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Long range transport of ultra cold atoms in a far-detuned 1D optical latticeApr 16 2012We present a novel method to transport ultra cold atoms in a focused optical lattice over macroscopic distances of many Rayleigh ranges. With this method ultra cold atoms were transported over 5 cm in 250 ms without significant atom loss or heating. By ... More

High accuracy correction of blackbody radiation shift in an optical lattice clockAug 14 2012Oct 29 2012We have determined the frequency shift that blackbody radiation is inducing on the $5s^2$ $^1$S$_0$ -- $5s5p$ $^3$P$_0$ clock transition in strontium. Previously its uncertainty limited the uncertainty of strontium lattice clocks to $1\times10^{-16}$. ... More

Delivering pulsed and phase stable light to atoms of an optical clockAug 18 2011Feb 10 2012In optical clocks, transitions of ions or neutral atoms are interrogated using pulsed ultra-narrow laser fields. Systematic phase chirps of the laser or changes of the optical path length during the measurement cause a shift of the frequency seen by the ... More

Lattice-induced photon scattering in an optical lattice clockFeb 08 2018Jul 19 2018We investigate scattering of lattice laser radiation in a strontium optical lattice clock and its implications for operating clocks at interrogation times up to several tens of seconds. Rayleigh scattering does not cause significant decoherence of the ... More

A compact and efficient strontium oven for laser-cooling experimentsSep 25 2012Here we describe a compact and efficient strontium oven well suited for laser-cooling experiments. Novel design solutions allowed us to produce a collimated strontium atomic beam with a flux of 1.0\times10^13 s^-1 cm^-2 at the oven temperature of 450 ... More

Tackling the blackbody shift in a strontium optical lattice clockSep 10 2010A major obstacle for optical clocks is the frequency shift due to black body radiation. We discuss how one can tackle this problem in an optical lattice clock; in our case 87-Sr: firstly, by a measurement of the dc Stark shift of the clock transition ... More

8E-17 fractional laser frequency instability with a long room-temperature cavityFeb 09 2015Mar 31 2015We present a laser system based on a 48 cm long optical glass resonator. The large size requires a sophisticated thermal control and optimized mounting design. A self balancing mounting was essential to reliably reach sensitivities to acceleration of ... More

Ultra-stable laser with average fractional frequency drift rate below $5\times10^{-19}/\mathrm{s}$May 07 2014Cryogenic single-crystal optical cavities have the potential to provide highest dimensional stability. We have investigated the long-term performance of an ultra-stable laser system which is stabilized to a single-crystal silicon cavity operated at 124 ... More

A strontium lattice clock with $3 \times 10^{-17}$ inaccuracy and its frequencyDec 12 2013Aug 15 2014We have measured the absolute frequency of the optical lattice clock based on $^{87}$Sr at PTB with an uncertainty of $3.9\times 10^{-16}$ using two caesium fountain clocks. This is close to the accuracy of today's best realizations of the SI second. ... More

Study of the Born-Oppenheimer Approximation for Mass-Scaling of Cold Collision PropertiesJun 15 2007Asymptotic levels of the A $^1\Sigma_u^+$ state of the two isotopomers $^{39}{\rm K}_2$ and $^{39}{\rm K}^{41}{\rm K}$ up to the dissociation limit are investigated with a Doppler-free high resolution laser-spectroscopic experiment in a molecular beam. ... More

Absolute Frequency Atlas from 915 nm to 985 nm based on Laser Absorption Spectroscopy of IodineJan 04 2018This article reports on laser absorption spectroscopy of iodine gas between 915 nm and 985 nm. This wavelength range is scanned utilizing a narrow linewidth and mode-hop-free tunable diode-laser whose frequency is actively controlled using a calibrated ... More

Potassium ground state scattering parameters and Born-Oppenheimer potentials from molecular spectroscopyApr 18 2008We present precision measurements with MHz uncertainty of the energy gap between asymptotic and well bound levels in the electronic ground state X $^1\Sigma_{\mathrm{g}}^+$ of the $^{39}$K$_2$ molecule. The molecules are prepared in a highly collimated ... More

Lattice-induced photon scattering in an optical lattice clockFeb 08 2018We investigate scattering of lattice laser radiation in a strontium optical lattice clock and its implications for operating clocks at interrogation times up to several ten seconds. Rayleigh scattering does not cause significant decoherence of the atomic ... 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

Bringing Structure into Summaries: Crowdsourcing a Benchmark Corpus of Concept MapsApr 14 2017Jul 21 2017Concept maps can be used to concisely represent important information and bring structure into large document collections. Therefore, we study a variant of multi-document summarization that produces summaries in the form of concept maps. However, suitable ... 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.

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

The Lang-Trotter Conjecture on AverageSep 04 2006For an elliptic curve $E$ over $\ratq$ and an integer $r$ let $\pi_E^r(x)$ be the number of primes $p\le x$ of good reduction such that the trace of the Frobenius morphism of $E/\fie_p$ equals $r$. We consider the quantity $\pi_E^r(x)$ on average over ... 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

Recent Physics results with the COMPASS ExperimentNov 03 2005Nov 06 2005The COMPASS experiment has obtained first physics results in the field of polarized distribution functions for quarks and gluons using muon scattering off polarized deuterons. The analysis using open charm production and pairs of high $p_T$ hadrons is ... More

Selected Aspects of Neutron DecayApr 18 2005Precision measurements of neutron decay offer complementary access to particle physics at small distance scales or high energies. In particular they allow tests of the V-A structure of the weak interaction. Among many experimental activities which are ... More

Strangeness in Hadronic SystemsSep 23 1999This paper reviews different aspects of hadronic systems with strange quarks. It reviews production, spectroscopy and decay of baryons and hypernuclei with emphasis on recent results obtained in this field. It includes a comparison of different systems ... 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.

Degenerations of ideal hyperbolic triangulationsAug 16 2005Jun 07 2011Let M be a cusped 3-manifold, and let T be an ideal triangulation of M. The deformation variety D(T), a subset of which parameterises (incomplete) hyperbolic structures obtained on M using T, is defined and compactified by adding certain projective classes ... More

Distribution Functionals for Hard Particles in N DimensionsFeb 15 2015The current article completes our investigation of the hard-particle interaction by determining their distribution functionals. Beginning with a short review of the perturbation expansion of the free-energy functional, we derive two representations of ... 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

On distances and metrics in discrete ordered setsJun 30 2013Discrete partially ordered sets can be turned into distance spaces in several ways. The distance functions may or may not satisfy the triangle inequality, and restriction of the distance to finite chains may or may not coincide with the natural, difference-of-height ... More

Feasibility of giant fiber-optic gyroscopesJan 04 2013Mar 07 2013The availability of long-distance, underground fiber-optic links opens a perspective of implementing interferometric fiber-optic gyroscopes embracing very large areas. We discuss the potential sensitivity, some disturbances and approaches to overcome ... More

Convergence of tree-valued Cannings chainsAug 29 2016We consider sequences of tree-valued Markov chains that describe evolving genealogies in Cannings models, and we show their convergence in distribution to tree-valued Fleming-Viot processes. Under the conditions of M\"ohle and Sagitov, this convergence ... More

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

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

Multiplicative inverses in short intervalsAug 16 2012We give an alternative proof of a recent result by T.D. Browning and A. Haynes (arXiv:1204.6374v1) on multiplicative inverses in sequences of intervals and improve this result under additional conditions on the spacing of these intervals.

Oriented robot motion planning in Riemannian manifoldsOct 15 2018Feb 26 2019We consider the problem of robot motion planning in an oriented Riemannian manifold as a topological motion planning problem in its oriented frame bundle. For this purpose, we study the topological complexity of oriented frame bundles, derive an upper ... More

QCD Parameters Correlations from Heavy QuarkoniaJan 02 2018Dec 03 2018Correlations between the QCD coupling \alpha_s, the gluon condensate < \alpha_s G^2 >, and the c,b-quark running masses m_c,b in the MS-scheme are explicitly studied (for the first time) from the (axial-)vector and (pseudo)scalar charmonium and bottomium ... More

The possibility of Scale Relativistic signatures in the Brownian motion of micro-spheres in optical trapsJun 23 2017The development of a mechanics of non-differentiable paths suggested by Scale Relativity results in a foundation of Quantum Mechanics including Schr\"odinger's equation and all the other axioms under the assumption the path non-differentiability can be ... 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.

A Proposal for the Measurement and Documentation of Research Software Sustainability in Interactive Metadata RepositoriesAug 16 2016Aug 17 2016This paper proposes an interactive repository type for research software metadata which measures and documents software sustainability by accumulating metadata, and computing sustainability metrics over them. Such a repository would help to overcome technical ... 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

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

On the divisor class group of double solidsSep 28 1998Sep 29 1998For a double solid $V\to P_3(C)$ branched over a surface $B\subset P_3(C)$ with only ordinary nodes as singularities, we give a set of generators of the divisor class group $Pic(\tilde{V}})$ in terms of contact surfaces of $B$ with only superisolated ... 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.

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

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

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

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

Electromagnetic Scattering in Degenerate and Partially Degenerate Nuclear MatterFeb 27 2019I calculate the rate of electromagnetic scattering in degenerate and partially degenerate plasmas composed of electrons, muons, protons, and neutrons. Correlations with strong interactions, induced by the polarizability of electromagnetically and strongly ... 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

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.

Dark matter constraints on the parameter space and particle spectra in the nonminimal SUSY standard modelApr 04 1997Aug 19 1997We investigate the dark matter constraints for the nonminimal SUSY standard model (NMSSM). The cosmologically restricted mass spectra of the NMSSM are compared to the minimal SUSY standard model (MSSM). The differences of the two models concerning the ... 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

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

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

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

An Operational Petri Net Semantics for the Join-CalculusAug 14 2012We present a concurrent operational Petri net semantics for the join-calculus, a process calculus for specifying concurrent and distributed systems. There often is a gap between system specifications and the actual implementations caused by synchrony ... More

Hyperboloid preservation implies the Lorentz and Poincaré groups without dilationsSep 20 2010An analogue of the Alexandrov-Zeeman theorem, based on hyperboloid preservation, as opposed to light cone preservation, is provided. This characterizes exactly the Poincar\'e group, as opposed to the Poincar\'e group extended by dilations. The hyperbolic ... More

Wetting on Random Roughness: the Ubiquity of Wenzel PrewettingMar 23 2012The wetting properties of solid substrates with macroscopic random roughness are considered as a function of the microscopic contact angle of the wetting liquid and its partial pressure in the surrounding gas phase. It is shown that Wenzel prewetting, ... More

Normal surfaces in topologically finite 3-manifoldsJun 14 2004Jun 12 2007The concept of a normal surface in a triangulated, compact 3-manifold was generalised by Thurston to a spun-normal surface in a non-compact 3-manifold with ideal triangulation. This paper defines a boundary curve map which takes a spun-normal surface ... More

Gamma-ray Bursts and their Central EnginesJan 04 2004Jan 09 2004Gamma-ray bursts are the most luminous and probably the most relativistic events in the universe. The last few years have seen a tremendous increase in our knowledge of these events, but the source of the bursts still remains elusive. I will summarise ... More

Astrophysical Smooth Particle HydrodynamicsMar 29 2009Aug 05 2009The paper presents a detailed review of the smooth particle hydrodynamics (SPH) method with particular focus on its astrophysical applications. We start by introducing the basic ideas and concepts and thereby outline all ingredients that are necessary ... 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.

Exponential sums with coefficients of certain Dirichlet seriesAug 12 2011Sep 12 2011Under the generalized Lindel\"of Hypothesis in the t- and q-aspects, we bound exponential sums with coefficients of Dirichlet series belonging to a certain class. We use these estimates to establish a conditional result on squares of Hecke eigenvalues ... More

Exponential sums with Dirichlet coefficients of L-functionsJun 22 2012Oct 29 2012Improving and extending recent results of the author, we conditionally estimate exponential sums with Dirichlet coefficients of L-functions, both over all integers and over all primes in an interval. In particular, we establish new conditional results ... More

Taste-split staggered actions: eigenvalues, chiralities and Symanzik improvementFeb 04 2013Jul 26 2013The eigenvalue spectra of staggered fermions with an Adams and/or Hoelbling mass term are studied. The chiralities of the eigenmodes reflect whether the chirality linked to the unflavored approximate (\gamma_5 \times 1) or the flavored exact (\gamma_5 ... More

Local phase damping of single qubits sets an upper bound on the phase damping rate of entangled statesNov 30 2011Jan 27 2012I derive an inequality in which the phase damping rates of single qubits set an upper bound for the phase damping rate of entangled states of many qubits. The derivation is based on two assumptions: first, that the phase damping can be described by a ... More

Topological susceptibility in full QCD: lattice results versus the prediction from the QCD partition function with granularityMar 14 2001Jun 29 2001Recent lattice data from CP-PACS, UKQCD, SESAM/TXL and the Pisa group regarding the quark mass dependence of the topological susceptibility in 2-flavour QCD are compared to each other and to theoretical expectations. The latter get specified by referring ... More

Topologically Unquenched QCD: Prospects from an explorative study in 2-flavour QED(2)Mar 22 2000May 11 2000The concept of simulating a variant of QCD with sea quarks which interact with the gluon configuration only via global gluonic quantities like $\int F\tilde F dx$ and $\int FF dx$ is tested for the case of the massive 2-flavour Schwinger model. It is ... More

Physics of eta-prime with rooted staggered quarksMar 12 2012Sep 20 2012The quark-mass dependence of the eta in the Schwinger model, which -- like the eta-prime in QCD -- becomes massive through the axial anomaly, is studied on the lattice with N_f=0,1,2. Staggered quarks are used, with a rooted determinant for N_f=1. In ... More

M_pi^2 versus m_q: comparing CP-PACS and UKQCD data to Chiral Perturbation TheoryAug 26 2002Mar 21 2003I present a selection of CP-PACS and UKQCD data for the pseudo-Goldstone masses in $N_f=2$ QCD with doubly degenerate quarks. At least the more chiral points should be consistent with Chiral Perturbation Theory for the latter to be useful in an extrapolation ... More

Testing the Leutwyler-Smilga prediction regarding the global topological charge distribution on the latticeSep 12 2000I give a sketch of my recent attempt to test the prediction by Leutwyler and Smilga according to which, for QCD in a finite box with $N_{f} \geq 2$, the combination $x = V \Sigma m$ indicates whether the net topological charge of the gauge background ... More

Dynamic shape analysis and comparison of leaf growthFeb 03 2010In the statistical analysis of shape a goal beyond the analysis of static shapes lies in the quantification of `same' deformation of different shapes. Typically, shape spaces are modelled as Riemannian manifolds on which parallel transport along geodesics ... More

Small random instances of the stable roommates problemFeb 23 2015Let $p_n$ denote the probability that a random instance of the stable roommates problem of size $n$ admits a solution. We derive an explicit formula for $p_n$ and compute exact values of $p_n$ for $n\leq 12$.

The Tap code - a code similar to Morse code for communication by tappingApr 18 2013A code is presented for fast, easy and efficient communication over channels that allow only two signal types: a single sound (e.g. a knock), or no sound (i.e. silence). This is a true binary code while Morse code is a ternary code and does not work in ... More

A refinement of the Hodge stratification for connected reductive groupsJul 18 2013For connected reductive groups G over a finite extension F of Q_p and L the maximal unramified extension of F we study the sets H_{\mu, N}(G) of elements b in G(L) with given Hodge points of (b\sigma), (b\sigma)^2, ..., (b\sigma)^N. We explain the relationship ... More

On the Parameterized Intractability of Monadic Second-Order LogicMar 14 2012Mar 23 2012One of Courcelle's celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic (MSO_2) is fixed-parameter tractable (fpt) on C by linear time parameterized algorithms, where the parameter ... 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

An extension of disjunctive programming and its impact for compact tree formulationsJul 07 2010In the 1970's, Balas introduced the concept of disjunctive programming, which is optimization over unions of polyhedra. One main result of his theory is that, given linear descriptions for each of the polyhedra to be taken in the union, one can easily ... 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

J.-L. Lions' Problem Concerning Maximal Regularity of Equations Governed by Non-Autonomous FormsJan 29 2016Jul 15 2016An old problem due to J.-L. Lions going back to the 1960s asks whether the abstract Cauchy problem associated to non-autonomous forms has maximal regularity if the time dependence is merely assumed to be continuous or even measurable. We give a negative ... 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

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 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

Phase Transition in the Number Partitioning ProblemJul 06 1998Sep 21 1998Number partitioning is an NP-complete problem of combinatorial optimization. A statistical mechanics analysis reveals the existence of a phase transition that separates the easy from the hard to solve instances and that reflects the pseudo-polynomiality ... More

Status of the B^0_{(s)}-\bar B^0_{(s)}} mixing from QCD spectral sum RulesMar 18 2002In this talk, I present new results [1] obtained from QCD spectral sum rules (QSSR), on the bag constant parameters entering in the analysis of the B^0_{(s)}-\bar B^0_{(s)} mass-differences. Taking the average of the results from the Laplace and moment ... More

Light and heavy quark masses, Flavour breaking of chiral condensates, Meson weak leptonic decay constants in QCDFeb 21 2002We review the present status for the determinations of the light and heavy quark masses, the light quark chiral condensate and the decay constants of light and heavy-light (pseudo)scalar mesons from QCD spectral sum rules (QSSR). Bounds on the light quark ... More

A new perspective on the Holstein polaron problemJun 12 1996The single-polaron band structure of the Holstein model in one and two dimensions is studied using a new form of resummed strong-coupling perturbation theory. Well converged results are obtained for phonon frequencies of the order of the hopping integral ... More

On the meaning of mean shapeFeb 03 2010May 12 2011Various concepts of mean shape previously unrelated in the literature are brought into relation. In particular for non-manifolds such as Kendall's 3D shape space, this paper answers the question, for which means one may apply a two-sample test. The answer ... More

How Perfect Offline Wallets Can Still Leak Bitcoin Private KeysJan 02 2015ECDSA has become a popular choice as lightweight alternative to RSA and classic DL based signature algorithms in recent years. As standardized, the signature produced by ECDSA for a pair of a message and a key is not deterministic. This work shows how ... More

Mini-review on QCD spectral sum rulesSep 29 2014Oct 03 2014Taking the example of the most popular and well-established Borel / Laplace / Exponential sum rule (LSR), I shortly review some of its recent applications in hadron physics namely the estimates of non-perturbative condensates, the determination of the ... More

Improved f_{D*_(s)}, f_{B*_(s)} and f_{B_c} from QCD Laplace sum rulesApr 26 2014Jun 01 2015Anticipating future precise measurements of the D- and B-like (semi-)leptonic and hadronic decays for alternative determinations of the CKM mixing angles, we pursue our program on the D- and B-like mesons by improving the estimates of f_{D*_(s)} and f_{B*_(s)} ... More

Stable Roommates Problem with Random PreferencesJan 21 2014Jan 21 2015The stable roommates problem with $n$ agents has worst case complexity $O(n^2)$ in time and space. Random instances can be solved faster and with less memory, however. We introduce an algorithm that has average time and space complexity $O(n^\frac{3}{2})$ ... More

Improved light quark masses from pseudoscalar sum rulesJan 15 2014Aug 27 2014Using ratios of the inverse Laplace transform sum rules within stability criteria for the subtraction point \mu in addition to the ones of the usual tau spectral sum rule variable and continuum threshold t_c, we extract the \pi(1300) and K(1460) decay ... More

Huffman coding as an algorithm to construct chains in partition latticesJun 24 2013The Huffman coding algorithm is interpreted in the lattice of partitions of the source alphabet. Maximal chains in the partition lattice correspond to linear extensions of tree orders, and those among the chains that exhibit a simple greedy property correspond ... More

Decay Constants of Heavy-Light Mesons from QCDNov 18 2015Nov 29 2015We summarize recently improved results for the pseudoscalar [1,2] and vector [3] meson decay constants and their ratios from QCD spectral sum rules where N2LO + estimate of the N3LO PT and power corrections up to d< 6 dimensions have been included in ... More

On the number of colored Birch and Tverberg partitionsAug 02 2012Dec 09 2012In 2009, Blagojevic, Matschke & Ziegler established the first tight colored Tverberg theorem, but no lower bounds for the number of colored Tverberg partitions. We develop a colored version of our previous results (2008), and we extend our results from ... More