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Modular arithmetic for a modulus n {\displaystyle n} defines any two elements a {\displaystyle a} and b {\displaystyle b} that differ by a multiple of n {\displaystyle n} to be equivalent, denoted by a ≡ b ( mod n ) {\displaystyle a\equiv b{\pmod {n}}} . Every integer is equivalent to one of the integers from 0 {\displ... | Wikipedia - Mathematical group | null | null | null |
If the hour hand is on 9 {\displaystyle 9} and is advanced 4 {\displaystyle 4} hours, it ends up on 1 {\displaystyle 1} , as shown in the illustration. This is expressed by saying that 9 + 4 {\displaystyle 9+4} is congruent to 1 {\displaystyle 1} "modulo 12 {\displaystyle 12} " or, in symbols, For any prime number p {\... | Wikipedia - Mathematical group | null | null | null |
The group operation, multiplication modulo p {\displaystyle p} , replaces the usual product by its representative, the remainder of division by p {\displaystyle p} . For example, for p = 5 {\displaystyle p=5} , the four group elements can be represented by 1 , 2 , 3 , 4 {\displaystyle 1,2,3,4} . In this group, 4 ⋅ 4 ≡ ... | Wikipedia - Mathematical group | null | null | null |
The primality of p {\displaystyle p} ensures that the usual product of two representatives is not divisible by p {\displaystyle p} , and therefore that the modular product is nonzero. The identity element is represented by 1 {\displaystyle 1} , and associativity follows from the corresponding property of the integers. ... | Wikipedia - Mathematical group | null | null | null |
The inverse b {\displaystyle b} can be found by using Bézout's identity and the fact that the greatest common divisor gcd ( a , p ) {\displaystyle \gcd(a,p)} equals 1 {\displaystyle 1} . In the case p = 5 {\displaystyle p=5} above, the inverse of the element represented by 4 {\displaystyle 4} is that represented by 4 {... | Wikipedia - Mathematical group | null | null | null |
Hence all group axioms are fulfilled. This example is similar to ( Q ∖ { 0 } , ⋅ ) {\displaystyle \left(\mathbb {Q} \smallsetminus \left\{0\right\},\cdot \right)} above: it consists of exactly those elements in the ring Z / p Z {\displaystyle \mathbb {Z} /p\mathbb {Z} } that have a multiplicative inverse. These groups,... | Wikipedia - Mathematical group | null | null | null |
Modular arithmetic modifies usual arithmetic by only using the numbers { 0 , 1 , 2 , … , n − 1 } {\displaystyle \{0,1,2,\dots ,n-1\}} , for a natural number n {\displaystyle n} called the modulus. Any other natural number can be mapped into this system by replacing it by its remainder after division by n {\displaystyle... | Wikipedia - Prime number | null | null | null |
However, in this system of numbers, division by all nonzero numbers is possible if and only if the modulus is prime. For instance, with the prime number 7 {\displaystyle 7} as modulus, division by 3 {\displaystyle 3} is possible: 2 / 3 ≡ 3 mod 7 {\displaystyle 2/3\equiv 3{\bmod {7}}} , because clearing denominators by ... | Wikipedia - Prime number | null | null | null |
There is no valid solution to 2 / 3 ≡ x mod 6 {\displaystyle 2/3\equiv x{\bmod {6}}}: clearing denominators by multiplying by 3 {\displaystyle 3} causes the left-hand side to become 2 {\displaystyle 2} while the right-hand side becomes either 0 {\displaystyle 0} or 3 {\displaystyle 3} . In the terminology of abstract a... | Wikipedia - Prime number | null | null | null |
Summing this over all choices of a {\displaystyle a} gives the equation ∑ a = 1 p − 1 a p − 1 ≡ ( p − 1 ) ⋅ 1 ≡ − 1 ( mod p ) , {\displaystyle \sum _{a=1}^{p-1}a^{p-1}\equiv (p-1)\cdot 1\equiv -1{\pmod {p}},} valid whenever p {\displaystyle p} is prime. Giuga's conjecture says that this equation is also a sufficient co... | Wikipedia - Prime number | null | null | null |
is congruent to − 1 {\displaystyle -1} mod p {\displaystyle p} . For a composite number n = r ⋅ s {\displaystyle \;n=r\cdot s\;} this cannot hold, since one of its factors divides both n and ( n − 1 ) ! | Wikipedia - Prime number | null | null | null |
{\displaystyle (n-1)!} , and so ( n − 1 ) ! ≡ − 1 ( mod n ) {\displaystyle (n-1)!\equiv -1{\pmod {n}}} is impossible. | Wikipedia - Prime number | null | null | null |
Modular data centers typically come in two types of form factors. The more common type, referred to as containerized data centers or portable modular data centers, fits data center equipment (servers, storage and networking equipment) into a standard shipping container, which is then transported to a desired location. ... | Wikipedia - Modular data center | null | null | null |
Cisco makes an example of this type of data center, called the Cisco Containerized Data Center.Another form of modular data center fits data center equipment into a facility composed of prefabricated components that can be quickly built on a site and added to as capacity is needed. For example, HP's version of this typ... | Wikipedia - Modular data center | null | null | null |
Modular programming is a technique to refine imperative language programs. Refined programs may reduce the software size, separate responsibilities, and thereby mitigate software aging. A program module is a sequence of statements that are bounded within a block and together identified by a name. Modules have a functio... | Wikipedia - Software code | null | null | null |
The context of a module are the elements being performed upon. The logic of a module is how it performs the function.The module's name should be derived first by its function, then by its context. Its logic should not be part of the name. | Wikipedia - Software code | null | null | null |
For example, function compute_square_root( x ) or function compute_square_root_integer( i: integer ) are appropriate module names. However, function compute_square_root_by_division( x ) is not. The degree of interaction within a module is its level of cohesion. | Wikipedia - Software code | null | null | null |
Cohesion is a judgment of the relationship between a module's name and its function. The degree of interaction between modules is the level of coupling. Coupling is a judgement of the relationship between a module's context and the elements being performed upon. | Wikipedia - Software code | null | null | null |
Modularity and flexibility are key elements in allowing for a data center to grow and change over time. Data center modules are pre-engineered, standardized building blocks that can be easily configured and moved as needed.A modular data center may consist of data center equipment contained within shipping containers o... | Wikipedia - Internet data center | null | null | null |
Modulating a carrier increases the frequency range, or bandwidth, it occupies. Transmission channels are generally limited in the bandwidth they can carry. The bandwidth depends on the symbol (modulation) rate (not directly on the bit rate). As the bit rate is the product of the symbol rate and the number of bits encod... | Wikipedia - Modulation rate | null | null | null |
However, for each additional bit encoded in a symbol, the constellation of symbols (the number of states of the carrier) doubles in size. This makes the states less distinct from one another which in turn makes it more difficult for the receiver to detect the symbol correctly in the presence of disturbances on the chan... | Wikipedia - Modulation rate | null | null | null |
For example, ITU-T V.29 specifies 4 bits per symbol, at a symbol rate of 2,400 baud, giving an effective bit rate of 9,600 bits per second. The history of spread spectrum goes in the opposite direction, leading to fewer and fewer data bits per symbol in order to spread the bandwidth. In the case of GPS, we have a data ... | Wikipedia - Modulation rate | null | null | null |
If each chip is considered a symbol, each symbol contains far less than one bit (50 bit/s / 1,023 ksymbols/s ≈ 0.000,05 bits/symbol). The complete collection of M possible symbols over a particular channel is called a M-ary modulation scheme. Most modulation schemes transmit some integer number of bits per symbol b, re... | Wikipedia - Modulation rate | null | null | null |
Modulation is the process of varying a carrier signal, typically a sine wave to use that signal to convey information. One of the three key characteristics of a signal are usually modulated: its phase, frequency or amplitude. In digital modulation, the changes in the signal are chosen from a fixed list (the modulation ... | Wikipedia - Node-to-node data transfer | null | null | null |
Modulation is generally performed to overcome signal transmission issues such as to allow Easy (low loss, low dispersion) propagation as electromagnetic waves Multiplexing, the transmission of multiple data signals in one frequency band, on different carrier frequencies. Smaller, more directional antennasCarrier signal... | Wikipedia - Node-to-node data transfer | null | null | null |
Modulation-doped two-dimensional electron gases can be gated to create quantum dots. Electrons trapped in these dots can then be operated as quantum bits. == References == | Wikipedia - Modulation doping | null | null | null |
Modulators act to provide the waveform of the RF-pulse. There are two different radar modulator designs: High voltage switch for non-coherent keyed power-oscillators These modulators consist of a high voltage pulse generator formed from a high voltage supply, a pulse forming network, and a high voltage switch such as a... | Wikipedia - Fill pulse | null | null | null |
In this way, the transmitted pulse of RF radiation is kept to a defined and usually very short duration. Hybrid mixers, fed by a waveform generator and an exciter for a complex but coherent waveform. This waveform can be generated by low power/low-voltage input signals. In this case the radar transmitter must be a powe... | Wikipedia - Fill pulse | null | null | null |
Module: an abelian group M and a ring R acting as operators on M. The members of R are sometimes called scalars, and the binary operation of scalar multiplication is a function R × M → M, which satisfies several axioms. Counting the ring operations these systems have at least three operations. Vector space: a module wh... | Wikipedia - Algebraic structure | null | null | null |
Modules of the Heisenberg algebra can be constructed as Fock spaces π λ {\displaystyle \pi _{\lambda }} for λ ∈ C {\displaystyle \lambda \in \mathbb {C} } which are induced representations of the Heisenberg Lie algebra, given by a vacuum vector v λ {\displaystyle v_{\lambda }} satisfying b n v λ = 0 {\displaystyle b_{n... | Wikipedia - Vertex algebra | null | null | null |
These are used to construct lattice vertex algebras, which as vector spaces are direct sums of Heisenberg modules, when the image of Y {\displaystyle Y} is extended appropriately to module elements. The module category is not semisimple, since one may induce a representation of the abelian Lie algebra where b0 acts by ... | Wikipedia - Vertex algebra | null | null | null |
Modules over a ring are generalizations of vector spaces, which removes the restriction that coefficients belong to a field. Given a module M over a ring R, a linear form on M is a linear map from M to R, where the latter is considered as a module over itself. The space of linear forms is always denoted Homk(V, k), whe... | Wikipedia - Real and imaginary parts of a linear functional | null | null | null |
Modulo minor technicalities all Iwahori–Hecke algebras of finite type are cellular w.r.t. to the involution that maps the standard basis as T w ↦ T w − 1 {\displaystyle T_{w}\mapsto T_{w^{-1}}} . This includes for example the integral group algebra of the symmetric groups as well as all other finite Weyl groups. A basi... | Wikipedia - Cellular algebra | null | null | null |
Modus ponens represents an instance of the Law of total probability which for a binary variable is expressed as: where e.g. Pr ( Q ) {\displaystyle \Pr(Q)} denotes the probability of Q {\displaystyle Q} and the conditional probability Pr ( Q ∣ P ) {\displaystyle \Pr(Q\mid P)} generalizes the logical implication P → Q {... | Wikipedia - Forward reasoning | null | null | null |
Modus ponens represents an instance of the binomial deduction operator in subjective logic expressed as: where ω P A {\displaystyle \omega _{P}^{A}} denotes the subjective opinion about P {\displaystyle P} as expressed by source A {\displaystyle A} , and the conditional opinion ω Q | P A {\displaystyle \omega _{Q|P}^{A... | Wikipedia - Forward reasoning | null | null | null |
Modus tollens represents an instance of the abduction operator in subjective logic expressed as: where ω Q A {\displaystyle \omega _{Q}^{A}} denotes the subjective opinion about Q {\displaystyle Q} , and ( ω Q | P A , ω Q | ¬ P A ) {\displaystyle (\omega _{Q|P}^{A},\omega _{Q|\lnot P}^{A})} denotes a pair of binomial c... | Wikipedia - Modus tollens | null | null | null |
The conditional opinion ω Q | P A {\displaystyle \omega _{Q|P}^{A}} generalizes the logical statement P → Q {\displaystyle P\to Q} , i.e. in addition to assigning TRUE or FALSE the source A {\displaystyle A} can assign any subjective opinion to the statement. The case where ω Q A {\displaystyle \omega _{Q}^{A}} is an a... | Wikipedia - Modus tollens | null | null | null |
Modus tollens represents an instance of the law of total probability combined with Bayes' theorem expressed as: where the conditionals Pr ( P ∣ Q ) {\displaystyle \Pr(P\mid Q)} and Pr ( P ∣ ¬ Q ) {\displaystyle \Pr(P\mid \lnot Q)} are obtained with (the extended form of) Bayes' theorem expressed as: and In the equation... | Wikipedia - Modus tollens | null | null | null |
It is then easy to see that Pr ( P ) = 0 {\displaystyle \Pr(P)=0} when Pr ( Q ∣ P ) = 1 {\displaystyle \Pr(Q\mid P)=1} and Pr ( Q ) = 0 {\displaystyle \Pr(Q)=0} . This is because Pr ( ¬ Q ∣ P ) = 1 − Pr ( Q ∣ P ) = 0 {\displaystyle \Pr(\lnot Q\mid P)=1-\Pr(Q\mid P)=0} so that Pr ( P ∣ ¬ Q ) = 0 {\displaystyle \Pr(P\mid... | Wikipedia - Modus tollens | null | null | null |
Mogul lamps are also the subject of a mathematics problem concerning the number of possible combinations of power that can be obtained. As it turns out, the name "Six Way Lamp" is somewhat deceiving since there are in fact 16 possible combinations (without the night-light), including combinations with all lamps of eith... | Wikipedia - Mogul lamp | null | null | null |
Mohammad Karamudini, editor in chief | Wikipedia - Roshd Biological Education | null | null | null |
Mohan analyzes two widely used representative quantum mechanics textbooks against the learning challenges reported by Krijtenburg-Lewerissa and others. Both texts adopt language ('waves' and 'particles') familiar to students in other contexts without directly exploring the significant shifts in meaning required by quan... | Wikipedia - Teaching quantum mechanics | null | null | null |
Mohandess Payeh 1 and Mohandess Payeh 2 are titles used respectively for professional engineer and engineer-in-training in Iran. Ir is used as a pre-nominal in Hong Kong, Malaysia and Indonesia. Er is used as a pre-nominal in Singapore and P.E./P.Eng. ( professional engineer ) are used as post-nominal designations. | Wikipedia - Professional engineering | null | null | null |
P.E.Jp as a pre-nominal in Japan. Engr. or engineer is allowed before your name only if you have membership in IEB, in Bangladesh. | Wikipedia - Professional engineering | null | null | null |
R.E. and P.E. are used as post-nominal designations for engineers in Pakistan registered with the Pakistan Engineering Council (PEC) after completing a four years Bachelor of Engineering/Bachelor of Science in Engineering degree. | Wikipedia - Professional engineering | null | null | null |
R.E. ( registered engineer ) and P.E. ( professional engineer ) Mohandes is used as a pre-nominal in Arab countries like Iraq, Syria and Lebanon. | Wikipedia - Professional engineering | null | null | null |
Eng. or .م as a pre-nominal in Jordan (for engineers holding a university degree in engineering after five years of studies). Engr. | Wikipedia - Professional engineering | null | null | null |
or engineer is used as a pre-nominal in the Philippines for individuals passing the government regulated professional licensure examination, which is only given for certain fields of engineering. CEng (Sri Lanka) is used in Sri Lanka as a post-nominal abbreviation by corporate members of the Institution of Engineers, S... | Wikipedia - Professional engineering | null | null | null |
The term incorporated engineers is offered by the Institution of Incorporated Engineers, Sri Lanka. CEng (India) is used as post-nominal abbreviation in India by those who are registered as a chartered engineer with Institution of Engineers (India). Er is used before their name by chartered engineers who hold the IE d... | Wikipedia - Professional engineering | null | null | null |
Moi National Mathematics Contest — prepared and hosted by Mang'u High School but open to students from all Kenyan high schools | Wikipedia - Math competition | null | null | null |
Moisil proved that every LMn algebra can be embedded in a direct product (of copies) of the canonical L n {\displaystyle {\mathcal {L}}_{n}} algebra. As a corollary, every LMn algebra is a subdirect product of subalgebras of L n {\displaystyle {\mathcal {L}}_{n}} .The Heyting implication can be defined as: x ⇒ y = d e ... | Wikipedia - Łukasiewicz–Moisil algebra | null | null | null |
Mokhtarian & Mackworth (1992) suggest a numerical method for computing an approximation to the curve-shortening flow that maintains a discrete approximation to the curve and alternates between two steps: Resample the current curve by placing new sample points at a uniform spacing, as measured by normalized arc length. ... | Wikipedia - Curve-shortening flow | null | null | null |
Mole-Richardson 103B microphone boom Consoles from Audix, Glensound, Neve, Soundcraft | Wikipedia - Broadcast Engineering Conservation Group | null | null | null |
Molecular Ecology expects that data supporting the results in the paper should be archived in an appropriate public archive, such as GenBank, Gene Expression Omnibus, TreeBASE, Dryad, the Knowledge Network for Biocomplexity, your own institutional or funder repository, or as Supporting Information on the Molecular Ecol... | Wikipedia - Data repository | null | null | null |
Molecular biological methods involve studying the DNA of the parasite in order to identify it. PCR and RFLP are used to detect and amplify parasite DNA found in the feces, blood, or tissue of the host. These techniques are very sensitive, which is useful for diagnosing parasites even when they are present in very low n... | Wikipedia - Veterinary parasitology | null | null | null |
Molecular biology allows scientists to understand a gene's function using microbial culturing and mutagenesis. Searching for similar genes in other organisms and in metagenomic and metatranscriptomic data allows us to understand what processes could be relevant and important in a given ecosystem, providing insight into... | Wikipedia - Geobiology | null | null | null |
The presence of DNA sequences of the pmo gene in the environment can be used as a proxy for methanotrophy. A more generalizable tool is the 16S ribosomal RNA gene, which is found in bacteria and archaea. This gene evolves very slowly over time and is not usually horizontally transferred, and so it is often used to dist... | Wikipedia - Geobiology | null | null | null |
In this way, genes are clues to organismal metabolism and identity. Genetics enables us to ask 'who is there?' and 'what are they doing?' This approach is called metagenomics. | Wikipedia - Geobiology | null | null | null |
Molecular biology and bioinformatics: AB1 – In DNA sequencing, chromatogram files used by instruments from Applied Biosystems ACE – A sequence assembly format ASN.1 – Abstract Syntax Notation One, is an International Standards Organization (ISO) data representation format used to achieve interoperability between platfo... | Wikipedia - List of file formats | null | null | null |
FASTA – The FASTA format, for sequence data. Sometimes also given as FNA or FAA (Fasta Nucleic Acid or Fasta Amino Acid). FASTQ – The FASTQ format, for sequence data with quality. | Wikipedia - List of file formats | null | null | null |
Sometimes also given as QUAL. GCPROJ – The Genome Compiler project. Advanced format for genetic data to be designed, shared and visualized. GenBank – The flatfile format used by the NCBI to represent database records for nucleotide and peptide sequences from the GenBank and RefSeq databases GFF – The General feature fo... | Wikipedia - List of file formats | null | null | null |
Molecular biology is the process of synthesis and regulation of a cell's DNA, RNA, and protein. Molecular biology consists of different techniques including Polymerase chain reaction, Gel electrophoresis, and macromolecule blotting to manipulate DNA.Polymerase chain reaction is done by placing a mixture of the desired ... | Wikipedia - Biomedicine | null | null | null |
This jelly-like sheet will have wells for DNA to be poured into. An electric current is applied so that the DNA, which is negatively charged due to its phosphate groups is attracted to the positive electrode. | Wikipedia - Biomedicine | null | null | null |
Different rows of DNA will move at different speeds because some DNA pieces are larger than others. Thus if two DNA samples show a similar pattern on the gel electrophoresis, one can tell that these DNA samples match.Macromolecule blotting is a process performed after gel electrophoresis. An alkaline solution is prepar... | Wikipedia - Biomedicine | null | null | null |
A sponge is placed into the solution and an agarose gel is placed on top of the sponge. Next, nitrocellulose paper is placed on top of the agarose gel and a paper towels are added on top of the nitrocellulose paper to apply pressure. The alkaline solution is drawn upwards towards the paper towel. | Wikipedia - Biomedicine | null | null | null |
During this process, the DNA denatures in the alkaline solution and is carried upwards to the nitrocellulose paper. The paper is then placed into a plastic bag and filled with a solution full of the DNA fragments, called the probe, found in the desired sample of DNA. The probes anneal to the complementary DNA of the ba... | Wikipedia - Biomedicine | null | null | null |
Afterwards, probes are washed off and the only ones present are the ones that have annealed to complementary DNA on the paper. Next the paper is stuck onto an x ray film. The radioactivity of the probes creates black bands on the film, called an autoradiograph. | Wikipedia - Biomedicine | null | null | null |
As a result, only similar patterns of DNA to that of the probe are present on the film. This allows us the compare similar DNA sequences of multiple DNA samples. The overall process results in a precise reading of similarities in both similar and different DNA sample. | Wikipedia - Biomedicine | null | null | null |
Molecular biology studies the common genetic and developmental mechanisms of animals and plants, attempting to answer the questions regarding the mechanisms of genetic inheritance and the structure of the gene. In 1953, James Watson and Francis Crick described the structure of DNA and the interactions within the molecu... | Wikipedia - Zoology | null | null | null |
Molecular genetics, the study of gene structure and function, has been among the most prominent sub-fields of molecular biology since the early 2000s. Other branches of biology are informed by molecular biology, by either directly studying the interactions of molecules in their own right such as in cell biology and dev... | Wikipedia - Zoology | null | null | null |
Molecular biophysics Biological membranes Cell membranes Bioenergetics Channels, receptors and transporters Enzyme kinetics Molecular motors Phospholipids Proteins Biofilms Supramolecular assemblies Nucleic acids | Wikipedia - Biophysical techniques | null | null | null |
Molecular biophysics typically addresses biological questions similar to those in biochemistry and molecular biology, seeking to find the physical underpinnings of biomolecular phenomena. Scientists in this field conduct research concerned with understanding the interactions between the various systems of a cell, inclu... | Wikipedia - Protein chemistry | null | null | null |
Protein dynamics can be observed by neutron spin echo spectroscopy. Conformational change in structure can be measured using techniques such as dual polarisation interferometry, circular dichroism, SAXS and SANS. Direct manipulation of molecules using optical tweezers or AFM, can also be used to monitor biological even... | Wikipedia - Protein chemistry | null | null | null |
Molecular biophysics typically addresses biological questions similar to those in biochemistry and molecular biology, seeking to find the physical underpinnings of biomolecular phenomena. Scientists in this field conduct research concerned with understanding the interactions between the various systems of a cell, inclu... | Wikipedia - Biophysics | null | null | null |
Fluorescent imaging techniques, as well as electron microscopy, x-ray crystallography, NMR spectroscopy, atomic force microscopy (AFM) and small-angle scattering (SAS) both with X-rays and neutrons (SAXS/SANS) are often used to visualize structures of biological significance. Protein dynamics can be observed by neutron... | Wikipedia - Biophysics | null | null | null |
Direct manipulation of molecules using optical tweezers or AFM, can also be used to monitor biological events where forces and distances are at the nanoscale. Molecular biophysicists often consider complex biological events as systems of interacting entities which can be understood e.g. through statistical mechanics, t... | Wikipedia - Biophysics | null | null | null |
In addition to traditional (i.e. molecular and cellular) biophysical topics like structural biology or enzyme kinetics, modern biophysics encompasses an extraordinarily broad range of research, from bioelectronics to quantum biology involving both experimental and theoretical tools. It is becoming increasingly common f... | Wikipedia - Biophysics | null | null | null |
Medical physics, a branch of biophysics, is any application of physics to medicine or healthcare, ranging from radiology to microscopy and nanomedicine. For example, physicist Richard Feynman theorized about the future of nanomedicine. He wrote about the idea of a medical use for biological machines (see nanomachines).... | Wikipedia - Biophysics | null | null | null |
Molecular capsules are chemical scaffolds designed to capture and hold a guest molecule (see molecular encapsulation). Szumna and coworkers developed a novel molecular capsule with a chiral interior. This capsule is made of two halves, like a plastic easter egg (Figure 6). Salt bridge interactions between the two halve... | Wikipedia - Salt bridge (protein) | null | null | null |
Molecular cloning is used to isolate and then transfer a DNA sequence of interest into a plasmid vector. This recombinant DNA technology was first developed in the 1960s. In this technique, a DNA sequence coding for a protein of interest is cloned using polymerase chain reaction (PCR), and/or restriction enzymes, into ... | Wikipedia - Molecular Biology | null | null | null |
The plasmid vector usually has at least 3 distinctive features: an origin of replication, a multiple cloning site (MCS), and a selective marker (usually antibiotic resistance). Additionally, upstream of the MCS are the promoter regions and the transcription start site, which regulate the expression of cloned gene. This... | Wikipedia - Molecular Biology | null | null | null |
Introducing DNA into bacterial cells can be done by transformation via uptake of naked DNA, conjugation via cell-cell contact or by transduction via viral vector. Introducing DNA into eukaryotic cells, such as animal cells, by physical or chemical means is called transfection. Several different transfection techniques ... | Wikipedia - Molecular Biology | null | null | null |
The plasmid may be integrated into the genome, resulting in a stable transfection, or may remain independent of the genome and expressed temporarily, called a transient transfection.DNA coding for a protein of interest is now inside a cell, and the protein can now be expressed. A variety of systems, such as inducible p... | Wikipedia - Molecular Biology | null | null | null |
Molecular computing is an unconventional form of computing that utilizes chemical reactions to perform computations. Data is represented by variations in chemical concentrations, and the goal of this type of computing is to use the smallest stable structures, such as single molecules, as electronic components. This fie... | Wikipedia - Unconventional computing | null | null | null |
Molecular dimers are often formed by the reaction of two identical compounds e.g.: 2A → A−A. In this example, monomer "A" is said to dimerize to give the dimer "A−A". An example is a diaminocarbene, which dimerize to give a tetraaminoethylene: 2 C ( NR 2 ) 2 ⟶ ( R 2 N ) 2 C = C ( NR 2 ) 2 {\displaystyle {\ce {2 C(NR2)2... | Wikipedia - Dimerisation (chemistry) | null | null | null |
Upon heating, it "cracks" (undergoes a retro-Diels-Alder reaction) to give identical monomers: C 10 H 12 ⟶ 2 C 5 H 6 {\displaystyle {\ce {C10H12 -> 2 C5H6}}} Many nonmetallic elements occur as dimers: hydrogen, nitrogen, oxygen, and the halogens (i.e. fluorine, chlorine, bromine and iodine). Noble gases can form dimers... | Wikipedia - Dimerisation (chemistry) | null | null | null |
Mercury occurs as a mercury(I) cation (Hg2+2), formally a dimeric ion. Other metals may form a proportion of dimers in their vapour phase. Known metallic dimers include dilithium (Li2), disodium (Na2), dipotassium (K2), dirubidium (Rb2) and dicaesium (Cs2). | Wikipedia - Dimerisation (chemistry) | null | null | null |
Such elemental dimers are homonuclear diatomic molecules. Many small organic molecules, most notably formaldehyde, easily form dimers. The dimer of formaldehyde (CH2O) is dioxetane (C2H4O2). Borane (BH3) occurs as the dimer diborane (B2H6), due to the high Lewis acidity of the boron center. | Wikipedia - Dimerisation (chemistry) | null | null | null |
Molecular docking (also referred to only as docking) is a method used to predict the orientation coordinates of a molecule (ligand) when bound to another one (receptor or target). The binding may be mostly through non-covalent interactions while covalently linked binding can also be studied. Molecular docking aims to p... | Wikipedia - Structural bioinformatics | null | null | null |
Molecular dynamics (MD) is a computational method for simulating interactions between molecules and their atoms during a given period of time. This method allows the observation of the behavior of molecules and their interactions, considering the system as a whole. To calculate the behavior of the systems and, thus, de... | Wikipedia - Structural bioinformatics | null | null | null |
Molecular dynamics (MD) is usually preferable to Monte Carlo (MC), so it is desirable to have a MD algorithm incorporating the basic WL idea for flat energy sampling. That algorithm is Statistical Temperature Molecular Dynamics (STMD), developed by Jaegil Kim et al at Boston University. An essential first step was made... | Wikipedia - Wang and Landau algorithm | null | null | null |
STMC is centered on an intensive quantity, the statistical temperature, T ( E ) = 1 / ( d S ( E ) / d E ) {\displaystyle T(E)=1/(dS(E)/dE)} , where E is the potential energy. When combined with the relation, Ω ( E ) = e S ( E ) {\displaystyle \Omega (E)=e^{S(E)}} , where we set k B = 1 {\displaystyle k_{B}=1} , the WL ... | Wikipedia - Wang and Landau algorithm | null | null | null |
The details are given in Ref. With an initial guess for T ( E ) {\displaystyle T(E)} and the range restricted to lie between T L {\displaystyle T_{L}} and T U {\displaystyle T_{U}} , the simulation proceeds as in WLMC, with significant numerical differences. An interpolation of T ~ ( E ) {\displaystyle {\tilde {T}}(E)}... | Wikipedia - Wang and Landau algorithm | null | null | null |
Different values of S ( E ) {\displaystyle S(E)} are available within the same energy bin when evaluating the acceptance probability. When histogram fluctuations are less than 20% of the mean, f {\displaystyle f} is reduced according to f → f {\displaystyle f\rightarrow {\sqrt {f}}} . STMC was compared with WL for the ... | Wikipedia - Wang and Landau algorithm | null | null | null |
Upon increasing energy bin size, STMC gets the same results over a considerable range, while the performance of WL deteriorates rapidly. STMD can use smaller initial values of f d = f − 1 {\displaystyle f_{d}=f-1} for more rapid convergence. In sum, STMC needs fewer steps to obtain the same quality of results. | Wikipedia - Wang and Landau algorithm | null | null | null |
Now consider the main result, STMD. It is based on the observation that in a standard MD simulation at temperature T 0 {\displaystyle T_{0}} with forces derived from the potential energy E ( ) {\displaystyle E()} , where {\displaystyle } denotes all the positions, the sampling weight for a configuration is e − E ( )... | Wikipedia - Wang and Landau algorithm | null | null | null |
For flat energy sampling, let the effective potential be T 0 S ( E ) {\displaystyle T_{0}S(E)} - entropic molecular dynamics. Then the weight is e − S ( E ) {\displaystyle e^{-S(E)}} . Since the density of states is e + S ( E ) {\displaystyle e^{+S(E)}} , their product gives flat energy sampling. | Wikipedia - Wang and Landau algorithm | null | null | null |
The forces are calculated as F = ( − d / d x ) T 0 S ( E ) = T 0 ( d S / d E ) ( − d / d x ) E ( ) = ( T 0 / T ( E ) ) F 0 {\displaystyle F=(-d/dx)T_{0}S(E)=T_{0}(dS/dE)(-d/dx)E()=(T_{0}/T(E))F^{0}} where F 0 {\displaystyle F^{0}} denotes the usual force derived from the potential energy. Scaling the usual forces by t... | Wikipedia - Wang and Landau algorithm | null | null | null |
As the simulation converges to flat energy sampling, the running estimate T ~ ( E ) {\displaystyle {\tilde {T}}(E)} converges to the true T ( E ) {\displaystyle T(E)} . Technical details including steps to speed convergence are described in and.In STMD T 0 {\displaystyle T_{0}} is called the kinetic temperature as it c... | Wikipedia - Wang and Landau algorithm | null | null | null |
Any canonical average can be calculated with reweighting, but the statistical temperature, T ( E ) {\displaystyle T(E)} , is immediately available with no additional analysis. It is extremely valuable for studying phase transitions. | Wikipedia - Wang and Landau algorithm | null | null | null |
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