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 $\mathbb{N}$-actions, their theory essentially reduces to the theory of minimal systems, but with $\mathbb{Z}$-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