PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers

Time-dependent partial differential equations (PDEs) are ubiquitous in science and engineering. Recently, mostly due to the high computational cost of traditional solution techniques, deep neural network based surrogates have gained increased interest. The practical utility of such neural PDE solvers relies on their ability to provide accurate, stable predictions over long time horizons, which is a notoriously hard problem. In this work, we present a large-scale analysis of common temporal rollout strategies, identifying the neglect of non-dominant spatial frequency information, often associated with high frequencies in PDE solutions, as the primary pitfall limiting stable, accurate rollout performance. Based on these insights, we draw inspiration from recent advances in diffusion models to introduce PDE-Refiner; a novel model class that enables more accurate modeling of all frequency components via a multistep refinement process. We validate PDE-Refiner on challenging benchmarks of complex fluid dynamics, demonstrating stable and accurate rollouts that consistently outperform state-of-the-art models, including neural, numerical, and hybrid neural-numerical architectures. We further demonstrate that PDE-Refiner greatly enhances data efficiency, since the denoising objective implicitly induces a novel form of spectral data augmentation. Finally, PDE-Refiner's connection to diffusion models enables an accurate and efficient assessment of the model's predictive uncertainty, allowing us to estimate when the surrogate becomes inaccurate.Comment: Project website: https://phlippe.github.io/PDERefiner

Dynamic reconfiguration of human brain networks during learning

Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two attributes -- flexibility and selection -- must operate over multiple temporal scales as performance of a skill changes from being slow and challenging to being fast and automatic. Such selective adaptability is naturally provided by modular structure, which plays a critical role in evolution, development, and optimal network function. Using functional connectivity measurements of brain activity acquired from initial training through mastery of a simple motor skill, we explore the role of modularity in human learning by identifying dynamic changes of modular organization spanning multiple temporal scales. Our results indicate that flexibility, which we measure by the allegiance of nodes to modules, in one experimental session predicts the relative amount of learning in a future session. We also develop a general statistical framework for the identification of modular architectures in evolving systems, which is broadly applicable to disciplines where network adaptability is crucial to the understanding of system performance.Comment: Main Text: 19 pages, 4 figures Supplementary Materials: 34 pages, 4 figures, 3 table

From Teamchef Arminius to Hermann Junior: glocalised discourse about a national foundation myth

If for much of the nineteenth and twentieth centuries, the ‘Battle of the Teutoburg Forest’, fought in 9 CE between Roman armies and Germanic tribes, was predominantly a reference point for nationalist and chauvinist discourses in Germany, the first decade of the twenty-first century has seen attempts to link public remembrance with local/regional identities on the one hand and international/intercultural contact on the other. In the run up to and during the ‘anniversary year’ of 2009, German media, sports institutions and various other official institutions articulating tourist, economic and political interests attempted to create a new ‘glocalised’ version of the public memory of the Teutoburg battle. Combining methods of Cognitive Linguistics and Critical Discourse Analysis, the paper analyses the narrative and argumentative topoi employed in this re-orientation of public memory, with a special emphasis on hybrid, post-national identity-construction. Das zweitausendjährige Gedenkjahr der „Schlacht im Teutoburger Wald“ im Jahr 2009 bot eine günstige Gelegenheit, die bis in die zweite Hälfte des 20. Jahrhunderts dominante Tradition nationalistisch–chauvinistischer Deutungen des Sieges von germanischen Stämmen über drei römische Legionen zu korrigieren und zu überwinden. Der Aufsatz analysiert mit Hilfe diskurslinguistischer Methoden die Anstrengungen regionaler Institutionen und Medien, die nationale Vereinnahmung des historischen Gedenkens kritisch zu thematisieren sowie neue, zum eine lokal situierte, zum andern international orientierte Identifikationsangebote anzubieten. Die Analyse zeigt, dass solche „de-nationalisierten“ Identifikationsangebote zwar teilweise auch früher verwendet wurden, aber heutzutage rekontextualisiert und auf innovative Weise in den Vordergrund gestellt werden

Blurred Boundaries: Gender and Work-Family Interference in Cross-National Context

Although well theorized at the individual level, previous research has neglected the role of national context in shaping overall levels of nonwork-work and work-nonwork interference. This study fills this gap by examining how a national context of gender empowerment affects the likelihood of experiencing nonwork-work and work-nonwork interference at the individual and national levels. Controlling for individual-level differences in the distribution of job demands and resources, results from our multilevel models indicate that women's empowerment has significant net gender and parenthood effects on nonwork-work interference. By contrast, gender empowerment equally structures work-nonwork interference for these groups. Our results highlight the need to investigate interference bidirectionally and in a multilevel context. © The Author(s) 2013

ESR, raman and conductivity studies on fractionated poly(2-methoxyaniline-5-sulfonic acid)

Synthesis methods used to produce poly(2-methoxyaniline-5-sulfonic acid) (PMAS), a water soluble, self-doped conducting polymer, have been shown to form two distinctly different polymer fractions with molecular weights of approximately 2 kDa and 8 -10 kDa. The low molecular weight (LMWT) PMAS fraction is redox inactive and non-conducting while the high molecular weight (HMWT) PMAS is electro-active with electrical conductivities of 0.94 0.05 S cm-1. Previous investigations have illustrated the different photochemical and electrochemical properties of these fractions, but have not correlated these properties with the structural and electronic interactions that drive them. Incomplete purification of the PMAS mixture, typically via bag dialysis, has been shown to result in a mixture of approximately 50:50 HMWT:LMWT PMAS with electrical conductivity significantly lower at approximately 0.10 to 0.26 S cm-1. The difference between the electrical conductivities of these fractions has been investigated by the controlled addition of the non-conducting LMWT PMAS fraction into the HMWT PMAS composite film with the subsequent electronic properties investigated by solid-state ESR and Raman spectroscopies. These studies illustrate strong electronic intereactions of the insulating LMWT PMAS with the emeraldine salt HMWT PMAS to substantially alter the population of the electronic charge carriers in the conducting polymer. ESR studies on these mixtures, when compared to HMWT PMAS, exhibited a lower level of electron spin in the presence of LMWT PMAS indicative of the the formation of low spin bipolarons without a change the oxidation state of the conducting HMWT fraction

The Biological Standard of Living in the two Germanies.

Physical stature is used as a proxy for the biological standard of living in the two Germanies before and after unification in an analysis of a cross-sectional sample (1998) of adult heights, as well as among military recruits of the 1990s. West Germans tended to be taller than East Germans throughout the period under consideration. Contrary to official proclamations of a classless society, there were substantial social differences in physical stature in East-Germany. Social differences in height were greater in the East among females, and less among males than in the West. The difficulties experienced by the East-German population after 1961 is evident in the increase in social inequality of physical stature thereafter, as well as in the increasing gap relative to the height of the West-German population. After unification, however, there is a tendency for East-German males, but not of females, to catch up with their West-German counterparts

Weak Lensing from Space I: Instrumentation and Survey Strategy

A wide field space-based imaging telescope is necessary to fully exploit the technique of observing dark matter via weak gravitational lensing. This first paper in a three part series outlines the survey strategies and relevant instrumental parameters for such a mission. As a concrete example of hardware design, we consider the proposed Supernova/Acceleration Probe (SNAP). Using SNAP engineering models, we quantify the major contributions to this telescope's Point Spread Function (PSF). These PSF contributions are relevant to any similar wide field space telescope. We further show that the PSF of SNAP or a similar telescope will be smaller than current ground-based PSFs, and more isotropic and stable over time than the PSF of the Hubble Space Telescope. We outline survey strategies for two different regimes - a ``wide'' 300 square degree survey and a ``deep'' 15 square degree survey that will accomplish various weak lensing goals including statistical studies and dark matter mapping.Comment: 25 pages, 8 figures, 1 table, replaced with Published Versio

Supernova / Acceleration Probe: A Satellite Experiment to Study the Nature of the Dark Energy

The Supernova / Acceleration Probe (SNAP) is a proposed space-based experiment designed to study the dark energy and alternative explanations of the acceleration of the Universe's expansion by performing a series of complementary systematics-controlled measurements. We describe a self-consistent reference mission design for building a Type Ia supernova Hubble diagram and for performing a wide-area weak gravitational lensing study. A 2-m wide-field telescope feeds a focal plane consisting of a 0.7 square-degree imager tiled with equal areas of optical CCDs and near infrared sensors, and a high-efficiency low-resolution integral field spectrograph. The SNAP mission will obtain high-signal-to-noise calibrated light-curves and spectra for several thousand supernovae at redshifts between z=0.1 and 1.7. A wide-field survey covering one thousand square degrees resolves ~100 galaxies per square arcminute. If we assume we live in a cosmological-constant-dominated Universe, the matter density, dark energy density, and flatness of space can all be measured with SNAP supernova and weak-lensing measurements to a systematics-limited accuracy of 1%. For a flat universe, the density-to-pressure ratio of dark energy can be similarly measured to 5% for the present value w0 and ~0.1 for the time variation w'. The large survey area, depth, spatial resolution, time-sampling, and nine-band optical to NIR photometry will support additional independent and/or complementary dark-energy measurement approaches as well as a broad range of auxiliary science programs. (Abridged)Comment: 40 pages, 18 figures, submitted to PASP, http://snap.lbl.go

Putting the pieces together: Integration for forest landscape restoration implementation

© 2019 John Wiley & Sons, Ltd. The concept of forest landscape restoration (FLR) is being widely adopted around the globe by governmental, non-governmental agencies, and the private sector, all of whom see FLR as an approach that contributes to multiple global sustainability goals. Originally, FLR was designed with a clearly integrative dimension across sectors, stakeholders, space and time, and in particular across the natural and social sciences. Yet, in practice, this integration remains a challenge in many FLR efforts. Reflecting this lack of integration are the continued narrow sectoral and disciplinary approaches taken by forest restoration projects, often leading to marginalisation of the most vulnerable populations, including through land dispossessions. This article aims to assess what lessons can be learned from other associated fields of practice for FLR implementation. To do this, 35 scientists came together to review the key literature on these concepts to suggest relevant lessons and guidance for FLR. We explored the following large-scale land use frameworks or approaches: land sparing/land sharing, the landscape approach, agroecology, and socio-ecological systems. Also, to explore enabling conditions to promote integrated decision making, we reviewed the literature on understanding stakeholders and their motivations, tenure and property rights, polycentric governance, and integration of traditional and Western knowledge. We propose lessons and guidance for practitioners and policymakers on ways to improve integration in FLR planning and implementation. Our findings highlight the need for a change in decision-making processes for FLR, better understanding of stakeholder motivations and objectives for FLR, and balancing planning with flexibility to enhance social–ecological resilience.The Frank Jackson Foundatio