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2015


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Fabrication and X-ray testing of true kinoform lenses with high efficiencies

Keskinbora, K., Sanli, U., Grévent, C., Schütz, G.

{Proceedings of SPIE}, 9592, SPIE, Bellingham, Washington, 2015 (article)

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DOI [BibTex]

2015


DOI [BibTex]


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Signaling equilibria in sensorimotor interactions

Leibfried, F, Grau-Moya, J, Braun, DA

Cognition, 141, pages: 73-86, August 2015 (article)

Abstract
Although complex forms of communication like human language are often assumed to have evolved out of more simple forms of sensorimotor signaling, less attention has been devoted to investigate the latter. Here, we study communicative sensorimotor behavior of humans in a two-person joint motor task where each player controls one dimension of a planar motion. We designed this joint task as a game where one player (the sender) possesses private information about a hidden target the other player (the receiver) wants to know about, and where the sender's actions are costly signals that influence the receiver's control strategy. We developed a game-theoretic model within the framework of signaling games to investigate whether subjects' behavior could be adequately described by the corresponding equilibrium solutions. The model predicts both separating and pooling equilibria, in which signaling does and does not occur respectively. We observed both kinds of equilibria in subjects and found that, in line with model predictions, the propensity of signaling decreased with increasing signaling costs and decreasing uncertainty on the part of the receiver. Our study demonstrates that signaling games, which have previously been applied to economic decision-making and animal communication, provide a framework for human signaling behavior arising during sensorimotor interactions in continuous and dynamic environments.

ei

DOI [BibTex]

DOI [BibTex]


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Focused ion beam micromachining enables novel optics for X-ray microscopy

Keskinbora, K., Sanli, U., Grévent, C., Hirscher, M., Schütz, G.

{Microscopy and Microanalysis}, 21(Suppl 3):1983-1984, Springer-Verlag New York, New York, NY, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Selectable nanopattern arrays for nanolithographic imprint and etch-mask applications

Jeong, H., Mark, A. G., Lee, T., Son, K., Chen, W., Alarcón-Correa, M., Kim, I., Schütz, G., Fischer, P.

{Advanced Science}, 2(2), Wiley-VCH, Weinheim, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Grain boundaries as a source of ferromagnetism and increased solubility of Ni in nanograined ZnO

Straumal, B. B., Mazilkin, A. A., Protasova, S. G., Stakhanova, S. V., Straumal, P. B., Bulatov, M. F., Schütz, G., Tietze, T., Goering, E., Baretzky, B.

{Reviews on Advanced Materials Science}, 41, pages: 61-71, 2015 (article)

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[BibTex]

[BibTex]


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Gyrational modes of benzenelike magnetic vortex molecules

Adolff, C. F., Hänze, M., Pues, M., Weigand, M., Meier, G.

{Physical Review B}, 92(2), American Physical Society, Woodbury, NY, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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"Job-Sharing" storage of hydrogen in Ru/Li2O nanocomposites

Fu, L., Tang, K., Oh, H., Kandavel, M., Bräuniger, T., Vinod Chandran, C., Menzel, A., Hirscher, M., Samuelis, D., Maier, J.

{Nano Letters}, 15(6):4170-4175, American Chemical Society, Washington, DC, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Overview of the multilayer-Fresnel zone plate and the kinoform lens development at MPI for Intelligent Systems

Sanli, U., Keskinbora, K., Grévent, C., Schütz, G.

{Proceedings of SPIE}, 9510, SPIE, Bellingham, Washington, 2015 (article)

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DOI [BibTex]


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Transition matrix elements for electron-phonon scattering: Phenomenological theory and ab initio electron theory

Illg, C., Haag, M., Müller, B. Y., Czycholl, G., Fähnle, M.

{Physical Review B}, 92(19), American Physical Society, Woodbury, NY, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Phase evolution in single-crystalline LiFePO4 followed by in situ scanning X-ray microscopy of a micrometre-sized battery

Ohmer, N., Fenk, B., Samuelis, D., Chen, C., Maier, J., Weigand, M., Goering, E., Schütz, G.

{Nature Communications}, 6, Nature Publishing Group, London, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Nitrogen-rich covalent triazine frameworks as high-performance platforms for selective carbon capture and storage

Hug, S., Stegbauer, L., Oh, H., Hirscher, M., Lotsch, B. V.

{Chemistry of Materials}, 27(23):8001-8010, American Chemical Society, Washington, D.C., 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Novel plasticity rule can explain the development of sensorimotor intelligence

Der, R., Martius, G.

Proceedings of the National Academy of Sciences, 112(45):E6224-E6232, 2015 (article)

Abstract
Grounding autonomous behavior in the nervous system is a fundamental challenge for neuroscience. In particular, self-organized behavioral development provides more questions than answers. Are there special functional units for curiosity, motivation, and creativity? This paper argues that these features can be grounded in synaptic plasticity itself, without requiring any higher-level constructs. We propose differential extrinsic plasticity (DEP) as a new synaptic rule for self-learning systems and apply it to a number of complex robotic systems as a test case. Without specifying any purpose or goal, seemingly purposeful and adaptive rhythmic behavior is developed, displaying a certain level of sensorimotor intelligence. These surprising results require no system-specific modifications of the DEP rule. They rather arise from the underlying mechanism of spontaneous symmetry breaking, which is due to the tight brain body environment coupling. The new synaptic rule is biologically plausible and would be an interesting target for neurobiological investigation. We also argue that this neuronal mechanism may have been a catalyst in natural evolution.

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link (url) DOI Project Page [BibTex]

link (url) DOI Project Page [BibTex]


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Multilayer Fresnel zone plates for X-ray microscopy

Sanli, U. T., Keskinbora, K., Grévent, C., Szeghalmi, A., Knez, M., Schütz, G.

{Microscopy and Microanalysis}, 21(Suppl 3):1987-1988, Springer-Verlag New York, New York, NY, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Interfacial dominated ferromagnetism in nanograined ZnO: a \muSR and DFT study

Tietze, T., Audehm, P., Chen, Y., Schütz, G., Straumal, B. B., Protasova, S. G., Mazilkin, A. A., Straumal, P. B., Prokscha, T., Luetkens, H., Salman, Z., Suter, A., Baretzky, B., Fink, K., Wenzel, W., Danilov, D., Goering, E.

{Scientific Reports}, 5, pages: 8871-8876, Nature Publishing Group, London, UK, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Preparation of a ferromagnetic barrier in YBa2Cu3O7-delta thinner than the coherence length

Soltan, S., Albrecht, J., Goering, E., Schütz, G., Mustafa, L., Keimer, B., Habermeier, H.

{Journal of Applied Physics}, 118(22), AIP Publishing, New York, NY, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Microanalytical methods for in-situ high-resolution analysis of rock varnish at the micrometer to nanometer scale

Macholdt, D. S., Jochum, K. P., Pöhlker, C., Stoll, B., Weis, U., Weber, B., Müller, M., Kapl, M., Buhre, S., Kilcoyne, A. L. D., Weigand, M., Scholz, D., Al-Amri, A. M., Andreae, M. O.

{Chemical Geology}, 411, pages: 57-68, Elsevier, Amsterdam, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Chemical composition, microstructure, and hygroscopic properties of aerosol particles at the Zotino Tall Tower Observatory (ZOTTO), Siberia, during a summer campaign

Mikhailov, E. F., Mironov, G. N., Pöhlker, C., Chi, X., Krüger, M., Shiraiwa, M., Förster, J., Pöschl, U., Vlasenko, S. S., Ryshkevich, T. I., Weigand, M., Kilcoyne, A. L. D., Andreae, M.

{Atmospheric Chemistry and Physics}, 15(15):8847-8869, European Geosciences Union, Katlenburg-Lindau, Germany, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Orbital reflectometry of PrNiO3/PrAlO3 superlattices

Wu, M., Benckiser, E., Audehm, P., Goering, E., Wochner, P., Christiani, G., Logvenov, G., Habermeier, H., Keimer, B.

{Physical Review B}, 91(19), American Physical Society, Woodbury, NY, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Dynamic domain wall chirality rectification by rotating magnetic fields

Bisig, A., Mawass, M., Stärk, M., Moutafis, C., Rhensius, J., Heidler, J., Gliga, S., Weigand, M., Tyliszczak, T., Van Waeyenberge, B., Stoll, H., Schütz, G., Kläui, M.

{Applied Physics Letters}, 106(12), American Institute of Physics, Melville, NY, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Imaging spin dynamics on the nanoscale using X-ray microscopy

Stoll, H., Noske, M., Weigand, M., Richter, K., Krüger, B., Reeve, R. M., Hänze, M., Adolff, C. F., Stein, F., Meier, G., Kläui, M., Schütz, G.

{Frontiers in Physics}, 3, Frontiers Media, Lausanne, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Structure Learning in Bayesian Sensorimotor Integration

Genewein, T, Hez, E, Razzaghpanah, Z, Braun, DA

PLoS Computational Biology, 11(8):1-27, August 2015 (article)

Abstract
Previous studies have shown that sensorimotor processing can often be described by Bayesian learning, in particular the integration of prior and feedback information depending on its degree of reliability. Here we test the hypothesis that the integration process itself can be tuned to the statistical structure of the environment. We exposed human participants to a reaching task in a three-dimensional virtual reality environment where we could displace the visual feedback of their hand position in a two dimensional plane. When introducing statistical structure between the two dimensions of the displacement, we found that over the course of several days participants adapted their feedback integration process in order to exploit this structure for performance improvement. In control experiments we found that this adaptation process critically depended on performance feedback and could not be induced by verbal instructions. Our results suggest that structural learning is an important meta-learning component of Bayesian sensorimotor integration.

ei

DOI [BibTex]

DOI [BibTex]


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Unique high-temperature performance of highly consensed MnBi permanent magnets

Chen, Y., Gregori, G., Leineweber, A., Qu, F., Chen, C., Tietze, T., Kronmüller, H., Schütz, G., Goering, E.

{Scripta Materialia}, 107, pages: 131-135, Pergamon, Tarrytown, NY, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Quantifying Emergent Behavior of Autonomous Robots

Martius, G., Olbrich, E.

Entropy, 17(10):7266, 2015 (article)

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Electrical determination of vortex state in submicron magnetic elements

Gangwar, A., Bauer, H. G., Chauleau, J., Noske, M., Weigand, M., Stoll, H., Schütz, G., Back, C. H.

{Physical Review B}, 91(9), American Physical Society, Woodbury, NY, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Mechanisms for the symmetric and antisymmetric switching of a magnetic vortex core: Differences and common aspects

Noske, M., Stoll, H., Fähnle, M., Hertel, R., Schütz, G.

{Physical Review B}, 91(1), American Physical Society, Woodbury, NY, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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High resolution, high efficiency mulitlayer Fresnel zone plates for soft and hard X-rays

Sanli, U., Keskinbora, K., Gregorczyk, K., Leister, J., Teeny, N., Grévent, C., Knez, M., Schütz, G.

{Proceedings of SPIE}, 9592, SPIE, Bellingham, Washington, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Macroscopic drift current in the inverse Faraday effect

Hertel, R., Fähnle, M.

{Physical Review B}, 91(2), American Physical Society, Woodbury, NY, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Single-step 3D nanofabrication of kinoform optics via gray-scale focused ion beam lithography for efficient X-ray focusing

Keskinbora, K., Grévent, C., Hirscher, M., Weigand, M., Schütz, G.

{Advanced Optical Materials}, 3, pages: 792-800, WILEY-VCH Verlag GmbH Co. KGaA, Weinheim, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Band structure engineering of two-dimensional magnonic vortex crystals

Behncke, C., Hänze, M., Adolff, C. F., Weigand, M., Meier, G.

{Physical Review B}, 91(22), American Physical Society, Woodbury, NY, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Towards denoising XMCD movies of fast magnetization dynamics using extended Kalman filter

Kopp, M., Harmeling, S., Schütz, G., Schölkopf, B., Fähnle, M.

{Ultramicroscopy}, 148, pages: 115-122, North-Holland, Amsterdam, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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A Reward-Maximizing Spiking Neuron as a Bounded Rational Decision Maker

Leibfried, F, Braun, DA

Neural Computation, 27(8):1686-1720, July 2015 (article)

Abstract
Rate distortion theory describes how to communicate relevant information most efficiently over a channel with limited capacity. One of the many applications of rate distortion theory is bounded rational decision making, where decision makers are modeled as information channels that transform sensory input into motor output under the constraint that their channel capacity is limited. Such a bounded rational decision maker can be thought to optimize an objective function that trades off the decision maker's utility or cumulative reward against the information processing cost measured by the mutual information between sensory input and motor output. In this study, we interpret a spiking neuron as a bounded rational decision maker that aims to maximize its expected reward under the computational constraint that the mutual information between the neuron's input and output is upper bounded. This abstract computational constraint translates into a penalization of the deviation between the neuron's instantaneous and average firing behavior. We derive a synaptic weight update rule for such a rate distortion optimizing neuron and show in simulations that the neuron efficiently extracts reward-relevant information from the input by trading off its synaptic strengths against the collected reward.

ei

DOI [BibTex]

DOI [BibTex]


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Magnetic moments induce strong phonon renormalization in FeSi

Krannich, S., Sidis, Y., Lamago, D., Heid, R., Mignot, J., von Löhneysen, H., Ivanov, A., Steffens, P., Keller, T., Wang, L., Goering, E., Weber, F.

{Nature Communications}, 6, Nature Publishing Group, London, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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What is epistemic value in free energy models of learning and acting? A bounded rationality perspective

Ortega, PA, Braun, DA

Cognitive Neuroscience, 6(4):215-216, December 2015 (article)

Abstract
Free energy models of learning and acting do not only care about utility or extrinsic value, but also about intrinsic value, that is, the information value stemming from probability distributions that represent beliefs or strategies. While these intrinsic values can be interpreted as epistemic values or exploration bonuses under certain conditions, the framework of bounded rationality offers a complementary interpretation in terms of information-processing costs that we discuss here.

ei

DOI [BibTex]

DOI [BibTex]


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Perpendicular magnetisation from in-plane fields in nano-scaled antidot lattices

Gräfe, J., Haering, F., Tietze, T., Audehm, P., Weigand, M., Wiedwald, U., Ziemann, P., Gawronski, P., Schütz, G., Goering, E. J.

{Nanotechnology}, 26(22), IOP Pub., Bristol, UK, 2015 (article)

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DOI Project Page [BibTex]

DOI Project Page [BibTex]


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Theory of ultrafast demagnetization after femtosecond laser pulses

Fähnle, M., Illg, C., Haag, M., Teeny, N.

{Acta Physica Polonica A}, 127(2):170-175, Państwowe Wydawnictwo Naukowe, Warszawa, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Non-linear radial spinwave modes in thin magnetic disks

Helsen, M., Gangwar, Ajay, De Clercq, J., Vansteenkiste, A., Weigand, M., Back, C. H., Van Waeyenberge, B.

{Applied Physics Letters}, 106(3), American Institute of Physics, Melville, NY, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Hydrogen isotope separation in metal-organic frameworks: Kinetic or chemical affinity quantum-sieving?

Savchenko, I., Mavrandonakis, A., Heine, T., Oh, H., Teufel, J., Hirscher, M.

{Microporous and Mesoporous Materials}, 216, pages: 133-137, Elsevier, Amsterdam, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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High-resolution dichroic imaging of magnetic flux distributions in superconductors with scanning x-ray microscopy

Ruoß, S., Stahl, C., Weigand, M., Schütz, G., Albrecht, J.

{Applied Physics Letters}, 106, American Institute of Physics, Melville, NY, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Preparation and characterisation of epitaxial Pt/Cu/FeMn/Co thin films on (100)-oriented MgO single crystals

Schmidt, M., Gräfe, J., Audehm, P., Phillipp, F., Schütz, G., Goering, E.

{Physica Status Solidi A}, 212(10):2114-2123, Wiley-VCH, Weinheim, 2015 (article)

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DOI [BibTex]

DOI [BibTex]


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Probing the magnetic moments of [MnIII6CrIII]3+ single-molecule magnets - A cross comparison of XMCD and spin-resolved electron spectroscopy

Helmstedt, A., Dohmeier, N., Müller, N., Gryzia, A., Brechling, A., Heinzmann, U., Hoeke, V., Krickemeyer, E., Glaser, T., Leicht, P., Fonin, M., Tietze, T., Joly, L., Kuepper, K.

{Journal of Electron Spectroscopy and Related Phenomena}, 198, pages: 12-19, Elsevier B.V., Amsterdam, 2015 (article)

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DOI [BibTex]

DOI [BibTex]

2003


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Texture and haptic cues in slant discrimination: Measuring the effect of texture type on cue combination

Rosas, P., Wichmann, F., Ernst, M., Wagemans, J.

Journal of Vision, 3(12):26, 2003 Fall Vision Meeting of the Optical Society of America, December 2003 (poster)

Abstract
In a number of models of depth cue combination the depth percept is constructed via a weighted average combination of independent depth estimations. The influence of each cue in such average depends on the reliability of the source of information. (Young, Landy, & Maloney, 1993; Ernst & Banks, 2002.) In particular, Ernst & Banks (2002) formulate the combination performed by the human brain as that of the minimum variance unbiased estimator that can be constructed from the available cues. Using slant discrimination and slant judgment via probe adjustment as tasks, we have observed systematic differences in performance of human observers when a number of different types of textures were used as cue to slant (Rosas, Wichmann & Wagemans, 2003). If the depth percept behaves as described above, our measurements of the slopes of the psychometric functions provide the predicted weights for the texture cue for the ranked texture types. We have combined these texture types with object motion but the obtained results are difficult to reconcile with the unbiased minimum variance estimator model (Rosas & Wagemans, 2003). This apparent failure of such model might be explained by the existence of a coupling of texture and motion, violating the assumption of independence of cues. Hillis, Ernst, Banks, & Landy (2002) have shown that while for between-modality combination the human visual system has access to the single-cue information, for within-modality combination (visual cues: disparity and texture) the single-cue information is lost, suggesting a coupling between these cues. Then, in the present study we combine the different texture types with haptic information in a slant discrimination task, to test whether in the between-modality condition the texture cue and the haptic cue to slant are combined as predicted by an unbiased, minimum variance estimator model.

ei

Web DOI [BibTex]

2003


Web DOI [BibTex]


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Concentration Inequalities for Sub-Additive Functions Using the Entropy Method

Bousquet, O.

Stochastic Inequalities and Applications, 56, pages: 213-247, Progress in Probability, (Editors: Giné, E., C. Houdré and D. Nualart), November 2003 (article)

Abstract
We obtain exponential concentration inequalities for sub-additive functions of independent random variables under weak conditions on the increments of those functions, like the existence of exponential moments for these increments. As a consequence of these general inequalities, we obtain refinements of Talagrand's inequality for empirical processes and new bounds for randomized empirical processes. These results are obtained by further developing the entropy method introduced by Ledoux.

ei

PostScript [BibTex]

PostScript [BibTex]


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Statistical Learning Theory, Capacity and Complexity

Schölkopf, B.

Complexity, 8(4):87-94, July 2003 (article)

Abstract
We give an exposition of the ideas of statistical learning theory, followed by a discussion of how a reinterpretation of the insights of learning theory could potentially also benefit our understanding of a certain notion of complexity.

ei

Web DOI [BibTex]


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Dealing with large Diagonals in Kernel Matrices

Weston, J., Schölkopf, B., Eskin, E., Leslie, C., Noble, W.

Annals of the Institute of Statistical Mathematics, 55(2):391-408, June 2003 (article)

Abstract
In kernel methods, all the information about the training data is contained in the Gram matrix. If this matrix has large diagonal values, which arises for many types of kernels, then kernel methods do not perform well: We propose and test several methods for dealing with this problem by reducing the dynamic range of the matrix while preserving the positive definiteness of the Hessian of the quadratic programming problem that one has to solve when training a Support Vector Machine, which is a common kernel approach for pattern recognition.

ei

PDF DOI [BibTex]

PDF DOI [BibTex]


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The em Algorithm for Kernel Matrix Completion with Auxiliary Data

Tsuda, K., Akaho, S., Asai, K.

Journal of Machine Learning Research, 4, pages: 67-81, May 2003 (article)

ei

PDF [BibTex]

PDF [BibTex]


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Constructing Descriptive and Discriminative Non-linear Features: Rayleigh Coefficients in Kernel Feature Spaces

Mika, S., Rätsch, G., Weston, J., Schölkopf, B., Smola, A., Müller, K.

IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(5):623-628, May 2003 (article)

Abstract
We incorporate prior knowledge to construct nonlinear algorithms for invariant feature extraction and discrimination. Employing a unified framework in terms of a nonlinearized variant of the Rayleigh coefficient, we propose nonlinear generalizations of Fisher‘s discriminant and oriented PCA using support vector kernel functions. Extensive simulations show the utility of our approach.

ei

DOI [BibTex]

DOI [BibTex]


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Tractable Inference for Probabilistic Data Models

Csato, L., Opper, M., Winther, O.

Complexity, 8(4):64-68, April 2003 (article)

Abstract
We present an approximation technique for probabilistic data models with a large number of hidden variables, based on ideas from statistical physics. We give examples for two nontrivial applications. © 2003 Wiley Periodicals, Inc.

ei

PDF GZIP Web [BibTex]

PDF GZIP Web [BibTex]


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Feature selection and transduction for prediction of molecular bioactivity for drug design

Weston, J., Perez-Cruz, F., Bousquet, O., Chapelle, O., Elisseeff, A., Schölkopf, B.

Bioinformatics, 19(6):764-771, April 2003 (article)

Abstract
Motivation: In drug discovery a key task is to identify characteristics that separate active (binding) compounds from inactive (non-binding) ones. An automated prediction system can help reduce resources necessary to carry out this task. Results: Two methods for prediction of molecular bioactivity for drug design are introduced and shown to perform well in a data set previously studied as part of the KDD (Knowledge Discovery and Data Mining) Cup 2001. The data is characterized by very few positive examples, a very large number of features (describing three-dimensional properties of the molecules) and rather different distributions between training and test data. Two techniques are introduced specifically to tackle these problems: a feature selection method for unbalanced data and a classifier which adapts to the distribution of the the unlabeled test data (a so-called transductive method). We show both techniques improve identification performance and in conjunction provide an improvement over using only one of the techniques. Our results suggest the importance of taking into account the characteristics in this data which may also be relevant in other problems of a similar type.

ei

Web [BibTex]


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Use of the Zero-Norm with Linear Models and Kernel Methods

Weston, J., Elisseeff, A., Schölkopf, B., Tipping, M.

Journal of Machine Learning Research, 3, pages: 1439-1461, March 2003 (article)

Abstract
We explore the use of the so-called zero-norm of the parameters of linear models in learning. Minimization of such a quantity has many uses in a machine learning context: for variable or feature selection, minimizing training error and ensuring sparsity in solutions. We derive a simple but practical method for achieving these goals and discuss its relationship to existing techniques of minimizing the zero-norm. The method boils down to implementing a simple modification of vanilla SVM, namely via an iterative multiplicative rescaling of the training data. Applications we investigate which aid our discussion include variable and feature selection on biological microarray data, and multicategory classification.

ei

PDF PostScript PDF [BibTex]

PDF PostScript PDF [BibTex]