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2020


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Effect of the soft layer thickness of magnetization reversal process of exchange-spring nanomagnet patterns

Son, K., Schütz, G., Goering, E.

{Current Applied Physics}, 20(4):477-483, Elsevier B.V., Amsterdam, 2020 (article)

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DOI [BibTex]

2020



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Tuning the magnetic properties of permalloy-based magnetoplasmonic crystals for sensor applications

Murzin, D. V., Belyaev, V. K., Groß, F., Gräfe, J., Rivas, M., Rodionova, V. V.

{Japanese Journal of Applied Physics}, 59(SE), IOP Publishing Ltd, Bristol, England, 2020 (article)

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DOI [BibTex]

DOI [BibTex]


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Creating zero-field skyrmions in exchange-biased multilayers through X-ray illumination

Guang, Y., Bykova, I., Liu, Y., Yu, G., Goering, E., Weigand, M., Gräfe, J., Kim, S. K., Zhang, J., Zhang, H., Yan, Z., Wan, C., Feng, J., Wang, X., Guo, C., Wei, H., Peng, Y., Tserkovnyak, Y., Han, X., Schütz, G.

{Nature Communications}, 11, Nature Publishing Group, London, 2020 (article)

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DOI [BibTex]

DOI [BibTex]


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Element-resolved study of the evolution of magnetic response in FexN compounds

Chen, Y., Gölden, D., Dirba, I., Huang, M., Gutfleisch, O., Nagel, P., Merz, M., Schuppler, S., Schütz, G., Alff, L., Goering, E.

{Journal of Magnetism and Magnetic Materials}, 498, NH, Elsevier, Amsterdam, 2020 (article)

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DOI [BibTex]

DOI [BibTex]


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The role of temperature and drive current in skyrmion dynamics

Litzius, K., Leliaert, J., Bassirian, P., Rodrigues, D., Kromin, S., Lemesh, I., Zazvorka, J., Lee, K., Mulkers, J., Kerber, N., Heinze, D., Keil, N., Reeve, R. M., Weigand, M., Van Waeyenberge, B., Schütz, G., Everschor-Sitte, K., Beach, G. S. D., Kläui, M.

{Nature Electronics}, 3(1):30-36, Springer Nature, London, 2020 (article)

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DOI [BibTex]

DOI [BibTex]


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Magnetic flux penetration into micron-sized superconductor/ferromagnet bilayers

Simmendinger, J., Weigand, M., Schütz, G., Albrecht, J.

{Superconductor Science and Technology}, 33(2), IOP Pub., Bristol, 2020 (article)

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DOI [BibTex]

DOI [BibTex]


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Fabrication and temperature-dependent magnetic properties of large-area L10-FePt/Co exchange-spring magnet nanopatterns

Son, K., Schütz, G.

{Physica E: Low-Dimensional Systems And Nanostructures}, 115, North-Holland, Amsterdam, 2020 (article)

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DOI [BibTex]

DOI [BibTex]


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How to functionalise metal-organic frameworks to enable guest nanocluster embedment

King, J., Zhang, L., Doszczeczko, S., Sambalova, O., Luo, H., Rohman, F., Phillips, O., Borgschulte, A., Hirscher, M., Addicoat, M., Szilágyi, P. A.

{Journal of Materials Chemistry A}, 8(9):4889-4897, Royal Society of Chemistry, Cambridge, UK, 2020 (article)

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DOI [BibTex]

DOI [BibTex]


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Thermal nucleation and high-resolution imaging of submicrometer magnetic bubbles in thin thulium iron garnet films with perpendicular anisotropy

Büttner, F., Mawass, M. A., Bauer, J., Rosenberg, E., Caretta, L., Avci, C. O., Gräfe, J., Finizio, S., Vaz, C. A. F., Novakovic, N., Weigand, M., Litzius, K., Förster, J., Träger, N., Groß, F., Suzuki, D., Huang, M., Bartell, J., Kronast, F., Raabe, J., Schütz, G., Ross, C. A., Beach, G. S. D.

{Physical Review Materials}, 4(1), American Physical Society, College Park, MD, 2020 (article)

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DOI [BibTex]

DOI [BibTex]


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Generation and characterization of focused helical x-ray beams

Loetgering, L., Baluktsian, M., Keskinbora, K., Horstmeyer, R., Wilhein, T., Schütz, G., Eikema, K. S. E., Witte, S.

Science Advances, 6(7), American Association for the Advancement of Science, 2020 (article)

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Generation and characterization of focused helical x-ray beams link (url) DOI [BibTex]

Generation and characterization of focused helical x-ray beams link (url) DOI [BibTex]


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Materials for hydrogen-based energy storage - past, recent progress and future outlook

Hirscher, M., Yartys, V. A., Baricco, M., Bellosta von Colbe, J., Blanchard, D., Bowman Jr., R. C., Broom, D. P., Buckley, C. E., Chang, F., Chen, P., Cho, Y. W., Crivello, J., Cuevas, F., David, W. I. F., de Jongh, P. E., Denys, R. V., Dornheim, M., Felderhoff, M., Filinchuk, Y., Froudakis, G. E., Grant, D. M., Gray, E. M., Hauback, B. C., He, T., Humphries, T. D., Jensen, T. R., Kim, S., Kojima, Y., Latroche, M., Li, H., Lotostskyy, M. V., Makepeace, J. W., M\oller, K. T., Naheed, L., Ngene, P., Noréus, D., Nyg\aard, M. M., Orimo, S., Paskevicius, M., Pasquini, L., Ravnsbaek, D. B., Sofianos, M. V., Udovic, T. J., Vegge, T., Walker, G. S., Webb, C. J., Weidenthaler, C., Zlotea, C.

{Journal of Alloys and Compounds}, 827, Elsevier B.V., Lausanne, Switzerland, 2020 (article)

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DOI [BibTex]

DOI [BibTex]

2018


Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective
Probabilistic Solutions To Ordinary Differential Equations As Non-Linear Bayesian Filtering: A New Perspective

Tronarp, F., Kersting, H., Särkkä, S., Hennig, P.

ArXiv preprint 2018, arXiv:1810.03440 [stat.ME], October 2018 (article)

Abstract
We formulate probabilistic numerical approximations to solutions of ordinary differential equations (ODEs) as problems in Gaussian process (GP) regression with non-linear measurement functions. This is achieved by defining the measurement sequence to consists of the observations of the difference between the derivative of the GP and the vector field evaluated at the GP---which are all identically zero at the solution of the ODE. When the GP has a state-space representation, the problem can be reduced to a Bayesian state estimation problem and all widely-used approximations to the Bayesian filtering and smoothing problems become applicable. Furthermore, all previous GP-based ODE solvers, which were formulated in terms of generating synthetic measurements of the vector field, come out as specific approximations. We derive novel solvers, both Gaussian and non-Gaussian, from the Bayesian state estimation problem posed in this paper and compare them with other probabilistic solvers in illustrative experiments.

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link (url) Project Page [BibTex]

2018



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Convergence Rates of Gaussian ODE Filters

Kersting, H., Sullivan, T. J., Hennig, P.

arXiv preprint 2018, arXiv:1807.09737 [math.NA], July 2018 (article)

Abstract
A recently-introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution $x$ and its first $q$ derivatives a priori as a Gauss--Markov process $\boldsymbol{X}$, which is then iteratively conditioned on information about $\dot{x}$. We prove worst-case local convergence rates of order $h^{q+1}$ for a wide range of versions of this Gaussian ODE filter, as well as global convergence rates of order $h^q$ in the case of $q=1$ and an integrated Brownian motion prior, and analyse how inaccurate information on $\dot{x}$ coming from approximate evaluations of $f$ affects these rates. Moreover, we present explicit formulas for the steady states and show that the posterior confidence intervals are well calibrated in all considered cases that exhibit global convergence---in the sense that they globally contract at the same rate as the truncation error.

pn

link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences

Kanagawa, M., Hennig, P., Sejdinovic, D., Sriperumbudur, B. K.

Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

Abstract
This paper is an attempt to bridge the conceptual gaps between researchers working on the two widely used approaches based on positive definite kernels: Bayesian learning or inference using Gaussian processes on the one side, and frequentist kernel methods based on reproducing kernel Hilbert spaces on the other. It is widely known in machine learning that these two formalisms are closely related; for instance, the estimator of kernel ridge regression is identical to the posterior mean of Gaussian process regression. However, they have been studied and developed almost independently by two essentially separate communities, and this makes it difficult to seamlessly transfer results between them. Our aim is to overcome this potential difficulty. To this end, we review several old and new results and concepts from either side, and juxtapose algorithmic quantities from each framework to highlight close similarities. We also provide discussions on subtle philosophical and theoretical differences between the two approaches.

pn

arXiv [BibTex]

arXiv [BibTex]


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Transmission x-ray microscopy at low temperatures: Irregular supercurrent flow at small length scales

Simmendinger, J., Ruoss, S., Stahl, C., Weigand, M., Gräfe, J., Schütz, G., Albrecht, J.

{Physical Review B}, 97(13), American Physical Society, Woodbury, NY, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Counterfactual Mean Embedding: A Kernel Method for Nonparametric Causal Inference

Muandet, K., Kanagawa, M., Saengkyongam, S., Marukata, S.

Arxiv e-prints, arXiv:1805.08845v1 [stat.ML], 2018 (article)

Abstract
This paper introduces a novel Hilbert space representation of a counterfactual distribution---called counterfactual mean embedding (CME)---with applications in nonparametric causal inference. Counterfactual prediction has become an ubiquitous tool in machine learning applications, such as online advertisement, recommendation systems, and medical diagnosis, whose performance relies on certain interventions. To infer the outcomes of such interventions, we propose to embed the associated counterfactual distribution into a reproducing kernel Hilbert space (RKHS) endowed with a positive definite kernel. Under appropriate assumptions, the CME allows us to perform causal inference over the entire landscape of the counterfactual distribution. The CME can be estimated consistently from observational data without requiring any parametric assumption about the underlying distributions. We also derive a rate of convergence which depends on the smoothness of the conditional mean and the Radon-Nikodym derivative of the underlying marginal distributions. Our framework can deal with not only real-valued outcome, but potentially also more complex and structured outcomes such as images, sequences, and graphs. Lastly, our experimental results on off-policy evaluation tasks demonstrate the advantages of the proposed estimator.

ei pn

arXiv [BibTex]

arXiv [BibTex]


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Model-based Kernel Sum Rule: Kernel Bayesian Inference with Probabilistic Models

Nishiyama, Y., Kanagawa, M., Gretton, A., Fukumizu, K.

Arxiv e-prints, arXiv:1409.5178v2 [stat.ML], 2018 (article)

Abstract
Kernel Bayesian inference is a powerful nonparametric approach to performing Bayesian inference in reproducing kernel Hilbert spaces or feature spaces. In this approach, kernel means are estimated instead of probability distributions, and these estimates can be used for subsequent probabilistic operations (as for inference in graphical models) or in computing the expectations of smooth functions, for instance. Various algorithms for kernel Bayesian inference have been obtained by combining basic rules such as the kernel sum rule (KSR), kernel chain rule, kernel product rule and kernel Bayes' rule. However, the current framework only deals with fully nonparametric inference (i.e., all conditional relations are learned nonparametrically), and it does not allow for flexible combinations of nonparametric and parametric inference, which are practically important. Our contribution is in providing a novel technique to realize such combinations. We introduce a new KSR referred to as the model-based KSR (Mb-KSR), which employs the sum rule in feature spaces under a parametric setting. Incorporating the Mb-KSR into existing kernel Bayesian framework provides a richer framework for hybrid (nonparametric and parametric) kernel Bayesian inference. As a practical application, we propose a novel filtering algorithm for state space models based on the Mb-KSR, which combines the nonparametric learning of an observation process using kernel mean embedding and the additive Gaussian noise model for a state transition process. While we focus on additive Gaussian noise models in this study, the idea can be extended to other noise models, such as the Cauchy and alpha-stable noise models.

pn

arXiv [BibTex]

arXiv [BibTex]


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Assessment methodology of promising porous materials for near ambient temperature hydrogen storage applications

Minuto, F. D., Balderas-Xicohténcatl, R., Policicchio, A., Hirscher, M., Agostino, R. G.

{International Journal of Hydrogen Energy}, 43(31):14550-14556, Elsevier, Amsterdam, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


A probabilistic model for the numerical solution of initial value problems
A probabilistic model for the numerical solution of initial value problems

Schober, M., Särkkä, S., Philipp Hennig,

Statistics and Computing, Springer US, 2018 (article)

Abstract
We study connections between ordinary differential equation (ODE) solvers and probabilistic regression methods in statistics. We provide a new view of probabilistic ODE solvers as active inference agents operating on stochastic differential equation models that estimate the unknown initial value problem (IVP) solution from approximate observations of the solution derivative, as provided by the ODE dynamics. Adding to this picture, we show that several multistep methods of Nordsieck form can be recast as Kalman filtering on q-times integrated Wiener processes. Doing so provides a family of IVP solvers that return a Gaussian posterior measure, rather than a point estimate. We show that some such methods have low computational overhead, nontrivial convergence order, and that the posterior has a calibrated concentration rate. Additionally, we suggest a step size adaptation algorithm which completes the proposed method to a practically useful implementation, which we experimentally evaluate using a representative set of standard codes in the DETEST benchmark set.

pn

PDF Code DOI Project Page [BibTex]


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Incorporation of Terbium into a Microalga Leads to Magnetotactic Swimmers

Santomauro, G., Singh, A., Park, B. W., Mohammadrahimi, M., Erkoc, P., Goering, E., Schütz, G., Sitti, M., Bill, J.

Advanced Biosystems, 2(12):1800039, 2018 (article)

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[BibTex]

[BibTex]


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Thermodynamics, kinetics and selectivity of H2 and D2 on zeolite 5A below 77K

Xiong, R., Balderas-Xicohténcatl, R., Zhang, L., Li, P., Yao, Y., Sang, G., Chen, C., Tang, T., Luo, D., Hirscher, M.

{Microporous and Mesoporous Materials}, 264, pages: 22-27, Elsevier, Amsterdam, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Volumetric hydrogen storage capacity in metal-organic frameworks

Balderas-Xicohténcatl, R., Schlichtenmayer, M., Hirscher, M.

{Energy Technology}, 6(3):578-582, Wiley-VCH, Weinheim, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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3D nanoprinted plastic kinoform x-ray optics

Sanli, U. T., Ceylan, H., Bykova, I., Weigand, M., Sitti, M., Schütz, G., Keskinbora, K.

{Advanced Materials}, 30(36), Wiley-VCH, Weinheim, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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High volumetric hydrogen storage capacity using interpenetrated metal-organic frameworks

Balderas-Xicohténcatl, R., Schmieder, P., Denysenko, D., Volkmer, D., Hirscher, M.

{Energy Technology}, 6(3):510-512, Wiley-VCH, Weinheim, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Thick permalloy films for the imaging of spin texture dynamics in perpendicularly magnetized systems

Finizio, S., Wintz, S., Bracher, D., Kirk, E., Semisalova, A. S., Förster, J., Zeissler, K., We\ssels, T., Weigand, M., Lenz, K., Kleibert, A., Raabe, J.

{Physical Review B}, 98(10), American Physical Society, Woodbury, NY, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Dynamic Janus metasurfaces in the visible spectral region

Yu, P., Li, J., Zhang, S., Jin, Z., Schütz, G., Qiu, C., Hirscher, M., Liu, N.

{Nano Letters}, 18(7):4584-4589, American Chemical Society, Washington, DC, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Review of ultrafast demagnetization after femtosecond laser pulses: A complex interaction of light with quantum matter

Fähnle, M., Haag, M., Illg, C., Müller, B. Y., Weng, W., Tsatsoulis, T., Huang, H., Briones Paz, J. Z., Teeny, N., Zhang, L., Kuhn, T.

{American Journal of Modern Physics}, 7(2):68-74, Science Publishing Group, New York, NY, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Direct observation of Zhang-Li torque expansion of magnetic droplet solitons

Chung, S., Tuan Le, Q., Ahlberg, M., Awad, A. A., Weigand, M., Bykova, I., Khymyn, R., Dvornik, M., Mazraati, H., Houshang, A., Jiang, S., Nguyen, T. N. A., Goering, E., Schütz, G., Gräfe, J., \AAkerman, J.

{Physical Review Letters}, 120(21), American Physical Society, Woodbury, N.Y., 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Current-induced skyrmion generation through morphological thermal transitions in chiral ferromagnetic heterostructures

Lemesh, I., Litzius, K., Böttcher, M., Bassirian, P., Kerber, N., Heinze, D., Zázvorka, J., Büttner, F., Caretta, L., Mann, M., Weigand, M., Finizio, S., Raabe, J., Im, M., Stoll, H., Schütz, G., Dupé, B., Kläui, M., Beach, G. S. D.

{Advanced Materials}, 30(49), Wiley-VCH, Weinheim, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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3d nanofabrication of high-resolution multilayer Fresnel zone plates

Sanli, U. T., Jiao, C., Baluktsian, M., Grévent, C., Hahn, K., Wang, Y., Srot, V., Richter, G., Bykova, I., Weigand, M., Schütz, G., Keskinbora, K.

{Advanced Science}, 5(9), Wiley-VCH, Weinheim, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Photocatalytic CO2 reduction by Cr-substituted Ba2(In2-xCrx)O5\mbox⋅(H2O)δ(0.04 ≤x ≤0.60)

Yoon, S., Gaul, M., Sharma, S., Son, K., Hagemann, H., Ziegenbalg, D., Schwingenschlogl, U., Widenmeyer, M., Weidenkaff, A.

{Solid State Sciences}, 78, pages: 22-29, Elsevier Masson SAS, Paris, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Correction of axial position uncertainty and systematic detector errors in ptychographic diffraction imaging

Loetgering, L., Rose, M., Keskinbora, K., Baluktsian, M., Dogan, G., Sanli, U., Bykova, I., Weigand, M., Schütz, G., Wilhein, T.

{Optical Engineering}, 57(8), The Society, Redondo Beach, Calif., 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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The role of surface oxides on hydrogen sorption kinetics in titanium thin films

Hadjixenophontos, E., Michalek, L., Roussel, M., Hirscher, M., Schmitz, G.

{Applied Surface Science}, 441, pages: 324-330, Elsevier B.V., Amsterdam, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Ferromagnetism in nitrogen and fluorine substituted BaTiO3

Yoon, S., Son, K., Ebbinghaus, S. G., Widenmeyer, M., Weidenkaff, A.

{Journal of Alloys and Compounds}, 749, pages: 628-633, Elsevier B.V., Lausanne, Switzerland, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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New concepts for 3d optics in x-ray microscopy

Sanli, U., Ceylan, H., Jiao, C., Baluktsian, M., Grevent, C., Hahn, K., Wang, Y., Srot, V., Richter, G., Bykova, I., Weigand, M., Sitti, M., Schütz, G., Keskinbora, K.

{Microscopy and Microanalysis}, 24(Suppl 2):288-289, Cambridge University Press, New York, NY, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Spin-wave interference in magnetic vortex stacks

Behncke, C., Adolff, C. F., Lenzing, N., Hänze, M., Schulte, B., Weigand, M., Schütz, G., Meier, G.

{Communications Physics}, 1, Nature Publishing Group, London, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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High-throughput synthesis of modified Fresnel zone plate arrays via ion beam lithography

Keskinbora, K., Sanli, U. T., Baluktsian, M., Grévent, C., Weigand, M., Schütz, G.

{Beilstein Journal of Nanotechnology}, 9, pages: 2049-2056, Beilstein-Institut, Frankfurt am Main, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Deterministic creation and deletion of a single magnetic skyrmion observed by direct time-resolved X-ray microscopy

Woo, S., Song, K. M., Zhang, X., Ezawa, M., Zhou, Y., Liu, X., Weigand, M., Finizio, S., Raabe, J., Park, M.-C., Lee, K.-Y., Choi, J. W., Min, B.-C., Koo, H. C., Chang, J.

{Nature Electronics}, 1(5):288-296, Springer Nature, London, 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Magnetic skyrmion as a nonlinear resistive element: A potential building block for reservoir computing

Prychynenko, D., Sitte, M., Litzius, K., Krüger, B., Bourianoff, G., Kläui, M., Sinova, J., Everschor-Sitte, K.

{Physical Review Applied}, 9(1), American Physical Society, College Park, Md. [u.a.], 2018 (article)

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DOI [BibTex]

DOI [BibTex]


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Tunable geometrical frustration in magnoic vortex crystals

Behncke, C., Adolff, C. F., Wintz, S., Hänze, M., Schulte, B., Weigand, M., Finizio, S., Raabe, J., Meier, G.

{Scientific Reports}, 8, Nature Publishing Group, London, UK, 2018 (article)

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DOI [BibTex]

DOI [BibTex]

2017


Probabilistic Line Searches for Stochastic Optimization
Probabilistic Line Searches for Stochastic Optimization

Mahsereci, M., Hennig, P.

Journal of Machine Learning Research, 18(119):1-59, November 2017 (article)

pn

link (url) Project Page [BibTex]

2017


link (url) Project Page [BibTex]


Early Stopping Without a Validation Set
Early Stopping Without a Validation Set

Mahsereci, M., Balles, L., Lassner, C., Hennig, P.

arXiv preprint arXiv:1703.09580, 2017 (article)

Abstract
Early stopping is a widely used technique to prevent poor generalization performance when training an over-expressive model by means of gradient-based optimization. To find a good point to halt the optimizer, a common practice is to split the dataset into a training and a smaller validation set to obtain an ongoing estimate of the generalization performance. In this paper we propose a novel early stopping criterion which is based on fast-to-compute, local statistics of the computed gradients and entirely removes the need for a held-out validation set. Our experiments show that this is a viable approach in the setting of least-squares and logistic regression as well as neural networks.

ps pn

link (url) Project Page Project Page [BibTex]


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Krylov Subspace Recycling for Fast Iterative Least-Squares in Machine Learning

Roos, F. D., Hennig, P.

arXiv preprint arXiv:1706.00241, 2017 (article)

Abstract
Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time approximations, such as spectral and inducing-point methods, have been suggested and are now in wide use. These are low-rank approximations that choose the low-rank space a priori and do not refine it over time. While this allows linear cost in the data-set size, it also causes a finite, uncorrected approximation error. Authors from numerical linear algebra have explored ways to iteratively refine such low-rank approximations, at a cost of a small number of matrix-vector multiplications. This idea is particularly interesting in the many situations in machine learning where one has to solve a sequence of related symmetric positive definite linear problems. From the machine learning perspective, such deflation methods can be interpreted as transfer learning of a low-rank approximation across a time-series of numerical tasks. We study the use of such methods for our field. Our empirical results show that, on regression and classification problems of intermediate size, this approach can interpolate between low computational cost and numerical precision.

pn

link (url) Project Page [BibTex]


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Convergence Analysis of Deterministic Kernel-Based Quadrature Rules in Misspecified Settings

Kanagawa, M., Sriperumbudur, B. K., Fukumizu, K.

Arxiv e-prints, arXiv:1709.00147v1 [math.NA], 2017 (article)

Abstract
This paper presents convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less smooth than a Sobolev RKHS based on which a quadrature rule is constructed. We provide convergence guarantees based on two different assumptions on a quadrature rule: one on quadrature weights, and the other on design points. More precisely, we show that convergence rates can be derived (i) if the sum of absolute weights remains constant (or does not increase quickly), or (ii) if the minimum distance between distance design points does not decrease very quickly. As a consequence of the latter result, we derive a rate of convergence for Bayesian quadrature in misspecified settings. We reveal a condition on design points to make Bayesian quadrature robust to misspecification, and show that, under this condition, it may adaptively achieve the optimal rate of convergence in the Sobolev space of a lesser order (i.e., of the unknown smoothness of a test integrand), under a slightly stronger regularity condition on the integrand.

pn

arXiv [BibTex]

arXiv [BibTex]


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Functionalised metal-organic frameworks: a novel approach to stabilising single metal atoms

Szilágyi, P. Á., Rogers, D. M., Zaiser, I., Callini, E., Turner, S., Borgschulte, A., Züttel, A., Geerlings, H., Hirscher, M., Dam, B.

{Journal of Materials Chemistry A}, 5(30):15559-15566, Royal Society of Chemistry, Cambridge, UK, 2017 (article)

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DOI [BibTex]

DOI [BibTex]


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Exploiting diffusion barrier and chemical affinity of metal-organic frameworks for efficient hydrogen isotope separation

Kim, J. Y., Balderas-Xicohténcatl, R., Zhang, L., Kang, S. G., Hirscher, M., Oh, H., Moon, H. R.

{Journal of the American Chemical Society}, 139(42):15135-15141, American Chemical Society, Washington, DC, 2017 (article)

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DOI [BibTex]

DOI [BibTex]


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Facile fabrication of mesoporous silica micro-jets with multi-functionalities

Vilela, D., Hortelao, A. C., Balderas-Xicohténcatl, R., Hirscher, M., Hahn, K., Ma, X., Sánchez, S.

{Nanoscale}, 9(37):13990-13997, Royal Society of Chemistry, Cambridge, UK, 2017 (article)

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DOI [BibTex]

DOI [BibTex]


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Selective hydrogen isotope separation via breathing transition in MIL-53(Al)

Kim, J. Y., Zhang, L., Balderas-Xicohténcatl, R., Park, J., Hirscher, M., Moon, H. R., Oh, H.

{Journal of the American Chemical Society}, 139(49):17743-17746, American Chemical Society, Washington, DC, 2017 (article)

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DOI [BibTex]

DOI [BibTex]


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Efficient synthesis for large-scale production and characterization for hydrogen storage of ligand exchanged MOF-74/174/184-M (M\textequalsMg2+, Ni2+)

Oh, H., Maurer, S., Balderas-Xicohténcatl, R., Arnold, L., Magdysyuk, O. V., Schütz, G., Müller, U., Hirscher, M.

{International Journal of Hydrogen Energy}, 42(2):1027-1035, Elsevier, Amsterdam, 2017 (article)

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DOI [BibTex]

DOI [BibTex]