Subshifts of quasi-finite type

We introduce subshifts of quasi-finite type as a generalization of the well-known subshifts of finite type. This generalization is much less rigid and therefore contains the symbolic dynamics of many non-uniform systems, e.g., piecewise monotonic maps of the interval with positive entropy. Yet many properties remain: existence of finitely many ergodic invariant probabilities of maximum entropy; lots of periodic points; meromorphic extension of the Artin-Mazur zeta function.Comment: added examples, more precise estimates on periodic points and classificatio

Puzzles of Quasi-Finite Type, Zeta Functions and Symbolic Dynamics for Multi-Dimensional Maps

We introduce "puzzles of quasi-finite type" which are the counterparts of our subshifts of quasi-finite type (Invent. Math. 159 (2005)) in the setting of combinatorial puzzles as defined in complex dynamics. We are able to analyze these dynamics defined by entropy conditions rather completely, obtaining a complete classification with respect to large entropy measures and a description of their measures with maximum entropy and periodic orbits. These results can in particular be applied to entropy-expanding maps like (x,y)-->(1.8-x^2+sy,1.9-y^2+sx) for small s. We prove in particular the meromorphy of the Artin-Mazur zeta function on a large disk. This follows from a similar new result about strongly positively recurrent Markov shifts where the radius of meromorphy is lower bounded by an "entropy at infinity" of the graph.Comment: accepted by Annales de l'Institut Fourier, final revised versio

Cell-Free and User-Centric Massive MIMO at Millimeter Wave Frequencies

In a cell-free (CF) massive MIMO architecture a very large number of distributed access points (APs) simultaneously and jointly serves a much smaller number of mobile stations (MSs); a variant of the cell-free technique is the user-centric (UC) approach, wherein each AP just decodes a reduced set of MSs, practically the ones that are received best. This paper introduces and analyzes the CF and UC architectures at millimeter wave (mmWave) frequencies. First of all, a multiuser clustered channel model is introduced in order to account for the correlation among the channels of nearby users; then, an uplink multiuser channel estimation scheme is described along with low-complexity hybrid analog/digital beamforming architectures. Interestingly, in the proposed scheme no channel estimation is needed at the MSs, and the beamforming schemes used at the MSs are channel-independent and have a very simple structure. Numerical results show that the considered architectures provide good performance, especially in lightly loaded systems, with the UC approach outperforming the CF one.Comment: presented at the 28th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (IEEE PIMRC 2017), Montreal (CA), October 201

A probabilistic study of neural complexity

G. Edelman, O. Sporns, and G. Tononi have introduced the neural complexity of a family of random variables, defining it as a specific average of mutual information over subfamilies. We show that their choice of weights satisfies two natural properties, namely exchangeability and additivity, and we call any functional satisfying these two properties an intricacy. We classify all intricacies in terms of probability laws on the unit interval and study the growth rate of maximal intricacies when the size of the system goes to infinity. For systems of a fixed size, we show that maximizers have small support and exchangeable systems have small intricacy. In particular, maximizing intricacy leads to spontaneous symmetry breaking and failure of uniqueness.Comment: minor edit

Uniqueness of equilibrium measures for countable Markov shifts and multidimensional piecewise expanding maps

We prove that potentials with summable variations on topologically transitive countable Markov shifts have at most one equilibrium measure. We apply this to multidimensional piecewise expanding maps using their Markov diagrams