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15,600 | Discrete element method Divided differences Finite difference coefficient Finite difference method Finite element method Finite volume method Numerical differentiation Numerical integration Numerical methods for ordinary differential equations | Discrete calculus | 0.814271 |
15,601 | In technical language, integral calculus studies a certain linear operator. The Riemann sum inputs a function and outputs a function, which gives the algebraic sum of areas between the part of the graph of the input and the x-axis. A motivating example is the distances traveled in a given time. | Discrete calculus | 0.814271 |
15,602 | The codifferential δ: C k → C k − 1 {\displaystyle \delta :C^{k}\to C^{k-1}} is an operator defined on k {\displaystyle k} -forms by: δ = ( − 1 ) n ( k − 1 ) + 1 ⋆ d ⋆ = ( − 1 ) k ⋆ − 1 d ⋆ , {\displaystyle \delta =(-1)^{n(k-1)+1}{\star }d{\star }=(-1)^{k}\,{\star }^{-1}d{\star },} where d {\displaystyle d} is the exte... | Discrete calculus | 0.814271 |
15,603 | . , {\displaystyle ,,...,} , then for any 0 {\displaystyle 0} -cochain f {\displaystyle f} ∫ σ d f = f ( a n ) − f ( a 0 ) {\displaystyle \int _{\sigma }df=f(a_{n})-f(a_{0})} Fundamental theorem of calculus II: if the graph is a tree, g {\displaystyle g} is a 1 {\displaystyle 1} -cochain, and a function ( 0 {\displays... | Discrete calculus | 0.814271 |
15,604 | {\displaystyle \int _{\sigma }g=\sum _{\sigma }g{\big (}{\big )}.} These are the properties: Constant rule: If c {\displaystyle c} is a constant, then d c = 0 {\displaystyle dc=0} Linearity: if a {\displaystyle a} and b {\displaystyle b} are constants, d ( a f + b g ) = a d f + b d g , ∫ σ ( a f + b g ) = a ∫ σ f + b ∫... | Discrete calculus | 0.814271 |
15,605 | These are their properties: Constant rule: If c {\displaystyle c} is a constant, then Δ c = 0 {\displaystyle \Delta c=0} Linearity: if a {\displaystyle a} and b {\displaystyle b} are constants, Δ ( a f + b g ) = a Δ f + b Δ g , ∑ ( a f + b g ) = a ∑ f + b ∑ g {\displaystyle \Delta (af+bg)=a\,\Delta f+b\,\Delta g,\quad ... | Discrete calculus | 0.814271 |
15,606 | During the 20th century discrete calculus remains interlinked with infinitesimal calculus especially differential forms but also starts to draw from algebraic topology as both develop. The main contributions come from the following individuals: Henri Poincaré: triangulations (barycentric subdivision, dual triangulation... | Discrete calculus | 0.814271 |
15,607 | The early history of discrete calculus is the history of calculus. Such basic ideas as the difference quotients and the Riemann sums appear implicitly or explicitly in definitions and proofs. After the limit is taken, however, they are never to be seen again. However, the Kirchhoff's voltage law (1847) can be expressed... | Discrete calculus | 0.814271 |
15,608 | In discrete calculus, this is a construction that creates from forms higher order forms: adjoining two cochains of degree p {\displaystyle p} and q {\displaystyle q} to form a composite cochain of degree p + q {\displaystyle p+q} . For cubical complexes, the wedge product is defined on every cube seen as a vector space... | Discrete calculus | 0.814271 |
15,609 | The fundamental theorem of calculus: If a function f {\displaystyle f} is defined on a partition of the interval {\displaystyle } , b = a + n h {\displaystyle b=a+nh} , and if F {\displaystyle F} is a function whose difference quotient is f {\displaystyle f} , then we have: ∑ i = 0 n − 1 f ( a + i h + h / 2 ) Δ x = F ... | Discrete calculus | 0.814271 |
15,610 | As this computation is carried out for each n {\displaystyle n} , the new function is defined at the points: a , a + h , a + 2 h , … , a + n h , … {\displaystyle a,a+h,a+2h,\ldots ,a+nh,\ldots } The fundamental theorem of calculus states that differentiation and integration are inverse operations. More precisely, it re... | Discrete calculus | 0.814271 |
15,611 | {\displaystyle {\begin{aligned}{\frac {\Delta f}{\Delta x}}(x)&={(x+h)^{2}-x^{2} \over {h}}\\&={x^{2}+2hx+h^{2}-x^{2} \over {h}}\\&={2hx+h^{2} \over {h}}\\&=2x+h.\end{aligned}}} The difference quotient of the difference quotient is called the second difference quotient and it is defined at a + h , a + 2 h , a + 3 h , …... | Discrete calculus | 0.814271 |
15,612 | In formal terms, the difference quotient is a linear operator which takes a function as its input and produces a second function as its output. This is more abstract than many of the processes studied in elementary algebra, where functions usually input a number and output another number. For example, if the doubling f... | Discrete calculus | 0.814271 |
15,613 | Discrete differential calculus is the study of the definition, properties, and applications of the difference quotient of a function. The process of finding the difference quotient is called differentiation. Given a function defined at several points of the real line, the difference quotient at that point is a way of e... | Discrete calculus | 0.814271 |
15,614 | The study of the concepts of change starts with their discrete form. The development is dependent on a parameter, the increment Δ x {\displaystyle \Delta x} of the independent variable. If we so choose, we can make the increment smaller and smaller and find the continuous counterparts of these concepts as limits. Infor... | Discrete calculus | 0.814271 |
15,615 | Differential calculus concerns incremental rates of change and the slopes of piece-wise linear curves. Integral calculus concerns accumulation of quantities and the areas under piece-wise constant curves. These two points of view are related to each other by the fundamental theorem of discrete calculus. | Discrete calculus | 0.814271 |
15,616 | Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. The word calculus is a Latin word, meaning originally "small pebble"; as such pebbles were u... | Discrete calculus | 0.814271 |
15,617 | In nuclear medicine, it is used to build models of radiation transport in targeted tumor therapies. In economics, calculus allows for the determination of maximal profit by calculating both marginal cost and marginal revenue, as well as modeling of markets.Discrete calculus can be used in conjunction with other mathema... | Discrete calculus | 0.814271 |
15,618 | It can be used to efficiently calculate sums of rectangular domains in images, to rapidly extract features and detect object; another algorithm that could be used is the summed area table. In the realm of medicine, calculus can be used to find the optimal branching angle of a blood vessel so as to maximize flow. From t... | Discrete calculus | 0.814271 |
15,619 | In engineering, difference equations are used to plot a course of a spacecraft within zero gravity environments, to model heat transfer, diffusion, and wave propagation. The discrete analogue of Green's theorem is applied in an instrument known as a planimeter, which is used to calculate the area of a flat surface on a... | Discrete calculus | 0.814271 |
15,620 | Maxwell's theory of electromagnetism and Einstein's theory of general relativity have been expressed in the language of discrete calculus. Chemistry uses calculus in determining reaction rates and radioactive decay (exponential decay). In biology, population dynamics starts with reproduction and death rates to model po... | Discrete calculus | 0.814271 |
15,621 | An example of the use of discrete calculus in mechanics is Newton's second law of motion: historically stated it expressly uses the term "change of motion" which implies the difference quotient saying The change of momentum of a body is equal to the resultant force acting on the body and is in the same direction. Commo... | Discrete calculus | 0.814271 |
15,622 | Discrete calculus is used for modeling either directly or indirectly as a discretization of infinitesimal calculus in every branch of the physical sciences, actuarial science, computer science, statistics, engineering, economics, business, medicine, demography, and in other fields wherever a problem can be mathematical... | Discrete calculus | 0.814271 |
15,623 | The hazards of synthetic biology include biosafety hazards to workers and the public, biosecurity hazards stemming from deliberate engineering of organisms to cause harm, and environmental hazards. The biosafety hazards are similar to those for existing fields of biotechnology, mainly exposure to pathogens and toxic ch... | Synthetic Biology | 0.81427 |
15,624 | Synthetic biology has traditionally been divided into four different engineering approaches: top down, parallel, orthogonal and bottom up.To replicate emergent behaviours from natural biology and build artificial life, unnatural chemicals are used. The other looks for interchangeable components from biological systems ... | Synthetic Biology | 0.81427 |
15,625 | Synthetic biology (SynBio) is a multidisciplinary field of science that focuses on living systems and organisms, and it applies engineering principles to develop new biological parts, devices, and systems or to redesign existing systems found in nature.It is a branch of science that encompasses a broad range of methodo... | Synthetic Biology | 0.81427 |
15,626 | Lastly, environmental hazards include adverse effects on biodiversity and ecosystem services, including potential changes to land use resulting from agricultural use of synthetic organisms. Synthetic biology is an example of a dual-use technology with the potential to be used in ways that could intentionally or uninten... | Synthetic Biology | 0.81427 |
15,627 | The commission did not recommend policy or oversight changes and called for continued funding of the research and new funding for monitoring, study of emerging ethical issues and public education.Synthetic biology, as a major tool for biological advances, results in the "potential for developing biological weapons, pos... | Synthetic Biology | 0.81427 |
15,628 | In January 2009, the Alfred P. Sloan Foundation funded the Woodrow Wilson Center, the Hastings Center, and the J. Craig Venter Institute to examine the public perception, ethics and policy implications of synthetic biology.On July 9–10, 2009, the National Academies' Committee of Science, Technology & Law convened a sym... | Synthetic Biology | 0.81427 |
15,629 | Some ethical issues relate to biosecurity, where biosynthetic technologies could be deliberately used to cause harm to society and/or the environment. Since synthetic biology raises ethical issues and biosecurity issues, humanity must consider and plan on how to deal with potentially harmful creations, and what kinds o... | Synthetic Biology | 0.81427 |
15,630 | It is also known as perpendicular engineering. This strategy, also referred to as "chemical synthetic biology," principally seeks to alter or enlarge the genetic codes of living systems utilising artificial DNA bases and/or amino acids. This subfield is also connected to xenobiology, a newly developed field that combin... | Synthetic Biology | 0.81427 |
15,631 | In organic chemistry, acid hydrolysis is a hydrolysis process in which a protic acid is used to catalyze the cleavage of a chemical bond via a nucleophilic substitution reaction, with the addition of the elements of water (H2O). For example, in the conversion of cellulose or starch to glucose. For the case of esters an... | Acid hydrolysis | 0.814261 |
15,632 | The functions of C ( z ) {\displaystyle \mathbf {C} (z)} form an algebraic field, known as the field of rational functions on the sphere. For example, given the function f ( z ) = 6 z 2 + 1 2 z 2 − 50 {\displaystyle f(z)={\frac {6z^{2}+1}{2z^{2}-50}}} we may define f ( ± 5 ) = ∞ {\displaystyle f(\pm 5)=\infty } , since... | Extended complex numbers | 0.814253 |
15,633 | In projective geometry, the sphere can be thought of as the complex projective line P 1 ( C ) {\displaystyle \mathbf {P} ^{1}(\mathbf {C} )} , the projective space of all complex lines in C 2 {\displaystyle \mathbf {C} ^{2}} . As with any compact Riemann surface, the sphere may also be viewed as a projective algebraic ... | Extended complex numbers | 0.814253 |
15,634 | For example, any rational function on the complex plane can be extended to a holomorphic function on the Riemann sphere, with the poles of the rational function mapping to infinity. More generally, any meromorphic function can be thought of as a holomorphic function whose codomain is the Riemann sphere. In geometry, th... | Extended complex numbers | 0.814253 |
15,635 | There are various approaches to determining the vectors x i {\displaystyle x_{i}} . Usually, MDS is formulated as an optimization problem, where ( x 1 , … , x M ) {\displaystyle (x_{1},\ldots ,x_{M})} is found as a minimizer of some cost function, for example, a r g m i n x 1 , … , x M ∑ i < j ( ‖ x i − x j ‖ − d i , j... | Multidimensional Scaling | 0.814253 |
15,636 | Instantaneous acceleration, meanwhile, is the limit of the average acceleration over an infinitesimal interval of time. In the terms of calculus, instantaneous acceleration is the derivative of the velocity vector with respect to time: As acceleration is defined as the derivative of velocity, v, with respect to time t ... | Uniform acceleration | 0.814252 |
15,637 | Applying the standard technique of proof by cases to recursively defined sets or functions, as in the preceding sections, yields structural induction — a powerful generalization of mathematical induction widely used to derive proofs in mathematical logic and computer science. | Mathematical recursion | 0.814252 |
15,638 | In set theory, this is a theorem guaranteeing that recursively defined functions exist. Given a set X, an element a of X and a function f: X → X, the theorem states that there is a unique function F: N → X {\displaystyle F:\mathbb {N} \to X} (where N {\displaystyle \mathbb {N} } denotes the set of natural numbers inclu... | Mathematical recursion | 0.814252 |
15,639 | The first synthetic ion channel was constructed by partial substitution on the primary rim of β-cyclodextrin. Other substituted β-cyclodextrins have since been reported, including thiol-modified cyclodextrins, an anion-selective oligobutylene channel, and various poly-ethyleneoxide linked starburst oligomers. Structure... | Synthetic ion channels | 0.814245 |
15,640 | Through this pore, ions flow down the potential and electrochemical gradient rapidly (>106/second), the maximum flux limited by the geometry and dimensions of the pore. At some later instant the pore may close or collapse, whereupon the current returns to zero. This open-state current, originating and amplified from a ... | Synthetic ion channels | 0.814245 |
15,641 | An "ion-channel forming" molecule can often show multiple types of conductance activities in planar bilayer membranes. Each of these modes of action can be characterized by their open duration (sub-ms---hours), related to whether the active structure is kinetically labile, unit conductance (pS---nS), related to the geo... | Synthetic ion channels | 0.814245 |
15,642 | Most (but not all; see minimalist channels) synthetic channels have chemical structures substantially larger than typical small molecules (molecular weights ~1-5kDa). This originates from the need to be amphiphilic, that is, have both sufficient hydrophobic portions to allow partitioning into lipid bilayer, as well as ... | Synthetic ion channels | 0.814245 |
15,643 | Semi-synthetic bio-hybrid channels constructed by modifications of natural ion channels had been constructed. Leveraging modern synthetic organic chemistry, these allows pinpoint modifications of existing structures to either elucidate their transport mechanisms or to graft on new functionalities. Gramicidin and alamet... | Synthetic ion channels | 0.814245 |
15,644 | In pattern recognition and machine learning, a feature vector is an n-dimensional vector of numerical features that represent some object. Many algorithms in machine learning require a numerical representation of objects, since such representations facilitate processing and statistical analysis. When representing image... | Feature vector | 0.814244 |
15,645 | In tandem mass spectrometry in space, the separation elements are physically separated and distinct, although there is a physical connection between the elements to maintain high vacuum. These elements can be sectors, transmission quadrupole, or time-of-flight. When using multiple quadrupoles, they can act as both mass... | Data-dependent acquisition | 0.814241 |
15,646 | The content of MIM/OMIM is based on selection and review of the published peer-reviewed biomedical literature. Updating of content is performed by a team of science writers and curators under the direction of Ada Hamosh at the McKusick-Nathans Institute of Genetic Medicine of Johns Hopkins University. While OMIM is fre... | Online Mendelian Inheritance in Man | 0.814238 |
15,647 | OMIM is the online continuation of Victor A. McKusick's Mendelian Inheritance in Man (MIM), which was published in 12 editions between 1966 and 1998. Nearly all of the 1,486 entries in the first edition of MIM discussed phenotypes.MIM/OMIM is produced and curated at the Johns Hopkins School of Medicine (JHUSOM). OMIM b... | Online Mendelian Inheritance in Man | 0.814238 |
15,648 | There is then an associated action of the Lie algebra so(3) of SO(3); the operators describing the action of so(3) on our Hilbert space are the (total) angular momentum operators. The relationship between the angular momentum operator and the rotation operators is the same as the relationship between Lie algebras and L... | Relative angular momentum | 0.814235 |
15,649 | In physics, angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a mag... | Relative angular momentum | 0.814235 |
15,650 | Arthur Samuel first used the term in its game-theoretic sense in his seminal paper on machine learning in checkers in 1959, but with a slightly different meaning: the "ply", in Samuel's terminology, is actually the depth of analysis ("Certain expressions were introduced which we will find useful. These are: Ply, define... | Ply (game theory) | 0.814231 |
15,651 | William Boyd was an American immunochemist and biochemist who became famous for his research on the genetics of race in the 1950s. During the 1940s, Boyd and Karl O. Renkonen independently discovered that lectins react differently to various blood types, after finding that the crude extracts of the lima bean and tufted... | Genetic history | 0.814224 |
15,652 | Finally, archaeogenetics has been used to study the occupation of Australia and New Guinea. The Indigenous people of Australia and New Guinea are phenotypically very similar, but mtDNA has shown that this is due to convergence from living in similar conditions. Non-coding regions of mt-DNA have shown “no similarities” ... | Genetic history | 0.814224 |
15,653 | He also focused on the biological significance of polymorphisms. His work provided the foundation for archaeogenetics because it facilitated the separation of genetic evidence for biological relationships between people. This genetic evidence was previously used for that purpose. It also provided material that could be... | Genetic history | 0.814224 |
15,654 | Archaeogenetics provides us with genetic evidence of ancient population group migrations, domestication events, and plant and animal evolution. The ancient DNA cross referenced with the DNA of relative modern genetic populations allows researchers to run comparison studies that provide a more complete analysis when anc... | Genetic history | 0.814224 |
15,655 | Archaeogenetics is the study of ancient DNA using various molecular genetic methods and DNA resources. This form of genetic analysis can be applied to human, animal, and plant specimens. Ancient DNA can be extracted from various fossilized specimens including bones, eggshells, and artificially preserved tissues in huma... | Genetic history | 0.814224 |
15,656 | Archaeogenetics has been used to understand the development of domestication of plants and animals. | Genetic history | 0.814224 |
15,657 | The information gained from genetics studies on current populations helps guide the Archaeologist's search for documenting these ancestors.Archaeogenetics has been used to trace the domestication of pigs throughout the old world. These studies also reveal evidence about the details of early farmers. Methods of Archaeog... | Genetic history | 0.814224 |
15,658 | Archaeogenetics has been used to study the domestication of animals. By analyzing genetic diversity in domesticated animal populations researchers can search for genetic markers in DNA to give valuable insight about possible traits of progenitor species. These traits are then used to help distinguish archaeological rem... | Genetic history | 0.814224 |
15,659 | Archaeogenetics has been used to better understand the populating of the Americas from Asia. Native American mtDNA haplogroups have been estimated to be between 15 and 20 kya, although there is some variation in these estimates. Genetic data has been used to propose various theories regarding how the Americas were colo... | Genetic history | 0.814224 |
15,660 | Analysis of mtDNA shows that modern humans occupied Eurasia in a single migratory event between 60 and 70 kya. Genetic evidence shows that occupation of the Near East and Europe happened no earlier than 50 kya. Studying haplogroup U has shown separate dispersals from the Near East both into Europe and into North Africa... | Genetic history | 0.814224 |
15,661 | Archaeogenetics has also been used to study hunter-gatherer populations in the region, such as the Ainu from Japan and Negrito groups in the Philippines. For example, the Pan-Asian SNP study found that Negrito populations in Malaysia and the Negrito populations in the Philippines were more closely related to non-Negrit... | Genetic history | 0.814224 |
15,662 | The combination of genetics and archeological findings have been used to trace the earliest signs of plant domestication around the world. However, since the nuclear, mitochondrial, and chloroplast genomes used to trace domestication's moment of origin have evolved at different rates, its use to trace genealogy have be... | Genetic history | 0.814224 |
15,663 | In vector computer graphics, CAD systems, and geographic information systems, geometric primitive (or prim) is the simplest (i.e. 'atomic' or irreducible) geometric shape that the system can handle (draw, store). Sometimes the subroutines that draw the corresponding objects are called "geometric primitives" as well. Th... | Line primitives | 0.814222 |
15,664 | Reducing energy loads of main systems equipment providing heating, cooling and water heating can be achieved by upgrading physical equipment including replacing older equipment with newer, more energy-efficient units, upgrading the building envelope with insulation and higher-grade windows, creating more efficient zoni... | Miscellaneous electric loads | 0.814222 |
15,665 | The corresponding formula for a continuous function (or waveform) f(t) defined over the interval T 1 ≤ t ≤ T 2 {\displaystyle T_{1}\leq t\leq T_{2}} is f RMS = 1 T 2 − T 1 ∫ T 1 T 2 2 d t , {\displaystyle f_{\text{RMS}}={\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{}^{2}\,{\rm {d}}t}}},} and the RMS for a func... | Root mean squared | 0.81422 |
15,666 | The RMS value of a set of values (or a continuous-time waveform) is the square root of the arithmetic mean of the squares of the values, or the square of the function that defines the continuous waveform. In physics, the RMS current value can also be defined as the "value of the direct current that dissipates the same ... | Root mean squared | 0.81422 |
15,667 | The RMS can be computed in the frequency domain, using Parseval's theorem. For a sampled signal x = x ( t = n T ) {\displaystyle x=x(t=nT)} , where T {\displaystyle T} is the sampling period, ∑ n = 1 N x 2 = 1 N ∑ m = 1 N | X | 2 , {\displaystyle \sum _{n=1}^{N}{x^{2}}={\frac {1}{N}}\sum _{m=1}^{N}\left|X\right|^{2}... | Root mean squared | 0.81422 |
15,668 | In the area of system identification, a dynamical system is structurally identifiable if it is possible to infer its unknown parameters by measuring its output over time. This problem arises in many branch of applied mathematics, since dynamical systems (such as the ones described by ordinary differential equations) ar... | Structural identifiability | 0.814219 |
15,669 | SourceA model of a possible glucose homeostasis mechanism is given by the differential equations G ˙ = u ( 0 ) + u − ( c + s i I ) G , β ˙ = β ( 1.4583 ⋅ 10 − 5 1 + ( 8.4 G ) 1.7 − 1.7361 ⋅ 10 − 5 1 + ( G 8.4 ) 8.5 ) , I ˙ = p β G 2 α 2 + G 2 − γ I , {\displaystyle {\begin{aligned}&{\dot {G}}=u(0)+u-(c+s_{\mathrm {i} }... | Structural identifiability | 0.814219 |
15,670 | The Institute of Applied Biochemistry is a research laboratory and bioweapons production facility located in Omutninsk, Kirov Oblast. For a time in the 1980s, the facility was directed by Ken Alibek.Wild rodents like rats that live in the woods outside the factory are chronically infected with the "Schu-4 military stra... | Institute of Applied Biochemistry | 0.814212 |
15,671 | In computer science research, Plan 9 has been used as a grid computing platform and as a vehicle for research into ubiquitous computing without middleware. In commerce, Plan 9 underlies Coraid storage systems. However, Plan 9 has never approached Unix in popularity, and has been primarily a research tool: t looks like ... | ANSI/POSIX Environment | 0.81421 |
15,672 | The possibility of inertialess travel was first suggested in Theoretical and Physical Chemistry, published in 1912 by the Tellurian chemist Samuel Lawrence Bigelow, an alumnus of Harvard. The first faster-than-light drive, which achieved only partial neutralization of inertia, was developed on the planet Nevia. Soon th... | Inertialess drive | 0.814209 |
15,673 | The Nevian faster-than-light drive apparently had no noticeable physiological effects even to an observer as well-trained as Conway Costigan. An alternative explanation is possible, however. There is no mention of the neutralization of inertia until the third installment; the physics in the first two installments seems... | Inertialess drive | 0.814209 |
15,674 | The transformation model may be written as T {\displaystyle T} , using which the transformed, registered model point set is: The output of a point set registration algorithm is therefore the optimal transformation T ⋆ {\displaystyle T^{\star }} such that M {\displaystyle {\mathcal {M}}} is best aligned to S {\displayst... | Point-set registration | 0.814205 |
15,675 | Graduated non-convexity (GNC) is a general-purpose framework for solving non-convex optimization problems without initialization. It has achieved success in early vision and machine learning applications. The key idea behind GNC is to solve the hard non-convex problem by starting from an easy convex problem. Specifical... | Point-set registration | 0.814205 |
15,676 | Given two point sets, rigid registration yields a rigid transformation which maps one point set to the other. A rigid transformation is defined as a transformation that does not change the distance between any two points. Typically such a transformation consists of translation and rotation. In rare cases, the point set... | Point-set registration | 0.814205 |
15,677 | In the M step, an unconstrained optimization on a matrix Lie group is designed to efficiently update the rigid transformation of the registration. Taking advantage of the local geometric covariances, the method shows a superior performance in accuracy and robustness to noise and outliers, compared with the baseline CPD... | Point-set registration | 0.814205 |
15,678 | Outlier removal methods seek to pre-process the set of highly corrupted correspondences before estimating the spatial transformation. The motivation of outlier removal is to significantly reduce the number of outlier correspondences, while maintaining inlier correspondences, so that optimization over the transformation... | Point-set registration | 0.814205 |
15,679 | At each iteration, the method first randomly samples 3 out of the total number of N {\displaystyle N} correspondences and computes a hypothesis ( l , R , t ) {\displaystyle (l,R,t)} using Horn's method, then the method evaluates the constraints in (cb.4) to count how many correspondences actually agree with such a hypo... | Point-set registration | 0.814205 |
15,680 | Maximum consensus seeks to find the largest set of correspondences that are consistent with the generative model (cb.1) for some choice of spatial transformation ( l , R , t ) {\displaystyle (l,R,t)} . Formally speaking, maximum consensus solves the following optimization: where | I | {\displaystyle \vert {\mathcal {I}... | Point-set registration | 0.814205 |
15,681 | Therefore, at each level of the hyper-parameter μ {\displaystyle \mu } , the following optimization is solved: Black and Rangarajan proved that the objective function of each optimization (cb.6) can be dualized into a sum of weighted least squares and a so-called outlier process function on the weights that determine t... | Point-set registration | 0.814205 |
15,682 | An variant of coherent point drift called CPD with Local Surface Geometry (LSG-CPD) for rigid point cloud registration. The method adaptively adds different levels of point-to-plane penalization on top of the point-to-point penalization based on the flatness of the local surface. This results in GMM components with ani... | Point-set registration | 0.814205 |
15,683 | In 2021, media outlets reported that the world's first synthetic coffee products have been created by two biotechnology companies, still awaiting regulatory approvals for near-term commercialization. Such products – which can be produced via cellular agriculture in bioreactors and for which multiple companies' R&D have... | Cellular agriculture | 0.814203 |
15,684 | Cellular agriculture focuses on the production of agricultural products from cell cultures using a combination of biotechnology, tissue engineering, molecular biology, and synthetic biology to create and design new methods of producing proteins, fats, and tissues that would otherwise come from traditional agriculture. ... | Cellular agriculture | 0.814203 |
15,685 | As biotechnological processes are scaled, experiments start to become increasingly expensive, as bioreactors of increasing volume will have to be created. Each increase in size will require a re-optimization of various parameters such as unit operations, fluid dynamics, mass transfer, and reaction kinetics. | Cellular agriculture | 0.814203 |
15,686 | Today, cheese making processes use rennet enzymes from genetically engineered bacteria, fungi, or yeasts because they are unadulterated, more consistent, and less expensive than animal-derived rennet.In 2004, Jason Matheny founded New Harvest, whose mission is to "accelerate breakthroughs in cellular agriculture". New ... | Cellular agriculture | 0.814203 |
15,687 | A joint program between New Harvest and the Tissue Engineering Research Center (TERC), an NIH-supported initiative established in 2004 to advance tissue engineering. The fellowship program offers funding for Masters and PhD students at Tufts university who are interested in bioengineering tunable structures, mechanics,... | Cellular agriculture | 0.814203 |
15,688 | The Numerical Recipes books cover a range of topics that include both classical numerical analysis (interpolation, integration, linear algebra, differential equations, and so on), signal processing (Fourier methods, filtering), statistical treatment of data, and a few topics in machine learning (hidden Markov model, su... | Numerical Recipes | 0.814202 |
15,689 | Since for atomic and molecular gases, the classical ideal gas law is well suited in most cases, let us describe the equation of state for elementary particles with mass m {\displaystyle m} and spin s {\displaystyle s} that takes into account quantum effects. In the following, the upper sign will always correspond to Fe... | Peng-Robinson equation of state | 0.814196 |
15,690 | Destiny is NASA's first permanent operating orbital research station since Skylab was vacated in February 1974. The Boeing Company began construction of the 14.5-tonne (32,000 lb) research laboratory in 1995 at the Michoud Assembly Facility and then the Marshall Space Flight Center in Huntsville, Alabama. Destiny was s... | Destiny Laboratory Module | 0.814196 |
15,691 | Scale-space theory is a framework for multi-scale signal representation developed by the computer vision, image processing and signal processing communities with complementary motivations from physics and biological vision. It is a formal theory for handling image structures at different scales, by representing an imag... | Scale space | 0.814195 |
15,692 | In the area of classical computer vision, scale-space theory has established itself as a theoretical framework for early vision, with Gaussian derivatives constituting a canonical model for the first layer of receptive fields. With the introduction of deep learning, there has also been work on also using Gaussian deriv... | Scale space | 0.814195 |
15,693 | Equivalently, the scale-space family can be defined as the solution of the diffusion equation (for example in terms of the heat equation), ∂ t L = 1 2 ∇ 2 L , {\displaystyle \partial _{t}L={\frac {1}{2}}\nabla ^{2}L,} with initial condition L ( x , y ; 0 ) = f ( x , y ) {\displaystyle L(x,y;0)=f(x,y)} . This formulatio... | Scale space | 0.814194 |
15,694 | The need for different approaches led to the birth of Physics of Failure at the Rome Air Development Center (RADC). Under the auspices of the RADC, the first Physics of Failure in Electronics Symposium was held in September 1962. The goal of the program was to relate the fundamental physical and chemical behavior of ma... | Physics of Failure | 0.814193 |
15,695 | Within the electronics industry, the major driver for the implementation of Physics of Failure was the poor performance of military weapon systems during World War II. During the subsequent decade, the United States Department of Defense funded an extensive amount of effort to especially improve the reliability of elec... | Physics of Failure | 0.814193 |
15,696 | There are some limitations with the use of physics of failure in design assessments and reliability prediction. The first is physics of failure algorithms typically assume a ‘perfect design’. Attempting to understand the influence of defects can be challenging and often leads to Physics of Failure (PoF) predictions lim... | Physics of Failure | 0.814193 |
15,697 | Leveraging this success, additional physics-of-failure based algorithms have been derived for the three other major degradation mechanisms (time dependent dielectric breakdown , hot carrier injection , and negative bias temperature instability ) in modern integrated circuits (equations shown below). More recent work ha... | Physics of Failure | 0.814193 |
15,698 | Black used this knowledge, in combination with experimental findings, to describe the failure rate due to electromigration as M T T F = A ( J − n ) e E a k T {\displaystyle MTTF=A(J^{-n})e^{\frac {Ea}{kT}}} where A is a constant based on the cross-sectional area of the interconnect, J is the current density, Ea is the ... | Physics of Failure | 0.814193 |
15,699 | The initial focus of physics of failure techniques tended to be limited to degradation mechanisms in integrated circuits. This was primarily because the rapid evolution of the technology created a need to capture and predict performance several generations ahead of existing product. One of the first major successes und... | Physics of Failure | 0.814193 |
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