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Improving students' understanding of rotating frames of reference using videos from different perspectivesFeb 26 2019The concepts of the Coriolis and the centrifugal force are essential in various scientific fields and they are standard components of introductory physics lectures. In this paper we explore how students understand and apply concepts of rotating frames ... More

Fast Bayesian Optimization of Machine Learning Hyperparameters on Large DatasetsMay 23 2016Mar 07 2017Bayesian optimization has become a successful tool for hyperparameter optimization of machine learning algorithms, such as support vector machines or deep neural networks. Despite its success, for large datasets, training and validating a single configuration ... More

Event-Based Modeling with High-Dimensional Imaging Biomarkers for Estimating Spatial Progression of DementiaMar 08 2019Event-based models (EBM) are a class of disease progression models that can be used to estimate temporal ordering of neuropathological changes from cross-sectional data. Current EBMs only handle scalar biomarkers, such as regional volumes, as inputs. ... More

Multimodal Machine Learning-based Knee Osteoarthritis Progression Prediction from Plain Radiographs and Clinical DataApr 12 2019Knee osteoarthritis (OA) is the most common musculoskeletal disease without a cure, and current treatment options are limited to symptomatic relief. Prediction of OA progression is a very challenging and timely issue, and it could, if resolved, accelerate ... More

BOHB: Robust and Efficient Hyperparameter Optimization at ScaleJul 04 2018Modern deep learning methods are very sensitive to many hyperparameters, and, due to the long training times of state-of-the-art models, vanilla Bayesian hyperparameter optimization is typically computationally infeasible. On the other hand, bandit-based ... More

Characterizing finite length local cohomology in terms of bounds on Koszul cohomologyOct 02 2018Oct 17 2018Let $(R,m, \kappa)$ be a local ring. We give a characterization of $R$-modules $M$ whose local cohomology is finite length up to some index in terms of asymptotic vanishing of Koszul cohomology on parameter ideals up to the same index. In particular, ... More

Multiscale Analysis and Localization of Random OperatorsAug 16 2007A discussion of the method of multiscale analysis in the study of localization of random operators based on lectures given at \emph{Random Schr\"odinger operators: methods, results, and perspectives}, \'Etats de la recherche, Universit\'e Paris 13, June ... More

Maximal Fermi charts and geometry of inflationary universesOct 29 2012Jul 09 2015A proof is given that the maximal Fermi coordinate chart for any comoving observer in a broad class of Robertson-Walker spacetimes consists of all events within the cosmological event horizon, if there is one, or is otherwise global. Exact formulas for ... More

Hamiltonian spectral invariants, symplectic spinors and Frobenius structures IIJan 17 2019Feb 02 2019In this article, we continue our study of 'Frobenius structures' and symplectic spectral invariants in the context of symplectic spinors. By studying the case of $C^1$-small Hamiltonian mappings on symplectic manifolds $M$ admitting a metaplectic structure ... More

Inverting the spherical Radon transform for physically meaningful functionsJul 28 2003In this paper we refer to the reconstruction formulas given in L.-E. Andersson's On the determination of a function from spherical averages, which are often used in applications such as SAR and SONAR. We demonstrate that the first one of these formulas ... More

Unique continuation principle for spectral projections of Schr\" odinger operators and optimal Wegner estimates for non-ergodic random Schr\" odinger operatorsSep 21 2012Jan 09 2013We prove a unique continuation principle for spectral projections of Schr\" odinger operators. We consider a Schr\" odinger operator $H= -\Delta + V$ on $\mathrm{L}^2(\mathbb{R}^d)$, and let $H_{\Lambda}$ denote its restriction to a finite box $\Lambda$ ... More

Totally geodesic submanifolds of the complex quadricMar 07 2006In this article, relations between the root space decomposition of a Riemannian symmetric space of compact type and the root space decompositions of its totally geodesic submanifolds (symmetric subspaces) are described. These relations provide an approach ... More

Anderson localization for one-frequency quasi-periodic block Jacobi operatorsSep 09 2016Apr 29 2017We consider a one-frequency, quasi-periodic, block Jacobi operator, whose blocks are generic matrix-valued analytic functions. We establish Anderson localization for this type of operator under the assumption that the coupling constant is large enough ... More

Asynchronous Stochastic Gradient MCMC with Elastic CouplingDec 02 2016We consider parallel asynchronous Markov Chain Monte Carlo (MCMC) sampling for problems where we can leverage (stochastic) gradients to define continuous dynamics which explore the target distribution. We outline a solution strategy for this setting based ... More

A Discriminative Event Based Model for Alzheimer's Disease Progression ModelingFeb 21 2017The event-based model (EBM) for data-driven disease progression modeling estimates the sequence in which biomarkers for a disease become abnormal. This helps in understanding the dynamics of disease progression and facilitates early diagnosis by staging ... More

Asynchronous Stochastic Gradient MCMC with Elastic CouplingDec 02 2016Dec 08 2016We consider parallel asynchronous Markov Chain Monte Carlo (MCMC) sampling for problems where we can leverage (stochastic) gradients to define continuous dynamics which explore the target distribution. We outline a solution strategy for this setting based ... More

Towards Automated Deep Learning: Efficient Joint Neural Architecture and Hyperparameter SearchJul 18 2018While existing work on neural architecture search (NAS) tunes hyperparameters in a separate post-processing step, we demonstrate that architectural choices and other hyperparameter settings interact in a way that can render this separation suboptimal. ... More

Bayesian Effect Selection in Structured Additive Distributional Regression ModelsFeb 27 2019We propose a novel spike and slab prior specification with scaled beta prime marginals for the importance parameters of regression coefficients to allow for general effect selection within the class of structured additive distributional regression. This ... More

Near-infrared wavefront sensing for the VLT interferometerAug 12 2008The very large telescope (VLT) interferometer (VLTI) in its current operating state is equipped with high-order adaptive optics (MACAO) working in the visible spectrum. A low-order near-infrared wavefront sensor (IRIS) is available to measure non-common ... More

Bayesian structured additive distributional regression with an application to regional income inequality in GermanySep 17 2015We propose a generic Bayesian framework for inference in distributional regression models in which each parameter of a potentially complex response distribution and not only the mean is related to a structured additive predictor. The latter is composed ... More

Fast Bayesian Optimization of Machine Learning Hyperparameters on Large DatasetsMay 23 2016Bayesian optimization has become a successful tool for hyperparameter optimization of machine learning algorithms, such as support vector machines or deep neural networks. But it is still costly if each evaluation of the objective requires training and ... More

Reasoning About Pragmatics with Neural Listeners and SpeakersApr 02 2016Sep 26 2016We present a model for pragmatically describing scenes, in which contrastive behavior results from a combination of inference-driven pragmatics and learned semantics. Like previous learned approaches to language generation, our model uses a simple feature-driven ... More

Automatic normal orientation in point clouds of building interiorsJan 19 2019Orienting surface normals correctly and consistently is a fundamental problem in geometry processing. Applications such as visualization, feature detection, and geometry reconstruction often rely on the availability of correctly oriented normals. Many ... More

Ac-conductivity and electromagnetic energy absorption for the Anderson model in linear response theoryMar 03 2014We continue our study of the ac-conductivity in linear response theory for the Anderson model using the conductivity measure. We establish further properties of the conductivity measure, including nontriviality at nonzero temperature, the high temperature ... More

Reliability of regulatory networks and its evolutionMay 27 2008The problem of reliability of the dynamics in biological regulatory networks is studied in the framework of a generalized Boolean network model with continuous timing and noise. Using well-known artificial genetic networks such as the repressilator, we ... More

Reliability of genetic networks is evolvableJul 10 2007Control of the living cell functions with remarkable reliability despite the stochastic nature of the underlying molecular networks -- a property presumably optimized by biological evolution. We here ask to what extent the property of a stochastic dynamical ... More

About the Complexity of Two-Stage Stochastic IPsJan 04 2019Feb 21 2019We consider so called $2$-stage stochastic integer programs (IPs) and their generalized form of multi-stage stochastic IPs. A $2$-stage stochastic IP is an integer program of the form $\max \{ c^T x \mid Ax = b, l \leq x \leq u, x \in \mathbb{Z}^{nt + ... More

Velocity addition formulas in Robertson-Walker spacetimesMar 17 2015Universal velocity addition formulas analogous to the well-known formula in special relativity are found for four geometrically defined relative velocities in a large class of Robertson-Walker spacetimes. Explicit examples are given. The special relativity ... More

Ballistic Behavior for Random Schrödinger Operators on the Bethe StripJun 08 2011Jul 13 2011The Bethe Strip of width $m$ is the cartesian product $\B\times\{1,...,m\}$, where $\B$ is the Bethe lattice (Cayley tree). We consider Anderson-like Hamiltonians $H_\lambda=\frac12 \Delta \otimes 1 + 1 \otimes A+\lambda \Vv$ on a Bethe strip with connectivity ... More

Bootstrap multiscale analysis and localization for multi-particle continuous Anderson HamiltoniansNov 17 2013Apr 15 2014We extend the bootstrap multiscale analysis developed by Germinet and Klein to the multi-particle continuous Anderson Hamiltonian, obtaining Anderson localization with finite multiplicity of eigenvalues, decay of eigenfunction correlations, and a strong ... More

Fermi coordinates, simultaneity, and expanding space in Robertson-Walker cosmologiesOct 04 2010Mar 05 2011Explicit Fermi coordinates are given for geodesic observers comoving with the Hubble flow in expanding Robertson-Walker spacetimes, along with exact expressions for the metric tensors in Fermi coordinates. For the case of non inflationary cosmologies, ... More

A comprehensive proof of localization for continuous Anderson models with singular random potentialsMay 01 2011Sep 21 2012We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of localization ... More

Absolutely Continuous Spectrum for Random Schroedinger Operators on the Bethe StripJan 22 2011Jan 03 2012The Bethe Strip of width $m$ is the cartesian product $\B\times\{1,...,m\}$, where $\B$ is the Bethe lattice (Cayley tree). We prove that Anderson models on the Bethe strip have "extended states" for small disorder. More precisely, we consider Anderson-like ... More

Concentration around the mean for maxima of empirical processesJun 29 2005In this paper we give optimal constants in Talagrand's concentration inequalities for maxima of empirical processes associated to independent and eventually nonidentically distributed random variables. Our approach is based on the entropy method introduced ... More

A comparative review of recent researches in geometryJul 20 2008Felix Klein's so-called Erlangen Program was published in 1872 as professoral dissertation. It proposed a new solution to the problem how to classify and characterize geometries on the basis of projective geometry and group theory. The given translation ... More

Embeddings, Normal Invariants and Functor CalculusAug 27 2014May 13 2015This paper investigates the space of codimension zero embeddings of a Poincare duality space in a disk. One of our main results exhibits a tower that interpolates from the space of Poincare immersions to a certain space of "unlinked" Poincare embeddings. ... More

An eigensystem approach to Anderson localizationSep 28 2015Sep 07 2016We introduce a new approach for proving localization (pure point spectrum with exponentially decaying eigenfunctions, dynamical localization) for the Anderson model at high disorder. In contrast to the usual strategy, we do not study finite volume Green's ... More

Ground state energy of trimmed discrete Schrödinger operators and localization for trimmed Anderson modelsJan 22 2013Mar 16 2013We consider discrete Schr\"odinger operators of the form $H=-\Delta +V$ on $\ell^2(\Z^d)$, where $\Delta$ is the discrete Laplacian and $V$ is a bounded potential. Given $\Gamma \subset \Z^d$, the $\Gamma$-trimming of $H$ is the restriction of $H$ to ... More

The conductivity measure for the Anderson modelSep 21 2007We study the ac-conductivity in linear response theory for the Anderson tight-binding model. We define the electrical ac-conductivity and calculate the linear-response current at zero temperature for arbitrary Fermi energy. In particular, the Fermi energy ... More

Weak Limit of the 3-State Quantum Walk on the LineApr 04 2014May 21 2014We revisit the one dimensional discrete time quantum walk with 3 states and the Grover coin. We derive analytic expressions for observed the localization, an long time approximation for the probability density function (PDF). We also connect the time ... More

Streaming KernelizationMay 06 2014Kernelization is a formalization of preprocessing for combinatorially hard problems. We modify the standard definition for kernelization, which allows any polynomial-time algorithm for the preprocessing, by requiring instead that the preprocessing runs ... More

Critical point correlations in random gaussian fieldsNov 22 2011We consider fluctuations in the distribution of critical points - saddle points, minima and maxima - of random gaussian fields. We calculate the asymptotic limits of the two point correlation function for various critical point densities, for both long ... More

Possible solution of the Coriolis attenuation problemNov 05 1996The most consistently useful simple model for the study of odd deformed nuclei, the particle-rotor model (strong coupling limit of the core-particle coupling model) has nevertheless been beset by a long-standing problem: It is necessary in many cases ... More

Interaction of Impurity Atoms in Bose-Einstein-CondensatesJul 30 2004The interaction of two spatially separated impurity atoms through phonon exchange in a Bose-Einstein condensate is studied within a Bogoliubov approach. The impurity atoms are held by deep and narrow trap potentials and experience level shifts which consist ... More

Continuity, positivity and simplicity of the Lyapunov exponents for quasi-periodic cocyclesMar 22 2016Mar 16 2017An analytic quasi-periodic cocycle is a linear cocycle over a fixed ergodic torus translation of one or several variables, where the fiber action depends analytically on the base point. Consider the space of all such cocycles of any given dimension and ... More

Optimal control for the thin-film equation: Convergence of a multi-parameter approach to track state constraints avoiding degeneraciesOct 08 2014Aug 08 2015We consider an optimal control problem subject to the thin-film equation which is deduced from the Navier--Stokes equation. The PDE constraint lacks well-posedness for general right-hand sides due to possible degeneracies; state constraints are used to ... More

The Liouville equation for singular ergodic magnetic Schrödinger operatorsNov 24 2008Oct 08 2009We study the time evolution of a density matrix in a quantum mechanical system described by an ergodic magnetic Schr\"odinger operator with singular magnetic and electric potentials, the electric field being introduced adiabatically. We construct a unitary ... More

A shortcut to (sun)flowers: Kernels in logarithmic space or linear timeApr 30 2015We investigate whether kernelization results can be obtained if we restrict kernelization algorithms to run in logarithmic space. This restriction for kernelization is motivated by the question of what results are attainable for preprocessing via simple ... More

Finite-Size Corrections for Ground States of Edwards-Anderson Spin GlassesOct 28 2011May 30 2012Extensive computations of ground state energies of the Edwards-Anderson spin glass on bond-diluted, hypercubic lattices are conducted in dimensions d=3,..,7. Results are presented for bond-densities exactly at the percolation threshold, p=p_c, and deep ... More

The generating of Fractal Images Using MathCAD ProgramMar 24 2009This paper presents the graphic representation in the z-plane of the first three iterations of the algorithm that generates the Sierpinski Gasket. It analyzes the influence of the f(z) map when we represent fractal images.

Projection methods for ill-posed problems revisitedJul 13 2015The discretization of least-squares problems for linear ill-posed operator equations in Hilbert spaces is considered. The main subject of this article concerns conditions for convergence of the associated discretized minimum-norm least-squares solution ... More

Twisted Reidemeister torsion, the Thurston norm and fibered manifoldsJan 29 2013We prove that the twisted Reidemeister torsion of a 3-manifold corresponding to a fibered class is monic and we show that it gives lower bounds on the Thurston norm. The former fixes a flawed proof in [FV10], the latter gives a quick alternative argument ... More

Reidemeister torsion, the Thurston norm and Harvey's invariantsAug 31 2005Feb 25 2006Recently twisted and higher order Alexander polynomials were used by Cochran, Harvey, Friedl--Kim and Turaev to give lower bounds on the Thurston norm. We first show how Reidemeister torsion relates to these Alexander polynomials. We then give lower bounds ... More

A Hidden Signal in the Ulam sequenceJul 01 2015Jul 06 2016The Ulam sequence is defined as $a_1 =1, a_2 = 2$ and $a_n$ being the smallest integer that can be written as the sum of two distinct earlier elements in a unique way. This gives $$1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 26, 28, 36, 38, 47, \dots$$ Ulam remarked ... More

New Bounds for the Traveling Salesman ConstantNov 25 2013Mar 27 2014Let $X_1, X_2, \dots, X_n$ be independent and uniformly distributed random variables in the unit square $[0,1]^2$ and let $L(X_1, \dots, X_n)$ be the length of the shortest traveling salesman path through these points. In 1959, Beardwood, Halton $\&$ ... More

Nonextensive statistical mechanics and complex scale-free networksSep 07 2006One explanation for the impressive recent boom in network theory might be that it provides a promising tool for an understanding of complex systems. Network theory is mainly focusing on discrete large-scale topological structures rather than on microscopic ... More

Aging Exponents in Self-Organized CriticalityJun 11 1997Aug 07 1997In a recent Letter [Phys. Rev. Lett. 79, 889 (1997) and cond-mat/9702054] we have demonstrated that the avalanches in the Bak-Sneppen model display aging behavior similar to glassy systems. Numerical results for temporal correlations show a broad distribution ... More

Stiffness of the Edwards-Anderson Model in all DimensionsAug 01 2005Sep 23 2005A comprehensive description in all dimensions is provided for the scaling exponent $y$ of low-energy excitations in the Ising spin glass introduced by Edwards and Anderson. A combination of extensive numerical as well as theoretical results suggest that ... More

Morita theory in abelian, derived and stable model categoriesOct 10 2003This is a survey paper, based on lectures given at the Workshop on "Structured ring spectra and their applications" which took place January 21-25, 2002, at the University of Glasgow. The term `Morita theory' is usually used for results concerning equivalences ... More

Neutron skin thickness of heavy nuclei with $α$-particle correlations and the slope of the nuclear symmetry energyMar 12 2014Jun 16 2014The formation of $\alpha$-particle clusters on the surface of heavy nuclei is described in a generalized relativistic mean-field model with explicit cluster degrees of freedom. The effects on the size of the neutron skin of Sn nuclei and ${}^{208}$Pb ... More

Fermions and the scattering equationsDec 18 2014Mar 03 2015This paper investigates how tree-level amplitudes with massless quarks, gluons and/or massless scalars transforming under a single copy of the gauge group can be expressed in the context of the scattering equations as a sum over the inequivalent solutions ... More

The SISCone jet algorithm optimised for low particle multiplicitiesAug 09 2011Dec 10 2011The SISCone jet algorithm is a seedless infrared-safe cone jet algorithm. There exists an implementation which is highly optimised for a large number of final state particles. However, in fixed-order perturbative calculations with a small number of final ... More

Does one need the O(epsilon)- and O(epsilon^2)-terms of one-loop amplitudes in an NNLO calculation ?Jul 26 2011Sep 12 2011This article discusses the occurences of one-loop amplitudes within a next-to-next-to-leading order calculation. In an NNLO calculation the one-loop amplitude enters squared and one would therefore naively expect that the O(epsilon)- and O(epsilon^2)-terms ... More

Automated calculations for multi-leg processesJul 23 2007Jul 26 2007The search for signals of new physics at the forthcoming LHC experiments involves the analysis of final states characterised by a high number of hadronic jets or identified particles. Precise theoretical predictions for these processes require the computation ... More

Hopf algebra structures in particle physicsOct 14 2003In the recent years, Hopf algebras have been introduced to describe certain combinatorial properties of quantum field theories. I will give a basic introduction to these algebras and review some occurrences in particle physics.

Moments of event shapes in electron-positron annihilation at NNLOSep 28 2009Nov 10 2009This article gives the perturbative NNLO results for the moments of the most commonly used event shape variables associated to three-jet events in electron-positron annihilation: Thrust, heavy jet mass, wide jet broadening, total jet broadening, C parameter ... More

Introduction to Monte Carlo methodsJun 23 2000These lectures given to graduate students in high energy physics, provide an introduction to Monte Carlo methods. After an overview of classical numerical quadrature rules, Monte Carlo integration together with variance-reducing techniques is introduced. ... More

Calculational techniques (not only) for single top productionMay 29 2000A next-to-leading order calculation for single top production including spin-dependent observables requires efficient techniques for the calculation of the relevant loop amplitudes. We discuss the adaption of dimensional regularization, the spinor helicity ... More

Coherent states and geodesics: cut locus and conjugate locusFeb 22 1995Sep 15 1995The intimate relationship between coherent states and geodesics is pointed out. For homogenous manifolds on which the exponential from the Lie algebra to the Lie group equals the geodesic exponential, and in particular for symmetric spaces, it is proved ... More

Symmetry Dependence of Localization in Quasi- 1- dimensional Disordered WiresMar 26 2000Jun 25 2000The crossover in energy level statistics of a quasi-1-dimensional disordered wire as a function of its length L is used, in order to derive its averaged localization length, without magnetic field, in a magnetic field and for moderate spin orbit scattering ... More

Indirect Detection of Dark Matter with gamma raysOct 10 2013Feb 12 2014The details of what constitutes the majority of the mass that makes up dark matter in the Universe remains one of the prime puzzles of cosmology and particle physics today - eighty years after the first observational indications. Today, it is widely accepted ... More

The asymptotic rank of metric spacesJan 08 2007Oct 20 2008In this article we define and study a notion of asymptotic rank for metric spaces and show in our main theorem that for a large class of spaces, the asymptotic rank is characterized by the growth of the higher filling functions. For a proper, cocompact, ... More

Nilpotent groups without exactly polynomial Dehn functionApr 16 2010We prove super-quadratic lower bounds for the growth of the filling area function of a certain class of Carnot groups. This class contains groups for which it is known that their Dehn function grows no faster than $n^2\log n$. We therefore obtain the ... More

Expectation bubbles in a spin model of markets: Intermittency from frustration across scalesMay 10 2001May 16 2001A simple spin model is studied, motivated by the dynamics of traders in a market where expectation bubbles and crashes occur. The dynamics is governed by interactions which are frustrated across different scales: While ferromagnetic couplings connect ... More

A Remark on Non-equivalent Star Products via Reduction for CP^nFeb 17 1998In this paper we construct non-equivalent star products on CP^n by phase space reduction. It turns out that the non-equivalent star products occur very natural in the context of phase space reduction by deforming the momentum map of the U(1)-action on ... More

The Covariant Picard Groupoid in Differential GeometrySep 23 2005In this article we discuss some general results on the covariant Picard groupoid in the context of differential geometry and interpret the problem of lifting Lie algebra actions to line bundles in the Picard groupoid approach.

Flavor physics with $Λ_b$ baryonsJan 13 2014Feb 26 2015At the LHC, bottom baryons are being produced in unprecedented quantities, which opens up a new field for flavor physics. For example, the decay $\Lambda_b \to p \mu^- \bar{\nu}$ can be used to obtain a novel determination of the CKM matrix element $|V_{ub}|$, ... More

Infinite multiplicity of abelian subalgebras in free group subfactorsFeb 07 2004We obtain an estimate of Voiculescu's (modified) free entropy dimension for generators of a ${II}_1$-factor $\mc{M}$ with a subfactor $\mc{N}$ containing an abelian subalgebra $\mc{A}$ of finite multiplicity. It implies in particular that the interpolated ... More

Algorithms for lattice QCD: progress and challengesNov 25 2010The development of improved algorithms for QCD on the lattice has enabled us to do calculations at small quark masses and get control over the chiral extrapolation. Also finer lattices have become possible, however, a severe slowing down associated with ... More

Algorithms for dynamical overlap fermionsSep 28 2006An overview of the current status of algorithmic approaches to dynamical overlap fermions is given. In particular the issue of changing the topological sector is discussed.

Hyperon-nucleon interaction and baryonic contact terms in SU(3) chiral effective field theoryDec 16 2013In this proceeding we summarize results for baryonic contact terms derived within SU(3) chiral effective field theory. The four-baryon contact terms, necessary for the description of the hyperon-nucleon interaction, include SU(3) symmetric and explicit ... More

A model of semimetallic behavior in strongly correlated electron systemsNov 17 1998Metals with values of the resistivity and the Hall coefficient much larger than typical ones, e.g., of sodium, are called semimetals. We suggest a model for semimetals which takes into account the strong Coulomb repulsion of the charge carriers, especially ... More

New opportunities with spectro-interferometry and spectro-astrometryDec 15 2013Latest-generation spectro-interferometric instruments combine a milliarcsecond angular resolution with spectral capabilities, resulting in an immensely increased information content. Here, I present methodological work and results that illustrate the ... More

Power correction analyses in e+e- annihilationSep 29 2000The current status of theoretical work and experimental analyses on power corrections in QCD for e+e- annihilation will be reviewed. Measurements of the number of active quark flavours n_f and the QCD colour factors C_A and C_F derived from QCD fits to ... More

Full signature invariants for $L_0(F(t))$May 28 2003We find full invariants for detecting non--zero elements in ${L}_0(F(t))\otimes \Q$, this group plays an important role in topology in the work done by Casson and Gordon.

Non-equilibrium almost-stationary states and linear response for gapped quantum systemsAug 11 2017Mar 18 2019We prove the validity of linear response theory at zero temperature for perturbations of gapped Hamiltonians describing interacting fermions on a lattice. As an essential innovation, our result requires the spectral gap assumption only for the unperturbed ... More

Changing the topology of Tensor NetworksMar 07 2012In many applications, it is needed to change the topology of a tensor network directly and without approximation. This work will introduce a general scheme that satisfies these needs. We will describe the procedure by two examples and show its efficiency ... More

Counting Finite Languages by Total Word LengthJan 25 2010We investigate the number of sets of words that can be formed from a finite alphabet, counted by the total length of the words in the set. An explicit expression for the counting sequence is derived from the generating function, and asymptotics for large ... More

Simple Models of Quasihomogeneous Projective 3-FoldsMay 08 1998Let X be a projective complex 3-fold, quasihomogeneous with respect to an action of a linear algebraic group. We show that X is a compactification of SL_2/G, G a discrete subgroup, or that X can be equivariantly transformed into the 3-dim. projective ... More

Lasso and equivalent quadratic penalized modelsJan 10 2014The least absolute shrinkage and selection operator (lasso) and ridge regression produce usually different estimates although input, loss function and parameterization of the penalty are identical. In this paper we look for ridge and lasso models with ... More

A differential equation with monodromy group $2.J_2$Apr 27 2015We construct a sixth order differential equation having the central extension of $C_2$ by the Hall-Janko group $J_2$ as monodromy group. Moreover it arises from an iterated application of tensor products and convolution operations from a first order differential ... More

Spectral Triples on Carnot ManifoldsApr 22 2014We analyze whether one can construct a spectral triple for a Carnot manifold $M$, which detects its Carnot-Carath\'{e}odory metric and its graded dimension. Therefore we construct self-adjoint horizontal Dirac operators $D^H$ and show that each horizontal ... More

A Geometric Approach to Noncommutative Principal BundlesAug 01 2011From a geometrical point of view it is, so far, not sufficiently well understood what should be a "noncommutative principal bundle". Still, there is a well-developed abstract algebraic approach using the theory of Hopf algebras. An important handicap ... More

A Counterexample to Guillemin's Zollfrei ConjectureFeb 11 2013We construct Zollfrei Lorentzian metrics on every nontrivial orientable circle bundle over a orientable closed surface. Further we prove a weaker version of Guillemin's conjecture assuming global hyperbolicity of the universal cover.

Large deviations for empirical path measures in cycles of integer partitionsFeb 02 2007Feb 05 2007Consider a large system of $N$ Brownian motions in $\mathbb{R}^d$ on some fixed time interval $[0,\beta]$ with symmetrised initial-terminal condition. That is, for any $i$, the terminal location of the $i$-th motion is affixed to the initial point of ... More

The Group of Hamiltonian Homeomorphisms in the L^\infty-normMay 08 2007The group Hameo (M,\omega) of Hamiltonian homeomorphisms of a connected symplectic manifold (M,\omega) was defined and studied in [7] and further in [6]. In these papers, the authors consistently used the L^{(1,\infty)}-Hofer norm (and not the L^\infty-Hofer ... More

Geometry on totally separably closed schemesMar 10 2015Nov 21 2016We prove, for quasicompact separated schemes over ground fields, that Cech cohomology coincides with sheaf cohomology with respect to the Nisnevich topology. This is a partial generalization of Artin's result that for noetherian schemes such an equality ... More

Algebraic versus topological triangulated categoriesJul 16 2008The most commonly known triangulated categories arise from chain complexes in an abelian category by passing to chain homotopy classes or inverting quasi-isomorphisms. Such examples are called `algebraic' because they originate from abelian (or at least ... More

The AS-Cohen-Macaulay property for quantum flag manifolds of minuscule weightJul 10 2007It is shown that quantum homogeneous coordinate rings of generalised flag manifolds corresponding to minuscule weights, their Schubert varieties, big cells, and determinantal varieties are AS-Cohen-Macaulay. The main ingredient in the proof is the notion ... More

Regularity of quotients by an automorphism of order $p$Jan 05 2010Let $B$ be a regular local ring and $G\subset\Aut(B)$ a finite group of local automorphisms. Assume that $G$ is cyclic of prime order $p$, where $p$ is equal to the residue characteristic of $B$. We give conditions under which the ring of invariants $A=B^G$ ... More