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Concurrent Spatial and Channel Squeeze & Excitation in Fully Convolutional NetworksMar 07 2018Jun 08 2018Fully convolutional neural networks (F-CNNs) have set the state-of-the-art in image segmentation for a plethora of applications. Architectural innovations within F-CNNs have mainly focused on improving spatial encoding or network connectivity to aid gradient ... More

Diverse Landmark Sampling from Determinantal Point Processes for Scalable Manifold LearningMar 11 2015High computational costs of manifold learning prohibit its application for large point sets. A common strategy to overcome this problem is to perform dimensionality reduction on selected landmarks and to successively embed the entire dataset with the ... More

Likelihood-Free Inference and Generation of Molecular GraphsMay 24 2019Recent methods for generating novel molecules use graph representations of molecules and employ various forms of graph convolutional neural networks for inference. However, training requires solving an expensive graph isomorphism problem, which previous ... More

Data Augmentation with Manifold Exploring Geometric Transformations for Increased Performance and RobustnessJan 14 2019In this paper we propose a novel augmentation technique that improves not only the performance of deep neural networks on clean test data, but also significantly increases their robustness to random transformations, both affine and projective. Inspired ... More

'Squeeze & Excite' Guided Few-Shot Segmentation of Volumetric ImagesFeb 04 2019Deep neural networks enable highly accurate image segmentation, but require large amounts of manually annotated data for supervised training. Few-shot learning aims to address this shortcoming by learning a new class from a few annotated support examples. ... More

`Project & Excite' Modules for Segmentation of Volumetric Medical ScansJun 11 2019Jun 12 2019Fully Convolutional Neural Networks (F-CNNs) achieve state-of-the-art performance for image segmentation in medical imaging. Recently, squeeze and excitation (SE) modules and variations thereof have been introduced to recalibrate feature maps channel- ... More

Deep Multi-Structural Shape Analysis: Application to NeuroanatomyJun 04 2018We propose a deep neural network for supervised learning on neuroanatomical shapes. The network directly operates on raw point clouds without the need for mesh processing or the identification of point correspondences, as spatial transformer networks ... More

DeepNAT: Deep Convolutional Neural Network for Segmenting NeuroanatomyFeb 27 2017We introduce DeepNAT, a 3D Deep convolutional neural network for the automatic segmentation of NeuroAnaTomy in T1-weighted magnetic resonance images. DeepNAT is an end-to-end learning-based approach to brain segmentation that jointly learns an abstract ... More

Recalibrating Fully Convolutional Networks with Spatial and Channel 'Squeeze & Excitation' BlocksAug 23 2018In a wide range of semantic segmentation tasks, fully convolutional neural networks (F-CNNs) have been successfully leveraged to achieve state-of-the-art performance. Architectural innovations of F-CNNs have mainly been on improving spatial encoding or ... More

Gaussian Process Uncertainty in Age Estimation as a Measure of Brain AbnormalityApr 04 2018Multivariate regression models for age estimation are a powerful tool for assessing abnormal brain morphology associated to neuropathology. Age prediction models are built on cohorts of healthy subjects and are built to reflect normal aging patterns. ... More

Detect, Quantify, and Incorporate Dataset Bias: A Neuroimaging Analysis on 12,207 IndividualsApr 28 2018Neuroimaging datasets keep growing in size to address increasingly complex medical questions. However, even the largest datasets today alone are too small for training complex models or for finding genome wide associations. A solution is to grow the sample ... More

Sparse Projections of Medical Images onto ManifoldsMar 22 2013Mar 28 2013Manifold learning has been successfully applied to a variety of medical imaging problems. Its use in real-time applications requires fast projection onto the low-dimensional space. To this end, out-of-sample extensions are applied by constructing an interpolation ... More

Bayesian QuickNAT: Model Uncertainty in Deep Whole-Brain Segmentation for Structure-wise Quality ControlNov 24 2018We introduce Bayesian QuickNAT for the automated quality control of whole-brain segmentation on MRI T1 scans. Next to the Bayesian fully convolutional neural network, we also present inherent measures of segmentation uncertainty that allow for quality ... More

Inherent Brain Segmentation Quality Control from Fully ConvNet Monte Carlo SamplingApr 19 2018Jun 08 2018We introduce inherent measures for effective quality control of brain segmentation based on a Bayesian fully convolutional neural network, using model uncertainty. Monte Carlo samples from the posterior distribution are efficiently generated using dropout ... More

Keypoint Transfer for Fast Whole-Body SegmentationJun 22 2018We introduce an approach for image segmentation based on sparse correspondences between keypoints in testing and training images. Keypoints represent automatically identified distinctive image locations, where each keypoint correspondence suggests a transformation ... More

A Multi-Armed Bandit to Smartly Select a Training Set from Big Medical DataMay 23 2017May 29 2017With the availability of big medical image data, the selection of an adequate training set is becoming more important to address the heterogeneity of different datasets. Simply including all the data does not only incur high processing costs but can even ... More

QuickNAT: A Fully Convolutional Network for Quick and Accurate Segmentation of NeuroanatomyJan 12 2018Nov 24 2018Whole brain segmentation from structural magnetic resonance imaging (MRI) is a prerequisite for most morphological analyses, but is computationally intense and can therefore delay the availability of image markers after scan acquisition. We introduce ... More

BrainTorrent: A Peer-to-Peer Environment for Decentralized Federated LearningMay 16 2019Access to sufficient annotated data is a common challenge in training deep neural networks on medical images. As annotating data is expensive and time-consuming, it is difficult for an individual medical center to reach large enough sample sizes to build ... More

InfiNet: Fully Convolutional Networks for Infant Brain MRI SegmentationOct 11 2018We present a novel, parameter-efficient and practical fully convolutional neural network architecture, termed InfiNet, aimed at voxel-wise semantic segmentation of infant brain MRI images at iso-intense stage, which can be easily extended for other segmentation ... More

Error Corrective Boosting for Learning Fully Convolutional Networks with Limited DataMay 02 2017Jul 02 2017Training deep fully convolutional neural networks (F-CNNs) for semantic image segmentation requires access to abundant labeled data. While large datasets of unlabeled image data are available in medical applications, access to manually labeled data is ... More

`Project & Excite' Modules for Segmentation of Volumetric Medical ScansJun 11 2019Fully Convolutional Neural Networks (F-CNNs) achieve state-of-the-art performance for image segmentation in medical imaging. Recently, squeeze and excitation (SE) modules and variations thereof have been introduced to recalibrate feature maps channel- ... More

Deep Shape Analysis on Abdominal Organs for Diabetes PredictionAug 06 2018Morphological analysis of organs based on images is a key task in medical imaging computing. Several approaches have been proposed for the quantitative assessment of morphological changes, and they have been widely used for the analysis of the effects ... More

ReLayNet: Retinal Layer and Fluid Segmentation of Macular Optical Coherence Tomography using Fully Convolutional NetworkApr 07 2017Jul 07 2017Optical coherence tomography (OCT) is used for non-invasive diagnosis of diabetic macular edema assessing the retinal layers. In this paper, we propose a new fully convolutional deep architecture, termed ReLayNet, for end-to-end segmentation of retinal ... More

On spatial and temporal multilevel dynamics and scaling effects in epileptic seizuresMar 30 2011Jul 29 2011Epileptic seizures are one of the most well-known dysfunctions of the nervous system. During a seizure, a highly synchronized behavior of neural activity is observed that can cause symptoms ranging from mild sensual malfunctions to the complete loss of ... More

Duck Traps: Two-dimensional Critical Manifolds in Planar SystemsAug 30 2018Nov 05 2018In this work we consider two-dimensional critical manifolds in planar fast-slow systems near fold and so-called canard (=`duck') points. These higher-dimension, and lower-codimension, situation is directly motivated by the case of hysteresis operators ... More

On the relativistic KMS condition for the P(φ)_2 modelSep 29 2006The relativistic KMS condition introduced by Bros and Buchholz provides a link between quantum statistical mechanics and quantum field theory. We show that for the $P(\phi)_2$ model at positive temperature, the two point function for fields satisfies ... More

Spectral properties and chiral symmetry violations of (staggered) domain wall fermions in the Schwinger modelFeb 26 2016Jul 05 2016We follow up on a suggestion by Adams and construct explicit domain wall fermion operators with staggered kernels. We compare different domain wall formulations, namely the standard construction as well as Borici's modified and Chiu's optimal construction, ... More

Friction force: from mechanics to thermodynamicsNov 17 2009Jul 01 2010We study some mechanical problems in which a friction force is acting on the system. Using the fundamental concepts of state, time evolution and energy conservation we explain how to extend Newtonian mechanics to thermodynamics. We arrive at the two laws ... More

Thermal Quantum Fields with Spatially Cut-off Interactions in 1+1 Space-time DimensionsJul 25 2003We construct interacting quantum fields in 1+1 space-time dimensions, representing charged or neutral scalar bosons at positive temperature and zero chemical potential. Our work is based on prior work by Klein and Landau and Hoegh-Krohn. Generalized path ... More

Relaxed Logarithmic Barrier Function Based Model Predictive Control of Linear SystemsMar 11 2015In this paper, we investigate the use of relaxed logarithmic barrier functions in the context of linear model predictive control. We present results that allow to guarantee asymptotic stability of the corresponding closed-loop system, and discuss further ... More

A stabilizing iteration scheme for model predictive control based on relaxed barrier functionsMar 15 2016Apr 06 2016We propose and analyze a stabilizing iteration scheme for the algorithmic implementation of model predictive control for linear discrete-time systems. Polytopic input and state constraints are considered and handled by means of so-called relaxed logarithmic ... More

Staggered domain wall fermionsSep 16 2016We construct domain wall fermions with a staggered kernel and investigate their spectral and chiral properties numerically in the Schwinger model. In some relevant cases we see an improvement of chirality by more than an order of magnitude as compared ... More

Differential Characters and Geometric ChainsMar 26 2013Apr 09 2013We study Cheeger-Simons differential characters and provide geometric descriptions of the ring structure and of the fiber integration map. The uniqueness of differential cohomology (up to unique natural transformation) is proved by deriving an explicit ... More

Distances and large deviations in the spatial preferential attachment modelSep 26 2018Sep 27 2018We investigate two asymptotic properties of a spatial preferential-attachment model introduced by E. Jacob and P. M\"orters (2013). First, in a regime of strong linear reinforcement, we show that typical distances are at most of doubly-logarithmic order. ... More

Thermal Quantum Fields without Cut-offs in 1+1 Space-time DimensionsMar 26 2004We construct interacting quantum fields in 1+1 dimensional Minkowski space, representing neutral scalar bosons at positive temperature. Our work is based on prior work by Klein and Landau and Hoegh-Krohn

Removable presymplectic singularities and the local splitting of Dirac structuresOct 20 2014Oct 27 2015We call a singularity of a presymplectic form $\omega$ removable in its graph if its graph extends to a smooth Dirac structure over the singularity. An example for this is the symplectic form of a magnetic monopole. A criterion for the removability of ... More

MPL - a program for computations with iterated integrals on moduli spaces of curves of genus zeroOct 14 2015We introduce the computer program MPL for computations with homotopy invariant iterated integrals on moduli spaces $\mathcal{M}_{0,n}$ of curves of genus 0 with $n$ ordered marked points. The program is an implementation of the algorithms presented in ... More

Discrete Complex Structure on Surfel SurfacesFeb 12 2008This paper defines a theory of conformal parametrization of digital surfaces made of surfels equipped with a normal vector. The main idea is to locally project each surfel to the tangent plane, therefore deforming its aspect-ratio. It is a generalization ... More

No information or horizon paradoxes for Th. SmithsMay 04 2015'Th'e 'S'tatistical 'm'echanician 'i'n 'th'e 's'treet (our Th. Smiths) must be surprised upon hearing popular versions of some of today's most discussed paradoxes in astronomy and cosmology. In fact, rather standard reminders of the meaning of thermal ... More

Many-body theory of degenerate systems: A simple exampleDec 05 2003The hierarchy of Green functions for (quasi)degenerate systems, presented in cond-mat/0308058, is calculated in detail for the case of a system with closed shells plus a single electron in a two-fold degenerate level. The complete hierarchy is derived ... More

Renormalization of QED in an external fieldFeb 08 2002The Schwinger equations of QED are rewritten in three different ways as integral equations involving functional derivatives, which are called weak field, strong field, and SCF quantum electrodynamics. The perturbative solutions of these equations are ... More

Quantum field theory of degenerate systemsJul 22 2003To set up a self-consistent quantum field theory of degenerate systems, the unperturbed state should be described by a density matrix instead of a pure state. This increases the combinatorial complexity of the many-body equations. Hopf algebraic techniques ... More

Vacuum Polarisation Tensors in Constant Electromagnetic Fields: Part IIFeb 25 2000In the second part of this series we apply the ``string-inspired'' technique to the calculation of one-loop amplitudes involving both vectors and axialvectors, as well as a general constant electromagnetic background field. The vector-axialvector two-point ... More

Cataclysmic Variables in Globular ClustersDec 05 2011Feb 10 2012Every massive globular cluster (GC) is expected to harbour a significant population of cataclysmic variables (CVs). In this review, I first explain why GC CVs matter astrophysically, how many and what types are theoretically predicted to exist and what ... More

Far-Ultraviolet Surveys of Globular Clusters: Hunting for the Products of Stellar Collisions and Near MissesJul 02 2004Globular clusters are gravitationally bound stellar systems containing on the order of 100,000 stars. Due to the high stellar densities in the cores of these clusters, close encounters and even physical collisions between stars are inevitable. These dynamical ... More

On the Calculation of QED Amplitudes in a Constant FieldJul 08 1998It is explained how first-quantized worldline path integrals can be used as an efficient alternative to Feynman diagrams in the calculation of QED amplitudes and effective actions. The examples include the one-loop photon splitting amplitude, the two-loop ... More

On the Stability of Contention Resolution Diversity Slotted ALOHAMar 21 2012In this paper a Time Division Multiple Access (TDMA) based Random Access (RA) channel with Successive Interference Cancellation (SIC) is considered for a finite user population and reliable retransmission mechanism on the basis of Contention Resolution ... More

Isotropy of Angular Frequencies and Weak Chimeras With Broken SymmetryDec 04 2015Oct 28 2016The notion of a weak chimeras provides a tractable definition for chimera states in networks of finitely many phase oscillators. Here we generalize the definition weak chimera to a more general class of equivariant dynamical systems by characterizing ... More

The Reeh-Schlieder property for ground statesJan 24 2000Feb 10 2000Recently it has been shown that the Reeh-Schlieder property w.r.t. thermal equilibrium states is a direct consequence of locality, additivity and the relativistic KMS condition. Here we extend this result to ground states.

Cluster Estimates for Modular StructuresApr 02 1998Apr 07 1999The basic ingredients of Tomita-Takesaki modular theory are used to establish cluster estimates. Applications to thermal quantum field theory are discussed.

Magnetoelectric bistabilities in ferromagnetic resonant tunneling structuresJul 28 2008The conditions for the occurrence of pronounced magnetoelectric bistabilities in the resonant tunneling through a ferromagnetic quantum well are theoretically investigated. The bistability appears due to the mutual feedback of the carriers Coulomb interaction ... More

Ricci curvature bounds for warped productsSep 06 2012Nov 09 2013We prove generalized lower Ricci curvature bounds for warped products over complete Finsler manifolds. On the one hand our result covers a theorem of Bacher and Sturm concerning euclidean and spherical cones. On the other hand it can be seen in analogy ... More

Obata's rigidity theorem for metric measure spacesOct 20 2014Apr 13 2015We prove Obata's rigidity theorem for metric measure spaces that satisfy a Riemannian curvature-dimension condition. Additionally, we show that a lower bound $K$ for the generalized Hessian of a sufficiently regular function $u$ holds if and only if $u$ ... More

Nominal Unification RevisitedDec 22 2010Nominal unification calculates substitutions that make terms involving binders equal modulo alpha-equivalence. Although nominal unification can be seen as equivalent to Miller's higher-order pattern unification, it has properties, such as the use of first-order ... More

Orthogonal bundles over curves in characteristic twoNov 11 2008Dec 09 2008Let X be a smooth projective curve of genus g \geq 2 defined over a field of characteristic two. We give examples of stable orthogonal bundles with unstable underlying vector bundles and use them to give counterexamples to Behrend's conjecture on the ... More

Auxiliary matrices on both sides of the equatorAug 12 2004Aug 17 2004The spectra of previously constructed auxiliary matrices for the six-vertex model at roots of unity are investigated for spin-chains of even and odd length. The two cases show remarkable differences. In particular, it is shown that for even roots of unity ... More

Lie algebraic structures in integrable models, affine Toda field theoryAug 25 2000Sep 01 2000The most prominent class of integrable quantum field theories in 1+1 dimensions is affine Toda theory. Distinguished by a rich underlying Lie algebraic structure these models have in recent years attracted much attention not only as test laboratories ... More

A Q-operator for the quantum transfer matrixOct 12 2006Oct 24 2006Baxter's Q-operator for the quantum transfer matrix of the XXZ spin-chain is constructed employing the representation theory of quantum groups. The spectrum of this Q-operator is discussed and novel functional relations which describe the finite temperature ... More

The characteristic polynomial of a random unitary matrix and Gaussian multiplicative chaos - The $L^2$-phaseOct 03 2014Oct 02 2015We study the characteristic polynomial of Haar distributed random unitary matrices. We show that after a suitable normalization, as one increases the size of the matrix, powers of the absolute value of the characteristic polynomial as well as powers of ... More

Exact asymptotics of the freezing transition of a logarithmically correlated random energy modelMay 12 2011Aug 26 2011We consider a logarithmically correlated random energy model, namely a model for directed polymers on a Cayley tree, which was introduced by Derrida and Spohn. We prove asymptotic properties of a generating function of the partition function of the model ... More

LHC Phenomenology of the Three-Site Higgsless ModelNov 08 2010We investigate the potential of the LHC for discovering the heavy vector and fermion resonances present in the Three-Site Higgsless Model. To this end, the model was implemented into the WHIZARD parton-level Monte Carlo eventgenerator. The results of ... More

On quasi-normal modes, area quantization and Bohr correspondence principleMar 18 2015Mar 30 2015In Int. Journ. Mod. Phys. D 14, 181 (2005), the author Khriplovich verbatim claims that "the correspondence principle does not dictate any relation between the asymptotics of quasinormal modes and the spectrum of quantized black holes" and that "this ... More

Bohr-like black holesMar 11 2015The idea that black holes (BHs) result in highly excited states representing both the "hydrogen atom" and the "quasi-thermal emission" in quantum gravity is today an intuitive but general conviction. In this paper it will be shown that such an intuitive ... More

Gravitational Waves Astronomy: a cornerstone for gravitational theoriesJun 28 2010Realizing a gravitational wave (GW) astronomy in next years is a great challenge for the scientific community. By giving a significant amount of new information, GWs will be a cornerstone for a better understanding of gravitational physics. In this paper ... More

An oscillating Universe from the linearized R^{2} theory of gravityFeb 18 2008Feb 19 2008An oscillating Universe which arises from the linearized R^{2} theory of gravity is discussed, showing that some observative evidences like the cosmological redshift and the Hubble law are in agreement with the model. In this context Dark Energy is seen ... More

Massive gravitational waves from the R^2 theory of gravity: production and response of interferometersNov 30 2007We show that from the R^{2} high order gravity theory it is possible to produce, in the linearized approch, particles which can be seen like massive modes of gravitational waves (GWs). The presence of the mass generates a longitudinal force in addition ... More

The Virgo - MiniGRAIL cross correlation for the detection of scalar gravitational wavesJun 26 2007Jul 05 2007After a review of the frequency - dependent angular pattern of interferometers in the TT gauge for scalar gravitational waves (SGWs), which has been recently analysed by Capozziello and Corda, in this letter the result is used to study the cross correlation ... More

Extension of the frequency-range of interferometers for the ''magnetic'' components of gravitational waves?Oct 31 2006Mar 26 2007Recently, with an enlighting treatment, Baskaran and Grishchuk have shown the presence and importance of the so-called ``magnetic'' components of gravitational waves (GWs), which have to be taken into account in the context of the total response functions ... More

Quasi-normal modes: the "electrons" of black holes as "gravitational atoms"? Implications for the black hole information puzzleFeb 26 2015Mar 31 2015Some recent important results on black hole (BH) quantum physics concerning the BH effective state and the natural correspondence between Hawking radiation and BH quasi-normal modes (QNMs) are reviewed, clarified and refined. Such a correspondence permits ... More

Quantum transitions of minimum energy for Hawking quanta in highly excited black holes: problems for loop quantum gravity?Dec 03 2012Dec 12 2013By analysing some recent results by Yoon, which arise from loop quantum gravity and from the assumption of the locality of photon emission in a black hole, we argue that they are not consistent with our recent semi-classical results for highly excited ... More

Effective temperature, Hawking radiation and quasinormal modesMay 17 2012Parikh and Wilczek have shown that Hawking radiation's spectrum cannot be strictly thermal. Such a non-strictly thermal character implies that the spectrum is also not strictly continuous and thus generates a natural correspondence between Hawking radiation ... More

General relativity and OPERA ExperimentJan 21 2012Nov 08 2012In his paper "A very simple solution to the OPERA neutrino velocity problem" the author J. Manuel Garcia-Islas claims to have very easily solved and explained within the general theory of relativity that OPERA's neutrinos are not traveling faster than ... More

A clarification on a common misconception about interferometric detectors of gravitational wavesMar 24 2011The aims of this letter are two. First, to show the angular gauge-invariance on the response of interferometers to gravitational waves (GWs). In this process, after resuming for completeness results on the Transverse-Traceless (TT) gauge, where, in general, ... More

Presentation of the Second Big Challenge Symposium - The Big Challenge of Cosmological Understanding: Gravitation, Dark Matter and Dark Energy. Towards New ScenariosJul 23 2010This Symposium is devoted to the Memory of Lev Kofman, June-17-1957-November-12-2009. The accelerated expansion of the Universe, which is today observed, shows that cosmological dynamics is dominated by the so-called Dark Energy field which provides a ... More

Will gravitational waves confirm Einstein's General Relativity?Jul 13 2009Jul 21 2009Even if Einstein's General Relativity achieved a great success and overcame lots of experimental tests, it also showed some shortcomings and flaws which today advise theorists to ask if it is the definitive theory of gravity. In this proceeding paper ... More

Consistent Dyson summation of Higgs propagators in nonlinear parameterizations revisitedJul 05 2004Dec 10 2004As we demonstrate in a process independent way, in a nonlinear parameterization of the scalar sector of the standard model the Dyson summation of the Higgs self energy can be performed without violating the Ward Identities. This implies also the Goldstone ... More

Higgsless fermion masses and unitarityFeb 11 2004Apr 20 2004We discuss the consistency of fermion mass generation by boundary conditions and brane localized terms in higher dimensional Higgsless models of gauge symmetry breaking. The sum rules imposed by tree-level unitarity and Ward Identities are applied to ... More

Twistor-inspired construction of massive quark amplitudesSep 09 2008Oct 30 2008The analog of the Cachazo-Svrvcek-Witten rules for scattering amplitudes with massive quarks is derived following an approach previously employed for amplitudes with massive scalars. A prescription for the external wave-functions is given that leads to ... More

From Tree Unitarity to Top Quark Physics in 5D Higgsless ModelsSep 26 2005In five dimensional models of Higgsless electroweak symmetry breaking, tree level unitarity in gauge boson scattering is restored by the exchange of gauge boson Kaluza-Klein modes instead of a Higgs boson. Unitarity of scattering amplitudes involving ... More

Theory status of four-fermion production at e-e+ collidersDec 17 2015The status of predictions for four-fermion production at e-e+ colliders is reviewed with an emphasis on the developments after the LEP2 era and an outlook to the challenges posed by the precision program at future colliders.

Algebraic quantum theoryApr 08 2004The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global program based on ... More

When is the underlying space of an orbifold a topological manifold?Jul 18 2013We answer the question posed by Davis: "When is the underlying space of an orbifold a topological manifold". It amounts to the classification of finite groups acting linearly on a Euclidean vector space such that the quotient space is homeomorphic to ... More

Warning signs for wave speed transitions of noisy Fisher-KPP invasion frontsDec 03 2012Invasion waves are a fundamental building block of theoretical ecology. In this study we aim to take the first steps to link propagation failure and fast acceleration of traveling waves to critical transitions (or tipping points). The approach is based ... More

Normal Hyperbolicity and Unbounded Critical ManifoldsApr 04 2012Aug 01 2013This work is motivated by mathematical questions arising in differential equation models for autocatalytic reactions. In particular, this paper answers an open question posed by Guckenheimer and Scheper [SIAM J. Appl. Dyn. Syst. 10-1 (2011), pp. 92-128] ... More

Deterministic continutation of stochastic metastable equilibria via Lyapunov equations and ellipsoidsJun 17 2011Jan 09 2012Numerical continuation methods for deterministic dynamical systems have been one of the most successful tools in applied dynamical systems theory. Continuation techniques have been employed in all branches of the natural sciences as well as in engineering ... More

Introduction to Potential Theory via ApplicationsApr 29 2008We introduce the basic concepts related to subharmonic functions and potentials, mainly for the case of the complex plane and prove the Riesz decomposition theorem. Beyond the elementary facts of the theory we deviate slightly from the usual path of exposition ... More

The Curse of InstabilityMay 16 2015High-dimensional computational challenges are frequently explained via the curse of dimensionality, i.e., increasing the number of dimensions leads to exponentially growing computational complexity. In this commentary, we argue that thinking on a different ... More

Scaling of Saddle-Node Bifurcations: Degeneracies and Rapid Quantitative ChangesJul 09 2008Jan 27 2012The scaling of the time delay near a "bottleneck" of a generic saddle-node bifurcation is well-known to be given by an inverse square-root law. We extend the analysis to several non-generic cases for smooth vector fields. We proceed to investigate $C^0$ ... More

Equivariant smoothing of piecewise linear manifoldsJul 09 2015We prove that every piecewise linear manifold of dimension up to four on which a finite group acts by piecewise linear homeomorphisms admits a compatible smooth structure with respect to which the group acts smoothly. This solves a challenge posed by ... More

A $L^\infty$ bound for the Cahn--Hilliard equation with relaxed non-smooth free energyNov 09 2015Phase field models are widely used to describe multiphase systems. Here a smooth indicator function, called phase field, is used to describe the spatial distribution of the phases under investigation. Material properties like density or viscosity are ... More

The Dirac Operator on Hyperbolic Manifolds of Finite VolumeOct 25 2000We study the spectrum of the Dirac operator on hyperbolic manifolds of finite volume. Depending on the spin structure it is either discrete or the whole real line. For link complements in S^3 we give a simple criterion in terms of linking numbers for ... More

Dependence on the spin structure of the Dirac spectrumJul 21 2000The theme is the influence of the spin structure on the Dirac spectrum of a spin manifold. We survey examples and results related to this question.

Embeddings into the Pancake Interconnection NetworkNov 26 2004Owing to its nice properties, the pancake is one of the Cayley graphs that were proposed as alternatives to the hypercube for interconnecting processors in parallel computers. In this paper, we present embeddings of rings, grids and hypercubes into the ... More

Multiplicate inverse forms of terminating hypergeometric seriesNov 18 2013The multiplicate form of Gould--Hsu's inverse series relations enables to investigate the dual relations of the Chu-Vandermonde-Gau{\ss}'s, the Pfaff-Saalsch\"utz's summation theorems and the binomial convolution formula due to Hagen and Rothe. Several ... More

Analysis of an Efficient Distributed Algorithm for Mutual Exclusion (Average-Case Analysis of Path Reversal)Nov 20 2006The algorithm analysed by Na\"{i}mi, Trehe and Arnold was the very first distributed algorithm to solve the mutual exclusion problem in complete networks by using a dynamic logical tree structure as its basic distributed data structure, viz. a path reversal ... More

Formation of Twin Clusters in a Galactic Tidal FieldJun 28 2001The formation of globular clusters is still an unsolved problem. Though most scenarios assume a massive molecular cloud as the progenitor, it is unclear, how the cloud is transformed into a star cluster. Here a scheme of supernova (SN) induced cluster ... More

Stein's method of exchangeable pairs for absolutely continuous, univariate distributions with applications to the Polya urn modelJul 02 2012Jul 21 2012We propose a way of finding a Stein type characterization of a given absolutely continuous distribution $\mu$ on $\R$ which is motivated by a regression property satisfied by an exchangeable pair $(W,W')$ where $\calL(W)$ is supposed or known to be close ... More

Supersymmetric Interpretation of the EGRET Excess in Diffuse Galactic Gamma RaysOct 24 2007Recently it was shown that the excess of diffuse Galactic gamma rays above 1 GeV could be interpreted as a Dark Matter annihilation signal. From the spectral shape of the excess it is possible to determine a range for the allowed WIMP mass which can be ... More

Schwarzian derivative and Numata Finsler structuresFeb 15 2008Jul 03 2008The flag curvature of the Numata Finsler structures is shown to admit a nontrivial prolongation to the one-dimensional case, revealing an unexpected link with the Schwarzian derivative of the diffeomorphisms associated with these Finsler structures.

On metrics on 2-orbifolds all of whose geodesics are closedMar 28 2016Jun 22 2016We show that the geodesic period spectrum of a Riemannian 2-orbifold all of whose geodesics are closed depends, up to a constant, only on its orbifold topology and compute it. In the manifold case we recover the fact proved by Gromoll, Grove and Pries ... More