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Discontinuities in the Maximum-Entropy InferenceAug 28 2013We revisit the maximum-entropy inference of the state of a finite-level quantum system under linear constraints. The constraints are specified by the expected values of a set of fixed observables. We point out the existence of discontinuities in this ... More

Quantum Convex SupportJan 16 2011Sep 08 2011Convex support, the mean values of a set of random variables, is central in information theory and statistics. Equally central in quantum information theory are mean values of a set of observables in a finite-dimensional C*-algebra A, which we call (quantum) ... More

Operator systems and convex sets with many normal conesJun 13 2016Sep 13 2016The state space of an operator system of $n$-by-$n$ matrices has, in a sense, many normal cones. Merely this convex geometrical property implies smoothness qualities and a clustering property of exposed faces. The latter holds since each exposed face ... More

A Note on Touching Cones and FacesOct 14 2010May 03 2011We study touching cones of a (not necessarily closed) convex set in a finitedimensional real Euclidean vector space and we draw relationships to other concepts in Convex Geometry. Exposed faces correspond to normal cones by an antitone lattice isomorphism. ... More

Continuity of the Maximum-Entropy InferenceFeb 14 2012Apr 21 2014We study the inverse problem of inferring the state of a finite-level quantum system from expected values of a fixed set of observables, by maximizing a continuous ranking function. We have proved earlier that the maximum-entropy inference can be a discontinuous ... More

Information topologies on non-commutative state spacesMar 29 2010Jan 18 2013We define an information topology (I-topology) and a reverse information topology (rI-topology) on the state space of a C*-subalgebra of Mat(n,C). These topologies arise from sequential convergence with respect to the relative entropy. We prove that open ... More

A variation principle for ground spacesApr 25 2017Mar 21 2018The ground spaces of a vector space of hermitian matrices, partially ordered by inclusion, form a lattice constructible from top to bottom in terms of intersections of maximal ground spaces. In this paper we characterize the lattice elements and the maximal ... More

Duality of non-exposed facesJul 12 2011Nov 28 2011Given any polar pair of convex bodies we study its conjugate face maps and we characterize conjugate faces of non-exposed faces in terms of normal cones. The analysis is carried out using the positive hull operator which defines lattice isomorphisms linking ... More

Maximum-entropy inference and inverse continuity of the numerical rangeFeb 13 2015Aug 13 2015We study the continuity of the maximum-entropy inference map for two observables in finite dimensions. We prove that the continuity is equivalent to the strong continuity of the set-valued inverse numerical range map. This gives a continuity condition ... More

On a theorem by KippenhahnMay 02 2017Kippenhahn discovered a real algebraic plane curve whose convex hull is the numerical range of a matrix. The correctness of this theorem was called into question when Chien and Nakazato found an example where the spatial analogue fails. They showed that ... More

Polyhedral Voronoi CellsMar 22 2010Voronoi cells of a discrete set in Euclidean space are known as generalized polyhedra. We identify polyhedral cells of a discrete set through a direction cone. For an arbitrary set we distinguish polyhedral from non-polyhedral cells using inversion at ... More

Entropy Distance: New Quantum PhenomenaJul 30 2010Sep 05 2012We study a curve of Gibbsian families of complex 3x3-matrices and point out new features, absent in commutative finite-dimensional algebras: a discontinuous maximum-entropy inference, a discontinuous entropy distance and non-exposed faces of the mean ... More

Pre-images of extreme points of the numerical range, and applicationsSep 18 2015May 19 2016We extend the pre-image representation of exposed points of the numerical range of a matrix to all extreme points. With that we characterize extreme points which are multiply generated, having at least two linearly independent pre-images, as the extreme ... More

A new signature of quantum phase transitions from the numerical rangeMar 01 2017Nov 30 2017The ground state energy of a finite-dimensional one-parameter Hamiltonian and the continuity of a maximum-entropy inference map are discussed in the context of quantum critical phenomena. The domain of the inference map is a convex compact set in the ... More

Kippenhahn's Theorem for joint numerical ranges and quantum statesJul 10 2019Kippenhahn's Theorem asserts that the numerical range of a matrix is the convex hull of a certain algebraic curve. Here, we show that the joint numerical range of finitely many hermitian matrices is similarly the convex hull of a semi-algebraic set. We ... More

Classification of joint numerical ranges of three hermitian matrices of size threeMar 20 2016Feb 11 2018The joint numerical range $W(F)$ of three hermitian $3$-by-$3$ matrices $F=(F_1,F_2,F_3)$ is a convex and compact subset in $\mathbb{R}^3$. Generically we find that $W(F)$ is a three-dimensional oval. Assuming $\dim(W(F))=3$, every one- or two-dimensional ... More

Geometry of the set of mixed quantum states: An apophatic approachDec 11 2011Dec 14 2011The set of quantum states consists of density matrices of order $N$, which are hermitian, positive and normalized by the trace condition. We analyze the structure of this set in the framework of the Euclidean geometry naturally arising in the space of ... More

Quantum Weak Coin FlippingNov 06 2018We investigate weak coin flipping, a fundamental cryptographic primitive where two distrustful parties need to remotely establish a shared random bit. A cheating player can try to bias the output bit towards a preferred value. For weak coin flipping the ... More

The MaxEnt extension of a quantum Gibbs family, convex geometry and geodesicsOct 31 2014We discuss methods to analyze a quantum Gibbs family in the ultra-cold regime where the norm closure of the Gibbs family fails due to discontinuities of the maximum-entropy inference. The current discussion of maximum-entropy inference and irreducible ... More

Continuity of the maximum-entropy inference: Convex geometry and numerical ranges approachFeb 06 2015We study the continuity of an abstract generalization of the maximum-entropy inference - a maximizer. It is defined as a right-inverse of a linear map restricted to a convex body which uniquely maximizes on each fiber of the linear map a continuous function ... More

Quantum Spin Hall Insulators with Interactions and Lattice AnisotropyJun 06 2011May 03 2012We investigate the interplay between spin-orbit coupling and electron-electron interactions on the honeycomb lattice combining the cellular dynamical mean-field theory and its real space extension with analytical approaches. We provide a thorough analysis ... More

Maximizing the divergence from a hierarchical model of quantum statesJun 03 2014Feb 12 2015We study many-party correlations quantified in terms of the Umegaki relative entropy (divergence) from a Gibbs family known as a hierarchical model. We derive these quantities from the maximum-entropy principle which was used earlier to define the closely ... More

A global minimization algorithm for Tikhonov functionals with sparsity constraintsJan 02 2014May 16 2014In this paper we present a globally convergent algorithm for the computation of a minimizer of the Tikhonov functional with sparsity promoting penalty term for nonlinear forward operators in Banach space. The dual TIGRA method uses a gradient descent ... More

A Parameterized Energy Correction Method for Electromagnetic Showers in BGO-ECAL of DAMPEMar 08 2017Apr 05 2017DAMPE is a space-based mission designed as a high energy particle detector measuring cosmic-rays and $\gamma-$rays which was successfully launched on Dec.17, 2015. The BGO electromagnetic calorimeter is one of the key sub-detectors of DAMPE for energy ... More

Random Subgroups of RationalsJan 15 2019Jan 17 2019This paper introduces and studies a notion of \emph{algorithmic randomness} for subgroups of rationals. Given a randomly generated additive subgroup $(G,+)$ of rationals, two main questions are addressed: first, what are the model-theoretic and recursion-theoretic ... More

Memory equations as reduced Markov processesApr 06 2018A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with such a memory ... More

Intrinsic Inference on the Mean Geodesic of Planar Shapes and Tree Discrimination by Leaf GrowthSep 16 2010For planar landmark based shapes, taking into account the non-Euclidean geometry of the shape space, a statistical test for a common mean first geodesic principal component (GPC) is devised. It rests on one of two asymptotic scenarios, both of which are ... More

A note on Diophantine approximation with Gaussian primesSep 28 2016We investigate the distribution of $p\theta$ modulo 1, where $\theta$ is a complex number which is not contained in $\mathbb{Q}(i)$, and $p$ runs over the Gaussian primes.

Introduction to Physical Implementations of Quantum Information ProcessingMar 01 2013This was a contribution to the lecture notes on the 44th IFF Spring School held at Forschungszentrum J\"ulich in 2013 on "Quantum Information Processing". The school as a whole had a strong focus on solid state systems. It was the purpose of this contribution ... More

Recent Progress in Lattice QCDJan 09 2013Recent progress in Lattice QCD is highlighted. After a brief introduction to the methodology of lattice computations the presentation focuses on three main topics: Hadron Spectroscopy, Hadron Structure and Lattice Flavor Physics. In each case a summary ... More

Gauge action improvement and smearingSep 23 2004Dec 28 2005The effect of repeatedly smearing SU(3) gauge configurations is investigated. Six gauge actions (Wilson, Symanzik, Iwasaki, DBW2, Beinlich-Karsch-Laermann, Langfeld; combined with a direct SU(3)-overrelaxation step) and three smearings (APE, HYP, EXP) ... More

Aspects of Quasi-Phasestructure of the Schwinger Model on a Cylinder with Broken Chiral SymmetryMay 19 1998Oct 05 1998We consider the N_f-flavour Schwinger Model on a thermal cylinder of circumference $\beta=1/T$ and of finite spatial length $L$. On the boundaries $x^1=0$ and $x^1=L$ the fields are subject to an element of a one-dimensional class of bag-inspired boundary ... More

Quantum phase transitions of topological insulators without gap closingOct 11 2013Aug 12 2016We consider two-dimensional Chern insulators and time-reversal invariant topological insulators and discuss the effect of perturbations breaking either particle-number conservation or time-reversal symmetry. The appearance of trivial mass terms is expected ... More

Interfacing Constraint-Based Grammars and Generation AlgorithmsAug 07 2000Constraint-based grammars can, in principle, serve as the major linguistic knowledge source for both parsing and generation. Surface generation starts from input semantics representations that may vary across grammars. For many declarative grammars, the ... More

Algorithmic Meta-TheoremsFeb 20 2009Algorithmic meta-theorems are general algorithmic results applying to a whole range of problems, rather than just to a single problem alone. They often have a "logical" and a "structural" component, that is they are results of the form: every computational ... More

Minimal even sets of nodesOct 20 1997We extend some results on even sets of nodes which have been proved for surfaces up to degree 6 to surfaces up to degree 10. In particular, we give a formula for the minimal cardinality of a nonempty even set of nodes.

A Projective Surface of Degree Eight with 168 NodesJul 19 1995The estimate for the maximal number of ordinary double points of a projective surface of degree eight is improved to $168\leq\mu(8)\leq 174$ by constructing a projective surface of degree eight with 168 nodes.

On the structure of semigroups on $L_p$ with a bounded $H{^\infty}$-calculusOct 17 2013Oct 07 2014We show that a bounded analytic semigroup on an $L_p$-space has a bounded $H^{\infty}(\Sigma_{\varphi})$-calculus for some $\varphi < \frac{\pi}{2}$ if and only if the semigroup can be obtained, after restricting to invariant subspaces, factorizing through ... More

Piecewise deterministic Markov processes driven by scalar conservation lawsJan 29 2019We investigate piecewise deterministic Markov processes (PDMP), where the deterministic dynamics follows a scalar conservation law and random jumps in the system are characterized by changes in the flux function. We show under which assumptions we can ... More

UV and IR divergences within Dimensional Regularization in Non-Commutative theories and Phenomenological ImplicationsAug 25 2002Oct 10 2002Using Dimensional Regularization (DR) for some two-point functions of a prototype Non-Comutative (NC) \phi^4 scalar theory in 4-dimensions, we explictly analyze, to one-loop, the IR and UV divergences of non-planar diagrams having quadratic divergences ... More

On the $p^λ$ problemDec 19 2005We deal with the distribution of the fractional parts of $p^{\lambda}$, $p$ running over the prime numbers and $\lambda$ being a fixed real number lying in the interval $(0,1)$. Roughly speaking, we study the following question: Given a real $\theta$, ... More

Addendum to "On the $p^λ$ problem"Dec 19 2005We prove that the conditions $\lambda<5/19$ and $L\le T^{1/2}$ in Theorems 3 and 4 of our recent paper "On the $p^{\lambda}$ problem" can be omitted.

Confined elasticae and the buckling of cylindrical shellsDec 12 2018Dec 25 2018For curves of prescribed length embedded into the unit disc in two dimensions, we obtain scaling results for the minimal elastic energy as the length just exceeds $2\pi$ and in the large length limit. In the small excess length case, we prove convergence ... More

Towards a characterization of Markov processes enjoying the time-inversion propertyJun 01 2005Apr 26 2007We give a necessary and sufficient condition for a homogeneous Markov process taking values in $\R^n$ to enjoy the time-inversion property of degree $\alpha$. The condition sets the shape for the semigroup densities of the process and allows to further ... More

The large sieve with sparse sets of moduliAug 22 2005Extending a method of D. Wolke, we establish a general result on the large sieve with sparse sets S of moduli which are in a sense well-distributed in arithmetic progressions. We then apply our result to the case when S consists of sqares. In this case ... More

On the number of Tverberg partitions in the prime power caseApr 22 2004We give an extension of the lower bound of Vucic and Zivaljevic for the number of Tverberg partitions from the prime to the prime power case. Our proof is inspired by the Z_p-index version of the proof in Matousek's book "Using the Borsuk-Ulam Theorem" ... More

Pathwise construction of tree-valued Fleming-Viot processesApr 14 2014Dec 27 2017In a random complete and separable metric space that we call the lookdown space, we encode the genealogical distances between all individuals ever alive in a lookdown model with simultaneous multiple reproduction events. We construct families of probability ... More

Elliptic curves with square-free $Δ$Mar 05 2015Jun 09 2015Under the Riemann Hypothesis for Dirichlet L-functions, we improve on the error term in a smoothed version of an estimate for the density of elliptic curves with square-free $\Delta=D/16$, where D is the discriminant, by T.D. Browning and the author. ... More

A note on Diophantine approximation with Gaussian primesSep 28 2016Nov 10 2017We investigate the distribution of $p\theta$ modulo 1, where $\theta$ is a complex number which is not contained in $\mathbb{Q}(i)$, and $p$ runs over the Gaussian primes.

Non-Autonomous Maximal $L^p$-Regularity for Rough Divergence Form Elliptic OperatorsNov 19 2015Aug 22 2016We obtain $L^p(L^q)$ maximal regularity estimates for time dependent second order elliptic operators in divergence form with rough dependencies in the spatial variables.

Singular moduli of higher level and special cyclesMay 11 2015Jun 25 2015We describe the complex multiplication (CM) values of modular functions for $\Gamma_0(N)$ whose divisor is given by a linear combination of Heegner divisors in terms of special cycles on the stack of CM elliptic curves. In particular, our results apply ... More

A primer on A-infinity-algebras and their Hochschild homologyJan 15 2016We present an elementary and self-contained construction of $A_\infty$-algebras, $A_\infty$-bimodules and their Hochschild homology and cohomology groups. In addition, we discuss the cup product in Hochschild cohomology and the spectral sequence of the ... More

Software and their Dependencies in Research Citation GraphsJun 14 2019Software is essential for a lot of research, but it is not featured in citation graphs which have the potential to assign credit for software contributions. This is due to a traditionalistic focus on textual research products. In this paper, I propose ... More

Maximal Regularity: Positive Counterexamples on UMD-Banach Lattices and Exact Intervals for the Negative Solution of the Extrapolation ProblemNov 16 2014Using methods from Banach space theory, we prove two new structural results on maximal regularity. The first says that there exist positive analytic semigroups on UMD-Banach lattices, namely $\ell_p(\ell_q)$ for $p \neq q \in (1, \infty)$, without maximal ... More

Generalized Gorensteinness and a homological determinant for preprojective algebrasJun 25 2018Studying invariant theory of commutative polynomial rings has motivated many developments in commutative algebra and algebraic geometry. Of particular interest has been to understand under what conditions we can obtain a fixed ring satisfying useful properties. ... More

A representation for exchangeable coalescent trees and generalized tree-valued Fleming-Viot processesAug 29 2016Dec 27 2017We give a de Finetti type representation for exchangeable random coalescent trees (formally described as semi-ultrametrics) in terms of sampling iid sequences from marked metric measure spaces. We apply this representation to define versions of tree-valued ... More

Vector valued theta functions associated with binary quadratic formsMay 11 2015Jun 02 2015We study the space of vector valued theta functions for the Weil representation of a positive definite even lattice of rank two with fundamental discriminant. We work out the relation of this space to the corresponding scalar valued theta functions of ... More

Spin 3/2 dimer modelJan 30 2009Apr 16 2009We present a parent Hamiltonian for weakly dimerized valence bond solid states for arbitrary half-integral S. While the model reduces for S=1/2 to the Majumdar-Ghosh Hamiltonian we discuss this model and its properties for S=3/2. Its degenerate ground ... More

Convergence issues in ChPT: a lattice perspectiveMay 24 2013This review addresses the practical convergence of the ChPT series in the p-regime. In the SU(2) framework there is a number of new results, and improved estimates of \bar\ell_3 and \bar\ell_4 are available. In the SU(3) framework few new lattice computations ... More

Logarithmic link smearing for full QCDSep 26 2007Mar 16 2009A Lie-algebra based recipe for smoothing gauge links in lattice field theory is presented, building on the matrix logarithm. With or without hypercubic nesting, this LOG/HYL smearing yields fat links which are differentiable w.r.t. the original ones. ... More

The phase transition in the multiflavour Schwinger modelSep 12 2000A summary is given of a quantization of the multiflavour Schwinger model on a finite-temperature cylinder with chirality-breaking boundary conditions at its spatial ends, and it is shown that the analytic expression for the chiral condensate implies that ... More

QCD in a finite box: Numerical test studies in the three Leutwyler-Smilga regimesAug 30 2000Nov 07 2000The Leutwyler-Smilga prediction regarding the (ir)relevance of the global topological charge for QCD in a finite box is subject to a test. To this end the lattice version of a suitably chosen analogue (massive 2-flavour Schwinger model) is analyzed in ... More

Inference on 3D Procrustes means: tree bole growth, rank-deficient diffusion tensors and perturbation modelsFeb 03 2010Feb 02 2011The Central Limit Theorem (CLT) for extrinsic and intrinsic means on manifolds is extended to a generalization of Fr\'echet means. Examples are the Procrustes mean for 3D Kendall shapes as well as a mean introduced by Ziezold. This allows for one-sample ... More

A Short Proof of the Reducibility of Hard-Particle Cluster IntegralsMay 18 2011The current article considers Mayer cluster integrals of n-dimensional hard particles in the n>1 dimensional flat Euclidean space. Extending results from Wertheim and Rosenfeld, we proof that the graphs are completely reducible into 1- and 2-point measures, ... More

Optimization of the Brillouin operator on the KNL architectureSep 06 2017Jul 09 2018Experiences with optimizing the matrix-times-vector application of the Brillouin operator on the Intel KNL processor are reported. Without adjustments to the memory layout, performance figures of 360 Gflop/s in single and 270 Gflop/s in double precision ... More

Three Dirac operators on two architectures with one piece of code and no hassleAug 16 2018Nov 20 2018A simple minded approach to implement three discretizations of the Dirac operator (staggered, Wilson, Brillouin) on two architectures (KNL and core i7) is presented. The idea is to use a high-level compiler along with OpenMP parallelization and SIMD pragmas, ... More

Entropy Analysis of Financial Time SeriesJul 25 2018This thesis applies entropy as a model independent measure to address three research questions concerning financial time series. In the first study we apply transfer entropy to drawdowns and drawups in foreign exchange rates, to study their correlation ... More

Foliations and the cohomology of moduli spaces of bounded global $G$-shtukasOct 19 2016For arbitrary reductive groups $G$ defined over a finite field, we decompose Newton strata in the special fiber of moduli spaces of global $G$-shtukas into a product of Rapoport-Zink spaces and Igusa varieties. This allows us to compare the $\ell$-adic ... More

The spectrum of light isovector mesons with $C=+1$ from the COMPASS experimentOct 04 2016Based on the largest event sample of diffractively produced $\pi^-\pi^-\pi^+$, obtained by a pion beam of $190~\rm{GeV/c}$ momentum, the COMPASS collaboration has performed the most advanced partial wave analysis on multi-body final states, using the ... More

Standard bases with respect to the Newton filtrationApr 15 1999The aim of this article is to introduce standard bases of ideals in polynomial rings with respect to a class of orderings which are not necessarily semigroup orderings. Our approach generalises the concept of standard bases with respect to semigroup orderings ... More

Diophantine approximation on lines in \mathbb{C}^2 with Gaussian prime constraints - enhanced versionJun 20 2017We study the problem of Diophantine approximation on lines in $\mathbb{C}^2$ with numerators and denominators restricted to Gaussian primes. To this end, we develop analogs of well-known results on small fractional parts of $p\gamma$, $p$ running over ... More

A Two Stage CVT / Eikonal Convection Mesh Deformation Approach for Large Nodal DeformationsNov 27 2014A two step mesh deformation approach for large nodal deformations, typically arising from non-parametric shape optimization, fluid-structure interaction or computer graphics, is considered. Two major difficulties, collapsed cells and an undesirable parameterization, ... More

On a topological fractional Helly theoremJun 20 2005We prove a new fractional Helly theorem for families of sets obeying topological conditions. More precisely, we show that the nerve of a finite family of open sets (and of subcomplexes of cell complexes) in R^d is k-Leray where k depends on the dimension ... More

m_c and m_b from M_B_c and new estimate of f_B_cJun 09 2019Jun 15 2019We extract (for the first time) the correlated values of the running masses m_c and m_b from M_Bc using QCD Laplace sum rules (LSR) within stability criteria where pertubative (PT) expressions at N2LO and non-perturbative (NP) gluon condensates at LO ... More

Note on antichain cutsets in discrete semimodular latticesFeb 26 2011The characterization of level sets of finite Boolean lattices as antichain cutsets, due to Rival and Zaguia, is seen to hold in all discrete semimodular lattices.

Non-Autonomous Maximal $L^p$-Regularity under Fractional Sobolev Regularity in TimeNov 28 2016We prove non-autonomous maximal $L^p$-regularity results on UMD spaces replacing the common H\"older assumption by a weaker fractional Sobolev regularity in time. This generalizes recent Hilbert space results by Dier and Zacher. In particular, on $L^q(\Omega)$ ... More

On a class of reducible trinomialsNov 04 2013In this short note we give an expression for some numbers $n$ such that the polynomial $x^{2p}-nx^p+1$ is reducible.

Spherical varieties over large fieldsMay 04 2018Oct 02 2018Let k_0 be a field of characteristic 0, k its algebraic closure, G a connected reductive group defined over k. Let H\subset G be a spherical subgroup. We assume that k_0 is a large field, for example, k_0 is either the field R of real numbers or a p-adic ... More

Calculating the correlation coefficients of graph-theoretical indicesAug 30 2006Using a generating function approach, the correlation coefficients of four different graph-theoretical indices, namely the number of independent vertex subsets, the number of matchings, the number of subtrees and the Wiener index, are asymptotically determined ... More

On the large sieve with sparse sets of moduliDec 12 2005Extending a method of D. Wolke, we establish a general result on the large sieve with sparse sets S of moduli which are in a sense well-distributed in arithmetic progressions. We then use this result together with Fourier techniques to obtain large sieve ... More

On the large sieve with square moduliAug 22 2005We prove an estimate for the large sieve with square moduli which improves a recent result of L. Zhao. Our method uses an idea of D. Wolke and some results from Fourier analysis.

Beyond the Rosenfeld Functional: Loop Contributions in Fundamental Measure TheoryAug 20 2012The Rosenfeld functional provides excellent results for the prediction of the fluid phase of hard convex particle systems but fails beyond the freezing point. The reason for this limitation is the neglect of orientational and distance correlations beyond ... More

Deriving the Rosenfeld Functional from the Virial ExpansionNov 22 2011Apr 19 2012In this article we replace the semi-heuristic derivation of the Rosenfeld functional of hard convex particles with the systematic calculation of Mayer clusters. It is shown that each cluster integral further decomposes into diagrams of intersection patterns ... More

On the number of Birch partitionsDec 28 2006Apr 17 2008Birch and Tverberg partitions are closely related concepts from discrete geometry. We show two properties for the number of Birch partitions: Evenness, and a lower bound. This implies the first non-trivial lower bound for the number of Tverberg partitions ... More

Helfrich's Energy and Constrained MinimisationAug 09 2016For every $g\in\mathbb{N}_0$ and $\epsilon>0$, we construct a smooth genus $g$ surface embedded into the unit ball with area $8\pi$ and Willmore energy smaller than $8\pi + \epsilon$. From this we deduce that a minimising sequence for Willmore's energy ... More

Regularity Properties of Sectorial Operators: Counterexamples and Open ProblemsJul 04 2014Oct 10 2015We give a survey on the different regularity properties of sectorial operators on Banach spaces. We present the main results and open questions in the theory and then concentrate on the known methods to construct various counterexamples.

The Kalton-Lancien Theorem Revisited: Maximal Regularity does not extrapolateOct 16 2012Sep 19 2013We give a new more explicit proof of a result by Kalton & Lancien stating that on each Banach space with an unconditional basis not isomorphic to a Hilbert space there exists a generator of a holomorphic semigroup which does not have maximal regularity. ... More

The square sieve and the large sieve with square moduliJun 19 2015Jun 07 2016We give a short alternative proof using Heath-Brown's square sieve of a bound of the author for the large sieve with square moduli.

Online learning as a way to tackle instabilities and biases in neural network parameterizationsJul 02 2019Over the last couple of years, machine learning parameterizations have emerged as a potential way to improve the representation of sub-grid processes in atmospheric models. All previous studies created a training dataset from a high-resolution simulation, ... More

Divide-and-conquer generating functions. Part I. Elementary sequencesJul 02 2003Divide-and-conquer functions satisfy equations in F(z),F(z^2),F(z^4)... Their generated sequences are mainly used in computer science, and they were analyzed pragmatically, that is, now and then a sequence was picked out for scrutiny. By giving several ... More

A representation for exchangeable coalescent trees and generalized tree-valued Fleming-Viot processesAug 29 2016We show that every exchangeable random semi-ultrametric on the integers can be obtained by sampling an iid sequence from a random marked metric measure space and adding the marks to the distances. We use this representation to define tree-valued Fleming-Viot ... More

Probing High-Energy Physics with High-Precision QED MeasurementsMar 05 2002I summarize our self-contained determinations of the lowest order hadronic contributions to the anomalous magnetic moments a_{\mu,\tau} of the muon and tau leptons, the running QED coupling \alpha(M_Z) and the muonium hyperfine splitting \nu. Using as ... More

Anomalous electronic conductance in quasicrystalsJul 27 1999Jul 31 1999Generic quantum interference effects occuring in 1D-quasicrystals are reviewed with emphasis on the joint effect of phason disorder on electronic localization and propagation modes. In close conjunction with properties of real materials, the contributions ... More

The Lorentz group and its finite field analogues: local isomorphism and approximationMay 08 2008Aug 04 2008Finite Lorentz groups acting on 4-dimensional vector spaces coordinatized by finite fields with a prime number of elements are represented as homomorphic images of countable, rational subgroups of the Lorentz group acting on real 4-dimensional space-time. ... More

$α_s(μ)$ from $M_{χ_{0c(0b)}}-M_{η_{c(b)}}$@N2LODec 19 2018This note complements and clarifies the results obtained in the original paper {\it QCD Parameters Correlations from Heavy Quarkonia} [1] where, here, we present a more detailed discussion of the \alpha_s-results obtained @ N2LO at two different subtraction ... More

Properties of the fixed ring of a preprojective algebraMay 08 2018Oct 24 2018For a finite group acting on a polynomial ring, the Chevalley-Shephard-Todd Theorem proves that the fixed subring is isomorphic to a polynomial ring if and only if the group is generated by pseudo-reflections. In recent years, progress was made in work ... More

Numerical evaluation of multi-loop integralsNov 28 2018We present updates on the development of pySecDec, a toolbox to numerically evaluate parameter integrals in the context of dimensional regularization. We discuss difficulties with loop integrals in the special kinematic condition where the squared momentum ... More

The structure of minimal surfaces in CAT(0) spacesAug 20 2018We prove that a minimal disc in a CAT(0) space is a local embedding away from a finite set of "branch points". On the way we establish several basic properties of minimal surfaces: monotonicity of area densities, density bounds, limit theorems and the ... More

The Neutron and the Universe - History of a RelationshipMay 11 2012We discuss selected topics in the field of particle- and astrophysics with neutrons. They have a direct link with our understanding of the history of the Universe and are related to recent, ongoing or future measurements. They deal with the structure ... More

The Puzzle of Neutron LifetimeFeb 01 2009Mar 06 2009In this paper we review the role of the neutron lifetime and discuss the present status of measurements. In view of the large discrepancy observed by the two most precise individual measurements so far we describe the different techniques and point out ... More