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Chemogenetics is the process by which macromolecules can be engineered to interact with previously unrecognized small molecules. Chemogenetics as a term was originally coined to describe the observed effects of mutations on chalcone isomerase activity on substrate specificities in the flowers of Dianthus caryophyllus. ...
Chemogenetics
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Chemogenetics and usage of DREADDs have allowed researchers to advance in biomedical research areas including many neurodegenerative and psychiatric conditions. Chemogenetics have been used in these fields to induce specific and reversible brain lesions and therefore, study specific activities of neuron population. Alt...
Chemogenetics
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The resolution in Optogenetic declines due to light scattering and illuminance declined levels as the distance between the subject and the light source increases. These factors, therefore, don’t allow for all cells to be affected by light and lead to a lower spatial resolution. Chemogenetics, however, does not require ...
Chemogenetics
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Optogenetics uses light-sensitive channels and pumps that are virally introduced into neurons. Cells' activity, having these channels, can then be manipulated by light. Chemogenetics, on the other hand, uses chemically engineered receptors and exogenous molecules specific for those receptors, to affect the activity of ...
Chemogenetics
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Speed of Light (The Foucault Method) Measuring the Speed of Light (video, Foucault method) BYU Physics & Astronomy
Foucault's measurements of the speed of light
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In relational algebra, a selection (sometimes called a restriction to avoid confusion with SQL's use of SELECT) is a unary operation written as σ a θ b ( R ) {\displaystyle \sigma _{a\theta b}(R)} or σ a θ v ( R ) {\displaystyle \sigma _{a\theta v}(R)} where: a {\displaystyle a} and b {\displaystyle b} are attribute na...
Function restriction
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The total energy is half the potential energy, the difference being the kinetic energy of the electron. This is also true for noncircular orbits by the virial theorem.A quantum ruleThe angular momentum L = mevr is an integer multiple of ħ: m e v r = n ℏ . {\displaystyle m_{\mathrm {e} }vr=n\hbar .}
Bohr atom
0.80397
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In high energy physics, it can be used to calculate the masses of heavy quark mesons. Calculation of the orbits requires two assumptions. Classical mechanicsThe electron is held in a circular orbit by electrostatic attraction.
Bohr atom
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In physics and engineering, mass flow rate is the mass of a substance which passes per unit of time. Its unit is kilogram per second in SI units, and slug per second or pound per second in US customary units. The common symbol is m ˙ {\displaystyle {\dot {m}}} (ṁ, pronounced "m-dot"), although sometimes μ (Greek lowerc...
Mass flow rate
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In six-dimensional geometry, a pentellated 6-cube is a convex uniform 6-polytope with 5th order truncations of the regular 6-cube. There are unique 16 degrees of pentellations of the 6-cube with permutations of truncations, cantellations, runcinations, and sterications. The simple pentellated 6-cube is also called an e...
Pentellated 6-cube
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In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by faces is a polyhedron. In more technical treatments of the geometry of polyhedra and higher-dimensional polytopes, the term is also used to mean an element of...
Ridge (geometry)
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In higher-dimensional geometry, the faces of a polytope are features of all dimensions. A face of dimension k is called a k-face. For example, the polygonal faces of an ordinary polyhedron are 2-faces. In set theory, the set of faces of a polytope includes the polytope itself and the empty set, where the empty set is f...
Ridge (geometry)
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Edward Miller of Pennsylvania began experimenting with them again in the late 1990s, as well as Francis Graham, a Kent State University, Ohio, physics professor. By 1999 both were flying rocket monocopters. Francis Graham wrote a book, Monocopters, with some theory of their flight characteristics, in 1999, sold by Apog...
Monocopter
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This is a list of geometric topology topics.
List of geometric topology topics
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Orientable manifold Connected sum Jordan-Schönflies theorem Signature (topology) Handle decomposition Handlebody h-cobordism theorem s-cobordism theorem Manifold decomposition Hilbert-Smith conjecture Mapping class group Orbifolds Examples Exotic sphere Homology sphere Lens space I-bundle
List of geometric topology topics
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Moise's Theorem (see also Hauptvermutung) Poincaré conjecture Thurston elliptization conjecture Thurston's geometrization conjecture Hyperbolic 3-manifolds Spherical 3-manifolds Euclidean 3-manifolds, Bieberbach Theorem, Flat manifolds, Crystallographic groups Seifert fiber space Heegaard splitting Waldhausen conjectur...
List of geometric topology topics
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Knot (mathematics) Link (knot theory) Wild knots Examples of knots Unknot Trefoil knot Figure-eight knot (mathematics) Borromean rings Types of knots Torus knot Prime knot Alternating knot Hyperbolic link Knot invariants Crossing number Linking number Skein relation Knot polynomials Alexander polynomial Jones polynomia...
List of geometric topology topics
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Born's interpretation of the wave function was criticized by Schrödinger, who had previously attempted to interpret it in real physical terms, but Albert Einstein's response became one of the earliest and most famous assertions that quantum mechanics is incomplete: Quantum mechanics is very worthy of respect. But an in...
Hidden-variables theory
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In June 1926, Max Born published a paper, "Zur Quantenmechanik der Stoßvorgänge" ("Quantum Mechanics of Collision Phenomena") in the scientific journal Zeitschrift für Physik, in which he was the first to clearly enunciate the probabilistic interpretation of the quantum wave function, which had been introduced by Erwin...
Hidden-variables theory
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Physicists such as Alain Aspect and Paul Kwiat have performed experiments that have found violations of these inequalities up to 242 standard deviations. This rules out local hidden-variable theories, but does not rule out non-local ones. Theoretically, there could be experimental problems that affect the validity of t...
Hidden-variables theory
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In 1964, John Bell showed through his famous theorem that if local hidden variables exist, certain experiments could be performed involving quantum entanglement where the result would satisfy a Bell inequality. If, on the other hand, statistical correlations resulting from quantum entanglement could not be explained by...
Hidden-variables theory
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Einstein, Podolsky, and Rosen argued while assuming local causality that quantum mechanics is an incomplete description of reality. Bell's theorem and the related Bell test experiments have subsequently ruled out nearly all local hidden variable theories, the exception being the superdeterminism loophole, which cannot ...
Hidden-variables theory
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In physics, hidden-variable theories are proposals to provide explanations of quantum mechanical phenomena through the introduction of (possibly unobservable) hypothetical entities. The existence of fundamental indeterminacy for some measurements is assumed as part of the mathematical formulation of quantum mechanics; ...
Hidden-variables theory
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In mathematics, the Jacobi curve is a representation of an elliptic curve different from the usual one defined by the Weierstrass equation. Sometimes it is used in cryptography instead of the Weierstrass form because it can provide a defence against simple and differential power analysis style (SPA) attacks; it is poss...
Jacobian curve
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Adding and doubling formulas are useful also to compute P, the n-th multiple of a point P on an elliptic curve: this operation is considered the most in elliptic curve cryptography. An elliptic curve E, over a field K can be put in the Weierstrass form y2 = x3 + ax + b, with a, b in K. What will be of importance later ...
Jacobian curve
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An allocation X is defined as essentially envy-free (EEF) if, for every agent i, there is a feasible allocation Yi with the same utility profile (all agents are indifferent between X and Yi) in which agent i does not envy anyone. Obviously, every EF allocation is EEF, since we can take Yi to be X for all i. Theorem 7 (...
Pareto-efficient envy-free division
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Patients with astigmatism need a cylindrical lens, or more generally a toric lens to see clearly. The geometry of a toric lens focuses light differently in different meridians. A meridian, in this case, is a plane that is incident with the optical axis. For example, a toric lens, when rotated correctly, could focus an ...
Eyeglass prescription
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The term "sphere" comes from the geometry of lenses. Lenses derive their power from curved surfaces. A spherical lens has the same curvature in every direction perpendicular to the optical axis. Spherical lenses are adequate correction when a person has no astigmatism. To correct for astigmatism, the "cylinder" and "ax...
Eyeglass prescription
0.803956
32,328
In molecular biology, the hydrogenase maturation protease family is a family of aspartic endopeptidases belonging to MEROPS family A31. The large subunit of -hydrogenase, as well as other nickel metalloenzymes, is synthesized as a precursor devoid of the metalloenzyme active site. This precursor undergoes a complex pos...
Hydrogenase maturation protease family
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32,329
Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger popu...
Statistical method
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The SSG relies on existing technology. The SuperSmart Grid would employ high voltage direct current (HVDC) cables in its first-generation implementation to integrate the European electricity market and possibly connect it to neighboring regions, such as North Africa, and their vast renewable energy resources, such as t...
SuperSmart Grid
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Unlike the more general development environments, data analysis simulators use a relatively simple static neural network that can be configured. A majority of the data analysis simulators on the market use backpropagating networks or self-organizing maps as their core. The advantage of this type of software is that it ...
Neural network software
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Unlike the research simulators, data analysis simulators are intended for practical applications of artificial neural networks. Their primary focus is on data mining and forecasting. Data analysis simulators usually have some form of preprocessing capabilities.
Neural network software
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The majority implementations of neural networks available are however custom implementations in various programming languages and on various platforms. Basic types of neural networks are simple to implement directly. There are also many programming libraries that contain neural network functionality and that can be use...
Neural network software
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32,334
In the study of biological neural networks however, simulation software is still the only available approach. In such simulators the physical biological and chemical properties of neural tissue, as well as the electromagnetic impulses between the neurons are studied. Commonly used biological network simulators include ...
Neural network software
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32,335
Historically, the most common type of neural network software was intended for researching neural network structures and algorithms. The primary purpose of this type of software is, through simulation, to gain a better understanding of the behavior and the properties of neural networks. Today in the study of artificial...
Neural network software
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Development environments for neural networks differ from the software described above primarily on two accounts – they can be used to develop custom types of neural networks and they support deployment of the neural network outside the environment. In some cases they have advanced preprocessing, analysis and visualizat...
Neural network software
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A range of products are being offered to produce and consume PMML. This ever-growing list includes the following neural network products: R: produces PMML for neural nets and other machine learning models via the package pmml. SAS Enterprise Miner: produces PMML for several mining models, including neural networks, lin...
Neural network software
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32,338
The data flow is controlled by a control system which is exchangeable as well as the adaptation algorithms. The other important feature is deployment capabilities. With the advent of component-based frameworks such as .NET and Java, component based development environments are capable of deploying the developed neural ...
Neural network software
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32,339
A more modern type of development environments that are currently favored in both industrial and scientific use are based on a component based paradigm. The neural network is constructed by connecting adaptive filter components in a pipe filter flow. This allows for greater flexibility as custom networks can be built a...
Neural network software
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32,340
In order for neural network models to be shared by different applications, a common language is necessary. The Predictive Model Markup Language (PMML) has been proposed to address this need. PMML is an XML-based language which provides a way for applications to define and share neural network models (and other data min...
Neural network software
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Neural network software is used to simulate, research, develop, and apply artificial neural networks, software concepts adapted from biological neural networks, and in some cases, a wider array of adaptive systems such as artificial intelligence and machine learning.
Neural network software
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32,342
Neural network simulators are software applications that are used to simulate the behavior of artificial or biological neural networks. They focus on one or a limited number of specific types of neural networks. They are typically stand-alone and not intended to produce general neural networks that can be integrated in...
Neural network software
0.803952
32,343
Bloch's theorem proves that the solutions to this differential equation can be written as follows: ψ n , k ( x ) = e i k ⋅ x u n , k ( x ) {\displaystyle \psi _{n,\mathbf {k} }(\mathbf {x} )=e^{i\mathbf {k} \cdot \mathbf {x} }u_{n,\mathbf {k} }(\mathbf {x} )} where k is a vector (called the wavevector), n is a discrete...
K.p method
0.803949
32,344
According to quantum mechanics (in the single-electron approximation), the quasi-free electrons in any solid are characterized by wavefunctions which are eigenstates of the following stationary Schrödinger equation: ( p 2 2 m + V ) ψ = E ψ {\displaystyle \left({\frac {p^{2}}{2m}}+V\right)\psi =E\psi } where p is the qu...
K.p method
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32,345
In solid-state physics, the k·p perturbation theory is an approximated semi-empirical approach for calculating the band structure (particularly effective mass) and optical properties of crystalline solids. It is pronounced "k dot p", and is also called the "k·p method". This theory has been applied specifically in the ...
K.p method
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32,346
Link Motion will further enhance its carputer into a “CarBrain”, using artificial intelligence (AI) and blockchain applications to make vehicles a more intelligent part of the traffic ecosystem. They have also integrated Keystone into the platform which is Irdeto’s new smartphone-based vehicle access solution that allo...
Link Motion
0.803948
32,347
Surface engineering is the sub-discipline of materials science which deals with the surface of solid matter. It has applications to chemistry, mechanical engineering, and electrical engineering (particularly in relation to semiconductor manufacturing). Solids are composed of a bulk material covered by a surface. The su...
Surface Engineering
0.803945
32,348
Play in most chess variants is sufficiently similar to chess that games can be recorded with algebraic notation, although additions to this are often required. For example, the third dimension in Millennium 3D Chess means that move notation needs to include the level number, as well as the rank and file—N2g3 means a kn...
Chess variants
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32,349
A groupoid S-scheme is a groupoid object in the category of schemes over some fixed base scheme S. If U = S {\displaystyle U=S} , then a groupoid scheme (where s = t {\displaystyle s=t} are necessarily the structure map) is the same as a group scheme. A groupoid scheme is also called an algebraic groupoid, to convey th...
Groupoid scheme
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32,350
The dissociation rate in chemistry, biochemistry, and pharmacology is the rate or speed at which a ligand dissociates from a protein, for instance, a receptor. It is an important factor in the binding affinity and intrinsic activity (efficacy) of a ligand at a receptor. The dissociation rate for a particular substrate ...
Dissociation rates
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32,351
Many programs using associative arrays will at some point need to store that data in a more permanent form, like in a computer file. A common solution to this problem is a generalized concept known as archiving or serialization, which produces a text or binary representation of the original objects that can be written ...
Associative arrays
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32,352
In physics, a pseudopotential or effective potential is used as an approximation for the simplified description of complex systems. Applications include atomic physics and neutron scattering. The pseudopotential approximation was first introduced by Hans Hellmann in 1934.
Fermi's pseudopotential
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32,353
There are now six classes open to both sexes, plus three classes for women and two junior classes. The latest worldwide statistics for 2011 indicate that Germany, the sport's birthplace, is still a center of the gliding world: it accounted for 27 percent of the world's glider pilots, and the three major glider manufact...
Ground launch
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32,354
Thus, specifying the cross section for a given reaction is a proxy for stating the probability that a given scattering process will occur. The measured reaction rate of a given process depends strongly on experimental variables such as the density of the target material, the intensity of the beam, the detection efficie...
Cross-section (physics)
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32,355
For example, in Rayleigh scattering, the intensity scattered at the forward and backward angles is greater than the intensity scattered sideways, so the forward differential scattering cross section is greater than the perpendicular differential cross section, and by adding all of the infinitesimal cross sections over ...
Cross-section (physics)
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32,356
For example, plasmonic nanoparticles can have light scattering cross sections for particular frequencies that are much larger than their actual cross-sectional areas. When two discrete particles interact in classical physics, their mutual cross section is the area transverse to their relative motion within which they m...
Cross-section (physics)
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32,357
In classical physics, this probability often converges to a deterministic proportion of excitation energy involved in the process, so that, for example, with light scattering off of a particle, the cross section specifies the amount of optical power scattered from light of a given irradiance (power per area). It is imp...
Cross-section (physics)
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32,358
In physics, the cross section is a measure of the probability that a specific process will take place when some kind of radiant excitation (e.g. a particle beam, sound wave, light, or an X-ray) intersects a localized phenomenon (e.g. a particle or density fluctuation). For example, the Rutherford cross-section is a mea...
Cross-section (physics)
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32,359
One major basis for this developmental theory is task analysis. The study of ideal tasks, including their instantiation in the real world, has been the basis of the branch of stimulus control called psychophysics. Tasks are defined as sequences of contingencies, each presenting stimuli and each requiring a behavior or ...
Model of hierarchical complexity
0.803934
32,360
In physics, the Young–Laplace equation () is an algebraic equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or wall tension, although use of the latter is only applicable if assuming that th...
Young–Laplace equation
0.803928
32,361
Boolean expressions are represented very similarly to algebraic expressions, the only difference being the specific values and operators used. Boolean expressions use true and false as constant values, and the operators include ∧ {\displaystyle \land } (AND), ∨ {\displaystyle \lor } (OR), ¬ {\displaystyle \neg } (NOT).
Binary expression tree
0.80392
32,362
Algebraic expression trees represent expressions that contain numbers, variables, and unary and binary operators. Some of the common operators are × (multiplication), ÷ (division), + (addition), − (subtraction), ^ (exponentiation), and - (negation). The operators are contained in the internal nodes of the tree, with th...
Binary expression tree
0.80392
32,363
A binary expression tree is a specific kind of a binary tree used to represent expressions. Two common types of expressions that a binary expression tree can represent are algebraic and boolean. These trees can represent expressions that contain both unary and binary operators.Like any binary tree, each node of a binar...
Binary expression tree
0.80392
32,364
The Asian Young Researchers Conference on Computational and Omics Biology (AYRCOB) is a conference series for young researchers and students who are conducting their research in the fields of computational, omics and systems biology in Asia. The main objectives of AYRCOB are to promote international exchange among youn...
Asian Young Researchers Conference on Computational and Omics Biology
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32,365
The AYRCOB has various sponsors including: China Beijing Genomics InstituteJapan The University of Tokyo Global COE Program (Deciphering Biosphere from Genome Big Bang) Japanese Society for BioinformaticsKorea Korean Bioinformation Center Korean University of Science and Technology (UST) Daejeon Convention and Visitors...
Asian Young Researchers Conference on Computational and Omics Biology
0.803918
32,366
The AYRCOB has several affiliated organizations including: China Beijing Genomics Institute (BGI)Japan The University of Tokyo Graduate University for Advanced StudiesKorea Yonsei University Ewha Womans University University of Science and Technology (UST)Singapore Nanyang Technological University National University o...
Asian Young Researchers Conference on Computational and Omics Biology
0.803918
32,367
Japan-Taiwan Young Researchers Conference on Computational and Systems Biology, 2008 was held at National Tsing Hua University, Taiwan The 2nd Taiwan-Japan Young Researchers Conference on Computational and Systems Biology, 2008 was held at CBRC, AIST, Japan 3rd AYRCOB, 2010 was held at National Cheng Kung University, T...
Asian Young Researchers Conference on Computational and Omics Biology
0.803918
32,368
A central role in their analysis is played by Zernike's circle polynomials that allow an efficient representation of the aberrations of any optical system with rotational symmetry. Recent analytic results have made it possible to extend Nijboer and Zernike's approach for point spread function evaluation to a large volu...
Point-spread function
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32,369
In observational astronomy, the experimental determination of a PSF is often very straightforward due to the ample supply of point sources (stars or quasars). The form and source of the PSF may vary widely depending on the instrument and the context in which it is used. For radio telescopes and diffraction-limited spac...
Point-spread function
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32,370
He adds, "non-human intelligent beings should exist that understand the language of advanced mathematics. However, none of the non-human intelligent beings that we know of confirm the status of (advanced) mathematics as an objective language." In the paper "On Math, Matter and Mind" the secularist viewpoint examined ar...
Mathematical multiverse hypothesis
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32,371
There was no Student Robotics competition in 2018. Due to some organisational issues within the charity, it was decided to take a year off to reorganise and ensure the longevity of the charity.Two alternate competitions were held with very similar characteristics and involved many of the original volunteers. SourceBots...
Student Robotics
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32,372
However, it is not a requirement that they use Python or the library. The main contents of the kit are: A Power Board (Central control and power distribution) Raspberry Pi 4 2GB with a KCH HAT Two Motor Boards (Boards for controlling brushed DC motors) A Ruggeduino Board (General purpose digital I/O and analogue input)...
Student Robotics
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32,373
Another group of volunteers (the Kit Team) develops and maintains a modular "robotics kit" that is provided to every team. The current revision of the kit uses a Raspberry Pi 4 as its central controller; previously both an Odroid U3 (2015 - 2022) and BeagleBoard have been used. Most competitors use the Python programmi...
Student Robotics
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32,374
The competitors may program their robot in Python via an IDE provided by Student Robotics. Student Robotics does not ban, nor support other methods than the IDE for programming their robots. The competition is free to enter although schools have to make their own travel arrangements and provide the materials to build a...
Student Robotics
0.803915
32,375
There is also a mini-game to introduce the teams to the kit. During the competition cycle, "Tech Days" held at various locations where teams are encouraged to work on their robot under the supervision of Student Robotics' Volunteers. Historically the competition has been hosted on the Highfield Campus of the University...
Student Robotics
0.803915
32,376
On the afternoon of the second day, the points from the league table determine the rounds for the knockout stage, which eventually determines the winners of the competition. Teams are introduced to the competition, and provided with their kit, at a "KickStart" event at the beginning of the academic year in October. Kic...
Student Robotics
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32,377
The competition is designed, organised and managed by a team of volunteers ("Blueshirts"). Most volunteers have previously competed in an annual competition and many have gone on to study robotics, computer science or engineering at university. The competition takes place over a weekend in April/May. There are a series...
Student Robotics
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32,378
This task involved moving and stacking cans of food in an arena, and marks the return of Student Robotics to an in-person competition following the COVID-19 pandemic. This competition year also marked a transition to Python 3 on the physical kit, and a new computer vision system based on OpenCV. 23 teams attended the c...
Student Robotics
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32,379
Multipliers are awarded for getting zones in a row or column. The 2013 competition final ended in a three-way tie, so a tie-breaker round was played. This tie breaker has been said to be the most tense match in Student Robotics history as it was won 3 seconds before the end. The video of this can be found here. Details...
Student Robotics
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32,380
Student Robotics is a registered charity that runs an annual robotics competition for teams of 16 to 19 year-olds. The charity aims to foster a world where engineering and artificial intelligence is accessible to young people with a stated mission "to bring the excitement of engineering and the challenge of coding to y...
Student Robotics
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32,381
The Cahn–Hilliard equation (after John W. Cahn and John E. Hilliard) is an equation of mathematical physics which describes the process of phase separation, by which the two components of a binary fluid spontaneously separate and form domains pure in each component. If c {\displaystyle c} is the concentration of the fl...
Cahn–Hilliard equation
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32,382
Tracking solutions seek to track the changes in the concept by continually updating the model. Methods for achieving this include online machine learning, frequent retraining on the most recently observed samples, and maintaining an ensemble of classifiers where one new classifier is trained on the most recent batch of...
Concept drift
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32,383
To prevent deterioration in prediction accuracy because of concept drift, reactive and tracking solutions can be adopted. Reactive solutions retrain the model in reaction to a triggering mechanism, such as a change-detection test, to explicitly detect concept drift as a change in the statistics of the data-generating p...
Concept drift
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32,384
In machine learning and predictive analytics this drift phenomenon is called concept drift. In machine learning, a common element of a data model are the statistical properties, such as probability distribution of the actual data. If they deviate from the statistical properties of the training data set, then the learne...
Concept drift
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32,385
Another important area is software engineering, where three types of data drift affecting data fidelity may be recognized. Changes in the software environment ("infrastructure drift") may invalidate software infrastructure configuration. "Structural drift" happens when the data schema changes, which may invalidate data...
Concept drift
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32,386
2014 Special Session on "Concept Drift, Domain Adaptation & Learning in Dynamic Environments" @IEEE IJCNN 2014 2013 RealStream Real-World Challenges for Data Stream Mining Workshop-Discussion at the ECML PKDD 2013, Prague, Czech Republic. LEAPS 2013 The 1st International Workshop on Learning stratEgies and dAta Proces...
Concept drift
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32,387
"A framework for generating data to simulate changing environments". AIAP'07: Proceedings of the 25th IASTED International Multi-Conference: artificial intelligence and applications. pp. 384–389. Code
Concept drift
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32,388
"Autopilot: Simulating Changing Concepts in Real Data" (PDF). Proceedings of the 19th Irish Conference on Artificial Intelligence & Cognitive Science. pp.
Concept drift
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32,389
Brazilian symposium on artificial intelligence. Springer. pp.
Concept drift
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32,390
The built up edge effectively changes tool geometry and rake steepness. It also reduces the contact area between the chip and the cutting tool, leading to: A reduction in the power demand of the cutting operation. Slight increase in tool life, since the cutting is partly being done by the built up edge rather than the ...
Built up edge
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32,391
Using gyrotrigonometry, a gyrovector addition can be found which operates according to the gyroparallelogram law. This is the coaddition to the gyrogroup operation. Gyroparallelogram addition is commutative. The gyroparallelogram law is similar to the parallelogram law in that a gyroparallelogram is a hyperbolic quadri...
Gyrovector space
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32,392
Gyrotrigonometry is the use of gyroconcepts to study hyperbolic triangles. Hyperbolic trigonometry as usually studied uses the hyperbolic functions cosh, sinh etc., and this contrasts with spherical trigonometry which uses the Euclidean trigonometric functions cos, sin, but with spherical triangle identities instead of...
Gyrovector space
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32,393
A gyrovector space is a mathematical concept proposed by Abraham A. Ungar for studying hyperbolic geometry in analogy to the way vector spaces are used in Euclidean geometry. Ungar introduced the concept of gyrovectors that have addition based on gyrogroups instead of vectors which have addition based on groups. Ungar ...
Gyrovector space
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32,394
Domenico Giulini, Algebraic and geometric structures of Special Relativity, A Chapter in "Special Relativity: Will it Survive the Next 100 Years? ", edited by Claus Lämmerzahl, Jürgen Ehlers, Springer, 2006.
Gyrovector space
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32,395
A review of one of the earlier gyrovector books says the following: "Over the years, there have been a handful of attempts to promote the non-Euclidean style for use in problem solving in relativity and electrodynamics, the failure of which to attract any substantial following, compounded by the absence of any positive...
Gyrovector space
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32,396
A proper velocity space model of hyperbolic geometry is given by proper velocities with vector addition given by the proper velocity addition formula: u ⊕ U v = u + v + { β u 1 + β u u ⋅ v c 2 + 1 − β v β v } u {\displaystyle \mathbf {u} \oplus _{U}\mathbf {v} =\mathbf {u} +\mathbf {v} +\left\{{\frac {\beta _{\mathbf {...
Gyrovector space
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32,397
The study of triangle centers traditionally is concerned with Euclidean geometry, but triangle centers can also be studied in hyperbolic geometry. Using gyrotrigonometry, expressions for trigonometric barycentric coordinates can be calculated that have the same form for both euclidean and hyperbolic geometry. In order ...
Gyrovector space
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32,398
The method or process of determining the resulting immission level is called noise calculation, its graphical representation is called noise map. Noise calculation is done for the following reasons: to calculate a current situation based on existing physics, mostly when a physical measurement at a location is impractic...
Noise calculation
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In the social sciences, ROC analysis is often called the ROC Accuracy Ratio, a common technique for judging the accuracy of default probability models. ROC curves are widely used in laboratory medicine to assess the diagnostic accuracy of a test, to choose the optimal cut-off of a test and to compare diagnostic accurac...
ROC curve
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