Split (1)

train · 115k rows

text stringlengths 2 4.67k	source dict
Stochastic optimization methods also include methods with random iterates. Some stochastic optimization methods use random iterates to solve stochastic problems, combining both meanings of stochastic optimization. Stochastic optimization methods generalize deterministic methods for deterministic problems. stochastic se...	{ "page_id": 50336055, "title": "Glossary of artificial intelligence" }
for unseen instances. This requires the learning algorithm to generalize from the training data to unseen situations in a "reasonable" way (see inductive bias). support vector machines In machine learning, support vector machines (SVMs, also support vector networks) are supervised learning models with associated learni...	{ "page_id": 50336055, "title": "Glossary of artificial intelligence" }
theory was developed as a geometrization of brain function (especially of the central nervous system) using tensors. TensorFlow A free and open-source software library for dataflow and differentiable programming across a range of tasks. It is a symbolic math library, and is also used for machine learning applications s...	{ "page_id": 50336055, "title": "Glossary of artificial intelligence" }
learning architecture that exploits a multi-head attention mechanism. Transformers address some of the limitations of long short-term memory, and became widely used in natural language processing, although it can also process other types of data such as images in the case of vision transformers. transhumanism Abbreviat...	{ "page_id": 50336055, "title": "Glossary of artificial intelligence" }
machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any algorithm. Turing test A test of a machine's ability to exhibit intelligent behaviour equivalent to, or indistinguishable from, that of a human, developed by Alan Turing i...	{ "page_id": 50336055, "title": "Glossary of artificial intelligence" }
other purposes as well, such as expressing business rules, enabling certain compiler optimizations, allowing for multiple dispatch, providing a form of documentation, etc. == U == unsupervised learning A type of self-organized Hebbian learning that helps find previously unknown patterns in data set without pre-existing...	{ "page_id": 50336055, "title": "Glossary of artificial intelligence" }
Colm P. O'Donnell is an Irish chemist and engineer. He is a professor of biosystems and food engineering at the University College Dublin who is active in the field of process analytical technology (PAT). He is also a head of university School of biosystems and food engineering — as well as a chairperson of the Dairy p...	{ "page_id": 58659130, "title": "Colm O'Donnell" }
Shotokuvirae is a kingdom of viruses. == Nomenclature == The kingdom, Shotokuvirae, was named after Japan's Empress Shotoku (718-770 AD), who reigned over Japan twice, first as Empress Koken and later as Empress Shotoku, and who created the world's earliest written record of a plant virus disease, which was a poem to h...	{ "page_id": 63770939, "title": "Shotokuvirae" }
Fluorescence-lifetime imaging microscopy or FLIM is an imaging technique based on the differences in the exponential decay rate of the photon emission of a fluorophore from a sample. It can be used as an imaging technique in confocal microscopy, two-photon excitation microscopy, and multiphoton tomography. The fluoresc...	{ "page_id": 1642813, "title": "Fluorescence-lifetime imaging microscopy" }
intensity and of the emitted light. This can be utilized for making non-intensity based measurements in chemical sensing. == Measurement == Fluorescence-lifetime imaging yields images with the intensity of each pixel determined by τ {\displaystyle \tau } , which allows one to view contrast between materials with differ...	{ "page_id": 1642813, "title": "Fluorescence-lifetime imaging microscopy" }
single photon avalanche photo diode (SPAD)) with respect to the excitation laser pulse. The recordings are repeated for multiple laser pulses and after enough recorded events, one is able to build a histogram of the number of events across all of these recorded time points. This histogram can then be fit to an exponent...	{ "page_id": 1642813, "title": "Fluorescence-lifetime imaging microscopy" }
as an LED, diode laser or a continuous wave source combined with an electro-optic modulator or an acousto-optic modulator. The fluorescence is (a.) demodulated and (b.) phase shifted; both quantities are related to the characteristic decay times of the fluorophore. Also, y-components to the excitation and fluorescence ...	{ "page_id": 1642813, "title": "Fluorescence-lifetime imaging microscopy" }
de-convolution problem is not straightforward and it is a slow process which in the early days of FLIM made it impractical for a pixel-by-pixel analysis. Non fitting methods are attractive because they offer a very fast solution to lifetime estimation. One of the major and straightforward techniques in this category is...	{ "page_id": 1642813, "title": "Fluorescence-lifetime imaging microscopy" }
Fourier transformation along with Laguerre gauss expansion have been used to estimate the lifetime in transformed space. These approaches are faster than the deconvolution based methods but they suffer from truncation and sampling problems. Moreover, application of methods like Laguerre gauss expansion is mathematicall...	{ "page_id": 1642813, "title": "Fluorescence-lifetime imaging microscopy" }
lamins A and B1 in distinct homopolymers at the nuclear envelope, which further interact with each other in higher order structures. FLIM imaging is particularly useful in neurons, where light scattering by brain tissue is problematic for ratiometric imaging. In neurons, FLIM imaging using pulsed illumination has been ...	{ "page_id": 1642813, "title": "Fluorescence-lifetime imaging microscopy" }
Androsterone sulfate, also known as 3α-hydroxy-5α-androstan-17-one 3α-sulfate, is an endogenous, naturally occurring steroid and one of the major urinary metabolites of androgens. It is a steroid sulfate which is formed from sulfation of androsterone by the steroid sulfotransferase SULT2A1 and can be desulfated back in...	{ "page_id": 54595901, "title": "Androsterone sulfate" }
The molecular formula C8H16O2 may refer to: Butyl butyrate Caprylic acid Cyclohexanedimethanol Ethyl hexanoate 2-Ethylhexanoic acid Hexyl acetate Manzanate Pentyl propanoate 2,2,4,4-Tetramethyl-1,3-cyclobutanediol Valproic acid	{ "page_id": 23662911, "title": "C8H16O2" }
Kate & Leopold is a 2001 American romantic comedy science fiction film that tells a story of a physicist by the name of Stuart (Liev Schreiber), who accidentally pulls his great‑great‑grandfather, Leopold (Hugh Jackman), through a time portal from 19th‑century New York to the present, where Leopold and Stuart's ex‑girl...	{ "page_id": 594240, "title": "Kate & Leopold" }
to the 21st century has caused a widespread "occlusion" of elevators, and may cause the disappearance of Stuart himself if Leopold does not go back to 1876 on Monday. Leopold is intrigued by the cynical and ambitious Kate McKay, Stuart's ex-girlfriend who lives downstairs. He says that she produces the impression of a ...	{ "page_id": 594240, "title": "Kate & Leopold" }
real". On Friday, Leopold hires a violinist and invites Kate to a rooftop dinner, which ends with a waltz and the first kiss. On Saturday, they stroll about Lower Manhattan and come across Uncle Millard's home at 1 Hanover Square, where Leopold retrieves a metal box with his boyhood treasures, including his mother's ri...	{ "page_id": 594240, "title": "Kate & Leopold" }
is to take place. Just when Leopold is about to announce his bride of convenience, Kate storms into the ballroom, and he instead announces her name, styled as "Kate McKay, of the McKays of Massapequa". Among the shocked guests, Kate and Leopold reunite with a kiss and dance a bridal waltz. Thus Kate turns out to be Stu...	{ "page_id": 594240, "title": "Kate & Leopold" }
the film has a weighted average score of 44 based on 27 reviews, indicating "mixed or average" reviews. Audiences surveyed by CinemaScore gave the film a grade B+ on scale of A to F. Roger Ebert of the Chicago Sun-Times wrote: "Meg Ryan does this sort of thing about as well as it can possibly be done, and after Sleeple...	{ "page_id": 594240, "title": "Kate & Leopold" }
The QTY Code is a design method to transform membrane proteins that are intrinsically insoluble in water into variants with water solubility, while retaining their structure and function. == Similar structures of amino acids == The QTY Code is based on two key molecular structural facts: 1) all 20 natural amino acids a...	{ "page_id": 66916675, "title": "QTY Code" }
amino acid turn, c) 3.6 amino acids and 360˚ per helical turn, and d) 5.4Å per helical turn. The 3 types of alpha-helices are: 1) mostly hydrophobic amino acids including Leucine (L), Isoleucine (I), Valine (V), Phenylalanine (F), Methionine (M) and Alanine (A) that are commonly found as the helical transmembrane segme...	{ "page_id": 66916675, "title": "QTY Code" }
severely infected COVID-19 patients, for whom cytokine storms often lead to death. == References == == Further reading == Hung, Chien-Lun; Kuo, Yun-Hsuan; Lee, Su Wei; Chiang, Yun-Wei (2021). "Protein Stability Depends Critically on the Surface Hydrogen-Bonding Network: A Case Study of Bid Protein". The Journal of Phys...	{ "page_id": 66916675, "title": "QTY Code" }
Smorodina, Eva; Diankin, Igor; Tao, Fei; Qing, Rui; Yang, Steve; Zhang, Shuguang (2022). "Structural informatic study of determined and AlphaFold2 predicted molecular structures of 13 human solute carrier transporters and their water-soluble QTY variants". Scientific Reports. 12 (1) 20103. Bibcode:2022NatSR..1220103S. ...	{ "page_id": 66916675, "title": "QTY Code" }
Chemokine Receptors and Potential Inhibitory Role of Their Truncated Isoforms Revealed through Combinatorial Prediction". International Journal of Molecular Sciences. 24 (22): 16266. doi:10.3390/ijms242216266. PMC 10671024. PMID 38003455. Li, Mengke; Qing, Rui; Tao, Fei; Xu, Ping; Zhang, Shuguang (2024). "Inhibitory ef...	{ "page_id": 66916675, "title": "QTY Code" }
In statistics, machine learning and algorithms, a tensor sketch is a type of dimensionality reduction that is particularly efficient when applied to vectors that have tensor structure. Such a sketch can be used to speed up explicit kernel methods, bilinear pooling in neural networks and is a cornerstone in many numeric...	{ "page_id": 64295245, "title": "Tensor sketch" }
O(kd_{2})} , respectively; including the Hadamard product gives overall time O ( d 1 d 2 + k d 1 + k d 2 ) {\displaystyle O(d_{1}d_{2}+kd_{1}+kd_{2})} . In most use cases this method is significantly faster than the full M ( y ⊗ z ) {\displaystyle M(y\otimes z)} requiring O ( k d ) = O ( k d 1 d 2 ) {\displaystyle O(kd...	{ "page_id": 64295245, "title": "Tensor sketch" }
{\displaystyle \mathbf {C} \in \mathbb {R} ^{3\times 3}} and D ∈ R 3 × 3 {\displaystyle \mathbf {D} \in \mathbb {R} ^{3\times 3}} be two matrices. Then the face-splitting product C ∙ D {\displaystyle \mathbf {C} \bullet \mathbf {D} } is C ∙ D = [ C 1 ⊗ D 1 C 2 ⊗ D 2 C 3 ⊗ D 3 ] = [ C 1 , 1 D 1 , 1 C 1 , 1 D 1 , 2 C 1 ,...	{ "page_id": 64295245, "title": "Tensor sketch" }
_{2}\\\hline \mathbf {C} _{3}\otimes \mathbf {D} _{3}\\\end{array}}\right]=\left[{\begin{array}{c c c c c c c c c }\mathbf {C} _{1,1}\mathbf {D} _{1,1}&\mathbf {C} _{1,1}\mathbf {D} _{1,2}&\mathbf {C} _{1,1}\mathbf {D} _{1,3}&\mathbf {C} _{1,2}\mathbf {D} _{1,1}&\mathbf {C} _{1,2}\mathbf {D} _{1,2}&\mathbf {C} _{1,2}\m...	{ "page_id": 64295245, "title": "Tensor sketch" }
show that, amazingly, this equals C ( x ⊗ y ) {\displaystyle C(x\otimes y)} – a count sketch of the tensor product! It turns out that this relation can be seen in terms of the face-splitting product as C ( 1 ) x ∗ C ( 2 ) y = F − 1 ( F C ( 1 ) x ∘ F C ( 2 ) y ) {\displaystyle C^{(1)}x\ast C^{(2)}y={\mathcal {F}}^{-1}({...	{ "page_id": 64295245, "title": "Tensor sketch" }
x ) 2 ] = ‖ x ‖ 2 2 {\displaystyle E[(T_{1}x)^{2}]=\\|x\\|_{2}^{2}} and E [ ( T 1 x ) p ] 1 / p ≤ a p ‖ x ‖ 2 {\displaystyle E[(T_{1}x)^{p}]^{1/p}\leq {\sqrt {ap}}\\|x\\|_{2}} . Let T ( 1 ) , … , T ( c ) {\displaystyle T^{(1)},\dots ,T^{(c)}} be independent consisting of T {\displaystyle T} and M = T ( 1 ) ∙ ⋯ ∙ T ( c ) {\...	{ "page_id": 64295245, "title": "Tensor sketch" }
sketches based on the face-splitting product, a different approach was developed in 2020 which applies M ( x ⊗ y ⊗ ⋯ ) = M ( 1 ) ( x ⊗ ( M ( 2 ) y ⊗ ⋯ ) ) {\displaystyle M(x\otimes y\otimes \cdots )=M^{(1)}(x\otimes (M^{(2)}y\otimes \cdots ))} We can achieve such an M {\displaystyle M} by letting M = M ( c ) ( M ( c − ...	{ "page_id": 64295245, "title": "Tensor sketch" }
is a k × d {\displaystyle k\times d} sampling matrix which is all zeros, except a single 1 in each row. If the diagonal matrix is replaced by one which has a tensor product of ± 1 {\displaystyle \pm 1} values on the diagonal, instead of being fully independent, it is possible to compute SHD ⁡ ( x ⊗ y ) {\displaystyle \...	{ "page_id": 64295245, "title": "Tensor sketch" }
2 ] ) = ( [ 1 0 0 1 1 0 ] ∙ [ 1 0 1 0 0 1 ] ) ( [ 1 1 1 − 1 ] [ σ 1 0 0 σ 2 ] [ x 1 x 2 ] ⊗ [ 1 1 1 − 1 ] [ ρ 1 0 0 ρ 2 ] [ y 1 y 2 ] ) = [ 1 0 0 1 1 0 ] [ 1 1 1 − 1 ] [ σ 1 0 0 σ 2 ] [ x 1 x 2 ] ∘ [ 1 0 1 0 0 1 ] [ 1 1 1 − 1 ] [ ρ 1 0 0 ρ 2 ] [ y 1 y 2 ] . {\displaystyle {\begin{aligned}&\operatorname {SHD} (x\otimes ...	{ "page_id": 64295245, "title": "Tensor sketch" }
+ 1 {\displaystyle \varepsilon ^{-2}(\log 1/\delta )^{c+1}} rows, then \| ‖ SHD ⁡ x ‖ 2 − ‖ x ‖ \| ≤ ε ‖ x ‖ 2 {\displaystyle \|\\|\operatorname {SHD} x\\|_{2}-\\|x\\|\|\leq \varepsilon \\|x\\|_{2}} for any vector x ∈ R d c {\displaystyle x\in \mathbb {R} ^{d^{c}}} with probability 1 − δ {\displaystyle 1-\delta } , while allowin...	{ "page_id": 64295245, "title": "Tensor sketch" }
{R} ^{d}} are the data points, y i {\displaystyle y_{i}} is the label of the i {\displaystyle i} th point (either −1 or +1), and y ^ ( x ′ ) {\displaystyle {\hat {y}}(\mathbf {x'} )} is the prediction of the class of x ′ {\displaystyle \mathbf {x'} } . The function k : R d × R d → R {\displaystyle k:\mathbb {R} ^{d}\ti...	{ "page_id": 64295245, "title": "Tensor sketch" }
n y i f ( x i ) {\displaystyle \sum _{i=1}^{n}y_{i}f(\mathbf {x} _{i})} can be computed in advance. The problem with this method is that the feature space can be very large. That is D >> d {\displaystyle D>>d} . For example, for the polynomial kernel k ( x , x ′ ) = ⟨ x , x ′ ⟩ 3 {\displaystyle k(x,x')=\langle x,x'\ran...	{ "page_id": 64295245, "title": "Tensor sketch" }
rows i , j {\displaystyle i,j} with the largest inner products ⟨ X i , Y j ⟩ {\displaystyle \langle X_{i},Y_{j}\rangle } . We could compute Z = X Y T ∈ R n × n {\displaystyle Z=XY^{T}\in \mathbb {R} ^{n\times n}} and simply look at all n 2 {\displaystyle n^{2}} possibilities. However, this would take at least n 2 {\dis...	{ "page_id": 64295245, "title": "Tensor sketch" }
radars" (PDF). Proc. Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-97), Lviv.: 73–74. Slyusar, V. I. (March 13, 1998). "A Family of Face Products of Matrices and its Properties" (PDF). Cybernetics and Systems Analysis C/C of Kibernetika I Sistemnyi Analiz.- 1999. 35 (3): 379–384. doi:10...	{ "page_id": 64295245, "title": "Tensor sketch" }
Cossaviricota is a phylum of viruses. The phylum is named after Yvonne Cossart who discovered Parvovirus B19, the causative pathogen of fifth disease. == Classes == The following classes are recognized: Mouviricetes Papovaviricetes Quintoviricetes == References ==	{ "page_id": 63770960, "title": "Cossaviricota" }
Methylation specific oligonucleotide microarray, also known as MSO microarray, was developed as a technique to map epigenetic methylation changes in DNA of cancer cells. The general process starts with modification of DNA with bisulfite, specifically to convert unmethylated cytosine in CpG sites to uracil, while leavin...	{ "page_id": 4264274, "title": "Methylation specific oligonucleotide microarray" }
modifications, as well as which tumour suppressor genes' transcription levels are affected. An interesting use of this microarray includes specific classification of cancers based on the methylation patterns alone, such as differentiating between classes of leukemia, suggesting that different classes of cancer show rel...	{ "page_id": 4264274, "title": "Methylation specific oligonucleotide microarray" }
A grain is a small, hard, dry fruit (caryopsis) – with or without an attached hull layer – harvested for human or animal consumption. A grain crop is a grain-producing plant. The two main types of commercial grain crops are cereals and legumes. After being harvested, dry grains are more durable than other staple foods,...	{ "page_id": 27988307, "title": "Grain" }
The three major pseudocereal grains are: amaranth (Amaranth family) also called kiwicha buckwheat (Smartweed family) quinoa (Amaranth family, formerly classified as Goosefoot family) == Pulses or grain legumes == Pulses or grain legumes, members of the pea family, have a higher protein content than most other plant foo...	{ "page_id": 27988307, "title": "Grain" }
transformation imposed by dominant members of a society seeking to expand control over labor and resources. == Trade == == Occupational safety and health == Those who handle grain at grain facilities may encounter numerous occupational hazards and exposures. Risks include grain entrapment, where workers are submerged i...	{ "page_id": 27988307, "title": "Grain" }
Viruses are only able to replicate themselves by commandeering the reproductive apparatus of cells and making them reproduce the virus's genetic structure and particles instead. How viruses do this depends mainly on the type of nucleic acid DNA or RNA they contain, which is either one or the other but never both. Virus...	{ "page_id": 4395348, "title": "Viral life cycle" }
host cell defenses or immune system and may increase the long-term "success" of the virus. This hiding is deemed latency. During this time, the virus does not produce any progeny, it remains inactive until external stimuli—such as light or stress—prompts it to activate. == See also == Kinetic class (virology) Viral phe...	{ "page_id": 4395348, "title": "Viral life cycle" }
The anal pore or cytoproct is a structure in various single-celled eukaryotes where waste is ejected after the nutrients from food have been absorbed into the cytoplasm. In ciliates, the anal pore (cytopyge) and cytostome are the only regions of the pellicle that are not covered by ridges, cilia or rigid covering. They...	{ "page_id": 32379221, "title": "Anal pore" }
vacuoles to be merged into the cell surface to be emptied. In ciliates, the anal cytostomes and cytopyge pore regions are not covered by either ridges or cilia or hard coatings like the other parts of the organism. As a food vacuole approaches the cytoproct region it actually starts to flatten out the surrounding cells...	{ "page_id": 32379221, "title": "Anal pore" }
the aboral end by two small pores, through which a small amount of egestion can take place. == References == == Bibliography == “Introduction to Ctenophora.” Introduction to the Ctenophora, https://ucmp.berkeley.edu/cnidaria/ctenophora.html. Pang, Kevin; Martindale, Mark Q. (December 2008). "Ctenophores". Current Biolo...	{ "page_id": 32379221, "title": "Anal pore" }
In chemical graph theory, the Padmakar–Ivan (PI) index is a topological index of a molecule, used in biochemistry. The Padmakar–Ivan index is a generalization introduced by Padmakar V. Khadikar and Iván Gutman of the concept of the Wiener index, introduced by Harry Wiener. The Padmakar–Ivan index of a graph G is the su...	{ "page_id": 56103252, "title": "Padmakar–Ivan index" }
Brownian motion is the random motion of particles suspended in a medium (a liquid or a gas). The traditional mathematical formulation of Brownian motion is that of the Wiener process, which is often called Brownian motion, even in mathematical sources. This motion pattern typically consists of random fluctuations in a ...	{ "page_id": 4436, "title": "Brownian motion" }
Jean Perrin in 1908. Perrin was awarded the Nobel Prize in Physics in 1926 "for his work on the discontinuous structure of matter". The many-body interactions that yield the Brownian pattern cannot be solved by a model accounting for every involved molecule. Consequently, only probabilistic models applied to molecular ...	{ "page_id": 4436, "title": "Brownian motion" }
of small dust particles is caused chiefly by true Brownian dynamics; Lucretius "perfectly describes and explains the Brownian movement by a wrong example". While Jan Ingenhousz described the irregular motion of coal dust particles on the surface of alcohol in 1785, the discovery of this phenomenon is often credited to ...	{ "page_id": 4436, "title": "Brownian motion" }
measured successfully. The velocity data verified the Maxwell–Boltzmann velocity distribution, and the equipartition theorem for a Brownian particle. == Statistical mechanics theories == === Einstein's theory === There are two parts to Einstein's theory: the first part consists in the formulation of a diffusion equatio...	{ "page_id": 4436, "title": "Brownian motion" }
magnitude q {\displaystyle q} , i.e., the probability density of the particle incrementing its position from x {\displaystyle x} to x + q {\displaystyle x+q} in the time interval τ {\displaystyle \tau } ). Further, assuming conservation of particle number, he expanded the number density ρ ( x , t + τ ) {\displaystyle \...	{ "page_id": 4436, "title": "Brownian motion" }
term is equal to one by the definition of probability, and the second and other even terms (i.e. first and other odd moments) vanish because of space symmetry. What is left gives rise to the following relation: ∂ ρ ∂ t = ∂ 2 ρ ∂ x 2 ⋅ ∫ − ∞ ∞ q 2 2 τ φ ( q ) d q + higher-order even moments. {\displaystyle {\frac {\part...	{ "page_id": 4436, "title": "Brownian motion" }
second moment is, however, non-vanishing, being given by E [ x 2 ] = 2 D t . {\displaystyle \mathbb {E} {\left[x^{2}\right]}=2Dt.} This equation expresses the mean squared displacement in terms of the time elapsed and the diffusivity. From this expression Einstein argued that the displacement of a Brownian particle is ...	{ "page_id": 4436, "title": "Brownian motion" }
6 π η r {\displaystyle \mu ={\tfrac {1}{6\pi \eta r}}} , where η is the dynamic viscosity of the fluid. In a state of dynamic equilibrium, and under the hypothesis of isothermal fluid, the particles are distributed according to the barometric distribution ρ = ρ o exp ⁡ ( − m g h k B T ) , {\displaystyle \rho =\rho _{o}...	{ "page_id": 4436, "title": "Brownian motion" }
N A . {\displaystyle {\frac {\mathbb {E} {\left[x^{2}\right]}}{2t}}=D=\mu k_{\text{B}}T={\frac {\mu RT}{N_{\text{A}}}}={\frac {RT}{6\pi \eta rN_{\text{A}}}}.} Here the first equality follows from the first part of Einstein's theory, the third equality follows from the definition of the Boltzmann constant as kB = R / NA...	{ "page_id": 4436, "title": "Brownian motion" }
for the viscosity. Introducing the ideal gas law per unit volume for the osmotic pressure, the formula becomes identical to that of Einstein's. The use of Stokes's law in Nernst's case, as well as in Einstein and Smoluchowski, is not strictly applicable since it does not apply to the case where the radius of the sphere...	{ "page_id": 4436, "title": "Brownian motion" }
2 ] = 2 D t = t 32 81 m u 2 π μ a = t 64 27 1 2 m u 2 3 π μ a , {\displaystyle \mathbb {E} {\left[(\Delta x)^{2}\right]}=2Dt=t{\frac {32}{81}}{\frac {mu^{2}}{\pi \mu a}}=t{\frac {64}{27}}{\frac {{\frac {1}{2}}mu^{2}}{3\pi \mu a}},} where μ is the viscosity coefficient, and a is the radius of the particle. Associating t...	{ "page_id": 4436, "title": "Brownian motion" }
{\sqrt {\frac {n}{2\pi }}},} showing that it increases as the square root of the total population. Suppose that a Brownian particle of mass M is surrounded by lighter particles of mass m which are traveling at a speed u. Then, reasons Smoluchowski, in any collision between a surrounding and Brownian particles, the velo...	{ "page_id": 4436, "title": "Brownian motion" }
the kinetic energy of the surrounding fluid particle, m u 2 / 2 {\displaystyle mu^{2}/2} . In 1906 Smoluchowski published a one-dimensional model to describe a particle undergoing Brownian motion. The model assumes collisions with M ≫ m where M is the test particle's mass and m the mass of one of the individual particl...	{ "page_id": 4436, "title": "Brownian motion" }
yields an approximation of the time evolution of the probability density function associated with the position of the particle going under a Brownian movement under the physical definition. The approximation becomes valid on timescales much larger than the timescale of individual atomic collisions, since it does not in...	{ "page_id": 4436, "title": "Brownian motion" }
frequently in pure and applied mathematics, economics and physics. The Wiener process Wt is characterized by four facts: W0 = 0 Wt is almost surely continuous Wt has independent increments W t − W s ∼ N ( 0 , t − s ) {\displaystyle W_{t}-W_{s}\sim {\mathcal {N}}(0,t-s)} (for 0 ≤ s ≤ t {\displaystyle 0\leq s\leq t} ). N...	{ "page_id": 4436, "title": "Brownian motion" }
of the origin infinitely often) whereas it is not recurrent in dimensions three and higher. Unlike the random walk, it is scale invariant. A d-dimensional Gaussian free field has been described as "a d-dimensional-time analog of Brownian motion." === Statistics === The Brownian motion can be modeled by a random walk. I...	{ "page_id": 4436, "title": "Brownian motion" }
} stands for the expected value. The power spectral density of Brownian motion is found to be S B M ( ω ) = 4 D ω 2 . {\displaystyle S_{BM}(\omega )={\frac {4D}{\omega ^{2}}}.} where D is the diffusion coefficient of Xt. For naturally occurring signals, the spectral content can be found from the power spectral density ...	{ "page_id": 4436, "title": "Brownian motion" }
formally defined power spectral density S ( ω ) {\displaystyle S(\omega )} , but its coefficient of variation γ = σ / μ {\displaystyle \gamma =\sigma /\mu } tends to 5 / 2 {\displaystyle {\sqrt {5}}/2} . This implies the distribution of S ( 1 ) ( ω , T ) {\displaystyle S^{(1)}(\omega ,T)} is broad even in the infinite ...	{ "page_id": 4436, "title": "Brownian motion" }
escape problem is that of calculating the mean escape time. This time diverges as the window shrinks, thus rendering the calculation a singular perturbation problem. == See also == == References == == Further reading == Brown, Robert (1828). "A brief account of microscopical observations made in the months of June, Jul...	{ "page_id": 4436, "title": "Brownian motion" }
Motion. (PDF version of this out-of-print book, from the author's webpage.) This is primarily a mathematical work, but the first four chapters discuss the history of the topic, in the era from Brown to Einstein. Pearle, P.; Collett, B.; Bart, K.; Bilderback, D.; Newman, D.; Samuels, S. (2010). "What Brown saw and you c...	{ "page_id": 4436, "title": "Brownian motion" }
Feature engineering is a preprocessing step in supervised machine learning and statistical modeling which transforms raw data into a more effective set of inputs. Each input comprises several attributes, known as features. By providing models with relevant information, feature engineering significantly enhances their p...	{ "page_id": 46207323, "title": "Feature engineering" }
are popular in multi-view feature engineering. == Predictive modelling == Feature engineering in machine learning and statistical modeling involves selecting, creating, transforming, and extracting data features. Key components include feature creation from existing data, transforming and imputing missing or invalid fe...	{ "page_id": 46207323, "title": "Feature engineering" }
tuple id propagation. === Open-source implementations === There are a number of open-source libraries and tools that automate feature engineering on relational data and time series: featuretools is a Python library for transforming time series and relational data into feature matrices for machine learning. MCMD: An ope...	{ "page_id": 46207323, "title": "Feature engineering" }
being used to either train models (by data scientists) or make predictions (by applications that have a trained model). It is a central location where you can either create or update groups of features created from multiple different data sources, or create and update new datasets from those feature groups for training...	{ "page_id": 46207323, "title": "Feature engineering" }
Chromium sulfate may refer to: Chromium(II) sulfate Chromium(III) sulfate	{ "page_id": 18682204, "title": "Chromium sulfate" }
Hydroxybutyraldehyde may refer to: 3-Hydroxybutyraldehyde (acetaldol), an aldol, formally the product of the dimerization of acetaldehyde 4-Hydroxybutyraldehyde, a chemical intermediate == See also == Hydroxybutanal	{ "page_id": 59183452, "title": "Hydroxybutyraldehyde" }
Harrington paradox is a notion in the environmental and ecological economics describing the compliance of firms to the environmental regulations. The paradox was first described in Winston Harrington's paper in 1988 and was based on the research over monitoring, realization and compliance to environmental regulations i...	{ "page_id": 26349919, "title": "Harrington paradox" }
Norway there is low frequency of monitoring and the fine system for minor violations is light can not bring strong evidence to the paradox, as major violations imply very strict punishments which is conforming to the rational crime theory. == External links == https://books.google.com/books?id=JQ0vBINSp_MC&pg=PA209 htt...	{ "page_id": 26349919, "title": "Harrington paradox" }
The molecular formula C18H34O2 (molar mass: 282.46 g/mol, exact mass: 282.2559 u) may refer to: Elaidic acid Octadecanolide Oleic acid Petroselinic acid	{ "page_id": 23662943, "title": "C18H34O2" }
Browning is the process of food turning brown due to the chemical reactions that take place within. The process of browning is one of the chemical reactions that take place in food chemistry and represents an interesting research topic regarding health, nutrition, and food technology. Though there are many different wa...	{ "page_id": 987492, "title": "Food browning" }
flavor in dried fruit such as figs and raisins. Examples of non-beneficial enzymatic browning: Fresh fruit and vegetables, including apples, potatoes, bananas and avocados. Oxidation of polyphenols is the major cause of melanosis in crustaceans such as shrimp. == Control of enzymatic browning == The control of enzymati...	{ "page_id": 987492, "title": "Food browning" }
and fruits. Refrigeration is also used during distribution and retailing of fruits and vegetables. Oxygen elimination − Presence of oxygen is crucial for enzymatic browning, therefore eliminating oxygen from the environment helps to slow down the browning reaction. Withdrawing air or replacing it with other gases (e.g....	{ "page_id": 987492, "title": "Food browning" }
initiation of the browning process. Also, they interfere with intermediate products of the following reactions and inhibit melanin formation. Ascorbic acid, N-acetylcysteine, L-cysteine, 4-hexylresorcinol, erythorbic acid, cysteine hydrochloride, glutathione are examples of antioxidants that have been studied for their...	{ "page_id": 987492, "title": "Food browning" }
partial vapor pressure of pure water at the same temperature). Caramelization is a process involving the pyrolysis of sugar. It is used extensively in cooking for the desired nutty flavor and brown color. As the process occurs, volatile chemicals are released, producing the characteristic caramel flavor. The other non-...	{ "page_id": 987492, "title": "Food browning" }
in the cytoplasm) triggers the oxidation of the grape. Thus, the initial browning of grapes occurs as a result of "compartmentalization modification" in the cells of the grape. == Implications in food industry and technology == Enzymatic browning affects the color, flavor, and nutritional value of foods, causing huge e...	{ "page_id": 987492, "title": "Food browning" }
shrimp, is a staple consumed by people all over the world. The browning of shrimp, which is actually referred to as melanosis, creates a great concern for food handlers and consumers. Melanosis mainly occurs during postmortem handling and refrigerated storage. Recent studies have found a plant extract that acts as an a...	{ "page_id": 987492, "title": "Food browning" }
The Hayashi rearrangement is the chemical reaction of ortho-benzoylbenzoic acids catalyzed by sulfuric acid or phosphorus pentoxide. This reaction proceeds through electrophilic acylium ion attack with a spiro intermediate. == References ==	{ "page_id": 8196452, "title": "Hayashi rearrangement" }
Papovaviricetes is a class of viruses. The class shares the name of an abolished family, Papovaviridae, which was split in 1999 into the two families Papillomaviridae and Polyomaviridae. The class was established in 2019 and takes its name from the former family. == Orders == The following orders are recognized: Sepoly...	{ "page_id": 63770985, "title": "Papovaviricetes" }
Oleosins are structural proteins found in vascular plant oil bodies and in plant cells. Oil bodies are not considered organelles because they have a single layer membrane and lack the pre-requisite double layer membrane in order to be considered an organelle. They are found in plant parts with high oil content that und...	{ "page_id": 10162537, "title": "Oleosin" }
cosmetics. == Usage == Oleosins provide an easy way of purifying proteins which have been produced recombinantly in plants. If the protein is made as a fusion protein with oleosin and a protease recognition site is incorporated between them, the fusion protein will sit in the membrane of the oil body, which can be easi...	{ "page_id": 10162537, "title": "Oleosin" }
Particulate organic matter (POM) is a fraction of total organic matter operationally defined as that which does not pass through a filter pore size that typically ranges in size from 0.053 millimeters (53 μm) to 2 millimeters. Particulate organic carbon (POC) is a closely related term often used interchangeably with PO...	{ "page_id": 49090922, "title": "Particulate organic matter" }
combustible, non-carbonate carbon that can be collected on a filter. The oceanographic community has historically used a variety of filters and pore sizes, most commonly 0.7, 0.8, or 1.0 μm glass or quartz fiber filters. The biomass of living zooplankton is intentionally excluded from POC through the use of a pre-filte...	{ "page_id": 49090922, "title": "Particulate organic matter" }
organic matter in soils can be grouped into four distinct categories on the basis of size, behaviour and persistence. These categories are arranged in order of decreasing ability to decompose. Each of them contribute to soil health in different ways. Dissolved organic matter (DOM): is the organic matter which dissolves...	{ "page_id": 49090922, "title": "Particulate organic matter" }
moist) and usually has a turnover time of less than 10 years. Less active parts may take 15 to 100 years to turnover. Where it is still at the soil surface and relatively fresh, particulate organic matter intercepts the energy of raindrops and protects physical soil surfaces from damage. As it is decomposes, particulat...	{ "page_id": 49090922, "title": "Particulate organic matter" }
and nutrients, rapid build-up of organic matter in water can result in eutrophication. Suspended organic materials can also serve as a potential vector for the pollution of water with fecal bacteria, toxic metals or organic compounds. == Marine ecosystems == Life and particulate organic matter in the ocean have fundame...	{ "page_id": 49090922, "title": "Particulate organic matter" }
Marine primary production can be divided into new production from allochthonous nutrient inputs to the euphotic zone, and regenerated production from nutrient recycling in the surface waters. The total new production in the ocean roughly equates to the sinking flux of particulate organic matter to the deep ocean, about...	{ "page_id": 49090922, "title": "Particulate organic matter" }
linearly with excess density (the difference from the water density) and the square of particle diameter (i.e., linearly with the particle area). Building on these expectations, many studies have tried to relate sinking velocity primarily to size, which has been shown to be a useful predictor for particles generated in...	{ "page_id": 49090922, "title": "Particulate organic matter" }

Subsets and Splits

No community queries yet

The top public SQL queries from the community will appear here once available.