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2011


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Learning, planning, and control for quadruped locomotion over challenging terrain

Kalakrishnan, Mrinal, Buchli, Jonas, Pastor, Peter, Mistry, Michael, Schaal, S.

International Journal of Robotics Research, 30(2):236-258, February 2011 (article)

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[BibTex]

2011


[BibTex]


Quantum-Cascade Laser-Based Vibrational Circular Dichroism
Quantum-Cascade Laser-Based Vibrational Circular Dichroism

Luedeke, S., Pfeifer, M., Fischer, P.

JOURNAL OF THE AMERICAN CHEMICAL SOCIETY, 133(15):5704-5707, 2011 (article)

Abstract
Vibrational circular dichroism (VCD) spectra were recorded with a tunable external-cavity quantum-cascade laser (QCL). In comparison with standard thermal light sources in the IR, QCLs provide orders of magnitude more power and are therefore promising for VCD studies in strongly absorbing solvents. The brightness of this novel light source is demonstrated with VCD and IR absorption measurements of a number of compounds, including proline in water.

pf

DOI [BibTex]

DOI [BibTex]


Actively coupled cavity ringdown spectroscopy with low-power broadband sources
Actively coupled cavity ringdown spectroscopy with low-power broadband sources

Petermann, C., Fischer, P.

OPTICS EXPRESS, 19(11):10164-10173, 2011 (article)

Abstract
We demonstrate a coupling scheme for cavity enhanced absorption spectroscopy that makes use of an intracavity acousto-optical modulator to actively switch light into (and out of) a resonator. This allows cavity ringdown spectroscopy (CRDS) to be implemented with broadband nonlaser light sources with spectral power densities of less than 30 mu W/nm. Although the acousto-optical element reduces the ultimate detection limit by introducing additional losses, it permits absorptivities to be measured with a high dynamic range, especially in lossy environments. Absorption measurements for the forbidden transition of gaseous oxygen in air at similar to 760nm are presented using a low-coherence cw-superluminescent diode. The same setup was electronically configured to cover absorption losses from 1.8 x 10(-8)cm(-1) to 7.5\% per roundtrip. This could be of interest in process analytical applications. (C) 2011 Optical Society of America

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DOI [BibTex]

DOI [BibTex]


Magnetically actuated propulsion at low Reynolds numbers: towards nanoscale control
Magnetically actuated propulsion at low Reynolds numbers: towards nanoscale control

Fischer, P., Ghosh, A.

NANOSCALE, 3(2):557-563, 2011 (article)

Abstract
Significant progress has been made in the fabrication of micron and sub-micron structures whose motion can be controlled in liquids under ambient conditions. The aim of many of these engineering endeavors is to be able to build and propel an artificial micro-structure that rivals the versatility of biological swimmers of similar size, e. g. motile bacterial cells. Applications for such artificial ``micro-bots'' are envisioned to range from microrheology to targeted drug delivery and microsurgery, and require full motion-control under ambient conditions. In this Mini-Review we discuss the construction, actuation, and operation of several devices that have recently been reported, especially systems that can be controlled by and propelled with homogenous magnetic fields. We describe the fabrication and associated experimental challenges and discuss potential applications.

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Video - Nanospropellers DOI [BibTex]


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Bayesian robot system identification with input and output noise

Ting, J., D’Souza, A., Schaal, S.

Neural Networks, 24(1):99-108, 2011, clmc (article)

Abstract
For complex robots such as humanoids, model-based control is highly beneficial for accurate tracking while keeping negative feedback gains low for compliance. However, in such multi degree-of-freedom lightweight systems, conventional identification of rigid body dynamics models using CAD data and actuator models is inaccurate due to unknown nonlinear robot dynamic effects. An alternative method is data-driven parameter estimation, but significant noise in measured and inferred variables affects it adversely. Moreover, standard estimation procedures may give physically inconsistent results due to unmodeled nonlinearities or insufficiently rich data. This paper addresses these problems, proposing a Bayesian system identification technique for linear or piecewise linear systems. Inspired by Factor Analysis regression, we develop a computationally efficient variational Bayesian regression algorithm that is robust to ill-conditioned data, automatically detects relevant features, and identifies input and output noise. We evaluate our approach on rigid body parameter estimation for various robotic systems, achieving an error of up to three times lower than other state-of-the-art machine learning methods

am

link (url) [BibTex]

link (url) [BibTex]


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Learning variable impedance control

Buchli, J., Stulp, F., Theodorou, E., Schaal, S.

International Journal of Robotics Research, 2011, clmc (article)

Abstract
One of the hallmarks of the performance, versatility, and robustness of biological motor control is the ability to adapt the impedance of the overall biomechanical system to different task requirements and stochastic disturbances. A transfer of this principle to robotics is desirable, for instance to enable robots to work robustly and safely in everyday human environments. It is, however, not trivial to derive variable impedance controllers for practical high degree-of-freedom (DOF) robotic tasks. In this contribution, we accomplish such variable impedance control with the reinforcement learning (RL) algorithm PISq ({f P}olicy {f I}mprovement with {f P}ath {f I}ntegrals). PISq is a model-free, sampling based learning method derived from first principles of stochastic optimal control. The PISq algorithm requires no tuning of algorithmic parameters besides the exploration noise. The designer can thus fully focus on cost function design to specify the task. From the viewpoint of robotics, a particular useful property of PISq is that it can scale to problems of many DOFs, so that reinforcement learning on real robotic systems becomes feasible. We sketch the PISq algorithm and its theoretical properties, and how it is applied to gain scheduling for variable impedance control. We evaluate our approach by presenting results on several simulated and real robots. We consider tasks involving accurate tracking through via-points, and manipulation tasks requiring physical contact with the environment. In these tasks, the optimal strategy requires both tuning of a reference trajectory emph{and} the impedance of the end-effector. The results show that we can use path integral based reinforcement learning not only for planning but also to derive variable gain feedback controllers in realistic scenarios. Thus, the power of variable impedance control is made available to a wide variety of robotic systems and practical applications.

am

link (url) [BibTex]

link (url) [BibTex]


Weak value amplified optical activity measurements
Weak value amplified optical activity measurements

Pfeifer, M., Fischer, P.

Opt. Express, 19(17):16508-16517, OSA, 2011 (article)

Abstract
We present a new form of optical activity measurement based on a modified weak value amplification scheme. It has recently been shown experimentally that the left- and right-circular polarization components refract with slightly different angles of refraction at a chiral interface causing a linearly polarized light beam to split into two. By introducing a polarization modulation that does not give rise to a change in the optical rotation it is possible to differentiate between the two circular polarization components even after post-selection with a linear polarizer. We show that such a modified weak value amplification measurement permits the sign of the splitting and thus the handedness of the optically active medium to be determined. Angular beam separations of Δθ ∼ 1 nanoradian, which corresponds to a circular birefringence of Δn ∼ 1 × 10−9, could be measured with a relative error of less than 1%.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Understanding haptics by evolving mechatronic systems

Loeb, G. E., Tsianos, G.A., Fishel, J.A., Wettels, N., Schaal, S.

Progress in Brain Research, 192, pages: 129, 2011 (article)

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[BibTex]

[BibTex]

2006


Chiral molecules split light: Reflection and refraction in a chiral liquid
Chiral molecules split light: Reflection and refraction in a chiral liquid

Ghosh, A., Fischer, P.

PHYSICAL REVIEW LETTERS, 97(17), 2006, Featured highlight ‘Fundamental optical physics: Refraction’ Nature Photonics, Nov. 2006. (article)

Abstract
A light beam changes direction as it enters a liquid at an angle from another medium, such as air. Should the liquid contain molecules that lack mirror symmetry, then it has been predicted by Fresnel that the light beam will not only change direction, but will actually split into two separate beams with a small difference in the respective angles of refraction. Here we report the observation of this phenomenon. We also demonstrate that the angle of reflection does not equal the angle of incidence in a chiral medium. Unlike conventional optical rotation, which depends on the path-length through the sample, the reported reflection and refraction phenomena arise within a few wavelengths at the interface and thereby suggest a new approach to polarimetry that can be used in microfluidic volumes.

Featured highlight ‘Fundamental optical physics: Refraction’ Nature Photonics, Nov. 2006.

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DOI [BibTex]

2006


DOI [BibTex]


Direct chiral discrimination in NMR spectroscopy
Direct chiral discrimination in NMR spectroscopy

Buckingham, A., Fischer, P.

CHEMICAL PHYSICS, 324(1):111-116, 2006 (article)

Abstract
Conventional nuclear magnetic resonance spectroscopy is unable to distinguish between the two mirror-image forms (enantiomers) of a chiral molecule. This is because the NMR spectrum is determined by the chemical shifts and spin-spin coupling constants which - in the absence of a chiral solvent - are identical for the two enantiomers. We discuss how chirality may nevertheless be directly detected in liquid-state NMR spectroscopy: In a chiral molecule, the rotating nuclear magnetic moment induces an electric dipole moment in the direction perpendicular to itself and to the permanent magnetic field of the spectrometer. We present computations of the precessing electric polarization following a pi/2 pulse. Our estimates indicate that the electric polarization should be detectable in favourable cases. We also predict that application of an electrostatic field induces a chirally sensitive magnetization oscillating in the direction of the permanent magnetic field. We show that the electric-field-perturbed chemical shift tensor, the nuclear magnetic shielding polarizability, underlies these chiral NMR effects. (c) 2005 Elsevier B.V. All rights reserved.

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DOI [BibTex]

DOI [BibTex]


NONLINEAR OPTICAL PROPERTIES OF CHIRAL LIQUIDS Electric-dipolar pseudoscalars in nonlinear optics
NONLINEAR OPTICAL PROPERTIES OF CHIRAL LIQUIDS Electric-dipolar pseudoscalars in nonlinear optics

Fischer, P., Champagne, B.

In NON-LINEAR OPTICAL PROPERTIES OF MATTER: FROM MOLECULES TO CONDENSED PHASES, 1, pages: 359-381, Challenges and Advances in Computational Chemistry and Physics, 2006 (incollection)

Abstract
We give all overview of linear and nonlinear optical processes that can be specific to chiral molecules in isotropic media. Specifically, we discuss the pseudoscalars that underlie nonlinear optical activity and chiral frequency conversion processes in fluids. We show that nonlinear optical techniques open entirely new ways of exploring chirality: Sum-frequency-generation (SFG) at second-order and BioCARS at fourth-order arise in the electric-dipole approximation and do not require circularly polarized light to detect chiral molecules in solution. Here the frequency conversion in itself is a measure of chirality. This is in contrast to natural optical activity phenomena which are based on the interference of radiation from induced oscillating electric and magnetic dipoles, and which are observed as a differential response to right and left circularly polarized light. We give examples from our SFG experiments in optically active solutions and show how the application of an additional static electric field to sum-frequency generation allows the absolute configuration of the chiral solute to be determined via all electric-dipolar process. Results from ab initio calculations of the SFG pseudoscalar are presented for a number of chiral molecules

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[BibTex]

[BibTex]


Ring-resonator-based frequency-domain optical activity measurements of a chiral liquid
Ring-resonator-based frequency-domain optical activity measurements of a chiral liquid

Vollmer, F., Fischer, P.

OPTICS LETTERS, 31(4):453-455, 2006 (article)

Abstract
Chiral liquids rotate the plane of polarization of linearly polarized light and are therefore optically active. Here we show that optical rotation can be observed in the frequency domain. A chiral liquid introduced in a fiber-loop ring resonator that supports left and right circularly polarized modes gives rise to relative frequency shifts that are a direct measure of the liquid's circular birefringence and hence of its optical activity. The effect is in principle not diminished if the circumference of the ring is reduced. The technique is similarly applicable to refractive index and linear birefringence measurements. (c) 2006 Optical Society of America.

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DOI [BibTex]


Sign of the refractive index in a gain medium with negative permittivity and permeability
Sign of the refractive index in a gain medium with negative permittivity and permeability

Chen, Y., Fischer, P., Wise, F.

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS, 23(1):45-50, 2006 (article)

Abstract
We show how the sign of the refractive index in any medium may be derived using a rigorous analysis based on Einstein causality. In particular, we consider left-handed materials, i.e., media that have negative permittivities and permeabilities at the frequency of interest. We find that the consideration of gain in such media can give rise to a positive refractive index. (c) 2006 Optical Society of America.

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DOI [BibTex]

DOI [BibTex]


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Approximate nearest neighbor regression in very high dimensions

Vijayakumar, S., DSouza, A., Schaal, S.

In Nearest-Neighbor Methods in Learning and Vision, pages: 103-142, (Editors: Shakhnarovich, G.;Darrell, T.;Indyk, P.), Cambridge, MA: MIT Press, 2006, clmc (inbook)

am

link (url) [BibTex]

link (url) [BibTex]

2000


Phenomenological damping in optical response tensors
Phenomenological damping in optical response tensors

Buckingham, A., Fischer, P.

PHYSICAL REVIEW A, 61(3), 2000 (article)

Abstract
Although perturbation theory applied to the optical response of a molecule or material system is only strictly valid far from resonances, it is often applied to ``near-resonance{''} conditions by means of complex energies incorporating damping. Inconsistent signs of the damping in optical response tensors have appeared in the recent literature, as have errors in the treatment of the perturbation by a static held. The ``equal-sign{''} convention used in a recent publication yields an unphysical material response, and Koroteev's intimation that linear electro-optical circular dichroism may exist in an optically active liquid under resonance conditions is also flawed. We show that the isotropic part of the Pockels tensor vanishes.

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DOI [BibTex]

2000


DOI [BibTex]


Ab initio investigation of the sum-frequency hyperpolarizability of small chiral molecules
Ab initio investigation of the sum-frequency hyperpolarizability of small chiral molecules

Champagne, B., Fischer, P., Buckingham, A.

CHEMICAL PHYSICS LETTERS, 331(1):83-88, 2000 (article)

Abstract
Using a sum-over-states procedure based on configuration interaction singles /6-311++G{*}{*}, we have computed the sum-frequency hyperpolarizability beta (ijk)(-3 omega; 2 omega, omega) Of two small chiral molecules, R-monofluoro-oxirane and R-(+)-propylene oxide. Excitation energies were scaled to fit experimental UV-absorption data and checked with ab initio values from time-dependent density functional theory. The isotropic part of the computed hyperpolarizabilities, beta(-3 omega; 2 omega, omega), is much smaller than that reported previously from sum-frequency generation experiments on aqueous solutions of arabinose. Comparison is made with a single-centre chiral model. (C) 2000 Elsevier Science B.V. All rights reserved.

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DOI [BibTex]

DOI [BibTex]


Three-wave mixing in chiral liquids
Three-wave mixing in chiral liquids

Fischer, P., Wiersma, D., Righini, R., Champagne, B., Buckingham, A.

PHYSICAL REVIEW LETTERS, 85(20):4253-4256, 2000 (article)

Abstract
Second-order nonlinear optical frequency conversion in isotropic systems is only dipole allowed for sum- and difference-frequency generation in chiral media. We develop a single-center chiral model of the three-wave mixing (sum:frequency generation) nonlinearity and estimate its magnitude. We also report results from ab initio calculations and from three- and four-wave mixing experiments in support of the theoretical estimates. We show that the second-order susceptibility in chiral liquids is much smaller than previously thought.

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DOI [BibTex]

DOI [BibTex]


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A brachiating robot controller

Nakanishi, J., Fukuda, T., Koditschek, D. E.

IEEE Transactions on Robotics and Automation, 16(2):109-123, 2000, clmc (article)

Abstract
We report on our empirical studies of a new controller for a two-link brachiating robot. Motivated by the pendulum-like motion of an apeâ??s brachiation, we encode this task as the output of a â??target dynamical system.â? Numerical simulations indicate that the resulting controller solves a number of brachiation problems that we term the â??ladder,â? â??swing-up,â? and â??ropeâ? problems. Preliminary analysis provides some explanation for this success. The proposed controller is implemented on a physical system in our laboratory. The robot achieves behaviors including â??swing locomotionâ? and â??swing upâ? and is capable of continuous locomotion over several rungs of a ladder. We discuss a number of formal questions whose answers will be required to gain a full understanding of the strengths and weaknesses of this approach.

am

link (url) [BibTex]

link (url) [BibTex]


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Biomimetic gaze stabilization

Shibata, T., Schaal, S.

In Robot learning: an Interdisciplinary approach, pages: 31-52, (Editors: Demiris, J.;Birk, A.), World Scientific, 2000, clmc (inbook)

Abstract
Accurate oculomotor control is one of the essential pre-requisites for successful visuomotor coordination. In this paper, we suggest a biologically inspired control system for learning gaze stabilization with a biomimetic robotic oculomotor system. In a stepwise fashion, we develop a control circuit for the vestibulo-ocular reflex (VOR) and the opto-kinetic response (OKR), and add a nonlinear learning network to allow adaptivity. We discuss the parallels and differences of our system with biological oculomotor control and suggest solutions how to deal with nonlinearities and time delays in the control system. In simulation and actual robot studies, we demonstrate that our system can learn gaze stabilization in real time in only a few seconds with high final accuracy.

am

link (url) [BibTex]

link (url) [BibTex]


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Interaction of rhythmic and discrete pattern generators in single joint movements

Sternad, D., Dean, W. J., Schaal, S.

Human Movement Science, 19(4):627-665, 2000, clmc (article)

Abstract
The study investigates a single-joint movement task that combines a translatory and cyclic component with the objective to investigate the interaction of discrete and rhythmic movement elements. Participants performed an elbow movement in the horizontal plane, oscillating at a prescribed frequency around one target and shifting to a second target upon a trigger signal, without stopping the oscillation. Analyses focused on extracting the mutual influences of the rhythmic and the discrete component of the task. Major findings are: (1) The onset of the discrete movement was confined to a limited phase window in the rhythmic cycle. (2) Its duration was influenced by the period of oscillation. (3) The rhythmic oscillation was "perturbed" by the discrete movement as indicated by phase resetting. On the basis of these results we propose a model for the coordination of discrete and rhythmic actions (K. Matsuoka, Sustained oscillations generated by mutually inhibiting neurons with adaptations, Biological Cybernetics 52 (1985) 367-376; Mechanisms of frequency and pattern control in the neural rhythm generators, Biological Cybernetics 56 (1987) 345-353). For rhythmic movements an oscillatory pattern generator is developed following models of half-center oscillations (D. Bullock, S. Grossberg, The VITE model: a neural command circuit for generating arm and articulated trajectories, in: J.A.S. Kelso, A.J. Mandel, M. F. Shlesinger (Eds.), Dynamic Patterns in Complex Systems. World Scientific. Singapore. 1988. pp. 305-326). For discrete movements a point attractor dynamics is developed close to the VITE model For each joint degree of freedom both pattern generators co-exist but exert mutual inhibition onto each other. The suggested modeling framework provides a unified account for both discrete and rhythmic movements on the basis of neuronal circuitry. Simulation results demonstrated that the effects observed in human performance can be replicated using the two pattern generators with a mutually inhibiting coupling.

am

link (url) [BibTex]

link (url) [BibTex]


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Dynamics of a bouncing ball in human performance

Sternad, D., Duarte, M., Katsumata, H., Schaal, S.

Physical Review E, 63(011902):1-8, 2000, clmc (article)

Abstract
On the basis of a modified bouncing-ball model, we investigated whether human movements utilize principles of dynamic stability in their performance of a similar movement task. Stability analyses of the model provided predictions about conditions indicative of a dynamically stable period-one regime. In a series of experiments, human subjects bounced a ball rhythmically on a racket and displayed these conditions supporting that they attuned to and exploited the dynamic stability properties of the task.

am

link (url) [BibTex]

link (url) [BibTex]

1998


Surface second-order nonlinear optical activity
Surface second-order nonlinear optical activity

Fischer, P., Buckingham, A.

JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS, 15(12):2951-2957, 1998 (article)

Abstract
Following the recent observation of a large second-harmonic intensity difference from a monolayer of chiral molecules with left and right circularly polarized light, the scattering theory is generalized and extended to predict linear and circular intensity differences for the more Versatile sum-frequency spectroscopy. Estimates indicate that intensity differences should be detectable for a typical experimental arrangement. The second-order nonlinear surface susceptibility tensor is given for different surface point groups in the electric dipole approximation; it is shown that nonlinear optical activity phenomena unambiguously probe molecular chirality only for molecular monolayers that are symmetric about the normal. Other surface symmetries can give rise to intensity differences from monolayers composed of achiral molecules. A water surface is predicted to show Linear and nonlinear optical activity in the presence of an electric field parallel to the surface. (C) 1998 Optical Society of America {[}S0740-3224(98)01311-3] OCIS codes: 190.0190, 190.4350, 240.6490.

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DOI [BibTex]

1998


DOI [BibTex]


Linear electro-optic effect in optically active liquids
Linear electro-optic effect in optically active liquids

Buckingham, A., Fischer, P.

CHEMICAL PHYSICS LETTERS, 297(3-4):239-246, 1998 (article)

Abstract
A linear effect of an electrostatic field F on the intensity of sum- and difference-frequency generation in a chiral liquid is predicted. It arises in the electric dipole approximation. The effect changes sign with the enantiomer and on reversing the direction of the electrostatic field. The sum-frequency generator chi(alpha beta gamma)((2)) (-omega(3);omega(1),omega(2)), where omega(3) = omega(1) + omega(2), and the electric field-induced sum-frequency generator chi(alpha beta gamma delta)((3))(-omega(3);omega(1),omega(2),0)F-delta interfere and their contributions to the scattering power can be distinguished. Encouraging predictions are given for a typical experimental arrangement. (C) 1998 Elsevier Science B.V. All rights reserved.

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DOI [BibTex]

DOI [BibTex]


Monolayers of hexadecyltrimethylammonium p-tosylate at the air-water interface. 1. Sum-frequency spectroscopy
Monolayers of hexadecyltrimethylammonium p-tosylate at the air-water interface. 1. Sum-frequency spectroscopy

Bell, G., Li, Z., Bain, C., Fischer, P., Duffy, D.

JOURNAL OF PHYSICAL CHEMISTRY B, 102(47):9461-9472, 1998 (article)

Abstract
Sum-frequency vibrational spectroscopy has been used to determine the structure of monolayers of the cationic surfactant, hexadecyltrimethylammonium p-tosylate (C(16)TA(+)Ts(-)), at the surface of water. Selective deuteration of the cation or the anion allowed the separate detection of sum-frequency spectra of the surfactant and of counterions that are bound to the monolayer. The p-tosylate ions an oriented with their methyl groups pointing away from the aqueous subphase and with the C-2 axis tilted, on average, by 30-40 degrees from the surface normal. The vibrational spectra of C(16)TA(+) indicate that the number of gauche defects in the monolayer does not change dramatically when bromide counterions are replaced by p-tosylate. The ends of the hydrocarbon chains of C16TA+ are, however, tilted much further from the surface normal in the presence of p-tosylate than in the presence of bromide. A quantitative analysis of the sum-frequency spectra requires a knowledge of the molecular hyperpolarizability tensor: the role of ab initio calculations and Raman spectroscopy in determining the components of this tensor is discussed.

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DOI [BibTex]

DOI [BibTex]


Ultraviolet resonance Raman study of drug binding in dihydrofolate reductase, gyrase, and catechol O-methyltransferase
Ultraviolet resonance Raman study of drug binding in dihydrofolate reductase, gyrase, and catechol O-methyltransferase

Couling, V., Fischer, P., Klenerman, D., Huber, W.

BIOPHYSICAL JOURNAL, 75(2):1097-1106, 1998 (article)

Abstract
This paper presents a study of the use of ultraviolet resonance Raman (UVRR) spectroscopic methods as a means of elucidating aspects of drug-protein interactions. Some of the RR vibrational bands of the aromatic amino acids tyrosine and tryptophan are sensitive to the microenvironment, and the use of UV excitation radiation allows selective enhancement of the spectral features of the aromatic amino acids, enabling observation specifically of their change in microenvironment upon drug binding. The three drug-protein systems investigated in this study are dihydrofolate reductase with its inhibitor trimethoprim, gyrase with novobiocin, and catechol O-methyltransferase with dinitrocatechol. It is demonstrated that UVRR spectroscopy has adequate sensitivity to be a useful means of detecting drug-protein interactions in those systems for which the electronic absorption of the aromatic amino acids changes because of hydrogen bonding and/or possible dipole-dipole and dipole-polarizability interactions with the ligand.

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DOI [BibTex]

DOI [BibTex]


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Constructive incremental learning from only local information

Schaal, S., Atkeson, C. G.

Neural Computation, 10(8):2047-2084, 1998, clmc (article)

Abstract
We introduce a constructive, incremental learning system for regression problems that models data by means of spatially localized linear models. In contrast to other approaches, the size and shape of the receptive field of each locally linear model as well as the parameters of the locally linear model itself are learned independently, i.e., without the need for competition or any other kind of communication. Independent learning is accomplished by incrementally minimizing a weighted local cross validation error. As a result, we obtain a learning system that can allocate resources as needed while dealing with the bias-variance dilemma in a principled way. The spatial localization of the linear models increases robustness towards negative interference. Our learning system can be interpreted as a nonparametric adaptive bandwidth smoother, as a mixture of experts where the experts are trained in isolation, and as a learning system which profits from combining independent expert knowledge on the same problem. This paper illustrates the potential learning capabilities of purely local learning and offers an interesting and powerful approach to learning with receptive fields. 

am

link (url) [BibTex]

link (url) [BibTex]


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Local adaptive subspace regression

Vijayakumar, S., Schaal, S.

Neural Processing Letters, 7(3):139-149, 1998, clmc (article)

Abstract
Incremental learning of sensorimotor transformations in high dimensional spaces is one of the basic prerequisites for the success of autonomous robot devices as well as biological movement systems. So far, due to sparsity of data in high dimensional spaces, learning in such settings requires a significant amount of prior knowledge about the learning task, usually provided by a human expert. In this paper we suggest a partial revision of the view. Based on empirical studies, we observed that, despite being globally high dimensional and sparse, data distributions from physical movement systems are locally low dimensional and dense. Under this assumption, we derive a learning algorithm, Locally Adaptive Subspace Regression, that exploits this property by combining a dynamically growing local dimensionality reduction technique  as a preprocessing step with a nonparametric learning technique, locally weighted regression, that also learns the region of validity of the regression. The usefulness of the algorithm and the validity of its assumptions are illustrated for a synthetic data set, and for data of the inverse dynamics of human arm movements and an actual 7 degree-of-freedom anthropomorphic robot arm. 

am

link (url) [BibTex]

link (url) [BibTex]