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The 1-vs-2 cycles conjecture or 2-cycle conjecture is an unproven computational hardness assumption asserting that solving the 1-vs-2 cycles problem in the massively parallel communication model requires at least a logarithmic number of rounds of communication, even for a randomized algorithm that succeeds with high probability (having a ...
The trace of J n is 1 if n is odd and 0 if n is even. In other words: tr ( J n ) = n mod 2 . {\displaystyle \operatorname {tr} (J_{n})=n{\bmod {2}}.} The determinant of J n is: det ( J n ) = ( − 1 ) n ( n − 1 ) 2 {\displaystyle \det(J_{n})=(-1)^{\frac {n(n-1)}{2}}} As a function of n , it has period 4, giving 1, 1, −1, −1 when n is ...
[2] [10] An alternative to these techniques is special computer hardware that allows memory to be accessed both in normal and in bit-reversed order. [12] The performance improvement of bit-reversals in both uniprocessor and multiprocessors has been paid a serious attention in high-performance computing fields.
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This happens trivially when n is a palindromic number; the nontrivial reverse divisors are 1089, 2178, 10989, 21978, 109989, 219978, 1099989, 2199978, ... (sequence A008919 in the OEIS ).
A mathematical or physical process is time-reversible if the dynamics of the process remain well-defined when the sequence of time-states is reversed.. A deterministic process is time-reversible if the time-reversed process satisfies the same dynamic equations as the original process; in other words, the equations are invariant or symmetrical under a change in the sign of time.
A graph and its transpose. In the mathematical and algorithmic study of graph theory, the converse, [1] transpose [2] or reverse [3] of a directed graph G is another directed graph on the same set of vertices with all of the edges reversed compared to the orientation of the corresponding edges in G.
[1] 3D LUTs are used extensively in the movie production chain, as part of the Digital Intermediate process. [2] [3] [4] Cubes may be of various sizes and bit depths. Often [when?] 33×33×33 cubes are used as 3D LUTs. [citation needed] The most common practice is to use RGB 10-bit/component log images as the input to the 3D LUT.