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References
External links
Dragon's Lair Project
arcade-history.com
1984 video games
Arcade video games
Konami games
LaserDisc video games
MSX games
Video games developed in Japan
Western (genre) video games
Konami arcade games | [
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Alice Burks (née Rowe, August 20, 1920 – November 21, 2017) was an American author of children's books and books about the history of electronic computers. Burks was born as Alice Rowe in East Cleveland, Ohio, in 1920. She began her undergraduate degree at Oberlin College on a competitive mathematics scholarship and transferred to the University of Pennsylvania in Philadelphia where she completed her B.A. in mathematics in 1944. During this period, she was employed as a human computer at the University of Pennsylvania's Moore School of Electrical Engineering. She retired from full-time work after marrying Moore School lecturer Dr. Arthur Burks, a mathematician who served as one of the principal engineers in the construction of the ENIAC, the world's first general-purpose electronic digital computer, built at the Moore School between 1943 and 1946. Unlike some of the Moore School women computers, Alice never worked directly with the ENIAC. At the conclusion of Arthur's work with the Moore School and at the Institute for Advanced Study in 1946, Alice moved with Arthur to Ann Arbor, Michigan, where he joined the faculty of the University of Michigan and helped to found the computer science department. She returned to school, earning an M.S. in educational psychology in 1957 from Michigan. | [
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Starting in the 1970s following the decision of Honeywell v. Sperry Rand, the federal court case that invalidated the ENIAC patent, she and husband Arthur championed the work of John Vincent Atanasoff, the Iowa State College physics professor whom the court had ruled invented the first electronic digital computer (a machine that came to be called the Atanasoff–Berry Computer) and from whom the subject matter of the ENIAC was ruled to be derived. In articles and two books, the first co-authored with Arthur, Mrs. Burks sought to bolster the judge's decision and highlight testimony and evidence from the case. This pitted the Burkses in a deeply acrimonious controversy against exponents of ENIAC inventors John Mauchly and J. Presper Eckert. Alice later lived in Ann Arbor, Michigan, where she was assisting her husband Arthur Burks with writing his memoirs and preparing his papers for university donation. Arthur died on May 14, 2008. Alice died in November 2017 at the age of 97. Bibliography
Children's books
See also
References
External links
Oral history interview with Alice R. Burks and Arthur W. Burks. Charles Babbage Institute, University of Minnesota. International Biographical Dictionary of Computer Pioneers
1920 births
2017 deaths
American children's writers
Human computers
Oberlin College alumni
University of Michigan School of Education alumni
Writers from Ann Arbor, Michigan | [
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Failing badly and failing well are concepts in systems security and network security (and engineering in general) describing how a system reacts to failure. The terms have been popularized by Bruce Schneier, a cryptographer and security consultant. Failing badly
A system that fails badly is one that has a catastrophic result when failure occurs. A single point of failure can thus bring down the whole system. Examples include:
Databases (such as credit card databases) protected only by a password. Once this security is breached, all data can be accessed. Fracture critical structures, such as buildings or bridges, that depend on a single column or truss, whose removal would cause a chain reaction collapse under normal loads. Security checks which concentrate on establishing identity, not intent (thus allowing, for example, suicide attackers to pass). Internet access provided by a single service provider. If the provider's network fails, all Internet connectivity is lost. Systems, including social ones, that rely on a single person, who, if absent or becomes permanently unavailable, halts the entire system. Brittle materials, such as "over-reinforced concrete", when overloaded, fail suddenly and catastrophically with no warning. Keeping the only copy of data in one central place. That data is lost forever when that place is damaged, such as the 1836 U.S. Patent Office fire, the American 1973 National Personnel Records Center fire, and the destruction of the Library of Alexandria. Failing well
A system that fails well is one that compartmentalizes or contains its failure. | [
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] |
Examples include:
Compartmentalized hulls in watercraft, ensuring that a hull breach in one compartment will not flood the entire vessel. Databases that do not allow downloads of all data in one attempt, limiting the amount of compromised data. Structurally redundant buildings conceived to resist loads beyond those expected under normal circumstances, or resist loads when the structure is damaged. Computer systems that restart or proceed to a stopped state when an invalid operation occurs. Access control systems that are locked when power is cut to the unit. Concrete structures which show fractures long before breaking under load, thus giving early warning. Armoured cockpit doors on airplanes, which confine a potential hijacker within the cabin even if they are able to bypass airport security checks. Internet connectivity provided by more than one vendor or discrete path, known as multihoming. Star or mesh networks, which can continue to operate when a node or connection has failed (though for a star network, failure of the central hub will still cause the network to fail). Ductile materials, such as "under-reinforced concrete", when overloaded, fail gradually – they yield and stretch, giving some warning before ultimate failure. Making a backup copy of all important data and storing it in a separate place. That data can be recovered from the other location when either place is damaged. Designing a system to 'fail well' has also been alleged to be a better use of limited security funds than the typical quest to eliminate all potential sources of errors and failure. See also
References
Engineering failures
Systems theory
Security engineering | [
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CTL* is a superset of computational tree logic (CTL) and linear temporal logic (LTL). It freely combines path quantifiers and temporal operators. Like CTL, CTL* is a branching-time logic. The formal semantics of CTL* formulae are defined with respect to a given Kripke structure. History
LTL had been proposed for the verification of computer programs, first by Amir Pnueli in 1977. Four years later in 1981 E. M. Clarke and E. A. Emerson invented CTL and CTL model checking. CTL* was defined by E. A. Emerson and Joseph Y. Halpern in 1983. CTL and LTL were developed independently before CTL*. Both sublogics have become standards in the model checking community, while CTL* is of practical importance because it provides an expressive testbed for representing and comparing these and other logics. This is surprising because the computational complexity of model checking in CTL* is not worse than that of LTL: they both lie in PSPACE. Syntax
The language of well-formed CTL* formulae is generated by the following unambiguous (with respect to bracketing) context-free grammar:
where ranges over a set of atomic formulas. Valid CTL*-formulae are built using the nonterminal . These formulae are called state formulae, while those created by the symbol are called path formulae. (The above grammar contains some redundancies; for example as well as implication and equivalence can be defined as just for Boolean algebras (or propositional logic) from negation and conjunction, and the temporal operators X and U are sufficient to define the other two.) The operators basically are the same as in CTL. | [
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However, in CTL, every temporal operator () has to be directly preceded by a quantifier, while in CTL* this is not required. The universal path quantifier may be defined in CTL* in the same way as for classical predicate calculus , although this in not possible in the CTL fragment. Examples of formulae
CTL* formula that is neither in LTL or in CTL:
LTL formula that is not in CTL:
CTL formula that is not in LTL:
CTL* formula that is in CTL and LTL:
Remark: When taking LTL as subset of CTL*, any LTL formula is implicitly prefixed with the universal path quantifier . Semantics
The semantics of CTL* are defined with respect to some Kripke structure. As the names imply, state formulae are interpreted with respect to the states of this structure, while path formulae are interpreted over paths on it. State formulae
If a state of the Kripke structure satisfies a state formula it is denoted . This relation is defined inductively as follows:
for all paths starting in
for some path starting in
Path formulae
The satisfaction relation for path formulae and a path is also defined inductively. For this, let denote the sub-path :
Decision problems
Model checking of CTL* is PSPACE-complete and the satisfiability problem is 2EXPTIME-complete. See also
Temporal logic
Kripke structure
Model checking
Reo Coordination Language
References
Amir Pnueli: The temporal logic of programs. Proceedings of the 18th Annual Symposium on Foundations of Computer Science (FOCS), 1977, 46–57. | [
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DOI= 10.1109/SFCS.1977.32
E. Allen Emerson, Joseph Y. Halpern: "Sometimes" and "not never" revisited: on branching versus linear time temporal logic. J. ACM 33, 1 (Jan. 1986), 151–178. DOI= http://doi.acm.org/10.1145/4904.4999
Ph. Schnoebelen: The Complexity of Temporal Logic Model Checking. Advances in Modal Logic 2002: 393–436
External links
CTL Teaching slides of professor Alessandro Artale at the Free University of Bozen-Bolzano
Logic in computer science
Temporal logic | [
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Grupa Lotos S.A. is a vertically integrated oil company based in Gdańsk, Poland. The company is listed in the Polish index WIG30. The Polish state is the majority shareholder with 53% percent. The company's main activity branches are: crude oil production, refining and marketing of oil products. The company is a leader in lubricants on the Polish market. Grupa Lotos is a producer of unleaded gasoline, diesel, fuel oils, aviation fuels, motor and industrial lubricants, bitumens and waxes. In 2018 the Polish oil refiner and retailer PKN Orlen announced its intent to acquire the company. The merger approval from the European Commission required significant asset divestments by both companies and is expected to reach closing in June or July 2022. Consolidation
Grupa Lotos is a holding composed of Grupa Lotos S.A. - the parent undertaking which manages the refinery in Gdańsk - and 18 direct subsidiaries, including Lotos Czechowice (former Rafineria Czechowice), Lotos Jasło (former Rafineria Jasło), crude oil exploration and production company Petrobaltic. In the end of June 2006 Grupa Lotos employed 5547 people. This is 112 employees more than in the end of 2005. Subsidiaries
LOTOS Paliwa
LOTOS Oil
LOTOS Asfalt
LOTOS Gaz w likwidacji
LOTOS Petrobaltic
LOTOS Exploration & Production Norge
LOTOS Infrastruktura
LOTOS Terminale
LOTOS Kolej
LOTOS Lab
LOTOS Ochrona
LOTOS Straż
LOTOS Serwis
LOTOS Geonafta
LOTOS-Air BP Polska
Profits
Grupa Lotos holding group consolidated net profit for the first quarter of 2006 financial year, estimated in accordance with IFRS reached approx. PLN 118 million. | [
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Grupa Lotos holding group consolidated net profit for whole 2005 financial year, estimated in accordance with IFRS reached approx. PLN 970 million. This is circa PLN 426 million more comparing to financial data from 2004. Capacity
Gdańsk refinery, owned by Grupa Lotos S.A., refines 6 million tons of crude oil per year. In 2005 Grupa Lotos holding group sold over 5.7 million tons of crude oil based products. Future
Retail Petrol Stations Network Development Programme, which launched at the end of 2004 assumes expansion of the network stations to 500 outlets. That will allow Grupa Lotos to increase its share in the retail fuel market to approx. 10% in 2012. Purchase of Esso and Slovnaft petrol stations networks in Poland (both networks hold high quality standards and possess sell volume higher than the average petrol station in Poland) indicates concrete acceleration in the process of creation a modern cross-country retail stations network. In 2020, state-run PKN Orlen plans to take over smaller rival Lotos, if it receives approval from the European Commission. The minister also suggested Poland should have greater control over the economy. Development
Grupa Lotos strategy aims chiefly at: accomplishment of Gdańsk refinery investment programme (10+ Program), development of crude oil production activity and further shares growth in retail and wholesale petrol market. References
External links
Grupa Lotos - Official Website of Grupa Lotos
Automotive fuel retailers
Companies based in Gdańsk
Energy companies established in 2003
Companies listed on the Warsaw Stock Exchange
Oil and gas companies of Poland
Government-owned companies of Poland
Polish brands
Lechia Gdańsk sponsors | [
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An incompressible string is a string with Kolmogorov complexity equal to its length, so that it has no shorter encodings. Example
Suppose we have the string 12349999123499991234, and we are using a compression method that works by putting a special character into the string (say '@') followed by a value that points to an entry in a lookup table (or dictionary) of repeating values. Let's imagine we have an algorithm that examines the string in 4 character chunks. Looking at our string, our algorithm might pick out the values 1234 and 9999 to place into its dictionary. Let's say 1234 is entry 0 and 9999 is entry 1. Now the string can become:
@0@1@0@1@0
Obviously, this is much shorter, although storing the dictionary itself will cost some space. However, the more repeats there are in the string, the better the compression will be. Our algorithm can do better though, if it can view the string in chunks larger than 4 characters. Then it can put 12349999 and 1234 into the dictionary, giving us:
@0@0@1
Even shorter. Now consider another string:
1234999988884321
This string is incompressible by our algorithm. The only repeats that occur are 88 and 99. | [
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If we were to store 88 and 99 in our dictionary, we would produce:
1234@1@1@0@04321
Unfortunately this is just as long as the original string, because our placeholders for items in the dictionary are 2 characters long, and the items they replace are the same length. Hence, this string is incompressible by our algorithm. References
Lossless compression algorithms
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In topology, Borel−Moore homology or homology with closed support is a homology theory for locally compact spaces, introduced by Armand Borel and John Moore in 1960. For reasonable compact spaces, Borel−Moore homology coincides with the usual singular homology. For non-compact spaces, each theory has its own advantages. In particular, a closed oriented submanifold defines a class in Borel–Moore homology, but not in ordinary homology unless the submanifold is compact. Note: Borel equivariant cohomology is an invariant of spaces with an action of a group G; it is defined as That is not related to the subject of this article. Definition
There are several ways to define Borel−Moore homology. They all coincide for reasonable spaces such as manifolds and locally finite CW complexes. Definition via sheaf cohomology
For any locally compact space X, Borel–Moore homology with integral coefficients is defined as the cohomology of the dual of the chain complex which computes sheaf cohomology with compact support. As a result, there is a short exact sequence analogous to the universal coefficient theorem:
In what follows, the coefficients are not written. Definition via locally finite chains
The singular homology of a topological space X is defined as the homology of the chain complex of singular chains, that is, finite linear combinations of continuous maps from the simplex to X. The Borel−Moore homology of a reasonable locally compact space X, on the other hand, is isomorphic to the homology of the chain complex of locally finite singular chains. Here "reasonable" means X is locally contractible, σ-compact, and of finite dimension. | [
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In more detail, let be the abelian group of formal (infinite) sums
where σ runs over the set of all continuous maps from the standard i-simplex Δi to X and each aσ is an integer, such that for each compact subset S of X, only finitely many maps σ whose image meets S have nonzero coefficient in u. Then the usual definition of the boundary ∂ of a singular chain makes these abelian groups into a chain complex:
The Borel−Moore homology groups are the homology groups of this chain complex. That is,
If X is compact, then every locally finite chain is in fact finite. So, given that X is "reasonable" in the sense above, Borel−Moore homology coincides with the usual singular homology for X compact. Definition via compactifications
Suppose that X is homeomorphic to the complement of a closed subcomplex S in a finite CW complex Y. Then Borel–Moore homology is isomorphic to the relative homology Hi(Y, S). Under the same assumption on X, the one-point compactification of X is homeomorphic to a finite CW complex. As a result, Borel–Moore homology can be viewed as the relative homology of the one-point compactification with respect to the added point. Definition via Poincaré duality
Let X be any locally compact space with a closed embedding into an oriented manifold M of dimension m. Then
where in the right hand side, relative cohomology is meant. Definition via the dualizing complex
For any locally compact space X of finite dimension, let be the dualizing complex of . Then
where in the right hand side, hypercohomology is meant. | [
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Properties
Borel−Moore homology is a covariant functor with respect to proper maps. That is, a proper map f: X → Y induces a pushforward homomorphism for all integers i. In contrast to ordinary homology, there is no pushforward on Borel−Moore homology for an arbitrary continuous map f. As a counterexample, one can consider the non-proper inclusion
Borel−Moore homology is a contravariant functor with respect to inclusions of open subsets. That is, for U open in X, there is a natural pullback or restriction homomorphism
For any locally compact space X and any closed subset F, with the complement, there is a long exact localization sequence:
Borel−Moore homology is homotopy invariant in the sense that for any space X, there is an isomorphism The shift in dimension means that Borel−Moore homology is not homotopy invariant in the naive sense. For example, the Borel−Moore homology of Euclidean space is isomorphic to in degree n and is otherwise zero. Poincaré duality extends to non-compact manifolds using Borel–Moore homology. Namely, for an oriented n-manifold X, Poincaré duality is an isomorphism from singular cohomology to Borel−Moore homology,
for all integers i. A different version of Poincaré duality for non-compact manifolds is the isomorphism from cohomology with compact support to usual homology:
A key advantage of Borel−Moore homology is that every oriented manifold M of dimension n (in particular, every smooth complex algebraic variety), not necessarily compact, has a fundamental class If the manifold M has a triangulation, then its fundamental class is represented by the sum of all the top dimensional simplices. | [
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In fact, in Borel−Moore homology, one can define a fundamental class for arbitrary (possibly singular) complex varieties. In this case the set of smooth points has complement of (real) codimension at least 2, and by the long exact sequence above the top dimensional homologies of and are canonically isomorphic. The fundamental class of is then defined to be the fundamental class of . Examples
Compact Spaces
Given a compact topological space its Borel-Moore homology agrees with its standard homology; that is,
Real line
The first non-trivial calculation of Borel-Moore homology is of the real line. First observe that any -chain is cohomologous to . Since this reduces to the case of a point , notice that we can take the Borel-Moore chain
since the boundary of this chain is and the non-existent point at infinity, the point is cohomologous to zero. Now, we can take the Borel-Moore chain
which has no boundary, hence is a homology class. This shows that
Real n-space
The previous computation can be generalized to the case We get
Infinite Cylinder
Using the Kunneth decomposition, we can see that the infinite cylinder has homology
Real n-space minus a point
Using the long exact sequence in Borel-Moore homology, we get the non-zero exact sequences
and
From the first sequence we get that
and from the second we get that
and
We can interpret these non-zero homology classes using the following observations:
There is the homotopy equivalence
A topological isomorphism
hence we can use the computation for the infinite cylinder to interpret as the homology class represented by and as
Plane with Points Removed
Let have -distinct points removed. | [
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-0.0603942871
] |
Notice the previous computation with the fact that Borel-Moore homology is an isomorphism invariant gives this computation for the case . In general, we will find a -class corresponding to a loop around a point, and the fundamental class in . Double Cone
Consider the double cone . If we take then the long exact sequence shows
Genus Two Curve with Three Points Removed
Given a genus two curve (Riemann surface) and three points , we can use the long exact sequence to compute the Borel-Moore homology of This gives
Since is only three points we have
This gives us that Using Poincare-duality we can compute
since deformation retracts to a one-dimensional CW-complex. Finally, using the computation for the homology of a compact genus 2 curve we are left with the exact sequence
showing
since we have the short exact sequence of free abelian groups
from the previous sequence. Notes
References
Survey articles
Books
Homology theory
Sheaf theory | [
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The Burns stanza is a verse form named after the Scottish poet Robert Burns, who used it in some fifty poems. It was not, however, invented by Burns, and prior to his use of it was known as the standard Habbie, after the piper Habbie Simpson (1550–1620). It is also sometimes known as the Scottish stanza or six-line stave. It is found in Middle English in the Romance of Octovian (Octavian). It was also found in mediaeval Provençal poems and miracle plays from the Middle Ages. The first notable poem written in this stanza was the "Lament for Habbie Simpson; or, the Life and Death of the Piper of Kilbarchan" by Robert Sempill the younger. The stanza was used frequently by major 18th-century Lowland Scots poets such as Robert Fergusson and Robert Burns, and has been used by subsequent poets. Major poems in the stanza include Burns's "To a Mouse", "To a Louse", "Address to the Deil" and "Death and Doctor Hornbook". The stanza is six lines in length and rhymes AAABAB, with tetrameter A lines and dimeter B lines. The second B line may or may not be repeated. Although the "Lament for Habbie" itself is strictly lyrical, subsequent uses have tended to be comic and satirical, as this passage from Burns shows:
A variation on the Burns stanza employs the rhyme scheme AABCCCB, with foreshortened third and seventh lines. | [
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This form is deployed, for example, in W. H. Auden's poem "Brother, who when the sirens roar" (also known as "A Communist to Others"):
Auden uses similar verse forms in other poems in the collection Look, Stranger! (also known as On This Island), such as "The Witnesses" and "Out on the Lawn I Lie in Bed" (also known as "Summer Night"). A more recent example can be seen in W. N. Herbert's "To a Mousse". References
Stanzaic form
Scottish literature
Scots language | [
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The following tables list the computational complexity of various algorithms for common mathematical operations. Here, complexity refers to the time complexity of performing computations on a multitape Turing machine. See big O notation for an explanation of the notation used. Note: Due to the variety of multiplication algorithms, below stands in for the complexity of the chosen multiplication algorithm. Arithmetic functions
Algebraic functions
Special functions
Many of the methods in this section are given in Borwein & Borwein. Elementary functions
The elementary functions are constructed by composing arithmetic operations, the exponential function (), the natural logarithm (), trigonometric functions (), and their inverses. The complexity of an elementary function is equivalent to that of its inverse, since all elementary functions are analytic and hence invertible by means of Newton's method. In particular, if either or in the complex domain can be computed with some complexity, then that complexity is attainable for all other elementary functions. Below, the size refers to the number of digits of precision at which the function is to be evaluated. It is not known whether is the optimal complexity for elementary functions. The best known lower bound is the trivial bound
. Non-elementary functions
Mathematical constants
This table gives the complexity of computing approximations to the given constants to correct digits. Number theory
Algorithms for number theoretical calculations are studied in computational number theory. Matrix algebra
The following complexity figures assume that arithmetic with individual elements has complexity O(1), as is the case with fixed-precision floating-point arithmetic or operations on a finite field. | [
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In 2005, Henry Cohn, Robert Kleinberg, Balázs Szegedy, and Chris Umans showed that either of two different conjectures would imply that the exponent of matrix multiplication is 2. Transforms
Algorithms for computing transforms of functions (particularly integral transforms) are widely used in all areas of mathematics, particularly analysis and signal processing. Notes
References
Further reading
Computer arithmetic algorithms
Computational complexity theory
Mathematics-related lists
Number theoretic algorithms
Unsolved problems in computer science | [
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An internal sort is any data sorting process that takes place entirely within the main memory of a computer. This is possible whenever the data to be sorted is small enough to all be held in the main memory. For sorting larger datasets, it may be necessary to hold only a chunk of data in memory at a time, since it won’t all fit. The rest of the data is normally held on some larger, but slower medium, like a hard-disk. Any reading or writing of data to and from this slower media can slow the sortation process considerably. This issue has implications for different sort algorithms. Some common internal sorting algorithms include:
Bubble Sort
Insertion Sort
Quick Sort
Heap Sort
Radix Sort
Selection sort
Consider a Bubblesort, where adjacent records are swapped in order to get them into the right order, so that records appear to “bubble” up and down through the dataspace. If this has to be done in chunks, then when we have sorted all the records in chunk 1, we move on to chunk 2, but we find that some of the records in chunk 1 need to “bubble through” chunk 2, and vice versa (i.e., there are records in chunk 2 that belong in chunk 1, and records in chunk 1 that belong in chunk 2 or later chunks). This will cause the chunks to be read and written back to disk many times as records cross over the boundaries between them, resulting in a considerable degradation of performance. | [
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If the data can all be held in memory as one large chunk, then this performance hit is avoided. On the other hand, some algorithms handle external sorting rather better. A Merge sort breaks the data up into chunks, sorts the chunks by some other algorithm (maybe bubblesort or Quick sort) and then recombines the chunks two by two so that each recombined chunk is in order. This approach minimises the number or reads and writes of data-chunks from disk, and is a popular external sort method. Sorting algorithms | [
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The correspondence problem refers to the problem of ascertaining which parts of one image correspond to which parts of another image, where differences are due to movement of the camera, the elapse of time, and/or movement of objects in the photos. Correspondence is a fundamental problem in computer vision — influential computer vision researcher Takeo Kanade famously once said that the three fundamental problems of computer vision are: “Correspondence, correspondence, and correspondence!” Indeed, correspondence is arguably the key building block in many related applications: optical flow (in which the two images are subsequent in time), dense stereo vision (in which two images are from a stereo camera pair), structure from motion (SfM) and visual SLAM (in which images are from different but partially overlapping views of a scene), and cross-scene correspondence (in which images are from different scenes entirely). Overview
Given two or more images of the same 3D scene, taken from different points of view, the correspondence problem refers to the task of finding a set of points in one image which can be identified as the same points in another image. To do this, points or features in one image are matched with the points or features in another image, thus establishing corresponding points or corresponding features, also known as homologous points or homologous features. The images can be taken from a different point of view, at different times, or with objects in the scene in general motion relative to the camera(s). | [
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The correspondence problem can occur in a stereo situation when two images of the same scene are used, or can be generalised to the N-view correspondence problem. In the latter case, the images may come from either N different cameras photographing at the same time or from one camera which is moving relative to the scene. The problem is made more difficult when the objects in the scene are in motion relative to the camera(s). A typical application of the correspondence problem occurs in panorama creation or image stitching — when two or more images which only have a small overlap are to be stitched into a larger composite image. In this case it is necessary to be able to identify a set of corresponding points in a pair of images in order to calculate the transformation of one image to stitch it onto the other image. Basic methods
There are two basic ways to find the correspondences between two images. Correlation-based – checking if one location in one image looks/seems like another in another image. Feature-based – finding features in the image and seeing if the layout of a subset of features is similar in the two images. To avoid the aperture problem a good feature should have local variation in two directions. Use
In computer vision the correspondence problem is studied for the case when a computer should solve it automatically with only images as input. Once the correspondence problem has been solved, resulting in a set of image points which are in correspondence, other methods can be applied to this set to reconstruct the position, motion and/or rotation of the corresponding 3D points in the scene. | [
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The correspondence problem is also the basis of the particle image velocimetry measurement technique, which is nowadays widely used in the fluid mechanics field to quantitatively measure fluid motion. Simple example
To find the correspondence between set A [1,2,3,4,5] and set B [3,4,5,6,7] find where they overlap and how far off one set is from the other. Here we see that the last three numbers in set A correspond with the first three numbers in set B. This shows that B is offset 2 to the left of A. Simple correlation-based example
A simple method is to compare small patches between rectified images. This works best with images taken with roughly the same point of view and either at the same time or with little to no movement of the scene between image captures, such as stereo images. A small window is passed over a number of positions in one image. Each position is checked to see how well it compares with the same location in the other image. Several nearby locations are compared for objects in one image which may not be at exactly the same image-location in the other image. It is possible that there is no fit that is good enough. This may mean that the feature is not present in both images, it has moved farther than your search accounted for, it has changed too much, or is being hidden by other parts of the image. See also
Stereoscopy
Parallax
Photogrammetry
Depth perception
Stereopsis
Computer vision
Fundamental matrix
Joint compatibility branch and bound algorithm
Epipolar geometry
Image registration
Birchfield–Tomasi dissimilarity
Scale-invariant feature transform (SIFT)
References
D. Scharstein and R. Szeliski. | [
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] |
A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspondence Algorithms. (PDF)
External links
Middlebury Stereo Vision page
Geometry in computer vision
Stereoscopy
zh:图像对应问题 | [
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The Dix–Hallpike test — or Nylén–Bárány test — is a diagnostic maneuver used to identify benign paroxysmal positional vertigo (BPPV). Procedure
When performing the Dix–Hallpike test, patients are lowered quickly to a supine position (lying horizontally with the face and torso facing up) with the neck extended 30 degrees below horizontal by the clinician performing the maneuver. The Dix–Hallpike and the side-lying testing position have yielded similar results. As such, the side-lying position can be used if the Dix–Hallpike cannot be performed easily. Steps:
The examiner looks for nystagmus (usually accompanied by vertigo). In BPPV, the nystagmus typically occurs in A or B only, and is torsional—the fast phase beating toward the lower ear. Its onset is usually delayed a few seconds, and it lasts 10–20 seconds. As the patient is returned to the upright position, transient nystagmus may occur in the opposite direction. Both nystagmus and vertigo typically decrease on repeat testing. Interpretation
Positive test result
A positive test is indicated by patient report of a reproduction of vertigo and clinician observation of nystagmus (involuntary eye movement). For some patients, this maneuver may be contraindicated, and a modification may be needed that also targets the posterior semicircular canal. Such patients include those who are too anxious about eliciting the uncomfortable symptoms of vertigo, and those who may not have the range of motion necessary to comfortably be in a supine position. The modification involves the patient moving from a seated position to side-lying without their head extending off the examination table, such as with Dix–Hallpike. | [
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The head is rotated 45 degrees away from the side being tested, and the eyes are examined for nystagmus. Negative test
If the test is negative, it makes benign positional vertigo a less likely diagnosis and central nervous system involvement should be considered. Advantages
Although there are alternative methods to administering the test, Cohen proposes advantages to the classic maneuver. The test can be easily administered by a single examiner, which prevents the need for external aid. Due to the position of the subject and the examiner, nystagmus, if present, can be observed directly by the examiner. Limitations
The negative predictive value of this test is not 100%. Some patients with a history of BPPV will not have a positive test result. The estimated sensitivity is 79%, along with an estimated specificity of 75%. The test may need to be performed more than once, as it is not always easy to demonstrate observable nystagmus that is typical of BPPV. Also, the test results can be affected by the speed with which the maneuver is conducted and the plane of the occiput. There are several disadvantages proposed by Cohen for the classic maneuver. Patients may be too tense, for fear of producing vertigo symptoms, which can prevent the necessary brisk passive movements for the test. A subject must have adequate cervical spine range of motion to allow neck extension, as well as trunk and hip range of motion to lie supine. From the previous point, the use of this maneuver can be limited by musculoskeletal and obesity issues in a subject. | [
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Precautions and contraindications
In rare cases a patient may be unable or unwilling to participate in the Dix–Hallpike test due to physical limitations. In these circumstances the side-lying test or other alternative tests may be used. Precautions
The Dix–Hallpike maneuver places a degree of stress on the patient's lower back; therefore, a cautious approach must be taken with patients who are suffering from back pain. Severe respiratory or cardiac problems may not allow a patient to tolerate the maneuver. For example a patient with orthopnoea may not be able to participate in the procedure, as the patient may have troubling breathing when lying down. Absolute contraindications
Neck surgery
Severe rheumatoid arthritis
Atlantoaxial and occipitoatlantal instability
Aplasia of odontoid process
Cervical myelopathy
Cervical radiculopathy
Carotid sinus syncope
Vascular dissection syndromes
See also
Tilt table test
Epley maneuver – used to treat BPPV
Footnotes
External links
Overview and diagrams at dizziness-and-balance.com
video of Dix–Hallpike test
Medical tests
Ear procedures | [
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A multifractal system is a generalization of a fractal system in which a single exponent (the fractal dimension) is not enough to describe its dynamics; instead, a continuous spectrum of exponents (the so-called singularity spectrum) is needed. Multifractal systems are common in nature. They include the length of coastlines, mountain topography, fully developed turbulence, real-world scenes, heartbeat dynamics, human gait and activity, human brain activity, and natural luminosity time series. Models have been proposed in various contexts ranging from turbulence in fluid dynamics to internet traffic, finance, image modeling, texture synthesis, meteorology, geophysics and more. The origin of multifractality in sequential (time series) data has been attributed to mathematical convergence effects related to the central limit theorem that have as foci of convergence the family of statistical distributions known as the Tweedie exponential dispersion models, as well as the geometric Tweedie models. The first convergence effect yields monofractal sequences, and the second convergence effect is responsible for variation in the fractal dimension of the monofractal sequences. Multifractal analysis is used to investigate datasets, often in conjunction with other methods of fractal and lacunarity analysis. The technique entails distorting datasets extracted from patterns to generate multifractal spectra that illustrate how scaling varies over the dataset. Multifrctal analysis has been used to decipher the generating rules and functionalities of complex networks. Multifractal analysis techniques have been applied in a variety of practical situations, such as predicting earthquakes and interpreting medical images. | [
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Definition
In a multifractal system , the behavior around any point is described by a local power law:
The exponent is called the singularity exponent, as it describes the local degree of singularity or regularity around the point . The ensemble formed by all the points that share the same singularity exponent is called the singularity manifold of exponent h, and is a fractal set of fractal dimension the singularity spectrum. The curve versus is called the singularity spectrum and fully describes the statistical distribution of the variable . In practice, the multifractal behaviour of a physical system is not directly characterized by its singularity spectrum . Rather, data analysis gives access to the multiscaling exponents . Indeed, multifractal signals generally obey a scale invariance property that yields power-law behaviours for multiresolution quantities, depending on their scale . Depending on the object under study, these multiresolution quantities, denoted by , can be local averages in boxes of size , gradients over distance , wavelet coefficients at scale , etc. For multifractal objects, one usually observes a global power-law scaling of the form:
at least in some range of scales and for some range of orders . When such behaviour is observed, one talks of scale invariance, self-similarity, or multiscaling. Estimation
Using so-called multifractal formalism, it can be shown that, under some well-suited assumptions, there exists a correspondence between the singularity spectrum and the multi-scaling exponents through a Legendre transform. | [
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While the determination of calls for some exhaustive local analysis of the data, which would result in difficult and numerically unstable calculations, the estimation of the relies on the use of statistical averages and linear regressions in log-log diagrams. Once the are known, one can deduce an estimate of thanks to a simple Legendre transform. Multifractal systems are often modeled by stochastic processes such as multiplicative cascades. The are statistically interpreted, as they characterize the evolution of the distributions of the as goes from larger to smaller scales. This evolution is often called statistical intermittency and betrays a departure from Gaussian models. Modelling as a multiplicative cascade also leads to estimation of multifractal properties. This methods works reasonably well, even for relatively small datasets. A maximum likely fit of a multiplicative cascade to the dataset not only estimates the complete spectrum but also gives reasonable estimates of the errors. Estimating multifractal scaling from box counting
Multifractal spectra can be determined from box counting on digital images. First, a box counting scan is done to determine how the pixels are distributed; then, this "mass distribution" becomes the basis for a series of calculations. The chief idea is that for multifractals, the probability of a number of pixels , appearing in a box , varies as box size , to some exponent , which changes over the image, as in (NB: For monofractals, in contrast, the exponent does not change meaningfully over the set). is calculated from the box-counting pixel distribution as in . | [
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= an arbitrary scale (box size in box counting) at which the set is examined
= the index for each box laid over the set for an
= the number of pixels or mass in any box, , at size
= the total boxes that contained more than 0 pixels, for each
is used to observe how the pixel distribution behaves when distorted in certain ways as in and :
= an arbitrary range of values to use as exponents for distorting the data set
When , equals 1, the usual sum of all probabilities, and when , every term is equal to 1, so the sum is equal to the number of boxes counted, . These distorting equations are further used to address how the set behaves when scaled or resolved or cut up into a series of -sized pieces and distorted by Q, to find different values for the dimension of the set, as in the following:
An important feature of is that it can also be seen to vary according to scale raised to the exponent in :
Thus, a series of values for can be found from the slopes of the regression line for the log of versus the log of for each , based on :
For the generalized dimension:
is estimated as the slope of the regression line for versus where:
Then is found from . The mean is estimated as the slope of the log-log regression line for versus , where:
In practice, the probability distribution depends on how the dataset is sampled, so optimizing algorithms have been developed to ensure adequate sampling. | [
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Applications
Multifractal analysis has been successfully used in many fields, including physical, information, and biological sciences. For example, the quantification of residual crack patterns on the surface of reinforced concrete shear walls. Dataset distortion analysis
Multifractal analysis has been used in several scientific fields to characterize various types of datasets. In essence, multifractal analysis applies a distorting factor to datasets extracted from patterns, to compare how the data behave at each distortion. This is done using graphs known as multifractal spectra, analogous to viewing the dataset through a "distorting lens", as shown in the illustration. Several types of multifractal spectra are used in practise. DQ vs Q
One practical multifractal spectrum is the graph of DQ vs Q, where DQ is the generalized dimension for a dataset and Q is an arbitrary set of exponents. The expression generalized dimension thus refers to a set of dimensions for a dataset (detailed calculations for determining the generalized dimension using box counting are described below). Dimensional ordering
The general pattern of the graph of DQ vs Q can be used to assess the scaling in a pattern. The graph is generally decreasing, sigmoidal around Q=0, where D(Q=0) ≥ D(Q=1) ≥ D(Q=2). As illustrated in the figure, variation in this graphical spectrum can help distinguish patterns. The image shows D(Q) spectra from a multifractal analysis of binary images of non-, mono-, and multi-fractal sets. As is the case in the sample images, non- and mono-fractals tend to have flatter D(Q) spectra than multifractals. | [
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The generalized dimension also gives important specific information. D(Q=0) is equal to the capacity dimension, which—in the analysis shown in the figures here—is the box counting dimension. D(Q=1) is equal to the information dimension, and D(Q=2) to the correlation dimension. This relates to the "multi" in multifractal, where multifractals have multiple dimensions in the D(Q) versus Q spectra, but monofractals stay rather flat in that area. versus
Another useful multifractal spectrum is the graph of versus (see calculations). These graphs generally rise to a maximum that approximates the fractal dimension at Q=0, and then fall. Like DQ versus Q spectra, they also show typical patterns useful for comparing non-, mono-, and multi-fractal patterns. In particular, for these spectra, non- and mono-fractals converge on certain values, whereas the spectra from multifractal patterns typically form humps over a broader area. Generalized dimensions of species abundance distributions in space
One application of Dq versus Q in ecology is characterizing the distribution of species. Traditionally the relative species abundances is calculated for an area without taking into account the locations of the individuals. An equivalent representation of relative species abundances are species ranks, used to generate a surface called the species-rank surface, which can be analyzed using generalized dimensions to detect different ecological mechanisms like the ones observed in the neutral theory of biodiversity, metacommunity dynamics, or niche theory. See also
Fractional Brownian motion
Detrended fluctuation analysis
Tweedie distributions
Markov switching multifractal
Weighted planar stochastic lattice (WPSL)
References
Further reading
External links
Movies of visualizations of multifractals
Fractals
Dimension theory | [
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In an electric power system, a fault or fault current is any abnormal electric current. For example, a short circuit is a fault in which a live wire touches a neutral or ground wire. An open-circuit fault occurs if a circuit is interrupted by a failure of a current-carrying wire (phase or neutral) or a blown fuse or circuit breaker. In three-phase systems, a fault may involve one or more phases and ground, or may occur only between phases. In a "ground fault" or "earth fault", current flows into the earth. The prospective short-circuit current of a predictable fault can be calculated for most situations. In power systems, protective devices can detect fault conditions and operate circuit breakers and other devices to limit the loss of service due to a failure. In a polyphase system, a fault may affect all phases equally, which is a "symmetric fault". If only some phases are affected, the resulting "asymmetric fault" becomes more complicated to analyse. The analysis of these types of faults is often simplified by using methods such as symmetrical components. The design of systems to detect and interrupt power system faults is the main objective of power-system protection. Transient fault
A transient fault is a fault that is no longer present if power is disconnected for a short time and then restored; or an insulation fault which only temporarily affects a device's dielectric properties which are restored after a short time. Many faults in overhead power lines are transient in nature. | [
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When a fault occurs, equipment used for power system protection operate to isolate the area of the fault. A transient fault will then clear and the power-line can be returned to service. Typical examples of transient faults include:
momentary tree contact
bird or other animal contact
lightning strike
conductor clashing
Transmission and distribution systems use an automatic re-close function which is commonly used on overhead lines to attempt to restore power in the event of a transient fault. This functionality is not as common on underground systems as faults there are typically of a persistent nature. Transient faults may still cause damage both at the site of the original fault or elsewhere in the network as fault current is generated. Persistent fault
A persistent fault is present regardless of power being applied. Faults in underground power cables are most often persistent due to mechanical damage to the cable, but are sometimes transient in nature due to lightning. Types of fault
Asymmetric fault
An asymmetric or unbalanced fault does not affect each of the phases equally. Common types of asymmetric fault, and their causes:
line-to-line fault - a short circuit between lines, caused by ionization of air, or when lines come into physical contact, for example due to a broken insulator. In transmission line faults, roughly 5% - 10% are asymmetric line-to-line faults. line-to-ground fault - a short circuit between one line and ground, very often caused by physical contact, for example due to lightning or other storm damage. In transmission line faults, roughly 65% - 70% are asymmetric line-to-ground faults. | [
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double line-to-ground fault - two lines come into contact with the ground (and each other), also commonly due to storm damage. In transmission line faults, roughly 15% - 20% are asymmetric double line-to-ground. Symmetric fault
A symmetric or balanced fault affects each of the phases equally. In transmission line faults, roughly 5% are symmetric. These faults are rare compared to asymmetric faults. Two kinds of symmetric fault are line to line to line (L-L-L) and line to line to line to ground (L-L-L-G). Symmetric faults account for 2 to 5% of all system faults. However, they can cause very severe damage to equipment even though the system remains balanced. Bolted fault
One extreme is where the fault has zero impedance, giving the maximum prospective short-circuit current. Notionally, all the conductors are considered connected to ground as if by a metallic conductor; this is called a "bolted fault". It would be unusual in a well-designed power system to have a metallic short circuit to ground but such faults can occur by mischance. In one type of transmission line protection, a "bolted fault" is deliberately introduced to speed up operation of protective devices. Ground fault (earth fault)
A ground fault (earth fault) is any failure that allows unintended connection of power circuit conductors with the earth. Such faults can cause objectionable circulating currents, or may energize the housings of equipment at a dangerous voltage. Some special power distribution systems may be designed to tolerate a single ground fault and continue in operation. | [
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Wiring codes may require an insulation monitoring device to give an alarm in such a case, so the cause of the ground fault can be identified and remedied. If a second ground fault develops in such a system, it can result in overcurrent or failure of components. Even in systems that are normally connected to ground to limit overvoltages, some applications require a Ground Fault Interrupter or similar device to detect faults to ground. Realistic faults
Realistically, the resistance in a fault can be from close to zero to fairly high relative to the load resistance. A large amount of power may be consumed in the fault, compared with the zero-impedance case where the power is zero. Also, arcs are highly non-linear, so a simple resistance is not a good model. All possible cases need to be considered for a good analysis. Arcing fault
Where the system voltage is high enough, an electric arc may form between power system conductors and ground. Such an arc can have a relatively high impedance (compared to the normal operating levels of the system) and can be difficult to detect by simple overcurrent protection. For example, an arc of several hundred amperes on a circuit normally carrying a thousand amperes may not trip overcurrent circuit breakers but can do enormous damage to bus bars or cables before it becomes a complete short circuit. Utility, industrial, and commercial power systems have additional protection devices to detect relatively small but undesired currents escaping to ground. | [
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In residential wiring, electrical regulations may now require arc-fault circuit interrupters on building wiring circuits, to detect small arcs before they cause damage or a fire. Analysis
Symmetric faults can be analyzed via the same methods as any other phenomena in power systems, and in fact many software tools exist to accomplish this type of analysis automatically (see power flow study). However, there is another method which is as accurate and is usually more instructive. First, some simplifying assumptions are made. It is assumed that all electrical generators in the system are in phase, and operating at the nominal voltage of the system. Electric motors can also be considered to be generators, because when a fault occurs, they usually supply rather than draw power. The voltages and currents are then calculated for this base case. Next, the location of the fault is considered to be supplied with a negative voltage source, equal to the voltage at that location in the base case, while all other sources are set to zero. This method makes use of the principle of superposition. To obtain a more accurate result, these calculations should be performed separately for three separate time ranges:
subtransient is first, and is associated with the largest currents
transient comes between subtransient and steady-state
steady-state occurs after all the transients have had time to settle
An asymmetric fault breaks the underlying assumptions used in three-phase power, namely that the load is balanced on all three phases. Consequently, it is impossible to directly use tools such as the one-line diagram, where only one phase is considered. | [
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However, due to the linearity of power systems, it is usual to consider the resulting voltages and currents as a superposition of symmetrical components, to which three-phase analysis can be applied. In the method of symmetric components, the power system is seen as a superposition of three components:
a positive-sequence component, in which the phases are in the same order as the original system, i.e., a-b-c
a negative-sequence component, in which the phases are in the opposite order as the original system, i.e., a-c-b
a zero-sequence component, which is not truly a three-phase system, but instead all three phases are in phase with each other. To determine the currents resulting from an asymmetric fault, one must first know the per-unit zero-, positive-, and negative-sequence impedances of the transmission lines, generators, and transformers involved. Three separate circuits are then constructed using these impedances. The individual circuits are then connected together in a particular arrangement that depends upon the type of fault being studied (this can be found in most power systems textbooks). Once the sequence circuits are properly connected, the network can then be analyzed using classical circuit analysis techniques. The solution results in voltages and currents that exist as symmetrical components; these must be transformed back into phase values by using the A matrix. Analysis of the prospective short-circuit current is required for selection of protective devices such as fuses and circuit breakers. | [
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If a circuit is to be properly protected, the fault current must be high enough to operate the protective device within as short a time as possible; also the protective device must be able to withstand the fault current and extinguish any resulting arcs without itself being destroyed or sustaining the arc for any significant length of time. The magnitude of fault currents differ widely depending on the type of earthing system used, the installation's supply type and earthing system, and its proximity to the supply. For example, for a domestic UK 230 V, 60 A TN-S or USA 120 V/240 V supply, fault currents may be a few thousand amperes. Large low-voltage networks with multiple sources may have fault levels of 300,000 amperes. A high-resistance-grounded system may restrict line to ground fault current to only 5 amperes. Prior to selecting protective devices, prospective fault current must be measured reliably at the origin of the installation and at the furthest point of each circuit, and this information applied properly to the application of the circuits. Detecting and locating faults
Overhead power lines are easiest to diagnose since the problem is usually obvious, e.g., a tree has fallen across the line, or a utility pole is broken and the conductors are lying on the ground. Locating faults in a cable system can be done either with the circuit de-energized, or in some cases, with the circuit under power. Fault location techniques can be broadly divided into terminal methods, which use voltages and currents measured at the ends of the cable, and tracer methods, which require inspection along the length of the cable. | [
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Terminal methods can be used to locate the general area of the fault, to expedite tracing on a long or buried cable. In very simple wiring systems, the fault location is often found through inspection of the wires. In complex wiring systems (for example, aircraft wiring) where the wires may be hidden, wiring faults are located with a Time-domain reflectometer. The time domain reflectometer sends a pulse down the wire and then analyzes the returning reflected pulse to identify faults within the electrical wire. In historic submarine telegraph cables, sensitive galvanometers were used to measure fault currents; by testing at both ends of a faulted cable, the fault location could be isolated to within a few miles, which allowed the cable to be grappled up and repaired. The Murray loop and the Varley loop were two types of connections for locating faults in cables
Sometimes an insulation fault in a power cable will not show up at lower voltages. A "thumper" test set applies a high-energy, high-voltage pulse to the cable. Fault location is done by listening for the sound of the discharge at the fault. While this test contributes to damage at the cable site, it is practical because the faulted location would have to be re-insulated when found in any case. In a high resistance grounded distribution system, a feeder may develop a fault to ground but the system continues in operation. The faulted, but energized, feeder can be found with a ring-type current transformer collecting all the phase wires of the circuit; only the circuit containing a fault to ground will show a net unbalanced current. | [
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] |
To make the ground fault current easier to detect, the grounding resistor of the system may be switched between two values so that the fault current pulses. Batteries
The prospective fault current of larger batteries, such as deep-cycle batteries used in stand-alone power systems, is often given by the manufacturer. In Australia, when this information is not given, the prospective fault current in amperes "should be considered to be 6 times the nominal battery capacity at the C A·h rate," according to AS 4086 part 2 (Appendix H). See also
Electrical safety
Fault (technology)
References
General
Power engineering
Engineering failures | [
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Structured light is the process of projecting a known pattern (often grids or horizontal bars) on to a scene. The way that these deform when striking surfaces allows vision systems to calculate the depth and surface information of the objects in the scene, as used in structured light 3D scanners. Invisible (or imperceptible) structured light uses structured light without interfering with other computer vision tasks for which the projected pattern will be confusing. Example methods include the use of infrared light or of extremely high frame rates alternating between two exact opposite patterns. Structured light is used by a number of police forces for the purpose of photographing fingerprints in a 3D scene. Where previously they would use tape to extract the fingerprint and flatten it out, they can now use cameras and flatten the fingerprint digitally, which allows the process of identification to begin before the officer has even left the scene. See also
Structured Illumination Microscopy (SIM)
Stereoscopy
3D scanner#Structured light
Structured-light 3D scanners often employed in a multiple-camera setup in conjunction with structured light to capture the geometry of the target
Dual photography
More advanced light stages make use of structured light to capture geometry of the target. The primary use of a light stage is an instrumentation setup for reflectance capture. | [
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] |
Depth map
Laser Dynamic Range Imager
Lidar
Range imaging
Kinect
Time-of-flight camera
External links
Projector-Camera Calibration Toolbox
Tutorial on Coded Light Projection Techniques
Structured light using pseudorandom codes
High-accuracy stereo depth maps using structured light
A comparative survey on invisible structured light
A Real-Time Laser Range Finding Vision System
Dual-frequency Pattern Scheme for High-speed 3-D Shape Measurement
High-Contrast Color-Stripe Pattern for Rapid Structured-Light Range Imaging
Image sensor technology in computer vision
Machine vision | [
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A surrogate model is an engineering method used when an outcome of interest cannot be easily measured or computed, so a model of the outcome is used instead. Most engineering design problems require experiments and/or simulations to evaluate design objective and constraint functions as a function of design variables. For example, in order to find the optimal airfoil shape for an aircraft wing, an engineer simulates the airflow around the wing for different shape variables (length, curvature, material, ..). For many real-world problems, however, a single simulation can take many minutes, hours, or even days to complete. As a result, routine tasks such as design optimization, design space exploration, sensitivity analysis and what-if analysis become impossible since they require thousands or even millions of simulation evaluations. One way of alleviating this burden is by constructing approximation models, known as surrogate models, metamodels or emulators, that mimic the behavior of the simulation model as closely as possible while being computationally cheap(er) to evaluate. Surrogate models are constructed using a data-driven, bottom-up approach. The exact, inner working of the simulation code is not assumed to be known (or even understood), solely the input-output behavior is important. A model is constructed based on modeling the response of the simulator to a limited number of intelligently chosen data points. This approach is also known as behavioral modeling or black-box modeling, though the terminology is not always consistent. When only a single design variable is involved, the process is known as curve fitting. | [
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Though using surrogate models in lieu of experiments and simulations in engineering design is more common, surrogate modeling may be used in many other areas of science where there are expensive experiments and/or function evaluations. Goals
The scientific challenge of surrogate modeling is the generation of a surrogate that is as accurate as possible, using as few simulation evaluations as possible. The process comprises three major steps which may be interleaved iteratively:
Sample selection (also known as sequential design, optimal experimental design (OED) or active learning)
Construction of the surrogate model and optimizing the model parameters (bias-variance trade-off)
Appraisal of the accuracy of the surrogate. The accuracy of the surrogate depends on the number and location of samples (expensive experiments or simulations) in the design space. Various design of experiments (DOE) techniques cater to different sources of errors, in particular, errors due to noise in the data or errors due to an improper surrogate model. Types of surrogate models
Popular surrogate modeling approaches are: polynomial response surfaces; kriging; more generalized Bayesian approaches, gradient-enhanced kriging (GEK); radial basis function; support vector machines; space mapping; artificial neural networks and Bayesian networks. Further methods recently explored are Fourier surrogate modeling and random forests
. For some problems, the nature of true function is not known a priori so it is not clear which surrogate model will be most accurate. In addition, there is no consensus on how to obtain the most reliable estimates of the accuracy of a given surrogate. Many other problems have known physics properties. | [
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In these cases, physics-based surrogates such as space-mapping based models are the most efficient. A recent survey of surrogate-assisted evolutionary optimization techniques can be found in. Spanning two decades of development and engineering applications, Rayas-Sanchez reviews aggressive space mapping exploiting surrogate models. Recently, Razavi et al. have published a state-of-the-art review of surrogate models used in water resources management field. Invariance properties
Recently proposed comparison-based surrogate models (e.g. ranking support vector machine) for evolutionary algorithms, such as CMA-ES, allow to preserve some invariance properties of surrogate-assisted optimizers:
1. Invariance with respect to monotonous transformations of the function (scaling)
2. Invariance with respect to orthogonal transformations of the search space (rotation). Applications
An important distinction can be made between two different applications of surrogate models: design optimization and design space approximation (also known as emulation). In surrogate model based optimization, an initial surrogate is constructed using some of the available budgets of expensive experiments and/or simulations. The remaining experiments/simulations are run for designs which the surrogate model predicts may have promising performance. The process usually takes the form of the following search/update procedure. 1. Initial sample selection (the experiments and/or simulations to be run)
2. Construct surrogate model
3. Search surrogate model (the model can be searched extensively, e.g. using a genetic algorithm, as it is cheap to evaluate)
4. Run and update experiment/simulation at a new location(s) found by search and add to sample
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Iterate steps 2 to 4 until out of time or design 'good enough'
Depending on the type of surrogate used and the complexity of the problem, the process may converge on a local or global optimum, or perhaps none at all. In design space approximation, one is not interested in finding the optimal parameter vector but rather in the global behavior of the system. Here the surrogate is tuned to mimic the underlying model as closely as needed over the complete design space. Such surrogates are a useful, cheap way to gain insight into the global behavior of the system. Optimization can still occur as a post-processing step, although with no update procedure (see above) the optimum found cannot be validated. Surrogate modeling software
Surrogate Modeling Toolbox (SMT: https://github.com/SMTorg/smt): is a Python package that contains a collection of surrogate modeling methods, sampling techniques, and benchmarking functions. This package provides a library of surrogate models that is simple to use and facilitates the implementation of additional methods. SMT is different from existing surrogate modeling libraries because of its emphasis on derivatives, including training derivatives used for gradient-enhanced modeling, prediction derivatives, and derivatives with respect to the training data. It also includes new surrogate models that are not available elsewhere: kriging by partial-least squares reduction and energy-minimizing spline interpolation. Surrogates.jl: is a Julia packages which offers tools like random forests, radial basis methods and kriging. | [
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] |
See also
Linear approximation
Response surface methodology
Kriging
Radial basis functions
Gradient-enhanced kriging (GEK)
OptiY
Space mapping
Surrogate endpoint
Surrogate data
Fitness approximation
Computer experiment
Conceptual model
Bayesian regression
Bayesian model selection
References
Reading
Queipo, N.V., Haftka, R.T., Shyy, W., Goel, T., Vaidyanathan, R., Tucker, P.K. (2005), “Surrogate-based analysis and optimization,” Progress in Aerospace Sciences, 41, 1–28. D. Gorissen, I. Couckuyt, P. Demeester, T. Dhaene, K. Crombecq, (2010), “A Surrogate Modeling and Adaptive Sampling Toolbox for Computer Based Design," Journal of Machine Learning Research, Vol. 11, pp. 2051−2055, July 2010. T-Q. Pham, A. Kamusella, H. Neubert, “Auto-Extraction of Modelica Code from Finite Element Analysis or Measurement Data," 8th International Modelica Conference, 20–22 March 2011 in Dresden. Forrester, Alexander, Andras Sobester, and Andy Keane, Engineering design via surrogate modelling: a practical guide, John Wiley & Sons, 2008. Bouhlel, M. A. and Bartoli, N. and Otsmane, A. and Morlier, J. (2016) "Improving kriging surrogates of high-dimensional design models by Partial Least Squares dimension reduction", Structural and Multidisciplinary Optimization 53 (5), 935-952
Bouhlel, M. A. and Bartoli, N. and Otsmane, A. and Morlier, J. | [
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(2016) "An improved approach for estimating the hyperparameters of the kriging model for high-dimensional problems through the partial least squares method", Mathematical Problems in Engineering
External links
Matlab code for surrogate modelling
Matlab SUrrogate MOdeling Toolbox – Matlab SUMO Toolbox
Surrogate Modeling Toolbox -- Python
Design of experiments
Numerical analysis
Scientific models
Mathematical modeling | [
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W32.Navidad is a mass-mailing worm program or virus, discovered in December 2000. It is designed to spread through email clients such as Microsoft Outlook while masquerading as an electronic Christmas card. Infected computers can be identified by blue eye icons which appear in the Windows system tray. Users who move their mouse cursor over the eye icons will be presented with a variety of different messages, including one which states: "Emmanuel-God is with us!May god bless u.And Ash, Lk, and LJ!!" References
Email worms
Hacking in the 2000s | [
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In Unix computing, lxrun is a compatibility layer to allow Linux binaries to run on UnixWare, SCO OpenServer and Solaris without recompilation. It was created by Mike Davidson. It has been an open source software project since 1997, and is available under the Mozilla Public License. Both SCO and Sun Microsystems began officially supporting lxrun in 1999. Timeline
August 22, 1997: lxrun is cited as a proof of concept of cross-platform binary compatibility at the 86open conference hosted by SCO in Santa Cruz, CA. August 29, 1997: lxrun's first mention on Usenet, in comp.unix.sco.misc. Most notably, the post mentions lxrun's availability in source and binary form from the SCO Skunkware FTP site. A later post in the thread mentions contributions by various authors, both inside and outside of SCO. October 1, 1997: The official lxrun website is established. June 19, 1998: Ronald Joe Record, Michael Hopkirk, and Steven Ginzburg present a paper on lxrun at the USENIX 1998 Technical Conference in New Orleans, LA. Mar 1, 1999: SCO announces Linux compatibility in UnixWare 7 and demonstrates lxrun at LinuxWorld Expo and Conference in San Jose, CA. May 12, 1999: Sun Microsystems announces support for Linux binaries on Solaris using lxrun. Current status
According to the official lxrun website, lxrun is now in "maintenance" mode, meaning that it is no longer being actively developed. | [
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] |
Reasons cited for the declining interest in lxrun include the wide availability of real Linux machines, and the availability of more capable emulation systems, such as SCO's Linux Kernel Personality (LKP), OpenSolaris BrandZ, and various virtual machine solutions. Newer Linux applications and host operating systems are not officially supported by lxrun. References
External links
Sun's Solaris get compatible with Linux apps (CNN, Fri 14 May 1999)
Lxrun - why wasn't it released under the GPL? (Pamela Jones, Groklaw, Wed 16 Aug 2006)
Linux
UNIX System V
Compatibility layers
Sun Microsystems software | [
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Przybylski's Star (pronounced or ), or HD 101065, is a rapidly oscillating Ap star at roughly from the Sun in the southern constellation of Centaurus. Scientific history
In 1961, the Polish-Australian astronomer Antoni Przybylski discovered that this star had a peculiar spectrum that would not fit into the standard framework for stellar classification. Przybylski's observations indicated unusually low amounts of iron and nickel in the star's spectrum, but higher amounts of unusual elements like strontium, holmium, niobium, scandium, yttrium, caesium, neodymium, praseodymium, thorium, ytterbium and uranium. In fact, at first Przybylski doubted that iron was present in the spectrum at all. Modern work shows that the iron group elements are somewhat below normal in abundance, but it is clear that the lanthanides and other exotic elements are highly over-abundant. Przybylski's Star also contains many different short-lived actinide elements with actinium, protactinium, neptunium, plutonium, americium, curium, berkelium, californium, and einsteinium being detected. The longest-lived isotope of einsteinium has a half-life of only 472 days. Other radioactive elements identified in this star include technetium and promethium. Compared to neighboring stars, HD 101065 has a high peculiar velocity of . Hypotheses
Because of the odd properties of this star, there are numerous hypotheses about why the oddities occur. One such theory is that the star contains some long-lived nuclides from the island of stability (such as 298Fl or 304120) and that the observed short-lived actinides are the daughters of these progenitors, occurring in secular equilibrium with their parents. | [
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Properties
HD 101065 is the prototype star of the rapidly oscillating Ap star (roAP) variable star class. In 1978, it was discovered to pulsate photometrically with a period of 12.15 min. A potential companion had also been detected, a 14th-magnitude star (in infrared) 8 arc seconds away. This could have meant a separation of just (0.02 light-years); however, Gaia Data Release 2 suggests that while those two stars appear to us as separated by a very close angle, the actual distance separating us from this second star is light-years which means more than twice further away than Przybylski's Star. See also
List of stars that dim oddly
Chemically peculiar star
Metallicity
References
External links
Przybylski's Most Unusual Star
Centaurus (constellation)
Astrophysics
F-type stars
Centauri, V816
101065
056709
Unsolved problems in astronomy
Rapidly oscillating Ap stars
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Druid is a hack and slash dungeon crawl developed by Electralyte Software and published by Firebird in 1986 for the Atari 8-bit family and Commodore 64. It was also ported to Amstrad CPC, ZX Spectrum, and by Nippon Dexter in 1988 for the MSX, although the MSX port was released in Japan only. Another Japanese port of Druid entitled was made for the Famicom Disk System by Jaleco in 1988. The game was followed by Druid II: Enlightenment and Warlock: The Avenger. Gameplay
Inspired by the arcade game Gauntlet, Druid is a fantasy-themed dungeon crawl where the player plays the part of Hasrinaxx, a druid who is trying to rid the world of the dark mage Acamantor and his army of demons. To do this, Hasrinaxx must travel through several levels. The first level is a normal landscape, and the ones after that are underground, each one deeper than the previous. Each level is infested with various enemies such as ghosts, giant insects, witches, and the four demon princes. Hasrinaxx can shoot these enemies with three different weapons: water, fire, and electricity, but they all come in a finite supply and are not equally effective on all enemies. Using a Chaos spell will destroy all enemies in the player's vicinity as well as replenish energy. The four demon princes can only be defeated with a Chaos spell; common weapons are ineffective against them. Hasrinaxx can also summon a golem to help him or turn invisible for a brief period. | [
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] |
In both Atari 8-bit and Commodore 64 versions, a second player can take control of the golem using joystick port 2. References
External links
Druid at Atari Mania
1986 video games
Amstrad CPC games
Atari 8-bit family games
Commodore 64 games
Video games about demons
Famicom Disk System games
Jaleco games
MSX games
Video games about old age
Video games developed in the United Kingdom
Video games scored by Tsukasa Tawada
ZX Spectrum games | [
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An Nv network is a term used in BEAM robotics referring to the small electrical Neural Networks that make up the bulk of BEAM-based robot control mechanisms. Basic Building blocks
The most basic component included in Nv Networks is the Nv Neuron. The purpose of an Nv Neuron is simply to take an input, do something with it, and give an output. the most common action of Nv Neurons is to give a delay. BEAM Nv Neurons
The standard for BEAM-based neurons is a capacitor that has one lead as an input, and the other going into the input line of an inverter. That inverter's output is the output of the neuron. The capacitor lead that is inputting into the inverter is pulled to ground with a resistor. The neuron functions because when an input is received (positive power on the input line), it charges the capacitor. Once the input is lost (negative power on the input line), the capacitor discharges into the inverter, causing the inverter to produce an output that is passed to the next neuron. The rate that the capacitor discharges is tied to the resistor that is pulling the input to the inverter to the negative. The larger the resistor, the longer it will take for the capacitor to fully discharge, and the longer it will take for that neuron to completely fire. Types of Networks
There are many common network topologies used in BEAM robots, the most common of which are listed here. | [
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Bicore
Probably the most utilized Nv Net topology in BEAM, the Bicore consists of two neurons placed in a loop that alternates current to the output. Input into the loop is given in the form of changing the resistance in each separate Neuron, which changes the rate at which the Neuron discharges, affecting the pace at which the loop oscillates. Master/Slave bicores
Another common topology is using two bicores in a master/slave layout where the master bicore leads the slave and sets the pace, while the slave bicore follows at an offset pace. This layout is most commonly used for dual-motor walkers. Larger networks
Other larger network topologies include the Tricore, and Quadcore which are laid out in a similar way the bicore is, except with more Neurons in the loop. More complex networks exist, but are not as common due to the simplistic nature of BEAM. Structure
A basic Nv network is built upon several Nv neurons in a loop. The loop's timing is often varied by input sensors. This difference in timing is often meant to affect the output pattern of the Nv loop. An example of this can be seen in a simple BEAM walker robot utilizing a bicore network (2 neurons). The neural network is set up to alternate current going to the main motor in a way where under equal input from the main sensors, the neurons oscillate at an equal pace to each other, producing a steady walking gait. When input (e.g. | [
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from light sensors) is present, the timing of each neuron in the loop is varied based on the input from the sensors, affecting the pace at which the loop oscillates. This affected pace is often used to alter the walking gait of a robot in order to steer it based on the input from its sensors. External articles and other references
BEAM NV Articles on the BEAM Robotics Wiki
On Bicores on the BEAM Robotics Wiki
Electrical circuits
BEAM robotics | [
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MuscleTech is a brand of dietary supplements, marketed by Iovate Health Sciences Inc., which includes Hydroxycut. It was owned by Canadian company Kerr Holdings which was acquired by the Xiwang Foodstuffs Company, a Chinese company, for $584 million in 2016. History
In 1998, MuscleTech launched Cell-Tech, a creatine-carbohydrate-alpha lipoic acid supplement. In December 2015, a settlement was reached that applies to protein shakes and beverages that include MuscleTech. In September 2018, Muscletech is partnering up Rob Gronkowski to create a high-protein candy bar. In April 2019, MuscleTech had partnered up with Tough Mudder. In July 2019, MuscleTech launched the Prime Series, a private label sports nutrition line exclusive to Amazon. In May 2020, a MuscleTech product made in the U.S. was linked to a death in Spain. MuscleTech's brand ambassadors include actor Henry Cavill, U.S. marathoner Ryan Hall, swimsuit model Camille Kostek and figure skater Gracie Gold. In April 2021, MuscleTech is announced the addition of a new general manager. MuscleTech, through its parent company Iovate Health Sciences, is a partner of the Metabolism & Sports Science Lab at the University of Toronto. References
External links
Official website
Sports nutrition and bodybuilding supplement companies | [
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The Character of Physical Law is a series of seven lectures by physicist Richard Feynman concerning the nature of the laws of physics. Feynman delivered the lectures in 1964 at Cornell University, as part of the Messenger Lectures series. The BBC recorded the lectures, and published a book under the same title the following year; Cornell published the BBC's recordings online in September 2015. In 2017 MIT Press published, with a new foreword by Frank Wilczek, a paperback reprint of the 1965 book. Topics
The lectures covered the following topics:
The law of gravitation, an example of physical law
The relation of mathematics and physics
The great conservation principles
Symmetry in physical law
The distinction of past and future
Probability and uncertainty - the quantum mechanical view of nature
Seeking new laws
Reception
Critical reception has been positive. The journal The Physics Teacher, in recommending it to both scientists and non-scientists alike, gave The Character of Physical Law a favorable review, writing that although the book was initially intended to supplement the recordings, it was "complete in itself and will appeal to a far wider audience". Selections
"In general we look for a new law by the following process. First we guess it. ...", –
See also
QED: The Strange Theory of Light and Matter
The Feynman Lectures on Physics
References
Lectures
Works by Richard Feynman
Physics books
1965 non-fiction books
Books of lectures | [
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The Free Software Foundation and the Open Knowledge Foundation approved CC0 as a recommended license to dedicate content to the public domain. The FSF and the Open Source Initiative, however, do not recommend the usage of this license for software due to inclusion of a clause expressly stating it does not grant patent licenses. In June 2016 an analysis of the Fedora Project's software packages placed CC0 as the 17th most popular license. The Unlicense software license, published around 2010, offers a public-domain waiver text with a fall-back public-domain-like license, inspired by permissive licenses but without an attribution clause. In 2015 GitHub reported that approximately 102,000 of their 5.1 million licensed projects, or 2%, use the Unlicense. The Zero Clause BSD license removes half a sentence from the OpenBSD template license, leaving only an unconditional grant of rights and a warranty disclaimer. It is listed by the Software Package Data Exchange as the Zero Clause BSD license, with the SPDX identifier "0BSD." It was first used by Rob Landley in Toybox and is OSI-approved. Reception
In the free-software community, there has been some controversy over whether a public domain dedication constitutes a valid open-source license. In 2004, lawyer Lawrence Rosen argued in the essay "Why the public domain isn't a license" that software could not truly be given into public domain, a position that faced opposition by Daniel J. Bernstein and others. In 2012, Rosen changed his mind, accepted CC0 as an open-source license, and admitted that, contrary to his previous claims, copyright can be waived away. | [
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In 2011, the Free Software Foundation added CC0 to its free software licenses and called it "the preferred method of releasing software in the public domain," while in general recommending the GNU General Public License. In February 2012, when the CC0 license was submitted to the Open Source Initiative for approval, controversy arose over a clause which excluded any relevant patents held by the copyright holder from the scope of the license. This clause was added with scientific data in mind rather than software, but some members of the OSI believed it could weaken users' defenses against software patents. As a result, Creative Commons withdrew their submission, and the license is not currently approved by the OSI. In June 2020, following a request for legacy approval, OSI formally recognized the Unlicense as an approved license meeting the OSD. Google does not allow its employees to contribute to projects under public domain equivalent licenses like the Unlicense and CC0, while allowing contributions to 0BSD licensed and US government PD projects. See also
Public domain
Public-domain mark
Public-domain software
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Notes
References
Permissive software licenses
Public domain
Public copyright licenses
Terms of service | [
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Intelligentsia Coffee is an American coffee roasting company and retailer based in Chicago, Illinois. Founded in 1995 by Doug Zell and Emily Mange, Intelligentsia is considered a major representative of third wave coffee. In 2015, Peet's Coffee & Tea (itself part of JAB Holding Company) acquired a majority stake in the company. History and locations
Aside from its headquarters at 1850 W. Fulton Street, Intelligentsia has several cafe retail locations throughout the Chicago area. They supply coffee to various Chicago-area cafes and restaurants, as well as other locations in the US and Canada. They generally buy their beans directly from growers in Central America, South America, East Africa, and Ethiopia. They currently operate four gas-powered Ideal Rapid Gothot Roasters at the Chicago Roasting Works. Two 90-kilo roasters and a 23-kilo reside in Chicago and a 40 kilo in Los Angeles. The machines date from the 1950s and were handcrafted from cast-iron and steel in Stuttgart, Germany. On August 17, 2007, Intelligentsia opened its first store outside of Chicago at Sunset Junction in Silver Lake, a district east of Hollywood in Los Angeles, California. Intelligentsia has opened two additional stores in the Los Angeles area, in Venice and Pasadena. In 2013, Intelligentsia opened its first store in New York City inside The High Line Hotel. The second New York City location opened in June 2014, inside the Urban Outfitters store in Herald Square. This is the first location to offer a full food menu. They also have 2 stores in Boston and one in Austin, Texas. | [
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A 2008 decision to stop serving 20-ounce coffee and espresso beverages in stores was met with controversy. Zell stated that the proportions are altered at such large quantities and certain drinks become watered-down, arguing that 20-ounce drinks end up "masking and adulterating the pure, intense flavors we work hard to source, roast and produce. We don't want this to just be a caffeine delivery device." In 2009 Intelligentsia acquired Ecco Caffè of Santa Rosa, California, and has retained the brand. In October 2015, it was announced that Peet's Coffee & Tea would buy a majority stake in Intelligentsia Coffee & Tea by the end of the year, as part of an expansion of Peet's into third wave coffee that also involved the acquisition of Stumptown Coffee Roasters. Intelligentsia was expected to continue operating independently, with founders Zell and Mange retaining a role in the company. The announcement came weeks after Intelligentsia had made known that it was seeking a private equity buy-out over $100 million. Honors
In 2006, Intelligentsia was included on several local and national best-of lists. One of their baristas also won national and international honors. It has been winning local best of list recognition from 2000 to 2005. In 2005, the local
recognition extended to national
recognition. In 2006, Intelligentsia was included on several local
and national "best" lists. | [
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See also
Blue Bottle Coffee
Counter Culture Coffee
La Colombe Coffee Roasters
Revelator Coffee
Stumptown Coffee Roasters
List of coffeehouse chains
List of coffee companies
Third wave of coffee
References
External links
Food and drink companies based in Chicago
Coffee houses of the United States
Retail companies established in 1995
Restaurants established in 1995
Coffee brands
1995 establishments in Illinois
2015 mergers and acquisitions | [
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Alteon WebSystems, originally known as Alteon Networks, is a division of Radware that produces application delivery controllers. Alteon was acquired by Nortel Networks on October 4, 2000. On February 22, 2009 Nortel Networks sold the Alteon application switching line to Radware. History
Alteon Networks was founded in 1996 by Mark Bryers, John Hayes, Ted Schroeder and Wayne Hathaway. Initial venture capital investors were Matrix Partners and Sutter Hill Ventures. Dominic Orr became chief executive in October 1996. Alteon introduced innovative products such as the ACEswitch 180, which was the first network switch to deliver Ethernet with selectable speed, 10/100 or 1000 Mbit/s, on every port via autonegotiation. Their ACEdirector Layer 4-7 switch was designed as an integrated services front-end and server load balancer. They also introduced Jumbo Frames (up to 9,000 bytes) with their ACEnic adapters, and supported by their switches. In addition to server switches, Alteon produced the first network interface controller (NIC) in 1997 that used Gigabit Ethernet (demonstrated at the Networld + Interop trade show in September 1996). Alteon's third generation Gigabit Ethernet NIC (code named "Tigon") became the basis for Broadcom's family of ethernet controllers (series BCM570x) and has shipped over 60 million copies. It was used in low-cost adapters from vendors such as 3Com. In July 2000, Nortel Networks announced it was buying Alteon for US$6 billion in stock. The deal had originally been announced with a value of $7.8 billion, but the stock market plummeted before the deal closed in October. | [
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Nortel rolled the ACEDirector and ACESwitch products into its Personal Internet product line, but one year later sales had slowed down. On February 22, 2009 Nortel Networks announced they would sell the Alteon application switching line to Radware, for $17.65 million. In November 2013, Radware announced the Alteon NG, marketed as an application delivery controller. References
1999 initial public offerings
2000 mergers and acquisitions
Dot-com bubble
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The Milne model was a special-relativistic cosmological model proposed by Edward Arthur Milne in 1935. It is mathematically equivalent to a special case of the FLRW model in the limit of zero energy density and it obeys the cosmological principle. The Milne model is also similar to Rindler space, a simple re-parameterization of flat Minkowski space. Since it features both zero energy density and maximally negative spatial curvature, the Milne model is inconsistent with cosmological observations. Cosmologists actually observe the universe's density parameter to be consistent with unity and its curvature to be consistent with flatness. Milne metric
The Milne universe is a special case of a more general Friedmann–Lemaître–Robertson–Walker model (FLRW). The Milne solution can be obtained from the more generic FLRW model by demanding that the energy density, pressure and cosmological constant all equal zero and the spatial curvature is negative. From these assumptions and the Friedmann equations it follows that the scale factor must depend on time coordinate linearly. Setting the spatial curvature and speed of light to unity the metric for a Milne universe can be expressed with hyperspherical coordinates as:
where
is the metric for a two-sphere and
is the curvature-corrected radial component for negatively curved space that varies between 0 and . The empty space that the Milne model describes can be identified with the inside of a light cone of an event in Minkowski space by a change of coordinates. Milne developed this model independent of general relativity but with awareness of special relativity. | [
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As he initially described it, the model has no expansion of space, so all of the redshift (except that caused by peculiar velocities) is explained by a recessional velocity associated with the hypothetical "explosion". However, the mathematical equivalence of the zero energy density () version of the FLRW metric to Milne's model implies that a full general relativistic treatment using Milne's assumptions would result in an increasing scale factor and associated metric expansion of space with the unique feature of a linearly increasing scale factor for all time since the deceleration parameter is uniquely zero for such a model. Incompatibility with observation
Even though the Milne model as a special case of a Friedmann-Robertson-Walker universe is a solution to General relativity, the assumption of zero energy content limits its use as a realistic description of the universe. Besides lacking the capability of describing matter Milne's universe is also incompatible with certain cosmological observations. In particular it makes no prediction of the cosmic microwave background radiation nor the abundance of light elements which are hallmark pieces of evidence that cosmologists agree support Big Bang cosmology over alternatives. Milne's density function
Milne proposed that the universe's density changes in time because of an initial outward explosion of matter. Milne's model assumes an inhomogeneous density function which is Lorentz Invariant (around the event t=x=y=z=0). When rendered graphically Milne's density distribution shows a three-dimensional spherical Lobachevskian pattern with outer edges moving outward at the speed of light. | [
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