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life while low-income populations will remain disproportionately low on vaccinations which hinders their ability to participate in non-essential activities. Due to the imbalance in the distribution of vaccines in the developing world, there are concerns about the inequity of vaccine passports for travellers. On 15 April 2021, the World Health Organization's emergency committee opposed vaccination passports, saying, "States parties are strongly encouraged to acknowledge the potential for requirements of proof of vaccination to deepen inequities and promote differential freedom of movement". However, many countries may increasingly consider the vaccination status of travellers when deciding to allow them entry or whether to require them to quarantine. "Some sort of vaccine certificate will be important" to reboot travel and tourism, according to Dr. David Nabarro, special envoy on COVID-19 for the WHO, in February 2021. In March 2021, Bernardo Mariano, the WHO's Director of Digital Health and Innovation, said that "We don't approve the fact that a vaccination passport should be a condition for travel." Lawmakers in several US states are also considering legislation to prohibit COVID-19 vaccination passports. Ethical concerns about vaccine passports have been raised by Human Rights Watch (HRW). According to HRW, requiring vaccine passports for work or travel could force people into taking tests or risk losing their jobs, create a perverse incentive for people to intentionally infect themselves to acquire immunity certificates, and risk creating a black market of forged or otherwise falsified vaccine cards. By restricting social, civic, and economic activities, vaccine passports may "compound existing gender, race, ethnicity, and nationality inequities." Immunity certificates also face privacy and human rights concerns. === Digital privacy === A security vulnerability in the app used by New Jersey and Utah briefly made it possible to request the QR codes of other users, containing encoded name, date of birth, and
|
{
"page_id": 68750333,
"source": null,
"title": "Vaccine passports during the COVID-19 pandemic"
}
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vaccination history information. On 24 September 2021, Saskatchewan Health Authority stated that digital vaccine records obtained in the province between 19 and 24 September may have accidentally contained the wrong QR code for the specific user. === Vaccination certificates === === Natural immunity === People may acquire a degree of natural immunity from SARS-CoV-2 when they are exposed to the live virus, and develop a primary immune response which produces antibodies that can recognize specific variants. As of May 2021, the WHO reported that more than 90% of individuals established recognizable antibodies within four weeks after an infection. For most people, these detectable antibodies roughly stay for at least 6–8 months. However, antibodies may not guarantee immunity from novel variants and mutations of SARS-CoV-2. The uncertainty of the science behind immunity to SARS-CoV-2 has raised issues over their applicability within passport frameworks. It has been argued that the primary difference is that vaccination certificates such as the Carte Jaune incentivize individuals to obtain vaccination against a disease, while immunity passports incentivize individuals to get infected with and recover from a disease. == See also == COVID-19 vaccine card COVID-19 vaccine Deployment of COVID-19 vaccines Electronic health record Living with COVID-19 Patient record access Vaccination requirements for international travel == References ==
|
{
"page_id": 68750333,
"source": null,
"title": "Vaccine passports during the COVID-19 pandemic"
}
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The endocochlear potential (EP; also called endolymphatic potential) is the positive voltage of 80-100mV seen in the cochlear endolymphatic spaces. Within the cochlea, the EP varies in magnitude all along its length. When a sound is presented, the endocochlear potential changes either positive or negative in the endolymph, depending on the stimulus. The change in the potential is called the summating potential. With the movement of the basilar membrane, a shear force is created and a small potential is generated due to a difference in potential between the endolymph (scala media, +80 mV) and the perilymph (vestibular and tympanic ducts, 0 mV). EP is highest in the basal turn of the cochlea (95 mV in mice) and decreases in the magnitude towards the apex (87 mV). In saccule and utricle, endolymphatic potential is about +9 mV and +3mV in the semicircular canal. EP is highly dependent on metabolism and ionic transport. An acoustic stimulus produces a simultaneous change in conductance at the membrane of the receptor cell. Because there is a steep gradient (150 mV), changes in membrane conductance are accompanied by rapid influx and efflux of ions which in turn produce the receptor potential. This is known as the Battery Hypothesis. The receptor potential for each hair cell causes a release of neurotransmitters at its basal pole, which elicits excitation of the afferent nerve fibres.
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{
"page_id": 27397118,
"source": null,
"title": "Endocochlear potential"
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A memory box is a box containing objects that serve as reminders. == Dementia == In cases of dementia, a memory box may be used as a form of therapy to remind the patient of their earlier life. == Deceased infants == Memory boxes are provided by some hospitals in the event of stillbirth, miscarriage, or other problem during or after childbirth. They contain objects belonging to or representing the deceased child to help relatives come to terms with their loss. Memory boxes are usually donated by local charities and organizations. Memory boxes for miscarriage, stillbirth and infant loss can contain the following items: lock of hair baby blanket special box to keep items in data card that states baby's name and birth information card/ink pad for taking foot/hand prints journal writing pen small stuffed animal to use in photos outfit that fits the baby air-dry clay for taking foot/hand molds disposable camera pocket kleenex bereavement books and information == References ==
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{
"page_id": 5835774,
"source": null,
"title": "Memory box"
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In the natural sciences, including physiology and engineering, a specific quantity generally refers to an intensive quantity obtained by the ratio of an extensive quantity of interest by another extensive quantity (usually mass or volume). If mass is the divisor quantity, the specific quantity is a massic quantity. If volume is the divisor quantity, the specific quantity is a volumic quantity. For example, massic leaf area is leaf area divided by leaf mass and volumic leaf area is leaf area divided by leaf volume. Derived SI units involve reciprocal kilogram (kg−1), e.g., square metre per kilogram (m2 · kg−1). Another kind of specific quantity, termed named specific quantity, is a generalization of the original concept. The divisor quantity is not restricted to mass, and name of the divisor is usually placed before "specific" in the full term (e.g., "thrust-specific fuel consumption"). Named and unnamed specific quantities are given for the terms below. == List == === Mass-specific quantities === Per unit of mass (short form of mass-specific): Specific absorption rate, power absorbed per unit mass of tissue at a given frequency Specific activity, radioactivity in becquerels per unit mass Specific energy, defined as energy per unit mass Specific internal energy, internal energy per unit mass Specific kinetic energy, kinetic energy of an object per unit of mass Specific enthalpy, enthalpy per unit mass Specific enzyme activity, activity per milligram of total protein Specific force, defined as the non-gravitational force per unit mass Specific growth rate, increase in cell mass per unit cell mass per unit time Specific heat capacity, heat capacity per unit mass, unless another unit is named, such as mole-specific heat capacity, or volume-specific heat capacity Specific latent heat, latent heat per unit mass Specific leaf area, leaf area per unit dry leaf mass Specific modulus, a materials
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{
"page_id": 60034047,
"source": null,
"title": "Specific quantity"
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property consisting of the elastic modulus per mass density of a material Specific orbital energy, orbital energy per unit mass Specific power, per unit of mass (or volume or area) Specific relative angular momentum, of two orbiting bodies is angular momentum per unit reduced mass, or the vector product of the relative position and the relative velocity Specific surface area, per unit of mass, volume, or cross-sectional area Specific volume, volume per unit mass, i.e. the reciprocal of density === Geometry specific quantities === Volume-specific quantity, the quotient of a physical quantity and volume ("per unit volume"), also called volumic quantities: Specific mass, actually meaning volume-specific mass, or mass per unit volume; same as density. Specific weight, weight per unit volume Charge density, the electric charge per volume Energy density, potential energy per unit volume Force density, force per unit volume Power density, power per unit volume Particle density (particle count), number of particles per unit volume Area-specific quantity, the quotient of a physical quantity and area ("per unit area"), also called areic quantities: Current density, the ratio of electric current to area Surface power density, power per unit area Specific surface energy, free energy per unit surface area Length-specific quantity, the quotient of a physical quantity and length ("per unit length"), also called lineic quantities: Linear charge density, charge per unit length Linear mass density, mass per unit length Linear number density, number of entities per unit length reciprocal length quantities === Other specific quantities === In chemistry: Molar quantities Concentration Per unit of other types. The dividing unit is sometimes added before the term "specific", and sometimes omitted. Brake-specific fuel consumption, fuel consumption per unit of braking power Thrust-specific fuel consumption, fuel consumption per unit of thrust Specific acid catalysis, in which the reaction rate is proportional to
|
{
"page_id": 60034047,
"source": null,
"title": "Specific quantity"
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the concentration of the protonated solvent molecules Specific acoustic impedance, ratio of sound pressure p to particle speed at a single frequency Specific capacity of a water well, quantity of water produced per (length) unit of drawdown Specific conductance, conductance per meter. Identical to electrical conductivity Specific detectivity of a photodetector Specific fuel consumption (disambiguation). Fuel consumption per unit thrust, or per unit power. Type defined as above. Specific gas constant, per molar mass Specific heat of vaporization, enthalpy of vaporization, vaporizing heat per mole Specific humidity, mass of water vapor per unit mass dry air Specific impulse, impulse (momentum change) per unit of propellant (either per unit of propellant mass, or per unit of propellant by Earth-weight) Specific melting heat, enthalpy of fusion; melting heat per mole Specific modulus, elastic modulus per mass density Specific resistance (disambiguation), several scientific meanings Specific rotation of a chemical, angle of optical rotation α of plane-polarized light per standard sample with a path length of one decimeter and a sample concentration of one gram per millilitre Specific speed, unitless figure of merit used to classify pump impellers (pump-specific) and turbines (turbine-specific). Ratio of performance against reference pump that needs one unit of speed to pump one unit volume per one unit hydraulic head pressure. For a turbine, it is performance measured against a reference turbine that develops one unit of power per one unit speed per one unit of hydraulic head. Specific storage, specific yield, and specific capacity, quantify the capacity of an aquifer to release groundwater from storage per unit decline in hydraulic head pressure Specific strength, material strength (pressure required at failure) per unit material density Specific surface area, per unit of mass, volume, or cross-sectional area Specific thrust, thrust per unit air intake rate == Usage == Reference tables Specific
|
{
"page_id": 60034047,
"source": null,
"title": "Specific quantity"
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properties are often used in reference tables as a means of recording material data in a manner that is independent of size or mass. This allows the data to be broadly applied while keeping the table compact. Ranking, classifying, and comparing Specific properties are useful for making comparisons about one attribute while cancelling out the effect of variations in another attribute. For instance, steel alloys are typically stronger than aluminum alloys but are also much denser. Greater strength allows less metal to be used, which makes the choice between the two metals less than obvious. To simplify the comparison, one would compare the specific strength (strength to weight ratio) of the two metals. A more everyday example relates to grocery shopping: a 2 kg package sells for a higher price than 1 kg package of the same foodstuff, but what matters is the "specific price", commonly called the unit cost (cost in currency units per kilogram). Mnemonics and qualitative reasoning In many instances, specific properties are more intuitive or are easier to remember than the original properties, whether in SI or imperial units. For instance, it is easier to conceptualize an acceleration of 2g than an acceleration of 19.6 meters per second squared. == See also == Intensive and extensive properties#Specific properties == References ==
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{
"page_id": 60034047,
"source": null,
"title": "Specific quantity"
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Chrome Azurol S is a histological dye used in biomedical research. Chrome Azural S (CAS) is a common spectrophotometric reagent for detection of certain metals like aluminum which can be toxic in excess and can contribute to people with neurodegenerative disorders. CAS is used to provide quantitative and qualitative information on molecules of interest like aluminum and siderophores. Qualitatively a color change can be observed while also allowing to quantitatively determine concentration of certain ions. == References ==
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{
"page_id": 62983169,
"source": null,
"title": "Chrome Azurol S"
}
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Fusarium graminearum Genome Database (FGDB) is genomic database on Fusarium graminearum, a plant pathogen which causes the wheat headblight disease. == See also == Gibberella zeae == References == == External links == http://mips.gsf.de/genre/proj/fusarium/ Archived 2009-06-17 at the Wayback Machine.
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{
"page_id": 31591427,
"source": null,
"title": "Fusarium graminearum genome database"
}
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Multiple sequence alignment (MSA) is the process or the result of sequence alignment of three or more biological sequences, generally protein, DNA, or RNA. These alignments are used to infer evolutionary relationships via phylogenetic analysis and can highlight homologous features between sequences. Alignments highlight mutation events such as point mutations (single amino acid or nucleotide changes), insertion mutations and deletion mutations, and alignments are used to assess sequence conservation and infer the presence and activity of protein domains, tertiary structures, secondary structures, and individual amino acids or nucleotides. Multiple sequence alignments require more sophisticated methodologies than pairwise alignments, as they are more computationally complex. Most multiple sequence alignment programs use heuristic methods rather than global optimization because identifying the optimal alignment between more than a few sequences of moderate length is prohibitively computationally expensive. However, heuristic methods generally cannot guarantee high-quality solutions and have been shown to fail to yield near-optimal solutions on benchmark test cases. == Problem statement == Given m {\displaystyle m} sequences S i {\displaystyle S_{i}} , i = 1 , ⋯ , m {\displaystyle i=1,\cdots ,m} similar to the form below: S := { S 1 = ( S 11 , S 12 , … , S 1 n 1 ) S 2 = ( S 21 , S 22 , ⋯ , S 2 n 2 ) ⋮ S m = ( S m 1 , S m 2 , … , S m n m ) {\displaystyle S:={\begin{cases}S_{1}=(S_{11},S_{12},\ldots ,S_{1n_{1}})\\S_{2}=(S_{21},S_{22},\cdots ,S_{2n_{2}})\\\,\,\,\,\,\,\,\,\,\,\vdots \\S_{m}=(S_{m1},S_{m2},\ldots ,S_{mn_{m}})\end{cases}}} A multiple sequence alignment is taken of this set of sequences S {\displaystyle S} by inserting any amount of gaps needed into each of the S i {\displaystyle S_{i}} sequences of S {\displaystyle S} until the modified sequences, S i ′ {\displaystyle S'_{i}} , all conform to length L ≥ max {
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n i ∣ i = 1 , … , m } {\displaystyle L\geq \max\{n_{i}\mid i=1,\ldots ,m\}} and no values in the sequences of S {\displaystyle S} of the same column consists of only gaps. The mathematical form of an MSA of the above sequence set is shown below: S ′ := { S 1 ′ = ( S 11 ′ , S 12 ′ , … , S 1 L ′ ) S 2 ′ = ( S 21 ′ , S 22 ′ , … , S 2 L ′ ) ⋮ S m ′ = ( S m 1 ′ , S m 2 ′ , … , S m L ′ ) {\displaystyle S':={\begin{cases}S'_{1}=(S'_{11},S'_{12},\ldots ,S'_{1L})\\S'_{2}=(S'_{21},S'_{22},\ldots ,S'_{2L})\\\,\,\,\,\,\,\,\,\,\,\vdots \\S'_{m}=(S'_{m1},S'_{m2},\ldots ,S'_{mL})\end{cases}}} To return from each particular sequence S i ′ {\displaystyle S'_{i}} to S i {\displaystyle S_{i}} , remove all gaps. == Graphing approach == A general approach when calculating multiple sequence alignments is to use graphs to identify all of the different alignments. When finding alignments via graph, a complete alignment is created in a weighted graph that contains a set of vertices and a set of edges. Each of the graph edges has a weight based on a certain heuristic that helps to score each alignment or subset of the original graph. === Tracing alignments === When determining the best suited alignments for each MSA, a trace is usually generated. A trace is a set of realized, or corresponding and aligned, vertices that has a specific weight based on the edges that are selected between corresponding vertices. When choosing traces for a set of sequences it is necessary to choose a trace with a maximum weight to get the best alignment of the sequences. == Alignment methods == There are various alignment methods used within multiple sequence to
|
{
"page_id": 4066308,
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"title": "Multiple sequence alignment"
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maximize scores and correctness of alignments. Each is usually based on a certain heuristic with an insight into the evolutionary process. Most try to replicate evolution to get the most realistic alignment possible to best predict relations between sequences. === Dynamic programming === A direct method for producing an MSA uses the dynamic programming technique to identify the globally optimal alignment solution. For proteins, this method usually involves two sets of parameters: a gap penalty and a substitution matrix assigning scores or probabilities to the alignment of each possible pair of amino acids based on the similarity of the amino acids' chemical properties and the evolutionary probability of the mutation. For nucleotide sequences, a similar gap penalty is used, but a much simpler substitution matrix, wherein only identical matches and mismatches are considered, is typical. The scores in the substitution matrix may be either all positive or a mix of positive and negative in the case of a global alignment, but must be both positive and negative, in the case of a local alignment. For n individual sequences, the naive method requires constructing the n-dimensional equivalent of the matrix formed in standard pairwise sequence alignment. The search space thus increases exponentially with increasing n and is also strongly dependent on sequence length. Expressed with the big O notation commonly used to measure computational complexity, a naïve MSA takes O(LengthNseqs) time to produce. To find the global optimum for n sequences this way has been shown to be an NP-complete problem. In 1989, based on Carrillo-Lipman Algorithm, Altschul introduced a practical method that uses pairwise alignments to constrain the n-dimensional search space. In this approach pairwise dynamic programming alignments are performed on each pair of sequences in the query set, and only the space near the n-dimensional intersection of these alignments
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"page_id": 4066308,
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is searched for the n-way alignment. The MSA program optimizes the sum of all of the pairs of characters at each position in the alignment (the so-called sum of pair score) and has been implemented in a software program for constructing multiple sequence alignments. In 2019, Hosseininasab and van Hoeve showed that by using decision diagrams, MSA may be modeled in polynomial space complexity. === Progressive alignment construction === The most widely used approach to multiple sequence alignments uses a heuristic search known as progressive technique (also known as the hierarchical or tree method) developed by Da-Fei Feng and Doolittle in 1987. Progressive alignment builds up a final MSA by combining pairwise alignments beginning with the most similar pair and progressing to the most distantly related. All progressive alignment methods require two stages: a first stage in which the relationships between the sequences are represented as a phylogenetic tree, called a guide tree, and a second step in which the MSA is built by adding the sequences sequentially to the growing MSA according to the guide tree. The initial guide tree is determined by an efficient clustering method such as neighbor-joining or unweighted pair group method with arithmetic mean (UPGMA), and may use distances based on the number of identical two-letter sub-sequences (as in FASTA rather than a dynamic programming alignment). Progressive alignments are not guaranteed to be globally optimal. The primary problem is that when errors are made at any stage in growing the MSA, these errors are then propagated through to the final result. Performance is also particularly bad when all of the sequences in the set are rather distantly related. Most modern progressive methods modify their scoring function with a secondary weighting function that assigns scaling factors to individual members of the query set in a nonlinear
|
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"page_id": 4066308,
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"title": "Multiple sequence alignment"
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fashion based on their phylogenetic distance from their nearest neighbors. This corrects for non-random selection of the sequences given to the alignment program. Progressive alignment methods are efficient enough to implement on a large scale for many (100s to 1000s) sequences. A popular progressive alignment method has been the Clustal family. ClustalW is used extensively for phylogenetic tree construction, in spite of the author's explicit warnings that unedited alignments should not be used in such studies and as input for protein structure prediction by homology modeling. European Bioinformatics Institute (EMBL-EBI) announced that CLustalW2 will expire in August 2015. They recommend Clustal Omega which performs based on seeded guide trees and HMM profile-profile techniques for protein alignments. An alternative tool for progressive DNA alignments is multiple alignment using fast Fourier transform (MAFFT). Another common progressive alignment method named T-Coffee is slower than Clustal and its derivatives but generally produces more accurate alignments for distantly related sequence sets. T-Coffee calculates pairwise alignments by combining the direct alignment of the pair with indirect alignments that aligns each sequence of the pair to a third sequence. It uses the output from Clustal as well as another local alignment program LALIGN, which finds multiple regions of local alignment between two sequences. The resulting alignment and phylogenetic tree are used as a guide to produce new and more accurate weighting factors. Because progressive methods are heuristics that are not guaranteed to converge to a global optimum, alignment quality can be difficult to evaluate and their true biological significance can be obscure. A semi-progressive method that improves alignment quality and does not use a lossy heuristic while running in polynomial time has been implemented in the program PSAlign. === Iterative methods === A set of methods to produce MSAs while reducing the errors inherent in progressive methods
|
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are classified as "iterative" because they work similarly to progressive methods but repeatedly realign the initial sequences as well as adding new sequences to the growing MSA. One reason progressive methods are so strongly dependent on a high-quality initial alignment is the fact that these alignments are always incorporated into the final result – that is, once a sequence has been aligned into the MSA, its alignment is not considered further. This approximation improves efficiency at the cost of accuracy. By contrast, iterative methods can return to previously calculated pairwise alignments or sub-MSAs incorporating subsets of the query sequence as a means of optimizing a general objective function such as finding a high-quality alignment score. A variety of subtly different iteration methods have been implemented and made available in software packages; reviews and comparisons have been useful but generally refrain from choosing a "best" technique. The software package PRRN/PRRP uses a hill-climbing algorithm to optimize its MSA alignment score and iteratively corrects both alignment weights and locally divergent or "gappy" regions of the growing MSA. PRRP performs best when refining an alignment previously constructed by a faster method. Another iterative program, DIALIGN, takes an unusual approach of focusing narrowly on local alignments between sub-segments or sequence motifs without introducing a gap penalty. The alignment of individual motifs is then achieved with a matrix representation similar to a dot-matrix plot in a pairwise alignment. An alternative method that uses fast local alignments as anchor points or seeds for a slower global-alignment procedure is implemented in the CHAOS/DIALIGN suite. A third popular iteration-based method named MUSCLE (multiple sequence alignment by log-expectation) improves on progressive methods with a more accurate distance measure to assess the relatedness of two sequences. The distance measure is updated between iteration stages (although, in its original form, MUSCLE
|
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contained only 2-3 iterations depending on whether refinement was enabled). === Consensus methods === Consensus methods attempt to find the optimal multiple sequence alignment given multiple different alignments of the same set of sequences. There are two commonly used consensus methods, M-COFFEE and MergeAlign. M-COFFEE uses multiple sequence alignments generated by seven different methods to generate consensus alignments. MergeAlign is capable of generating consensus alignments from any number of input alignments generated using different models of sequence evolution or different methods of multiple sequence alignment. The default option for MergeAlign is to infer a consensus alignment using alignments generated using 91 different models of protein sequence evolution. === Hidden Markov models === A hidden Markov model (HMM) is a probabilistic model that can assign likelihoods to all possible combinations of gaps, matches, and mismatches, to determine the most likely MSA or set of possible MSAs. HMMs can produce a single highest-scoring output but can also generate a family of possible alignments that can then be evaluated for biological significance. HMMs can produce both global and local alignments. Although HMM-based methods have been developed relatively recently, they offer significant improvements in computational speed, especially for sequences that contain overlapping regions. Typical HMM-based methods work by representing an MSA as a form of directed acyclic graph known as a partial-order graph, which consists of a series of nodes representing possible entries in the columns of an MSA. In this representation a column that is absolutely conserved (that is, that all the sequences in the MSA share a particular character at a particular position) is coded as a single node with as many outgoing connections as there are possible characters in the next column of the alignment. In the terms of a typical hidden Markov model, the observed states are the individual alignment
|
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columns and the "hidden" states represent the presumed ancestral sequence from which the sequences in the query set are hypothesized to have descended. An efficient search variant of the dynamic programming method, named the Viterbi algorithm, is generally used to successively align the growing MSA to the next sequence in the query set to produce a new MSA. This is distinct from progressive alignment methods because the alignment of prior sequences is updated at each new sequence addition. However, like progressive methods, this technique can be influenced by the order in which the sequences in the query set are integrated into the alignment, especially when the sequences are distantly related. Several software programs are available in which variants of HMM-based methods have been implemented and which are noted for their scalability and efficiency, although properly using an HMM method is more complex than using more common progressive methods. The simplest is Partial-Order Alignment (POA), and a similar more general method is implemented in the Sequence Alignment and Modeling System (SAM) software package. and HMMER. SAM has been used as a source of alignments for protein structure prediction to participate in the Critical Assessment of Structure Prediction (CASP) structure prediction experiment and to develop a database of predicted proteins in the yeast species S. cerevisiae. HHsearch is a software package for the detection of remotely related protein sequences based on the pairwise comparison of HMMs. A server running HHsearch (HHpred) was the fastest of 10 automatic structure prediction servers in the CASP7 and CASP8 structure prediction competitions. === Phylogeny-aware methods === Most multiple sequence alignment methods try to minimize the number of insertions/deletions (gaps) and, as a consequence, produce compact alignments. This causes several problems if the sequences to be aligned contain non-homologous regions, if gaps are informative in a phylogeny
|
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"page_id": 4066308,
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analysis. These problems are common in newly produced sequences that are poorly annotated and may contain frame-shifts, wrong domains or non-homologous spliced exons. The first such method was developed in 2005 by Löytynoja and Goldman. The same authors released a software package called PRANK in 2008. PRANK improves alignments when insertions are present. Nevertheless, it runs slowly compared to progressive and/or iterative methods which have been developed for several years. In 2012, two new phylogeny-aware tools appeared. One is called PAGAN that was developed by the same team as PRANK. The other is ProGraphMSA developed by Szalkowski. Both software packages were developed independently but share common features, notably the use of graph algorithms to improve the recognition of non-homologous regions, and an improvement in code making these software faster than PRANK. === Motif finding === Motif finding, also known as profile analysis, is a method of locating sequence motifs in global MSAs that is both a means of producing a better MSA and a means of producing a scoring matrix for use in searching other sequences for similar motifs. A variety of methods for isolating the motifs have been developed, but all are based on identifying short highly conserved patterns within the larger alignment and constructing a matrix similar to a substitution matrix that reflects the amino acid or nucleotide composition of each position in the putative motif. The alignment can then be refined using these matrices. In standard profile analysis, the matrix includes entries for each possible character as well as entries for gaps. Alternatively, statistical pattern-finding algorithms can identify motifs as a precursor to an MSA rather than as a derivation. In many cases when the query set contains only a small number of sequences or contains only highly related sequences, pseudocounts are added to normalize the distribution
|
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"page_id": 4066308,
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reflected in the scoring matrix. In particular, this corrects zero-probability entries in the matrix to values that are small but nonzero. Blocks analysis is a method of motif finding that restricts motifs to ungapped regions in the alignment. Blocks can be generated from an MSA or they can be extracted from unaligned sequences using a precalculated set of common motifs previously generated from known gene families. Block scoring generally relies on the spacing of high-frequency characters rather than on the calculation of an explicit substitution matrix. Statistical pattern-matching has been implemented using both the expectation-maximization algorithm and the Gibbs sampler. One of the most common motif-finding tools, named Multiple EM for Motif Elicitation (MEME), uses expectation maximization and hidden Markov methods to generate motifs that are then used as search tools by its companion MAST in the combined suite MEME/MAST. === Non-coding multiple sequence alignment === Non-coding DNA regions, especially transcription factor binding sites (TFBSs), are conserved, but not necessarily evolutionarily related, and may have converged from non-common ancestors. Thus, the assumptions used to align protein sequences and DNA coding regions are inherently different from those that hold for TFBS sequences. Although it is meaningful to align DNA coding regions for homologous sequences using mutation operators, alignment of binding site sequences for the same transcription factor cannot rely on evolutionary related mutation operations. Similarly, the evolutionary operator of point mutations can be used to define an edit distance for coding sequences, but this has little meaning for TFBS sequences because any sequence variation has to maintain a certain level of specificity for the binding site to function. This becomes specifically important when trying to align known TFBS sequences to build supervised models to predict unknown locations of the same TFBS. Hence, Multiple Sequence Alignment methods need to adjust the underlying
|
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evolutionary hypothesis and the operators used as in the work published incorporating neighbouring base thermodynamic information to align the binding sites searching for the lowest thermodynamic alignment conserving specificity of the binding site. == Optimization == === Genetic algorithms and simulated annealing === Standard optimization techniques in computer science – both of which were inspired by, but do not directly reproduce, physical processes – have also been used in an attempt to more efficiently produce quality MSAs. One such technique, genetic algorithms, has been used for MSA production in an attempt to broadly simulate the hypothesized evolutionary process that gave rise to the divergence in the query set. The method works by breaking a series of possible MSAs into fragments and repeatedly rearranging those fragments with the introduction of gaps at varying positions. A general objective function is optimized during the simulation, most generally the "sum of pairs" maximization function introduced in dynamic programming-based MSA methods. A technique for protein sequences has been implemented in the software program SAGA (Sequence Alignment by Genetic Algorithm) and its equivalent in RNA is called RAGA. The technique of simulated annealing, by which an existing MSA produced by another method is refined by a series of rearrangements designed to find better regions of alignment space than the one the input alignment already occupies. Like the genetic algorithm method, simulated annealing maximizes an objective function like the sum-of-pairs function. Simulated annealing uses a metaphorical "temperature factor" that determines the rate at which rearrangements proceed and the likelihood of each rearrangement; typical usage alternates periods of high rearrangement rates with relatively low likelihood (to explore more distant regions of alignment space) with periods of lower rates and higher likelihoods to more thoroughly explore local minima near the newly "colonized" regions. This approach has been implemented in
|
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the program MSASA (Multiple Sequence Alignment by Simulated Annealing). === Mathematical programming and exact solution algorithms === Mathematical programming and in particular mixed integer programming models are another approach to solve MSA problems. The advantage of such optimization models is that they can be used to find the optimal MSA solution more efficiently compared to the traditional DP approach. This is due in part, to the applicability of decomposition techniques for mathematical programs, where the MSA model is decomposed into smaller parts and iteratively solved until the optimal solution is found. Example algorithms used to solve mixed integer programming models of MSA include branch and price and Benders decomposition. Although exact approaches are computationally slow compared to heuristic algorithms for MSA, they are guaranteed to reach the optimal solution eventually, even for large-size problems. === Simulated quantum computing === In January 2017, D-Wave Systems announced that its qbsolv open-source quantum computing software had been successfully used to find a faster solution to the MSA problem. == Alignment visualization and quality control == The necessary use of heuristics for multiple alignment means that for an arbitrary set of proteins, there is always a good chance that an alignment will contain errors. For example, an evaluation of several leading alignment programs using the BAliBase benchmark found that at least 24% of all pairs of aligned amino acids were incorrectly aligned. These errors can arise because of unique insertions into one or more regions of sequences, or through some more complex evolutionary process leading to proteins that do not align easily by sequence alone. As the number of sequence and their divergence increases many more errors will be made simply because of the heuristic nature of MSA algorithms. Multiple sequence alignment viewers enable alignments to be visually reviewed, often by inspecting the quality
|
{
"page_id": 4066308,
"source": null,
"title": "Multiple sequence alignment"
}
|
of alignment for annotated functional sites on two or more sequences. Many also enable the alignment to be edited to correct these (usually minor) errors, in order to obtain an optimal 'curated' alignment suitable for use in phylogenetic analysis or comparative modeling. However, as the number of sequences increases and especially in genome-wide studies that involve many MSAs it is impossible to manually curate all alignments. Furthermore, manual curation is subjective. And finally, even the best expert cannot confidently align the more ambiguous cases of highly diverged sequences. In such cases it is common practice to use automatic procedures to exclude unreliably aligned regions from the MSA. For the purpose of phylogeny reconstruction (see below) the Gblocks program is widely used to remove alignment blocks suspect of low quality, according to various cutoffs on the number of gapped sequences in alignment columns. However, these criteria may excessively filter out regions with insertion/deletion events that may still be aligned reliably, and these regions might be desirable for other purposes such as detection of positive selection. A few alignment algorithms output site-specific scores that allow the selection of high-confidence regions. Such a service was first offered by the SOAP program, which tests the robustness of each column to perturbation in the parameters of the popular alignment program CLUSTALW. The T-Coffee program uses a library of alignments in the construction of the final MSA, and its output MSA is colored according to confidence scores that reflect the agreement between different alignments in the library regarding each aligned residue. Its extension, Transitive Consistency Score (TCS), uses T-Coffee libraries of pairwise alignments to evaluate any third party MSA. Pairwise projections can be produced using fast or slow methods, thus allowing a trade-off between speed and accuracy. Another alignment program that can output an MSA with
|
{
"page_id": 4066308,
"source": null,
"title": "Multiple sequence alignment"
}
|
confidence scores is FSA, which uses a statistical model that allows calculation of the uncertainty in the alignment. The HoT (Heads-Or-Tails) score can be used as a measure of site-specific alignment uncertainty due to the existence of multiple co-optimal solutions. The GUIDANCE program calculates a similar site-specific confidence measure based on the robustness of the alignment to uncertainty in the guide tree that is used in progressive alignment programs. An alternative, more statistically justified approach to assess alignment uncertainty is the use of probabilistic evolutionary models for joint estimation of phylogeny and alignment. A Bayesian approach allows calculation of posterior probabilities of estimated phylogeny and alignment, which is a measure of the confidence in these estimates. In this case, a posterior probability can be calculated for each site in the alignment. Such an approach was implemented in the program BAli-Phy. There are free programs available for visualization of multiple sequence alignments, for example Jalview and UGENE. == Phylogenetic use == Multiple sequence alignments can be used to create a phylogenetic tree. This is made possible by two reasons. The first is because functional domains that are known in annotated sequences can be used for alignment in non-annotated sequences. The other is that conserved regions known to be functionally important can be found. This makes it possible for multiple sequence alignments to be used to analyze and find evolutionary relationships through homology between sequences. Point mutations and insertion or deletion events (called indels) can be detected. Multiple sequence alignments can also be used to identify functionally important sites, such as binding sites, active sites, or sites corresponding to other key functions, by locating conserved domains. When looking at multiple sequence alignments, it is useful to consider different aspects of the sequences when comparing sequences. These aspects include identity, similarity, and homology.
|
{
"page_id": 4066308,
"source": null,
"title": "Multiple sequence alignment"
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|
Identity means that the sequences have identical residues at their respective positions. On the other hand, similarity has to do with the sequences being compared having similar residues quantitatively. For example, in terms of nucleotide sequences, pyrimidines are considered similar to each other, as are purines. Similarity ultimately leads to homology, in that the more similar sequences are, the closer they are to being homologous. This similarity in sequences can then go on to help find common ancestry. == See also == Alignment-free sequence analysis Cladistics Generalized tree alignment Multiple sequence alignment viewers PANDIT, a biological database covering protein domains Phylogenetics Sequence alignment software Structural alignment == References == === Survey articles === Duret, L.; S. Abdeddaim (2000). "Multiple alignment for structural functional or phylogenetic analyses of homologous sequences". In D. Higgins and W. Taylor (ed.). Bioinformatics sequence structure and databanks. Oxford: Oxford University Press. Notredame, C. (2002). "Recent progresses in multiple sequence alignment: a survey". Pharmacogenomics. 3 (1): 131–144. doi:10.1517/14622416.3.1.131. PMID 11966409. Thompson, J. D.; Plewniak, F.; Poch, O. (1999). "A comprehensive comparison of multiple sequence alignment programs". Nucleic Acids Research. 27 (13): 12682–2690. doi:10.1093/nar/27.13.2682. PMC 148477. PMID 10373585. Wallace, I.M.; Blackshields, G.; Higgins, D.G. (2005). "Multiple sequence alignments". Curr Opin Struct Biol. 15 (3): 261–266. doi:10.1016/j.sbi.2005.04.002. PMID 15963889. Notredame, C (2007). "Recent Evolutions of Multiple Sequence Alignment Algorithms". PLOS Computational Biology. 3 (8): e123. Bibcode:2007PLSCB...3..123N. doi:10.1371/journal.pcbi.0030123. PMC 1963500. PMID 17784778. == External links == ExPASy sequence alignment tools Archived Multiple Alignment Resource Page – from the Virtual School of Natural Sciences Tools for Multiple Alignments – from Pôle Bioinformatique Lyonnais An entry point to clustal servers and information An entry point to the main T-Coffee servers An entry point to the main MergeAlign server and information European Bioinformatics Institute servers: ClustalW2 – general purpose multiple sequence alignment program
|
{
"page_id": 4066308,
"source": null,
"title": "Multiple sequence alignment"
}
|
for DNA or proteins. Muscle – MUltiple Sequence Comparison by Log-Expectation T-coffee – multiple sequence alignment. MAFFT – Multiple Alignment using Fast Fourier Transform KALIGN – a fast and accurate multiple sequence alignment algorithm. === Lecture notes, tutorials, and courses === Multiple sequence alignment lectures – from the Max Planck Institute for Molecular Genetics Lecture Notes and practical exercises on multiple sequence alignments at the European Molecular Biology Laboratory (EMBL) Molecular Bioinformatics Lecture Notes Molecular Evolution and Bioinformatics Lecture Notes
|
{
"page_id": 4066308,
"source": null,
"title": "Multiple sequence alignment"
}
|
Single molecule fluorescent sequencing is one method of DNA sequencing. The core principle is the imaging of individual fluorophore molecules, each corresponding to one base. By working on single molecule level, amplification of DNA is not required, avoiding amplification bias. The method lends itself to parallelization by probing many sequences simultaneously, imaging all of them at the same time. The principle can be applied stepwise (e.g. the Helicos implementation), or in real time (as in the Pacific Biosciences implementation). == References ==
|
{
"page_id": 31001609,
"source": null,
"title": "Single molecule fluorescent sequencing"
}
|
Amitabh Singh is an Indian Space Scientist. He was Project Manager for Chandrayaan-1 Mission and Deputy Project Director & Operations Director for Chandrayaan-2 & 3 Mission at Indian Space Research Organization. He handled the optical payload data processing and on-board algorithm related to Chandrayaan-2 and Chandrayaan-3 Lander and Rover. He is also a Guest Faculty at Department of Physics, Electronics & Space Science of the Gujarat University. He is working for upcoming Chandrayaan missions. He has authored some books on Chandrayaan 1 and articles on Planetary Geomatics and Exploring the Moon in three dimension. He has been awarded the ISRS Young Achiever Award by the Indian Society of Remote Sensing, Dehradun. He was also Part of Chandrayaan-3 team who received Rastriya Vigyan team award 2024 == Early life == Amitabh Singh was born at Kubauli village of Samastipur district in Bihar. His wife is a senior doctor. == Education == === Anugrah Narayan College, Patna === He studied M.Sc (Electronics) from Department of Physics, A N College Patna. === BIT, Mesra === He studied M.Tech from Birla Institute of Technology, Mesra. == Bibliography == Chandrayaan-1 se liye gaye Chandrama Ke Pratibimb, ISBN 978-81-909978-8-1 Images of Moon from Chandrayaan-1, ISBN 978-81-909978-3-6 == Awards == ISRS Young Achiever Award (2008) 2024 Laurels for Team Achievement Award for Chandrayaan-3 by The International Academy of Astronautics (IAA) (2024) Rastriya Vigyan Team Award 2024 for Chandrayaan-3 Team (2024) == References ==
|
{
"page_id": 68946956,
"source": null,
"title": "Amitabh Singh"
}
|
A health claim on a food label and in food marketing is a claim by a manufacturer of food products that their food will reduce the risk of developing a disease or condition. For example, it is claimed by the manufacturers of oat cereals that oat bran can reduce cholesterol, which will lower the chances of developing serious heart conditions. Vague health claims include that the food inside is "healthy," "organic," "low fat," "non-GMO," "no sugar added," or "natural". Health claims are also made for over-the-counter drugs and prescription drugs, medical procedures, and medical devices, but these generally have a separate, much more stringent set of regulations. == Health claims in the United States == In the United States, health claims on nutrition facts labels are regulated by the U.S. Food and Drug Administration (FDA), while advertising is regulated by the Federal Trade Commission. Dietary supplements are regulated as a separate type of consumer item from food or over-the-counter drugs. === Food === ==== FDA guidelines ==== According to the FDA, "Authorized health claims in food labeling are claims that have been reviewed by FDA and are allowed on food products or dietary supplements to show that a food or food component may reduce the risk of a disease or a health-related condition." An authorized health claim is limited to evidence for reducing the risk of a disease, and does not apply to the diagnosis, cure, mitigation, or treatment of disease. It must be reviewed, evaluated, and publicly-announced by the FDA prior to use. Approval of a health claim by the FDA requires significant scientific agreement (SSA) among reputable scientists that the claim is based on publicly-available evidence that a relationship exists between an element and a disease. The SSA standard provides a high degree of confidence that the relationship
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{
"page_id": 265229,
"source": null,
"title": "Health claim"
}
|
between the element and the disease is valid. Based on scientific evidence, such claims may be used for marketing on foods or dietary supplements. The authorized health claim must be written in a way that helps consumers understand the importance of including the element in their daily diet. The FDA has guidelines for what is considered a misleading label, and also monitors and warns food manufacturers against labeling foods as having specific health effects when no evidence exists to support such statements, such as for one manufacturer in 2018. A qualified health claim is supported by some scientific evidence, but does not meet the significant scientific standard of evidence required for an authorized health claim. Qualified health claims must be accompanied by a disclaimer or other qualifying language to accurately communicate the level of scientific evidence supporting the claim. ==== Consumer advocacy ==== The use of the label “Healthy” on a variety of foods has been a particular issue for many food quality advocacy groups. In general, claims of health benefits for specific foodstuffs are not supported by scientific evidence and are not evaluated by national regulatory agencies. Additionally, research funded by manufacturers or marketers has been criticized to result in more favorable results than those from independently funded research. === Dietary supplements === In the United States, these claims, usually referred to as "qualified health claims", are regulated by the Food and Drug Administration (FDA) in the public interest. The rule in place before 2003 required "significant scientific consensus" before a claim could be made, applying characterization of a hierarchy of degrees of certainty: A: "There is significant scientific agreement for [the claim]." B: "Although there is some scientific evidence supporting [the claim], the evidence is not conclusive." C: "Some scientific evidence suggests [the claim]. However, the FDA has
|
{
"page_id": 265229,
"source": null,
"title": "Health claim"
}
|
determined that this evidence is limited and not conclusive." D: "Very limited and preliminary scientific research suggests [the claim]. The FDA concludes that there is little scientific evidence supporting this claim." See the Wikipedia article on dietary supplements for a description of current FDA policy. == Health claims in Canada == == Health claims in Europe == In the European Union, the European Food Safety Authority provides regulations on food labeling to address the quality of possible health foods. In the United Kingdom by law any health claim on food labels must be true and not misleading. Food producers may optionally use the (discontinued in 2010) Joint Health Claims Initiative to determine whether their claims are likely to be legally sustainable. In early 2005 the European PASSCLAIM project (Process for the Assessment of Scientific Support for Claims on Foods), sponsored by the European Union and coordinated by ILSI-Europe (https://web.archive.org/web/20090822045739/http://europe.ilsi.org/), ended. The aim of this project was to develop criteria for the scientific substantiation of claims on foods. Several hundreds of scientists from academia, research institutes, government and industry have contributed to the project. All the resulting papers can be downloaded for free from http://www.ilsi.org/Europe/Pages/PASSCLAIM_Pubs.aspx. The final consensus paper, comprising the final set of criteria, has been published in June 2005 in the European Journal of Nutrition. == References == == External links == New York Times article, "Looser Rules Proposed for Health Claims on Food Labels" Statutory Instrument 1996 No. 1499 UK Food Labelling Regulations 1996 https://ec.europa.eu/food/safety/labelling_nutrition/claims/register/public/ http://ec.europa.eu/food/food/labellingnutrition/claims/index_en.htm.
|
{
"page_id": 265229,
"source": null,
"title": "Health claim"
}
|
Aminopurine may refer to: 2-Aminopurine 6-Aminopurine (adenine)
|
{
"page_id": 23464973,
"source": null,
"title": "Aminopurine"
}
|
Srinivasan Varadarajan (31 March 1928 – 11 May 2022) was an Indian chemist, civil servant, corporate executive and the former chairman of several public sector undertakings such as Indian Petrochemicals Corporation Limited (IPCL), Petrofils Cooperative Limited, Engineers India Limited (EIL), and Bridge and Roof Company (India). == Education == Varadarajan hails from Tamil Nadu. He obtained two master's degrees (MA and MSc) from Madras University and Andhra University and two doctoral degrees (Ph.D.) from University of Delhi and University of Cambridge. He worked as a faculty member at several educational institutions such as Delhi University (1949–53), Massachusetts Institute of Technology (1956–57) and Department of Radiotherapeutics and University of Cambridge (1957–59). == Awards == The Government of India awarded him the third highest civilian honour of the Padma Bhushan in 1985 for his contributions to society. He was an elected fellow of the Indian National Science Academy (1983), Indian Academy of Sciences (1972) and The World Academy of Sciences (1997). == See also == List of University of Delhi people List of Madras University alumni List of University of Cambridge people == References ==
|
{
"page_id": 50400269,
"source": null,
"title": "Srinivasan Varadarajan"
}
|
The exodermis is a physiological barrier that has a role in root function and protection. The exodermis is a membrane of variable permeability responsible for the radial flow of water, ions, and nutrients. It is the outer layer of a plant's cortex. The exodermis serves a double function as it can protect the root from invasion by foreign pathogens and ensures that the plant does not lose too much water through diffusion through the root system and can properly replenish its stores at an appropriate rate. == Overview and function == The exodermis is a specialized type of hypodermis that develops Casparian strips in its cell wall, as well as further wall modifications. The Casparian strip is a band of hydrophobic, corky-like tissue that is found on the outside of the endodermis and the exodermis. Its main function is to prevent solution backflow into the cortex and to maintain root pressure. It is also involved in ensuring that soil is not pulled directly into the root system during nutrient uptake. Exodermis cells are found on the outermost layer of almost all seeded vascular plants and the outer layer of the cortex of many angiosperms including onion, hoya canoas, maize, and sunflower plants but not on seedless vascular plants. As with most plant species, there is a large variety in the thickness and permeability of the exodermis, to better allow the plants to be suited to their environments. Although the term barrier is used to describe the exodermis, the exodermis behaves more like a membrane through which different materials can pass through. It can modify its permeability so that in response to different external stimuli, it can change to better suit the root's requirements. This serves as a function for survival, as root systems are exposed to changing environmental conditions and
|
{
"page_id": 33623056,
"source": null,
"title": "Exodermis"
}
|
thus the plant needs to modify itself as necessary, either in thickening or thinning of Casparian strips or by changing the permeability of the band to certain ions. It also has been found to modify the permeability during the root growth and maturation. == Growth and Structure == Roots are specialized for the uptake of water, nutrients (including ions for proper function). Similar to the endodermis, the exodermis contains very compact cells and is surrounded by a Casparian band, two features which are used to restrict the flow of water to a symplastic fashion (through the cytoplasm) rather than apoplastic fashion which (through the cell wall) flow through passages through the cells' membranes called plasmodesmata. Plasmodesma are small junctions that provide a direct connection between the cytoplasm of two neighboring plant cells. Similar to gap junctions found in animal cells, they allow an easy connection between the two cells permitting the transfer of ions, water and intercellular communication. This connection in the cytoplasm allows for neighboring plants to act as if they have one cytoplasm; a feature that enables the proper function of the exodermis. The apoplast is located outside the plasma membrane of the root cells and is the location at which inorganic materials can diffuse easily according to their concentration gradient. This apoplastic region is broken up by Casparian strips. The Casparian band is involved in the exodermal cell's ability to regulate water flow movement through the membrane as it is the hydrophobic nature of this band that controls the water entry and exit from the root. Exodermal cells have also found to develop another layer of thickened, tertiary hydrophobic substance on the inside of their plasma membrane walls known as the suberin lamellae which form a protective layer on the inside of the cortex of the exodermis.
|
{
"page_id": 33623056,
"source": null,
"title": "Exodermis"
}
|
This layer is composed of a protein called suberin and is also hydrophobic meaning it also contributes to the ability of the exodermis to control water input. This added protection can result in the accelerated aging of the Casparian strips. Maturation of exodermal tissue occurs in three distinct stages: Stage 1 sees the development of the Casparian strips in the cell wall between the exodermis and the endodermis. Stage 2 includes the deposition of suberin and other hydrophobic polymers and cell membranes of individual exodermal cells. It also serves in forming the connection between the plasmodesma and the Casparian strip. Stage 3 includes the addition of cellulose and lignin with occasional deposition of suberin into the cell walls to strengthen them. Since suberin and the Casparian band are responsible for inhibiting nutrient and fluid uptake, it forces it across the exodermis and endodermis and into the root cortex. Exodermal cells can be found very close to the tip of the root, with some plants demonstrating exodermal cells as close to 30 mm from the tip. == Passage cells == A passage cell is short cells that form a thin layer along the long axis of the plant exodermis. These cells are a structural feature in the exodermis as they allow the uptake of ions Calcium and Magnesium, hence why they are commonly associated with exodermal cells. Their role does not correspond to any particular tissue meaning that they are found in all areas of the exodermis as they are needed. They are found frequently in herbaceous and woody species and are found to be more common in areas of lower rainfall, as the development of these cells decreases the amount of water lost through the radius of the plant. Although they do contain Casparian strips, the following development and maturation
|
{
"page_id": 33623056,
"source": null,
"title": "Exodermis"
}
|
of suberin lamellae and thicker cellulose walls do not progress. Passage cells are partially responsible for growth and development. As the plant ages and growth slows, the number of passage cells begin to decrease, resulting in a complete lack of passage cells altogether. In response to dehydration, some passage cells, particularly those located in aquatic environments, have developed pads that are composed of lignin and cellulose and are designed to close the cells to prevent further loss of ions and water to the environment via diffusion == Changes in response to external stimuli == Being involved in water uptake and regulation of solutes into and out of the membrane, the exodermal cells must adapt to their external environment to ensure that the plant can survive. Because there are so many individual species of plant, each with different environmental conditions and with different nutrient requirements, it is the variability of this membrane that provides the option to ensure appropriate nutrient levels are reached. Exodermal cells can modify their Casparian strips to fit changing stimuli. Exodermal barriers can change their permeability as necessary to ensure that adequate nutrients are reaching the plant. In microenvironments, where macronutrient levels are low (such as phosphorus, nitrogen and potassium) development in the exodermis, Casparian strips and the suberin lamellae. In areas with high-stress conditions such as heavy metal concentration, high salt concentration and other inorganic compounds, the exodermal cells are wider and shorter, ensuring that these toxic components cannot enter the root complex and cause damage to the system. Plants are found all over the world in a variety of different environmental conditions, each with their challenges in survival. There have been many investigations conducted into the specific nature of these cells for specific plants each with their specializations. In environments with low water supply, such
|
{
"page_id": 33623056,
"source": null,
"title": "Exodermis"
}
|
as in drought or desert conditions, the deposit of tertiary layers in the plant's exodermis can be found up far higher in the apex of the root system. In areas with a high water environment, such as wetlands and in areas that are predominantly anaerobic or hypoxic, plants' exodermis layers were found to develop patchy exodermal layers to aid the diffusion of oxygen into the root system more effectively. As the plant begins to age and mature the level of suberisation in the plant cells will increase, causing a decrease in the total amount of water that can enter the plant root complex. It will also cause an increase in the selectivity of the ions that are able to cross the barrier and be absorbed, slowly becoming more susceptible to large osmotic changes. The apoplastic nature of the exodermis means that selectivity should decrease with age not increase, however evidence and conflicting results between studies suggest otherwise and warrants further investigation. Lignin is a biopolymer that has been found to develop naturally in the Casparian strip to strengthen and thicken the cell wall of the plants. As the root begins to encounter higher soil density and conditions where the soil has higher water content, the root cortex and surrounding structures begin to thicken. In areas where there is less soil, (from high wind areas or poor soil quality) exodermal growth is severely hindered. == Xanthone Synthesis == Xanthones are a type of specialized bioactive constituents that are found to accumulate in the root system Hypericum perforatum. Xanthones are abundant in angiosperms with cDNA evidence suggesting that they are also present in Lusiaceae, Gentianaceae and Hypericaceae species. Xanthones are known to the Chemistry and Pharmacology industries for its potential use as an anti-depressant. It has also been found to actively treat
|
{
"page_id": 33623056,
"source": null,
"title": "Exodermis"
}
|
fungal infections on human skin. Xanthone derivatives are being used to generate new pharmacological products as they have a close link with Acetyl Coenzyme A (Acetyl CoA). The carbon backbone for xanthones is formed by Benzophenone synthase (BPS) and through a series of oxidation and condensation reactions, xanthones are produced. Xanthone messenger RNA and associated proteins are localized to the exodermis and Endodermis systems. Similar to other parts of the root system, the concentration of these molecules is dependent on the genetic variation and the environmental factors. The exodermis is involved in preventing the entry of pathogens into the cortex of the plant. In the root system with bacterial infections and invasion from rhizogenes, the concentration of BPS increases to fight off the pathogens. Particularly high concentrations of xanthones was also found in aerial root systems. Suberin Endodermis Cortex == References ==
|
{
"page_id": 33623056,
"source": null,
"title": "Exodermis"
}
|
The Physics of Superheroes is a popular science book by physics professor and long-time comic-book fan James Kakalios. First published in 2005, it explores the basic laws of physics. Kakalios does not set out to show where the world of superheroes contradicts modern science, granting the heroes one or more "miracle exceptions" from natural law. Instead, he focuses on examples of comic book scenes that can be used to understand the diverse laws of physics from an unusual angle, such as Gwen Stacy's death and Ant-Man's ability to punch his way out of a paper bag. Kakalios relates these elements of comic books to principles of physics, such as levers and torque, and in this way covers diverse topics, from mechanics to the quantum world. == See also == The Physics of Star Trek == References == == External links == The Physics of Superheroes webpage
|
{
"page_id": 10882063,
"source": null,
"title": "The Physics of Superheroes"
}
|
Olga Malinkiewicz (Polish pronunciation: [ˈɔlɡa malinˈkjɛvit͡ʂ]; born 26 November 1982) is a Polish physicist, inventor and entrepreneur. She is known for inventing a method of producing solar cells based on perovskites using inkjet printing. She is a co-founder and the Chief Technology Officer at Saule Technologies. She is the recipient of two European Inventor Awards (2024). == Biography == Malinkiewicz was born in 1982 in Wrocław, Poland. She started her studies at the Faculty of Physics at the University of Warsaw, where she obtained a Bachelor in 2005. She graduated from the Barcelona University of Technology in Barcelona in 2010. While still a student, in 2009 she started working at the ICFO Institute. In 2017, she obtained her PhD from ICMol – Institute for Molecular Science of the University of Valencia at the group of Dr. Henk Bolink, with a thesis on low cost, efficient hybrid solar cells. In 2014 she founded Saule Technologies, with private backing and turned down an offer of €1 million (US$1.3 million) for 10% of the start-up. The name of the company derives from Saulė, the goddess of the Sun in Baltic mythology. == Awards == During her studies, Olga developed a novel perovskite solar cell architecture allowing the fabrication of such devices at low temperatures, while retaining high efficiency. She has been granted with the Photonics21 Student Innovation award in a competition organised by the European Commission in 2014 for this achievement. She published an article on the subject in Nature Scientific Reports. In 2015 Olga was honored with an award in the Innovators Under 35 ranking, organized by MIT Technology Review for "developing a new technology that could spark a “social revolution” in renewable energies". In 2016, she was awarded the Knight's Cross of the Order of Polonia Restituta by the President of
|
{
"page_id": 58133523,
"source": null,
"title": "Olga Malinkiewicz"
}
|
Poland Andrzej Duda for her "outstanding contributions to the development of Polish science". For her future science and business activities, she was distinguished by the American Chemical Society as one of the top women entrepreneurs in new technologies. In 2021, she received the Lem's Planet Award in the technology category for her invention and commercialization of the printed perovskite-based solar cells. In 2024, as the first Polish woman scientist, she received two European Inventor Awards presented by the European Patent Office. The first award was granted in the Small and Medium-Sized Enterprises category while the second one was in the Popular Prize category. Malinkiewicz and her team were recognized for "advancing solar energy technology with their cost-effective and environmentally friendly perovskite solar cells", which was described as a visionary idea and a technology that can change the world. == Professional life == In 2015, she co-founded Saule Technologies (named after the Baltic sun goddess), along with two Polish businessmen. A partnership was signed in January 2018 with the Swedish construction company Skanska. The company is also looking for partnership with other companies operating in the Middle East. It is also working with Egis Group, a rigid plastics film producer, on the encapsulation of the cells. == See also == List of Poles Timeline of Polish science and technology == References ==
|
{
"page_id": 58133523,
"source": null,
"title": "Olga Malinkiewicz"
}
|
Adobe Firefly is a web app and family of generative artificial intelligence models for creative production. Its capabilities include text-to-image and text-to-video. It is part of Adobe Creative Cloud, and also powers features in other Creative Cloud apps, including Photoshop's Generative Fill tool. Its video models are currently being tested in an open beta phase, and its image generation tools are available via subscription. Adobe Firefly is developed using Adobe's Sensei platform. Firefly is trained with images from Creative Commons, Wikimedia and Flickr Commons as well as 300 million images and videos in Adobe Stock and the public domain. This dependency only on training data for which Adobe owns the license or which is public domain has led them to describe the models' output as "commercially safe". Firefly for Enterprise was released on June 22, 2023. == History == Adobe Firefly was first announced in September 2022 at Adobe's MAX conference. It was initially released as a public beta in March 2023, and is currently available to all Adobe Creative Cloud subscribers. Adobe Firefly is built on top of Adobe Sensei, the company's AI platform. Sensei has been used to power a variety of features in Adobe's creative software, such as object selection in Photoshop and image auto-enhancement in Lightroom. Firefly expanded its capabilities to Illustrator, Premiere Pro, and Express, particularly for generating photos, videos and audio to enhance or alter specific parts of the media. NVIDIA Picasso runs some Adobe Firefly models. Google planned to use Firefly in Bard (now Gemini) as its AI image generator, but ended up using their own Imagen model. Mattel, IBM, and Dentsu have also partnered with Adobe. The demo showed a capability for generating variations of photos. In April 2025, Adobe released Adobe Firefly Image 4 and Firefly Image 4 Ultra Model in
|
{
"page_id": 74124313,
"source": null,
"title": "Adobe Firefly"
}
|
Adobe Firefly Web Application. == References ==
|
{
"page_id": 74124313,
"source": null,
"title": "Adobe Firefly"
}
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Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually autonomous and logically consistent formulation of quantum mechanics. Its account of quantum jumps supplanted the Bohr model's electron orbits. It did so by interpreting the physical properties of particles as matrices that evolve in time. It is equivalent to the Schrödinger wave formulation of quantum mechanics, as manifest in Dirac's bra–ket notation. In some contrast to the wave formulation, it produces spectra of (mostly energy) operators by purely algebraic, ladder operator methods. Relying on these methods, Wolfgang Pauli derived the hydrogen atom spectrum in 1926, before the development of wave mechanics. == Development of matrix mechanics == In 1925, Werner Heisenberg, Max Born, and Pascual Jordan formulated the matrix mechanics representation of quantum mechanics. === Epiphany at Helgoland === In 1925 Werner Heisenberg was working in Göttingen on the problem of calculating the spectral lines of hydrogen. By May 1925 he began trying to describe atomic systems by observables only. On June 7, after weeks of failing to alleviate his hay fever with aspirin and cocaine, Heisenberg left for the pollen-free North Sea island of Helgoland. While there, in between climbing and memorizing poems from Goethe's West-östlicher Diwan, he continued to ponder the spectral issue and eventually realised that adopting non-commuting observables might solve the problem. He later wrote: It was about three o' clock at night when the final result of the calculation lay before me. At first I was deeply shaken. I was so excited that I could not think of sleep. So I left the house and awaited the sunrise on the top of a rock.: 275 === The three fundamental papers === After Heisenberg returned to Göttingen, he showed Wolfgang Pauli his
|
{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
}
|
calculations, commenting at one point: Everything is still vague and unclear to me, but it seems as if the electrons will no more move on orbits. On July 9 Heisenberg gave the same paper of his calculations to Max Born, saying that "he had written a crazy paper and did not dare to send it in for publication, and that Born should read it and advise him" prior to publication. Heisenberg then departed for a while, leaving Born to analyse the paper. In the paper, Heisenberg formulated quantum theory without sharp electron orbits. Hendrik Kramers had earlier calculated the relative intensities of spectral lines in the Sommerfeld model by interpreting the Fourier coefficients of the orbits as intensities. But his answer, like all other calculations in the old quantum theory, was only correct for large orbits. Heisenberg, after a collaboration with Kramers, began to understand that the transition probabilities were not quite classical quantities, because the only frequencies that appear in the Fourier series should be the ones that are observed in quantum jumps, not the fictional ones that come from Fourier-analyzing sharp classical orbits. He replaced the classical Fourier series with a matrix of coefficients, a fuzzed-out quantum analog of the Fourier series. Classically, the Fourier coefficients give the intensity of the emitted radiation, so in quantum mechanics the magnitude of the matrix elements of the position operator were the intensity of radiation in the bright-line spectrum. The quantities in Heisenberg's formulation were the classical position and momentum, but now they were no longer sharply defined. Each quantity was represented by a collection of Fourier coefficients with two indices, corresponding to the initial and final states. When Born read the paper, he recognized the formulation as one which could be transcribed and extended to the systematic language of matrices,
|
{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
}
|
which he had learned from his study under Jakob Rosanes at Breslau University. Born, with the help of his assistant and former student Pascual Jordan, began immediately to make the transcription and extension, and they submitted their results for publication; the paper was received for publication just 60 days after Heisenberg's paper. A follow-on paper was submitted for publication before the end of the year by all three authors. (A brief review of Born's role in the development of the matrix mechanics formulation of quantum mechanics along with a discussion of the key formula involving the non-commutativity of the probability amplitudes can be found in an article by Jeremy Bernstein. A detailed historical and technical account can be found in Mehra and Rechenberg's book The Historical Development of Quantum Theory. Volume 3. The Formulation of Matrix Mechanics and Its Modifications 1925–1926.) Up until this time, matrices were seldom used by physicists; they were considered to belong to the realm of pure mathematics. Gustav Mie had used them in a paper on electrodynamics in 1912 and Born had used them in his work on the lattices theory of crystals in 1921. While matrices were used in these cases, the algebra of matrices with their multiplication did not enter the picture as they did in the matrix formulation of quantum mechanics. Born, however, had learned matrix algebra from Rosanes, as already noted, but Born had also learned Hilbert's theory of integral equations and quadratic forms for an infinite number of variables as was apparent from a citation by Born of Hilbert's work Grundzüge einer allgemeinen Theorie der Linearen Integralgleichungen published in 1912. Jordan, too, was well equipped for the task. For a number of years, he had been an assistant to Richard Courant at Göttingen in the preparation of Courant and David
|
{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
}
|
Hilbert's book Methoden der mathematischen Physik I, which was published in 1924. This book, fortuitously, contained a great many of the mathematical tools necessary for the continued development of quantum mechanics. In 1926, John von Neumann became assistant to David Hilbert, and he would coin the term Hilbert space to describe the algebra and analysis which were used in the development of quantum mechanics. A linchpin contribution to this formulation was achieved in Dirac's reinterpretation/synthesis paper of 1925, which invented the language and framework usually employed today, in full display of the noncommutative structure of the entire construction. === Heisenberg's reasoning === Before matrix mechanics, the old quantum theory described the motion of a particle by a classical orbit, with well defined position and momentum X(t), P(t), with the restriction that the time integral over one period T of the momentum times the velocity must be a positive integer multiple of the Planck constant ∫ 0 T P d X d t d t = ∫ 0 T P d X = n h . {\displaystyle \int _{0}^{T}P\;{\frac {dX}{dt}}\;dt=\int _{0}^{T}P\;dX=nh.} While this restriction correctly selects orbits with more or less the right energy values En, the old quantum mechanical formalism did not describe time dependent processes, such as the emission or absorption of radiation. When a classical particle is weakly coupled to a radiation field, so that the radiative damping can be neglected, it will emit radiation in a pattern that repeats itself every orbital period. The frequencies that make up the outgoing wave are then integer multiples of the orbital frequency, and this is a reflection of the fact that X(t) is periodic, so that its Fourier representation has frequencies 2πn/T only. X ( t ) = ∑ n = − ∞ ∞ e 2 π i n t
|
{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
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/ T X n . {\displaystyle X(t)=\sum _{n=-\infty }^{\infty }e^{2\pi int/T}X_{n}.} The coefficients Xn are complex numbers. The ones with negative frequencies must be the complex conjugates of the ones with positive frequencies, so that X(t) will always be real, X n = X − n ∗ . {\displaystyle X_{n}=X_{-n}^{*}.} A quantum mechanical particle, on the other hand, cannot emit radiation continuously; it can only emit photons. Assuming that the quantum particle started in orbit number n, emitted a photon, then ended up in orbit number m, the energy of the photon is En − Em, which means that its frequency is En − Em/h. For large n and m, but with n − m relatively small, these are the classical frequencies by Bohr's correspondence principle E n − E m ≈ h ( n − m ) T . {\displaystyle E_{n}-E_{m}\approx {\frac {h(n-m)}{T}}.} In the formula above, T is the classical period of either orbit n or orbit m, since the difference between them is higher order in h. But for small n and m, or if n − m is large, the frequencies are not integer multiples of any single frequency. Since the frequencies that the particle emits are the same as the frequencies in the Fourier description of its motion, this suggests that something in the time-dependent description of the particle is oscillating with frequency En − Em/h. Heisenberg called this quantity Xnm, and demanded that it should reduce to the classical Fourier coefficients in the classical limit. For large values of n and m but with n − m relatively small, Xnm is the (n − m)th Fourier coefficient of the classical motion at orbit n. Since Xnm has opposite frequency to Xmn, the condition that X is real becomes X n m = X m
|
{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
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|
n ∗ . {\displaystyle X_{nm}=X_{mn}^{*}.} By definition, Xnm only has the frequency En − Em/h, so its time evolution is simple: X n m ( t ) = e 2 π i ( E n − E m ) t / h X n m ( 0 ) = e i ( E n − E m ) t / ℏ X n m ( 0 ) . {\displaystyle X_{nm}(t)=e^{2\pi i(E_{n}-E_{m})t/h}X_{nm}(0)=e^{i(E_{n}-E_{m})t/\hbar }X_{nm}(0).} This is the original form of Heisenberg's equation of motion. Given two arrays Xnm and Pnm describing two physical quantities, Heisenberg could form a new array of the same type by combining the terms XnkPkm, which also oscillate with the right frequency. Since the Fourier coefficients of the product of two quantities is the convolution of the Fourier coefficients of each one separately, the correspondence with Fourier series allowed Heisenberg to deduce the rule by which the arrays should be multiplied, ( X P ) m n = ∑ k = 0 ∞ X m k P k n . {\displaystyle (XP)_{mn}=\sum _{k=0}^{\infty }X_{mk}P_{kn}.} Born pointed out that this is the law of matrix multiplication, so that the position, the momentum, the energy, all the observable quantities in the theory, are interpreted as matrices. Under this multiplication rule, the product depends on the order: XP is different from PX. The X matrix is a complete description of the motion of a quantum mechanical particle. Because the frequencies in the quantum motion are not multiples of a common frequency, the matrix elements cannot be interpreted as the Fourier coefficients of a sharp classical trajectory. Nevertheless, as matrices, X(t) and P(t) satisfy the classical equations of motion; also see Ehrenfest's theorem, below. === Matrix basics === When it was introduced by Werner Heisenberg, Max Born and Pascual Jordan in 1925,
|
{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
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matrix mechanics was not immediately accepted and was a source of controversy, at first. Schrödinger's later introduction of wave mechanics was greatly favored. Part of the reason was that Heisenberg's formulation was in an odd mathematical language, for the time, while Schrödinger's formulation was based on familiar wave equations. But there was also a deeper sociological reason. Quantum mechanics had been developing by two paths, one led by Einstein, who emphasized the wave–particle duality he proposed for photons, and the other led by Bohr, that emphasized the discrete energy states and quantum jumps that Bohr discovered. De Broglie had reproduced the discrete energy states within Einstein's framework – the quantum condition is the standing wave condition, and this gave hope to those in the Einstein school that all the discrete aspects of quantum mechanics would be subsumed into a continuous wave mechanics. Matrix mechanics, on the other hand, came from the Bohr school, which was concerned with discrete energy states and quantum jumps. Bohr's followers did not appreciate physical models that pictured electrons as waves, or as anything at all. They preferred to focus on the quantities that were directly connected to experiments. In atomic physics, spectroscopy gave observational data on atomic transitions arising from the interactions of atoms with light quanta. The Bohr school required that only those quantities that were in principle measurable by spectroscopy should appear in the theory. These quantities include the energy levels and their intensities but they do not include the exact location of a particle in its Bohr orbit. It is very hard to imagine an experiment that could determine whether an electron in the ground state of a hydrogen atom is to the right or to the left of the nucleus. It was a deep conviction that such questions did not have
|
{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
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an answer. The matrix formulation was built on the premise that all physical observables are represented by matrices, whose elements are indexed by two different energy levels. The set of eigenvalues of the matrix were eventually understood to be the set of all possible values that the observable can have. Since Heisenberg's matrices are Hermitian, the eigenvalues are real. If an observable is measured and the result is a certain eigenvalue, the corresponding eigenvector is the state of the system immediately after the measurement. The act of measurement in matrix mechanics collapses the state of the system. If one measures two observables simultaneously, the state of the system collapses to a common eigenvector of the two observables. Since most matrices don't have any eigenvectors in common, most observables can never be measured precisely at the same time. This is the uncertainty principle. If two matrices share their eigenvectors, they can be simultaneously diagonalized. In the basis where they are both diagonal, it is clear that their product does not depend on their order because multiplication of diagonal matrices is just multiplication of numbers. The uncertainty principle, by contrast, is an expression of the fact that often two matrices A and B do not always commute, i.e., that AB − BA does not necessarily equal 0. The fundamental commutation relation of matrix mechanics, ∑ k ( X n k P k m − P n k X k m ) = i ℏ δ n m {\displaystyle \sum _{k}\left(X_{nk}P_{km}-P_{nk}X_{km}\right)=i\hbar \,\delta _{nm}} implies then that there are no states that simultaneously have a definite position and momentum. This principle of uncertainty holds for many other pairs of observables as well. For example, the energy does not commute with the position either, so it is impossible to precisely determine the position and energy
|
{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
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of an electron in an atom. === Nobel Prize === In 1928, Albert Einstein nominated Heisenberg, Born, and Jordan for the Nobel Prize in Physics. The announcement of the Nobel Prize in Physics for 1932 was delayed until November 1933. It was at that time that it was announced Heisenberg had won the Prize for 1932 "for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen" and Erwin Schrödinger and Paul Adrien Maurice Dirac shared the 1933 Prize "for the discovery of new productive forms of atomic theory". It might well be asked why Born was not awarded the Prize in 1932, along with Heisenberg, and Bernstein proffers speculations on this matter. One of them relates to Jordan joining the Nazi Party on May 1, 1933, and becoming a stormtrooper. Jordan's Party affiliations and Jordan's links to Born may well have affected Born's chance at the Prize at that time. Bernstein further notes that when Born finally won the Prize in 1954, Jordan was still alive, while the Prize was awarded for the statistical interpretation of quantum mechanics, attributable to Born alone. Heisenberg's reactions to Born for Heisenberg receiving the Prize for 1932 and for Born receiving the Prize in 1954 are also instructive in evaluating whether Born should have shared the Prize with Heisenberg. On November 25, 1933, Born received a letter from Heisenberg in which he said he had been delayed in writing due to a "bad conscience" that he alone had received the Prize "for work done in Göttingen in collaboration – you, Jordan and I". Heisenberg went on to say that Born and Jordan's contribution to quantum mechanics cannot be changed by "a wrong decision from the outside". In 1954, Heisenberg wrote an
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{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
}
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article honoring Max Planck for his insight in 1900. In the article, Heisenberg credited Born and Jordan for the final mathematical formulation of matrix mechanics and Heisenberg went on to stress how great their contributions were to quantum mechanics, which were not "adequately acknowledged in the public eye". == Mathematical development == Once Heisenberg introduced the matrices for X and P, he could find their matrix elements in special cases by guesswork, guided by the correspondence principle. Since the matrix elements are the quantum mechanical analogs of Fourier coefficients of the classical orbits, the simplest case is the harmonic oscillator, where the classical position and momentum, X(t) and P(t), are sinusoidal. === Harmonic oscillator === In units where the mass and frequency of the oscillator are equal to one (see nondimensionalization), the energy of the oscillator is H = 1 2 ( P 2 + X 2 ) . {\displaystyle H={\tfrac {1}{2}}\left(P^{2}+X^{2}\right).} The level sets of H are the clockwise orbits, and they are nested circles in phase space. The classical orbit with energy E is X ( t ) = 2 E cos ( t ) , P ( t ) = − 2 E sin ( t ) . {\displaystyle X(t)={\sqrt {2E}}\cos(t),\qquad P(t)=-{\sqrt {2E}}\sin(t)~.} The old quantum condition dictates that the integral of P dX over an orbit, which is the area of the circle in phase space, must be an integer multiple of the Planck constant. The area of the circle of radius √2E is 2πE. So E = n h 2 π = n ℏ , {\displaystyle E={\frac {nh}{2\pi }}=n\hbar \,,} or, in natural units where ħ = 1, the energy is an integer. The Fourier components of X(t) and P(t) are simple, and more so if they are combined into the quantities A
|
{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
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( t ) = X ( t ) + i P ( t ) = 2 E e − i t , A † ( t ) = X ( t ) − i P ( t ) = 2 E e i t . {\displaystyle A(t)=X(t)+iP(t)={\sqrt {2E}}\,e^{-it},\quad A^{\dagger }(t)=X(t)-iP(t)={\sqrt {2E}}\,e^{it}.} Both A and A† have only a single frequency, and X and P can be recovered from their sum and difference. Since A(t) has a classical Fourier series with only the lowest frequency, and the matrix element Amn is the (m − n)th Fourier coefficient of the classical orbit, the matrix for A is nonzero only on the line just above the diagonal, where it is equal to √2En. The matrix for A† is likewise only nonzero on the line below the diagonal, with the same elements. Thus, from A and A†, reconstruction yields 2 X ( 0 ) = ℏ [ 0 1 0 0 0 ⋯ 1 0 2 0 0 ⋯ 0 2 0 3 0 ⋯ 0 0 3 0 4 ⋯ ⋮ ⋮ ⋮ ⋮ ⋮ ⋱ ] , {\displaystyle {\sqrt {2}}X(0)={\sqrt {\hbar }}\;{\begin{bmatrix}0&{\sqrt {1}}&0&0&0&\cdots \\{\sqrt {1}}&0&{\sqrt {2}}&0&0&\cdots \\0&{\sqrt {2}}&0&{\sqrt {3}}&0&\cdots \\0&0&{\sqrt {3}}&0&{\sqrt {4}}&\cdots \\\vdots &\vdots &\vdots &\vdots &\vdots &\ddots \\\end{bmatrix}},} and 2 P ( 0 ) = ℏ [ 0 − i 1 0 0 0 ⋯ i 1 0 − i 2 0 0 ⋯ 0 i 2 0 − i 3 0 ⋯ 0 0 i 3 0 − i 4 ⋯ ⋮ ⋮ ⋮ ⋮ ⋮ ⋱ ] , {\displaystyle {\sqrt {2}}P(0)={\sqrt {\hbar }}\;{\begin{bmatrix}0&-i{\sqrt {1}}&0&0&0&\cdots \\i{\sqrt {1}}&0&-i{\sqrt {2}}&0&0&\cdots \\0&i{\sqrt {2}}&0&-i{\sqrt {3}}&0&\cdots \\0&0&i{\sqrt {3}}&0&-i{\sqrt {4}}&\cdots \\\vdots &\vdots &\vdots &\vdots &\vdots &\ddots \\\end{bmatrix}},} which, up to the choice of units, are the Heisenberg matrices for the harmonic oscillator. Both matrices are Hermitian,
|
{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
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since they are constructed from the Fourier coefficients of real quantities. Finding X(t) and P(t) is direct, since they are quantum Fourier coefficients so they evolve simply with time, X m n ( t ) = X m n ( 0 ) e i ( E m − E n ) t , P m n ( t ) = P m n ( 0 ) e i ( E m − E n ) t . {\displaystyle X_{mn}(t)=X_{mn}(0)e^{i(E_{m}-E_{n})t},\quad P_{mn}(t)=P_{mn}(0)e^{i(E_{m}-E_{n})t}~.} The matrix product of X and P is not hermitian, but has a real and imaginary part. The real part is one half the symmetric expression XP + PX, while the imaginary part is proportional to the commutator [ X , P ] = ( X P − P X ) . {\displaystyle [X,P]=(XP-PX).} It is simple to verify explicitly that XP − PX in the case of the harmonic oscillator, is iħ, multiplied by the identity. It is likewise simple to verify that the matrix H = 1 2 ( X 2 + P 2 ) {\displaystyle H={\tfrac {1}{2}}\left(X^{2}+P^{2}\right)} is a diagonal matrix, with eigenvalues Ei. === Conservation of energy === The harmonic oscillator is an important case. Finding the matrices is easier than determining the general conditions from these special forms. For this reason, Heisenberg investigated the anharmonic oscillator, with Hamiltonian H = 1 2 P 2 + 1 2 X 2 + ε X 3 . {\displaystyle H={\tfrac {1}{2}}P^{2}+{\tfrac {1}{2}}X^{2}+\varepsilon X^{3}~.} In this case, the X and P matrices are no longer simple off-diagonal matrices, since the corresponding classical orbits are slightly squashed and displaced, so that they have Fourier coefficients at every classical frequency. To determine the matrix elements, Heisenberg required that the classical equations of motion be obeyed as matrix equations, d X d t
|
{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
}
|
= P , d P d t = − X − 3 ε X 2 . {\displaystyle {\frac {dX}{dt}}=P~,\qquad {\frac {dP}{dt}}=-X-3\varepsilon X^{2}~.} He noticed that if this could be done, then H, considered as a matrix function of X and P, will have zero time derivative. d H d t = P ∗ d P d t + ( X + 3 ε X 2 ) ∗ d X d t = 0 , {\displaystyle {\frac {dH}{dt}}=P*{\frac {dP}{dt}}+\left(X+3\varepsilon X^{2}\right)*{\frac {dX}{dt}}=0~,} where A∗B is the anticommutator, A ∗ B = 1 2 ( A B + B A ) . {\displaystyle A*B={\tfrac {1}{2}}(AB+BA)~.} Given that all the off diagonal elements have a nonzero frequency; H being constant implies that H is diagonal. It was clear to Heisenberg that in this system, the energy could be exactly conserved in an arbitrary quantum system, a very encouraging sign. The process of emission and absorption of photons seemed to demand that the conservation of energy will hold at best on average. If a wave containing exactly one photon passes over some atoms, and one of them absorbs it, that atom needs to tell the others that they can't absorb the photon anymore. But if the atoms are far apart, any signal cannot reach the other atoms in time, and they might end up absorbing the same photon anyway and dissipating the energy to the environment. When the signal reached them, the other atoms would have to somehow recall that energy. This paradox led Bohr, Kramers and Slater to abandon exact conservation of energy. Heisenberg's formalism, when extended to include the electromagnetic field, was obviously going to sidestep this problem, a hint that the interpretation of the theory will involve wavefunction collapse. === Differentiation trick — canonical commutation relations === Demanding that the classical equations
|
{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
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of motion are preserved is not a strong enough condition to determine the matrix elements. The Planck constant does not appear in the classical equations, so that the matrices could be constructed for many different values of ħ and still satisfy the equations of motion, but with different energy levels. So, in order to implement his program, Heisenberg needed to use the old quantum condition to fix the energy levels, then fill in the matrices with Fourier coefficients of the classical equations, then alter the matrix coefficients and the energy levels slightly to make sure the classical equations are satisfied. This is clearly not satisfactory. The old quantum conditions refer to the area enclosed by the sharp classical orbits, which do not exist in the new formalism. The most important thing that Heisenberg discovered is how to translate the old quantum condition into a simple statement in matrix mechanics. To do this, he investigated the action integral as a matrix quantity, ∫ 0 T ∑ k P m k ( t ) d X k n d t d t ≈ ? J m n . {\displaystyle \int _{0}^{T}\sum _{k}P_{mk}(t){\frac {dX_{kn}}{dt}}dt\,\,{\stackrel {\scriptstyle ?}{\approx }}\,\,J_{mn}~.} There are several problems with this integral, all stemming from the incompatibility of the matrix formalism with the old picture of orbits. Which period T should be used? Semiclassically, it should be either m or n, but the difference is order ħ, and an answer to order ħ is sought. The quantum condition tells us that Jmn is 2πn on the diagonal, so the fact that J is classically constant tells us that the off-diagonal elements are zero. His crucial insight was to differentiate the quantum condition with respect to n. This idea only makes complete sense in the classical limit, where n is not an
|
{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
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integer but the continuous action variable J, but Heisenberg performed analogous manipulations with matrices, where the intermediate expressions are sometimes discrete differences and sometimes derivatives. In the following discussion, for the sake of clarity, the differentiation will be performed on the classical variables, and the transition to matrix mechanics will be done afterwards, guided by the correspondence principle. In the classical setting, the derivative is the derivative with respect to J of the integral which defines J, so it is tautologically equal to 1. d d J ∫ 0 T P d X = 1 = ∫ 0 T d t ( d P d J d X d t + P d d J d X d t ) = ∫ 0 T d t ( d P d J d X d t − d P d t d X d J ) {\displaystyle {\begin{aligned}{}{\frac {d}{dJ}}\int _{0}^{T}PdX&=1\\&=\int _{0}^{T}dt\left({\frac {dP}{dJ}}{\frac {dX}{dt}}+P{\frac {d}{dJ}}{\frac {dX}{dt}}\right)\\&=\int _{0}^{T}dt\left({\frac {dP}{dJ}}{\frac {dX}{dt}}-{\frac {dP}{dt}}{\frac {dX}{dJ}}\right)\end{aligned}}} where the derivatives dP/dJ and dX/dJ should be interpreted as differences with respect to J at corresponding times on nearby orbits, exactly what would be obtained if the Fourier coefficients of the orbital motion were differentiated. (These derivatives are symplectically orthogonal in phase space to the time derivatives dP/dt and dX/dt). The final expression is clarified by introducing the variable canonically conjugate to J, which is called the angle variable θ: The derivative with respect to time is a derivative with respect to θ, up to a factor of 2πT, 2 π T ∫ 0 T d t ( d P d J d X d θ − d P d θ d X d J ) = 1 . {\displaystyle {\frac {2\pi }{T}}\int _{0}^{T}dt\left({\frac {dP}{dJ}}{\frac {dX}{d\theta }}-{\frac {dP}{d\theta }}{\frac {dX}{dJ}}\right)=1\,.} So the quantum condition integral is the average value over
|
{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
}
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one cycle of the Poisson bracket of X and P. An analogous differentiation of the Fourier series of P dX demonstrates that the off-diagonal elements of the Poisson bracket are all zero. The Poisson bracket of two canonically conjugate variables, such as X and P, is the constant value 1, so this integral really is the average value of 1; so it is 1, as we knew all along, because it is dJ/dJ after all. But Heisenberg, Born and Jordan, unlike Dirac, were not familiar with the theory of Poisson brackets, so, for them, the differentiation effectively evaluated {X, P} in J,θ coordinates. The Poisson Bracket, unlike the action integral, does have a simple translation to matrix mechanics – it normally corresponds to the imaginary part of the product of two variables, the commutator. To see this, examine the (antisymmetrized) product of two matrices A and B in the correspondence limit, where the matrix elements are slowly varying functions of the index, keeping in mind that the answer is zero classically. In the correspondence limit, when indices m, n are large and nearby, while k, r are small, the rate of change of the matrix elements in the diagonal direction is the matrix element of the J derivative of the corresponding classical quantity. So it is possible to shift any matrix element diagonally through the correspondence, A ( m + r ) ( n + r ) − A m n ≈ r ( d A d J ) m n {\displaystyle A_{(m+r)(n+r)}-A_{mn}\approx r\;\left({\frac {dA}{dJ}}\right)_{mn}} where the right hand side is really only the (m − n)th Fourier component of dA/dJ at the orbit near m to this semiclassical order, not a full well-defined matrix. The semiclassical time derivative of a matrix element is obtained up to a factor of
|
{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
}
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i by multiplying by the distance from the diagonal, i k A m ( m + k ) ≈ ( T 2 π d A d t ) m ( m + k ) = ( d A d θ ) m ( m + k ) . {\displaystyle ikA_{m(m+k)}\approx \left({\frac {T}{2\pi }}{\frac {dA}{dt}}\right)_{m(m+k)}=\left({\frac {dA}{d\theta }}\right)_{m(m+k)}\,.} since the coefficient Am(m+k) is semiclassically the kth Fourier coefficient of the mth classical orbit. The imaginary part of the product of A and B can be evaluated by shifting the matrix elements around so as to reproduce the classical answer, which is zero. The leading nonzero residual is then given entirely by the shifting. Since all the matrix elements are at indices which have a small distance from the large index position (m,m), it helps to introduce two temporary notations: A[r,k] = A(m+r)(m+k) for the matrices, and dA/dJ[r] for the rth Fourier components of classical quantities, ( A B − B A ) [ 0 , k ] = ∑ r = − ∞ ∞ ( A [ 0 , r ] B [ r , k ] − A [ r , k ] B [ 0 , r ] ) = ∑ r ( A [ − r + k , k ] + ( r − k ) d A d J [ r ] ) ( B [ 0 , k − r ] + r d B d J [ r − k ] ) − ∑ r A [ r , k ] B [ 0 , r ] . {\displaystyle {\begin{aligned}(AB-BA)[0,k]&=\sum _{r=-\infty }^{\infty }{\bigl (}A[0,r]B[r,k]-A[r,k]B[0,r]{\bigr )}\\&=\sum _{r}\left(A[-r+k,k]+(r-k){\frac {dA}{dJ}}[r]\right)\left(B[0,k-r]+r{\frac {dB}{dJ}}[r-k]\right)-\sum _{r}A[r,k]B[0,r]\,.\end{aligned}}} Flipping the summation variable in the first sum from r to r′ = k − r, the matrix element becomes, ∑ r ′ ( A [
|
{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
}
|
r ′ , k ] − r ′ d A d J [ k − r ′ ] ) ( B [ 0 , r ′ ] + ( k − r ′ ) d B d J [ r ′ ] ) − ∑ r A [ r , k ] B [ 0 , r ] {\displaystyle \sum _{r'}\left(A[r',k]-r'{\frac {dA}{dJ}}[k-r']\right)\left(B[0,r']+(k-r'){\frac {dB}{dJ}}[r']\right)-\sum _{r}A[r,k]B[0,r]} and it is clear that the principal (classical) part cancels. The leading quantum part, neglecting the higher order product of derivatives in the residual expression, is then equal to ∑ r ′ ( d B d J [ r ′ ] ( k − r ′ ) A [ r ′ , k ] − d A d J [ k − r ′ ] r ′ B [ 0 , r ′ ] ) {\displaystyle \sum _{r'}\left({\frac {dB}{dJ}}[r'](k-r')A[r',k]-{\frac {dA}{dJ}}[k-r']r'B[0,r']\right)} so that, finally, ( A B − B A ) [ 0 , k ] = ∑ r ′ ( d B d J [ r ′ ] i d A d θ [ k − r ′ ] − d A d J [ k − r ′ ] i d B d θ [ r ′ ] ) {\displaystyle (AB-BA)[0,k]=\sum _{r'}\left({\frac {dB}{dJ}}[r']i{\frac {dA}{d\theta }}[k-r']-{\frac {dA}{dJ}}[k-r']i{\frac {dB}{d\theta }}[r']\right)} which can be identified with i times the kth classical Fourier component of the Poisson bracket. Heisenberg's original differentiation trick was eventually extended to a full semiclassical derivation of the quantum condition, in collaboration with Born and Jordan. Once they were able to establish that i ℏ { X , P } P B ⟼ [ X , P ] ≡ X P − P X = i ℏ , {\displaystyle i\hbar \{X,P\}_{\mathrm {PB} }\qquad \longmapsto \qquad [X,P]\equiv XP-PX=i\hbar \,,} this condition replaced and extended the old
|
{
"page_id": 396320,
"source": null,
"title": "Matrix mechanics"
}
|
quantization rule, allowing the matrix elements of P and X for an arbitrary system to be determined simply from the form of the Hamiltonian. The new quantization rule was assumed to be universally true, even though the derivation from the old quantum theory required semiclassical reasoning. (A full quantum treatment, however, for more elaborate arguments of the brackets, was appreciated in the 1940s to amount to extending Poisson brackets to Moyal brackets.) === State vectors and the Heisenberg equation === To make the transition to standard quantum mechanics, the most important further addition was the quantum state vector, now written |ψ⟩, which is the vector that the matrices act on. Without the state vector, it is not clear which particular motion the Heisenberg matrices are describing, since they include all the motions somewhere. The interpretation of the state vector, whose components are written ψm, was furnished by Born. This interpretation is statistical: the result of a measurement of the physical quantity corresponding to the matrix A is random, with an average value equal to ∑ m n ψ m ∗ A m n ψ n . {\displaystyle \sum _{mn}\psi _{m}^{*}A_{mn}\psi _{n}\,.} Alternatively, and equivalently, the state vector gives the probability amplitude ψn for the quantum system to be in the energy state n. Once the state vector was introduced, matrix mechanics could be rotated to any basis, where the H matrix need no longer be diagonal. The Heisenberg equation of motion in its original form states that Amn evolves in time like a Fourier component, A m n ( t ) = e i ( E m − E n ) t A m n ( 0 ) , {\displaystyle A_{mn}(t)=e^{i(E_{m}-E_{n})t}A_{mn}(0)~,} which can be recast in differential form d A m n d t = i ( E m −
|
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E n ) A m n , {\displaystyle {\frac {dA_{mn}}{dt}}=i(E_{m}-E_{n})A_{mn}~,} and it can be restated so that it is true in an arbitrary basis, by noting that the H matrix is diagonal with diagonal values Em, d A d t = i ( H A − A H ) . {\displaystyle {\frac {dA}{dt}}=i(HA-AH)~.} This is now a matrix equation, so it holds in any basis. This is the modern form of the Heisenberg equation of motion. Its formal solution is: A ( t ) = e i H t A ( 0 ) e − i H t . {\displaystyle A(t)=e^{iHt}A(0)e^{-iHt}~.} All these forms of the equation of motion above say the same thing, that A(t) is equivalent to A(0), through a basis rotation by the unitary matrix eiHt, a systematic picture elucidated by Dirac in his bra–ket notation. Conversely, by rotating the basis for the state vector at each time by eiHt, the time dependence in the matrices can be undone. The matrices are now time independent, but the state vector rotates, | ψ ( t ) ⟩ = e − i H t | ψ ( 0 ) ⟩ , d | ψ ⟩ d t = − i H | ψ ⟩ . {\displaystyle |\psi (t)\rangle =e^{-iHt}|\psi (0)\rangle ,\qquad {\frac {d|\psi \rangle }{dt}}=-iH|\psi \rangle \,.} This is the Schrödinger equation for the state vector, and this time-dependent change of basis amounts to transformation to the Schrödinger picture, with ⟨x|ψ⟩ = ψ(x). In quantum mechanics in the Heisenberg picture the state vector, |ψ⟩ does not change with time, while an observable A satisfies the Heisenberg equation of motion, The extra term is for operators such as A = ( X + t 2 P ) {\displaystyle A=\left(X+t^{2}P\right)} which have an explicit time dependence, in addition to the time
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dependence from the unitary evolution discussed. The Heisenberg picture does not distinguish time from space, so it is better suited to relativistic theories than the Schrödinger equation. Moreover, the similarity to classical physics is more manifest: the Hamiltonian equations of motion for classical mechanics are recovered by replacing the commutator above by the Poisson bracket (see also below). By the Stone–von Neumann theorem, the Heisenberg picture and the Schrödinger picture must be unitarily equivalent, as detailed below. == Further results == Matrix mechanics rapidly developed into modern quantum mechanics, and gave interesting physical results on the spectra of atoms. === Wave mechanics === Jordan noted that the commutation relations ensure that P acts as a differential operator. The operator identity [ a , b c ] = a b c − b c a = a b c − b a c + b a c − b c a = [ a , b ] c + b [ a , c ] {\displaystyle [a,bc]=abc-bca=abc-bac+bac-bca=[a,b]c+b[a,c]} allows the evaluation of the commutator of P with any power of X, and it implies that [ P , X n ] = − i n X n − 1 {\displaystyle \left[P,X^{n}\right]=-in~X^{n-1}} which, together with linearity, implies that a P-commutator effectively differentiates any analytic matrix function of X. Assuming limits are defined sensibly, this extends to arbitrary functions−but the extension need not be made explicit until a certain degree of mathematical rigor is required, Since X is a Hermitian matrix, it should be diagonalizable, and it will be clear from the eventual form of P that every real number can be an eigenvalue. This makes some of the mathematics subtle, since there is a separate eigenvector for every point in space. In the basis where X is diagonal, an arbitrary state can be
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"page_id": 396320,
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written as a superposition of states with eigenvalues x, | ψ ⟩ = ∫ x ψ ( x ) | x ⟩ , {\displaystyle |\psi \rangle =\int _{x}\psi (x)|x\rangle \,,} so that ψ(x) = ⟨x|ψ⟩, and the operator X multiplies each eigenvector by x, X | ψ ⟩ = ∫ x x ψ ( x ) | x ⟩ . {\displaystyle X|\psi \rangle =\int _{x}x\psi (x)|x\rangle ~.} Define a linear operator D which differentiates ψ, D ∫ x ψ ( x ) | x ⟩ = ∫ x ψ ′ ( x ) | x ⟩ , {\displaystyle D\int _{x}\psi (x)|x\rangle =\int _{x}\psi '(x)|x\rangle \,,} and note that ( D X − X D ) | ψ ⟩ = ∫ x [ ( x ψ ( x ) ) ′ − x ψ ′ ( x ) ] | x ⟩ = ∫ x ψ ( x ) | x ⟩ = | ψ ⟩ , {\displaystyle (DX-XD)|\psi \rangle =\int _{x}\left[\left(x\psi (x)\right)'-x\psi '(x)\right]|x\rangle =\int _{x}\psi (x)|x\rangle =|\psi \rangle \,,} so that the operator −iD obeys the same commutation relation as P. Thus, the difference between P and −iD must commute with X, [ P + i D , X ] = 0 , {\displaystyle [P+iD,X]=0\,,} so it may be simultaneously diagonalized with X: its value acting on any eigenstate of X is some function f of the eigenvalue x. This function must be real, because both P and −iD are Hermitian, ( P + i D ) | x ⟩ = f ( x ) | x ⟩ , {\displaystyle (P+iD)|x\rangle =f(x)|x\rangle \,,} rotating each state |x⟩ by a phase f(x), that is, redefining the phase of the wavefunction: ψ ( x ) → e − i f ( x ) ψ ( x ) . {\displaystyle \psi (x)\rightarrow e^{-if(x)}\psi
|
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(x)\,.} The operator iD is redefined by an amount: i D → i D + f ( X ) , {\displaystyle iD\rightarrow iD+f(X)\,,} which means that, in the rotated basis, P is equal to −iD. Hence, there is always a basis for the eigenvalues of X where the action of P on any wavefunction is known: P ∫ x ψ ( x ) | x ⟩ = ∫ x − i ψ ′ ( x ) | x ⟩ , {\displaystyle P\int _{x}\psi (x)|x\rangle =\int _{x}-i\psi '(x)|x\rangle \,,} and the Hamiltonian in this basis is a linear differential operator on the state-vector components, [ P 2 2 m + V ( X ) ] ∫ x ψ x | x ⟩ = ∫ x [ − 1 2 m ∂ 2 ∂ x 2 + V ( x ) ] ψ x | x ⟩ {\displaystyle \left[{\frac {P^{2}}{2m}}+V(X)\right]\int _{x}\psi _{x}|x\rangle =\int _{x}\left[-{\frac {1}{2m}}{\frac {\partial ^{2}}{\partial x^{2}}}+V(x)\right]\psi _{x}|x\rangle } Thus, the equation of motion for the state vector is but a celebrated differential equation, Since D is a differential operator, in order for it to be sensibly defined, there must be eigenvalues of X which neighbors every given value. This suggests that the only possibility is that the space of all eigenvalues of X is all real numbers, and that P is iD, up to a phase rotation. To make this rigorous requires a sensible discussion of the limiting space of functions, and in this space this is the Stone–von Neumann theorem: any operators X and P which obey the commutation relations can be made to act on a space of wavefunctions, with P a derivative operator. This implies that a Schrödinger picture is always available. Matrix mechanics easily extends to many degrees of freedom in a natural way. Each degree
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"page_id": 396320,
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of freedom has a separate X operator and a separate effective differential operator P, and the wavefunction is a function of all the possible eigenvalues of the independent commuting X variables. [ X i , X j ] = 0 [ P i , P j ] = 0 [ X i , P j ] = i δ i j . {\displaystyle {\begin{aligned}\left[X_{i},X_{j}\right]&=0\\[1ex]\left[P_{i},P_{j}\right]&=0\\[1ex]\left[X_{i},P_{j}\right]&=i\delta _{ij}\,.\end{aligned}}} In particular, this means that a system of N interacting particles in 3 dimensions is described by one vector whose components in a basis where all the X are diagonal is a mathematical function of 3N-dimensional space describing all their possible positions, effectively a much bigger collection of values than the mere collection of N three-dimensional wavefunctions in one physical space. Schrödinger came to the same conclusion independently, and eventually proved the equivalence of his own formalism to Heisenberg's. Since the wavefunction is a property of the whole system, not of any one part, the description in quantum mechanics is not entirely local. The description of several quantum particles has them correlated, or entangled. This entanglement leads to strange correlations between distant particles which violate the classical Bell's inequality. Even if the particles can only be in just two positions, the wavefunction for N particles requires 2N complex numbers, one for each total configuration of positions. This is exponentially many numbers in N, so simulating quantum mechanics on a computer requires exponential resources. Conversely, this suggests that it might be possible to find quantum systems of size N which physically compute the answers to problems which classically require 2N bits to solve. This is the aspiration behind quantum computing. === Ehrenfest theorem === For the time-independent operators X and P, ∂A/∂t = 0 so the Heisenberg equation above reduces to: i ℏ d A d
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"page_id": 396320,
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t = [ A , H ] = A H − H A , {\displaystyle i\hbar {\frac {dA}{dt}}=[A,H]=AH-HA,} where the square brackets [ , ] denote the commutator. For a Hamiltonian which is p2/2m + V(x), the X and P operators satisfy: d X d t = P m , d P d t = − ∇ V , {\displaystyle {\frac {dX}{dt}}={\frac {P}{m}},\quad {\frac {dP}{dt}}=-\nabla V,} where the first is classically the velocity, and second is classically the force, or potential gradient. These reproduce Hamilton's form of Newton's laws of motion. In the Heisenberg picture, the X and P operators satisfy the classical equations of motion. You can take the expectation value of both sides of the equation to see that, in any state |ψ⟩: d d t ⟨ X ⟩ = d d t ⟨ ψ | X | ψ ⟩ = 1 m ⟨ ψ | P | ψ ⟩ = 1 m ⟨ P ⟩ d d t ⟨ P ⟩ = d d t ⟨ ψ | P | ψ ⟩ = ⟨ ψ | ( − ∇ V ) | ψ ⟩ = − ⟨ ∇ V ⟩ . {\displaystyle {\begin{aligned}{\frac {d}{dt}}\langle X\rangle &={\frac {d}{dt}}\langle \psi |X|\psi \rangle ={\frac {1}{m}}\langle \psi |P|\psi \rangle ={\frac {1}{m}}\langle P\rangle \\[1.5ex]{\frac {d}{dt}}\langle P\rangle &={\frac {d}{dt}}\langle \psi |P|\psi \rangle =\langle \psi |(-\nabla V)|\psi \rangle =-\langle \nabla V\rangle \,.\end{aligned}}} So Newton's laws are exactly obeyed by the expected values of the operators in any given state. This is Ehrenfest's theorem, which is an obvious corollary of the Heisenberg equations of motion, but is less trivial in the Schrödinger picture, where Ehrenfest discovered it. === Transformation theory === In classical mechanics, a canonical transformation of phase space coordinates is one which preserves the structure of the Poisson brackets. The new variables x′,
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"page_id": 396320,
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p′ have the same Poisson brackets with each other as the original variables x, p. Time evolution is a canonical transformation, since the phase space at any time is just as good a choice of variables as the phase space at any other time. The Hamiltonian flow is the canonical transformation: x → x + d x = x + ∂ H ∂ p d t p → p + d p = p − ∂ H ∂ x d t . {\displaystyle {\begin{aligned}x&\rightarrow x+dx=x+{\frac {\partial H}{\partial p}}dt\\[1ex]p&\rightarrow p+dp=p-{\frac {\partial H}{\partial x}}dt~.\end{aligned}}} Since the Hamiltonian can be an arbitrary function of x and p, there are such infinitesimal canonical transformations corresponding to every classical quantity G, where G serves as the Hamiltonian to generate a flow of points in phase space for an increment of time s, d x = ∂ G ∂ p d s = { G , X } d s d p = − ∂ G ∂ x d s = { G , P } d s . {\displaystyle {\begin{aligned}dx&={\frac {\partial G}{\partial p}}ds=\left\{G,X\right\}ds\\[1ex]dp&=-{\frac {\partial G}{\partial x}}ds=\left\{G,P\right\}ds\,.\end{aligned}}} For a general function A(x,p) on phase space, its infinitesimal change at every step ds under this map is d A = ∂ A ∂ x d x + ∂ A ∂ p d p = { A , G } d s . {\displaystyle dA={\frac {\partial A}{\partial x}}dx+{\frac {\partial A}{\partial p}}dp=\{A,G\}ds\,.} The quantity G is called the infinitesimal generator of the canonical transformation. In quantum mechanics, the quantum analog G is now a Hermitian matrix, and the equations of motion are given by commutators, d A = i [ G , A ] d s . {\displaystyle dA=i[G,A]ds\,.} The infinitesimal canonical motions can be formally integrated, just as the Heisenberg equation of motion were integrated, A ′ =
|
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"page_id": 396320,
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U † A U {\displaystyle A'=U^{\dagger }AU} where U = eiGs and s is an arbitrary parameter. The definition of a quantum canonical transformation is thus an arbitrary unitary change of basis on the space of all state vectors. U is an arbitrary unitary matrix, a complex rotation in phase space, U † = U − 1 . {\displaystyle U^{\dagger }=U^{-1}\,.} These transformations leave the sum of the absolute square of the wavefunction components invariant, while they take states which are multiples of each other (including states which are imaginary multiples of each other) to states which are the same multiple of each other. The interpretation of the matrices is that they act as generators of motions on the space of states. For example, the motion generated by P can be found by solving the Heisenberg equation of motion using P as a Hamiltonian, d X = i [ X , P ] d s = d s d P = i [ P , P ] d s = 0 . {\displaystyle {\begin{aligned}dX&=i[X,P]ds=ds\\[1ex]dP&=i[P,P]ds=0\,.\end{aligned}}} These are translations of the matrix X by a multiple of the identity matrix, X → X + s I . {\displaystyle X\rightarrow X+sI~.} This is the interpretation of the derivative operator D: eiPs = eD, the exponential of a derivative operator is a translation (so Lagrange's shift operator). The X operator likewise generates translations in P. The Hamiltonian generates translations in time, the angular momentum generates rotations in physical space, and the operator X2 + P2 generates rotations in phase space. When a transformation, like a rotation in physical space, commutes with the Hamiltonian, the transformation is called a symmetry (behind a degeneracy) of the Hamiltonian – the Hamiltonian expressed in terms of rotated coordinates is the same as the original Hamiltonian. This means that
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"page_id": 396320,
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the change in the Hamiltonian under the infinitesimal symmetry generator L vanishes, d H d s = i [ L , H ] = 0 . {\displaystyle {\frac {dH}{ds}}=i[L,H]=0\,.} It then follows that the change in the generator under time translation also vanishes, d L d t = i [ H , L ] = 0 {\displaystyle {\frac {dL}{dt}}=i[H,L]=0} so that the matrix L is constant in time: it is conserved. The one-to-one association of infinitesimal symmetry generators and conservation laws was discovered by Emmy Noether for classical mechanics, where the commutators are Poisson brackets, but the quantum-mechanical reasoning is identical. In quantum mechanics, any unitary symmetry transformation yields a conservation law, since if the matrix U has the property that U − 1 H U = H {\displaystyle U^{-1}HU=H} so it follows that U H = H U {\displaystyle UH=HU} and that the time derivative of U is zero – it is conserved. The eigenvalues of unitary matrices are pure phases, so that the value of a unitary conserved quantity is a complex number of unit magnitude, not a real number. Another way of saying this is that a unitary matrix is the exponential of i times a Hermitian matrix, so that the additive conserved real quantity, the phase, is only well-defined up to an integer multiple of 2π. Only when the unitary symmetry matrix is part of a family that comes arbitrarily close to the identity are the conserved real quantities single-valued, and then the demand that they are conserved become a much more exacting constraint. Symmetries which can be continuously connected to the identity are called continuous, and translations, rotations, and boosts are examples. Symmetries which cannot be continuously connected to the identity are discrete, and the operation of space-inversion, or parity, and charge conjugation are examples.
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"page_id": 396320,
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The interpretation of the matrices as generators of canonical transformations is due to Paul Dirac. The correspondence between symmetries and matrices was shown by Eugene Wigner to be complete, if antiunitary matrices which describe symmetries which include time-reversal are included. === Selection rules === It was physically clear to Heisenberg that the absolute squares of the matrix elements of X, which are the Fourier coefficients of the oscillation, would yield the rate of emission of electromagnetic radiation. In the classical limit of large orbits, if a charge with position X(t) and charge q is oscillating next to an equal and opposite charge at position 0, the instantaneous dipole moment is q X(t), and the time variation of this moment translates directly into the space-time variation of the vector potential, which yields nested outgoing spherical waves. For atoms, the wavelength of the emitted light is about 10,000 times the atomic radius, and the dipole moment is the only contribution to the radiative field, while all other details of the atomic charge distribution can be ignored. Ignoring back-reaction, the power radiated in each outgoing mode is a sum of separate contributions from the square of each independent time Fourier mode of d, P ( ω ) = 2 3 ω 4 | d i | 2 . {\displaystyle P(\omega )={\tfrac {2}{3}}{\omega ^{4}}|d_{i}|^{2}~.} Now, in Heisenberg's representation, the Fourier coefficients of the dipole moment are the matrix elements of X. This correspondence allowed Heisenberg to provide the rule for the transition intensities, the fraction of the time that, starting from an initial state i, a photon is emitted and the atom jumps to a final state j, P i j = 2 3 ( E i − E j ) 4 | X i j | 2 . {\displaystyle P_{ij}={\tfrac {2}{3}}\left(E_{i}-E_{j}\right)^{4}\left|X_{ij}\right|^{2}\,.} This then
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"page_id": 396320,
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allowed the magnitude of the matrix elements to be interpreted statistically: they give the intensity of the spectral lines, the probability for quantum jumps from the emission of dipole radiation. Since the transition rates are given by the matrix elements of X, wherever Xij is zero, the corresponding transition should be absent. These were called the selection rules, which were a puzzle until the advent of matrix mechanics. An arbitrary state of the hydrogen atom, ignoring spin, is labelled by |n;l,m⟩, where the value of l is a measure of the total orbital angular momentum and m is its z-component, which defines the orbit orientation. The components of the angular momentum pseudovector are L i = ε i j k X j P k {\displaystyle L_{i}=\varepsilon _{ijk}X^{j}P^{k}} where the products in this expression are independent of order and real, because different components of X and P commute. The commutation relations of L with all three coordinate matrices X, Y, Z (or with any vector) are easy to find, [ L i , X j ] = i ε i j k X k , {\displaystyle \left[L_{i},X_{j}\right]=i\varepsilon _{ijk}X_{k}\,,} which confirms that the operator L generates rotations between the three components of the vector of coordinate matrices X. From this, the commutator of Lz and the coordinate matrices X, Y, Z can be read off, [ L z , X ] = i Y , [ L z , Y ] = − i X . {\displaystyle {\begin{aligned}\left[L_{z},X\right]&=iY\,,\\[1ex]\left[L_{z},Y\right]&=-iX\,.\end{aligned}}} This means that the quantities X + iY and X − iY have a simple commutation rule, [ L z , X + i Y ] = ( X + i Y ) , [ L z , X − i Y ] = − ( X − i Y ) . {\displaystyle {\begin{aligned}\left[L_{z},X+iY\right]&=(X+iY)\,,\\[1ex]\left[L_{z},X-iY\right]&=-(X-iY)\,.\end{aligned}}}
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"page_id": 396320,
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Just like the matrix elements of X + iP and X − iP for the harmonic oscillator Hamiltonian, this commutation law implies that these operators only have certain off diagonal matrix elements in states of definite m, L z ( ( X + i Y ) | m ⟩ ) = ( X + i Y ) L z | m ⟩ + ( X + i Y ) | m ⟩ = ( m + 1 ) ( X + i Y ) | m ⟩ {\displaystyle L_{z}{\bigl (}(X+iY)|m\rangle {\bigr )}=(X+iY)L_{z}|m\rangle +(X+iY)|m\rangle =(m+1)(X+iY)|m\rangle } meaning that the matrix (X + iY) takes an eigenvector of Lz with eigenvalue m to an eigenvector with eigenvalue m + 1. Similarly, (X − iY) decrease m by one unit, while Z does not change the value of m. So, in a basis of |l,m⟩ states where L2 and Lz have definite values, the matrix elements of any of the three components of the position are zero, except when m is the same or changes by one unit. This places a constraint on the change in total angular momentum. Any state can be rotated so that its angular momentum is in the z-direction as much as possible, where m = l. The matrix element of the position acting on |l,m⟩ can only produce values of m which are bigger by one unit, so that if the coordinates are rotated so that the final state is |l′,l′⟩, the value of l′ can be at most one bigger than the biggest value of l that occurs in the initial state. So l′ is at most l + 1. The matrix elements vanish for l′ > l + 1, and the reverse matrix element is determined by Hermiticity, so these vanish also when l′ < l
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"page_id": 396320,
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− 1: Dipole transitions are forbidden with a change in angular momentum of more than one unit. === Sum rules === The Heisenberg equation of motion determines the matrix elements of P in the Heisenberg basis from the matrix elements of X. P i j = m d d t X i j = i m ( E i − E j ) X i j , {\displaystyle P_{ij}=m{\frac {d}{dt}}X_{ij}=im\left(E_{i}-E_{j}\right)X_{ij}\,,} which turns the diagonal part of the commutation relation into a sum rule for the magnitude of the matrix elements: ∑ j P i j x j i − X i j p j i = i ∑ j 2 m ( E i − E j ) | X i j | 2 = i . {\displaystyle \sum _{j}P_{ij}x_{ji}-X_{ij}p_{ji}=i\sum _{j}2m\left(E_{i}-E_{j}\right)\left|X_{ij}\right|^{2}=i\,.} This yields a relation for the sum of the spectroscopic intensities to and from any given state, although to be absolutely correct, contributions from the radiative capture probability for unbound scattering states must be included in the sum: ∑ j 2 m ( E i − E j ) | X i j | 2 = 1 . {\displaystyle \sum _{j}2m\left(E_{i}-E_{j}\right)\left|X_{ij}\right|^{2}=1\,.} == See also == Interaction picture Bra–ket notation Introduction to quantum mechanics Heisenberg's entryway to matrix mechanics == References == == Further reading == Bernstein, Jeremy (2005). "Max Born and the quantum theory". American Journal of Physics. 73 (11). American Association of Physics Teachers (AAPT): 999–1008. Bibcode:2005AmJPh..73..999B. doi:10.1119/1.2060717. ISSN 0002-9505. Max Born The statistical interpretation of quantum mechanics. Nobel Lecture – December 11, 1954. Nancy Thorndike Greenspan, "The End of the Certain World: The Life and Science of Max Born" (Basic Books, 2005) ISBN 0-7382-0693-8. Also published in Germany: Max Born - Baumeister der Quantenwelt. Eine Biographie (Spektrum Akademischer Verlag, 2005), ISBN 3-8274-1640-X. Max Jammer The Conceptual Development
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{
"page_id": 396320,
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of Quantum Mechanics (McGraw-Hill, 1966) Jagdish Mehra and Helmut Rechenberg The Historical Development of Quantum Theory. Volume 3. The Formulation of Matrix Mechanics and Its Modifications 1925–1926. (Springer, 2001) ISBN 0-387-95177-6 B. L. van der Waerden, editor, Sources of Quantum Mechanics (Dover Publications, 1968) ISBN 0-486-61881-1 Aitchison, Ian J. R.; MacManus, David A.; Snyder, Thomas M. (2004). "Understanding Heisenberg's "magical" paper of July 1925: A new look at the calculational details". American Journal of Physics. 72 (11). American Association of Physics Teachers (AAPT): 1370–1379. arXiv:quant-ph/0404009. doi:10.1119/1.1775243. ISSN 0002-9505. S2CID 53118117. Thomas F. Jordan, Quantum Mechanics in Simple Matrix Form, (Dover publications, 2005) ISBN 978-0486445304 Merzbacher, E (1968). "Matrix methods in quantum mechanics". Am. J. Phys. 36 (9): 814–821. doi:10.1119/1.1975154. == External links == An Overview of Matrix Mechanics Matrix Methods in Quantum Mechanics Heisenberg Quantum Mechanics Archived 2010-02-16 at the Wayback Machine (The theory's origins and its historical developing 1925–27) Werner Heisenberg 1970 CBC radio Interview On Matrix Mechanics at MathPages
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"page_id": 396320,
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Quantum feedback or quantum feedback control is a class of methods to prepare and manipulate a quantum system in which that system's quantum state or trajectory is used to evolve the system towards some desired outcome. Just as in the classical case, feedback occurs when outputs from the system are used as inputs that control the dynamics (e.g. by controlling the Hamiltonian of the system). The feedback signal is typically filtered or processed in a classical way, which is often described as measurement based feedback. However, quantum feedback also allows the possibility of maintaining the quantum coherence of the output as the signal is processed (via unitary evolution), which has no classical analogue. == Measurement based feedback == In the closed loop quantum control, the feedback may be entirely dynamical (that is, the plant and controller form a single dynamical system and the controller with the two influencing each other through direct interaction). This is named Coherent Control. Alternatively, the feedback may be entirely information theoretic insofar as the controller gains information about the plant due to measurement of the plant. This is measurement-based control. == Coherent feedback == Unlike measurement based feedback, where the quantum state is measured (causing it to collapse) and control is conditioned on the classical measurement outcome, coherent feedback maintains the full quantum state and implements deterministic, non-destructive operations on the state, using fully quantum devices. One example is a mirror, reflecting photons (the quantum states) back to the emitter. == Notes == == References ==
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"page_id": 46926884,
"source": null,
"title": "Quantum feedback"
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Marti Alice Hearst is a professor in the School of Information at the University of California, Berkeley. She did early work in corpus-based computational linguistics, including some of the first work in automating sentiment analysis, and word sense disambiguation. She invented an algorithm that became known as "Hearst patterns" which applies lexico-syntactic patterns to recognize hyponymy (ISA) relations with high accuracy in large text collections, including an early application of it to WordNet; this algorithm is widely used in commercial text mining applications including ontology learning. Hearst also developed early work in automatic segmentation of text into topical discourse boundaries, inventing a now well-known approach called TextTiling. Hearst's research is on user interfaces for search engine technology and big data analytics. She did early work in user interfaces and information visualization for search user interfaces, inventing the TileBars query term visualization. Her Flamenco research project investigated and developed the now widely used faceted navigation approach for searching and browsing web sites and information collections. She wrote the first academic book on the topic of Search User Interfaces (Cambridge University Press, 2009). Hearst is an Edge Foundation contributing author and a member of the Usage panel of the American Heritage Dictionary of the English Language. Hearst received her B.A., M.S., and Ph.D. in computer science, all from Berkeley. In 2013 she became a fellow of the Association for Computing Machinery. She became a member of the CHI Academy in 2017, and has previously served as president of the Association for Computational Linguistics and on the advisory council of NSF's CISE Directorate. Additionally, she has been a member of the Web Board for CACM, the Usage Panel for the American Heritage Dictionary, the Edge.org panel of experts, the research staff at Xerox PARC, and the boards of ACM Transactions on the Web,
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{
"page_id": 38538277,
"source": null,
"title": "Marti Hearst"
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Computational Linguistics, ACM Transactions on Information Systems, and IEEE Intelligent Systems. Hearst has received an NSF CAREER award, an IBM Faculty Award, and an Okawa Foundation Fellowship. Her work on user interfaces has had a profound impact on the industry, earning Hearst two Google Research Awards and four Excellence in Teaching Awards.} She has also led projects worth over $3.5M in research grants. Hearst’s publications date back to 1990, when ‘A Hybrid Approach to Restricted Text Interpretation’ was published in Stanford University’s AAAI Spring Symposium on Text Based Intelligent Systems in March of that year. == References == == External links == Web page at UC Berkeley Website for Search User Interfaces book (text freely available and searchable) The Flamenco Faceted Navigation and Search Project
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{
"page_id": 38538277,
"source": null,
"title": "Marti Hearst"
}
|
A floc is a type of microbial aggregate that may be contrasted with biofilms and granules, or else considered a specialized type of biofilm. Flocs appear as cloudy suspensions of cells floating in water, rather than attached to and growing on a surface like most biofilms. The floc typically is held together by a matrix of extracellular polymeric substance (EPS), which may contain variable amounts of polysaccharide, protein, and other biopolymers. The formation and the properties of flocs may affect the performance of industrial water treatment bioreactors such as activated sludge systems where the flocs form a sludge blanket. Floc formation may benefit the constituent microorganisms in a number of ways, including protection from pH stress, resistance to predation, manipulation of microenvironments, and facilitation of mutualistic relationships in mixed microbial communities. In general, the mechanisms by which flocculating microbial aggregates hold together are poorly understood. However, work on the activated sludge bacterium Zoogloea resiniphila has shown that PEP-CTERM proteins must be expressed for flocs to form; in their absence, growth is planktonic, even though exopolysaccharide is produced. == See also == Yeast flocculation#Process == References ==
|
{
"page_id": 57805865,
"source": null,
"title": "Floc (biofilm)"
}
|
Affinity capture is a technique in molecular biology used to isolate desired compounds based on their chemical properties and a solid substrate. Commonly, plates out of solid materials such as glass are coated with various reagents to allow for covalent bonding of a capturing molecule such as an antibody. Afterwards, a solvent containing a desired compound for isolation is poured onto the plate, and the compound binds to the receptors on the plate (hence the capturing of the compound). Washing the plate and removing the desired compound completes the purification process. == Applications == Affinity capture has been used to isolate proteins by means of binding a peptide sequence to the solid substrate, thus allowing for protein capture. The process has also been examined for potential automation, but the unique circumstances for any given experiment may impede reproducibility. == See also == Chem-seq == References ==
|
{
"page_id": 55774252,
"source": null,
"title": "Affinity capture"
}
|
The roll center of a vehicle is the notional point at which the cornering forces in the suspension are reacted to the vehicle body. There are two definitions of roll center. The most commonly used is the geometric (or kinematic) roll center, whereas the Society of Automotive Engineers uses a force-based definition. == Definition == Geometric roll center is solely dictated by the suspension geometry, and can be found using principles of the instant center of rotation. Force based roll center, according to the US Society of Automotive Engineers, is "The point in the transverse vertical plane through any pair of wheel centers at which lateral forces may be applied to the sprung mass without producing suspension roll". The lateral location of the roll center is typically at the center-line of the vehicle when the suspension on the left and right sides of the car are mirror images of each other. The significance of the roll center can only be appreciated when the vehicle's center of mass is also considered. If there is a difference between the position of the center of mass and the roll center a moment arm is created. When the vehicle experiences angular velocity due to cornering, the length of the moment arm, combined with the stiffness of the springs and possibly anti-roll bars (also called 'anti-sway bar'), defines how much the vehicle will roll. This has other effects too, such as dynamic load transfer. == Application == When the vehicle rolls the roll centers migrate. The roll center height has been shown to affect behavior at the initiation of turns such as nimbleness and initial roll control. == Testing methods == Current methods of analyzing individual wheel instant centers have yielded more intuitive results of the effects of non-rolling weight transfer effects. This type of
|
{
"page_id": 1510452,
"source": null,
"title": "Roll center"
}
|
analysis is better known as the lateral-anti method. This is where one takes the individual instant center locations of each corner of the car and then calculates the resultant vertical reaction vector due to lateral force. This value then is taken into account in the calculation of a jacking force and lateral weight transfer. This method works particularly well in circumstances where there are asymmetries in left to right suspension geometry. The practical equivalent of the above is to push laterally at the tire contact patch and measure the ratio of the change in vertical load to the horizontal force. == See also == Weight distribution Vehicle metrics == References ==
|
{
"page_id": 1510452,
"source": null,
"title": "Roll center"
}
|
Diarylethene is the general name of a class of chemical compounds that have aromatic functional groups bonded to each end of a carbon–carbon double bond. The simplest example is stilbene, which has two geometric isomers, E and Z. Under the influence of light, these compounds can generally perform two kinds of reversible isomerizations: E to Z isomerizations, most common for stilbenes (and azobenzenes). This process goes through an excited state energy minimum where the aromatic rings lie at 90° to each other. This conformation drops to the ground state and generally relaxes to trans and cis forms in a 1:1 ratio, thus the quantum yield for E-Z isomerization is very rarely greater than 0.5. 6π electrocyclizations of the Z form, leading to an additional bond between the two aryl functionalities and a disruption of the aromatic character of these groups. The quantum yield of this reaction is generally less than 0.1, and in most diarylethenes the close-ring form is thermally unstable, reverting to the cis-form in a matter of seconds or minutes under ambient conditions. Thermal isomerization is also possible. In E-Z isomerization, the thermal equilibrium lies well towards the trans-form because of its lower energy (~15 kJ mol−1 in stilbene). The activation energy for thermal E-Z isomerization is 150–190 kJ mol−1 for stilbene, meaning that temperatures above 200°C are required to isomerize stilbene at a reasonable rate, but most derivatives have lower energy barriers (e.g. 65 kJ mol−1 for 4-aminostilbene). The activation energy of the electrocyclization is 73 kJ mol−1 for stilbene. Both processes are often applied in molecular switches and for photochromism (reversible state changes from exposure to light). After the 6π electrocyclization of the Z form to the "close-ring" form, most unsubstituted diarylethenes are prone to oxidation, leading to a re-aromatization of the π-system. The most common
|
{
"page_id": 1117237,
"source": null,
"title": "Diarylethene"
}
|
example is (E)-stilbene, which upon irradiation undergoes an E to Z isomerization, which can be followed by a 6π electrocyclization. Reaction of the product of this reaction with molecular oxygen affords phenanthrene, and it has been suggested by some studies that dehydrogenation may even occur spontaneously. The dihydrophenanthrene intermediate has never been isolated, but it has been detected spectroscopically in pump-probe experiments by virtue of its long wavelength optical absorption band. Although both the E-Z isomerization and the 6π electrocyclization are reversible processes, this oxidation renders the entire sequence irreversible. == Stabilization of the closed-ring form to oxidation == One solution to the problem of oxidation is to replace the hydrogens ortho to the carbon-carbon double bond by groups that can not be removed during the oxidation. Following the Woodward–Hoffmann rules, the photochemical 6π cyclization takes place in a conrotatory fashion, leading to products with an anti configuration of the methyl substituents. As both methyl groups are attached to a stereogenic center, two enantiomers (R,R and S,S) are formed, normally as a racemic mixture. This approach also has the advantage that the thermal (disrotatory) ring closure can not take place because of steric hindrance between the substitution groups. == Dithienylethenes == Ortho-substitution of the aromatic units results in a stabilization against oxidation, but the closed-ring form still has a low thermodynamic stability in most cases (e.g. 2,3-dimesityl-2-butene has a half-life of 90 seconds at 20°C). This problem can be addressed by lowering the aromaticity of the system. The most commonly used example are the dithienylethenes, i.e. alkenes with a thiophene ring on either side. Dithienylethene derivatives have shown different types of photochemical side reactions, e.g., oxidation or elimination reactions of the ring-closed isomer and formation of an annulated ring isomer as a byproduct of the photochromic reaction. In order to
|
{
"page_id": 1117237,
"source": null,
"title": "Diarylethene"
}
|
overcome the first, the 2-position of the thiophenes is substituted with a methyl group, preventing oxidation of the ring closed form. Also often the two free α-positions on the double bond are connected in a 5 or 6-membered ring in order to lock the double bond into the cis-form. This makes the dithienylethene undergo only open-closed ring isomerization, unconfused by E-Z isomerization. More recently, based on recent findings showing that by-product formation most likely occurs exclusively from the lowest singlet excited state, a superior fatigue resistance of dithienylethenes upon visible-light excitation has been achieved by attaching small triplet-sensitizing moieties to the diarylethene core via a π-conjugated linkage. The dithienylethenes are also of interest for the fact that their isomerization requires very little change of shape. This means that their isomerization in a solid matrix can take place much more quickly than with most other photochromic molecules. In the case of some analogs, photochromic behavior can even be carried out in single crystals without disrupting the crystal structure. == Applications == Typically, the open-ring isomers are colorless compounds, whereas the closed-ring isomers have colors dependent on their chemical structure, due to the extended conjugation along the molecular backbone. Therefore, many diarylethenes have photochromic behavior both in solution and in solid state. Moreover, these two isomers differ from one another not only in their absorption spectra but also in various physical and chemical properties, such as their refractive index, dielectric constant, and oxidation-reduction potential. These properties can be readily controlled by reversible isomerization between the open- and closed-ring states using photoirradiation, and thus they have been suggested for use in optical data storage and 3D optical data storage in particular. The closed form has a conjugated path from one end of the molecule to the other, whereas the open form has not.
|
{
"page_id": 1117237,
"source": null,
"title": "Diarylethene"
}
|
This allows for the electronic communication between functional groups attached to the far ends of the diarylethene to be switched on and off using UV and visible light. == References ==
|
{
"page_id": 1117237,
"source": null,
"title": "Diarylethene"
}
|
Photoinduced phase transition is a technique used in solid-state physics. It is a process to the nonequilibrium phases generated from an equilibrium by shining on high energy photons, and the nonequilibrium phase is a macroscopic excited domain that has new structural and electronic orders quite different from the starting ground state (equilibrium phase). == References ==
|
{
"page_id": 18353210,
"source": null,
"title": "Photoinduced phase transitions"
}
|
The molecular formula C26H27N5O2 may refer to: UH15-38 Vilazodone
|
{
"page_id": 37293116,
"source": null,
"title": "C26H27N5O2"
}
|
The molecular formula C10H13N3O may refer to: AL-34662 ODMA (drug)
|
{
"page_id": 61148222,
"source": null,
"title": "C10H13N3O"
}
|
An arteriovenous malformation (AVM) is an abnormal connection between arteries and veins, bypassing the capillary system. Usually congenital, this vascular anomaly is widely known because of its occurrence in the central nervous system (usually as a cerebral AVM), but can appear anywhere in the body. The symptoms of AVMs can range from none at all to intense pain or bleeding, and they can lead to other serious medical problems. == Signs and symptoms == Symptoms of AVMs vary according to their location. Most neurological AVMs produce few to no symptoms. Often the malformation is discovered as part of an autopsy or during treatment of an unrelated disorder (an "incidental finding"); in rare cases, its expansion or a micro-bleed from an AVM in the brain can cause epilepsy, neurological deficit, or pain. The most general symptoms of a cerebral AVM include headaches and epileptic seizures, with more specific symptoms that normally depend on its location and the individual, including: Difficulties with movement coordination, including muscle weakness and even paralysis; Vertigo (dizziness); Difficulties of speech (dysarthria) and communication, as found with aphasia; Difficulties with everyday activities, as found with apraxia; Abnormal sensations (numbness, tingling, or spontaneous pain); Memory and thought-related problems, such as confusion, dementia, or hallucinations. Cerebral AVMs may present themselves in a number of different ways: Bleeding (45% of cases) "parkinsonism" 4 symptoms in Parkinson's disease. Acute onset of severe headache. May be described as the worst headache of the patient's life. Depending on the location of bleeding, may be associated with new fixed neurologic deficit. In unruptured brain AVMs, the risk of spontaneous bleeding may be as low as 1% per year. After a first rupture, the annual bleeding risk may increase to more than 5%. Seizure or brain seizure (46%). Depending on the place of the AVM, it
|
{
"page_id": 3135,
"source": null,
"title": "Arteriovenous malformation"
}
|
can contribute to loss of vision. Headache (34%) Progressive neurologic deficit (21%) May be caused by mass effect or venous dilatations. Presence and nature of the deficit depend on location of lesion and the draining veins. Pediatric patients Heart failure Macrocephaly Prominent scalp veins === Pulmonary arteriovenous malformations === Pulmonary arteriovenous malformations are abnormal communications between the veins and arteries of the pulmonary circulation, leading to a right-to-left blood shunt. They have no symptoms in up to 29% of all cases, however they can give rise to serious complications including hemorrhage, and infection. They are most commonly associated with hereditary hemorrhagic telangiectasia. == Genetics == AVMs are usually congenital and are part of the RASopathy family of developmental syndromes. The understanding of the anomaly's genetic transmission patterns are incomplete, but there are known genetic mutations (for instance in the epithelial line, tumor suppressor PTEN gene) which can lead to an increased occurrence throughout the body. The anomaly can occur due to autosomal dominant diseases, such as hereditary hemorrhagic telangiectasia. == Pathophysiology == In the circulatory system, arteries carry blood away from the heart to the lungs and the rest of the body, where the blood normally passes through capillaries—where oxygen is released and waste products like carbon dioxide (CO2) absorbed—before veins return blood to the heart. An AVM interferes with this process by forming a direct connection of the arteries and veins, bypassing the capillary bed. AVMs can cause intense pain and lead to serious medical problems. Although AVMs are often associated with the brain and spinal cord, they can develop in other parts of the body. As an AVM lacks the dampening effect of capillaries on the blood flow, the AVM can get progressively larger over time as the amount of blood flowing through it increases, forcing the heart
|
{
"page_id": 3135,
"source": null,
"title": "Arteriovenous malformation"
}
|
to work harder to keep up with the extra blood flow. It also causes the surrounding area to be deprived of the functions of the capillaries. The resulting tangle of blood vessels, often called a nidus (Latin for 'nest'), has no capillaries. It can be extremely fragile and prone to bleeding because of the abnormally direct connections between high-pressure arteries and low-pressure veins. One indicator is a pulsing 'whoosh' sound caused by rapid blood flow through arteries and veins, which has been given the term bruit (French for 'noise'). If the AVM is severe, this may produce an audible symptom which can interfere with hearing and sleep as well as cause psychological distress. == Diagnosis == AVMs are diagnosed primarily by the following imaging methods: Computed tomography (CT) scan is a noninvasive X-ray to view the anatomical structures within the brain to detect blood in or around the brain. A newer technology called CT angiography involves the injection of contrast into the blood stream to view the arteries of the brain. This type of test provides the best pictures of blood vessels through angiography and soft tissues through CT. Magnetic resonance imaging (MRI) scan is a noninvasive test, which uses a magnetic field and radio-frequency waves to give a detailed view of the soft tissues of the brain. Magnetic resonance angiography (MRA) – scans created using magnetic resonance imaging to specifically image the blood vessels and structures of the brain. A magnetic resonance angiogram can be an invasive procedure, involving the introduction of contrast dyes (e.g., gadolinium MR contrast agents) into the vasculature (circulatory system) of a patient using a catheter inserted into an artery and passed through the blood vessels to the brain. Once the catheter is in place, the contrast dye is injected into the bloodstream and the
|
{
"page_id": 3135,
"source": null,
"title": "Arteriovenous malformation"
}
|
MR images are taken. Additionally or alternatively, flow-dependent or other contrast-free magnetic resonance imaging techniques can be used to determine the location and other properties of the vasculature. AVMs can occur in various parts of the body: brain (cerebral AV malformation) spleen lung kidney spinal cord liver intercostal space iris spermatic cord extremities – arm, shoulder, etc. AVMs may occur in isolation or as a part of another disease (for example, Sturge-Weber syndrome or hereditary hemorrhagic telangiectasia). AVMs have been shown to be associated with aortic stenosis. Bleeding from an AVM can be relatively mild or devastating. It can cause severe and less often fatal strokes. == Treatment == Treatment for AVMs in the brain can be symptomatic, and patients should be followed by a neurologist for any seizures, headaches, or focal neurologic deficits. AVM-specific treatment may also involve endovascular embolization, neurosurgery or radiosurgery. Embolization, that is, cutting off the blood supply to the AVM with coils, particles, acrylates, or polymers introduced by a radiographically guided catheter, may be used in addition to neurosurgery or radiosurgery, but is rarely successful in isolation except in smaller AVMs. A gamma knife may also be used. If a cerebral AVM is detected before a stroke occurs, usually the arteries feeding blood into the nidus can be closed off to avert the danger. Interventional therapy may be relatively risky in the short term. Treatment of lung AVMs is typically performed with endovascular embolization alone, which is considered the standard of care. == Epidemiology == The estimated detection rate of AVM in the US general population is 1.4/100,000 per year. This is approximately one-fifth to one-seventh the incidence of intracranial aneurysms. An estimated 300,000 Americans have AVMs, of whom 12% (approximately 36,000) will exhibit symptoms of greatly varying severity. == History == Hubert von Luschka
|
{
"page_id": 3135,
"source": null,
"title": "Arteriovenous malformation"
}
|
(1820–1875) and Rudolf Virchow (1821–1902) first described arteriovenous malformations in the mid-1800s. Herbert Olivecrona (1891–1980) performed the first surgical excision of an intracranial AVM in 1932. == Society and culture == === Notable cases === Actor Ricardo Montalbán was born with spinal AVM. During the filming of the 1951 film Across the Wide Missouri, Montalbán was thrown from his horse, knocked unconscious, and trampled by another horse which aggravated his AVM and resulted in a painful back injury that never healed. The pain increased as he aged, and in 1993, Montalbán underwent 9+1⁄2 hours of spinal surgery which left him paralyzed below the waist and using a wheelchair. Composer and lyricist William Finn was diagnosed with AVM and underwent gamma knife surgery in September 1992, soon after he won the 1992 Tony Award for best musical, awarded to "Falsettos". Finn wrote the 1998 Off-Broadway musical A New Brain about the experience. Phoenix Suns NBA basketball point guard AJ Price nearly died from AVM in 2004 while a student at the University of Connecticut. On December 13, 2006, Senator Tim Johnson of South Dakota was diagnosed with AVM and treated at George Washington University Hospital. Actor/comedian T. J. Miller was diagnosed with AVM in 2010; Miller had a seizure and was unable to sleep for a period. He successfully underwent surgery that had a mortality rate of 10%. On August 3, 2011, Mike Patterson of the Philadelphia Eagles collapsed on the field and had a seizure during a practice, leading to him being diagnosed with AVM. Former Florida Gators and Oakland Raiders linebacker Neiron Ball was diagnosed with AVM in 2011 while playing for Florida, but recovered and was cleared to play. On September 16, 2018, Ball was placed in a medically induced coma due to complications of the disease, which
|
{
"page_id": 3135,
"source": null,
"title": "Arteriovenous malformation"
}
|
lasted until his death on September 10, 2019. Indonesian actress Egidia Savitri died from complications of AVM on November 29, 2013. Jazz guitarist Pat Martino experienced an AVM and subsequently developed amnesia and manic depression. He eventually re-learned to play the guitar by listening to his own recordings from before the aneurysm. YouTube vlogger Nikki Lilly (Nikki Christou), winner of the 2016 season of Junior Bake Off was born with AVM, which has resulted in some facial disfigurement. Country music singer Drake White was diagnosed with AVM in January 2019, and is undergoing treatment. Model Lucy Markovic died in April 2025 at age 27 shortly after undergoing surgery to treat AVM. === Cultural depictions === In the HBO series Six Feet Under (2001), main character Nate Fisher discovers he has an AVM after being in a car accident and getting a precautionary cat scan at the hospital during Season 1. His AVM becomes a key focus during Season 2 and again in Season 5. In season 1 episode 9 of House (2004), titled "DNR", a jazz musician has an AVM and is misdiagnosed with ALS. Two season three episodes also involve AVM - "Top Secret" (episode 16), in which a veteran who believes himself to be suffering from Gulf War syndrome is found to have spinal and pulmonary AVM from hereditary hemorrhagic telangiectasia; and "Resignation" (episode 22), where the patient developed AVM in her intestines after drinking pipe cleaner fluid in a suicide attempt. In the 2005 Lifetime film Dawn Anna, the titular character learns she has AVM, and undergoes a serious operation and subsequent rehabilitation, which she recovers from. == See also == Foix–Alajouanine syndrome Haemangioma Klippel–Trénaunay syndrome Parkes Weber syndrome == References ==
|
{
"page_id": 3135,
"source": null,
"title": "Arteriovenous malformation"
}
|
Potassium nitride is an unstable chemical compound. Several syntheses were erroneously claimed in the 19th century, and by 1894 it was assumed that it did not exist. However, a synthesis of this compound was claimed in 2004. It is observed to have the anti-TiI3 structure below 233 K (−40 °C; −40 °F), although a Li3P-type structure should be more stable. Above this temperature, it converts to an orthorhombic phase. This compound was produced by the reaction of potassium metal and liquid nitrogen at 77 K (−196.2 °C; −321.1 °F) under vacuum: 6K + N2 → 2K3N This compound decomposes back into potassium and nitrogen at room temperature. This compound is unstable due to steric hindrance. == References ==
|
{
"page_id": 66653247,
"source": null,
"title": "Potassium nitride"
}
|
A voie verte or greenway is an autonomous communication route reserved for non-motorized traffic, such as pedestrians and cyclists. Voies vertes are developed with a view to integrated development that enhances the environment, heritage, quality of life, and user-friendliness. In Europe, they have been organized since October 1997 within the framework of the European Green Network to coordinate and regulate uses often prohibited in certain countries or that compete with motorized practices. == Context == In this regard, towpaths, old rural paths, and disused railway tracks are privileged mediums for the development of voies vertes. If managed appropriately (through sustainable gardening and restoration ecology, and without the use of pesticides in the surroundings, which can then potentially play a role in the green infraestructure and blue network), voires vertes are one of the elements of sustainable development policies in the relevant areas. For English speakers, greenways refers to voies vertes, but also more generally to "a road that is good from an environmental point of view" (Turner, 1995, or - in England, according to a survey cited by Turner in 2006: "a linear space containing elements planned, designed, and managed for multiple purposes, including ecological, recreational, cultural, aesthetic, and others compatible with the concept of sustainable land use") or a wide range of landscape and urban planning strategies including, to varying degrees, an environmental concern associated with transportation infrastructure, the edges of which have often acquired special value and are sometimes associated with the concept of a biological corridor in Europe. == History and evolution == From 1975 to 1995, voies vertes proliferated significantly in the urban landscapes of so-called developed countries. For example, by 1995, more than 500 communities were building them in North America alone. They address new human needs while also extending some of the functions of
|
{
"page_id": 76155969,
"source": null,
"title": "Voie verte"
}
|
ancient rural roads. More than simple facilities or landscaping, they increasingly aim to provide a counterbalance to the loss of natural landscape in the context of increasing urbanization and agricultural industrialization. As times changed, the notion of chemins verts ou corridors verts evolved to meet new needs and challenges. Three distinct stages (or "generations") of voies vertes can be identified as forms of urban and peri-urban landscape: The first generation consisted of wooded paths, bordered by grassy and flowered embankments or ancestral walking paths, complementary to road networks; Recreational and discovery trails, or routes away from traffic zones, providing access to rivers, streams, ridges, and urban fabric, allotment gardens, etc., followed. Generally, automobiles were excluded (Reserved lanes); The latest generation is often more multifunctional, primarily reserved for soft travel and leisure, sometimes also for landscape enhancement, while also seeking to address certain vital needs of fauna, and flora (and sometimes fungi, with the conservation of deadwood). Ditches, swales, and flood-prone areas can also play a roleb in water and flood management (in urban or rural areas). Path edges are designed and managed to act as wildlife corridors with a potential buffer strip. Like grassy strips or other types of buffer zones, some voies vertes also contribute to improving water quality (with, for example, ditches and swales serving as natural wetland). They also provide resources for outdoor education, landscape discovery, and interpretation. Planners must therefore adopt multidisciplinary approaches, sometimes merging formerly opposing disciplines such as civil engineering, architecture, landscape ecology, sustainable gardening, or wetland ecology. In France, the term voies vertes tends to overlap with that of the voies vertes in the cycle route and voies vertes network. == Network status == === Belgium === In Belgium, a network of 2200 km of voies vertes was already defined in 2003, of
|
{
"page_id": 76155969,
"source": null,
"title": "Voie verte"
}
|
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