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EST1 Drugs EST1 > Clinical implications > Cancer > Drugs This is the rate-limiting step in telomerase activity. It is associated with many cancer types. Various cancer cells and fibroblasts transformed with hTERT cDNA have high telomerase activity, while somatic cells do not.
Physical theories modified by general relativity Classical mechanics and special relativity Physical_theories_modified_by_general_relativity > Classical mechanics and special relativity Classical mechanics and special relativity are lumped together here because special relativity is in many ways intermediate between general relativity and classical mechanics, and shares many attributes with classical mechanics. In the following discussion, the mathematics of general relativity is used heavily. Also, under the principle of minimal coupling, the physical equations of special relativity can be turned into their general relativity counterparts by replacing the Minkowski metric (ηab) with the relevant metric of spacetime (gab) and by replacing any partial derivatives with covariant derivatives. In the discussions that follow, the change of metrics is implied.
Stacked bar graph Summary Bar_graph A bar chart or bar graph is a chart or graph that presents categorical data with rectangular bars with heights or lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally. A vertical bar chart is sometimes called a column chart.
Computer code Basic Computer_Program > Programming paradigms and languages > Imperative languages > Basic BASIC (1964) stands for "Beginner's All-Purpose Symbolic Instruction Code." It was developed at Dartmouth College for all of their students to learn. If a student did not go on to a more powerful language, the student would still remember Basic. A Basic interpreter was installed in the microcomputers manufactured in the late 1970s.
Mental causation Physicalist solutions Mental_causation > Traditional solutions > Physicalist solutions Behaviorists, in general, argue that mental events are merely dispositions to behave in certain ways. Another theory is the identity theory, according to which mental events are (either type- or token-) identical to physical events. A more recent view, known as functionalism, claims that mental events are individuated (or constituted by) the causal role they play. As such, mental events would fit directly into the causal realm, as they are simply certain causal (or functional) roles. Finally, there is eliminative materialism, which simply denies that there are any such mental events; thus, there is really no problem of mental causation at all.
Nonsymmetric gravitational theory Summary Nonsymmetric_gravitational_theory Later, in 1995, Moffat noted that the field corresponding with the antisymmetric part need not be massless, like the electromagnetic (or gravitational) fields. In its original form, the theory may be unstable, although this has only been shown in the case of the linearized version.In the weak field approximation where interaction between fields is not taken into account, NGT is characterized by a symmetric rank-2 tensor field (gravity), an antisymmetric tensor field, and a constant characterizing the mass of the antisymmetric tensor field. The antisymmetric tensor field is found to satisfy the equations of a Maxwell–Proca massive antisymmetric tensor field.
Behavioral epigenetics Discovery Behavioral_epigenetics > Discovery The glucocorticoid gene is activated, resulting in lowered stress response. Rat pups that receive a less nurturing upbringing are more sensitive to stress throughout their life-span. This pioneering work in rodents has been difficult to replicate in humans because of a general lack of availability of human brain tissue for measurement of epigenetic changes.
Bohm diffusion Further research Bohm_diffusion > Further research The concepts of negative temperature state, and of the convective cells contributed much to the understanding of the diffusion. The underlying physics may be explained as follows. The process can be a transport driven by the thermal fluctuations, corresponding to the lowest possible random electric fields.
Mirror symmetry conjecture Mathematical interpretation of B-model correlation functions Mirror_symmetry_conjecture > Ideas from string theory > B-model > Mathematical interpretation of B-model correlation functions Mathematically, the B-model is a variation of hodge structures which was originally given by the construction from the Dwork family.
TimesTen TimesTen Scaleout TimesTen > Deployment Modes > TimesTen Scaleout TimesTen Scaleout allows a single TimesTen database to span many machines. A shared-nothing architecture is used to distribute data across multiple TimesTen instances running on many machines. All machines can query and modify all data in the database, and all database ACID properties are fully supported. Multiple copies of data are kept for high availability. Databases provided by TimesTen Scaleout can be larger than the amount of RAM available on a single machine, and database throughput is scalable as more machines are added.
Kunstweg Summary Kunstweg The principles of iterative sine table calculation through the Kunstweg are as follows: cells in a column sum up the values of the two previous cells in the same column. The final cell's value is divided by two, and the next iteration starts. Finally, the values of the last column get normalized.
Computational phylogenetics Types of phylogenetic trees and networks Phylogenetic_inference > Types of phylogenetic trees and networks By contrast, unrooted trees plot the distances and relationships between input sequences without making assumptions regarding their descent. An unrooted tree can always be produced from a rooted tree, but a root cannot usually be placed on an unrooted tree without additional data on divergence rates, such as the assumption of the molecular clock hypothesis.The set of all possible phylogenetic trees for a given group of input sequences can be conceptualized as a discretely defined multidimensional "tree space" through which search paths can be traced by optimization algorithms. Although counting the total number of trees for a nontrivial number of input sequences can be complicated by variations in the definition of a tree topology, it is always true that there are more rooted than unrooted trees for a given number of inputs and choice of parameters.Both rooted and unrooted phylogenetic trees can be further generalized to rooted or unrooted phylogenetic networks, which allow for the modeling of evolutionary phenomena such as hybridization or horizontal gene transfer.
Oxide mineral Summary Oxide_minerals The oxide mineral class includes those minerals in which the oxide anion (O2−) is bonded to one or more metal alloys. The hydroxide-bearing minerals are typically included in the oxide class. Minerals with complex anion groups such as the silicates, sulfates, carbonates and phosphates are classed separately.
Power electronic AC/AC converters Industrial_electronics > AC/AC converters Phase-Angle Control: Various circuits exist to implement a phase-angle control on different waveforms, such as half-wave or full-wave voltage control. The power electronic components that are typically used are diodes, SCRs, and Triacs. With the use of these components, the user can delay the firing angle in a wave, which will only cause part of the wave to be in output.
Multithreading (computer architecture) Implementation specifics Multithreading_(computer_architecture) > Implementation specifics A major area of research is the thread scheduler that must quickly choose from among the list of ready-to-run threads to execute next, as well as maintain the ready-to-run and stalled thread lists. An important subtopic is the different thread priority schemes that can be used by the scheduler. The thread scheduler might be implemented totally in software, totally in hardware, or as a hardware/software combination.
LN-3 inertial navigation system Platform LN-3_inertial_navigation_system > Functional description > Platform The following characteristics of the platform are described: Three accelerometers in orthogonal directions provide the basic sensing elements. They measure acceleration along the two grid coordinate axes and the vertical (Z) axis. The Z accelerometer is not used by the LN3-2A itself but provides vertical acceleration data for the automatic flight control system. The east-west and north-south X and Y axes are used for the LN3-2A.
Base-pair substitution Functional categorization Nucleotide_substitution > Categorization > Functional categorization The likely effect is additional amino acids added to the amino terminus of the original protein. Frame-shift mutations are also possible in start-gain mutations, but typically do not affect translation of the original protein.
Space heating Heating Indoor_climate_control > Heating Heaters are appliances whose purpose is to generate heat (i.e. warmth) for the building. This can be done via central heating. Such a system contains a boiler, furnace, or heat pump to heat water, steam, or air in a central location such as a furnace room in a home, or a mechanical room in a large building. The heat can be transferred by convection, conduction, or radiation. Space heaters are used to heat single rooms and only consist of a single unit.
Power Chord Terminology Power_Chord > Terminology They can also be played with octave doublings of the root or fifth note, which makes a sound that is subjectively higher pitched with less power in the low frequencies, but still retains the character of a power chord. Another notation is ind, designating the chord as 'indeterminate'. This refers to the fact that a power chord is neither major nor minor, as there is no third present. This gives the power chord a chameleon-like property; if played where a major chord might be expected, it can sound like a major chord, but when played where a minor chord might be expected, it can sound minor.
Magnetobiology Effects Magnetobiology > Effects An example of a magnetobiological effect is the magnetic navigation by migrant animals by means of magnetoreception. Many animal orders, such as certain birds, marine turtles, reptiles, amphibians and salmonoid fishes are able to detect small variations of the geomagnetic field and its magnetic inclination to find their seasonal habitats. They are said to use an "inclination compass".
Semimagic square Moment of inertia Semimagic_square > Properties of magic squares > Moment of inertia The moment of inertia of a magic square has been defined as the sum over all cells of the number in the cell times the squared distance from the center of the cell to the center of the square; here the unit of measurement is the width of one cell. (Thus for example a corner cell of a 3×3 square has a distance of 2 , {\displaystyle {\sqrt {2}},} a non-corner edge cell has a distance of 1, and the center cell has a distance of 0.) Then all magic squares of a given order have the same moment of inertia as each other.
Analogical models Dynamical analogies Analogical_model > Dynamical analogies Doing so preserves the correct energy flow between domains, a useful feature when modelling a system as an integrated whole. Examples of systems that require unified modelling are mechatronics and audio electronics.The earliest such analogy is due to James Clerk Maxwell who, in 1873, associated mechanical force with electrical voltage. This analogy became so widespread that sources of voltage are still today referred to as electromotive force.
Differential privacy Summary Differential_privacy Another way to describe differential privacy is as a constraint on the algorithms used to publish aggregate information about a statistical database which limits the disclosure of private information of records in the database. For example, differentially private algorithms are used by some government agencies to publish demographic information or other statistical aggregates while ensuring confidentiality of survey responses, and by companies to collect information about user behavior while controlling what is visible even to internal analysts. Roughly, an algorithm is differentially private if an observer seeing its output cannot tell whether a particular individual's information was used in the computation. Differential privacy is often discussed in the context of identifying individuals whose information may be in a database. Although it does not directly refer to identification and reidentification attacks, differentially private algorithms provably resist such attacks.Differential privacy was developed by cryptographers and thus is often associated with cryptography, and draws much of its language from cryptography.
ICANN Trusted Community Representatives ICANN > Structure > Trusted Community Representatives As the operator of the IANA domain name functions, ICANN is responsible for the DNSSEC management of the root zone. While day-to-day operations are managed by ICANN and Verisign, the trust is rooted in a group of Trusted Community Representatives. The members of this group must not be affiliated with ICANN, but are instead members of the broader DNS community, volunteering to become a Trusted Community Representative. The role of the representatives are primarily to take part in regular key ceremonies at a physical location, organized by ICANN, and to safeguard the key materials in between.
Insulin therapy Principles Human_insulin > Principles A majority of insulin used clinically today is produced this way, although clinical experience has provided conflicting evidence on whether these insulins are any less likely to produce an allergic reaction. Adverse reactions have been reported; these include loss of warning signs that patients may slip into a coma through hypoglycemia, convulsions, memory lapse and loss of concentration. However, the International Diabetes Federation's position statement from 2005 is very clear in stating that "there is NO overwhelming evidence to prefer one species of insulin over another" and " animal insulins remain a perfectly acceptable alternative.
Time-evolving block decimation Introduction Time-evolving_block_decimation > Introduction With the Matrix Product States formalism being at the mathematical heart of DMRG, the TEBD scheme was adopted by the DMRG community, thus giving birth to the time dependent DMRG , t-DMRG for short. Around the same time, other groups have developed similar approaches in which quantum information plays a predominant role as, for example, in DMRG implementations for periodic boundary conditions , and for studying mixed-state dynamics in one-dimensional quantum lattice systems,. Those last approaches actually provide a formalism that is more general than the original TEBD approach, as it also allows to deal with evolutions with matrix product operators; this enables the simulation of nontrivial non-infinitesimal evolutions as opposed to the TEBD case, and is a crucial ingredient to deal with higher-dimensional analogues of matrix product states.
Heterogeneous gold catalysis Theoretical background Heterogeneous_gold_catalysis > Theoretical background Bulk metallic gold is known to be inert, exhibiting a surface reactivity at room temperature only towards a few substances such as formic acid and sulphur-containing compounds, e.g. H2S and thiols. Within heterogeneous catalysis, reactants adsorb onto the surface of the catalyst thus forming activated intermediates. However, if the adsorption is weak such as in the case of bulk gold, a sufficient perturbation of the reactant electronic structure does not occur and catalysis is hindered (Sabatier's principle).
Paradigms of AI Programming History Paradigms_of_AI_Programming > History The Lisp programming language has survived since 1958 as a primary language for Artificial Intelligence research. This text was published in 1992 as the Common Lisp standard was becoming widely adopted. Norvig introduces Lisp programming in the context of classic AI programs, including General Problem Solver (GPS) from 1959, ELIZA: Dialog with a Machine, from 1966, and STUDENT: Solving Algebra Word Problems, from 1964. The book covers more recent AI programming techniques, including Logic Programming, Object-Oriented Programming, Knowledge Representation, Symbolic Mathematics and Expert Systems.
Relational quantum mechanics Summary Relational_quantum_mechanics The terms "observer" and "observed" apply to any arbitrary system, microscopic or macroscopic. The classical limit is a consequence of aggregate systems of very highly correlated subsystems.
Clean programming language Features Concurrent_Clean > Features However, Clean deals with mutable state and input/output (I/O) through a uniqueness type system, in contrast to Haskell's use of monads. The compiler takes advantage of the uniqueness type system to generate more efficient code, because it knows that at any point during the execution of the program, only one reference can exist to a value with a unique type. Therefore, a unique value can be changed in place.An integrated development environment (IDE) for Microsoft Windows is included in the Clean distribution.
System virtual machine Emulation of a non-native system System_virtual_machine > Techniques > Emulation of a non-native system Virtual machines can also perform the role of an emulator, allowing software applications and operating systems written for another computer processor architecture to be run.
Insulinoma associated-2 Autoantibodies in Type 1 Diabetes Insulinoma_associated-2 > Overview > Autoantibodies in Type 1 Diabetes Autoantibodies targeting pancreatic islet cell can occur years before a hyperglycaemia is established, therefore these autoantibodies are used in prediction of Type 1 Diabetes. Islet cell autoantibodies are detected in serum, including ICA (islet cell cytoplasma autoantibodies), IAA (autoantibodies to insulin), GAD (glutamic acid decarboxylase), IA-2 (insulinoma-associated protein 2), and ZnT8 (zinc transporter of islet beta cells).However, it is not clear if a primary autoantigen exists and immune reaction against other molecules results from secondary antigen spreading, or multiple molecules represent a primary target.The first autoimmune targets are usually aimed against insulin or GAD, and it is unique to observe IA-2 or ZnT8 as the first autoantibodies. What set off the appearance of a first β-cell targeting autoantibody is unclear.The IAA antibody usually appears early in life, median age is 1.49.
Acidity constant Applications and significance Acid–base_equilibrium > Applications and significance This permits a technique called isoelectric focusing, which is used for separation of proteins by 2-D gel polyacrylamide gel electrophoresis. Buffer solutions also play a key role in analytical chemistry. They are used whenever there is a need to fix the pH of a solution at a particular value.
Cell-free system Metabolic manipulation Cell-free_system > Uses > Metabolic manipulation Engineering of metabolic processes have been achieved through cell-free systems. Bujara et al., for example, were able to use glycolytic network extracts, consisting of enzymes from E. coli that produced dihydroxyacetone phosphate, to analyze in real-time the metabolite concentrations while altering enzyme levels, with the end result of optimal production of dihydroxyacetone phosphate. Further, Calhoun and Swartz were able to use a glycolytic intermediate to fuel a cell-free system, enabling relatively inexpensive ATP generation compared to reagent usage in phosphoenolpyruvate reactions.
Thyrotoxic periodic paralysis Signs and symptoms Thyrotoxic_periodic_paralysis > Signs and symptoms This may explain why attacks are more common in summer when more people drink sugary drinks and engage in exercise. Exercise-related attacks tend to occur during a period of rest immediately after exercise; exercise may, therefore, be recommended to abort an attack.There may be symptoms of thyroid overactivity, such as weight loss, a fast or irregular heart rate, tremor, and perspiration; but such symptoms occur in only half of all cases. The most common type of hyperthyroidism, Graves' disease, may additionally cause eye problems (Graves' ophthalmopathy) and skin changes of the legs (pretibial myxedema). Thyroid disease may also cause muscle weakness in the form of thyrotoxic myopathy, but this is constant rather than episodic.
Algorithmic cooling Cooling Algorithmic_cooling > Background > Thermodynamics > Cooling The classical interpretation of "cooling" is transferring heat from one object to the other. However, the same process can be viewed as entropy transfer. For example, if two gas containers that are both in thermal equilibrium with two different temperatures are put in contact, entropy will be transferred from the "hotter" object (with higher entropy) to the "colder" one. This approach can be used when discussing the cooling of an object whose temperature is not always intuitively defined, e.g. a single particle. Therefore, the process of cooling spins can be thought of as a process of transferring entropy between spins, or outside of the system.
Blood poisoning History Bacterial_sepsis > History The genetic locus for this effect was dubbed Lps. These mice were also found to be hyper susceptible to infection by gram-negative bacteria. These observations were finally linked in 1998 by the discovery of the toll-like receptor gene 4 (TLR 4).
Inner core super-rotation Inner core anisotropy Inner_core_super-rotation > Seismic observations > Inner core anisotropy There may also be a different orientation of anisotropy in an "innermost inner core" (IMIC) with a radius of about 550 kilometers.A group at the University of Cambridge used travel time differentials to estimate the longitudes of the hemisphere boundaries with depth up to 90 kilometers below the inner core boundary. Combining this information with an estimate for the rate of growth for the inner core, they obtained a rate of 0.1–1° per million years.Estimates of the rotation rate based on travel time differentials have been inconsistent. Those based on the Sandwich Island earthquakes have the fastest rates, although they also have a weaker signal, with PKP(DF) barely emerging above the noise. Estimates based on other paths have been lower or even in the opposite direction. By one analysis, the rotation rate is constrained to be less than 0.1° per year.
Group (mathematics) Examples and applications Group_(mathematics) > Examples and applications Examples and applications of groups abound. A starting point is the group Z {\displaystyle \mathbb {Z} } of integers with addition as group operation, introduced above. If instead of addition multiplication is considered, one obtains multiplicative groups. These groups are predecessors of important constructions in abstract algebra.
Asexual reproduction Fission Reproduce_asexually > Types of asexual reproduction > Fission Prokaryotes (Archaea and Bacteria) reproduce asexually through binary fission, in which the parent organism divides in two to produce two genetically identical daughter organisms. Eukaryotes (such as protists and unicellular fungi) may reproduce in a functionally similar manner by mitosis; most of these are also capable of sexual reproduction. Multiple fission at the cellular level occurs in many protists, e.g. sporozoans and algae. The nucleus of the parent cell divides several times by mitosis, producing several nuclei. The cytoplasm then separates, creating multiple daughter cells.In apicomplexans, multiple fission, or schizogony appears either as merogony, sporogony or gametogony. Merogony results in merozoites, which are multiple daughter cells, that originate within the same cell membrane, sporogony results in sporozoites, and gametogony results in microgametes.
FBN1 gene Marfan Syndrome FBN1_gene > Marfan Syndrome Marfan syndrome (MFS) is an autosomal dominant disorder that affects the connective tissues of bodily systems such as the eyes, cardiovascular system, skeletal system, skin, pulmonary system and the dura. MFS affects approximately 1 in 5,000 individuals. MFS is not an easily diagnosed pathology with a scoring system called the Ghent nosology table used, rather than a single molecule test.
Crowding History Crowding > History Herman Bouma, in 1970, famously found what was later called Bouma's law, yet that paper was fully neglected for many years. In the coming three decades, the phenomenon was studied in experimental psychology, under different terms.
Exogenous variable Summary Exogenous_variable In an economic model, an exogenous variable is one whose measure is determined outside the model and is imposed on the model, and an exogenous change is a change in an exogenous variable. : p. 8: p. 202: p.
Gilding Chemical gilding Gilding > Chemical gilding Chemical gilding embraces those processes in which the gold is at some stage of chemical combination. These include cold gilding, wet gilding, fire gilding and depletion gilding.
Apical dendrite Cerebellum Apical_dendrite > Areas of interest > Cerebellum A defining characteristic of Purkinje cells in the cerebellum is the apical dendrite.
Telomere-binding protein Oral cancer Telomere-binding_protein > Clinical implications > Oral cancer Oral cancer also has a link to telomere-binding proteins, with TERF2 in particular. The overexpression of TERF2 has been a notable similarity across patients with oral malignancies in humans. Similar to UV-damaged cells, there was an overall genomic instability leading to uncapping of the telomeric ends.
Integrated information theory Related papers Integrated_information_theory > External links > Related papers Integrated Information Theory: An Updated Account (2012) (First presentation of IIT 3.0) Tononi, Giulio (2008). "Consciousness as Integrated Information: A Provisional Manifesto". The Biological Bulletin.
Thermal time constant Summary Time_constant In physics and engineering, the time constant, usually denoted by the Greek letter τ (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system. The time constant is the main characteristic unit of a first-order LTI system. In the time domain, the usual choice to explore the time response is through the step response to a step input, or the impulse response to a Dirac delta function input.
Rebound headache Causes Medication_overuse_headache > Causes If they are taking ergots (such as Ergotamine etc) , it may take about 2.7 years, and if they are taking analgesics (such as Naproxen etc), it may take about 4.8 years. So, the delay between taking medication too often and developing MOH varies based on the type of medication being used.The underlying mechanisms that lead to the development of the condition are still widely unknown and clarification of their role is hampered by a lack of experimental research or suitable animal models. Various pathophysiological abnormalities have been reported and they seem to have an important role in initiating and maintaining chronic headache (genetic disposition, receptor and enzyme physiology and regulation, psychological and behavioural factors, physical dependencies, recent functional imaging results).In some cases, individuals may be genetically predisposed to developing medication overuse headache.
RecycleUnits Algorithms RecycleUnits > Algorithms Note that a resolution proof can be seen as a general directed acyclic graph as opposed to a tree. After the recursive call the clause of the present node is updated. While doing so four different cases can occur.
Transition state theory Thermodynamic treatment Transition_state_theory > Development > Thermodynamic treatment In 1884, Jacobus van 't Hoff proposed the Van 't Hoff equation describing the temperature dependence of the equilibrium constant for a reversible reaction: A ↽ − − ⇀ B {\displaystyle {\ce {{A}<=> {B}}}} d ln ⁡ K d T = Δ U R T 2 {\displaystyle {\frac {d\ln K}{dT}}={\frac {\Delta U}{RT^{2}}}} where ΔU is the change in internal energy, K is the equilibrium constant of the reaction, R is the universal gas constant, and T is thermodynamic temperature. Based on experimental work, in 1889, Svante Arrhenius proposed a similar expression for the rate constant of a reaction, given as follows: d ln ⁡ k d T = Δ E R T 2 {\displaystyle {\frac {d\ln k}{dT}}={\frac {\Delta E}{RT^{2}}}} Integration of this expression leads to the Arrhenius equation k = A e − E a / R T {\displaystyle k=Ae^{-E_{a}/RT}} where k is the rate constant. A was referred to as the frequency factor (now called the pre-exponential coefficient), and Ea is regarded as the activation energy.
Metal testing Summary Metal_testing After the components are known they can be looked up and matched to known alloys. The original sample would be destroyed in the process. This type of testing is destructive.
Code on demand Cache Code_on_demand > Constraints > Cache The last constraint on the client-server communication is that responses from servers must be marked as cacheable or non-cacheable. An effective cache can reduce the number of client-server interactions, which contributes positively to the performance of the system. At least, from a user’s point of view.
Mechanical rectifier Summary Mechanical_rectifier A mechanical rectifier is a device for converting alternating current (AC) to direct current (DC) by means of mechanically operated switches. The best-known type is the commutator, which is an integral part of a DC dynamo, but before solid-state devices became available, independent mechanical rectifiers were used for certain applications. Before the invention of semiconductors, rectification at high currents involved serious losses. There were various vacuum/gas devices, such as the mercury arc rectifiers, thyratrons, ignitrons, and vacuum diodes.
PatchMatch Halting criterion PatchMatch > Algorithm > Halting criterion The often used halting criterion is set the iteration times to be about 4~5. Even with low iteration, the algorithm works well.
Deep Q-learning Algorithm Deep_Q-learning > Algorithm However, Q-learning can also learn in non-episodic tasks (as a result of the property of convergent infinite series). If the discount factor is lower than 1, the action values are finite even if the problem can contain infinite loops. For all final states s f {\displaystyle s_{f}} , Q ( s f , a ) {\displaystyle Q(s_{f},a)} is never updated, but is set to the reward value r {\displaystyle r} observed for state s f {\displaystyle s_{f}} . In most cases, Q ( s f , a ) {\displaystyle Q(s_{f},a)} can be taken to equal zero.
Epsilon, delta In non-standard calculus Limit_at_infinity > Other characterizations > In non-standard calculus In non-standard calculus the limit of a function is defined by: if and only if for all x ∈ R ∗ , {\displaystyle x\in \mathbb {R} ^{*},} f ∗ ( x ) − L {\displaystyle f^{*}(x)-L} is infinitesimal whenever x − a is infinitesimal. Here R ∗ {\displaystyle \mathbb {R} ^{*}} are the hyperreal numbers and f* is the natural extension of f to the non-standard real numbers. Keisler proved that such a hyperreal definition of limit reduces the quantifier complexity by two quantifiers. On the other hand, Hrbacek writes that for the definitions to be valid for all hyperreal numbers they must implicitly be grounded in the ε-δ method, and claims that, from the pedagogical point of view, the hope that non-standard calculus could be done without ε-δ methods cannot be realized in full. Bŀaszczyk et al. detail the usefulness of microcontinuity in developing a transparent definition of uniform continuity, and characterize Hrbacek's criticism as a "dubious lament".
Hadamard's maximal determinant problem Connection of the maximal determinant problems for {1, −1} and {0, 1} matrices Hadamard's_maximal_determinant_problem > Connection of the maximal determinant problems for {1, −1} and {0, 1} matrices Extract the (n−1)×(n−1) submatrix consisting of rows 2 through n and columns 2 through n. This matrix has elements 0 and −2. (The determinant of this submatrix is the same as that of the original matrix, as can be seen by performing a cofactor expansion on column 1 of the matrix obtained in Step 1.)
Proteinogenic amino acid Chemical properties Proteinogenic_amino_acids > Chemical properties Following is a table listing the one-letter symbols, the three-letter symbols, and the chemical properties of the side chains of the standard amino acids. The masses listed are based on weighted averages of the elemental isotopes at their natural abundances. Forming a peptide bond results in elimination of a molecule of water. Therefore, the protein's mass is equal to the mass of amino acids the protein is composed of minus 18.01524 Da per peptide bond.
Symmetry in mathematics Symmetry in quantum mechanics: bosons and fermions Mathematical_symmetry > Symmetry in representation theory > Symmetry in quantum mechanics: bosons and fermions In quantum mechanics, bosons have representatives that are symmetric under permutation operators, and fermions have antisymmetric representatives. This implies the Pauli exclusion principle for fermions. In fact, the Pauli exclusion principle with a single-valued many-particle wavefunction is equivalent to requiring the wavefunction to be antisymmetric. An antisymmetric two-particle state is represented as a sum of states in which one particle is in state | x ⟩ {\displaystyle \scriptstyle |x\rangle } and the other in state | y ⟩ {\displaystyle \scriptstyle |y\rangle }: | ψ ⟩ = ∑ x , y A ( x , y ) | x , y ⟩ {\displaystyle |\psi \rangle =\sum _{x,y}A(x,y)|x,y\rangle } and antisymmetry under exchange means that A(x,y) = −A(y,x).
4,294,967,295 Summary 4,294,967,295 The number 4,294,967,295 is a whole number equal to 232 − 1. It is a perfect totient number, meaning it is equal to the sum of its iterated totients. It follows 4,294,967,294 and precedes 4,294,967,296. It has a factorization of 3 ⋅ 5 ⋅ 17 ⋅ 257 ⋅ 65537 {\displaystyle 3\cdot 5\cdot 17\cdot 257\cdot 65537} . In computing, 4,294,967,295 is the highest unsigned (that is, not negative) 32-bit integer, which makes it the highest possible number a 32-bit system can store in memory.
Crystal field High-spin and low-spin Crystal_Field_Theory > Overview > High-spin and low-spin For example, NO2− is a strong-field ligand and produces a large Δ. The octahedral ion 3−, which has 5 d-electrons, would have the octahedral splitting diagram shown at right with all five electrons in the t2g level. This low spin state therefore does not follow Hund's rule. Conversely, ligands (like I− and Br−) which cause a small splitting Δ of the d-orbitals are referred to as weak-field ligands.
Two-way string-matching algorithm Summary Two-way_string-matching_algorithm In computer science, the two-way string-matching algorithm is a string-searching algorithm, discovered by Maxime Crochemore and Dominique Perrin in 1991. It takes a pattern of size m, called a “needle”, preprocesses it in linear time O(m), producing information that can then be used to search for the needle in any “haystack” string, taking only linear time O(n) with n being the haystack's length. The two-way algorithm can be viewed as a combination of the forward-going Knuth–Morris–Pratt algorithm (KMP) and the backward-running Boyer–Moore string-search algorithm (BM). Like those two, the 2-way algorithm preprocesses the pattern to find partially repeating periods and computes “shifts” based on them, indicating what offset to “jump” to in the haystack when a given character is encountered.
Velocity (character) Powers and abilities Velocity_(character) > Powers and abilities In issue #31, when she spends a day with her sister Cassie, Carin also demonstrates that her eyes can move at an incredible pace as well, allowing her to follow the path of a card while playing a game of three-card monte. The Brain Box also enhances her reaction time and ability to process sensory input, so she will be able to control herself and understand what she sees and hears when moving at high speed. Lately she has gained Ultra-Sapiens abilities. When activated, these allow her to sprout sharp ridges along the outer length of her arms and legs, as well as the ability to quickly heal from injuries.
Tactile signing Comparison to visual sign language Tactile_signing > Comparison to visual sign language Little data exists on the specifics of variation between visual and tactile sign language use. However, studies suggest a significant degree of difference. In hand-over-hand signing, elements of deaf sign languages known as 'non-manual features' (such as facial expression) will not be received, and will need to be substituted with supplementary information produced manually. Common non-manual features used in Deaf Sign languages that are absent in tactile signing include raised eyebrows as a question marker and a shaking head as a negation.
Consensus decision-making Objectives Rational_consensus > Objectives Characteristics of consensus decision-making include: Collaboration: Participants contribute to a shared proposal and shape it into a decision that meets the concerns of all group members as much as possible. Cooperation: Participants in an effective consensus process should strive to reach the best possible decision for the group and all of its members, rather than competing for personal preferences. Egalitarianism: All members of a consensus decision-making body should be afforded, as much as possible, equal input into the process.
Periodic table period Summary Period_(periodic_table) As atomic number increases, shells fill with electrons in approximately the order shown in the ordering rule diagram. The filling of each shell corresponds to a row in the table. In the s-block and p-block of the periodic table, elements within the same period generally do not exhibit trends and similarities in properties (vertical trends down groups are more significant). However, in the d-block, trends across periods become significant, and in the f-block elements show a high degree of similarity across periods.
Lagrange resolvents Summary Resolvent_(Galois_theory) In the case of a cubic equation, this resolvent is sometimes called the quadratic resolvent; its roots appear explicitly in the formulas for the roots of a cubic equation. The cubic resolvent of a quartic equation, which is a resolvent for the dihedral group of 8 elements. The Cayley resolvent is a resolvent for the maximal resoluble Galois group in degree five.
Respirometry Whole-animal metabolic rates Respirometry > Whole-animal metabolic rates The metabolism of an animal is estimated by determining rates of carbon dioxide production (VCO2) and oxygen consumption (VO2) of individual animals, either in a closed or an open-circuit respirometry system. Two measures are typically obtained: standard (SMR) or basal metabolic rate (BMR) and maximal rate (VO2max). SMR is measured while the animal is at rest (but not asleep) under specific laboratory (temperature, hydration) and subject-specific conditions (e.g., size or allometry), age, reproduction status, post-absorptive to avoid thermic effect of food).
Third-generation sequencing Alternative splicing Third-generation_sequencing > Transcriptomics > Alternative splicing Alternative splicing (AS) is the process by which a single gene may give rise to multiple distinct mRNA transcripts and consequently different protein translations. Some evidence suggests that AS is a ubiquitous phenomenon and may play a key role in determining the phenotypes of organisms, especially in complex eukaryotes; all eukaryotes contain genes consisting of introns that may undergo AS. In particular, it has been estimated that AS occurs in 95% of all human multi-exon genes. AS has undeniable potential to influence myriad biological processes. Advancing knowledge in this area has critical implications for the study of biology in general.
OAG (company) Recent history OAG_(company) > Recent history Reed Elsevier sold OAG to Electra Partners in 2001. After five years under private ownership OAG was bought by United Business Media in December 2006 to strengthen its aviation, transportation and travel business interests. UBM sold the majority of its data business to Electra Partners in 2013, who formed AXIO Data Group.In 2009 OAG started to supply airlines schedules and Minimum Connection Time (MCTs) to Global Distribution Systems Travelport and OAG also partners with the largest GDS in the world Amadeus and TravelSky.In June 2010 OAG created new technology (Schedules Dynamic) to deliver the most up-to-date airline schedule changes to airlines, OTAs, GDSs and treservation systems.OAG has a strategic partnership with IATA and contributes to its SSIM Standards Board and working groups.In 2012, OAG launched OAG Analyser to deliver airline schedule analysis via an online accessible tool. In 2013, OAG added to its analytical suite with the launch of Traffic Analyser, a product developed in partnership with Travelport; a leading distribution services and e-commerce provider for the global travel industry.In 2014, OAG acquired the services of real-time flight information solutions provider, Flight view, to expand its flight data business.
Chain reaction (chemistry) Summary Chain_reaction_(chemistry) Chemically, the equivalent to a snow avalanche is a spark causing a forest fire. In nuclear physics, a single stray neutron can result in a prompt critical event, which may finally be energetic enough for a nuclear reactor meltdown or (in a bomb) a nuclear explosion. Numerous chain reactions can be represented by a mathematical model based on Markov chains.
Molecular mixology Techniques Molecular_mixology > Techniques The techniques used by a mixologist are mostly bound to the new equipment which is provided by the molecular gastronomy. They are, for the most part, adaptations of new techniques for food preparation. Some techniques originally created for food applications can nowadays be commonly found in cocktail bars.
Resonance fluorescence Coupling photons to a molecule Resonance_fluorescence > Coupling photons to a molecule The sample which they excited was a Shpol'skii matrix which they had doped with the dyes they wished to use, dibenzanthanthrene. To improve the accuracy of the results, single-molecule fluorescence-excitation spectroscopy was used. The actual process for measuring the resonance was measuring the interference between the laser beam and the photons that were scattered from the molecule.
Object Process Methodology Design Object_Process_Methodology > Design Object-Process Methodology (OPM) is a systems modeling paradigm that integrates two aspects inherent in any system: its structure and its behavior. Structure is represented via objects and structural relations among them, such as aggregation-participation (whole-part relation) and generalization-specialization ("is-a" relation). Behavior is represented by processes and how they transform objects: How they create or consume objects, or how they change the states of an object. : 2 OPM offers a way to model systems of almost any domain, be it artificial or natural. : x
Digital privacy Information privacy Digital_privacy > Types of privacy > Information privacy The baseline for this concept was put forward in the late 1940s, and the third era of privacy development began in the 1990s.The European Union has various privacy laws that dictate how information may be collected and used by companies. Some of those laws are written to give agency to the preferences of individuals/consumers in how their data is used.
Contraction hierarchy Algorithm Contraction_hierarchies > Algorithm To calculate the distance between these two cities, the algorithm has to traverse all the edges along the way, adding up their length. Precomputing this distance once and storing it in an additional edge created between the two large cities will save calculations each time this highway has to be evaluated in a query. This additional edge is called a "shortcut" and has no counterpart in the real world. The contraction hierarchies algorithm has no knowledge about road types but is able to determine which shortcuts have to be created using the graph alone as input.
Cohomological dimension of a field Summary Cohomological_dimension In abstract algebra, cohomological dimension is an invariant of a group which measures the homological complexity of its representations. It has important applications in geometric group theory, topology, and algebraic number theory.
Sea Currents Sea > Physical science > Currents Wind blowing over the surface of the sea causes friction at the interface between air and sea. Not only does this cause waves to form, but it also makes the surface seawater move in the same direction as the wind. Although winds are variable, in any one place they predominantly blow from a single direction and thus a surface current can be formed. Westerly winds are most frequent in the mid-latitudes while easterlies dominate the tropics.
Inverse mapping Inverses and composition Inverse_mapping > Definitions > Inverses and composition Recall that if f is an invertible function with domain X and codomain Y, then f − 1 ( f ( x ) ) = x {\displaystyle f^{-1}\left(f(x)\right)=x} , for every x ∈ X {\displaystyle x\in X} and f ( f − 1 ( y ) ) = y {\displaystyle f\left(f^{-1}(y)\right)=y} for every y ∈ Y {\displaystyle y\in Y} .Using the composition of functions, this statement can be rewritten to the following equations between functions: f − 1 ∘ f = id X {\displaystyle f^{-1}\circ f=\operatorname {id} _{X}} and f ∘ f − 1 = id Y , {\displaystyle f\circ f^{-1}=\operatorname {id} _{Y},} where idX is the identity function on the set X; that is, the function that leaves its argument unchanged. In category theory, this statement is used as the definition of an inverse morphism. Considering function composition helps to understand the notation f −1. Repeatedly composing a function f: X→X with itself is called iteration. If f is applied n times, starting with the value x, then this is written as f n(x); so f 2(x) = f (f (x)), etc. Since f −1(f (x)) = x, composing f −1 and f n yields f n−1, "undoing" the effect of one application of f.
Coenzyme F420 hydrogenase Summary Coenzyme_F420_hydrogenase In enzymology, a coenzyme F420 hydrogenase (EC 1.12.98.1) is an enzyme that catalyzes the chemical reaction H2 + coenzyme F420 ⇌ {\displaystyle \rightleftharpoons } reduced coenzyme F420Thus, the two substrates of this enzyme are H2 and coenzyme F420, whereas its product is reduced coenzyme F420. This enzyme belongs to the family of oxidoreductases, specifically those acting on hydrogen as donor with other, known, acceptors. The systematic name of this enzyme class is hydrogen:coenzyme F420 oxidoreductase.
Small nucleolar RNA SNORA57 Summary Small_nucleolar_RNA_SNORA57 In molecular biology, Small nucleolar RNA SNORA57 (also known as U99 and MBI-64) is a non-coding RNA (ncRNA) molecule which functions in the biogenesis (modification) of other small nuclear RNAs (snRNAs). This type of modifying RNA is located in the nucleolus of the eukaryotic cell which is a major site of snRNA biogenesis. It is known as a small nucleolar RNA (snoRNA) and also often referred to as a "guide RNA".
Proof complexity Optimality and simulations between proof systems Proof_complexity > Optimality and simulations between proof systems Every propositional proof system P can be simulated by Extended Frege extended with axioms postulating soundness of P. The existence of an optimal (respectively p-optimal) proof system is known to follow from the assumption that NE=coNE (respectively E=NE).For many weak proof systems it is known that they do not simulate certain stronger systems (see below). However, the question remains open if the notion of simulation is relaxed. For example, it is open whether Resolution effectively polynomially simulates Extended Frege.
Multidimensional systems Applications Multidimensional_system > Applications Multidimensional systems or m-D systems are the necessary mathematical background for modern digital image processing with many applications in biomedicine, X-ray technology and satellite communications. There are also some studies combining m-D systems with partial differential equations (PDEs).
Darboux's formula Special cases Darboux's_formula > Special cases Taking φ to be a Bernoulli polynomial in Darboux's formula gives the Euler–Maclaurin summation formula. Taking φ to be (t − 1)n gives the formula for a Taylor series.
Composite numbers Summary Composite_number A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit.For example, the integer 14 is a composite number because it is the product of the two smaller integers 2 × 7.
Model-centered instruction Principles of Model-Centered Instruction Model-centered_instruction > Principles of Model-Centered Instruction The terms model and simulation are not synonymous; models can be expressed in a variety of computer-based and non-computer-based forms. 2. Problem solving: Interaction with systems or models should be focused by the solution of one or more carefully selected problems, expressed in terms of the model, with solutions being performed by the learner, by a peer, or by an expert.
Restricted Boltzmann machine Summary Restricted_Boltzmann_machine A restricted Boltzmann machine (RBM) (also called Restricted Sherrington–Kirkpatrick model with external field or restricted stochastic Ising–Lenz–Little model) is a generative stochastic artificial neural network that can learn a probability distribution over its set of inputs.RBMs were initially proposed under the name Harmonium by Paul Smolensky in 1986, and rose to prominence after Geoffrey Hinton and collaborators used fast learning algorithms for them in the mid-2000. RBMs have found applications in dimensionality reduction, classification, collaborative filtering, feature learning, topic modelling and even many body quantum mechanics. They can be trained in either supervised or unsupervised ways, depending on the task. As their name implies, RBMs are a variant of Boltzmann machines, with the restriction that their neurons must form a bipartite graph: a pair of nodes from each of the two groups of units (commonly referred to as the "visible" and "hidden" units respectively) may have a symmetric connection between them; and there are no connections between nodes within a group.
Standard Model of Particle Physics Higgs boson Standard_Model_of_Particle_Physics > Particle content > Higgs boson As the Higgs boson is massive, it must interact with itself. Because the Higgs boson is a very massive particle and also decays almost immediately when created, only a very high-energy particle accelerator can observe and record it.
Information source (mathematics) Summary Information_source_(mathematics) In mathematics, an information source is a sequence of random variables ranging over a finite alphabet Γ, having a stationary distribution. The uncertainty, or entropy rate, of an information source is defined as H { X } = lim n → ∞ H ( X n | X 0 , X 1 , … , X n − 1 ) {\displaystyle H\{\mathbf {X} \}=\lim _{n\to \infty }H(X_{n}|X_{0},X_{1},\dots ,X_{n-1})} where X 0 , X 1 , … , X n {\displaystyle X_{0},X_{1},\dots ,X_{n}} is the sequence of random variables defining the information source, and H ( X n | X 0 , X 1 , … , X n − 1 ) {\displaystyle H(X_{n}|X_{0},X_{1},\dots ,X_{n-1})} is the conditional information entropy of the sequence of random variables. Equivalently, one has H { X } = lim n → ∞ H ( X 0 , X 1 , … , X n − 1 , X n ) n + 1 . {\displaystyle H\{\mathbf {X} \}=\lim _{n\to \infty }{\frac {H(X_{0},X_{1},\dots ,X_{n-1},X_{n})}{n+1}}.}
Electric armour Overview Electromagnetic_armour > Overview Electric armour is a newer reactive armour technology. This armour is made up of two or more conductive plates separated by an air gap or by an insulating material, creating a high-power capacitor. In operation, a high-voltage power source charges the armour. When an incoming body penetrates the plates, it closes the circuit to discharge the capacitor, dumping a great deal of energy into the penetrator, vaporizing it or even turning it into a plasma, significantly diffusing the attack.Another version of electric armour uses layers of plates of electromagnetic metal with silicone spacers on alternate sides. The damage to the exterior of the armour passes electricity into the plates causing them to magnetically move together. As the process is completed at the speed of electricity the plates are moving when struck by the projectile causing the projectile energy to be deflected whilst the energy is also dissipated in parting the magnetically attracted plates.
Nanoscale vacuum-channel transistor Immunity to radiation Nanoscale_vacuum-channel_transistor > Advantages > Immunity to radiation The radiation can ionize the atoms in a solid-state transistor. These ionized atoms and corresponding electrons can interfere with the electron transport between the source and collector. However, no ionization occur in the vacuum-channel transistors. Therefore, a vacuum-channel transistor can be used in a high radiation environment such as outer space or inside a nuclear reactor.
Focal plane Focal points and planes Nodal_point > Explanation > Focal points and planes The front focal point of an optical system, by definition, has the property that any ray that passes through it will emerge from the system parallel to the optical axis. The rear (or back) focal point of the system has the reverse property: rays that enter the system parallel to the optical axis are focused such that they pass through the rear focal point. The front and rear (or back) focal planes are defined as the planes, perpendicular to the optic axis, which pass through the front and rear focal points. An object infinitely far from the optical system forms an image at the rear focal plane.
Diatomaceous Earth Filtration Diatomaceous_Earth > Usages > Filtration It has a high porosity because it is composed of microscopically small, hollow particles. Diatomaceous earth (sometimes referred to by trademarked brand names such as Celite) is used in chemistry as a filtration aid, to increase flow rate, and filter very fine particles that would otherwise pass through or clog filter paper. It is also used to filter water, particularly in the drinking water treatment process and in fish tanks, and other liquids, such as beer and wine. It can also filter syrups, sugar, and honey without removing or altering their color, taste, or nutritional properties.
Shannon Entropy Limitations of entropy in cryptography Information_entropy > Aspects > Limitations of entropy in cryptography Entropy fails to capture the number of guesses required if the possible keys are not chosen uniformly. Instead, a measure called guesswork can be used to measure the effort required for a brute force attack.Other problems may arise from non-uniform distributions used in cryptography. For example, a 1,000,000-digit binary one-time pad using exclusive or.
Filter thread Uses Photographic_filter > Uses Filters in photography can be classified according to their use: Clear and ultraviolet Color correction Color conversion (or light balance) Color separation, also called color subtraction Contrast enhancement Infrared Neutral density, including the graduated neutral density filter and solar filter Polarizing Special effects of various kinds, including Graduated color, called color grads Cross screen and star diffractors Diffusion and contrast reduction Spot Close-up or macro diopters, and split diopters or split focus
Inertial frames Newtonian mechanics Galilean_frame_of_reference > Newton's inertial frame of reference > Newtonian mechanics There are several approaches to this issue. One approach is to argue that all real forces drop off with distance from their sources in a known manner, so we have only to be sure that a body is far enough away from all sources to ensure that no force is present. A possible issue with this approach is the historically long-lived view that the distant universe might affect matters (Mach's principle).
Memory ordering Optimization under as-if Memory_ordering > Compile-time memory ordering > Additional difficulties and complications > Optimization under as-if It is the responsibility of the programmer to consult the language specification to avoid writing ill-formed programs where the semantics are potentially changed as a result of any legal compiler optimization. Fortran traditionally places a high burden on the programmer to be aware of these issues, with the systems programming languages C and C++ not far behind. Some high-level languages eliminate pointer constructions altogether, as this level of alertness and attention to detail is considered too high to reliably maintain even among professional programmers.
Quadratic integers Summary Quadratic_integer In number theory, quadratic integers are a generalization of the usual integers to quadratic fields. Quadratic integers are algebraic integers of degree two, that is, solutions of equations of the form x2 + bx + c = 0with b and c (usual) integers. When algebraic integers are considered, the usual integers are often called rational integers. Common examples of quadratic integers are the square roots of rational integers, such as √2, and the complex number i = √−1, which generates the Gaussian integers.
Bacterial skin infection Viral Skin_infection > Causes > Viral Virus-related cutaneous conditions caused by these obligate intracellular agents derive from both DNA and RNA viruses. Some examples of viral skin infections include: Warts, benign proliferative skin lesions that are caused by human papilloma virus (HPV). Warts vary in shape, size, appearance, and location on the body where they occur. For example, plantar warts (verrucae plantaris), occur on the soles of the feet and appear as thick calluses.