In graph theory, there are several different types of object called cycles, principally a closed walk and a simple cycle; also, e.g., an element of the cycle space of the graph.
A closed walk consists of a sequence of vertices starting and ending at the same vertex, with each two consecutive vertices in the sequence adjacent to each other in the graph. In a directed graph, each edge must be traversed by the walk consistently with its direction: the edge must be oriented from the earlier of two consecutive vertices to the later of the two vertices in the sequence. The choice of starting vertex is not important: traversing the same cyclic sequence of edges from different starting vertices produces the same closed walk.
A simple cycle may be defined either as a closed walk with no repetitions of vertices and edges allowed, other than the repetition of the starting and ending vertex, or as the set of edges in such a walk. The two definitions are equivalent in directed graphs, where simple cycles are also called directed cycles: the cyclic sequence of vertices and edges in a walk is completely determined by the set of edges that it uses. In undirected graphs the set of edges of a cycle can be traversed by a walk in either of two directions, giving two possible directed cycles for every undirected cycle. (For closed walks more generally, in directed or undirected graphs, the multiset of edges does not unambiguously determine the vertex ordering.) A circuit can be a closed walk allowing repetitions of vertices but not edges; however, it can also be a simple cycle, so explicit definition is recommended when it is used.
Cycle is an album by the Japanese noise musician Merzbow. It features recordings of Masami Akita's pet chickens. Material from this album was performed live at Radio Nova in Oslo, which was released as Mini Cycle / Yoshino Tamago / Yonos Bigfoot.
All music composed by Masami Akita.
In algebraic topology, a simplicial k-chain is a formal linear combination of k-simplices.
Integration is defined on chains by taking the linear combination of integrals over the simplices in the chain with coefficients typically integers. The set of all k-chains forms a group and the sequence of these groups is called a chain complex.
The boundary of a chain is the linear combination of boundaries of the simplices in the chain. The boundary of a k-chain is a (k−1)-chain. Note that the boundary of a simplex is not a simplex, but a chain with coefficients 1 or −1 – thus chains are the closure of simplices under the boundary operator.
Example 1: The boundary of a path is the formal difference of its endpoints: it is a telescoping sum. To illustrate, if the 1-chain is a path from point
to point
, where
,
and
are its constituent 1-simplices, then
Example 2: The boundary of the triangle is a formal sum of its edges with signs arranged to make the traversal of the boundary counterclockwise.
T.A.O. is a fictional character in the Wildstorm universe.
The Tactical Augmented Organism was created by Optigen, a subsidiary of the Halo Corporation, on behalf of International Operations. As a child, he grew at an amazing rate. The scientists working on him thought that he was imprisoned in his test tube, but at nights he would sneak out and use the lab's computers to learn more about the world outside.
When Savant and Mister Majestic were reforming the WildC.A.Ts, Savant read the files on TAO. The scientist of Optigen was unwilling to let TAO go until TAO handed him a note with several numbers on it. The scientist immediately agreed to release TAO. When asked what the numbers meant, TAO explained to his new teammates that the top one was the phone number of the scientist's wife, the other four were the phone numbers of the scientist's mistresses. Despite seemingly having no superhuman powers, TAO's intelligence and manipulative nature appeared to be quite an asset to the new WildC.A.Ts. He manipulated Mister Majestic into agreeing to recruit the murderous cyborg Ladytron.
Tao is an RIAA Gold-certified album by Rock singer Rick Springfield. It was released in 1985 on RCA Records. It was belatedly released on CD in 1990.
All songs written by Rick Springfield, except where noted.
With Tao, Springfield decided to experiment with new wave and synthrock. Springfield noted in a 2012 interview, "Tao had a lot of European influences and I perhaps went a little bit too far in that direction. The production was more European orientated, with the massive synths and that stuff actually did it really well in Europe, especially in Germany, 'Celebrate Youth' was a hit." Springfield considers Tao to be his finest album to date. "We just had a lot of new ideas. It is probably the one I experimented on the most. Whatever I thought of we tried it. It was just when sampling was just starting, we got really into the drum sampling. But we started on just a DMX. A little DMX drum machine, all the original drum tracks were laid down on that, and then we triggered other drum samples from that. It was built up track by track. That is still my favorite album." Springfield recalls, "I had stopped listening to American rock by 1984. In fact, I was getting increasingly interested in what was going on in other types of music, especially with artists who were English."
Nintendo is one of the world's biggest video game developing companies, having created multiple successful franchises. Because of its storied history, the developer employs a methodical system of software and hardware development that is mainly centralized within its offices in Kyoto and Tokyo, in cooperation with its division Nintendo of America in Redmond, Washington. The company also owns several worldwide subsidiaries and funds partner affiliates that contribute technology and software for the Nintendo brand.
Nintendo Co., Ltd (NCL) has a central office located in Minami-ku, Kyoto, Kyoto Prefecture, Japan (34°58′11.89″N 135°45′22.33″E / 34.9699694°N 135.7562028°E / 34.9699694; 135.7562028) and a nearby building, its pre-2000 headquarters, now serving as a research and development building, located in Higashiyama-ku, Kyoto, Kyoto Prefecture, Japan (34°58′29.00″N 135°46′10.48″E / 34.9747222°N 135.7695778°E / 34.9747222; 135.7695778). Its original Kyoto headquarters can still be found at (34°59′30.03″N 135°45′58.66″E / 34.9916750°N 135.7662944°E / 34.9916750; 135.7662944). Additionally, Nintendo has a third operation in Tokyo, Japan, where research and development, manufacturing, and clerical work are conducted. All three offices are interconnected and have video conferences often for communication and presentation purposes.
You're powerful
You're unshakeable
You're powerful
You're unshakeable
You wreck me
You rule me
You turn me upside down (ya know)
Your glory
Pervades me
You conquer without a sound
You shake me
You break me
You make me whole again (ya know)
Your nature
Unchanging
All fails, but You remain
And when the ground begins to shake
And when my courage starts to fade
I let my fears go
When You
Breathe
The lifeless rise up
Invade me
With violence
And heal me
You're mighty