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Most of the metadata for the plate collection is contained in 663 bound volumes and about 500 looseleaf logbooks. Photographs of all of the logbook pages are available on the DASCH website. The effort to digitize this information began at Harvard. Some was done in India. | Wikipedia - Digital Access to a Sky Century @ Harvard | null | null | null |
The effort later moved to the American Museum of Natural History where volunteers worked under the supervision of Dr Michael Shara, Curator of the Department of Astrophysics and Holly Klug, Department. of Volunteer Services.In August 2014, the transcription of the Harvard plate logbooks was taken over by the Smithsonia... | Wikipedia - Digital Access to a Sky Century @ Harvard | null | null | null |
Most of the oomycetes produce two distinct types of spores. The main dispersive spores are asexual, self-motile spores called zoospores, which are capable of chemotaxis (movement toward or away from a chemical signal, such as those released by potential food sources) in surface water (including precipitation on plant s... | Wikipedia - Water mould | null | null | null |
Most of the packages have limitations of some sort. Several of the programs, including Easyreg, Epidata and Instat, do not appear to handle missing data or do not handle it well. While EpiInfo has many statistical procedures, correlation is not one of them. Rather correlation is found by regression. | Wikipedia - Free statistics software | null | null | null |
This means that EpiInfo will not produce a single table showing correlations among multiple variables. According to the Zelig installation manual, use of Zelig requires that R and several of its libraries already be installed, and the installation also requires some degree of background in R. One limit of MicrOsiris is... | Wikipedia - Free statistics software | null | null | null |
The output can be saved, though, as a text file and then used. One limitation is specific to programs that were developed by individuals. Support for these programs is limited to the time that the author has available. | Wikipedia - Free statistics software | null | null | null |
While the authors may, and often do, respond fairly quickly when there are few people asking questions, if too many people ask questions or the author is otherwise busy, support would correspondingly be slower. R is both written by and used by a large number of people all over the world, and many forums and other inter... | Wikipedia - Free statistics software | null | null | null |
Most of the physical laws that govern the dynamics of a system can be described by partial differential equations. For example, the Navier–Stokes equations are a set of partial differential equations derived from the conservation laws (i.e., conservation of mass, momentum, and energy) that govern fluid mechanics. The s... | Wikipedia - Physics-informed neural networks | null | null | null |
In this setting, these governing equations must be solved while accounting for prior assumptions, linearization, and adequate time and space discretization. Recently, solving the governing partial differential equations of physical phenomena using deep learning has emerged as a new field of scientific machine learning ... | Wikipedia - Physics-informed neural networks | null | null | null |
In general, deep neural networks could approximate any high-dimensional function given that sufficient training data are supplied. However, such networks do not consider the physical characteristics underlying the problem, and the level of approximation accuracy provided by them is still heavily dependent on careful sp... | Wikipedia - Physics-informed neural networks | null | null | null |
On the other hand, physics-informed neural networks (PINNs) leverage governing physical equations in neural network training. Namely, PINNs are designed to be trained to satisfy the given training data as well as the imposed governing equations. In this fashion, a neural network can be guided with training data that do... | Wikipedia - Physics-informed neural networks | null | null | null |
Potentially, an accurate solution of partial differential equations can be found without knowing the boundary conditions. Therefore, with some knowledge about the physical characteristics of the problem and some form of training data (even sparse and incomplete), PINN may be used for finding an optimal solution with hi... | Wikipedia - Physics-informed neural networks | null | null | null |
PINNs can be thought of as a meshfree alternative to traditional approaches (e.g., CFD for fluid dynamics), and new data-driven approaches for model inversion and system identification. Notably, the trained PINN network can be used for predicting the values on simulation grids of different resolutions without the need ... | Wikipedia - Physics-informed neural networks | null | null | null |
Most of the properties of the quantum Fourier transform follow from the fact that it is a unitary transformation. This can be checked by performing matrix multiplication and ensuring that the relation F F † = F † F = I {\displaystyle FF^{\dagger }=F^{\dagger }F=I} holds, where F † {\displaystyle F^{\dagger }} is the He... | Wikipedia - Quantum Fourier transform | null | null | null |
From the unitary property it follows that the inverse of the quantum Fourier transform is the Hermitian adjoint of the Fourier matrix, thus F − 1 = F † {\displaystyle F^{-1}=F^{\dagger }} . Since there is an efficient quantum circuit implementing the quantum Fourier transform, the circuit can be run in reverse to perfo... | Wikipedia - Quantum Fourier transform | null | null | null |
Most of the requirements for a classical digital signature scheme also apply to the quantum digital signature scheme. In detail The scheme has to provide security against tampering by The sender after the message was signed (see bit commitment) The receiver A third party Creating a signed message has to be easy Every r... | Wikipedia - Quantum digital signature | null | null | null |
Most of the same principles of the scalar case hold for more general theories with additional fields. Each field requires the introduction of its own fictitious current, with antiparticle fields requiring their own separate currents. Acting on the partition function with a derivative of a current brings down its associ... | Wikipedia - Partition function (quantum field theory) | null | null | null |
For partition functions with Grassmann valued fermion fields, the sources are also Grassmann valued. For example, a theory with a single Dirac fermion ψ ( x ) {\displaystyle \psi (x)} requires the introduction of two Grassmann currents η {\displaystyle \eta } and η ¯ {\displaystyle {\bar {\eta }}} so that the partition... | Wikipedia - Partition function (quantum field theory) | null | null | null |
Most of the series acceleration techniques developed for alternating series can be profitably applied to the evaluation of the eta function. One particularly simple, yet reasonable method is to apply Euler's transformation of alternating series, to obtain Note that the second, inside summation is a forward difference. | Wikipedia - Dirichlet eta function | null | null | null |
Most of the short term forecast approaches use numerical weather prediction models (NWP) that provide an important estimation of the development of weather variables. The models used included the Global Forecast System (GFS) or data provided by the European Center for Medium Range Weather Forecasting (ECMWF). These two... | Wikipedia - Solar power forecasting | null | null | null |
Among others, HIRLAM, WRF or MM5. Since these NWP models are highly complex and difficult to run on local computers, these variables are usually considered as exogeneous inputs to solar irradiance models and ingested form the respective data provider. | Wikipedia - Solar power forecasting | null | null | null |
Best forecasting results are achieved with data assimilation. Some researchers argue for the use of post-processing techniques, once the models’ output is obtained, in order to obtain a probabilistic point of view of the accuracy of the output. This is usually done with ensemble techniques that mix different outputs of... | Wikipedia - Solar power forecasting | null | null | null |
Most of the small finds from the de Vaux excavations were taken back to Jerusalem to be used in later excavation reports for Qumran, but the death of Roland de Vaux brought a halt to the reports and the small finds were left to gather dust on shelves in museum backrooms. In the late 1980s, archaeologist Robert Donceel ... | Wikipedia - Qumran-Essene hypothesis | null | null | null |
In 1992 Pauline Donceel-Voute put forward the Roman villa model in an attempt to explain these artifacts. In 2002 archaeologists Minna and Kenneth Lönnqvist published their archaeological and spatial studies at Qumran bringing another view to the settlement interpretations including the astronomical orientations of som... | Wikipedia - Qumran-Essene hypothesis | null | null | null |
Most of the subseafloor is anoxic because oxygen is removed by aerobic microorganisms within the first few centimeters of the sediment. Below the oxygen-replete seafloor, methanogens produce methane that is either used by other organisms or becomes trapped in gas hydrates. These other organisms that utilize methane for... | Wikipedia - Methane gas | null | null | null |
Most of the work on classification problems has focused on three dimensions, particularly on the classification of crystal nets, i.e., of periodic graphs that could serve as descriptions or designs for placement of atoms or molecular objects, with bonds indicated by edges, in a crystal. One of the more popular classifi... | Wikipedia - Periodic Graph (Geometry) | null | null | null |
Even though the graph isomorphism problem is polynomial time reducible to crystal net topological equivalence (making topological equivalence a candidate for being "computationally intractable" in the sense of not being polynomial time computable), a crystal net is generally regarded as novel if and only if no topologi... | Wikipedia - Periodic Graph (Geometry) | null | null | null |
The cycles of a crystal net are related to another invariant, that of the coordination sequence (or shell map in topology), which is defined as follows. First, a distance sequence from a vertex v in a graph is the sequence n1, n2, n3, ..., where ni is the number of vertices of distance i from v. The coordination sequen... | Wikipedia - Periodic Graph (Geometry) | null | null | null |
See for a mathematical aspect of topological density which is closely related to the large deviation property of simple random walks. Another invariant arises from the relationship between tessellations and Euclidean graphs. If we regard a tessellation as an assembly of (possibly polyhedral) solid regions, (possibly po... | Wikipedia - Periodic Graph (Geometry) | null | null | null |
(In addition, the adjacency graph of the tiles induces another Euclidean graph.) If there are finitely many prototiles in the tessellation, and the tessellation is periodic, then the resulting Euclidean graph will be periodic. Going in the reverse direction, the prototiles of a tessellation whose 1-skeleton is (topolog... | Wikipedia - Periodic Graph (Geometry) | null | null | null |
Most of the work on organothorium compounds has focused on the cyclopentadienyl complexes and cyclooctatetraenyls. Like many of the early and middle actinides (up to americium, and also expected for curium), thorium forms a cyclooctatetraenide complex: the yellow Th(C8H8)2, thorocene. It is isotypic with the better-kno... | Wikipedia - Thorium | null | null | null |
It is unstable in air and decomposes in water or at 190 °C. Half sandwich compounds are also known, such as (η8-C8H8)ThCl2(THF)2, which has a piano-stool structure and is made by reacting thorocene with thorium tetrachloride in tetrahydrofuran.The simplest of the cyclopentadienyls are Th(C5H5)3 and Th(C5H5)4: many deri... | Wikipedia - Thorium | null | null | null |
The chloride derivative is prepared by heating thorium tetrachloride with limiting KC5H5 used (other univalent metal cyclopentadienyls can also be used). The alkyl and aryl derivatives are prepared from the chloride derivative and have been used to study the nature of the Th–C sigma bond.Other organothorium compounds ... | Wikipedia - Thorium | null | null | null |
Tetrabenzylthorium, Th(CH2C6H5)4, and tetraallylthorium, Th(CH2CH=CH2)4, are known, but their structures have not been determined. They decompose slowly at room temperature. Thorium forms the monocapped trigonal prismatic anion 3−, heptamethylthorate(IV), which forms the salt 3 (tmeda = (CH3)2NCH2CH2N(CH3)2). Although ... | Wikipedia - Thorium | null | null | null |
Most of the work on substitution models has focused on DNA/RNA and protein sequence evolution. Models of DNA sequence evolution, where the alphabet corresponds to the four nucleotides (A, C, G, and T), are probably the easiest models to understand. DNA models can also be used to examine RNA virus evolution; this reflec... | Wikipedia - Substitution model | null | null | null |
In fact, substitution models can be developed for any biological characters that can be encoded using a specific alphabet (e.g., amino acid sequences combined with information about the conformation of those amino acids in three-dimensional protein structures). The majority of substitution models used for evolutionary ... | Wikipedia - Substitution model | null | null | null |
This means that substitution models can be viewed as implying a specific multinomial distribution for site pattern frequencies. If we consider a multiple sequence alignment of four DNA sequences there are 256 possible site patterns so there are 255 degrees of freedom for the site pattern frequencies. | Wikipedia - Substitution model | null | null | null |
However, it is possible to specify the expected site pattern frequencies using five degrees of freedom if using the Jukes-Cantor model of DNA evolution, which is a simple substitution model that allows one to calculate the expected site pattern frequencies only the tree topology and the branch lengths (given four taxa ... | Wikipedia - Substitution model | null | null | null |
Most of them may be stated for general polygons as well, but expectation of more efficient algorithms warrants a separate consideration Orthogonal range searching Orthogonal convex hull construction Boolean operations on polygons for orthogonal polygons (e.g., intersection and union) Motion planning/path planning/routi... | Wikipedia - Orthogonal polygons | null | null | null |
Most of these calculi can be formalized as abstract relation algebras, such that reasoning can be carried out at a symbolic level. For computing solutions of a constraint network, the path-consistency algorithm is an important tool. | Wikipedia - Spatial reasoning | null | null | null |
Most often in Lagrangian mechanics, the Lagrangian L(q, dq/dt, t) is in configuration space, where q = (q1, q2,..., qn) is an n-tuple of the generalized coordinates. The Euler–Lagrange equations of motion are (One overdot indicates one time derivative). Introducing the definition of canonical momentum for each generali... | Wikipedia - Position and momentum spaces | null | null | null |
A Legendre transformation is performed to change the variables in the total differential of the generalized coordinate space Lagrangian; where the definition of generalized momentum and Euler–Lagrange equations have replaced the partial derivatives of L. The product rule for differentials allows the exchange of differe... | Wikipedia - Position and momentum spaces | null | null | null |
Most often, a panel antenna will be constructed as multiple "bays" - each consisting of an individual dipole placed before a shared reflector - with all of these bays connected in parallel to increase received signal strength. These forms of antennae were introduced in the late 1980s as a "C.F.R." by C.F.R. America (Ci... | Wikipedia - Panel antenna | null | null | null |
Most often, hexapods are controlled by gaits, which allow the robot to move forward, turn, and perhaps side-step. Some of the most common gaits are as follows: Alternating tripod: 3 legs on the ground at a time. Quadruped. | Wikipedia - Hexapod (robotics) | null | null | null |
Crawl: move just one leg at a time.Gaits for hexapods are often stable, even in slightly rocky and uneven terrain. Motion may also be nongaited, which means the sequence of leg motions is not fixed, but rather chosen by the computer in response to the sensed environment. This may be most helpful in very rocky terrain, ... | Wikipedia - Hexapod (robotics) | null | null | null |
Most often, the weights used in implementations of Huffman coding represent numeric probabilities, but the algorithm given above does not require this; it requires only that the weights form a totally ordered commutative monoid, meaning a way to order weights and to add them. The Huffman template algorithm enables one ... | Wikipedia - Huffman tree | null | null | null |
Most operators in the table below are generalisations of binary logic and probability operators. For example addition is simply a generalisation of addition of probabilities. Some operators are only meaningful for combining binomial opinions, and some also apply to multinomial opinion. | Wikipedia - Subjective logic | null | null | null |
Most operators are binary, but complement is unary, and abduction is ternary. See the referenced publications for mathematical details of each operator. Transitive source combination can be denoted in a compact or expanded form. | Wikipedia - Subjective logic | null | null | null |
For example, the transitive trust path from analyst/source A {\displaystyle A\,\!} via source B {\displaystyle B\,\!} to the variable X {\displaystyle X\,\!} | Wikipedia - Subjective logic | null | null | null |
can be denoted as {\displaystyle \,\!} in compact form, or as : {\displaystyle :\,\!} in expanded form. | Wikipedia - Subjective logic | null | null | null |
Here, {\displaystyle \,\!} expresses that A {\displaystyle A} has some trust/distrust in source B {\displaystyle B} , whereas {\displaystyle \,\!} expresses that B {\displaystyle B} has an opinion about the state of variable X {\displaystyle X} which is given as an advice to A {\displaystyle A} . The expanded form is... | Wikipedia - Subjective logic | null | null | null |
Most optical communications use amplitude modulation where the quantum noise is predominantly the shot noise. A laser's quantum noise, when not considering shot noise, is the uncertainty of its electric field's amplitude and phase. That uncertainty becomes observable when a quantum amplifier preserves phase. The phase ... | Wikipedia - Quantum noise | null | null | null |
Most organic solvents are denaturing, including: Ethanol | Wikipedia - DNA denaturation | null | null | null |
Most organoplatinum(0) compounds contain alkene and alkyne ligands. Carbonyl complexes are rare, and the analogue of Ni(CO)4 is elusive. The alkene and alkyne ligands serve as two-electron donors, for example in the complexes (PPh3)2Pt(C2H4) and (PPh3)2Pt(C2Ph2). The ethylene ligand in (PPh3)2Pt(C2H4) is labile and exc... | Wikipedia - Organoplatinum chemistry | null | null | null |
A general synthetic route to (PPh3)2Pt(un) (un = alkene, alkyne) is reduction of potassium tetrachloroplatinate with ethanolic potassium hydroxide or hydrazine in presence of a phosphine ligand such as triphenylphosphine and the alkene or alkyne. Such reactions proceed via the intermediacy of cis-dichlorobis(triphenylp... | Wikipedia - Organoplatinum chemistry | null | null | null |
Nitrogen-based ligands do not often support the formation of platinum complexes of alkenes and alkynes. Zerovalent organoplatinum complexes lacking phosphine ligands are often prepared via PtCl2(COD). Li2C8H8 + PtCl2(COD) + 3 C7H10 → + 2 LiCl + C8H8 + C8H12 Pt(C7H10)3 + 2 COD → Pt(COD)2 + 3 C7H10where C7H10 is norborn... | Wikipedia - Organoplatinum chemistry | null | null | null |
Most packages are able to import data from Excel or CSV (text with commas separating values). One consideration is whether there are missing data. Some packages, like PSPP and MicrOsiris, can automatically deal with the missing data. So for example, say one set of data look like this: In this data set, Sam is missing h... | Wikipedia - Free statistics software | null | null | null |
When some packages, like PSPP or MicrOsiris, read in or import the original data set, the packages will recognize that those values are missing, and do their calculations accordingly. MicrOsiris automatically assigns 1.5 or 1.6 billion to blanks as missing, and these values are excluded from analysis.Other packages nee... | Wikipedia - Free statistics software | null | null | null |
Most pages in SCOP contain a search box. Entering "trypsin +human" retrieves several proteins, including the protein trypsinogen from humans. Selecting that entry displays a page that includes the "lineage", which is at the top of most SCOP pages. Human trypsonogen lineageRoot: scop Class: All beta proteins Fold: Tryp... | Wikipedia - Structural Classification of Proteins | null | null | null |
Most paleontologists accept that Tyrannosaurus was both an active predator and a scavenger like most large carnivores. By far the largest carnivore in its environment, T. rex was most likely an apex predator, preying upon hadrosaurs, armored herbivores like ceratopsians and ankylosaurs, and possibly sauropods. A study ... | Wikipedia - Tyrannosaurus rex | null | null | null |
Even higher estimates were made by Mason B. Meers in 2003. This allowed it to crush bones during repetitive biting and fully consume the carcasses of large dinosaurs. | Wikipedia - Tyrannosaurus rex | null | null | null |
Stephan Lautenschlager and colleagues calculated that Tyrannosaurus was capable of a maximum jaw gape of around 80 degrees, a necessary adaptation for a wide range of jaw angles to power the creature's strong bite.A debate exists, however, about whether Tyrannosaurus was primarily a predator or a pure scavenger. The de... | Wikipedia - Tyrannosaurus rex | null | null | null |
Ever since the first discovery of Tyrannosaurus most scientists have speculated that it was a predator; like modern large predators it would readily scavenge or steal another predator's kill if it had the opportunity.Paleontologist Jack Horner has been a major proponent of the view that Tyrannosaurus was not a predator... | Wikipedia - Tyrannosaurus rex | null | null | null |
Other paleontologists such as Thomas Holtz Jr. argued that there are plenty of modern-day predators that do not use their forelimbs to hunt such as wolves, hyenas, and secretary birds as well as other extinct animals thought to be predators that would not have used their forelimbs such as phorusrhacids. Tyrannosaurs ha... | Wikipedia - Tyrannosaurus rex | null | null | null |
These suggest a highly developed sense of smell which could sniff out carcasses over great distances, as modern vultures do. Research on the olfactory bulbs of dinosaurs has shown that Tyrannosaurus had the most highly developed sense of smell of 21 sampled dinosaurs. Tyrannosaur teeth could crush bone, and therefore c... | Wikipedia - Tyrannosaurus rex | null | null | null |
Karen Chin and colleagues have found bone fragments in coprolites (fossilized feces) that they attribute to tyrannosaurs, but point out that a tyrannosaur's teeth were not well adapted to systematically chewing bone like hyenas do to extract marrow. Since at least some of Tyrannosaurus's potential prey could move quick... | Wikipedia - Tyrannosaurus rex | null | null | null |
The eye sockets of tyrannosaurs are positioned so that the eyes would point forward, giving them binocular vision slightly better than that of modern hawks. It is not obvious why natural selection would have favored this long-term trend if tyrannosaurs had been pure scavengers, which would not have needed the advanced ... | Wikipedia - Tyrannosaurus rex | null | null | null |
A 2021 study focused on the vision and hearing of the small theropod Shuvuuia, to which Tyrannosaurus was compared suggests that Tyrannosaurus was diurnal and would have hunted predominantly during daylight hours, a feature it shared with Dromaeosaurus, a third dinosaur compared to Shuvuuia in the study. A skeleton of ... | Wikipedia - Tyrannosaurus rex | null | null | null |
Despite the consensus that the tail bites were caused by Tyrannosaurus, there has been some evidence to show that they might have been created by other factors. For example, a 2014 study suggested that the tail injuries might have been due to Edmontosaurus individuals stepping on each other, while another study in 2020... | Wikipedia - Tyrannosaurus rex | null | null | null |
It is not known what the exact nature of the interaction was, though: either animal could have been the aggressor. Since the Triceratops wounds healed, it is most likely that the Triceratops survived the encounter and managed to overcome the Tyrannosaurus. In a battle against a bull Triceratops, the Triceratops would l... | Wikipedia - Tyrannosaurus rex | null | null | null |
Studies of Sue found a broken and healed fibula and tail vertebrae, scarred facial bones and a tooth from another Tyrannosaurus embedded in a neck vertebra, providing evidence for aggressive behavior. Studies on hadrosaur vertebrae from the Hell Creek Formation that were punctured by the teeth of what appears to be a l... | Wikipedia - Tyrannosaurus rex | null | null | null |
These chambers might have trapped pieces of carcass with bacteria, giving Tyrannosaurus a deadly, infectious bite much like the Komodo dragon was thought to have. Jack Horner and Don Lessem, in a 1993 popular book, questioned Abler's hypothesis, arguing that Tyrannosaurus's tooth serrations as more like cubes in shape ... | Wikipedia - Tyrannosaurus rex | null | null | null |
Most particle physics experiments use some form of calorimetry. Often it is the most practical way to detect and measure neutral particles from an interaction. In addition, calorimeters are necessary for calculating "missing energy" which can be attributed to particles that rarely interact with matter and escape the de... | Wikipedia - Electromagnetic calorimeter | null | null | null |
Most past proposals for the development of space mirrors are specifically to slow the progression of climate change on Earth. Deflecting a small amount of the sun’s energy from the Earth’s atmosphere would reduce the amount of energy entering the ecosystem of the Earth. | Wikipedia - Space mirror (geoengineering) | null | null | null |
Most people with 1p36 deletion syndrome have some structural abnormality of the brain, and approximately half have epilepsy or other seizures. Almost all children exhibit some degree of hypotonia. Common structural brain abnormalities include agenesis of the corpus callosum, cerebral cortical atrophy, gait abnormalitie... | Wikipedia - 1p36 deletion syndrome | null | null | null |
Most performance analysis tools use dynamic program analysis techniques. | Wikipedia - Dynamic data-flow analysis | null | null | null |
Most phases of matter can be understood through the lens of spontaneous symmetry breaking. For example, crystals are periodic arrays of atoms that are not invariant under all translations (only under a small subset of translations by a lattice vector). Magnets have north and south poles that are oriented in a specific ... | Wikipedia - Spontaneous symmetry breaking | null | null | null |
In addition to these examples, there are a whole host of other symmetry-breaking phases of matter — including nematic phases of liquid crystals, charge- and spin-density waves, superfluids, and many others. There are several known examples of matter that cannot be described by spontaneous symmetry breaking, including: ... | Wikipedia - Spontaneous symmetry breaking | null | null | null |
Most phorusrhacids were very fast runners. All members possessed a large, sharp beak, a powerful neck and sharp talons. However, even with these attributes, the phorusrhacids are often assumed to have preyed on relatively small animals (about the size of a rabbit) that could be dispatched with a minimum of struggle. Th... | Wikipedia - Terror Bird | null | null | null |
This is disputable as many big-game hunting predators such as Smilodon, great white sharks and Allosaurus have weaker bite forces and often laterally weak skulls as adaptations towards, not away from, killing large prey, relying instead on the presence of a cutting edge, a wide gape made possible by the reduction of ja... | Wikipedia - Terror Bird | null | null | null |
Generally speaking, it is thought that a terror bird would use its feet to injure prey by kicking it, and to hold the prey down and dispatch by pecking at it with its large beak. Larger prey may also have been attacked by pecking and kicking, or by using the beak as a blade to strike at or slash vital organs. It has be... | Wikipedia - Terror Bird | null | null | null |
Most physical phenomena are modeled by partial differential equations. To solve them, one usually decomposes the space in which the solutions are searched into small, mutually interacting cells. For linear systems this interaction involves linear functions. For nonlinear systems, this interaction is often approximated ... | Wikipedia - Linear Algebra | null | null | null |
Linear models are frequently used for complex nonlinear real-world systems because it makes parametrization more manageable. In both cases, very large matrices are generally involved. Weather forecasting (or more specifically, parametrization for atmospheric modeling) is a typical example of a real-world application, w... | Wikipedia - Linear Algebra | null | null | null |
Most plants have the ability to close their stomata at the start of water stress, at least partially, to restrict rates of transpiration. They use signals or hormones sent up from the roots and through the transpiration stream. Since roots are the parts responsible for water searching and uptake, they can detect the co... | Wikipedia - Xerophyte | null | null | null |
During the day and especially during mid-day when the sun is at its peak, most stomata of xerophytes are close. Not only do more stomata open at night in the presence of mist or dew, the size of stomatal opening or aperture is larger at night compared to during the day. This phenomenon was observed in xeromorphic speci... | Wikipedia - Xerophyte | null | null | null |
Most popular methods for predicting RNA and DNA's secondary structure involve dynamic programming. One of the early attempts at predicting RNA secondary structure was made by Ruth Nussinov and co-workers who developed a dynamic programming-based algorithm that maximized the length and number of a series of "blocks" (po... | Wikipedia - Nucleic acid structure prediction | null | null | null |
Nussinov et al. later published an adapted approach with improved performance that increased the RNA size limit to ~1,000 bases by folding increasingly sized subsections while storing the results of prior folds, now known as the Nussinov algorithm. In 1981, Michael Zuker and Patrick Stiegler proposed a refined approach... | Wikipedia - Nucleic acid structure prediction | null | null | null |
For longer fragments, recursion on the optimal free energy changes determined for shorter sequences speeds the determination of the lowest folding free energy. Once the lowest free energy of the complete sequence is calculated, the exact structure of RNA molecule is determined.Dynamic programming algorithms are commonl... | Wikipedia - Nucleic acid structure prediction | null | null | null |
These methods rely on pre-calculated parameters which estimate the free energy associated with certain types of base-pairing interactions, including Watson-Crick and Hoogsteen base pairs. Depending on the complexity of the method, single base pairs may be considered, and short two- or three-base segments, to incorporat... | Wikipedia - Nucleic acid structure prediction | null | null | null |
Most printers overlap the black dots slightly, so there is not an exact one-to-one relationship to dot frequency (in dots per unit area) and lightness. Tone scale linearization may be applied to the source image to get the printed image to look correct. | Wikipedia - Error diffusion | null | null | null |
Most problems can be formulated in terms of a search space and target in several different manners. For example, for the traveling salesman problem a solution can be a route visiting all cities and the goal is to find the shortest route. But a solution can also be a path, and being a cycle is part of the target. A loca... | Wikipedia - Local search algorithm | null | null | null |
This requires a neighborhood relation to be defined on the search space. As an example, the neighborhood of vertex cover is another vertex cover only differing by one node. For boolean satisfiability, the neighbors of a boolean assignment are those that have a single variable in an opposite state. | Wikipedia - Local search algorithm | null | null | null |
The same problem may have multiple distinct neighborhoods defined on it; local optimization with neighborhoods that involve changing up to k components of the solution is often referred to as k-opt. Typically, every candidate solution has more than one neighbor solution; the choice of which one to select is taken using... | Wikipedia - Local search algorithm | null | null | null |
When no improving neighbors are present, local search is stuck at a locally optimal point. This local-optima problem can be cured by using restarts (repeated local search with different initial conditions), randomization, or more complex schemes based on iterations, like iterated local search, on memory, like reactive ... | Wikipedia - Local search algorithm | null | null | null |
The search can terminate after a given time bound, or when the best solution found thus far has not improved in a given number of steps. Local search is an anytime algorithm: it can return a valid solution even if it's interrupted at any time after finding the first valid solution. Local search is typically an approxim... | Wikipedia - Local search algorithm | null | null | null |
Most processes in a streamer discharge are two-body processes, where an electron collides with a neutral molecule. An important example is impact ionization, where an electron ionizes a neutral molecule. Therefore, the mean free path is inversely proportional to the gas number density. If the electric field is changed ... | Wikipedia - Streamer discharge | null | null | null |
In other words, if the ratio between electric field E {\displaystyle E} and number density N {\displaystyle N} is constant, we expect similar dynamics. Typical lengths scale as 1 / N {\displaystyle 1/N} , as they are related to the mean free path. This also motivates the Townsend unit, which is a physical unit of the E... | Wikipedia - Streamer discharge | null | null | null |
Most programming languages and language implementations do not support a Scheme-like numerical tower, though some languages provide limited or inconsistent support if implementation simplicity permits. Python, for example, provides a similar structure via PEP3141, citing Scheme's example, though in practice rational nu... | Wikipedia - Numerical tower | null | null | null |
While 1 / 3 in Python is treated as a call to divide 1 by 3, yielding a float, the inclusion of rationals inside a complex number, though clearly permissible, implicitly coerces them from rationals into floats or ints, even in cases where this is incorrect. Smalltalk is another programming language that follows this mo... | Wikipedia - Numerical tower | null | null | null |
Most programs available for protein analysis are not written for proteins that have undergone post-translational modifications. Some programs will accept post-translational modifications to aid in protein identification but then ignore the modification during further protein analysis. It is important to account for the... | Wikipedia - Call-map proteomics | null | null | null |
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