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Kepler 10b Nomenclature and history Kepler-10b > Nomenclature and history In order to measure the mass of a planet, and rule out other phenomena that can mimic the presence of a planet transiting a star, candidate transiting planets are followed up with the radial velocity method of detecting extrasolar planets.Kepler-10b's discovery was based on eight months of data collected with the Kepler telescope from May 2009 to January 2010. The planet's first transits were observed in July 2009. According to the collected data, Kepler-10 dimmed by one part in ten thousand every 0.83 days.
Software verification and validation Validation vs. verification Software_verification_and_validation > Definitions > Validation vs. verification According to the Capability Maturity Model (CMMI-SW v1.1), Software Validation: The process of evaluating software during or at the end of the development process to determine whether it satisfies specified requirements. Software Verification: The process of evaluating software to determine whether the products of a given development phase satisfy the conditions imposed at the start of that phase. Validation during the software development process can be seen as a form of User Requirements Specification validation; and, that at the end of the development process is equivalent to Internal and/or External Software validation. Verification, from CMMI's point of view, is evidently of the artifact kind.
Biquadratic function Ferrari's solution Fourth-degree_equation > Solution > Solution methods > Ferrari's solution This implies that the discriminant in y of this quadratic equation is zero, that is m is a root of the equation ( − q ) 2 − 4 ( 2 m ) ( m 2 + p m + p 2 4 − r ) = 0 , {\displaystyle (-q)^{2}-4(2m)\left(m^{2}+pm+{\frac {p^{2}}{4}}-r\right)=0,\,} which may be rewritten as This is the resolvent cubic of the quartic equation. The value of m may thus be obtained from Cardano's formula. When m is a root of this equation, the right-hand side of equation (1) is the square ( 2 m y − q 2 2 m ) 2 .
Electric conductance Relation to resistivity and conductivity Electric_resistance > Relation to resistivity and conductivity For this reason, the geometrical cross-section is different from the effective cross-section in which current actually flows, so resistance is higher than expected. Similarly, if two conductors near each other carry AC current, their resistances increase due to the proximity effect. At commercial power frequency, these effects are significant for large conductors carrying large currents, such as busbars in an electrical substation, or large power cables carrying more than a few hundred amperes.
Coefficient of friction Angle of friction Frictional_force > Dry friction > Angle of friction For certain applications, it is more useful to define static friction in terms of the maximum angle before which one of the items will begin sliding. This is called the angle of friction or friction angle. It is defined as: and thus: where θ {\displaystyle \theta } is the angle from horizontal and μs is the static coefficient of friction between the objects. This formula can also be used to calculate μs from empirical measurements of the friction angle.
Subgenual cingulate Involvement in depression Subgenual_cingulate > Involvement in depression 1% initially reported positive effects, but had a depression relapse before the year follow up completed. There were no side effects or complications reported from the treatment.A recent study found that transcranial magnetic stimulation is more clinically effective treating depression when targeted specifically to Brodmann area 46, because this area has intrinsic functional connectivity (negative correlation) with area 25.Another recent study has found that the responses of area 25 to viewing sad stimuli are affected by cortisol. This suggests that depression related changes in the activity in area 25 could be due to hypothalamic–pituitary–adrenal axis dysregulation.
High resolution computed tomography Applications High-resolution_computed_tomography > Lung disease > Applications The major pulmonary complication is bronchiolitis obliterans, which may be a sign of lung graft rejection. HRCT has better sensitivity for bronchiolitis obliterans than conventional radiography. Some transplant centers may arrange annual HRCT to screen for this.
Osmoregulation in rock doves Transport mechanisms of osmoregulation Osmoregulation_in_rock_doves > Transport mechanisms of osmoregulation Water flows from the epithelial cells into the blood via osmosis. Since osmosis occurs, the osmolarity of the filtrate remains isotonic. Sodium/Potassium/ATPase transporter is located in the basolateral membrane of the epithelial cell, which is opposite of the lumen of the proximal tubule, and actively pumps sodium out of the cell into the blood.
Cathode bias Design Cathode_bias > Design To find the correct resistor value, first the tube operating point is determined. The plate current, the grid voltage relative to the cathode and the screen current (if applicable) are noted for the operating point. The cathode bias resistor value is found by dividing the absolute value of the operating point grid voltage by the operating point cathode current (plate current plus screen current). The power dissipated by the cathode bias resistor is the product of the square of the cathode current and the resistance in ohms.
Carbon–boron bond Reactions Organoboron_compound > Reactions Organoboranes (R3B) and borates (R4B−, generated via addition of R− to R3B) possess boron–carbon bonds that are polarized toward carbon. Thus, the carbon attached to boron is nucleophilic, and in borates this property may be harnessed to transfer one of the R groups to an electrophilic center either inter- or (more often) intramolecularly. In the latter case, the nucleophilic R group is able to undergo 1,2-migration towards an electrophilic carbon attached to boron. The resulting reorganized borane can then be oxidized or subjected to protonolysis to afford organic products.
Banach-Saks theorem Generalizations Weak_convergence_(Hilbert_space) > Generalizations The definition of weak convergence can be extended to Banach spaces. A sequence of points ( x n ) {\displaystyle (x_{n})} in a Banach space B is said to converge weakly to a point x in B if for any bounded linear functional f {\displaystyle f} defined on B {\displaystyle B} , that is, for any f {\displaystyle f} in the dual space B ′ {\displaystyle B'} . If B {\displaystyle B} is an Lp space on Ω {\displaystyle \Omega } and p < + ∞ {\displaystyle p<+\infty } , then any such f {\displaystyle f} has the form for some y ∈ L q ( Ω ) {\displaystyle y\in \,L^{q}(\Omega )} , where μ {\displaystyle \mu } is the measure on Ω {\displaystyle \Omega } and 1 p + 1 q = 1 {\displaystyle {\frac {1}{p}}+{\frac {1}{q}}=1} are conjugate indices. In the case where B {\displaystyle B} is a Hilbert space, then, by the Riesz representation theorem, for some y {\displaystyle y} in B {\displaystyle B} , so one obtains the Hilbert space definition of weak convergence.
Rule-based machine translation Components Rule-based_machine_translation > Components The RBMT system contains: a SL morphological analyser - analyses a source language word and provides the morphological information; a SL parser - is a syntax analyser which analyses source language sentences; a translator - used to translate a source language word into the target language; a TL morphological generator - works as a generator of appropriate target language words for the given grammatica information; a TL parser - works as a composer of suitable target language sentences; Several dictionaries - more specifically a minimum of three dictionaries:a SL dictionary - needed by the source language morphological analyser for morphological analysis,a bilingual dictionary - used by the translator to translate source language words into target language words,a TL dictionary - needed by the target language morphological generator to generate target language words.The RBMT system makes use of the following: a Source Grammar for the input language which builds syntactic constructions from input sentences; a Source Lexicon which captures all of the allowable vocabulary in the domain; Source Mapping Rules which indicate how syntactic heads and grammatical functions in the source language are mapped onto domain concepts and semantic roles in the interlingua; a Domain Model/Ontology which defines the classes of domain concepts and restricts the fillers of semantic roles for each class; Target Mapping Rules which indicate how domain concepts and semantic roles in the interlingua are mapped onto syntactic heads and grammatical functions in the target language; a Target Lexicon which contains appropriate target lexemes for each domain concept; a Target Grammar for the target language which realizes target syntactic constructions as linearized output sentences.
Elementary geometry Complex geometry Geometry > Contemporary geometry > Complex geometry The primary objects of study in complex geometry are complex manifolds, complex algebraic varieties, and complex analytic varieties, and holomorphic vector bundles and coherent sheaves over these spaces. Special examples of spaces studied in complex geometry include Riemann surfaces, and Calabi–Yau manifolds, and these spaces find uses in string theory. In particular, worldsheets of strings are modelled by Riemann surfaces, and superstring theory predicts that the extra 6 dimensions of 10 dimensional spacetime may be modelled by Calabi–Yau manifolds.
Oxidative phosphorylation Summary Oxidative_phosphorylation Oxidative phosphorylation (UK , US ) or electron transport-linked phosphorylation or terminal oxidation is the metabolic pathway in which cells use enzymes to oxidize nutrients, thereby releasing chemical energy in order to produce adenosine triphosphate (ATP). In eukaryotes, this takes place inside mitochondria. Almost all aerobic organisms carry out oxidative phosphorylation.
Mo2Cl8 Summary Mo2Cl8 Potassium octachlorodimolybdate (systematically named potassium bis(tetrachloromolybdate)(Mo–Mo)(4−)) is an inorganic compound with the chemical formula K4. It is known as a red-coloured, microcrystalline solid. The anion is of historic interest as one of the earliest illustrations of a quadruple bonding. The salt is usually obtained as the pink-coloured dihydrate.
Tradition Works cited Tradition > References > Works cited Model-based reasoning: science, technology, values. Springer. pp.
Very smooth hash Examples of VSN and VSSR Very_smooth_hash > VSN and VSSR > Examples of VSN and VSSR This is a trivial modular square root, because 3 2 ≱ n {\displaystyle 3^{2}\not \geq n} and so the modulus is not involved when squaring. The integer b 2 = 15 {\displaystyle b_{2}=15} is also Very Smooth Quadratic Residue modulo n {\displaystyle n} . All prime factors are smaller than 7.37 and the Modular Square Root is x 2 = 20 {\displaystyle x_{2}=20} since 20 2 = 400 ≡ 15 {\displaystyle 20^{2}=400\equiv 15} (mod n {\displaystyle n} ).
Prosecutor's fallacy Findings in psychology Prosecutor's_fallacy > Findings in psychology Teaching people to translate these kinds of Bayesian reasoning problems into natural frequency formats is more effective than merely teaching them to plug probabilities (or percentages) into Bayes' theorem. It has also been shown that graphical representations of natural frequencies (e.g., icon arrays, hypothetical outcome plots) help people to make better inferences.Why are natural frequency formats helpful? One important reason is that this information format facilitates the required inference because it simplifies the necessary calculations.
Engineering Seismology Earthquake prediction Engineering_Seismology > Seismology and society > Earthquake prediction Forecasting a probable timing, location, magnitude and other important features of a forthcoming seismic event is called earthquake prediction. Various attempts have been made by seismologists and others to create effective systems for precise earthquake predictions, including the VAN method. Most seismologists do not believe that a system to provide timely warnings for individual earthquakes has yet been developed, and many believe that such a system would be unlikely to give useful warning of impending seismic events.
Oxyphil cell (parathyroid) Structure Oxyphil_cell_(parathyroid) > Structure Oxyphil cells may be binucleated and proteins found within their cytoplasms are basic, resulting in acidophilic cytoplasms. Cytochemically, oxyphil cells and C cells are fairly similar. Oxyphil cells are much larger in size (12–20 μm) compared with chief cells (6–8 μm) and also stain lighter than chief cells. Oxyphil cells have a cytoplasm filled with many, large mitochondria. Oxyphil cells have abundant cytoplasmic glycogen and ribosomes that are interspersed between the mitochondria. The endoplasmic reticulum, Golgi apparatuses, and secretory granules are poorly developed in oxyphil cells of normal parathyroid glands
Intestinal gas Odor Rectal_gases > Management > Odor Bismuth The odor created by flatulence is commonly treated with bismuth subgallate, available over-the-counter in the US as Devrom. Bismuth subgallate is commonly used by individuals who have had ostomy surgery, bariatric surgery, faecal incontinence and irritable bowel syndrome. Bismuth subsalicylate is a compound that binds hydrogen sulfide, and one study reported a dose of 524 mg four times a day for 3–7 days bismuth subsalicylate yielded a >95% reduction in faecal hydrogen sulfide release in both humans and rats. Another bismuth compound, bismuth subnitrate was also shown to bind to hydrogen sulfide.
Inductive impedance History Electrical_impedance > History Perhaps the earliest use of complex numbers in circuit analysis was by Johann Victor Wietlisbach in 1879 in analysing the Maxwell bridge. Wietlisbach avoided using differential equations by expressing AC currents and voltages as exponential functions with imaginary exponents (see § Validity of complex representation). Wietlisbach found the required voltage was given by multiplying the current by a complex number (impedance), although he did not identify this as a general parameter in its own right.The term impedance was coined by Oliver Heaviside in July 1886. Heaviside recognised that the "resistance operator" (impedance) in his operational calculus was a complex number.
Scientific methods Relationship with mathematics Scientific_studies > Relationship with mathematics Building on Pólya's work, Imre Lakatos argued that mathematicians actually use contradiction, criticism, and revision as principles for improving their work. In like manner to science, where truth is sought, but certainty is not found, in Proofs and Refutations, what Lakatos tried to establish was that no theorem of informal mathematics is final or perfect. This means that we should not think that a theorem is ultimately true, only that no counterexample has yet been found.
Vortex cooler Phenomenological approach Vortex_cooler > Method of operation > Phenomenological approach This approach relies on observation and experimental data. It is specifically tailored to the geometrical shape of the vortex tube and the details of its flow and is designed to match the particular observables of the complex vortex tube flow, namely turbulence, acoustic phenomena, pressure fields, air velocities and many others. The earlier published models of the vortex tube are phenomenological. They are: Radial pressure difference: centrifugal compression and air expansion Radial transfer of angular momentum Radial acoustic streaming of energy Radial heat pumpingMore on these models can be found in recent review articles on vortex tubes.The phenomenological models were developed at an earlier time when the turbine equation of Euler was not thoroughly analyzed; in the engineering literature, this equation is studied mostly to show the work output of a turbine; while temperature analysis is not performed since turbine cooling has more limited application unlike power generation, which is the main application of turbines.
Cache language model Summary Cache_language_model A cache language model is a type of statistical language model. These occur in the natural language processing subfield of computer science and assign probabilities to given sequences of words by means of a probability distribution. Statistical language models are key components of speech recognition systems and of many machine translation systems: they tell such systems which possible output word sequences are probable and which are improbable. The particular characteristic of a cache language model is that it contains a cache component and assigns relatively high probabilities to words or word sequences that occur elsewhere in a given text.
Armature (electrical) Summary Armature_(electrical) In electrical engineering, the armature is the winding (or set of windings) of an electric machine which carries alternating current. The armature windings conduct AC even on DC machines, due to the commutator action (which periodically reverses current direction) or due to electronic commutation, as in brushless DC motors. The armature can be on either the rotor (rotating part) or the stator (stationary part), depending on the type of electric machine.
Transcription translation feedback loop General mechanisms of TTFL Transcription_translation_feedback_loop > General mechanisms of TTFL Across species, proteins involved in the TTFL contain common structural motifs such PAS domains, involved in protein-protein interactions, and bHLH domains, involved in DNA binding.Once enough modified protein products accumulate in the cytoplasm, they are transported into the nucleus where they inhibit the positive element from the promoter to stop transcription of clock genes. The clock gene is thus transcribed at low levels until its protein products are degraded, allowing for positive regulatory elements to bind to the promoter and restart transcription. The negative feedback loop of the TTFL has multiple properties important for the cellular circadian clock.
Pati–Salam model Vector superfields Pati–Salam_model > Minimal supersymmetric Pati–Salam > Vector superfields Those associated with the SU(4) × SU(2)L × SU(2)R gauge symmetry
Diffusion rate Diffusion in the context of different disciplines Diffusion > Diffusion in the context of different disciplines The concept of diffusion is widely used in: physics (particle diffusion), chemistry, biology, sociology, economics, and finance (diffusion of people, ideas and of price values). However, in each case the substance or collection undergoing diffusion is "spreading out" from a point or location at which there is a higher concentration of that substance or collection. There are two ways to introduce the notion of diffusion: either a phenomenological approach starting with Fick's laws of diffusion and their mathematical consequences, or a physical and atomistic one, by considering the random walk of the diffusing particles.In the phenomenological approach, diffusion is the movement of a substance from a region of high concentration to a region of low concentration without bulk motion. According to Fick's laws, the diffusion flux is proportional to the negative gradient of concentrations.
Mirror-symmetry breaking In biology Mirror-symmetry_breaking > In biology Biological organisms easily discriminate between molecules with different chiralities. This can affect physiological reactions such as smell and taste.
CING (biomolecular NMR structure) Summary CING_(biomolecular_NMR_structure) In biomolecular structure, CING stands for the Common Interface for NMR structure Generation and is known for structure and NMR data validation.NMR spectroscopy provides diverse data on the solution structure of biomolecules. CING combines many external programs and internalized algorithms to direct an author of a new structure or a biochemist interested in an existing structure to regions of the molecule that might be problematic in relation to the experimental data. The source code is maintained open to the public at Google Code. There is a secure web interface iCing available for new data.
Wallace effect Gene flow Wallace_effect > Arguments against reinforcement > Gene flow : 369 In addition, specific alleles that have the selective advantage within the overlapped populations are only useful within that population. However, if they are selectively advantageous, gene flow should allow the alleles to spread throughout both populations. To prevent this, the alleles would have to be deleterious or neutral.
H2MoO4 Summary Molybdic_acid Molybdic acid refers to hydrated forms of molybdenum trioxide and related species. The monohydrate (MoO3·H2O) and the dihydrate (MoO3·2H2O) are well characterized. They are yellow diamagnetic solids.
Simple Sequence Repeat Mutation mechanisms and mutation rates Short_tandem_repeat_polymorphism > Mutation mechanisms and mutation rates The actual cause of mutations in microsatellites is debated. One proposed cause of such length changes is replication slippage, caused by mismatches between DNA strands while being replicated during meiosis. DNA polymerase, the enzyme responsible for reading DNA during replication, can slip while moving along the template strand and continue at the wrong nucleotide.
Power series On the set of exponents Power_series > Examples > On the set of exponents Negative powers are not permitted in a power series; for instance, 1 + x − 1 + x − 2 + ⋯ {\textstyle 1+x^{-1}+x^{-2}+\cdots } is not considered a power series (although it is a Laurent series). Similarly, fractional powers such as x 1 2 {\textstyle x^{\frac {1}{2}}} are not permitted (but see Puiseux series). The coefficients a n {\textstyle a_{n}} are not allowed to depend on x {\textstyle x} , thus for instance: is not a power series.
Performance tuning Summary Performance_tuning This limit within the system is referred to as a bottleneck. A handful of techniques are used to improve performance. Among them are code optimization, load balancing, caching strategy, distributed computing and self-tuning.
Contactless energy transfer 19th century developments and dead ends Wireless_energy_transfer > History > 19th century developments and dead ends Transmission of electrical energy without wires was observed by many inventors and experimenters, but lack of a coherent theory attributed these phenomena vaguely to electromagnetic induction. A concise explanation of these phenomena would come from the 1860s Maxwell's equations by James Clerk Maxwell, establishing a theory that unified electricity and magnetism to electromagnetism, predicting the existence of electromagnetic waves as the "wireless" carrier of electromagnetic energy. Around 1884 John Henry Poynting defined the Poynting vector and gave Poynting's theorem, which describe the flow of power across an area within electromagnetic radiation and allow for a correct analysis of wireless power transfer systems.
Minimal polynomial (field theory) Summary Minimal_polynomial_(field_theory) In field theory, a branch of mathematics, the minimal polynomial of an element α of a field extension is, roughly speaking, the polynomial of lowest degree having coefficients in the field, such that α is a root of the polynomial. If the minimal polynomial of α exists, it is unique. The coefficient of the highest-degree term in the polynomial is required to be 1. More formally, a minimal polynomial is defined relative to a field extension E/F and an element of the extension field E/F.
Pre-engineered building Project professionals and manufacturer-designed buildings Pre-engineered_building > Project professionals and manufacturer-designed buildings The structural Engineer of Record is responsible to specify the design parameters for the project (e.g. materials, loads, design standards, service limits) and to ensure that the element and assembly designs by others are consistent in the global context of the finished building. The specialty engineer is responsible to design only those elements which the manufacturer is commercially obligated to supply (e.g. by contract) and to communicate the assembly procedures, design assumptions and responses, to the extent that the design relies on or affects work by others, to the Engineer of Record – usually described in the manufacturer's erection drawings and assembly manuals. The manufacturer produces an engineered product but does not typically provide engineering services to the project.
RNA replication Replication process Viral_replicase > Replication process Termination of the nascent RNA chain produced by RdRp is not completely known, however, it has been shown that RdRp termination is sequence-independent.One major drawback of RNA-dependent RNA polymerase replication is the immense error rate during transcription. RdRps are known to have a lack of fidelity on the order of 104 nucleotides, which is thought to be a direct result of its insufficient proofreading abilities. This high rate of variation is favored in viral genomes as it allows for the pathogen to overcome defenses developed by hosts trying to avoid infection allowing for evolutionary growth.
Population cycle Relationships between predators and prey Population_cycle > Relationships between predators and prey There is also an interaction between prey with periodic cycles and predators. As the population expands, there is more food available for predators. As it contracts, there is less food available for predators, putting pressure on their population numbers.
Shift-reduce conflict Bottom-up parse stack Shift-reduce_conflict > Overview > Bottom-up parse stack The base or bottom of the stack is on the left and holds the leftmost, oldest parse fragment. Every reduction step acts only on the rightmost, newest parse fragments. (This accumulative parse stack is very unlike the predictive, leftward-growing parse stack used by top-down parsers.)
Interrupts in 65xx processors ABORT interrupt Interrupts_in_65xx_processors > ABORT interrupt The interrupt disable flag is set in the status register. PB is loaded with $00. The program counter is loaded from the ABORT vector (see tables).As the address pushed to the stack is that of the aborted instruction rather than the contents of the program counter, executing an RTI (ReTurn from Interrupt) following an ABORT interrupt will cause the processor to return to the aborted instruction, rather than the next instruction, as would be the case with the other interrupts.
Algorand Consensus algorithm Algorand > Design > Consensus algorithm In this second phase, a new committee is formed via cryptographic sortition. When users have determined that they are in this second-phase voting committee, they analyze the proposed blocks they have received (including verification of first-phase committee membership) and vote on whether any of the blocks should be adopted. If the voting committee achieves consensus on a new block, then the new block is disseminated across the network.Within the Algorand consensus algorithm, membership in both committees changes every time the phase is run.
Neonatal infection Herpes Simplex Virus (HSV) Neonatal_infection > Etiologies > Viruses > Herpes Simplex Virus (HSV) It can be difficult to distinguish between HSV CNS disease and other causes of neonatal meningitis; therefore, it is recommended to start empiric acyclovir in all cases of neonatal meningitis. Disseminated disease: 25–30% of neonatal HSV infections. Disease is defined by multi-organ involvement, including liver, lungs CNS, heart, kidney, GI tract, and skin. Neonates with disseminated HSV infection present with nonspecific symptoms of neonatal sepsis. All infants with signs of neonatal sepsis should undergo testing for HSV and empiric antiviral therapy.
Multinomial formula Number of ways to select according to a distribution Multinomial_theorem > Interpretations > Number of ways to select according to a distribution In statistical mechanics and combinatorics, if one has a number distribution of labels, then the multinomial coefficients naturally arise from the binomial coefficients. Given a number distribution {ni} on a set of N total items, ni represents the number of items to be given the label i. (In statistical mechanics i is the label of the energy state.) The number of arrangements is found by Choosing n1 of the total N to be labeled 1.
Berman–Hartmanis conjecture Summary Berman–Hartmanis_conjecture In structural complexity theory, the Berman–Hartmanis conjecture is an unsolved conjecture named after Leonard C. Berman and Juris Hartmanis that states that all NP-complete languages look alike, in the sense that they can be related to each other by polynomial time isomorphisms.
Anne R. Douglass Research Anne_R._Douglass > Research Her model on the movement of chlorofluorocarbons (CFCs) in the atmosphere has implications for what would have happened to the ozone layer in the absence of international agreements to reduce atmospheric CFCs levels.Douglass was the co-lead of the validation program for NASA's Aura satellite which is designed to collect data on ozone, climate, and air quality. In 2010, Douglass took over the project scientist position. The ozone data collected by the Aura satellites plays a key role in ozone assessments which guides Douglass's participation in the Montreal Protocol. In 2018, Douglass's research shows decreases in ozone depletion above Antarctica which indicates an improvement in the ozone hole that may fully heal by 2070.
Bacterial protein Summary Protein_function Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, responding to stimuli, providing structure to cells and organisms, and transporting molecules from one location to another. Proteins differ from one another primarily in their sequence of amino acids, which is dictated by the nucleotide sequence of their genes, and which usually results in protein folding into a specific 3D structure that determines its activity. A linear chain of amino acid residues is called a polypeptide.
Friction drive Summary Friction_drive As the "gear ratio" is a function of the distance from the center of the driven disk, any finite thickness on the driven disk means the inner and outer edges are being driven at different speeds. This causes considerable friction on the bearing surface, wearing it out and giving off significant amounts of heat. This results in a sweet spot that limits it to certain low-torque roles.
Dopamine Immune system Prolactin-inhibiting_hormone > Functions > Outside the central nervous system > Immune system In the immune system dopamine acts upon receptors present on immune cells, especially lymphocytes. Dopamine can also affect immune cells in the spleen, bone marrow, and circulatory system. In addition, dopamine can be synthesized and released by immune cells themselves. The main effect of dopamine on lymphocytes is to reduce their activation level. The functional significance of this system is unclear, but it affords a possible route for interactions between the nervous system and immune system, and may be relevant to some autoimmune disorders.
Glycogen branching enzyme Summary Starch_branching_enzyme 1,4-alpha-glucan-branching enzyme, also known as brancher enzyme or glycogen-branching enzyme is an enzyme that in humans is encoded by the GBE1 gene.Glycogen branching enzyme is an enzyme that adds branches to the growing glycogen molecule during the synthesis of glycogen, a storage form of glucose. More specifically, during glycogen synthesis, a glucose 1-phosphate molecule reacts with uridine triphosphate (UTP) to become UDP-glucose, an activated form of glucose. The activated glucosyl unit of UDP-glucose is then transferred to the hydroxyl group at the C-4 of a terminal residue of glycogen to form an α-1,4-glycosidic linkage, a reaction catalyzed by glycogen synthase. Importantly, glycogen synthase can only catalyze the synthesis of α-1,4-glycosidic linkages.
Bridge failure Bridge traffic loading Bridge > Bridge traffic loading Notably, in Europe, it is the maximum value expected in 1000 years. Bridge standards generally include a load model, deemed to represent the characteristic maximum load to be expected in the return period. In the past, these load models were agreed by standard drafting committees of experts but today, this situation is changing.
Linear cryptanalysis Summary Linear_cryptanalysis In cryptography, linear cryptanalysis is a general form of cryptanalysis based on finding affine approximations to the action of a cipher. Attacks have been developed for block ciphers and stream ciphers. Linear cryptanalysis is one of the two most widely used attacks on block ciphers; the other being differential cryptanalysis. The discovery is attributed to Mitsuru Matsui, who first applied the technique to the FEAL cipher (Matsui and Yamagishi, 1992).
Differential entropy Definition Differential_entropy > Definition Unlike the discrete analog, the differential entropy has an offset that depends on the units used to measure X {\displaystyle X} . : 183–184 For example, the differential entropy of a quantity measured in millimeters will be log(1000) more than the same quantity measured in meters; a dimensionless quantity will have differential entropy of log(1000) more than the same quantity divided by 1000. One must take care in trying to apply properties of discrete entropy to differential entropy, since probability density functions can be greater than 1.
Animal psychopathology Stress Animal_psychopathology > Behavioral disorders > Stress When animals experience stress, they are generally more alert than when they are not stressed. It may help them be better aware of unfamiliar environments and possible threats to their life in these environments. Yerkes and Dodson developed a law that explains the empirical relationship between arousal and performance illustrated by an inverted U-shape graph.
Adjustable-focus eyeglasses Methods Adjustable-focus_eyeglasses > Methods The appropriate addition range depends on the user's level of refractive error. A tiny mechanism, actuated by the slider, simultaneously controls both flexible lenses to assure appropriate near vision tracking in both eyes. Another type of opto-mechanical lens is the design of Joshua Silver, and uses liquid pressure against a diaphragm to control focus of a lens.
Limiting similarity Criticism Limiting_similarity > Criticism The key weakness of the theory of limiting similarity is that it is highly system specific and thus difficult to test in practice. In actual environments, one resource axis is inadequate and a specific analysis must be done for each given pair of species. In practice it is necessary to take into account: individual variations in resource utilization curves within a species and how these should be weighted in calculating a common curve whether the resource in question is a present in a deterministic or stochastic distribution and if this changes over time effects of intraspecific competition vs interspecific competitionWhile these complications don't invalidate the concept, they render limiting similarity exceedingly difficult to test in practice and useful for little more than didacticism. Furthermore, Hubbell and Foster point out that extinction via competition can take an extremely long time and the importance of limiting similarity in extinction may even be superseded by speciation.
Caretaker gene Pathways to cancer via the caretakers Caretaker_gene > Genes in context > Pathways to cancer via the caretakers Caretaker genes provide genome stability by preventing the accumulation of these mutations. Factors that contribute to genome stabilization include proper cell-cycle checkpoints, DNA repair pathways, and other actions that ensure cell survival following DNA damage. Specific DNA maintenance operations encoded by caretaker genes include nucleotide excision repair, base excision repair, non-homologous end joining recombination pathways, mismatch repair pathways, and telomere metabolism.
Tuberculin test False positive result Tuberculin_test > False positive result According to the Ohio Department of Health and US Department of Health, the Bacillus Calmette–Guérin (BCG) vaccine does not protect against TB infection. It does, though, give 80% of children protection against tuberculous meningitis and miliary tuberculosis. Therefore, a positive TST/PPD in a person who has received BCG vaccine is interpreted as latent TB infection (LTBI).
Dynamic optimality Knuth's dynamic programming algorithm Dynamic_optimality > Static optimality > Knuth's dynamic programming algorithm In 1971, Knuth published a relatively straightforward dynamic programming algorithm capable of constructing the statically optimal tree in only O(n2) time. In this work, Knuth extended and improved the dynamic programming algorithm by Edgar Gilbert and Edward F. Moore introduced in 1958. Gilbert's and Moore's algorithm required O ( n 3 ) {\displaystyle O(n^{3})} time and O ( n 2 ) {\displaystyle O(n^{2})} space and was designed for a particular case of optimal binary search trees construction (known as optimal alphabetic tree problem) that considers only the probability of unsuccessful searches, that is, ∑ i = 1 n A i = 0 {\textstyle \sum _{i=1}^{n}A_{i}=0} . Knuth's work relied upon the following insight: the static optimality problem exhibits optimal substructure; that is, if a certain tree is statically optimal for a given probability distribution, then its left and right subtrees must also be statically optimal for their appropriate subsets of the distribution (known as monotonicity property of the roots).
Gas-rich meteorites Meteorites Gas-rich_meteorites > Meteorites This meteoritics-related list is incomplete; you can help by expanding it. Interplanetary dust, like c-chondrites and enstatites, contain hosts for these gases and often measurable gas contents. So too do a fraction of micrometeorites.
Normalizing factor Bayes' theorem Normalization_factor > Bayes' theorem {\displaystyle P(H_{0}\|D)\propto P(D\|H_{0})P(H_{0}).} Since P(H\|D) is a probability, the sum over all possible (mutually exclusive) hypotheses should be 1, leading to the conclusion that P ( H 0 \| D ) = P ( D \| H 0 ) P ( H 0 ) ∑ i P ( D \| H i ) P ( H i ) . {\displaystyle P(H_{0}\|D)={\frac {P(D\|H_{0})P(H_{0})}{\displaystyle \sum _{i}P(D\|H_{i})P(H_{i})}}.}
Metabolic Control Analysis Control coefficients Metabolic_Control_Analysis > Control coefficients A control coefficient measures the relative steady state change in a system variable, e.g. pathway flux (J) or metabolite concentration (S), in response to a relative change in a parameter, e.g. enzyme activity or the steady-state rate ( v i {\displaystyle v_{i}} ) of step i {\displaystyle i} . The two main control coefficients are the flux and concentration control coefficients. Flux control coefficients are defined by C v i J = ( d J d p p J ) / ( ∂ v i ∂ p p v i ) = d ln ⁡ J d ln ⁡ v i {\displaystyle C_{v_{i}}^{J}=\left({\frac {dJ}{dp}}{\frac {p}{J}}\right){\bigg /}\left({\frac {\partial v_{i}}{\partial p}}{\frac {p}{v_{i}}}\right)={\frac {d\ln J}{d\ln v_{i}}}} and concentration control coefficients by C v i S = ( d S d p p S ) / ( ∂ v i ∂ p p v i ) = d ln ⁡ S d ln ⁡ v i {\displaystyle C_{v_{i}}^{S}=\left({\frac {dS}{dp}}{\frac {p}{S}}\right){\bigg /}\left({\frac {\partial v_{i}}{\partial p}}{\frac {p}{v_{i}}}\right)={\frac {d\ln S}{d\ln v_{i}}}} .
Infinite string Analysis Bi-infinite_string > Use in other fields of mathematics > Analysis In analysis, when talking about sequences, one will generally consider sequences of the form ( x 1 , x 2 , x 3 , … ) or ( x 0 , x 1 , x 2 , … ) {\displaystyle (x_{1},x_{2},x_{3},\dots ){\text{ or }}(x_{0},x_{1},x_{2},\dots )} which is to say, infinite sequences of elements indexed by natural numbers. A sequence may start with an index different from 1 or 0. For example, the sequence defined by xn = 1/log(n) would be defined only for n ≥ 2.
Gene manipulation Medicine Genetically_Modified > Applications > Medicine The work was widely condemned as unethical, dangerous, and premature. Currently, germline modification is banned in 40 countries. Scientists that do this type of research will often let embryos grow for a few days without allowing it to develop into a baby.Researchers are altering the genome of pigs to induce the growth of human organs, with the aim of increasing the success of pig to human organ transplantation. Scientists are creating "gene drives", changing the genomes of mosquitoes to make them immune to malaria, and then looking to spread the genetically altered mosquitoes throughout the mosquito population in the hopes of eliminating the disease.
Lemma (morphology) Pronunciation Lemma_(morphology) > Pronunciation A word may have different pronunciations, depending on its phonetic environment (the neighbouring sounds) or on the degree of stress in a sentence. An example of the latter is the weak and strong forms of certain English function words like some and but (pronounced /sʌm/, /bʌt/ when stressed but /s(ə)m/, /bət/ when unstressed). Dictionaries usually give the pronunciation used when the word is pronounced alone (its isolation form) and with stress, but they may also note common weak forms of pronunciation.
Selfish DNA Homing endonucleases Selfish_DNA > Examples > Homing endonucleases This gives homing endonucleases an allele frequency dynamics rather similar to a segregation distortion system, and generally unless opposed by strong countervailing selection, they are expected to go to fixation in a population. CRISPR-Cas9 technology allows the artificial construction of homing endonuclease systems. These so-called "gene drive" systems pose a combination of great promise for biocontrol but also potential risk.
Nucleoside-modified messenger RNA Background Nucleoside-modified_messenger_RNA > Background mRNA is produced by synthesising a ribonucleic acid (RNA) strand from nucleotide building blocks according to a deoxyribonucleic acid (DNA) template, a process that is called transcription. When the building blocks provided to the RNA polymerase include non-standard nucleosides such as pseudouridine — instead of the standard adenosine, cytidine, guanosine, and uridine nucleosides — the resulting mRNA is described as nucleoside-modified.Production of protein begins with assembly of ribosomes on the mRNA, the latter then serving as a blueprint for the synthesis of proteins by specifying their amino acid sequence based on the genetic code in the process of protein biosynthesis called translation.
Hydrosere Phytoplankton stage Hydrosere > Stages > Phytoplankton stage Phytoplanktons (cyanobacteria), green algae (Spirogyra, Oedogonium), diatoms, etc. are the pioneer colonizers in the initial stage, starting from a water body, such as a pond. Their spores are carried by air to the pond. The phytoplankton are followed by zooplankton. They settle down to the bottom of the pond after death, and decay into humus that mixes with silt and clay particles brought into the basin by run off water and wave action and form soil. As soil builds up, the pond becomes shallower and further environmental changes follow.
Electrical Conductor Summary Electrical_Conductor This momentum transfer model makes metal an ideal choice for a conductor; metals, characteristically, possess a delocalized sea of electrons which gives the electrons enough mobility to collide and thus affect a momentum transfer. As discussed above, electrons are the primary mover in metals; however, other devices such as the cationic electrolyte(s) of a battery, or the mobile protons of the proton conductor of a fuel cell rely on positive charge carriers. Insulators are non-conducting materials with few mobile charges that support only insignificant electric currents.
Linearised Einstein field equations Summary Linearized_gravity In the theory of general relativity, linearized gravity is the application of perturbation theory to the metric tensor that describes the geometry of spacetime. As a consequence, linearized gravity is an effective method for modeling the effects of gravity when the gravitational field is weak. The usage of linearized gravity is integral to the study of gravitational waves and weak-field gravitational lensing.
Sample distribution Mean Statistical_distribution > Mean The mean of the empirical distribution is an unbiased estimator of the mean of the population distribution. E n ( X ) = 1 n ( ∑ i = 1 n x i ) {\displaystyle E_{n}(X)={\frac {1}{n}}\left(\sum _{i=1}^{n}{x_{i}}\right)} which is more commonly denoted x ¯ {\displaystyle {\bar {x}}}
Permutation (music) Summary Permutation_(music) The rest of the numbers are counted half-step-wise such that: B = 0, C = 1, C♯/D♭ = 2, D = 3, D♯/E♭ = 4, E = 5, F = 6, F♯/G♭ = 7, G = 8, G♯/A♭ = 9, A = 10, and A♯/B♭ = 11. Prime zero is retrieved entirely by choice of the composer. To receive the retrograde of any given prime, the numbers are simply rewritten backwards.
Tangent (trigonometry) In calculus Tangent_(trigonometry) > In calculus In calculus, there are two equivalent definitions of trigonometric functions, either using power series or differential equations. These definitions are equivalent, as starting from one of them, it is easy to retrieve the other as a property. However the definition through differential equations is somehow more natural, since, for example, the choice of the coefficients of the power series may appear as quite arbitrary, and the Pythagorean identity is much easier to deduce from the differential equations.
Subject-oriented programming Subject-oriented programming as a "third dimension" Subject-oriented_programming > Dimensions > Subject-oriented programming as a "third dimension" Method dispatch in object oriented programming can be thought of as "two dimensional" in the sense that the code executed depends on both the method name and the object in question. This can be contrasted with procedural programming, where a procedure name resolves directly, or one dimensionally, onto a subroutine, and also to subject oriented programming, where the sender or subject is also relevant to dispatch, constituting a third dimension.
Foil resistors Production resistors Foil_resistors > Standards > Production resistors Resistor characteristics are quantified and reported using various national standards. In the US, MIL-STD-202 contains the relevant test methods to which other standards refer. There are various standards specifying properties of resistors for use in equipment: IEC 60062 (IEC 62) / DIN 40825 / BS 1852 / IS 8186 / JIS C 5062 etc. (Resistor color code, RKM code, date code) EIA RS-279 / DIN 41429 (Resistor color code) IEC 60063 (IEC 63) / JIS C 5063 (Standard E series values) MIL-PRF-26 MIL-PRF-39007 (Fixed power, established reliability) MIL-PRF-55342 (Surface-mount thick and thin film) MIL-PRF-914 MIL-R-11 Standard Canceled MIL-R-39017 (Fixed, General Purpose, Established Reliability) MIL-PRF-32159 (zero ohm jumpers) UL 1412 (fusing and temperature limited resistors)There are other United States military procurement MIL-R- standards.
Electronic band structure Names of bands near the Fermi level (conduction band, valence band) Band_structure > Basic concepts > Filling of bands > Names of bands near the Fermi level (conduction band, valence band) The closest band above the band gap is called the conduction band, and the closest band beneath the band gap is called the valence band. The name "valence band" was coined by analogy to chemistry, since in semiconductors (and insulators) the valence band is built out of the valence orbitals. In a metal or semimetal, the Fermi level is inside of one or more allowed bands.
Lens (vertebrate anatomy) Development Lens_nucleus > Structure > Development These signals also induce the synthesis of proteins called crystallins. As the name suggests the crystallins can form a clear highly refractive jelly.
Invariant chain Cancer Invariant_chain > Clinical significance > Cancer Found on a number of cancer cell types. Possible cancer therapy target. See milatuzumab.
Band theory Theory in crystals Theory_of_electrons_in_solids > Theory in crystals The ansatz is the special case of electron waves in a periodic crystal lattice using Bloch's theorem as treated generally in the dynamical theory of diffraction. Every crystal is a periodic structure which can be characterized by a Bravais lattice, and for each Bravais lattice we can determine the reciprocal lattice, which encapsulates the periodicity in a set of three reciprocal lattice vectors (b1, b2, b3). Now, any periodic potential V(r) which shares the same periodicity as the direct lattice can be expanded out as a Fourier series whose only non-vanishing components are those associated with the reciprocal lattice vectors. So the expansion can be written as: where K = m1b1 + m2b2 + m3b3 for any set of integers (m1, m2, m3). From this theory, an attempt can be made to predict the band structure of a particular material, however most ab initio methods for electronic structure calculations fail to predict the observed band gap.
Pulmonary tuberculosis Pulmonary Epidemiology_of_tuberculosis > Signs and symptoms > Pulmonary If a tuberculosis infection does become active, it most commonly involves the lungs (in about 90% of cases). Symptoms may include chest pain and a prolonged cough producing sputum. About 25% of people may not have any symptoms (i.e., they remain asymptomatic). Occasionally, people may cough up blood in small amounts, and in very rare cases, the infection may erode into the pulmonary artery or a Rasmussen's aneurysm, resulting in massive bleeding.
Gravitational damping Quantum gravity, wave-particle aspects, and graviton Gravitational_Radiation > Properties and behaviour > Quantum gravity, wave-particle aspects, and graviton If such a particle exists, it is expected to be massless (because the gravitational force appears to have unlimited range) and must be a spin-2 boson. It can be shown that any massless spin-2 field would give rise to a force indistinguishable from gravitation, because a massless spin-2 field must couple to (interact with) the stress–energy tensor in the same way that the gravitational field does; therefore if a massless spin-2 particle were ever discovered, it would be likely to be the graviton without further distinction from other massless spin-2 particles. Such a discovery would unite quantum theory with gravity.
In vitro mutagenesis Applications Site-specific_mutagenesis > Applications Site-directed mutagenesis is used to generate mutations that may produce a rationally designed protein that has improved or special properties (i.e.protein engineering). Investigative tools – specific mutations in DNA allow the function and properties of a DNA sequence or a protein to be investigated in a rational approach. Furthermore, single amino-acid changes by site-directed mutagenesis in proteins can help understand the importance of post-translational modifications.
Two New Sciences Reactions by commentators Two_New_Sciences > Reactions by commentators So great a contribution to physics was Two New Sciences that scholars have long maintained that the book anticipated Isaac Newton's laws of motion. Galileo ... is the father of modern physics—indeed of modern science Part of Two New Sciences was pure mathematics, as has been pointed out by the mathematician Alfréd Rényi, who said that it was the most significant book on mathematics in over 2000 years: Greek mathematics did not deal with motion, and so they never formulated mathematical laws of motion, even though Archimedes developed differentiation and integration. Two New Sciences opened the way to treating physics mathematically by treating motion mathematically for the first time. The Greek mathematician Zeno had designed his paradoxes to prove that motion could not be treated mathematically, and that any attempt to do so would lead to paradoxes.
Mathematical model Elements of a mathematical model Mathematical_models_in_physics > Elements of a mathematical model Mathematical models can take many forms, including dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures. In general, mathematical models may include logical models. In many cases, the quality of a scientific field depends on how well the mathematical models developed on the theoretical side agree with results of repeatable experiments. Lack of agreement between theoretical mathematical models and experimental measurements often leads to important advances as better theories are developed. In the physical sciences, a traditional mathematical model contains most of the following elements: Governing equations Supplementary sub-models Defining equations Constitutive equations Assumptions and constraints Initial and boundary conditions Classical constraints and kinematic equations
Quadratic voting Summary Quadratic_funding By increasing voter credit costs, this demonstrates an individual's support and interests toward the particular decision. If money is used, it is eventually cycled back to the voters based upon per capita. Both E. Glen Weyl and Steven Lalley published research in 2017 in which they claim to demonstrate that this decision-making policy expedites efficiency as the number of voters increases.
VisualFEA Overview VisualFEA > Overview VisualFEA is a full-fledged finite element analysis program with many easy-to-use but powerful features, which can be classified largely into four parts: finite element processing, pre-processing, post-processing and educational simulation. All the functions are integrated into a single executable module, which is a characteristic of the program distinguished from other finite element analysis programs generally composed of multiple modules. The whole procedure from pre-processing to analysis, and to post-processing can be completed on the spot without launching one program after another, or without pipelining data from one program to another.
Purdie methylation Summary Epigenetic_methylation In biological systems, methylation is catalyzed by enzymes; such methylation can be involved in modification of heavy metals, regulation of gene expression, regulation of protein function, and RNA processing. In vitro methylation of tissue samples is also one method for reducing certain histological staining artifacts. The reverse of methylation is demethylation.
Content negotiation Mechanisms Content_negotiation > Mechanisms HTTP provides for several different content negotiation mechanisms including: server-driven (or proactive), agent-driven (or reactive), transparent, and/or hybrid combinations thereof.
Glossary of probability and statistics O Glossary_of_probability_and_statistics > O opinion poll optimal decision optimal design outlier
Ising lattice Local field Ising_lattice > Four dimensions and above > Local field {\displaystyle \langle H(x_{1})H(x_{2})\cdots H(x_{n})\rangle ={\int DH\,e^{-\int d^{d}x\left}H(x_{1})H(x_{2})\cdots H(x_{n}) \over \int DH\,e^{-\int d^{d}x\left}}.} The denominator in this expression is called the partition function:and the integral over all possible values of H is a statistical path integral. It integrates exp(βF) over all values of H, over all the long wavelength fourier components of the spins. F is a "Euclidean" Lagrangian for the field H. It is similar to the Lagrangian in of a scalar field in quantum field theory, the difference being that all the derivative terms enter with a positive sign, and there is no overall factor of i (thus "Euclidean").
Web Accessibility Directive Implications of this Directive Web_Accessibility_Directive > Implications of this Directive The Directive: addresses websites and apps of public sector organizations; refers to specific standards, such as EN 301 549; requires the publication of an accessibility statement for websites and mobile apps; calls for a feedback mechanism for users to flag accessibility problems; expects regular accessibility monitoring and corresponding public reports by Member States.The EC is also supporting the financing of research and pilot projects such as W3C-WAI - WAI-Tools to establish uniform accessibility testing rules; W3C-WAI - WAI-Guide to design educational material; WADcher to develop a WAD platform prototype for evaluation, monitoring and reporting for WAD; Funka Nu AB - We4Authors to facilitates the incorporation of accessibility features as the default option in authoring tools.
Hohmann orbit Summary Hohmann_orbit In astronautics, the Hohmann transfer orbit () is an orbital maneuver used to transfer a spacecraft between two orbits of different altitudes around a central body. Examples would be used for travel between low Earth orbit and the Moon, or another solar planet or asteroid. In the idealized case, the initial and target orbits are both circular and coplanar. The maneuver is accomplished by placing the craft into an elliptical transfer orbit that is tangential to both the initial and target orbits.
Quantum thermodynamics Dynamical view Quantum_thermodynamics > Dynamical view The Markov property imposes that the system and bath are uncorrelated at all times ρ S B = ρ s ⊗ ρ B {\displaystyle \rho _{\rm {SB}}=\rho _{s}\otimes \rho _{\rm {B}}} . The L-GKS equation is unidirectional and leads any initial state ρ S {\displaystyle \rho _{\rm {S}}} to a steady state solution which is an invariant of the equation of motion ρ ˙ S ( t → ∞ ) = 0 {\displaystyle {\dot {\rho }}_{\rm {S}}(t\rightarrow \infty )=0} .The Heisenberg picture supplies a direct link to quantum thermodynamic observables. The dynamics of a system observable represented by the operator, O {\displaystyle O} , has the form: d O d t = i ℏ + L D ∗ ( O ) + ∂ O ∂ t {\displaystyle {\frac {dO}{dt}}={\frac {i}{\hbar }}+L_{\rm {D}}^{*}(O)+{\frac {\partial O}{\partial t}}} where the possibility that the operator, O {\displaystyle O} is explicitly time-dependent, is included.
Pulse-Doppler radar History Pulse-Doppler_radar > History Doppler weather effects (precipitation) were also found to degrade conventional radar and moving target indicator radar, which can mask aircraft reflections. This phenomenon was adapted for use with weather radar in the 1950s after declassification of some World War II systems. Pulse-Doppler radar was developed during World War II to overcome limitations by increasing pulse repetition frequency.
Legal theory Natural law Legal_studies > Natural law The strong natural law thesis holds that if a human law fails to be in response to compelling reasons, then it is not properly a "law" at all. This is captured, imperfectly, in the famous maxim: lex iniusta non est lex (an unjust law is no law at all). The weak natural law thesis holds that if a human law fails to be in response to compelling reasons, then it can still be called a "law", but it must be recognised as a defective law.Notions of an objective moral order, external to human legal systems, underlie natural law. What is right or wrong can vary according to the interests one is focused on. John Finnis, one of the most important of modern natural lawyers, has argued that the maxim "an unjust law is no law at all" is a poor guide to the classical Thomist position.
Simple random samples Introduction Simple_random_samples > Introduction The principle of simple random sampling is that every set of items has the same probability of being chosen. For example, suppose N college students want to get a ticket for a basketball game, but there are only X < N tickets for them, so they decide to have a fair way to see who gets to go. Then, everybody is given a number in the range from 0 to N-1, and random numbers are generated, either electronically or from a table of random numbers. Numbers outside the range from 0 to N-1 are ignored, as are any numbers previously selected.
Probability models An example Statistical_models > An example In this example, the model is determined by (1) specifying S {\displaystyle S} and (2) making some assumptions relevant to P {\displaystyle {\mathcal {P}}} . There are two assumptions: that height can be approximated by a linear function of age; that errors in the approximation are distributed as i.i.d. Gaussian. The assumptions are sufficient to specify P {\displaystyle {\mathcal {P}}} —as they are required to do.
Allotropes of sulfur Cyclo-Sn (n = 9–15, 18, 20) Allotrope_of_sulfur > Solid cyclo-sulfur allotropes > Cyclo-Sn (n = 9–15, 18, 20) These allotropes have been synthesised by various methods for example, treating titanocene pentasulfide and a dichlorosulfane of suitable sulfur chain length, Sn−5Cl2: (η5-C5H5)2TiS5 + Sn−5Cl2 → cyclo-Sn + (η5-C5H5)2TiCl2or alternatively treating a dichlorosulfane, Sn−mCl2 and a polysulfane, H2Sm: Sn−mCl2 + H2Sm → cyclo-Sn + 2 HClS12, S18, and S20 can also be prepared from S8. With the exception of cyclo-S12, the rings contain S–S bond lengths and S-S-S bond angle that differ one from another.Cyclo-S12 is the most stable cyclo-allotrope. Its structure can be visualised as having sulfur atoms in three parallel planes, 3 in the top, 6 in the middle and three in the bottom.Two forms (α-, β-) of cyclo-S9 are known, one of which has been characterized.Two forms of cyclo-S18 are known where the conformation of the ring is different. To differentiate these structures, rather than using the normal crystallographic convention of α-, β-, etc., which in other cyclo-Sn compounds refer to different packings of essentially the same conformer, these two conformers have been termed endo- and exo-.

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