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100 | Euler method Backward Euler method Trapezoidal rule (differential equations) Linear multistep methods Runge–Kutta methods Euler integration Multigrid methods (MG methods), a group of algorithms for solving differential equations using a hierarchy of discretizations Partial differential equation: Finite difference metho... | List of algorithms | 0.860834 |
101 | This method is an upgraded modification to combinatorial probe anchor ligation technology (cPAL) described by Complete Genomics which has since become part of Chinese genomics company BGI in 2013. The two companies have refined the technology to allow for longer read lengths, reaction time reductions and faster time to... | Genomic sequencing | 0.860495 |
102 | Sometimes, a set is endowed with more than one feature simultaneously, which allows mathematicians to study the interaction between the different structures more richly. For example, an ordering imposes a rigid form, shape, or topology on the set, and if a set has both a topology feature and a group feature, such that ... | Mathematical structure | 0.860057 |
103 | In mathematics, a structure is a set endowed with some additional features on the set (e.g. an operation, relation, metric, or topology). Often, the additional features are attached or related to the set, so as to provide it with some additional meaning or significance. A partial list of possible structures are measure... | Mathematical structure | 0.860057 |
104 | In statistics, the gradient of the least-squares regression best-fitting line for a given sample of data may be written as: m = r s y s x {\displaystyle m={\frac {rs_{y}}{s_{x}}}} ,This quantity m is called as the regression slope for the line y = m x + c {\displaystyle y=mx+c} . The quantity r {\displaystyle r} is Pea... | Slope of a line | 0.860053 |
105 | By moving the two points closer together so that Δy and Δx decrease, the secant line more closely approximates a tangent line to the curve, and as such the slope of the secant approaches that of the tangent. Using differential calculus, we can determine the limit, or the value that Δy/Δx approaches as Δy and Δx get clo... | Slope of a line | 0.860053 |
106 | For a line, the secant between any two points is the line itself, but this is not the case for any other type of curve. For example, the slope of the secant intersecting y = x2 at (0,0) and (3,9) is 3. (The slope of the tangent at x = 3⁄2 is also 3 − a consequence of the mean value theorem.) | Slope of a line | 0.860053 |
107 | The concept of a slope is central to differential calculus. For non-linear functions, the rate of change varies along the curve. The derivative of the function at a point is the slope of the line tangent to the curve at the point, and is thus equal to the rate of change of the function at that point. If we let Δx and Δ... | Slope of a line | 0.860053 |
108 | When the curve is given by a series of points in a diagram or in a list of the coordinates of points, the slope may be calculated not at a point but between any two given points. When the curve is given as a continuous function, perhaps as an algebraic expression, then the differential calculus provides rules giving a ... | Slope of a line | 0.860053 |
109 | The concept of slope applies directly to grades or gradients in geography and civil engineering. Through trigonometry, the slope m of a line is related to its angle of inclination θ by the tangent function m = tan ( θ ) {\displaystyle m=\tan(\theta )} Thus, a 45° rising line has a slope of +1 and a 45° falling line h... | Slope of a line | 0.860053 |
110 | Intended to be equivalent to an introductory college course in mechanics for physics or engineering majors, the course modules are: Kinematics Newton's laws of motion Work, energy and power Systems of particles and linear momentum Circular motion and rotation Oscillations and gravitation.Methods of calculus are used wh... | AP Physics C: Mechanics | 0.859946 |
111 | Additionally, tables of equations, information, and constants are provided for all portions of the exam as of 2015. This and AP Physics C: Electricity and Magnetism are the shortest AP exams, with total testing time of 90 minutes.The topics covered by the exam are as follows: As a result of the 2019-20 coronavirus pand... | AP Physics C: Mechanics | 0.859946 |
112 | Advanced Placement (AP) Physics C: Mechanics (also known as AP Mechanics) is an introductory physics course administered by the College Board as part of its Advanced Placement program. It is intended to proxy a one-semester calculus-based university course in mechanics. The content of Physics C: Mechanics overlaps with... | AP Physics C: Mechanics | 0.859946 |
113 | The AP examination for AP Physics C: Mechanics is separate from the AP examination for AP Physics C: Electricity and Magnetism. Before 2006, test-takers paid only once and were given the choice of taking either one or two parts of the Physics C test. | AP Physics C: Mechanics | 0.859946 |
114 | telephone monopoly, presented its Bellboy radio paging system at the Seattle World's Fair. Bellboy was the first commercial system for personal paging. It also marked one of the first consumer applications of the transistor (invented by Bell Labs in 1947), for which three Bell Labs inventors received a Nobel Prize in P... | Paging system | 0.859617 |
115 | When unspecified, constants indicate classes of similar objects, commonly functions, all equal up to a constant—technically speaking, this may be viewed as 'similarity up to a constant'. Such constants appear frequently when dealing with integrals and differential equations. Though unspecified, they have a specific val... | Mathematical constant | 0.858972 |
116 | Kepler proved that it is the limit of the ratio of consecutive Fibonacci numbers. The golden ratio has the slowest convergence of any irrational number. It is, for that reason, one of the worst cases of Lagrange's approximation theorem and it is an extremal case of the Hurwitz inequality for Diophantine approximations. | Mathematical constant | 0.858972 |
117 | The number φ, also called the golden ratio, turns up frequently in geometry, particularly in figures with pentagonal symmetry. Indeed, the length of a regular pentagon's diagonal is φ times its side. The vertices of a regular icosahedron are those of three mutually orthogonal golden rectangles. Also, it appears in the ... | Mathematical constant | 0.858972 |
118 | In a similar fashion, constants appear in the solutions to differential equations where not enough initial values or boundary conditions are given. For example, the ordinary differential equation y' = y(x) has solution Cex where C is an arbitrary constant. When dealing with partial differential equations, the constants... | Mathematical constant | 0.858972 |
119 | A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a special symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. Constants arise in many areas of mathematics, with constants such as e an... | Mathematical constant | 0.858972 |
120 | The Euler–Mascheroni constant is defined as the following limit: γ = lim n → ∞ ( ( ∑ k = 1 n 1 k ) − ln n ) {\displaystyle {\begin{aligned}\gamma &=\lim _{n\to \infty }\left(\left(\sum _{k=1}^{n}{\frac {1}{k}}\right)-\ln n\right)\\\end{aligned}}} The Euler–Mascheroni constant appears in Mertens' third theorem and has... | Mathematical constant | 0.858972 |
121 | The term "imaginary" was coined because there is no (real) number having a negative square. There are in fact two complex square roots of −1, namely i and −i, just as there are two complex square roots of every other real number (except zero, which has one double square root). In contexts where the symbol i is ambiguou... | Mathematical constant | 0.858972 |
122 | Euler's number e, also known as the exponential growth constant, appears in many areas of mathematics, and one possible definition of it is the value of the following expression: e = lim n → ∞ ( 1 + 1 n ) n {\displaystyle e=\lim _{n\to \infty }\left(1+{\frac {1}{n}}\right)^{n}} The constant e is intrinsically related t... | Mathematical constant | 0.858972 |
123 | Abbreviations used: R – Rational number, I – Irrational number (may be algebraic or transcendental), A – Algebraic number (irrational), T – Transcendental number Gen – General, NuT – Number theory, ChT – Chaos theory, Com – Combinatorics, Inf – Information theory, Ana – Mathematical analysis | Mathematical constant | 0.858972 |
124 | The constant π (pi) has a natural definition in Euclidean geometry as the ratio between the circumference and diameter of a circle. It may be found in many other places in mathematics: for example, the Gaussian integral, the complex roots of unity, and Cauchy distributions in probability. However, its ubiquity is not l... | Mathematical constant | 0.858972 |
125 | In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers) and providing an output (which may also be a number). A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variab... | Response variable | 0.858803 |
126 | Although bubble sort is one of the simplest sorting algorithms to understand and implement, its O(n2) complexity means that its efficiency decreases dramatically on lists of more than a small number of elements. Even among simple O(n2) sorting algorithms, algorithms like insertion sort are usually considerably more eff... | Bubble Sort | 0.858795 |
127 | Euclidean geometry has two fundamental types of measurements: angle and distance. The angle scale is absolute, and Euclid uses the right angle as his basic unit, so that, for example, a 45-degree angle would be referred to as half of a right angle. The distance scale is relative; one arbitrarily picks a line segment wi... | 2D geometry | 0.85879 |
128 | Angle bisector theorem Butterfly theorem Ceva's theorem Heron's formula Menelaus' theorem Nine-point circle Pythagorean theorem | 2D geometry | 0.85879 |
129 | In recent years, multiple websites that maintain lists of conceptual questions have been created by instructors for various disciplines. Some books on physics provide many examples of conceptual questions as well.Multiple conceptual questions can be assembled into a concept inventory to test the working knowledge of st... | Conceptual question | 0.85854 |
130 | Conceptual problems are often formulated as multiple-choice questions, making them easy to use during in-class discussions, particularly when utilizing active learning, peer instruction, and audience response. An example of a conceptual question in undergraduate thermodynamics is provided below: During adiabatic expans... | Conceptual question | 0.85854 |
131 | Algorithm selection is not limited to single domains but can be applied to any kind of algorithm if the above requirements are satisfied. Application domains include: hard combinatorial problems: SAT, Mixed Integer Programming, CSP, AI Planning, TSP, MAXSAT, QBF and Answer Set Programming combinatorial auctions in mach... | Algorithm selection | 0.858412 |
132 | We distinguish between two kinds of features: Static features are in most cases some counts and statistics (e.g., clauses-to-variables ratio in SAT). These features ranges from very cheap features (e.g. number of variables) to very complex features (e.g., statistics about variable-clause graphs). Probing features (some... | Algorithm selection | 0.858412 |
133 | In machine learning, algorithm selection is better known as meta-learning. The portfolio of algorithms consists of machine learning algorithms (e.g., Random Forest, SVM, DNN), the instances are data sets and the cost metric is for example the error rate. So, the goal is to predict which machine learning algorithm will ... | Algorithm selection | 0.858412 |
134 | The algorithm selection problem is mainly solved with machine learning techniques. By representing the problem instances by numerical features f {\displaystyle f} , algorithm selection can be seen as a multi-class classification problem by learning a mapping f i ↦ A {\displaystyle f_{i}\mapsto {\mathcal {A}}} for a giv... | Algorithm selection | 0.858412 |
135 | This method can be used to recombine structural elements or entire protein domains. This method is based on phosphorothioate chemistry which allows the specific cleavage of phosphorothiodiester bonds. The first step in the process begins with amplification of fragments that need to be recombined along with the vector b... | Protein engineering | 0.858274 |
136 | Computing methods have been used to design a protein with a novel fold, named Top7, and sensors for unnatural molecules. The engineering of fusion proteins has yielded rilonacept, a pharmaceutical that has secured Food and Drug Administration (FDA) approval for treating cryopyrin-associated periodic syndrome. Another c... | Protein engineering | 0.858274 |
137 | In Euclidean geometry, a plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space R 3 {\displaystyle \mathbb {R} ^{3}} . A prototypical example is one of a room's walls, infinitely extended and assumed infinitesimal thin. While a pair of rea... | Plane equation | 0.857835 |
138 | Euclid set forth the first great landmark of mathematical thought, an axiomatic treatment of geometry. He selected a small core of undefined terms (called common notions) and postulates (or axioms) which he then used to prove various geometrical statements. Although the plane in its modern sense is not directly given a... | Plane equation | 0.857835 |
139 | These restrictions were relaxed by Aiken et al.This extended lambda calculus was intended to serve as a provably memory-safe intermediate representation for compiling Standard ML programs into machine code, but building a translator that would produce good results on large programs faced a number of practical limitatio... | Region-based memory management | 0.857812 |
140 | In 1994, this work was generalized in a seminal work by Tofte and Talpin to support type polymorphism and higher-order functions in Standard ML, a functional programming language, using a different algorithm based on type inference and the theoretical concepts of polymorphic region types and the region calculus. Their ... | Region-based memory management | 0.857812 |
141 | Algorithms were also used in Babylonian astronomy. Babylonian clay tablets describe and employ algorithmic procedures to compute the time and place of significant astronomical events.Algorithms for arithmetic are also found in ancient Egyptian mathematics, dating back to the Rhind Mathematical Papyrus c. 1550 BC. | Algorithm | 0.85781 |
142 | Muhammad ibn Mūsā al-Khwārizmī, a Persian mathematician, wrote the Al-jabr in the 9th century. The terms "algorism" and "algorithm" are derived from the name al-Khwārizmī, while the term "algebra" is derived from the book Al-jabr. In Europe, the word "algorithm" was originally used to refer to the sets of rules and tec... | Algorithm | 0.85781 |
143 | Plant breeding is the science of changing the traits of plants in order to produce desired characteristics. It has been used to improve the quality of nutrition in products for humans and animals. The goals of plant breeding are to produce crop varieties that boast unique and superior traits for a variety of applicatio... | Plant breeding | 0.857804 |
144 | Improvements in nutritional value for forage crops from the use of analytical chemistry and rumen fermentation technology have been recorded since 1960; this science and technology gave breeders the ability to screen thousands of samples within a small amount of time, meaning breeders could identify a high performing h... | Plant breeding | 0.857804 |
145 | Cereal Genomics. Methods in Molecular Biology. Vol. | Plant breeding | 0.857804 |
146 | ; Spillane, C. (1999) Biotechnology assisted participatory plant breeding: Complement or contradiction? CGIAR Program on Participatory Research and Gender Analysis, Working Document No.4, CIAT: Cali. | Plant breeding | 0.857804 |
147 | (ISBN 9781439802427), CRC Press, Boca Raton, FL, USA, pp 584 Schlegel, Rolf (2007) Concise Encyclopedia of Crop Improvement: Institutions, Persons, Theories, Methods, and Histories (ISBN 9781560221463), CRC Press, Boca Raton, FL, USA, pp 423 Schlegel, Rolf (2014) Dictionary of Plant Breeding, 2nd ed., (ISBN 978-1439802... | Plant breeding | 0.857804 |
148 | In molecular biology, an actomyosin contractile ring is a prominent structure during cytokinesis. It forms perpendicular to the axis of the spindle apparatus towards the end of telophase, in which sister chromatids are identically separated at the opposite sides of the spindle forming nuclei (Figure 1). The actomyosin ... | Actomyosin ring | 0.857732 |
149 | In mathematics, a quadratic-linear algebra is an algebra over a field with a presentation such that all relations are sums of monomials of degrees 1 or 2 in the generators. They were introduced by Polishchuk and Positselski (2005, p.101). An example is the universal enveloping algebra of a Lie algebra, with generators ... | Quadratic-linear algebra | 0.857728 |
150 | In computer science, a search algorithm is an algorithm designed to solve a search problem. Search algorithms work to retrieve information stored within particular data structure, or calculated in the search space of a problem domain, with either discrete or continuous values. Although search engines use search algorit... | Search algorithms | 0.857714 |
151 | Specific applications of search algorithms include: Problems in combinatorial optimization, such as: The vehicle routing problem, a form of shortest path problem The knapsack problem: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total wei... | Search algorithms | 0.857714 |
152 | Protein structure prediction is the inference of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of its folding and its secondary and tertiary structure from its primary structure. Structure prediction is fundamentally different from the inverse problem of protein desig... | Protein chemistry | 0.85758 |
153 | For example, they could be used to identify and destroy cancer cells. Molecular nanotechnology is a speculative subfield of nanotechnology regarding the possibility of engineering molecular assemblers, biological machines which could re-order matter at a molecular or atomic scale. Nanomedicine would make use of these n... | Protein chemistry | 0.85758 |
154 | Molecular biophysics is a rapidly evolving interdisciplinary area of research that combines concepts in physics, chemistry, engineering, mathematics and biology. It seeks to understand biomolecular systems and explain biological function in terms of molecular structure, structural organization, and dynamic behaviour at... | Protein chemistry | 0.85758 |
155 | Computational biology involves the development and application of data-analytical and theoretical methods, mathematical modeling and computational simulation techniques to the study of biological, ecological, behavioral, and social systems. The field is broadly defined and includes foundations in biology, applied mathe... | Protein chemistry | 0.85758 |
156 | Molecular biophysics typically addresses biological questions similar to those in biochemistry and molecular biology, seeking to find the physical underpinnings of biomolecular phenomena. Scientists in this field conduct research concerned with understanding the interactions between the various systems of a cell, inclu... | Protein chemistry | 0.85758 |
157 | In graph theory, Graph equations are equations in which the unknowns are graphs. One of the central questions of graph theory concerns the notion of isomorphism. We ask: When are two graphs the same? (i.e., graph isomorphism) The graphs in question may be expressed differently in terms of graph equations.What are the g... | Graph equation | 0.857529 |
158 | The table below summarizes how algebraic expressions compare with several other types of mathematical expressions by the type of elements they may contain, according to common but not universal conventions. A rational algebraic expression (or rational expression) is an algebraic expression that can be written as a quot... | Algebraic expression | 0.857402 |
159 | Usually, π is constructed as a geometric relationship, and the definition of e requires an infinite number of algebraic operations. A rational expression is an expression that may be rewritten to a rational fraction by using the properties of the arithmetic operations (commutative properties and associative properties ... | Algebraic expression | 0.857402 |
160 | In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). For example, 3x2 − 2xy + c is an algebraic expression. Since taking th... | Algebraic expression | 0.857402 |
161 | In 1658, in the first edition of The New World of English Words, it says: Algorithme, (a word compounded of Arabick and Spanish,) the art of reckoning by Cyphers. In 1706, in the sixth edition of The New World of English Words, it says: Algorithm, the Art of computing or reckoning by numbers, which contains the five pr... | Algorithmic problem | 0.857278 |
162 | Total weight that can be carried is no more than some fixed number X. So, the solution must consider weights of items as well as their value. Quantum algorithm They run on a realistic model of quantum computation. The term is usually used for those algorithms which seem inherently quantum, or use some essential feature... | Algorithmic problem | 0.857278 |
163 | In mathematics and computer science, an algorithm ( ) is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to d... | Algorithmic problem | 0.857278 |
164 | In digital electronics and computer science (fields of applied logic engineering and mathematics), truth tables can be used to reduce basic boolean operations to simple correlations of inputs to outputs, without the use of logic gates or code. For example, a binary addition can be represented with the truth table: wher... | Truth tables | 0.857206 |
165 | This may be due to a lack of mathematical knowledge; some problems were only solved after centuries of effort. But this also reflects that, in general, no such method can exist: some problems are known to be unsolvable by an algorithm, such as Hilbert's tenth problem, which was proved unsolvable in 1970. For several cl... | Equation solving | 0.857109 |
166 | Equations involving linear or simple rational functions of a single real-valued unknown, say x, such as 8 x + 7 = 4 x + 35 or 4 x + 9 3 x + 4 = 2 , {\displaystyle 8x+7=4x+35\quad {\text{or}}\quad {\frac {4x+9}{3x+4}}=2\,,} can be solved using the methods of elementary algebra. | Equation solving | 0.857109 |
167 | The most common type of equation is a polynomial equation (commonly called also an algebraic equation) in which the two sides are polynomials. The sides of a polynomial equation contain one or more terms. | Mathematical equations | 0.85657 |
168 | An algebraic number is a number that is a solution of a non-zero polynomial equation in one variable with rational coefficients (or equivalently — by clearing denominators — with integer coefficients). Numbers such as π that are not algebraic are said to be transcendental. Almost all real and complex numbers are transc... | Mathematical equations | 0.85657 |
169 | A parametric equation for a curve expresses the coordinates of the points of the curve as functions of a variable, called a parameter. For example, x = cos t y = sin t {\displaystyle {\begin{aligned}x&=\cos t\\y&=\sin t\end{aligned}}} are parametric equations for the unit circle, where t is the parameter. Together,... | Mathematical equations | 0.85657 |
170 | In pure mathematics, differential equations are studied from several different perspectives, mostly concerned with their solutions — the set of functions that satisfy the equation. Only the simplest differential equations are solvable by explicit formulas; however, some properties of solutions of a given differential e... | Mathematical equations | 0.85657 |
171 | A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. They are solved by finding an expression for... | Mathematical equations | 0.85657 |
172 | The smallest and most basic number field is the field Q {\displaystyle \mathbb {Q} } of rational numbers. Many properties of general number fields are modeled after the properties of Q {\displaystyle \mathbb {Q} } . At the same time, many other properties of algebraic number fields are substantially different from the ... | Degree of a number field | 0.856411 |
173 | Both types of functions encode the arithmetic behavior of Q {\displaystyle \mathbb {Q} } and K {\displaystyle K} , respectively. For example, Dirichlet's theorem asserts that in any arithmetic progression a , a + m , a + 2 m , … {\displaystyle a,a+m,a+2m,\ldots } with coprime a {\displaystyle a} and m {\displaystyle m}... | Degree of a number field | 0.856411 |
174 | An integral basis for a number field K {\displaystyle K} of degree n {\displaystyle n} is a set B = {b1, …, bn}of n algebraic integers in K {\displaystyle K} such that every element of the ring of integers O K {\displaystyle {\mathcal {O}}_{K}} of K {\displaystyle K} can be written uniquely as a Z-linear combination of... | Degree of a number field | 0.856411 |
175 | In the United Kingdom, the original boxes (prior to the introduction of the Happy Meal-sized nugget boxes) were of 6, 9, and 20 nuggets. According to Schur's theorem, since 6, 9, and 20 are (setwise) relatively prime, any sufficiently large integer can be expressed as a (non-negative, integer) linear combination of the... | Coin problem | 0.856384 |
176 | One special case of the coin problem is sometimes also referred to as the McNugget numbers. The McNuggets version of the coin problem was introduced by Henri Picciotto, who placed it as a puzzle in Games Magazine in 1987, and included it in his algebra textbook co-authored with Anita Wah. Picciotto thought of the appli... | Coin problem | 0.856384 |
177 | Reasons for this may be that silicon is less versatile than carbon in forming compounds, that the compounds formed by silicon are unstable, and that it blocks the flow of heat.Even so, biogenic silica is used by some Earth life, such as the silicate skeletal structure of diatoms. According to the clay hypothesis of A. ... | Hypothetical types of biochemistry | 0.856269 |
178 | This may suggest a greater variety of complex carbon compounds throughout the cosmos, providing less of a foundation on which to build silicon-based biologies, at least under the conditions prevalent on the surface of planets. Also, even though Earth and other terrestrial planets are exceptionally silicon-rich and carb... | Hypothetical types of biochemistry | 0.856269 |
179 | Silicon, on the other hand, interacts with very few other types of atoms. Moreover, where it does interact with other atoms, silicon creates molecules that have been described as "monotonous compared with the combinatorial universe of organic macromolecules". This is because silicon atoms are much bigger, having a larg... | Hypothetical types of biochemistry | 0.856269 |
180 | Silicon dioxide, also known as silica and quartz, is very abundant in the universe and has a large temperature range where it is liquid. However, its melting point is 1,600 to 1,725 °C (2,912 to 3,137 °F), so it would be impossible to make organic compounds in that temperature, because all of them would decompose. Sili... | Hypothetical types of biochemistry | 0.856269 |
181 | An algorithm is said to run in sub-linear time (often spelled sublinear time) if T ( n ) = o ( n ) {\displaystyle T(n)=o(n)} . In particular this includes algorithms with the time complexities defined above. The specific term sublinear time algorithm commonly refers to randomized algorithms that sample a small fraction... | Polynomial time | 0.85612 |
182 | Whatever name is applied, it deals with the ways in which plants respond to their environment and so overlaps with the field of ecology. Environmental physiologists examine plant response to physical factors such as radiation (including light and ultraviolet radiation), temperature, fire, and wind. | Plant Physiology | 0.856078 |
183 | The ripening of fruit and loss of leaves in the winter are controlled in part by the production of the gas ethylene by the plant. Finally, plant physiology includes the study of plant response to environmental conditions and their variation, a field known as environmental physiology. Stress from water loss, changes in ... | Plant Physiology | 0.856078 |
184 | Major subdisciplines of plant physiology include phytochemistry (the study of the biochemistry of plants) and phytopathology (the study of disease in plants). The scope of plant physiology as a discipline may be divided into several major areas of research. First, the study of phytochemistry (plant chemistry) is includ... | Plant Physiology | 0.856078 |
185 | Plant physiology is a subdiscipline of botany concerned with the functioning, or physiology, of plants. Closely related fields include plant morphology (structure of plants), plant ecology (interactions with the environment), phytochemistry (biochemistry of plants), cell biology, genetics, biophysics and molecular biol... | Plant Physiology | 0.856078 |
186 | Paradoxically, the subdiscipline of environmental physiology is on the one hand a recent field of study in plant ecology and on the other hand one of the oldest. Environmental physiology is the preferred name of the subdiscipline among plant physiologists, but it goes by a number of other names in the applied sciences.... | Plant Physiology | 0.856078 |
187 | Baudrit, C., and D. Dubois (2006). Practical representations of incomplete probabilistic knowledge. Computational Statistics & Data Analysis 51: 86–108. Baudrit, C., D. Dubois, D. Guyonnet (2006). | Probability box | 0.855952 |
188 | There may be uncertainty about the shape of a probability distribution because the sample size of the empirical data characterizing it is small. Several methods in traditional statistics have been proposed to account for this sampling uncertainty about the distribution shape, including Kolmogorov–Smirnov and similar co... | Probability box | 0.855952 |
189 | P-boxes and probability bounds analysis have been used in many applications spanning many disciplines in engineering and environmental science, including: Engineering design Expert elicitation Analysis of species sensitivity distributions Sensitivity analysis in aerospace engineering of the buckling load of the frontsk... | Probability box | 0.855952 |
190 | Many algorithms where quantum speedups occur in quantum computing are instances of the hidden subgroup problem. The following list outlines important instances of the HSP, and whether or not they are solvable. | Hidden subgroup problem | 0.855947 |
191 | The hidden subgroup problem is especially important in the theory of quantum computing for the following reasons. Shor's quantum algorithm for factoring and discrete logarithm (as well as several of its extensions) relies on the ability of quantum computers to solve the HSP for finite Abelian groups. The existence of e... | Hidden subgroup problem | 0.855947 |
192 | The hidden subgroup problem (HSP) is a topic of research in mathematics and theoretical computer science. The framework captures problems such as factoring, discrete logarithm, graph isomorphism, and the shortest vector problem. This makes it especially important in the theory of quantum computing because Shor's quantu... | Hidden subgroup problem | 0.855947 |
193 | Thus, |X| ≤ |F| and |F| ≤ |X|, so, by the Schröder–Bernstein theorem, |F| = |X|. This means precisely that there is a bijection j between X and F. Finally, for x, y ∈ X define x • y = j−1(j(x) Δ j(y)). This turns (X, •) into a group. Hence every set admits a group structure. | Group structure and the axiom of choice | 0.855938 |
194 | Any nonempty finite set has a group structure as a cyclic group generated by any element. Under the assumption of the axiom of choice, every infinite set X is equipotent with a unique cardinal number |X| which equals an aleph. Using the axiom of choice, one can show that for any family S of sets |⋃S| ≤ |S| × sup { |s|:... | Group structure and the axiom of choice | 0.855938 |
195 | In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation by members of the group of which it is a part. In other words, a subgroup N {\displaystyle N} of the group G {\displaystyle G} is normal in G {\displaystyle G} if and... | Normal subgroup | 0.855827 |
196 | {\displaystyle \sigma ^{2}>0.\,} Then the sequence of random variables Z n = ∑ i = 1 n ( X i − μ ) σ n {\displaystyle Z_{n}={\frac {\sum _{i=1}^{n}(X_{i}-\mu )}{\sigma {\sqrt {n}}}}\,} converges in distribution to a standard normal random variable. For some classes of random variables, the classic central limit theorem... | Mathematical probability | 0.855788 |
197 | The central limit theorem (CLT) explains the ubiquitous occurrence of the normal distribution in nature, and this theorem, according to David Williams, "is one of the great results of mathematics. "The theorem states that the average of many independent and identically distributed random variables with finite variance ... | Mathematical probability | 0.855788 |
198 | Most introductions to probability theory treat discrete probability distributions and continuous probability distributions separately. The measure theory-based treatment of probability covers the discrete, continuous, a mix of the two, and more. | Mathematical probability | 0.855788 |
199 | In probability theory, there are several notions of convergence for random variables. They are listed below in the order of strength, i.e., any subsequent notion of convergence in the list implies convergence according to all of the preceding notions. Weak convergence A sequence of random variables X 1 , X 2 , … , {\di... | Mathematical probability | 0.855788 |
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