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Russell-style universes In a specific context Russell-style_universes > In a specific context Perhaps the simplest version is that any set can be a universe, so long as the object of study is confined to that particular set. If the object of study is formed by the real numbers, then the real line R, which is the real number set, could be the universe under consideration. Implicitly, this is the universe that Georg Cantor was using when he first developed modern naive set theory and cardinality in the 1870s and 1880s in applications to real analysis. The only sets that Cantor was originally interested in were subsets of R. This concept of a universe is reflected in the use of Venn diagrams. |
Albert Bridge, London Present day Albert_Bridge,_London > Present day In 1990, the tidal flow system was abandoned and Albert Bridge was converted back to two-way traffic. A traffic island was installed on the south end of the bridge to prevent larger vehicles from using it. In the early years of the 21st century the Chelsea area experienced a growth in the popularity of large four-wheel drive cars (so-called Chelsea tractors), many of which were over the two-ton weight limit; it was estimated that one third of all vehicles using the bridge were over the weight limit. In July 2006 the 27-foot (8.2 m) wide roadway was narrowed to a single lane in each direction to reduce the load. |
DYA framework Quality attributes for communication DYA_framework > DYA infrastructure > The DYA infrastructure architecture process > Quality attributes for communication Quality attributes also provide a way to check and report on delivered results. To stop disciplines talking at cross purposes, unequivocal agreement is needed on the quality attributes each discipline brings into the architectural process. |
Primary progressive multiple sclerosis Signs and symptoms Multiple_Sclerosis > Signs and symptoms Stress may also trigger an attack. Women with MS who become pregnant experience fewer relapses; however, during the first months after delivery the risk increases. Overall, pregnancy does not seem to influence long-term disability. Many events have been found not to affect relapse rates including vaccination, breast feeding, physical trauma, and Uhthoff's phenomenon. |
Rapidly exploring random tree Variants and improvements for motion planning Rapidly_exploring_random_tree > Variants and improvements for motion planning RRT-Rope, a method for fast near-optimal path planning using a deterministic shortening approach, very effective in open and large environments. Parti-game directed RRTs (PDRRTs), a method that combines RRTs with the parti-game method to refine the search where it is needed (for example around obstacles) to be able to plan faster and solve more motion planning problems than RRT Closed-loop rapidly exploring random (CL-RRT), an extension of RRT that samples an input to a stable closed-loop system consisting of the vehicle and a controllerIt has been shown that, under 'mild technical conditions', the cost of the best path in the RRT converges almost surely to a non-optimal value. For that reason, it is desirable to find variants of the RRT that converges to an optimum, like RRT*. Below follows is a list of RRT*-based methods (starting with RRT* itself). |
GIS vector file format Vector formats GIS_vector_file_format > Vector formats This is the basis of most modern file formats, including spatial databases that include a geometry column along with the other attributes in a single relational table. Other formats, such as GeoJSON, use different structures for geometry and attributes, but combine them for each object in the same file.Geospatial topology is often an important part of vector data, representing the inherent spatial relationships (especially adjacency) between objects. Topology has been managed in vector file formats in four ways. |
Noisy qubit channel Important examples Quantum_channel > Channel capacity > Important examples The entanglement-assisted teleportation scheme allows one to transmit quantum information using a classical channel. Superdense coding. achieves two bit per qubit. These results indicate the significant role played by entanglement in quantum communication. |
Peer mentoring Peer tutoring Peer_mentoring > In education > Peer tutoring There are many benefits for both the peer tutor and tutee in this relationship; one aspect of this is that the tutor can establish a rapport with the tutee in a way that a teacher cannot. Tutors themselves benefit from working with students. The skills a tutor develops can be applied to other aspects in life including graduate school or a future job. |
Cell lineage tree Embryogenesis Cell_lineage_tree > Embryogenesis As an embryo develops from a fertilized egg, the single egg cell splits into many cells, which grow in number and migrate to the appropriate locations inside the embryo at appropriate times during development. As the embryo's cells grow in number and migrate, they also differentiate into an increasing number of different cell types, ultimately turning into the stable, specialized cell types characteristic of the adult organism. Each of the cells in an embryo contains the same genome, characteristic of the species, but the level of activity of each of the many thousands of genes that make up the complete genome varies with, and determines, a particular cell's type (e.g. neuron, bone cell, skin cell, muscle cell, etc.). During embryo development (embryogenesis), many cell types are present which are not present in the adult organism. |
Rolling-element bearings Life calculation models Rolling-element_bearing > Bearing failure > Life calculation models By the 1990s, real bearings were found to give service lives up to 14 times longer than those predicted. An explanation was put forward based on fatigue life; if the bearing was loaded to never exceed the fatigue strength, then the Lundberg-Palmgren mechanism for failure by fatigue would simply never occur. |
Dirichlet eta function Zeros Dirichlet_eta_function > Zeros The zeros of the eta function include all the zeros of the zeta function: the negative even integers (real equidistant simple zeros); the zeros along the critical line, none of which are known to be multiple and over 40% of which have been proven to be simple, and the hypothetical zeros in the critical strip but not on the critical line, which if they do exist must occur at the vertices of rectangles symmetrical around the x-axis and the critical line and whose multiplicity is unknown. In addition, the factor 1 − 2 1 − s {\displaystyle 1-2^{1-s}} adds an infinite number of complex simple zeros, located at equidistant points on the line ℜ ( s ) = 1 {\displaystyle \Re (s)=1} , at s n = 1 + 2 n π i / ln ( 2 ) {\displaystyle s_{n}=1+2n\pi i/\ln(2)} where n is any nonzero integer. Under the Riemann hypothesis, the zeros of the eta function would be located symmetrically with respect to the real axis on two parallel lines ℜ ( s ) = 1 / 2 , ℜ ( s ) = 1 {\displaystyle \Re (s)=1/2,\Re (s)=1} , and on the perpendicular half line formed by the negative real axis. |
Aldosterone escape Summary Aldosterone_escape Aldosterone initially results in an increase in Na+ reabsorption in these patients through stimulation of ENaC channels in principal cells of the renal collecting tubules. Increased ENaC channels situated in the apical membranes of the principal cells allow for more Na+ reabsorption, which may cause a transient increase in fluid reabsorption as well. However, within a few days, Na+ reabsorption returns to normal as evidenced by normal urinary Na+ levels in these patients. |
Stress (biology) Summary General_adaptation_syndrome There are two kinds of stress hormone levels. Resting (basal) cortisol levels are normal everyday quantities that are essential for standard functioning. Reactive cortisol levels are increases in cortisol in response to stressors. |
Agathis australis Root structure and soil interaction Agathis_australis > Root structure and soil interaction In a process known as leaching, these acidic molecules pass through the soil layers with the help of rainfall, and release other nutrients trapped in clay such as nitrogen and phosphorus. This leaves these important nutrients unavailable to other trees, as they are washed down into deeper layers. This process is known as podsolization, and changes the soil colour to a dull grey. |
Potential Energy Potential energy for a linear spring Magnetic_potential_energy > Potential energy for a linear spring A horizontal spring exerts a force F = (−kx, 0, 0) that is proportional to its deformation in the axial or x direction. The work of this spring on a body moving along the space curve s(t) = (x(t), y(t), z(t)), is calculated using its velocity, v = (vx, vy, vz), to obtain For convenience, consider contact with the spring occurs at t = 0, then the integral of the product of the distance x and the x-velocity, xvx, is x2/2. The function is called the potential energy of a linear spring. Elastic potential energy is the potential energy of an elastic object (for example a bow or a catapult) that is deformed under tension or compression (or stressed in formal terminology). It arises as a consequence of a force that tries to restore the object to its original shape, which is most often the electromagnetic force between the atoms and molecules that constitute the object. If the stretch is released, the energy is transformed into kinetic energy. |
Faster than light travel Possible distance away from Earth Faster_than_light > Superluminal travel of non-information > Possible distance away from Earth If they were then to return to Earth, the traveler would arrive on Earth thousands of years from the time when they originally left. Their travel speed would not have been observed from Earth as being superluminal — neither for that matter would it appear to be so from the traveler's perspective– but the traveler would instead have experienced a length contraction of the universe in their direction of travel. After the traveler reverses course, the Earth will seem to experience much more time passing than the traveler does. So while the traveler's (ordinary) coordinate speed cannot exceed c, their proper speed, or distance traveled from the Earth's point of reference divided by proper time, can be much greater than c. This is seen in statistical studies of muons traveling much further than c times their half-life (at rest), if traveling close to c. |
Signaling cascade Stem cells Biochemical_cascade > Cell-specific biochemical cascades > Stem cells In old adult stem cells, let-7 microRNA expression increases, reducing Hmga2 levels and increasing p16Ink4a and p19Arf levels. This reduces the sensitivity of stem cells to mitogenic signals by inhibiting cyclin-CDK complexes. As a result, either stem cells cannot enter the cell cycle, or cell division slows in many tissues.Extrinsic regulation is made by signals from the niche, where stem cells are found, which is able to promote quiescent state and cell cycle activation in somatic stem cells. |
Fortschritt E 512 Technical description Fortschritt_E_512 > Technical description With a cylinder bore of 120 mm and a stroke of 145 mm, it displaces 6.56 dm3. It is rated 77 kW at 2000 min−1, and produces a maximum torque of 392 N·m at 1350 min−1.The torque is sent from the engine to a manual three-speed gearbox, and to the main drive wheel, from which the threshing drum, the straw walkers, sieves, fan, corn conveyor, corn elevator, and header are driven. The three-speed gearbox is used solely for converting the torque that is sent to the front wheels. |
Algorithmically random sequence Properties and examples of Martin-Löf random sequences Algorithmic_randomness > Properties and examples of Martin-Löf random sequences Every sequence is Turing reducible to some random sequence. (Kučera 1985/1989, Gács 1986). Thus there are random sequences of arbitrarily high Turing degree. |
Collection (abstract data type) Linear collections Collection_(abstract_data_type) > Linear collections Many collections define a particular linear ordering, with access to one or both ends. The actual data structure implementing such a collection need not be linear—for example, a priority queue is often implemented as a heap, which is a kind of tree. Important linear collections include: lists; stacks; queues; priority queues; double-ended queues; double-ended priority queues. |
Maxwell’s equations Integral equations Maxwell's_theory > Formulation in terms of electric and magnetic fields (microscopic or in vacuum version) > Key to the notation > Integral equations In the integral equations, Ω is any volume with closed boundary surface ∂Ω, and Σ is any surface with closed boundary curve ∂Σ,The equations are a little easier to interpret with time-independent surfaces and volumes. Time-independent surfaces and volumes are "fixed" and do not change over a given time interval. For example, since the surface is time-independent, we can bring the differentiation under the integral sign in Faraday's law: Maxwell's equations can be formulated with possibly time-dependent surfaces and volumes by using the differential version and using Gauss and Stokes formula appropriately. |
Distributed parameter systems Duality between controllability and observability Distributed_parameter_system > Linear time-invariant distributed-parameter systems > Duality between controllability and observability As in the finite-dimensional case, controllability and observability are dual concepts (at least when for the domain of Φ {\displaystyle \Phi } and the co-domain of Ψ {\displaystyle \Psi } the usual L2 choice is made). The correspondence under duality of the different concepts is: Exact controllability ↔ Exact observability, Approximate controllability ↔ Approximate observability, Null controllability ↔ Final state observability. |
Shift 2: Unleashed Development Shift_2:_Unleashed > Development "The simulation genre, really, is just a numbers game at the moment; it's all about, 'We've got the greatest physics engine, and we're going to add 1,000 cars, tracks etcetera.' It's quite a dry experience. We want to turn that on its head, by adding in social features, such as Autolog. |
Epigenetic alteration Twins Epigenetics > Medicine > Twins This supports the notion that microenvironment at early stages of embryonic development can be quite important for the establishment of epigenetic marks. Congenital genetic disease is well understood and it is clear that epigenetics can play a role, for example, in the case of Angelman syndrome and Prader–Willi syndrome. These are normal genetic diseases caused by gene deletions or inactivation of the genes but are unusually common because individuals are essentially hemizygous because of genomic imprinting, and therefore a single gene knock out is sufficient to cause the disease, where most cases would require both copies to be knocked out. |
Invariant (computer science) Examples Invariant_(computer_science) > Examples On the other hand, multiplication does not have this same property, as distance is not invariant under multiplication. Angles and ratios of distances are invariant under scalings, rotations, translations and reflections. These transformations produce similar shapes, which is the basis of trigonometry. |
Undertow (water waves) Oceanography Undertow_(wave_action) > Oceanography An "undertow" is a steady, offshore-directed compensation flow, which occurs below waves near the shore. Physically, nearshore, the wave-induced mass flux between wave crest and trough is onshore directed. This mass transport is localized in the upper part of the water column, i.e. above the wave troughs. To compensate for the amount of water being transported towards the shore, a second-order (i.e. proportional to the wave height squared), offshore-directed mean current takes place in the lower section of the water column. |
Mathematical physicist Relativity and quantum relativistic theories Mathematical_physicist > Scope > Relativity and quantum relativistic theories The special and general theories of relativity require a rather different type of mathematics. This was group theory, which played an important role in both quantum field theory and differential geometry. This was, however, gradually supplemented by topology and functional analysis in the mathematical description of cosmological as well as quantum field theory phenomena. In the mathematical description of these physical areas, some concepts in homological algebra and category theory are also important. |
Equilibrium temperature Calculation of equilibrium temperature Planetary_equilibrium_temperature > Calculation of equilibrium temperature The planet absorbs the radiation that isn't reflected by the albedo, and heats up. One may assume that the planet radiates energy like a blackbody at some temperature according to the Stefan–Boltzmann law. Thermal equilibrium exists when the power supplied by the star is equal to the power emitted by the planet. The temperature at which this balance occurs is the planetary equilibrium temperature. |
Recombinant organism Mammals Genetically_modified_organisms > Animals > Mammals Then researchers would have to wait until the animal reached breeding age and then offspring would be screened for the presence of the gene in every cell. The development of the CRISPR-Cas9 gene editing system as a cheap and fast way of directly modifying germ cells, effectively halving the amount of time needed to develop genetically modified mammals. Mammals are the best models for human disease, making genetic engineered ones vital to the discovery and development of cures and treatments for many serious diseases. |
Universal stress protein Tuberculosis Universal_stress_protein > Clinical significance > Tuberculosis These conditions have been found to upregulate a particular USP gene called rv2623, as well as an additional 50 genes involved in long-term persistence in the mammalian host. It was suggested this USP gene was involved in inducing the latent response within the mammalian host. This stage of the infection is currently chronic with no effective treatments. |
Glossary of elementary quantum mechanics Kinematical postulates Glossary_of_elementary_quantum_mechanics > Formalism > Kinematical postulates Total wave function of a particle For single-particle system, the total wave function Ψ {\displaystyle \Psi } of a particle can be expressed as a product of spatial wave function and the spinor. The total wave functions are in the tensor product space of the Hilbert space of the spatial part (which is spanned by the position eigenstates) and the Hilbert space for the spin. Wave function The word "wave function" could mean one of following: A vector in Hilbert space which can represent a state; synonymous to "ket" or "state vector". |
Isotopic analysis by nuclear magnetic resonance Advantages of the method Isotopic_analysis_by_nuclear_magnetic_resonance > Principle > Advantages of the method The isotopic ratios of a molecule can also be determined by isotope ratio mass spectrometry (IRMS), sample quantity for IRMS is much lower than for NMR, and there is the possibility of coupling the mass spectrometer to a chromatographic system to enable on-line purification or analyses of several components of a complex mixture. However the sample is burnt after a physical transformation such as combustion or pyrolysis. Therefore, it gives a mean value of the concentration of the isotope studied between all sites of the molecule. |
History of general relativity The development of the Einstein field equations History_of_general_relativity > Creation of general relativity > The development of the Einstein field equations This predicted the non-Newtonian perihelion precession of Mercury, and so had Einstein very excited. However, it was soon realized that they were inconsistent with the local conservation of energy–momentum unless the universe had a constant density of mass–energy–momentum. In other words, air, rock and even a vacuum should all have the same density. |
Random polytope Example uses Random_polytope > Example uses Minimal caps Macbeath regions Approximations (approximations of convex bodies see properties of definition 1) Economic cap covering theorem (see relation from properties of definition 1 to floating bodies) == References == |
Asymptotically safe gravity Summary Asymptotically_safe_gravity The essence of asymptotic safety is the observation that nontrivial renormalization group fixed points can be used to generalize the procedure of perturbative renormalization. In an asymptotically safe theory the couplings do not need to be small or tend to zero in the high energy limit but rather tend to finite values: they approach a nontrivial UV fixed point. The running of the coupling constants, i.e. their scale dependence described by the renormalization group (RG), is thus special in its UV limit in the sense that all their dimensionless combinations remain finite. |
Wigner's friend QBism and Bayesian interpretations Wigner's_friend > Responses in different interpretations of quantum mechanics > QBism and Bayesian interpretations In the interpretation known as QBism, advocated by N. David Mermin among others, the Wigner's-friend situation does not lead to a paradox, because there is never a uniquely correct wavefunction for any system. Instead, a wavefunction is a statement of personalist Bayesian probabilities, and moreover, the probabilities that wavefunctions encode are probabilities for experiences that are also personal to the agent who experiences them. Jaynes expresses this as follows: "There is a paradox only if we suppose that a density matrix (i.e. a probability distribution) is something 'physically real' and 'absolute'. But now the dilemma disappears when we recognize the 'relativity principle' for probabilities. |
Pierre Bourdieu Habitus and doxa Pierre_Bourdieu > Objective (field) and subjective (habitus) > Habitus and doxa Doxa refers to the learned, fundamental, deep-founded, unconscious beliefs, and values, taken as self-evident universals, that inform an agent's actions and thoughts within a particular field. Doxa tends to favor the particular social arrangement of the field, thus privileging the dominant and taking their position of dominance as self-evident and universally favorable. Therefore, the categories of understanding and perception that constitute a habitus, being congruous with the objective organization of the field, tend to reproduce the very structures of the field. A doxic situation may be thought of as a situation characterized by a harmony between the objective, external structures and the 'subjective', internal structures of the habitus. |
Translational kinetic energy Without vectors and calculus Kinetic_Energy > Kinetic energy for non-relativistic velocity > Kinetic energy of rigid bodies > Derivation > Without vectors and calculus The work W done by a force F on an object over a distance s parallel to F equals W = F ⋅ s {\displaystyle W=F\cdot s} .Using Newton's Second Law F = m a {\displaystyle F=ma} with m the mass and a the acceleration of the object and s = a t 2 2 {\displaystyle s={\frac {at^{2}}{2}}} the distance traveled by the accelerated object in time t, we find with v = a t {\displaystyle v=at} for the velocity v of the object W = m a a t 2 2 = m ( a t ) 2 2 = m v 2 2 . {\displaystyle W=ma{\frac {at^{2}}{2}}={\frac {m(at)^{2}}{2}}={\frac {mv^{2}}{2}}.} |
Biomechanics Renaissance Biomechanics > History > Renaissance The next major biomechanic would not be around until 1452, with the birth of Leonardo da Vinci. Da Vinci was an artist and mechanic and engineer. He contributed to mechanics and military and civil engineering projects. He had a great understanding of science and mechanics and studied anatomy in a mechanics context. |
Divisor (ring theory) Properties Divisibility_(ring_theory) > Properties Statements about divisibility in a commutative ring R {\displaystyle R} can be translated into statements about principal ideals. For instance, One has a ∣ b {\displaystyle a\mid b} if and only if ( b ) ⊆ ( a ) {\displaystyle (b)\subseteq (a)} . Elements a and b are associates if and only if ( a ) = ( b ) {\displaystyle (a)=(b)} . An element u is a unit if and only if u is a divisor of every element of R. An element u is a unit if and only if ( u ) = R {\displaystyle (u)=R} . |
History of cancer chemotherapy Antifolates History_of_cancer_chemotherapy > Antifolates Dr. Richard Lewisohn of Mount Sinai Hospital in New York administered the drug, and over the course of several months, Ruth's condition began to improve. However, Ruth died the following year.In 1951, Jane C. Wright demonstrated the use of methotrexate in solid tumors, showing remission in breast cancer. Wright's group was the first to demonstrate use of the drug in solid tumors, as opposed to leukemias, which are cancers of the marrow. Several years later at the National Cancer Institute, Roy Hertz and Min Chiu Li then demonstrated complete remission in women with choriocarcinoma and chorioadenoma in 1956, discovering that methotrexate alone could cure choriocarcinoma (1958), a germ-cell malignancy that originates in trophoblastic cells of the placenta. In 1960 Wright et al. produced remissions in mycosis fungoides. |
Pierre Duhem Works in English translation Pierre_Duhem > Works > Works in English translation Ampère's Force Law: A Modern Introduction. Alan Aversa (trans.). doi:10.13140/RG.2.2.31100.03206/1. |
Population geneticist Gene flow Population_Genetics > Four processes > Gene flow Gene flow is hindered by mountain ranges, oceans and deserts or even human-made structures such as the Great Wall of China, which has hindered the flow of plant genes.Gene flow is the exchange of genes between populations or species, breaking down the structure. Examples of gene flow within a species include the migration and then breeding of organisms, or the exchange of pollen. Gene transfer between species includes the formation of hybrid organisms and horizontal gene transfer. |
Metastatic tumor Diagnosis Metastatic_cancer > Diagnosis Still, the determination of the primary tumor can often be very difficult, and the pathologist may have to use several adjuvant techniques, such as immunohistochemistry, FISH (fluorescent in situ hybridization), and others. Despite the use of techniques, in some cases the primary tumor remains unidentified. Metastatic cancers may be found at the same time as the primary tumor, or months or years later. |
Biophysical techniques Biophysical techniques Biophysical_techniques > Biophysical techniques One of the main benefits of using optical techniques which make up biophotonics is that they preserve the integrity of the biological cells being examined. Calcium imaging – various optical techniques for recording the location and concentration of calcium. Typically this is done in cell and tissue samples using either genetically encoded or chemically derived fluorescent calcium indicating dyes. |
Bordwell thermodynamic cycle Summary Bordwell_thermodynamic_cycle A Bordwell thermodynamic cycle use experimentally determined and reasonable estimates of Gibbs free energy (ΔG˚) values to determine unknown and experimentally inaccessible values. |
SI defining constant Impact on reproducibility SI_defining_constants > Impact on reproducibility In practice, G can only be measured with a relative uncertainty of the order of 10−5, which would have resulted in the upper limit of the kilogram's reproducibility being around 10−5 whereas the then-current international prototype of the kilogram can be measured with a reproducibility of 1.2 × 10−8. The physical constants were chosen on the basis of minimal uncertainty associated with measuring the constant and the degree of independence of the constant in respect of other constants that were being used. Although the BIPM has developed a standard mise en pratique (practical technique) for each type of measurement, the mise en pratique used to make the measurement is not part of the measurement's definition – it is merely an assurance that the measurement can be done without exceeding the specified maximum uncertainty. |
Molybdenum(IV) telluride Colour Molybdenum_ditelluride > Physical properties > Colour In powdered form MoTe2 is black.Very thin crystals of MoTe2 can be made using sticky tape. When they are thin around 500 nm thick red light can be transmitted. Even thinner layers can be orange or transparent. An absorption edge occurs in the spectrum with wavelengths longer than 6720 Å transmitted and shorter wavelengths heavily attenuated. At 77 K this edge changes to 6465 Å. This corresponds to deep red. |
Angular wave vector Definition Angular_wavevector > Definition A sinusoidal traveling wave follows the equation ψ ( r , t ) = A cos ( k ⋅ r − ω t + φ ) , {\displaystyle \psi (\mathbf {r} ,t)=A\cos(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi ),} where: r is position, t is time, ψ is a function of r and t describing the disturbance describing the wave (for example, for an ocean wave, ψ would be the excess height of the water, or for a sound wave, ψ would be the excess air pressure). A is the amplitude of the wave (the peak magnitude of the oscillation), φ is a phase offset, ω is the (temporal) angular frequency of the wave, describing how many radians it traverses per unit of time, and related to the period T by the equation ω = 2 π T , {\displaystyle \omega ={\tfrac {2\pi }{T}},} k is the angular wave vector of the wave, describing how many radians it traverses per unit of distance, and related to the wavelength by the equation | k | = 2 π λ . {\displaystyle |\mathbf {k} |={\tfrac {2\pi }{\lambda }}.} The equivalent equation using the wave vector and frequency is ψ ( r , t ) = A cos ( 2 π ( ν ~ ⋅ r − f t ) + φ ) , {\displaystyle \psi \left(\mathbf {r} ,t\right)=A\cos \left(2\pi \left({\tilde {\boldsymbol {\nu }}}\cdot {\mathbf {r} }-ft\right)+\varphi \right),} where: f {\displaystyle f} is the frequency ν ~ {\displaystyle {\tilde {\boldsymbol {\nu }}}} is the wave vector |
Unique key Summary Unique_key > Summary Depending on its design, a database table may have many candidate keys but at most one candidate key may be distinguished as the primary key. A key constraint applies to the set of tuples in a table at any given point in time. A key is not necessarily a unique identifier across the population of all possible instances of tuples that could be stored in a table but it does imply a data integrity rule that duplicates should not be allowed in the database table. |
Mobile Security Wi-Fi Mobile_Security > Attacks based on communication > Attacks based on communication networks > Wi-Fi An attacker can try to eavesdrop on Wi-Fi communications to derive information (e.g., username, password). This type of attack is not unique to smartphones, but they are very vulnerable to these attacks because often Wi-Fi is their only means of communication and access the internet. The security of wireless networks (WLAN) is thus an important subject. Initially, wireless networks were secured by WEP keys. |
Lorentz interval Lorentz transformations Space-time_interval > Basic mathematics of spacetime > Lorentz transformations Terence is an official at the starting line, while Stella is a participant. At time t = t′ = 0, Stella's spaceship accelerates instantaneously to a speed of 0.5 c. The distance from Earth to Mars is 300 light-seconds (about 90.0×106 km). Terence observes Stella crossing the finish-line clock at t = 600.00 s. But Stella observes the time on her ship chronometer to be t ′ = γ ( t − v x / c 2 ) = 519.62 s {\displaystyle t^{\prime }=\gamma \left(t-vx/c^{2}\right)=519.62\ {\text{s}}} as she passes the finish line, and she calculates the distance between the starting and finish lines, as measured in her frame, to be 259.81 light-seconds (about 77.9×106 km). 1). |
Non-specific effect of vaccines Influence of pre-existing specific immunity Non-specific_effect_of_vaccines > Influence of pre-existing specific immunity The beneficial non-specific effects of live vaccines are stronger with earlier vaccination, possibly due to maternal antibodies. Boosting with live vaccines also seems to enhance the beneficial effects. |
Repeat associated small interfering RNA Summary Repeat_associated_small_interfering_RNA They are distinct from microRNA (miRNA) in size (26–31 nucleotides as opposed to 21–24 nt), lack of sequence conservation, increased complexity, and independence of Dicer for biogenesis, at least in animals. (Plant Dcl2 may play a role in rasi/piRNA biogenesis. )Double-stranded RNAs capable of silencing repeat elements, then known as repeat associated small interfering RNA (rasiRNA), were proposed in Drosophila in 2001. By 2008, it was still unclear how piRNAs are generated, but potential methods had been suggested, and it was certain their biogenesis pathway is distinct from miRNA and siRNA, while rasiRNA is now considered a piRNA subspecies. |
Dermatitis Corticosteroids Dermatitis > Management > Medications > Corticosteroids In severe cases, oral or injectable corticosteroids may be used. While these usually bring about rapid improvements, they have greater side effects. |
Volume transmission Serotonin pharmacology Volume_transmission > Neuromodulatory systems > Serotonin system > Serotonin pharmacology Selective serotonin reuptake inhibitors (SSRIs) such as fluoxetine are widely used antidepressants that specifically block the reuptake of serotonin with less effect on other transmitters. Tricyclic antidepressants also block reuptake of biogenic amines from the synapse, but may primarily effect serotonin or norepinephrine or both. They typically take 4 to 6 weeks to alleviate any symptoms of depression. They are considered to have immediate and long-term effects. |
Average case analysis Sorting algorithms Average_case_analysis > Examples > Sorting algorithms Also, when implemented with the "shortest first" policy, the worst-case space complexity is instead bounded by O(log(n)). Heapsort has O(n) time when all elements are the same. Heapify takes O(n) time and then removing elements from the heap is O(1) time for each of the n elements. |
Matrix differentiation Notation Matrix_derivative > Notation The vector and matrix derivatives presented in the sections to follow take full advantage of matrix notation, using a single variable to represent a large number of variables. In what follows we will distinguish scalars, vectors and matrices by their typeface. We will let M(n,m) denote the space of real n×m matrices with n rows and m columns. Such matrices will be denoted using bold capital letters: A, X, Y, etc. An element of M(n,1), that is, a column vector, is denoted with a boldface lowercase letter: a, x, y, etc. An element of M(1,1) is a scalar, denoted with lowercase italic typeface: a, t, x, etc. XT denotes matrix transpose, tr(X) is the trace, and det(X) or |X| is the determinant. |
Occurrences of Grandi's series Power series Occurrences_of_Grandi's_series > Power series The power series most famously associated with Grandi's series is its ordinary generating function, f ( x ) = 1 − x + x 2 − x 3 + ⋯ = 1 1 + x . {\displaystyle f(x)=1-x+x^{2}-x^{3}+\cdots ={\frac {1}{1+x}}.} |
Hydraulic torque wrench Summary Hydraulic_torque_wrench The hydraulic torque wrench was invented by George A. Sturdevant in Houston, Texas. The concept of a hydraulic powered torque wrench was first introduced on the market sometime in the early 1960s in a primitive form, and several key advances have been developed by manufacturers since that time which provided major advancements in the technology and usability of the tools far beyond the original concept tool. Newer tools offer benefits such as lighter weights, smaller nose radius dimensions for fitting into tight spaces, use of exotic alloys, actuation triggers on the tool itself, multi-position reaction members, 360° × 360° hose swivels, and the ability to run multiple tools simultaneously from a single power pack. |
Erythrocyte sedimentation rate Relation to C-reactive protein Erythrocyte_sedimentation_rate > Relation to C-reactive protein Such inflammation may not be enough to raise the level of ESR. Those with high ESR usually do not have demonstrable inflammation. However, in cases of low grade bacterial infections of bone and joints such as coagulase negative staphylococcus (CoNS), and systemic lupus erythematosus (SLE), ESR can be a good marker for the inflammatory process. |
Pendant drop method Pendant drop test Water_droplets > Pendant drop test In the pendant drop test, a drop of liquid is suspended from the end of a tube or by any surface by surface tension. The force due to surface tension is proportional to the length of the boundary between the liquid and the tube, with the proportionality constant usually denoted γ {\displaystyle \gamma } . Since the length of this boundary is the circumference of the tube, the force due to surface tension is given by F γ = π d γ {\displaystyle \,F_{\gamma }=\pi d\gamma } where d is the tube diameter. The mass m of the drop hanging from the end of the tube can be found by equating the force due to gravity ( F g = m g {\displaystyle F_{g}=mg} ) with the component of the surface tension in the vertical direction ( F γ sin α {\displaystyle F_{\gamma }\sin \alpha } ) giving the formula m g = π d γ sin α {\displaystyle \,mg=\pi d\gamma \sin \alpha } where α is the angle of contact with the tube's front surface, and g is the acceleration due to gravity. |
Salt (chemistry) Solubility Potassium_salt > Properties > Solubility Many ionic compounds exhibit significant solubility in water or other polar solvents. Unlike molecular compounds, salts dissociate in solution into anionic and cationic components. The lattice energy, the cohesive forces between these ions within a solid, determines the solubility. |
Local Universe Particles Physical_universe > Composition > Particles Of central importance is the Standard Model, a theory that is concerned with electromagnetic interactions and the weak and strong nuclear interactions. The Standard Model is supported by the experimental confirmation of the existence of particles that compose matter: quarks and leptons, and their corresponding "antimatter" duals, as well as the force particles that mediate interactions: the photon, the W and Z bosons, and the gluon. The Standard Model predicted the existence of the recently discovered Higgs boson, a particle that is a manifestation of a field within the universe that can endow particles with mass. |
Java Enterprise Edition Specifications Java_EE > Specifications Jakarta EE includes several specifications that serve different purposes, like generating web pages, reading and writing from a database in a transactional way, managing distributed queues. The Jakarta EE APIs include several technologies that extend the functionality of the base Java SE APIs, such as Jakarta Enterprise Beans, connectors, servlets, Jakarta Server Pages and several web service technologies. |
Lateral raise Shoulder fly Chest_fly > Equipment > Shoulder fly The shoulder fly (also known as a lateral raise) works the deltoid muscle of the shoulder. The movement starts with the arms straight, and the hands holding weights at the sides or in front of the body. Body is in a slight forward-leaning position with hips and knees bent a little. Arms are kept straight or slightly bent, and raised through an arc of movement in the coronal plane that terminates when the hands are at approximately shoulder height. |
Fourier optics Eigenfunction (natural mode) solutions: background and overview Fourier_optics > The plane wave spectrum: the foundation of Fourier optics > Eigenfunction (natural mode) solutions: background and overview In certain physics applications such as in the computation of bands in a periodic volume, it is often a case that the elements of a matrix will be very complicated functions of frequency and wavenumber, and the matrix will be non-singular (I.e., it has the inverse matrix.) for most combinations of frequency and wavenumber, but will also be singular (I.e., it does not have the inverse matrix.) for certain specific combinations. |
Key finding attacks Analytical key finding Key_finding_attacks > Approaches > Analytical key finding While statistical key finding can be effective for reducing the amount of memory that needs to be searched, it still requires high-entropy areas to be tested to check if they contain the correct key material. In certain cases, particularly in the context of public key encryption systems, it is possible to determine patterns that must occur in the key material and then limit the search to areas where these patterns are found. Shamir and van Someren demonstrated one example of this analytical approach for finding private RSA keys where the public key is known and has a small public exponent. In the RSA system the public key is a pair ( n , e ) {\displaystyle (n,e)} , where n = p . |
Bioenergetic systems Coupled reactions Bioenergetic_systems > Coupled reactions The ATP–CP system neither uses oxygen nor produces lactic acid if oxygen is unavailable and is thus called alactic anaerobic. This is the primary system behind very short, powerful movements like a golf swing, a 100 m sprint or powerlifting. |
Messenger particles Particle and field viewpoints Exchange_particle > Particle and field viewpoints Photons, W bosons, and Z bosons, excitations of the electroweak gauge fields. Higgs bosons, excitations of one component of the Higgs field, which gives mass to fundamental particles.In addition, composite particles such as mesons, as well as quasiparticles, can be described as excitations of an effective field. Gravity is not a part of the Standard Model, but it is thought that there may be particles called gravitons which are the excitations of gravitational waves. The status of this particle is still tentative, because the theory is incomplete and because the interactions of single gravitons may be too weak to be detected. |
Signal-recognition particle Mechanism Signal_recognition_particle > Mechanism In eukaryotes, SRP binds to the signal sequence of a newly synthesized peptide as it emerges from the ribosome. This binding leads to the slowing of protein synthesis known as "elongation arrest", a conserved function of SRP that facilitates the coupling of the protein translation and the protein translocation processes. SRP then targets this entire complex (the ribosome-nascent chain complex) to the protein-conducting channel, also known as the translocon, in the endoplasmic reticulum (ER) membrane. This occurs via the interaction and docking of SRP with its cognate SRP receptor that is located in close proximity to the translocon. |
Gauge–gravity duality Second superstring revolution Strings_theory > History > Second superstring revolution Petr Hořava and Witten found the eleven-dimensional formulation of the heterotic string theories, showing that orbifolds solve the chirality problem. Witten noted that the effective description of the physics of D-branes at low energies is by a supersymmetric gauge theory, and found geometrical interpretations of mathematical structures in gauge theory that he and Nathan Seiberg had earlier discovered in terms of the location of the branes. In 1997, Juan Maldacena noted that the low energy excitations of a theory near a black hole consist of objects close to the horizon, which for extreme charged black holes looks like an anti-de Sitter space. |
EXEC 8 CPU dispatch EXEC_8 > History > The Exec > Performing work > CPU dispatch The Dispatcher, I/O completions, and I/O initiation are some examples. All locks used by both of these priorities are spin locks as the only way they can be set by someone else is on another processor and the design requires that they only be set for very short instruction sequences. High Exec priority is used by the operator command handler and some other functions that may have to run even when a real time program has control. |
Asymmetric multiprocessing Summary Asymmetric_multiprocessing An asymmetric multiprocessing (AMP or ASMP) system is a multiprocessor computer system where not all of the multiple interconnected central processing units (CPUs) are treated equally. For example, a system might allow (either at the hardware or operating system level) only one CPU to execute operating system code or might allow only one CPU to perform I/O operations. Other AMP systems might allow any CPU to execute operating system code and perform I/O operations, so that they were symmetric with regard to processor roles, but attached some or all peripherals to particular CPUs, so that they were asymmetric with respect to the peripheral attachment. Asymmetric multiprocessing was the only method for handling multiple CPUs before symmetric multiprocessing (SMP) was available. It has also been used to provide less expensive options on systems where SMP was available. |
TCP hole punching Types of NAT TCP_hole_punching > Types of NAT The availability of TCP hole punching depends on the type of computer port allocation used by the NAT. For two peers behind a NAT to connect to each other via TCP simultaneous open, they need to know a little bit about each other. One thing that they absolutely need to know is the "location" of the other peer, or the remote endpoint. The remote endpoint is the data of the IP address and a port that the peer will connect to. |
Information processing Information processing model: the working memory Information_processing > In cognitive psychology > Models and theories > Information processing model: the working memory According to Linden (2007), "The capacity of STM had initially been estimated at "seven plus or minus two" items (Miller 1956), which fits the observation from neuropsychological testing that the average digit span of healthy adults is about seven (Cowan and others 2005). However, it emerged that these numbers of items can only be retained if they are grouped into so-called chunks, using perceptual or conceptual associations between individual stimuli." Its duration is of 5–20 seconds before it is out of the subject's mind. |
Group cognition Writings on Small-Group Cognition Group_cognition > Writings on Group Cognition > Writings on Small-Group Cognition It reflects on the design-based research methodology for analyzing group cognition and provides some analyzed examples of small group cognitive interaction. It includes philosophic, technical, historical, mathematical and pedagogical considerations—providing a multi-faceted view of the VMT research project. • Stahl is a monograph analyzing the work of a group of three students as they become introduced to dynamic mathematics during eight hour-long online sessions using VMT with GeoGebra. |
Cache algorithm Overview Cache_algorithms > Overview The actual hit ratio varies widely from one application to another. In particular, video and audio streaming applications often have a hit ratio close to zero, because each bit of data in the stream is read once for the first time (a compulsory miss), used, and then never read or written again. Even worse, many cache algorithms (in particular, LRU) allow this streaming data to fill the cache, pushing out of the cache information that will be used again soon (cache pollution).Other things to consider: Items with different cost: keep items that are expensive to obtain, e.g. those that take a long time to get. |
Key–value database Types and examples Key–value_database > Types and examples Key–value databases can use consistency models ranging from eventual consistency to serializability. Some support ordering of keys. Some maintain data in memory (RAM), while others employ solid-state drives or rotating disks. Every entity (record) is a set of key–value pairs. |
Multi-access edge computing Distributed computing in the RAN Mobile_edge_computing > Distributed computing in the RAN MEC provides a distributed computing environment for application and service hosting. It also has the ability to store and process content close to cellular subscribers, for faster response time. Applications can also be exposed to real-time radio access network (RAN) information.The key element is the MEC application server, which is integrated at the RAN element. This server provides computing resources, storage capacity, connectivity and access to RAN information. |
Space tether missions Description Space_tether_missions > Description The sub-satellite is released from the base assisted by a spring ejection system, centrifugal force or gravity gradient effects. Tethers can be deployed for a range of applications, including electrodynamic propulsion, momentum exchange, artificial gravity, deployment of sensors or antennas etc. Tether deployment may be followed by a station-keeping phase (in particular if the target state is a vertical system orientation), and, sometimes, if the deployment system allows, a retraction.The station-keeping phase and retraction phase need active control for stability, especially when atmospheric effects are taken into account. When there are no simplifying assumptions, the dynamics become overly difficult because they are then governed by a set of ordinary and partial nonlinear, non-autonomous and coupled differential equations. These conditions create a list of dynamical issues to consider: Three-dimensional rigid body dynamics (librational motion) of the station and subsatellite Swinging in-plane and out-of-plane motions of the tether of finite mass Offset of the tether attachment point from the base-satellite center of mass as well as controlled variations of the offset Transverse vibrations of the tether External forces |
Limit supremum Sequences of sets Limit_supremum > Sequences of sets Hence, it is the infimum of the limit points. Because ordering is by set inclusion, then the outer limit will always contain the inner limit (i.e., lim inf Xn ⊆ lim sup Xn). Hence, when considering the convergence of a sequence of sets, it generally suffices to consider the convergence of the outer limit of that sequence.The difference between the two definitions involves how the topology (i.e., how to quantify separation) is defined. In fact, the second definition is identical to the first when the discrete metric is used to induce the topology on X. |
Lightning Memory-Mapped Database Performance Lightning_Memory-Mapped_Database > Performance The benchmarks showed the underlying filesystem as having a big influence on performance. JFS with an external journal performs well, especially compared to other modern systems like Btrfs and ZFS. Zimbra has tested back-mdb vs back-hdb performance in OpenLDAP, with LMDB clearly outperforming the BDB based back-hdb. |
Products in algebraic topology The cup product Products_in_algebraic_topology > The cup product H p ( X ) ⊗ H q ( X ) → H p + q ( X ) {\displaystyle H^{p}(X)\otimes H^{q}(X)\to H^{p+q}(X)} This product can be understood as induced by the exterior product of differential forms in de Rham cohomology. It makes the singular cohomology of a connected manifold into a unitary supercommutative ring. |
Linear density Summary Linear_mass_density Linear density is the measure of a quantity of any characteristic value per unit of length. Linear mass density (titer in textile engineering, the amount of mass per unit length) and linear charge density (the amount of electric charge per unit length) are two common examples used in science and engineering. The term linear density is most often used when describing the characteristics of one-dimensional objects, although linear density can also be used to describe the density of a three-dimensional quantity along one particular dimension. Just as density is most often used to mean mass density, the term linear density likewise often refers to linear mass density. However, this is only one example of a linear density, as any quantity can be measured in terms of its value along one dimension. |
Branch migration Prokaryotes Branch_migration > Mechanism > Prokaryotes The mechanism for prokaryotic branch migration has been studied many times in Escherichia coli. In E. coli, the proteins RuvA and RuvB come together and form a complex that facilitates the process in a number of ways. RuvA is a tetramer and binds to the DNA at the Holliday junction when it is in the open X form. The protein binds in a way that the DNA entering/departing the junction is still free to rotate and slide through. |
Eisenmenger's syndrome Pathogenesis Eisenmenger_syndrome > Pathogenesis Scar (dead lung tissue) does not contribute to oxygen transfer, therefore decreasing the useful volume of the pulmonary vasculature. The scar tissue also provides less flexibility and compliance than normal lung tissue, causing further increases in pulmonary blood pressure, and the weakened heart must pump harder to continue supplying the lungs, leading to damage of more capillaries. It is because of this maladaptive response that at the onset of Eisenmenger syndrome, the damage is considered irreversible, even if the underlying heart defect is corrected after the fact.Eventually, due to increased resistance and decreased compliance of the pulmonary vessels, elevated pulmonary pressures cause the myocardium of the right heart to hypertrophy (RVH). |
Teriflunomide Mechanisms of action Teriflunomide > Mechanisms of action Teriflunomide is an immunomodulatory drug inhibiting pyrimidine de novo synthesis by blocking the enzyme dihydroorotate dehydrogenase. It is uncertain whether this explains its effect on MS lesions.Teriflunomide inhibits rapidly dividing cells, including activated T cells, which are thought to drive the disease process in MS. Teriflunomide may decrease the risk of infections compared to chemotherapy-like drugs because of its more-limited effects on the immune system.It has been found that teriflunomide blocks the transcription factor NF-κB. It also inhibits tyrosine kinase enzymes, but only in high doses not clinically used. |
Riemann–Stieltjes Integral Riemann integral Riemann–Stieltjes_Integral > Examples and special cases > Riemann integral The standard Riemann integral is a special case of the Riemann–Stieltjes integral where g ( x ) = x {\displaystyle g(x)=x} . |
E = mc² Alternative version Mass–energy_equivalence > History > Einstein: mass–energy equivalence > Alternative version However, if the same process is considered in a frame that moves with velocity v to the left, the pulse moving to the left is redshifted, while the pulse moving to the right is blue shifted. The blue light carries more momentum than the red light, so that the momentum of the light in the moving frame is not balanced: the light is carrying some net momentum to the right. The object has not changed its velocity before or after the emission. |
FtsZ Summary FtsZ The hypothesis was that cell division mutants of E. coli would grow as filaments due to the inability of the daughter cells to separate from one another. FtsZ is found in almost all bacteria, many archaea, all chloroplasts and some mitochondria, where it is essential for cell division. FtsZ assembles the cytoskeletal scaffold of the Z ring that, along with additional proteins, constricts to divide the cell in two. |
PAC learning Definitions and terminology PAC_learning > Definitions and terminology In the character recognition problem, the instance space is X = { 0 , 1 } n {\displaystyle X=\{0,1\}^{n}} . In the interval problem the instance space, X {\displaystyle X} , is the set of all bounded intervals in R {\displaystyle \mathbb {R} } , where R {\displaystyle \mathbb {R} } denotes the set of all real numbers. A concept is a subset c ⊂ X {\displaystyle c\subset X} . |
Elementary mathematics Basic two-dimensional geometry Elementary_mathematics > Strands of elementary mathematics > Basic two-dimensional geometry A circle is a simple shape of two-dimensional geometry that is the set of all points in a plane that are at a given distance from a given point, the center.The distance between any of the points and the center is called the radius. It can also be defined as the locus of a point equidistant from a fixed point. A perimeter is a path that surrounds a two-dimensional shape. |
Names for the number 0 in English "O" ("oh") Names_for_the_number_0_in_English > "O" ("oh") Another example is James Bond's designation, 007, which is always read as "double-o seven", not "double-zero seven", "zero-zero seven", or "o o seven".The letter "o" ("oh") is also used in spoken English as the name of the number 0 when saying times in the 24-hour clock, particularly in English used by both British and American military forces. Thus 16:05 is "sixteen oh five", and 08:30 is "oh eight thirty".The use of O as a number can lead to confusion as in the ABO blood group system. |
Mean-field theory Non-interacting spins approximation Mean-field_approximation > Applications > Ising model > Non-interacting spins approximation {\displaystyle h^{\text{eff.}}} . We thus have two equations between m {\displaystyle m} and h eff. |
Polonium tetranitrate Synthesis Polonium_tetranitrate > Synthesis Dissolution of metallic polonium in concentrated nitric acid: P o + 8 H N O 3 → P o ( N O 3 ) 4 + 4 N O 2 ↑ + 4 H 2 O {\displaystyle {\mathsf {Po+8HNO_{3}\ {\xrightarrow {}}\ Po(NO_{3})_{4}+4NO_{2}\uparrow +4H_{2}O}}} |
Abiogenesis Chemiosmosis Origins_of_life > Producing biology > Chemiosmosis The energy required to release strongly bound ATP has its origin in protons that move across the membrane. In modern cells, those proton movements are caused by the pumping of ions across the membrane, maintaining an electrochemical gradient. In the first organisms, the gradient could have been provided by the difference in chemical composition between the flow from a hydrothermal vent and the surrounding seawater, or perhaps meteoric quinones that were conducive to the development of chemiosmotic energy across lipid membranes if at a terrestrial origin. |
Evolution of Infectious Disease Evolution Evolution_of_Infectious_Disease > Evolution If an organism lives a moderately healthy lifestyle, including its diet, physical activity, and decreased stress, its chances of fighting off infectious diseases increase. Host resistance pivots around how well a host's immune system can fight off a disease and rid their body of the pathogens. Although a healthy lifestyle can help a host, infectious diseases seem to evolve so quickly that a new generation of a disease may have emerged before scientists have the chance to make a vaccination for the first generation. Pathogens adapt to the medications and form a resistance to them which causes the new generations of pathogens to be more detrimental than the previous generations. After many generations have emerged, scientists must continuously form new vaccinations to combat the components of the disease that evolve every time a generation appears. |
Epigenome editing General concept Epigenome_editing > General concept Although DNA methylation at gene promoters typically correlates with gene repression, methylation at gene bodies is correlated with gene activation, and DNA methylation may also play a role in gene splicing. The ability to directly target and edit individual methylation sites is critical to determining the exact function of DNA methylation at a specific site. Epigenome editing is a powerful tool that allows this type of analysis. |
Gnome sort Summary Gnome_sort The average running time is O(n2) but tends towards O(n) if the list is initially almost sorted.Dick Grune described the sorting method with the following story: Gnome Sort is based on the technique used by the standard Dutch Garden Gnome (Du. : tuinkabouter). Here is how a garden gnome sorts a line of flower pots. Basically, he looks at the flower pot next to him and the previous one; if they are in the right order he steps one pot forward, otherwise, he swaps them and steps one pot backward. Boundary conditions: if there is no previous pot, he steps forwards; if there is no pot next to him, he is done. |
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