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9,058 | # European influence in Afghanistan
## Mohammed Zahir Shah, 1933--1973 {#mohammed_zahir_shah_19331973}
In 1933, after the assassination of Nadir Khan, Mohammed Zahir Shah became king. In 1940, the Afghan legation in Berlin asked that if Germany won the Second World War would the *Reich* give all of British India up t... | 287 | European influence in Afghanistan | 9 |
9,067 | # Division ring
In algebra, a **division ring**, also called a **skew field** (or, occasionally, a **sfield**), is a nontrivial ring in which division by nonzero elements is defined. Specifically, it is a nontrivial ring`{{refn|In this article, rings have a {{math|1}}.}}`{=mediawiki} in which every nonzero element `{{... | 276 | Division ring | 0 |
9,067 | # Division ring
## Relation to fields and linear algebra {#relation_to_fields_and_linear_algebra}
All fields are division rings, and every non-field division ring is noncommutative. The best known example is the ring of quaternions. If one allows only rational instead of real coefficients in the constructions of the ... | 772 | Division ring | 1 |
9,067 | # Division ring
## Main theorems {#main_theorems}
**Wedderburn\'s little theorem**: All finite division rings are commutative and therefore finite fields. (Ernst Witt gave a simple proof.)
**Frobenius theorem**: The only finite-dimensional associative division algebras over the reals are the reals themselves, the co... | 196 | Division ring | 2 |
9,069 | # Dia (software)
**Dia** (`{{IPAc-en|ˈ|d|iː|ə}}`{=mediawiki}) is free and open source general-purpose diagramming software, developed originally by Alexander Larsson. It uses a controlled single document interface (SDI) similar to GIMP and Inkscape.
## Features
Dia has a modular design with several shape packages av... | 283 | Dia (software) | 0 |
9,074 | # Design Science License
**Design Science License** (**DSL**) is a copyleft license for any type of free content such as text, images, music. Unlike other open source licenses, the DSL was intended to be used on any type of copyrightable work, including documentation and source code. It was the first "generalized copy... | 91 | Design Science License | 0 |
9,082 | # Dispute resolution
**Dispute resolution** or **dispute settlement** is the process of resolving disputes between parties. The term *dispute resolution* is *conflict resolution* through legal means.
Prominent venues for dispute settlement in international law include the International Court of Justice (formerly the ... | 348 | Dispute resolution | 0 |
9,082 | # Dispute resolution
## Legal dispute resolution {#legal_dispute_resolution}
The legal system provides resolutions for many different types of disputes. Some disputants will not reach agreement through a collaborative process. Some disputes need the coercive power of the state to enforce a resolution. Perhaps more im... | 567 | Dispute resolution | 1 |
9,085 | # Catan: Cities & Knights
***Catan: Cities & Knights*** (*Städte und Ritter*), formerly *The Cities and Knights of Catan*, is an expansion to the board game *The Settlers of Catan* for three to four players (five to six player play is also possible with the *Settlers* and *Cities & Knights* five to six player extensio... | 882 | Catan: Cities & Knights | 0 |
9,085 | # Catan: Cities & Knights
## Barbarian attacks {#barbarian_attacks}
*Cities & Knights* introduces a third die, known as the event die, which serves two functions. The first applies to the concept of barbarians, a periodic foe that all players must work together to defend against. Three of the sides of the event die h... | 692 | Catan: Cities & Knights | 1 |
9,085 | # Catan: Cities & Knights
## Progress cards {#progress_cards}
The other significant outcome of the event die is Progress cards, which replace development cards. Because of the mechanics of progress cards explained below, one of the two white dice used in *Settlers* is replaced by a red die.
Progress cards are organi... | 392 | Catan: Cities & Knights | 2 |
9,085 | # Catan: Cities & Knights
## City walls {#city_walls}
City walls are a minor addition to *Cities & Knights* that increase the number of resource and commodity cards a player is allowed in their hand before having to discard on a roll of 7. However, they do not protect the player from the robber or barbarians. Only ci... | 729 | Catan: Cities & Knights | 3 |
9,086 | # Catan: Seafarers
***Catan: Seafarers***, or ***Seafarers of Catan*** in older editions, (*Die Seefahrer von Catan*) is an expansion of the board game *Catan* for three to four players (five-to-six-player play is also possible with both of the respective five-to-six-player extensions). The main feature of this expans... | 594 | Catan: Seafarers | 0 |
9,086 | # Catan: Seafarers
## Scenarios
Unlike *The Settlers of Catan* and *Catan: Cities & Knights*, in which the only random element of setup is the placement of land tiles, number tokens, and harbors in an identically shaped playing area, *Catan: Seafarers* has a number of different scenarios or maps from which to choose.... | 830 | Catan: Seafarers | 1 |
9,086 | # Catan: Seafarers
## Scenarios
### The Pirate Island {#the_pirate_island}
*The Pirate Island*, introduced in newer editions, is the first scenario which changes the mechanics of new gameplay elements introduced in *Seafarers*. *The Pirate Island* had previously been available as a downloadable scenario (but only in ... | 732 | Catan: Seafarers | 2 |
9,086 | # Catan: Seafarers
## Reception
*The Seafarers of Catan* was reviewed in the online second volume of *Pyramid* | 18 | Catan: Seafarers | 3 |
9,087 | # Dynamical system
In mathematics, a **dynamical system** is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion ... | 299 | Dynamical system | 0 |
9,087 | # Dynamical system
## Overview
The concept of a dynamical system has its origins in Newtonian mechanics. There, as in other natural sciences and engineering disciplines, the evolution rule of dynamical systems is an implicit relation that gives the state of the system for only a short time into the future. (The relat... | 524 | Dynamical system | 1 |
9,087 | # Dynamical system
## History
Many people regard French mathematician Henri Poincaré as the founder of dynamical systems. Poincaré published two now classical monographs, \"New Methods of Celestial Mechanics\" (1892--1899) and \"Lectures on Celestial Mechanics\" (1905--1910). In them, he successfully applied the resu... | 369 | Dynamical system | 2 |
9,087 | # Dynamical system
## Formal definition {#formal_definition}
In the most general sense, a **dynamical system** is a tuple (*T*, *X*, Φ) where *T* is a monoid, written additively, *X* is a non-empty set and Φ is a function
$$\Phi: U \subseteq (T \times X) \to X$$ with
$$\mathrm{proj}_{2}(U) = X$$ (where $\mathrm{pro... | 354 | Dynamical system | 3 |
9,087 | # Dynamical system
## Formal definition {#formal_definition}
### Geometrical definition {#geometrical_definition}
In the geometrical definition, a dynamical system is the tuple $\langle \mathcal{T}, \mathcal{M}, f\rangle$. $\mathcal{T}$ is the domain for time -- there are many choices, usually the reals or the integ... | 517 | Dynamical system | 4 |
9,087 | # Dynamical system
## Formal definition {#formal_definition}
### Measure theoretical definition {#measure_theoretical_definition}
A dynamical system may be defined formally as a measure-preserving transformation of a measure space, the triplet (*T*, (*X*, Σ, *μ*), Φ). Here, *T* is a monoid (usually the non-negative i... | 498 | Dynamical system | 5 |
9,087 | # Dynamical system
## Construction of dynamical systems {#construction_of_dynamical_systems}
The concept of *evolution in time* is central to the theory of dynamical systems as seen in the previous sections: the basic reason for this fact is that the starting motivation of the theory was the study of time behavior of... | 326 | Dynamical system | 6 |
9,087 | # Dynamical system
## Examples
- Arnold\'s cat map
- Baker\'s map is an example of a chaotic piecewise linear map
- Billiards and outer billiards
- Bouncing ball dynamics
- Circle map
- Complex quadratic polynomial
- Double pendulum
- Dyadic transformation
- Dynamical system simulation
- Hénon map... | 600 | Dynamical system | 7 |
9,087 | # Dynamical system
## Local dynamics {#local_dynamics}
The qualitative properties of dynamical systems do not change under a smooth change of coordinates (this is sometimes taken as a definition of qualitative): a *singular point* of the vector field (a point where *v*(*x*) = 0) will remain a singular point under smo... | 824 | Dynamical system | 8 |
9,087 | # Dynamical system
## Bifurcation theory {#bifurcation_theory}
When the evolution map Φ^*t*^ (or the vector field it is derived from) depends on a parameter μ, the structure of the phase space will also depend on this parameter. Small changes may produce no qualitative changes in the phase space until a special value... | 280 | Dynamical system | 9 |
9,087 | # Dynamical system
## Ergodic systems {#ergodic_systems}
In many dynamical systems, it is possible to choose the coordinates of the system so that the volume (really a ν-dimensional volume) in phase space is invariant. This happens for mechanical systems derived from Newton\'s laws as long as the coordinates are the ... | 551 | Dynamical system | 10 |
9,087 | # Dynamical system
## Nonlinear dynamical systems and chaos {#nonlinear_dynamical_systems_and_chaos}
Simple nonlinear dynamical systems, including piecewise linear systems, can exhibit strongly unpredictable behavior, which might seem to be random, despite the fact that they are fundamentally deterministic. This unpr... | 386 | Dynamical system | 11 |
9,090 | # Dhimmi
***`{{Transliteration|ar|ALA|Dhimmī}}`{=mediawiki}*** (*ذمي* *`{{Transliteration|ar|DIN|ḏimmī}}`{=mediawiki}*, `{{IPA|ar|ˈðimmiː|IPA}}`{=mediawiki}, collectively *أهل الذمة* *`{{Transliteration|ar|DIN|ʾahl aḏ-ḏimmah}}`{=mediawiki}/`{{Transliteration|ar|ALA|dhimmah}}`{=mediawiki}* \"the people of the covenant\... | 512 | Dhimmi | 0 |
9,090 | # Dhimmi
## The \"Dhimma contract\" {#the_dhimma_contract}
Based on Quranic verses and Islamic traditions, *sharia* law distinguishes between Muslims, followers of other Abrahamic religions, and Pagans or people belonging to other polytheistic religions. As monotheists, Jews and Christians have traditionally been con... | 1,178 | Dhimmi | 1 |
9,090 | # Dhimmi
## The \"Dhimma contract\" {#the_dhimma_contract}
### Views of modern Islamic scholars on the status of non-Muslims in an Islamic society {#views_of_modern_islamic_scholars_on_the_status_of_non_muslims_in_an_islamic_society}
- The Iranian Shi\'a Muslim Ayatollah Ruhollah Khomeini indicates in his book *Isl... | 789 | Dhimmi | 2 |
9,090 | # Dhimmi
## Dhimmi communities {#dhimmi_communities}
Jews and Christians living under early Muslim rule were considered dhimmis, a status that was later also extended to other non-Muslims like Hindus and Buddhists. They were allowed to \"freely practice their religion, and to enjoy a large measure of communal autonom... | 505 | Dhimmi | 3 |
9,090 | # Dhimmi
## Dhimmi communities {#dhimmi_communities}
### Christians
According to historians Lewis and Stillman, local Christians in Syria, Iraq, and Egypt were non-Chalcedonians and many may have felt better off under early Muslim rule than under that of the Byzantine Orthodox of Constantinople. In 1095, Pope Urban I... | 872 | Dhimmi | 4 |
9,090 | # Dhimmi
## Restrictions
There were a number of restrictions on dhimmis. In a modern sense the dhimmis would be described as second-class citizens. According to historian Marshall Hodgson, from very early times Muslim rulers would very often humiliate and punish dhimmis (usually Christians or Jews that refused to con... | 364 | Dhimmi | 5 |
9,090 | # Dhimmi
## Restrictions
### Jizya tax {#jizya_tax}
Payment of the *jizya* obligated Muslim authorities to protect dhimmis in civil and military matters. Sura 9 (At-Tawba), verse 29 stipulates that *jizya* be exacted from non-Muslims as a condition required for jihad to cease. Islamic jurists required adult, free, he... | 803 | Dhimmi | 6 |
9,090 | # Dhimmi
## Relevant texts {#relevant_texts}
### Quranic verses as a basis for Islamic policies toward dhimmis {#quranic_verses_as_a_basis_for_islamic_policies_toward_dhimmis}
Lewis states
- Al-Baqara 256 \"Let there be no compulsion in religion: \...\",`{{qref|2|256|s=y}}`{=mediawiki} means non-Muslims should no... | 618 | Dhimmi | 7 |
9,090 | # Dhimmi
## Cultural interactions and cultural differences {#cultural_interactions_and_cultural_differences}
During the Middle Ages, local associations known as *futuwwa* clubs developed across the Islamic lands. There were usually several futuwwah in each town. These clubs catered to varying interests, primarily spo... | 486 | Dhimmi | 8 |
9,091 | # Doctor V64
The **Doctor V64** (also referred to simply as the **V64**) is a development and backup device made by Bung Enterprises Ltd that is used in conjunction with the Nintendo 64. The Doctor V64 also had the ability to play video CDs and audio CDs. Additionally, it could apply stereo 3D effects to the audio.
#... | 697 | Doctor V64 | 0 |
9,091 | # Doctor V64
## Legal issues {#legal_issues}
### Role in piracy {#role_in_piracy}
The Doctor V64 unit was the first commercially available backup device for the Nintendo 64 unit. Though the unit was sold as a development machine, it could be modified to enable the creation and use of commercial game backups. Unlike ... | 292 | Doctor V64 | 1 |
9,091 | # Doctor V64
## Main menu {#main_menu}
The Doctor V64 implemented text-based menu-driven screens. The menus consisted of white text superimposed over a black background. Utilizing the buttons on the V64 unit, a user would navigate the menus and issue commands. Though the menu was mainly designed for game developers, ... | 448 | Doctor V64 | 2 |
9,091 | # Doctor V64
## Detailed specifications {#detailed_specifications}
### CD-ROM access speed {#cd_rom_access_speed}
Most early V64 models shipped with a standard IDE 8X CD-ROM . During the manufacturing lifetime of the device, latter V64 models shipped with 16X and eventually 20X drives. V64 units could be purchased w... | 482 | Doctor V64 | 3 |
9,110 | # Diophantus
**Diophantus of Alexandria** (*Diophantos*) (`{{IPAc-en|d|aɪ|oʊ|ˈ|f|æ|n|t|ə|s}}`{=mediawiki}; `{{fl|250 CE}}`{=mediawiki}) was a Greek mathematician who was the author of the *Arithmetica* in thirteen books, ten of which are still extant, made up of arithmetical problems that are solved through algebraic ... | 450 | Diophantus | 0 |
9,110 | # Diophantus
## *Arithmetica*
*Arithmetica* is the major work of Diophantus and the most prominent work on premodern algebra in Greek mathematics. It is a collection of 290 algebraic problems giving numerical solutions of determinate equations (those with a unique solution) and indeterminate equations. *Arithmetica* ... | 719 | Diophantus | 1 |
9,110 | # Diophantus
## Other works {#other_works}
Another work by Diophantus, *On Polygonal Numbers* is transmitted in an incomplete form in four Byzantine manuscripts along with the *Arithmetica*. Two other lost works by Diophantus are known: *Porisms* and *On Parts*.
Recently, Wilbur Knorr has suggested that another book... | 274 | Diophantus | 2 |
9,110 | # Diophantus
## Influence
Diophantus\' work has had a large influence in history. Although Joseph-Louis Lagrange called Diophantus \"the inventor of algebra\", he did not invent it, however his work *Arithmetica* created a foundation for work on algebra and in fact much of advanced mathematics is based on algebra. Di... | 1,017 | Diophantus | 3 |
9,110 | # Diophantus
## Influence
### Rediscovery of books IV-VII {#rediscovery_of_books_iv_vii}
In 1968, Fuat Sezgin found four previously unknown books of *Arithmetica* at the shrine of Imam Rezā in the holy Islamic city of Mashhad in northeastern Iran. The four books are thought to have been translated from Greek to Arabi... | 231 | Diophantus | 4 |
9,118 | # Duke Kahanamoku
thumb\|upright=1.2\|Signature
**Duke Paoa Kahinu Mokoe Hulikohola Kahanamoku** (August 24, 1890 -- January 22, 1968) was a Hawaiian competition swimmer, lifeguard, and popularizer of the sport of surfing. A Native Hawaiian, he was born three years before the overthrow of the Hawaiian Kingdom. He liv... | 584 | Duke Kahanamoku | 0 |
9,118 | # Duke Kahanamoku
## Career
Kahanamoku easily qualified for the U.S. Olympic swimming team in 1912. At the 1912 Summer Olympics in Stockholm, he won a gold medal in the 100-meter freestyle, and a silver medal with the second-place U.S. team in the men\'s 4×200-meter freestyle relay.
During the 1920 Olympics in Antwe... | 618 | Duke Kahanamoku | 1 |
9,118 | # Duke Kahanamoku
## *Duncan v. Kahanamoku* {#duncan_v._kahanamoku}
In 1946, Kahanamoku was the *pro forma* defendant in the landmark Supreme Court case *Duncan v. Kahanamoku*. While Kahanamoku was a military police officer during World War II, he arrested Duncan, a civilian shipfitter, for public intoxication.
At t... | 741 | Duke Kahanamoku | 2 |
9,129 | # Don Tennant
**Donald G. Tennant** (November 23, 1922 -- December 8, 2001) was an American advertising agency executive.
He worked at the Leo Burnett agency in Chicago, Illinois. The agency placed anthropomorphic faces of \'critters\' on packaged goods. Tennant was in charge of the Marlboro account and invented the ... | 52 | Don Tennant | 0 |
9,146 | # Dolly (sheep)
**Dolly** (5 July 1996 -- 14 February 2003) was a female Finn-Dorset sheep and the first mammal that was cloned from an adult somatic cell. She was cloned by associates of the Roslin Institute in Scotland, using the process of nuclear transfer from a cell taken from a mammary gland. Her cloning proved ... | 644 | Dolly (sheep) | 0 |
9,146 | # Dolly (sheep)
## Death
On 14 February 2003, Dolly was euthanised because she had a progressive lung disease and severe arthritis. A Finn Dorset such as Dolly has a life expectancy of around 11 to 12 years, but Dolly lived 6.5 years. A post-mortem examination showed she had a form of lung cancer called ovine pulmona... | 303 | Dolly (sheep) | 1 |
9,146 | # Dolly (sheep)
## Legacy
After cloning was successfully demonstrated through the production of Dolly, many other large mammals were cloned, including pigs, deer, horses and bulls. The attempt to clone argali (mountain sheep) did not produce viable embryos. The attempt to clone a banteng bull was more successful, as ... | 466 | Dolly (sheep) | 2 |
9,259 | # Equivalence relation
Equivalence}} `{{stack|{{Binary relations}}}}`{=mediawiki}
In mathematics, an **equivalence relation** is a binary relation that is reflexive, symmetric, and transitive. The equipollence relation between line segments in geometry is a common example of an equivalence relation. A simpler example... | 384 | Equivalence relation | 0 |
9,259 | # Equivalence relation
## Examples
### Simple example {#simple_example}
On the set $X = \{a, b, c\}$, the relation $R = \{(a, a), (b, b), (c, c), (b, c), (c, b)\}$ is an equivalence relation. The following sets are equivalence classes of this relation: $[a] = \{a\}, ~~~~ [b] = [c] = \{b, c\}.$
The set of all equiva... | 441 | Equivalence relation | 1 |
9,259 | # Equivalence relation
## Connections to other relations {#connections_to_other_relations}
- A partial order is a relation that is reflexive, `{{em|[[Antisymmetric relation|antisymmetric]]}}`{=mediawiki}, and transitive.
- Equality is both an equivalence relation and a partial order. Equality is also the only rel... | 497 | Equivalence relation | 2 |
9,259 | # Equivalence relation
## Related important definitions {#related_important_definitions}
Let $a, b \in X$, and $\sim$ be an equivalence relation. Some key definitions and terminology follow:
### Equivalence class {#equivalence_class}
A subset $Y$ of $X$ such that $a \sim b$ holds for all $a$ and $b$ in $Y$, and nev... | 703 | Equivalence relation | 3 |
9,259 | # Equivalence relation
## Generating equivalence relations {#generating_equivalence_relations}
- Given any set $X,$ an equivalence relation over the set $[X \to X]$ of all functions $X \to X$ can be obtained as follows. Two functions are deemed equivalent when their respective sets of fixpoints have the same cardin... | 376 | Equivalence relation | 4 |
9,259 | # Equivalence relation
## Algebraic structure {#algebraic_structure}
Much of mathematics is grounded in the study of equivalences, and order relations. Lattice theory captures the mathematical structure of order relations. Even though equivalence relations are as ubiquitous in mathematics as order relations, the alge... | 1,091 | Equivalence relation | 5 |
9,281 | # Evolutionary linguistics
**Evolutionary linguistics** or **Darwinian linguistics** is a sociobiological approach to the study of language. Evolutionary linguists consider linguistics as a subfield of sociobiology and evolutionary psychology. The approach is also closely linked with evolutionary anthropology, cogniti... | 266 | Evolutionary linguistics | 0 |
9,281 | # Evolutionary linguistics
## History
### 1863--1945: social Darwinism {#social_darwinism}
Although pre-Darwinian theorists had compared languages to living organisms as a metaphor, the comparison was first taken literally in 1863 by the historical linguist August Schleicher who was inspired by Charles Darwin\'s *On... | 773 | Evolutionary linguistics | 1 |
9,281 | # Evolutionary linguistics
## Approaches
Evolutionary linguistics is often divided into functionalism and formalism, concepts which are not to be confused with functionalism and formalism in the humanistic reference. Functional evolutionary linguistics considers languages as adaptations to human mind. The formalist v... | 553 | Evolutionary linguistics | 2 |
9,281 | # Evolutionary linguistics
## Criticism
Evolutionary linguistics has been criticised by advocates of (humanistic) structural and functional linguistics. Ferdinand de Saussure commented on 19th century evolutionary linguistics: `{{Blockquote|text=
"Language was considered a specific sphere, a fourth natural kingdom; t... | 289 | Evolutionary linguistics | 3 |
9,286 | # Ethical non-naturalism
**Ethical non-naturalism** (or **moral non-naturalism**) is the meta-ethical view which claims that:
1. Ethical sentences express propositions.
2. Some such propositions are true.
3. Those propositions are made true by objective features of the world, independent of human opinion.
4. Thes... | 727 | Ethical non-naturalism | 0 |
9,307 | # Demand-pull inflation
`{{Macroeconomics sidebar}}`{=mediawiki}
**Demand-pull inflation** occurs when aggregate demand in an economy is more than aggregate supply. It involves inflation rising as real gross domestic product rises and unemployment falls, as the economy moves along the Phillips curve. This is commonly... | 393 | Demand-pull inflation | 0 |
9,308 | # Cost-push inflation
`{{Macroeconomics sidebar}}`{=mediawiki} **Cost-push inflation** is a purported type of inflation caused by increases in the cost of important goods or services where no suitable alternative is available.
## Cause
As businesses face higher prices for underlying inputs, they are forced to increa... | 352 | Cost-push inflation | 0 |
9,309 | # Extractor (mathematics)
An $(N,M,D,K,\epsilon)$ -**extractor** is a bipartite graph with $N$ nodes on the left and $M$ nodes on the right such that each node on the left has $D$ neighbors (on the right), which has the added property that for any subset $A$ of the left vertices of size at least $K$, the distribution ... | 261 | Extractor (mathematics) | 0 |
9,313 | # Expander graph
In graph theory, an **expander graph** is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander constructions have spawned research in pure and applied mathematics, with several applications to complexity theory, design of robust computer... | 702 | Expander graph | 0 |
9,313 | # Expander graph
## Definitions
### Spectral expansion {#spectral_expansion}
When `{{mvar|G}}`{=mediawiki} is `{{mvar|d}}`{=mediawiki}-regular, a linear algebraic definition of expansion is possible based on the eigenvalues of the adjacency matrix `{{math|1=''A'' = ''A''(''G'')}}`{=mediawiki} of `{{mvar|G}}`{=mediawi... | 396 | Expander graph | 1 |
9,313 | # Expander graph
## Definitions
### Expander families {#expander_families}
A family $(G_i)_{i \in \mathbb N}$ of $d$-regular graphs of increasing size is an **expander family** if $h(G_i)$ is bounded away from zero.
| 32 | Expander graph | 2 |
9,313 | # Expander graph
## Relationships between different expansion properties {#relationships_between_different_expansion_properties}
The expansion parameters defined above are related to each other. In particular, for any `{{mvar|d}}`{=mediawiki}-regular graph `{{mvar|G}}`{=mediawiki},
$$h_{\text{out}}(G) \le h(G) \le d... | 281 | Expander graph | 3 |
9,313 | # Expander graph
## Constructions
There are four general strategies for explicitly constructing families of expander graphs. The first strategy is algebraic and group-theoretic, the second strategy is analytic and uses additive combinatorics, the third strategy is combinatorial and uses the zig-zag and related graph ... | 1,070 | Expander graph | 4 |
9,313 | # Expander graph
## Applications and useful properties {#applications_and_useful_properties}
The original motivation for expanders is to build economical robust networks (phone or computer): an expander with bounded degree is precisely an asymptotic robust graph with the number of edges growing linearly with size (nu... | 556 | Expander graph | 5 |
9,313 | # Expander graph
## Applications and useful properties {#applications_and_useful_properties}
### AKS sorting network and approximate halvers {#aks_sorting_network_and_approximate_halvers}
Sorting networks take a set of inputs and perform a series of parallel steps to sort the inputs. A parallel step consists of perfo... | 587 | Expander graph | 6 |
9,320 | # Ericales
The **Ericales** are a large and diverse order of flowering plants in the asterid group of the eudicots. Well-known and economically important members of this order include tea and ornamental camellias, persimmon, ebony, blueberry, cranberry, lingonberry, huckleberry, kiwifruit, Brazil nut, argan, sapote, a... | 640 | Ericales | 0 |
9,324 | # Easter egg
**Easter eggs**, also called **Paschal eggs**, are eggs that are decorated for the Christian holiday of Easter, which celebrates the resurrection of Jesus. As such, Easter eggs are commonly used during the season of Eastertide (Easter season). The oldest tradition, which continues to be used in Central an... | 915 | Easter egg | 0 |
9,324 | # Easter egg
## Traditions and customs {#traditions_and_customs}
### Lenten tradition {#lenten_tradition}
The Easter egg tradition may also have merged into the celebration of the end of the privations of Lent. Traditionally, eggs are among the foods forbidden on fast days, including all of Lent, an observance which... | 1,051 | Easter egg | 1 |
9,324 | # Easter egg
## Traditions and customs {#traditions_and_customs}
### Use of Easter eggs in decorations {#use_of_easter_eggs_in_decorations}
In some Mediterranean countries, especially in Lebanon, chicken eggs are boiled and decorated by dye and/or painting and used as decoration around the house. Then, on Easter Day,... | 267 | Easter egg | 2 |
9,324 | # Easter egg
## Easter egg games {#easter_egg_games}
### Egg hunts {#egg_hunts}
An egg hunt is a game in which decorated eggs, which may be hard-boiled chicken eggs, chocolate eggs, or artificial eggs containing candies, are hidden for children to find. The eggs often vary in size, and may be hidden both indoors and... | 712 | Easter egg | 3 |
9,324 | # Easter egg
## Variants
### Chocolate
Chocolate eggs first appeared at the court of Louis XIV in Versailles and in 1725 the widow Giambone in Turin started producing chocolate eggs by filling empty chicken egg shells with molten chocolate. In 1873, J.S. Fry & Sons produced the first hollow chocolate egg making a sm... | 435 | Easter egg | 4 |
9,324 | # Easter egg
## Legends
### Christian traditions {#christian_traditions}
While the origin of Easter eggs can be explained in the symbolic terms described above, among followers of Eastern Christianity the legend says that Mary Magdalene was bringing cooked eggs to share with the other women at the tomb of Jesus, and... | 665 | Easter egg | 5 |
9,332 | # Errol Morris
**Errol Mark Morris** (born February 5, 1948) is an American film director known for documentaries that interrogate the epistemology of their subjects, and the invention of the Interrotron. In 2003, his *The Fog of War: Eleven Lessons from the Life of Robert S. McNamara* won the Academy Award for Best D... | 525 | Errol Morris | 0 |
9,332 | # Errol Morris
## Career
After leaving UC Berkeley, he became a regular at the Pacific Film Archive. As Tom Luddy, the director of the archive at the time, later remembered: \"He was a film noir nut. He claimed we weren\'t showing the real film noir. So I challenged him to write the program notes. Then, there was his... | 871 | Errol Morris | 1 |
9,332 | # Errol Morris
## Career
### *The Thin Blue Line* {#the_thin_blue_line}
In 1985, Morris became interested in Dr. James Grigson, a psychiatrist in Dallas. Under Texas law, the death penalty can only be issued if the jury is convinced that the defendant is not only guilty, but will commit further violent crimes in the ... | 573 | Errol Morris | 2 |
9,332 | # Errol Morris
## Career
### *A Brief History of Time* and *Fast, Cheap & Out of Control* {#a_brief_history_of_time_and_fast_cheap_out_of_control}
Morris wanted to make a film about Albert Einstein\'s brain and approached Amblin Entertainment about it. Gordon Freeman had acquired the rights to Stephen Hawking\'s best... | 663 | Errol Morris | 3 |
9,332 | # Errol Morris
## Career
### Commercials
Although Morris has achieved fame as a documentary filmmaker, he is also an accomplished director of television commercials. In 2002, Morris directed a series of television ads for Apple Computer as part of a popular \"Switch\" campaign. The commercials featured ex-Windows use... | 665 | Errol Morris | 4 |
9,332 | # Errol Morris
## Style and legacy {#style_and_legacy}
To conduct interviews, Morris invented a machine, called the Interrotron, which allows the interviewer and his subject to make eye-contact with each other while both staring through the camera lens itself. He explains the device as follows:
Author Marsha McCread... | 366 | Errol Morris | 5 |
9,332 | # Errol Morris
## Filmography
### Feature films {#feature_films}
- *Gates of Heaven* (1978)
- *Vernon, Florida* (1981)
- *The Thin Blue Line* (1988)
- *The Dark Wind* (1991), fiction movie
- *A Brief History of Time* (1991)
- *Fast, Cheap & Out of Control* (1997)
- *Mr. Death: The Rise and Fall of Fred... | 327 | Errol Morris | 6 |
9,332 | # Errol Morris
## Accolades
- *Gates of Heaven* (1978) was long featured on Roger Ebert\'s list of the ten greatest films ever made.
- Golden Horse for Best Foreign Film at the Taiwan International Film Festival for *The Thin Blue Line* (1988)
- New York Film Critics Circle and the National Society of Film Crit... | 334 | Errol Morris | 7 |
9,333 | # Ethan Allen
**Ethan Allen** (`{{OldStyleDate|January 21, 1738||January 10, 1737}}`{=mediawiki} -- February 12, 1789) was an American farmer, writer, military officer and politician. He is best known as one of the founders of Vermont and for the capture of Fort Ticonderoga during the American Revolutionary War, and w... | 334 | Ethan Allen | 0 |
9,333 | # Ethan Allen
## Early life {#early_life}
Allen was born in Litchfield, Connecticut Colony, the first child of Joseph and Mary Baker Allen, both descended from English Puritans. The family moved to the town of Cornwall shortly after his birth due to his father\'s quest for freedom of religion during the Great Awakeni... | 775 | Ethan Allen | 1 |
9,333 | # Ethan Allen
## New Hampshire Grants {#new_hampshire_grants}
New Hampshire Governor Benning Wentworth was selling land grants west of the Connecticut River as early as 1749, an area to which New Hampshire had always laid claim. Many of these grants were sold at relatively low prices to land speculators, with Wentwor... | 401 | Ethan Allen | 2 |
9,333 | # Ethan Allen
## New Hampshire Grants {#new_hampshire_grants}
### Green Mountain Boys {#green_mountain_boys}
On Allen\'s return to Bennington, the settlers met at the Catamount Tavern to discuss their options. These discussions resulted in the formation of the Green Mountain Boys in 1770, with local militia companies... | 922 | Ethan Allen | 3 |
9,333 | # Ethan Allen
## Revolutionary War {#revolutionary_war}
### Capture of Fort Ticonderoga {#capture_of_fort_ticonderoga}
Allen received a message from members of an irregular Connecticut militia in late April, following the battles of Lexington and Concord, that they were planning to capture Fort Ticonderoga and reque... | 373 | Ethan Allen | 4 |
9,333 | # Ethan Allen
## Revolutionary War {#revolutionary_war}
### Raids on St. John {#raids_on_st._john}
On the following day, a detachment of the Boys under Seth Warner\'s command went to nearby Fort Crown Point and captured the small garrison there. On May 14, following the arrival of 100 men recruited by Arnold\'s capta... | 960 | Ethan Allen | 5 |
9,333 | # Ethan Allen
## Revolutionary War {#revolutionary_war}
### Capture
The American invasion of Quebec departed from Ticonderoga on August 28. On September 4, the army had occupied the Île aux Noix in the Richelieu River, a few miles above Fort St. John, which they then prepared to besiege. On September 8, Schuyler sent... | 338 | Ethan Allen | 6 |
9,333 | # Ethan Allen
## Imprisonment
Much of what is known of Allen\'s captivity is known only from his own account of the time; where contemporary records are available, they tend to confirm those aspects of his story.
Allen was first placed aboard `{{HMS|Gaspée|1773|6}}`{=mediawiki}, a brig anchored at Montreal. He was k... | 654 | Ethan Allen | 7 |
9,333 | # Ethan Allen
## Vermont Republic {#vermont_republic}
### Return home {#return_home}
Following his visit to Valley Forge, Allen traveled to Salisbury, arriving on May 25, 1778. There he learned that his brother Heman had died just the previous week and that his brother Zimri, who had been caring for Allen\'s family ... | 927 | Ethan Allen | 8 |
9,333 | # Ethan Allen
## Later years {#later_years}
As the war had ended with the 1783 Treaty of Paris, and the United States, operating under the Articles of Confederation, resisted any significant action with respect to Vermont, Allen\'s historic role as an agitator became less important, and his public role in Vermont\'s ... | 381 | Ethan Allen | 9 |
9,333 | # Ethan Allen
## Later years {#later_years}
### Second marriage {#second_marriage}
Allen met his second wife, a young widow named Frances \"Fanny\" Montresor Brush Buchanan, early in 1784; and after a brief courtship, they wed on February 16, 1784. Fanny came from a notably Loyalist background (including Crean Brush,... | 761 | Ethan Allen | 10 |
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