Probability density adjoint for sensitivity analysis of the Mean of Chaos

Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quantities in chaotic dynamical systems. The following paper presents a new method for sensitivity analysis of {\em ergodic} chaotic dynamical systems, the density adjoint method. The method involves solving the governing equations for the system's invariant measure and its adjoint on the system's attractor manifold rather than in phase-space. This new approach is derived for and demonstrated on one-dimensional chaotic maps and the three-dimensional Lorenz system. It is found that the density adjoint computes very finely detailed adjoint distributions and accurate sensitivities, but suffers from large computational costs.Comment: 29 pages, 27 figure

A flexible modeling framework to estimate interregional trade patterns and input-output accounts

This study implements and tests a mathematical programming model to estimate interregional, interindustry transaction flows in a national system of economic regions based on an interregional accounting framework and initial information of interregional shipments. A national input-output (IO) table, regional data on gross output, value-added, exports, imports and final demand at sector level are used as inputs to generate an interregional IO account that reconciles regional economic statistics and interregional transaction data. The model is tested using data from a multi-regional global input-output database and shows remarkable capacity to discover true interregional trade patterns from highly distorted initial estimates.Scientific Research&Science Parks,Information Technology,Environmental Economics&Policies,Statistical&Mathematical Sciences,ICT Policy and Strategies,Statistical&Mathematical Sciences,Information Technology,Scientific Research&Science Parks,Science Education,Geographical Information Systems

Entanglement dynamics at flat surfaces: investigations using multi-chain molecular dynamics and a single-chain slip-spring model

The dynamics of an entangled polymer melt confined in a channel by parallel plates is investigated by Molecular Dynamics (MD) simulations of a detailed, multi-chain model. A Primitive Path Analysis predicts that the density of entanglements remains approximately constant throughout the gap and drops to lower values only in the immediate vicinity of the surface. Based on these observations, we propose a coarse-grained, single-chain slip-spring model with a uniform density of slip-spring anchors and slip-links. The slip-spring model is compared to the Kremer-Grest MD bead-spring model via equilibrium correlation functions of chain orientations. Reasonably good agreement between the single-chain model and the detailed multi-chain model is obtained for chain relaxation dynamics, both away from the surface and for chains whose center of mass positions are at a distance from the surface that is less than the bulk chain radius of gyration, without introducing any additional model parameters. Our results suggest that there is no considerable drop in topological interactions for chains in the vicinity of a single flat surface. We infer from the slip-spring model that the experimental plateau modulus of a confined polymer melt may be different to a corresponding unconfined system even if there is no drop in topological interactions for the confined case

Testing a Simple Structural Model of Endogenous Growth

The efect of taxation on growth is embodied in a model of a small open economy with endogenous growth. The structural model is estimated on post-war panel data for 76 countries and the bootstrap is used to produce the model’s sampling variation. Panel data regressions of growth on taxation do not reject this model but do reject a model with no tax effects.endogenous growth, taxation, business regulation, bootstrap, model validation.

Least Squares Shadowing method for sensitivity analysis of differential equations

For a parameterized hyperbolic system $\frac{du}{dt}=f(u,s)$ the derivative of the ergodic average $\langle J \rangle = \lim_{T \to \infty}\frac{1}{T}\int_0^T J(u(t),s)$ to the parameter $s$ can be computed via the Least Squares Shadowing algorithm (LSS). We assume that the sytem is ergodic which means that $\langle J \rangle$ depends only on $s$ (not on the initial condition of the hyperbolic system). After discretizing this continuous system using a fixed timestep, the algorithm solves a constrained least squares problem and, from the solution to this problem, computes the desired derivative $\frac{d\langle J \rangle}{ds}$. The purpose of this paper is to prove that the value given by the LSS algorithm approaches the exact derivative when the discretization timestep goes to $0$ and the timespan used to formulate the least squares problem grows to infinity.Comment: 21 pages, this article complements arXiv:1304.3635 and analyzes LSS for the case of continuous hyperbolic system