Sensors in the built environment ensure safety and comfort by tracking contaminants occupied space. In event of contaminant release, it is important to use limited sensor data rapidly accurately identify release location contaminant. Identification will enable subsequent remediation as well evacuation decision-making. previous work, we used an operator theoretic approach—based on Perron–Frobeni...

Let K be a closed convex cone with dual K∗ in a finite-dimensional real Hilbert space V . A positive operator on K is a linear operator L on V such that L (K) ⊆ K. Positive operators generalize the nonnegative matrices and are essential to the Perron-Frobenius theory. We say that L is a Z-operator on K if 〈L (x), s〉 ≤ 0 for all (x, s) ∈ K ×K such that 〈x, s〉 = 0. The Z-operators are generalizat...

We analyze the effects of stochastic perturbations in a physical example occurring as a higher-dimensional dynamical system. The physical model is that of a class- B laser, which is perturbed stochastically with finite noise. The effect of the noise perturbations on the dynamics is shown to change the qualitative nature of the dynamics experimentally from a stochastic periodic attractor to one ...

Given a discrete-time random dynamical system represented by cocycle of non-singular measurable maps, we may obtain information on quantities studying the Perron–Frobenius operators associated to maps. Of particular interest is second-largest Lyapunov exponent for operators, λ2, which can tell us about mixing rates and decay correlations in system. We prove generalized theorem cocycles bounded ...

We study ergodicity of bounded, sub-additive and non-negatively homogeneous maps on finite dimensional spaces which we call upper transition operators. We show that ergodicity coincides with the necessary and sufficient condition for a generalised Perron-Frobenius theorem for upper transition operators. We show that ergodicity is equivalent with regular absorningness of the upper transition ope...

The subleading eigenvalues and associated eigenfunctions of the Perron-Frobenius operator for 2-dimensional area-preserving maps are numerically investigated. We closely examine validity so-called Ulam method, a numerical scheme believed to provide operator, both linear nonlinear on torus. For case, second-largest investigated by calculating Fokker-Planck with sufficiently small diffusivity. On...

We study the properties of the Google matrix of an Ulam network generated by intermittency maps. This network is created by the Ulam method which gives a matrix approximant for the Perron-Frobenius operator of dynamical map. The spectral properties of eigenvalues and eigenvectors of this matrix are analyzed. We show that the PageRank of the system is characterized by a power law decay with the ...

We study the correspondence between phase-space localization of quantum (quasi-)energy eigenstates and classical correlation decay, given by Ruelle-Pollicott resonances of the Frobenius-Perron operator. It will be shown that scarred (quasi-)energy eigenstates are correlated: Pairs of eigenstates strongly overlap in phase space (scar in same phase-space regions) if the difference of their eigene...