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ISOLLE: LLE with geodesic distance

Claudio Varini, Andreas Degenhard, Tim W. Nattkemper
2006 Neurocomputing  
Andreas Degenhard received his Master Degree in Theoretical Physics from the University of Muenster, Germany in 1995 and the Ph.D. degree in Mathematical Physics from the University of Bielefeld, Germany  ... 
doi:10.1016/j.neucom.2005.12.120 fatcat:3m7glhplvzh37jb3hgdyw7kdgq

ISOLLE: Locally Linear Embedding with Geodesic Distance [chapter]

Claudio Varini, Andreas Degenhard, Tim Nattkemper
2005 Lecture Notes in Computer Science  
Locally Linear Embedding (LLE) has recently been proposed as a method for dimensional reduction of high-dimensional nonlinear data sets. In LLE each data point is reconstructed from a linear combination of its n nearest neighbors, which are typically found using the Euclidean Distance. We propose an extension of LLE which consists in performing the search for the neighbors with respect to the geodesic distance (ISOLLE). In this study we show that the usage of this metric can lead to a more
more » ... ate preservation of the data structure. The proposed approach is validated on both real-world and synthetic data.
doi:10.1007/11564126_34 fatcat:jwezbbe3nngc5c6nbvvx27ld2m

Coarse-Grained Lattice Model for Molecular Recognition

Hans Behringer, Andreas Degenhard, Friederike Schmid
2006 Physical Review Letters  
doi:10.1103/physrevlett.97.128101 pmid:17026000 fatcat:i7264w6ou5c4lnqhlbidaboqre

Developing and analyzing idealized models for molecular recognition

Hans Behringer, Thorsten Bogner, Alexey Polotsky, Andreas Degenhard, Friederike Schmid
2007 Journal of Biotechnology  
We study equilibrium aspects of molecular recognition of two biomolecules using idealized model systems and methods from statistical physics. Starting from the basic experimental findings we demonstrate exemplarily how an idealized coarsegrained model for the investigation of molecular recognition of two biomolecules can be developed. In addition we provide details regarding two model systems for the recognition of a flexible and a rigid biomolecule respectively, the latter taking into account
more » ... onformational changes. We focus particularly on the interplay and influence of the correlations of the residue distributions of the biomolecules on the recognition process.
doi:10.1016/j.jbiotec.2007.01.035 pmid:17368607 fatcat:uschgih3trbqto4zy6axxsrk5e

Half Fourier Acquisition Applied to Time Series Analysis of Contrast Agent Uptake [chapter]

Andreas Degenhard, Christine Tanner, Carmel Hayes, David J. Hawkes, Martin O. Leach
2001 Lecture Notes in Computer Science  
Magnetic Resonance Imaging (MRI) has emerged as a powerful tool in medical diagnosis and research. Dynamic Contrast Enhanced MRI (DCE-MRI), which involves the administration of a paramagnetic contrast medium, has been shown to provide additional sensitivity in detecting abnormality. In particular, in imaging of the breast and axilla the ability to differentiate between benign and malignant lesions depends, in part, on the enhancement profile. Evaluation of this requires a sufficient temporal
more » ... olution in the time series acquisition. Faster imaging in general requires that images are acquired with a lower spatial resolution or signal to noise ratio. In this paper we investigate a novel approach for increasing the temporal resolution in DCE-MRI without decreasing the accuracy of the measurement. The results clearly indicate a superior image quality compared to standard half Fourier techniques and the algorithm correctly recovers the time series characteristics of T1 and T * 2 -weighted time series data.
doi:10.1007/3-540-45468-3_104 fatcat:2r3i2f76n5bwbft4la6j5qna2q

Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations [article]

Andreas Degenhard, Javier Rodriguez-Laguna
2001 arXiv   pre-print
We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems. We examine dynamical scaling characteristics in the short-time and the long-time evolution regime providing only a reduced number of degrees of freedom to the evolution process.
arXiv:cond-mat/0106156v2 fatcat:ckth5ibmk5gl7cqwtmwkohyfpi

Molecular Recognition in a Lattice Model: An Enumeration Study

Thorsten Bogner, Andreas Degenhard, Friederike Schmid
2004 Physical Review Letters  
We investigate the mechanisms underlying selective molecular recognition of single heteropolymers at chemically structured planar surfaces. To this end, we study systems with two-letter (HP) lattice heteropolymers by exact enumeration techniques. Selectivity for a particular surface is defined by an adsorption energy criterium. We analyze the distributions of selective sequences and the role of mutations. A particularly important factor for molecular recognition is the small-scale structure on the polymers.
doi:10.1103/physrevlett.93.268108 pmid:15698030 fatcat:aab6epppyfgdvk3fjvo23dtqse

Polymer adsorption onto random planar surfaces: Interplay of polymer and surface correlations

Alexey Polotsky, Friederike Schmid, Andreas Degenhard
2004 Journal of Chemical Physics  
We study the adsorption of homogeneous or heterogeneous polymers onto heterogeneous planar surfaces with exponentially decaying site-site correlations, using a variational reference system approach. As a main result, we derive simple equations for the adsorption-desorption transition line. We show that the adsorption threshold is the same for systems with quenched and annealed disorder. The results are discussed with respect to their implications for the physics of molecular recognition.
doi:10.1063/1.1778137 pmid:15332921 fatcat:3nin6bf5k5bgtnzhcbk5rrabpe

Visual exploratory analysis of DCE-MRI data in breast cancer by dimensional data reduction: A comparative study

Claudio Varini, Andreas Degenhard, Tim W. Nattkemper
2006 Biomedical Signal Processing and Control  
Andreas Degenhard for their devotion to this work, their enthusiasm and the many fruitful discussions. • Prof. Dr.  ...  Degenhard and T. W. Nattkemper. Visualisation of Breast Tumours DCE-MRI Data using LLE, C. Varini, T. W. Nattkemper, A. Degenhard and A. Wismüller.  ... 
doi:10.1016/j.bspc.2006.05.001 fatcat:aikhbzzg35gvlgcd4n3w7czgom

Coarse-grained lattice model for investigating the role of cooperativity in molecular recognition

Hans Behringer, Andreas Degenhard, Friederike Schmid
2007 Physical Review E  
Equilibrium aspects of molecular recognition of rigid biomolecules are investigated using coarse-grained lattice models. The analysis is carried out in two stages. First an ensemble of probe molecules is designed with respect to the target biomolecule. The recognition ability of the probe ensemble is then investigated by calculating the free energy of association. The influence of cooperative and anti-cooperative effects accompanying the association of the target and probe molecules is studied.
more » ... Numerical findings are presented and compared to analytical results which can be obtained in the limit of dominating cooperativity and in the mean-field formulation of the models.
doi:10.1103/physreve.76.031914 pmid:17930278 fatcat:cfywrzvjjnc4nknae466ybrth4

A non-perturbative real-space renormalization group scheme

Andreas Degenhard
2000 Journal of Physics A: Mathematical and General  
Based on the original idea of the density matrix renormalization group (DMRG), i.e. to include the missing boundary conditions between adjacent blocks of the blocked quantum system, we present a rigorous and nonperturbative mathematical formulation for the real-space renormalization group (RG) idea invented by L.P. Kadanoff and further developed by K.G. Wilson. This is achieved by using additional Hilbert spaces called auxiliary spaces in the construction of each single isolated block, which is
more » ... then named a superblock according to the original nomenclature. On this superblock we define two maps called embedding and truncation for successively integrating out the small scale structure. Our method overcomes the known difficulties of the numerical DMRG, i.e. limitation to zero temperature and one space dimension.
doi:10.1088/0305-4470/33/35/306 fatcat:byvhm5xtcraghpnv4un6qigkcq

Random copolymer adsorption: Morita approximation compared to exact numerical simulations

Alexey Polotsky, Andreas Degenhard, Friederike Schmid
2009 Journal of Chemical Physics  
We study the adsorption of ideal random lattice copolymers with correlations in the sequences on homogeneous substrates with two different methods: An analytical solution of the problem based on the constrained annealed approximation introduced by Morita in 1964 and the generating functional (GF) technique, and direct numerical simulations of lattice chains averaged over many realizations of random sequences. Both methods allow to calculate the free energy and different conformational
more » ... stics of the adsorbed chain. The comparison of the results for random copolymers with different degree of correlations and different types of nonadsorbing monomers (neutral or repelling from the surface) shows not only qualitative but a very good quantitative agreement, especially in the cases of Bernoullian and quasi-alternating random sequences.
doi:10.1063/1.3193723 pmid:19673584 fatcat:mcwxsv5xxjgejhck2bkidr5ria

Apertureless scanning near-field optical microscopy of sparsely labeled tobacco mosaic viruses and the intermediate filament desmin

Alexander Harder, Mareike Dieding, Volker Walhorn, Sven Degenhard, Andreas Brodehl, Christina Wege, Hendrik Milting, Dario Anselmetti
2013 Beilstein Journal of Nanotechnology  
Both fluorescence imaging and atomic force microscopy (AFM) are highly versatile and extensively used in applications ranging from nanotechnology to life sciences. In fluorescence microscopy luminescent dyes serve as position markers. Moreover, they can be used as active reporters of their local vicinity. The dipolar coupling of the tip with the incident light and the fluorophore give rise to a local field and fluorescence enhancement. AFM topographic imaging allows for resolutions down to the
more » ... tomic scale. It can be operated in vacuum, under ambient conditions and in liquids. This makes it ideal for the investigation of a wide range of different samples. Furthermore an illuminated AFM cantilever tip apex exposes strongly confined non-propagating electromagnetic fields that can serve as a coupling agent for single dye molecules. Thus, combining both techniques by means of apertureless scanning near-field optical microscopy (aSNOM) enables concurrent high resolution topography and fluorescence imaging. Commonly, among the various (apertureless) SNOM approaches metallic or metallized probes are used. Here, we report on our custom-built aSNOM setup, which uses commercially available monolithic silicon AFM cantilevers. The field enhancement confined to the tip apex facilitates an optical resolution down to 20 nm. Furthermore, the use of standard mass-produced AFM cantilevers spares elaborate probe production or modification processes. We investigated tobacco mosaic viruses and the intermediate filament protein desmin. Both are mixed complexes of building blocks, which are fluorescently labeled to a low degree. The simultaneous recording of topography and fluorescence data allows for the exact localization of distinct building blocks within the superordinate structures.
doi:10.3762/bjnano.4.60 pmid:24062977 pmcid:PMC3778390 fatcat:jzp2pc5lk5dqplsphz67qe7eia

Influence of sequence correlations on the adsorption of random heteropolymers onto homogeneous planar surfaces

Alexey Polotsky, Friederike Schmid, Andreas Degenhard
2004 Journal of Chemical Physics  
Using a reference system approach, we develop an analytical theory for the adsorption of random heteropolymers with exponentially decaying and/or oscillating sequence correlations on planar homogeneous surfaces. We obtain a simple equation for the adsorption-desorption transition line. This result as well as the validity of the reference system approach is tested by a comparison with numerical lattice calculations.
doi:10.1063/1.1647045 pmid:15267512 fatcat:o5rf3vcd6feztasv6ivvh6gtae

Quantitative evaluation of free-form deformation registration for dynamic contrast-enhanced MR mammography

Christine Tanner, Julia A. Schnabel, Derek L. G. Hill, David J. Hawkes, Andreas Degenhard, Martin O. Leach, D. Rodney Hose, Margaret A. Hall-Craggs, Sasha I. Usiskin
2007 Medical Physics (Lancaster)  
In this paper, we present an evaluation study of a set of registration strategies for the alignment of sequences of 3D dynamic contrast-enhanced magnetic resonance breast images. The accuracy of the optimal registration strategies was determined on unseen data. The evaluation is based on the simulation of physically plausible breast deformations using finite element methods and on contrast-enhanced image pairs without visually detectable motion artifacts. The configuration of the finite element
more » ... model was chosen according to its ability to predict in vivo breast deformations for two volunteers. We computed transformations for ten patients with 12 simulated deformations each. These deformations were applied to the postcontrast image to model patient motion occurring between pre-and postcontrast image acquisition. The original precontrast images were registered to the corresponding deformed postcontrast images. The performance of several registration configurations ͑rigid, affine, B-spline based nonrigid, single-resolution, multi-resolution, and volume-preserving͒ was optimized for five of the ten patients. The images were most accurately aligned with volume-preserving single-resolution nonrigid registration employing 40 or 20 mm control point spacing. When tested on the remaining five patients the optimal configurations reduced the average mean registration error from 1.40 to 0.45 mm for the whole breast tissue and from 1.20 to 0.32 mm for the enhancing lesion. These results were obtained on average within 26 ͑81͒ min for 40 ͑20͒ mm control point spacing. The visual appearance of the difference images from 30 patients was significantly improved after 20 mm volume-preserving single-resolution nonrigid registration in comparison to no registration or rigid registration. No substantial volume changes within the region of the enhancing lesions were introduced by this nonrigid registration.
doi:10.1118/1.2712040 pmid:17500454 fatcat:osrxpji4rne7pary2makt5yqlu
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