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Positively finitely related profinite groupsNov 22 2016We define and study the class of positively finitely related (PFR) profinite groups. Positive finite relatedness is a probabilistic property of profinite groups which provides a first step to defining higher finiteness properties of profinite groups which ... More

A geometric approach to divergent points of higher dimensional Collatz mappingsNov 18 2015We define generalized Collatz mappings on free abelian groups of finite rank and study their iteration trajectories. Using geometric arguments we describe cones of points having a divergent trajectory and we deduce lower bounds for the density of the ... More

On $p$-adic limits of topological invariantsNov 01 2018The purpose of this article is to define and study new invariants of topological spaces: the $p$-adic Betti numbers and the $p$-adic torsion. These invariants take values in the $p$-adic numbers and are constructed from a virtual pro-$p$ completion of ... More

Lefschetz numbers of symplectic involutions on arithmetic groupsFeb 05 2013The reduced norm-one group G of a central simple algebra is an inner form of the special linear group, and an involution on the algebra induces an automorphism of G. We study the action of such automorphisms in the cohomology of arithmetic subgroups of ... More

On lower bounds for cohomology growth in p-adic analytic towersMay 22 2013Jan 09 2014Let p and l be two distinct prime numbers and let G be a group. We study the asymptotic behaviour of the mod-l Betti numbers in p-adic analytic towers of finite index subgroups. If X is a finite l-group of automorphisms of G, our main theorem allows to ... More

The growth of Betti numbers and approximation theoremsSep 03 2017These short lecture notes provide a brief introduction to the field of homology growth. They are composed out of two lectures, which I have given at the Borel seminar 2017 in Les Diablerets. We give a proof of L\"uck's approximation theorem, discuss generalizations ... More

Characters, $L^2$-Betti numbers and an equivariant approximation theoremFeb 08 2017Mar 01 2017Let $G$ be a group with a finite subgroup $H$. We define the $L^2$-multiplicity of an irreducible representation of $H$ in the $L^2$-homology of a proper $G$-CW-complex. These invariants generalize the $L^2$-Betti numbers. Our main results are approximation ... More

Groups acting on rooted trees and their representations on the boundaryJan 08 2018Apr 03 2018We consider groups that act on spherically symmetric rooted trees and study the associated representation of the group on the space of locally constant functions on the boundary of the tree. We introduce and discuss the new notion of locally 2-transitive ... More

On the growth of the first Betti number of arithmetic hyperbolic 3-manifoldsApr 17 2012We calculate the Lefschetz number of a Galois automorphism in the cohomology of certain arithmetic congruence groups arising from orders in quaternion algebras over number fields. As an application we give a lower bound for the first Betti number of a ... More

Zeta functions associated to admissible representations of compact p-adic Lie groupsJul 26 2017Feb 27 2019Let $G$ be a profinite group. A strongly admissible smooth representation $\rho$ of $G$ over $\mathbb{C}$ decomposes as a direct sum $\rho \cong \bigoplus_{\pi \in \mathrm{Irr}(G)} m_\pi(\rho) \, \pi$ of irreducible representations with finite multiplicities ... More

On equivariant Euler-Poincaré characteristic in sheaf cohomologyJul 04 2013Let X be a topological Hausdorff space together with a continuous action of a finite group G. Let R be the ring of integers of a number field F. Let E be a G-sheaf of flat R-modules over X and let $\Phi$ be a G-stable paracompactifying family of supports ... More

Zeta functions associated to admissible representations of compact p-adic Lie groupsJul 26 2017Aug 05 2018Let $G$ be a profinite group. A strongly admissible smooth representation $\rho$ of $G$ over $\mathbb{C}$ decomposes as a direct sum $\rho \cong \bigoplus_{\pi \in \mathrm{Irr}(G)} m_\pi(\rho) \, \pi$ of irreducible representations with finite multiplicities ... More

Equivariant Benjamini-Schramm Convergence of Simplicial Complexes and $\ell^2$-MultiplicitiesMay 14 2019We define a variant of Benjamini-Schramm convergence for finite simplicial complexes with the action of a fixed finite group G which leads to the notion of random rooted simplicial G-complexes. For every random rooted simplicial G-complex we define a ... More

On geometric aspects of diffuse groupsNov 24 2014Dec 02 2014Bowditch introduced the notion of diffuse groups as a geometric variation of the unique product property. We elaborate on various examples and non-examples, keeping the geometric point of view from Bowditch's paper. In particular, we discuss fundamental ... More

Profinite invariants of arithmetic groupsJan 04 2019Jan 21 2019We prove that the sign of the Euler characteristic of arithmetic groups with CSP is determined by the profinite completion. In contrast, we construct examples showing that this is not true for the Euler characteristic itself and that the sign of the Euler ... More

Remarks on Seshadri constantsJul 09 1995Given a smooth complex projective variety $X$ and an ample line bundle $L$ on $X$. Fix a point $x\in X$. We consider the question, are there conditions which guarantee the maxima of the Seshadri constant of $L$ at $x$, i.e $\eps(L,x)=\root n \of {L^n}$? ... More

Does black-hole evaporation imply that physics is non-unitary, and if so, what must the laws of physics look like? An EssayMay 10 2009Stephen Hawking's discovery of black hole evaporation had the remarkable consequence that information is destroyed by a black hole, which can only be accommodated by modifying the laws of quantum mechanics. Different attempts to evade the information ... More

Fractal algebras of discretization sequencesOct 06 2011These are the lecture notes for a course at the Summer School on "Applied Analysis" at the Technical University Chemnitz in September 2011. We start with the definition of a fractal algebra and show that the fractal property is enormously useful for several ... More

The slippage paradoxMar 11 2011Buying or selling assets leads to transaction costs for the investor. On one hand, it is well know to all market practionaires that the transaction costs are positive on average and present therefore systematic loss. On the other hand, for every trade, ... More

On Sharpness of Error Bounds for Single Hidden Layer Feedforward Neural NetworksNov 13 2018A new quantitative extension of the uniform boundedness principle is used to show sharpness of error bounds for sigmoid and ReLU function approximation. Neural networks perform such operations. Best possible approximation errors of neural networks with ... More

Curvature Bounds for Neighborhoods of Self-Similar SetsOct 11 2010In some recent work, fractal curvatures C^f_k(F) and fractal curvature measures C^f_k(F, .), k = 0, ..., d, have been determined for all self-similar sets F in R^d, for which the parallel neighborhoods satisfy a certain regularity condition and a certain ... More

Area estimates for two-dimensional immersions of mean curvature type in Euclidean spaces of higher codimensionMar 12 2007We establish area bounds for two-dimensional immersions in R^3 and R^n. Namely, for \mu-stable immersions in R^3 (R^n), for graphs in $\mathbb R^3$ which solve quasilinear equations in divergence form, and for graphs which are critical for Fermat-type ... More

mu-Stability of 2-immersions of prescribed mean curvature and flat normal bundle in Euclidean spaces of higher codimensionJan 22 2007We present three ways to establish general stability inequalities for various classes of 2-immersions in Euclidean spaces of higher codimension

Gauge techniques in time and frequency domain TLMJun 13 2000Mar 22 2009Typical features of the Transmission Line Matrix (TLM) algorithm in connection with stub loading techniques and prone to be hidden in common frequency domain formulations are elucidated within the propagator approach to TLM. In particular, the latter ... More

Dimension Functions on the Spectrum over Bounded Geodesics and Applications to Diophantine ApproximationMar 27 2014Sep 05 2014The set B of geodesic rays avoiding a suitable obstacle in a complete negatively curved Riemannian manifold determines a spectrum S. While various properties of this spectrum are known, we define and study dimension functions on S in terms of the Hausdorff-dimension ... More

(Failure of the) Wisdom of the crowds in an endogenous opinion dynamics model with multiply biased agentsSep 14 2013We study an endogenous opinion (or, belief) dynamics model where we endogenize the social network that models the link (`trust') weights between agents. Our network adjustment mechanism is simple: an agent increases her weight for another agent if that ... More

Intersecting 1-factors and nowhere-zero 5-flowsJun 24 2013Let $G$ be a bridgeless cubic graph, and $\mu_2(G)$ the minimum number $k$ such that two 1-factors of $G$ intersect in $k$ edges. A cyclically $n$-edge-connected cubic graph $G$ has a nowhere-zero 5-flow if (1) $n \geq 6$ and $\mu_2(G) \leq 2$ or (2) ... More

Contracted Lorentz invariance for gravity with a preferred foliationJan 08 2013Sep 06 2013In canonical gravity, the choice of a local time direction is not obviously compatible with local Lorentz invariance. One way to address this issue is to view gravity as a gauge theory on observer space, rather than spacetime. In a Lorentz covariant theory ... More

On some many-valued abstract logics and their Epsilon-T-style extensionsSep 24 2012Logical systems with classical negation and means for sentential or propositional self-reference involve, in some way, paradoxical statements such as the liar. However, the paradox disappears if one replaces classical by an appropriate non-classical negation ... More

DG-algebras and derived A-infinity algebrasNov 28 2007Jul 21 2009A differential graded algebra can be viewed as an A-infinity algebra. By a theorem of Kadeishvili, a dga over a field admits a quasi-isomorphism from a minimal A-infinity algebra. We introduce the notion of a derived A-infinity algebra and show that any ... More

The quantization complexity of diffusion processesNov 26 2004We investigate the high resolution coding problem for solutions of stochastic differential equations in the L^p[0,1]- and the C[0,1]-space. Tight asymptotic estimates are found under weak regularity assumptions. The main technical tool is a decoupling ... More

Strongly Polynomial 2-Approximations of Discrete Wasserstein BarycentersApr 18 2017Oct 23 2018Wasserstein barycenters correspond to optimal solutions of transportation problems for several marginals, which arise in a wide range of fields. In many applications, data is given as a set of probability measures with finite support. The discrete barycenters ... More

Arveson dichotomy and essential fractalityJul 26 2011The notions of fractal and essentially fractal algebras of approximation sequences and of the Arveson dichotomy have proved extremely useful for several spectral approximation problems. The purpose of this short note is threefold: to present a short new ... More

Dual Scattering Channel Schemes Extending the Johns AlgorithmSep 16 2003Apr 17 2006Dual scattering channel schemes extend the transmission line matrix numerical method (JOHNS' TLM algorithm) in two directions. For one point, transmission line links are replaced by abstract scattering channels in terms of paired distributions (characteristic ... More

Residual based Error Estimate and Quasi-Interpolation on Polygonal Meshes for High Order BEM-based FEMNov 29 2015Only a few numerical methods can treat boundary value problems on polygonal and polyhedral meshes. The BEM-based Finite Element Method is one of the new discretization strategies, which make use of and benefits from the flexibility of these general meshes ... More

Directional H2-matrix compression for high-frequency problemsOct 23 2015Jun 17 2017Standard numerical algorithms like the fast multipole method or $\mathcal{H}$-matrix schemes rely on low-rank approximations of the underlying kernel function. For high-frequency problems, the ranks grow rapidly as the mesh is refined, and standard techniques ... More

CP Violation Makes Left-Right Symmetric Extensions With Non-Hermitian Mass Matrices Appear UnnaturalFeb 01 2010Mar 31 2010Following a similar recent analysis for CP violation in the electroweak sector of the standard model, we estimate the naturalness of a magnitude of CP violation (measured by the Jarlskog invariant J) close to the observed value in extensions of the standard ... More

A Modification of the Social Force Model by ForesightDec 03 2009The motion of pedestrian crowds (e.g. for simulation of an evacuation situation) can be modeled as a multi-body system of self driven particles with repulsive interaction. We use a few simple situations to determine the simplest allowed functional form ... More

Geometric Aspects of Gauge and Spacetime SymmetriesMar 03 2011We investigate several problems in relativity and particle physics where symmetries play a central role; in all cases geometric properties of Lie groups and their quotients are related to physical effects. The first part is concerned with symmetries in ... More

Multilevel Monte Carlo algorithms for Lévy-driven SDEs with Gaussian correctionJan 07 2011We introduce and analyze multilevel Monte Carlo algorithms for the computation of $\mathbb {E}f(Y)$, where $Y=(Y_t)_{t\in[0,1]}$ is the solution of a multidimensional L\'{e}vy-driven stochastic differential equation and $f$ is a real-valued function on ... More

Oded Schramm: From Circle Packing to SLEJul 12 2010In this note, I will describe some highlights of Oded Schramm's work in circle packings and the Koebe conjecture, as well as on SLE.

Spatial discretization of restricted group algebrasFeb 22 2010We consider spatial discretizations by the finite section method of the restricted group algebra of a finitely generated discrete group, which is represented as a concrete operator algebra via its left-regular representation. Special emphasis is paid ... More

GLR-Parsing of Word Lattices Using a Beam Search MethodJun 22 1995This paper presents an approach that allows the efficient integration of speech recognition and language understanding using Tomita's generalized LR-parsing algorithm. For this purpose the GLRP-algorithm is revised so that an agenda mechanism can be used ... More

Homotopy of Rational Maps and the Quantization of SkyrmionsOct 31 2002The Skyrme model is a classical field theory which models the strong interaction between atomic nuclei. It has to be quantized in order to compare it to nuclear physics. When the Skyrme model is semi-classically quantized it is important to take the Finkelstein-Rubinstein ... More

Finkelstein-Rubinstein constraints for the Skyrme model with pion massesSep 13 2005The Skyrme model is a classical field theory modelling the strong interaction between atomic nuclei. It has to be quantized in order to compare it to nuclear physics. When the Skyrme model is semi-classically quantized it is important to take the Finkelstein-Rubinstein ... More

Remarks on Nitsche's functional: The rotationally symmetric caseSep 23 2004We investigate existence and stability of rotationally symmetric critical immersions of variational problems of higher order which were considered by Nitsche.

Lower S-Dimension of Fractal SetsMar 19 2010Oct 11 2010The interrelations between (upper and lower) Minkowski contents and (upper and lower) surface area based contents (S-contents) as well as between their associated dimensions have recently been investigated for general sets in R^d (cf. [3]). While the ... More

DSC numerical solution of the Oberbeck-Boussinesq equationsMay 04 2005Jul 06 2005Dual Scattering Channel schemes generalise Johns' TLM algorithm and replace the latter in situations where the transmission line picture of wave propagation fails. This is notoriously the case in applications to fluid dynamics, for instance. In this paper, ... More

Dual scattering channel schemes and transmission line methodsJun 25 2004Jun 30 2004Dual scattering channel (DSC) schemes naturally extend the transmission line matrix (TLM) numerical method beyond the lines set up by P.B.JOHNS and coworkers. Conceptually, DSC schemes retain from TLM the typical formal splitting of the computed fields ... More

Adaptive compression of large vectorsMay 31 2015Numerical algorithms for elliptic partial differential equations frequently employ error estimators and adaptive mesh refinement strategies in order to reduce the computational cost. We can extend these techniques to general vectors by splitting the vectors ... More

Master Equation and Two Heat ReservoirsAug 16 2006We analyze a simple spin-flip process under the presence of two heat reservoirs. While one flip process is triggered by a bath at temperature $T$, the inverse process is activated by a bath at a different temperature $T ^{\prime}$. The situation can be ... More

On the stability of dual scattering channel schemesMay 06 2004Jun 08 2004Dual scattering channel (DSC) schemes generalize Johns' TLM algorithm in replacing transmission lines with abstract scattering channels in terms of paired distributions. A well known merit of TLM schemes is unconditional stability, a property that is ... More

The Anderson impurity model with a narrow-band host: from orbital physics to the Kondo effectMay 10 2011A particle-hole symmetric Anderson impurity model with a metallic host of narrow bandwidth is studied within the framework of the local moment approach. The resultant single-particle spectra are compared to unrestricted Hartree-Fock, second order perturbation ... More

Boltzmann Collision TermOct 31 2005We derive the Boltzmann equation for scalar fields using the Schwinger-Keldysh formalism. The focus lies on the derivation of the collision term. We show that the relevant self-energy diagrams have a factorization property. The collision term assumes ... More

Quantization of SkyrmionsOct 16 2006The Skyrme model is a nonlinear classical field theory which models the strong interaction between atomic nuclei. In order to compare the predictions of the Skyrme model with nuclear physics, it has to be quantized. We show, summarizing earlier work, ... More

S^3 Skyrmions and the Rational Map AnsatzJun 19 2000Oct 28 2002This paper discusses multi-skyrmions on the 3-sphere with variable radius L using the rational map ansatz. For baryon number B = 3,...,9 this ansatz produces the lowest energy solutions known so far. By considering the geometry of the model we find an ... More

Logarithmic structures on topological K-theory spectraApr 03 2012Oct 23 2013We study a modified version of Rognes' logarithmic structures on structured ring spectra. In our setup, we obtain canonical logarithmic structures on connective K-theory spectra which approximate the respective periodic spectra. The inclusion of the p-complete ... More

Universal Toda brackets of ring spectraNov 27 2006Oct 15 2007We construct and examine the universal Toda bracket of a highly structured ring spectrum R. This invariant of R is a cohomology class in the Mac Lane cohomology of the graded ring of homotopy groups of R which carries information about R and the category ... More

Hamiltonian dynamics of several rigid bodies interacting with point vorticesFeb 11 2013Oct 28 2013We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the Hamiltonian formulation ... More

2D Numerical Simulation of Stellar ConvectionMar 06 2000The dynamics and thermal structure of the surface layers of stars with outer convection zones can be studied in some detail by means of numerical simulations of time-dependent compressible convection. In an effort to investigate the properties of ``stellar ... More

Kinetic induced phase transitionJul 27 1999An Ising model with local Glauber dynamics is studied under the influence of additional kinetic restrictions for the spin-flip rates depending on the orientation of neighboring spins. Even when the static interaction between the spins is completely eliminated ... More

On the stability of the tangent bundle of Fano manifoldsJul 10 1994By using the classification of Fano 3-folds we prove: Let $X$ be Fano 3-fold. Assume that the tangent bundle $T_X$ of $X$ is not stable (i.e. semi-stable or unstable). Then $b_2\geq 2$ and a relative tangent sheaf $T_{X/Y}$ of a contraction $f:X\longrightarrow ... More

Kernel Regression by Mode Calculation of the Conditional Probability DistributionNov 21 2008The most direct way to express arbitrary dependencies in datasets is to estimate the joint distribution and to apply afterwards the argmax-function to obtain the mode of the corresponding conditional distribution. This method is in practice difficult, ... More

On the Iterated Hairpin CompletionOct 18 2010Mar 09 2011The (bounded) hairpin completion and its iterated versions are operations on formal lan- guages which have been inspired by the hairpin formation in DNA-biochemistry. The paper answers two questions asked in the literature about the iterated hairpin completion. ... More

Dynamical modeling and the interactions with the ISMSep 22 2011This paper is a review of some of the recent modeling efforts to improve our understanding of structure formation and evolution of planetary nebulae including their interaction with the interstellar medium. New propositions have been made for the formation ... More

2-point functions in quantum cosmologyAug 30 2011We discuss the path-integral formulation of quantum cosmology with a massless scalar field as a sum-over-histories, with particular reference to loop quantum cosmology. Exploiting the analogy with the relativistic particle, we give a complete overview ... More

Asymptotic normality of integer compositions inside a rectangleMar 03 2012Among all restricted integer compositions with at most $m$ parts, each of which has size at most $l$, choose one uniformly at random. Which integer does this composition represent? In the current note, we show that underlying distribution is, for large ... More

Classical GR as a topological theory with linear constraintsNov 24 2010Sep 23 2011We investigate a formulation of continuum 4d gravity in terms of a constrained topological (BF) theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum gravity. ... More

Directional H2-matrix compression for high-frequency problemsOct 23 2015Jun 11 2016Standard numerical algorithms like the fast multipole method or $\mathcal{H}$-matrix schemes rely on low-rank approximations of the underlying kernel function. For high-frequency problems, the ranks grow rapidly as the mesh is refined, and standard techniques ... More

Epistemic extensions of combined classical and intuitionistic propositional logicNov 04 2016Logic L was introduced by Lewitzka [8] as a modal system that combines intuitionistic and classical logic: L is a conservative extension of CPC and it contains a copy of IPC via embedding $\varphi\mapsto\square\varphi$. In this article, we consider L3, ... More

W+jets as a background to top physics: the quest for many jetsJul 20 2010The latest progress in calculating electroweak gauge boson production in association with QCD jets at hadron colliders is summarized. Particular emphasis is given to the recently completed QCD one-loop calculations of W+3jets and Wb final states. Furthermore ... More

Fermions coupled to Skyrmions on S^3Apr 30 2003This paper discusses Skyrmions on the 3-sphere coupled to fermions. The resulting Dirac equation commutes with a generalized angular momentum G. For G = 0 the Dirac equation can be solved explicitly for a constant Skyrme configuration and also for a SO(4) ... More

Large eddy approximation of turbulent flow in DSC schemesMar 30 2006Aug 28 2008Large eddy approximation of turbulent flow is given a natural setting within the DSC framework of computational fluid dynamics. Periodic cellular coarse-graining prevents the nodal flow from piling up and preserves its large patterns. The coarsening operations ... More

1-factor and cycle covers of cubic graphsSep 20 2012Jan 29 2015Let $G$ be a bridgeless cubic graph. Consider a list of $k$ 1-factors of $G$. Let $E_i$ be the set of edges contained in precisely $i$ members of the $k$ 1-factors. Let $\mu_k(G)$ be the smallest $|E_0|$ over all lists of $k$ 1-factors of $G$. Any list ... More

Localization results for Minkowski contentsOct 10 2016It was shown recently that the Minkowski content of a bounded set $A$ in $\mathbb{R}^d$ with volume zero can be characterized in terms of the asymptotic behaviour of the boundary surface area of its parallel sets $A_r$ as the parallel radius $r$ tends ... More

On Sharpness of Error Bounds for Single Hidden Layer Feedforward Neural NetworksNov 13 2018Mar 14 2019A new non-linear variant of a quantitative extension of the uniform boundedness principle is used to show sharpness of error bounds for approximation by sums of sigmoid and ReLU functions. Single hidden layer feedforward neural networks perform such operations. ... More

Adaptive compression of large vectorsMay 31 2015Apr 09 2017Numerical algorithms for elliptic partial differential equations frequently employ error estimators and adaptive mesh refinement strategies in order to reduce the computational cost. We can extend these techniques to general vectors by splitting the vectors ... More

Hierarchical matrix arithmetic with accumulated updatesMar 27 2017Jul 31 2018Hierarchical matrices can be used to construct efficient preconditioners for partial differential and integral equations by taking advantage of low-rank structures in triangular factorizations and inverses of the corresponding stiffness matrices. The ... More

Executing the same binary on several operating systemsDec 16 2006Apr 12 2015We notice a way to execute a binary file on Windows and ELF-based systems. It can be used to create software installers and other applications not exceeding 64 kilo bytes.

Opinion dynamics and wisdom under out-group discriminationJun 13 2013Oct 10 2016We study a DeGroot-like opinion dynamics model in which agents may oppose other agents. As an underlying motivation, in our setup, agents want to adjust their opinions to match those of the agents of their 'in-group' and, in addition, they want to adjust ... More

On the stability of dual scattering channel schemesMay 06 2004May 19 2004This paper was withdrawn by arXiv administrators. It is an erroneous duplicate submission of math.NA/0405095.

HelloWorld! An Instructive Case for the Transformation Tool ContestNov 21 2011This case comprises several primitive tasks that can be solved straight away with most transformation tools. The aim is to cover the most important kinds of primitive operations on models, i.e. create, read, update and delete (CRUD). To this end, tasks ... More

Stirling's approximation for central extended binomial coefficientsMar 09 2012Aug 04 2016We derive asymptotic formulas for central extended binomial coefficients, which are generalizations of binomial coefficients. To do so, we relate the exact distribution of the sum of independent discrete uniform random variables to the asymptotic distribution, ... More

Necessity as justified truthMay 16 2012Jun 03 2012We present a logic for the reasoning about necessity and justifications which is independent from relational semantics. We choose the concept of justification -- coming from a class of "Justification Logics" (Artemov 2008, Fitting 2009) -- as the primitive ... More

Tutte's 5-Flow Conjecture for Highly Cyclically Connected Cubic GraphsJul 04 2006Sep 20 2012In 1954, Tutte conjectured that every bridgeless graph has a nowhere-zero 5-flow. Let $\omega$ be the minimum number of odd cycles in a 2-factor of a bridgeless cubic graph. Tutte's conjecture is equivalent to its restriction to cubic graphs with $\omega ... More

Anisotropic polygonal and polyhedral discretizations in finite element analysisOct 28 2017New interpolation and quasi-interpolation operators of Cl\'ement- and Scott-Zhang-type are analyzed on anisotropic polygonal and polyhedral meshes. Since no reference element is available, an appropriate linear mapping to a reference configuration plays ... More

The Space of Connections as the Arena for (Quantum) GravityNov 11 2011Nov 17 2011We review some properties of the space of connections as the natural arena for canonical (quantum) gravity, and compare to the case of the superspace of 3-metrics. We detail how a 1-parameter family of metrics on the space of connections arises from the ... More

Spectra of units for periodic ring spectra and group completion of graded E-infinity spacesNov 29 2011Aug 13 2015We construct a new spectrum of units for a commutative symmetric ring spectrum that detects the difference between a periodic ring spectrum and its connective cover. It is augmented over the sphere spectrum. The homotopy cofiber of its augmentation map ... More

Lectures on normal Coulomb frames in the normal bundle of twodimensional immersionen of higher codimensionOct 12 2009We establish existence and regularity results for normal Coulomb frames in the normal bundle of two-dimensional surfaces of disc-type embedded in Euclidean spaces of higher dimensions.

Linear Incongruences for Generalized Eta-QuotientsDec 19 2016Apr 17 2018For a given generalized eta-quotient, we show that linear progressions whose residues fulfill certain quadratic equations do not give rise to a linear congruence modulo any prime. This recovers known results for classical eta-quotients, especially the ... More

Why Johnny Can't Use Stego: a Human-oriented Perspective on the Application of SteganographySep 21 2016Steganography is the discipline that deals with concealing the existence of secret communications. Existing research already provided several fundamentals for defining steganography and presented a multitude of hiding methods and countermeasures for this ... More

From Reaction-Diffusion Systems to Confined Brownian MotionMay 02 2016Jun 22 2016In this note, we demonstrated for the first time that one can derive an expression for the effective diffusion coefficient, equal to the Lifson-Jackson formula, using a subsequent homogenization of the 1D reaction-diffusion-advection equation. The latter ... More

BPHZ Renormalization in Configuration Space for the $\mathcal{A}^4$-ModelSep 28 2017Recent developments for BPHZ renormalization performed in configuration space are reviewed and applied to the model of a scalar quantum field with quartic self-interaction. An extension of the results regarding the short-distance expansion and the Zimmermann ... More

Manifold calculus adapted for simplicial complexesFeb 18 2017Nov 20 2017We develop a generalization of manifold calculus in the sense of Goodwillie-Weiss where the manifold is replaced by a simplicial complex. We consider functors from the category of open subsets of a fixed simplical complex into the category of topological ... More

Epistemic extensions of combined classical and intuitionistic propositional logicNov 04 2016Feb 27 2017Logic $L$ was introduced by Lewitzka [7] as a modal system that combines intuitionistic and classical logic: $L$ is a conservative extension of CPC and it contains a copy of IPC via the embedding $\varphi\mapsto\square\varphi$. In this article, we consider ... More

Maximum principles for non-Markovian semi-martingales with jumps and moreDec 07 2014We find a maximum principle for general non-Markovian semi-martingales. We do so by describing the adjoint processes with non-anticipating stochastic derivatives in a martingale random field setting. In the case of the L\'evy processes this extends maximum ... More

Perturbing a quantum gravity condensateNov 04 2014Feb 03 2015In a recent proposal using the group field theory approach, a spatially homogeneous (generally anisotropic) universe is described as a quantum gravity condensate of "atoms of space," which allows the derivation of an effective cosmological Friedmann equation ... More

Spontaneous breaking of Lorentz symmetry for canonical gravityOct 05 2012Oct 08 2012In the Ashtekar-Barbero formulation of canonical general relativity based on an SU(2) connection, Lorentz covariance is a subtle issue which has been the focus of some debate. Here we present a Lorentz covariant formulation generalising the notion of ... More

Schmidt Games and Conditions on Resonant SetsOct 03 2012Sep 18 2013Winning sets of Schmidt's game enjoy a remarkable rigidity. Therefore, this game (and modifications of it) have been applied to many examples of complete metric spaces (X, d) to show that the set of "badly approximable points", with respect to a given ... More

DSC Approach to Computational Fluid DynamicsOct 04 2005Apr 01 2006This paper presents the Dual Scattering Channel numerical solution of the Navier-Stokes Equations for quasi-incompressible flow in the Oberbeck-Boussinesq approximation. The implementation in hexahedral non-orthogonal mesh is outlined. A numerical example ... More