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Face-centered cubic crystallization of atomistic configurationsJul 02 2014We address the question of whether three-dimensional crystals are minimizers of classical many-body energies. This problem is of conceptual relevance as it presents a significant milestone towards understanding, on the atomistic level, phenomena such ... More

Asymptotic Analysis of the Ginzburg-Landau Functional on Point CloudsApr 17 2016Nov 10 2016The Ginzburg-Landau functional is a phase transition model which is suitable for clustering or classification type problems. We study the asymptotics of a sequence of Ginzburg-Landau functionals with anisotropic interaction potentials on point clouds ... More

Rescaled Objective Solutions of Fokker-Planck and Boltzmann equationsMay 25 2018Dec 11 2018We study the long-time behavior of symmetric solutions of the nonlinear Boltzmann equation and a closely related nonlinear Fokker-Planck equation. If the symmetry of the solutions corresponds to shear flows, the existence of stationary solutions can be ... More

Long Range Particle Dynamics and the Linear Boltzmann EquationDec 12 2017This paper gives the first full proof of the justification of the linear Boltzmann equation from an underlying long range particle evolution. We suppose that a tagged particle is interacting with a background via a two body potential that is decaying ... More

Asymptotic Analysis of the Ginzburg-Landau Functional on Point CloudsApr 17 2016The Ginzburg-Landau functional is a phase transition model which is suitable for clustering or classification type problems. We study the asymptotics of a sequence of Ginzburg-Landau functionals with anisotropic interaction potentials on point clouds ... More

The Derivation of the Linear Boltzmann Equation from a Rayleigh Gas Particle ModelMar 24 2016A linear Boltzmann equation is derived in the Boltzmann-Grad scaling for the deterministic dynamics of many interacting particles with random initial data. We study a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with background ... More

The Derivation of the Linear Boltzmann Equation from a Rayleigh Gas Particle ModelMar 24 2016Apr 02 2017A linear Boltzmann equation is derived in the Boltzmann-Grad scaling for the deterministic dynamics of many interacting particles with random initial data. We study a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with background ... More

Energy transport by acoustic modes of harmonic latticesNov 21 2006We study the large scale evolution of a scalar lattice excitation which satisfies a discrete wave-equation in three dimensions. We assume that the dispersion relation associated to the elastic coupling constants of the wave-equation is acoustic, i.e., ... More

Surface energy and boundary layers for a chain of atoms at low temperatureApr 12 2019We analyze the surface energy and boundary layers for a chain of atoms at low temperature for an interaction potential of Lennard-Jones type. The pressure (stress) is assumed small but positive and bounded away from zero, while the temperature $\beta^{-1}$ ... More

Convergence of the $k$-Means Minimization Problem using $Γ$-ConvergenceJan 06 2015Apr 03 2015The $k$-means method is an iterative clustering algorithm which associates each observation with one of $k$ clusters. It traditionally employs cluster centers in the same space as the observed data. By relaxing this requirement, it is possible to apply ... More

Optimality of the triangular lattice for a particle system with Wasserstein interactionDec 31 2012Nov 07 2013We prove strong crystallization results in two dimensions for an energy that arises in the theory of block copolymers. The energy is defined on sets of points and their weights, or equivalently on the set of atomic measures. It consists of two terms; ... More

Thermalization of rate-independent processes by entropic regularizationSep 17 2012We consider the effective behaviour of a rate-independent process when it is placed in contact with a heat bath. The method used to "thermalize" the process is an interior-point entropic regularization of the Moreau--Yosida incremental formulation of ... More

Equivalence of ensembles, condensation and glassy dynamics in the Bose-Hubbard HamiltonianMar 29 2019We study mathematically the equilibrium properties of the Bose-Hubbard Hamiltonian in the limit of a vanishing hopping amplitude. This system conserves the energy and the number of particles. We establish the equivalence between the microcanonical and ... More

Nonlinear Elasticity from Atomistic MechanicsFeb 17 2012Apr 06 2012We present sharp convergence results for the Cauchy--Born approximation of general classical atomistic interactions, for both static and dynamic problems, for small data.

Recursion Relations for Long-Range Integrable Spin Chains with Open Boundary ConditionsJan 04 2012Apr 26 2012It is well known that integrable charges for short-range (e.g. nearest-neighbor) spin chains with periodic boundary conditions can be recursively generated by a so-called boost operator. In the past, this iterative construction has been generalized to ... More

On the Structure of Monodromy Algebras and Drinfeld DoublesSep 18 1996Oct 11 1996We give a review and some new relations on the structure of the monodromy algebra (also called loop algebra) associated with a quasitriangular Hopf algebra H. It is shown that as an algebra it coincides with the so-called braided group constructed by ... More

Local cohomology and F-stabilityApr 28 2009Jun 25 2009We study the relationship between the Frobenius stability of an Artinian module over an F-injective ring and its stable part.

Standard Model statistics of a Type II orientifoldDec 15 2005Dec 22 2005We analyse four-dimensional, supersymmetric intersecting D-brane models in a toroidal orientifold background from a statistical perspective. The distribution and correlation of observables, like gauge groups and couplings, are discussed. We focus on models ... More

Statistics in the Landscape of Intersecting Brane ModelsOct 12 2007Mar 24 2008An approach towards a statistical survey of four dimensional supersymmetric vacua in the string theory landscape is described and illustrated with three examples of ensembles of intersecting D-brane models. The question whether it is conceivable to make ... More

On not testing the foreign-language effect: A comment on Costa, Foucart, Arnon, Aparici, and Apesteguia (2014)Jun 25 2015In their first five studies, Costa, Foucart, Arnon, Aparici, and Apesteguia (2014) fail to provide a statistical test of the foreign-language effect. Instead, the authors employ a procedure in which they test the framing effects separately for the native ... More

Blocks with a generalized quaternion defect group and three simple modules over a 2-adic ringJun 16 2015We show that two blocks of generalized quaternion defect with three simple modules over a sufficiently large $2$-adic ring $\mathcal O$ are Morita-equivalent if and only if the corresponding blocks over the residue field of $\mathcal O$ are Morita-equivalent. ... More

Superfluidity in driven non-equilibrium Bose-Einstein condensates due to balanced forcesNov 10 2016In this letter an analytical proof of the existence and suppression of superfluidity in open Bose- Einstein condensates (BEC) such as those of Exciton-Polaritons (Polaritons) or the atom laser is given. To test superfluidity in the mean-field regime of ... More

Automatic Calculation of supersymmetric Renormalization Group Equations and Self EnergiesFeb 03 2010Jan 11 2011SARAH is a Mathematica package for studying supersymmetric models. It calculates for a given model the masses, tadpole equations and all vertices at tree-level. Those information can be used by \SARAH to write model files for CalcHep/CompHep or FeynArts/FormCalc. ... More

Automation of non-SUSY two-loop RGEs with PyR@TE: latest developmentsOct 29 2015In light of the conspicuous absence of SUSY in the energy range explored by the LHC during run I, non-supersymmetric BSM scenarios are becoming more and more attractive. One key ingredient in exploring such BSM physics are the renormalization group equations ... More

On the impact of kinetic mixing in beta functions at two-loopAug 25 2016Sep 06 2016Kinetic mixing is a fundamental property of models with a gauge symmetry involving several $\mathrm{U}(1)$ group factors. In this paper, we perform a numerical study of the impact of kinetic mixing on beta functions at two-loop. To do so, we use the recently ... More

Lectures on Yangian SymmetryJun 09 2016Jul 26 2016In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional ... More

A closer look at non-decoupling D-TermsMar 18 2016May 09 2016Non-Decoupling D-Terms are an attractive possibility to enhance the tree-level mass of the standard model like Higgs boson in supersymmetric models. We discuss here for the case of a new Abelian gauge group two effects usually neglected in literature: ... More

Analytical calculation of the axis angle 2V from extinction measurements on the spindle stageFeb 27 2017A concise derivation of the "Joel equations", which allow for the determination of the axis angle 2V from measurements of extinction directions on a spindle stage, is provided starting from the wave-equation. Only analytic methods and no geometric arguments ... More

Lower bounds on the size of general Schrödinger-cat states from experimental dataOct 11 2016Mar 20 2017Experimental progress with meso- and macroscopic quantum states (i.e., general Schrodinger-cat states) was recently accompanied by theoretical proposals on how to measure the merit of these efforts. So far, experiment and theory were disconnected as theoretical ... More

Instantaneous non-local computation of low T-depth quantum circuitsNov 09 2015Sep 26 2016Instantaneous non-local quantum computation requires multiple parties to jointly perform a quantum operation, using pre-shared entanglement and a single round of simultaneous communication. We study this task for its close connection to position-based ... More

Beyond superfluidity in driven non-equilibrium Bose-Einstein condensatesNov 10 2016Apr 04 2017The phenomenon of superfluidity in open Bose-Einstein condensates (BEC) is analysed numerically and analytically. It is found that a superfluid phase is feasible even above the speed of sound, when forces due to inhomogeneous non-equilibrium processes ... More

Levine's motivic comparison theorem revisitedJan 22 2007For a field of characteristic zero, M. Levine has proved that his category of triangulated motives is equivalent to the one constructed by V. Voevodsky. In this paper we show that the strategy of Levine's proof can be applied on every perfect field to ... More

Dealing with cross-country heterogeneity in panel VARs using finite mixture modelsApr 04 2018In this paper, we provide a parsimonious means to estimate panel VARs with stochastic volatility. We assume that coefficients associated with domestic lagged endogenous variables arise from a Gaussian mixture model. Shrinkage on the cluster size is introduced ... More

Vector Field Twisting of Lie-AlgebrasJul 11 2006Aug 10 2006In quantum groups coproducts of Lie-algebras are twisted in terms of generators of the corresponding universal enveloping algebra. If representations are considered, twists also serve as starproducts that accordingly quantize representation spaces. In ... More

Sharp estimates of the Kobayashi metric and Gromov hyperbolicityJan 03 2008Let D be a smooth relatively compact and strictly J-pseudoconvex domain in a four dimensional almost complex manifold (M,J). We give sharp estimates of the Kobayashi metric. Our approach is based on an asymptotic quantitative description of both the domain ... More

The Cosmological Constant and Discrete Space-TimesOct 16 2006In this thesis the cosmological constant is investigated from two points of view. First, we study the influence of a time-dependent cosmological constant on the late-time expansion of the universe. Thereby, we consider several combinations of scaling ... More

Perturbations in the relaxation mechanism for a large cosmological constantSep 11 2009Jan 12 2010Recently, a mechanism for relaxing a large cosmological constant (CC) has been proposed [arxiv:0902.2215], which permits solutions with low Hubble rates at late times without fine-tuning. The setup is implemented in the LXCDM framework, and we found a ... More

On the Monodromy and Galois Group of Conics Lying on Heisenberg Invariant Quartic K3 SurfacesNov 04 2015In "Curves on Heisenberg invariant quartic surfaces in projective 3-space", Eklund showed that a general $(\mathbb{Z}/2\mathbb{Z})^{4}$-invariant quartic K3 surface contains at least $320$ conics. In this paper we analyse the field of definition of those ... More

Special subvarieties of Drinfeld modular varietiesMar 22 2005Feb 28 2009We explore an analogue of the Andr\'e-Oort conjecture for subvarieties of Drinfeld modular varieties. The conjecture states that a subvariety $X$ of a Drinfeld modular variety contains a Zariski-dense set of complex multiplication (CM) points if and only ... More

Invariance of the BFV-complexDec 12 2008Nov 21 2010The BFV-formalism was introduced to handle classical systems, equipped with symmetries. It associates a differential graded Poisson algebra to any coisotropic submanifold $S$ of a Poisson manifold $(M,\Pi)$. However the assignment (coisotropic submanifold) ... More

Improved Delsarte bounds for spherical codes in small dimensionsJan 27 2005Mar 10 2008We present an extension of the Delsarte linear programming method. For several dimensions it yields improved upper bounds for kissing numbers and for spherical codes. Musin's recent work on kissing numbers in dimensions three and four can be viewed in ... More

A projector based convergence proof of the Ginelli algorithm for covariant Lyapunov vectorsFeb 23 2018Linear perturbations of solutions of dynamical systems exhibit different asymptotic growth rates, which are naturally characterized by so-called covariant Lyapunov vectors (CLVs). Due to an increased interest of CLVs in applications, several algorithms ... More

Random colorings and automorphism breaking in locally finite graphsApr 24 2013A colouring of a graph G is called distinguishing if its stabiliser in Aut G is trivial. It has been conjectured that, if every automorphism of a locally finite graph moves infinitely many vertices, then there is a distinguishing 2-colouring. We study ... More

The Galois action on M-Origamis and their Teichmüller curvesAug 28 2014We consider a rather special class of translation surfaces (called M-Origamis in this work) that are obtained from dessins by a construction introduced by Martin M\"oller. We give a new proof with a more combinatorial flavour of M\"oller's theorem that ... More

The super-critical contact process has a spectral gapOct 23 2013We consider the super-critical contact process on $\mathbb{Z}^d$. It is known that measures which dominate the upper invariant measure $\mu$ converge exponentially fast to $\mu$. However, the same is not true for measures which are below $\mu$, as the ... More

Update of the flavour-physics constraints in the NMSSMDec 07 2015We consider the impact of several flavour-changing observables in the $B$- and the Kaon sectors on the parameter space of the NMSSM, in a minimal flavour violating version of this model. Our purpose consists in updating our previous results in arXiv:0710.3714 ... More

xSLHA: an Les Houches Accord reader for Python and MathematicaDec 11 2018The format defined by the SUSY Les Houches Accord (SLHA) is widely used in high energy physics to store and exchange information. It is no longer applied only to a few supersymmetric models, but the general structure is adapted to all kind of models. ... More

On the 2-Abelian Complexity of the Thue-Morse WordApr 15 2014Jun 02 2015We show that the 2-abelian complexity of the infinite Thue-Morse word is 2-regular, and other properties of the 2-abelian complexity, most notably that it is a concatenation of palindromes of increasing length. We also show sharp bounds for the length ... More

A Probabilistic Look at Conservative Growth-Fragmentation EquationsSep 08 2016Nov 02 2016In this note, we consider general growth-fragmentation equations from a probabilistic point of view. Using Foster-Lyapunov techniques, we study the recurrence of the associated Markov process depending on the growth and fragmentation rates. We prove the ... More

Bounds for the annealed return probability on large finite percolation clustersNov 30 2008Aug 26 2012Bounds for the expected return probability of the delayed random walk on finite clusters of an invariant percolation on transitive unimodular graphs are derived. They are particularly suited for the case of critical Bernoulli percolation and the associated ... More

Optimal regularity for two-dimensional Pfaffian systems and the fundamental theorem of surface theoryApr 16 2019We prove that a Pfaffian system with coefficients in the critical space $L^2_\mathrm{loc}$ on a simply connected open subset of $\mathbb{R}^2$ has a non-trivial solution in $W^{1,2}_\mathrm{loc}$ if the coefficients are antisymmetric and satisfy a compatibility ... More

Representing Isabelle in LFSep 14 2010LF has been designed and successfully used as a meta-logical framework to represent and reason about object logics. Here we design a representation of the Isabelle logical framework in LF using the recently introduced module system for LF. The major novelty ... More

Beyond-MSSM Higgs sectorsSep 25 2014Oct 28 2014This is a compact overview of Higgs sectors in extensions of the MSSM. The focus is on the summary of the main features of models with additional singlets and triplets as well as of models with Dirac gauginos. In addition, also important aspects of models ... More

SARAH 3.2: Dirac Gauginos, UFO output, and moreJul 04 2012Feb 12 2013SARAH is a Mathematica package optimized for the fast, efficient and precise study of supersymmetric models beyond the MSSM: a new model can be defined in a short form and all vertices are derived. This allows SARAH to create model files for FeynArts/FormCalc, ... More

Challenge IEEE-ISBI/TCB : Application of Covariance matrices and wavelet marginalsOct 10 2014This short memo aims at explaining our approach for the challenge IEEE-ISBI on Bone Texture Characterization. In this work, we focus on the use of covariance matrices and wavelet marginals in an SVM classifier.

The Picard Group of Various Families of $(\mathbb{Z}/2\mathbb{Z})^{4}$-invariant Quartic K3 SurfacesNov 05 2015The subject of this paper is the study of various families of quartic K3 surfaces which are invariant under a certain $(\mathbb{Z}/2\mathbb{Z})^{4}$ action. In particular, we describe families whose general member contains $8,16,24$ or $32$ lines as well ... More

The Impact of Credit Risk and Implied Volatility on Stock ReturnsMay 30 2010This paper examines the possibility of using derivative-implied risk premia to explain stock returns. The rapid development of derivative markets has led to the possibility of trading various kinds of risks, such as credit and interest rate risk, separately ... More

Warped Extra Dimensions: Flavor, Precision Tests and Higgs PhysicsDec 29 2011In this thesis, the phenomenology of the Randall-Sundrum setup is investigated. In this context models with and without an enlarged SU(2)_L x SU(2)_R x U(1)_X x P_{LR} gauge symmetry, which removes corrections to the T parameter and to the Z b_L \bar ... More

Basic Orders for Defect Two Blocks of $\Z_p\Sym_n$Nov 30 2010We show how basic orders for defect two blocks of symmetric groups over the ring of $p$-adic integers can be constructed by purely combinatorial means.

Fuzzy Characterization of Near-Earth-AsteroidsMay 23 2009Due to close encounters with the inner planets, Near-Earth-Asteroids (NEAs) can have very chaotic orbits. Because of this chaoticity, a statistical treatment of the dynamical properties of NEAs becomes difficult or even impossible. We propose a new way ... More

Cycle modules and the intersection A-infinity algebraJun 27 2009Given a cycle module M with a ring structure we show that the cycle complex with coefficients in M of a smooth scheme of finite type over a field has a A-infinity algebra structure. In the case of Milnor K-theory this gives a homotopy model for the classical ... More

The Shafarevich-Tate group in cyclotomic Z_p-extensions at supersingular primesJun 10 2011We study the asymptotic growth of the p-primary component of the Shafarevich-Tate group in the cyclotomic direction at any odd prime of good supersingular reduction, generalizing work of Kobayashi. This explains formulas obtained by Kurihara, Perrin-Riou, ... More

The $L^2$-torsion polytope of amenable groupsApr 24 2017Jan 29 2018We introduce the notion of groups of polytope class and show that torsion-free amenable groups satisfying the Atiyah Conjecture possess this property. A direct consequence is the homotopy invariance of the $L^2$-torsion polytope among $G$-CW-complexes ... More

Filtering out the cosmological constant in the Palatini formalism of modified gravityJul 15 2010Jan 20 2011According to theoretical physics the cosmological constant (CC) is expected to be much larger in magnitude than other energy densities in the universe, which is in stark contrast to the observed Big Bang evolution. We address this old CC problem not by ... More

Gravity and Quantum Fields in Discrete Space-TimesOct 27 2006In a 6D model, where the extra dimensions form a discretised curved disk, we investigate the mass spectra and profiles of gravitons and Dirac fermions. The discretisation is performed in detail leading to a star-like geometry. In addition, we use the ... More

Attack Trees in IsabelleMar 17 2018May 15 2018In this paper, we present a proof theory for attack trees. Attack trees are a well established and useful model for the construction of attacks on systems since they allow a stepwise exploration of high level attacks in application scenarios. Using the ... More

The CLIC Detector ConceptFeb 16 2018The Compact Linear Collider (CLIC) is a concept for a future linear collider that would provide e$^+$e$^-$ collisions at up to 3 TeV. The physics aims require a detector system with excellent jet energy and track momentum resolution, highly efficient ... More

Accessing Masses Beyond Collider Reach - in EFTNov 08 2017We demonstrate how masses of new states, beyond direct experimental reach, could nevertheless be extracted in the framework of effective field theory (EFT), given broad assumptions on the underlying UV physics, however not sticking to a particular setup ... More

Uniformly distributed sequences in the orthogonal group and on the Grassmannian manifoldMay 16 2014Sep 17 2014Quasi-Monte Carlo methods replaced classical Monte Carlo methods in many areas of numerical analysis over the last decades. The purpose of this paper is to extend quasi-Monte Carlo methods into a new direction. We construct and implement a uniformly distributed ... More

Generalized orthogonal matching pursuit for multiple measurements - A structural approachMay 23 2017Sparse data approximation has become a popular research topic in signal processing. However, in most cases only a single measurement vector (SMV) is considered. In applications, the multiple measurement vector (MMV) case is more usual, i.e., the sparse ... More

Reopen parameter regions in Two-Higgs Doublet ModelsMay 10 2017Dec 06 2017The stability of the electroweak potential is a very important constraint for models of new physics. At the moment, it is standard for Two-Higgs doublet models (THDM), singlet or triplet extensions of the standard model to perform these checks at tree-level. ... More

Reconstruction of Function Fields from their pro-l abelian divisorial InertiaOct 10 2018Let $\Pi^c_K\to\Pi_K$ be the maximal pro-$\ell$ abelian-by-central, respectively abelian, Galois groups of a function field $K|k$ with $k$ algebraically closed and ${\rm char}\neq\ell$. We show that $K|k$ can be functorially reconstructed by group theoretical ... More

Quantitative Robustness of Localized Support Vector MachinesMar 01 2019The huge amount of available data nowadays is a challenge for kernel-based machine learning algorithms like SVMs with respect to runtime and storage capacities. Local approaches might help to relieve these issues and to improve statistical accuracy. It ... More

Simulation ModelingDec 21 2018With the rise of computers, simulation models have emerged beside the more traditional statistical and mathematical models as a third pillar for ecological analysis. Broadly speaking, a simulation model is an algorithm, typically implemented as a computer ... More

On $α$-largeness and the Paris-Harrington principle in $\mathrm{RCA}_0$ and $\mathrm{RCA}_0^{\displaystyle{*}}$Nov 28 2016Jul 14 2018We examine, within $\mathrm{RCA}_0$, the treatment by Ketonen and Solovay on the use of $\alpha$-largeness for giving an upper bound for the Paris--Harrington principle. This proof works fine in $\mathrm{RCA}_0^{\displaystyle{*}}$ for every fixed standard ... More

Lévy processes with values in locally convex Suslin spacesOct 02 2015We provide a L\'evy-It\^o decomposition of sample paths of L\'evy processes with values in complete locally convex Suslin spaces. This class of state spaces contains the well investigated examples of separable Banach spaces, as well as Fr\'echet or distribution ... More

Testability of the exclusion restriction in continuous instrumental variable modelsJun 25 2018In this note we prove Pearl's conjecture, showing that the exclusion restriction of an instrument cannot be tested without structural assumptions in general instrumental variable models with a continuously distributed endogenous variable. This stands ... More

Counting Algebraic Curves with Tropical GeometryJun 09 2012Tropical geometry is a piecewise linear "shadow" of algebraic geometry. It allows for the computation of several cohomological invariants of an algebraic variety. In particular, its application to enumerative algebraic geometry led to significant progress. ... More

Computing Node Polynomials for Plane CurvesJun 01 2010Mar 09 2011According to the G\"ottsche conjecture (now a theorem), the degree N^{d, delta} of the Severi variety of plane curves of degree d with delta nodes is given by a polynomial in d, provided d is large enough. These "node polynomials" N_delta(d) were determined ... More

When is an origami set a ring?Apr 27 2018Starting with a flat sheet of paper, points can be constructed as the intersection of two folds. The set of constructible points clearly depends on which folds are admissible. In this paper, we study the situation where a fold is admissible if its slope ... More

Phase transition results for three Ramsey-like theoremsMar 22 2016We classify a sharp phase transition threshold for Friedman's finite adjacent Ramsey theorem. We extend the method for showing this result to two previously known classifications involving Ramsey theorem variants: the Paris--Harrington theorem and the ... More

On "finitary" Ramsey's theoremAug 09 2015Nov 29 2016We examine a version of Ramsey's theorem based on Tao, Gaspar and Kohlenbach's "finitary" infinite pigeonhole principle.We will show that the "finitary" infinite Ramsey's theorem naturally gives rise to statements at the level of the infinite Ramsey's ... More

Symmetries, psudosymmetries and conservation laws in Lagrangian and Hamiltonian $k$-symplectic formalismsOct 16 2014In this paper we will present Lagrangian and Hamiltonian $k$-symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using symmetries and pseudosymmetries, ... More

Brownian Motions on Metric Graphs with Non-Local Boundary Conditions I: CharacterizationMay 17 2018A classification for Brownian motions on metric graphs, that is, right continuous strong Markov processes which behave like a one-dimensional Brownian motion on the edges and feature effects like Walsh skewness, stickiness and jumps at the vertices, is ... More

Torsion bounds for elliptic curves and Drinfeld modulesOct 17 2008We derive asymptotically optimal upper bounds on the number of L-rational torsion points on a given elliptic curve or Drinfeld module defined over a finitely generated field K, as a function of the degree [L:K]. Our main tool is the adelic openness of ... More

The weight in a Serre-type conjecture for tame n-dimensional Galois representationsMar 03 2008Jul 04 2011We formulate a Serre-type conjecture for n-dimensional Galois representations that are tamely ramified at p. The weights are predicted using a representation-theoretic recipe. For n = 3 some of these weights were not predicted by the previous conjecture ... More

Intersection patterns of finite sets and of convex setsJul 04 2016The main result is a common generalization of results on lower bounds for the chromatic number of r-uniform hypergraphs and some of the major theorems in Tverberg-type theory, which is concerned with the intersection pattern of faces in a simplicial complex ... More

Monoide des enlacements et facteurs orthogonaux (Monoids of linking pairings and orthogonal summands)Mar 14 2005Jun 17 2005A linking pairing is a symetric bilinear pairing lambda: GxG --> Q/Z on a finite abelian group. The set of isomorphism classes of linking pairings is a non-cancellative monoid E under orthogonal sum, which is infinitely generated and infinitely related. ... More

Cops, robbers, and infinite graphsOct 30 2014Mar 30 2015Cops and robbers is a game between two players, where one tries to catch the other by moving along the edges of a graph. It is well known that on a finite graph the cop has a winning strategy if and only if the graph is constructible and that finiteness ... More

Model-Independent Pricing of Asian Options via Optimal Martingale TransportDec 03 2014In this article we discuss the problem of calculating optimal model-independent (robust) bounds for the price of Asian options with discrete and continuous averaging. We will give geometric characterisations of the maximising and the minimising pricing ... More

Reverse mathematics of the finite downwards closed subsets of $\mathbb{N}^k$ ordered by inclusion and adjacent Ramsey for fixed dimensionOct 04 2016Oct 04 2017We show that the well-partial orderedness of the finite downwards closed subsets of $\mathbb{N}^k$ ,ordered by inclusion, is equivalent to the well-foundedness of the ordinal $\omega^{\omega^\omega}$. This was conjectured to be the case by Hatzikiriakou ... More

Integral points of bounded height on a log Fano threefoldJan 24 2019We determine an asymptotic formula for the number of integral points of bounded height on a blow-up of $\mathbb{P}^3$ outside certain planes using universal torsors.

Lifting of morphisms to quotient presentationsSep 30 2002In this article we investigate algebraic morphisms between toric varieties. Given presentations of toric varieties as quotients we are interested in the question when a morphism admits a lifting to these quotient presentations. We show that this can be ... More

A study of a hamiltonian model for martensitic phase transformations including microkinetic energyNov 19 1998How can a system in a macroscopically stable state explore energetically more favorable states, which are far away from the current equilibrium state? Based on continuum mechanical considerations we derive a Boussinesq-type equation which models the dynamics ... More

A Query Language for Formal Mathematical LibrariesApr 20 2012One of the most promising applications of mathematical knowledge management is search: Even if we restrict attention to the tiny fragment of mathematics that has been formalized, the amount exceeds the comprehension of an individual human. Based on the ... More

A Probabilistic Look at Growth-Fragmentation EquationsSep 08 2016In this note, we consider general growth-fragmentation equations from a probabilistic point of view. Using Foster-Lyapunov techniques, we study the recurrence of the associated Markov process depending on the growth and fragmentation rates. We prove the ... More

On the IYB-property in some solvable groupsApr 07 2013A finite group $G$ is called Involutive Yang-Baxter (IYB) if there exists a bijective 1-cocycle $\chi: G \longrightarrow M$ for some $\mathbb Z G$-module $M$. It is known that every IYB-group is solvable, but it is still an open question whether the converse ... More

Top physics prospects at LHCJun 24 2005With a high instantaneous luminosity and the large top quark pair production cross section, the Large Hadron Collider (LHC) will be a "top factory" allowing the analysis of millions of top events. After a short description of the top quark pair production ... More

Multiple scattering induced negative refraction of matter wavesNov 13 2014Mar 04 2016Starting from fundamental multiple scattering theory it is shown that negative refraction indices are feasible for matter waves passing a well-defined ensemble of scatterers. A simple approach to this topic is presented and explicit examples for systems ... More

Chiral Four-Dimensional Heterotic Covariant LatticesOct 17 2014In the covariant lattice formalism, chiral four-dimensional heterotic string vacua are obtained from certain even self-dual lattices which completely decompose into a left-mover and a right-mover lattice. The main purpose of this work is to classify all ... More