Diffeomorphism type via aperiodicity in Reeb dynamics

Data Skeletonization via Reeb Graphs

Recovering hidden structure from complex and noisy non-linear data is one of the most fundamental problems in machine learning and statistical inference. While such data is often high-dimensional, it is of interest to approximate it with a low-dimensional or even one-dimensional space, since many important aspects of data are often intrinsically low-dimensional. Furthermore, there are many scen...

Aperiodicity in Tree Automata

Asymptotic Stabilization of Feedback Linearizable Systems via Estimated Diffeomorphism

The traditional feedback linearization method often requires the full system parameter and state information. In this paper, we consider an asymptotic stabilization problem of a class of feedback linearizable nonlinear systems by using less than the full parameter/state information. First, our approach is to classify system parameters into two categories — ‘directly used parameters’ and ‘indire...

When periodicities enforce aperiodicity

Non-periodic tilings and local rules are commonly used to model the long range aperiodic order of quasicrystals and the finite-range energetic interactions that stabilize them. This paper focuses on planar rhombus tilings, that are tilings of the Euclidean plane which can be seen as an approximation of a real plane embedded in a higher dimensional space. Our main result is a characterization of...

Positive Recurrence and Aperiodicity

Drop the term ∑ i1,...in 6=k λinpinin−1 · · · pi1j we obtain λj > Pk(X1 = j, Rk > 1) + Pk(X2 = j, Rk > 2) + · · ·+ Pk(Xn = j, Rk > n) → γ j as n→∞ (where Rk is the first return time of k) So we have λ > γ(k). If in addition P is invariant, then we proved earlier that γ(k) is invariant, so μ = λ − γ(k) is also invariant with μ > 0 and μk = λk − γ (k) k = 0. Since P is irreducible, for any i ∈ I,...