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Predictive and Self Triggering for Event-based State EstimationSep 23 2016Event-based state estimation can achieve estimation quality comparable to traditional time-triggered methods, but with a significantly lower number of samples. In networked estimation problems, this reduction in sampling instants does, however, not necessarily ... More

Distributed Event-based State EstimationNov 16 2015An event-based state estimation approach for reducing communication in a networked control system is proposed. Multiple distributed sensor-actuator-agents observe a dynamic process and sporadically exchange their measurements and inputs over a bus network. ... More

Online learning with stability guarantees: A memory-based real-time model predictive controllerDec 22 2018Jan 08 2019We propose and analyze a real-time model predictive control (MPC) scheme that utilizes stored data to improve its performance by learning the value function online with stability guarantees. The suboptimality of the applied control input resulting from ... More

Depth-Based Object Tracking Using a Robust Gaussian FilterFeb 19 2016We consider the problem of model-based 3D-tracking of objects given dense depth images as input. Two difficulties preclude the application of a standard Gaussian filter to this problem. First of all, depth sensors are characterized by fat-tailed measurement ... More

Feedback Control Goes Wireless: Guaranteed Stability over Low-power Multi-hop NetworksApr 24 2018Feb 19 2019Closing feedback loops fast and over long distances is key to emerging applications; for example, robot motion control and swarm coordination require update intervals of tens of milliseconds. Low-power wireless technology is preferred for its low cost, ... More

Event-triggered LearningApr 05 2019Efficient exchange of information is an essential aspect of intelligent collective behavior. Event-triggered control and estimation achieve some efficiency by replacing continuous data exchange between agents with intermittent, or event-triggered communication. ... More

Resource-aware IoT Control: Saving Communication through Predictive TriggeringJan 19 2019The Internet of Things (IoT) interconnects multiple physical devices in large-scale networks. When the 'things' coordinate decisions and act collectively on shared information, feedback is introduced between them. Multiple feedback loops are thus closed ... More

Automatic LQR Tuning Based on Gaussian Process Global OptimizationMay 06 2016This paper proposes an automatic controller tuning framework based on linear optimal control combined with Bayesian optimization. With this framework, an initial set of controller gains is automatically improved according to a pre-defined performance ... More

A Local Information Criterion for Dynamical SystemsMay 27 2018Encoding a sequence of observations is an essential task with many applications. The encoding can become highly efficient when the observations are generated by a dynamical system. A dynamical system imposes regularities on the observations that can be ... More

Evaluating Low-Power Wireless Cyber-Physical SystemsApr 25 2018Simulation tools and testbeds have been proposed to assess the performance of control designs and wireless protocols in isolation. A cyber-physical system (CPS), however, integrates control with network elements, which must be evaluated together under ... More

Trajectory-Based Off-Policy Deep Reinforcement LearningMay 14 2019Policy gradient methods are powerful reinforcement learning algorithms and have been demonstrated to solve many complex tasks. However, these methods are also data-inefficient, afflicted with high variance gradient estimates, and frequently get stuck ... More

Event-triggered Learning for Resource-efficient Networked ControlMar 05 2018Sep 27 2018Common event-triggered state estimation (ETSE) algorithms save communication in networked control systems by predicting agents' behavior, and transmitting updates only when the predictions deviate significantly. The effectiveness in reducing communication ... More

Event-triggered Pulse Control with Model Learning (if Necessary)Mar 19 2019In networked control systems, communication is a shared and therefore scarce resource. Event-triggered control (ETC) can achieve high performance control with a significantly reduced amount of samples compared to classical, periodic control schemes. However, ... More

Learning an Approximate Model Predictive Controller with GuaranteesJun 11 2018A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of nonlinear systems. ... More

On the Design of LQR Kernels for Efficient Controller LearningSep 20 2017Finding optimal feedback controllers for nonlinear dynamic systems from data is hard. Recently, Bayesian optimization (BO) has been proposed as a powerful framework for direct controller tuning from experimental trials. For selecting the next query point ... More

A New Perspective and Extension of the Gaussian FilterApr 29 2015Jun 05 2015The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. GFs represent the belief of the current state by a Gaussian with the ... More

Efficient Encoding of Dynamical Systems through Local ApproximationsMay 24 2018Sep 27 2018An efficient representation of observed data has many benefits in various domains of engineering and science. Representing static data sets, such as images, is a living branch in machine learning and eases downstream tasks, such as classification, regression, ... More

Deep Reinforcement Learning for Event-Triggered ControlSep 13 2018Event-triggered control (ETC) methods can achieve high-performance control with a significantly lower number of samples compared to usual, time-triggered methods. These frameworks are often based on a mathematical model of the system and specific designs ... More

Data-efficient Auto-tuning with Bayesian Optimization: An Industrial Control StudyDec 15 2018Dec 18 2018Bayesian optimization is proposed for automatic learning of optimal controller parameters from experimental data. A probabilistic description (a Gaussian process) is used to model the unknown function from controller parameters to a user-defined cost. ... More

Gait learning for soft microrobots controlled by light fieldsSep 10 2018Soft microrobots based on photoresponsive materials and controlled by light fields can generate a variety of different gaits. This inherent flexibility can be exploited to maximize their locomotion performance in a given environment and used to adapt ... More

Robust Gaussian Filtering using a Pseudo MeasurementSep 14 2015May 30 2016Many sensors, such as range, sonar, radar, GPS and visual devices, produce measurements which are contaminated by outliers. This problem can be addressed by using fat-tailed sensor models, which account for the possibility of outliers. Unfortunately, ... More

Model-Based Policy Search for Automatic Tuning of Multivariate PID ControllersMar 08 2017PID control architectures are widely used in industrial applications. Despite their low number of open parameters, tuning multiple, coupled PID controllers can become tedious in practice. In this paper, we extend PILCO, a model-based policy search framework, ... More

Probabilistic Recurrent State-Space ModelsJan 31 2018Feb 10 2018State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series data. Fully ... More

Feedback Control Goes Wireless: Guaranteed Stability over Low-power Multi-hop NetworksApr 24 2018Nov 02 2018Closing feedback loops fast and over long distances is key to emerging applications; for example, robot motion control and swarm coordination require update intervals of tens of milliseconds. Low-power wireless is preferred for its low cost, small form ... More

Virtual vs. Real: Trading Off Simulations and Physical Experiments in Reinforcement Learning with Bayesian OptimizationMar 03 2017In practice, the parameters of control policies are often tuned manually. This is time-consuming and frustrating. Reinforcement learning is a promising alternative that aims to automate this process, yet often requires too many experiments to be practical. ... More

Fast and Tiny Structural Self-Indexes for XMLDec 28 2010XML document markup is highly repetitive and therefore well compressible using dictionary-based methods such as DAGs or grammars. In the context of selectivity estimation, grammar-compressed trees were used before as synopsis for structural XPath queries. ... More

XPath Node Selection over Grammar-Compressed TreesNov 21 2013XML document markup is highly repetitive and therefore well compressible using grammar-based compression. Downward, navigational XPath can be executed over grammar-compressed trees in PTIME: the query is translated into an automaton which is executed ... More

String States on AdS_3 x S^3 from the SupergroupAug 01 2012Oct 24 2012In the hybrid formulation of string theory on AdS_3 x S^3, the compactification-independent physical spectrum at the first massive level is determined. We find that these states transform in representations of the Lie superalgebra psl(2|2) and present ... More

Surgery stable curvature conditionsMar 26 2013We give a simple criterion for a pointwise curvature condition to be stable under surgery. Namely, a curvature condition $C$, which is understood to be an open, convex, O(n)-invariant cone in the space of algebraic curvature operators, is stable under ... More

B_s-B_s-bar mixing and lepton flavor violation in SUSY SO(10)May 27 2005We present a quantitative analysis of the flavor physics of a SUSY SO(10) model proposed by Chang, Masiero, and Murayama, linking b -> s transitions to the large observed atmospheric neutrino mixing. We consider B_s-B_s-bar mixing and tau -> mu gamma ... More

Kernels of representations and coideal subalgebras of Hopf algebrasDec 14 2010We define left and right kernels of representations of Hopf algebras. In the case of group algebras, left and right kernels coincide and they are the usual kernels of modules. In the general case we show that these kernels coincide with the categorical ... More

Information Theoretic Resources in Quantum TheoryMar 19 2013Resource identification and quantification is an essential element of both classical and quantum information theory. Entanglement is one of these resources, arising when quantum communication and nonlocal operations are expensive to perform. In the first ... More

Quantifying entanglement when measurements are imperfect or restrictedNov 19 2010Oct 30 2012Motivated by the increasing ability of experimentalists to perform detector tomography, we consider how to incorporate the imperfections and restrictions of available measurements directly into the quantification of entanglement. Exploiting the idea that ... More

A simple test for the existence of two accretion modes in Active Galactic NucleiFeb 20 2005By analogy to the different accretion states observed in black-hole X-ray binaries (BHXBs), it appears plausible that accretion disks in active galactic nuclei (AGN) undergo a state transition between a radiatively efficient and inefficient accretion ... More

Dimer Models, Integrable Systems and Quantum Teichmuller SpaceMay 09 2011Jul 05 2011We introduce a correspondence between dimer models (and hence superconformal quivers) and the quantum Teichmuller space of the Riemann surfaces associated to them by mirror symmetry. Via the untwisting map, every brane tiling gives rise to a tiling of ... More

Shortcuts to adiabaticity: Suppression of pair production in driven Dirac dynamicsNov 02 2015Dec 09 2015Achieving effectively adiabatic dynamics in finite time is a ubiquitous goal in virtually all areas of modern physics. So-called shortcuts to adiabaticity refer to a set of methods and techniques that allow to produce in a short time the same final state ... More

Theoretical foundations and applications of the Loop-Tree Duality in Quantum Field TheoriesSep 23 2015The Loop-Tree Duality (LTD) is a novel perturbative method in QFT that establishes a relation between loop-level and tree-level scattering amplitudes. This is achieved by directly applying the Residue Theorem to the loop-energy-integration. The result ... More

A Geometric Approach to Pairwise Bayesian Alignment of Functional Data Using Importance SamplingMay 26 2015Mar 03 2016We present a Bayesian model for pairwise nonlinear registration of functional data. We utilize the geometry of the space of warping functions to define appropriate prior distributions and sample from the posterior using importance sampling. A simple square-root ... More

Resolutions for unit groups of ordersSep 28 2016Oct 27 2016We present a general algorithm for constructing a free resolution for unit groups of orders in semisimple rational algebras. The approach is based on computing a contractible $G$-complex employing the theory of minimal classes of quadratic forms and Opgenorth's ... More

Barrett: out-of-core processing of MultiNest outputAug 02 2016Barrett is a Python package for processing and visualising statistical inferences made using the nested sampling algorithm MultiNest. The main differential feature from competitors are full out-of-core processing allowing barrett to handle arbitrarily ... More

Quantum computation with three-electron double quantum dots at an optimal operation pointJul 13 2015The author analyzes quantum computation with the hybrid qubit (HQ) that is encoded using the three-electron configuration of a double quantum dot. All gate operations are controlled with electric signals, while the qubit remains at an optimal operation ... More

Aging dynamics of non-linear elastic interfaces: the Kardar-Parisi-Zhang equationAug 20 2007In this work, the out-of-equilibrium dynamics of the Kardar-Parisi-Zhang equation in (1+1) dimensions is studied by means of numerical simulations, focussing on the two-times evolution of an interface in the absence of any disordered environment. This ... More

Quantum Zeno suppression of dipole-dipole forcesNov 23 2016We consider inter-atomic forces due to resonant dipole-dipole interactions within a dimer of highly excited Rydberg atoms, embedded in an ultra-cold gas. These forces rely on a coherent superposition of two-atom electronic states, which is destroyed by ... More

Improving the Accuracy and Efficiency of MAP Inference for Markov LogicJun 13 2012In this work we present Cutting Plane Inference (CPI), a Maximum A Posteriori (MAP) inference method for Statistical Relational Learning. Framed in terms of Markov Logic and inspired by the Cutting Plane Method, it can be seen as a meta algorithm that ... More

Towards a Data Reduction for the Minimum Flip Supertree ProblemApr 22 2011In computational phylogenetics, the problem of constructing a supertree of a given set of rooted input trees can be formalized in different ways, to cope with contradictory information in the input. We consider the Minimum Flip Supertree problem, where ... More

Data Assimilation: The Schrödinger PerspectiveJul 22 2018Apr 10 2019Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using probabilistic particle-based ... More

Asymptotic efficiency for covariance estimation under noise and asynchronicitySep 07 2018The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds for a fundamental parametric model give ... More

Superstrings in General BackgroundsJul 31 2008Mar 12 2009The thesis divides into three parts. The first is devoted to a careful study of very convenient superspace conventions which are a basic tool for the second part. A theorem is formulated that gives a clear statement about when the signs of a superspace ... More

A Remark on Coclosed G_2-StructuresMay 03 2010Aug 19 2010We prove that Einstein coclosed G_2-structures are nearly parallel.

A criterion for transience of multidimensional branching random walk in random environmentMay 14 2007We develop a criterion for transience for a general model of branching Markov chains. In the case of multi-dimensional branching random walk in random environment (BRWRE) this criterion becomes explicit. In particular, we show that \emph{Condition L} ... More

Brane-World chargesOct 12 2000Mar 27 2001As opposed to usual Einstein gravity in four dimensions, the Brane-World scenario allows the construction of a local density of gravitational energy (and also of momentum, of angular momentum, etc...). This is a direct consequence of the hypothesis that ... More

Periodic-Orbit Approach to Universality in Quantum ChaosDec 20 2005We show that in the semiclassical limit, classically chaotic systems have universal spectral statistics. Concentrating on short-time statistics, we identify the pairs of classical periodic orbits determining the small-$\tau$ behavior of the spectral form ... More

Asymptotic efficiency for covariance estimation under noise and asynchronicitySep 07 2018May 06 2019The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds are established for a general Gaussian framework ... More

Geometric interpretations of a counterexample to Hilbert's 14th problem, and rings of bounded polynomials on semialgebraic setsMay 10 2011Dec 31 2012We interpret a counterexample to Hilbert's 14th problem by S. Kuroda geometrically in two ways: As ring of regular functions on a smooth rational quasiprojective variety over any field K of characteristic 0, and, in the special case where K are the real ... More

Controlling nonlinear PDEs using low-dimensional bilinear approximations obtained from dataJan 18 2018May 14 2019In a recent article, we presented a framework to control nonlinear partial differential equations (PDEs) by means of Koopman operator based reduced models and concepts from switched systems. The main idea was to transform a control system into a set of ... More

The quintic nonlinear Schrödinger equation on three-dimensional Zoll manifoldsJan 24 2011Oct 14 2011Let (M,g) be a three-dimensional smooth compact Riemannian manifold such that all geodesics are simple and closed with a common minimal period, such as the 3-sphere S^3 with canonical metric. In this work the global well-posedness problem for the quintic ... More

A Gaussian mixture ensemble transform filterFeb 15 2011Jul 06 2011We generalize the popular ensemble Kalman filter to an ensemble transform filter where the prior distribution can take the form of a Gaussian mixture or a Gaussian kernel density estimator. The design of the filter is based on a continuous formulation ... More

Tangency properties of sets with finite geometric curvature energiesFeb 02 2012Apr 03 2012We investigate inverse thickness $1/\Delta$ and the integral Menger curvature energies $\mathcal{U}_{p}^{\alpha}$, $\mathcal{I}_{p}^{\alpha}$ and $\mathcal{M}_{p}^{\alpha}$, to find that finite $1/\Delta$ or $\mathcal{U}_{p}^{\alpha}$ implies the existence ... More

First passage percolation in Euclidean space and on random tessellationsNov 07 2016There are various models of first passage percolation (FPP) in $\mathbb R^d$. We want to start a very general study of this topic. To this end we generalize the first passage percolation model on the lattice $\mathbb Z^d$ to $\mathbb R^d$ and adapt the ... More

An L2-quotient algorithm for finitely presented groups on arbitrarily many generatorsFeb 27 2014We generalize the Plesken-Fabia\'nska $\mathrm{L}_2$-quotient algorithm for finitely presented groups on two or three generators to allow an arbitrary number of generators. The main difficulty lies in a constructive description of the invariant ring of ... More

On a three dimensional analogue to the holomorphic z-powersJul 11 2010The main objective of this article is a constructive generalization of the holomorphic power and Laurent series expansions in C to dimension 3 using the framework of hypercomplex function theory. For this reason, deals the first part of this article with ... More

The functors Wbar and Diag o Nerve are simplicially homotopy equivalentApr 07 2008Given a simplicial group G, there are two known classifying simplicial set constructions, the Kan classifying simplicial set Wbar G and Diag N G, where N denotes the dimensionwise nerve. They are known to be weakly homotopy equivalent. We will show that ... More

Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagramJan 27 2008The local geometry of a Riemannian symmetric space is described completely by the Riemannian metric and the Riemannian curvature tensor of the space. In the present article I describe how to compute these tensors for any Riemannian symmetric space from ... More

Totally geodesic submanifolds of the complex and the quaternionic 2-GrassmanniansSep 17 2007In this article, I classify the totally geodesic submanifolds in the complex 2-Grassmannians and in the quaternionic 2-Grassmannians. It turns out that for both of these spaces, the earlier classification of maximal totally geodesic submanifolds in Riemannian ... More

Vafa-Witten Estimates for Compact Symmetric SpacesMay 10 2006Aug 31 2006We give an optimal upper bound for the first eigenvalue of the untwisted Dirac operator on a compact symmetric space G/H with rk G-rk H\le 1 with respect to arbitrary Riemannian metrics. We also prove a rigidity statement.

Eigenvectors of tensors - A primerOct 10 2018We give an introduction to the theory and to some applications of eigenvectors of tensors (in other words, invariant one-dimensional subspaces of homogeneous polynomial maps), including a review of some concepts that are useful for their discussion. The ... More

Uniform Error Estimation for Convection-Diffusion ProblemsMar 03 2014Let us consider the singularly perturbed model problem $Lu:=-\varepsilon\Delta u-bu_x+c u =f$ with homogeneous Dirichlet boundary conditions on $\Gamma=\partial\Omega$ $u|_\Gamma =0$ on the unit-square $\Omega=(0,1)^2$. Assuming that $b>0$ is of order ... More

Determining Aschbacher classes using charactersFeb 26 2014Let $\Delta\colon G \to \mathrm{GL}(n, K)$ be an absolutely irreducible representation of an arbitrary group $G$ over an arbitrary field $K$; let $\chi\colon G \to K\colon g \mapsto \mathrm{tr}(\Delta(g))$ be its character. In this paper, we assume knowledge ... More

On auto-equivalences and complete derived invariants of gentle algebrasApr 09 2019We study triangulated categories which can be modeled by an oriented marked surface $\mathcal{S}$ and a line field $\eta$ on $\mathcal{S}$. This includes bounded derived categories of gentle algebras and -- conjecturally -- all partially wrapped Fukaya ... More

Discrete ThicknessJan 22 2014We investigate the relationship between a discrete version of thickness and its smooth counterpart. These discrete energies are defined on equilateral polygons with $n$ vertices. It will turn out that the smooth ropelength, which is the scale invariant ... More

Data Assimilation: The Schrödinger PerspectiveJul 22 2018May 01 2019Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using probabilistic particle-based ... More

Feature-based groupwise registration of historical aerial images to present-day ortho-photo mapsNov 22 2018In this paper, we address the registration of historical WWII images to present-day ortho-photo maps for the purpose of geolocalization. Due to the challenging nature of this problem, we propose to register the images jointly as a group rather than in ... More

A model for the behaviour of fluid droplets based on mean curvature flowFeb 17 2011May 27 2011During his experiments W. D. Ristenpart made a very remarkable discovery. If two oppositely charged droplets of fluid are close enough, at first they attract each other and touch eventually. Surprisingly after that the droplets are repelled from each ... More

The Effect of Hole Ice on the Propagation and Detection of Light in IceCubeApr 17 2019IceCube is a neutrino observatory at Earth's South Pole that uses glacial ice as detector medium. Secondary particles from neutrino interactions produce Cherenkov light, which is detected by an array of photo detectors deployed within the ice. In distinction ... More

Eberhard-type theorems with two kinds of polygonsJan 03 2019Eberhard-type theorems are statements about the realizability of a polytope (or more general polyhedral maps) given the valency of its vertices and sizes of its polygonal faces up to a linear linear degree of freedom. We present new theorems of Eberhard-type ... More

The Strong Colors of Flowers - The Structure of Graphs with Chordal SquaresNov 09 2017A proper vertex coloring of a graph is a mapping of its vertices on a set of colors, such that two adjacent vertices are not mapped to the same color. This constraint may be interpreted in terms of the distance between to vertices and so a more general ... More

On the irreducible representations of generalized quantum doublesFeb 20 2012A description of all the irreducible representations of generalized quantum doubles associated to skew pairings of semisimple Hopf algebras is given. In particular a description of the irreducible representations of semisimple Drinfeld doubles is obtained. ... More

Backward-Backward Splitting in Hadamard SpacesSep 23 2013Sep 30 2013The backward-backward algorithm is a tool for finding minima of a regularization of the sum of two convex functions in Hilbert spaces. We generalize this setting to Hadamard spaces and prove the convergence of an error-tolerant version of the backward-backward ... More

Mellin moments of heavy flavor contributions to F_2(x,Q^2) at NNLOOct 16 2009This thesis is concerned with the calculation of fixed moments of the O(a_s^3) heavy flavor contributions to the Wilson coefficients of the structure function F_2(x,Q^2) in the limit Q^2 >> m^2, neglecting power corrections. The massive Wilson coefficients ... More

Accurate variational electronic structure calculations with the density matrix renormalization groupMay 06 2014During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. The underlying matrix product state (MPS) ansatz is a low-rank decomposition of the full configuration interaction ... More

Turbulent spectra in real-time gauge field evolutionDec 12 2008We investigate ultraviolet fixed points in the real-time evolution of non-Abelian gauge fields. Classical-statistical lattice simulations reveal equal-time correlation functions with a spectral index 3/2. Analytical understanding of this result is achieved ... More

Supersymmetry beyond minimal flavour violationAug 14 2008Nov 18 2008We review the sources and phenomenology of non-minimal flavour violation in the MSSM. We discuss in some detail the most important theoretical and experimental constraints, as well as promising observables to look for supersymmetric effects at the LHC ... More

On strategies for determination and characterization of the underlying eventSep 04 2010Sep 22 2010We discuss the problem of the separation and description of the underlying event (UE) within two existing approaches to UE measurement: the "traditional" method, widely used at Tevatron, and a recently proposed jet-area/median method. A simple toy model ... More

Wilson Loops, Bianchi Constraints and Duality in Abelian Lattice ModelsAug 05 1998Nov 18 1998We introduce new modified Abelian lattice models, with inhomogeneous local interactions, in which a sum over topological sectors are included in the defining partition function. The dual models, on lattices with arbitrary topology, are constructed and ... More

Bipartite Field Theories: from D-Brane Probes to Scattering AmplitudesJul 03 2012Dec 20 2012We introduce and initiate the investigation of a general class of 4d, N=1 quiver gauge theories whose Lagrangian is defined by a bipartite graph on a Riemann surface, with or without boundaries. We refer to such class of theories as Bipartite Field Theories ... More

Depth Two Hopf Subalgebras of Semisimple Hopf algebrasJul 18 2008Let H be a finite dimensional semisimple Hopf algebra over an algebraically closed field of characteristic zero. In this note we give a short proof of the fact that a Hopf subalgebra of H is a depth two subalgebra if and only if it is normal Hopf subalgebra. ... More

Categorical Hopf kernels and representations of semisimple Hopf algebrasOct 11 2010In the category of semisimple Hopf algebras the Hopf kernels introduced by Andruskiewitsch and Devoto in \cite{AD} coincide with kernels of representation as introduced in \cite{Bker}. Some new results concerning the normality of kernels are also presented. ... More

The Chordal Loewner Equation and Monotone Probability TheoryMay 21 2016Jun 21 2016In [5], O. Bauer interpreted the chordal Loewner equation in terms of non-commutative probability theory. We follow this perspective and identify the chordal Loewner equations as the non-autonomous versions of evolution equations for semigroups in monotone ... More

Second-order perturbation theory for 3He and pd scattering in pionless EFTSep 11 2016This work implements pionless effective field theory with the two-nucleon system expanded around the unitarity limit at second order perturbation theory. The expansion is found to converge well. All Coulomb effects are treated in perturbation theory, ... More

Composition, collimation, contamination: the jet of Cygnus X-1Sep 26 2005We model the observed size and brightness of the VLBA radio core of the jet in Cygnus X-1 to derive an expression for the jet power as a function of basic jet parameters. We apply this expression to recent constraints on the jet power from observations ... More

Self-exciting Point Processes: Infections and ImplementationsFeb 12 2018This is a comment on Reinhart's "Review of Self-Exciting Spatio-Temporal Point Processes and Their Applications" (arXiv:1708.02647v1). I contribute some experiences from modelling the spread of infectious diseases. Furthermore, I try to complement the ... More

Average Cost of QuickXsort with Pivot SamplingMar 15 2018May 17 2018QuickXsort is a strategy to combine Quicksort with another sorting method X, so that the result has essentially the same comparison cost as X in isolation, but sorts in place even when X requires a linear-size buffer. We solve the recurrence for QuickXsort ... More

H1 Diffractive Structure Function Measurements and QCD FitsDec 15 2004Measurements of diffractive structure functions in ep collisions and diffractive parton densities extracted from QCD fits are presented.

Asymptotic Rasmussen InvariantFeb 12 2007We use simple properties of the Rasmussen invariant of knots to study its asymptotic behaviour on the orbits of a smooth volume preserving vector field on a compact domain in the 3-space. A comparison with the asymptotic signature allows us to prove that ... More

One-dimensional quantum wires: A pedestrian approach to bosonizationAug 01 2007Sep 08 2009In these lecture notes we will consider systems in which the motion of electrons is confined to one dimension (1D). In these so-called quantum wires electron-electron interaction effects play an important role because the restricted dimensions enhance ... More

Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal OperatorsFeb 06 1996May 28 1996Field theory calculations predict multiplicative logarithmic corrections to correlation functions from marginally irrelevant operators. However, for the numerically most suitable model - the spin-1/2 chain - these corrections have been controversial. ... More

An Accurate Determination of the Exchange Constant in Sr_2CuO_3 from Recent Theoretical ResultsAug 10 1995Feb 08 1996Data from susceptibility measurements on Sr_2CuO_3 are compared with recent theoretical predictions for the magnetic susceptibility of the antiferromagnetic spin-1/2 Heisenberg chain. The experimental data fully confirms the theoretical predictions and ... More

A Schanuel Property for $j$Jan 20 2017Oct 01 2017I give a model-theoretic setting for the modular $j$ function and its derivatives. These structures, here called $j$-fields, provide an adequate setting for interpreting the Ax-Schanuel theorem for $j$ (Pila-Tsimerman 2015). Following the ideas of M. ... More

Integrability of Moufang Foundations - A Contribution to the Classification of Twin BuildingsOct 20 2014Buildings have been introduced by J. Tits in order to study semi-simple algebraic groups from a geometrical point of view. One of the most important results in the theory of buildings is the classification of irreducible spherical buildings of rank at ... More

Polylogarithmic Cuts in Models of V^0Mar 25 2013Mar 29 2013We study initial cuts of models of weak two-sorted Bounded Arithmetics with respect to the strength of their theories and show that these theories are stronger than the original one. More explicitly we will see that polylogarithmic cuts of models of $\mathbf{V}^0$ ... More