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ACT AIEEE in India AP ASVAB AMC Australian Mathematics Competition CFA CISSP CLEP COMLEX CLAT Hong Kong Diploma of Secondary Education F = ma, leading up to the United States Physics Olympiad FE GCE Ordinary Level GED GRE GATE IB Diploma Programme science subject exams IIT-JEE in India, which had, until 2006, a high-stakes phase after the initial MCQ based screening phase Indonesian National Exam LSAT MCAT Multistate Bar Examination NCLEX PLAB for non-EEA medical graduates to practice in the UK PSAT SAT Test of English as a Foreign Language TOEIC USMLE NTSE NEET(UG) in India UGC NET in India UPSC CSE Preliminary in India
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Multiple choice question
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1
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The process of completing the square makes use of the algebraic identity x 2 + 2 h x + h 2 = ( x + h ) 2 , {\displaystyle x^{2}+2hx+h^{2}=(x+h)^{2},} which represents a well-defined algorithm that can be used to solve any quadratic equation. : 207 Starting with a quadratic equation in standard form, ax2 + bx + c = 0 Divide each side by a, the coefficient of the squared term. Subtract the constant term c/a from both sides.
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Quadratic equations
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2
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In algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.) The numbers a, b, and c are the coefficients of the equation and may be distinguished by respectively calling them, the quadratic coefficient, the linear coefficient and the constant coefficient or free term.The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side. A quadratic equation has at most two solutions.
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Quadratic equations
| 0.884408
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3
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The equation given by Fuss' theorem, giving the relation among the radius of a bicentric quadrilateral's inscribed circle, the radius of its circumscribed circle, and the distance between the centers of those circles, can be expressed as a quadratic equation for which the distance between the two circles' centers in terms of their radii is one of the solutions. The other solution of the same equation in terms of the relevant radii gives the distance between the circumscribed circle's center and the center of the excircle of an ex-tangential quadrilateral. Critical points of a cubic function and inflection points of a quartic function are found by solving a quadratic equation.
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Quadratic equations
| 0.884408
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4
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Given the cosine or sine of an angle, finding the cosine or sine of the angle that is half as large involves solving a quadratic equation. The process of simplifying expressions involving the square root of an expression involving the square root of another expression involves finding the two solutions of a quadratic equation. Descartes' theorem states that for every four kissing (mutually tangent) circles, their radii satisfy a particular quadratic equation.
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Quadratic equations
| 0.884408
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5
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{\displaystyle x={\frac {{\sqrt {4ac+b^{2}}}-b}{2a}}.} The Bakhshali Manuscript written in India in the 7th century AD contained an algebraic formula for solving quadratic equations, as well as quadratic indeterminate equations (originally of type ax/c = y). Muhammad ibn Musa al-Khwarizmi (9th century), possibly inspired by Brahmagupta, developed a set of formulas that worked for positive solutions.
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Quadratic equation
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6
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In the days before calculators, people would use mathematical tables—lists of numbers showing the results of calculation with varying arguments—to simplify and speed up computation. Tables of logarithms and trigonometric functions were common in math and science textbooks. Specialized tables were published for applications such as astronomy, celestial navigation and statistics. Methods of numerical approximation existed, called prosthaphaeresis, that offered shortcuts around time-consuming operations such as multiplication and taking powers and roots.
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Quadratic equation
| 0.881942
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7
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Statistics show that waste collection is one of the most dangerous jobs, at times more dangerous than police work, but consistently less dangerous than commercial fishing and ranch and farm work. On-the-job hazards include broken glass, medical waste such as syringes, caustic chemicals, objects falling out of overloaded containers, diseases that may accompany solid waste, asbestos, dog attacks and pests, inhaling dust, smoke and chemical fumes, severe weather, traffic accidents, and unpleasant smells that can make someone physically sick.Risks also exist from working in close proximity to traffic hazards, and in using the heavy machinery (such as container lifters and compactors) found on collection vehicles.
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Garbage collector
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8
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Students reconstructed a chain of events in the Dr. Biology laboratory and field site, writing their own narrative for the story. Early in 2007, Ask A Biologist became one of the early content channels on iTunes U with its audio podcast of the same name. Hosted by Dr. Biology, the program was soon listed as one of five great courses by Macworld.
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Ask a Biologist
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The Virtual Bird Aviary, included the majority of bird species found in the Southwest United States including more than 400 vocal recordings and companion sonograms, bird images, text descriptions, and range maps. In 2005, the website was peer reviewed by the Multimedia Educational Resource for Learning and Online Teaching (MERLOT), earning a "five out of five star" rating.In 2006, the website introduced the Mysterious World of Dr. Biology a comic book adventure. The activity encouraged students to piece together a mystery.
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Ask a Biologist
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10
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Ask A Biologist is a pre-kindergarten through high school program dedicated to answering questions from students, their teachers, and parents. The primary focus of the program is to connect students and teachers with working scientists through a question and answer Web e-mail form. The companion website also includes a large collection of free content and activities that can be used inside, as well as outside, of the classroom. The award-winning program has been continuously running for more than 14 years, with the assistance of more than 150 volunteer scientists, faculty, and graduate students in biology and related fields. In 2010 the program released its new website interface and features that became the subject for articles in the journals Science and PLoS Biology.
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Ask a Biologist
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Stories about Biology Stories about Biologists Games and Simulations Body Depot Biology Bits PLOSable Image Gallery Puzzles – Word Search & Crossword Coloring Pages Mysterious World of Dr. Biology comic book adventure activity Audio Podcasts Co-host Contest Ugly Bug Contest Bird Finder Tool Virtual Pocket Seed Experiment Biology Virtual Reality Tours
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Ask a Biologist
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In 2011, statistics of each post-translational modification experimentally and putatively detected have been compiled using proteome-wide information from the Swiss-Prot database. The 10 most common experimentally found modifications were as follows:
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Post-translational modification
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In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, Fs = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram. He published the solution of his anagram in 1678 as: ut tensio, sic vis ("as the extension, so the force" or "the extension is proportional to the force").
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Spring Constant
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In the shorter term, efforts are underway to commercialize algae-based fuels such as diesel, gasoline, and jet fuel. Cyanobacteria have been also engineered to produce ethanol and experiments have shown that when one or two CBB genes are being over expressed, the yield can be even higher.Cyanobacteria may possess the ability to produce substances that could one day serve as anti-inflammatory agents and combat bacterial infections in humans. Cyanobacteria's photosynthetic output of sugar and oxygen has been demonstrated to have therapeutic value in rats with heart attacks. While cyanobacteria can naturally produce various secondary metabolites, they can serve as advantageous hosts for plant-derived metabolites production owing to biotechnological advances in systems biology and synthetic biology.Spirulina's extracted blue color is used as a natural food coloring.Researchers from several space agencies argue that cyanobacteria could be used for producing goods for human consumption in future crewed outposts on Mars, by transforming materials available on this planet.
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Cyanobacteria
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are estimated at 12–15 Mb, as large as yeast. Recent research has suggested the potential application of cyanobacteria to the generation of renewable energy by directly converting sunlight into electricity. Internal photosynthetic pathways can be coupled to chemical mediators that transfer electrons to external electrodes.
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Cyanobacteria
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Since DNA is an informative macromolecule in terms of transmission from one generation to another, DNA sequencing is used in evolutionary biology to study how different organisms are related and how they evolved. In February 2021, scientists reported, for the first time, the sequencing of DNA from animal remains, a mammoth in this instance, over a million years old, the oldest DNA sequenced to date.
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DNA Sequencing
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Systems of linear inequalities can be simplified by Fourier–Motzkin elimination.The cylindrical algebraic decomposition is an algorithm that allows testing whether a system of polynomial equations and inequalities has solutions, and, if solutions exist, describing them. The complexity of this algorithm is doubly exponential in the number of variables. It is an active research domain to design algorithms that are more efficient in specific cases.
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System of inequalities
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DNA sequencing may be used to determine the sequence of individual genes, larger genetic regions (i.e. clusters of genes or operons), full chromosomes, or entire genomes of any organism. DNA sequencing is also the most efficient way to indirectly sequence RNA or proteins (via their open reading frames). In fact, DNA sequencing has become a key technology in many areas of biology and other sciences such as medicine, forensics, and anthropology.
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Next Generation Sequencing
| 0.869318
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The problem of managing the deallocation of garbage is well-known in computer science. Several approaches are taken: Many operating systems reclaim the memory and resources used by a process or program when it terminates. Simple or short-lived programs which are designed to run in such environments can exit and allow the operating system to perform any necessary reclamation. In systems or programming languages with manual memory management, the programmer must explicitly arrange for memory to be deallocated when it is no longer used.
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Garbage (computer science)
| 0.868862
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In computer science, garbage includes data, objects, or other regions of the memory of a computer system (or other system resources), which will not be used in any future computation by the system, or by a program running on it. Because every computer system has a finite amount of memory, and most software produces garbage, it is frequently necessary to deallocate memory that is occupied by garbage and return it to the heap, or memory pool, for reuse.
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Garbage (computer science)
| 0.868862
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The grade distributions for the Physics C: Electricity and Magnetism scores since 2010 were:
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AP Physics C: Electricity and Magnetism
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The exam is typically administered on a Monday afternoon in May. The exam is configured in two categories: a 35-question multiple choice section and a 3-question free response section. Test takers are allowed to use an approved calculator during the entire exam. The test is weighted such that each section is worth half of the final score. This and AP Physics C: Mechanics are the shortest AP exams, with total testing time of 90 minutes (45 minutes for each section).The topics covered by the exam are as follows:
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AP Physics C: Electricity and Magnetism
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E&M is equivalent to an introductory college course in electricity and magnetism for physics or engineering majors. The course modules are: Electrostatics Conductors, capacitors, and dielectrics Electric circuits Magnetic fields Electromagnetism.Methods of calculus are used wherever appropriate in formulating physical principles and in applying them to physical problems. Therefore, students should have completed or be concurrently enrolled in a calculus class.
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AP Physics C: Electricity and Magnetism
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Advanced Placement (AP) Physics C: Electricity and Magnetism (also known as AP Physics C: E&M or AP E&M) is an introductory physics course administered by the College Board as part of its Advanced Placement program. It is intended to proxy a second-semester calculus-based university course in electricity and magnetism. The content of Physics C: E&M overlaps with that of AP Physics 2, but Physics 2 is algebra-based and covers other topics outside of electromagnetism, while Physics C is calculus-based and only covers electromagnetism. Physics C: E&M may be combined with its mechanics counterpart to form a year-long course that prepares for both exams.
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AP Physics C: Electricity and Magnetism
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The AP examination for AP Physics C: Electricity and Magnetism is separate from the AP examination for AP Physics C: Mechanics. Before 2006, test-takers paid only once and were given the choice of taking either one or two parts of the Physics C test.
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AP Physics C: Electricity and Magnetism
| 0.868815
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The mathematical abstraction of the statistics of coin flipping is described by means of the Bernoulli process; a single flip of a coin is a Bernoulli trial. In the study of statistics, coin-flipping plays the role of being an introductory example of the complexities of statistics. A commonly treated textbook topic is that of checking if a coin is fair.
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Coin-tossing problem
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A geometry: it is equipped with a metric and is flat. A topology: there is a notion of open sets.There are interfaces among these: Its order and, independently, its metric structure induce its topology. Its order and algebraic structure make it into an ordered field. Its algebraic structure and topology make it into a Lie group, a type of topological group.
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Mathematical structures
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The set of real numbers has several standard structures: An order: each number is either less or more than any other number. Algebraic structure: there are operations of multiplication and addition that make it into a field. A measure: intervals of the real line have a specific length, which can be extended to the Lebesgue measure on many of its subsets. A metric: there is a notion of distance between points.
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Mathematical structures
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In 1939, the French group with the pseudonym Nicolas Bourbaki saw structures as the root of mathematics. They first mentioned them in their "Fascicule" of Theory of Sets and expanded it into Chapter IV of the 1957 edition. They identified three mother structures: algebraic, topological, and order.
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Mathematical structures
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In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists. Sorting is also often useful for canonicalizing data and for producing human-readable output. Formally, the output of any sorting algorithm must satisfy two conditions: The output is in monotonic order (each element is no smaller/larger than the previous element, according to the required order). The output is a permutation (a reordering, yet retaining all of the original elements) of the input.For optimum efficiency, the input data should be stored in a data structure which allows random access rather than one that allows only sequential access.
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Sorting Algorithm
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Given three fields arranged in a tower, say K a subfield of L which is in turn a subfield of M, there is a simple relation between the degrees of the three extensions L/K, M/L and M/K: = ⋅ . {\displaystyle =\cdot .} In other words, the degree going from the "bottom" to the "top" field is just the product of the degrees going from the "bottom" to the "middle" and then from the "middle" to the "top". It is quite analogous to Lagrange's theorem in group theory, which relates the order of a group to the order and index of a subgroup — indeed Galois theory shows that this analogy is more than just a coincidence.
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Degree of an extension
| 0.867439
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In mathematics, more specifically field theory, the degree of a field extension is a rough measure of the "size" of the field extension. The concept plays an important role in many parts of mathematics, including algebra and number theory — indeed in any area where fields appear prominently.
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Degree of an extension
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An ideal constant-force spring is a spring for which the force it exerts over its range of motion is a constant, that is, it does not obey Hooke's law. In reality, "constant-force springs" do not provide a truly constant force and are constructed from materials which do obey Hooke's law. Generally constant-force springs are constructed as a rolled ribbon of spring steel such that the spring is in a rolled up form when relaxed. As the spring is unrolled, the material coming off the roll (un)bends from the radius of the roll into a straight line between the reel and the load. Because the material tension-stiffness of the straight section is orders of magnitude greater than the bending stiffness of the ribbon, the straight section does not stretch significantly, the restoring force comes primarily from the deformation of the portion of the ribbon near the roll. Because the geometry of that region remains nearly constant as the spring unrolls (with material coming off the roll joining the curved section, and material in the curved section joining the straight section), the resulting force is nearly constant.
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Constant-force spring
| 0.866986
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This series of steps continues for a specific number of cycles, as determined by user-defined instrument settings. The 3' blocking groups were originally conceived as either enzymatic or chemical reversal The chemical method has been the basis for the Solexa and Illumina machines. Sequencing by reversible terminator chemistry can be a four-colour cycle such as used by Illumina/Solexa, or a one-colour cycle such as used by Helicos BioSciences. Helicos BioSciences used “virtual Terminators”, which are unblocked terminators with a second nucleoside analogue that acts as an inhibitor. These terminators have the appropriate modifications for terminating or inhibiting groups so that DNA synthesis is terminated after a single base addition.
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Next-Generation Sequencing
| 0.86686
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In the theory of quadratic forms, the parabola is the graph of the quadratic form x2 (or other scalings), while the elliptic paraboloid is the graph of the positive-definite quadratic form x2 + y2 (or scalings), and the hyperbolic paraboloid is the graph of the indefinite quadratic form x2 − y2. Generalizations to more variables yield further such objects. The curves y = xp for other values of p are traditionally referred to as the higher parabolas and were originally treated implicitly, in the form xp = kyq for p and q both positive integers, in which form they are seen to be algebraic curves. These correspond to the explicit formula y = xp/q for a positive fractional power of x. Negative fractional powers correspond to the implicit equation xp yq = k and are traditionally referred to as higher hyperbolas. Analytically, x can also be raised to an irrational power (for positive values of x); the analytic properties are analogous to when x is raised to rational powers, but the resulting curve is no longer algebraic and cannot be analyzed by algebraic geometry.
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Parabola
| 0.865891
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If one replaces the real numbers by an arbitrary field, many geometric properties of the parabola y = x 2 {\displaystyle y=x^{2}} are still valid: A line intersects in at most two points. At any point ( x 0 , x 0 2 ) {\displaystyle (x_{0},x_{0}^{2})} the line y = 2 x 0 x − x 0 2 {\displaystyle y=2x_{0}x-x_{0}^{2}} is the tangent.Essentially new phenomena arise, if the field has characteristic 2 (that is, 1 + 1 = 0 {\displaystyle 1+1=0} ): the tangents are all parallel. In algebraic geometry, the parabola is generalized by the rational normal curves, which have coordinates (x, x2, x3, ..., xn); the standard parabola is the case n = 2, and the case n = 3 is known as the twisted cubic. A further generalization is given by the Veronese variety, when there is more than one input variable.
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Parabola
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Any parabola can be described in a suitable coordinate system by an equation y = a x 2 {\displaystyle y=ax^{2}} . Proof: straightforward calculation for the unit parabola y = x 2 {\displaystyle y=x^{2}} . Application: The 4-points property of a parabola can be used for the construction of point P 4 {\displaystyle P_{4}} , while P 1 , P 2 , P 3 {\displaystyle P_{1},P_{2},P_{3}} and Q 2 {\displaystyle Q_{2}} are given. Remark: the 4-points property of a parabola is an affine version of the 5-point degeneration of Pascal's theorem.
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Parabola
| 0.865891
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This can be done with calculus, or by using a line that is parallel to the axis of symmetry of the parabola and passes through the midpoint of the chord. The required point is where this line intersects the parabola. Then, using the formula given in Distance from a point to a line, calculate the perpendicular distance from this point to the chord. Multiply this by the length of the chord to get the area of the parallelogram, then by 2/3 to get the required enclosed area.
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Parabola
| 0.865891
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A theorem equivalent to this one, but different in details, was derived by Archimedes in the 3rd century BCE. He used the areas of triangles, rather than that of the parallelogram. See The Quadrature of the Parabola.
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Parabola
| 0.865891
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The above proofs of the reflective and tangent bisection properties use a line of calculus. Here a geometric proof is presented. In this diagram, F is the focus of the parabola, and T and U lie on its directrix. P is an arbitrary point on the parabola.
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Parabola
| 0.865891
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Let three tangents to a parabola form a triangle. Then Lambert's theorem states that the focus of the parabola lies on the circumcircle of the triangle. : Corollary 20 Tsukerman's converse to Lambert's theorem states that, given three lines that bound a triangle, if two of the lines are tangent to a parabola whose focus lies on the circumcircle of the triangle, then the third line is also tangent to the parabola.
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Parabola
| 0.865891
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Application: The 2-points–2-tangents property can be used for the construction of the tangent of a parabola at point P 2 {\displaystyle P_{2}} , if P 1 , P 2 {\displaystyle P_{1},P_{2}} and the tangent at P 1 {\displaystyle P_{1}} are given. Remark 1: The 2-points–2-tangents property of a parabola is an affine version of the 3-point degeneration of Pascal's theorem. Remark 2: The 2-points–2-tangents property should not be confused with the following property of a parabola, which also deals with 2 points and 2 tangents, but is not related to Pascal's theorem.
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Parabola
| 0.865891
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A short calculation shows: line Q 1 Q 2 {\displaystyle Q_{1}Q_{2}} has slope 2 x 0 {\displaystyle 2x_{0}} which is the slope of the tangent at point P 0 {\displaystyle P_{0}} . Application: The 3-points-1-tangent-property of a parabola can be used for the construction of the tangent at point P 0 {\displaystyle P_{0}} , while P 1 , P 2 , P 0 {\displaystyle P_{1},P_{2},P_{0}} are given. Remark: The 3-points-1-tangent-property of a parabola is an affine version of the 4-point-degeneration of Pascal's theorem.
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Parabola
| 0.865891
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At higher speeds, such as in ballistics, the shape is highly distorted and does not resemble a parabola. Another hypothetical situation in which parabolas might arise, according to the theories of physics described in the 17th and 18th centuries by Sir Isaac Newton, is in two-body orbits, for example, the path of a small planetoid or other object under the influence of the gravitation of the Sun. Parabolic orbits do not occur in nature; simple orbits most commonly resemble hyperbolas or ellipses.
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Parabola
| 0.865891
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In nature, approximations of parabolas and paraboloids are found in many diverse situations. The best-known instance of the parabola in the history of physics is the trajectory of a particle or body in motion under the influence of a uniform gravitational field without air resistance (for instance, a ball flying through the air, neglecting air friction). The parabolic trajectory of projectiles was discovered experimentally in the early 17th century by Galileo, who performed experiments with balls rolling on inclined planes. He also later proved this mathematically in his book Dialogue Concerning Two New Sciences.
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Parabola
| 0.865891
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The same effects occur with sound and other waves. This reflective property is the basis of many practical uses of parabolas. The parabola has many important applications, from a parabolic antenna or parabolic microphone to automobile headlight reflectors and the design of ballistic missiles. It is frequently used in physics, engineering, and many other areas.
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Parabola
| 0.865891
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Electrodynamic fields are electric fields which do change with time, for instance when charges are in motion. In this case, a magnetic field is produced in accordance with Ampère's circuital law (with Maxwell's addition), which, along with Maxwell's other equations, defines the magnetic field, B {\displaystyle \mathbf {B} } , in terms of its curl: where J {\displaystyle \mathbf {J} } is the current density, μ 0 {\displaystyle \mu _{0}} is the vacuum permeability, and ε 0 {\displaystyle \varepsilon _{0}} is the vacuum permittivity. That is, both electric currents (i.e. charges in uniform motion) and the (partial) time derivative of the electric field directly contributes to the magnetic field. In addition, the Maxwell–Faraday equation states These represent two of Maxwell's four equations and they intricately link the electric and magnetic fields together, resulting in the electromagnetic field. The equations represent a set of four coupled multi-dimensional partial differential equations which, when solved for a system, describe the combined behavior of the electromagnetic fields. In general, the force experienced by a test charge in an electromagnetic field is given by the Lorentz force law:
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Electrical field
| 0.86507
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In computer science, manual memory management refers to the usage of manual instructions by the programmer to identify and deallocate unused objects, or garbage. Up until the mid-1990s, the majority of programming languages used in industry supported manual memory management, though garbage collection has existed since 1959, when it was introduced with Lisp. Today, however, languages with garbage collection such as Java are increasingly popular and the languages Objective-C and Swift provide similar functionality through Automatic Reference Counting. The main manually managed languages still in widespread use today are C and C++ – see C dynamic memory allocation.
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Manual memory management
| 0.864882
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A graded quadratic algebra A is determined by a vector space of generators V = A1 and a subspace of homogeneous quadratic relations S ⊂ V ⊗ V (Polishchuk & Positselski 2005, p. 6). Thus A = T ( V ) / ⟨ S ⟩ {\displaystyle A=T(V)/\langle S\rangle } and inherits its grading from the tensor algebra T(V). If the subspace of relations is instead allowed to also contain inhomogeneous degree 2 elements, i.e. S ⊂ k ⊕ V ⊕ (V ⊗ V), this construction results in a filtered quadratic algebra. A graded quadratic algebra A as above admits a quadratic dual: the quadratic algebra generated by V* and with quadratic relations forming the orthogonal complement of S in V* ⊗ V*.
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Quadratic algebra
| 0.864868
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Tensor algebra, symmetric algebra and exterior algebra of a finite-dimensional vector space are graded quadratic (in fact, Koszul) algebras. Universal enveloping algebra of a finite-dimensional Lie algebra is a filtered quadratic algebra.
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Quadratic algebra
| 0.864868
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In mathematics, a quadratic algebra is a filtered algebra generated by degree one elements, with defining relations of degree 2. It was pointed out by Yuri Manin that such algebras play an important role in the theory of quantum groups. The most important class of graded quadratic algebras is Koszul algebras.
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Quadratic algebra
| 0.864868
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Note that there are 3 translation "windows", or reading frames, depending on where you start reading the code. Finally, use the table at Genetic code to translate the above into a structural formula as used in chemistry. This will give you the primary structure of the protein.
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Protein translation
| 0.864804
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In Systema Naturae, Linnaeus described the genera Volvox and Corallina, and a species of Acetabularia (as Madrepora), among the animals. In 1768, Samuel Gottlieb Gmelin (1744–1774) published the Historia Fucorum, the first work dedicated to marine algae and the first book on marine biology to use the then new binomial nomenclature of Linnaeus. It included elaborate illustrations of seaweed and marine algae on folded leaves.W.
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Algae
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Alginic acid, or alginate, is extracted from brown algae. Its uses range from gelling agents in food, to medical dressings. Alginic acid also has been used in the field of biotechnology as a biocompatible medium for cell encapsulation and cell immobilization. Molecular cuisine is also a user of the substance for its gelling properties, by which it becomes a delivery vehicle for flavours. Between 100,000 and 170,000 wet tons of Macrocystis are harvested annually in New Mexico for alginate extraction and abalone feed.
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Algae
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It developed over time to chromosomal analysis, then genetic marker analysis, and eventual genomic analysis. Identifying traits and their underlying genetics allowed for transferring useful genes and the traits they controlled from either wild or mutant plants to crop plants. Understanding and manipulating of plant genetics was in its heyday during the Green Revolution brought about by Norman Borlaug. During this time, the molecule of heredity, DNA, was also discovered, which allowed scientists to actually examine and manipulate genetic information directly.
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Plant genetics
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The strict requirements for producing hybrid seed led to the development of careful population and inbred line maintenance, keeping plants isolated and unable to out-cross, which produced plants that better allowed researchers to tease out different genetic concepts. The structure of these populations allowed scientist such a T. Dobzhansky, S. Wright, and R.A. Fisher to develop evolutionary biology concepts as well as explore speciation over time and the statistics underlying plant genetics.
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Plant genetics
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Castle discovered that while individual traits may segregate and change over time with selection, that when selection is stopped and environmental effects are taken into account, the genetic ratio stops changing and reach a sort of stasis, the foundation of Population Genetics. This was independently discovered by G. H. Hardy and W. Weinberg, which ultimately gave rise to the concept of Hardy–Weinberg equilibrium published in 1908.For a more thorough exploration of the history of population genetics, see History of Population Genetics by Bob Allard. Around this same time, genetic and plant breeding experiments in maize began.
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Plant genetics
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His discoveries, deduction of segregation ratios, and subsequent laws have not only been used in research to gain a better understanding of plant genetics, but also play a large role in plant breeding. Mendel's works along with the works of Charles Darwin and Alfred Wallace on selection provided the basis for much of genetics as a discipline.
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Mendel died in 1884. The significance of Mendel's work was not recognized until the turn of the 20th century. Its rediscovery prompted the foundation of modern genetics.
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Mendel's work tracked many phenotypic traits of pea plants, such as their height, flower color, and seed characteristics. Mendel showed that the inheritance of these traits follows two particular laws, which were later named after him. His seminal work on genetics, “Versuche über Pflanzen-Hybriden” (Experiments on Plant Hybrids), was published in 1866, but went almost entirely unnoticed until 1900 when prominent botanists in the UK, like Sir Gavin de Beer, recognized its importance and re-published an English translation.
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The earliest evidence of plant domestication found has been dated to 11,000 years before present in ancestral wheat. While initially selection may have happened unintentionally, it is very likely that by 5,000 years ago farmers had a basic understanding of heredity and inheritance, the foundation of genetics. This selection over time gave rise to new crop species and varieties that are the basis of the crops we grow, eat and research today. The field of plant genetics began with the work of Gregor Johann Mendel, who is often called the "father of genetics".
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Genetic modification has been the cause for much research into modern plant genetics, and has also led to the sequencing of many plant genomes. Today there are two predominant procedures of transforming genes in organisms: the "Gene gun" method and the Agrobacterium method.
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Arabidopsis thaliana, also known as thale cress, has been the model organism for the study of plant genetics. As Drosophila, a species of fruit fly, was to the understanding of early genetics, so has been A. thaliana to the understanding of plant genetics. It was the first plant to ever have its genome sequenced in the year 2000. It has a small genome, making the initial sequencing more attainable.
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In plant breeding, people create hybrids between plant species for economic and aesthetic reasons. For example, the yield of Corn has increased nearly five-fold in the past century due in part to the discovery and proliferation of hybrid corn varieties. Plant genetics can be used to predict which combination of plants may produce a plant with Hybrid vigor, or conversely many discoveries in Plant genetics have come from studying the effects of hybridization.
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Speciation can be easier in many plants due to unique genetic abilities, such as being well adapted to polyploidy. Plants are unique in that they are able to produce energy-dense carbohydrates via photosynthesis, a process which is achieved by use of chloroplasts. Chloroplasts, like the superficially similar mitochondria, possess their own DNA. Chloroplasts thus provide an additional reservoir for genes and genetic diversity, and an extra layer of genetic complexity not found in animals. The study of plant genetics has major economic impacts: many staple crops are genetically modified to increase yields, confer pest and disease resistance, provide resistance to herbicides, or to increase their nutritional value.
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Much of Mendel's work with plants still forms the basis for modern plant genetics. Plants, like all known organisms, use DNA to pass on their traits. Animal genetics often focuses on parentage and lineage, but this can sometimes be difficult in plant genetics due to the fact that plants can, unlike most animals, be self-fertile.
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Plant genetics is the study of genes, genetic variation, and heredity specifically in plants. It is generally considered a field of biology and botany, but intersects frequently with many other life sciences and is strongly linked with the study of information systems. Plant genetics is similar in many ways to animal genetics but differs in a few key areas. The discoverer of genetics was Gregor Mendel, a late 19th-century scientist and Augustinian friar.
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Arora, Sanjeev; Barak, Boaz (2009), Computational Complexity: A Modern Approach, Cambridge University Press, ISBN 978-0-521-42426-4, Zbl 1193.68112 Downey, Rod; Fellows, Michael (1999), Parameterized complexity, Monographs in Computer Science, Berlin, New York: Springer-Verlag, ISBN 9780387948836 Du, Ding-Zhu; Ko, Ker-I (2000), Theory of Computational Complexity, John Wiley & Sons, ISBN 978-0-471-34506-0 Garey, Michael R.; Johnson, David S. (1979), Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman, ISBN 0-7167-1045-5 Goldreich, Oded (2008), Computational Complexity: A Conceptual Perspective, Cambridge University Press van Leeuwen, Jan, ed. (1990), Handbook of theoretical computer science (vol.
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In the computer science subfield of algorithmic information theory, Chaitin's constant is the real number representing the probability that a randomly chosen Turing machine will halt, formed from a construction due to Argentine-American mathematician and computer scientist Gregory Chaitin. Chaitin's constant, though not being computable, has been proven to be transcendental and normal. Chaitin's constant is not universal, depending heavily on the numerical encoding used for Turing machines; however, its interesting properties are independent of the encoding.
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The square root of 2, often known as root 2, radical 2, or Pythagoras' constant, and written as √2, is the positive algebraic number that, when multiplied by itself, gives the number 2. It is more precisely called the principal square root of 2, to distinguish it from the negative number with the same property. Geometrically the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational.
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Secosteroids (Latin seco, "to cut") are a subclass of steroidal compounds resulting, biosynthetically or conceptually, from scission (cleavage) of parent steroid rings (generally one of the four). Major secosteroid subclasses are defined by the steroid carbon atoms where this scission has taken place. For instance, the prototypical secosteroid cholecalciferol, vitamin D3 (shown), is in the 9,10-secosteroid subclass and derives from the cleavage of carbon atoms C-9 and C-10 of the steroid B-ring; 5,6-secosteroids and 13,14-steroids are similar.Norsteroids (nor-, L. norma; "normal" in chemistry, indicating carbon removal) and homosteroids (homo-, Greek homos; "same", indicating carbon addition) are structural subclasses of steroids formed from biosynthetic steps. The former involves enzymic ring expansion-contraction reactions, and the latter is accomplished (biomimetically) or (more frequently) through ring closures of acyclic precursors with more (or fewer) ring atoms than the parent steroid framework.Combinations of these ring alterations are known in nature.
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The product of the prior and the likelihood, when normalized, results in a posterior probability distribution that incorporates all the information known to date. By Aumann's agreement theorem, Bayesian agents whose prior beliefs are similar will end up with similar posterior beliefs. However, sufficiently different priors can lead to different conclusions, regardless of how much information the agents share.
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Augustus De Morgan and George Boole improved the exposition of the theory. In 1906, Andrey Markov introduced the notion of Markov chains, which played an important role in stochastic processes theory and its applications. The modern theory of probability based on measure theory was developed by Andrey Kolmogorov in 1931.On the geometric side, contributors to The Educational Times included Miller, Crofton, McColl, Wolstenholme, Watson, and Artemas Martin. See integral geometry for more information.
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The objective wave function evolves deterministically but, according to the Copenhagen interpretation, it deals with probabilities of observing, the outcome being explained by a wave function collapse when an observation is made. However, the loss of determinism for the sake of instrumentalism did not meet with universal approval. Albert Einstein famously remarked in a letter to Max Born: "I am convinced that God does not play dice". Like Einstein, Erwin Schrödinger, who discovered the wave function, believed quantum mechanics is a statistical approximation of an underlying deterministic reality. In some modern interpretations of the statistical mechanics of measurement, quantum decoherence is invoked to account for the appearance of subjectively probabilistic experimental outcomes.
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Physicists face the same situation in the kinetic theory of gases, where the system, while deterministic in principle, is so complex (with the number of molecules typically the order of magnitude of the Avogadro constant 6.02×1023) that only a statistical description of its properties is feasible. Probability theory is required to describe quantum phenomena. A revolutionary discovery of early 20th century physics was the random character of all physical processes that occur at sub-atomic scales and are governed by the laws of quantum mechanics.
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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 1/2;} however, when taking a second ball, the probability of it being either a red ball or a blue ball depends on the ball previously taken. For example, if a red ball was taken, then the probability of picking a red ball again would be 1 / 3 , {\displaystyle 1/3,} since only 1 red and 2 blue balls would have been remaining. And if a blue ball was taken previously, the probability of taking a red ball will be 2 / 3. {\displaystyle 2/3.}
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The theory of behavioral finance emerged to describe the effect of such groupthink on pricing, on policy, and on peace and conflict.In addition to financial assessment, probability can be used to analyze trends in biology (e.g., disease spread) as well as ecology (e.g., biological Punnett squares). As with finance, risk assessment can be used as a statistical tool to calculate the likelihood of undesirable events occurring, and can assist with implementing protocols to avoid encountering such circumstances. Probability is used to design games of chance so that casinos can make a guaranteed profit, yet provide payouts to players that are frequent enough to encourage continued play.Another significant application of probability theory in everyday life is reliability. Many consumer products, such as automobiles and consumer electronics, use reliability theory in product design to reduce the probability of failure. Failure probability may influence a manufacturer's decisions on a product's warranty.The cache language model and other statistical language models that are used in natural language processing are also examples of applications of probability theory.
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An example of the use of probability theory in equity trading is the effect of the perceived probability of any widespread Middle East conflict on oil prices, which have ripple effects in the economy as a whole. An assessment by a commodity trader that a war is more likely can send that commodity's prices up or down, and signals other traders of that opinion. Accordingly, the probabilities are neither assessed independently nor necessarily rationally.
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Probability theory is applied in everyday life in risk assessment and modeling. The insurance industry and markets use actuarial science to determine pricing and make trading decisions. Governments apply probabilistic methods in environmental regulation, entitlement analysis, and financial regulation.
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Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These concepts have been given an axiomatic mathematical formalization in probability theory, which is used widely in areas of study such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy to, for example, draw inferences about the expected frequency of events. Probability theory is also used to describe the underlying mechanics and regularities of complex systems.
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In Cox's theorem, probability is taken as a primitive (i.e., not further analyzed), and the emphasis is on constructing a consistent assignment of probability values to propositions. In both cases, the laws of probability are the same, except for technical details. There are other methods for quantifying uncertainty, such as the Dempster–Shafer theory or possibility theory, but those are essentially different and not compatible with the usually-understood laws of probability.
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In probability theory and applications, Bayes' rule relates the odds of event A 1 {\displaystyle A_{1}} to event A 2 , {\displaystyle A_{2},} before (prior to) and after (posterior to) conditioning on another event B . {\displaystyle B.} The odds on A 1 {\displaystyle A_{1}} to event A 2 {\displaystyle A_{2}} is simply the ratio of the probabilities of the two events.
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In quantum mechanics, the measurement problem is the problem of how, or whether, wave function collapse occurs. The inability to observe such a collapse directly has given rise to different interpretations of quantum mechanics and poses a key set of questions that each interpretation must answer. The wave function in quantum mechanics evolves deterministically according to the Schrödinger equation as a linear superposition of different states. However, actual measurements always find the physical system in a definite state.
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The heuristic method In optimization problems, heuristic algorithms can be used to find a solution close to the optimal solution in cases where finding the optimal solution is impractical. These algorithms work by getting closer and closer to the optimal solution as they progress. In principle, if run for an infinite amount of time, they will find the optimal solution.
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For some problems they can find the optimal solution while for others they stop at local optima, that is, at solutions that cannot be improved by the algorithm but are not optimum. The most popular use of greedy algorithms is for finding the minimal spanning tree where finding the optimal solution is possible with this method. Huffman Tree, Kruskal, Prim, Sollin are greedy algorithms that can solve this optimization problem.
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For optimization problems there is a more specific classification of algorithms; an algorithm for such problems may fall into one or more of the general categories described above as well as into one of the following: Linear programming When searching for optimal solutions to a linear function bound to linear equality and inequality constraints, the constraints of the problem can be used directly in producing the optimal solutions. There are algorithms that can solve any problem in this category, such as the popular simplex algorithm. Problems that can be solved with linear programming include the maximum flow problem for directed graphs. If a problem additionally requires that one or more of the unknowns must be an integer then it is classified in integer programming.
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In rapid succession the following appeared: Alonzo Church, Stephen Kleene and J.B. Rosser's λ-calculus a finely honed definition of "general recursion" from the work of Gödel acting on suggestions of Jacques Herbrand (cf. Gödel's Princeton lectures of 1934) and subsequent simplifications by Kleene. Church's proof that the Entscheidungsproblem was unsolvable, Emil Post's definition of effective calculability as a worker mindlessly following a list of instructions to move left or right through a sequence of rooms and while there either mark or erase a paper or observe the paper and make a yes-no decision about the next instruction. Alan Turing's proof of that the Entscheidungsproblem was unsolvable by use of his "a- machine"—in effect almost identical to Post's "formulation", J. Barkley Rosser's definition of "effective method" in terms of "a machine". Kleene's proposal of a precursor to "Church thesis" that he called "Thesis I", and a few years later Kleene's renaming his Thesis "Church's Thesis" and proposing "Turing's Thesis".
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The field of metagenomics involves identification of organisms present in a body of water, sewage, dirt, debris filtered from the air, or swab samples from organisms. Knowing which organisms are present in a particular environment is critical to research in ecology, epidemiology, microbiology, and other fields. Sequencing enables researchers to determine which types of microbes may be present in a microbiome, for example.
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Louis Georges Gouy in 1910 and David Leonard Chapman in 1913 both observed that capacitance was not a constant and that it depended on the applied potential and the ionic concentration. The "Gouy–Chapman model" made significant improvements by introducing a diffuse model of the DL. In this model, the charge distribution of ions as a function of distance from the metal surface allows Maxwell–Boltzmann statistics to be applied. Thus the electric potential decreases exponentially away from the surface of the fluid bulk.Gouy-Chapman layers may bear special relevance in bioelectrochemistry.
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For example, the color temperature of an A0V star is about 15000 K compared to an effective temperature of about 9500 K.For most applications in astronomy (e.g., to place a star on the HR diagram or to determine the temperature of a model flux fitting an observed spectrum) the effective temperature is the quantity of interest. Various color-effective temperature relations exist in the literature. There relations also have smaller dependencies on other stellar parameters, such as the stellar metallicity and surface gravity
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In astronomy, the color temperature is defined by the local slope of the SPD at a given wavelength, or, in practice, a wavelength range. Given, for example, the color magnitudes B and V which are calibrated to be equal for an A0V star (e.g. Vega), the stellar color temperature T C {\displaystyle T_{C}} is given by the temperature for which the color index B − V {\displaystyle B-V} of a black-body radiator fits the stellar one. Besides the B − V {\displaystyle B-V} , other color indices can be used as well. The color temperature (as well as the correlated color temperature defined above) may differ largely from the effective temperature given by the radiative flux of the stellar surface.
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Color temperature has important applications in lighting, photography, videography, publishing, manufacturing, astrophysics and other fields. In practice, color temperature is most meaningful for light sources that correspond somewhat closely to the color of some black body, i.e., light in a range going from red to orange to yellow to white to bluish white. Although the concept of correlated color temperature extends the definition to any visible light, the color temperature of a green or a purple light rarely is useful information.
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Most research in the area of memory models revolves around: Designing a memory model that allows a maximal degree of freedom for compiler optimizations while still giving sufficient guarantees about race-free and (perhaps more importantly) race-containing programs. Proving program optimizations that are correct with respect to such a memory model.The Java Memory Model was the first attempt to provide a comprehensive threading memory model for a popular programming language. After it was established that threads could not be implemented safely as a library without placing certain restrictions on the implementation and, in particular, that the C and C++ standards (C99 and C++03) lacked necessary restrictions, the C++ threading subcommittee set to work on suitable memory model; in 2005, they submitted C working document n1131 to get the C Committee on board with their efforts. The final revision of the proposed memory model, C++ n2429, was accepted into the C++ draft standard at the October 2007 meeting in Kona. The memory model was then included in the next C++ and C standards, C++11 and C11.
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The memory model stipulates that changes to the values of shared variables only need to be made visible to other threads when such a synchronization barrier is reached. Moreover, the entire notion of a race condition is defined over the order of operations with respect to these memory barriers.These semantics then give optimizing compilers a higher degree of freedom when applying optimizations: the compiler needs to make sure only that the values of (potentially shared) variables at synchronization barriers are guaranteed to be the same in both the optimized and unoptimized code. In particular, reordering statements in a block of code that contains no synchronization barrier is assumed to be safe by the compiler.
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Or for some compilers assume no multi-threaded execution (so better optimized code can be produced), which can lead to optimizations that are incompatible with multi-threading - these can often lead to subtle bugs, that don't show up in early testing. Modern programming languages like Java therefore implement a memory model. The memory model specifies synchronization barriers that are established via special, well-defined synchronization operations such as acquiring a lock by entering a synchronized block or method.
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A memory model allows a compiler to perform many important optimizations. Compiler optimizations like loop fusion move statements in the program, which can influence the order of read and write operations of potentially shared variables. Changes in the ordering of reads and writes can cause race conditions. Without a memory model, a compiler is not allowed to apply such optimizations to multi-threaded programs in general, or only in special cases.
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Using protein markers, gene-linkage studies were able to map the mutation to chromosome 7. Chromosome walking and chromosome jumping techniques were then used to identify and sequence the gene. In 1989, Lap-Chee Tsui led a team of researchers at the Hospital for Sick Children in Toronto that discovered the gene responsible for CF. CF represents a classic example of how a human genetic disorder was elucidated strictly by the process of forward genetics.
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She was the first to describe the characteristic cystic fibrosis of the pancreas and to correlate it with the lung and intestinal disease prominent in CF. She also first hypothesized that CF was a recessive disease and first used pancreatic enzyme replacement to treat affected children. In 1952, Paul di Sant'Agnese discovered abnormalities in sweat electrolytes; a sweat test was developed and improved over the next decade.The first linkage between CF and another marker (paraoxonase) was found in 1985 by Hans Eiberg, indicating that only one locus exists for CF. In 1988, the first mutation for CF, ΔF508, was discovered by Francis Collins, Lap-Chee Tsui, and John R. Riordan on the seventh chromosome. Subsequent research has found over 1,000 different mutations that cause CF.Because mutations in the CFTR gene are typically small, classical genetics techniques had been unable to accurately pinpoint the mutated gene.
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A*: special case of best-first search that uses heuristics to improve speed B*: a best-first graph search algorithm that finds the least-cost path from a given initial node to any goal node (out of one or more possible goals) Backtracking: abandons partial solutions when they are found not to satisfy a complete solution Beam search: is a heuristic search algorithm that is an optimization of best-first search that reduces its memory requirement Beam stack search: integrates backtracking with beam search Best-first search: traverses a graph in the order of likely importance using a priority queue Bidirectional search: find the shortest path from an initial vertex to a goal vertex in a directed graph Breadth-first search: traverses a graph level by level Brute-force search: an exhaustive and reliable search method, but computationally inefficient in many applications D*: an incremental heuristic search algorithm Depth-first search: traverses a graph branch by branch Dijkstra's algorithm: a special case of A* for which no heuristic function is used General Problem Solver: a seminal theorem-proving algorithm intended to work as a universal problem solver machine. Iterative deepening depth-first search (IDDFS): a state space search strategy Jump point search: an optimization to A* which may reduce computation time by an order of magnitude using further heuristics Lexicographic breadth-first search (also known as Lex-BFS): a linear time algorithm for ordering the vertices of a graph Uniform-cost search: a tree search that finds the lowest-cost route where costs vary SSS*: state space search traversing a game tree in a best-first fashion similar to that of the A* search algorithm F*: special algorithm to merge the two arrays
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List of algorithms
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