14,249 research outputs found
Subshifts with sparse traces
We study two-dimensional subshifts whose horizontal trace (a.k.a. projective
subdynamics) contains only points of finite support. Our main result is a
classification result for such subshifts satisfying a minimality property. As
corollaries, we obtain new proofs for various known results on traces of SFTs,
nilpotency and decidability of cellular automata, topological full groups and
the subshift of prime numbers. We also construct various (sofic) examples
illustrating the concepts.Comment: 43 pages, 9 figures. Fixed some broken definitions, elaborated on
some proofs (kept the informal style). Added an example on path extraction,
results otherwise unchanged. Comments welcome
Inverse boundary value problems for the magnetic Schroedinger equation
We survey recent results on inverse boundary value problems for the magnetic
Schroedinger equation
A note on directional closing
We show that directional closing in the sense of Guillon-Kari-Zinoviadis and
Franks-Kra is not closed under conjugacy. This implies that being polygonal in
the sense of Franks-Kra is not closed under conjugacy.Comment: 4 pages, 2 figure
Decidability and Universality of Quasiminimal Subshifts
We introduce the quasiminimal subshifts, subshifts having only finitely many
subsystems. With -actions, their theory essentially reduces to the
theory of minimal systems, but with -actions, the class is much
larger. We show many examples of such subshifts, and in particular construct a
universal system with only a single proper subsystem, refuting a conjecture of
[Delvenne, K\r{u}rka, Blondel, '05].Comment: 40 pages, 1 figure, submitted to JCS
Toeplitz subshift whose automorphism group is not finitely generated
We compute an explicit representation of the (topological) automorphism group
or a particular Toeplitz subshift. The automorphism group is a (non-finitely
generated) subgroup of rational numbers under addition and the shift map
corresponds to the rational number 1. The group is the additive subgroup of the
rational numbers generated by the powers of 5/2.Comment: 22 pages. Comments and corrections welcome
A Sum-Product Model as a Physical Basis for Shadow Fading
Shadow fading (slow fading) effects play a central role in mobile
communication system design and analysis. Experimental evidence indicates that
shadow fading exhibits log-normal power distribution almost universally, and
yet it is still not well understood what causes this. In this paper, we propose
a versatile sum-product signal model as a physical basis for shadow fading.
Simulation results imply that the proposed model results in log-normally
distributed local mean power regardless of the distributions of the
interactions in the radio channel, and hence it is capable of explaining the
log-normality in a wide variety of propagation scenarios. The sum-product model
also includes as its special cases the conventional product model as well as
the recently proposed sum model, and improves upon these by: a) being
applicable in both global and local distance scales; b) being more plausible
from physical point of view; c) providing better goodness-of-fit to log-normal
distribution than either of these models.Comment: 23 pages, 9 figs. To be revised and maybe submitte
Minimal subshifts with a language pivot property
We construct a binary minimal subshift whose words of length n form a
connected subset of the Hamming graph for each n.Comment: 6 page
Semiclassical pseudodifferential calculus and the reconstruction of a magnetic field
We give a procedure for reconstructing a magnetic field and electric
potential from boundary measurements related to the magnetic Schroedinger
operator in three and higher dimensions
On Nilpotency and Asymptotic Nilpotency of Cellular Automata
We prove a conjecture of P. Guillon and G. Richard by showing that cellular
automata that eventually fix all cells to a fixed symbol 0 are nilpotent on
S^Z^d for all d. We also briefly discuss nilpotency on other subshifts, and
show that weak nilpotency implies nilpotency in all subshifts and all
dimensions, since we do not know a published reference for this.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249
When are group shifts of finite type?
It is known that a group shift on a polycyclic group is necessarily of finite
type. We show that, for trivial reasons, if a group does not satisfy the
maximal condition on subgroups, then it admits non-SFT abelian group shifts. In
particular, we show that if group is elementarily amenable or satisfies the
Tits alternative, then it is virtually polycyclic if and only if all its group
shifts are of finite type. Our theorems are minor elaborations of results of
Schmidt and Osin.Comment: 8 pages; fixed a typo IN THE TITL
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