We consider the problem of measuring margin robust feasibility solutions to a system nonlinear equations. study special case quadratic equations, which shows up in many practical applications such as power grid and other infrastructure networks. This is generalization quadratically constrained programming (QCQP), NP-Hard general setting. develop approaches based on topological degree theory est...

We consider the problem of maximizing asymptotic growth rate an investor under drift uncertainty in setting stochastic portfolio theory (SPT). As work Kardaras and Robertson we take as inputs (i) a Markovian volatility matrix $c(x)$ (ii) invariant density $p(x)$ for market weights, but additionally impose long-only constraints on investor. Our principal contribution is proving uniqueness existe...

Infrastructure systems, such as power, transportation, telecommunication, and water are composed of multiple components which interconnected interdependent to produce distribute essential goods services. So, the robustness infrastructure systems resist disturbances is crucial for durable performance modern societies. Multilayer networks have been used model multiplicity interrelation percolatio...

This paper proposes a class of parametric multiple-index time series models that involve linear combinations trends, stationary variables and unit root processes as regressors. The inclusion the three different types series, along with use structure for these to circumvent curse dimensionality, is due both theoretical practical considerations. M-type estimators (including OLS, LAD, Huber’s esti...