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Bound

A Wisdom Archive on Bound

Bound

A selection of articles related to Bound

We recommend this article: Bound - 1, and also this: Bound - 2.
bound, Bound

ARTICLES RELATED TO Bound

Bound: Encyclopedia II - Heap - Heap applications

Heaps are favourite data structures for many applications. Heap sort: One of the best sorting methods being in-place and with no quadratic worst case scenarios. Selection algorithms: Finding the min, max or both of them, median or even any kth element in sublinear time can be done dynamically with heaps. Graph algorithms: By using heaps as internal traversal data structures, run time will be reduced by an order of polynomial. One more advantage of heap over tree in some applications is construction of heap can be don ...

See also:

Heap, Heap - Variants, Heap - Comparison of theoretic bounds for variants, Heap - Heap applications

Read more here: » Heap: Encyclopedia II - Heap - Heap applications

Bound: Encyclopedia II - Haibane Renmei - Plot Summary

The series starts out with two parallel scenes. One contains the image of a girl falling from the sky, cradling a crow; it tries to stop her fall, but cannot. The other consists of a group of Haibane finding a large cocoon growing in a storage room. When the cocoon breaks open, the teenage girl inside is brought to the guest room, where she is cared for by several Haibane, mostly one named Reki. All the girl can remember is her dream of falling. As Haibane are traditionally named based on their dreams within the cocoon, she is named Rakka (" ...

See also:

Haibane Renmei, Haibane Renmei - Characters, Haibane Renmei - Plot Summary, Haibane Renmei - Haibane, Haibane Renmei - Sin-Bound, Haibane Renmei - Context and Interpretation

Read more here: » Haibane Renmei: Encyclopedia II - Haibane Renmei - Plot Summary

Bound: Encyclopedia II - Haibane Renmei - Haibane

The Haibane are a race of people who resemble angels in that they have wings and haloes. However, their wings are short, not functional, and rather than white they are charcoal grey. Furthermore, their haloes are forged for them by the Haibane Renmei, although it is likely the case that they can still only be worn by a Haibane. Haibane are born from cocoons that grow from small seeds that appear in places such as Old Home (in all the depicted cases they in fact grow in uninhabited rooms). In the introduction sequence to the anime the ...

See also:

Haibane Renmei, Haibane Renmei - Characters, Haibane Renmei - Plot Summary, Haibane Renmei - Haibane, Haibane Renmei - Sin-Bound, Haibane Renmei - Context and Interpretation

Read more here: » Haibane Renmei: Encyclopedia II - Haibane Renmei - Haibane

Bound: Encyclopedia II - Alternating Turing machine - Example

Perhaps the simplest problem for alternating machines to solve is the quantified boolean formula problem, which is a generalization of the boolean satisfiability problem in which each variable can be bound by either an existential or a universal quantifier. The alternating machine branches existentially to try all possible values of an existentially quantified variable and universally to try all possible values of a universally quantified variable, in the left-to-right order in which they are bound. After deciding a value for all quantified ...

See also:

Alternating Turing machine, Alternating Turing machine - Definitions, Alternating Turing machine - Informal Description, Alternating Turing machine - Formal Definition, Alternating Turing machine - Machine with k alternations, Alternating Turing machine - Resource bounds, Alternating Turing machine - Example, Alternating Turing machine - Complexity classes and comparison to deterministic Turing machines

Read more here: » Alternating Turing machine: Encyclopedia II - Alternating Turing machine - Example

Bound: Encyclopedia II - Whaling in Japan - Japanese whaling since the suspension of commercial whaling

Whaling in Japan - Whales taken by Japan while not bound by IWC suspension. Whaling in Japan - Whales taken under Special Permit scientific whaling. ...

See also:

Whaling in Japan, Whaling in Japan - History, Whaling in Japan - Japanese whaling since the suspension of commercial whaling, Whaling in Japan - Whales taken by Japan while not bound by IWC suspension, Whaling in Japan - Whales taken under Special Permit scientific whaling

Read more here: » Whaling in Japan: Encyclopedia II - Whaling in Japan - Japanese whaling since the suspension of commercial whaling

Bound: Encyclopedia II - Hermitian adjoint - Properties

Immediate properties: A** = A (A + B )* = A* + B* (λA)* = λ* A*, where λ* denotes the complex conjugate of the complex number λ (AB)* = B* A* If we define the operator norm of A by then . Moreover, The set of bounded linear operators on a Hilbert space H together with the adjoint operation and the opera ...

See also:

Hermitian adjoint, Hermitian adjoint - Definition for bounded operators, Hermitian adjoint - Properties, Hermitian adjoint - Hermitian operators, Hermitian adjoint - Adjoints of unbounded operators, Hermitian adjoint - Other adjoints

Read more here: » Hermitian adjoint: Encyclopedia II - Hermitian adjoint - Properties

Bound: Encyclopedia II - Hermitian adjoint - Hermitian operators

A bounded operator A : H → H is called Hermitian or self-adjoint if A = A* which is equivalent to In some sense, these operators play the role of the real numbers (being equal to their own "complex conjugate"). They serve as the model of real-valued observables in quantum mechanics. See the article on self-adjoint operators for a full treatment. ...

See also:

Hermitian adjoint, Hermitian adjoint - Definition for bounded operators, Hermitian adjoint - Properties, Hermitian adjoint - Hermitian operators, Hermitian adjoint - Adjoints of unbounded operators, Hermitian adjoint - Other adjoints

Read more here: » Hermitian adjoint: Encyclopedia II - Hermitian adjoint - Hermitian operators

Bound: Encyclopedia II - Joint entropy - Properties

Joint entropy - Greater than subsystem entropies. The joint entropy is always at least equal to the entropies of the original system; adding a new system can never reduce the available uncertainty. This inequality is an equality if and only if Y is a (deterministic) function of X. Joint entropy - Subadditivity. Two systems, considered together, can never have more entropy than the sum of the entropy in each of them. This is an ex ...

See also:

Joint entropy, Joint entropy - Background, Joint entropy - Definition, Joint entropy - Properties, Joint entropy - Greater than subsystem entropies, Joint entropy - Subadditivity, Joint entropy - Bounds, Joint entropy - Relations to Other Entropy Measures

Read more here: » Joint entropy: Encyclopedia II - Joint entropy - Properties

Bound: Encyclopedia II - Hermitian adjoint - Other adjoints

The equation is formally similar to the defining properties of pairs of adjoint functors in category theory, and this is where adjoint functors got their name. ...

See also:

Hermitian adjoint, Hermitian adjoint - Definition for bounded operators, Hermitian adjoint - Properties, Hermitian adjoint - Hermitian operators, Hermitian adjoint - Adjoints of unbounded operators, Hermitian adjoint - Other adjoints

Read more here: » Hermitian adjoint: Encyclopedia II - Hermitian adjoint - Other adjoints

Bound: Encyclopedia II - Busy beaver - Examples of Busy Beaver Turing machines

These are tables of rules for Turing machines that generate Σ(1), Σ(2), and the best known lower bound for Σ(6) and S(6). The latter entry is listed because it is truly remarkable. In the tables, the columns represent the current state and the rows represent the current symbol read from the tape. The table entries indicate the symbol to write onto the tape, the new state, and the direction to move over the tape. Each machine begins in state A with an infinite tape that contains all 0's. Thus, the initial symbol read from the tape is a 0. Result Key: (st ...

See also:

Busy beaver, Busy beaver - Definition and known values, Busy beaver - Generalizations, Busy beaver - Trivial proof for uncomputability of Sn and Σn, Busy beaver - Examples of Busy Beaver Turing machines, Busy beaver - Exact values and lower bounds for some Snm and Σnm

Read more here: » Busy beaver: Encyclopedia II - Busy beaver - Examples of Busy Beaver Turing machines

Bound: Encyclopedia II - Empty set - Properties

(Here we use mathematical symbols.) For any set A, the empty set is a subset of A: ∀A: ⊆ A For any set A, the union of A with the empty set is A: ∀A: A ∪ = A For any set A, the intersection of A with the empty set is the empty set: ∀A: A ∩ = For any set A, the Cartesian product of A and the empty set is empty: ...

See also:

Empty set, Empty set - Notation, Empty set - Properties, Empty set - Common problems, Empty set - Axiomatic set theory, Empty set - Does it exist or is it necessary?, Empty set - Operations on the empty set, Empty set - Bounds, Empty set - The empty set and zero, Empty set - Category theory

Read more here: » Empty set: Encyclopedia II - Empty set - Properties

Bound: Encyclopedia II - Whaling in Japan - History

The oldest written mention of whaling in Japanese records is from Kojiki, the oldest known Japanese historical book. It dates back to 712. Since then, whaling has been frequently mentioned in Japanese historical sources. Whales have long been a source of food, oil, and material. A famous saying goes: "There's nothing to throw away from a whale except its voice." In 1852, a US naval officer Matthew Perry forced open Japan's doors to the world. One of the purposes was to obtain a b ...

See also:

Whaling in Japan, Whaling in Japan - History, Whaling in Japan - Japanese whaling since the suspension of commercial whaling, Whaling in Japan - Whales taken by Japan while not bound by IWC suspension, Whaling in Japan - Whales taken under Special Permit scientific whaling

Read more here: » Whaling in Japan: Encyclopedia II - Whaling in Japan - History

Bound: Encyclopedia II - Empty set - Notation

The standard notation for denoting the empty set is the symbol or ∅, introduced by the Bourbaki group (specifically André Weil) in 1939. [1] This should not be confused with the Scandinavian vowel Øø and the Greek letter Φ. Another common notation for the empty set is {}. For comparison, see the three signs together: ∅ Øø Φ – the empty set sign is based on a geometric circle, whereas the Scandinav ...

See also:

Empty set, Empty set - Notation, Empty set - Properties, Empty set - Common problems, Empty set - Axiomatic set theory, Empty set - Does it exist or is it necessary?, Empty set - Operations on the empty set, Empty set - Bounds, Empty set - The empty set and zero, Empty set - Category theory

Read more here: » Empty set: Encyclopedia II - Empty set - Notation

Bound: Encyclopedia II - Empty set - Common problems

The empty set is not the same thing as nothing; it is a set with nothing inside it, and a set is something. This often causes difficulty among those who first encounter it. It may be helpful to think of a set as a bag containing its elements; an empty bag may be empty, but the bag itself certainly exists. Some people balk at the first property listed above, that the empty set is a subset of any set A. By the definition of subset, this claim means that for every element x of {}, x belong ...

See also:

Empty set, Empty set - Notation, Empty set - Properties, Empty set - Common problems, Empty set - Axiomatic set theory, Empty set - Does it exist or is it necessary?, Empty set - Operations on the empty set, Empty set - Bounds, Empty set - The empty set and zero, Empty set - Category theory

Read more here: » Empty set: Encyclopedia II - Empty set - Common problems

Bound: Encyclopedia II - Busy beaver - Definition and known values

The two functions defined below, called Busy Beaver functions, were introduced in 1962 by Tibor Rado as simple examples of noncomputable functions: Σ(n): the largest number of 1's printable by an n-state machine before halting, and S(n): the largest number of steps taken by an n-state machine before halting. Both of these functions are noncomputable, because they grow faster than any computable function. E ...

See also:

Busy beaver, Busy beaver - Definition and known values, Busy beaver - Generalizations, Busy beaver - Trivial proof for uncomputability of Sn and Σn, Busy beaver - Examples of Busy Beaver Turing machines, Busy beaver - Exact values and lower bounds for some Snm and Σnm

Read more here: » Busy beaver: Encyclopedia II - Busy beaver - Definition and known values

Bound: Encyclopedia II - Busy beaver - Trivial proof for uncomputability of Sn and Σn

Suppose that S(n) is a computable function and let EvalS denote a TM, evaluating S(n). Given a tape with n 1s it will produce S(n) 1's on the tape and then halt. Let Clean denote a Turing machine cleaning the sequence of 1s initially written on the tape. Let Double denote a Turing machine evaluating function n + n. Given a tape with n 1s it will produce 2n 1s on the tape and then halt. Let us create the composition Double|EvalS| ...

See also:

Busy beaver, Busy beaver - Definition and known values, Busy beaver - Generalizations, Busy beaver - Trivial proof for uncomputability of Sn and Σn, Busy beaver - Examples of Busy Beaver Turing machines, Busy beaver - Exact values and lower bounds for some Snm and Σnm

Read more here: » Busy beaver: Encyclopedia II - Busy beaver - Trivial proof for uncomputability of Sn and Σn

Bound: Encyclopedia II - Alpha-beta pruning - Improvements over minimax

The benefit of alpha-beta pruning lies in the fact that branches of the search tree can be eliminated. The search time can in this way be limited to the 'more promising' subtree, and a deeper search can be performed in the same time. Like its predecessor, it belongs to the branch and bound class of algorithms. The optimisation typically reduces the effective branching factor by two compared to simple Minimax, or equivalently doubles the number of nodes that can be searched in a given time. The algorithm does even better ...

See also:

Alpha-beta pruning, Alpha-beta pruning - Improvements over minimax, Alpha-beta pruning - Heuristic improvements, Alpha-beta pruning - Other algorithms, Alpha-beta pruning - Pseudocode, Alpha-beta pruning - External references

Read more here: » Alpha-beta pruning: Encyclopedia II - Alpha-beta pruning - Improvements over minimax

Bound: Encyclopedia II - Alternating Turing machine - Definitions

Alternating Turing machine - Informal Description. The definition of NP uses the existential mode of computation: if any choice leads to an accepting state, then the whole computation accepts. The definition of co-NP uses the universal mode of computation: if all choices lead to an accepting state, then the whole computation accepts. An alternating Turing machine (or to be more precise, the definition of acce ...

See also:

Alternating Turing machine, Alternating Turing machine - Definitions, Alternating Turing machine - Informal Description, Alternating Turing machine - Formal Definition, Alternating Turing machine - Machine with k alternations, Alternating Turing machine - Resource bounds, Alternating Turing machine - Example, Alternating Turing machine - Complexity classes and comparison to deterministic Turing machines

Read more here: » Alternating Turing machine: Encyclopedia II - Alternating Turing machine - Definitions

Bound: Encyclopedia II - Spectrum functional analysis - Spectrum of unbounded operators

One can extend the definition of spectrum for unbounded operators on a Banach space X, operators which are no longer elements in the Banach algebra B(X). One proceeds in a manner similar to the bounded case. A complex number λ is said to be in the complement of the spectrum of a linear operator if the operator is surjective, with its inverse a bounded operator. A complex number λ is then in the spectrum if this property fails to hold. The spectrum ...

See also:

Spectrum functional analysis, Spectrum functional analysis - Definition, Spectrum functional analysis - Basic properties, Spectrum functional analysis - Spectrum of a bounded operator, Spectrum functional analysis - Classification of points in the spectrum of an operator, Spectrum functional analysis - Point spectrum, Spectrum functional analysis - Approximate point spectrum, Spectrum functional analysis - Compression spectrum, Spectrum functional analysis - Further results, Spectrum functional analysis - Spectrum of unbounded operators

Read more here: » Spectrum functional analysis: Encyclopedia II - Spectrum functional analysis - Spectrum of unbounded operators

Bound: Encyclopedia II - Low-discrepancy sequence - The Erdős-Turan-Koksma inequality

It is computationally hard to find the exact value of the discrepancy of large point sets. The Paul Erdős-Turán-Koksma inequality provides an upper bound. Let x1,...,xN be points in Is and H be an arbitrary positive integer. Then where ...

See also:

Low-discrepancy sequence, Low-discrepancy sequence - Definition of discrepancy, Low-discrepancy sequence - The Koksma-Hlawka inequality, Low-discrepancy sequence - The formula of Hlawka-Zaremba, Low-discrepancy sequence - The L2 version of the Koksma-Hlawka inequality, Low-discrepancy sequence - The Erdős-Turan-Koksma inequality, Low-discrepancy sequence - The main conjectures, Low-discrepancy sequence - The best-known sequences, Low-discrepancy sequence - Lower bounds, Low-discrepancy sequence - Applications

Read more here: » Low-discrepancy sequence: Encyclopedia II - Low-discrepancy sequence - The Erdős-Turan-Koksma inequality

Bound: Encyclopedia II - Sarin gas attack on the Tokyo subway - Background

AUM Shinrikyō (オウム真理教, literally, "AUM the True Teaching") is the former name of a controversial religious group based in Japan. The group gained international notoriety in 1995, when its founder and a group of followers were accused of masterminding the poison gas attack. The name AUM Shinrikyō derives from the Hindu syllable "aum" (pronounced "ohm") meaning "powers of creation and destruction of a universe," and the Japanese words "shinri" ("truth") and "kyō" ("teaching," "doctrine"). In 2000, after the attack, ...

See also:

Sarin gas attack on the Tokyo subway, Sarin gas attack on the Tokyo subway - Background, Sarin gas attack on the Tokyo subway - The main perpetrators, Sarin gas attack on the Tokyo subway - Hayashi Ikuo, Sarin gas attack on the Tokyo subway - Hirose Ken'ichi, Sarin gas attack on the Tokyo subway - Toyoda Tōru, Sarin gas attack on the Tokyo subway - Yokoyama Masato, Sarin gas attack on the Tokyo subway - Hayashi Yasuo, Sarin gas attack on the Tokyo subway - The attack, Sarin gas attack on the Tokyo subway - Chiyoda line, Sarin gas attack on the Tokyo subway - Marunouchi line Ogikubo-bound, Sarin gas attack on the Tokyo subway - Marunouchi line Ikebukuro-bound, Sarin gas attack on the Tokyo subway - Hibiya line departing Naka-meguro, Sarin gas attack on the Tokyo subway - Hibiya line Naka-meguro-bound, Sarin gas attack on the Tokyo subway - Aftermath, Sarin gas attack on the Tokyo subway - The injured, Sarin gas attack on the Tokyo subway - Emergency services, Sarin gas attack on the Tokyo subway - AUM/Aleph today

Read more here: » Sarin gas attack on the Tokyo subway: Encyclopedia II - Sarin gas attack on the Tokyo subway - Background

Bound: Encyclopedia II - Sarin gas attack on the Tokyo subway - The main perpetrators

Ten men were responsible for carrying out the attacks; five released the sarin, while the other five served as get-away drivers. The teams were: Hayashi Ikuo (林 郁夫) and Niimi Tomomitsu (新見 智光) Hirose Ken'ichi (広瀬 健一) and Kitamura Kōichi (北村 浩一) Toyoda Tōru (豊田 亨) and Takahashi Katsuya (高橋 克也) Yokoyama Masato (横山 真人) and Tonozaki Kiyotaka (外崎 清隆) Hayashi Yasuo (林 泰男, no relation to Hayashi Ikuo) and Sugimoto Shigeo (杉本 繁郎) ...

See also:

Sarin gas attack on the Tokyo subway, Sarin gas attack on the Tokyo subway - Background, Sarin gas attack on the Tokyo subway - The main perpetrators, Sarin gas attack on the Tokyo subway - Hayashi Ikuo, Sarin gas attack on the Tokyo subway - Hirose Ken'ichi, Sarin gas attack on the Tokyo subway - Toyoda Tōru, Sarin gas attack on the Tokyo subway - Yokoyama Masato, Sarin gas attack on the Tokyo subway - Hayashi Yasuo, Sarin gas attack on the Tokyo subway - The attack, Sarin gas attack on the Tokyo subway - Chiyoda line, Sarin gas attack on the Tokyo subway - Marunouchi line Ogikubo-bound, Sarin gas attack on the Tokyo subway - Marunouchi line Ikebukuro-bound, Sarin gas attack on the Tokyo subway - Hibiya line departing Naka-meguro, Sarin gas attack on the Tokyo subway - Hibiya line Naka-meguro-bound, Sarin gas attack on the Tokyo subway - Aftermath, Sarin gas attack on the Tokyo subway - The injured, Sarin gas attack on the Tokyo subway - Emergency services, Sarin gas attack on the Tokyo subway - AUM/Aleph today

Read more here: » Sarin gas attack on the Tokyo subway: Encyclopedia II - Sarin gas attack on the Tokyo subway - The main perpetrators




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