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Newton's cradle Other examples of this effect Newton's_cradle > Physics explanation > Simple solution > Other examples of this effect The surrounding atoms, molecules, or sub-volumes experiencing the pressure wave act to constrain each other similarly to how the string constrains the cradle's balls to a straight line. As a medical example, lithotripsy shock waves can be sent through the skin and tissue without harm to burst kidney stones. The side of the stones opposite to the incoming pressure wave bursts, not the side receiving the initial strike. In the Indian game carrom, a striker stops after hitting a stationery playing piece, transferring all of its momentum into the piece that was hit.
Meudon Great Refractor Design and construction Meudon_Great_Refractor > Design and construction There are two objective lenses, one is designed for the human eye, and the other for photography. The 62 cm lens is designed to focus blue light, which is the color desired for the film emulsion. (It would be another century before CCD imaging came into force). The lenses in the telescope are a type of glass lens that has two parts, usually called an achromat.
Demyelinating disease Summary Demyelinating_disease A demyelinating disease refers to any disease affecting the nervous system where the myelin sheath surrounding neurons is damaged. This damage disrupts the transmission of signals through the affected nerves, resulting in a decrease in their conduction ability. Consequently, this reduction in conduction can lead to deficiencies in sensation, movement, cognition, or other functions depending on the nerves affected. Various factors can contribute to the development of demyelinating diseases, including genetic predisposition, infectious agents, autoimmune reactions, and other unknown factors.
Ucode system Structure and Resolution mechanism Ucode_system > Structure and Resolution mechanism The ucode server architecture is similar to the familiar Internet DNS resolution service. Like DNS, the ucode resolution mechanism consists of hierarchical levels. The ucode resolution mechanism is three tiered as follows: uID center maintains the root server Top level domain (TLD) servers are under root Second level domain (SLD) servers are under TLDThe root server is maintained by uID Center in Tokyo. TLD servers are in place in Japan, other Asian countries and in Europe (Oulu, Finland). The number of TLD and SLD servers is not limited.
Building material Metal Building_material > Man-made substances > Metal Corrosion is metal's prime enemy when it comes to longevity. Steel is a metal alloy whose major component is iron, and is the usual choice for metal structural building materials. It is strong, flexible, and if refined well and/or treated lasts a long time.
Fornix of the brain Structure Hippocampal_commissure > Structure The left and right parts separate, but there is also an anterior/posterior divergence. The posterior fibers (called the postcommissural fornix) of each side continue through the hypothalamus to the mammillary bodies; then to the anterior nuclei of thalamus. The anterior fibers (precommissural fornix) end at the septal nuclei of the basal forebrain and nucleus accumbens of each half of the brain.
Surgical shock Summary Surgical_shock Surgical shock is the shock to the circulation resulting from surgery. It is commonly due to a loss of blood which results in insufficient blood volume. == References ==
Kolmogorov's axioms The numeric bound Kolmogorov's_axioms > Consequences > The numeric bound It immediately follows from the monotonicity property that 0 ≤ P ( E ) ≤ 1 ∀ E ∈ F . {\displaystyle 0\leq P(E)\leq 1\qquad \forall E\in F.}
Holomorphic Fock space Weyl calculus Schrödinger_representation > Weyl calculus Defining in general W ( F ) = 1 2 π ∫ F ( z ) W ( z ) d x d y , {\displaystyle W(F)={1 \over 2\pi }\int F(z)W(z)\,dxdy,} the product of two such operators is given by the formula W ( F ) W ( G ) = W ( F ⋆ G ) , {\displaystyle W(F)W(G)=W(F\star G),} where the twisted convolution or Moyal product is given by F ⋆ G ( z ) = 1 2 π ∫ F ( z 1 ) G ( z 2 − z 1 ) e i ( x 1 y 2 − y 1 x 2 ) d x 1 d y 1 . {\displaystyle F\star G(z)={1 \over 2\pi }\int F(z_{1})G(z_{2}-z_{1})e^{i(x_{1}y_{2}-y_{1}x_{2})}\,dx_{1}dy_{1}.} The smoothing operators correspond to W(F) or ψ(a) with F or a Schwartz functions on R2.
Bivalve molluscs Nervous system Bivalve_molluscs > Anatomy > Nervous system The sedentary habits of the bivalves have meant that in general the nervous system is less complex than in most other molluscs. The animals have no brain; the nervous system consists of a nerve network and a series of paired ganglia. In all but the most primitive bivalves, two cerebropleural ganglia are on either side of the oesophagus. The cerebral ganglia control the sensory organs, while the pleural ganglia supply nerves to the mantle cavity.
Sound velocity probe Summary Sound_velocity_probe A sound velocity probe is a device that is used for measuring the speed of sound, specifically in the water column, for oceanographic and hydrographic research purposes.
Kinodynamic planning Summary Kinodynamic_planning These techniques for kinodynamic planning have been shown to work well in practice. However, none of these heuristic techniques can guarantee the optimality of the computed solution (i.e., they have no performance guarantees), and none can be mathematically proven to be faster than the original PTAS algorithms (i.e., none have a provably lower computational complexity). == References ==
Finite potential barrier (QM) Remarks and applications Finite_potential_barrier_(QM) > Remarks and applications On the other hand, many systems only change along one coordinate direction and are translationally invariant along the others; they are separable. The Schrödinger equation may then be reduced to the case considered here by an ansatz for the wave function of the type: Ψ ( x , y , z ) = ψ ( x ) ϕ ( y , z ) {\displaystyle \Psi (x,y,z)=\psi (x)\phi (y,z)} . For another, related model of a barrier, see Delta potential barrier (QM), which can be regarded as a special case of the finite potential barrier. All results from this article immediately apply to the delta potential barrier by taking the limits V 0 → ∞ , a → 0 {\displaystyle V_{0}\to \infty ,\;a\to 0} while keeping V 0 a = λ {\displaystyle V_{0}a=\lambda } constant.
Chaotic dynamical system A popular but inaccurate analogy for chaos Chaotic_dynamical_system > A popular but inaccurate analogy for chaos The sensitive dependence on initial conditions (i.e., butterfly effect) has been illustrated using the following folklore: For want of a nail, the shoe was lost. For want of a shoe, the horse was lost. For want of a horse, the rider was lost. For want of a rider, the battle was lost.
Brain injuries Long term psychological and physiological effects Brain_damage > Signs and symptoms > Long term psychological and physiological effects There are multiple responses of the body to brain injury, occurring at different times after the initial occurrence of damage, as the functions of the neurons, nerve tracts, or sections of the brain can be affected by damage. The immediate response can take many forms. Initially, there may be symptoms such as swelling, pain, bruising, or loss of consciousness.
PH meter Calibration and operation PH_electrode > Design and use > Calibration and operation For general purposes, buffers at pH 4.00 and pH 10.00 are suitable. The pH meter has one calibration control to set the meter reading equal to the value of the first standard buffer and a second control to adjust the meter reading to the value of the second buffer. A third control allows the temperature to be set.
Velocity Scalar velocities Velocity_vector > Relative velocity > Scalar velocities In the one-dimensional case, the velocities are scalars and the equation is either: if the two objects are moving in opposite directions, or: if the two objects are moving in the same direction.
Vertical queue Concept usage Vertical_queue > Concept usage The first vehicle to arrive at the point of congestion would thus be at the bottom of the vertical queue. Vehicles incur no delay traveling to the point of congestion, and travel to the point at which the vertical queue occurs without hindrance. The vehicles only incur delay while in congestion or at the stop line.
Impact of the COVID-19 pandemic on other health issues Summary Impact_of_the_COVID-19_pandemic_on_other_health_issues As of June 2020, 40% of U.S. adults were experiencing adverse mental health symptoms, with 11% having seriously considered to attempt suicide. The research data suggest that the pandemic has negative effects on both weight loss and food health monitoring but the effects were short lived results.Paying attention and taking measures to prevent mental health problems and post-traumatic stress syndrome, particularly in women, is already a need.
Functional reactive programming Interactive FRP Functional_reactive_programming > Interactive FRP It has been pointed out that the ordinary FRP model, from inputs to outputs, is poorly suited to interactive programs. Lacking the ability to "run" programs within a mapping from inputs to outputs may mean one of the following solutions has to be used: Create a data structure of actions which appear as the outputs. The actions must be run by an external interpreter or environment. This inherits all of the difficulties of the original stream I/O system of Haskell.
Perceptual load theory Summary Perceptual_load_theory Perceptual load theory is a psychological theory of attention. It was presented by Nilli Lavie in the mid-nineties as a potential resolution to the early/late selection debate.This debate relates to the "cocktail party problem": how do people at a cocktail party select the conversation they are listening to and ignore the others? The models of attention proposed prior to Lavie's theory differed in their proposals for the point in the information processing stream where the selection of target information occurs, leading to a heated debate about whether the selection occurs "early" or "late". There were also arguments about to what degree distracting stimuli are processed.
Nuclear C-algebra Examples Nuclear_C-algebra > Examples The commutative unital C ∗ {\displaystyle ^{*}} algebra of (real or complex-valued) continuous functions on a compact Hausdorff space as well as the noncommutative unital algebra of n × n {\displaystyle n\times n} real or complex matrices are nuclear (cf. here).
Sample standard deviation Confidence interval of a sampled standard deviation Standard_deviations > Estimation > Confidence interval of a sampled standard deviation A larger population of N = 10 has 9 degrees of freedom for estimating the standard deviation. The same computations as above give us in this case a 95% CI running from 0.69 × SD to 1.83 × SD. So even with a sample population of 10, the actual SD can still be almost a factor 2 higher than the sampled SD.
Principle of sufficient reason History Principle_of_sufficient_reason > History The modern formulation of the principle is usually ascribed to early Enlightenment philosopher Gottfried Leibniz. Leibniz formulated it, but was not an originator. The idea was conceived of and utilized by various philosophers who preceded him, including Anaximander, Parmenides, Archimedes, Plato and Aristotle, Cicero, Avicenna, Thomas Aquinas, and Spinoza. One often pointed to is in Anselm of Canterbury: his phrase quia Deus nihil sine ratione facit (because God does nothing without reason) and the formulation of the ontological argument for the existence of God.
Adiponectin Discovery Adiponectin > Discovery The gene was investigated for variants that predispose to type 2 diabetes. Several single nucleotide polymorphisms in the coding region and surrounding sequence were identified from several different populations, with varying prevalences, degrees of association and strength of effect on type 2 diabetes. Berberine, an isoquinoline alkaloid, has been shown to increase adiponectin expression, which partly explains its beneficial effects on metabolic disturbances. Mice fed the omega-3 fatty acids eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA) have shown increased plasma adiponectin. Curcumin, capsaicin, gingerol, and catechins have also been found to increase adiponectin expression.Phylogenetic distribution includes expression in birds and fish.
Long-bolt engine Advantages Long-bolt_engine > Advantages This permits the block and crankcase to be made lighter and less stiff, whilst still reducing the amount of deflection and twist exhibited in service. When a ladder-frame main bearing cap is used, the crankcase assembly becomes considerably stiffer.These advantages are primarily for the initial production of engines, particularly when this is a robot-based assembly. Secondary advantages may also be gained of improved service life.
Early life of Isaac Newton Universal law of gravitation Early_life_of_Isaac_Newton > Universal law of gravitation At a meeting of the Royal Society on 11 January 1672, Oldenburg, the secretary, read a letter from Paris describing the procedure followed by Jean Picard in measuring a degree, and specifically stating the precise length that he calculated it to be. It is probable that Newton had become acquainted with this measurement of Picard's, and that he was therefore led to make use of it when his thoughts were redirected to the subject. This estimate of the Earth's magnitude, giving 691 miles (1112 km) to 10°, made the two results, the discrepancy between which Newton had regarded as a disproof of his conjecture, to agree so exactly that he now regarded his conjecture as fully established.
Certainty equivalence principle Summary Certainty_equivalence_principle Stochastic control or stochastic optimal control is a sub field of control theory that deals with the existence of uncertainty either in observations or in the noise that drives the evolution of the system. The system designer assumes, in a Bayesian probability-driven fashion, that random noise with known probability distribution affects the evolution and observation of the state variables. Stochastic control aims to design the time path of the controlled variables that performs the desired control task with minimum cost, somehow defined, despite the presence of this noise. The context may be either discrete time or continuous time.
Latent class model Related methods Latent_class_analysis > Related methods Modified to handle discrete data, this constrained analysis is known as LCA. Discrete latent trait models further constrain the classes to form from segments of a single dimension: essentially allocating members to classes on that dimension: an example would be assigning cases to social classes on a dimension of ability or merit. As a practical instance, the variables could be multiple choice items of a political questionnaire.
Bar recursion Summary Bar_recursion Bar recursion is a generalized form of recursion developed by C. Spector in his 1962 paper. It is related to bar induction in the same fashion that primitive recursion is related to ordinary induction, or transfinite recursion is related to transfinite induction.
Nigrostriatal pathway Levodopa-induced dyskinesia Nigrostriatal_pathway > Clinical significance > Parkinson's disease > Levodopa-induced dyskinesia Levodopa-induced dyskinesias (LID) is a complication associated with long-term use of the Parkinson's treatment L-DOPA, characterized by involuntary movement and muscle contractions. This disorder occurs in up to 90% of patients after 9 years of treatment. The use of L-DOPA in patients can lead to interruption of nigrostriatal dopamine projections as well as changes in the post-synaptic neurons in the basal ganglia.
Adiabatic shear band Deformation Adiabatic_shear_band > Deformation During work hardening, the micro-structure, distortion of grain structure and the generation and glide of dislocations all occur. The remainder of the plastic work done – which can be as much as 90% of the total, is dissipated as heat. If the plastic deformation is carried out under dynamic conditions, such as by drop forging, then the plastic deformation is localized more as the forging hammer speed is increased.
Coherent effects in semiconductor optics Photon echoes of excitons Coherent_effects_in_semiconductor_optics > Selected coherent effects > Photon echoes of excitons When photon echo experiments are performed in semiconductors with exciton resonances, it is essential to include many-body effects in the theoretical analysis since they may qualitatively alter the dynamics. For example, numerical solutions of the SBEs have demonstrated that the dynamical reduction of the band gap which originates from the Coulomb interaction among the photoexcited electrons and holes is able to generate a photon echo even for resonant excitation of a single discrete exciton resonance with a pulse of sufficient intensity.Besides the rather simple effect of inhomogeneous broadening, spatial fluctuations of the energy, i.e., disorder, which in semiconductor nanostructure may, e.g., arise from imperfection of the interfaces between different materials, can also lead to a decay of the photon echo amplitude with increasing time delay.
Construction of the real numbers On models Constructions_of_real_numbers > Axiomatic definitions > Axioms > On models Saying that any two models are isomorphic means that for any two models ( R , 0 R , 1 R , + R , × R , ≤ R ) {\displaystyle (\mathbb {R} ,0_{\mathbb {R} },1_{\mathbb {R} },+_{\mathbb {R} },\times _{\mathbb {R} },\leq _{\mathbb {R} })} and ( S , 0 S , 1 S , + S , × S , ≤ S ) , {\displaystyle (S,0_{S},1_{S},+_{S},\times _{S},\leq _{S}),} there is a bijection f: R → S {\displaystyle f\colon \mathbb {R} \to S} that preserves both the field operations and the order. Explicitly, f is both injective and surjective. f(0ℝ) = 0S and f(1ℝ) = 1S.
Pyramorphix Number of combinations Pyramorphix > Master Pyramorphix > Number of combinations There are six edge pieces which are fixed in position relative to one another, each of which has four possible orientations. If the puzzle is solved apart from these pieces, the number of edge twists will always be even, making 46/2 possibilities for these pieces.
Homogeneous electron gas Zero-temperature phase diagram of jellium in three and two dimensions Uniform_electron_gas > Zero-temperature phase diagram of jellium in three and two dimensions To minimize the kinetic energy, the single-electron states are delocalized, in a state very close to the Slater determinant (non-interacting state) constructed from plane waves. Here the lowest-momentum plane-wave states are doubly occupied by spin-up and spin-down electrons, giving a paramagnetic Fermi fluid. At lower densities, where the interaction energy is more important, it is energetically advantageous for the electron gas to spin-polarize (i.e., to have an imbalance in the number of spin-up and spin-down electrons), resulting in a ferromagnetic Fermi fluid.
Array programming Mathematical reasoning and language notation Array_programming > Mathematical reasoning and language notation The matrix left-division operator concisely expresses some semantic properties of matrices. As in the scalar equivalent, if the (determinant of the) coefficient (matrix) A is not null then it is possible to solve the (vectorial) equation A * x = b by left-multiplying both sides by the inverse of A: A−1 (in both MATLAB and GNU Octave languages: A^-1). The following mathematical statements hold when A is a full rank square matrix: A^-1 (A x)==A^-1 * (b) (A^-1 * A)* x ==A^-1 * b (matrix-multiplication associativity) x = A^-1 * bwhere == is the equivalence relational operator. The previous statements are also valid MATLAB expressions if the third one is executed before the others (numerical comparisons may be false because of round-off errors).
Buckingham π theorem Speed Buckingham_pi_theorem > Examples > Speed In linear algebra, the set of vectors with this property is known as the kernel (or nullspace) of the dimensional matrix. In this particular case its kernel is one-dimensional. The dimensional matrix as written above is in reduced row echelon form, so one can read off a non-zero kernel vector to within a multiplicative constant: If the dimensional matrix were not already reduced, one could perform Gauss–Jordan elimination on the dimensional matrix to more easily determine the kernel.
Epinephrine (neurotransmitter) Mechanism of action Epinephrine_(neurotransmitter) > Mechanism of action It increases peripheral resistance via α1 receptor-dependent vasoconstriction and increases cardiac output by binding to β1 receptors. The goal of reducing peripheral circulation is to increase coronary and cerebral perfusion pressures and therefore increase oxygen exchange at the cellular level. While adrenaline does increase aortic, cerebral, and carotid circulation pressure, it lowers carotid blood flow and end-tidal CO2 or ETCO2 levels. It appears that adrenaline improve macrocirculation at the expense of the capillary beds where perfusion takes place.
Stack canary Bypass countermeasures Stack_canary > Protection schemes > Bypass countermeasures The previous mitigations make the steps of the exploitation harder. But it is still possible to exploit a stack buffer overflow if some vulnerabilities are presents or if some conditions are met.
Gershgorin circle theorem Example Gershgorin_circle_theorem > Example {\displaystyle D(10,2),\;D(8,0.6),\;D(2,3),\;{\text{and}}\;D(-11,3).} Note that we can improve the accuracy of the last two discs by applying the formula to the corresponding columns of the matrix, obtaining D ( 2 , 1.2 ) {\displaystyle D(2,1.2)} and D ( − 11 , 2.2 ) {\displaystyle D(-11,2.2)} . The eigenvalues are 9.8218, 8.1478, 1.8995, −10.86.
Piperacillin Pharmacodynamics Piperacillin > Pharmacology > Pharmacodynamics Similar results are found in a study where a select number of β-lactam susceptible pathogens consisting of Enterococcus faecalis, Klebsiella pneumoniae and Citrobacter freundii were used to test a ~10g every 24 hour dosing interval for continuous infusion.Organisms with a piperacillin-tazobactam MIC values equal to 32 or less than 16ml/I lead to 50% T>MIC when extended-interval intermittent administrations under two different dosing intervals (8.1g and 6.75g every 12 hours) were used against them. The pharmacodynamic target attainments corresponding to pathogens with MIC values of 16 mg/I are found to reach 92% when a more traditional 4 hour dosing regime is utilized to administer at irregular intervals. One study using the Monte Carlo simulation produced contradicting results to the previous studies, deducing that inadequate pharmacodynamic targets were achieved (T>MIC > 50%) for similar ESBL-producing bacteria, applying to both continuous and high dosage intermittent infusion.
Field coupling Angular momentum coupling Coupling_(physics) > Quantum mechanics > Angular momentum coupling When angular momenta from two separate sources interact with each other, they are said to be coupled. For example, two electrons orbiting around the same nucleus may have coupled angular momenta. Due to the conservation of angular momentum and the nature of the angular momentum operator, the total angular momentum is always the sum of the individual angular momenta of the electrons, or Spin-Orbit interaction (also known as spin-orbit coupling) is a special case of angular momentum coupling. Specifically, it is the interaction between the intrinsic spin of a particle, S, and its orbital angular momentum, L. As they are both forms of angular momentum, they must be conserved. Even if energy is transferred between the two, the total angular momentum, J, of the system must be constant, J = L + S {\displaystyle \mathbf {J} =\mathbf {L} +\mathbf {S} } .
Autoreactive lymphocyte Function Autoreactive_lymphocyte > Function The atypical lymphocytes have been best studied from blood of patients with infectious mononucleosis. Early studies suspect that atypical lymphocytes could have both T or B cells features; now it is more suggested that reactive lymphocytes are activated T-lymphocytes produced in response to infected B-lymphocytes.Reactive lymphocytes have been found to accumulate in areas of inflammation like the liver and pharynx of individuals with infectious mononucleosis and skin window preparations. In infectious mononucleosis, the atypical lymphocytes are one component of a normal immune system that helps to control potentially fatal Epstein-Barr virus-induced B-cell lymphoma in human.
Intestinal cancer Pathogenesis Bowel_cancer > Pathogenesis DCC commonly has a deleted segment of a chromosome in colorectal cancer.Approximately 70% of all human genes are expressed in colorectal cancer, with just over 1% of having increased expression in colorectal cancer compared to other forms of cancer. Some genes are oncogenes: they are overexpressed in colorectal cancer. For example, genes encoding the proteins KRAS, RAF, and PI3K, which normally stimulate the cell to divide in response to growth factors, can acquire mutations that result in over-activation of cell proliferation.
Personality development Evolutionary Personality_development > Theories > Evolutionary The evolutionary theory of personality development is primarily based on the evolutionary process of natural selection. From the evolutionary perspective, evolution resulted in variations of the human mind. Natural selection refined these variations based on their beneficence to humans. Due to human complexity, many opposing personality traits proved to be beneficial in a variety of ways.
Electron shell model History K_shell > History During this period Bohr was working with Walther Kossel, whose papers in 1914 and in 1916 called the orbits "shells". Sommerfeld retained Bohr's planetary model, but added mildly elliptical orbits (characterized by additional quantum numbers ℓ and m) to explain the fine spectroscopic structure of some elements. The multiple electrons with the same principal quantum number (n) had close orbits that formed a "shell" of positive thickness instead of the circular orbit of Bohr's model which orbits called "rings" were described by a plane.The existence of electron shells was first observed experimentally in Charles Barkla's and Henry Moseley's X-ray absorption studies.
C8H10FN3O3S Summary C8H10FN3O3S The molecular formula C8H10FN3O3S (molar mass: 247.24 g/mol, exact mass: 247.0427 u) may refer to: Emtricitabine (FTC) Racivir
RNA World Hypothesis Implications RNA_World_Hypothesis > Implications RNAs are known to play roles in other cellular catalytic processes, specifically in the targeting of enzymes to specific RNA sequences. In eukaryotes, the processing of pre-mRNA and RNA editing take place at sites determined by the base pairing between the target RNA and RNA constituents of small nuclear ribonucleoproteins (snRNPs). Such enzyme targeting is also responsible for gene down regulation through RNA interference (RNAi), where an enzyme-associated guide RNA targets specific mRNA for selective destruction. Likewise, in eukaryotes the maintenance of telomeres involves copying of an RNA template that is a constituent part of the telomerase ribonucleoprotein enzyme. Another cellular organelle, the vault, includes a ribonucleoprotein component, although the function of this organelle remains to be elucidated.
Eigenvalues and eigenvectors of the second derivative Neumann case Eigenvalues_and_eigenvectors_of_the_second_derivative > Derivation of Eigenvalues and Eigenvectors in the Discrete Case > Neumann case Relabeling the indices in the formula above and combining with the zero eigenvalue, we obtain, λ k = − 4 h 2 sin 2 ⁡ ( ( k − 1 ) π 2 n ) , k = 1 , . .
Iterated prisoner dilemma Stochastic iterated prisoner's dilemma Iterated_prisoner's_dilemma > The iterated prisoner's dilemma > Stochastic iterated prisoner's dilemma In a stochastic iterated prisoner's dilemma game, strategies are specified in terms of "cooperation probabilities". In an encounter between player X and player Y, X's strategy is specified by a set of probabilities P of cooperating with Y. P is a function of the outcomes of their previous encounters or some subset thereof. If P is a function of only their most recent n encounters, it is called a "memory-n" strategy. A memory-1 strategy is then specified by four cooperation probabilities: P = { P c c , P c d , P d c , P d d } {\displaystyle P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}} , where Pcd is the probability that X will cooperate in the present encounter given that the previous encounter was characterized by X cooperating and Y defecting.
Point-coincidence argument Meaning of coordinate invariance Point-coincidence_argument > Meaning of coordinate invariance In General Relativity, every separate local quantity which is used to describe the geometry is itself a local dynamical field, with its own equation of motion. This produces severe restrictions, because the equation of motion has to be a sensible one. It must determine the future from initial conditions, it must not have runaway instabilities for small perturbations, it must define a positive definite energy for small deviations. If one takes the point of view that coordinate invariance is trivially true, the principle of coordinate invariance simply states that the metric itself is dynamical and its equation of motion does not involve a fixed background geometry.
Osmotic concentration Definition Osmotic_strength > Definition However, φ can also be larger than 1 (e.g. for sucrose). For salts, electrostatic effects cause φ to be smaller than 1 even if 100% dissociation occurs (see Debye–Hückel equation); n is the number of particles (e.g. ions) into which a molecule dissociates. For example: glucose has n of 1, while NaCl has n of 2; C is the molar concentration of the solute; the index i represents the identity of a particular solute.Osmolarity can be measured using an osmometer which measures colligative properties, such as Freezing-point depression, Vapor pressure, or Boiling-point elevation.
Random Sequence Modern approaches Random_Sequence > Modern approaches This definition is often called Kolmogorov–Loveland stochasticity. But this method was considered too weak by Alexander Shen who showed that there is a Kolmogorov–Loveland stochastic sequence which does not conform to the general notion of randomness. In 1966 Per Martin-Löf introduced a new notion which is now generally considered the most satisfactory notion of algorithmic randomness.
HTTP Strict Transport Security Applicability HTTP_Strict_Transport_Security > Applicability Additionally, no warnings are presented to the user during the downgrade process, making the attack fairly subtle to all but the most vigilant. Marlinspike's sslstrip tool fully automates the attack.HSTS addresses this problem by informing the browser that connections to the site should always use TLS/SSL. The HSTS header can be stripped by the attacker if this is the user's first visit.
Receiver Operating Characteristic Curve Explorer and Tester Background – ROC curves in biomarker discovery Receiver_Operating_Characteristic_Curve_Explorer_and_Tester > Background – ROC curves in biomarker discovery Medical biomarkers fall into 5 major categories: 1) diagnostic (used to identify if you have a disease or condition); 2) prognostic (used to determine how well you will do with the disease or condition); 3) predictive (used to determine if you may get the disease); 4) efficacy or monitoring (used to determine how well a drug or treatment is doing in fighting the disease) and 5) exposure (used to determine if you have been exposed to a drug, food, toxin or other kind of substance). Good biomarkers should exhibit good sensitivity (the fraction of correctly identified true positives) and good specificity (the fraction of correctly identified true negatives). A perfect biomarker or biomarker panel would be 100% sensitive (predict all people in the sick group as being sick) and 100% specific (not predicting anyone from the healthy group as being sick).
Gene expression programming Neural networks Gene_expression_programming > Neural networks This output (zero or one in this simple case) depends on the threshold of each unit, that is, if the total incoming activation is equal to or greater than the threshold, then the output is one, zero otherwise. The above NN-tree can be linearized as follows: 0123456789012 DDDabab654321where the structure in positions 7–12 (Dw) encodes the weights. The values of each weight are kept in an array and retrieved as necessary for expression.
Oort constants Uses Oort_constants > Uses Since R0 can be determined by other means (such as by carefully tracking the motions of stars near the Milky Way's central supermassive black hole), knowing A {\displaystyle A} and B {\displaystyle B} allows us to determine V0. It can also be shown that the mass density ρ R {\displaystyle \rho _{R}} can be given by: ρ R = B 2 − A 2 2 π G {\displaystyle \rho _{R}={\frac {B^{2}-A^{2}}{2\pi G}}} So the Oort constants can tell us something about the mass density at a given radius in the disk. They are also useful to constrain mass distribution models for the Galaxy. As well, in the epicyclic approximation for nearly circular stellar orbits in a disk, the epicyclic frequency κ {\displaystyle \kappa } is given by κ 2 = − 4 B Ω {\displaystyle \kappa ^{2}=-4B\Omega } , where Ω {\displaystyle \Omega } is the angular velocity. Therefore, the Oort constants can tell us a great deal about motions in the galaxy.
Proportional font Font metrics Proportional_spacing > Typeface anatomy > Font metrics Typefaces that can be substituted for one another in a document without changing the document's text flow are said to be "metrically identical" (or "metrically compatible"). Several typefaces have been created to be metrically compatible with widely used proprietary typefaces to allow the editing of documents set in such typefaces in digital typesetting environments where these typefaces are not available. For instance, the free and open-source Liberation fonts and Croscore fonts have been designed as metrically compatible substitutes for widely used Microsoft fonts.
Hereditarily countable set The collection of all h. c. sets Hereditarily_countable_set > Results > The collection of all h. c. sets The class of all hereditarily countable sets can be proven to be a set from the axioms of Zermelo–Fraenkel set theory (ZF) and is set is designated H ℵ 1 {\displaystyle H_{\aleph _{1}}} . In particular, the existence does not require any form of the axiom of choice. Constructive Zermelo-Freankel (CZF) does not prove the class to be a set.
Velocity vector Polar coordinates Velocity > Polar coordinates It is also the dot product of velocity and transverse direction, or the product of the angular speed ω {\displaystyle \omega } and the radius (the magnitude of the position). such that Angular momentum in scalar form is the mass times the distance to the origin times the transverse velocity, or equivalently, the mass times the distance squared times the angular speed. The sign convention for angular momentum is the same as that for angular velocity.
Glossary of calculus E Glossary_of_calculus > E It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who treated it in his book Institutionum calculi integralis (published 1768–1870). exponential function In mathematics, an exponential function is a function of the form where b is a positive real number, and in which the argument x occurs as an exponent.
Desmos (graphing) Features Desmos_(graphing) > Features The tool comes pre-programmed with 36 different example graphs for the purpose of teaching new users about the tool and the mathematics involved.Another popular use of the calculator involves the creation of graphic arts using equations and inequalities. The calculator also has an audiotrace function, which can be used to make music. As of April 2017, Desmos also released a browser-based 2D interactive geometry tool, with supporting features including the plotting of points, lines, circles, and polygons.
Digital video fingerprinting Summary Digital_video_fingerprinting Video fingerprinting or video hashing are a class of dimension reduction techniques in which a system identifies, extracts, and then summarizes characteristic components of a video as a unique or a set of multiple perceptual hashes or fingerprints, enabling that video to be uniquely identified. This technology has proven to be effective at searching and comparing video files.
Crash (computing) Application crashes Crash_(computing) > Application crashes An application typically crashes when it performs an operation that is not allowed by the operating system. The operating system then triggers an exception or signal in the application. Unix applications traditionally responded to the signal by dumping core.
Cache-oblivious algorithm Summary Cache-oblivious_algorithm Eventually, one reaches a subproblem size that fits into the cache, regardless of the cache size. For example, an optimal cache-oblivious matrix multiplication is obtained by recursively dividing each matrix into four sub-matrices to be multiplied, multiplying the submatrices in a depth-first fashion. In tuning for a specific machine, one may use a hybrid algorithm which uses loop tiling tuned for the specific cache sizes at the bottom level but otherwise uses the cache-oblivious algorithm.
Computability theory (computation) Automorphism problems Computability_theory_(computation) > Areas of research > Automorphism problems Besides the lattice of computably enumerable sets, automorphisms are also studied for the structure of the Turing degrees of all sets as well as for the structure of the Turing degrees of c.e. sets. In both cases, Cooper claims to have constructed nontrivial automorphisms which map some degrees to other degrees; this construction has, however, not been verified and some colleagues believe that the construction contains errors and that the question of whether there is a nontrivial automorphism of the Turing degrees is still one of the main unsolved questions in this area.
Signal level Dynamic range Signal_level > Definition > Dynamic range The concepts of signal-to-noise ratio and dynamic range are closely related. Dynamic range measures the ratio between the strongest un-distorted signal on a channel and the minimum discernible signal, which for most purposes is the noise level. SNR measures the ratio between an arbitrary signal level (not necessarily the most powerful signal possible) and noise. Measuring signal-to-noise ratios requires the selection of a representative or reference signal.
Classifier constructions in sign languages Classification Classifier_constructions_in_sign_languages > Description > Classification Extension morphemes: Movement does not represent actual motion, but the outline of the entity's shape or perimeter. It can also represent the configuration of multiple similar entities, such as a line of books.Whole entity classifiers and handling classifiers are the most established classifier types.
Quantum dot cellular automaton State transition Quantum_dot_cellular_automata > State transition There is a connection between quantum-dot cells and cellular automata. Cells can only be in one of 2 states and the conditional change of state in a cell is dictated by the state of its adjacent neighbors. However, a method to control data flow is necessary to define the direction in which state transition occurs in QCA cells. The clocks of a QCA system serve two purposes: powering the automaton, and controlling data flow direction. QCA clocks are areas of conductive material under the automaton’s lattice, modulating the electron tunneling barriers in the QCA cells above it.
Mathesis universalis René Descartes Mathesis_universalis > René Descartes In Descartes' corpus the term mathesis universalis appears only in the Rules for the Direction of the Mind. In the discussion of Rule Four, Descartes' provides his clearest description of mathesis universalis: Rule Four We need a method if we are to investigate the truth of things. I began my investigation by inquiring what exactly is generally meant by the term 'mathematics' and why it is that, in addition to arithmetic and geometry, sciences such as astronomy, music, optics, mechanics, among others, are called branches of mathematics. This made me realize that there must be a general science which explains all the points that can be raised concerning order and measure irrespective of the subject-matter, and that this science should be termed mathesis universalis — a venerable term with a well-established meaning — for it covers everything that entitles these other sciences to be called branches of mathematics.
Dangling bonds Magnetic Dangling_bonds > Properties > Magnetic Ferromagnetic properties in various carbon nanostructures can be described using dangling bonds and may be used to create metal-free organic spintronics and polymeric ferromagnetic materials (see Applications). Creating dangling bonds with unpaired electrons can, for example, be achieved by cutting or putting large mechanical strain on a polymer. In this process, covalent bonds between carbon atoms are broken. One electron can end up on each of the carbon atoms that originally contributed to the bond, leading to two unpaired dangling bonds.
Adaptive feedback cancellation Jammer Suppression Adaptive_feedback_cancellation > Applications > Jammer Suppression Jammer suppression is a way to reject interference with large signals that are much stronger than traditional signals. This process uses an adaptive filter, and its algorithm has applications in all types of signal suppression.
Rydberg matter Physical Rydberg_matter > Physical Bonding in Rydberg matter is caused by delocalisation of the high-energy electrons to form an overall lower energy state. The way in which the electrons delocalise is to form standing waves on loops surrounding nuclei, creating quantised angular momentum and the defining characteristics of Rydberg matter. It is a generalised metal by way of the quantum numbers influencing loop size but restricted by the bonding requirement for strong electron correlation; it shows exchange-correlation properties similar to covalent bonding. Electronic excitation and vibrational motion of these bonds can be studied by Raman spectroscopy.
6174 Other "Kaprekar's constants" 6174 > Other "Kaprekar's constants" There can be analogous fixed points for digit lengths other than four; for instance, if we use 3-digit numbers, then most sequences (i.e., other than repdigits such as 111) will terminate in the value 495 in at most 6 iterations. Sometimes these numbers (495, 6174, and their counterparts in other digit lengths or in bases other than 10) are called "Kaprekar constants".
Dimension (physical quantity) Formalisms Numerical_value_equation > Dimensionless concepts > Formalisms Paradoxically, dimensional analysis can be a useful tool even if all the parameters in the underlying theory are dimensionless, e.g., lattice models such as the Ising model can be used to study phase transitions and critical phenomena. Such models can be formulated in a purely dimensionless way. As we approach the critical point closer and closer, the distance over which the variables in the lattice model are correlated (the so-called correlation length, ξ {\displaystyle \xi } ) becomes larger and larger.
NSSL Doppler History NSSL_Doppler > History In the early 1940s, radar operators throughout Europe noticed that, when using radar to track objects otherwise concealed due to distance, haze, or otherwise, precipitation was also visible, causing issues when it came to masking and objects within cores of precipitation. Into the late-1940s, scientists from Europe and the United States began to expand on the idea of radar for meteorological applications. In the mid-1950s, the advent of Doppler radar came into light, and many radars in the United States were soon Doppler.
Lie's third theorem Summary Lie's_third_theorem In the mathematics of Lie theory, Lie's third theorem states that every finite-dimensional Lie algebra g {\displaystyle {\mathfrak {g}}} over the real numbers is associated to a Lie group G {\displaystyle G} . The theorem is part of the Lie group–Lie algebra correspondence. Historically, the third theorem referred to a different but related result. The two preceding theorems of Sophus Lie, restated in modern language, relate to the infinitesimal transformations of a group action on a smooth manifold.
Sequence alignment Dot-matrix methods Sequence_identity > Pairwise alignment > Dot-matrix methods The dot-matrix approach, which implicitly produces a family of alignments for individual sequence regions, is qualitative and conceptually simple, though time-consuming to analyze on a large scale. In the absence of noise, it can be easy to visually identify certain sequence features—such as insertions, deletions, repeats, or inverted repeats—from a dot-matrix plot. To construct a dot-matrix plot, the two sequences are written along the top row and leftmost column of a two-dimensional matrix and a dot is placed at any point where the characters in the appropriate columns match—this is a typical recurrence plot. Some implementations vary the size or intensity of the dot depending on the degree of similarity of the two characters, to accommodate conservative substitutions.
Mathematical formula Summary Formula In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula. The informal use of the term formula in science refers to the general construct of a relationship between given quantities. The plural of formula can be either formulas (from the most common English plural noun form) or, under the influence of scientific Latin, formulae (from the original Latin).
Normal probability plot Summary Normal_probability_plot With modern computers normal plots are commonly made with software. The normal probability plot is a special case of the Q–Q probability plot for a normal distribution. The theoretical quantiles are generally chosen to approximate either the mean or the median of the corresponding order statistics.
Mitotic catastrophe Term usage Mitotic_catastrophe > Term usage Multiple attempts to specifically define mitotic catastrophe have been made since the term was first used to describe a temperature dependent lethality in the yeast, Schizosaccharomyces pombe, that demonstrated abnormal segregation of chromosomes. The term has been used to define a mechanism of cellular death that occurs while a cell is in mitosis or as a method of oncosuppression that prevents potentially tumorigenic cells from dividing. This oncosuppression is accomplished by initiating a form of cell death such as apoptosis or necrosis or by inducing cellular senescence.
Ohms Law External links and further reading Ohm’s_law > External links and further reading (1963). "Resistance to Ohm's Law". American Journal of Physics.
Environment of evolutionary adaptedness Evolutionary psychology and culture Evolutionary_psychologists > Evolutionary psychology and culture Evolutionary psychologists thereby see physical and psychological characteristics of humans as genetically programmed. Even then, when evolutionary psychologists acknowledge the influence of the environment on human development, they understand the environment only as an activator or trigger for the programmed developmental instructions encoded in genes. Evolutionary psychologists, for example, believe that the human brain is made up of innate modules, each of which is specialised only for very specific tasks, e. g. an anxiety module.
Hamiltonian (control theory) The Hamiltonian of control compared to the Hamiltonian of mechanics Hamiltonian_(control_theory) > The Hamiltonian of control compared to the Hamiltonian of mechanics The associated conditions for a maximum are d p d t = − ∂ H ∂ q {\displaystyle {\frac {dp}{dt}}=-{\frac {\partial H}{\partial q}}} d q d t = ∂ H ∂ p {\displaystyle {\frac {dq}{dt}}=~~{\frac {\partial H}{\partial p}}} ∂ H ∂ u = 0 {\displaystyle {\frac {\partial H}{\partial u}}=0} This definition agrees with that given by the article by Sussmann and Willems. (see p. 39, equation 14). Sussmann and Willems show how the control Hamiltonian can be used in dynamics e.g. for the brachistochrone problem, but do not mention the prior work of Carathéodory on this approach.
Air condition Mini-split and multi-split systems Air_conditioner > Types of air conditioner > Mini-split and multi-split systems Both were first sold in Japan. Variable refrigerant flow systems when compared with central plant cooling from an air handler, eliminate the need for large cool air ducts, air handlers, and chillers; instead cool refrigerant is transported through much smaller pipes to the indoor units in the spaces to be conditioned, thus allowing for less space above dropped ceilings and a lower structural impact, while also allowing for more individual and independent temperature control of spaces, and the outdoor and indoor units can be spread across the building. Variable refrigerant flow indoor units can also be turned off individually in unused spaces. The lower start-up power of VRF's DC inverter compressors and their inherent DC power requirements also allow VRF solar-powered heat pumps to be run using DC-providing solar panels.
Melitta filter system Overview Filter_basket > Overview Both bleached and unbleached filters are made.Typically, coffee filters are made up of filaments approximately 20 micrometres wide, which allow particles through that are less than approximately 10 to 15 micrometres.Some baristas claim that paper filters exhibit a "paperish" taste and recommend to wash out the filter with a flush of hot water before filling the ground coffee into the filter. Since paper filters filter out some components the resulting coffee is said to taste somewhat fruitier compared to permanent filters. For a filter to be compatible with a filter holder (in the case of drip coffee preparation also called a dripper) or coffee maker, the filter needs to be a specific shape and size.
Stack machines Temporary / local values Zero_address_arithmetic > Comparison with register machines > Temporary / local values Some in the industry believe that stack machines execute more data cache cycles for temporary values and local variables than do register machines.On stack machines, temporary values often get spilled into memory, whereas on machines with many registers these temps usually remain in registers. (However, these values often need to be spilled into "activation frames" at the end of a procedure's definition, basic block, or at the very least, into a memory buffer during interrupt processing). Values spilled to memory add more cache cycles.
Kernel thread M:N (hybrid threading) Thread_management > Scheduling > Threading models > M:N (hybrid threading) M:N maps some M number of application threads onto some N number of kernel entities, or "virtual processors." This is a compromise between kernel-level ("1:1") and user-level ("N:1") threading. In general, "M:N" threading systems are more complex to implement than either kernel or user threads, because changes to both kernel and user-space code are required. In the M:N implementation, the threading library is responsible for scheduling user threads on the available schedulable entities; this makes context switching of threads very fast, as it avoids system calls. However, this increases complexity and the likelihood of priority inversion, as well as suboptimal scheduling without extensive (and expensive) coordination between the userland scheduler and the kernel scheduler.
Seidel triangle Sum of powers Generalized_Bernoulli_numbers > Applications of the Bernoulli numbers > Sum of powers {\displaystyle S_{m}(n)={\frac {1}{m+1}}\sum _{k=0}^{m}(-1)^{k}{\binom {m+1}{k}}B_{k}^{-{}}n^{m+1-k}.} Bernoulli's formula is sometimes called Faulhaber's formula after Johann Faulhaber who also found remarkable ways to calculate sums of powers. Faulhaber's formula was generalized by V. Guo and J. Zeng to a q-analog.
Geometric camera calibration Extrinsic parameters Geometric_camera_calibration > Formulation > Extrinsic parameters When a camera is used, light from the environment is focused on an image plane and captured. This process reduces the dimensions of the data taken in by the camera from three to two (light from a 3D scene is stored on a 2D image). Each pixel on the image plane therefore corresponds to a shaft of light from the original scene.
Motor drive (photography) Summary Motor_drive_(photography) A motor drive, in the field of photography, is a powered film transport mechanism. Historically, film loading, advancing, and rewinding were all manually driven functions.The desires of professional photographers for more efficient shooting, particularly in sports and wildlife photography, and the desires of amateur and novice photographers for easier to use cameras both drove the development of automatic film transport. Some early developments were made with clockwork drives, but most development in the field has been in the direction of electrically driven transport. At first, motor drives were external units that attached to the basic camera body, normally beneath it, with an interface consisting of a physical drive socket and some electrical contacts to signal the drive when to actuate.
Artificial powered exoskeleton Classification Powered_exoskeleton > Classification The active class comprises exoskeletons that give “active” aid to the user; in other words, these exoskeletons perform the movements without the need for the user to apply energy. The energy needed to perform the movement is supplied by an external source. On the other hand, the passive class comprises exoskeletons that need the user to perform the movement to work; these exoskeletons do not have power sources.
Thermometric titration Thermometric titrations Thermometric_titration > Thermometric titrations Where reaction kinetics are slow, and direct titrations between titrant and titrand are not possible, indirect or back-titrations often can be devised to solve the problem. Catalytically enhanced endpoints can be used in some instances where the temperature change at the endpoint is very small and endpoints would not be detected satisfactorily by the titration software. The suitability of a particular chemical reaction as a candidate for a thermometric titration procedure can generally be predicted on the basis of the estimated amount of analyte present in the sample and the enthalpy of the reaction.
Cervical segments Motor organization Cervical_segments > Function > Motor organization The DL neurons are involved in distal limb control. Therefore, these DL neurons are found specifically only in the cervical and lumbosacral enlargements within the spinal cord. There is no decussation in the lateral corticospinal tract after the decussation at the medullary pyramids.
Small nuclear RNA In the spliceosome Small_nuclear_RNA > In the spliceosome Spliceosomes catalyse splicing, an integral step in eukaryotic precursor messenger RNA maturation. A splicing mistake in even a single nucleotide can be devastating to the cell, and a reliable, repeatable method of RNA processing is necessary to ensure cell survival. The spliceosome is a large, protein-RNA complex that consists of five small nuclear RNAs (U1, U2, U4, U5, and U6) and over 150 proteins. The snRNAs, along with their associated proteins, form ribonucleoprotein complexes (snRNPs), which bind to specific sequences on the pre-mRNA substrate.
What-if analysis One-at-a-time (OAT) What-if_analysis > Sensitivity analysis methods > One-at-a-time (OAT) This increases the comparability of the results (all 'effects' are computed with reference to the same central point in space) and minimizes the chances of computer program crashes, more likely when several input factors are changed simultaneously. OAT is frequently preferred by modelers because of practical reasons. In case of model failure under OAT analysis the modeler immediately knows which is the input factor responsible for the failure.Despite its simplicity however, this approach does not fully explore the input space, since it does not take into account the simultaneous variation of input variables.
Political demography Youth bulges Political_demography > Age structure and politics > Youth bulges A second avenue of inquiry considers age structures: be these 'youth bulges' or aging populations. Young populations are associated with a ratio of dependents to producers: a high proportion of the population under age 16 puts pressure on resources. A 'youth bulge' of those in the 16-30 bracket creates a different set of problems. A large population of adolescents entering the labor force and electorate strains at the seams of the economy and polity, which were designed for smaller populations.
Matrix decomposition QZ decomposition Matrix_factorization > Decompositions based on eigenvalues and related concepts > QZ decomposition Decomposition (real version): A = Q S Z T {\displaystyle A=QSZ^{\mathsf {T}}} and B = Q T Z T {\displaystyle B=QTZ^{\mathsf {T}}} where A, B, Q, Z, S, and T are matrices containing real numbers only. In this case Q and Z are orthogonal matrices, the T superscript represents transposition, and S and T are block upper triangular matrices. The blocks on the diagonal of S and T are of size 1×1 or 2×2.
Infinite dimensional Lebesgue measure Summary Infinite-dimensional_Lebesgue_measure Alternatively, one may consider Lebesgue measure on finite-dimensional subspaces of the larger space and consider so-called prevalent and shy sets. The Hilbert cube carries the product Lebesgue measure, and the compact topological group given by the Tychonoff product of infinitely many copies of the circle group is infinite-dimensional, and carries a Haar measure that is translation-invariant. These two spaces can be mapped onto each other in a measure preserving way by unwrapping the circles into intervals. The infinite product of the additive real numbers has the analogous product Haar measure, which is precisely the infinite dimensional analog of Lebesgue measure.

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