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Equilibrium vapor pressure may differ significantly from saturation vapor pressure depending on the size of droplets and presence of other particles which act as cloud condensation nuclei.However, these terms are used inconsistently, and some authors use "saturation vapor pressure" outside the narrow meaning given by the AMS Glossary. For example, a text on atmospheric convection states, "The Kelvin effect causes the saturation vapor pressure over the curved surface of the droplet to be greater than that over a flat water surface" (emphasis added).The still-current term saturation vapor pressure derives from the obsolete theory that water vapor dissolves into air, and that air at a given temperature can only hold a certain amount of water before becoming "saturated". Actually, as stated by Dalton's law (known since 1802), the partial pressure of water vapor or any substance does not depend on air at all, and the relevant temperature is that of the liquid. Nevertheless, the erroneous belief persists among the public and even meteorologists, aided by the misleading terms saturation pressure and supersaturation and the related definition of relative humidity. | https://en.wikipedia.org/wiki/Saturation_pressure |
In meteorology, to see how effectively a mathematical model predicts the behavior of the atmosphere. In bioinformatics, the root-mean-square deviation of atomic positions is the measure of the average distance between the atoms of superimposed proteins. In structure based drug design, the RMSD is a measure of the difference between a crystal conformation of the ligand conformation and a docking prediction. | https://en.wikipedia.org/wiki/Root_mean_squared_error |
In economics, the RMSD is used to determine whether an economic model fits economic indicators. Some experts have argued that RMSD is less reliable than Relative Absolute Error. In experimental psychology, the RMSD is used to assess how well mathematical or computational models of behavior explain the empirically observed behavior. | https://en.wikipedia.org/wiki/Root_mean_squared_error |
In GIS, the RMSD is one measure used to assess the accuracy of spatial analysis and remote sensing. In hydrogeology, RMSD and NRMSD are used to evaluate the calibration of a groundwater model. In imaging science, the RMSD is part of the peak signal-to-noise ratio, a measure used to assess how well a method to reconstruct an image performs relative to the original image. | https://en.wikipedia.org/wiki/Root_mean_squared_error |
In computational neuroscience, the RMSD is used to assess how well a system learns a given model. In protein nuclear magnetic resonance spectroscopy, the RMSD is used as a measure to estimate the quality of the obtained bundle of structures. Submissions for the Netflix Prize were judged using the RMSD from the test dataset's undisclosed "true" values. | https://en.wikipedia.org/wiki/Root_mean_squared_error |
In the simulation of energy consumption of buildings, the RMSE and CV(RMSE) are used to calibrate models to measured building performance. In X-ray crystallography, RMSD (and RMSZ) is used to measure the deviation of the molecular internal coordinates deviate from the restraints library values. In control theory, the RMSE is used as a quality measure to evaluate the performance of a state observer. In fluid dynamics, normalized root-mean-square deviation (NRMSD), coefficient of variation (CV), and percent RMS are used to quantify the uniformity of flow behavior such as velocity profile, temperature distribution, or gas species concentration. The value is compared to industry standards to optimize the design of flow and thermal equipment and processes. | https://en.wikipedia.org/wiki/Root_mean_squared_error |
In meteorology, training denotes repeated areas of rain, typically associated with thunderstorms, that move over the same region in a relatively short period of time. Training thunderstorms are capable of producing excessive rainfall totals, often causing flash flooding. The name training is derived from how a train and its cars travel along a track (moving along a single path), without the track moving. | https://en.wikipedia.org/wiki/Training_(meteorology) |
In meteorology, weather datasets are acquired over many years of record and, as part of this, measurements at certain stations may cease occasionally while, at around the same time, measurements may start at nearby locations. There are then questions as to whether, if the records are combined to form a single longer set of records, those records can be considered homogeneous over time. An example of homogeneity testing of wind speed and direction data can be found in Romanić et al., 2015. | https://en.wikipedia.org/wiki/Heterogeneity_(statistics) |
In meteorology, where changes and effects of complex interactions in the atmosphere are studied, the weather reports often use fuzzy expressions indicating a broad trend, likelihood or level. The main reason is that the forecast can rarely be totally exact for any given location. In biology, protein complexes with multiple structural forms are called fuzzy complexes. | https://en.wikipedia.org/wiki/Fuzzy_concept |
The different conformations can result in different, even opposite functions. The conformational ensemble is modulated by the environmental conditions. | https://en.wikipedia.org/wiki/Fuzzy_concept |
Post-translational modifications or alternative splicing can also impact the ensemble and thereby the affinity or specificity of interactions. Genetic fuzzy systems use algorithms or genetic programming which simulate natural evolutionary processes, in order to understand their structures and parameters. In medical diagnosis, the assessment of what the symptoms of a patient are often cannot be very exactly specified, since there are many possible qualitative and quantitative gradations in severity, incidence or frequency that could occur. | https://en.wikipedia.org/wiki/Fuzzy_concept |
Different symptoms may also overlap to some extent. These gradations can be difficult to measure, it may cost a lot of time and money, and so the medical professionals might use approximate "fuzzy" categories in their judgement of a medical condition or a patient's condition. Although it may not be exact, the diagnosis is often useful enough for treatment purposes. | https://en.wikipedia.org/wiki/Fuzzy_concept |
Fuzzy logic is increasingly employed in diagnostic and medical equipment capable of measuring gradations of a condition. In information services, fuzzy concepts are frequently encountered because a customer or client asks a question about something which could be interpreted in different ways, or, a document is transmitted of a type or meaning which cannot be easily allocated to a known type or category, or to a known procedure. It might take considerable inquiry to "place" the information, or establish in what framework it should be understood. | https://en.wikipedia.org/wiki/Fuzzy_concept |
In phenomenology, which aims to study the structure of subjective experience without preconceptions, an important insight is that how someone experiences something can be influenced both by the influence of the thing being experienced itself, but also by how the person responds to it. Thus, the actual experience the person has, is shaped by an "interactive object-subject relationship". To describe this experience, fuzzy categories are often necessary, since it is often impossible to predict or describe with great exactitude what the interaction will be, and how it is experienced. | https://en.wikipedia.org/wiki/Fuzzy_concept |
In translation work, fuzzy concepts are analyzed for the purpose of good translation. A concept in one language may not have quite the same meaning or significance in another language, or it may not be feasible to translate it literally, or at all. Some languages have concepts which do not exist in another language, raising the problem of how one would most easily render their meaning. | https://en.wikipedia.org/wiki/Fuzzy_concept |
In computer-assisted translation, a technique called fuzzy matching is used to find the most likely translation of a piece of text, using previous translated texts as a basis. In hypnotherapy, fuzzy language is deliberately used for the purpose of trance induction. Hypnotic suggestions are often couched in a somewhat vague, general or ambiguous language requiring interpretation by the subject. | https://en.wikipedia.org/wiki/Fuzzy_concept |
The intention is to distract and shift the conscious awareness of the subject away from external reality to her own internal state. In response to the somewhat confusing signals she gets, the awareness of the subject spontaneously tends to withdraw inward, in search of understanding or escape. In business and economics, it was discovered that "we are guided less by a correct exact knowledge of our self-interest than by a socially learned, evolved, intuitive grasp derived from mental shortcuts (frames, reference points, envy, addiction, temptation, fairness)". | https://en.wikipedia.org/wiki/Fuzzy_concept |
Thus, economic preferences are often fuzzy preferences, a highly important point for suppliers of products and services. Fuzzy set empirical methodologies are increasingly used by economic analysts to analyze the extent to which members of a population belong to a specific market category, because that can make a big difference to business results. In sexology, sex and gender are conceptualized by gender pluralists as a spectrum or continuum, or a set of scaled characteristics. | https://en.wikipedia.org/wiki/Fuzzy_concept |
Thus, the idea that people are either heterosexual men, heterosexual women, gay, lesbian, bisexual or transsexual is far too simplistic; gender identity is a matter of degree, a graded concept, which for that very reason is a fuzzy concept with unsharp boundaries. For example, somebody who is "mainly" heterosexual, may occasionally have had non-heterosexual contacts, without this warranting a definite "bisexual" label. A great variety of sexual orientations are possible and can co-exist. | https://en.wikipedia.org/wiki/Fuzzy_concept |
In the course of history, typical male or female gender roles and gender characteristics can also gradually change, so that the extent to which they express "masculine" or "feminine" traits is, at any time, a matter of degree, i.e. fuzzy. In politics, it can be highly important and problematic how exactly a conceptual distinction is drawn, or indeed whether a distinction is drawn at all; distinctions used in administration may be deliberately sharpened, or kept fuzzy, due to some political motive or power relationship. Politicians may be deliberately vague about some things, and very clear and explicit about others; if there is information that proves their case, they become very precise, but if the information doesn't prove their case, they become vague or say nothing. | https://en.wikipedia.org/wiki/Fuzzy_concept |
In statistical research, it is an aim to measure the magnitudes of phenomena. For this purpose, phenomena have to be grouped and categorized, so that distinct and discrete counting units can be defined. It must be possible to allocate all observations to mutually exclusive categories, so that they are properly quantifiable. | https://en.wikipedia.org/wiki/Fuzzy_concept |
Survey observations do not spontaneously transform themselves into countable data; they have to be identified, categorized and classified in such a way, that identical observations can be grouped together, and that observations are not counted twice or more. A well-designed questionnaire ensures that the questions are interpreted in the same way by all respondents, and that the respondents are really able to answer them within the formats provided. Again, for this purpose, it is a requirement that the concepts being used are exactly and comprehensibly defined for all concerned, and not fuzzy. | https://en.wikipedia.org/wiki/Fuzzy_concept |
There could be a margin of measurement error, but the amount of error must be kept within tolerable limits, and preferably its magnitude should be known. In theology an attempt is made to define more precisely the meaning of spiritual concepts, which refer to how human beings construct the meaning of human existence, and, often, the relationship people have with a supernatural world. Many spiritual concepts and beliefs are fuzzy, to the extent that, although abstract, they often have a highly personalized meaning, or involve personal interpretation of a type that is not easy to define in a cut-and-dried way. | https://en.wikipedia.org/wiki/Fuzzy_concept |
A similar situation occurs in psychotherapy. The Dutch theologian Kees de Groot has explored the imprecise notion that psychotherapy is like an "implicit religion", defined as a "fuzzy concept" (it all depends on what one means by "psychotherapy" and "religion"). The philosopher of spirituality Ken Wilber argued that "nothing is 100% right or wrong", things merely "vary in their degree of incompleteness and dysfunction"; no one and nothing is 100% good or evil, each just varies "in their degree of ignorance and disconnection". | https://en.wikipedia.org/wiki/Fuzzy_concept |
This insight suggests, that all human valuations can be considered as graded concepts, where each qualitative judgement has at least implicitly a sense of quantitative proportion attached to it. In the legal system, it is essential that rules are interpreted and applied in a standard way, so that the same sorts of cases and the same sorts of circumstances are treated equally. Otherwise one would be accused of arbitrariness, which would not serve the interests of justice. | https://en.wikipedia.org/wiki/Fuzzy_concept |
Consequently, lawmakers aim to devise definitions and categories which are sufficiently precise, so that they are not open to different interpretations. For this purpose, it is critically important to remove fuzziness, and differences of interpretation are typically resolved through a court ruling based on evidence. Alternatively, some other procedure is devised which permits the correct distinction to be discovered and made. In administration, archiving and accounting, fuzziness problems in interpretation and boundary problems can arise, because it is not clear to what category exactly a case, item, document, transaction or piece of data belongs. In principle, each case, event or item must be allocated to the correct category in a procedure, but it may be, that it is difficult to make the appropriate or relevant distinctions. | https://en.wikipedia.org/wiki/Fuzzy_concept |
In meteorology, wind speed, or wind flow speed, is a fundamental atmospheric quantity caused by air moving from high to low pressure, usually due to changes in temperature. Wind speed is now commonly measured with an anemometer. Wind speed affects weather forecasting, aviation and maritime operations, construction projects, growth and metabolism rate of many plant species, and has countless other implications. Wind direction is usually almost parallel to isobars (and not perpendicular, as one might expect), due to Earth's rotation. | https://en.wikipedia.org/wiki/Wind_velocity |
In method of action, the preparation is identical to that of caffeine base as the citrate counter ion dissociates in water. Doses of caffeine citrate, due to the added weight of the citrate moiety, are understandably higher than with caffeine base, i.e., it takes a larger dose to get the same amount of caffeine. The ratio of therapeutic doses of caffeine base to its citrate salt is typically 1:2. Dosing should therefore be clearly distinguished. | https://en.wikipedia.org/wiki/Caffeine_citrate |
In method of moments, an alternative to the original (non-generalized) Method of Moments (MoM) is described, and references to some applications and a list of theoretical advantages and disadvantages relative to the traditional method are provided. This Bayesian-Like MoM (BL-MoM) is distinct from all the related methods described above, which are subsumed by the GMM. The literature does not contain a direct comparison between the GMM and the BL-MoM in specific applications. | https://en.wikipedia.org/wiki/Generalized_Method_of_Moments |
In method ringing, a branch of change ringing, the ringing pattern known as plain hunt is the simplest method of generating continuously changing sequences, and is a fundamental building-block of method ringing. | https://en.wikipedia.org/wiki/Plain_hunt |
In method ringing, plain hunt is the simplest form of generating changing permutations in a continuous fashion, and is a fundamental building-block of change ringing methods. It consists of a plain undeviating course of a bell between the first and last places in the striking order, with two strikes in the first and last position to enable a turn-around. Thus each bell moves one position at each succeeding change, unless they reach the first or last position, when they remain there for two changes then proceed to the other end of the sequence.This simple rule can be extended to any number of bells. | https://en.wikipedia.org/wiki/Method_ringing |
In method ringing, plain hunt is the simplest form of generating changing permutations in a continuous fashion, and is a fundamental building-block of many change ringing methods. The accompanying diagram shows plain hunt on six bells. The course of two bells only are shown for clarity. Each row in the diagram shows the order of striking after each change. | https://en.wikipedia.org/wiki/Change_ringing |
Plain hunt consists of a plain undeviating course of a bell between the first and last places in the striking order, by moving a place in the sequence at each change, but with two strikes in the first and last position to enable a turn-around as the internal bells change over. Thus each bell moves one position at each succeeding change, unless they reach the first or last position, where they remain for two changes then proceed to the other end of the sequence. All of the bells are doing this at every change, without any words of command.This simple rule can be extended to any number of bells, however it repeats the sequence after twice the number of bells hunting. | https://en.wikipedia.org/wiki/Change_ringing |
In methods of general perturbations, general differential equations, either of motion or of change in the orbital elements, are solved analytically, usually by series expansions. The result is usually expressed in terms of algebraic and trigonometric functions of the orbital elements of the body in question and the perturbing bodies. This can be applied generally to many different sets of conditions, and is not specific to any particular set of gravitating objects. | https://en.wikipedia.org/wiki/Orbital_perturbation_analysis_(spacecraft) |
Historically, general perturbations were investigated first. The classical methods are known as variation of the elements, variation of parameters or variation of the constants of integration. In these methods, it is considered that the body is always moving in a conic section, however the conic section is constantly changing due to the perturbations. | https://en.wikipedia.org/wiki/Orbital_perturbation_analysis_(spacecraft) |
If all perturbations were to cease at any particular instant, the body would continue in this (now unchanging) conic section indefinitely; this conic is known as the osculating orbit and its orbital elements at any particular time are what are sought by the methods of general perturbations.General perturbations takes advantage of the fact that in many problems of celestial mechanics, the two-body orbit changes rather slowly due to the perturbations; the two-body orbit is a good first approximation. General perturbations is applicable only if the perturbing forces are about one order of magnitude smaller, or less, than the gravitational force of the primary body. In the Solar System, this is usually the case; Jupiter, the second largest body, has a mass of about 1/1000 that of the Sun. General perturbation methods are preferred for some types of problems, as the source of certain observed motions are readily found. This is not necessarily so for special perturbations; the motions would be predicted with similar accuracy, but no information on the configurations of the perturbing bodies (for instance, an orbital resonance) which caused them would be available. | https://en.wikipedia.org/wiki/Orbital_perturbation_analysis_(spacecraft) |
In methods of special perturbations, numerical datasets, representing values for the positions, velocities and accelerative forces on the bodies of interest, are made the basis of numerical integration of the differential equations of motion. In effect, the positions and velocities are perturbed directly, and no attempt is made to calculate the curves of the orbits or the orbital elements.Special perturbations can be applied to any problem in celestial mechanics, as it is not limited to cases where the perturbing forces are small. Once applied only to comets and minor planets, special perturbation methods are now the basis of the most accurate machine-generated planetary ephemerides of the great astronomical almanacs. Special perturbations are also used for modeling an orbit with computers. | https://en.wikipedia.org/wiki/Gravitational_perturbation |
In methylmalonic acidemia, the body is unable to break down the amino acids methionine, threonine, isoleucine and valine; as a result methylmalonic acid builds up in the blood and tissues. Those afflicted with this disorder are either lacking functional copies or adequate levels of one or more of the following enzymes: methylmalonyl-CoA mutase, methylmalonyl-CoA epimerase, or those involved in adenosylcobalamin synthesis. | https://en.wikipedia.org/wiki/Methylmalonic_aciduria |
In metric f(R) gravity, one arrives at the field equations by varying the action with respect to the metric and not treating the connection Γ α β μ {\displaystyle \Gamma _{\alpha \beta }^{\mu }} independently. For completeness we will now briefly mention the basic steps of the variation of the action. The main steps are the same as in the case of the variation of the Einstein–Hilbert action (see the article for more details) but there are also some important differences. | https://en.wikipedia.org/wiki/F(R)_theory |
The variation of the determinant is as always: The Ricci scalar is defined as Therefore, its variation with respect to the inverse metric g μ ν {\displaystyle g^{\mu \nu }} is given by For the second step see the article about the Einstein–Hilbert action. Since δ Γ μ ν λ {\displaystyle \delta \Gamma _{\mu \nu }^{\lambda }} is the difference of two connections, it should transform as a tensor. Therefore, it can be written as Substituting into the equation above: where ∇ μ {\displaystyle \nabla _{\mu }} is the covariant derivative and ◻ = g μ ν ∇ μ ∇ ν {\displaystyle \square =g^{\mu \nu }\nabla _{\mu }\nabla _{\nu }} is the d'Alembert operator. Denoting F ( R ) = d f d R {\displaystyle F(R)={\frac {df}{dR}}} , the variation in the action reads: Doing integration by parts on the second and third terms (and neglected the boundary contributions), we get: By demanding that the action remains invariant under variations of the metric, δ S δ g μ ν = 0 {\displaystyle {\frac {\delta S}{\delta g^{\mu \nu }}}=0} , one obtains the field equations: where T μ ν {\displaystyle T_{\mu \nu }} is the energy–momentum tensor defined as where L m {\displaystyle {\mathcal {L}}_{m}} is the matter Lagrangian. | https://en.wikipedia.org/wiki/F(R)_theory |
In metric geometry, a geodesic bicombing distinguishes a class of geodesics of a metric space. The study of metric spaces with distinguished geodesics traces back to the work of the mathematician Herbert Busemann. The convention to call a collection of paths of a metric space bicombing is due to William Thurston. By imposing a weak global non-positive curvature condition on a geodesic bicombing several results from the theory of CAT(0) spaces and Banach space theory may be recovered in a more general setting. | https://en.wikipedia.org/wiki/Geodesic_bicombing |
In metric geometry, a geodesic is a curve which is everywhere locally a distance minimizer. More precisely, a curve γ: I → M from an interval I of the reals to the metric space M is a geodesic if there is a constant v ≥ 0 such that for any t ∈ I there is a neighborhood J of t in I such that for any t1, t2 ∈ J we have d ( γ ( t 1 ) , γ ( t 2 ) ) = v | t 1 − t 2 | . {\displaystyle d(\gamma (t_{1}),\gamma (t_{2}))=v\left|t_{1}-t_{2}\right|.} This generalizes the notion of geodesic for Riemannian manifolds. | https://en.wikipedia.org/wiki/Geodesic |
However, in metric geometry the geodesic considered is often equipped with natural parameterization, i.e. in the above identity v = 1 and d ( γ ( t 1 ) , γ ( t 2 ) ) = | t 1 − t 2 | . {\displaystyle d(\gamma (t_{1}),\gamma (t_{2}))=\left|t_{1}-t_{2}\right|.} If the last equality is satisfied for all t1, t2 ∈ I, the geodesic is called a minimizing geodesic or shortest path. In general, a metric space may have no geodesics, except constant curves. At the other extreme, any two points in a length metric space are joined by a minimizing sequence of rectifiable paths, although this minimizing sequence need not converge to a geodesic. | https://en.wikipedia.org/wiki/Geodesic |
In metric geometry, an injective metric space, or equivalently a hyperconvex metric space, is a metric space with certain properties generalizing those of the real line and of L∞ distances in higher-dimensional vector spaces. These properties can be defined in two seemingly different ways: hyperconvexity involves the intersection properties of closed balls in the space, while injectivity involves the isometric embeddings of the space into larger spaces. However it is a theorem of Aronszajn & Panitchpakdi (1956) that these two different types of definitions are equivalent. | https://en.wikipedia.org/wiki/Injective_metric_space |
In metric geometry, asymptotic dimension of a metric space is a large-scale analog of Lebesgue covering dimension. The notion of asymptotic dimension was introduced by Mikhail Gromov in his 1993 monograph Asymptotic invariants of infinite groups in the context of geometric group theory, as a quasi-isometry invariant of finitely generated groups. As shown by Guoliang Yu, finitely generated groups of finite homotopy type with finite asymptotic dimension satisfy the Novikov conjecture. Asymptotic dimension has important applications in geometric analysis and index theory. | https://en.wikipedia.org/wiki/Asymptotic_dimension |
In metric geometry, the Karlsruhe metric is a measure of distance that assumes travel is only possible along rays through the origin and circular arcs centered at the origin. The name alludes to the layout of the city of Karlsruhe, which has radial streets and circular avenues around a central point. This metric is also called Moscow metric.In this metric, there are two types of shortest paths. | https://en.wikipedia.org/wiki/Karlsruhe_metric |
One possibility, when the two points are on nearby rays, combines a circular arc through the nearer to the origin of the two points and a segment of a ray through the farther of the two points. Alternatively, for points on rays that are nearly opposite, it is shorter to follow one ray all the way to the origin and then follow the other ray back out. Therefore, the Karlsruhe distance between two points d k ( p 1 , p 2 ) {\displaystyle d_{k}(p_{1},p_{2})} is the minimum of the two lengths that would be obtained for these two types of path. That is, it equals where ( r i , φ i ) {\displaystyle (r_{i},\varphi _{i})} are the polar coordinates of p i {\displaystyle p_{i}} and δ ( p 1 , p 2 ) = min ( | φ 1 − φ 2 | , 2 π − | φ 1 − φ 2 | ) {\displaystyle \delta (p_{1},p_{2})=\min(|\varphi _{1}-\varphi _{2}|,2\pi -|\varphi _{1}-\varphi _{2}|)} is the angular distance between the two points. | https://en.wikipedia.org/wiki/Karlsruhe_metric |
In metric geometry, the Reshetnyak gluing theorem gives information on the structure of a geometric object built by using as building blocks other geometric objects, belonging to a well defined class. Intuitively, it states that a manifold obtained by joining (i.e. "gluing") together, in a precisely defined way, other manifolds having a given property inherit that very same property. The theorem was first stated and proved by Yurii Reshetnyak in 1968. | https://en.wikipedia.org/wiki/Reshetnyak_gluing_theorem |
In metric geometry, the discrete metric takes the value one for distinct points and zero otherwise. When applied coordinate-wise to the elements of a vector space, the discrete distance defines the Hamming distance, which is important in coding and information theory. In the field of real or complex numbers, the distance of the discrete metric from zero is not homogeneous in the non-zero point; indeed, the distance from zero remains one as its non-zero argument approaches zero. However, the discrete distance of a number from zero does satisfy the other properties of a norm, namely the triangle inequality and positive definiteness. | https://en.wikipedia.org/wiki/Equivalent_norm |
When applied component-wise to vectors, the discrete distance from zero behaves like a non-homogeneous "norm", which counts the number of non-zero components in its vector argument; again, this non-homogeneous "norm" is discontinuous. In signal processing and statistics, David Donoho referred to the zero "norm" with quotation marks. Following Donoho's notation, the zero "norm" of x {\displaystyle x} is simply the number of non-zero coordinates of x , {\displaystyle x,} or the Hamming distance of the vector from zero. | https://en.wikipedia.org/wiki/Equivalent_norm |
When this "norm" is localized to a bounded set, it is the limit of p {\displaystyle p} -norms as p {\displaystyle p} approaches 0. Of course, the zero "norm" is not truly a norm, because it is not positive homogeneous. Indeed, it is not even an F-norm in the sense described above, since it is discontinuous, jointly and severally, with respect to the scalar argument in scalar–vector multiplication and with respect to its vector argument. Abusing terminology, some engineers omit Donoho's quotation marks and inappropriately call the number-of-non-zeros function the L 0 {\displaystyle L^{0}} norm, echoing the notation for the Lebesgue space of measurable functions. | https://en.wikipedia.org/wiki/Equivalent_norm |
In metric geometry, the metric envelope or tight span of a metric space M is an injective metric space into which M can be embedded. In some sense it consists of all points "between" the points of M, analogous to the convex hull of a point set in a Euclidean space. The tight span is also sometimes known as the injective envelope or hyperconvex hull of M. It has also been called the injective hull, but should not be confused with the injective hull of a module in algebra, a concept with a similar description relative to the category of R-modules rather than metric spaces. The tight span was first described by Isbell (1964), and it was studied and applied by Holsztyński in the 1960s. It was later independently rediscovered by Dress (1984) and Chrobak & Larmore (1994); see Chepoi (1997) for this history. The tight span is one of the central constructions of T-theory. | https://en.wikipedia.org/wiki/Hyperconvex_hull |
In metric graph theory, a convex subgraph of an undirected graph G is a subgraph that includes every shortest path in G between two of its vertices. Thus, it is analogous to the definition of a convex set in geometry, a set that contains the line segment between every pair of its points. Convex subgraphs play an important role in the theory of partial cubes and median graphs. In particular, in median graphs, the convex subgraphs have the Helly property: if a family of convex subgraphs has the property that all pairwise intersections are nonempty, then the whole family has a nonempty intersection. | https://en.wikipedia.org/wiki/Convex_subgraph |
In metric space theory and Riemannian geometry, the Riemannian circle is a great circle with a characteristic length. It is the circle equipped with the intrinsic Riemannian metric of a compact one-dimensional manifold of total length 2π, or the extrinsic metric obtained by restriction of the intrinsic metric to the two-dimensional surface of the sphere, rather than the extrinsic metric obtained by restriction of the Euclidean metric to the unit circle of the two-dimensional Cartesian plane. The distance between a pair of points on the surface of the sphere is defined to be the length of the shorter of the two arcs into which the circle is partitioned by the two points. It is named after German mathematician Bernhard Riemann. | https://en.wikipedia.org/wiki/Riemannian_circle |
In metric spaces, a set is compact if and only if it is complete and totally bounded; without the axiom of choice only the forward direction holds. Precompact sets share a number of properties with compact sets. Like compact sets, a finite union of totally bounded sets is totally bounded. Unlike compact sets, every subset of a totally bounded set is again totally bounded. The continuous image of a compact set is compact. The uniformly continuous image of a precompact set is precompact. | https://en.wikipedia.org/wiki/Totally_bounded |
In metric theories of gravitation such as general relativity, curvature scalars play an important role in telling distinct spacetimes apart. Two of the most basic curvature invariants in general relativity are the Kretschmann scalar R a b c d R a b c d {\displaystyle R_{abcd}\,R^{abcd}} and the Chern–Pontryagin scalar, R a b c d ⋆ R a b c d {\displaystyle R_{abcd}\,{{}^{\star }\!R}^{abcd}} These are analogous to two familiar quadratic invariants of the electromagnetic field tensor in classical electromagnetism. An important unsolved problem in general relativity is to give a basis (and any syzygies) for the zero-th order invariants of the Riemann tensor. They have limitations because many distinct spacetimes cannot be distinguished on this basis. In particular, so called VSI spacetimes (including pp-waves as well as some other Petrov type N and III spacetimes) cannot be distinguished from Minkowski spacetime using any number of polynomial curvature invariants (of any order). | https://en.wikipedia.org/wiki/Curvature_invariant |
In metric theories of gravitation, particularly general relativity, a static spherically symmetric perfect fluid solution (a term which is often abbreviated as ssspf) is a spacetime equipped with suitable tensor fields which models a static round ball of a fluid with isotropic pressure. Such solutions are often used as idealized models of stars, especially compact objects such as white dwarfs and especially neutron stars. In general relativity, a model of an isolated star (or other fluid ball) generally consists of a fluid-filled interior region, which is technically a perfect fluid solution of the Einstein field equation, and an exterior region, which is an asymptotically flat vacuum solution. | https://en.wikipedia.org/wiki/Static_spherically_symmetric_perfect_fluid |
These two pieces must be carefully matched across the world sheet of a spherical surface, the surface of zero pressure. (There are various mathematical criteria called matching conditions for checking that the required matching has been successfully achieved.) Similar statements hold for other metric theories of gravitation, such as the Brans–Dicke theory. | https://en.wikipedia.org/wiki/Static_spherically_symmetric_perfect_fluid |
In this article, we will focus on the construction of exact ssspf solutions in our current Gold Standard theory of gravitation, the theory of general relativity. To anticipate, the figure at right depicts (by means of an embedding diagram) the spatial geometry of a simple example of a stellar model in general relativity. The euclidean space in which this two-dimensional Riemannian manifold (standing in for a three-dimensional Riemannian manifold) is embedded has no physical significance, it is merely a visual aid to help convey a quick impression of the kind of geometrical features we will encounter. | https://en.wikipedia.org/wiki/Static_spherically_symmetric_perfect_fluid |
In metric theories of gravitation, particularly general relativity, a test particle is an idealized model of a small object whose mass is so small that it does not appreciably disturb the ambient gravitational field. According to the Einstein field equations, the gravitational field is locally coupled not only to the distribution of non-gravitational mass–energy, but also to the distribution of momentum and stress (e.g. pressure, viscous stresses in a perfect fluid). In the case of test particles in a vacuum solution or electrovacuum solution, this turns out to imply that in addition to the tidal acceleration experienced by small clouds of test particles (spinning or not), spinning test particles may experience additional accelerations due to spin-spin forces. | https://en.wikipedia.org/wiki/Test_body |
In metric-affine f(R) gravity, one generalizes things even further, treating both the metric and connection independently, and assuming the matter Lagrangian depends on the connection as well. | https://en.wikipedia.org/wiki/F(R)_gravity |
In metrology (test and measurement science), a synthetic instrument is software that performs a specific synthesis, analysis, or measurement function. A Synthetic Measurement System (SMS) is a common, general purpose, physical hardware platform that is intended to perform many kinds of synthesis, analysis, or measurement functions using Synthetic Instruments. Typically the generic SMS hardware is dual cascade of three subsystems: digital processing and control, analog-to-digital or digital-to-analog conversion (codec), and signal conditioning. | https://en.wikipedia.org/wiki/Synthetic_instrument |
One cascade is for stimulus, one for response. Sandwiched between them is the device under test (DUT) that is being measured. A synthetic instrument is the opposite of the retronym natural instrument. | https://en.wikipedia.org/wiki/Synthetic_instrument |
Although the word “synthetic” in the phrase synthetic instrument might seem to imply that synthetic instruments are synthesizers: that they only do synthesis; this is incorrect. The instrument itself is being synthesized; nothing is implied about what the instrument does. A synthetic instrument might indeed be a synthesizer, but it could just as easily be an analyzer, or some hybrid of the two. | https://en.wikipedia.org/wiki/Synthetic_instrument |
Synthetic instruments are implemented on generic hardware, i.e., generic meaning that the underlying hardware is not explicitly designed to perform the particular measurement. This is probably the most salient characteristic of a synthetic instrument. Measurement specificity is encapsulated totally in software. | https://en.wikipedia.org/wiki/Synthetic_instrument |
The hardware does not define the measurement. An analogy to this relationship between specific measurement hardware versus generic hardware with its function totally defined in software is the relationship between specific digital circuits and a general purpose CPU. A specific digital circuit can be designed and hardwired with digital logic parts to perform a specific calculation. | https://en.wikipedia.org/wiki/Synthetic_instrument |
Alternatively, a microprocessor (or, better yet, a gate array) could be used to perform the same calculation using appropriate software. One case is specific, the other generic, with the specificity encapsulated in software. | https://en.wikipedia.org/wiki/Synthetic_instrument |
At the software level, portability of measurement description is the key attribute that distinguishes a synthetic instrument from the more commonly found instrumentation software—software that is limited to hardware scripting and data flow processing. Not all measurement related software systems inherently provide for the abstract, portable synthesis of measurements. Even if they do have such provisions, they may not typically be applied that way by users, especially if the system encourages non-abstracted access to hardware. | https://en.wikipedia.org/wiki/Synthetic_instrument |
Application software packages such as Measure Foundry and LabVIEW are typically used with explicit structural links to the natural measurements made by specific hardware and therefore usually are not synthesizing measurements from an abstract description. On the other hand, should a software system be used to synthesize measurement functions as descriptive behavioral constructs, rather than hardware referenced structural data flow descriptions, this is true measurement synthesis. An analogy here is the distinction between a non portable structural description and an abstract behavioral description of digital logic that we see in HDL systems like Verilog. | https://en.wikipedia.org/wiki/Synthetic_instrument |
Synthetic instruments in test and measurement are conceptually related to the software synthesizer in audio or music. A musical instrument synthesizer synthesizes the sound of specific instruments from generic hardware. Of course, a significant difference in these concepts is that musical instrument synthesizers typically only generate musical sound, whereas a synthetic instrument in test and measurement may be equally likely to generate or to measure some signal or parameter. | https://en.wikipedia.org/wiki/Synthetic_instrument |
A similar term commonly used in test and measurement, Virtual instrumentation, is a superset of synthetic instrumentation. All synthetic instruments are virtual instruments; however, the two terms are different when virtual instrument software mirrors and augments non-generic instrument hardware, providing a soft front panel, or managing the data flow to and from a natural instrument. In this case, the PC and accompanying software is supplementing the analysis and presentation capabilities of the natural instrument. | https://en.wikipedia.org/wiki/Synthetic_instrument |
The essential point is this: synthetic instruments are synthesized. The whole is greater than the sum of the parts. To use Buckminster Fuller's word, synthetic instruments are synergistic instruments. | https://en.wikipedia.org/wiki/Synthetic_instrument |
Like a triangle is more than three lines, synthetic instruments are more than the triangle of hardware (Control, Codec, Conditioning) they are implemented on. Therefore, one way to tell if you have a true synthetic instrument is to examine the hardware design alone and to try to figure out what sort of instrument it might be. If all you can determine are basic category facts, like the fact that it can be categorized as a stimulus or response instrument, but not anything about what it's particularly designed to create or measure—if the measurement specificity is all hidden in software—then you likely have a true synthetic instrument. The DoD has created a standards body called the Synthetic Instrument Working Group (SIWG) whose role is to define standards for interoperability of synthetic instrument systems. The SIWG defines a synthetic instruments (SI) as: A reconfigurable system that links a series of elemental hardware and software components with standardized interfaces to generate signals or make measurements using numeric processing techniques. | https://en.wikipedia.org/wiki/Synthetic_instrument |
In metrology (the science of measurement), a standard (or etalon) is an object, system, or experiment that bears a defined relationship to a unit of measurement of a physical quantity. Standards are the fundamental reference for a system of weights and measures, against which all other measuring devices are compared. Historical standards for length, volume, and mass were defined by many different authorities, which resulted in confusion and inaccuracy of measurements. Modern measurements are defined in relationship to internationally standardized reference objects, which are used under carefully controlled laboratory conditions to define the units of length, mass, electrical potential, and other physical quantities. | https://en.wikipedia.org/wiki/Secondary_standard |
In metrology and the fields that it serves (such as manufacturing, machining, and engineering), total indicator reading (TIR), also known by the newer name full indicator movement (FIM), is the difference between the maximum and minimum measurements, that is, readings of an indicator, on the planar, cylindrical, or contoured surface of a part, showing its amount of deviation from flatness, roundness (circularity), cylindricity, concentricity with other cylindrical features, or similar conditions. The indicator traditionally would be a dial indicator; today dial-type and digital indicators coexist. The earliest expansion of "TIR" was total indicated run-out and concerned cylindrical or tapered (conical) parts, where "run-out" (noun) refers to any imperfection of form that causes a rotating part such as a shaft to "run out" (verb), that is, to not rotate with perfect smoothness. | https://en.wikipedia.org/wiki/Total_indicator_reading |
These conditions include being out-of-round (that is, lacking sufficient roundness); eccentricity (that is, lacking sufficient concentricity); or being bent axially (regardless of whether the surfaces are perfectly round and concentric at every cross-sectional point). The purpose of emphasizing the "total" in TIR was to duly maintain the distinction between per-side differences and both-sides-considered differences, which requires perennial conscious attention in lathe work. For example, all depths of cut in lathe work must account for whether they apply to the radius (that is, per side) or to the diameter (that is, total). | https://en.wikipedia.org/wiki/Total_indicator_reading |
Similarly, in shaft-straightening operations, where calibrated amounts of bending force are applied laterally to the shaft, the "total" emphasis corresponds to a bend of half that magnitude. If a shaft has 0.1 mm TIR, it is "out of straightness" by half that total, i.e., 0.05 mm. Today TIR in its more inclusive expansion, "total indicator reading", concerns all kinds of features, from round to flat to contoured. | https://en.wikipedia.org/wiki/Total_indicator_reading |
One example of how the "total" emphasis can apply to flat surfaces as well as round ones is in the topic of surface roughness, where both peaks and valleys count toward an assessment of the magnitude of roughness. Statistical methods such as root mean square (RMS) duly address the "total" idea in this respect. The newer name "full indicator movement" (FIM) was coined to emphasize the requirement of zero cosine error. | https://en.wikipedia.org/wiki/Total_indicator_reading |
Whereas dial test indicators will give a foreshortened reading if their tips are on an angle to the surface being measured (cosine error), a drawing callout of FIM is defined as referring to the distance traveled by the extremity of the tip—not by the lesser amount that its lever-like action moves the needle. Thus a FIM requirement is only met when the measured part itself is truly in geometric compliance—not merely when the needle sweeps a certain arc of the dial. The "TIR" abbreviation is still more widely known and used than "FIM". This is natural given that (1) many part designs that are still being manufactured are made from decades-old engineering drawings, which still say "TIR"; and (2) generations of machinists were trained with the term "TIR", whereas only recent curriculum uses "FIM". | https://en.wikipedia.org/wiki/Total_indicator_reading |
In metrology at macro scale achieving traceability is quite easy and artefacts like scales, laser interferometers, step gauges, and straight edges are used. At nanoscale a crystalline highly oriented pyrolytic graphite (HOPG), mica or silicon surface is considered suitable used as calibration artefact for achieving traceability. But it is not always possible to ensure traceability. Like what is a straight edge at nanoscale and even if take the same standard as that for macroscale there is no way to calibrate it accurately at nanoscale. | https://en.wikipedia.org/wiki/Nanometrology |
This so because the requisite internationally or nationally accepted reference standards are not always there. Also the measurement equipment required to ensure traceability has not been developed. The generally used for traceability are miniaturisation of traditional metrology standards hence there is a need for establishing nanoscale standards. Also there is a need to establish some kind of uncertainty estimation model. Traceability is one of the fundamental requirements for manufacturing and assembly of products when multiple producers are there. | https://en.wikipedia.org/wiki/Nanometrology |
In metrology, measurement uncertainty is the expression of the statistical dispersion of the values attributed to a measured quantity. All measurements are subject to uncertainty and a measurement result is complete only when it is accompanied by a statement of the associated uncertainty, such as the standard deviation. By international agreement, this uncertainty has a probabilistic basis and reflects incomplete knowledge of the quantity value. | https://en.wikipedia.org/wiki/Measurement_uncertainty |
It is a non-negative parameter.The measurement uncertainty is often taken as the standard deviation of a state-of-knowledge probability distribution over the possible values that could be attributed to a measured quantity. Relative uncertainty is the measurement uncertainty relative to the magnitude of a particular single choice for the value for the measured quantity, when this choice is nonzero. This particular single choice is usually called the measured value, which may be optimal in some well-defined sense (e.g., a mean, median, or mode). Thus, the relative measurement uncertainty is the measurement uncertainty divided by the absolute value of the measured value, when the measured value is not zero. | https://en.wikipedia.org/wiki/Measurement_uncertainty |
In metrology, specifically axial-flow turbine meters, the Strouhal number is used in combination with the Roshko number to give a correlation between flow rate and frequency. The advantage of this method over the frequency/viscosity versus K-factor method is that it takes into account temperature effects on the meter. St = f U C 3 , {\displaystyle {\text{St}}={\frac {f}{U}}C^{3},} where, f = meter frequency, U = flow rate, C = linear coefficient of expansion for the meter housing material.This relationship leaves Strouhal dimensionless, although a dimensionless approximation is often used for C3, resulting in units of pulses/volume (same as K-factor). | https://en.wikipedia.org/wiki/Strouhal_number |
This relationship between flow and frequency can also be found in the aeronautical field. Considering pulsating methane-air coflow jet diffusion flames, we get St = a w j U j {\displaystyle {\text{St}}={\dfrac {aw_{j}}{U_{j}}}} ,where, a = fuel jet radius w = the modulation frequency U = exit velocity of the fuel jetFor a small Strouhal number (St=0.1) the modulation forms a deviation in the flow that travels very far downstream. As the Strouhal number grows, the non-dimensional frequency approaches the natural frequency of a flickering flame, and eventually will have greater pulsation than the flame. | https://en.wikipedia.org/wiki/Strouhal_number |
In metrology, such as when performed in support of science, engineering or manufacturing objectives, dynamic range refers to the range of values that can be measured by a sensor or metrology instrument. Often this dynamic range of measurement is limited at one end of the range by saturation of a sensing signal sensor or by physical limits that exist on the motion or other response capability of a mechanical indicator. The other end of the dynamic range of measurement is often limited by one or more sources of random noise or uncertainty in signal levels that may be described as defining the sensitivity of the sensor or metrology device. When digital sensors or sensor signal converters are a component of the sensor or metrology device, the dynamic range of measurement will be also related to the number of binary digits (bits) used in a digital numeric representation in which the measured value is linearly related to the digital number. | https://en.wikipedia.org/wiki/Dynamic_range |
For example, a 12-bit digital sensor or converter can provide a dynamic range in which the ratio of the maximum measured value to the minimum measured value is up to 212 = 4096. Metrology systems and devices may use several basic methods to increase their basic dynamic range. These methods include averaging and other forms of filtering, correction of receivers characteristics, repetition of measurements, nonlinear transformations to avoid saturation, etc. In more advance forms of metrology, such as multiwavelength digital holography, interferometry measurements made at different scales (different wavelengths) can be combined to retain the same low-end resolution while extending the upper end of the dynamic range of measurement by orders of magnitude. | https://en.wikipedia.org/wiki/Dynamic_range |
In metropolitan areas, FOMA uses the UMTS band I around 2100 MHz, which has been originally assigned to IMT-2000 services worldwide, except in the Americas. In order to improve coverage in rural and mountainous areas, NTT DoCoMo also offers FOMA services in the 800 MHz band originally assigned to the 2G PDC mova service, which corresponds to UMTS band VI and is similar to band V used in the United States. These extended service areas are branded FOMA Plus-Area (FOMAプラスエリア) and require multiband terminals. == References == | https://en.wikipedia.org/wiki/Freedom_of_Mobile_Multimedia_Access |
In metropolitan areas, stray voltage issues have become a major concern. Many of these areas have large amounts of aging underground and aboveground electrical distribution equipment in crowded public spaces. Even a low rate of insulation failures or current leakage can result in hazardous exposure to the general public. Consolidated Edison in New York City has had frequent incidents of stray voltage, including the electrocution death of Jodie S. Lane in 2004, while walking her dog in Manhattan. | https://en.wikipedia.org/wiki/Stray_voltage |
In 2009, the Jodie S. Lane Public Safety Foundation announced a publicly accessible website with maps showing thousands of reported stray voltage locations in New York City. In addition, the Foundation sponsors the "Jodie S. Lane Stray Voltage Detection, Mitigation & Prevention Conference", an annual meeting attended by power utilities and regulators from around the country to discuss stray voltage detection programs. The Foundation also initiated and advocates regular mobile scanning by utility companies for stray voltage hazards. | https://en.wikipedia.org/wiki/Stray_voltage |
In Boston, NSTAR Electric (formerly Boston Edison) has also had problems with hazardous stray voltages, which have killed several dogs during the 1990s. As a result, the City of Boston government started a program to detect, report on, and repair stray voltage hazards.Toronto Hydro pulled all employees off regular duty on the weekend of January 30, 2009 to deal with ongoing stray voltage problems in the city. This came after as many as five children were shocked though none suffered serious injury. The stray voltage problem had claimed the lives of two dogs in the previous few months.In March 2013, Californian Simona Wilson won a $4 million lawsuit against her power company after stray voltage from a substation near her house repeatedly shocked her and members of her family whenever they were in the shower.The United States Social Security Administration, Administrative Law Judge, Edward Bergtholdt, in an August 17, 2000 decision awarded Michael Gunner permanent disability from exposure to stray voltage. | https://en.wikipedia.org/wiki/Stray_voltage |
In metropolitan areas, the scale and intensity of collaboration is a key determinant of whether or not polycentric networks function properly. Metropolitan planning organizations (MPOs) have given researchers a unique opportunity to study the scale and intensity of collaboration. A 2015 study of 381 MPOs in the United States, found a direct link between the MPO's scale and performance. | https://en.wikipedia.org/wiki/Polycentric_networks |
The study concluded that more intense MPO collaboration across both vertical and horizontal stakeholders improved performance. The study found that MPOs that focused more on vertical collaboration (between the state and higher-up agencies) saw a decrease in their perceived performance. The study looked at 15 indicators including condition of transportation network, mobility for disadvantaged populations, air quality, highway congestion, public participation, extent of coordination and stakeholder involvement, satisfaction among general public, satisfaction among local stakeholders, compliance with federal and state rules, transportation systems security, accessibility, reliability, and safety, travel demand model accuracy and project implementation. | https://en.wikipedia.org/wiki/Polycentric_networks |
In mice (Mus musculus), laterality in paw usage has been shown to be a learned behavior (rather than inherited), due to which, in any population, half of the mice become left-handed while the other half becomes right-handed. The learning occurs by a gradual reinforcement of randomly occurring weak asymmetries in paw choice early in training, even when training in an unbiased world. Meanwhile, reinforcement relies on short-term and long-term memory skills that are strain-dependent, causing strains to differ in the degree of laterality of its individuals. Long-term memory of previously gained laterality in handedness due to training is heavily diminished in mice with absent corpus callosum and reduced hippocampal commissure. Regardless of the amount of past training and consequent biasing of paw choice, there is a degree of randomness in paw choice that is not removed by training, which may provide adaptability to changing environments. | https://en.wikipedia.org/wiki/Laterality |
In mice T is expressed in the inner cell mass of the blastocyst stage embryo (but not in the majority of mouse embryonic stem cells) followed by the primitive streak (see image). In later development expression is localised to the node and notochord. In Xenopus laevis Xbra (the Xenopus T homologue, also recently renamed t) is expressed in the mesodermal marginal zone of the pre-gastrula embryo followed by localisation to the blastopore and notochord at the mid-gastrula stage. | https://en.wikipedia.org/wiki/T-box_transcription_factor_T |
In mice and humans the spontaneous mutation rate in the male germ line is significantly lower than in somatic cells. Furthermore, although the spontaneous mutation rate in the male germ line increases with age, the rate of increase is lower than in somatic tissues. Within the testicular spermatogonial stem cell population the integrity of DNA appears to be maintained by highly effective DNA damage surveillance and protective DNA repair processes. | https://en.wikipedia.org/wiki/Germline_mutation |
The progressive increase in the mutation rate with age in the male germ line may be a result of a decline in the accuracy of the repair of DNA damages, or of an increase in DNA replication errors. Once spermatogenesis is complete, the differentiated spermatozoa that are formed no longer have the capability for DNA repair, and are thus vulnerable to attack by prevalent oxidative free radicals that cause oxidative DNA damage. Such damaged spermatozoa may undergo programmed cell death (apoptosis). | https://en.wikipedia.org/wiki/Germline_mutation |
In mice and humans, alterations in serotonin levels and signalling have been shown to regulate bone mass. Mice that lack brain serotonin have osteopenia, while mice that lack gut serotonin have high bone density. In humans, increased blood serotonin levels have been shown to be a significant negative predictor of low bone density. Serotonin can also be synthesized, albeit at very low levels, in the bone cells. | https://en.wikipedia.org/wiki/Serotonin |
It mediates its actions on bone cells using three different receptors. Through 5-HT1B receptors, it negatively regulates bone mass, while it does so positively through 5-HT2B receptors and 5-HT2C receptors. | https://en.wikipedia.org/wiki/Serotonin |
There is very delicate balance between physiological role of gut serotonin and its pathology. Increase in the extracellular content of serotonin results in a complex relay of signals in the osteoblasts culminating in FoxO1/ Creb and ATF4 dependent transcriptional events. Following the 2008 findings that gut serotonin regulates bone mass, the mechanistic investigations into what regulates serotonin synthesis from the gut in the regulation of bone mass have started. | https://en.wikipedia.org/wiki/Serotonin |
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