Related papers: Symbol Frequencies in Surjective Cellular Automata
Classical cellular automata represent a class of explicit discrete spacetime lattice models in which complex large-scale phenomena emerge from simple deterministic rules. With the goal to uncover different physically distinct classes of…
Given a finite set of local constraints, we seek a cellular automaton (i.e., a local and uniform algorithm) that self-stabilises on the configurations that satisfy these constraints. More precisely, starting from a finite perturbation of a…
Any reliable biomarker has to be specific, generalizable, and reproducible across individuals and contexts. The exact values of such a biomarker must represent similar health states in different individuals and at different times within the…
The ergodic spectral efficiency (SE) in interference-limited multiple-input multiple-output (MIMO) downlink cellular systems is characterized based on stochastic geometry. A single user is served by using singular value decomposition…
A sequence of null hypotheses regarding the number of negligible effects (zero effects) in orthogonal saturated designs is formulated. Two step-up simultaneous testing procedures are proposed to identify active effects (nonzero effects)…
In multiple testing scenarios, typically the sign of a parameter is inferred when its estimate exceeds some significance threshold in absolute value. Typically, the significance threshold is chosen to control the experimentwise type I error…
We propose a protocol for a controlled experiment to measure a weak value of the electron's spin in a solid state device. The weak value is obtained by a two step procedure -- weak measurement followed by a strong one (post-selection),…
A probability measure is a characteristic measure of a topological dynamical system if it is invariant to the automorphism group of the system. We show that zero entropy shifts always admit characteristic measures. We use similar techniques…
Sensors and actuators based on resonant micro-electro-mechanical systems (MEMS), such as scanning micro mirrors, are well-established in automotive and consumer products. As the areas of application broaden, the requirements for the MEMS…
We prove existence of (at most denumerable many) absolutely continuous invariant probability measures for random one-dimensional dynamical systems with asymptotic expansion. If the rate of expansion (Lyapunov exponents) is bounded away from…
Given a heterogeneous Gaussian sequence model with unknown mean $\theta \in \mathbb R^d$ and known covariance matrix $\Sigma = \operatorname{diag}(\sigma_1^2,\dots, \sigma_d^2)$, we study the signal detection problem against sparse…
Deviation of ergodic sums is studied for substitution dynamical systems with a matrix that admits eigenvalues of modulus 1. We consider the corresponding eigenfunctions, and in Theorem 1.1 we prove that the limit inferior of the ergodic…
Let $X=(X_1,\ldots,X_n)$ be a vector of i.i.d. random variables where $X_i$'s take values over $\mathbb{N}$. The purpose of this paper is to study the number of weakly increasing subsequences of $X$ of a given length $k$, and the number of…
We explain and restate the results from our recent paper arXiv:1503.08000.v3 in standard language for substitutions and $S$-adic systems in symbolic dynamics. We then produce as rather direct application an $S$-adic system (with finite set…
For a continuous semicascade on a metrizable compact set $\Omega $, we consider the weak$^{*}$ convergence of generalized operator ergodic means in ${\rm End}\, \, C^{*} (\Omega)$. We discuss conditions on the dynamical system under which…
The periodogram is a popular tool that tests whether a signal consists only of noise or if it also includes other components. The main issue of this method is to define a critical detection threshold that allows identification of a…
Ergodic optimization aims to describe dynamically invariant probability measures that maximize the integral of a given function. The Dyck and Motzkin shifts are well-known examples of transitive subshifts over a finite alphabet that are not…
We consider the problem of estimating the total probability of all symbols that appear with a given frequency in a string of i.i.d. random variables with unknown distribution. We focus on the regime in which the block length is large yet no…
We investigate the problem of jointly testing multiple hypotheses and estimating a random parameter of the underlying distribution in a sequential setup. The aim is to jointly infer the true hypothesis and the true parameter while using on…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…