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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 Apri...	{ "page_id": 68750333, "title": "Vaccine passports during the COVID-19 pandemic" }
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 acqu...	{ "page_id": 68750333, "title": "Vaccine passports during the COVID-19 pandemic" }
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 endoly...	{ "page_id": 27397118, "title": "Endocochlear potential" }
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 d...	{ "page_id": 5835774, "title": "Memory box" }
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 ...	{ "page_id": 60034047, "title": "Specific quantity" }
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...	{ "page_id": 60034047, "title": "Specific quantity" }
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 conductivi...	{ "page_id": 60034047, "title": "Specific quantity" }
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 w...	{ "page_id": 60034047, "title": "Specific quantity" }
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 in...	{ "page_id": 62983169, "title": "Chrome Azurol S" }
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.	{ "page_id": 31591427, "title": "Fusarium graminearum genome database" }
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 highligh...	{ "page_id": 4066308, "title": "Multiple sequence alignment" }
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...	{ "page_id": 4066308, "title": "Multiple sequence alignment" }
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 a...	{ "page_id": 4066308, "title": "Multiple sequence alignment" }
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 u...	{ "page_id": 4066308, "title": "Multiple sequence alignment" }
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 h...	{ "page_id": 4066308, "title": "Multiple sequence alignment" }
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 inco...	{ "page_id": 4066308, "title": "Multiple sequence alignment" }
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-COFF...	{ "page_id": 4066308, "title": "Multiple sequence alignment" }
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...	{ "page_id": 4066308, "title": "Multiple sequence alignment" }
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 a...	{ "page_id": 4066308, "title": "Multiple sequence alignment" }
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 ...	{ "page_id": 4066308, "title": "Multiple sequence alignment" }
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 === ...	{ "page_id": 4066308, "title": "Multiple sequence alignment" }
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 use...	{ "page_id": 4066308, "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 an...	{ "page_id": 4066308, "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-speci...	{ "page_id": 4066308, "title": "Multiple sequence alignment" }
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. Simi...	{ "page_id": 4066308, "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 lect...	{ "page_id": 4066308, "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 parallelizatio...	{ "page_id": 31001609, "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 Chandraya...	{ "page_id": 68946956, "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 se...	{ "page_id": 265229, "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 ...	{ "page_id": 265229, "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 ...	{ "page_id": 265229, "title": "Health claim" }
Aminopurine may refer to: 2-Aminopurine 6-Aminopurine (adenine)	{ "page_id": 23464973, "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...	{ "page_id": 50400269, "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 ...	{ "page_id": 33623056, "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 o...	{ "page_id": 33623056, "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 t...	{ "page_id": 33623056, "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...	{ "page_id": 33623056, "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 ...	{ "page_id": 33623056, "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 ...	{ "page_id": 33623056, "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 exc...	{ "page_id": 10882063, "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. S...	{ "page_id": 58133523, "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 c...	{ "page_id": 58133523, "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 ar...	{ "page_id": 74124313, "title": "Adobe Firefly" }
Adobe Firefly Web Application. == References ==	{ "page_id": 74124313, "title": "Adobe Firefly" }
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 interpreti...	{ "page_id": 396320, "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 B...	{ "page_id": 396320, "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 He...	{ "page_id": 396320, "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 ...	{ "page_id": 396320, "title": "Matrix mechanics" }
/ 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 ...	{ "page_id": 396320, "title": "Matrix mechanics" }
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)....	{ "page_id": 396320, "title": "Matrix mechanics" }
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 w...	{ "page_id": 396320, "title": "Matrix mechanics" }
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 Heisen...	{ "page_id": 396320, "title": "Matrix mechanics" }
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...	{ "page_id": 396320, "title": "Matrix mechanics" }
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". == Mat...	{ "page_id": 396320, "title": "Matrix mechanics" }
( 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 ...	{ "page_id": 396320, "title": "Matrix mechanics" }
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^{...	{ "page_id": 396320, "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...	{ "page_id": 396320, "title": "Matrix mechanics" }
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...	{ "page_id": 396320, "title": "Matrix mechanics" }
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 vari...	{ "page_id": 396320, "title": "Matrix mechanics" }
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 av...	{ "page_id": 396320, "title": "Matrix mechanics" }
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 ...	{ "page_id": 396320, "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. Th...	{ "page_id": 396320, "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, h...	{ "page_id": 396320, "title": "Matrix mechanics" }
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 ...	{ "page_id": 396320, "title": "Matrix mechanics" }
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 rec...	{ "page_id": 396320, "title": "Matrix mechanics" }
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 ~.} Def...	{ "page_id": 396320, "title": "Matrix mechanics" }
(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 )...	{ "page_id": 396320, "title": "Matrix mechanics" }
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\\[1...	{ "page_id": 396320, "title": "Matrix mechanics" }
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}}=-\nabl...	{ "page_id": 396320, "title": "Matrix mechanics" }
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 ...	{ "page_id": 396320, "title": "Matrix mechanics" }
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...	{ "page_id": 396320, "title": "Matrix mechanics" }
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...	{ "page_id": 396320, "title": "Matrix mechanics" }
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 phy...	{ "page_id": 396320, "title": "Matrix mechanics" }
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 shoul...	{ "page_id": 396320, "title": "Matrix mechanics" }
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 ⟩ {\disp...	{ "page_id": 396320, "title": "Matrix mechanics" }
− 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...	{ "page_id": 396320, "title": "Matrix mechanics" }
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, 1...	{ "page_id": 396320, "title": "Matrix mechanics" }
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 ...	{ "page_id": 46926884, "title": "Quantum feedback" }
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...	{ "page_id": 38538277, "title": "Marti Hearst" }
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 E...	{ "page_id": 38538277, "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...	{ "page_id": 57805865, "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...	{ "page_id": 55774252, "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. == ...	{ "page_id": 1510452, "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 t...	{ "page_id": 1510452, "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 reversibl...	{ "page_id": 1117237, "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 dihyd...	{ "page_id": 1117237, "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...	{ "page_id": 1117237, "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, "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 star...	{ "page_id": 18353210, "title": "Photoinduced phase transitions" }
The molecular formula C26H27N5O2 may refer to: UH15-38 Vilazodone	{ "page_id": 37293116, "title": "C26H27N5O2" }
The molecular formula C10H13N3O may refer to: AL-34662 ODMA (drug)	{ "page_id": 61148222, "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 AV...	{ "page_id": 3135, "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 arteriovenou...	{ "page_id": 3135, "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 dir...	{ "page_id": 3135, "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 live...	{ "page_id": 3135, "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 filmi...	{ "page_id": 3135, "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 ...	{ "page_id": 3135, "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-ty...	{ "page_id": 66653247, "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 ...	{ "page_id": 76155969, "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...	{ "page_id": 76155969, "title": "Voie verte" }

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