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200 | They are needed to convert high voltage mains electricity into low voltage electricity which can be safely used in homes. Maxwell's formulation of the law is given in the Maxwell–Faraday equation—the fourth and final of Maxwell's equations—which states that a time-varying magnetic field produces an electric field. Toge... | Introduction to electromagnetism | 0.854357 |
201 | In physics, fields are entities that interact with matter and can be described mathematically by assigning a value to each point in space and time. Vector fields are fields which are assigned both a numerical value and a direction at each point in space and time. Electric charges produce a vector field called the elect... | Introduction to electromagnetism | 0.854357 |
202 | The discovery that certain toxic chemicals administered in combination can cure certain cancers ranks as one of the greatest in modern medicine. Childhood ALL (Acute Lymphoblastic Leukemia), testicular cancer, and Hodgkins disease, previously universally fatal, are now generally curable diseases. They have also proved ... | Combination chemotherapy | 0.854107 |
203 | Molecular genetics has uncovered signalling networks that regulate cellular activities such as proliferation and survival. In a particular cancer, such a network may be radically altered, due to a chance somatic mutation. Targeted therapy inhibits the metabolic pathway that underlies that type of cancer's cell division... | Combination chemotherapy | 0.854107 |
204 | The nearest neighbour search problem arises in numerous fields of application, including: Pattern recognition – in particular for optical character recognition Statistical classification – see k-nearest neighbor algorithm Computer vision – for point cloud registration Computational geometry – see Closest pair of points... | Nearest neighbor problem | 0.853979 |
205 | In the special case where the data is a dense 3D map of geometric points, the projection geometry of the sensing technique can be used to dramatically simplify the search problem. This approach requires that the 3D data is organized by a projection to a two-dimensional grid and assumes that the data is spatially smooth... | Nearest neighbor problem | 0.853979 |
206 | While speech recognition is mainly based on deep learning because most of the industry players in this field like Google, Microsoft and IBM reveal that the core technology of their speech recognition is based on this approach, speech-based emotion recognition can also have a satisfactory performance with ensemble learn... | Ensemble Methods | 0.853971 |
207 | As an ensemble, the Bayes optimal classifier represents a hypothesis that is not necessarily in H {\displaystyle H} . The hypothesis represented by the Bayes optimal classifier, however, is the optimal hypothesis in ensemble space (the space of all possible ensembles consisting only of hypotheses in H {\displaystyle H}... | Ensemble Methods | 0.853971 |
208 | The content within the book is written using a question and answer format. It contains some 250 questions, which The Science Teacher states each are answered with a "concise and well-formulated essay that is informative and readable." The Science Teacher review goes on to state that many of the answers given in the boo... | A Question and Answer Guide to Astronomy | 0.853932 |
209 | A Question and Answer Guide to Astronomy is a book about astronomy and cosmology, and is intended for a general audience. The book was written by Pierre-Yves Bely, Carol Christian, and Jean-Rene Roy, and published in English by Cambridge University Press in 2010. It was originally written in French. | A Question and Answer Guide to Astronomy | 0.853932 |
210 | The degree can be used to generalize Bézout's theorem in an expected way to intersections of n hypersurfaces in Pn. == Notes == | Degree (algebraic geometry) | 0.853916 |
211 | A generalization of Bézout's theorem asserts that, if an intersection of n projective hypersurfaces has codimension n, then the degree of the intersection is the product of the degrees of the hypersurfaces. The degree of a projective variety is the evaluation at 1 of the numerator of the Hilbert series of its coordinat... | Degree (algebraic geometry) | 0.853916 |
212 | This is a generalization of Bézout's theorem (For a proof, see Hilbert series and Hilbert polynomial § Degree of a projective variety and Bézout's theorem). The degree is not an intrinsic property of the variety, as it depends on a specific embedding of the variety in an affine or projective space. The degree of a hype... | Degree (algebraic geometry) | 0.853916 |
213 | In mathematics, the degree of an affine or projective variety of dimension n is the number of intersection points of the variety with n hyperplanes in general position. For an algebraic set, the intersection points must be counted with their intersection multiplicity, because of the possibility of multiple components. ... | Degree (algebraic geometry) | 0.853916 |
214 | Actin was first observed experimentally in 1887 by W.D. Halliburton, who extracted a protein from muscle that 'coagulated' preparations of myosin that he called "myosin-ferment". However, Halliburton was unable to further refine his findings, and the discovery of actin is credited instead to Brunó Ferenc Straub, a youn... | F actin | 0.853902 |
215 | It is possible that actin could be applied to nanotechnology as its dynamic ability has been harnessed in a number of experiments including those carried out in acellular systems. The underlying idea is to use the microfilaments as tracks to guide molecular motors that can transport a given load. That is actin could be... | F actin | 0.853902 |
216 | Actin is used in scientific and technological laboratories as a track for molecular motors such as myosin (either in muscle tissue or outside it) and as a necessary component for cellular functioning. It can also be used as a diagnostic tool, as several of its anomalous variants are related to the appearance of specifi... | F actin | 0.853902 |
217 | Actin can spontaneously acquire a large part of its tertiary structure. However, the way it acquires its fully functional form from its newly synthesized native form is special and almost unique in protein chemistry. The reason for this special route could be the need to avoid the presence of incorrectly folded actin m... | F actin | 0.853902 |
218 | A number of natural toxins that interfere with actin's dynamics are widely used in research to study actin's role in biology. Latrunculin – a toxin produced by sponges – binds to G-actin preventing it from joining microfilaments. Cytochalasin D – produced by certain fungi – serves as a capping factor, binding to the (+... | F actin | 0.853902 |
219 | This is the topic of the scientific field of structural biology, which employs techniques such as X-ray crystallography, NMR spectroscopy, cryo-electron microscopy (cryo-EM) and dual polarisation interferometry, to determine the structure of proteins. Protein structures range in size from tens to several thousand amino... | Protein Structure | 0.853837 |
220 | Quantum electrodynamics (QED), a relativistic quantum field theory of electrodynamics, is among the most stringently tested theories in physics. The most precise and specific tests of QED consist of measurements of the electromagnetic fine-structure constant, α, in various physical systems. Checking the consistency of ... | Tests of electromagnetism | 0.853791 |
221 | For example, molecular dynamics (MD) is commonly used to analyze the dynamic movements of biological molecules. In 1975, the first simulation of a biological folding process using MD was published in Nature. Recently, protein structure prediction was significantly improved by a new machine learning method called AlphaF... | Structural Biology | 0.853673 |
222 | Recent developments in the field have included the generation of X-ray free electron lasers, allowing analysis of the dynamics and motion of biological molecules, and the use of structural biology in assisting synthetic biology.In the late 1930s and early 1940s, the combination of work done by Isidor Rabi, Felix Bloch,... | Structural Biology | 0.853673 |
223 | In 1912 Max Von Laue directed X-rays at crystallized copper sulfate generating a diffraction pattern. These experiments led to the development of X-ray crystallography, and its usage in exploring biological structures. In 1951, Rosalind Franklin and Maurice Wilkins used X-ray diffraction patterns to capture the first i... | Structural Biology | 0.853673 |
224 | For example, researchers have used structural biology to better understand Met, a protein encoded by a protooncogene that is an important drug target in cancer. Similar research has been conducted for HIV targets to treat people with AIDS. Researchers are also developing new antimicrobials for mycobacterial infections ... | Structural Biology | 0.853673 |
225 | For example, structural biology tools have enabled virologists to understand how the HIV envelope allows the virus to evade human immune responses.Structural biology is also an important component of drug discovery. Scientists can identify targets using genomics, study those targets using structural biology, and develo... | Structural Biology | 0.853673 |
226 | Structural biologists have made significant contributions towards understanding the molecular components and mechanisms underlying human diseases. For example, cryo-EM and ssNMR have been used to study the aggregation of amyloid fibrils, which are associated with Alzheimer's disease, Parkinson's disease, and type II di... | Structural Biology | 0.853673 |
227 | The Faraday paradox was a once inexplicable aspect of the reaction between nitric acid and steel. Around 1830, the English scientist Michael Faraday found that diluted nitric acid would attack steel, but concentrated nitric acid would not. The attempt to explain this discovery led to advances in electrochemistry. | Faraday paradox (electrochemistry) | 0.85354 |
228 | Discrete Mathematics: Deals with separate and distinct mathematical structures, including topics such as combinatorics, graph theory, and algorithms. 8. Decision Mathematics: Applies mathematical techniques to solve real-world problems related to optimization, networks, and decision-making. 9. Financial Mathematics: Ap... | Advanced level mathematics | 0.853341 |
229 | 6. Statistics: Involves collecting, analyzing, and interpreting data, including topics like probability, hypothesis testing, regression analysis, and sampling. 7. | Advanced level mathematics | 0.853341 |
230 | Applied Mathematics: Focuses on practical applications of mathematical concepts to solve real-world problems in various fields. 5. Mechanics: Focuses on the study of motion, forces, and vectors, particularly relevant for physics or engineering interests. | Advanced level mathematics | 0.853341 |
231 | 3. Pure Mathematics: Explores advanced topics in algebra, calculus, and mathematical proofs. 4. | Advanced level mathematics | 0.853341 |
232 | ```List of subjects in A Level Mathematics``` 1. Core Mathematics: Covers foundational topics like algebra, calculus, trigonometry, and coordinate geometry. 2. Further Mathematics: Expands upon Core Mathematics with additional areas such as complex numbers, matrices, differential equations, and numerical methods. | Advanced level mathematics | 0.853341 |
233 | Prior to the 2017 reform, the basic A-Level course consisted of six modules, four pure modules (C1, C2, C3, and C4) and two applied modules in Statistics, Mechanics and/or Decision Mathematics. The C1 through C4 modules are referred to by A-level textbooks as "Core" modules, encompassing the major topics of mathematics... | Advanced level mathematics | 0.853341 |
234 | Paper 1: Pure Mathematics Paper 2: Pure Mathematics and Statistics Paper 3: Pure Mathematics and Mechanics | Advanced level mathematics | 0.853341 |
235 | Paper 1: Pure Mathematics Paper 2: Content on Paper 1 plus Mechanics Paper 3: Content on Paper 1 plus Statistics | Advanced level mathematics | 0.853341 |
236 | Paper 1: Pure Mathematics 1 Paper 2: Pure Mathematics 2 Paper 3: Statistics and Mechanics | Advanced level mathematics | 0.853341 |
237 | Most students will complete three modules in one year, which will create an AS-level qualification in their own right and will complete the A-level course the following year—with three more modules. The system in which mathematics is assessed is changing for students starting courses in 2017 (as part of the A-level ref... | Advanced level mathematics | 0.853341 |
238 | Advanced Level (A-Level) Mathematics is a qualification of further education taken in the United Kingdom (and occasionally other countries as well). In the UK, A-Level exams are traditionally taken by 17-18 year-olds after a two-year course at a sixth form or college. Advanced Level Further Mathematics is often taken b... | Advanced level mathematics | 0.853341 |
239 | Module: an abelian group M and a ring R acting as operators on M. The members of R are sometimes called scalars, and the binary operation of scalar multiplication is a function R × M → M, which satisfies several axioms. Counting the ring operations these systems have at least three operations. Vector space: a module wh... | Algebraic structure | 0.853092 |
240 | Associativity An operation ∗ {\displaystyle *} is associative if for every x, y and z in the algebraic structure. Left distributivity An operation ∗ {\displaystyle *} is left distributive with respect to another operation + {\displaystyle +} if for every x, y and z in the algebraic structure (the second operation is de... | Algebraic structure | 0.853092 |
241 | An axiom of an algebraic structure often has the form of an identity, that is, an equation such that the two sides of the equals sign are expressions that involve operations of the algebraic structure and variables. If the variables in the identity are replaced by arbitrary elements of the algebraic structure, the equa... | Algebraic structure | 0.853092 |
242 | In statistics, the multiple comparisons, multiplicity or multiple testing problem occurs when one considers a set of statistical inferences simultaneously or infers a subset of parameters selected based on the observed values.The more inferences are made, the more likely erroneous inferences become. Several statistical... | Multiple comparisons problem | 0.85289 |
243 | A number of Nobel Prizes have been awarded for steroid research, including: 1927 (Chemistry) Heinrich Otto Wieland — Constitution of bile acids and sterols and their connection to vitamins 1928 (Chemistry) Adolf Otto Reinhold Windaus — Constitution of sterols and their connection to vitamins 1939 (Chemistry) Adolf Bute... | Steroid biosynthesis | 0.852769 |
244 | Steroids can be classified based on their chemical composition. One example of how MeSH performs this classification is available at the Wikipedia MeSH catalog. Examples of this classification include: In biology, it is common to name the above steroid classes by the number of carbon atoms present when referring to hor... | Steroid biosynthesis | 0.852769 |
245 | In solving mathematical equations, particularly linear simultaneous equations, differential equations and integral equations, the terminology homogeneous is often used for equations with some linear operator L on the LHS and 0 on the RHS. In contrast, an equation with a non-zero RHS is called inhomogeneous or non-homog... | Sides of an equation | 0.852767 |
246 | The statement is: a set of polynomials S in K {\displaystyle K} has a common zero in an algebraically closed field containing K, if and only if 1 does not belong to the ideal generated by S, that is, if 1 is not a linear combination of elements of S with polynomial coefficients. The second version generalizes the fact... | Polynomial expression | 0.852759 |
247 | The Nullstellensatz (German for "zero-locus theorem") is a theorem, first proved by David Hilbert, which extends to the multivariate case some aspects of the fundamental theorem of algebra. It is foundational for algebraic geometry, as establishing a strong link between the algebraic properties of K {\displaystyle K} ... | Polynomial expression | 0.852759 |
248 | Polynomial rings occur and are often fundamental in many parts of mathematics such as number theory, commutative algebra, and algebraic geometry. In ring theory, many classes of rings, such as unique factorization domains, regular rings, group rings, rings of formal power series, Ore polynomials, graded rings, have bee... | Polynomial expression | 0.852759 |
249 | In mathematics, especially in the field of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more indeterminates (traditionally also called variables) with coefficients in another ring, often a field. Often, the term "polynomial... | Polynomial expression | 0.852759 |
250 | M. vaginatus stabilizes soil using a polysaccharide sheath that binds to sand particles and absorbs water.Some of these organisms contribute significantly to global ecology and the oxygen cycle. The tiny marine cyanobacterium Prochlorococcus was discovered in 1986 and accounts for more than half of the photosynthesis o... | Blue-green Algae | 0.852634 |
251 | One of the most critical processes determining cyanobacterial eco-physiology is cellular death. Evidence supports the existence of controlled cellular demise in cyanobacteria, and various forms of cell death have been described as a response to biotic and abiotic stresses. However, cell death research in cyanobacteria ... | Blue-green Algae | 0.852633 |
252 | For detailed discussions of some solution methods see: Tschirnhaus transformation (general method, not guaranteed to succeed); Bezout method (general method, not guaranteed to succeed); Ferrari method (solutions for degree 4); Euler method (solutions for degree 4); Lagrange method (solutions for degree 4); Descartes me... | Polynomial equation | 0.852539 |
253 | For example, x 5 − 3 x + 1 = 0 {\displaystyle x^{5}-3x+1=0} is an algebraic equation with integer coefficients and y 4 + x y 2 − x 3 3 + x y 2 + y 2 + 1 7 = 0 {\displaystyle y^{4}+{\frac {xy}{2}}-{\frac {x^{3}}{3}}+xy^{2}+y^{2}+{\frac {1}{7}}=0} is a multivariate polynomial equation over the rationals. Some but not all... | Polynomial equation | 0.852539 |
254 | In mathematics, an algebraic equation or polynomial equation is an equation of the form P = 0 {\displaystyle P=0} where P is a polynomial with coefficients in some field, often the field of the rational numbers. For many authors, the term algebraic equation refers only to univariate equations, that is polynomial equati... | Polynomial equation | 0.852539 |
255 | "Some researchers suggest that AI designers specify their desired goals by listing forbidden actions or by formalizing ethical rules (as with Asimov's Three Laws of Robotics). However, Russell and Norvig argued that this approach overlooks the complexity of human values: "It is certainly very hard, and perhaps impossib... | Alignment problem | 0.852467 |
256 | In the field of artificial intelligence (AI), AI alignment research aims to steer AI systems towards humans' intended goals, preferences, or ethical principles. An AI system is considered aligned if it advances the intended objectives. A misaligned AI system pursues some objectives, but not the intended ones.It can be ... | Alignment problem | 0.852467 |
257 | After novel geometries such as hyperbolic and projective geometry had emerged, Klein used group theory to organize them in a more coherent way. Further advancing these ideas, Sophus Lie founded the study of Lie groups in 1884.The third field contributing to group theory was number theory. | Group axioms | 0.852381 |
258 | Dudek, Wiesław A. (2001), "On some old and new problems in n-ary groups" (PDF), Quasigroups and Related Systems, 8: 15–36, MR 1876783. Eliel, Ernest; Wilen, Samuel; Mander, Lewis (1994), Stereochemistry of Organic Compounds, Wiley, ISBN 978-0-471-01670-0 Ellis, Graham (2019), "6.4 Triangle groups", An Invitation to Com... | Group axioms | 0.852381 |
259 | (2002), Universal Algebra and Applications in Theoretical Computer Science, London: CRC Press, ISBN 978-1-58488-254-1. Dove, Martin T (2003), Structure and Dynamics: An Atomic View of Materials, Oxford University Press, p. 265, ISBN 0-19-850678-3. | Group axioms | 0.852381 |
260 | (2001), "On three-dimensional space groups", Beiträge zur Algebra und Geometrie, 42 (2): 475–507, arXiv:math.MG/9911185, MR 1865535. Coornaert, M.; Delzant, T.; Papadopoulos, A. | Group axioms | 0.852381 |
261 | (1993), Group Theory and Chemistry, New York: Dover Publications, ISBN 978-0-486-67355-4. Borel, Armand (1991), Linear Algebraic Groups, Graduate Texts in Mathematics, vol. 126 (2nd ed. | Group axioms | 0.852381 |
262 | Any finite abelian group is isomorphic to a product of finite cyclic groups; this statement is part of the fundamental theorem of finitely generated abelian groups. Any group of prime order p {\displaystyle p} is isomorphic to the cyclic group Z p {\displaystyle \mathrm {Z} _{p}} (a consequence of Lagrange's theorem). ... | Group axioms | 0.852381 |
263 | This way, the group operation, which may be abstractly given, translates to the multiplication of matrices making it accessible to explicit computations.A group action gives further means to study the object being acted on. On the other hand, it also yields information about the group. Group representations are an orga... | Group axioms | 0.852381 |
264 | Finally, the inverse of a / b {\displaystyle a/b} is b / a {\displaystyle b/a} , therefore the axiom of the inverse element is satisfied. The rational numbers (including zero) also form a group under addition. Intertwining addition and multiplication operations yields more complicated structures called rings and – if d... | Group axioms | 0.85238 |
265 | As of the 20th century, groups gained wide recognition by the pioneering work of Ferdinand Georg Frobenius and William Burnside, who worked on representation theory of finite groups, Richard Brauer's modular representation theory and Issai Schur's papers. The theory of Lie groups, and more generally locally compact gro... | Group axioms | 0.85238 |
266 | Certain abelian group structures had been used implicitly in Carl Friedrich Gauss's number-theoretical work Disquisitiones Arithmeticae (1798), and more explicitly by Leopold Kronecker. In 1847, Ernst Kummer made early attempts to prove Fermat's Last Theorem by developing groups describing factorization into prime numb... | Group axioms | 0.85238 |
267 | At first, Galois's ideas were rejected by his contemporaries, and published only posthumously. More general permutation groups were investigated in particular by Augustin Louis Cauchy. Arthur Cayley's On the theory of groups, as depending on the symbolic equation θ n = 1 {\displaystyle \theta ^{n}=1} (1854) gives the f... | Group axioms | 0.85238 |
268 | (1994), An introduction to homological algebra, Cambridge Studies in Advanced Mathematics, vol. 38, Cambridge University Press, ISBN 978-0-521-55987-4, MR 1269324, OCLC 36131259 Weinberg, Steven (1972), Gravitation and Cosmology, New York: John Wiley & Sons, ISBN 0-471-92567-5. Welsh, Dominic (1989), Codes and Cryptogr... | Group axioms | 0.85238 |
269 | Schwartzman, Steven (1994), The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English, Mathematical Association of America, ISBN 978-0-88385-511-9. Shatz, Stephen S. (1972), Profinite Groups, Arithmetic, and Geometry, Princeton University Press, ISBN 978-0-691-08017-8, MR 0347778 Simons... | Group axioms | 0.85238 |
270 | Rosen, Kenneth H. (2000), Elementary Number Theory and its Applications (4th ed. ), Addison-Wesley, ISBN 978-0-201-87073-2, MR 1739433. | Group axioms | 0.85238 |
271 | Naber, Gregory L. (2003), The Geometry of Minkowski Spacetime, New York: Dover Publications, ISBN 978-0-486-43235-9, MR 2044239. Neukirch, Jürgen (1999), Algebraic Number Theory, Grundlehren der mathematischen Wissenschaften, vol. | Group axioms | 0.85238 |
272 | Kuga, Michio (1993), Galois' Dream: Group Theory and Differential Equations, Boston, MA: Birkhäuser Boston, ISBN 978-0-8176-3688-3, MR 1199112. Kurzweil, Hans; Stellmacher, Bernd (2004), The Theory of Finite Groups, Universitext, Berlin, New York: Springer-Verlag, ISBN 978-0-387-40510-0, MR 2014408. Lay, David (2003), ... | Group axioms | 0.85238 |
273 | 588–596, ISBN 0-201-02918-9. Gollmann, Dieter (2011), Computer Security (2nd ed. ), West Sussex, England: John Wiley & Sons, Ltd., ISBN 978-0-470-74115-3 Hatcher, Allen (2002), Algebraic Topology, Cambridge University Press, ISBN 978-0-521-79540-1. | Group axioms | 0.85238 |
274 | A Lie group is a group that also has the structure of a differentiable manifold; informally, this means that it looks locally like a Euclidean space of some fixed dimension. Again, the definition requires the additional structure, here the manifold structure, to be compatible: the multiplication and inverse maps are re... | Group axioms | 0.85238 |
275 | In particular the equation P = Q {\displaystyle P=Q} is equivalent to P − Q = 0 {\displaystyle P-Q=0} . It follows that the study of algebraic equations is equivalent to the study of polynomials. A polynomial equation over the rationals can always be converted to an equivalent one in which the coefficients are integers... | Polynomial equations | 0.852345 |
276 | A Diophantine equation is a (usually multivariate) polynomial equation with integer coefficients for which one is interested in the integer solutions. Algebraic geometry is the study of the solutions in an algebraically closed field of multivariate polynomial equations. Two equations are equivalent if they have the sam... | Polynomial equations | 0.852345 |
277 | In particular, it includes the study of equations that involve nth roots and, more generally, algebraic expressions. This makes the term algebraic equation ambiguous outside the context of the old problem. So the term polynomial equation is generally preferred when this ambiguity may occur, specially when considering m... | Polynomial equations | 0.852345 |
278 | The term "algebraic equation" dates from the time when the main problem of algebra was to solve univariate polynomial equations. This problem was completely solved during the 19th century; see Fundamental theorem of algebra, Abel–Ruffini theorem and Galois theory. Since then, the scope of algebra has been dramatically ... | Polynomial equations | 0.852345 |
279 | The study of algebraic equations is probably as old as mathematics: the Babylonian mathematicians, as early as 2000 BC could solve some kinds of quadratic equations (displayed on Old Babylonian clay tablets). Univariate algebraic equations over the rationals (i.e., with rational coefficients) have a very long history. ... | Polynomial equations | 0.852345 |
280 | 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 | 0.852345 |
281 | There is a vast body of methods for solving various kinds of differential equations, both numerically and analytically. A particular class of problem that can be considered to belong here is integration, and the analytic methods for solving this kind of problems are now called symbolic integration. Solutions of differe... | Solving equations | 0.852289 |
282 | Equations involving matrices and vectors of real numbers can often be solved by using methods from linear algebra. | Solving equations | 0.852289 |
283 | Smaller systems of linear equations can be solved likewise by methods of elementary algebra. For solving larger systems, algorithms are used that are based on linear algebra. See Gaussian elimination | Solving equations | 0.852289 |
284 | This is because of the large number of genes involved; this makes the trait very variable and people are of many different heights. Despite a common misconception, the green/blue eye traits are also inherited in this complex inheritance model. Inheritance can also be complicated when the trait depends on the interactio... | Introduction to genetics | 0.852251 |
285 | Genetics is the study of genes and tries to explain what they are and how they work. Genes are how living organisms inherit features or traits from their ancestors; for example, children usually look like their parents because they have inherited their parents' genes. Genetics tries to identify which traits are inherit... | Introduction to genetics | 0.852251 |
286 | The combination of mutations creating new alleles at random, and natural selection picking out those that are useful, causes an adaptation. This is when organisms change in ways that help them to survive and reproduce. Many such changes, studied in evolutionary developmental biology, affect the way the embryo develops ... | Introduction to genetics | 0.852251 |
287 | A population of organisms evolves when an inherited trait becomes more common or less common over time. For instance, all the mice living on an island would be a single population of mice: some with white fur, some gray. If over generations, white mice became more frequent and gray mice less frequent, then the color of... | Introduction to genetics | 0.852251 |
288 | Cystic fibrosis, for example, is caused by mutations in a single gene called CFTR and is inherited as a recessive trait.Other diseases are influenced by genetics, but the genes a person gets from their parents only change their risk of getting a disease. Most of these diseases are inherited in a complex way, with eithe... | Introduction to genetics | 0.852251 |
289 | Subsequent authors have greatly extended Dehn's algorithm and applied it to a wide range of group theoretic decision problems.It was shown by Pyotr Novikov in 1955 that there exists a finitely presented group G such that the word problem for G is undecidable. It follows immediately that the uniform word problem is also... | Word problem for groups | 0.85202 |
290 | The oldest result relating algebraic structure to solvability of the word problem is Kuznetsov's theorem: A recursively presented simple group S has solvable word problem.To prove this let ⟨X|R⟩ be a recursive presentation for S. Choose a ∈ S such that a ≠ 1 in S. If w is a word on the generators X of S, then let: S w ... | Word problem for groups | 0.85202 |
291 | There are a number of results that relate solvability of the word problem and algebraic structure. The most significant of these is the Boone-Higman theorem: A finitely presented group has solvable word problem if and only if it can be embedded in a simple group that can be embedded in a finitely presented group.It is ... | Word problem for groups | 0.85202 |
292 | The following will be proved as an example of the use of this technique: Theorem: A finitely presented residually finite group has solvable word problem.Proof: Suppose G = ⟨X|R⟩ is a finitely presented, residually finite group. Let S be the group of all permutations of N, the natural numbers, that fixes all but finitel... | Word problem for groups | 0.85202 |
293 | For instance, the Higman embedding theorem can be used to construct a group containing an isomorphic copy of every finitely presented group with solvable word problem. It seems natural to ask whether this group can have solvable word problem. But it is a consequence of the Boone-Rogers result that: Corollary: There is ... | Word problem for groups | 0.85202 |
294 | The criterion given above, for the solvability of the word problem in a single group, can be extended by a straightforward argument. This gives the following criterion for the uniform solvability of the word problem for a class of finitely presented groups: To solve the uniform word problem for a class K of groups, it ... | Word problem for groups | 0.85202 |
295 | Classification of malware codes such as computer viruses, computer worms, trojans, ransomware and spywares with the usage of machine learning techniques, is inspired by the document categorization problem. Ensemble learning systems have shown a proper efficacy in this area. | Ensemble learning | 0.851909 |
296 | Bayesian model averaging (BMA) makes predictions by averaging the predictions of models weighted by their posterior probabilities given the data. BMA is known to generally give better answers than a single model, obtained, e.g., via stepwise regression, especially where very different models have nearly identical perfo... | Ensemble learning | 0.851908 |
297 | R: at least three packages offer Bayesian model averaging tools, including the BMS (an acronym for Bayesian Model Selection) package, the BAS (an acronym for Bayesian Adaptive Sampling) package, and the BMA package. Python: scikit-learn, a package for machine learning in Python offers packages for ensemble learning inc... | Ensemble learning | 0.851908 |
298 | According to Snopes.com, more recent (1999 and 1988) versions identify the problem as a question in "a physics degree exam at the University of Copenhagen" and the student was Niels Bohr, and includes the following answers: Tying a piece of string to the barometer, lowering the barometer from the roof to the ground, an... | Barometer question | 0.851886 |
299 | Neither of two available options (pass or fail) was morally acceptable.By mutual agreement with the student and the examiner, Calandra gave the student another opportunity to answer, warning the student the answer would require demonstrating some knowledge of physics. The student came up with several possible answers, ... | Barometer question | 0.851886 |
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