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Phase- coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber linkJun 18 2009We have explored the performance of two "dark fibers" of a commercial telecommunication fiber link for a remote comparison of optical clocks. The two fibers, linking the Leibniz University of Hanover (LUH) with the Physi-kalisch-Technische Bundesanstalt ... 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

Thermal noise in optical cavities revisitedNov 21 2011Thermal noise of optical reference cavities sets a fundamental limit to the frequency instability of ultra-stable lasers. Using Levin's formulation of the fluctuation-dissipation theorem we correct the analytical estimate for the spacer contribution given ... More

Tuning the Thermal Expansion Properties of Optical Reference Cavities with Fused Silica MirrorsFeb 10 2010We investigate the thermal expansion of low thermal noise Fabry-Perot cavities made of Low Thermal Expansion (LTE) glass spacers and Fused Silica (FS) mirrors. The different thermal expansion of mirror and spacer deforms the mirror. This deformation strongly ... More

On the relation between uncertainties of weighted frequency averages and the various types of Allan deviationsApr 02 2015Apr 27 2015The power spectral density in Fourier frequency domain, and the different variants of the Allan deviation (ADEV) in dependence on the averaging time are well established tools to analyse the fluctuation properties and frequency instability of an oscillatory ... More

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 photoassociation of $^{40}$Ca near the ${^3P_1}+{^1S_0}$ asymptote and its Zeeman effectJun 27 2013We report on the first measurement of narrow photoassociation lines of $^{40}$Ca near the ${^3P_1}+{^1S_0}$ asymptote related to the molecular states $^3\Pi_u$ and $^3\Sigma^+_u$. The highly accurate binding energies and Zeeman splittings are well described ... More

Wavelength dependent ac-Stark shift of the 1S0 - 3P1 transition at 657 nm in CaJun 04 2004We have measured the ac-Stark shift of the 4s2 1S0 - 4s4p 3P1 line in 40Ca for perturbing laser wavelengths between 780 nm and 1064 nm with a time domain Ramsey-Borde atom interferometer. We found a zero crossing of the shift for the mS = 0 - mP = 0 transition ... 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

Bose-Einstein condensation of alkaline earth atoms: $^{40}${Ca}Aug 03 2009Sep 02 2009We have achieved Bose-Einstein condensation of $^{40}$Ca, the first for an alkaline earth element. The influence of elastic and inelastic collisions associated with the large ground state s-wave scattering length of $^{40}$Ca was measured. From these ... 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

Nonlinear Zeeman effect in photoassociation spectra of $^{40}$Ca near the $^3$P$_1$+$^1$S$_0$ asymptoteJun 12 2015We present calculations of the Zeeman effect of narrow photoassociation lines of $^{40}$Ca near the $^3$P$_1$ + $^1$S$_0$ asymptote. Using a coupled-channel model we find a nonlinear Zeeman effect that even at low fields of a few mT amounts to several ... More

Demonstration of a Transportable 1 Hz-Linewidth LaserOct 13 2010May 18 2011We present the setup and test of a transportable clock laser at 698 nm for a strontium lattice clock. A master-slave diode laser system is stabilized to a rigidly mounted optical reference cavity. The setup was transported by truck over 400 km from Braunschweig ... More

Noise and instability of an optical lattice clockJul 17 2015Nov 03 2015We present an analysis of the different types of noise from the detection and interrogation laser in our strontium lattice clock. We develop a noise model showing that in our setup quantum projection noise--limited detection is possible if more than 130~atoms ... More

Reducing the effect of thermal noise in optical cavitiesDec 14 2012Dec 17 2013Thermal noise in optical cavities imposes a severe limitation in the stability of the most advanced frequency standards at a level of a few 10^(-16) (s/t)^(1/2) for long averaging times t. In this paper we describe two schemes for reducing the effect ... More

Geodesy and metrology with a transportable optical clockMay 11 2017The advent of novel measurement instrumentation can lead to paradigm shifts in scientific research. Optical atomic clocks, due to their unprecedented stability and uncertainty, are already being used to test physical theories and herald a revision of ... 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

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

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

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 compact, robust, and transportable ultra-stable laser with a fractional frequency instability of $1\times10^{-15}$Oct 20 2014We present a compact and robust transportable ultra-stable laser system with minimum fractional frequency instability of $1\times10^{-15}$ at integration times between 1 to 10 s. The system was conceived as a prototype of a subsystem of a microwave-optical ... More

Free Lévy Processes on Dual GroupsMar 23 2002We give a short introduction to the theory of L\'evy processes on dual groups. As examples we consider L\'evy processes with additive increments and L\'evy processes on the dual affine group.

Monotone and Boolean Convolutions for Non-compactly Supported Probability MeasuresMar 14 2007Jul 03 2009The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the multiplicative boolean ... More

An ensemble related to discrete orthogonal polynomials and its application to tilings of a half-hexagonJan 19 2011Jun 28 2013We discuss asymptotic properties of a family of discrete probability measures which may be used to model particle configurations with a wall on a set of discrete nodes. The correlations are shown to be determinantal and are expressed in terms of discrete ... More

Co-Indexing Labelled DRSs to Represent and Reason with AmbiguitiesJul 25 1995The paper addresses the problem of representing ambiguities in a way that allows for monotonic disambiguation and for direct deductive computation. The paper focuses on an extension of the formalism of underspecified DRSs to ambiguities introduced by ... More

Dilute Birman--Wenzl--Murakami Algebra and $D^{(2)}_{n+1}$ modelsFeb 14 1994A ``dilute'' generalisation of the Birman--Wenzl--Murakami algebra is considered. It can be ``Baxterised'' to a solution of the Yang--Baxter algebra. The $D^{(2)}_{n+1}$ vertex models are examples of corresponding solvable lattice models and can be regarded ... More

An Indirect Genetic Algorithm for Set Covering ProblemsMar 20 2008This paper presents a new type of genetic algorithm for the set covering problem. It differs from previous evolutionary approaches first because it is an indirect algorithm, i.e. the actual solutions are found by an external decoder function. The genetic ... More

The roughening transition of interfaces in disordered mediaOct 29 1997Competing pinning effects on a D-dimensional interface by weak impurity disorder and a periodic potential of the underlying crystal lattice are analyzed for $2<D<4$. We use both the Gaussian variational method (GVM) and the functional renormalization ... More

On Cloning Context-FreenessJul 22 1997To Rogers (1994) we owe the insight that monadic second order predicate logic with multiple successors (MSO) is well suited in many respects as a realistic formal base for syntactic theorizing. However, the agreeable formal properties of this logic come ... More

Artificial Immune Systems (AIS) - A New Paradigm for Heuristic Decision MakingJan 28 2008May 16 2008Over the last few years, more and more heuristic decision making techniques have been inspired by nature, e.g. evolutionary algorithms, ant colony optimisation and simulated annealing. More recently, a novel computational intelligence technique inspired ... More

Quantum deformations of fundamental groups of oriented 3-manifoldsFeb 27 2002Feb 27 2002We compute two-term skein modules of framed oriented links in oriented 3-manifolds. They contain the self-writhe and total linking number invariants of framed oriented links in a universal way. The relations in a natural presentation of the skein module ... More

Correlators in N=1 SYM(2+1)Apr 30 2001We present a calculation of the correlator <0|T^{++}(r) T^{++}(0) |0> in N=1 SYM theory in 2+1 dimensions. In the calculation, we use supersymmetric discrete light-cone quantization (SDLCQ), which preserves the supersymmetry at every step of the calculation. ... More

On the Role of the Annihilation Channel in Front Form PositroniumMay 12 1997The annihilation channel is implemented into the front form calculations of the positronium spectrum presented in a previous publication. The effective Hamiltonian is calculated analytically. Its eigensolutions are obtained numerically. A complete separation ... More

Hitting probabilities for random convex bodies and lattices of trianglesDec 18 2013In the first part of this paper, we obtain symmetric formulae for the probabilities that a plane convex body hits exactly 1, 2, 3, 4, 5 or 6 triangles of a lattice of congruent triangles in the plane. Furthermore, a very simple formula for the expectation ... More

Random chords and point distances in regular polygonsApr 12 2012Sep 05 2012In this paper we obtain the chord length distribution function for any regular polygon. From this function we conclude the density function and the distribution function of the distance between two uniformly and independently distributed random points ... More

Measures and geometric probabilities for ellipses intersecting circlesDec 06 2016Santal\'o calculated the measures for all positions of a moving line segment in which it lies inside a fixed circle and intersects this circle in one or two points. From these measures he concluded hitting probabilities for a line segment thrown randomly ... More

On Reasoning with AmbiguitiesFeb 21 1995Feb 22 1995The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations and different ... More

Trigonometric R Matrices related to `Dilute' Birman--Wenzl--Murakami AlgebraFeb 16 1994Explicit expressions for three series of $R$ matrices which are related to a ``dilute'' generalisation of the Birman--Wenzl--Murakami are presented. Of those, one series is equivalent to the quantum $R$ matrices of the $D^{(2)}_{n+1}$ generalised Toda ... More

Buffon's problem with a star of needles and a lattice of parallelogramsSep 24 2012A star of n (n greater than or equal to 2) line segments (needles) of equal length with common endpoint and constant angular spacing is randomly placed onto a lattice which is the union of two families of equidistant lines in the plane with angle alpha ... More

The mean width of the oloid and integral geometric applications of itApr 25 2016The oloid is the convex hull of two circles with equal radius in perpendicular planes so that the center of each circle lies on the other circle. We calculate the mean width of the oloid in two ways, first via the integral of mean curvature, and then ... More

Buffon's problem with a pivot needleJan 14 2014Jan 16 2014In this paper, we solve Buffon's needle problem for a needle consisting of two line segments connected in a pivot point.

A spectral sequence for Iwasawa adjointsJul 24 2013We establish a purely algebraic tool for studying the Iwasawa adjoints of some natural Iwasawa modules for $p$-adic Lie group extensions of number fields, by relating them to certain continuous Galois cohomology groups via a spectral sequence.

Exact solution of two classes of prudent polygonsSep 30 2008Jan 26 2010Prudent walks are self-avoiding walks on the square lattice which never step into the direction of an already occupied vertex. We study the closed version of these walks, called prudent polygons, where the last vertex is adjacent to the first one. More ... More

Dilute Algebras and Solvable Lattice ModelsNov 24 1995The definition of a dilute braid-monoid algebra is briefly reviewed. The construction of solvable vertex and interaction-round-a-face models built on representations of the dilute Temperley-Lieb and Birman-Wenzl-Murakami algebras is discussed.

Representations of Two-Colour BWM Algebras and Solvable Lattice ModelsDec 03 1996Many of the known solutions of the Yang-Baxter equation, which are related to solvable lattice models of vertex- and IRF-type, yield representations of the Birman-Wenzl-Murakami algebra. From these, representations of a two-colour generalization of the ... More

What is Stochastic Independence?Jun 03 2002The notion of a tensor product with projections or with inclusions is defined. It is shown that the definition of stochastic independence relies on such a structure and that independence can be defined in an arbitrary category with a tensor product with ... More

Note on a Positronium Model from Flow Equations in Front Form DynamicsAug 13 1998Jan 16 2001In this note we address the problem of solving for the positronium mass spectrum. We use front-form dynamics together with the method of flow equations. For a special choice of the similarity function, the calculations can be simplified by analytically ... More

Frobenius algebras and skein modules of surfaces in 3-manifoldsFeb 27 2008For each Frobenius algebra there is defined a skein module of surfaces embedded in a given 3-manifold and bounding a prescribed curve system in the boundary. The skein relations are local and generate the kernel of a certain natural extension of the corresponding ... More

Empty simplices of polytopes and graded Betti numbersDec 14 2005The conjecture of Kalai, Kleinschmidt, and Lee on the number of empty simplices of a simplicial polytope is established by relating it to the first graded Betti numbers of the polytope. The proof allows us to derive explicit optimal bounds on the number ... More

Killing forms on G2 and Spin7 manifoldsOct 04 2004Killing forms on Riemannian manifolds are differential forms whose covariant derivative is totally skew-symmetric. We show that on a compact manifold with holonomy G2 or Spin7 any Killing form has to be parallel. The main tool is a universal Weitzenboeck ... More

SYM Correlators and the Maldacena ConjectureAug 21 2002We report on progress in evaluating quantum filed theories with supersymmetric discrete light-cone quantization (SDLCQ). We compare the method to lattice gauge theory and point out its relevance for lattice calculations. As an exciting application we ... More

Analytical solution to the Schrodinger equation of a laser-driven correlated two-particle systemJan 31 2002The time-dependent quantum system of two laser-driven electrons in a harmonic oscillator potential is analysed, taking into account the repulsive Coulomb interaction between both particles. The Schrodinger equation of the two-particle system is shown ... More

Improved bounds on the number of ternary square-free wordsMay 29 2001Aug 02 2001Improved upper and lower bounds on the number of square-free ternary words are obtained. The upper bound is based on the enumeration of square-free ternary words up to length 110. The lower bound is derived by constructing generalised Brinkhuis triples. ... More

Testing SDLCQ in 2+1 dimensionsMar 13 2000The SDLCQ regularization is known to explicitly preserve supersymmetry in 1+1 dimensions. To test this property in higher dimensions, we consider supersymmetric Yang-Mills theory on R x S^1 x S^1. In particular, we choose one of the compact directions ... More

Basis Invariants in Non--Abelian Gauge TheoriesJan 23 1997Feb 05 1997A basis of Lorentz and gauge-invariant monomials in non--Abelian gauge theories with matter is described, applicable for the inverse mass expansion of effective actions. An algorithm to convert an arbitrarily given invariant expression into a linear combination ... More

Recent HERA Results and Future ProspectsJun 10 1998A few selected HERA results are presented and the prospects for future measurements with high luminosity are discussed, which will become available after the planned luminosity upgrade of the HERA storage ring planned for 2000.

A remark concerning sinc integralsApr 22 2014We give a simple proof of Hanspeter Schmid's result that $K_n:=2\int_0^\infty\cos t\,\prod_{k=0}^n\mathrm{sinc}\left(\frac{t}{2k+1}\right)\mathrm{d}t=\pi/2$ if $n\in\{0,1,\ldots,55\}$, and $K_n<\pi/2$ if $n\geq 56$. Furthermore, we present two sinc integrals ... More

Classification of Polynomial Mappings Between Commutative GroupsDec 21 2012Jan 28 2014Some polynomials $P$ with rational coefficients give rise to well defined maps between cyclic groups, $\Z_q\longrightarrow\Z_r$, $x+q\Z\longmapsto P(x)+r\Z$. More generally, there are polynomials in several variables with tuples of rational numbers as ... More

The distribution function of the distance between two random points in a right-angled triangleAug 30 2012Sep 17 2012In this paper we obtain the density function and the distribution function of the distance between two uniformly and independently distributed random points in any right-angled triangle. The density function is derived from the chord length distribution ... 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

Towards Quantum Simulating QCDSep 25 2014Quantum link models provide an alternative non-perturbative formulation of Abelian and non-Abelian lattice gauge theories. They are ideally suited for quantum simulation, for example, using ultracold atoms in an optical lattice. This holds the promise ... More

High-resolution spectroscopy and high-density monitoring in X-rays of NovaeSep 10 2012The 21st century X-ray observatories XMM-Newton, Chandra, and Swift gave us completely new insights into the X-ray behaviour of nova outbursts. These new-generation X-ray observatories provide particularly high spectral resolution and high density in ... More

Absolute Continuity under Time Shift for Ornstein-Uhlenbeck type Processes with Delay or AnticipationNov 27 2014The paper is concerned with one-dimensional two-sided Ornstein-Uhlenbeck type processes with delay or anticipation. We prove existence and uniqueness requiring almost sure boundedness on the left half-axis in case of delay and almost sure boundedness ... More

Decomposition driven interface evolution for layers of binary mixtures: {II}. Influence of convective transport on linear stabilitySep 03 2010We study the linear stability with respect to lateral perturbations of free surface films of polymer mixtures on solid substrates. The study focuses on the stability properties of the stratified and homogeneous steady film states studied in Part I [U. ... More

Monomial and toric ideals associated to Ferrers graphsSep 13 2006Each partition $\lambda = (\lambda_1, \lambda_2, ..., \lambda_n)$ determines a so-called Ferrers tableau or, equivalently, a Ferrers bipartite graph. Its edge ideal, dubbed Ferrers ideal, is a squarefree monomial ideal that is generated by quadrics. We ... More

Numerical MacaulificationFeb 10 2012An unpublished example due to Joe Harris from 1983 (or earlier) gave two smooth space curves with the same Hilbert function, but one of the curves was arithmetically Cohen-Macaulay (ACM) and the other was not. Starting with an arbitrary homogeneous ideal ... More

Weighted uniform consistency of kernel density estimators with general bandwidth sequencesJul 09 2006Sep 29 2006We are interested in the rate of consistency of kernel density estimators with respect to the weighted sup-norm determined by some unbounded weight function. This problem has been considered by Gine, Koltchinskii and Zinn (2004) for a deterministic bandwidth ... More

Mosco Type Convergence of Bilinear Forms and Weak Convergence of $n$-Particle SystemsSep 21 2012Feb 09 2015It is well known that Mosco (type) convergence is a tool in order to verify weak convergence of finite dimensional distributions of sequences of stochastic processes. In the present paper we are concerned with the concept of Mosco type convergence for ... More

Generalized Killing spinors on spheresOct 01 2013We study generalized Killing spinors on round spheres $\mathbb{S}^n$. We show that on the standard sphere $\mathbb{S}^8$ any generalized Killing spinor has to be an ordinary Killing spinor. Moreover we classify generalized Killing spinors on $\mathbb{S}^n$ ... More

Some comments on pinwheel tilings and their diffractionFeb 08 2011The pinwheel tiling is the paradigm for a substitution tiling with circular symmetry, in the sense that the corresponding autocorrelation is circularly symmetric. As a consequence, its diffraction measure is also circularly symmetric, so the pinwheel ... More

DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCLFeb 27 2017May 30 2017We present the latest major release version 6.0 of the quantified Boolean formula (QBF) solver DepQBF, which is based on QCDCL. QCDCL is an extension of the conflict-driven clause learning (CDCL) paradigm implemented in state of the art propositional ... More

An Optical Clock with Ultracold Neutral AtomsMay 16 2002Nov 20 2002We demonstrate how to realize an optical clock with neutral atoms that is competitive to the currently best single ion optical clocks in accuracy and superior in stability. Using ultracold atoms in a Ca optical frequency standard we show how to reduce ... More

Optical frequency transfer via 146 km fiber link with 10^{-19} relative accuracyApr 17 2009We demonstrate the long-distance transmission of an ultra-stable optical frequency derived directly from a state-of-the-art optical frequency standard. Using an active stabilization system we deliver the frequency via a 146 km long underground fiber link ... More

Localized Flux Lines and the Bose GlassJul 16 1996Columnar defects provide effective pinning centers for magnetic flux lines in high--$T_{\rm c}$ superconductors. Utilizing a mapping of the statistical mechanics of directed lines to the quantum mechanics of two--dimensional bosons, one expects an entangled ... More

Interaction dependence of composite fermion effective massesDec 02 1996We estimate the composite fermion effective mass for a general two particle potential r^{-\alpha} using exact diagonalization for polarized electrons in the lowest Landau level on a sphere. Our data for the ground state energy at filling fraction \nu=1/2 ... More

libtissue - implementing innate immunityMar 01 2010Mar 09 2010In a previous paper the authors argued the case for incorporating ideas from innate immunity into articficial immune systems (AISs) and presented an outline for a conceptual framework for such systems. A number of key general properties observed in the ... More

Clifford structures on Riemannian manifoldsDec 21 2009Oct 19 2011We introduce the notion of even Clifford structures on Riemannian manifolds, a framework generalizing almost Hermitian and quaternion-Hermitian geometries. We give the complete classification of manifolds carrying parallel even Clifford structures: K\"ahler, ... More

The singular continuous diffraction measure of the Thue-Morse chainSep 03 2008Sep 29 2008The paradigm for singular continuous spectra in symbolic dynamics and in mathematical diffraction is provided by the Thue-Morse chain, in its realisation as a binary sequence with values in $\{\pm 1\}$. We revisit this example and derive a functional ... More

Vanshing Theorems for Quaternionic Kaehler ManifoldsJan 11 2000We discuss a peculiar interplay between the representation theory of the holonomy group of a Riemannian manifold, the Weitzenboeck formula for the Hodge-Laplace operator on forms and the Lichnerowicz formula for twisted Dirac operators. For quaternionic ... More

ISGDR- bulk or surface mode ?Jul 05 1999A polarization and response function for finite systems and temperatures is derived from linearizing the Vlasov equation. Besides the Lindhard response function in local density approximation we obtain an additional contribution due to the surface. This ... More

Simulation Optimization of the Crossdock Door Assignment ProblemMar 11 2008The purpose of this report is to present the Crossdock Door Assignment Problem, which involves assigning destinations to outbound dock doors of Crossdock centres such that travel distance by material handling equipment is minimized. We propose a two fold ... More

Exploiting problem structure in a genetic algorithm approach to a nurse rostering problemFeb 14 2008May 16 2008There is considerable interest in the use of genetic algorithms to solve problems arising in the areas of scheduling and timetabling. However, the classical genetic algorithm paradigm is not well equipped to handle the conflict between objectives and ... More

Strategic Alert Throttling for Intrusion Detection SystemsJan 28 2008May 16 2008Network intrusion detection systems are themselves becoming targets of attackers. Alert flood attacks may be used to conceal malicious activity by hiding it among a deluge of false alerts sent by the attacker. Although these types of attacks are very ... More

Partnering Strategies for Fitness Evaluation in a Pyramidal Evolutionary AlgorithmJan 23 2008Mar 03 2008This paper combines the idea of a hierarchical distributed genetic algorithm with different inter-agent partnering strategies. Cascading clusters of sub-populations are built from bottom up, with higher-level sub-populations optimising larger parts of ... More

The Weitzenböck MachineFeb 01 2007In this article we give a unified treatment of the construction of all possible Weitzenb\"ock formulas for all irreducible, non--symmetric holonomy groups. The resulting classification is two--fold, we construct explicitly a basis of the space of Weitzenb\"ock ... More

Homometric model sets and window covariogramsOct 12 2006Two Delone sets are called homometric when they share the same autocorrelation or Patterson measure. A model set LAMBDA within a given cut and project scheme is a Delone set that is defined through a window W in internal space. The autocorrelation measure ... More

Phenomenology of brane-world cosmological modelsOct 27 2004Nov 16 2004We present a brief review of brane-world models - models in which our observable Universe with its standard matter fields is assumed as localized on a domain wall (three-brane) in a higher dimensional surrounding (bulk) spacetime. Models of this type ... More

Moderate deviation probabilities for open convex sets: nonlogarithmic behaviorOct 06 2004Precise asymptotics for moderate deviation probabilities are established for open convex sets in both the finite- and infinite-dimensional settings. Our results are based on the existence of dominating points for these sets, a related representation formula, ... More

Maximal length of trapped one-dimensional Bose-Einstein condensatesSep 08 2004I discuss a Bogoliubov inequality for obtaining a rigorous bound on the maximal axial extension of inhomogeneous one-dimensional Bose-Einstein condensates. An explicit upper limit for the aspect ratio of a strongly elongated, harmonically trapped Thomas-Fermi ... More

The modified XXZ Heisenberg chain, conformal invariance, surface exponents of c<1 systems, and hidden symmetries of the finite chainsNov 10 2003The spin-1/2 XXZ Heisenberg chain with two types of boundary terms is considered. For the first type, the Hamiltonian is hermitian but not for the second type which includes the U_{q}[SU(2)] symmetric case. It is shown that for a certain `tuning' between ... More

A maximum principle for the mutation-selection equilibrium of nucleotide sequencesMar 12 2003Aug 27 2003We study the equilibrium behaviour of a deterministic four-state mutation-selection model as a model for the evolution of a population of nucleotide sequences in sequence space. The mutation model is the Kimura 3ST mutation scheme, and the selection scheme ... More

Motion of Quantized Vortices as Elementary ObjectsJul 29 1999Jan 10 2000The general local, nondissipative equations of motion for a quantized vortex moving in an uncharged laboratory superfluid are derived from a relativistic, co-ordinate invariant framework, having vortices as its elementary objects in the form of stable ... More

Parallel spinors and holonomy groupsMar 11 1999In this paper we complete the classification of spin manifolds admitting parallel spinors, in terms of the Riemannian holonomy groups. More precisely, we show that on a given n-dimensional Riemannian manifold, spin structures with parallel spinors are ... More

The Complete Solution of the Classical SL(2,R)/U(1) Gauged WZNW Field TheoryMay 29 1998We prove that any gauged WZNW model has a Lax pair representation, and give explicitly the general solution of the classical equations of motion of the SL(2,R)/U(1) theory. We calculate the symplectic structure of this solution by solving a differential ... More

Kauffman state sums and bracket deformationAug 22 2006Aug 06 2007We derive a formula expanding the bracket with respect to a natural deformation parameter. The expansion is in terms of a two-variable polynomial algebra of diagram resolutions generated by basic operations involving the Goldman bracket. A functorial ... More

Feature selection in detection of adverse drug reactions from the Health Improvement Network (THIN) databaseSep 02 2014Adverse drug reaction (ADR) is widely concerned for public health issue. ADRs are one of most common causes to withdraw some drugs from market. Prescription event monitoring (PEM) is an important approach to detect the adverse drug reactions. The main ... More

The correlation measures of finite sequences: limiting distributions and minimum valuesApr 01 2014Feb 03 2015Three measures of pseudorandomness of finite binary sequences were introduced by Mauduit and S\'ark\"ozy in 1997 and have been studied extensively since then: the normality measure, the well-distribution measure, and the correlation measure of order r. ... More

The peak sidelobe level of random binary sequencesMay 26 2011Mar 17 2014Let $A_n=(a_0,a_1,\dots,a_{n-1})$ be drawn uniformly at random from $\{-1,+1\}^n$ and define \[ M(A_n)=\max_{0<u<n}\,\Bigg|\sum_{j=0}^{n-u-1}a_ja_{j+u}\Bigg|\quad\text{for $n>1$}. \] It is proved that $M(A_n)/\sqrt{n\log n}$ converges in probability to ... More

Betti numbers of monomial ideals and shifted skew shapesDec 15 2007We present two new problems on lower bounds for resolution Betti numbers of monomial ideals generated in a fixed degree. The first concerns any such ideal and bounds the total Betti numbers, while the second concerns ideals that are quadratic and bihomogeneous ... More

Criteria for componentwise linearityAug 19 2011Oct 11 2011We establish characteristic-free criteria for the componentwise linearity of graded ideals. As applications, we classify the componentwise linear ideals among the Gorenstein ideals, the standard determinantal ideals, and the ideals generated by the submaximal ... More