This paper presents an analytical model for downlink rate allocation in Code Division Multiple Access (CDMA) mobile networks. By discretizing the coverage area into small segments, the transmit power requirements are characterized via a matrix representation that separates user and system characteristics. We obtain a closed-form analytical expression for the so-called Perron-Frobenius eigenvalu...

This paper models and analyses downlink power assignment feasibility in Code Division Multiple Access (CDMA) mobile networks. By discretizing the area into small segments, the power requirements are characterized via a matrix representation that separates user and system characteristics. We obtain a closed-form analytical expression of the so-called Perron-Frobenius eigenvalue of that matrix, w...

Our proof is built on Perron-Frobenius theorem, a seminal work in matrix theory (Meyer 2000). By Perron-Frobenius theorem, the power iteration algorithm for predicting top K persuaders converges to a unique C and this convergence is independent of the initialization of C if the persuasion probability matrix P is nonnegative, irreducible, and aperiodic (Heath 2002). We first show that P is nonne...

A pseudo-Anosov surface automorphism φ has associated to it an algebraic unit λφ called the dilatation of φ. It is known that in many cases λφ appears as the spectral radius of a Perron–Frobenius matrix preserving a symplectic form L. We investigate what algebraic units could potentially appear as dilatations by first showing that every algebraic unit λ appears as an eigenvalue for some integra...

The spectral radius of a matrix A is the maximum norm of all eigenvalues of A. In previous work we already formalized that for a complex matrix A, the values in A grow polynomially in n if and only if the spectral radius is at most one. One problem with the above characterization is the determination of all complex eigenvalues. In case A contains only non-negative real values, a simplification ...

Exploring long-term implications of valuation leads us to recover and use a distorted probability measure that reflects the long-term implications for risk pricing. This measure is typically distinct from the physical and the risk neutral measures that are well known in mathematical finance. We apply a generalized version of Perron-Frobenius theory to construct this probability measure and pres...

We introduce complex cones and associated projective gauges, generalizing a real Birkhoff cone and its Hilbert metric to complex vector spaces. We deduce a variety of spectral gap theorems in complex Banach spaces. We prove a dominated complex cone-contraction Theorem and use it to extend the classical Perron-Frobenius Theorem to complex matrices, Jentzsch’s Theorem to complex integral operator...

The celebrated Perron–Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. H...