We introduce and compare some notions of complexity for orbits in dynamical systems and prove: (i) that the complexity of the orbits of random points equals the Kolmogorov鈥揝ina entropy of the system, (ii) that
Topological Sort Shortest Paths Min Spanning Trees 4 Class NP Problems NP-Problems: Problems for which there is no known polynomial-time algorithms, "intractable" problems NP means non-deterministically polynomial. If we have a candidate for a solution, we can verify it in ...
The term ‘mathematically complex’ initially has nothing in common with our concept of complexity, especially since it was formed in the nineteenth century. The term was introduced by Carl FriedrichGauss, who significantly expanded the known sets of numbers by embedding the number line into a plan...
The running time of topological sort is O(|V|+|E|). Let Nl denote the set of all rotations at Level l, and Nl+1 denote the ones at level l+1. Then, for any Level l, if the union set of all rotations of size 2 in Level l and Level l+1 contains all the non-fixed men, ...
we propose a special case of the QCMP in which all two-qubit interactions of a given IG can be compressed into a single time slice of the quantum circuit; this simplification can be likened to a sort of “lightcone" path through a configuration space, which we explain in detail in Secti...
Principled approach to the selection of the embedding dimension of networks ArticleOpen access18 June 2021 Seismic shocks and financial systems: a topological perspective on Borsa Istanbul after the earthquake ArticleOpen access26 November 2024
Ak-page upward book embedding(kUBE) of a directed acyclic graphGis a book embeddings ofGonkpages with the additional requirement that the vertices appear in a topological ordering along the spine of the book. ThekUBE Testingproblem, which asks whether a graph admits akUBE, was introduced in 199...
While the multi faith prayer room can be found in vastly different contexts, the interiors of the space hold an uncanny similarity from one example to the other. The pallet of colors, textures, finishes and furniture tend to all suggest some sort of neutrality. As the name states, these ...
To sort out the problem of complexity, authors in mechanics–physics-based economics have put forward various suggestions. The simplest reaction is to carefully circumscribe the scope of economics. Citing Schumpeter (1911/1934), Knight (1935/1999) emphasized (at the time when the intellectual founda...
we propose a special case of the QCMP in which all two-qubit interactions of a given IG can be compressed into a single time slice of the quantum circuit; this simplification can be likened to a sort of “lightcone" path through a configuration space, which we explain in detail in Secti...