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5,200 | This relaxes the requirement that a molecule contains two or more atoms, since the noble gases are individual atoms. Atoms and complexes connected by non-covalent interactions, such as hydrogen bonds or ionic bonds, are typically not considered single molecules.Concepts similar to molecules have been discussed since an... | Molecular theory | 0.826414 |
5,201 | A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and biochemistry, the distinction from ions is dropped and molecule is often used when re... | Molecular theory | 0.826414 |
5,202 | A specialized icosahedron die provides the answers of the Magic 8 Ball, conventionally used to provide answers to yes-or-no questions. Dice can be used to generate random numbers for use in passwords and cryptography applications. The Electronic Frontier Foundation describes a method by which dice can be used to genera... | Normal dice | 0.826414 |
5,203 | It is highly likely that the Pythagoreans used the Platonic solids as dice. They referred to such dice as "the dice of the gods" and they sought to understand the universe through an understanding of geometry in polyhedra. Polyhedral dice are commonly used in role-playing games. | Normal dice | 0.826414 |
5,204 | The Euclidean distance between two points of the plane with Cartesian coordinates ( x 1 , y 1 ) {\displaystyle (x_{1},y_{1})} and ( x 2 , y 2 ) {\displaystyle (x_{2},y_{2})} is This is the Cartesian version of Pythagoras's theorem. In three-dimensional space, the distance between points ( x 1 , y 1 , z 1 ) {\displaysty... | Cartesian coordinate plane | 0.826412 |
5,205 | Control design as regression problem of the second kind: MLC may also identify arbitrary nonlinear control laws which minimize the cost function of the plant. In this case, neither a model, nor the control law structure, nor the optimizing actuation command needs to be known. The optimization is only based on the contr... | Machine learning control | 0.826411 |
5,206 | One example is the computation of sensor feedback from a known full state feedback. A neural network is commonly used technique for this task. | Machine learning control | 0.826411 |
5,207 | Machine learning control (MLC) is a subfield of machine learning, intelligent control and control theory which solves optimal control problems with methods of machine learning. Key applications are complex nonlinear systems for which linear control theory methods are not applicable. | Machine learning control | 0.826411 |
5,208 | However, the definition was still in flux. After the 1985 lecture at the Chinese Academy of Sciences in Beijing, in 1997 C. F. Jeff Wu again suggested that statistics should be renamed data science. He reasoned that a new name would help statistics shed inaccurate stereotypes, such as being synonymous with accounting o... | Data Science | 0.826407 |
5,209 | In 1962, John Tukey described a field he called "data analysis", which resembles modern data science. In 1985, in a lecture given to the Chinese Academy of Sciences in Beijing, C. F. Jeff Wu used the term "data science" for the first time as an alternative name for statistics. Later, attendees at a 1992 statistics symp... | Data Science | 0.826407 |
5,210 | Many statisticians, including Nate Silver, have argued that data science is not a new field, but rather another name for statistics. Others argue that data science is distinct from statistics because it focuses on problems and techniques unique to digital data. Vasant Dhar writes that statistics emphasizes quantitative... | Data Science | 0.826407 |
5,211 | Data science is an interdisciplinary field focused on extracting knowledge from typically large data sets and applying the knowledge and insights from that data to solve problems in a wide range of application domains. The field encompasses preparing data for analysis, formulating data science problems, analyzing data,... | Data Science | 0.826407 |
5,212 | According to the 1957 physics textbook by Max Jammer, the term work was introduced in 1826 by the French mathematician Gaspard-Gustave Coriolis as "weight lifted through a height", which is based on the use of early steam engines to lift buckets of water out of flooded ore mines. According to Rene Dugas, French enginee... | Work (physics) | 0.826406 |
5,213 | In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force strength and the distance traveled. A force is said to do positive work if when app... | Work (physics) | 0.826406 |
5,214 | Given a field k and a field K containing k, one defines the relative algebraic closure of k in K to be the subfield of K consisting of all elements of K that are algebraic over k, that is all elements of K that are a root of some nonzero polynomial with coefficients in k. | Algebraic extension | 0.82638 |
5,215 | The following three properties hold: If E is an algebraic extension of F and F is an algebraic extension of K then E is an algebraic extension of K. If E and F are algebraic extensions of K in a common overfield C, then the compositum EF is an algebraic extension of K. If E is an algebraic extension of F and E > K > F ... | Algebraic extension | 0.82638 |
5,216 | In mathematics, an algebraic extension is a field extension L/K such that every element of the larger field L is algebraic over the smaller field K; that is, every element of L is a root of a non-zero polynomial with coefficients in K. A field extension that is not algebraic, is said to be transcendental, and must cont... | Algebraic extension | 0.82638 |
5,217 | Adaptive comparative judgement is a technique borrowed from psychophysics which is able to generate reliable results for educational assessment – as such it is an alternative to traditional exam script marking. In the approach, judges are presented with pairs of student work and are then asked to choose which is better... | Adaptive comparative judgement | 0.826376 |
5,218 | "There is no such thing as absolute judgement" The science of comparative judgement began with Louis Leon Thurstone of the University of Chicago. A pioneer of psychophysics, he proposed several ways to construct scales for measuring sensation and other psychological properties. One of these was the law of comparative j... | Adaptive comparative judgement | 0.826376 |
5,219 | A rotating magnetic field is produced by external magnetic coils perpendicular to the axis of the machine, and the direction of this field is rotated about the axis. When the rotation frequency is between the ion and electron gyro-frequencies, the electrons in the plasma co-rotate with the magnetic field (are "dragged"... | Field-Reversed Configuration | 0.826373 |
5,220 | At low s-parameter, most ions inside an FRC follow large betatron orbits (their average gyroradius is about half the size of the plasma) which are typical in accelerator physics rather than plasma physics. These FRCs are very stable because the plasma is not dominated by usual small gyroradius particles like other ther... | Field-Reversed Configuration | 0.826373 |
5,221 | The FRC was first observed in laboratories in the late 1950s during theta pinch experiments with a reversed background magnetic field. The original idea was attributed to the Greek scientist and engineer Nicholas C. Christofilos who developed the concept of E-layers for the Astron fusion reactor.The first studies were ... | Field-Reversed Configuration | 0.826373 |
5,222 | Derived units may have their own unit name, such as the watt (J/s) and lux (cd/m2), or may just be expressed as combinations of base units, such as velocity (m/s) and acceleration (m/s2).The metric system was designed to have properties that make it easy to use and widely applicable, including units based on the natura... | Metric unit | 0.826352 |
5,223 | Classifier performance depends greatly on the characteristics of the data to be classified. There is no single classifier that works best on all given problems (a phenomenon that may be explained by the no-free-lunch theorem). Various empirical tests have been performed to compare classifier performance and to find the... | Statistical classifier | 0.826343 |
5,224 | Terminology across fields is quite varied. In statistics, where classification is often done with logistic regression or a similar procedure, the properties of observations are termed explanatory variables (or independent variables, regressors, etc.), and the categories to be predicted are known as outcomes, which are ... | Statistical classifier | 0.826343 |
5,225 | In statistics, classification is the problem of identifying which of a set of categories (sub-populations) an observation (or observations) belongs to. Examples are assigning a given email to the "spam" or "non-spam" class, and assigning a diagnosis to a given patient based on observed characteristics of the patient (s... | Statistical classifier | 0.826343 |
5,226 | In introductory physics textbooks, the standard basis vectors are often denoted i , j , k {\displaystyle \mathbf {i} ,\mathbf {j} ,\mathbf {k} } instead (or x ^ , y ^ , z ^ {\displaystyle \mathbf {\hat {x}} ,\mathbf {\hat {y}} ,\mathbf {\hat {z}} } , in which the hat symbol ^ typically denotes unit vectors). In this ca... | Opposite vector | 0.826339 |
5,227 | In any dimension (and, in particular, higher dimensions), it is possible to define the exterior product, which (among other things) supplies an algebraic characterization of the area and orientation in space of the n-dimensional parallelotope defined by n vectors. In a pseudo-Euclidean space, a vector's squared length ... | Opposite vector | 0.826339 |
5,228 | In the geometrical and physical settings, it is sometimes possible to associate, in a natural way, a length or magnitude and a direction to vectors. In addition, the notion of direction is strictly associated with the notion of an angle between two vectors. If the dot product of two vectors is defined—a scalar-valued p... | Opposite vector | 0.826339 |
5,229 | Computer science has been a part of the school curricula from age 14 or age 16 in a few countries for a few decades, but has typically as an elective subject. Primary and secondary computer science education is relatively new in the United States with many K-12 CS teachers facing obstacles to integrating CS instruction... | Computer science education | 0.826338 |
5,230 | The Association for Computing Machinery (ACM) runs a Special Interest Group (SIG) on Computer science education known as SIGCSE which celebrated its 50th anniversary in 2018, making it one of the oldest and longest running ACM Special Interest Groups. An outcome of computing education research are Parsons problems. | Computer science education | 0.826338 |
5,231 | The history of computer science education can be traced back to the early days of computing, when programming was primarily done by scientists and mathematicians. As computers became more widely used in industry and government, the need for skilled programmers grew, and universities began to offer courses in computer s... | Computer science education | 0.826338 |
5,232 | In 2011, women earned half of the computer science degrees in Malaysia. In 2001, 55 percent of computer science graduates in Guyana were women. == References == | Computer science education | 0.826338 |
5,233 | Computer Science is perceived as a male dominated field, pursued by people who are nerdy and lack social skills. All these characteristics seem to be more damaging for a woman as compared to a man. Therefore, in order to break these stereotypes and to engage more women in computer science, it is crucial that there are ... | Computer science education | 0.826338 |
5,234 | In many countries, there is a significant gender gap in computer science education. In 2015, 15.3% of computer science students graduating from non-doctoral granting institutions in the US were women while at doctoral granting institutions, the figure was 16.6%. The number of female PhD recipients in the US was 19.3% i... | Computer science education | 0.826338 |
5,235 | Computing education research (CER) or Computer science education research is an interdisciplinary field that focuses on studying the teaching and learning of computer science. It is a subfield of both computer science and education research, and is concerned with understanding how computer science is taught, learned, a... | Computer science education | 0.826338 |
5,236 | Computer science education researchers are interested in promoting diversity and inclusion in computer science education. This may involve studying the factors that contribute to under representation of certain groups in computer science, and developing interventions to promote inclusivity and equity. | Computer science education | 0.826338 |
5,237 | Computer science education researchers are interested in developing effective ways to assess student learning outcomes. This may involve developing new measures of student knowledge or skills, or evaluating the effectiveness of different assessment methods. | Computer science education | 0.826338 |
5,238 | Computer science education research emerged as a field of study in the 1970s, when researchers began to explore the effectiveness of different approaches to teaching computer programming. Since then, the field has grown to encompass a wide range of topics related to computer science education, including curriculum desi... | Computer science education | 0.826338 |
5,239 | As technology becomes increasingly integrated into all aspects of society, the demand for skilled computer scientists is growing. According to the Bureau of Labor Statistics, employment of computer and information technology occupations is projected to "grow 21 percent from 2021 to 2031", much faster than the average f... | Computer science education | 0.826338 |
5,240 | Computer science education or computing education is the field of teaching and learning the discipline of computer science, and computational thinking. The field of computer science education encompasses a wide range of topics, from basic programming skills to advanced algorithm design and data analysis. It is a rapidl... | Computer science education | 0.826338 |
5,241 | The curriculum for computer science education varies depending on the level of education and country. At the elementary and middle school level, computer science education usually focuses on block or visual programming languages such as Scratch using basic programming concepts, such as loops, conditionals, and variable... | Computer science education | 0.826338 |
5,242 | Teaching methods in computer science education vary depending on the level of education and the goals of the program. At the elementary and middle school level, computer science education may focus on interactive games and puzzles to teach programming concepts. In high school and college, computer science education may... | Computer science education | 0.826338 |
5,243 | Researchers in computer science education seek to design curricula that are effective and engaging for students. This may involve studying the effectiveness of different programming languages, or developing new pedagogical approaches that promote active learning. | Computer science education | 0.826338 |
5,244 | Researchers in computer science education are interested in exploring different teaching methods and instructional strategies. This may involve studying the effectiveness of lectures, online tutorials, or peer-to-peer learning. | Computer science education | 0.826338 |
5,245 | One of the primary goals of computer science education research is to improve the teaching and learning of computer science. To this end, researchers study a variety of topics, including: | Computer science education | 0.826338 |
5,246 | Having the expression for the expected value of z, which will involve partial derivatives and the means and variances of the random variables x, set up the expression for the expectation of the variance: V a r ≡ E ) 2 ] {\displaystyle {\rm {Var}}\,\,\,\equiv \,\,{\rm {E}}\left\,}\right)^{2}}\right]} that is, find ( z... | Experimental uncertainty analysis | 0.826336 |
5,247 | For example, an experimental uncertainty analysis of an undergraduate physics lab experiment in which a pendulum can estimate the value of the local gravitational acceleration constant g. The relevant equation for an idealized simple pendulum is, approximately, T = 2 π L g E q ( 1 ) {\displaystyle T\,=\,2\,\pi \,{\sqr... | Experimental uncertainty analysis | 0.826336 |
5,248 | In fact, a substantial portion of mathematical statistics is concerned with the general problem of deriving the complete frequency distribution of such functions, from which the can then be derived.To illustrate, a simple example of this process is to find the mean and variance of the derived quantity z = x2 where th... | Experimental uncertainty analysis | 0.826336 |
5,249 | Thus M S e = σ 2 + β 2 {\displaystyle {\rm {MSe}}\,\,\,=\,\,\,\sigma ^{2}+\,\,\,\beta ^{2}} where β is the bias (distance). This is a statistical application of the parallel-axis theorem from mechanics.In summary, the linearized approximation for the expected value (mean) and variance of a nonlinearly-transformed rando... | Experimental uncertainty analysis | 0.826336 |
5,250 | Next, suppose that it is impractical to use the direct approach to find the dependence of the derived quantity (g) upon the input, measured parameters (L, T, θ). Is there an alternative method? From calculus, the concept of the total differential is useful here: d z = ∂ z ∂ x 1 d x 1 + ∂ z ∂ x 2 d x 2 + ∂ z ∂ x 3 d x 3... | Experimental uncertainty analysis | 0.826336 |
5,251 | For simplicity, consider only the measured time as a random variable, so that the derived quantity, the estimate of g, amounts to g ^ = k T 2 {\displaystyle {\hat {g}}=\,\,{k \over {T^{2}}}} where k collects the factors in Eq(2) that for the moment are constants. Again applying the rules for probability calculus, a PDF... | Experimental uncertainty analysis | 0.826336 |
5,252 | The definition was first proposed by Eva M. Neumann-Held, suggesting that a redefinition of our view of the "gene" in relation to developmental genetics. This concept claims that the definition is too general. We therefore need to either clarify its definition or stop using the term "gene". In the Cycles of Contingency... | Process molecular gene concept | 0.826323 |
5,253 | Since the advent of computers and artificial intelligence, computer programs have been adapted that attempt to simulate the implicit learning process observed in the AGL paradigm. The AI programs first adapted to simulate both natural and artificial grammar learning used the following basic structure: Given A set of gr... | Artificial grammar learning | 0.826315 |
5,254 | In robotics, the exploration problem deals with the use of a robot to maximize the knowledge over a particular area. The exploration problem arises in robotic mapping and search & rescue situations, where an environment might be dangerous or inaccessible to humans. | Exploration problem | 0.826314 |
5,255 | The exploration problem naturally arises in situations in which a robot is utilized to survey an area that is dangerous or inaccessible for humans. The field of robotic explorations draws from various fields of information gathering and decision theory, and have been studied as far back as the 1950s. The earliest work ... | Exploration problem | 0.826314 |
5,256 | Shortly after launch, the SEP sensors on ACE detected solar events that had unexpected characteristics. Unlike most large, shock-accelerated SEP events, these were highly enriched in iron and helium-3, as are the much smaller, flare-associated impulsive SEP events. Within the first year of operations, ACE found many of... | Advanced Composition Explorer | 0.826309 |
5,257 | Particle acceleration is ubiquitous in nature and understanding its nature is one of the fundamental problems of space plasma astrophysics. The unique data set obtained by ACE measurements have been used to: Make direct measurements of charge and/or mass-dependent fractionation during solar energetic particle and inter... | Advanced Composition Explorer | 0.826309 |
5,258 | Within each telescope, particle trajectories are measured with a pair of two-dimensional silicon strip detectors instrumented with custom very-large-scale integrated (VLSI) electronics to provide both position and energy-loss measurements. SIS was specially designed to achieve excellent mass resolution under the extrem... | Advanced Composition Explorer | 0.826309 |
5,259 | Let L be a language in PP. Let L c {\displaystyle L^{c}} denote the complement of L. By the definition of PP there is a polynomial-time probabilistic algorithm A with the property that x ∈ L ⇒ Pr > 1 2 and x ∉ L ⇒ Pr ≤ 1 2 . {\displaystyle x\in L\Rightarrow \Pr>{\frac {1}{2}}\quad {\text{and}}\quad x\not \in L\Righta... | PP (complexity) | 0.826284 |
5,260 | Mathematical practice comprises the working practices of professional mathematicians: selecting theorems to prove, using informal notations to persuade themselves and others that various steps in the final proof are convincing, and seeking peer review and publication, as opposed to the end result of proven and publishe... | Mathematical practice | 0.826282 |
5,261 | Importantly for the general theory of binary encoding, he added that this method could be used with any objects at all: "provided those objects be capable of a twofold difference only; as by Bells, by Trumpets, by Lights and Torches, by the report of Muskets, and any instruments of like nature".George Boole published a... | Binary Code | 0.826254 |
5,262 | The Ifá/Ifé system of divination in African religions, such as of Yoruba, Igbo, and Ewe, consists of an elaborate traditional ceremony producing 256 oracles made up by 16 symbols with 256 = 16 x 16. An initiated priest, or Babalawo, who had memorized oracles, would request sacrifice from consulting clients and make pra... | Binary Code | 0.826254 |
5,263 | The advantage of using balls rather than squares is that this definition generalizes to any metric space. In other words, the box definition is extrinsic — one assumes the fractal space S is contained in a Euclidean space, and defines boxes according to the external geometry of the containing space. However, the dimens... | Box-counting dimension | 0.826248 |
5,264 | In mathematics, a system of bilinear equations is a special sort of system of polynomial equations, where each equation equates a bilinear form with a constant (possibly zero). More precisely, given two sets of variables represented as coordinate vectors x and y, then each equation of the system can be written where, i... | System of bilinear equations | 0.826239 |
5,265 | For example, a spinning top is subject to gravitational torque making it lean over and change the angular momentum about the nutation axis, but neglecting friction at the point of spinning contact, it has a conserved angular momentum about its spinning axis, and another about its precession axis. Also, in any planetary... | Conservation of Angular Momentum | 0.826214 |
5,266 | In Cartesian coordinates: or more compactly in index notation: The angular velocity can also be defined as an anti-symmetric second order tensor, with components ωij. The relation between the two anti-symmetric tensors is given by the moment of inertia which must now be a fourth order tensor: Again, this equation in L ... | Conservation of Angular Momentum | 0.826214 |
5,267 | In modern (20th century) theoretical physics, angular momentum (not including any intrinsic angular momentum – see below) is described using a different formalism, instead of a classical pseudovector. In this formalism, angular momentum is the 2-form Noether charge associated with rotational invariance. As a result, an... | Conservation of Angular Momentum | 0.826214 |
5,268 | There are two main types of topology for a spacetime M. | Global geometry | 0.826212 |
5,269 | The Alexandrov topology on spacetime, is the coarsest topology such that both Y + ( E ) {\displaystyle Y^{+}(E)} and Y − ( E ) {\displaystyle Y^{-}(E)} are open for all subsets E ⊂ M {\displaystyle E\subset M} . Here the base of open sets for the topology are sets of the form Y + ( x ) ∩ Y − ( y ) {\displaystyle Y^{+}(... | Global geometry | 0.826212 |
5,270 | Spacetime topology is the topological structure of spacetime, a topic studied primarily in general relativity. This physical theory models gravitation as the curvature of a four dimensional Lorentzian manifold (a spacetime) and the concepts of topology thus become important in analysing local as well as global aspects ... | Global geometry | 0.826212 |
5,271 | An extension of Mantel's Theorem provides an explicit lower bound on triangle densities in terms of edge densities.Theorem (Goodman). t ( K 3 , G ) ≥ t ( K 2 , G ) ( 2 t ( K 2 , G ) − 1 ) . {\displaystyle t(K_{3},G)\geq t(K_{2},G)(2t(K_{2},G)-1).} | Homomorphism density | 0.826177 |
5,272 | A more complete description of the relationship between t ( K 3 , G ) {\displaystyle t(K_{3},G)} and t ( K 2 , G ) {\displaystyle t(K_{2},G)} was proven by Razborov. His work from 2008 completes the understanding of a homomorphism inequality problem, the description of D 2 , 3 {\displaystyle D_{2,3}} , which is the reg... | Homomorphism density | 0.826177 |
5,273 | It is sufficient to prove this inequality for any graph G {\displaystyle G} . Say G {\displaystyle G} is a graph on n {\displaystyle n} vertices, and { λ i } i = 1 n {\displaystyle \{\lambda _{i}\}_{i=1}^{n}} are the eigenvalues of its adjacency matrix A G {\displaystyle A_{G}} . By spectral graph theory, we know hom ... | Homomorphism density | 0.826177 |
5,274 | A converse inequality to Goodman's Theorem is a special case of Kruskal–Katona theorem, which states that t ( K 3 , G ) ≤ t ( K 2 , G ) 3 / 2 {\displaystyle t(K_{3},G)\leq t(K_{2},G)^{3/2}} . It turns out that both of these inequalities are tight for specific edge densities. Proof. | Homomorphism density | 0.826177 |
5,275 | A classic example is Turán's Theorem, which states that if t ( K r , W ) = 0 {\displaystyle t(K_{r},W)=0} , then t ( K 2 , W ) ≤ ( 1 − 1 r − 1 ) {\displaystyle t(K_{2},W)\leq \left(1-{\frac {1}{r-1}}\right)} . A special case of this is Mantel's Theorem, which states that if t ( K 3 , W ) = 0 {\displaystyle t(K_{3},W)=0... | Homomorphism density | 0.826177 |
5,276 | However, we get a much harder problem, in fact an undecidable one, when we have a homomorphism inequalities on a more general set of graphs H i {\displaystyle H_{i}} :Theorem (Hatami, Norine). Let a 1 , ⋯ , a n {\displaystyle a_{1},\cdots ,a_{n}} be real constants, and { H i } i = 1 n {\displaystyle \{H_{i}\}_{i=1}^{n}... | Homomorphism density | 0.826177 |
5,277 | In some situations, deciding whether such an inequality is true or not can be simplified, such as it is the case in the following theorem.Theorem (Bollobás). Let a 1 , ⋯ , a n {\displaystyle a_{1},\cdots ,a_{n}} be real constants. Then, the inequality ∑ i = 1 n a i t ( K i , G ) ≥ 0 {\displaystyle \sum _{i=1}^{n}a_{i}t... | Homomorphism density | 0.826177 |
5,278 | The Lagrangian can be useful in analyzing extremal problems. The quantity is defined to be L ( H ) = max x 1 , … , x n ≥ 0 x 1 + ⋯ x n = 1 ∑ e ∈ E ( H ) ∏ v ∈ e x v {\displaystyle L(H)=\max _{\begin{matrix}x_{1},\ldots ,x_{n}\geq 0\\x_{1}+\cdots x_{n}=1\end{matrix}}\sum _{e\in E(H)}\prod _{v\in e}x_{v}} .One useful fac... | Homomorphism density | 0.826177 |
5,279 | Many results in extremal graph theory can be described by inequalities involving homomorphism densities associated to a graph. The following are a sequence of examples relating the density of triangles to the density of edges. | Homomorphism density | 0.826177 |
5,280 | In the mathematical field of extremal graph theory, homomorphism density with respect to a graph H {\displaystyle H} is a parameter t ( H , − ) {\displaystyle t(H,-)} that is associated to each graph G {\displaystyle G} in the following manner: t ( H , G ) := | hom ( H , G ) | | V ( G ) | | V ( H ) | {\displaystyle t... | Homomorphism density | 0.826177 |
5,281 | In computational geometry, Klee's measure problem is the problem of determining how efficiently the measure of a union of (multidimensional) rectangular ranges can be computed. Here, a d-dimensional rectangular range is defined to be a Cartesian product of d intervals of real numbers, which is a subset of Rd. The probl... | Klee's measure problem | 0.826157 |
5,282 | Franco P. Preparata and Michael I. Shamos (1985). Computational Geometry (Springer-Verlag, Berlin). Klee's Measure Problem, from Professor Jeff Erickson's list of open problems in computational geometry. (Accessed November 8, 2005, when the last update was July 31, 1998.) == References == | Klee's measure problem | 0.826157 |
5,283 | Chan, Timothy M. (2013), "Klee's measure problem made easy", Proceedings of the 54th IEEE Symposium on Foundations of Computer Science (FOCS) (PDF), pp. 410–419, CiteSeerX 10.1.1.643.26, doi:10.1109/FOCS.2013.51, ISBN 978-0-7695-5135-7, S2CID 11648588. | Klee's measure problem | 0.826157 |
5,284 | (1998), "On the Klee's measure problem in small dimensions", Proceedings of the 25th Conference on Current Trends in Theory and Practice of Informatics (SOFSEM-98), Lecture Notes in Computer Science, vol. 1521, Berlin: Springer-Verlag, pp. 304–311, doi:10.1007/3-540-49477-4_22, ISBN 978-3-540-65260-1. | Klee's measure problem | 0.826157 |
5,285 | Klee, Victor (1977), "Can the measure of ∪ {\displaystyle \cup } be computed in less than O ( n log n ) {\displaystyle O(n\log n)} steps? ", American Mathematical Monthly, 84 (4): 284–285, doi:10.2307/2318871, JSTOR 2318871, MR 0436661. Bentley, Jon L. (1977), Algorithms for Klee's rectangle problems, Unpublished no... | Klee's measure problem | 0.826157 |
5,286 | Papers not selected for publication in PLOS Computational Biology were published in edited form in the Journal of Computational Biology as usual.As of 2016 the conference started a partnership with Cell Systems. Each year, a subset of work accepted at RECOMB is also considered for publication in a special issue of Cell... | Research in Computational Molecular Biology | 0.826151 |
5,287 | The first conference was held at the Sandia National Laboratories in Santa Fe, New Mexico.A series of RECOMB Satellite meetings was established by Pavel Pevzner in 2001. These meetings cover specialist aspects of bioinformatics, including massively parallel sequencing, comparative genomics, regulatory genomics and bioi... | Research in Computational Molecular Biology | 0.826151 |
5,288 | Research in Computational Molecular Biology (RECOMB) is an annual academic conference on the subjects of bioinformatics and computational biology. The conference has been held every year since 1997 and is a major international conference in computational biology, alongside the ISMB and ECCB conferences. The conference ... | Research in Computational Molecular Biology | 0.826151 |
5,289 | What follows is an example to make the above discussion concrete, using the formalism developed in the article on the mathematical formulation of quantum mechanics. Let n denote a complete set of (discrete) quantum numbers for specifying single-particle states (for example, for the particle in a box problem, take n to ... | Indistinguishable particles | 0.82615 |
5,290 | This phase factor here is called the mutual statistics. Finally, in the case M = R , {\displaystyle M=\mathbb {R} ,} the space \ {coincident points} is not connected, so even if particle I and particle II are identical, they can still be distinguished via labels such as "the particle on the left" and "the particle on ... | Indistinguishable particles | 0.82615 |
5,291 | This is described by the infinite cyclic group generated by making a counterclockwise half-turn interchange. Unlike the previous case, performing this interchange twice in a row does not recover the original state; so such an interchange can generically result in a multiplication by exp(iθ) for any real θ (by unitarity... | Indistinguishable particles | 0.82615 |
5,292 | This interchange is an involution, so its only effect is to multiply the phase by a square root of 1. If the root is +1, then the points have Bose statistics, and if the root is –1, the points have Fermi statistics. In the case M = R 2 , {\displaystyle M=\mathbb {R} ^{2},} the universal covering space of \ {coincident... | Indistinguishable particles | 0.82615 |
5,293 | To understand why particle statistics work the way that they do, note first that particles are point-localized excitations and that particles that are spacelike separated do not interact. In a flat d-dimensional space M, at any given time, the configuration of two identical particles can be specified as an element of M... | Indistinguishable particles | 0.82615 |
5,294 | The spin-statistics theorem relates the exchange symmetry of identical particles to their spin. It states that bosons have integer spin, and fermions have half-integer spin. Anyons possess fractional spin. | Indistinguishable particles | 0.82615 |
5,295 | These exotic particles are known as anyons, and they obey fractional statistics. Experimental evidence for the existence of anyons exists in the fractional quantum Hall effect, a phenomenon observed in the two-dimensional electron gases that form the inversion layer of MOSFETs. There is another type of statistic, known... | Indistinguishable particles | 0.82615 |
5,296 | Systems of many identical fermions are described by Fermi–Dirac statistics. Parastatistics are also possible. In certain two-dimensional systems, mixed symmetry can occur. | Indistinguishable particles | 0.82615 |
5,297 | These statistical properties are described as Bose–Einstein statistics. Particles which exhibit antisymmetric states are called fermions. Antisymmetry gives rise to the Pauli exclusion principle, which forbids identical fermions from sharing the same quantum state. | Indistinguishable particles | 0.82615 |
5,298 | In quantum mechanics the free rotation of a molecule is quantized, so that the rotational energy and the angular momentum can take only certain fixed values, which are related simply to the moment of inertia, I {\displaystyle I} , of the molecule. For any molecule, there are three moments of inertia: I A {\displaystyle... | Microwave spectroscope | 0.826143 |
5,299 | Understanding electron and ion current collection to and from the surrounding ambient plasma is critical for most EDT systems. Any exposed conducting section of the EDT system can passively ('passive' and 'active' emission refers to the use of pre-stored energy in order to achieve the desired effect) collect electron o... | Electrodynamic tether | 0.826141 |
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