Differential encoding of losses and gains in the human striatum.

Studies on human monetary prediction and decision making emphasize the role of the striatum in encoding prediction errors for financial reward. However, less is known about how the brain encodes financial loss. Using Pavlovian conditioning of visual cues to outcomes that simultaneously incorporate the chance of financial reward and loss, we show that striatal activation reflects positively signed prediction errors for both. Furthermore, we show functional segregation within the striatum, with more anterior regions showing relative selectivity for rewards and more posterior regions for losses. These findings mirror the anteroposterior valence-specific gradient reported in rodents and endorse the role of the striatum in aversive motivational learning about financial losses, illustrating functional and anatomical consistencies with primary aversive outcomes such as pain.

Analysis of amorphous indium-gallium-zinc-oxide thin-film transistor contact metal using Pilling-Bedworth theory and a variable capacitance diode model

It is widely reported that threshold voltage and on-state current of amorphous indium-gallium-zinc-oxide bottom-gate thin-film transistors are strongly influenced by the choice of source/drain contact metal. Electrical characterisation of thin-film transistors indicates that the electrical properties depend on the type and thickness of the metal(s) used. Electron transport mechanisms and possibilities for control of the defect state density are discussed. Pilling-Bedworth theory for metal oxidation explains the interaction between contact metal and amorphous indium-gallium-zinc-oxide, which leads to significant trap formation. Charge trapping within these states leads to variable capacitance diode-like behavior and is shown to explain the thin-film transistor operation. © 2013 AIP Publishing LLC.

Differential geometry and design coupling in MDO

The notion of coupling within a design, particularly within the context of Multidisciplinary Design Optimization (MDO), is much used but ill-defined. There are many different ways of measuring design coupling, but these measures vary in both their conceptions of what design coupling is and how such coupling may be calculated. Within the differential geometry framework which we have previously developed for MDO systems, we put forth our own design coupling metric for consideration. Our metric is not commensurate with similar types of coupling metrics, but we show that it both provides a helpful geo- metric interpretation of coupling (and uncoupledness in particular) and exhibits greater generality and potential for analysis than those similar metrics. Furthermore, we discuss how the metric might be profitably extended to time-varying problems and show how the metric's measure of coupling can be applied to multi-objective optimization problems (in unconstrained optimization and in MDO). © 2013 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

On the application of differential geometry to MDO

Multidisciplinary Design Optimization (MDO) is a methodology for optimizing large coupled systems. Over the years, a number of different MDO decomposition strategies, known as architectures, have been developed, and various pieces of analytical work have been done on MDO and its architectures. However, MDO lacks an overarching paradigm which would unify the field and promote cumulative research. In this paper, we propose a differential geometry framework as such a paradigm: Differential geometry comes with its own set of analysis tools and a long history of use in theoretical physics. We begin by outlining some of the mathematics behind differential geometry and then translate MDO into that framework. This initial work gives new tools and techniques for studying MDO and its architectures while producing a naturally arising measure of design coupling. The framework also suggests several new areas for exploration into and analysis of MDO systems. At this point, analogies with particle dynamics and systems of differential equations look particularly promising for both the wealth of extant background theory that they have and the potential predictive and evaluative power that they hold. © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

A differential lyapunov framework for contraction analysis

Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is inferred from infinitesimal contraction of the Finsler metrics through integration along solutions curves. © 2013 IEEE.

Unified form language: A domain-specific language for weak formulations of partial differential equations

We present the Unified Form Language (UFL), which is a domain-specific language for representing weak formulations of partial differential equations with a view to numerical approximation. Features of UFL include support for variational forms and functionals, automatic differentiation of forms and expressions, arbitrary function space hierarchies formultifield problems, general differential operators and flexible tensor algebra. With these features, UFL has been used to effortlessly express finite element methods for complex systems of partial differential equations in near-mathematical notation, resulting in compact, intuitive and readable programs. We present in this work the language and its construction. An implementation of UFL is freely available as an open-source software library. The library generates abstract syntax tree representations of variational problems, which are used by other software libraries to generate concrete low-level implementations. Some application examples are presented and libraries that support UFL are highlighted. © 2014 ACM.

Differential equation based length scales to improve DES and RANS simulations

Surprisingly expensive to compute wall distances are still used in a range of key turbulence and peripheral physics models. Potentially economical, accuracy improving differential equation based distance algorithms are considered. These involve elliptic Poisson and hyperbolic natured Eikonal equation approaches. Numerical issues relating to non-orthogonal curvilinear grid solution of the latter are addressed. Eikonal extension to a Hamilton-Jacobi (HJ) equation is discussed. Use of this extension to improve turbulence model accuracy and, along with the Eikonal, enhance Detached Eddy Simulation (DES) techniques is considered. Application of the distance approaches is studied for various geometries. These include a plane channel flow with a wire at the centre, a wing-flap system, a jet with co-flow and a supersonic double-delta configuration. Although less accurate than the Eikonal, Poisson method based flow solutions are extremely close to those using a search procedure. For a moving grid case the Poisson method is found especially efficient. Results show the Eikonal equation can be solved on highly stretched, non-orthogonal, curvilinear grids. A key accuracy aspect is that metrics must be upwinded in the propagating front direction. The HJ equation is found to have qualitative turbulence model improving properties. © 2003 by P. G. Tucker.