Graph Kernels

We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexity of kernel computation between unlabeled graphs with n vertices from O(n^6) to O(n^3). We find a spectral decomposition approach even more efficient when computing entire kernel matrices. For labeled graphs we develop conjugate gradient and fixed-point methods that take O(dn^3) time per iteration, where d is the size of the label set. By extending the necessary linear algebra to Reproducing Kernel Hilbert Spaces (RKHS) we obtain the same result for d-dimensional edge kernels, and O(n^4) in the infinite-dimensional case; on sparse graphs these algorithms only take O(n^2) time per iteration in all cases. Experiments on graphs from bioinformatics and other application domains show that these techniques can speed up computation of the kernel by an order of magnitude or more. We also show that certain rational kernels (Cortes et al., 2002, 2003, 2004) when specialized to graphs reduce to our random walk graph kernel. Finally, we relate our framework to R-convolution kernels (Haussler, 1999) and provide a kernel that is close to the optimal assignment kernel of Fröhlich et al. (2006) yet provably positive semi-definite

Neural Message Passing with Edge Updates for Predicting Properties of Molecules and Materials

Neural message passing on molecular graphs is one of the most promising methods for predicting formation energy and other properties of molecules and materials. In this work we extend the neural message passing model with an edge update network which allows the information exchanged between atoms to depend on the hidden state of the receiving atom. We benchmark the proposed model on three publicly available datasets (QM9, The Materials Project and OQMD) and show that the proposed model yields superior prediction of formation energies and other properties on all three datasets in comparison with the best published results. Furthermore we investigate different methods for constructing the graph used to represent crystalline structures and we find that using a graph based on K-nearest neighbors achieves better prediction accuracy than using maximum distance cutoff or the Voronoi tessellation graph

Non-collinear magnetoconductance of a quantum dot

We study theoretically the linear conductance of a quantum dot connected to ferromagnetic leads. The dot level is split due to a non-collinear magnetic field or intrinsic magnetization. The system is studied in the non-interacting approximation, where an exact solution is given, and, furthermore, with Coulomb correlations in the weak tunneling limit. For the non-interacting case, we find an anti-resonance for a particular direction of the applied field, non-collinear to the parallel magnetization directions of the leads. The anti-resonance is destroyed by the correlations, giving rise to an interaction induced enhancement of the conductance. The angular dependence of the conductance is thus distinctly different for the interacting and non-interacting cases when the magnetizations of the leads are parallel. However, for anti-parallel lead magnetizations the interactions do not alter the angle dependence significantly.Comment: 7 pages, 7 figure

Signatures of nonadiabatic O2 dissociation at Al(111): First-principles fewest-switches study

Recently, spin selection rules have been invoked to explain the discrepancy between measured and calculated adsorption probabilities of molecular oxygen reacting with Al(111). In this work, we inspect the impact of nonadiabatic spin transitions on the dynamics of this system from first principles. For this purpose the motion on two distinct potential-energy surfaces associated to different spin configurations and possible transitions between them are inspected by means of the Fewest Switches algorithm. Within this framework we especially focus on the influence of such spin transitions on observables accessible to molecular beam experiments. On this basis we suggest experimental setups that can validate the occurrence of such transitions and discuss their feasibility.Comment: 13 pages, 7 figure

Quantum Breathing Mode of Interacting Particles in a One-dimensional Harmonic Trap

Extending our previous work, we explore the breathing mode---the [uniform] radial expansion and contraction of a spatially confined system. We study the breathing mode across the transition from the ideal quantum to the classical regime and confirm that it is not independent of the pair interaction strength (coupling parameter). We present the results of time-dependent Hartree-Fock simulations for 2 to 20 fermions with Coulomb interaction and show how the quantum breathing mode depends on the particle number. We validate the accuracy of our results, comparing them to exact Configuration Interaction results for up to 8 particles

Materials property prediction using symmetry-labeled graphs as atomic-position independent descriptors

Computational materials screening studies require fast calculation of the properties of thousands of materials. The calculations are often performed with Density Functional Theory (DFT), but the necessary computer time sets limitations for the investigated material space. Therefore, the development of machine learning models for prediction of DFT calculated properties are currently of interest. A particular challenge for \emph{new} materials is that the atomic positions are generally not known. We present a machine learning model for the prediction of DFT-calculated formation energies based on Voronoi quotient graphs and local symmetry classification without the need for detailed information about atomic positions. The model is implemented as a message passing neural network and tested on the Open Quantum Materials Database (OQMD) and the Materials Project database. The test mean absolute error is 20 meV on the OQMD database and 40 meV on Materials Project Database. The possibilities for prediction in a realistic computational screening setting is investigated on a dataset of 5976 ABSe$_3$ selenides with very limited overlap with the OQMD training set. Pretraining on OQMD and subsequent training on 100 selenides result in a mean absolute error below 0.1 eV for the formation energy of the selenides.Comment: 14 pages including references and 13 figure

Nonlocal lattice fermion models on the 2d torus

Abelian fermion models described by the SLAC action are considered on a finite 2d lattice. It is shown that modification of these models by introducing additional Pauli - Villars regularization supresses nonlocal effects and provides agreement with the continuum results in vectorial U(1) models. In the case of chiral fermions the phase of the determinant differs from the continuum one.Comment: 16 pages, LaTeX, 5 eps figures, uses epsf.sty, rotate.st

The german camera evaluation project - results from the geometry group

The so-called German camera evaluation project was initiated by the German society of Photogrammetry, Remote Sensing and Geoinformation (DGPF) in order to allow for comprehensive empirical test on photogrammetric digital airborne camera systems. During this test, the digital camera systems DMC, Ultracam-X, ADS40 (2nd generation), JAS-150, Quattro DigiCAM and AIC-x1 were flown in the test site Vaihingen/Enz in summer 2008. In addition, RMK analogue images and ALS50 LiDAR data were recorded for comparison, while reference measurements on the ground were made available as well. Parts of the test field were also covered from hyper-spectral sensor flights, namely the AISA+ and ROSIS system. After data collection all this material was prepared, documented and distributed to more than 30 institutions which participated in the evaluation and formed the project network of expertise. This evaluation phase included topics like the analysis of geometric accuracy and sensor calibration, the radiometric performance including on-site radiometric calibration and multi-spectral land classifications. Additionally, the performance of photogrammetric surface model generation and the potential of manual stereo plotting from digital images were investigated. Within this paper, the major findings from the geometric evaluations, namely sensor orientation and height model generation are presented

To read or not to read

• De manier waarop vakliteratuur wordt gebruikt in kwalitatief onderzoek, alsmede het tijdstip waarop, zijn fundamentele onderzoeksdilemma’s. • De gefundeerde theoriebenadering staat kritisch tegenover het gebruik van vakliteratuur. • Het gebruik van vakliteratuur brengt gevaren met zich mee, onder andere omdat de onderzoeker zich alleen zou kunnen richten op die zaken waarvan hij uit de literatuur heeft begrepen dat ze relevant zijn. • Bestaande vakliteratuur gebruiken brengt ook kansen met zich mee. Het helpt bijvoorbeeld het onderzoek richting te geven door handvatten te bieden voor het ontwikkelen van de voorlopige vraag en het verschaffen van conceptuele helderheid. • De keuze voor het wel of niet gebruiken van vakliteratuur en voor de manier waarop dient te worden bevraagd en geëxpliciteerd in zowel de onderzoeksopzet, het lopende onderzoek als het eindproduct

Reflecting on the role of literature in qualitative public administration research:learning from grounded theory

When undertaking qualitative research, public administration scholars must walk a thin line between being theoretically sensitive and imposing preconceived ideas on their work. This article identifies opportunities and pitfalls in using literature in qualitative public administration research. Whereas the opportunities are already well known within the discipline, the pitfalls remain underexposed. We identify potential pitfalls by using insights from the grounded theory approach. To illustrate how opportunities can be optimally exploited, and pitfalls avoided, we provide examples of high quality public administration research. Finally, we derive recommendations for public administration scholars when using literature in their qualitative research. These recommendations can help improve qualitative methods in the public administration discipline