predominantly used for detecting chromosomal abnormalities in humans.
Methylation-sensitive restriction enzymes
Methylation sensitive restriction enzymes paired with PCR is a way to evaluate methylation in DNA - specifically the CpG sites. If DNA is methylated, the restriction enzymes will not cleave the strand. Contrarily, if the DNA is not methylated, the enzymes will cleave the strand and it will be amplified by PCR.
Bisulfite sequencing
Bisulfite sequencing is another way to evaluate DNA methylation. Cytosine will be changed to uracil from being treated with sodium bisulfite, whereas methylated cytosines will not be affected.
Nanopore sequencing
Certain sequencing methods, such as nanopore sequencing, allow sequencing of native DNA. Native (=unamplified) DNA retains the epigenetic modifications which would otherwise be lost during the amplification step. Nanopore basecaller models can distinguish between the signals obtained for epigenetically modified bases and unaltered based and provide an epigenetic profile in addition to the sequencing result.
Structural inheritance | Epigenetics | Wikipedia | 445 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
In ciliates such as Tetrahymena and Paramecium, genetically identical cells show heritable differences in the patterns of ciliary rows on their cell surface. Experimentally altered patterns can be transmitted to daughter cells. It seems existing structures act as templates for new structures. The mechanisms of such inheritance are unclear, but reasons exist to assume that multicellular organisms also use existing cell structures to assemble new ones.
Nucleosome positioning
Eukaryotic genomes have numerous nucleosomes. Nucleosome position is not random, and determine the accessibility of DNA to regulatory proteins. Promoters active in different tissues have been shown to have different nucleosome positioning features. This determines differences in gene expression and cell differentiation. It has been shown that at least some nucleosomes are retained in sperm cells (where most but not all histones are replaced by protamines). Thus nucleosome positioning is to some degree inheritable. Recent studies have uncovered connections between nucleosome positioning and other epigenetic factors, such as DNA methylation and hydroxymethylation.
Histone variants
Different histone variants are incorporated into specific regions of the genome non-randomly. Their differential biochemical characteristics can affect genome functions via their roles in gene regulation, and maintenance of chromosome structures.
Genomic architecture
The three-dimensional configuration of the genome (the 3D genome) is complex, dynamic and crucial for regulating genomic function and nuclear processes such as DNA replication, transcription and DNA-damage repair.
Functions and consequences
In the brain
Memory
Memory formation and maintenance are due to epigenetic alterations that cause the required dynamic changes in gene transcription that create and renew memory in neurons.
An event can set off a chain of reactions that result in altered methylations of a large set of genes in neurons, which give a representation of the event, a memory.
Areas of the brain important in the formation of memories include the hippocampus, medial prefrontal cortex (mPFC), anterior cingulate cortex and amygdala, as shown in the diagram of the human brain in this section. | Epigenetics | Wikipedia | 433 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
When a strong memory is created, as in a rat subjected to contextual fear conditioning (CFC), one of the earliest events to occur is that more than 100 DNA double-strand breaks are formed by topoisomerase IIB in neurons of the hippocampus and the medial prefrontal cortex (mPFC). These double-strand breaks are at specific locations that allow activation of transcription of immediate early genes (IEGs) that are important in memory formation, allowing their expression in mRNA, with peak mRNA transcription at seven to ten minutes after CFC.
Two important IEGs in memory formation are EGR1 and the alternative promoter variant of DNMT3A, DNMT3A2. EGR1 protein binds to DNA at its binding motifs, 5′-GCGTGGGCG-3′ or 5′-GCGGGGGCGG-3', and there are about 12,000 genome locations at which EGR1 protein can bind. EGR1 protein binds to DNA in gene promoter and enhancer regions. EGR1 recruits the demethylating enzyme TET1 to an association, and brings TET1 to about 600 locations on the genome where TET1 can then demethylate and activate the associated genes.
The DNA methyltransferases DNMT3A1, DNMT3A2 and DNMT3B can all methylate cytosines (see image this section) at CpG sites in or near the promoters of genes. As shown by Manzo et al., these three DNA methyltransferases differ in their genomic binding locations and DNA methylation activity at different regulatory sites. Manzo et al. located 3,970 genome regions exclusively enriched for DNMT3A1, 3,838 regions for DNMT3A2 and 3,432 regions for DNMT3B. When DNMT3A2 is newly induced as an IEG (when neurons are activated), many new cytosine methylations occur, presumably in the target regions of DNMT3A2. Oliviera et al. found that the neuronal activity-inducible IEG levels of Dnmt3a2 in the hippocampus determined the ability to form long-term memories. | Epigenetics | Wikipedia | 476 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
Rats form long-term associative memories after contextual fear conditioning (CFC). Duke et al. found that 24 hours after CFC in rats, in hippocampus neurons, 2,097 genes (9.17% of the genes in the rat genome) had altered methylation. When newly methylated cytosines are present in CpG sites in the promoter regions of genes, the genes are often repressed, and when newly demethylated cytosines are present the genes may be activated. After CFC, there were 1,048 genes with reduced mRNA expression and 564 genes with upregulated mRNA expression. Similarly, when mice undergo CFC, one hour later in the hippocampus region of the mouse brain there are 675 demethylated genes and 613 hypermethylated genes. However, memories do not remain in the hippocampus, but after four or five weeks the memories are stored in the anterior cingulate cortex. In the studies on mice after CFC, Halder et al. showed that four weeks after CFC there were at least 1,000 differentially methylated genes and more than 1,000 differentially expressed genes in the anterior cingulate cortex, while at the same time the altered methylations in the hippocampus were reversed.
The epigenetic alteration of methylation after a new memory is established creates a different pool of nuclear mRNAs. As reviewed by Bernstein, the epigenetically determined new mix of nuclear mRNAs are often packaged into neuronal granules, or messenger RNP, consisting of mRNA, small and large ribosomal subunits, translation initiation factors and RNA-binding proteins that regulate mRNA function. These neuronal granules are transported from the neuron nucleus and are directed, according to 3′ untranslated regions of the mRNA in the granules (their "zip codes"), to neuronal dendrites. Roughly 2,500 mRNAs may be localized to the dendrites of hippocampal pyramidal neurons and perhaps 450 transcripts are in excitatory presynaptic nerve terminals (dendritic spines). The altered assortments of transcripts (dependent on epigenetic alterations in the neuron nucleus) have different sensitivities in response to signals, which is the basis of altered synaptic plasticity. Altered synaptic plasticity is often considered the neurochemical foundation of learning and memory. | Epigenetics | Wikipedia | 512 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
Aging
Epigenetics play a major role in brain aging and age-related cognitive decline, with relevance to life extension.
Other and general
In adulthood, changes in the epigenome are important for various higher cognitive functions. Dysregulation of epigenetic mechanisms is implicated in neurodegenerative disorders and diseases. Epigenetic modifications in neurons are dynamic and reversible. Epigenetic regulation impacts neuronal action, affecting learning, memory, and other cognitive processes.
Early events, including during embryonic development, can influence development, cognition, and health outcomes through epigenetic mechanisms.
Epigenetic mechanisms have been proposed as "a potential molecular mechanism for effects of endogenous hormones on the organization of developing brain circuits".
Nutrients could interact with the epigenome to "protect or boost cognitive processes across the lifespan".
A review suggests neurobiological effects of physical exercise via epigenetics seem "central to building an 'epigenetic memory' to influence long-term brain function and behavior" and may even be heritable.
With the axo-ciliary synapse, there is communication between serotonergic axons and antenna-like primary cilia of CA1 pyramidal neurons that alters the neuron's epigenetic state in the nucleus via the signalling distinct from that at the plasma membrane (and longer-term).
Epigenetics also play a major role in the brain evolution in and to humans.
Development
Developmental epigenetics can be divided into predetermined and probabilistic epigenesis. Predetermined epigenesis is a unidirectional movement from structural development in DNA to the functional maturation of the protein. "Predetermined" here means that development is scripted and predictable. Probabilistic epigenesis on the other hand is a bidirectional structure-function development with experiences and external molding development. | Epigenetics | Wikipedia | 400 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
Somatic epigenetic inheritance, particularly through DNA and histone covalent modifications and nucleosome repositioning, is very important in the development of multicellular eukaryotic organisms. The genome sequence is static (with some notable exceptions), but cells differentiate into many different types, which perform different functions, and respond differently to the environment and intercellular signaling. Thus, as individuals develop, morphogens activate or silence genes in an epigenetically heritable fashion, giving cells a memory. In mammals, most cells terminally differentiate, with only stem cells retaining the ability to differentiate into several cell types ("totipotency" and "multipotency"). In mammals, some stem cells continue producing newly differentiated cells throughout life, such as in neurogenesis, but mammals are not able to respond to loss of some tissues, for example, the inability to regenerate limbs, which some other animals are capable of. Epigenetic modifications regulate the transition from neural stem cells to glial progenitor cells (for example, differentiation into oligodendrocytes is regulated by the deacetylation and methylation of histones). Unlike animals, plant cells do not terminally differentiate, remaining totipotent with the ability to give rise to a new individual plant. While plants do utilize many of the same epigenetic mechanisms as animals, such as chromatin remodeling, it has been hypothesized that some kinds of plant cells do not use or require "cellular memories", resetting their gene expression patterns using positional information from the environment and surrounding cells to determine their fate.
Epigenetic changes can occur in response to environmental exposure – for example, maternal dietary supplementation with genistein (250 mg/kg) have epigenetic changes affecting expression of the agouti gene, which affects their fur color, weight, and propensity to develop cancer. Ongoing research is focused on exploring the impact of other known teratogens, such as diabetic embryopathy, on methylation signatures. | Epigenetics | Wikipedia | 426 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
Controversial results from one study suggested that traumatic experiences might produce an epigenetic signal that is capable of being passed to future generations. Mice were trained, using foot shocks, to fear a cherry blossom odor. The investigators reported that the mouse offspring had an increased aversion to this specific odor. They suggested epigenetic changes that increase gene expression, rather than in DNA itself, in a gene, M71, that governs the functioning of an odor receptor in the nose that responds specifically to this cherry blossom smell. There were physical changes that correlated with olfactory (smell) function in the brains of the trained mice and their descendants. Several criticisms were reported, including the study's low statistical power as evidence of some irregularity such as bias in reporting results. Due to limits of sample size, there is a probability that an effect will not be demonstrated to within statistical significance even if it exists. The criticism suggested that the probability that all the experiments reported would show positive results if an identical protocol was followed, assuming the claimed effects exist, is merely 0.4%. The authors also did not indicate which mice were siblings, and treated all of the mice as statistically independent. The original researchers pointed out negative results in the paper's appendix that the criticism omitted in its calculations, and undertook to track which mice were siblings in the future.
Transgenerational
Epigenetic mechanisms were a necessary part of the evolutionary origin of cell differentiation. Although epigenetics in multicellular organisms is generally thought to be a mechanism involved in differentiation, with epigenetic patterns "reset" when organisms reproduce, there have been some observations of transgenerational epigenetic inheritance (e.g., the phenomenon of paramutation observed in maize). Although most of these multigenerational epigenetic traits are gradually lost over several generations, the possibility remains that multigenerational epigenetics could be another aspect to evolution and adaptation.
As mentioned above, some define epigenetics as heritable. | Epigenetics | Wikipedia | 410 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
A sequestered germ line or Weismann barrier is specific to animals, and epigenetic inheritance is more common in plants and microbes. Eva Jablonka, Marion J. Lamb and Étienne Danchin have argued that these effects may require enhancements to the standard conceptual framework of the modern synthesis and have called for an extended evolutionary synthesis. Other evolutionary biologists, such as John Maynard Smith, have incorporated epigenetic inheritance into population-genetics models or are openly skeptical of the extended evolutionary synthesis (Michael Lynch). Thomas Dickins and Qazi Rahman state that epigenetic mechanisms such as DNA methylation and histone modification are genetically inherited under the control of natural selection and therefore fit under the earlier "modern synthesis".
Two important ways in which epigenetic inheritance can differ from traditional genetic inheritance, with important consequences for evolution, are:
rates of epimutation can be much faster than rates of mutation
the epimutations are more easily reversible
In plants, heritable DNA methylation mutations are 100,000 times more likely to occur compared to DNA mutations. An epigenetically inherited element such as the PSI+ system can act as a "stop-gap", good enough for short-term adaptation that allows the lineage to survive for long enough for mutation and/or recombination to genetically assimilate the adaptive phenotypic change. The existence of this possibility increases the evolvability of a species.
More than 100 cases of transgenerational epigenetic inheritance phenomena have been reported in a wide range of organisms, including prokaryotes, plants, and animals. For instance, mourning-cloak butterflies will change color through hormone changes in response to experimentation of varying temperatures.
The filamentous fungus Neurospora crassa is a prominent model system for understanding the control and function of cytosine methylation. In this organism, DNA methylation is associated with relics of a genome-defense system called RIP (repeat-induced point mutation) and silences gene expression by inhibiting transcription elongation.
The yeast prion PSI is generated by a conformational change of a translation termination factor, which is then inherited by daughter cells. This can provide a survival advantage under adverse conditions, exemplifying epigenetic regulation which enables unicellular organisms to respond rapidly to environmental stress. Prions can be viewed as epigenetic agents capable of inducing a phenotypic change without modification of the genome. | Epigenetics | Wikipedia | 506 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
Direct detection of epigenetic marks in microorganisms is possible with single molecule real time sequencing, in which polymerase sensitivity allows for measuring methylation and other modifications as a DNA molecule is being sequenced. Several projects have demonstrated the ability to collect genome-wide epigenetic data in bacteria.
Epigenetics in bacteria
While epigenetics is of fundamental importance in eukaryotes, especially metazoans, it plays a different role in bacteria. Most importantly, eukaryotes use epigenetic mechanisms primarily to regulate gene expression which bacteria rarely do. However, bacteria make widespread use of postreplicative DNA methylation for the epigenetic control of DNA-protein interactions. Bacteria also use DNA adenine methylation (rather than DNA cytosine methylation) as an epigenetic signal. DNA adenine methylation is important in bacteria virulence in organisms such as Escherichia coli, Salmonella, Vibrio, Yersinia, Haemophilus, and Brucella. In Alphaproteobacteria, methylation of adenine regulates the cell cycle and couples gene transcription to DNA replication. In Gammaproteobacteria, adenine methylation provides signals for DNA replication, chromosome segregation, mismatch repair, packaging of bacteriophage, transposase activity and regulation of gene expression. There exists a genetic switch controlling Streptococcus pneumoniae (the pneumococcus) that allows the bacterium to randomly change its characteristics into six alternative states that could pave the way to improved vaccines. Each form is randomly generated by a phase variable methylation system. The ability of the pneumococcus to cause deadly infections is different in each of these six states. Similar systems exist in other bacterial genera. In Bacillota such as Clostridioides difficile, adenine methylation regulates sporulation, biofilm formation and host-adaptation.
Medicine
Epigenetics has many and varied potential medical applications. | Epigenetics | Wikipedia | 415 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
Twins
Direct comparisons of identical twins constitute an optimal model for interrogating environmental epigenetics. In the case of humans with different environmental exposures, monozygotic (identical) twins were epigenetically indistinguishable during their early years, while older twins had remarkable differences in the overall content and genomic distribution of 5-methylcytosine DNA and histone acetylation. The twin pairs who had spent less of their lifetime together and/or had greater differences in their medical histories were those who showed the largest differences in their levels of 5-methylcytosine DNA and acetylation of histones H3 and H4.
Dizygotic (fraternal) and monozygotic (identical) twins show evidence of epigenetic influence in humans. DNA sequence differences that would be abundant in a singleton-based study do not interfere with the analysis. Environmental differences can produce long-term epigenetic effects, and different developmental monozygotic twin subtypes may be different with respect to their susceptibility to be discordant from an epigenetic point of view.
A high-throughput study, which denotes technology that looks at extensive genetic markers, focused on epigenetic differences between monozygotic twins to compare global and locus-specific changes in DNA methylation and histone modifications in a sample of 40 monozygotic twin pairs. In this case, only healthy twin pairs were studied, but a wide range of ages was represented, between 3 and 74 years. One of the major conclusions from this study was that there is an age-dependent accumulation of epigenetic differences between the two siblings of twin pairs. This accumulation suggests the existence of epigenetic "drift". Epigenetic drift is the term given to epigenetic modifications as they occur as a direct function with age. While age is a known risk factor for many diseases, age-related methylation has been found to occur differentially at specific sites along the genome. Over time, this can result in measurable differences between biological and chronological age. Epigenetic changes have been found to be reflective of lifestyle and may act as functional biomarkers of disease before clinical threshold is reached. | Epigenetics | Wikipedia | 455 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
A more recent study, where 114 monozygotic twins and 80 dizygotic twins were analyzed for the DNA methylation status of around 6000 unique genomic regions, concluded that epigenetic similarity at the time of blastocyst splitting may also contribute to phenotypic similarities in monozygotic co-twins. This supports the notion that microenvironment at early stages of embryonic development can be quite important for the establishment of epigenetic marks. Congenital genetic disease is well understood and it is clear that epigenetics can play a role, for example, in the case of Angelman syndrome and Prader–Willi syndrome. These are normal genetic diseases caused by gene deletions or inactivation of the genes but are unusually common because individuals are essentially hemizygous because of genomic imprinting, and therefore a single gene knock out is sufficient to cause the disease, where most cases would require both copies to be knocked out.
Genomic imprinting
Some human disorders are associated with genomic imprinting, a phenomenon in mammals where the father and mother contribute different epigenetic patterns for specific genomic loci in their germ cells. The best-known case of imprinting in human disorders is that of Angelman syndrome and Prader–Willi syndrome – both can be produced by the same genetic mutation, chromosome 15q partial deletion, and the particular syndrome that will develop depends on whether the mutation is inherited from the child's mother or from their father.
In the Överkalix study, paternal (but not maternal) grandsons of Swedish men who were exposed during preadolescence to famine in the 19th century were less likely to die of cardiovascular disease. If food was plentiful, then diabetes mortality in the grandchildren increased, suggesting that this was a transgenerational epigenetic inheritance. The opposite effect was observed for females – the paternal (but not maternal) granddaughters of women who experienced famine while in the womb (and therefore while their eggs were being formed) lived shorter lives on average.
Examples of drugs altering gene expression from epigenetic events
The use of beta-lactam antibiotics can alter glutamate receptor activity and the action of cyclosporine on multiple transcription factors. Additionally, lithium can impact autophagy of aberrant proteins, and opioid drugs via chronic use can increase the expression of genes associated with addictive phenotypes. | Epigenetics | Wikipedia | 500 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
Parental nutrition, in utero exposure to stress or endocrine disrupting chemicals, male-induced maternal effects such as the attraction of differential mate quality, and maternal as well as paternal age, and offspring gender could all possibly influence whether a germline epimutation is ultimately expressed in offspring and the degree to which intergenerational inheritance remains stable throughout posterity. However, whether and to what extent epigenetic effects can be transmitted across generations remains unclear, particularly in humans.
Addiction
Addiction is a disorder of the brain's reward system which arises through transcriptional and neuroepigenetic mechanisms and occurs over time from chronically high levels of exposure to an addictive stimulus (e.g., morphine, cocaine, sexual intercourse, gambling). Transgenerational epigenetic inheritance of addictive phenotypes has been noted to occur in preclinical studies. However, robust evidence in support of the persistence of epigenetic effects across multiple generations has yet to be established in humans; for example, an epigenetic effect of prenatal exposure to smoking that is observed in great-grandchildren who had not been exposed.
Research
The two forms of heritable information, namely genetic and epigenetic, are collectively called dual inheritance. Members of the APOBEC/AID family of cytosine deaminases may concurrently influence genetic and epigenetic inheritance using similar molecular mechanisms, and may be a point of crosstalk between these conceptually compartmentalized processes.
Fluoroquinolone antibiotics induce epigenetic changes in mammalian cells through iron chelation. This leads to epigenetic effects through inhibition of α-ketoglutarate-dependent dioxygenases that require iron as a co-factor.
Various pharmacological agents are applied for the production of induced pluripotent stem cells (iPSC) or maintain the embryonic stem cell (ESC) phenotypic via epigenetic approach. Adult stem cells like bone marrow stem cells have also shown a potential to differentiate into cardiac competent cells when treated with G9a histone methyltransferase inhibitor BIX01294. | Epigenetics | Wikipedia | 439 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
Cell plasticity, which is the adaptation of cells to stimuli without changes in their genetic code, requires epigenetic changes. These have been observed in cell plasticity in cancer cells during epithelial-to-mesenchymal transition and also in immune cells, such as macrophages. Interestingly, metabolic changes underly these adaptations, since various metabolites play crucial roles in the chemistry of epigenetic marks. This includes for instance alpha-ketoglutarate, which is required for histone demethylation, and acetyl-Coenzyme A, which is required for histone acetylation.
Epigenome editing
Epigenetic regulation of gene expression that could be altered or used in epigenome editing are or include mRNA/lncRNA modification, DNA methylation modification and histone modification.
CpG sites, SNPs and biological traits
Methylation is a widely characterized mechanism of genetic regulation that can determine biological traits. However, strong experimental evidences correlate methylation patterns in SNPs as an important additional feature for the classical activation/inhibition epigenetic dogma. Molecular interaction data, supported by colocalization analyses, identify multiple nuclear regulatory pathways, linking sequence variation to disturbances in DNA methylation and molecular and phenotypic variation.
UBASH3B locus
UBASH3B encodes a protein with tyrosine phosphatase activity, which has been previously linked to advanced neoplasia. SNP rs7115089 was identified as influencing DNA methylation and expression of this locus, as well as and Body Mass Index (BMI). In fact, SNP rs7115089 is strongly associated with BMI and with genetic variants linked to other cardiovascular and metabolic traits in GWASs. New studies suggesting UBASH3B as a potential mediator of adiposity and cardiometabolic disease. In addition, animal models demonstrated that UBASH3B expression is an indicator of caloric restriction that may drive programmed susceptibility to obesity and it is associated with other measures of adiposity in human peripherical blood. | Epigenetics | Wikipedia | 439 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
NFKBIE locus
SNP rs730775 is located in the first intron of NFKBIE and is a cis eQTL for NFKBIE in whole blood. Nuclear factor (NF)-κB inhibitor ε (NFKBIE) directly inhibits NF-κB1 activity and is significantly co-expressed with NF-κB1, also, it is associated with rheumatoid arthritis. Colocalization analysis supports that variants for the majority of the CpG sites in SNP rs730775 cause genetic variation at the NFKBIE locus which is suggestible linked to rheumatoid arthritis through trans acting regulation of DNA methylation by NF-κB.
FADS1 locus
Fatty acid desaturase 1 (FADS1) is a key enzyme in the metabolism of fatty acids. Moreover, rs174548 in the FADS1 gene shows increased correlation with DNA methylation in people with high abundance of CD8+ T cells. SNP rs174548 is strongly associated with concentrations of arachidonic acid and other metabolites in fatty acid metabolism, blood eosinophil counts. and inflammatory diseases such as asthma. Interaction results indicated a correlation between rs174548 and asthma, providing new insights about fatty acid metabolism in CD8+ T cells with immune phenotypes.
Pseudoscience
As epigenetics is in the early stages of development as a science and is surrounded by sensationalism in the public media, David Gorski and geneticist Adam Rutherford have advised caution against the proliferation of false and pseudoscientific conclusions by new age authors making unfounded suggestions that a person's genes and health can be manipulated by mind control. Misuse of the scientific term by quack authors has produced misinformation among the general public. | Epigenetics | Wikipedia | 379 | 49033 | https://en.wikipedia.org/wiki/Epigenetics | Biology and health sciences | Genetics and taxonomy | null |
In male human anatomy, the glans penis or penile glans, commonly referred to as the glans, (; from Latin glans meaning "acorn") is the bulbous structure at the distal end of the human penis that is the human male's most sensitive erogenous zone and primary anatomical source of sexual pleasure. The glans penis is present in the male reproductive organs of humans and most other mammals where it may appear smooth, spiny, elongated or divided. It is externally lined with mucosal tissue, which creates a smooth texture and glossy appearance. In humans, the glans is located over the distal ends of the corpora cavernosa and is a continuation of the corpus spongiosum of the penis. At the summit appears the urinary meatus and at the base forms the corona glandis. An elastic band of tissue, known as the frenulum, runs on its ventral surface. In men who are not circumcised, it is completely or partially covered by a fold of skin called the foreskin. In adults, the foreskin can generally be retracted over and past the glans manually or sometimes automatically during an erection.
The glans penis develops as the terminal end of the genital tubercle during the embryonic development of the male fetus. The tubercle is present in the embryos of both sexes as an outgrowth in the caudal region that later develops into a primordial phallus. Exposure to male hormones (androgens) initiates the tubercle's development into a penis making the glans penis anatomically homologous to the clitoral glans in females.
The glans is more commonly known as the "head" or the "tip" of the penis, and colloquially referred to in British English and Irish English as the "bellend".
Structure | Glans penis | Wikipedia | 391 | 49084 | https://en.wikipedia.org/wiki/Glans%20penis | Biology and health sciences | Reproductive system | Biology |
The glans penis is a body of spongy erectile tissue that is moulded on the rounded ends of the two corpora cavernosa penis, extending farther on their upper than on their lower surfaces. It is the expanded cap of the corpus spongiosum, a sponge-like region that surrounds the male urethra within the penis maintaining it as a viable channel for ejaculation. The glans is covered by a stratified squamous epithelium and a dense layer of connective tissue equivalent to the dermis of typical skin. The papillary layer of the dermis blends into the dense connective tissue forming the tunica albuginea of the corpus spongiosum behind the glans. The external lining with mucosal tissue is responsible for its typical smooth texture and appearance.
The increase of arterial flow during erection fills the erectile tissue with blood causing the glans to grow in size and sensitivity. While the penis is rigid when erect, the glans itself remains slightly softer. The soft cushiony texture of the glans absorbs impact during rigorous instances of copulation. The proportional size of the glans penis can vary among males. While the shape of the glans is typically acorn-like, in some men it might be wider in circumference than the shaft, giving the penis a mushroom-like appearance, while in others it might be narrower and more akin to a probe in shape. Some researchers have suggested that the glans has evolved to become acorn-, mushroom- or cone-shaped so that during copulation it acts to remove any semen still there from previous sex partners, but this is not supported when looking at primate relatives who have different mating behaviors. | Glans penis | Wikipedia | 366 | 49084 | https://en.wikipedia.org/wiki/Glans%20penis | Biology and health sciences | Reproductive system | Biology |
At the summit of the glans is the slit-like vertical external urethral orifice, called the urinary meatus, through which urine, semen and pre-ejaculatory fluid exit the penis. The circumference of the base of the glans forms a rounded projecting border, the corona glandis, overhanging a deep retroglandular groove known as the coronal sulcus. Behind the corona is the neck of the penis, which separates the glans and the penile shaft. Ventrally, the two glans wings merge on the midline forming the septum glandis and a triangle or a V-shaped area under it. The frenulum is the highly vascularized elastic band of tissue located on the underside of the glans that connects the foreskin to the head of the penis. The frenulum is supple enough to allow the retraction of the foreskin over the glans and pull it back when the erection is gone. In flaccid state, it tightens to narrow the foreskin opening.
Innervation
The glans and the frenulum are innervated by the bilateral dorsal nerve of the penis and the perineal nerve, both divisions of the pudendal nerve. Branches of the dorsal nerve extend through the glans ventrolaterally displaying a three-dimensional innervation pattern. The main branches form smaller bundles of nerves that expand outwards into the tissue of the glans. The rich innervation of the glans penis reveals its function as a primary anatomical source of male sexual pleasure. Yang & Bradley argue; "the distinct pattern of innervation of the glans emphasizes its role as a sensory structure". While Yang & Bradley's (1998) report "showed no areas in the glans to be more densely innervated than others.", Halata & Munger (1986) report that the density of several nerve terminals is greatest in the corona glandis. | Glans penis | Wikipedia | 416 | 49084 | https://en.wikipedia.org/wiki/Glans%20penis | Biology and health sciences | Reproductive system | Biology |
Halata & Spathe (1997) reported; "the glans penis contains a predominance of free nerve endings, numerous genital end bulbs and rarely Pacinian and Ruffinian corpuscles. Merkel nerve endings and Meissner's corpuscles (mechanoreceptors typically found in thick glabrous skin) are not present". The genital end bulbs, that are present throughout the glans, are most numerous in the corona and near the frenulum. Simple, Pacinian and Ruffinian corpuscles are identified predominantly in the corona glandis. The most numerous nerve terminals are free nerve endings present in almost every dermal papilla of the glans, as well as scattered throughout the deeper dermis.
Blood supply
The glans penis receives blood from the internal pudental artery through its branch, the dorsal artery of the penis, which also supplies the foreskin, and the penile shaft. Behind the corona, the terminal branches of the dorsal arteries anastomose with the axial arteries through perforating branches before they end in the glans. Branches of the dorsal artery curve around each side of the distal shaft to enter the glans and the frenulum ventrally. Venous drainage of the penis begins at the base of the glans. Small tributaries deriving from the corona form a venous plexus at the neck of the penis, known as the retro-coronal, or retro-balanic, plexus. Smaller paired venules run into the frenulum and the glans from its ventral surface. The deep dorsal vein, one of the two dorsal veins of the penis, serves as a common vessel receiving blood drained from the glans and the two corpora cavernosa through the circumflex veins that surround them. | Glans penis | Wikipedia | 380 | 49084 | https://en.wikipedia.org/wiki/Glans%20penis | Biology and health sciences | Reproductive system | Biology |
Foreskin
The glans is completely or partially covered by a double-layered fold of skin, known as the foreskin. In adults, glans exposure can be easily achieved by manual retraction of the foreskin or sometimes automatically during erection. The degree of automatic foreskin retraction varies considerably depending on the foreskin length. The foreskin can be characterized as long when the preputial orifice extends beyond the glans during erection or medium when the orifice is located around the meatus. The primary purpose of the foreskin is considered to be the covering of the glans and the urinary meatus, while also maintaining the mucosa in a moist environment.
Foreskin rectractability gradually increases with age. In infancy the foreskin is fused to the glans, it remains non retractable in early childhood and it continues to be tight during preadolescence. The skin begins to loosen up significantly during puberty allowing the glans to be completely exposed when needed. By the age of eighteen most boys will have a fully retractable foreskin.
In some cases, for cultural, medical, or prophylactic reasons some men undergo circumcision or were circumcised as infants, a procedure where the foreskin is partially or completely removed from the penis. The glans of circumcised men remains fully exposed and dry. Several studies have suggested the glans is generally equally sensitive in both circumcised and uncircumcised penises.
Development
The glans develops as the terminal end of a phallic structure, called the genital tubercle, which forms in the embryo regardless of sex during the early weeks of pregnancy. Initially undifferentiated, the tubercle develops into a penis during the development of the reproductive system depending on the exposure to male hormones, such as androgens. In mammals, sexual differentiation is determined by the sperm that carries either an X or a Y (male) chromosome. The Y chromosome contains a sex-determining gene (SRY) that encodes a transcription factor for the protein TDF (testis determining factor) and triggers the creation of testosterone for the embryo's development into a male. | Glans penis | Wikipedia | 463 | 49084 | https://en.wikipedia.org/wiki/Glans%20penis | Biology and health sciences | Reproductive system | Biology |
Although the sex of the infant is determined from the moment of conception, the complete external differentiation of the organs begins about eight or nine weeks after conception. Some sources state that the process will be completed by the twelfth week, while others state that it is clearly evident by the thirteenth week and that the sex organs are fully developed by the sixteenth week.
Both the penis and clitoris develop from the same tissues that become the glans and shaft of the penis and this shared embryonic origin makes these two organs homologous (different versions of the same structure). In the female fetus the absence of testosterone will stop the growth of the phallus causing the tubercle to shrink and form the clitoris. In the male fetus the presence of a Y chromosome leads to the development of the testes, which secrete a large amount of hormones called androgens. These hormones will cause the masculinization of the phenotypically indifferent organs. When exposed to testosterone, the genital tubercle elongates to form the penis. By fusion of the urogenital folds—elongated spindle-shaped structures that contribute to the formation of the urethral groove on the belly aspect of the genital tubercle—the urogenital sinus closes completely to form the spongy urethra and the labioscrotal swellings unite to form the scrotum. The secretion of testosterone during this phase plays a decisive role in the final shaping of the penis. After birth, testosterone levels drop significantly until puberty.
Clinical significance
The epithelium of the glans penis consists of mucosal tissue. Birley et al. report that excessive washing with soap may dry the mucous membrane which covers the glans penis and cause non-specific dermatitis. The condition is described as an inflammation of the skin, often caused by an irritating substance or a contact allergy. Sensitivity to chemicals in certain products can cause an allergic reaction, including irritation, itching and rash. | Glans penis | Wikipedia | 410 | 49084 | https://en.wikipedia.org/wiki/Glans%20penis | Biology and health sciences | Reproductive system | Biology |
Inflammation of the glans penis is known as balanitis. It is a treatable condition that occurs in about 3–11% of males (up to 35% of diabetic males). Edwards reported that it is generally more common in males who have poor hygiene habits or have not been circumcised. It has many causes, including irritation or infection with a wide variety of pathogens. Symptoms of balanitis may appear suddenly or develop gradually. They might include pain, irritation, redness or red patches on the glans penis. Careful identification of the cause with the aid of patient history, physical examination, swabs and cultures, and biopsy are essential in order to determine the proper treatment.
The meatus (opening) of the urethra located at the tip of the glans might become subject to meatal stenosis, a condition mostly seen as a late complication of circumcision. It occurs in about 2–20% of circumcised boys and it is rarely seen in uncircumcised men. It is characterized by a narrowing of the meatus, which might cause sudden or often urges to urinate and burning during the process.
For some individuals who experience difficulty in achieving full glanular engorgement of glans penis, they may be diagnosed with soft glans syndrome (glans insufficiency syndrome). It is often undiagnosed in the general population due to the lack of a standardized nomenclature.
Other animals
Mammals
Carnivores
Male felids are able to urinate backwards by curving the tip of the glans penis backward. In cats, the glans penis is covered with spines. Penile spines also occur on the glans of male and female spotted hyenas. In male dogs the glans penis is smooth and consists of two parts called the bulbus glandis and pars longa glandis. The glans of a fossa's penis extends about halfway down the shaft and is spiny except at the tip. In comparison, the glans of felids is short and spiny, while that of viverrids is smooth and long. | Glans penis | Wikipedia | 456 | 49084 | https://en.wikipedia.org/wiki/Glans%20penis | Biology and health sciences | Reproductive system | Biology |
Rodents
The glans penis of the marsh rice rat is long and robust, averaging long and broad. Winkelmann's mouse can most readily be distinguished from its close relatives by its partially corrugated glans penis. In Thomasomys ucucha, the glans penis is rounded, short, and small and is superficially divided into left and right halves by a trough at the top and a ridge at the bottom. Most of the glans is covered with spines, except for an area near the tip. The glans penis of a male cape ground squirrel is large with a prominent baculum.
Perissodactyls
When erect, the glans of a horse's penis increases by 3 to . The urethra opens within the urethral fossa, a small pouch at the distal end of the glans. Unlike the human glans, the glans of a horse's penis extends backwards on its shaft.
Marsupials, monotremes and bats
The shape of the glans varies among different marsupial species. In most marsupials, the glans is divided, but male macropods have an undivided glans penis.
The glans penis is also divided into two parts in platypuses and echidnas.
Males of Racey's pipistrelle bat have a narrow, egg-shaped glans penis. | Glans penis | Wikipedia | 295 | 49084 | https://en.wikipedia.org/wiki/Glans%20penis | Biology and health sciences | Reproductive system | Biology |
Ohm's law states that the electric current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the three mathematical equations used to describe this relationship:
where is the current through the conductor, V is the voltage measured across the conductor and R is the resistance of the conductor. More specifically, Ohm's law states that the R in this relation is constant, independent of the current. If the resistance is not constant, the previous equation cannot be called Ohm's law, but it can still be used as a definition of static/DC resistance. Ohm's law is an empirical relation which accurately describes the conductivity of the vast majority of electrically conductive materials over many orders of magnitude of current. However some materials do not obey Ohm's law; these are called non-ohmic.
The law was named after the German physicist Georg Ohm, who, in a treatise published in 1827, described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire. Ohm explained his experimental results by a slightly more complex equation than the modern form above (see below).
In physics, the term Ohm's law is also used to refer to various generalizations of the law; for example the vector form of the law used in electromagnetics and material science:
where J is the current density at a given location in a resistive material, E is the electric field at that location, and σ (sigma) is a material-dependent parameter called the conductivity, defined as the inverse of resistivity ρ (rho). This reformulation of Ohm's law is due to Gustav Kirchhoff.
History
In January 1781, before Georg Ohm's work, Henry Cavendish experimented with Leyden jars and glass tubes of varying diameter and length filled with salt solution. He measured the current by noting how strong a shock he felt as he completed the circuit with his body. Cavendish wrote that the "velocity" (current) varied directly as the "degree of electrification" (voltage). He did not communicate his results to other scientists at the time, and his results were unknown until James Clerk Maxwell published them in 1879. | Ohm's law | Wikipedia | 458 | 49090 | https://en.wikipedia.org/wiki/Ohm%27s%20law | Physical sciences | Electrical circuits | null |
Francis Ronalds delineated "intensity" (voltage) and "quantity" (current) for the dry pile—a high voltage source—in 1814 using a gold-leaf electrometer. He found for a dry pile that the relationship between the two parameters was not proportional under certain meteorological conditions.
Ohm did his work on resistance in the years 1825 and 1826, and published his results in 1827 as the book Die galvanische Kette, mathematisch bearbeitet ("The galvanic circuit investigated mathematically"). He drew considerable inspiration from Joseph Fourier's work on heat conduction in the theoretical explanation of his work. For experiments, he initially used voltaic piles, but later used a thermocouple as this provided a more stable voltage source in terms of internal resistance and constant voltage. He used a galvanometer to measure current, and knew that the voltage between the thermocouple terminals was proportional to the junction temperature. He then added test wires of varying length, diameter, and material to complete the circuit. He found that his data could be modeled through the equation
where x was the reading from the galvanometer, ℓ was the length of the test conductor, a depended on the thermocouple junction temperature, and b was a constant of the entire setup. From this, Ohm determined his law of proportionality and published his results.
In modern notation we would write,
where is the open-circuit emf of the thermocouple, is the internal resistance of the thermocouple and is the resistance of the test wire. In terms of the length of the wire this becomes,
where is the resistance of the test wire per unit length. Thus, Ohm's coefficients are, | Ohm's law | Wikipedia | 360 | 49090 | https://en.wikipedia.org/wiki/Ohm%27s%20law | Physical sciences | Electrical circuits | null |
Ohm's law was probably the most important of the early quantitative descriptions of the physics of electricity. We consider it almost obvious today. When Ohm first published his work, this was not the case; critics reacted to his treatment of the subject with hostility. They called his work a "web of naked fancies" and the Minister of Education proclaimed that "a professor who preached such heresies was unworthy to teach science." The prevailing scientific philosophy in Germany at the time asserted that experiments need not be performed to develop an understanding of nature because nature is so well ordered, and that scientific truths may be deduced through reasoning alone. Also, Ohm's brother Martin, a mathematician, was battling the German educational system. These factors hindered the acceptance of Ohm's work, and his work did not become widely accepted until the 1840s. However, Ohm received recognition for his contributions to science well before he died.
In the 1850s, Ohm's law was widely known and considered proved. Alternatives such as "Barlow's law", were discredited, in terms of real applications to telegraph system design, as discussed by Samuel F. B. Morse in 1855.
The electron was discovered in 1897 by J. J. Thomson, and it was quickly realized that it was the particle (charge carrier) that carried electric currents in electric circuits. In 1900, the first (classical) model of electrical conduction, the Drude model, was proposed by Paul Drude, which finally gave a scientific explanation for Ohm's law. In this model, a solid conductor consists of a stationary lattice of atoms (ions), with conduction electrons moving randomly in it. A voltage across a conductor causes an electric field, which accelerates the electrons in the direction of the electric field, causing a drift of electrons which is the electric current. However the electrons collide with atoms which causes them to scatter and randomizes their motion, thus converting kinetic energy to heat (thermal energy). Using statistical distributions, it can be shown that the average drift velocity of the electrons, and thus the current, is proportional to the electric field, and thus the voltage, over a wide range of voltages. | Ohm's law | Wikipedia | 449 | 49090 | https://en.wikipedia.org/wiki/Ohm%27s%20law | Physical sciences | Electrical circuits | null |
The development of quantum mechanics in the 1920s modified this picture somewhat, but in modern theories the average drift velocity of electrons can still be shown to be proportional to the electric field, thus deriving Ohm's law. In 1927 Arnold Sommerfeld applied the quantum Fermi-Dirac distribution of electron energies to the Drude model, resulting in the free electron model. A year later, Felix Bloch showed that electrons move in waves (Bloch electrons) through a solid crystal lattice, so scattering off the lattice atoms as postulated in the Drude model is not a major process; the electrons scatter off impurity atoms and defects in the material. The final successor, the modern quantum band theory of solids, showed that the electrons in a solid cannot take on any energy as assumed in the Drude model but are restricted to energy bands, with gaps between them of energies that electrons are forbidden to have. The size of the band gap is a characteristic of a particular substance which has a great deal to do with its electrical resistivity, explaining why some substances are electrical conductors, some semiconductors, and some insulators.
While the old term for electrical conductance, the mho (the inverse of the resistance unit ohm), is still used, a new name, the siemens, was adopted in 1971, honoring Ernst Werner von Siemens. The siemens is preferred in formal papers.
In the 1920s, it was discovered that the current through a practical resistor actually has statistical fluctuations, which depend on temperature, even when voltage and resistance are exactly constant; this fluctuation, now known as Johnson–Nyquist noise, is due to the discrete nature of charge. This thermal effect implies that measurements of current and voltage that are taken over sufficiently short periods of time will yield ratios of V/I that fluctuate from the value of R implied by the time average or ensemble average of the measured current; Ohm's law remains correct for the average current, in the case of ordinary resistive materials.
Ohm's work long preceded Maxwell's equations and any understanding of frequency-dependent effects in AC circuits. Modern developments in electromagnetic theory and circuit theory do not contradict Ohm's law when they are evaluated within the appropriate limits. | Ohm's law | Wikipedia | 456 | 49090 | https://en.wikipedia.org/wiki/Ohm%27s%20law | Physical sciences | Electrical circuits | null |
Scope
Ohm's law is an empirical law, a generalization from many experiments that have shown that current is approximately proportional to electric field for most materials. It is less fundamental than Maxwell's equations and is not always obeyed. Any given material will break down under a strong-enough electric field, and some materials of interest in electrical engineering are "non-ohmic" under weak fields.
Ohm's law has been observed on a wide range of length scales. In the early 20th century, it was thought that Ohm's law would fail at the atomic scale, but experiments have not borne out this expectation. As of 2012, researchers have demonstrated that Ohm's law works for silicon wires as small as four atoms wide and one atom high.
Microscopic origins
The dependence of the current density on the applied electric field is essentially quantum mechanical in nature; (see Classical and quantum conductivity.) A qualitative description leading to Ohm's law can be based upon classical mechanics using the Drude model developed by Paul Drude in 1900.
The Drude model treats electrons (or other charge carriers) like pinballs bouncing among the ions that make up the structure of the material. Electrons will be accelerated in the opposite direction to the electric field by the average electric field at their location. With each collision, though, the electron is deflected in a random direction with a velocity that is much larger than the velocity gained by the electric field. The net result is that electrons take a zigzag path due to the collisions, but generally drift in a direction opposing the electric field.
The drift velocity then determines the electric current density and its relationship to E and is independent of the collisions. Drude calculated the average drift velocity from p = −eEτ where p is the average momentum, −e is the charge of the electron and τ is the average time between the collisions. Since both the momentum and the current density are proportional to the drift velocity, the current density becomes proportional to the applied electric field; this leads to Ohm's law.
Hydraulic analogy | Ohm's law | Wikipedia | 421 | 49090 | https://en.wikipedia.org/wiki/Ohm%27s%20law | Physical sciences | Electrical circuits | null |
A hydraulic analogy is sometimes used to describe Ohm's law. Water pressure, measured by pascals (or PSI), is the analog of voltage because establishing a water pressure difference between two points along a (horizontal) pipe causes water to flow. The water volume flow rate, as in liters per second, is the analog of current, as in coulombs per second. Finally, flow restrictors—such as apertures placed in pipes between points where the water pressure is measured—are the analog of resistors. We say that the rate of water flow through an aperture restrictor is proportional to the difference in water pressure across the restrictor. Similarly, the rate of flow of electrical charge, that is, the electric current, through an electrical resistor is proportional to the difference in voltage measured across the resistor. More generally, the hydraulic head may be taken as the analog of voltage, and Ohm's law is then analogous to Darcy's law which relates hydraulic head to the volume flow rate via the hydraulic conductivity.
Flow and pressure variables can be calculated in fluid flow network with the use of the hydraulic ohm analogy. The method can be applied to both steady and transient flow situations. In the linear laminar flow region, Poiseuille's law describes the hydraulic resistance of a pipe, but in the turbulent flow region the pressure–flow relations become nonlinear.
The hydraulic analogy to Ohm's law has been used, for example, to approximate blood flow through the circulatory system.
Circuit analysis
In circuit analysis, three equivalent expressions of Ohm's law are used interchangeably:
Each equation is quoted by some sources as the defining relationship of Ohm's law,
or all three are quoted, or derived from a proportional form,
or even just the two that do not correspond to Ohm's original statement may sometimes be given.
The interchangeability of the equation may be represented by a triangle, where V (voltage) is placed on the top section, the I (current) is placed to the left section, and the R (resistance) is placed to the right. The divider between the top and bottom sections indicates division (hence the division bar). | Ohm's law | Wikipedia | 451 | 49090 | https://en.wikipedia.org/wiki/Ohm%27s%20law | Physical sciences | Electrical circuits | null |
Resistive circuits
Resistors are circuit elements that impede the passage of electric charge in agreement with Ohm's law, and are designed to have a specific resistance value R. In schematic diagrams, a resistor is shown as a long rectangle or zig-zag symbol. An element (resistor or conductor) that behaves according to Ohm's law over some operating range is referred to as an ohmic device (or an ohmic resistor) because Ohm's law and a single value for the resistance suffice to describe the behavior of the device over that range.
Ohm's law holds for circuits containing only resistive elements (no capacitances or inductances) for all forms of driving voltage or current, regardless of whether the driving voltage or current is constant (DC) or time-varying such as AC. At any instant of time Ohm's law is valid for such circuits.
Resistors which are in series or in parallel may be grouped together into a single "equivalent resistance" in order to apply Ohm's law in analyzing the circuit.
Reactive circuits with time-varying signals
When reactive elements such as capacitors, inductors, or transmission lines are involved in a circuit to which AC or time-varying voltage or current is applied, the relationship between voltage and current becomes the solution to a differential equation, so Ohm's law (as defined above) does not directly apply since that form contains only resistances having value R, not complex impedances which may contain capacitance (C) or inductance (L).
Equations for time-invariant AC circuits take the same form as Ohm's law. However, the variables are generalized to complex numbers and the current and voltage waveforms are complex exponentials.
In this approach, a voltage or current waveform takes the form Ae, where t is time, s is a complex parameter, and A is a complex scalar. In any linear time-invariant system, all of the currents and voltages can be expressed with the same s parameter as the input to the system, allowing the time-varying complex exponential term to be canceled out and the system described algebraically in terms of the complex scalars in the current and voltage waveforms.
The complex generalization of resistance is impedance, usually denoted Z; it can be shown that for an inductor,
and for a capacitor,
We can now write, | Ohm's law | Wikipedia | 507 | 49090 | https://en.wikipedia.org/wiki/Ohm%27s%20law | Physical sciences | Electrical circuits | null |
where V and I are the complex scalars in the voltage and current respectively and Z is the complex impedance.
This form of Ohm's law, with Z taking the place of R, generalizes the simpler form. When Z is complex, only the real part is responsible for dissipating heat.
In a general AC circuit, Z varies strongly with the frequency parameter s, and so also will the relationship between voltage and current.
For the common case of a steady sinusoid, the s parameter is taken to be , corresponding to a complex sinusoid . The real parts of such complex current and voltage waveforms describe the actual sinusoidal currents and voltages in a circuit, which can be in different phases due to the different complex scalars.
Linear approximations
Ohm's law is one of the basic equations used in the analysis of electrical circuits. It applies to both metal conductors and circuit components (resistors) specifically made for this behaviour. Both are ubiquitous in electrical engineering. Materials and components that obey Ohm's law are described as "ohmic" which means they produce the same value for resistance (R = V/I) regardless of the value of V or I which is applied and whether the applied voltage or current is DC (direct current) of either positive or negative polarity or AC (alternating current). | Ohm's law | Wikipedia | 275 | 49090 | https://en.wikipedia.org/wiki/Ohm%27s%20law | Physical sciences | Electrical circuits | null |
In a true ohmic device, the same value of resistance will be calculated from R = V/I regardless of the value of the applied voltage V. That is, the ratio of V/I is constant, and when current is plotted as a function of voltage the curve is linear (a straight line). If voltage is forced to some value V, then that voltage V divided by measured current I will equal R. Or if the current is forced to some value I, then the measured voltage V divided by that current I is also R. Since the plot of I versus V is a straight line, then it is also true that for any set of two different voltages V1 and V2 applied across a given device of resistance R, producing currents I1 = V1/R and I2 = V2/R, that the ratio (V1 − V2)/(I1 − I2) is also a constant equal to R. The operator "delta" (Δ) is used to represent a difference in a quantity, so we can write ΔV = V1 − V2 and ΔI = I1 − I2. Summarizing, for any truly ohmic device having resistance R, V/I = ΔV/ΔI = R for any applied voltage or current or for the difference between any set of applied voltages or currents. | Ohm's law | Wikipedia | 279 | 49090 | https://en.wikipedia.org/wiki/Ohm%27s%20law | Physical sciences | Electrical circuits | null |
There are, however, components of electrical circuits which do not obey Ohm's law; that is, their relationship between current and voltage (their I–V curve) is nonlinear (or non-ohmic). An example is the p–n junction diode (curve at right). As seen in the figure, the current does not increase linearly with applied voltage for a diode. One can determine a value of current (I) for a given value of applied voltage (V) from the curve, but not from Ohm's law, since the value of "resistance" is not constant as a function of applied voltage. Further, the current only increases significantly if the applied voltage is positive, not negative. The ratio V/I for some point along the nonlinear curve is sometimes called the static, or chordal, or DC, resistance, but as seen in the figure the value of total over total varies depending on the particular point along the nonlinear curve which is chosen. This means the "DC resistance" V/I at some point on the curve is not the same as what would be determined by applying an AC signal having peak amplitude volts or amps centered at that same point along the curve and measuring . However, in some diode applications, the AC signal applied to the device is small and it is possible to analyze the circuit in terms of the dynamic, small-signal, or incremental resistance, defined as the one over the slope of the V–I curve at the average value (DC operating point) of the voltage (that is, one over the derivative of current with respect to voltage). For sufficiently small signals, the dynamic resistance allows the Ohm's law small signal resistance to be calculated as approximately one over the slope of a line drawn tangentially to the V–I curve at the DC operating point. | Ohm's law | Wikipedia | 379 | 49090 | https://en.wikipedia.org/wiki/Ohm%27s%20law | Physical sciences | Electrical circuits | null |
Temperature effects
Ohm's law has sometimes been stated as, "for a conductor in a given state, the electromotive force is proportional to the current produced. "That is, that the resistance, the ratio of the applied electromotive force (or voltage) to the current, "does not vary with the current strength."The qualifier "in a given state" is usually interpreted as meaning "at a constant temperature," since the resistivity of materials is usually temperature dependent. Because the conduction of current is related to Joule heating of the conducting body, according to Joule's first law, the temperature of a conducting body may change when it carries a current. The dependence of resistance on temperature therefore makes resistance depend upon the current in a typical experimental setup, making the law in this form difficult to directly verify. Maxwell and others worked out several methods to test the law experimentally in 1876, controlling for heating effects. Usually, the measurements of a sample resistance are carried out at low currents to prevent Joule heating. However, even a small current causes heating(cooling) at the first(second) sample contact due to the Peltier effect. The temperatures at the sample contacts become different, their difference is linear in current. The voltage drop across the circuit includes additionally the Seebeck thermoelectromotive force which again is again linear in current. As a result, there exists a thermal correction to the sample resistance even at negligibly small current. The magnitude of the correction could be comparable with the sample resistance.
Relation to heat conductions
Ohm's principle predicts the flow of electrical charge (i.e. current) in electrical conductors when subjected to the influence of voltage differences; Jean-Baptiste-Joseph Fourier's principle predicts the flow of heat in heat conductors when subjected to the influence of temperature differences.
The same equation describes both phenomena, the equation's variables taking on different meanings in the two cases. Specifically, solving a heat conduction (Fourier) problem with temperature (the driving "force") and flux of heat (the rate of flow of the driven "quantity", i.e. heat energy) variables also solves an analogous electrical conduction (Ohm) problem having electric potential (the driving "force") and electric current (the rate of flow of the driven "quantity", i.e. charge) variables. | Ohm's law | Wikipedia | 491 | 49090 | https://en.wikipedia.org/wiki/Ohm%27s%20law | Physical sciences | Electrical circuits | null |
The basis of Fourier's work was his clear conception and definition of thermal conductivity. He assumed that, all else being the same, the flux of heat is strictly proportional to the gradient of temperature. Although undoubtedly true for small temperature gradients, strictly proportional behavior will be lost when real materials (e.g. ones having a thermal conductivity that is a function of temperature) are subjected to large temperature gradients.
A similar assumption is made in the statement of Ohm's law: other things being alike, the strength of the current at each point is proportional to the gradient of electric potential. The accuracy of the assumption that flow is proportional to the gradient is more readily tested, using modern measurement methods, for the electrical case than for the heat case.
Other versions
Ohm's law, in the form above, is an extremely useful equation in the field of electrical/electronic engineering because it describes how voltage, current and resistance are interrelated on a "macroscopic" level, that is, commonly, as circuit elements in an electrical circuit. Physicists who study the electrical properties of matter at the microscopic level use a closely related and more general vector equation, sometimes also referred to as Ohm's law, having variables that are closely related to the V, I, and R scalar variables of Ohm's law, but which are each functions of position within the conductor. Physicists often use this continuum form of Ohm's Law:
where is the electric field vector with units of volts per meter (analogous to of Ohm's law which has units of volts), is the current density vector with units of amperes per unit area (analogous to of Ohm's law which has units of amperes), and ρ "rho" is the resistivity with units of ohm·meters (analogous to of Ohm's law which has units of ohms). The above equation is also written as where "sigma" is the conductivity which is the reciprocal of .
The voltage between two points is defined as: | Ohm's law | Wikipedia | 421 | 49090 | https://en.wikipedia.org/wiki/Ohm%27s%20law | Physical sciences | Electrical circuits | null |
with the element of path along the integration of electric field vector E. If the applied E field is uniform and oriented along the length of the conductor as shown in the figure, then defining the voltage V in the usual convention of being opposite in direction to the field (see figure), and with the understanding that the voltage V is measured differentially across the length of the conductor allowing us to drop the Δ symbol, the above vector equation reduces to the scalar equation:
Since the field is uniform in the direction of wire length, for a conductor having uniformly consistent resistivity ρ, the current density will also be uniform in any cross-sectional area and oriented in the direction of wire length, so we may write:
Substituting the above 2 results (for E and J respectively) into the continuum form shown at the beginning of this section:
The electrical resistance of a uniform conductor is given in terms of resistivity by:
where ℓ is the length of the conductor in SI units of meters, is the cross-sectional area (for a round wire if is radius) in units of meters squared, and ρ is the resistivity in units of ohm·meters.
After substitution of R from the above equation into the equation preceding it, the continuum form of Ohm's law for a uniform field (and uniform current density) oriented along the length of the conductor reduces to the more familiar form:
A perfect crystal lattice, with low enough thermal motion and no deviations from periodic structure, would have no resistivity, but a real metal has crystallographic defects, impurities, multiple isotopes, and thermal motion of the atoms. Electrons scatter from all of these, resulting in resistance to their flow.
The more complex generalized forms of Ohm's law are important to condensed matter physics, which studies the properties of matter and, in particular, its electronic structure. In broad terms, they fall under the topic of constitutive equations and the theory of transport coefficients.
Magnetic effects
If an external B-field is present and the conductor is not at rest but moving at velocity , then an extra term must be added to account for the current induced by the Lorentz force on the charge carriers.
In the rest frame of the moving conductor this term drops out because . There is no contradiction because the electric field in the rest frame differs from the E-field in the lab frame: .
Electric and magnetic fields are relative, see Lorentz transformation. | Ohm's law | Wikipedia | 493 | 49090 | https://en.wikipedia.org/wiki/Ohm%27s%20law | Physical sciences | Electrical circuits | null |
If the current is alternating because the applied voltage or E-field varies in time, then reactance must be added to resistance to account for self-inductance, see electrical impedance. The reactance may be strong if the frequency is high or the conductor is coiled.
Conductive fluids
In a conductive fluid, such as a plasma, there is a similar effect. Consider a fluid moving with the velocity in a magnetic field . The relative motion induces an electric field which exerts electric force on the charged particles giving rise to an electric current . The equation of motion for the electron gas, with a number density , is written as
where , and are the charge, mass and velocity of the electrons, respectively. Also, is the frequency of collisions of the electrons with ions which have a velocity field . Since, the electron has a very small mass compared with that of ions, we can ignore the left hand side of the above equation to write
where we have used the definition of the current density, and also put which is the electrical conductivity. This equation can also be equivalently written as
where is the electrical resistivity. It is also common to write instead of which can be confusing since it is the same notation used for the magnetic diffusivity defined as . | Ohm's law | Wikipedia | 258 | 49090 | https://en.wikipedia.org/wiki/Ohm%27s%20law | Physical sciences | Electrical circuits | null |
A vacuum cleaner, also known simply as a vacuum, is a device that uses suction, and often agitation, in order to remove dirt and other debris from carpets and hard floors.
The dirt is collected into a dust bag or a plastic bin. Vacuum cleaners, which are used in homes as well as in commercial settings, exist in a variety of sizes and types, including stick vacuums, handheld vacuums, upright vacuums, and canister vacuums. Specialized shop vacuums can be used to clean both solid debris and liquids.
Name
Although vacuum cleaner and the short form vacuum are neutral names, in some countries (UK, Ireland) hoover is used instead as a genericized trademark, and as a verb. The name comes from the Hoover Company, one of the first and most influential companies in the development of the device. In New Zealand, particularly the Southland region, it is sometimes called a lux, likewise a genericized trademark and used as a verb. The device is also sometimes called a sweeper although the same term also refers to a carpet sweeper, a similar invention.
History
The vacuum cleaner evolved from the carpet sweeper via manual vacuum cleaners. The first manual models, using bellows, were developed in the 1860s, and the first motorized designs appeared at the turn of the 20th century, with the first decade being the boom decade.
Manual vacuums
In 1860 a manual vacuum cleaner was invented by Daniel Hess of West Union, Iowa. Called a "carpet sweeper", it gathered dust with a rotating brush and had a bellows for generating suction.
Another early model (1869) was the "Whirlwind", invented in Chicago in 1868 by Ives W. McGaffey. The bulky device worked with a belt driven fan cranked by hand that made it awkward to operate, although it was commercially marketed with mixed success.
A similar model was constructed by Melville R. Bissell of Grand Rapids, Michigan in 1876, who also manufactured carpet sweepers. The company later added portable vacuum cleaners to its line of cleaning tools.
Powered vacuum cleaners | Vacuum cleaner | Wikipedia | 421 | 49105 | https://en.wikipedia.org/wiki/Vacuum%20cleaner | Technology | Household appliances | null |
The end of the 19th century saw the introduction of powered cleaners, although early types used some variation of blowing air to clean instead of suction. One appeared in 1898 when John S. Thurman of St. Louis, Missouri, submitted a patent (U.S. No. 634,042) for a "pneumatic carpet renovator" which blew dust into a receptacle. Thurman's system, powered by an internal combustion engine, traveled to the customer's residence on a horse-drawn wagon as part of a door-to-door cleaning service. Corrine Dufour of Savannah, Georgia, received two patents in 1899 and 1900 for another blown-air system that seems to have featured the first use of an electric motor.
In 1901 powered vacuum cleaners using suction were invented independently by British engineer Hubert Cecil Booth and American inventor David T. Kenney. Booth also may have coined the word "vacuum cleaner". Booth's horse-drawn combustion-engine-powered "Puffing Billy", maybe derived from Thurman's blown-air design, relied upon just suction with air pumped through a cloth filter and was offered as part of his cleaning services. Kenney's was a stationary steam-engine-powered system with pipes and hoses reaching into all parts of the building.
Domestic vacuum cleaner
The first vacuum-cleaning device to be portable and marketed at the domestic market was built in 1905 by Walter Griffiths, a manufacturer in Birmingham, England. His Griffith's Improved Vacuum Apparatus for Removing Dust from Carpets resembled modern-day cleaners; it was portable, easy to store, and powered by "any one person (such as the ordinary domestic servant)", who would have the task of compressing a bellows-like contraption to suck up dust through a removable, flexible pipe, to which a variety of shaped nozzles could be attached.
In 1906 James B. Kirby developed his first of many vacuums called the "Domestic Cyclone". It used water for dirt separation. Later revisions came to be known as the Kirby Vacuum Cleaner. The Cleveland, Ohio factory was built in 1916 and remains open currently, and all Kirby vacuum cleaners are manufactured in the United States. | Vacuum cleaner | Wikipedia | 460 | 49105 | https://en.wikipedia.org/wiki/Vacuum%20cleaner | Technology | Household appliances | null |
In 1907 department store janitor James Murray Spangler (1848–1915) of Canton, Ohio, invented the first portable electric vacuum cleaner, obtaining a patent for the Electric Suction Sweeper on 2 June 1908. Crucially, in addition to suction from an electric fan that blew the dirt and dust into a soap box and one of his wife's pillow cases, Spangler's design utilized a rotating brush to loosen debris. Unable to produce the design himself due to lack of funding, he sold the patent in 1908 to local leather goods manufacturer William Henry Hoover (1849–1932), who had Spangler's machine redesigned with a steel casing, casters, and attachments, founding the company that in 1922 was renamed the Hoover Company. Their first vacuum was the 1908 Model O, which sold for $60 ($ in dollars). Subsequent innovations included the beater bar in 1919 ("It beats as it sweeps as it cleans"), disposal filter bags in the 1920s, and an upright vacuum cleaner in 1926.
In Continental Europe, the Fisker and Nielsen company in Denmark was the first to sell vacuum cleaners in 1910. The design weighed just and could be operated by a single person. The Swedish company Electrolux launched their Model V in 1921 with the innovation of being able to lie on the floor on two thin metal runners. In the 1930s the German company Vorwerk started marketing vacuum cleaners of their own design which they sold through direct sales.
Post-Second World War
For many years after their introduction, vacuum cleaners remained a luxury item, but after the Second World War, they became common among the middle classes. Vacuums tend to be more common in Western countries, because in most other parts of the world, wall-to-wall carpeting is uncommon and homes have tile or hardwood floors, which are easily swept, wiped or mopped manually without power assist.
The last decades of the 20th century saw the more widespread use of technologies developed earlier, including filterless cyclonic dirt separation, central vacuum systems and rechargeable hand-held vacuums. In addition, miniaturized computer technology and improved batteries allowed the development of a new type of machine—the autonomous robotic vacuum cleaner. In 1997 Electrolux of Sweden demonstrated the Electrolux Trilobite, the first autonomous cordless robotic vacuum cleaner on the BBC-TV program Tomorrow's World, introducing it to the consumer market in 2001. | Vacuum cleaner | Wikipedia | 496 | 49105 | https://en.wikipedia.org/wiki/Vacuum%20cleaner | Technology | Household appliances | null |
Recent developments
In 2004 a British company released AiRider, a hovering vacuum cleaner that floats on a cushion of air, similar to a hovercraft, to make it light-weight and easier to maneuver (compared to using wheels).
A British inventor has developed a new cleaning technology known as Air Recycling Technology, which, instead of using a vacuum, uses an air stream to collect dust from the carpet. This technology was tested by the Market Transformation Programme (MTP) and shown to be more energy-efficient than the vacuum method. Although working prototypes exist, Air Recycling Technology is not currently used in any production cleaner.
Modern configurations
A wide variety of technologies, designs, and configurations are available for both domestic and commercial cleaning jobs.
Upright
Upright vacuum cleaners are popular in the US, UK, and numerous Commonwealth countries, but unusual in some Continental European countries. They take the form of a cleaning head, onto which a handle and bag are attached. Upright designs generally employ a rotating brushroll or beater bar, which removes dirt through a combination of sweeping and vibration. There are two types of upright vacuums; dirty-air/direct fan (found mostly on commercial vacuums), or clean-air/fan-bypass (found on most of today's domestic vacuums).
The older of the two designs, direct-fan cleaners have a large impeller (fan) mounted close to the suction opening, through which the dirt passes directly, before being blown into a bag. The motor is often cooled by a separate cooling fan. Because of their large-bladed fans, and comparatively short airpaths, direct-fan cleaners create a very efficient airflow from a low amount of power, and make effective carpet cleaners. Their "above-floor" cleaning power is less efficient, since the airflow is lost when it passes through a long hose, and the fan has been optimized for airflow volume and not suction. | Vacuum cleaner | Wikipedia | 396 | 49105 | https://en.wikipedia.org/wiki/Vacuum%20cleaner | Technology | Household appliances | null |
Fan-bypass uprights have their motor mounted after the filter bag. Dust is removed from the airstream by the bag, and usually a filter, before it passes through the fan. The fans are smaller, and are usually a combination of several moving and stationary turbines working in sequence to boost power. The motor is cooled by the airstream passing through it. Fan-bypass vacuums are good for both carpet and above-floor cleaning, since their suction does not significantly diminish over the distance of a hose, as it does in direct-fan cleaners. However, their air-paths are much less efficient, and can require more than twice as much power as direct-fan cleaners to achieve the same results.
The most common upright vacuum cleaners use a drive-belt powered by the suction motor to rotate the brush-roll. However, a more common design of dual motor upright is available. In these cleaners, the suction is provided via a large motor, while the brushroll is powered by a separate, smaller motor, which does not create any suction. The brush-roll motor can sometimes be switched off, so hard floors can be cleaned without the brush-roll scattering the dirt. It may also have an automatic cut-off feature which shuts the motor off if the brush-roll becomes jammed, protecting it from damage.
Canister
Canister models (in the UK also often called cylinder models) dominate the European market. They have the motor and dust collectors (using a bag or bagless) in a separate unit, usually mounted on wheels, which is connected to the vacuum head by a flexible hose. Their main advantage is flexibility, as the user can attach different heads for different tasks, and maneuverability (the head can reach under furniture and makes it very easy to vacuum stairs and vertical surfaces). Many cylinder models have power heads as standard or add-on equipment containing the same sort of mechanical beaters as in upright units, making them as efficient on carpets as upright models. Such beaters are driven by a separate electric motor or a turbine which uses the suction power to spin the brushroll via a drive belt. | Vacuum cleaner | Wikipedia | 438 | 49105 | https://en.wikipedia.org/wiki/Vacuum%20cleaner | Technology | Household appliances | null |
Drum
Drum or shop vac models are essentially heavy-duty industrial versions of cylinder vacuum cleaners, where the canister consists of a large vertically positioned drum which can be stationary or on wheels. Smaller versions, for use in garages or small workshops, are usually electrically powered. Larger models, which can store over , are often hooked up to compressed air, utilizing the Venturi effect to produce a partial vacuum. Built-in dust collection systems are also used in many workshops.
Wet/dry
Wet or wet/dry vacuum cleaners are a specialized form of cylinder/drum models that can be used to clean up wet or liquid spills. They are generally designed to be used both indoors and outdoors and to accommodate both wet and dry debris; some are also equipped with an exhaust port or detachable blower for reversing the airflow, a useful function for everything from clearing a clogged hose to blowing dust into a corner for easy collection.
Shop vacs are able to collect large, bulky or otherwise inconvenient material that would damage or foul household vacuum cleaners, like sawdust, swarf, and liquids.
They use wide hoses, which open directly into the collection chamber (usually a bucket-like cylinder constituting the body of the vacuum). As the airstream enters the larger volume, its flow slows down, allowing the material to drop into the chamber before air is sucked out through the filter and to the vacuum's exhaust.
Shop vacs' performance can be evaluated by a number of metrics. Commonly used ones include the motor's rating (using power measurements like watts or horsepower), the vacuum's ability to develop suction (using pressure measurements like inches of water), and total airflow through the system (using volume rate measurements like cubic feet per minute).
Related to the wet vacuum is the extraction vacuum cleaner used mainly in hot water extraction, a method of cleaning hard-to-move pieces of fabric like carpets. These machines are able to spray hot soapy water and then suck it back out of the fabric, removing dirt in the process.
Wet vacuum cleaners have been modified by end users, adding an internally-mounted sump pump for continuous removal of liquids without having to stop to empty the tank. | Vacuum cleaner | Wikipedia | 462 | 49105 | https://en.wikipedia.org/wiki/Vacuum%20cleaner | Technology | Household appliances | null |
Pneumatic
Pneumatic or pneumatic wet/dry vacuum cleaners are a specialized form of wet/dry models that hook up to compressed air. They commonly can accommodate both wet and dry soilage, a useful feature in industrial plants and manufacturing facilities.
Backpack
Backpack vacuum cleaners are commonly used for commercial cleaning: they allow the user to move rapidly about a large area. They are essentially small canister vacuums strapped onto the user's back.
Hand-held
Lightweight hand-held vacuum cleaners, either powered from rechargeable batteries or mains power, are also popular for cleaning up smaller spills. Frequently seen examples include the Black & Decker DustBuster, which was introduced in 1979, and numerous handheld models by Dirt Devil, which were first introduced in 1984. Some battery-powered handheld vacuums are wet/dry rated; the appliance must be partially disassembled and cleaned after picking up wet materials to avoid developing unpleasant odors.
Robotic
In the late 1990s and early 2000s, several companies developed robotic vacuum cleaners, a form of carpet sweeper usually equipped with limited suction power. Some prominent brands are Roomba, Neato, and bObsweep. These machines move autonomously while collecting surface dust and debris into a dustbin. They can usually navigate around furniture and come back to a docking station to charge their batteries, and a few are able to empty their dust containers into the dock as well. Most models are equipped with motorized brushes and a vacuum motor to collect dust and debris. While most robotic vacuum cleaners are designed for home use, some models are appropriate for operation in offices, hotels, hospitals, etc.
In December 2009, Neato Robotics launched the world's first robotic vacuum cleaner which uses a rotating laser-based range-finder (a form of lidar) to scan and map its surrounding. It uses this map to clean the floor methodically, even if it requires the robot to return to its base multiple times to recharge itself. In many cases it will notice when an area of the floor that was previously inaccessible becomes reachable, such as when a dog wakes up from a nap, and return to vacuum that area.
Cyclonic | Vacuum cleaner | Wikipedia | 451 | 49105 | https://en.wikipedia.org/wiki/Vacuum%20cleaner | Technology | Household appliances | null |
Portable vacuum cleaners working on the cyclonic separation principle became popular in the 1990s. This dirt separation principle was well known and often used in central vacuum systems. Cleveland's P.A. Geier Company had obtained a patent on a cyclonic vacuum cleaner as early as 1928, which was later sold to Health-Mor in 1939, introducing the Filter Queen cyclonic canister vacuum cleaner.
In 1979, James Dyson introduced a portable unit with cyclonic separation, adapting this design from industrial saw mills. He launched his cyclone cleaner first in Japan in the 1980s at a cost of about US$1800 and in 1993 released the Dyson DC01 upright in the UK for £200. Critics expected that people would not buy a vacuum cleaner at twice the price of a conventional unit, but the Dyson design later became the most popular cleaner in the UK.
Cyclonic cleaners do not use filtration bags. Instead, the dust is separated in a detachable cylindrical collection vessel or bin. Air and dust are sucked at high speed into the collection vessel at a direction tangential to the vessel wall, creating a fast-spinning vortex. The dust particles and other debris move to the outside of the vessel by centrifugal force, where they fall due to gravity.
In fixed-installation central vacuum cleaners, the cleaned air may be exhausted directly outside without need for further filtration. A well-designed cyclonic filtration system loses suction power due to airflow restriction only when the collection vessel is almost full. This is in marked contrast to filter bag systems, which lose suction when pores in the filter become clogged as dirt and dust are collected.
In portable cyclonic models, the cleaned air from the center of the vortex is expelled from the machine after passing through a number of successively finer filters at the top of the container. The first filter is intended to trap particles which could damage the subsequent filters that remove fine dust particles. The filters must regularly be cleaned or replaced to ensure that the machine continues to perform efficiently.
Since Dyson's success in raising public awareness of cyclonic separation, several other companies have introduced cyclone models. Competing manufacturers include Hoover, Bissell, Bosch, Eureka, Electrolux and Vax. This high level of competition means the cheapest models are generally no more expensive than a conventional cleaner.
Central | Vacuum cleaner | Wikipedia | 485 | 49105 | https://en.wikipedia.org/wiki/Vacuum%20cleaner | Technology | Household appliances | null |
Central vacuum cleaners, also known as built-in or ducted, are a type of canister/cylinder model which has the motor and dirt filtration unit located in a central location in a building, and connected by pipes to fixed vacuum inlets installed throughout the building. Only the hose and cleaning head need be carried from room to room, and the hose is commonly 8 m (25 ft) long, allowing a large range of movement without changing vacuum inlets. Plastic or metal piping connects the inlets to the central unit. The vacuum head may be unpowered, or have beaters operated by an electric motor or by an air-driven turbine.
The dirt bag or collection bin in a central vacuum system is usually so large that emptying or changing needs to be done less often, perhaps a few times per year for an ordinary household. The central unit usually stays in stand-by, and is turned on by a switch on the handle of the hose. Alternately, the unit powers up when the hose is plugged into the wall inlet, when the metal hose connector makes contact with two prongs in the wall inlet and control current is transmitted through low voltage wires to the main unit.
A central vacuum typically produces greater suction than common portable vacuum cleaners because a larger fan and more powerful motor can be used when they are not required to be portable. A cyclonic separation system, if used, does not lose suction as the collection container fills up, until the container is nearly full. This is in marked contrast to filter-bag designs, which start losing suction immediately as pores in the filter become clogged by accumulated dirt and dust.
A benefit to allergy sufferers is that unlike a standard vacuum cleaner, which must blow some of the dirt collected back into the room being cleaned (no matter how efficient its filtration), a central vacuum removes all the dirt collected to the central unit. Since this central unit is usually located outside the living area, no dust is recirculated back into the room being cleaned. Also it is possible on most newer models to vent the exhaust entirely outside, even with the unit inside the living quarters.
Another benefit of the central vacuum is, because of the remote location of the motor unit, there is much less noise in the room being cleaned than with a standard vacuum cleaner.
Constellation | Vacuum cleaner | Wikipedia | 479 | 49105 | https://en.wikipedia.org/wiki/Vacuum%20cleaner | Technology | Household appliances | null |
Introduced in 1954, The Hoover Company's Constellation was of the cylinder type and lacked wheels. Instead the vacuum cleaner floated on its exhaust, operating as a hovercraft, although that was not true of the earliest models, which had a rotating hose, the intention being that the user would place the unit in the center of the room, and work around the cleaner.
The Constellation was changed and updated over the years until discontinued in 1975. Later Constellations routed all of the exhaust under the vacuum using an airfoil. The updated design was quiet even by modern standards, particularly on carpet, because it muffled the sound. Those models float on carpet or bare floor although, on hard flooring, the exhaust air tends to scatter any fluff or debris around.
Hoover re-released an updated version of the later-model Constellation in the US (model # S3341 in Pearl White and # S3345 in stainless steel). Changes included a HEPA filtration bag, a 12-amp motor, a turbine-powered brush roll, and a redesigned version of the handle. The same model was marketed in the UK under the Maytag brand, called the Satellite because of licensing restrictions. It was sold from 2006 to 2009.
Vehicles
See vacuum truck for very big vacuum cleaners mounted on vehicles.
Other
Some other vacuum cleaners include an electric mop in the same machine: for a dry and a later wet clean.
The iRobot company developed the Scooba, a robotic wet vacuum cleaner that carries its own cleaning solution, applies it and scrubs the floor, and vacuums the dirty water into a collection tank.
Technology
A vacuum's suction is caused by a difference in air pressure. A fan driven by an electric motor (often a universal motor) reduces the pressure inside the machine. Atmospheric pressure then pushes the air through the carpet and into the nozzle, and so the dust is literally pushed into the bag.
Tests have shown that vacuuming can kill 100% of young fleas and 96% of adult fleas.
Exhaust filtration | Vacuum cleaner | Wikipedia | 419 | 49105 | https://en.wikipedia.org/wiki/Vacuum%20cleaner | Technology | Household appliances | null |
Vacuums by their nature cause dust to become airborne, by exhausting air that is not completely filtered. This can cause health problems since the operator ends up inhaling respirable dust, which is also redeposited into the area being cleaned. There are several methods manufacturers use to control this problem, some of which may be combined in a single appliance. Typically a filter is positioned so that the incoming air passes through it before it reaches the fan, and then the filtered air passes through the motor for cooling purposes. Some other designs use a completely separate air intake for cooling.
It is nearly impossible for a practical air filter to completely remove all ultrafine particles from a dirt-laden airstream. An ultra-efficient air filter will immediately clog up and become ineffective during everyday use, and practical filters are a compromise between filtering effectiveness and restriction of airflow. One way to sidestep this problem is to exhaust partially filtered air to the outdoors, which is a design feature of some central vacuum systems. Specially engineered portable vacuums may also utilize this design, but are more awkward to set up and use, requiring temporary installation of a separate exhaust hose to an exterior window. | Vacuum cleaner | Wikipedia | 239 | 49105 | https://en.wikipedia.org/wiki/Vacuum%20cleaner | Technology | Household appliances | null |
Bag: The most common method to capture the debris vacuumed up involves a paper or fabric bag that allows air to pass through, but attempts to trap most of the dust and debris. The bag may become clogged with fine dust before it is full. The bag may be disposable, or designed to be cleaned and re-used.
Bagless: In non-cyclonic bagless models, the role of the bag is taken by a removable container and a reusable filter, equivalent to a reusable fabric bag.
Cyclonic separation: A vacuum cleaner employing this method is also bagless. It causes intake air to be cycled or spun so fast that most of the dust is forced out of the air and falls into a collection bin. The operation is similar to that of a centrifuge. Centrifugal separators eliminate the problem of a bag becoming clogged with fine dust.
Water filtration: First seen commercially in the 1920s in the form of the Newcombe Separator (later to become the Rexair Rainbow), a water filtration vacuum cleaner uses a water bath as a filter. It forces the dirt-laden intake air to pass through water before it is exhausted, so that wet dust cannot become airborne. The water trap filtration and low speed may also allow the user to use the machine as a stand-alone air purifier and humidifier unit. The dirty water must be dumped out and the appliance must be cleaned after each use, to avoid growth of bacteria and mold, causing unpleasant odors.
Ultra fine air filter: Also called HEPA filtered, this method is used as a secondary filter after the air has passed through the rest of the machine. It is meant to remove any remaining dust that could harm the operator. Some vacuum cleaners also use an activated charcoal filter to remove odors.
Ordinary vacuum cleaners should never be used to clean up asbestos fibers, even if fitted with a HEPA filter. Specially-designed machines are required to safely clean up asbestos.
Attachments
Most vacuum cleaners are supplied with numerous specialized attachments, such as tools, brushes and extension wands, which allow them to reach otherwise inaccessible places or to be used for cleaning a variety of surfaces. The most common of these tools are:
Hard floor brush (for non-upright designs)
Powered floor nozzle (for canister designs)
Dusting brush
Crevice tool
Upholstery nozzle
Specifications | Vacuum cleaner | Wikipedia | 508 | 49105 | https://en.wikipedia.org/wiki/Vacuum%20cleaner | Technology | Household appliances | null |
The performance of a vacuum cleaner can be measured by several parameters:
Airflow, in litres per second [l/s] or cubic feet per minute (CFM or ft3/min)
Air speed, in metres per second [m/s] or miles per hour [mph]
Suction, vacuum, or water lift, in pascals [Pa] or inches of water
Other specifications of a vacuum cleaner are:
Weight, in kilograms [kg] or pounds [lb]
Noise, in decibels [dB]
Power cord length and hose length (as applicable)
Suction (Pa)
The suction is the maximum pressure difference that the pump can create. For example, a typical domestic model has a suction of about negative 20 kPa. This means that it can lower the pressure inside the hose from normal atmospheric pressure (about 100 kPa) by 20 kPa. The higher the suction rating, the more powerful the cleaner. One inch of water is equivalent to about 249 Pa; hence, the typical suction is of water.
Input power (W)
The power consumption of a vacuum cleaner, in watts, is often the only figure stated. Many North American vacuum manufacturers give the current only in amperes (e.g. "6 amps"), and the consumer is left to multiply that by the line voltage of 120 volts to get the approximate power ratings in watts. The rated input power does not indicate the effectiveness of the cleaner, only how much electricity it consumes.
After August 2014, due to EU rules, manufacture of vacuum cleaners with a power consumption greater than 1600 watts were banned within the EU, and from 2017 no vacuum cleaner with a wattage greater than 900 watts was permitted.
Output power (AW)
The amount of input power that is converted into airflow at the end of the cleaning hose is sometimes stated, and is measured in airwatts: the measurement units are simply watts. The word "air" is used to clarify that this is output power, not input electrical power.
The airwatt is derived from English units. ASTM International defines the airwatt as 0.117354 × F × S, where F is the rate of air flow in ft3/min and S is the pressure in inches of water. This makes one airwatt equal to 0.9983 watts. | Vacuum cleaner | Wikipedia | 481 | 49105 | https://en.wikipedia.org/wiki/Vacuum%20cleaner | Technology | Household appliances | null |
Peak horsepower
The peak horsepower of a vacuum cleaner is often measured by removal of any cooling fans and calculating power based on the motor's power plus the rotational inertial energy stored the motor armature and centrifugal blower. A peak horsepower rating is often an impractical figure and is only valid for a very short period. Continuous power is typically far lower.
Cultural references
Vacuum cleaners have become closely associated with housecleaning, and artists have sometimes used them to symbolize the banality and routine of everyday life and culture. Visual artist Jeff Koons exhibited his The New series of household vacuums enshrined in museum-quality vitrines, such as New Shelton Wet/Dry Doubledecker (1981) at the Museum of Modern Art and New Hoover Convertibles, Green, Blue; New Hoover Convertibles, Green, Blue; Doubledecker (1981–1987) at the Whitney Museum of American Art. In 2002, fashion designer Tara Subkoff used topless models wielding upright vacuum cleaners to promote her controversial fashion label "Imitation of Christ".
In 2018, Paulius Markevičius organized performances of Dance for the Vacuum-Cleaner and Father choreographed by Greta Grinevičiūtė, and premiered in Vilnius, Lithuania. In 2019, Sandrina Lindgren choreographed dancers in Requiem for Vacuum Cleaning in the Barker Theatre of Turku, Finland, with each performer operating multiple machines simultaneously.
Musician Frank Zappa used vacuum cleaners in many of his different performances and on promotional artwork. Other performers have used a vacuum cleaner hose or wand as a modernized version of the Australian Aboriginal didgeridoo, or used the whine of the motor for techno music.
In 1996, Mister Rogers' Neighborhood episode #1702 featured vacuum cleaners, including dancing, magic, and a segment showing how a small Dirt Devil canister vacuum was manufactured. | Vacuum cleaner | Wikipedia | 377 | 49105 | https://en.wikipedia.org/wiki/Vacuum%20cleaner | Technology | Household appliances | null |
Phoenix is a minor constellation in the southern sky. Named after the mythical phoenix, it was first depicted on a celestial atlas by Johann Bayer in his 1603 Uranometria. The French explorer and astronomer Nicolas Louis de Lacaille charted the brighter stars and gave their Bayer designations in 1756. The constellation stretches from roughly −39° to −57° declination, and from 23.5h to 2.5h of right ascension. The constellations Phoenix, Grus, Pavo and Tucana, are known as the Southern Birds.
The brightest star, Alpha Phoenicis, is named Ankaa, an Arabic word meaning 'the Phoenix'. It is an orange giant of apparent magnitude 2.4. Next is Beta Phoenicis, actually a binary system composed of two yellow giants with a combined apparent magnitude of 3.3. Nu Phoenicis has a dust disk, while the constellation has ten star systems with known planets and the recently discovered galaxy clusters El Gordo and the Phoenix Cluster—located 7.2 and 5.7 billion light years away respectively, two of the largest objects in the visible universe. Phoenix is the radiant of two annual meteor showers: the Phoenicids in December, and the July Phoenicids.
History
Phoenix was the largest of the 12 constellations established by Petrus Plancius from the observations of Pieter Dirkszoon Keyser and Frederick de Houtman. It first appeared on a 35-cm diameter celestial globe published in 1597 (or 1598) in Amsterdam by Plancius with Jodocus Hondius. The first depiction of this constellation in a celestial atlas was in Johann Bayer's Uranometria of 1603. De Houtman included it in his southern star catalog the same year under the Dutch name Den voghel Fenicx, "The Bird Phoenix", symbolising the phoenix of classical mythology. One name of the brightest star Alpha Phoenicis—Ankaa—is derived from the , and was coined sometime after 1800 in relation to the constellation. | Phoenix (constellation) | Wikipedia | 420 | 49123 | https://en.wikipedia.org/wiki/Phoenix%20%28constellation%29 | Physical sciences | Other | Astronomy |
Celestial historian Richard Allen noted that unlike the other constellations introduced by Plancius and La Caille, Phoenix has actual precedent in ancient astronomy, as the Arabs saw this formation as representing young ostriches, Al Ri'āl, or as a griffin or eagle. In addition, the same group of stars was sometimes imagined by the Arabs as a boat, Al Zaurak, on the nearby river Eridanus. He observed, "the introduction of a Phoenix into modern astronomy was, in a measure, by adoption rather than by invention."
The Chinese incorporated Phoenix's brightest star, Ankaa (Alpha Phoenicis), and stars from the adjacent constellation Sculptor to depict Bakui, a net for catching birds. Phoenix and the neighbouring constellation of Grus together were seen by Julius Schiller as portraying Aaron the High Priest. These two constellations, along with nearby Pavo and Tucana, are called the Southern Birds.
Characteristics
Phoenix is a small constellation bordered by Fornax and Sculptor to the north, Grus to the west, Tucana to the south, touching on the corner of Hydrus to the south, and Eridanus to the east and southeast. The bright star Achernar is nearby. The three-letter abbreviation for the constellation, as adopted by the International Astronomical Union in 1922, is "Phe". The official constellation boundaries, as set by Belgian astronomer Eugène Delporte in 1930, are defined by a polygon of 10 segments. In the equatorial coordinate system, the right ascension coordinates of these borders lie between and , while the declination coordinates are between −39.31° and −57.84°. This means it remains below the horizon to anyone living north of the 40th parallel in the Northern Hemisphere, and remains low in the sky for anyone living north of the equator. It is most visible from locations such as Australia and South Africa during late Southern Hemisphere spring. Most of the constellation lies within, and can be located by, forming a triangle of the bright stars Achernar, Fomalhaut and Beta Ceti—Ankaa lies roughly in the centre of this.
Features
Stars | Phoenix (constellation) | Wikipedia | 439 | 49123 | https://en.wikipedia.org/wiki/Phoenix%20%28constellation%29 | Physical sciences | Other | Astronomy |
A curved line of stars comprising Alpha, Kappa, Mu, Beta, Nu and Gamma Phoenicis was seen as a boat by the ancient Arabs. French explorer and astronomer Nicolas Louis de Lacaille charted and designated 27 stars with the Bayer designations Alpha through to Omega in 1756. Of these, he labelled two stars close together Lambda, and assigned Omicron, Psi and Omega to three stars, which subsequent astronomers such as Benjamin Gould felt were too dim to warrant their letters. A different star was subsequently labelled Psi Phoenicis, while the other two designations fell out of use.
Ankaa is the brightest star in the constellation. It is an orange giant of apparent visual magnitude 2.37 and spectral type K0.5IIIb, 77 light years distant from Earth and orbited by a secondary object about which little is known. Lying close by Ankaa is Kappa Phoenicis, a main sequence star of spectral type A5IVn and apparent magnitude 3.90. Located centrally in the asterism, Beta Phoenicis is the second brightest star in the constellation and another binary star. Together the stars, both yellow giants of spectral type G8, shine with an apparent magnitude of 3.31, though the components are of individual apparent magnitudes of 4.0 and 4.1 and orbit each other every 168 years. Zeta Phoenicis or Wurren is an Algol-type eclipsing binary, with an apparent magnitude fluctuating between 3.9 and 4.4 with a period of around 1.7 days (40 hours); its dimming results from the component two blue-white B-type stars, which orbit and block out each other from Earth. The two stars are 0.05 AU from each other, while a third star is around 600 AU away from the pair, and has an orbital period exceeding 5000 years. The system is around 300 light years distant. In 1976, researchers Clausen, Gyldenkerne, and Grønbech calculated that a nearby 8th magnitude star is a fourth member of the system. | Phoenix (constellation) | Wikipedia | 427 | 49123 | https://en.wikipedia.org/wiki/Phoenix%20%28constellation%29 | Physical sciences | Other | Astronomy |
AI Phe is an eclipsing binary star identified in 1972. Its long mutual eclipses and combination of spectroscopic and astrometric data allows precise measurement of the masses and radii of the stars which is viewed as a potential cross-check on stellar properties and distances independent on Ceiphid Variables and such techniques. The long eclipse events require space-based observations to avoid Solar interference.
Gamma Phoenicis is a red giant of spectral type M0IIIa and varies between magnitudes 3.39 and 3.49. It lies 235 light years away. Psi Phoenicis is another red giant, this time of spectral type M4III, and has an apparent magnitude that ranges between 4.3 and 4.5 over a period of around 30 days. Lying 340 light years away, it has around 85 times the diameter, but only 85% of the mass, of the Sun. W Phoenicis is a Mira variable, ranging from magnitude 8.1 to 14.4 over 333.95 days. A red giant, its spectrum ranges between M5e and M6e. Located 6.5 degrees west of Ankaa is SX Phoenicis, a variable star which ranges from magnitude 7.1 to 7.5 over a period of a mere 79 minutes. Its spectral type varies between A2 and F4. It gives its name to a group of stars known as SX Phoenicis variables. Rho and BD Phoenicis are Delta Scuti variables—short period (six hours at most) pulsating stars that have been used as standard candles and as subjects to study astroseismology. Rho is spectral type F2III, and ranges between magnitudes 5.20 and 5.26 over a period of 2.85 hours. BD is of spectral type A1V, and ranges between magnitudes 5.90 and 5.94. | Phoenix (constellation) | Wikipedia | 391 | 49123 | https://en.wikipedia.org/wiki/Phoenix%20%28constellation%29 | Physical sciences | Other | Astronomy |
Nu Phoenicis is a yellow-white main sequence star of spectral type F9V and magnitude 4.96. Lying some 49 light years distant, it is around 1.2 times as massive as the Sun, and likely to be surrounded by a disk of dust. It is the closest star in the constellation that is visible with the unaided eye. Gliese 915 is a white dwarf only 26 light years away. It is of magnitude 13.05, too faint to be seen with the naked eye. White dwarfs are extremely dense stars compacted into a volume the size of the Earth. With around 85% of the mass of the Sun, Gliese 915 has a surface gravity of 108.39 ± 0.01 (2.45 · 108) cm·s−2, or approximately 250,000 of Earth's.
Ten stars have been found to have planets to date, and four planetary systems have been discovered with the SuperWASP project. HD 142 is a yellow giant that has an apparent magnitude of 5.7, and has a planet (HD 142 b) 1.36 times the mass of Jupiter which orbits every 328 days. HD 2039 is a yellow subgiant with an apparent magnitude of 9.0 around 330 light years away which has a planet (HD 2039 b) six times the mass of Jupiter. WASP-18 is a star of magnitude 9.29 which was discovered to have a hot Jupiter-like planet (WASP-18b) taking less than a day to orbit the star. The planet is suspected to be causing WASP-18 to appear older than it really is. WASP-4 and WASP-5 are solar-type yellow stars around 1000 light years distant and of 13th magnitude, each with a single planet larger than Jupiter. WASP-29 is an orange dwarf of spectral type K4V and visual magnitude 11.3, which has a planetary companion of similar size and mass to Saturn. The planet completes an orbit every 3.9 days.
WISE J003231.09-494651.4 and WISE J001505.87-461517.6 are two brown dwarfs discovered by the Wide-field Infrared Survey Explorer, and are 63 and 49 light years away respectively. Initially hypothesised before they were belatedly discovered, brown dwarfs are objects more massive than planets, but which are of insufficient mass for hydrogen fusion characteristic of stars to occur. Many are being found by sky surveys. | Phoenix (constellation) | Wikipedia | 504 | 49123 | https://en.wikipedia.org/wiki/Phoenix%20%28constellation%29 | Physical sciences | Other | Astronomy |
Phoenix contains HE0107-5240, possibly one of the oldest stars yet discovered. It has around 1/200,000 the metallicity that the Sun has and hence must have formed very early in the history of the universe. With a visual magnitude of 15.17, it is around 10,000 times dimmer than the faintest stars visible to the naked eye and is 36,000 light years distant.
Deep-sky objects
The constellation does not lie on the galactic plane of the Milky Way, and there are no prominent star clusters. NGC 625 is a dwarf irregular galaxy of apparent magnitude 11.0 and lying some 12.7 million light years distant. Only 24000 light years in diameter, it is an outlying member of the Sculptor Group. NGC 625 is thought to have been involved in a collision and is experiencing a burst of active star formation. NGC 37 is a lenticular galaxy of apparent magnitude 14.66. It is approximately 42 kiloparsecs (137,000 light-years) in diameter and about 12.9 billion years old. Robert's Quartet (composed of the irregular galaxy NGC 87, and three spiral galaxies NGC 88, NGC 89 and NGC 92) is a group of four galaxies located around 160 million light-years away which are in the process of colliding and merging. They are within a circle of radius of 1.6 arcmin, corresponding to about 75,000 light-years. Located in the galaxy ESO 243-49 is HLX-1, an intermediate-mass black hole—the first one of its kind identified. It is thought to be a remnant of a dwarf galaxy that was absorbed in a collision with ESO 243-49. Before its discovery, this class of black hole was only hypothesized.
Lying within the bounds of the constellation is the gigantic Phoenix cluster, which is around 7.3 million light years wide and 5.7 billion light years away, making it one of the most massive galaxy clusters. It was first discovered in 2010, and the central galaxy is producing an estimated 740 new stars a year. Larger still is El Gordo, or officially ACT-CL J0102-4915, whose discovery was announced in 2012. Located around 7.2 billion light years away, it is composed of two subclusters in the process of colliding, resulting in the spewing out of hot gas, seen in X-rays and infrared images. | Phoenix (constellation) | Wikipedia | 501 | 49123 | https://en.wikipedia.org/wiki/Phoenix%20%28constellation%29 | Physical sciences | Other | Astronomy |
Meteor showers
Phoenix is the radiant of two annual meteor showers. The Phoenicids, also known as the December Phoenicids, were first observed on 3 December 1887. The shower was particularly intense in December 1956, and is thought related to the breakup of the short-period comet 289P/Blanpain. It peaks around 4–5 December, though is not seen every year. A very minor meteor shower peaks around July 14 with around one meteor an hour, though meteors can be seen anytime from July 3 to 18; this shower is referred to as the July Phoenicids. | Phoenix (constellation) | Wikipedia | 123 | 49123 | https://en.wikipedia.org/wiki/Phoenix%20%28constellation%29 | Physical sciences | Other | Astronomy |
A hallucination is a perception in the absence of an external stimulus that has the compelling sense of reality. They are distinguishable from several related phenomena, such as dreaming (REM sleep), which does not involve wakefulness; pseudohallucination, which does not mimic real perception, and is accurately perceived as unreal; illusion, which involves distorted or misinterpreted real perception; and mental imagery, which does not mimic real perception, and is under voluntary control. Hallucinations also differ from "delusional perceptions", in which a correctly sensed and interpreted stimulus (i.e., a real perception) is given some additional significance.
Hallucinations can occur in any sensory modality—visual, auditory, olfactory, gustatory, tactile, proprioceptive, equilibrioceptive, nociceptive, thermoceptive and chronoceptive. Hallucinations are referred to as multimodal if multiple sensory modalities occur.
A mild form of hallucination is known as a disturbance, and can occur in most of the senses above. These may be things like seeing movement in peripheral vision, or hearing faint noises or voices. Auditory hallucinations are very common in schizophrenia. They may be benevolent (telling the subject good things about themselves) or malicious, cursing the subject. 55% of auditory hallucinations are malicious in content, for example, people talking about the subject, not speaking to them directly. Like auditory hallucinations, the source of the visual counterpart can also be behind the subject. This can produce a feeling of being looked or stared at, usually with malicious intent. Frequently, auditory hallucinations and their visual counterpart are experienced by the subject together.
Hypnagogic hallucinations and hypnopompic hallucinations are considered normal phenomena. Hypnagogic hallucinations can occur as one is falling asleep and hypnopompic hallucinations occur when one is waking up. Hallucinations can be associated with drug use (particularly deliriants), sleep deprivation, psychosis, neurological disorders, and delirium tremens. Many hallucinations happen also during sleep paralysis. | Hallucination | Wikipedia | 451 | 49159 | https://en.wikipedia.org/wiki/Hallucination | Biology and health sciences | Miscellaneous | null |
The word "hallucination" itself was introduced into the English language by the 17th-century physician Sir Thomas Browne in 1646 from the derivation of the Latin word alucinari meaning to wander in the mind. For Browne, hallucination means a sort of vision that is "depraved and receive[s] its objects erroneously".
Classification
Hallucinations may be manifested in a variety of forms. Various forms of hallucinations affect different senses, sometimes occurring simultaneously, creating multiple sensory hallucinations for those experiencing them.
Auditory
Auditory hallucinations (also known as paracusia) are the perception of sound without outside stimulus. Auditory hallucinations can be divided into elementary and complex, along with verbal and nonverbal. These hallucinations are the most common type of hallucination, with auditory verbal hallucinations being more common than nonverbal. Elementary hallucinations are the perception of sounds such as hissing, whistling, an extended tone, and more. In many cases, tinnitus is an elementary auditory hallucination. However, some people who experience certain types of tinnitus, especially pulsatile tinnitus, are actually hearing the blood rushing through vessels near the ear. Because the auditory stimulus is present in this situation, it does not qualify it as a hallucination.
Complex hallucinations are those of voices, music, or other sounds that may or may not be clear, may or may not be familiar, and may be friendly, aggressive, or among other possibilities. A hallucination of a single individual person of one or more talking voices is particularly associated with psychotic disorders such as schizophrenia, and hold special significance in diagnosing these conditions. | Hallucination | Wikipedia | 348 | 49159 | https://en.wikipedia.org/wiki/Hallucination | Biology and health sciences | Miscellaneous | null |
In schizophrenia, voices are normally perceived coming from outside the person, but in dissociative disorders they are perceived as originating from within the person, commenting in their head instead of behind their back. Differential diagnosis between schizophrenia and dissociative disorders is challenging due to many overlapping symptoms, especially Schneiderian first rank symptoms such as hallucinations. However, many people who do not have a diagnosable mental illness may sometimes hear voices as well. One important example to consider when forming a differential diagnosis for a patient with paracusia is lateral temporal lobe epilepsy. Despite the tendency to associate hearing voices, or otherwise hallucinating, and psychosis with schizophrenia or other psychiatric illnesses, it is crucial to take into consideration that, even if a person does exhibit psychotic features, they do not necessarily have a psychiatric disorder on its own. Disorders such as Wilson's disease, various endocrine diseases, numerous metabolic disturbances, multiple sclerosis, systemic lupus erythematosus, porphyria, sarcoidosis, and many others can present with psychosis.
Musical hallucinations are also relatively common in terms of complex auditory hallucinations and may be the result of a wide range of causes ranging from hearing-loss (such as in musical ear syndrome, the auditory version of Charles Bonnet syndrome), lateral temporal lobe epilepsy, arteriovenous malformation, stroke, lesion, abscess, or tumor.
The Hearing Voices Movement is a support and advocacy group for people who hallucinate voices, but do not otherwise show signs of mental illness or impairment.
High caffeine consumption has been linked to an increase in likelihood of one experiencing auditory hallucinations. A study conducted by the La Trobe University School of Psychological Sciences revealed that as few as five cups of coffee a day (approximately 500 mg of caffeine) could trigger the phenomenon.
Visual | Hallucination | Wikipedia | 386 | 49159 | https://en.wikipedia.org/wiki/Hallucination | Biology and health sciences | Miscellaneous | null |
A visual hallucination is "the perception of an external visual stimulus where none exists". A separate but related phenomenon is a visual illusion, which is a distortion of a real external stimulus. Visual hallucinations are classified as simple or complex:
Simple visual hallucinations (SVH) are also referred to as non-formed visual hallucinations and elementary visual hallucinations. These terms refer to lights, colors, geometric shapes, and indiscrete objects. These can be further subdivided into phosphenes which are SVH without structure, and photopsias which are SVH with geometric structures.
Complex visual hallucinations (CVH) are also referred to as formed visual hallucinations. CVHs are clear, lifelike images or scenes such as people, animals, objects, places, etc.
For example, one may report hallucinating a giraffe. A simple visual hallucination is an amorphous figure that may have a similar shape or color to a giraffe (looks like a giraffe), while a complex visual hallucination is a discrete, lifelike image that is, unmistakably, a giraffe.
Command
Command hallucinations are hallucinations in the form of commands; they appear to be from an external source, or can appear coming from the subject's head. The contents of the hallucinations can range from the innocuous to commands to cause harm to the self or others. Command hallucinations are often associated with schizophrenia. People experiencing command hallucinations may or may not comply with the hallucinated commands, depending on the circumstances. Compliance is more common for non-violent commands. | Hallucination | Wikipedia | 345 | 49159 | https://en.wikipedia.org/wiki/Hallucination | Biology and health sciences | Miscellaneous | null |
Command hallucinations are sometimes used to defend a crime that has been committed, often homicides. In essence, it is a voice that one hears and it tells the listener what to do. Sometimes the commands are quite benign directives such as "Stand up" or "Shut the door." Whether it is a command for something simple or something that is a threat, it is still considered a "command hallucination." Some helpful questions that can assist one in determining if they may have this includes: "What are the voices telling you to do?", "When did your voices first start telling you to do things?", "Do you recognize the person who is telling you to harm yourself (or others)?", "Do you think you can resist doing what the voices are telling you to do?"
Olfactory
Phantosmia (olfactory hallucinations), smelling an odor that is not actually there, and parosmia (olfactory illusions), inhaling a real odor but perceiving it as different scent than remembered, are distortions to the sense of smell (olfactory system), and in most cases, are not caused by anything serious and will usually go away on their own in time. It can result from a range of conditions such as nasal infections, nasal polyps, dental problems, migraines, head injuries, seizures, strokes, or brain tumors. Environmental exposures can sometimes cause it as well, such as smoking, exposure to certain types of chemicals (e.g., insecticides or solvents), or radiation treatment for head or neck cancer. It can also be a symptom of certain mental disorders such as depression, bipolar disorder, intoxication, substance withdrawal, or psychotic disorders (e.g., schizophrenia). The perceived odors are usually unpleasant and commonly described as smelling burned, foul, spoiled, or rotten.
Tactile
Tactile hallucinations are the illusion of tactile sensory input, simulating various types of pressure to the skin or other organs. One subtype of tactile hallucination, formication, is the sensation of insects crawling underneath the skin and is frequently associated with prolonged cocaine use. However, formication may also be the result of normal hormonal changes such as menopause, or disorders such as peripheral neuropathy, high fevers, Lyme disease, skin cancer, and more. | Hallucination | Wikipedia | 497 | 49159 | https://en.wikipedia.org/wiki/Hallucination | Biology and health sciences | Miscellaneous | null |
Gustatory
This type of hallucination is the perception of taste without a stimulus. These hallucinations, which are typically strange or unpleasant, are relatively common among individuals who have certain types of focal epilepsy, especially temporal lobe epilepsy. The regions of the brain responsible for gustatory hallucination in this case are the insula and the superior bank of the sylvian fissure.
Sexual
Sexual hallucinations are the perception of erogenous or orgasmic stimuli. They may be unimodal or multimodal in nature and frequently involve sensation in the genital region, though it is not exclusive. Frequent examples of sexual hallucinations include the sensation of being penetrated, experiencing orgasm, feeling as if one is being touched in an erogenous zone, sensing stimulation in the genitals, feeling the fondling of one's breasts or buttocks and tastes or smells related to sexual activity. Visualizations of sexual content and auditory voices making sexually explicit remarks may sometimes be included in this classification. While it features components of other classifications, sexual hallucinations are distinct due to the orgasmic component and unique presentation.
The regions of the brain responsible differ by the subsection of sexual hallucination. In orgasmic auras, the mesial temporal lobe, right amygdala and hippocampus are involved. In males, genital specific sensations are related to the postcentral gyrus and arousal and ejaculation are linked to stimulation in the posterior frontal lobe. In females, however, the hippocampus and amygdala are connected. Limited studies have been done to understand the mechanism of action behind sexual hallucinations in epilepsy, substance use, and post-traumatic stress disorder etiologies.
Somatic
Somatic hallucinations refer to an interoceptive sensory experience in the absence of stimulus. Somatic hallucinations can be broken down into further subcategories: general, algesic, kinesthetic, and cenesthopathic. | Hallucination | Wikipedia | 414 | 49159 | https://en.wikipedia.org/wiki/Hallucination | Biology and health sciences | Miscellaneous | null |
Cenesthopathic- Effecting the cenesthetic sensory modality, cenesthopathic hallucinations are a pathological alteration in the sense of bodily existence, caused by aberrant bodily sensations. Most often, cenesthopathic hallucinations will refer to sensation in the visceral organs. Therefore, it is also known as visceral hallucinations. Manifestations are often subjective, hard to describe and unique to the sufferer. Common manifestations include pressure, burning, tickling, or tightening in various body systems. While these hallucinations can be experienced by a variety of psychiatric and neurological disorder, cenesthopathic schizophrenia is recognized by the ICD as a subtype of schizophrenia marked by primarily cenesthopathic hallucinations and other body image aberrations.
Kinesthetic- Kinesthetic hallucinations, effecting the sensory modality of the same name, are the sensation of movement of the limbs or other body parts without actual movement.
Algesic- Algesic hallucinations, effecting the algesic sensory modality, refers to a perceived perception of pain.
General- General somatic hallucination refers to somatic hallucinations not otherwise categorized by the above subsections. Common examples include when an individual feels that their body is being mutilated, i.e. twisted, torn, or disemboweled. Other reported cases are invasion by animals in the person's internal organs, such as snakes in the stomach or frogs in the rectum. The general feeling that one's flesh is decomposing is also classified under this type of this hallucination.
Multimodal
A hallucination involving sensory modalities is called multimodal, analogous to unimodal hallucinations which have only one sensory modality. The multiple sensory modalities can occur at the same time (simultaneously) or with a delay (serial), be related or unrelated to each other, and be consistent with reality (congruent) or not (incongruent). For example, a person talking in a hallucination would be congruent with reality, but a cat talking would not be.
Multimodal hallucinations are correlated to poorer mental health outcomes, and are often experienced as feeling more real.
Cause
Hallucinations can be caused by a number of factors.
Hypnagogic hallucination | Hallucination | Wikipedia | 499 | 49159 | https://en.wikipedia.org/wiki/Hallucination | Biology and health sciences | Miscellaneous | null |
These hallucinations occur just before falling asleep and affect a high proportion of the population: in one survey 37% of the respondents experienced them twice a week. The hallucinations can last from seconds to minutes; all the while, the subject usually remains aware of the true nature of the images. These may be associated with narcolepsy. Hypnagogic hallucinations are sometimes associated with brainstem abnormalities, but this is rare.
Peduncular hallucinosis
Peduncular means pertaining to the peduncle, which is a neural tract running to and from the pons on the brain stem. These hallucinations usually occur in the evenings, but not during drowsiness, as in the case of hypnagogic hallucination. The subject is usually fully conscious and then can interact with the hallucinatory characters for extended periods of time. As in the case of hypnagogic hallucinations, insight into the nature of the images remains intact. The false images can occur in any part of the visual field, and are rarely polymodal.
Delirium tremens
One of the more enigmatic forms of visual hallucination is the highly variable, possibly polymodal delirium tremens. It is associated with withdrawal in alcohol use disorder. Individuals with delirium tremens may be agitated and confused, especially in the later stages of this disease. Insight is gradually reduced with the progression of this disorder. Sleep is disturbed and occurs for a shorter period of time, with rapid eye movement sleep. | Hallucination | Wikipedia | 319 | 49159 | https://en.wikipedia.org/wiki/Hallucination | Biology and health sciences | Miscellaneous | null |
Parkinson's disease and Lewy body dementia
Parkinson's disease is linked with Lewy body dementia for their similar hallucinatory symptoms. Presence hallucinations can be an early indicator of cognitive decline in Parkinson's Disease. The symptoms strike during the evening in any part of the visual field, and are rarely polymodal. The segue into hallucination may begin with illusions where sensory perception is greatly distorted, but no novel sensory information is present. These typically last for several minutes, during which time the subject may be either conscious and normal or drowsy/inaccessible. Insight into these hallucinations is usually preserved and REM sleep is usually reduced. Parkinson's disease is usually associated with a degraded substantia nigra pars compacta, but recent evidence suggests that PD affects a number of sites in the brain. Some places of noted degradation include the median raphe nuclei, the noradrenergic parts of the locus coeruleus, and the cholinergic neurons in the parabrachial area and pedunculopontine nuclei of the tegmentum.
Migraine coma
This type of hallucination is usually experienced during the recovery from a comatose state. The migraine coma can last for up to two days, and a state of depression is sometimes comorbid. The hallucinations occur during states of full consciousness, and insight into the hallucinatory nature of the images is preserved. It has been noted that ataxic lesions accompany the migraine coma.
Migraine attacks
Migraine attacks may result in visual hallucinations including auras and in rarer cases, auditory hallucinations. | Hallucination | Wikipedia | 335 | 49159 | https://en.wikipedia.org/wiki/Hallucination | Biology and health sciences | Miscellaneous | null |
Charles Bonnet syndrome
Charles Bonnet syndrome is the name given to visual hallucinations experienced by a partially or severely sight impaired person. The hallucinations can occur at any time and can distress people of any age, as they may not initially be aware that they are hallucinating. They may fear for their own mental health initially, which may delay them sharing with carers until they start to understand it themselves. The hallucinations can frighten and disconcert as to what is real and what is not. The hallucinations can sometimes be dispersed by eye movements, or by reasoned logic such as, "I can see fire but there is no smoke and there is no heat from it" or perhaps, "We have an infestation of rats but they have pink ribbons with a bell tied on their necks." Over elapsed months and years, the hallucinations may become more or less frequent with changes in ability to see. The length of time that the sight impaired person can have these hallucinations varies according to the underlying speed of eye deterioration. A differential diagnosis are ophthalmopathic hallucinations.
Focal epilepsy
Visual hallucinations due to focal seizures differ depending on the region of the brain where the seizure occurs. For example, visual hallucinations during occipital lobe seizures are typically visions of brightly colored, geometric shapes that may move across the visual field, multiply, or form concentric rings and generally persist from a few seconds to a few minutes. They are usually unilateral and localized to one part of the visual field on the contralateral side of the seizure focus, typically the temporal field. However, unilateral visions moving horizontally across the visual field begin on the contralateral side and move toward the ipsilateral side. | Hallucination | Wikipedia | 365 | 49159 | https://en.wikipedia.org/wiki/Hallucination | Biology and health sciences | Miscellaneous | null |
Temporal lobe seizures, on the other hand, can produce complex visual hallucinations of people, scenes, animals, and more as well as distortions of visual perception. Complex hallucinations may appear to be real or unreal, may or may not be distorted with respect to size, and may seem disturbing or affable, among other variables. One rare but notable type of hallucination is heautoscopy, a hallucination of a mirror image of one's self. These "other selves" may be perfectly still or performing complex tasks, may be an image of a younger self or the present self, and tend to be briefly present. Complex hallucinations are a relatively uncommon finding in temporal lobe epilepsy patients. Rarely, they may occur during occipital focal seizures or in parietal lobe seizures.
Distortions in visual perception during a temporal lobe seizure may include size distortion (micropsia or macropsia), distorted perception of movement (where moving objects may appear to be moving very slowly or to be perfectly still), a sense that surfaces such as ceilings and even entire horizons are moving farther away in a fashion similar to the dolly zoom effect, and other illusions. Even when consciousness is impaired, insight into the hallucination or illusion is typically preserved.
Drug-induced hallucination
Drug-induced hallucinations are caused by hallucinogens, dissociatives, and deliriants, including many drugs with anticholinergic actions and certain stimulants, which are known to cause visual and auditory hallucinations. Some psychedelics such as lysergic acid diethylamide (LSD) and psilocybin can cause hallucinations that range in the spectrum of mild to intense. | Hallucination | Wikipedia | 363 | 49159 | https://en.wikipedia.org/wiki/Hallucination | Biology and health sciences | Miscellaneous | null |
Hallucinations, pseudohallucinations, or intensification of pareidolia, particularly auditory, are known side effects of opioids to different degrees—it may be associated with the absolute degree of agonism or antagonism of especially the kappa opioid receptor, sigma receptors, delta opioid receptor and the NMDA receptors or the overall receptor activation profile as synthetic opioids like those of the pentazocine, levorphanol, fentanyl, pethidine, methadone and some other families are more associated with this side effect than natural opioids like morphine and codeine and semi-synthetics like hydromorphone, amongst which there also appears to be a stronger correlation with the relative analgesic strength. Three opioids, Cyclazocine (a benzormorphan opioid/pentazocine relative) and two levorphanol-related morphinan opioids, Cyclorphan and Dextrorphan are classified as hallucinogens, and Dextromethorphan as a dissociative. These drugs also can induce sleep (relating to hypnagogic hallucinations) and especially the pethidines have atropine-like anticholinergic activity, which was possibly also a limiting factor in the use, the psychotomimetic side effects of potentiating morphine, oxycodone, and other opioids with scopolamine (respectively in the Twilight Sleep technique and the combination drug Skophedal, which was eukodal (oxycodone), scopolamine and ephedrine, called the "wonder drug of the 1930s" after its invention in Germany in 1928, but only rarely specially compounded today) (q.q.v.).
Sensory deprivation hallucination
Hallucinations can be caused by sensory deprivation when it occurs for prolonged periods of time, and almost always occurs in the modality being deprived (visual for blindfolded/darkness, auditory for muffled conditions, etc.)
Experimentally-induced hallucinations
Anomalous experiences, such as so-called benign hallucinations, may occur in a person in a state of good mental and physical health, even in the apparent absence of a transient trigger factor such as fatigue, intoxication or sensory deprivation. | Hallucination | Wikipedia | 490 | 49159 | https://en.wikipedia.org/wiki/Hallucination | Biology and health sciences | Miscellaneous | null |
The evidence for this statement has been accumulating for more than a century. Studies of benign hallucinatory experiences go back to 1886 and the early work of the Society for Psychical Research, which suggested approximately 10% of the population had experienced at least one hallucinatory episode in the course of their life. More recent studies have validated these findings; the precise incidence found varies with the nature of the episode and the criteria of "hallucination" adopted, but the basic finding is now well-supported.
Non-celiac gluten sensitivity
There is tentative evidence of a relationship with non-celiac gluten sensitivity, the so-called "gluten psychosis".
Pathophysiology
Dopaminergic and serotonergic hallucinations
It has been reported that in serotonergic hallucinations, the person maintains an awareness that they are hallucinating, unlike dopaminergic hallucinations.
Neuroanatomy
Hallucinations are associated with structural and functional abnormalities in primary and secondary sensory cortices. Reduced grey matter in regions of the superior temporal gyrus/middle temporal gyrus, including Broca's area, is associated with auditory hallucinations as a trait, while acute hallucinations are associated with increased activity in the same regions along with the hippocampus, parahippocampus, and the right hemispheric homologue of Broca's area in the inferior frontal gyrus. Grey and white matter abnormalities in visual regions are associated with hallucinations in diseases such as Alzheimer's disease, further supporting the notion of dysfunction in sensory regions underlying hallucinations.
One proposed model of hallucinations posits that over-activity in sensory regions, which is normally attributed to internal sources via feedforward networks to the inferior frontal gyrus, is interpreted as originating externally due to abnormal connectivity or functionality of the feedforward network. This is supported by cognitive studies of those with hallucinations, who have demonstrated abnormal attribution of self generated stimuli. | Hallucination | Wikipedia | 425 | 49159 | https://en.wikipedia.org/wiki/Hallucination | Biology and health sciences | Miscellaneous | null |
Disruptions in thalamocortical circuitry may underlie the observed top down and bottom up dysfunction. Thalamocortical circuits, composed of projections between thalamic and cortical neurons and adjacent interneurons, underlie certain electrophysical characteristics (gamma oscillations) that are associated with sensory processing. Cortical inputs to thalamic neurons enable attentional modulation of sensory neurons. Dysfunction in sensory afferents, and abnormal cortical input may result in pre-existing expectations modulating sensory experience, potentially resulting in the generation of hallucinations. Hallucinations are associated with less accurate sensory processing, and more intense stimuli with less interference are necessary for accurate processing and the appearance of gamma oscillations (called "gamma synchrony"). Hallucinations are also associated with the absence of reduction in P50 amplitude in response to the presentation of a second stimuli after an initial stimulus; this is thought to represent failure to gate sensory stimuli, and can be exacerbated by dopamine release agents.
Abnormal assignment of salience to stimuli may be one mechanism of hallucinations. Dysfunctional dopamine signaling may lead to abnormal top down regulation of sensory processing, allowing expectations to distort sensory input.
Treatments
There are few treatments for many types of hallucinations. However, for those hallucinations caused by mental disease, a psychologist or psychiatrist should be consulted, and treatment will be based on the observations of those doctors. Antipsychotic and atypical antipsychotic medication may also be utilized to treat the illness if the symptoms are severe and cause significant distress. For other causes of hallucinations there is no factual evidence to support any one treatment is scientifically tested and proven. However, abstaining from hallucinogenic drugs, stimulant drugs, managing stress levels, living healthily, and getting plenty of sleep can help reduce the prevalence of hallucinations. In all cases of hallucinations, medical attention should be sought out and informed of one's specific symptoms. Meta-analyses show that cognitive behavioral therapy and metacognitive training can also reduce the severity of hallucinations. Furthermore, there are recovery movements all around the world that advocate for individuals with schizophrenia or voice-hearers (individuals that hear voices). The Hearing Voices Movement, starting in Europe, is a great example of utilizing the knowledge and experience of voice hearers and combining it with experts in disorders such as schizophrenia, such as psychiatrists. | Hallucination | Wikipedia | 512 | 49159 | https://en.wikipedia.org/wiki/Hallucination | Biology and health sciences | Miscellaneous | null |
Epidemiology
Prevalence of hallucinations varies depending on underlying medical conditions, which sensory modalities are affected, age and culture. auditory hallucinations are the most well studied and most common sensory modality of hallucinations, with an estimated lifetime prevalence of 9.6%. Children and adolescents have been found to experience similar rates (12.7% and 12.4% respectively) which occur mostly during late childhood and adolescence. This is compared with adults and those over 60 (with rates of 5.8% and 4.8% respectively). For those with schizophrenia, the lifetime prevalence of hallucinations is 80% and the estimated prevalence of visual hallucinations is 27%, compared to 79% for auditory hallucinations. A 2019 study suggested 16.2% of adults with hearing impairment experience hallucinations, with prevalence rising to 24% in the most hearing impaired group.
A risk factor for multimodal hallucinations is prior experience of unimodal hallucinations. In 90% cases of psychosis, a visual hallucination occurs in combination with another sensory modality, most often being auditory or somatic. In schizophrenia, multimodal hallucinations are twice as common as unimodal ones.
A 2015 review of 55 publications from 1962 to 2014 found 16–28.6% of those experiencing hallucinations report at least some religious content in them, along with 20–60% reporting some religious content in delusions. There is some evidence for delusions being a risk factor for religious hallucinations, with and 61.7% of people having experienced any delusion and 75.9% of those having experienced a religious delusion found to also experience hallucinations. | Hallucination | Wikipedia | 351 | 49159 | https://en.wikipedia.org/wiki/Hallucination | Biology and health sciences | Miscellaneous | null |
In mathematics, a real interval is the set of all real numbers lying between two fixed endpoints with no "gaps". Each endpoint is either a real number or positive or negative infinity, indicating the interval extends without a bound. A real interval can contain neither endpoint, either endpoint, or both endpoints, excluding any endpoint which is infinite.
For example, the set of real numbers consisting of , , and all numbers in between is an interval, denoted and called the unit interval; the set of all positive real numbers is an interval, denoted ; the set of all real numbers is an interval, denoted ; and any single real number is an interval, denoted .
Intervals are ubiquitous in mathematical analysis. For example, they occur implicitly in the epsilon-delta definition of continuity; the intermediate value theorem asserts that the image of an interval by a continuous function is an interval; integrals of real functions are defined over an interval; etc.
Interval arithmetic consists of computing with intervals instead of real numbers for providing a guaranteed enclosure of the result of a numerical computation, even in the presence of uncertainties of input data and rounding errors.
Intervals are likewise defined on an arbitrary totally ordered set, such as integers or rational numbers. The notation of integer intervals is considered in the special section below.
Definitions and terminology
An interval is a subset of the real numbers that contains all real numbers lying between any two numbers of the subset.
The endpoints of an interval are its supremum, and its infimum, if they exist as real numbers. If the infimum does not exist, one says often that the corresponding endpoint is Similarly, if the supremum does not exist, one says that the corresponding endpoint is
Intervals are completely determined by their endpoints and whether each endpoint belong to the interval. This is a consequence of the least-upper-bound property of the real numbers. This characterization is used to specify intervals by mean of , which is described below.
An does not include any endpoint, and is indicated with parentheses. For example, is the interval of all real numbers greater than and less than . (This interval can also be denoted by , see below). The open interval consists of real numbers greater than , i.e., positive real numbers. The open intervals are thus one of the forms | Interval (mathematics) | Wikipedia | 471 | 49172 | https://en.wikipedia.org/wiki/Interval%20%28mathematics%29 | Mathematics | Real analysis | null |
where and are real numbers such that When in the first case, the resulting interval is the empty set which is a degenerate interval (see below). The open intervals are those intervals that are open sets for the usual topology on the real numbers.
A is an interval that includes all its endpoints and is denoted with square brackets. For example, means greater than or equal to and less than or equal to . Closed intervals have one of the following forms in which and are real numbers such that
The closed intervals are those intervals that are closed sets for the usual topology on the real numbers. The empty set and are the only intervals that are both open and closed.
A has two endpoints and includes only one of them. It is said left-open or right-open depending on whether the excluded endpoint is on the left or on the right. These intervals are denoted by mixing notations for open and closed intervals. For example, means greater than and less than or equal to , while means greater than or equal to and less than . The half-open intervals have the form
Every closed interval is a closed set of the real line, but an interval that is a closed set need not be a closed interval. For example, intervals and are also closed sets in the real line. Intervals and are neither an open set nor a closed set. If one allows an endpoint in the closed side to be an infinity (such as ), the result will not be an interval, since it is not even a subset of the real numbers. Instead, the result can be seen as an interval in the extended real line, which occurs in measure theory, for example.
In summary, a set of the real numbers is an interval, if and only if it is an open interval, a closed interval, or a half-open interval.
A is any set consisting of a single real number (i.e., an interval of the form ). Some authors include the empty set in this definition. A real interval that is neither empty nor degenerate is said to be proper, and has infinitely many elements. | Interval (mathematics) | Wikipedia | 425 | 49172 | https://en.wikipedia.org/wiki/Interval%20%28mathematics%29 | Mathematics | Real analysis | null |
An interval is said to be left-bounded or right-bounded, if there is some real number that is, respectively, smaller than or larger than all its elements. An interval is said to be bounded, if it is both left- and right-bounded; and is said to be unbounded otherwise. Intervals that are bounded at only one end are said to be half-bounded. The empty set is bounded, and the set of all reals is the only interval that is unbounded at both ends. Bounded intervals are also commonly known as finite intervals.
Bounded intervals are bounded sets, in the sense that their diameter (which is equal to the absolute difference between the endpoints) is finite. The diameter may be called the length, width, measure, range, or size of the interval. The size of unbounded intervals is usually defined as , and the size of the empty interval may be defined as (or left undefined).
The centre (midpoint) of a bounded interval with endpoints and is , and its radius is the half-length . These concepts are undefined for empty or unbounded intervals.
An interval is said to be left-open if and only if it contains no minimum (an element that is smaller than all other elements); right-open if it contains no maximum; and open if it contains neither. The interval , for example, is left-closed and right-open. The empty set and the set of all reals are both open and closed intervals, while the set of non-negative reals, is a closed interval that is right-open but not left-open. The open intervals are open sets of the real line in its standard topology, and form a base of the open sets.
An interval is said to be left-closed if it has a minimum element or is left-unbounded, right-closed if it has a maximum or is right unbounded; it is simply closed if it is both left-closed and right closed. So, the closed intervals coincide with the closed sets in that topology.
The interior of an interval is the largest open interval that is contained in ; it is also the set of points in which are not endpoints of . The closure of is the smallest closed interval that contains ; which is also the set augmented with its finite endpoints.
For any set of real numbers, the interval enclosure or interval span of is the unique interval that contains , and does not properly contain any other interval that also contains . | Interval (mathematics) | Wikipedia | 510 | 49172 | https://en.wikipedia.org/wiki/Interval%20%28mathematics%29 | Mathematics | Real analysis | null |
An interval is a subinterval of interval if is a subset of . An interval is a proper subinterval of if is a proper subset of .
However, there is conflicting terminology for the terms segment and interval, which have been employed in the literature in two essentially opposite ways, resulting in ambiguity when these terms are used. The Encyclopedia of Mathematics defines interval (without a qualifier) to exclude both endpoints (i.e., open interval) and segment to include both endpoints (i.e., closed interval), while Rudin's Principles of Mathematical Analysis calls sets of the form [a, b] intervals and sets of the form (a, b) segments throughout. These terms tend to appear in older works; modern texts increasingly favor the term interval (qualified by open, closed, or half-open), regardless of whether endpoints are included.
Notations for intervals
The interval of numbers between and , including and , is often denoted . The two numbers are called the endpoints of the interval. In countries where numbers are written with a decimal comma, a semicolon may be used as a separator to avoid ambiguity.
Including or excluding endpoints
To indicate that one of the endpoints is to be excluded from the set, the corresponding square bracket can be either replaced with a parenthesis, or reversed. Both notations are described in International standard ISO 31-11. Thus, in set builder notation,
Each interval , , and represents the empty set, whereas denotes the singleton set . When , all four notations are usually taken to represent the empty set.
Both notations may overlap with other uses of parentheses and brackets in mathematics. For instance, the notation is often used to denote an ordered pair in set theory, the coordinates of a point or vector in analytic geometry and linear algebra, or (sometimes) a complex number in algebra. That is why Bourbaki introduced the notation to denote the open interval. The notation too is occasionally used for ordered pairs, especially in computer science.
Some authors such as Yves Tillé use to denote the complement of the interval ; namely, the set of all real numbers that are either less than or equal to , or greater than or equal to .
Infinite endpoints
In some contexts, an interval may be defined as a subset of the extended real numbers, the set of all real numbers augmented with and . | Interval (mathematics) | Wikipedia | 484 | 49172 | https://en.wikipedia.org/wiki/Interval%20%28mathematics%29 | Mathematics | Real analysis | null |
In this interpretation, the notations , , , and are all meaningful and distinct. In particular, denotes the set of all ordinary real numbers, while denotes the extended reals.
Even in the context of the ordinary reals, one may use an infinite endpoint to indicate that there is no bound in that direction. For example, is the set of positive real numbers, also written as The context affects some of the above definitions and terminology. For instance, the interval = is closed in the realm of ordinary reals, but not in the realm of the extended reals.
Integer intervals
When and are integers, the notation ⟦a, b⟧, or or or just , is sometimes used to indicate the interval of all integers between and included. The notation is used in some programming languages; in Pascal, for example, it is used to formally define a subrange type, most frequently used to specify lower and upper bounds of valid indices of an array.
Another way to interpret integer intervals are as sets defined by enumeration, using ellipsis notation.
An integer interval that has a finite lower or upper endpoint always includes that endpoint. Therefore, the exclusion of endpoints can be explicitly denoted by writing , , or . Alternate-bracket notations like or are rarely used for integer intervals.
Properties
The intervals are precisely the connected subsets of It follows that the image of an interval by any continuous function from to is also an interval. This is one formulation of the intermediate value theorem.
The intervals are also the convex subsets of The interval enclosure of a subset is also the convex hull of
The closure of an interval is the union of the interval and the set of its finite endpoints, and hence is also an interval. (The latter also follows from the fact that the closure of every connected subset of a topological space is a connected subset.) In other words, we have
The intersection of any collection of intervals is always an interval. The union of two intervals is an interval if and only if they have a non-empty intersection or an open end-point of one interval is a closed end-point of the other, for example
If is viewed as a metric space, its open balls are the open bounded intervals , and its closed balls are the closed bounded intervals . In particular, the metric and order topologies in the real line coincide, which is the standard topology of the real line. | Interval (mathematics) | Wikipedia | 485 | 49172 | https://en.wikipedia.org/wiki/Interval%20%28mathematics%29 | Mathematics | Real analysis | null |
Any element of an interval defines a partition of into three disjoint intervals 1, 2, 3: respectively, the elements of that are less than , the singleton and the elements that are greater than . The parts 1 and 3 are both non-empty (and have non-empty interiors), if and only if is in the interior of . This is an interval version of the trichotomy principle.
Dyadic intervals
A dyadic interval is a bounded real interval whose endpoints are and where and are integers. Depending on the context, either endpoint may or may not be included in the interval.
Dyadic intervals have the following properties:
The length of a dyadic interval is always an integer power of two.
Each dyadic interval is contained in exactly one dyadic interval of twice the length.
Each dyadic interval is spanned by two dyadic intervals of half the length.
If two open dyadic intervals overlap, then one of them is a subset of the other.
The dyadic intervals consequently have a structure that reflects that of an infinite binary tree.
Dyadic intervals are relevant to several areas of numerical analysis, including adaptive mesh refinement, multigrid methods and wavelet analysis. Another way to represent such a structure is p-adic analysis (for ).
Generalizations
Balls
An open finite interval is a 1-dimensional open ball with a center at and a radius of The closed finite interval is the corresponding closed ball, and the interval's two endpoints form a 0-dimensional sphere. Generalized to -dimensional Euclidean space, a ball is the set of points whose distance from the center is less than the radius. In the 2-dimensional case, a ball is called a disk.
If a half-space is taken as a kind of degenerate ball (without a well-defined center or radius), a half-space can be taken as analogous to a half-bounded interval, with its boundary plane as the (degenerate) sphere corresponding to the finite endpoint.
Multi-dimensional intervals
A finite interval is (the interior of) a 1-dimensional hyperrectangle. Generalized to real coordinate space an axis-aligned hyperrectangle (or box) is the Cartesian product of finite intervals. For this is a rectangle; for this is a rectangular cuboid (also called a "box"). | Interval (mathematics) | Wikipedia | 492 | 49172 | https://en.wikipedia.org/wiki/Interval%20%28mathematics%29 | Mathematics | Real analysis | null |
Allowing for a mix of open, closed, and infinite endpoints, the Cartesian product of any intervals, is sometimes called an -dimensional interval.
A facet of such an interval is the result of replacing any non-degenerate interval factor by a degenerate interval consisting of a finite endpoint of The faces of comprise itself and all faces of its facets. The corners of are the faces that consist of a single point of
Convex polytopes
Any finite interval can be constructed as the intersection of half-bounded intervals (with an empty intersection taken to mean the whole real line), and the intersection of any number of half-bounded intervals is a (possibly empty) interval. Generalized to -dimensional affine space, an intersection of half-spaces (of arbitrary orientation) is (the interior of) a convex polytope, or in the 2-dimensional case a convex polygon.
Domains
An open interval is a connected open set of real numbers. Generalized to topological spaces in general, a non-empty connected open set is called a domain.
Complex intervals
Intervals of complex numbers can be defined as regions of the complex plane, either rectangular or circular.
Intervals in posets and preordered sets
Definitions
The concept of intervals can be defined in arbitrary partially ordered sets or more generally, in arbitrary preordered sets. For a preordered set and two elements one similarly defines the intervals
where means Actually, the intervals with single or no endpoints are the same as the intervals with two endpoints in the larger preordered set
defined by adding new smallest and greatest elements (even if there were ones), which are subsets of In the case of one may take to be the extended real line.
Convex sets and convex components in order theory
A subset of the preordered set is (order-)convex if for every and every we have Unlike in the case of the real line, a convex set of a preordered set need not be an interval. For example, in the totally ordered set of rational numbers, the set
is convex, but not an interval of since there is no square root of two in | Interval (mathematics) | Wikipedia | 431 | 49172 | https://en.wikipedia.org/wiki/Interval%20%28mathematics%29 | Mathematics | Real analysis | null |
Let be a preordered set and let The convex sets of contained in form a poset under inclusion. A maximal element of this poset is called a convex component of By the Zorn lemma, any convex set of contained in is contained in some convex component of but such components need not be unique. In a totally ordered set, such a component is always unique. That is, the convex components of a subset of a totally ordered set form a partition.
Properties
A generalization of the characterizations of the real intervals follows. For a non-empty subset of a linear continuum the following conditions are equivalent.
The set is an interval.
The set is order-convex.
The set is a connected subset when is endowed with the order topology.
For a subset of a lattice the following conditions are equivalent.
The set is a sublattice and an (order-)convex set.
There is an ideal and a filter such that
Applications
In general topology
Every Tychonoff space is embeddable into a product space of the closed unit intervals Actually, every Tychonoff space that has a base of cardinality is embeddable into the product of copies of the intervals.
The concepts of convex sets and convex components are used in a proof that every totally ordered set endowed with the order topology is completely normal or moreover, monotonically normal.
Topological algebra
Intervals can be associated with points of the plane, and hence regions of intervals can be associated with regions of the plane. Generally, an interval in mathematics corresponds to an ordered pair taken from the direct product of real numbers with itself, where it is often assumed that . For purposes of mathematical structure, this restriction is discarded, and "reversed intervals" where are allowed. Then, the collection of all intervals can be identified with the topological ring formed by the direct sum of with itself, where addition and multiplication are defined component-wise.
The direct sum algebra has two ideals, { [x,0] : x ∈ R } and { [0,y] : y ∈ R }. The identity element of this algebra is the condensed interval . If interval is not in one of the ideals, then it has multiplicative inverse . Endowed with the usual topology, the algebra of intervals forms a topological ring. The group of units of this ring consists of four quadrants determined by the axes, or ideals in this case. The identity component of this group is quadrant I. | Interval (mathematics) | Wikipedia | 489 | 49172 | https://en.wikipedia.org/wiki/Interval%20%28mathematics%29 | Mathematics | Real analysis | null |
Every interval can be considered a symmetric interval around its midpoint. In a reconfiguration published in 1956 by M Warmus, the axis of "balanced intervals" is used along with the axis of intervals that reduce to a point. Instead of the direct sum the ring of intervals has been identified with the hyperbolic numbers by M. Warmus and D. H. Lehmer through the identification
where
This linear mapping of the plane, which amounts of a ring isomorphism, provides the plane with a multiplicative structure having some analogies to ordinary complex arithmetic, such as polar decomposition. | Interval (mathematics) | Wikipedia | 121 | 49172 | https://en.wikipedia.org/wiki/Interval%20%28mathematics%29 | Mathematics | Real analysis | null |
In mathematics, especially group theory, two elements and of a group are conjugate if there is an element in the group such that This is an equivalence relation whose equivalence classes are called conjugacy classes. In other words, each conjugacy class is closed under for all elements in the group.
Members of the same conjugacy class cannot be distinguished by using only the group structure, and therefore share many properties. The study of conjugacy classes of non-abelian groups is fundamental for the study of their structure. For an abelian group, each conjugacy class is a set containing one element (singleton set).
Functions that are constant for members of the same conjugacy class are called class functions.
Definition
Let be a group. Two elements are conjugate if there exists an element such that in which case is called of and is called a conjugate of
In the case of the general linear group of invertible matrices, the conjugacy relation is called matrix similarity.
It can be easily shown that conjugacy is an equivalence relation and therefore partitions into equivalence classes. (This means that every element of the group belongs to precisely one conjugacy class, and the classes and are equal if and only if and are conjugate, and disjoint otherwise.) The equivalence class that contains the element is
and is called the conjugacy class of The of is the number of distinct (nonequivalent) conjugacy classes. All elements belonging to the same conjugacy class have the same order.
Conjugacy classes may be referred to by describing them, or more briefly by abbreviations such as "6A", meaning "a certain conjugacy class with elements of order 6", and "6B" would be a different conjugacy class with elements of order 6; the conjugacy class 1A is the conjugacy class of the identity which has order 1. In some cases, conjugacy classes can be described in a uniform way; for example, in the symmetric group they can be described by cycle type.
Examples
The symmetric group consisting of the 6 permutations of three elements, has three conjugacy classes:
No change . The single member has order 1.
Transposing two . The 3 members all have order 2.
A cyclic permutation of all three . The 2 members both have order 3. | Conjugacy class | Wikipedia | 507 | 49176 | https://en.wikipedia.org/wiki/Conjugacy%20class | Mathematics | Abstract algebra | null |
These three classes also correspond to the classification of the isometries of an equilateral triangle.
The symmetric group consisting of the 24 permutations of four elements, has five conjugacy classes, listed with their description, cycle type, member order, and members: | Conjugacy class | Wikipedia | 57 | 49176 | https://en.wikipedia.org/wiki/Conjugacy%20class | Mathematics | Abstract algebra | null |
No change. Cycle type = [14]. Order = 1. Members = { (1, 2, 3, 4) }. The single row containing this conjugacy class is shown as a row of black circles in the adjacent table.
Interchanging two (other two remain unchanged). Cycle type = [1221]. Order = 2. Members = { (1, 2, 4, 3), (1, 4, 3, 2), (1, 3, 2, 4), (4, 2, 3, 1), (3, 2, 1, 4), (2, 1, 3, 4) }). The 6 rows containing this conjugacy class are highlighted in green in the adjacent table.
A cyclic permutation of three (other one remains unchanged). Cycle type = [1131]. Order = 3. Members = { (1, 3, 4, 2), (1, 4, 2, 3), (3, 2, 4, 1), (4, 2, 1, 3), (4, 1, 3, 2), (2, 4, 3, 1), (3, 1, 2, 4), (2, 3, 1, 4) }). The 8 rows containing this conjugacy class are shown with normal print (no boldface or color highlighting) in the adjacent table.
A cyclic permutation of all four. Cycle type = [41]. Order = 4. Members = { (2, 3, 4, 1), (2, 4, 1, 3), (3, 1, 4, 2), (3, 4, 2, 1), (4, 1, 2, 3), (4, 3, 1, 2) }). The 6 rows containing this conjugacy class are highlighted in orange in the adjacent table.
Interchanging two, and also the other two. Cycle type = [22]. Order = 2. Members = { (2, 1, 4, 3), (4, 3, 2, 1), (3, 4, 1, 2) }). The 3 rows containing this conjugacy class are shown with boldface entries in the adjacent table.
The proper rotations of the cube, which can be characterized by permutations of the body diagonals, are also described by conjugation in | Conjugacy class | Wikipedia | 509 | 49176 | https://en.wikipedia.org/wiki/Conjugacy%20class | Mathematics | Abstract algebra | null |
In general, the number of conjugacy classes in the symmetric group is equal to the number of integer partitions of This is because each conjugacy class corresponds to exactly one partition of into cycles, up to permutation of the elements of
In general, the Euclidean group can be studied by conjugation of isometries in Euclidean space.
Example
Let G =
a = ( 2 3 )
x = ( 1 2 3 )
x−1 = ( 3 2 1 )
Then xax−1
= ( 1 2 3 ) ( 2 3 ) ( 3 2 1 ) = ( 3 1 )
= ( 3 1 ) is Conjugate of ( 2 3 )
Properties
The identity element is always the only element in its class, that is
If is abelian then for all , i.e. for all (and the converse is also true: if all conjugacy classes are singletons then is abelian).
If two elements belong to the same conjugacy class (that is, if they are conjugate), then they have the same order. More generally, every statement about can be translated into a statement about because the map is an automorphism of called an inner automorphism. See the next property for an example.
If and are conjugate, then so are their powers and (Proof: if then ) Thus taking th powers gives a map on conjugacy classes, and one may consider which conjugacy classes are in its preimage. For example, in the symmetric group, the square of an element of type (3)(2) (a 3-cycle and a 2-cycle) is an element of type (3), therefore one of the power-up classes of (3) is the class (3)(2) (where is a power-up class of ).
An element lies in the center of if and only if its conjugacy class has only one element, itself. More generally, if denotes the of i.e., the subgroup consisting of all elements such that then the index is equal to the number of elements in the conjugacy class of (by the orbit-stabilizer theorem).
Take and let be the distinct integers which appear as lengths of cycles in the cycle type of (including 1-cycles). Let be the number of cycles of length in for each (so that ). Then the number of conjugates of is:
Conjugacy as group action | Conjugacy class | Wikipedia | 509 | 49176 | https://en.wikipedia.org/wiki/Conjugacy%20class | Mathematics | Abstract algebra | null |
For any two elements let
This defines a group action of on The orbits of this action are the conjugacy classes, and the stabilizer of a given element is the element's centralizer.
Similarly, we can define a group action of on the set of all subsets of by writing
or on the set of the subgroups of
Conjugacy class equation
If is a finite group, then for any group element the elements in the conjugacy class of are in one-to-one correspondence with cosets of the centralizer This can be seen by observing that any two elements and belonging to the same coset (and hence, for some in the centralizer ) give rise to the same element when conjugating :
That can also be seen from the orbit-stabilizer theorem, when considering the group as acting on itself through conjugation, so that orbits are conjugacy classes and stabilizer subgroups are centralizers. The converse holds as well.
Thus the number of elements in the conjugacy class of is the index of the centralizer in ; hence the size of each conjugacy class divides the order of the group.
Furthermore, if we choose a single representative element from every conjugacy class, we infer from the disjointness of the conjugacy classes that
where is the centralizer of the element Observing that each element of the center forms a conjugacy class containing just itself gives rise to the class equation:
where the sum is over a representative element from each conjugacy class that is not in the center.
Knowledge of the divisors of the group order can often be used to gain information about the order of the center or of the conjugacy classes.
Example
Consider a finite -group (that is, a group with order where is a prime number and ). We are going to prove that .
Since the order of any conjugacy class of must divide the order of it follows that each conjugacy class that is not in the center also has order some power of where But then the class equation requires that From this we see that must divide so | Conjugacy class | Wikipedia | 444 | 49176 | https://en.wikipedia.org/wiki/Conjugacy%20class | Mathematics | Abstract algebra | null |
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