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Company (renamed Alcoa in 1907) and Aluminium Industrie AG. The British Aluminium Company, Produits Chimiques d’Alais et de la Camargue, and Société Electro-Métallurgique de Froges also joined the cartel. By the mid-20th century, aluminium had become a part of everyday life and an essential component of housewares. In ...	{ "page_id": 904, "source": null, "title": "Aluminium" }
to grow in the 1970s with the rise of energy cost. Production moved from the industrialized countries to countries where production was cheaper. Production costs in the late 20th century changed because of advances in technology, lower energy prices, exchange rates of the United States dollar, and alumina prices. The B...	{ "page_id": 904, "source": null, "title": "Aluminium" }
in Latin, so this name was not adopted universally. This name was criticized by contemporary chemists from France, Germany, and Sweden, who insisted the metal should be named for the oxide, alumina, from which it would be isolated. The English name alum does not come directly from Latin, whereas alumine/alumina comes f...	{ "page_id": 904, "source": null, "title": "Aluminium" }
England and Germany Davy's spelling aluminum was initially used; until German chemist Friedrich Wöhler published his account of the Wöhler process in 1827 in which he used the spelling aluminium, which caused that spelling's largely wholesale adoption in England and Germany, with the exception of a small number of what...	{ "page_id": 904, "source": null, "title": "Aluminium" }
also acknowledges this spelling. IUPAC official publications use the -ium spelling as primary, and they list both where it is appropriate. == Production and refinement == The production of aluminium starts with the extraction of bauxite rock from the ground. The bauxite is processed and transformed using the Bayer proc...	{ "page_id": 904, "source": null, "title": "Aluminium" }
solution and discarded. The solution, free of solids, is seeded with small crystals of aluminium hydroxide; this causes decomposition of the [Al(OH)4]− ions to aluminium hydroxide. After about half of aluminium has precipitated, the mixture is sent to classifiers. Small crystals of aluminium hydroxide are collected to ...	{ "page_id": 904, "source": null, "title": "Aluminium" }
aluminium with a purity of above 99%. Further purification can be done by the Hoopes process. This process involves the electrolysis of molten aluminium with a sodium, barium, and aluminium fluoride electrolyte. The resulting aluminium has a purity of 99.99%. Electric power represents about 20 to 40% of the cost of pro...	{ "page_id": 904, "source": null, "title": "Aluminium" }
almost always alloyed, which markedly improves its mechanical properties, especially when tempered. For example, the common aluminium foils and beverage cans are alloys of 92% to 99% aluminium. The main alloying agents for both wrought and cast aluminium are copper, zinc, magnesium, manganese, and silicon (e.g., duralu...	{ "page_id": 904, "source": null, "title": "Aluminium" }
inert alumina. Another principal use is as a drying agent or absorbent. Several sulfates of aluminium have industrial and commercial application. Aluminium sulfate (in its hydrate form) is produced on the annual scale of several millions of metric tons. About two-thirds is consumed in water treatment. The next major ap...	{ "page_id": 904, "source": null, "title": "Aluminium" }
to allow the protein in the vaccine to achieve sufficient potency as an immune stimulant. Until 2004, most of the adjuvants used in vaccines were aluminium-adjuvanted. == Biology == Despite its widespread occurrence in the Earth's crust, aluminium has no known function in biology. At pH 6–9 (relevant for most natural w...	{ "page_id": 904, "source": null, "title": "Aluminium" }
can cause anemia. During the 1988 Camelford water pollution incident, people in Camelford had their drinking water contaminated with aluminium sulfate for several weeks. A final report into the incident in 2013 concluded it was unlikely that this had caused long-term health problems. Aluminium has been suspected of bei...	{ "page_id": 904, "source": null, "title": "Aluminium" }
of aluminium in nerve and bone tissues. === Treatment === In case of suspected sudden intake of a large amount of aluminium, the only treatment is deferoxamine mesylate which may be given to help eliminate aluminium from the body by chelation therapy. However, this should be applied with caution as this reduces not onl...	{ "page_id": 904, "source": null, "title": "Aluminium" }
the environment on each step of the production process. The major challenge is the emission of greenhouse gases. These gases result from electrical consumption of the smelters and the byproducts of processing. The most potent of these gases are perfluorocarbons, namely CF4 and C2F6, from the smelting process. Biodegrad...	{ "page_id": 904, "source": null, "title": "Aluminium" }
Institute of Technology Press, 2014. == External links == Aluminium at The Periodic Table of Videos (University of Nottingham) Toxicological Profile for Aluminum (PDF) (September 2008) – 357-page report from the United States Department of Health and Human Services, Public Health Service, Agency for Toxic Substances an...	{ "page_id": 904, "source": null, "title": "Aluminium" }
A generalized compound is a mixture of chemical compounds of constant composition, despite possible changes in the total amount. The concept is used in the Dynamic Energy Budget theory, where biomass is partitioned into a limited set of generalised compounds, which contain a high percentage of organic compounds. The am...	{ "page_id": 5637003, "source": null, "title": "Generalised compound" }
This page provides supplementary chemical data on carbon monoxide. == Material safety data sheet == The handling of this chemical may incur notable safety precautions. It is highly recommended that you seek the material safety data sheet (MSDS) for this chemical from a reliable source such as SIRI, and follow its direc...	{ "page_id": 2163601, "source": null, "title": "Carbon monoxide (data page)" }
This page provides supplementary chemical data on n-hexane. == Material Safety Data Sheet == The handling of this chemical may incur notable safety precautions. It is highly recommend that you seek the Material Safety Datasheet (MSDS) for this chemical from a reliable source and follow its directions. eChemPortal Scien...	{ "page_id": 11404178, "source": null, "title": "Hexane (data page)" }
Semi-deciduous or semi-evergreen is a botanical term which refers to plants that lose their foliage for a very short period, when old leaves fall off and new foliage growth is starting. This phenomenon occurs in tropical and sub-tropical woody species, for example in Dipteryx odorata. Semi-deciduous or semi-evergreen m...	{ "page_id": 5768086, "source": null, "title": "Semi-deciduous" }
Nano spray dryers refer to using spray drying to create particles in the nanometer range. Spray drying is a gentle method for producing powders with a defined particle size out of solutions, dispersions, and emulsions which is widely used for pharmaceuticals, food, biotechnology, and other industrial materials synthesi...	{ "page_id": 24118168, "source": null, "title": "Nano spray dryer" }
small sample amounts and the high yields, it is ideal for spray drying expensive substances in basic research. The following list shows examples of what is possible: Inhalable drugs for dry powder inhalers (DPI‘s) Nano- and microencapsulation of liposomes Stabilization of heat-sensitive vaccines, insulin, growth hormon...	{ "page_id": 24118168, "source": null, "title": "Nano spray dryer" }
advantage of a laminar flow is that the particles fall straight down from the spray head and do not stick to the glass wall. The laminar flow is produced by pressing the air through a porous metal foam. == Electrostatic particle collector == To collect the very fine particles a new technology is used in the field of "n...	{ "page_id": 24118168, "source": null, "title": "Nano spray dryer" }
In machine learning, the kernel perceptron is a variant of the popular perceptron learning algorithm that can learn kernel machines, i.e. non-linear classifiers that employ a kernel function to compute the similarity of unseen samples to training samples. The algorithm was invented in 1964, making it the first kernel c...	{ "page_id": 41485209, "source": null, "title": "Kernel perceptron" }
i α i y i K ( x i , x ′ ) {\displaystyle \operatorname {sgn} \sum _{i}\alpha _{i}y_{i}K(\mathbf {x} _{i},\mathbf {x'} )} . Here, K is some kernel function. Formally, a kernel function is a non-negative semidefinite kernel (see Mercer's condition), representing an inner product between samples in a high-dimensional spac...	{ "page_id": 41485209, "source": null, "title": "Kernel perceptron" }
{x} )\\&=\operatorname {sgn} \left(\sum _{i}^{n}\alpha _{i}y_{i}\mathbf {x} _{i}\right)^{\mathsf {T}}\mathbf {x} \\&=\operatorname {sgn} \sum _{i}^{n}\alpha _{i}y_{i}(\mathbf {x} _{i}\cdot \mathbf {x} )\end{aligned}}} Plugging these two equations into the training loop turn it into the dual perceptron algorithm. Finall...	{ "page_id": 41485209, "source": null, "title": "Kernel perceptron" }
with the kernel perceptron is that it does not regularize, making it vulnerable to overfitting. The NORMA online kernel learning algorithm can be regarded as a generalization of the kernel perceptron algorithm with regularization. The sequential minimal optimization (SMO) algorithm used to learn support vector machines...	{ "page_id": 41485209, "source": null, "title": "Kernel perceptron" }
Charusita Chakravarty (5 May 1964 – 29 March 2016) was an Indian academic and scientist. She was a professor of chemistry at the Indian Institute of Technology, Delhi since 1999. In 2009 she was conferred Shanti Swarup Bhatnagar Prize for Science and Technology in the field of chemical science. In 1999, she received B....	{ "page_id": 42206106, "source": null, "title": "Charusita Chakravarty" }
degree, even though she had a PhD from Cambridge. She did get an offer from IIT Kanpur, and then went on to accept a position in IIT Delhi's Department of Chemistry, where she continued to teach till her death. Soon after joining IIT Delhi, she submitted a research proposal to the Department of Science and Technology a...	{ "page_id": 42206106, "source": null, "title": "Charusita Chakravarty" }
silica, beryllium fluoride and water. Mol. Phys. 2008, 106, 1925. Agarwal, M. and Chakravarty, C. Waterlike structural and excess entropy anomalies in liquid beryllium fluoride. J. Phys. Chem. B, 2007, 111, 13294. Sharma, R., Nath, Chakraborty, S. N. and Charusita C. Entropy, Diffusivity and Structural Order in Liquids...	{ "page_id": 42206106, "source": null, "title": "Charusita Chakravarty" }
The Bacterial protein tyrosine-kinase database (BYKdb) is a specialized database of computer-annotated bacterial tyrosine-kinases that share no resemblance with their eukaryotic counterparts. == See also == Tyrosine-kinases == References == == External links == http://bykdb.ibcp.fr	{ "page_id": 34472859, "source": null, "title": "BYKdb" }
Detached eddy simulation (DES) is a modification of a Reynolds-averaged Navier–Stokes equations (RANS) model in which the model switches to a subgrid scale formulation in regions fine enough for large eddy simulation (LES) calculations. == Details == Regions near solid boundaries and where the turbulent length scale is...	{ "page_id": 2884506, "source": null, "title": "Detached eddy simulation" }
In molecular biology mir-216 microRNA is a short RNA molecule. MicroRNAs function to regulate the expression levels of other genes by several mechanisms. == See also == MicroRNA == References == == Further reading == == External links == Page for mir-216 microRNA precursor family at Rfam	{ "page_id": 36373405, "source": null, "title": "Mir-216 microRNA precursor family" }
A list of particle accelerators used for particle physics experiments. Some early particle accelerators that more properly did nuclear physics, but existed prior to the separation of particle physics from that field, are also included. Although a modern accelerator complex usually has several stages of accelerators, on...	{ "page_id": 3343262, "source": null, "title": "List of accelerators in particle physics" }
accelerator with a center-of-mass energy around the GUT scale. It would be light-weeks across and require the construction of a Dyson swarm around the Sun. Planckatron is an accelerator with a center-of-mass energy of the order of the Planck scale. It is estimated that the radius of the Planckatron would have to be rou...	{ "page_id": 3343262, "source": null, "title": "List of accelerators in particle physics" }
The rangeland health refers to the degree to which the integrity of the soil and ecological processes of rangeland ecosystems are sustained. The attributes evaluated during rangeland health assessments are 1) Soil and Site Stability 2) Hydrologic Function 3) Biotic Integrity. == References ==	{ "page_id": 72745888, "source": null, "title": "Rangeland health" }
Epis (, Haitian Creole: epis) is a blend of peppers, garlic, and herbs that is used as a flavor base for many foods in Haitian cuisine. Some refer to it as a pesto sauce. It is also known as epise and zepis. It is essential for Haitian cuisine. == Background == Epis has Taino and African origins. It also has similariti...	{ "page_id": 67371936, "source": null, "title": "Epis" }
See also == Sofrito Holy trinity Tempering (spices) Mirepoix Sauce == References ==	{ "page_id": 67371936, "source": null, "title": "Epis" }
Tellurium oxide may refer to: Tellurium monoxide, TeO Tellurium dioxide, TeO2 Tellurium trioxide, TeO3	{ "page_id": 27591586, "source": null, "title": "Tellurium oxide" }
V. Parmeswaran Nair is a physicist, currently a Distinguished Professor at City College of New York, holding it since September 2011, and is also a published author. == Early life and education == Nair received a bachelor degree in 1976 and a masters degree in 1978 at the University of Kerala in India. He also received...	{ "page_id": 52429737, "source": null, "title": "V. Parmeswaran Nair" }
A pheromone trap is a type of insect trap that uses pheromones to lure insects. Sex pheromones and aggregating pheromones are the most common types used. A pheromone-impregnated lure is encased in a conventional trap such as a bottle trap, delta trap, water-pan trap, or funnel trap. Pheromone traps are used both to cou...	{ "page_id": 24118186, "source": null, "title": "Pheromone trap" }
and when they fly off, the pheromones make them attractive to other males. It is hoped that if enough males chase other males instead of females, egg-laying will be severely impeded. Some difficulties surrounding pheromone traps include sensitivity to bad weather, their ability to attract pests from neighboring areas, ...	{ "page_id": 24118186, "source": null, "title": "Pheromone trap" }
CompHEP is a software package for automatic computations in high energy physics from Lagrangians to collision events or particle decays. CompHEP is based on quantum theory of gauge fields, namely it uses the technique of squared Feynman diagrams at the tree-level approximation. By default, CompHEP includes the Standard...	{ "page_id": 12125099, "source": null, "title": "CompHEP" }
In mathematical statistics, the Kullback–Leibler (KL) divergence (also called relative entropy and I-divergence), denoted D KL ( P ∥ Q ) {\displaystyle D_{\text{KL}}(P\parallel Q)} , is a type of statistical distance: a measure of how much a model probability distribution Q is different from a true probability distribu...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
a measured probability distribution. Distribution Q represents instead a theory, a model, a description or an approximation of P. The Kullback–Leibler divergence D KL ( P ∥ Q ) {\displaystyle D_{\text{KL}}(P\parallel Q)} is then interpreted as the average difference of the number of bits required for encoding samples o...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
symmetrized divergence does not satisfy the triangle inequality. Numerous references to earlier uses of the symmetrized divergence and to other statistical distances are given in Kullback (1959, pp. 6–7, §1.3 Divergence). The asymmetric "directed divergence" has come to be known as the Kullback–Leibler divergence, whil...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
→ 0 + x log ⁡ ( x ) = 0 . {\displaystyle \lim _{x\to 0^{+}}x\,\log(x)=0\,.} For distributions P and Q of a continuous random variable, relative entropy is defined to be the integral D KL ( P ∥ Q ) = ∫ − ∞ ∞ p ( x ) log ⁡ p ( x ) q ( x ) d x , {\displaystyle D_{\text{KL}}(P\parallel Q)=\int _{-\infty }^{\infty }p(x)\,\l...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
the entropy of P relative to Q. Continuing in this case, if μ {\displaystyle \mu } is any measure on X {\displaystyle {\mathcal {X}}} for which densities p and q with P ( d x ) = p ( x ) μ ( d x ) {\displaystyle P(dx)=p(x)\mu (dx)} and Q ( d x ) = q ( x ) μ ( d x ) {\displaystyle Q(dx)=q(x)\mu (dx)} exist (meaning that...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
in the relation. Sometimes, as in this article, it may be described as the divergence of P from Q or as the divergence from Q to P. This reflects the asymmetry in Bayesian inference, which starts from a prior Q and updates to the posterior P. Another common way to refer to D KL ( P ∥ Q ) {\displaystyle D_{\text{KL}}(P\...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
ln ⁡ 3 − 50 ln ⁡ 5 ) ≈ 0.0852996 , {\displaystyle {\begin{aligned}D_{\text{KL}}(P\parallel Q)&=\sum _{x\in {\mathcal {X}}}P(x)\,\ln {\frac {P(x)}{Q(x)}}\\&={\frac {9}{25}}\ln {\frac {9/25}{1/3}}+{\frac {12}{25}}\ln {\frac {12/25}{1/3}}+{\frac {4}{25}}\ln {\frac {4/25}{1/3}}\\&={\frac {1}{25}}\left(32\ln 2+55\ln 3-50\ln...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
often called the information gain achieved if P would be used instead of Q which is currently used. By analogy with information theory, it is called the relative entropy of P with respect to Q. Expressed in the language of Bayesian inference, D KL ( P ∥ Q ) {\displaystyle D_{\text{KL}}(P\parallel Q)} is a measure of th...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
one to minimize relative entropy by geometric means, for example by information projection and in maximum likelihood estimation. The relative entropy is the Bregman divergence generated by the negative entropy, but it is also of the form of an f-divergence. For probabilities over a finite alphabet, it is unique in bein...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
as representing an implicit probability distribution q ( x i ) = 2 − ℓ i {\displaystyle q(x_{i})=2^{-\ell _{i}}} over X, where ℓ i {\displaystyle \ell _{i}} is the length of the code for x i {\displaystyle x_{i}} in bits. Therefore, relative entropy can be interpreted as the expected extra message-length per datum that...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
P ) {\displaystyle H(P)} to make D KL ( P ∥ Q ) {\displaystyle D_{\text{KL}}(P\parallel Q)} agree more closely with our notion of distance, as the excess loss. The resulting function is asymmetric, and while this can be symmetrized (see § Symmetrised divergence), the asymmetric form is more useful. See § Interpretation...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
be transmitted to identify a value x drawn from X, if a code is used corresponding to the probability distribution Q, rather than the "true" distribution P. No upper-bound exists for the general case. However, it is shown that if P and Q are two discrete probability distributions built by distributing the same discrete...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
) \| d y d x \| d x = ∫ y a y b p ~ ( y ) log ⁡ p ~ ( y ) q ~ ( y ) d y {\displaystyle {\begin{aligned}D_{\text{KL}}(P\parallel Q)&=\int _{x_{a}}^{x_{b}}p(x)\,\log {\frac {p(x)}{q(x)}}\,dx\\[6pt]&=\int _{x_{a}}^{x_{b}}{\tilde {p}}(y(x))\left\|{\frac {dy}{dx}}\right\|\log {\frac {{\tilde {p}}(y(x))\,\left\|{\frac {dy}{dx}}\r...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
KL ( P 2 ∥ Q 2 ) . {\displaystyle D_{\text{KL}}(P\parallel Q)=D_{\text{KL}}(P_{1}\parallel Q_{1})+D_{\text{KL}}(P_{2}\parallel Q_{2}).} Relative entropy D KL ( P ∥ Q ) {\displaystyle D_{\text{KL}}(P\parallel Q)} is convex in the pair of probability measures ( P , Q ) {\displaystyle (P,Q)} , i.e. if ( P 1 , Q 1 ) {\disp...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
0 , Σ 1 . {\displaystyle \Sigma _{0},\Sigma _{1}.} If the two distributions have the same dimension, k, then the relative entropy between the distributions is as follows: D KL ( N 0 ∥ N 1 ) = 1 2 [ tr ⁡ ( Σ 1 − 1 Σ 0 ) − k + ( μ 1 − μ 0 ) T Σ 1 − 1 ( μ 1 − μ 0 ) + ln ⁡ det Σ 1 det Σ 0 ] . {\displaystyle D_{\text{KL}}\l...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
i i ( L 0 ) i i ) . {\displaystyle D_{\text{KL}}\left({\mathcal {N}}_{0}\parallel {\mathcal {N}}_{1}\right)={\frac {1}{2}}\left(\sum _{i,j=1}^{k}{\left(M_{ij}\right)}^{2}-k+\|y\|^{2}+2\sum _{i=1}^{k}\ln {\frac {(L_{1})_{ii}}{(L_{0})_{ii}}}\right).} A special case, and a common quantity in variational inference, is the re...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
< B ≤ D {\displaystyle C\leq A<B\leq D} ). Then the information gain is: D KL ( p ∥ q ) = log ⁡ D − C B − A {\displaystyle D_{\text{KL}}\left({\mathcal {p}}\parallel {\mathcal {q}}\right)=\log {\frac {D-C}{B-A}}} Intuitively, the information gain to a k times narrower uniform distribution contains log 2 ⁡ k {\displayst...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
the sufficient statistics T ( x ) = x {\displaystyle T(x)=x} , the natural parameter θ = log ⁡ λ {\displaystyle \theta =\log \lambda } , and log partition function A ( θ ) = e θ {\displaystyle A(\theta )=e^{\theta }} . As such, the divergence between two Poisson distributions with means λ 1 {\displaystyle \lambda _{1}}...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
. {\displaystyle D_{\text{KL}}(\mu \parallel \lambda )=(\mu -\log \lambda )\mu -{\frac {\mu ^{2}}{2}}+\lambda .} == Relation to metrics == While relative entropy is a statistical distance, it is not a metric on the space of probability distributions, but instead it is a divergence. While metrics are symmetric and gener...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
a small amount from the parameter value θ 0 {\displaystyle \theta _{0}} . Specifically, up to first order one has (using the Einstein summation convention) P ( θ ) = P ( θ 0 ) + Δ θ j P j ( θ 0 ) + ⋯ {\displaystyle P(\theta )=P(\theta _{0})+\Delta \theta _{j}\,P_{j}(\theta _{0})+\cdots } with Δ θ j = ( θ − θ 0 ) j {\di...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
θ ) ∥ P ( θ 0 ) ) {\displaystyle g_{jk}(\theta _{0})=\left.{\frac {\partial ^{2}}{\partial \theta _{j}\,\partial \theta _{k}}}\right\|_{\theta =\theta _{0}}D_{\text{KL}}(P(\theta )\parallel P(\theta _{0}))} must be positive semidefinite. Letting θ 0 {\displaystyle \theta _{0}} vary (and dropping the subindex 0) the Hess...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
\left.\int _{x=0}^{\infty }{\frac {\partial p(x,\rho )}{\partial \rho }}\right\|_{\rho =0}\,dx=\left.\int _{x=0}^{\infty }{\frac {\partial ^{2}p(x,\rho )}{\partial \rho ^{2}}}\right\|_{\rho =0}\,dx=0} then: D ( p ( x , 0 ) ∥ p ( x , ρ ) ) = c ρ 2 2 + O ( ρ 3 ) as ρ → 0. {\displaystyle {\mathcal {D}}(p(x,0)\parallel p(x,\...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
not the fact that i = m {\displaystyle i=m} . === Mutual information === The mutual information, I ⁡ ( X ; Y ) = D KL ( P ( X , Y ) ∥ P ( X ) P ( Y ) ) = E X ⁡ { D KL ( P ( Y ∣ X ) ∥ P ( Y ) ) } = E Y ⁡ { D KL ( P ( X ∣ Y ) ∥ P ( X ) ) } {\displaystyle {\begin{aligned}\operatorname {I} (X;Y)&=D_{\text{KL}}(P(X,Y)\paral...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
{\displaystyle P_{U}(X)} , from the true distribution P ( X ) {\displaystyle P(X)} — i.e. less the expected number of bits saved, which would have had to be sent if the value of X were coded according to the uniform distribution P U ( X ) {\displaystyle P_{U}(X)} rather than the true distribution P ( X ) {\displaystyle...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
of bits which would have to be transmitted to identify X from N equally likely possibilities, less the relative entropy of the product distribution P U ( X ) P ( Y ) {\displaystyle P_{U}(X)P(Y)} from the true joint distribution P ( X , Y ) {\displaystyle P(X,Y)} — i.e. less the expected number of bits saved which would...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
a set of possibilities, if a coding scheme is used based on a given probability distribution q, rather than the "true" distribution p. The cross entropy for two distributions p and q over the same probability space is thus defined as follows. H ( p , q ) = E p ⁡ [ − log ⁡ q ] = H ( p ) + D KL ( p ∥ q ) . {\displaystyle...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
⁡ p ( x ∣ y , I ) , {\displaystyle \mathrm {H} {\big (}p(x\mid y,I){\big )}=-\sum _{x}p(x\mid y,I)\log p(x\mid y,I),} which may be less than or greater than the original entropy H ( p ( x ∣ I ) ) {\displaystyle \mathrm {H} (p(x\mid I))} . However, from the standpoint of the new probability distribution one can estimate...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
⁡ p ( x ∣ y 1 , y 2 , I ) p ( x ∣ I ) {\displaystyle \sum _{x}p(x\mid y_{1},y_{2},I)\log {\frac {p(x\mid y_{1},y_{2},I)}{p(x\mid I)}}} may be ≤ or > than ∑ x p ( x ∣ y 1 , I ) log ⁡ p ( x ∣ y 1 , I ) p ( x ∣ I ) {\textstyle \sum _{x}p(x\mid y_{1},I)\log {\frac {p(x\mid y_{1},I)}{p(x\mid I)}}} and so the combined inform...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
H 0 {\displaystyle H_{0}} : the mean information per sample for discriminating in favor of a hypothesis H 1 {\displaystyle H_{1}} against a hypothesis H 0 {\displaystyle H_{0}} , when hypothesis H 1 {\displaystyle H_{1}} is true. Another name for this quantity, given to it by I. J. Good, is the expected weight of evide...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
to how well each reflects the particular circumstances of the problem in question. === Principle of minimum discrimination information === The idea of relative entropy as discrimination information led Kullback to propose the Principle of Minimum Discrimination Information (MDI): given new facts, a new distribution f s...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
( x ∣ a ) {\displaystyle q(x\mid a)} . (Note that often the later expected value is called the conditional relative entropy (or conditional Kullback–Leibler divergence) and denoted by D KL ( q ( x ∣ a ) ∥ p ( x ∣ a ) ) {\displaystyle D_{\text{KL}}(q(x\mid a)\parallel p(x\mid a))} ) This is minimized if q ( x ∣ a ) = p ...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
KL ( p ∥ m ) {\displaystyle D_{\text{KL}}(p\parallel m)} subject to some constraint. This has led to some ambiguity in the literature, with some authors attempting to resolve the inconsistency by redefining cross-entropy to be D KL ( p ∥ m ) {\displaystyle D_{\text{KL}}(p\parallel m)} , rather than H ( p , m ) {\displa...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
{\displaystyle G=U+PV-TS} is minimized instead. The change in free energy under these conditions is a measure of available work that might be done in the process. Thus available work for an ideal gas at constant temperature T o {\displaystyle T_{o}} and pressure P o {\displaystyle P_{o}} is W = Δ G = N k T o Θ ( V / V ...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
For density matrices P and Q on a Hilbert space, the quantum relative entropy from Q to P is defined to be D KL ( P ∥ Q ) = Tr ⁡ ( P ( log ⁡ P − log ⁡ Q ) ) . {\displaystyle D_{\text{KL}}(P\parallel Q)=\operatorname {Tr} (P(\log P-\log Q)).} In quantum information science the minimum of D KL ( P ∥ Q ) {\displaystyle D_...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
likelihood and maximum spacing estimators. == Symmetrised divergence == Kullback & Leibler (1951) also considered the symmetrized function: D KL ( P ∥ Q ) + D KL ( Q ∥ P ) {\displaystyle D_{\text{KL}}(P\parallel Q)+D_{\text{KL}}(Q\parallel P)} which they referred to as the "divergence", though today the "KL divergence"...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
the two distributions, M = 1 2 ( P + Q ) . {\displaystyle M={\tfrac {1}{2}}\left(P+Q\right).} We can also interpret D JS {\displaystyle D_{\text{JS}}} as the capacity of a noisy information channel with two inputs giving the output distributions P and Q. The Jensen–Shannon divergence, like all f-divergences, is locally...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
as absolute entropy serves as theoretical background for data compression, relative entropy serves as theoretical background for data differencing – the absolute entropy of a set of data in this sense being the data required to reconstruct it (minimum compressed size), while the relative entropy of a target set of data...	{ "page_id": 1115052, "source": null, "title": "Kullback–Leibler divergence" }
A polar organic chemical integrative sampler (POCIS) is a passive sampling device which allows for the in situ collection of a time-integrated average of hydrophilic organic contaminants developed by researchers with the United States Geological Survey in Columbia, Missouri. POCIS provides a means for estimating the to...	{ "page_id": 42927021, "source": null, "title": "Polar organic chemical integrative sampler" }
pharmaceutical and personal care products in surface waters. The United States Geological Survey (USGS) has been heavily involved in the development of passive samplers and has articles in their database regarding the development of POCIS as early as 2000. The USGS Columbia Environmental Research Center (CERC) is a sel...	{ "page_id": 42927021, "source": null, "title": "Polar organic chemical integrative sampler" }
membranes which are then compressed between two stainless steel rings which expose a sampling area. A standard POCIS disk consists of a sampling surface area to sorbent mass ratio of approximately 180 cm2g. Because the amount of chemical sampled is directly related to the sample surface area, it is sometimes necessary ...	{ "page_id": 42927021, "source": null, "title": "Polar organic chemical integrative sampler" }
across the water boundary layer. The thickness of this layer is dependent on water flow and turbulence around the sampler and can significantly alter sampling rates. Second, the contaminant must transport across the membrane either through the water-filled pores or through the membrane itself. Finally, contaminants tra...	{ "page_id": 42927021, "source": null, "title": "Polar organic chemical integrative sampler" }
in the water without being buried in the sediment. It is ideal to place the sampler in moving water in order to increase sampling rates, however, areas with an extremely turbulent water flow should be avoided as to prevent damage to the POCIS device. Passive samplers are very vulnerable to vandalism and it is therefore...	{ "page_id": 42927021, "source": null, "title": "Polar organic chemical integrative sampler" }
1 μL). === Relevant contaminants === Any compound with a log Kow of less than or equal to 3 can concentrate in a POCIS sampler. Applicable classes of contaminants measured by POCIS are pharmaceuticals, household and industrial products, hormones, herbicides, and polar pesticides (Table 1). Currently, there are two POCI...	{ "page_id": 42927021, "source": null, "title": "Polar organic chemical integrative sampler" }
fractionation depending on the desired use of the sample. === Data analysis === After the sample has been processed, the extract can be analysed using a variety of data analysis techniques. The chemical analysis and analytical instrumentation used depends on the goal of the study. Many analyses require multiple samples...	{ "page_id": 42927021, "source": null, "title": "Polar organic chemical integrative sampler" }
are designed to mimic the bioconcentration of contaminants in fatty tissues (ITRC, 2006). Contaminants applicable to the use of an SPMD include, but are not limited to, polychlorinated biphenyls (PCBs), polycyclic aromatic hydrocarbons (PAHs), organochlorine pesticides, dioxins, and furans. The SPMD consist of a thin-w...	{ "page_id": 42927021, "source": null, "title": "Polar organic chemical integrative sampler" }
The marsh organ is a collection of plastic pipes attached to a wooden framework that is placed in marshes to measure the effects of inundation time and flood frequency on the productivity of marsh vegetation. The information is used for scientific research purposes. The marsh organ was developed by James Morris from th...	{ "page_id": 67568559, "source": null, "title": "Marsh organ" }
added nutrients and much more. Over time, scientists can gather information such as total plant biomass accumulation, total organic matter, peat formation, decomposition rates, and sedimentation. The data can be used to forecast the future health of the marsh being studied, and to infer how the marsh will respond to se...	{ "page_id": 67568559, "source": null, "title": "Marsh organ" }
while the species Carex lyngbyei survived significantly better around the highest tidal height. Both species also showed sensitivity to competitors, with S. tabernaemontani being the only species to germinate in the presence of competition. == External stressors == Along with the stress of rising sea levels, marsh vege...	{ "page_id": 67568559, "source": null, "title": "Marsh organ" }
marsh organ setup, researchers discovered that for marsh elevations higher than optimum expected at low sea level rise rates, acceleration in the rate of sea level rise will enhance root growth, organic accretion and wetland stability altogether. But, for sub-optimum marsh elevations expected at rapid sea level rise ra...	{ "page_id": 67568559, "source": null, "title": "Marsh organ" }
T790M, also known as Thr790Met, is a gatekeeper mutation of the epidermal growth factor receptor (EGFR). The mutation substitutes a threonine (T) with a methionine (M) at position 790 of exon 20, affecting the ATP binding pocket of the EGFR kinase domain. Threonine is a small polar amino acid; methionine is a larger no...	{ "page_id": 48563120, "source": null, "title": "T790M" }
Chlorodifluoroethane has the following isomers: 2-Chloro-1,1-difluoroethane (R-142) 1-Chloro-1,2-difluoroethane (R-142a) 1-Chloro-1,1-difluoroethane (R-142b)	{ "page_id": 40698799, "source": null, "title": "Chlorodifluoroethane" }
In molecular biology mir-241 microRNA is a short RNA molecule. MicroRNAs function to regulate the expression levels of other genes by several mechanisms. == See also == MicroRNA == References == == Further reading == == External links == Page for mir-241 microRNA precursor family at Rfam	{ "page_id": 36373427, "source": null, "title": "Mir-241 microRNA precursor family" }
Ubiquitin-conjugating enzymes, also known as E2 enzymes and more rarely as ubiquitin-carrier enzymes, perform the second step in the ubiquitination reaction that targets a protein for degradation via the proteasome. The ubiquitination process covalently attaches ubiquitin, a short protein of 76 amino acids, to a lysine...	{ "page_id": 8258485, "source": null, "title": "Ubiquitin-conjugating enzyme" }
proteins which can act as both and E2 and an E3 containing domains which cover both E2 and E3 functionality. == Isozymes == The following human genes encode ubiquitin-conjugating enzymes: == See also == Ubiquitin Ubiquitin-activating enzyme Ubiquitin ligase == References == == External links == Eukaryotic Linear Motif ...	{ "page_id": 8258485, "source": null, "title": "Ubiquitin-conjugating enzyme" }
The regulation of science refers to use of law, or other ruling, by academic or governmental bodies to allow or restrict science from performing certain practices, or researching certain scientific areas. Science could be regulated by legislation if areas are seen as harmful, immoral, or dangerous. For these reasons sc...	{ "page_id": 1311669, "source": null, "title": "Regulation of science" }
IRBs to review all the research done at the institution. These boards, generally composed of both scientific peers from the institution and lay persons, are tasked with assessing the risks and benefits associated with the use of human subjects, in addition to the adequacy of the protection and consent of the participan...	{ "page_id": 1311669, "source": null, "title": "Regulation of science" }
and sale of drugs. The Center for Drug Evaluation and Research (CDER) is responsible for reviewing new drug applications and requires clinical trials as proof of effectiveness. The Center for Biologics Evaluation and Research (CBER) is responsible for implementing federal regulations of biopharmaceuticals such as vacci...	{ "page_id": 1311669, "source": null, "title": "Regulation of science" }
a Supreme Court ruling in Epperson v. Arkansas in 1968. Since 2001, there has been a resurgence of anti-evolution bills, one of which, the Louisiana Science Education Act, was passed. This Act allows public schools to use supplementary material that is critical of the scientific theories such as evolution and global wa...	{ "page_id": 1311669, "source": null, "title": "Regulation of science" }
Kovács reagent is a biochemical reagent consisting of isoamyl alcohol, para-dimethylaminobenzaldehyde (DMAB), and concentrated hydrochloric acid. It is used for the diagnostical indole test, to determine the ability of the organism to split indole from the amino acid tryptophan. The indole produced yields a red complex...	{ "page_id": 34407360, "source": null, "title": "Kovac's reagent" }

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