Stability Verification of Neural Network Controllers using Mixed-Integer Programming

We propose a framework for the stability verification of Mixed-Integer Linear Programming (MILP) representable control policies. This framework compares a fixed candidate policy, which admits an efficient parameterization and can be evaluated at a low computational cost, against a fixed baseline policy, which is known to be stable but expensive to evaluate. We provide sufficient conditions for the closed-loop stability of the candidate policy in terms of the worst-case approximation error with respect to the baseline policy, and we show that these conditions can be checked by solving a Mixed-Integer Quadratic Program (MIQP). Additionally, we demonstrate that an outer and inner approximation of the stability region of the candidate policy can be computed by solving an MILP. The proposed framework is sufficiently general to accommodate a broad range of candidate policies including ReLU Neural Networks (NNs), optimal solution maps of parametric quadratic programs, and Model Predictive Control (MPC) policies. We also present an open-source toolbox in Python based on the proposed framework, which allows for the easy verification of custom NN architectures and MPC formulations. We showcase the flexibility and reliability of our framework in the context of a DC-DC power converter case study and investigate its computational complexity

Climate model and proxy data constraints on ocean warming across the Paleocene-Eocene Thermal Maximum

Constraining the greenhouse gas forcing, climatic warming and estimates of climate sensitivity across ancient large transient warming events is a major challenge to the palaeoclimate research community. Here we provide a new compilation and synthesis of the available marine proxy temperature data across the largest of these hyperthermals, the Paleocene-Eocene Thermal Maximum (PETM). This includes the application of consistent temperature calibrations to all data, including the most recent set of calibrations for archaeal lipid-derived palaeothermometry. This compilation provides the basis for an informed discussion of the likely range of PETM warming, the biases present in the existing record and an initial assessment of the geographical pattern of PETM ocean warming. To aid interpretation of the geographic variability of the proxy-derived estimates of PETM warming, we present a comparison of this data with the patterns of warming produced by high pCO2 simulations of Eocene climates using the Hadley Centre atmosphere-ocean general circulation model (AOGCM) HadCM3L. On the basis of this comparison and taking into account the patterns of intermediate-water warming we estimate that the global mean surface temperature anomaly for the PETM is within the range of 4 to 5°C

Comparative Study of 3-Dimensional Woven Joint Architectures for Composite Spacecraft Structures

The National Aeronautics and Space Administration (NASA) Exploration Systems Mission Directorate initiated an Advanced Composite Technology (ACT) Project through the Exploration Technology Development Program in order to support the polymer composite needs for future heavy lift launch architectures. As an example, the large composite structural applications on Ares V inspired the evaluation of advanced joining technologies, specifically 3D woven composite joints, which could be applied to traditionally manufactured barrel segments. Implementation of these 3D woven joint technologies may offer enhancements in damage tolerance without sacrificing weight. However, baseline mechanical performance data is needed to properly analyze the joint stresses and subsequently design/down-select a preform architecture. Six different configurations were designed and prepared for this study; each consisting of a different combination of warp/fill fiber volume ratio and preform interlocking method (z-fiber, fully interlocked, or hybrid). Tensile testing was performed for this study with the enhancement of a dual camera Digital Image Correlation (DIC) system which provides the capability to measure full-field strains and three dimensional displacements of objects under load. As expected, the ratio of warp/fill fiber has a direct influence on strength and modulus, with higher values measured in the direction of higher fiber volume bias. When comparing the z-fiber weave to a fully interlocked weave with comparable fiber bias, the z-fiber weave demonstrated the best performance in two different comparisons. We report the measured tensile strengths and moduli for test coupons from the 6 different weave configurations under study

An optical fiber hydrogen sensor using a palladium-coated ball lens

A self-referenced optical fiber refractometer using a ball lens as a sensor head has been developed and characterized. A 350-μm ball lens created at the tip of a single mode fiber has been coated with a 40-nm optically thin layer of palladium that reacts with hydrogen to form a hydride, which has a lower reflectivity than pure palladium. Optical reflectance measurements from the tip of the ball lens were performed to determine the hydrogen response. The change in reflectivity is proportional to the hydrogen concentration in the range 0% to 1% hydrogen in air with a detection limit down to 10 ppm (1σ) in air. This technique offers a simple sensor head arrangement, with a larger sampling area (~40 times) than a typical single-mode fiber core. A statistical image analysis of a palladium film, with cracks created by accelerated failure, confirms that the anticipated sensor area for a ball lens sensor head has a more predictable reflectivity than that of a bare fiber core

Implicit complexity for coinductive data: a characterization of corecurrence

We propose a framework for reasoning about programs that manipulate coinductive data as well as inductive data. Our approach is based on using equational programs, which support a seamless combination of computation and reasoning, and using productivity (fairness) as the fundamental assertion, rather than bi-simulation. The latter is expressible in terms of the former. As an application to this framework, we give an implicit characterization of corecurrence: a function is definable using corecurrence iff its productivity is provable using coinduction for formulas in which data-predicates do not occur negatively. This is an analog, albeit in weaker form, of a characterization of recurrence (i.e. primitive recursion) in [Leivant, Unipolar induction, TCS 318, 2004].Comment: In Proceedings DICE 2011, arXiv:1201.034

The impact of body mass index on labour management and mode of delivery : A retrospective matched cohort study

FUNDINGBWM is supported by an NHMRC Investigator grant (GNT1176437). BWM reports consultancy, research funding and travel support from Merck.ACKNOWLEDGEMENTSOpen access publishing facilitated by Monash University, as part of the Wiley - Monash University agreement via the Council of Australian University Librarians.Peer reviewedPublisher PD

Dynamic communities in multichannel data: An application to the foreign exchange market during the 2007--2008 credit crisis

We study the cluster dynamics of multichannel (multivariate) time series by representing their correlations as time-dependent networks and investigating the evolution of network communities. We employ a node-centric approach that allows us to track the effects of the community evolution on the functional roles of individual nodes without having to track entire communities. As an example, we consider a foreign exchange market network in which each node represents an exchange rate and each edge represents a time-dependent correlation between the rates. We study the period 2005-2008, which includes the recent credit and liquidity crisis. Using dynamical community detection, we find that exchange rates that are strongly attached to their community are persistently grouped with the same set of rates, whereas exchange rates that are important for the transfer of information tend to be positioned on the edges of communities. Our analysis successfully uncovers major trading changes that occurred in the market during the credit crisis.Comment: 8 pages, 6 figures, accepted for publication in Chao