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

Challenging physiognomy: questioning the idea that facial characteristics are indicative of personality

Physiognomy; the idea that facial characteristics are indicative of personality has persisted within the science of psychology despite some questionable supporting evidence. Indeed the idea is not unreasonable if certain premise can be supported. The aim of this research was to test three related premise in order to ascertain whether people could accurately judge the personality of a stranger from only a superficial exposure. An experiment was devised which exposed participants to one of eight video clips. The video clips were all of the same person but varied in duration, whether the eyes were visible, and whether the person was talking. One hundred and forty participants took part in the study. After watching one of the video clips each participant was asked to assess the personality of the person in the video using a standard personality questionnaire. The null results challenge the findings of previous research in support of physiognomy

Near-Zero-Power Temperature Sensing via Tunneling Currents Through Complementary Metal-Oxide-Semiconductor Transistors.

Temperature sensors are routinely found in devices used to monitor the environment, the human body, industrial equipment, and beyond. In many such applications, the energy available from batteries or the power available from energy harvesters is extremely limited due to limited available volume, and thus the power consumption of sensing should be minimized in order to maximize operational lifetime. Here we present a new method to transduce and digitize temperature at very low power levels. Specifically, two pA current references are generated via small tunneling-current metal-oxide-semiconductor field effect transistors (MOSFETs) that are independent and proportional to temperature, respectively, which are then used to charge digitally-controllable banks of metal-insulator-metal (MIM) capacitors that, via a discrete-time feedback loop that equalizes charging time, digitize temperature directly. The proposed temperature sensor was integrated into a silicon microchip and occupied 0.15 mm2 of area. Four tested microchips were measured to consume only 113 pW with a resolution of 0.21 °C and an inaccuracy of ±1.65 °C, which represents a 628× reduction in power compared to prior-art without a significant reduction in performance

Least Squares Shadowing Sensitivity Analysis of a Modified Kuramoto-Sivashinsky Equation

Computational methods for sensitivity analysis are invaluable tools for scientists and engineers investigating a wide range of physical phenomena. However, many of these methods fail when applied to chaotic systems, such as the Kuramoto-Sivashinsky (K-S) equation, which models a number of different chaotic systems found in nature. The following paper discusses the application of a new sensitivity analysis method developed by the authors to a modified K-S equation. We find that least squares shadowing sensitivity analysis computes accurate gradients for solutions corresponding to a wide range of system parameters.Comment: 23 pages, 14 figures. Submitted to Chaos, Solitons and Fractals, in revie

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

Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations

The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged quantity. This failure is known to be caused by ill-conditioned initial value problems. This paper overcomes this failure by replacing the initial value problem with the well-conditioned "least squares shadowing (LSS) problem". The LSS problem is then linearized in our sensitivity analysis algorithm, which computes a derivative that converges to the derivative of the infinitely long time average. We demonstrate our algorithm in several dynamical systems exhibiting both periodic and chaotic oscillations.Comment: submitted to JCP in revised for

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