Learning the Solution Operator of Boundary Value Problems using Graph Neural Networks

As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently. In this work, we design a general solution operator for two different time-independent PDEs using graph neural networks (GNNs) and spectral graph convolutions. We train the networks on simulated data from a finite elements solver on a variety of shapes and inhomogeneities. In contrast to previous works, we focus on the ability of the trained operator to generalize to previously unseen scenarios. Specifically, we test generalization to meshes with different shapes and superposition of solutions for a different number of inhomogeneities. We find that training on a diverse dataset with lots of variation in the finite element meshes is a key ingredient for achieving good generalization results in all cases. With this, we believe that GNNs can be used to learn solution operators that generalize over a range of properties and produce solutions much faster than a generic solver. Our dataset, which we make publicly available, can be used and extended to verify the robustness of these models under varying conditions

The Determinants and Effects of Board Nomination Committees*

This article assesses the corporate governance-related antecedents of nomination committee adoption, and the impact of nomination committees' existence and their composition on board independence and board demographic diversity. We conducted a longitudinal study of board composition amongst 210 Swiss public companies from January 2001 through December 2003, a period during which the Swiss (Stock) Exchange (SWX) introduced new corporate governance-related disclosure guidelines. We find firms with nomination committees are more likely to have a higher number of independent and foreign directors, but not more likely to have a higher number of female board members. Further, the existence of nomination committees is associated with a higher degree of nationality diversity but is not related to board educational diversity. We also find that nomination committee composition matters in the nomination of independent and foreign, but not of female directors. Our results suggest that understanding different board roles and composition require a multi-theoretical approach, and that agency theory, resource-dependence theory and group effectiveness theory help to explain different aspects of board composition and effectiveness. Finally, the article discusses the concept of diversity and appropriate ways to study diversity in a boardroom contex

The curse of extremes: generalist career experience and CEO initial compensation

Studies argue that generalist CEOs are more valued by the market for executive labor and receive higher initial compensation. Challenging this prevailing assumption, we acknowledge the drawbacks of extensive career mobility and predict an inverted U-shape relationship between CEO generalist career experience and CEO initial compensation. Integrating the generalism and specialization views of human capital, we postulate that at an initial level, the acquisition of experience-breadth from different firms and industries enables CEOs to broaden their knowledge-base, obtain a variety of skills, and thus increase their labor-market value and initial compensation. After a threshold, however, the accumulation of extensive levels of career generalism through frequent job-hopping across firm and industry contexts gradually causes a lack of experience-depth and insufficient career specialization – thereby triggering lower CEO market-value and initial pay. Data from 197 CEO appointments in large publicly traded firms support our predictions. Our results also show that the observed inverted U-shape relationship varies with factors nested at different layers of context – highlighting the contingent nature of this area of research

Towards Learning Self-Organized Criticality of Rydberg Atoms using Graph Neural Networks

Self-Organized Criticality (SOC) is a ubiquitous dynamical phenomenon believed to be responsible for the emergence of universal scale-invariant behavior in many, seemingly unrelated systems, such as forest fires, virus spreading or atomic excitation dynamics. SOC describes the buildup of large-scale and long-range spatio-temporal correlations as a result of only local interactions and dissipation. The simulation of SOC dynamics is typically based on Monte-Carlo (MC) methods, which are however numerically expensive and do not scale beyond certain system sizes. We investigate the use of Graph Neural Networks (GNNs) as an effective surrogate model to learn the dynamics operator for a paradigmatic SOC system, inspired by an experimentally accessible physics example: driven Rydberg atoms. To this end, we generalize existing GNN simulation approaches to predict dynamics for the internal state of the node. We show that we can accurately reproduce the MC dynamics as well as generalize along the two important axes of particle number and particle density. This paves the way to model much larger systems beyond the limits of traditional MC methods. While the exact system is inspired by the dynamics of Rydberg atoms, the approach is quite general and can readily be applied to other systems

Mapping correlations between nitrogen concentrations in atmospheric deposition and mosses for natural landscapes in Europe

Recent investigations proved that nitrogen (N) concentrations in mosses are primarily determined byatmospheric deposition. The correlations are country- and N compound-specific and agree well withspatial patterns and temporal trends across Europe as a whole and in single European countries. Thisstudy investigates whether correlations between the concentration of N in atmospheric deposition andmosses within the units of an ecological land classification of Europe can be established. To this end, N measurements from the 2005 European moss survey and modelled N atmospheric deposition in 2005were intersected with a map of European landscapes. Then, considering minimum numbers of samplingsites required across Europe, in single European countries and within the landscapes of Europe andaccounting for spatial auto-correlation, the correlations between the N concentration in mosses andcorresponding deposition were calculated and mapped for each of those landscape units containingmoss sampling sites. Using an example of one landscape with positive correlation and one landscape withno correlation between N concentrations in deposition and in mosses, influencing factors were rankedbased on investigating the multivariate interactions between moss concentrations and, amongst others,atmospheric deposition, land use, elevation or moss species by classification and regression trees. Fromthis study it could be concluded that the numbers of sampling sites within Europe and most participatingcountries as well as within most of the landscapes covering Europe are sufficient. Spatial patterns ofcorrelations between the atmospheric N deposition and N concentration in mosses could be provento vary across the landscapes of Europe. Where clear positive correlations between N concentrationsin deposition and mosses exist in landscapes, multivariate ranking identifies the deposition as maininfluencing factor. In cases with no correlation between deposition and N concentrations in mosses,other factors such as e.g. moss species collected may be of importance. Therefore, mosses were proved toserve as biological indicators for atmospheric depositions and ecologically defined land classes could beidentified as more complex indicators which allow relating exposure monitoring with effects assessment

Frequency and Polarization Agile RFID Patch Antenna with Reduced Dimensions

This paper presents a frequency and polarization reconfigurable UHF RFID patch antenna based on a switchable feeding network. For best integration of the antenna, its size and ground plane are much smaller with respect to the canonical patch antenna design, however the proposed design is able to cover the EU and US frequency bands of the RFID standard. State-of-the-art CMOS switches are employed as key element for selecting the desired polarization and proper matching network. The switches provide also a simple solution for high power applications in contrast to concepts based on PIN diodes or varactors. Simulated results have shown good performance. Considering its flexible and inexpensive structure, the proposed system is a promising alternative to aperture tuning and circular polarized antenna approaches

Blueprint for a microwave trapped ion quantum computer

The availability of a universal quantum computer may have a fundamental impact on a vast number of research fields and on society as a whole. An increasingly large scientific and industrial community is working toward the realization of such a device. An arbitrarily large quantum computer may best be constructed using a modular approach. We present a blueprint for a trapped ion–based scalable quantum computer module, making it possible to create a scalable quantum computer architecture based on long-wavelength radiation quantum gates. The modules control all operations as stand-alone units, are constructed using silicon microfabrication techniques, and are within reach of current technology. To perform the required quantum computations, the modules make use of long-wavelength radiation–based quantum gate technology. To scale this microwave quantum computer architecture to a large size, we present a fully scalable design that makes use of ion transport between different modules, thereby allowing arbitrarily many modules to be connected to construct a large-scale device. A high error–threshold surface error correction code can be implemented in the proposed architecture to execute fault-tolerant operations. With appropriate adjustments, the proposed modules are also suitable for alternative trapped ion quantum computer architectures, such as schemes using photonic interconnects

Photodisintegration of the Three-Nucleon Systems and their Polarizabilities

The total photodisintegration cross sections of three-body nuclei are calculated with semirealistic NN potentials below pion threshold. Full final state interaction with Coulomb force is taken into account via the Lorentz integral transform method. The experimental total cross sections are well described and the sum rule $\sigma_{-1}(^3$H) agrees with elastic electron scattering data. The calculated ^3He polarizability is 0.15 fm^3.Comment: 9 pages, Latex (REVTEX), 3 Postscript figures, to appear in Phys. Lett.

Mesoporous tertiary oxides via a novel amphiphilic approach

We report a facile biomimetic sol-gel synthesis using the sponge phase formed by the lipid monoolein as a structure-directing template, resulting in high phase purity, mesoporous dysprosium- and gadolinium titanates. The stability of monoolein in a 1,4-butanediol and water mixture complements the use of a simple sol-gel metal oxide synthesis route. By judicious control of the lipid/solvent concentration, the sponge phase of monoolein can be directly realised in the pyrochlore material, leading to a porous metal oxide network with an average pore diameter of 10 nm

Differential effects of apolipoprotein E isoforms on phosphorylation at specific sites on tau by glycogen synthase kinase-3β identified by nano-electrospray mass spectrometry

AbstractPreviously published data have shown an allele-specific variation in the in vitro binding of apolipoprotein E (apoE) to tau, which prompted the hypothesis that apoE binding may protect tau from phosphorylation, apoE3 being more efficient than apoE4. We have, therefore, investigated the effects of apoE on tau phosphorylation in vitro by the proline-directed kinase, glycogen synthase kinase (GSK)-3β. The phosphopeptide maps of tau alone, of tau with apoE3 and of tau with apoE4 were very similar. When apoE2 was present a further four spots were evident. Additionally, of the 15 peptides phosphorylated in the presence or absence of apoE, subtle differences, some isoform-specific, in the relative amounts of phosphorylation were observed