id int32 0 100k | text stringlengths 20 3.54k | source stringlengths 1 104 | similarity float32 0.8 0.91 |
|---|---|---|---|
3,600 | In such a situation, the distributed charges taken as a group always carries a whole number of elementary charge units. Yet one can point to zones within the assemblage where less than a full charge resides, such as the area around an atom's nucleus. This is possible in part because particles are not like mathematical ... | Atomic charge | 0.834343 |
3,601 | If h denotes the altitude in a right triangle and p and q the segments on the hypotenuse then the theorem can be stated as: h = p q {\displaystyle h={\sqrt {pq}}} or in term of areas: h 2 = p q . {\displaystyle h^{2}=pq.} The latter version yields a method to square a rectangle with ruler and compass, that is to constr... | Geometric mean theorem | 0.834342 |
3,602 | Examples of the most studied classes of algebraic varieties are: plane algebraic curves, which include lines, circles, parabolas, ellipses, hyperbolas, cubic curves like elliptic curves and quartic curves like lemniscates, and Cassini ovals. A point of the plane belongs to an algebraic curve if its coordinates satisfy ... | Mathematical equation | 0.834341 |
3,603 | Some of Bhaskara's contributions to mathematics include the following: A proof of the Pythagorean theorem by calculating the same area in two different ways and then cancelling out terms to get a2 + b2 = c2. In Lilavati, solutions of quadratic, cubic and quartic indeterminate equations are explained. Solutions of indet... | Bhāskara II | 0.834339 |
3,604 | In engineering, electromechanics combines processes and procedures drawn from electrical engineering and mechanical engineering. Electromechanics focuses on the interaction of electrical and mechanical systems as a whole and how the two systems interact with each other. This process is especially prominent in systems s... | Electromechanical engineering | 0.834338 |
3,605 | An algorithm is said to run in sub-linear time (often spelled sublinear time) if T ( n ) = o ( n ) {\displaystyle T(n)=o(n)} . In particular this includes algorithms with the time complexities defined above. The specific term sublinear time algorithm commonly refers to randomized algorithms that sample a small fraction... | Polynomial time | 0.834331 |
3,606 | (10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000; short scale: ten duotrigintillion; long scale: ten thousand sexdecillion, or ten sexdecillard) Mathematics: There are 157 152 858 401 024 063 281 013 959 519 483 771 508 510 790 313 968 742 344 694 684 829 502 629 88... | Orders of magnitude (numbers) | 0.834331 |
3,607 | In abstract algebra, the integers, the rational numbers, the real numbers, and the complex numbers can be abstracted to more general algebraic structures, such as a commutative ring, which is a mathematical structure where addition, subtraction, and multiplication behave as they do in the more familiar number systems, ... | Division by zero | 0.83433 |
3,608 | The converse of the triangle inequality theorem is also true: if three real numbers are such that each is less than the sum of the others, then there exists a triangle with these numbers as its side lengths and with positive area; and if one number equals the sum of the other two, there exists a degenerate triangle (th... | Triangular inequality | 0.834327 |
3,609 | One of the easiest ways of doing this is to find a counterexample which exhibits one property but not the other. In Counterexamples in Topology, Steen and Seebach, together with five students in an undergraduate research project at St. Olaf College, Minnesota in the summer of 1967, canvassed the field of topology for s... | Counterexamples in Topology | 0.834326 |
3,610 | The algebraic equations are the basis of a number of areas of modern mathematics: Algebraic number theory is the study of (univariate) algebraic equations over the rationals (that is, with rational coefficients). Galois theory was introduced by Évariste Galois to specify criteria for deciding if an algebraic equation m... | Polynomial equations | 0.834325 |
3,611 | In a non-deterministic model of computation, such as non-deterministic Turing machines, some choices may be done at some steps of the computation. In complexity theory, one considers all possible choices simultaneously, and the non-deterministic time complexity is the time needed, when the best choices are always done.... | Asymptotic complexity | 0.834324 |
3,612 | Parallel axis theorem – also known as Huygens–Steiner theorem, or just as Steiner's theorem, named after Christiaan Huygens and Jakob Steiner, can be used to determine the moment of inertia or the second moment of area of a rigid body about any axis, given the body's moment of inertia about a parallel axis through the ... | Glossary of aerospace engineering | 0.834323 |
3,613 | Finally, the Thomas–Fermi model assumes that the electrons are in equilibrium, meaning that the total chemical potential is the same at all points. (In electrochemistry terminology, "the electrochemical potential of electrons is the same at all points". In semiconductor physics terminology, "the Fermi level is flat".) ... | Thomas–Fermi screening length | 0.834313 |
3,614 | Under the effect of surface tension, the liquid meniscus assumes a semi-spherical shape at the tip of the emitter. Application of the positive voltage V {\displaystyle V\,} will induce the electric field: E = 2 V r ln ( 4 d / r ) {\displaystyle E={2V \over r\ln(4d/r)}} where r {\displaystyle r\,} is the liquid radius... | Electrospray | 0.834311 |
3,615 | See Algebraic structure for details. In this context, given an algebraic structure S, a substructure of S is a subset that is closed under all operations of S, including the auxiliary operations that are needed for avoiding existential quantifiers. A substructure is an algebraic structure of the same type as S. It foll... | Reflexive transitive closure | 0.834309 |
3,616 | The latter question is answered by Sperner's theorem, which gave rise to much of extremal set theory. The types of questions addressed in this case are about the largest possible graph which satisfies certain properties. For example, the largest triangle-free graph on 2n vertices is a complete bipartite graph Kn,n. | Combinatorial theory | 0.834301 |
3,617 | Elementary discrete mathematics courses sometimes leave students with the impression that the subject matter of set theory is no more than these properties. For more about elementary set theory, see set, set theory, algebra of sets, and naive set theory. For an introduction to set theory at a higher level, see also axi... | Simple theorems in the algebra of sets | 0.834295 |
3,618 | A group is said to be quasi-nilpotent if every element acts as an inner automorphism on every chief factor. The generalized Fitting subgroup is the unique largest subnormal quasi-nilpotent subgroup, and is equal to the set of all elements which act as inner automorphisms on every chief factor of the whole group (Hupper... | Generalized Fitting subgroup | 0.834292 |
3,619 | In computer science and object-oriented programming, a passive data structure (PDS), also termed a plain old data structure or plain old data (POD), is a record, in contrast with objects. It is a data structure that is represented only as passive collections of field values (instance variables), without using object-or... | Plain old data structure | 0.834292 |
3,620 | In 2014 an SNP array was released for B. napus by Dalton-Morgan et al., and another by Clarke et al., in 2016, both of which have since become widely used in molecular breeding. In a demonstration of the importance of epigenetics, Hauben et al., 2009 found that isogenic lines did not have identical energy use efficienc... | Brassica napus | 0.83429 |
3,621 | There are two distinct senses of the word "undecidable" in contemporary use. The first of these is the sense used in relation to Gödel's theorems, that of a statement being neither provable nor refutable in a specified deductive system. The second sense is used in relation to computability theory and applies not to sta... | Algorithmically unsolvable problem | 0.83429 |
3,622 | The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI unit for electric dipole moment is the coulomb-meter (C⋅m). The debye (D) is another unit of measurement used in atomic physics and chemistry... | Electric dipole | 0.834289 |
3,623 | In computer science, a search data structure is any data structure that allows the efficient retrieval of specific items from a set of items, such as a specific record from a database. The simplest, most general, and least efficient search structure is merely an unordered sequential list of all the items. Locating the ... | Search data structure | 0.834289 |
3,624 | Biochemistry deals with the chemistry of the growth and activity of living organisms. It is a chemistry where most reactions are controlled by complex proteins called enzymes and are moderated and limited by hormones. The chemistry is always highly complex and is still not fully understood. Decomposition of organic mat... | Chemical change | 0.834281 |
3,625 | It is shown in below table. Effectively, while it is not possible to construct a 3×3 table with entries +1 and −1 such that the product of the elements in each row equals +1 and the product of elements in each column equals −1, it is possible to do so with the richer algebraic structure based on spin matrices. The play... | Quantum pseudo-telepathy | 0.83428 |
3,626 | When writing sequences for systematic biology it may be necessary to have IUPAC codes that mean "any of the two" or "any of the three". The IUPAC code R (any purine) is complementary to Y (any pyrimidine) and M (amino) to K (keto). W (weak) and S (strong) are usually not swapped but have been swapped in the past by som... | Reverse complement | 0.834279 |
3,627 | However, they are usually disguised so as to make the solutions difficult. The problems given in the IMO are largely designed to require creativity and the ability to solve problems quickly. Thus, the prominently featured problems are algebraic inequalities, complex numbers, and construction-oriented geometrical proble... | International Mathematical Olympiad | 0.834275 |
3,628 | Microfluidic devices can combine several analytical steps into one device. This technology has been coined by some as the "lab on a chip" technology. Most current molecular biology methods use some form of MEMS, including microarray technology and next generation sequencing instruments. | Microfluidic whole genome haplotyping | 0.83427 |
3,629 | In this case, they are a superset of the rational numbers, but are again order-isomorphic. It is also possible to apply the theorem to other linear orders whose elements are not defined as numbers. For instance, the binary strings that end in a 1, in their lexicographic order, form another isomorphic ordering. | Cantor's isomorphism theorem | 0.83427 |
3,630 | "The GSRS is used to generate permanent, unique identifiers for substances in regulated products, such as ingredients in drug and biological products. The GSRS uses molecular structure, protein and nucleic sequences and descriptive information to generate the UNII. The preferred means for defining a chemical substance ... | Unique Ingredient Identifier | 0.834266 |
3,631 | Lookup speed How quickly a word can be found in the inverted index. The speed of finding an entry in a data structure, compared with how quickly it can be updated or removed, is a central focus of computer science. Maintenance How the index is maintained over time. Fault tolerance How important it is for the service to... | Search engine indexing | 0.834265 |
3,632 | In geometry, various formalisms exist to express a rotation in three dimensions as a mathematical transformation. In physics, this concept is applied to classical mechanics where rotational (or angular) kinematics is the science of quantitative description of a purely rotational motion. The orientation of an object at ... | Rotation representation (mathematics) | 0.83426 |
3,633 | : 282 In effect, Khayyam's work is an effort to unify algebra and geometry. : 241 This particular geometric solution of cubic equations has been further investigated by M. Hachtroudi and extended to solving fourth-degree equations. | Omar Khayyam | 0.834258 |
3,634 | Similarly, codon pair optimization, a combination of dinucelotide and codon optimization, has also been successfully used to increase expression.The most studied application of k-mers for decreasing translational efficiency is codon-pair manipulation for attenuating viruses in order to create vaccines. Researchers were... | K-mer | 0.83425 |
3,635 | Both Floyd's and Brent's algorithms use only a constant number of memory cells, and take a number of function evaluations that is proportional to the distance from the start of the sequence to the first repetition. Several other algorithms trade off larger amounts of memory for fewer function evaluations. The applicati... | Cycle detection | 0.834249 |
3,636 | The class field tower problem asks whether this tower is always finite; Hasse (1926) attributed this question to Furtwangler, though Furtwangler said he had heard it from Schreier. Another consequence of the Golod–Shafarevich theorem is that such towers may be infinite (in other words, do not always terminate in a fiel... | Golod–Shafarevich theorem | 0.834249 |
3,637 | The extended Euclidean algorithm is also the main tool for computing multiplicative inverses in simple algebraic field extensions. An important case, widely used in cryptography and coding theory, is that of finite fields of non-prime order. In fact, if p is a prime number, and q = pd, the field of order q is a simple ... | Extended Euclidean algorithm | 0.834246 |
3,638 | As the commutator subgroup is generated by commutators, a perfect group may contain elements that are products of commutators but not themselves commutators. Øystein Ore proved in 1951 that the alternating groups on five or more elements contained only commutators, and conjectured that this was so for all the finite no... | Grün's lemma | 0.834245 |
3,639 | Those who have a greater desire to study math would go on one track, studying algebra. Those who did not have a large interest in math would go another route, studying general mathematics, which eliminated the problem of students being held back. Finally, grades 10-12 built math maturity. | National Council of Teachers of Mathematics | 0.834245 |
3,640 | When this abuse of notation may be confusing, one may distinguish between these structures by denoting ( Z , + ) {\displaystyle (\mathbb {Z} ,+)} the group of integers with addition, and ( Z , + , ⋅ ) {\displaystyle (\mathbb {Z} ,+,\cdot )} the ring of integers. Similarly, a topological space consists of a set X (the u... | Abuse of notation | 0.834242 |
3,641 | For an atomic nucleus, which can be regarded as an ion having stripped off all electrons, the charge number is identical with the atomic number Z, which corresponds to the number of protons in ordinary atomic nuclei. Unlike in chemistry, subatomic particles with electric charges of two elementary charges (e.g. some del... | Charge number | 0.83424 |
3,642 | The baseline lengths presently in use range from 16 to 508 meters (52 to 1,667 ft). The radio frequencies accessible to this telescope range from 194–408 gigahertz (1.545–0.735 mm) which includes rotational transitions of dozens of molecular species as well as continuum emission from interstellar dust grains. Although ... | Submillimeter Array | 0.834232 |
3,643 | In the light of later work on Galois theory, the principles of these proofs have been clarified. It is straightforward to show from analytic geometry that constructible lengths must come from base lengths by the solution of some sequence of quadratic equations. In terms of field theory, such lengths must be contained i... | Constructible polygon | 0.834232 |
3,644 | If A is a Euclidean algebra, it must contain R. If it is strictly larger than R, the argument above shows that it contains C. If it is larger than C, it contains H. If it is larger still, it must contain O. But there the process must stop, because O is not associative. In fact H is not commutative and a(b j) = (b a) j ... | Euclidean Hurwitz algebra | 0.83423 |
3,645 | Various bioinformatics tools can be used to analyze end-sequence profiling. Common ones include BreakDancer, PEMer, Variation Hunter, common LAW, GASV, and Spanner. ESP can be used to map structural variation at high-resolution in disease tissue. This technique is mainly used on tumor samples from different cancer type... | End-sequence profiling | 0.834226 |
3,646 | : 48 Theorem. Let S1, S2, ..., Sm be a collection of sets such that S i 1 ∪ S i 2 ∪ ⋯ ∪ S i k {\displaystyle S_{i_{1}}\cup S_{i_{2}}\cup \dots \cup S_{i_{k}}} contains at least k elements for k = 1,2,...,m and for all k-combinations { i 1 , i 2 , … , i k {\displaystyle i_{1},i_{2},\ldots ,i_{k}} } of the integers 1,2,.... | Transversal (group theory) | 0.834225 |
3,647 | The fact that people believe that they have this ability is in line with the illusion of control.In this study, the researchers wanted to test if they could manipulate a coin toss, and counter the gambler's fallacy by having the participant focus on the person tossing the coin. In contrast, they attempted to initiate t... | Hot-hand fallacy | 0.83422 |
3,648 | Equivalent label sequences can occur in many ways – which makes scoring a non-trivial task, but there is an efficient forward–backward algorithm for that. CTC scores can then be used with the back-propagation algorithm to update the neural network weights. Alternative approaches to a CTC-fitted neural network include a... | Connectionist temporal classification | 0.83422 |
3,649 | Depending on the field of physics, it may be advantageous to choose one or another extended set of dimensional symbols. In electromagnetism, for example, it may be useful to use dimensions of T, L, M and Q, where Q represents the dimension of electric charge. In thermodynamics, the base set of dimensions is often exten... | Unit commensurability | 0.834219 |
3,650 | Sometimes a group can be reconstructed from a subgroup and quotient (plus some additional data), by the semidirect product construction; D 4 {\displaystyle \mathrm {D} _{4}} is an example. The first isomorphism theorem implies that any surjective homomorphism ϕ: G → H {\displaystyle \phi \colon G\to H} factors canonica... | Group (mathematics) | 0.834214 |
3,651 | A mathematical model (for example in biology, climate change, economics or engineering) can be highly complex, and as a result, its relationships between inputs and outputs may be poorly understood. In such cases, the model can be viewed as a black box, i.e. the output is an "opaque" function of its inputs. Quite often... | Sensitivity analysis | 0.834214 |
3,652 | Example areas of study are radio waves, usually emitted by cold objects such as interstellar gas and dust clouds; the cosmic microwave background radiation which is the redshifted light from the Big Bang; pulsars, which were first detected at microwave frequencies. The study of these waves requires very large radio tel... | Stellar physics | 0.834211 |
3,653 | In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include false and true. In logic, mathematics and theoretical computer science, a Boolean domain is usually written as {0, 1}, or B . {\displaystyle \mathbb {B} .} The algebraic structure that natural... | Boolean domain | 0.834209 |
3,654 | Optical character recognition for printed text (nearing par-human for Latin-script typewritten text) Object recognition Various robotics tasks that may require advances in robot hardware as well as AI, including: Stable bipedal locomotion: Bipedal robots can walk, but are less stable than human walkers (as of 2017) Hum... | Progress in artificial intelligence | 0.834208 |
3,655 | Hirschhorn et al. (1999) show that a pizza sliced in the same way as the pizza theorem, into a number n of sectors with equal angles where n is divisible by four, can also be shared equally among n/4 people. For instance, a pizza divided into 12 sectors can be shared equally by three people as well as by two; however, ... | Pizza theorem | 0.834205 |
3,656 | CS Theory Stack Exchange. Retrieved 21 November 2014. "Is there an algorithm that provably exists although we don't know what it is?". Computer Science Stack Exchange. Retrieved 21 November 2014. | Non-constructive algorithm existence proofs | 0.834204 |
3,657 | Concentrating sunlight: A mirrored surface with high specular reflection is used to concentrate light from the Sun into a small cooking area. Depending on the geometry of the surface, sunlight could be concentrated by several orders of magnitude producing temperatures high enough to melt salt and metal. Such high tempe... | Solar cookers | 0.834203 |
3,658 | NLTK includes graphical demonstrations and sample data. It is accompanied by a book that explains the underlying concepts behind the language processing tasks supported by the toolkit, plus a cookbook.NLTK is intended to support research and teaching in NLP or closely related areas, including empirical linguistics, cog... | Natural Language Toolkit | 0.834201 |
3,659 | Working set is a concept in computer science which defines the amount of memory that a process requires in a given time interval. | Process working set | 0.834198 |
3,660 | It has applications in a wide range of disciplines, including mechanical, civil, chemical and biomedical engineering, geophysics, oceanography, meteorology, astrophysics, and biology. Fluid staticsFluid statics, or hydrostatics, is the branch of fluid mechanics that studies "fluids at rest and the pressure in a fluid o... | Glossary of engineering: A–L | 0.834197 |
3,661 | Computational biology has assisted evolutionary biology by: Using DNA data to reconstruct the tree of life with computational phylogenetics Fitting population genetics models (either forward time or backward time) to DNA data to make inferences about demographic or selective history Building population genetics models ... | Computational evolutionary biology | 0.834195 |
3,662 | In computer science, pointer analysis, or points-to analysis, is a static code analysis technique that establishes which pointers, or heap references, can point to which variables, or storage locations. It is often a component of more complex analyses such as escape analysis. A closely related technique is shape analys... | Pointer analysis | 0.834192 |
3,663 | As early as the 1860s, experiments demonstrated that biologically relevant molecules can be produced from interaction of simple carbon sources with abundant inorganic catalysts. The spontaneous formation of complex polymers from abiotically generated monomers under the conditions posited by the "soup" theory is not str... | Primordial sea | 0.83419 |
3,664 | Bertrand's box paradox is a veridical paradox in elementary probability theory. It was first posed by Joseph Bertrand in his 1889 work Calcul des Probabilités. There are three boxes: a box containing two gold coins, a box containing two silver coins, a box containing one gold coin and one silver coin.The question is to... | Bertrand's box paradox | 0.834187 |
3,665 | — Anatoly Petrov — 19 February 1970 — "General regularities in the reactions of conjugated systems" XXVII. — Vladimir Engelhardt — 18 March 1971 — "Ways and objective knowledge of chemistry in life" XXVIII. — Jacob Sirkin — 3 March 1972 — "non-rigid molecules" XXIX. | Mendeleev readings | 0.834184 |
3,666 | Differential calculus Integral calculus Multivariable calculus Fractional calculus Differential Geometry | Outline of calculus | 0.834183 |
3,667 | Note: A “cost metric” need not be a monetary value; cost may be measured in production time, peak or total memory requirements, power consumption, or some informal metric like “ease of explanation”, or a combination of the above (e.g., multi-objective optimization). The idea of a geodesic is general, and should be unde... | Feature-oriented programming | 0.834181 |
3,668 | When asked about the purpose of sight in humans and animals, even elementary-school children can answer that animals have vision to help them find food and avoid danger (function/adaptation). Biologists have three additional explanations: sight is caused by a particular series of evolutionary steps (phylogeny), the mec... | Tinbergen's four questions | 0.834173 |
3,669 | How many shoes are being worn?" The crystallized approach to solving the problem would involve the application of high school-level algebra. Algebra is an acculturational product. | Fluid intelligence | 0.834171 |
3,670 | Nonetheless, it was shown in that for every fixed l and m, its Graver basis G ( A ) {\displaystyle G(A)} can be computed in time which is polynomial in n. The results mentioned above allow then to solve this problem in polynomial time for fixed l and m and variable n. Note that if only one side l of the table is fixed ... | Graver basis | 0.83417 |
3,671 | Hubble is unable to see further back than very early reionization at about z≈11.1 (galaxy GN-z11, 400 million years cosmic time).The design emphasizes the near to mid-infrared for several reasons: high-redshift (very early and distant) objects have their visible emissions shifted into the infrared, and therefore their ... | James Webb Space Telescope | 0.834169 |
3,672 | bang-bang control A controller that switches a final element on or off instead of providing a proportional response. Barlow's wheel A demonstration of electromagnetic principles. Bartlett's bisection theorem A mathematical theorem used in network analysis. | Glossary of electrical and electronics engineering | 0.834166 |
3,673 | However, if we represent each divisor of n by the set of its prime factors, we find that this nonconcrete Boolean algebra is isomorphic to the concrete Boolean algebra consisting of all sets of prime factors of n, with union corresponding to least common multiple, intersection to greatest common divisor, and complement... | Boolean operator (Boolean algebra) | 0.834164 |
3,674 | In the surface layer, oxygen, DOC, POC and chlorophyll need to be in low levels in order for cyanobacteria to respire. As depth increases, many branches and sub branches of microbes create specific niches based on the chemistry and nutrient availability of that depth.Microorganisms including foraminifera, meiobenthic, ... | Blue hole | 0.834164 |
3,675 | However, it is possible to define a conditional probability for some zero-probability events using a σ-algebra of such events (such as those arising from a continuous random variable).For example, in a bag of 2 red balls and 2 blue balls (4 balls in total), the probability of taking a red ball is 1 / 2 ; {\displaystyle... | Probability | 0.834159 |
3,676 | The book is just over 1100 pages, of which the first 383 are dedicated to mathematics—Penrose's goal is to acquaint inquisitive readers with the mathematical tools needed to understand the remainder of the book in depth. Physics enters the discussion on page 383 with the topic of spacetime. From there it moves on to fi... | The Road to Reality | 0.834158 |
3,677 | It is convenient to consider the i-th n-ary symbol to be nfi as done below in the section on truth tables. An equational theory in a given language consists of equations between terms built up from variables using symbols of that language. Typical equations in the language of Boolean algebra are x∧y = y∧x, x∧x = x, x∧¬... | Boolean algebras canonically defined | 0.834156 |
3,678 | The algebraic specification therefore describes all possible states of the data element, and all possible transitions between states.For a more complicated example, the integers can be specified (among many other ways, and choosing one of the many formalisms) with two constructors 1: Z (_ - _): Z × Z -> Z and three equ... | Algebraic specification | 0.834156 |
3,679 | Additive and multiplicative number theory, perfect numbers, congruence modulo integer power, Witten zeta values; history of mathematics, history of arts. | Tianxin Cai | 0.834152 |
3,680 | In abstract algebra, the term associator is used in different ways as a measure of the non-associativity of an algebraic structure. Associators are commonly studied as triple systems. | Associator | 0.834149 |
3,681 | Mathematical Contest in Modeling (MCM) — team contest for undergraduates Mathematical Kangaroo — worldwide competition. Mental Calculation World Cup — contest for the best mental calculators Primary Mathematics World Contest (PMWC) — worldwide competition Rocket City Math League (RCML) — Competition run by students at ... | Math competition | 0.834148 |
3,682 | . . In the next chapter the techniques of generalization, specialization and analogy are presented as possible strategies for plausible reasoning. In the remaining chapters, these ideas are illustrated by discussing the discovery of several results in various fields of mathematics like number theory, geometry, etc. and... | Mathematics and Plausible Reasoning | 0.834148 |
3,683 | To do this, they extracted DNA from around 2,000 soil samples to build metagenomic libraries that captured the genetic diversity of the environmental microbiome. They then designed degenerate primers to amplify genes likely to be similar to the BGC that make daptomycin by using a polymerase chain reaction (PCR) procedu... | Malacidin | 0.834148 |
3,684 | They discovered two key issues with the computational machines that processed neural networks. The first issue was that single-layer neural networks were incapable of processing the exclusive-or circuit. The second significant issue was that computers were not sophisticated enough to effectively handle the long run tim... | Neural networks | 0.834145 |
3,685 | The numbers for a particular subject, by which the two kinds of intelligence are multiplied to obtain the expected score, are posited by the hypothesis to be the same for all intelligence level pairs, and are called "factor loading" for this subject. For example, the hypothesis may hold that the predicted average stude... | Principal factor analysis | 0.834145 |
3,686 | Methods based on chemical modifications are now available where MNP can be linked to a protein molecule via a single specific amino acid (such as N- or C- termini), thus avoiding reduction in activity due to the free access of the substrate to the active site. Moreover, site-directed immobilization also avoids modifyin... | Magnetic nanoparticles | 0.834144 |
3,687 | Several areas of mathematics led to the study of groups. Lagrange's 1770 study of the solutions of the quintic equation led to the Galois group of a polynomial. Gauss's 1801 study of Fermat's little theorem led to the ring of integers modulo n, the multiplicative group of integers modulo n, and the more general concept... | Abstract Algebra | 0.834143 |
3,688 | A common criticism of neural networks, particularly in robotics, is that they require too much training for real-world operation. Potential solutions include randomly shuffling training examples, by using a numerical optimization algorithm that does not take too large steps when changing the network connections followi... | Artificial Neural Network | 0.834137 |
3,689 | In silico PCR refers to computational tools used to calculate theoretical polymerase chain reaction (PCR) results using a given set of primers (probes) to amplify DNA sequences from a sequenced genome or transcriptome.These tools are used to optimize the design of primers for target DNA or cDNA sequences. Primer optimi... | In silico PCR | 0.834133 |
3,690 | In particle physics, a system of natural units in which the speed of light in vacuum c and the reduced Planck constant ħ are dimensionless and equal to unity is widely used: c = ħ = 1. In these units, both distances and times are expressed in inverse energy units (while energy and mass are expressed in the same units, ... | Mega electronvolt | 0.834129 |
3,691 | In Euclidean geometry, Ptolemy's inequality relates the six distances determined by four points in the plane or in a higher-dimensional space. It states that, for any four points A, B, C, and D, the following inequality holds: A B ¯ ⋅ C D ¯ + B C ¯ ⋅ D A ¯ ≥ A C ¯ ⋅ B D ¯ . {\displaystyle {\overline {AB}}\cdot {\overli... | Ptolemy's inequality | 0.834128 |
3,692 | Next, they depend on our being at a special spot at the edge of the Milky Way galaxy and they did not suggest the radiation is isotropic. The estimates would yield very different predictions if Earth happened to be located elsewhere in the universe. The 1948 results of Alpher and Herman were discussed in many physics s... | Primordial gravitational wave | 0.834128 |
3,693 | It sealed in the importance of there being proofs, or "witnesses", that the answer for an instance is yes and there being proofs, or "witnesses", that the answer for an instance is no. In this blossom algorithm paper, Edmonds also characterizes feasible problems as those solvable in polynomial time; this is one of the ... | Jack Edmonds | 0.834127 |
3,694 | The Complexity of Set Constraints (Technical report). Computer Science Department, Cornell University. 93–1352. | Set constraint | 0.834123 |
3,695 | While the intent of the energy conditions is to provide simple criteria that rule out many unphysical situations while admitting any physically reasonable situation, in fact, at least when one introduces an effective field modeling of some quantum mechanical effects, some possible matter tensors which are known to be p... | Energy condition | 0.83412 |
3,696 | In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible. Quasigroups differ from groups mainly in that the associative and identity element properties are optional. A quasigroup with an identity element is called a loop. | Quasigroup | 0.834117 |
3,697 | All these 10 laboratories are required to share 5% of positive samples to INSACOG for further research and studies. A National Centre for Disease Control (NCDC) nodal unit maintain a database of all samples of the new variants. Two national genomic sequencing database centers are appointed 1) National Institute of Biom... | INSACOG | 0.834111 |
3,698 | Sequential locality, a special case of spatial locality, occurs when data elements are arranged and accessed linearly, such as traversing the elements in a one-dimensional array. Locality is a type of predictable behavior that occurs in computer systems. Systems that exhibit strong locality of reference are great candi... | Application locality | 0.834105 |
3,699 | CNVseq detects copy number variations supported on a statistical model derived from array-comparative genomic hybridization. Sequences alignment are performed by BLAT, calculations are executed by R modules and is fully automated using Perl. There are few other bioinformatics tools that can call CNA from RNA-Seq. | List of RNA-Seq bioinformatics tools | 0.834102 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.