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Bound | A Wisdom Archive on Bound | | Bound A selection of articles related to Bound | |
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| ARTICLES RELATED TO Bound | | | |  Bound: Encyclopedia II - Scene graph - Scene-graph and Bounding Volume Hierarchies BVHsBounding Volume Hierarchies (BVHs) are useful for numerous tasks - including efficient culling and speeding up collision detection between objects. A BVH is a spatial structure but doesn't have to partition the geometry (see spatial partitioning, below).
A BVH is a tree of bounding volumes (often spheres, AABBs or/and OBBs). At the bottom of the hierarchy the size of the volume is just large enough to encompass a single object tightly (or possibly even some smaller fraction of an object in high resolution BVHs), as you walk up the hie ...
See also:Scene graph, Scene graph - Introduction, Scene graph - Scene-graphs in graphics editing tools, Scene graph - Scene-graphs in games and 3D applications, Scene graph - Scene-graph Implementation, Scene graph - Scene-graph Operations and Dispatch, Scene graph - Scene-graph and Bounding Volume Hierarchies BVHs, Scene graph - Scene-graphs and Spatial Partitioning, Scene graph - When it is useful to combine them, Scene graph - PHIGS Read more here: » Scene graph: Encyclopedia II - Scene graph - Scene-graph and Bounding Volume Hierarchies BVHs |
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| | | | | Bound: Encyclopedia II - Prime number theorem - Bounds on the prime counting function The prime number theorem is an asymptotic result. Hence, it cannot be used to bound π(x).
However, some bounds on π(x) are known, for instance
The first inequality holds for all x ≥ 17 and the second one for x > 1.
Another useful bound is
...
See also:Prime number theorem, Prime number theorem - Statement of the theorem, Prime number theorem - The prime counting function in terms of the logarithmic integral, Prime number theorem - The issue of depth, Prime number theorem - The prime number theorem for arithmetic progressions, Prime number theorem - Bounds on the prime counting function, Prime number theorem - Approximations for the nth prime number, Prime number theorem - Gaps between primes, Prime number theorem - Table of πx x / ln x and Lix, Prime number theorem - Analogue for irreducible polynomials over a finite field Read more here: » Prime number theorem: Encyclopedia II - Prime number theorem - Bounds on the prime counting function |
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| | | | | Bound: Encyclopedia II - Birthday paradox - An upper bound and a different perspective The argument below is adapted from an argument of Paul Halmos.2
Recollect from above that the probability that no two birthdays coincide is
We are interested in the smallest n such that p(n) > 1/2; or equivalently, the smallest n such that p(n) < 1/2.
Substituting, as above, 1 - k/365 with e−k/365, and using the inequality 1 − x< ...
See also:Birthday paradox, Birthday paradox - Understanding the paradox, Birthday paradox - Calculating the probability, Birthday paradox - Approximations, Birthday paradox - Same birthday as you, Birthday paradox - Reverse problem, Birthday paradox - Sample calculations, Birthday paradox - Generalization, Birthday paradox - Applications, Birthday paradox - An upper bound and a different perspective, Birthday paradox - Empirical test, Birthday paradox - Near matches, Birthday paradox - Collision counting, Birthday paradox - Notes Read more here: » Birthday paradox: Encyclopedia II - Birthday paradox - An upper bound and a different perspective |
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| | | | | Bound: Encyclopedia II - Low-discrepancy sequence - Lower bounds Let s = 1. Then
for any finite point set x1, ..., xN.
Let s = 2. W. M. Schmidt proved that for any finite point set x1, ..., xN,
where
For arbitrary dimensions s > 1, K.F. Roth proved that
for any finite point set x1, ..., xN. Th ...
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 - Lower bounds |
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| | | | | Bound: Encyclopedia II - Entropy in thermodynamics and information theory - The von Neumann-Landauer bound A theoretical application of this formal equivalence of thermodynamic entropy and information-theoretic entropy in the discrete case yields a lower bound on the amount of heat generated by an irreversible computational process, known as the von Neumann-Landauer bound.
Rolf Landauer argued in a 1961 paper that computational operations that are logically irreversible are also physically irreversible in the sense that reversing them would break the second law of thermodynamics. This result is known as Landauer's principle. ...
See also:Entropy in thermodynamics and information theory, Entropy in thermodynamics and information theory - Introduction, Entropy in thermodynamics and information theory - Equivalence of Form of Defining Equations, Entropy in thermodynamics and information theory - Discrete Case, Entropy in thermodynamics and information theory - Continuous Case, Entropy in thermodynamics and information theory - The von Neumann-Landauer bound, Entropy in thermodynamics and information theory - Black Holes, Entropy in thermodynamics and information theory - The Fluctuation Theorem, Entropy in thermodynamics and information theory - Topics of Recent Research, Entropy in thermodynamics and information theory - Is information quantized?, Entropy in thermodynamics and information theory - See Also Read more here: » Entropy in thermodynamics and information theory: Encyclopedia II - Entropy in thermodynamics and information theory - The von Neumann-Landauer bound |
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| | | | | | | | | Bound: Encyclopedia II - Supremum - Supremum of a set of real numbers In analysis the supremum or least upper bound of a set S of real numbers is denoted by sup(S) and is defined to be the smallest real number that is greater than or equal to every number in S. An important property of the real numbers is its completeness: every nonempty set of real numbers that is bounded above has a supremum. If, in addition, we define sup(S) = −∞ when S is empty and sup(S) = +∞ when S is not bounded above, then every set o ...
See also:Supremum, Supremum - Supremum of a set of real numbers, Supremum - Approximation property, Supremum - Additive property, Supremum - Comparison property, Supremum - Suprema within partially ordered sets, Supremum - Comparison with other order theoretical notions, Supremum - Greatest elements, Supremum - Maximal elements, Supremum - Minimal upper bounds, Supremum - Least-upper-bound property Read more here: » Supremum: Encyclopedia II - Supremum - Supremum of a set of real numbers |
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| | | | | Bound: Encyclopedia II - Supremum - Suprema within partially ordered sets Least upper bounds are important concepts in order theory, where they are also called joins (especially in lattice theory). As in the special case treated above, a supremum of a given set is just the least element of the set of its upper bounds, provided that such an element exists.
Formally, we have: For subsets S of arbitrary partially ordered sets (P, ≤), a supremum or least upper bound of S is an element u in P such that
x ≤ u for all x i ...
See also:Supremum, Supremum - Supremum of a set of real numbers, Supremum - Approximation property, Supremum - Additive property, Supremum - Comparison property, Supremum - Suprema within partially ordered sets, Supremum - Comparison with other order theoretical notions, Supremum - Greatest elements, Supremum - Maximal elements, Supremum - Minimal upper bounds, Supremum - Least-upper-bound property Read more here: » Supremum: Encyclopedia II - Supremum - Suprema within partially ordered sets |
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| | | | | | | | Bound: Encyclopedia II - Supremum - Comparison with other order theoretical notions
Supremum - Greatest elements.
The difference between the supremum of a set and the greatest element of a set may not be immediately obvious. The difference is exemplified by the set of negative real numbers. Since 0 is not a negative number, this set has no greatest element: for every element of the set, there is another, larger element. For instance, for any negative real number x, there is a negative real number x/2, which is greater. On the other hand, the upper bounds of the set of negative real ...
See also:Supremum, Supremum - Supremum of a set of real numbers, Supremum - Approximation property, Supremum - Additive property, Supremum - Comparison property, Supremum - Suprema within partially ordered sets, Supremum - Comparison with other order theoretical notions, Supremum - Greatest elements, Supremum - Maximal elements, Supremum - Minimal upper bounds, Supremum - Least-upper-bound property Read more here: » Supremum: Encyclopedia II - Supremum - Comparison with other order theoretical notions |
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| | | | | Bound: Encyclopedia II - Woody Guthrie - Legacy By the time of Guthrie's death, his work had been discovered by a new audience, introduced to them in part through Bob Dylan, who visited Guthrie in the last years of his life and described him as "my last hero." Dylan later went on to write Last Thoughts on Woody Guthrie, a five-page tribute, and included "Song to Woody" on his first, eponymous album (1962).
In 1964, Phil Ochs's debut album, All the News That's Fit to Sing, included the song "Bound for Glory," a tribute to Guthrie and a criticism of revisionism and ignorance among modern audiences who preferred to forget some of Guthrie's more cont ...
See also:Woody Guthrie, Woody Guthrie - Life and career, Woody Guthrie - Legacy Read more here: » Woody Guthrie: Encyclopedia II - Woody Guthrie - Legacy |
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| | | | | Bound: Encyclopedia II - Gela - Very brief history Around 688 BC, the city was founded by colonists from Rhodos and Crete, 45 years after Syracuse. The city was named after the river Gela. The Greek had many colonies in the south of current Italy, and for many centuries the Greek influence has been great here. Aischylos died in this city in 456 BC. From Gela, other parts of the island were also hellenized. Much archeological research has been taken place in and around the city, and the archaeological museum exhibits many artefacts from the earlier periods of the city's history, among which t ...
See also:Gela, Gela - Very brief history, Gela - Bounding communes, Gela - Population history, Gela - Sights in and around Gela Read more here: » Gela: Encyclopedia II - Gela - Very brief history |
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| | | | | Bound: Encyclopedia II - Ribosome - Atomic structure The atomic structure of the 50S large subunit ribosome from the archeal, Haloarcula marismortui was published in Science on August 11, 2000 by N. Ban et al.
Soon after the structure of the 30S from Thermus thermophilus was published in Cell on September 1, 2000, by F. Schluenzen et. al.. Shortly after a more detailed structure was published in Nature on September 21, 2000 by B. T. Wimberly, et al..
Using these coordinates, M. M. Yusupov, et al. were able to reconstruct the entire Thermus thermophilus 70S particle at low resolution, which ...
See also:Ribosome, Ribosome - Overview, Ribosome - Free ribosomes, Ribosome - Membrane bound ribosomes, Ribosome - Atomic structure, Ribosome - External link Read more here: » Ribosome: Encyclopedia II - Ribosome - Atomic structure |
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| | | | | | Bound: Encyclopedia II - SSX - Gameplay Players may choose any one of a number of riders, each with their own statistics and boarding style. A course is selected and the player is given the option of racing down the course or participating in a competition to do tricks.
Each course is filled with ramps, rails, and other assorted objects. Performing tricks fills up the player's boost meter, which can then be used for additional acceleration, making tricks important even in a race. Players also have the option of practicing or explo ...
See also:SSX, SSX - Gameplay, SSX - SSX and SSX Tricky, SSX - SSX 3, SSX - SSX Out of Bounds, SSX - SSX On Tour Read more here: » SSX: Encyclopedia II - SSX - Gameplay |
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| | | | | Bound: Encyclopedia II - SSX - SSX and SSX Tricky SSX was released only for the PlayStation 2 for its launch in October 2000. SSX was developed by EA Canada, SSX Tricky by EA Sports. SSX Tricky was released November 5, 2001 for the PlayStation 2, GameCube, and Xbox. SSX Tricky was so similar to the original that many considered it an "upgrade" rather than a sequel.
In SSX and SSX Tricky, winning medals in a variety of events, unlocks new courses, characters, and boards, as well as improved the boarder's abilities. New outfits may be ea ...
See also:SSX, SSX - Gameplay, SSX - SSX and SSX Tricky, SSX - SSX 3, SSX - SSX Out of Bounds, SSX - SSX On Tour Read more here: » SSX: Encyclopedia II - SSX - SSX and SSX Tricky |
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| | | | | Bound: Encyclopedia II - SSX - SSX 3 SSX 3 was released on October 20, 2003 on all the same platforms SSX Tricky was released on, as well as the Gizmondo. It was developed by EA Canada.
The most obvious change to the series is the location. In earlier games, individual tracks were located around the world. In SSX 3, the entire game takes place on one mountain, with three peaks and several individual runs. Runs are designated as "race," "freestyle," "half pipe," "big air," or "back country" tracks, and are designed accordingly. Tracks are connected; ...
See also:SSX, SSX - Gameplay, SSX - SSX and SSX Tricky, SSX - SSX 3, SSX - SSX Out of Bounds, SSX - SSX On Tour Read more here: » SSX: Encyclopedia II - SSX - SSX 3 |
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