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Complex projective space Introduction Complex_projective_space > Introduction The notion of a projective plane arises out of the idea of perspection in geometry and art: that it is sometimes useful to include in the Euclidean plane an additional "imaginary" line that represents the horizon that an artist, painting the plane, might see. Following each direction from the origin, there is a different point on the horizon, so the horizon can be thought of as the set of all directions from the origin. The Euclidean plane, together with its horizon, is called the real projective plane, and the horizon is sometimes called a line at infinity.
H4K20me H4K20me3 H4K20me > Lysine Methylation > H4K20me3 The loss of H4K20me3 defines cancer along with a reduction of H4K16ac.H4K20me3 is involved in Hutchinson-Gilford Progeria syndrome where patients have premature and very rapid aging caused by de novo mutations that occurs in a gene that encodes lamin A. Lamin A is made but isn't processed properly. This poor processing creates a really abnormal nuclear morphology and disorganized heterochromatin. Patients also don't have appropriate DNA repair, and they also have increased genomic instability.
Fanconi anaemia Myelodysplastic syndromes Fanconi_anemia > Pathogenesis > Myelodysplastic syndromes MDSs, formerly known as preleukemia, are a group of bone marrow neoplastic diseases that share many of the morphologic features of AML, with some important differences. First, the percentage of undifferentiated progenitor cells, blast cells, is always less than 20%, with considerably more dysplasia, defined as cytoplasmic and nuclear morphologic changes in erythroid, granulocytic, and megakaryocytic precursors, than what is usually seen in cases of AML. These changes reflect delayed apoptosis or a failure of programmed cell death. When left untreated, MDS can lead to AML in about 30% of cases.
Hypothesis test Neyman–Pearson hypothesis testing Statistical_hypothesis_testing > Neyman–Pearson hypothesis testing A simple method of solution is to select the hypothesis with the highest probability for the Geiger counts observed. The typical result matches intuition: few counts imply no source, many counts imply two sources and intermediate counts imply one source. Notice also that usually there are problems for proving a negative.
Inferring horizontal gene transfer Model-based reconciliation methods Inferring_horizontal_gene_transfer > Phylogenetic methods > Explicit phylogenetic methods > Model-based reconciliation methods More refined models account for the biased frequency of HGT between closely related lineages, reflecting the loss of efficiency of HR with phylogenetic distance, for ILS, or for the fact that the actual donor of most HGT belong to extinct or unsampled lineages. Further extensions of DTL models are being developed towards an integrated description of the genome evolution processes. In particular, some of them consider horizontal at multiple scales—modelling independent evolution of gene fragments or recognising co-evolution of several genes (e.g., due to co-transfer) within and across genomes.
Gateleg table Summary Gateleg_table A gateleg table is a type of furniture first introduced in England in the 16th century. The table top has a fixed section and one or two hinged leaves, which, when not in use, fold down below the fixed section to hang vertically.
Synthetic hormones Summary Hormonal_medication Hormones are used to communicate between organs and tissues. In vertebrates, hormones are responsible for regulating a variety of physiological processes and behavioral activities such as digestion, metabolism, respiration, sensory perception, sleep, excretion, lactation, stress induction, growth and development, movement, reproduction, and mood manipulation. In plants, hormones modulate almost all aspects of development, from germination to senescence.Hormones affect distant cells by binding to specific receptor proteins in the target cell, resulting in a change in cell function.
Advance Steel Features Advance_Steel > Features This means that users can create their own customized macros for specialist requirements. Advance Steel imports and exports to the following file formats: GTC DWG IFC 2x3 CIS/2 SDNF PSS KISS (“Keep it Simple, Steel”) DSTV DXFThe main functions of Advance Steel concern: Creation of 3D model using a library of construction elements (i.e., beams, plates, bolts, welds, etc.) Sheet metal and plate work Advanced tools for element collision detection Clear workshop drawings, automatically labeled and dimensioned Checking the model in order to insure a correctly built 3D model and accurate bills of materials Automatic creation of general arrangement and shop drawings, fabrication drawings, fitting drawings, isometric views and fabrication drawings Drawing creation workflow management (revision control, automatic update, etc.) Automatic creation of lists / bills of materials and NC files Multi-user technology - all users involved in a project can work simultaneously and securely on the same model, without errors.Advance Steel provides instruments for modeling complex structures such as straight and spiral stairs, railings, and ladders. The program creates all necessary documents (including NC files) for the stair fabrication.
Interrupts in 65xx processors ABORT interrupt Interrupts_in_65xx_processors > ABORT interrupt In order for the processor to correctly respond to an abort, system logic must assert (negate) the ABORTB input as soon as a valid address has been placed on the bus and it has been determined that the address constitutes a page fault, memory access violation or other anomaly (e.g., attempted execution of a privileged instruction). Hence the logic must not assert ABORTB until the processor has asserted the VDA or VPA signals. Also, ABORTB must remain asserted until the fall of the phase-two clock and then be immediately released. If these timing constraints are not observed, the abort interrupt handler itself may be aborted, causing registers and/or memory to be changed in a possibly-undefined manner.
Electrical characteristics of dynamic loudspeakers Minimum impedance Electrical_characteristics_of_dynamic_loudspeakers > Load impedance and amplifiers > Minimum impedance This is the minimum value in the impedance vs. frequency relationship, which is always higher than the DC resistance of the voice coil, i.e., as measured by an ohmmeter. Minimum impedance is significant because the lower the impedance, the higher the current must be at the same drive voltage. The output devices of an amplifier are rated for a certain maximum current level, and when this is exceeded the device(s) sometimes, more or less promptly, fail.
Fermat's right triangle theorem Fermat's proof Fermat's_right_triangle_theorem > Fermat's proof During his lifetime, Fermat challenged several other mathematicians to prove the non-existence of a Pythagorean triangle with square area, but did not publish the proof himself. However, he wrote a proof in his copy of Diophantus's Arithmetica, the same copy in which he wrote that he could prove Fermat's Last Theorem. Fermat's son Clement-Samuel published an edition of this book, including Fermat's marginal notes with the proof of the right triangle theorem, in 1670.Fermat's proof is a proof by infinite descent. It shows that, from any example of a Pythagorean triangle with square area, one can derive a smaller example.
Table of elements The order of subshell filling Periodic_Table > Atomic structures of the elements > Electron configurations > The order of subshell filling Oxygen (1s2 2s2 2p4), fluorine (1s2 2s2 2p5), and neon (1s2 2s2 2p6) then complete the already singly filled 2p orbitals; the last of these fills the second shell completely.Starting from element 11, sodium, the second shell is full, making the second shell a core shell for this and all heavier elements. The eleventh electron begins the filling of the third shell by occupying a 3s orbital, giving a configuration of 1s2 2s2 2p6 3s1 for sodium. This configuration is abbreviated 3s1, where represents neon's configuration.
Inertial Mass Inertial vs. gravitational mass Mass > Definitions > Inertial vs. gravitational mass This says that the ratio of gravitational to inertial mass of any object is equal to some constant K if and only if all objects fall at the same rate in a given gravitational field. This phenomenon is referred to as the "universality of free-fall". In addition, the constant K can be taken as 1 by defining our units appropriately.
Philosophy of statistics Topics of interest Philosophy_of_statistics > Topics of interest Distinctions between induction and logical deduction relevant to inferences from data and evidence arise, such as when frequentist interpretations are compared with degrees of certainty derived from Bayesian inference. However, the difference between induction and ordinary reasoning is not generally appreciated. Leo Breiman exposed the diversity of thinking in his article on 'The Two Cultures', making the point that statistics has several kinds of inference to make, modelling and prediction amongst them.
Ring of integers Multiplicative structure Rings_of_integers > Multiplicative structure In a ring of integers, every element has a factorization into irreducible elements, but the ring need not have the property of unique factorization: for example, in the ring of integers Z, the element 6 has two essentially different factorizations into irreducibles: 6 = 2 ⋅ 3 = ( 1 + − 5 ) ( 1 − − 5 ) . {\displaystyle 6=2\cdot 3=(1+{\sqrt {-5}})(1-{\sqrt {-5}}).} A ring of integers is always a Dedekind domain, and so has unique factorization of ideals into prime ideals.The units of a ring of integers OK is a finitely generated abelian group by Dirichlet's unit theorem. The torsion subgroup consists of the roots of unity of K. A set of torsion-free generators is called a set of fundamental units.
Colebrook–White equation Turbulent flow in smooth conduits Swamee–Jain_equation > Flow regime > Turbulent flow in smooth conduits The Blasius correlation is the simplest equation for computing the Darcy friction factor. Because the Blasius correlation has no term for pipe roughness, it is valid only to smooth pipes. However, the Blasius correlation is sometimes used in rough pipes because of its simplicity. The Blasius correlation is valid up to the Reynolds number 100000.
Vitamin D Difference between substrates Vitamin_D > Mechanism of action > Difference between substrates Vitamin D3 can alternatively be hydroxylated to calcifediol by sterol 27-hydroxylase (CYP27A1), but vitamin D2 cannot. Ergocalciferol can be directly hydroxylated at position 24 by CYP27A1. This hydroxylation also leads to a greater degree of inactivation: the activity of calcitriol decreases to 60% of original after 24-hydroxylation, whereas ercalcitriol undergoes a 10-fold decrease in activity on conversion to ercalcitetrol.It is disputed whether these differences lead to a measurable drop in efficacy (see § Food fortification).
Physical volume Design Volume_manager > Design Systems can use LVs as raw block devices just like disk partitions: creating mountable file systems on them, or using them as swap storage. Striped LVs allocate each successive LE from a different PV; depending on the size of the LE, this can improve performance on large sequential reads by bringing to bear the combined read-throughput of multiple PVs. Administrators can grow LVs (by concatenating more LEs) or shrink them (by returning LEs to the pool).
Occipital pole of cerebrum Composition Occipital_pole_of_cerebrum > Composition The large expanse of medullary matter now exposed, surrounded by the convoluted margin of gray substance, is called the centrum semiovale. The blood supply to the centrum semiovale is from the superficial middle cerebral artery. The cortical branches of this artery descend to provide blood to the centrum semiovale.
Decentralized application Examples Decentralized_application > Examples Augur – prediction market platform. Cryptokitties – game built on Ethereum. It slowed Ethereum down due to insufficient transaction processing and exposed the scaling limitations of public blockchains. Stacks project – a platform for developing decentralized applications.
Finite element method in structural mechanics History Finite_element_method_in_structural_mechanics > History Torus-shaped elements for axisymmetric problems such as membranes, thick plates, shells, and solids. The cross-section of the elements are similar to the previously described types: one-dimensional for thin plates and shells, and two-dimensional for solids, thick plates and shells. Three-dimensional elements for modeling 3-D solids such as machine components, dams, embankments or soil masses. Common element shapes include tetrahedrals and hexahedrals. Nodes are placed at the vertexes and possibly in the element faces or within the element.
Gerbe Cohomological classification Gerbe > Cohomological classification For example, in topology, many examples of gerbes can be constructed by considering gerbes banded by the group U ( 1 ) {\displaystyle U(1)} . As the classifying space B ( U ( 1 ) ) = K ( Z , 2 ) {\displaystyle B(U(1))=K(\mathbb {Z} ,2)} is the second Eilenberg-Maclane space for the integers, a bundle gerbe banded by U ( 1 ) {\displaystyle U(1)} on a topological space X {\displaystyle X} is constructed from a homotopy class of maps in = {\displaystyle =} which is exactly the third singular homology group H 3 ( X , Z ) {\displaystyle H^{3}(X,\mathbb {Z} )} . It has been found that all gerbes representing torsion cohomology classes in H 3 ( X , Z ) {\displaystyle H^{3}(X,\mathbb {Z} )} are represented by a bundle of finite dimensional algebras End ( V ) {\displaystyle {\text{End}}(V)} for a fixed complex vector space V {\displaystyle V} .
Symbiotic bacteria Chemosynthetic Bacteria and Mussels Symbiotic_bacteria > Examples of Symbiotic Relationships > Chemosynthetic Bacteria and Mussels Symbiotic, chemosynthetic bacteria that have been discovered associated with mussels (Bathymodiolus) located near hydrothermal vents have a gene that enables them to utilize hydrogen as a source of energy, in preference to sulphur or methane as their energy source for production of energy.
Chebyshev inequality Example Chebyshev's_inequality > Example Suppose we randomly select a journal article from a source with an average of 1000 words per article, with a standard deviation of 200 words. We can then infer that the probability that it has between 600 and 1400 words (i.e. within k = 2 standard deviations of the mean) must be at least 75%, because there is no more than 1⁄k2 = 1/4 chance to be outside that range, by Chebyshev's inequality. But if we additionally know that the distribution is normal, we can say there is a 75% chance the word count is between 770 and 1230 (which is an even tighter bound).
Nonlinear scalar field theory Feynman path integral Scalar_field_(quantum_field_theory) > Quantum scalar field theory > Feynman path integral Any unconstrained momenta are integrated over all values. The result is divided by a symmetry factor, which is the number of ways the lines and vertices of the graph can be rearranged without changing its connectivity. Do not include graphs containing "vacuum bubbles", connected subgraphs with no external lines.The last rule takes into account the effect of dividing by ~Z. The Minkowski-space Feynman rules are similar, except that each vertex is represented by −ig, while each internal line is represented by a propagator i/(q2−m2+iε), where the ε term represents the small Wick rotation needed to make the Minkowski-space Gaussian integral converge.
Boltzmann entropy History Boltzmann_entropy_formula > History The equation was originally formulated by Ludwig Boltzmann between 1872 and 1875, but later put into its current form by Max Planck in about 1900. To quote Planck, "the logarithmic connection between entropy and probability was first stated by L. Boltzmann in his kinetic theory of gases".A 'microstate' is a state specified in terms of the constituent particles of a body of matter or radiation that has been specified as a macrostate in terms of such variables as internal energy and pressure. A macrostate is experimentally observable, with at least a finite extent in spacetime.
Pictogram Standardization Pictogram > Standardization Pictographs can often transcend languages in that they can communicate to speakers of a number of tongues and language families equally effectively, even if the languages and cultures are completely different. This is why road signs and similar pictographic material are often applied as global standards expected to be understood by nearly all. A standard set of pictographs was defined in the international standard ISO 7001: Public Information Symbols. Other common sets of pictographs are the laundry symbols used on clothing tags and the chemical hazard symbols as standardized by the GHS system. Pictograms have been popularized in use on the web and in software, better known as "icons" displayed on a computer screen in order to help user navigate a computer system or mobile device.
Trigeminal neuralgia Signs and symptoms Trigeminal_neuralgia > Signs and symptoms This disorder is characterized by episodes of severe facial pain along the trigeminal nerve divisions. The trigeminal nerve is a paired cranial nerve that has three major branches: the ophthalmic nerve (V1), the maxillary nerve (V2), and the mandibular nerve (V3). One, two, or all three branches of the nerve may be affected. Trigeminal neuralgia most commonly involves the middle branch (the maxillary nerve or V2) and lower branch (mandibular nerve or V3) of the trigeminal nerve.An individual attack usually lasts from a few seconds to several minutes or hours, but these can repeat for hours with very short intervals between attacks.
Sensitivity (control systems) Summary Sensitivity_(control_systems) In control engineering, the sensitivity (or more precisely, the sensitivity function) of a control system measures how variations in the plant parameters affects the closed-loop transfer function. Since the controller parameters are typically matched to the process characteristics and the process may change, it is important that the controller parameters are chosen in such a way that the closed loop system is not sensitive to variations in process dynamics. Moreover, the sensitivity function is also important to analyse how disturbances affects the system.
Aspect Oriented Programming Motivation and basic concepts Aspect-oriented_software_development > Motivation and basic concepts For example, a security module can include advice that performs a security check before accessing a bank account. The pointcut defines the times (join points) when one can access a bank account, and the code in the advice body defines how the security check is implemented. That way, both the check and the places can be maintained in one place.
Invertible matrix Summary Inverse_of_a_matrix In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular, nondegenerate or (rarely used) regular), if there exists an n-by-n square matrix B such that A B = B A = I n , {\displaystyle \mathbf {AB} =\mathbf {BA} =\mathbf {I} _{n},} where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A−1. Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.Over a field, a square matrix that is not invertible is called singular or degenerate. A square matrix with entries in a field is singular if and only if its determinant is zero.
Fair allocation of items and money MInimum subsidy procedures Fair_allocation_of_items_and_money > Additive agents > MInimum subsidy procedures For any ε > 0, it finds an allocation with subsidy at most O P T + ε ⋅ S {\displaystyle OPT+\varepsilon \cdot S} , where S is the maximum value that an agent assigns to all objects. The algorithm uses dynamic programming and runs in time O ( ( m / ε ) n 2 + 1 ) {\displaystyle O((m/\varepsilon )^{n^{2}+1})} . For a variable number of agents, a trivial approximation algorithm attains O P T + ( n − 1 ) ⋅ S {\displaystyle OPT+(n-1)\cdot S} .
Axiom Summary Logical_axioms An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word ἀξίωμα (axíōma), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.The precise definition varies across fields of study. In classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. In modern logic, an axiom is a premise or starting point for reasoning.In mathematics, an axiom may be a "logical axiom" or a "non-logical axiom".
Historical myth Physics Historical_myth > Science, technology, and mathematics > Physics Although a common classroom experiment is often explained this way, Bernoulli's principle only applies within a flow field, and the air above and below the paper is in different flow fields. The paper rises because the air follows the curve of the paper and a curved streamline will develop pressure differences perpendicular to the airflow. The Coriolis effect does not cause water to consistently drain from basins in a clockwise/counter-clockwise direction depending on the hemisphere.
Didier Sornette The Global Earthquake Forecasting System Didier_Sornette > Theory of earthquakes and fault networks > The Global Earthquake Forecasting System Tree potentials and ground potentials 4. Soil conductivity changes 5. Groundwater chemistry changes 6.
Dioecy In botany Dioecious_plant > In botany Land plants (embryophytes) differ from animals in that their life cycle involves alternation of generations. In animals, typically an individual produces gametes of one kind, either sperm or egg cells. The gametes have half the number of chromosomes of the individual producing them, so are haploid. Without further dividing, a sperm and an egg cell fuse to form a zygote that develops into a new individual.
Antisymmetric exchange Magnetic skyrmions Antisymmetric_exchange > Applications > Magnetic skyrmions A magnetic skyrmion is a magnetic texture that occurs in the magnetization field. They exist in spiral or hedgehog configurations that are stabilized by the Dzyaloshinskii-Moriya interaction. Skyrmions are topological in nature, making them promising candidates for future spintronic devices.
Thoracic aortic aneurysm Screening Thoracic_aortic_aneurysm > Screening Guidelines were issued in March 2010 for early detection of thoracic aortic disease, by the American College of Cardiology, the American Heart Association, and other groups. Among the recommendations: First-degree relatives of people with thoracic aortic aneurysm or dissection should have aortic imaging to identify asymptomatic disease. People with symptoms suggestive of thoracic aortic dissection should be routinely evaluated "to establish a pretest risk of disease that can then be used to guide diagnostic decisions." People diagnosed with Marfan syndrome should immediately have an echocardiogram to measure the aorta and followed up six months later to check for aortic enlargement.
Molar entropy Statistical mechanics Entropy > Definitions and descriptions > Statistical mechanics For instance, Rosenfeld's excess-entropy scaling principle states that reduced transport coefficients throughout the two-dimensional phase diagram are functions uniquely determined by the excess entropy.The most general interpretation of entropy is as a measure of the extent of uncertainty about a system. The equilibrium state of a system maximizes the entropy because it does not reflect all information about the initial conditions, except for the conserved variables. This uncertainty is not of the everyday subjective kind, but rather the uncertainty inherent to the experimental method and interpretative model.The interpretative model has a central role in determining entropy.
History of special relativity Electromagnetic mass History_of_special_relativity > Aether and electrodynamics of moving bodies > Electromagnetic mass He recognized that electromagnetic energy behaves like a fictitious fluid with mass density of m = E / c 2 {\displaystyle \scriptstyle {m=E/c^{2}}} (or E = m c 2 {\displaystyle \scriptstyle {E=mc^{2}}} ) and defined a fictitious electromagnetic momentum as well. However, he arrived at a radiation paradox which was fully explained by Einstein in 1905.Walter Kaufmann (1901–1903) was the first to confirm the velocity dependence of electromagnetic mass by analyzing the ratio e / m {\displaystyle \scriptstyle {e/m}} (where e {\displaystyle \scriptstyle {e}} is the charge and m {\displaystyle \scriptstyle {m}} the mass) of cathode rays. He found that the value of e / m {\displaystyle \scriptstyle {e/m}} decreased with the speed, showing that, assuming the charge constant, the mass of the electron increased with the speed.
Hard-core predicate Summary Hard-core_predicate Suppose f is a strong one-way function. Define g(x, r) = (f(x), r) where |r| = 2|x|.
Stoichiometric coefficient Notation variants Chemical_equations > Structure > Notation variants The standard notation for chemical equations only permits all reactants on one side, all products on the other, and all stoichiometric coefficients positive. For example, the usual form of the equation for dehydration of methanol to dimethylether is: 2 CH 3 OH ⟶ CH 3 OCH 3 + H 2 O {\displaystyle {\ce {2 CH3OH -> CH3OCH3 + H2O}}} Sometimes an extension is used, where some substances with their stoichiometric coefficients are moved above or below the arrow, preceded by a plus sign or nothing for a reactant, and by a minus sign for a product. Then the same equation can look like this: 2 CH 3 OH → − H 2 O CH 3 OCH 3 {\displaystyle {\ce {2CH3OH->CH3OCH3}}} Such notation serves to hide less important substances from the sides of the equation, to make the type of reaction at hand more obvious, and to facilitate chaining of chemical equations. This is very useful in illustrating multi-step reaction mechanisms.
Solubility equilibrium Phase effect Solubility_constant > Effects of conditions > Phase effect However, kinetic factors may favor the formation the unfavorable precipitate (e.g. aragonite), which is then said to be in a metastable state.In pharmacology, the metastable state is sometimes referred to as amorphous state. Amorphous drugs have higher solubility than their crystalline counterparts due to the absence of long-distance interactions inherent in crystal lattice. Thus, it takes less energy to solvate the molecules in amorphous phase. The effect of amorphous phase on solubility is widely used to make drugs more soluble.
Ontological catalogue Selected bibliography Theory_of_Categories > Selected bibliography Categories of Being: Essays on Metaphysics and Logic. New York: Oxford University Press. Hoffman, J., and Rosenkrantz, G. S.,1994.
Network address translator Type of NAT and NAT traversal, role of port preservation for TCP Port_address_translation > Type of NAT and NAT traversal, role of port preservation for TCP TCP hole punching requires the NAT to follow the port preservation design for TCP. For a given outgoing TCP communication, the same port numbers are used on both sides of the NAT. NAT port preservation for outgoing TCP connections is crucial for TCP NAT traversal because, under TCP, one port can only be used for one communication at a time, so programs bind distinct TCP sockets to ephemeral ports for each TCP communication, rendering NAT port prediction impossible for TCP.On the other hand, for UDP, NATs do not need port preservation.
Hot transition Vibrational hot bands Hot_band > Vibrational hot bands In the harmonic approximation, the normal modes of a molecule are not coupled, and all vibrational quantum levels are equally spaced, so hot bands would not be distinguishable from so-called "fundamental" transitions arising from the overall vibrational ground state. However, vibrations of real molecules always have some anharmonicity, which causes coupling between different vibrational modes that in turn shifts the observed frequencies of hot bands in vibrational spectra. Because anharmonicity decreases the spacing between adjacent vibrational levels, hot bands exhibit red shifts (appear at lower frequencies than the corresponding fundamental transitions). The magnitude of the observed shift is correlated to the degree of anharmonicity in the corresponding normal modes.
Human nervous system Summary Nervous_System Spinal nerves are mixed nerves that serve both functions. The PNS is divided into three separate subsystems, the somatic, autonomic, and enteric nervous systems. Somatic nerves mediate voluntary movement.
Risk of infection Assessment Risk_of_infection > Assessment The patient should be asked about a history of repeated infections, symptoms of infection, recent travel to high-risk areas, and their immunization history. They should also be assessed for objective signs such as the presence of wounds, fever, or signs of nutritional deficiency
Brunel truss Summary Brunel_truss The Royal Albert Bridge is a railway bridge which spans the River Tamar in England between Plymouth, Devon and Saltash, Cornwall. Its unique design consists of two 455-foot (138.7 m) lenticular iron trusses 100 feet (30.5 m) above the water, with conventional plate-girder approach spans. This gives it a total length of 2,187.5 feet (666.8 m). It carries the Cornish Main Line railway in and out of Cornwall.
Photovoltaic Effect Physics Photovoltaic_Effect > Physics In addition to the direct photovoltaic excitation of free electrons, an electric current can also arise through the Seebeck effect. When conductive or semiconductive material is heated by absorption of electromagnetic radiation, the heating can lead to increased temperature gradients in the semiconductor material or differentials between materials. These thermal differences in turn may generate a voltage because the electron energy levels are shifted differently in different areas, creating a potential difference between those areas which in turn create an electric current. The relative contributions of the photovoltaic effect versus the Seebeck effect depend on many characteristics of the constituent materials.All above effects generate direct current, the first demonstration of the alternating current photovoltaic effect (AC PV) was done by Dr. Haiyang Zou and Prof. Zhong Lin Wang at the Georgia Institute of Technology in 2017.
Fungal cell Internal membranes Eucaryotic_cells > Distinguishing features > Internal membranes Various tube- and sheet-like extensions of the nuclear membrane form the endoplasmic reticulum, which is involved in protein transport and maturation. It includes the rough endoplasmic reticulum, covered in ribosomes which synthesize proteins; these enter the interior space or lumen. Subsequently, they generally enter vesicles, which bud off from the smooth endoplasmic reticulum. In most eukaryotes, these protein-carrying vesicles are released and further modified in stacks of flattened vesicles (cisternae), the Golgi apparatus.Vesicles may be specialized; for instance, lysosomes contain digestive enzymes that break down biomolecules in the cytoplasm.
International Society for Computational Biology Summary International_Society_for_Computational_Biology The International Society for Computational Biology (ISCB) is a scholarly society for researchers in computational biology and bioinformatics. The society was founded in 1997 to provide a stable financial home for the Intelligent Systems for Molecular Biology (ISMB) conference and has grown to become a larger society working towards advancing understanding of living systems through computation and for communicating scientific advances worldwide. In addition to ISMB, the society also organizes a growing number of smaller, more regionally or topically focused conferences and presents a number of annual scientific achievement awards, including the Overton Prize and the ISCB Senior Scientist Awards.
Rare gas Compounds Rare_gas > Chemical properties > Compounds (On the other hand, flerovium, despite being in group 14, is predicted to be unusually volatile, which suggests noble gas-like properties. )The noble gases—including helium—can form stable molecular ions in the gas phase. The simplest is the helium hydride molecular ion, HeH+, discovered in 1925.
Proofs by contradiction Summary Indirect_proof In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite,and reductio ad impossibile.A mathematical proof employing proof by contradiction usually proceeds as follows: The proposition to be proved is P. We assume P to be false, i.e., we assume ¬P. It is then shown that ¬P implies falsehood. This is typically accomplished by deriving two mutually contradictory assertions, Q and ¬Q, and appealing to the law of noncontradiction. Since assuming P to be false leads to a contradiction, it is concluded that P is in fact true.An important special case is the existence proof by contradiction: in order to demonstrate that an object with a given property exists, we derive a contradiction from the assumption that all objects satisfy the negation of the property.
Bayesian decision theory Empirical Bayes estimators Bayes_risk > Empirical Bayes estimators For example, if independent observations of different parameters are performed, then the estimation performance of a particular parameter can sometimes be improved by using data from other observations. There are parametric and non-parametric approaches to empirical Bayes estimation. Parametric empirical Bayes is usually preferable since it is more applicable and more accurate on small amounts of data.
Astrophysical simulations Summary Computational_Astrophysics Computational astrophysics refers to the methods and computing tools developed and used in astrophysics research. Like computational chemistry or computational physics, it is both a specific branch of theoretical astrophysics and an interdisciplinary field relying on computer science, mathematics, and wider physics. Computational astrophysics is most often studied through an applied mathematics or astrophysics programme at PhD level. Well-established areas of astrophysics employing computational methods include magnetohydrodynamics, astrophysical radiative transfer, stellar and galactic dynamics, and astrophysical fluid dynamics. A recently developed field with interesting results is numerical relativity.
Training data set Test data set Training_dataset > Test data set To do this, the final model is used to predict classifications of examples in the test set. Those predictions are compared to the examples' true classifications to assess the model's accuracy.In a scenario where both validation and test datasets are used, the test data set is typically used to assess the final model that is selected during the validation process.
Energy Efficiency Ratio Summary Seasonal_Energy_Efficiency_Ratio In the United States, the efficiency of air conditioners is often rated by the seasonal energy efficiency ratio (SEER) which is defined by the Air Conditioning, Heating, and Refrigeration Institute, a trade association, in its 2008 standard AHRI 210/240, Performance Rating of Unitary Air-Conditioning and Air-Source Heat Pump Equipment. A similar standard is the European seasonal energy efficiency ratio (ESEER). The SEER rating of a unit is the cooling output during a typical cooling-season divided by the total electric energy input during the same period.
Transition metal thiolate complex Reactions Transition_metal_thiolate_complex > Reactions Thiolates are relatively basic ligands, being derived from conjugate acids with pKa's of 6.5 (thiophenol) to 10.5 (butanethiol). Consequently, thiolate ligand often bridge pairs of metals. One example is Fe2(SCH3)2(CO)6. Thiolate ligands, especially when nonbridging, are susceptible to attack by electrophiles including acids, alkylating agents, and oxidants.
Lamellar tearing Cold cracking Lamellar_tearing > Types > Cracks > Cold cracking In addition, a slower cooling rate means a longer time at an elevated temperature, which allows more hydrogen to escape. A slower cooling rate is achieved by using high heat input and maintaining it during the welding.The alloy composition of the base metal also has an essential role in the likelihood of a cold crack occurring, since that composition relates to the hardenability of materials. With high cooling rates, the risk of forming a hard, brittle structure in the weld metal and HAZ is more likely.
Service Control Point Summary Service_Control_Point These are realized using Intelligent Network Application Part (INAP) that sits above Transaction Capabilities Application Part (TCAP) on the SS7 protocol stack. The TCAP is part of the top or 7th layer of the OSI layer breakdown. SCPs are connected with either SSPs or STPs.
Resistor–transistor logic Advantages Resistor-transistor_logic > Advantages The primary advantage of RTL technology was that it used a minimum number of transistors. In circuits using discrete components, before integrated circuits, transistors were the most expensive component to produce. Early IC logic production (such as Fairchild's in 1961) used the same approach briefly, but quickly transitioned to higher-performance circuits such as diode–transistor logic and then transistor–transistor logic (starting in 1963 at Sylvania Electric Products), since diodes and transistors were no more expensive than resistors in the IC.
Stacker 4 Summary Stacker_3 Stac Electronics, originally incorporated as State of the Art Consulting and later shortened to Stac, Inc., was a technology company founded in 1983. It is known primarily for its Lempel–Ziv–Stac lossless compression algorithm and Stacker disk compression utility for compressing data for storage.
Natural Computation Systems biology Cellular_computing > Nature as information processing > Systems biology Other approaches to describing accurately and succinctly protein–protein interactions include the use of textual bio-calculus or pi-calculus enriched with stochastic features.Transport networks refer to the separation and transport of substances mediated by lipid membranes. Some lipids can self-assemble into biological membranes. A lipid membrane consists of a lipid bilayer in which proteins and other molecules are embedded, being able to travel along this layer. Through lipid bilayers, substances are transported between the inside and outside of membranes to interact with other molecules. Formalisms depicting transport networks include membrane systems and brane calculi.
MATHLAB Applications MATHLAB > Applications MATHLAB 68 has been used to solve electrical linear circuits using an acausal modeling approach for symbolic circuit analysis. This application was developed as a plug-in for MATHLAB 68 (open-source), building on MATHLAB's linear algebra facilities (Laplace transforms, inverse Laplace transforms and linear algebra manipulation).
Animal vaccination Next generation vaccines Animal_vaccination > Vaccine production > Next generation vaccines Currently, there is research being undergone into plant vaccines, which come under the category of vector vaccines. Domestic chickens have been vaccinated against Pasteurella anatis using bacterial outer membrane vesicles purified by hydrostatic filtration dialysis.
Band structure Tight binding model Theory_of_electrons_in_solids > Theory in crystals > Tight binding model The Wannier functions are localized near atomic sites, like atomic orbitals, but being defined in terms of Bloch functions they are accurately related to solutions based upon the crystal potential. Wannier functions on different atomic sites R are orthogonal. The Wannier functions can be used to form the Schrödinger solution for the n-th energy band as: The TB model works well in materials with limited overlap between atomic orbitals and potentials on neighbouring atoms.
Data lineage Big data debugging Data_lineage > Rationale > Big data debugging Big data analytics is the process of examining large data sets to uncover hidden patterns, unknown correlations, market trends, customer preferences and other useful business information. They apply machine learning algorithms etc. to the data which transforms the data. Due to the humongous size of the data, there could be unknown features in the data, possibly even outliers.
Spring tides Forces Tidal_current > Physics > Forces These bodies have strong gravitational fields that diminish with distance and cause the ocean's surface to deviate from the geoid. They establish a new equilibrium ocean surface which bulges toward the moon on one side and away from the moon on the other side. The earth's rotation relative to this shape causes the daily tidal cycle. The ocean surface tends toward this equilibrium shape, which is constantly changing, and never quite attains it. When the ocean surface is not aligned with it, it's as though the surface is sloping, and water accelerates in the down-slope direction.
Network game Summary Two_player A multiplayer video game is a video game in which more than one person can play in the same game environment at the same time, either locally on the same computing system (couch co-op), on different computing systems via a local area network, or via a wide area network, most commonly the Internet (e.g. World of Warcraft, Call of Duty, DayZ). Multiplayer games usually require players to share a single game system or use networking technology to play together over a greater distance; players may compete against one or more human contestants, work cooperatively with a human partner to achieve a common goal, or supervise other players' activity. Due to multiplayer games allowing players to interact with other individuals, they provide an element of social communication absent from single-player games.
Skin friction line Additional sources Skin_friction_line > References > Additional sources Chapman, G. T. Topological classification of flow separation on three-dimensional bodies AIAA, Aerospace Sciences Meeting, 24th, Reno, NV, Jan. 6–9, 1986. 22 p. Skin friction lines | CSA New developments and applications of skin-friction measuring techniques - Abstract - Measurement Science and Technology - IOPscience
Alfred Werner Coordination chemistry Alfred_Werner > Research > Coordination chemistry In 1893, Werner was the first to propose correct structures for coordination compounds containing complex ions, in which a central transition metal atom is surrounded by neutral or anionic ligands. For example, it was known that cobalt forms a "complex" hexamine cobalt (III) chloride, with formula CoCl3•6NH3, but the nature of the association indicated by the dot was mysterious. Werner proposed the structure Cl3, with the Co3+ ion surrounded by six NH3 at the vertices of an octahedron. The three Cl− are dissociated as free ions, which Werner confirmed by measuring the conductivity of the compound in an aqueous solution, and also by chloride anion analysis using precipitation with silver nitrate.
Premenstrual dysphoric disorder DSM-5 Premenstrual_dysphoric_disorder > Diagnosis > DSM-5 A sense of being overwhelmed or out of control. Physical symptoms such as breast tenderness or swelling, joint or muscle pain, a sensation of "bloating", or weight gain.Severity Criterion D: The symptoms observed in Criteria A-C are associated with clinically significant distress or interference with work, school, usual social activities, or relationships with others (e.g., avoidance of social activities; decreased productivity and efficiency at work, school, or home). Consideration of Other Psychiatric Disorders Criterion E: The disturbance is not merely an exacerbation of the symptoms of another disorder, such as major depressive disorder, panic disorder, persistent depressive disorder (Dysthymia), or a personality disorder—although it may co-occur with any of these disorders.Confirmation of the Disorder Criterion F: Criterion A should be confirmed by prospective daily ratings during at least two symptomatic cycles.
Opportunity Cost Comparative advantage versus absolute advantage Opportunity_Cost > Use of opportunity cost > Comparative advantage versus absolute advantage For example, if Country A can produce 1 tonne of wool using less manpower compared to Country B, then it is more efficient and has an absolute advantage over wool production, even if it does not have a comparative advantage because it has a higher opportunity cost (5 tonnes of tea).Absolute advantage refers to how efficiently resources are used whereas comparative advantage refers to how little is sacrificed in terms of opportunity cost. When a country produces what it has the comparative advantage of, even if it does not have an absolute advantage, and trades for those products it does not have a comparative advantage over, it maximises its output since the opportunity cost of its production is lower than its competitors. By focusing on specialising this way, it also maximises its level of consumption.
Direct mapped cache Advantages Set_associative > Fully associative cache > Advantages Fully associative cache structure provides us the flexibility of placing memory block in any of the cache lines and hence full utilization of the cache. The placement policy provides better cache hit rate. It offers the flexibility of utilizing a wide variety of replacement algorithms if a cache miss occurs
Acceleration (special relativity) Summary Acceleration_(special_relativity) In such frames, effects arise which are analogous to homogeneous gravitational fields, which have some formal similarities to the real, inhomogeneous gravitational fields of curved spacetime in general relativity. In the case of hyperbolic motion one can use Rindler coordinates, in the case of uniform circular motion one can use Born coordinates. Concerning the historical development, relativistic equations containing accelerations can already be found in the early years of relativity, as summarized in early textbooks by Max von Laue (1911, 1921) or Wolfgang Pauli (1921). For instance, equations of motion and acceleration transformations were developed in the papers of Hendrik Antoon Lorentz (1899, 1904), Henri Poincaré (1905), Albert Einstein (1905), Max Planck (1906), and four-acceleration, proper acceleration, hyperbolic motion, accelerating reference frames, Born rigidity, have been analyzed by Einstein (1907), Hermann Minkowski (1907, 1908), Max Born (1909), Gustav Herglotz (1909), Arnold Sommerfeld (1910), von Laue (1911), Friedrich Kottler (1912, 1914), see section on history.
Doppler Shift Compensation Constant frequency vs. frequency modulated pulses Doppler_Shift_Compensation > Bat echolocation calls > Constant frequency vs. frequency modulated pulses For FM bats, the frequency of the Doppler shifted echoes still falls within their range of auditory responsiveness. Hence, they do not need a DSC mechanism to optimize their echolocation behavior.
Plane group Why there are exactly seventeen groups P6m_symmetry > Formal definition and discussion > Why there are exactly seventeen groups Examples632: 5/6 + 2/3 + 1/2 = 2 3*3: 2/3 + 1 + 2/6 = 2 4*2: 3/4 + 1 + 1/4 = 2 22×: 1/2 + 1/2 + 1 = 2Now enumeration of all wallpaper groups becomes a matter of arithmetic, of listing all feature strings with values summing to 2. Feature strings with other sums are not nonsense; they imply non-planar tilings, not discussed here. (When the orbifold Euler characteristic is negative, the tiling is hyperbolic; when positive, spherical or bad).
Abzyme Summary Abzyme Studying them has yielded important insights into reaction mechanisms, enzyme structure and function, catalysis, and the immune system itself.Enzymes function by lowering the activation energy of the transition state of a chemical reaction, thereby enabling the formation of an otherwise less-favorable molecular intermediate between the reactant(s) and the product(s). If an antibody is developed to bind to a molecule that is structurally and electronically similar to the transition state of a given chemical reaction, the developed antibody will bind to, and stabilize, the transition state, just like a natural enzyme, lowering the activation energy of the reaction, and thus catalyzing the reaction. By raising an antibody to bind to a stable transition-state analog, a new and unique type of enzyme is produced.
Strain rate Simple deformations Strain_rate > Definition > Simple deformations This description fits the laminar flow of a fluid between two solid plates that slide parallel to each other (a Couette flow) or inside a circular pipe of constant cross-section (a Poiseuille flow). In those cases, the state of the material at some time t {\displaystyle t} can be described by the displacement X ( y , t ) {\displaystyle X(y,t)} of each layer, since an arbitrary starting time, as a function of its distance y {\displaystyle y} from the fixed wall. Then the strain in each layer can be expressed as the limit of the ratio between the current relative displacement X ( y + d , t ) − X ( y , t ) {\displaystyle X(y+d,t)-X(y,t)} of a nearby layer, divided by the spacing d {\displaystyle d} between the layers: ϵ ( y , t ) = lim d → 0 X ( y + d , t ) − X ( y , t ) d = ∂ X ∂ y ( y , t ) {\displaystyle \epsilon (y,t)=\lim _{d\rightarrow 0}{\frac {X(y+d,t)-X(y,t)}{d}}={\frac {\partial X}{\partial y}}(y,t)} Therefore, the strain rate is ϵ ˙ ( y , t ) = ( ∂ ∂ t ∂ X ∂ y ) ( y , t ) = ( ∂ ∂ y ∂ X ∂ t ) ( y , t ) = ∂ V ∂ y ( y , t ) {\displaystyle {\dot {\epsilon }}(y,t)=\left({\frac {\partial }{\partial t}}{\frac {\partial X}{\partial y}}\right)(y,t)=\left({\frac {\partial }{\partial y}}{\frac {\partial X}{\partial t}}\right)(y,t)={\frac {\partial V}{\partial y}}(y,t)} where V ( y , t ) {\displaystyle V(y,t)} is the current linear speed of the material at distance y {\displaystyle y} from the wall.
Action (physics) Single relativistic particle Action_(physics) > The action principle > Single relativistic particle When relativistic effects are significant, the action of a point particle of mass m travelling a world line C parametrized by the proper time τ {\displaystyle \tau } is If instead, the particle is parametrized by the coordinate time t of the particle and the coordinate time ranges from t1 to t2, then the action becomes where the Lagrangian is
Ampicillin sodium Pharmacokinetics Ampicillin_sodium > Pharmacology > Pharmacokinetics Ampicillin is well-absorbed from the GI tract (though food reduces its absorption), and reaches peak concentrations in one to two hours. The bioavailability is around 62% for parenteral routes. Unlike other penicillins, which usually bind 60–90% to plasma proteins, ampicillin binds to only 15–20%.Ampicillin is distributed through most tissues, though it is concentrated in the liver and kidneys. It can also be found in the cerebrospinal fluid when the meninges become inflamed (such as, for example, meningitis).
Adrenal gland Addison's disease Adrenal_glands > Clinical significance > Adrenal insufficiency > Addison's disease Addison's disease refers to primary hypoadrenalism, which is a deficiency in glucocorticoid and mineralocorticoid production by the adrenal gland. In the Western world, Addison's disease is most commonly an autoimmune condition, in which the body produces antibodies against cells of the adrenal cortex. Worldwide, the disease is more frequently caused by infection, especially from tuberculosis.
Sextuple bond Aromatics Sextuple_bond > Ligand effects > Aromatics Calculating its frontier molecular orbitals sug­gests the existence of relatively stable singlet and triplet states, with a sextuple bond in the singlet state. But that state is the excited one; the triplet ground state should exhibit a formal quintuple bond. Similarly, for the dibenzene complexes Cr2(C6H6)2, Mo2(C6H6)2, and W2(C6H6)2, molecular bonding orbitals for the triplet states with symmetries D6h and D6d indicate the possibility of an intermetallic sex­tuple bond. Quantum chemistry calculations reveal, however, that the corre­sponding D2h singlet geometry is stabler than the D6h triplet state by 3–39 kcal/mol, depending on the central metal.
Genetic barrier Genetic isolation and speciation Genetic_isolation > Genetic isolation and speciation A genetic species is a collection of biologically compatible crossbreeding natural populations genetically distinct from genetically related people. In contrast to the biological species concept, the genetic species concept emphasizes genetic isolation rather than reproductive separation. The finding of genetically separate but not reproductively isolated species advances our knowledge of biodiversity, speciation, related issues, and organism evolution. Consider the development of two allopatric populations.
Serotonin-norepinephrine reuptake inhibitors History Serotonin–noradrenaline_reuptake_inhibitor > History Imipramine was found to affect numerous neurotransmitter systems and to block the reuptake of norepinephrine and serotonin from the synapse, therefore increasing the levels of these neurotransmitters. Use of MAOIs and TCAs gave major advances in treatment of depression but their use was limited by unpleasant side effects and significant safety and toxicity issues.Throughout the 1960s and 1970s, the catecholamine hypothesis of emotion and its relation to depression was of wide interest and that the decreased levels of certain neurotransmitters, such as norepinephrine, serotonin, and dopamine might play a role in the pathogenesis of depression. This led to the development of fluoxetine, the first SSRI.
Bode Plot Examples using Bode plots Gain_margin > Gain margin and phase margin > Examples using Bode plots Figure 7 shows the corresponding phase comparison: the phase of the feedback amplifier is nearly zero out to the frequency f180 where the open-loop gain has a phase of −180°. In this vicinity, the phase of the feedback amplifier plunges abruptly downward to become almost the same as the phase of the open-loop amplifier. (Recall, AFB ≈ AOL for small AOL.)
Causes of hearing loss Noise Causes_of_hearing_loss > Noise While these exchange rates may indicate a wider zone of comfort or safety, they can significantly underestimate the damage caused by loud noise. For example, at 100 dB (nightclub music level), a 3 dB exchange rate would limit exposure to 15 minutes; the 5 dB exchange rate allows an hour. Many people are unaware of the presence of environmental sound at damaging levels, or of the level at which sound becomes harmful.
Cerebral edema Osmotic therapy Cytotoxic_edema > Treatment > Specific measures > Osmotic therapy The goal of osmotic therapy is to create a higher concentration of ions within the vasculature at the blood–brain barrier. This will create an osmotic pressure gradient and will cause the flow of water out of the brain and into the vasculature for drainage elsewhere. An ideal osmotic agent produces a favorable osmotic pressure gradient, is nontoxic, and is not filtered out by the blood–brain barrier. Hypertonic saline and mannitol are the main osmotic agents in use, while loop diuretics can aid in the removal of the excess fluid pulled out of the brain.
Fracture in polymers Fatigue Fracture_in_polymers > Fracture Mechanics in Polymers > Fatigue Crack Nucleation ApproachThe crack nucleation approach considers that polymers will eventually crack under a history of stress and strains. Study under this proposal is first adapted by Auguest Wöhler in the 1860s, who aimed to study railroad axles. Two important parameters are involved in this conversation: maximum principal strain and strain energy density.
Steady State Biochemistry Steady_State > Applications > Biochemistry In biochemistry, the study of biochemical pathways is an important topic. Such pathways will often display steady-state behavior where the chemical species are unchanging, but there is a continuous dissipation of flux through the pathway. Many, but not all, biochemical pathways evolve to stable, steady states. As a result, the steady state represents an important reference state to study. This is also related to the concept of homeostasis, however, in biochemistry, a steady state can be stable or unstable such as in the case of sustained oscillations or bistable behavior.
Bacteria swarm Fish Swarm_behaviour > Biological swarming > Marine life > Fish JSTOR 1543482. PMID 12087003. S2CID 377484.
Spaces of test functions and distributions Definitions of test functions and distributions Spaces_of_test_functions_and_distributions > Definitions of test functions and distributions {\displaystyle {\mathcal {D}}(U).} To define the space of distributions we must first define the canonical LF-topology, which in turn requires that several other locally convex topological vector spaces (TVSs) be defined first. First, a (non-normable) topology on C ∞ ( U ) {\displaystyle C^{\infty }(U)} will be defined, then every C ∞ ( K ) {\displaystyle C^{\infty }(K)} will be endowed with the subspace topology induced on it by C ∞ ( U ) , {\displaystyle C^{\infty }(U),} and finally the (non-metrizable) canonical LF-topology on C c ∞ ( U ) {\displaystyle C_{c}^{\infty }(U)} will be defined. The space of distributions, being defined as the continuous dual space of C c ∞ ( U ) , {\displaystyle C_{c}^{\infty }(U),} is then endowed with the (non-metrizable) strong dual topology induced by C c ∞ ( U ) {\displaystyle C_{c}^{\infty }(U)} and the canonical LF-topology (this topology is a generalization of the usual operator norm induced topology that is placed on the continuous dual spaces of normed spaces). This finally permits consideration of more advanced notions such as convergence of distributions (both sequences and nets), various (sub)spaces of distributions, and operations on distributions, including extending differential equations to distributions.
Endosymbiosis hypothesis Nuclear membrane Symbiogenesis > Endosymbiosis of protomitochondria > Nuclear membrane Digesting engulfed cells without energy-producing mitochondria would have been challenging for the host cell. On this view, membrane-bound bubbles or vesicles leaving the protomitochondria may have formed the nuclear envelope.The process of symbiogenesis by which the early eukaryotic cell integrated the proto-mitochondrion likely included protection of the archaeal host genome from the release of reactive oxygen species. These would have been formed during oxidative phosphorylation and ATP production by the proto-mitochondrion.
E2 elimination E2 mechanism E2_elimination > E2 mechanism The E2 mechanism, where E2 stands for bimolecular elimination, involves a one-step mechanism in which carbon-hydrogen and carbon-halogen bonds break to form a double bond (C=C Pi bond). The specifics of the reaction are as follows: E2 is a single step elimination, with a single transition state. It is typically undergone by primary substituted alkyl halides, but is possible with some secondary alkyl halides and other compounds. The reaction rate is second order, because it's influenced by both the alkyl halide and the base (bimolecular).
Lazy evaluation Java Infinite_list > Laziness and eagerness > Simulating laziness in eager languages > Java What may not be obvious is that, at the end of the loop, the program has constructed a linked list of 11 objects and that all of the actual additions involved in computing the result are done in response to the call to a.eval() on the final line of code. This call recursively traverses the list to perform the necessary additions. We can build a Java class that memoizes a lazy object as follows: This allows the previous example to be rewritten to be far more efficient. Where the original ran in time exponential in the number of iterations, the memoized version runs in linear time: Note that Java's lambda expressions are just syntactic sugar. Anything you can write with a lambda expression can be rewritten as a call to construct an instance of an anonymous inner class implementing the interface, and any use of an anonymous inner class can be rewritten using a named inner class, and any named inner class can be moved to the outermost nesting level.
Powerful number Summary Powerful_number A powerful number is a positive integer m such that for every prime number p dividing m, p2 also divides m. Equivalently, a powerful number is the product of a square and a cube, that is, a number m of the form m = a2b3, where a and b are positive integers. Powerful numbers are also known as squareful, square-full, or 2-full. Paul Erdős and George Szekeres studied such numbers and Solomon W. Golomb named such numbers powerful. The following is a list of all powerful numbers between 1 and 1000: 1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 72, 81, 100, 108, 121, 125, 128, 144, 169, 196, 200, 216, 225, 243, 256, 288, 289, 324, 343, 361, 392, 400, 432, 441, 484, 500, 512, 529, 576, 625, 648, 675, 676, 729, 784, 800, 841, 864, 900, 961, 968, 972, 1000, ... (sequence A001694 in the OEIS).
Biological research Eukaryotes Biological_research > Diversity > Eukaryotes Like groupings such as algae, invertebrates, or protozoans, the protist grouping is not a formal taxonomic group but is used for convenience. Most protists are unicellular; these are called microbial eukaryotes.Plants are mainly multicellular organisms, predominantly photosynthetic eukaryotes of the kingdom Plantae, which would exclude fungi and some algae. Plant cells were derived by endosymbiosis of a cyanobacterium into an early eukaryote about one billion years ago, which gave rise to chloroplasts.
Biodemography Overview Biodemography > Overview As a consequence, it is an interdisciplinary concept, but maintains biological roots. The hierarchical organizations that are inherent to both biology (cell, organ, individual) and demography (individual cohort, population) form a chain in which the individual serves as the link between the lower mechanistic levels, and the higher functional levels. Biodemography serves to inform research on human aging through theory building using mathematical and statistical modeling, hypothesis testing using experimental methods, and coherence-seeking using genetics and evolutionary concepts.
Model-theoretic approach Compactness and the Löwenheim-Skolem theorem Homogeneous_model > Fundamental notions of first-order model theory > Compactness and the Löwenheim-Skolem theorem The compactness theorem states that a set of sentences S is satisfiable if every finite subset of S is satisfiable. The analogous statement with consistent instead of satisfiable is trivial, since every proof can have only a finite number of antecedents used in the proof. The completeness theorem allows us to transfer this to satisfiability.