72,413 research outputs found
Scaling universalities of kth-nearest neighbor distances on closed manifolds
Take N sites distributed randomly and uniformly on a smooth closed surface.
We express the expected distance from an arbitrary point on the
surface to its kth-nearest neighboring site, in terms of the function A(l)
giving the area of a disc of radius l about that point. We then find two
universalities. First, for a flat surface, where A(l)=\pi l^2, the k-dependence
and the N-dependence separate in . All kth-nearest neighbor distances
thus have the same scaling law in N. Second, for a curved surface, the average
\int d\mu over the surface is a topological invariant at leading and
subleading order in a large N expansion. The 1/N scaling series then depends,
up through O(1/N), only on the surface's topology and not on its precise shape.
We discuss the case of higher dimensions (d>2), and also interpret our results
using Regge calculus.Comment: 14 pages, 2 figures; submitted to Advances in Applied Mathematic
Symmetry-protected Topological Phases at Finite Temperature
We have applied the recently developed theory of topological Uhlmann numbers
to a representative model of a topological insulator in two dimensions, the
Qi-Wu-Zhang model. We have found a stable symmetry-protected topological (SPT)
phase under external thermal fluctuations in two-dimensions. A complete phase
diagram for this model is computed as a function of temperature and coupling
constants in the original Hamiltonian. It shows the appearance of large stable
phases of matter with topological properties compatible with thermal
fluctuations or external noise and the existence of critical lines separating
abruptly trivial phases from topological phases. These novel critical
temperatures represent thermal topological phase transitions. The initial part
of the paper comprises a self-contained explanation of the Uhlmann geometric
phase needed to understand the topological properties that it may acquire when
applied to topological insulators and superconductors.Comment: Contribution to the focus issue on "Artificial Graphene". Edited by
Maciej Lewenstein, Vittorio Pellegrini, Marco Polini and Mordechai (Moti)
Sege
Edge usage, motifs and regulatory logic for cell cycling genetic networks
The cell cycle is a tightly controlled process, yet its underlying genetic
network shows marked differences across species. Which of the associated
structural features follow solely from the ability to impose the appropriate
gene expression patterns? We tackle this question in silico by examining the
ensemble of all regulatory networks which satisfy the constraint of producing a
given sequence of gene expressions. We focus on three cell cycle profiles
coming from baker's yeast, fission yeast and mammals. First, we show that the
networks in each of the ensembles use just a few interactions that are
repeatedly reused as building blocks. Second, we find an enrichment in network
motifs that is similar in the two yeast cell cycle systems investigated. These
motifs do not have autonomous functions, but nevertheless they reveal a
regulatory logic for cell cycling based on a feed-forward cascade of activating
interactions.Comment: 9 pages, 9 figures, to be published in Phys. Rev.
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