Results for "Christian Grünzweig"

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Laue three dimensional neutron diffractionFeb 08 2019This article presents a measurement technique and data analysis tool to perform 3D grain distribution mapping and indexing of oligocrystalline samples using neutrons: Laue three-dimensional neutron diffraction (Laue3DND). The approach builds on forward ... More
Dendritic flux avalanches in Niobium single crystal near critical temperatureAug 12 2013We report on the observation of dendritic flux avalanches in a large Niobium single crystal. In contrast to avalanches observed in thin films, they appear only in a very narrow temperature interval of about a tenth of a Kelvin near the critical temperature ... More
Decay of Quantum Correlations in Atom Optics Billiards with Chaotic and Mixed DynamicsApr 21 2004We perform echo spectroscopy on ultra cold atoms in atom optics billiards, to study their quantum dynamics. The detuning of the trapping laser is used to change the ``perturbation'', which causes a decay in the echo coherence. Two different regimes are ... More
Thermal Quantum Fields without Cut-offs in 1+1 Space-time DimensionsMar 26 2004We construct interacting quantum fields in 1+1 dimensional Minkowski space, representing neutral scalar bosons at positive temperature. Our work is based on prior work by Klein and Landau and Hoegh-Krohn
Counting atoms in a deep optical microtrapNov 25 2010Jan 17 2011We demonstrate a method to count small numbers of atoms held in a deep, microscopic optical dipole trap by collecting fluorescence from atoms exposed to a standing wave of light that is blue detuned from resonance. While scattering photons, the atoms ... More
Hyperfine Spectroscopy of Optically Trapped AtomsSep 28 2004We perform spectroscopy on the hyperfine splitting of $^{85}$Rb atoms trapped in far-off-resonance optical traps. The existence of a spatially dependent shift in the energy levels is shown to induce an inherent dephasing effect, which causes a broadening ... More
On spatial and temporal multilevel dynamics and scaling effects in epileptic seizuresMar 30 2011Jul 29 2011Epileptic seizures are one of the most well-known dysfunctions of the nervous system. During a seizure, a highly synchronized behavior of neural activity is observed that can cause symptoms ranging from mild sensual malfunctions to the complete loss of ... More
Duck Traps: Two-dimensional Critical Manifolds in Planar SystemsAug 30 2018Nov 05 2018In this work we consider two-dimensional critical manifolds in planar fast-slow systems near fold and so-called canard (=`duck') points. These higher-dimension, and lower-codimension, situation is directly motivated by the case of hysteresis operators ... More
On the relativistic KMS condition for the P(φ)_2 modelSep 29 2006The relativistic KMS condition introduced by Bros and Buchholz provides a link between quantum statistical mechanics and quantum field theory. We show that for the $P(\phi)_2$ model at positive temperature, the two point function for fields satisfies ... More
Friction force: from mechanics to thermodynamicsNov 17 2009Jul 01 2010We study some mechanical problems in which a friction force is acting on the system. Using the fundamental concepts of state, time evolution and energy conservation we explain how to extend Newtonian mechanics to thermodynamics. We arrive at the two laws ... More
Thermal Quantum Fields with Spatially Cut-off Interactions in 1+1 Space-time DimensionsJul 25 2003We construct interacting quantum fields in 1+1 space-time dimensions, representing charged or neutral scalar bosons at positive temperature and zero chemical potential. Our work is based on prior work by Klein and Landau and Hoegh-Krohn. Generalized path ... More
Spectral properties and chiral symmetry violations of (staggered) domain wall fermions in the Schwinger modelFeb 26 2016Jul 05 2016We follow up on a suggestion by Adams and construct explicit domain wall fermion operators with staggered kernels. We compare different domain wall formulations, namely the standard construction as well as Borici's modified and Chiu's optimal construction, ... More
Echo spectroscopy and Atom Optics BilliardsDec 02 2002Dec 03 2002We discuss a recently demonstrated type of microwave spectroscopy of trapped ultra-cold atoms known as "echo spectroscopy" [M.F. Andersen et. al., Phys. Rev. Lett., in press (2002)]. Echo spectroscopy can serve as an extremely sensitive experimental tool ... More
Relaxed Logarithmic Barrier Function Based Model Predictive Control of Linear SystemsMar 11 2015In this paper, we investigate the use of relaxed logarithmic barrier functions in the context of linear model predictive control. We present results that allow to guarantee asymptotic stability of the corresponding closed-loop system, and discuss further ... More
A stabilizing iteration scheme for model predictive control based on relaxed barrier functionsMar 15 2016Apr 06 2016We propose and analyze a stabilizing iteration scheme for the algorithmic implementation of model predictive control for linear discrete-time systems. Polytopic input and state constraints are considered and handled by means of so-called relaxed logarithmic ... More
Revivals of Coherence in Chaotic Atom-Optics BilliardsDec 31 2003We investigate the coherence properties of thermal atoms confined in optical dipole traps where the underlying classical dynamics is chaotic. A perturbative expression derived for the coherence of the echo scheme of [Andersen et. al., Phys. Rev. Lett. ... More
Suppression of Dephasing of Optically Trapped AtomsJul 29 2003Ultra-cold atoms trapped in an optical dipole trap and prepared in a coherent superposition of their hyperfine ground states, decohere as they interact with their environment. We demonstrate than the loss in coherence in an "echo" experiment, which is ... More
Single beam atom sorting machineAug 10 2011We create two overlapping one-dimensional optical lattices using a single laser beam, a spatial light modulator and a high numerical aperture lens. These lattices have the potential to trap single atoms, and using the dynamic capabilities of the spatial ... More
Differential Characters and Geometric ChainsMar 26 2013Apr 09 2013We study Cheeger-Simons differential characters and provide geometric descriptions of the ring structure and of the fiber integration map. The uniqueness of differential cohomology (up to unique natural transformation) is proved by deriving an explicit ... More
Staggered domain wall fermionsSep 16 2016We construct domain wall fermions with a staggered kernel and investigate their spectral and chiral properties numerically in the Schwinger model. In some relevant cases we see an improvement of chirality by more than an order of magnitude as compared ... More
Distances and large deviations in the spatial preferential attachment modelSep 26 2018Sep 27 2018We investigate two asymptotic properties of a spatial preferential-attachment model introduced by E. Jacob and P. M\"orters (2013). First, in a regime of strong linear reinforcement, we show that typical distances are at most of doubly-logarithmic order. ... More
On the Vacuum Polarization Density Caused by an External FieldJul 01 2003Feb 11 2004We consider an external potential, $-\lambda \phi$, due to one or more nuclei. Following the Dirac picture such a potential polarizes the vacuum. The polarization density as derived in physics literature, after a well known renormalization procedure, ... More
Quantum field theory meets Hopf algebraNov 14 2006Sep 11 2010This paper provides a primer in quantum field theory (QFT) based on Hopf algebra and describes new Hopf algebraic constructions inspired by QFT concepts. The following QFT concepts are introduced: chronological products, S-matrix, Feynman diagrams, connected ... More
A differential identity for Green functionsFeb 15 2006If P is a differential operator with constant coefficients, an identity is derived to calculate the action of exp(P) on the product of two functions. In many-body theory, P describes the interaction Hamiltonian and the identity yields a hierarchy of Green ... More
Quantum groups and interacting quantum fieldsAug 19 2002If C is a cocommutative coalgebra, a bialgebra structure can be given to the symmetric algebra S(C). The symmetric product is twisted by a Laplace pairing and the twisted product of any number of elements of S(C) is calculated explicitly. This is used ... More
Continuous-Variable Quantum Key Distribution with Entanglement in the MiddleMay 07 2012We analyze the performance of continuous-variable quantum key distribution protocols where the entangled source originates not from one of the trusted parties, Alice or Bob, but from the malicious eavesdropper in the middle. This is in contrast to the ... More
Tight Running Time Lower Bounds for Vertex Deletion ProblemsNov 17 2015May 17 2016For a graph class $\Pi$, the $\Pi$-Vertex Deletion problem has as input an undirected graph $G=(V,E)$ and an integer $k$ and asks whether there is a set of at most $k$ vertices that can be deleted from $G$ such that the resulting graph is a member of ... More
A quantum-information-theoretic complement to a general-relativistic implementation of a beyond-Turing computerMay 21 2014Jun 11 2014There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable (even in principle) can exceed ... More
Vacuum Polarisation Tensors in Constant Electromagnetic Fields: Part IJan 27 2000Dec 29 2000The string-inspired technique is used for the calculation of vacuum polarisation tensors in constant electromagnetic fields. In the first part of this series, we give a detailed exposition of the method for the case of the QED one-loop N-photon amplitude ... More
Modules Whose Small Submodules Have Krull DimensionJul 21 1998The main aim of this paper is to show that an AB5*-module whose small submodules have Krull dimension has a radical having Krull dimension. The proof uses the notion of dual Goldie dimension.
Blue Stragglers in Globular Clusters: Observations, Statistics and PhysicsJun 13 2014This chapter explores how we might use the observed {\em statistics} of blue stragglers in globular clusters to shed light on their formation. This means we will touch on topics also discussed elsewhere in this book, such as the discovery and implications ... More
Dualité onde-corpuscule formée par une masselotte oscillante dans un milieu élastique : étude théorique et similitudes quantiquesSep 29 2016We introduce a dual wave-particle macroscopic system, where a bead oscillator oscillates in an elastic media which obeys the Klein-Gordon equation. This theoretical system comes mainly from bouncing drops experiments and also a sliding bead on a vibrating ... More
Local duality and mixed Hodge modulesApr 22 2009We establish a relationship between the graded quotients of a filtered holonomic D-module, their sheaf-theoretic duals, and the characteristic variety, in case the filtered D-module underlies a polarized Hodge module on a smooth algebraic variety. The ... More
Nuclearity and split for thermal quantum field theoriesNov 26 1998Jan 05 2000We review the heuristic arguments suggesting that any thermal quantum field theory, which can be interpreted as a quantum statistical mechanics of (interacting) relativistic particles, obeys certain restrictions on its number of local degrees of freedom. ... More
On nodal sets for Dirac and Laplace operatorsJul 10 1997We prove that the nodal set (zero set) of a solution of a generalized Dirac equation on a Riemannian manifold has codimension 2 at least. If the underlying manifold is a surface, then the nodal set is discrete. We obtain a quick proof of the fact that ... More
On the geometry of metric measure spaces with variable curvature boundsJun 10 2015Sep 09 2015Motivated by a classical comparison result of J. C. F. Sturm we introduce a curvature-dimension condition CD(k,N) for general metric measure spaces and variable lower curvature bound k. In the case of non-zero constant lower curvature our approach coincides ... More
Immersions of surfaces in almost complex 4-manifoldsAug 31 2000In this note, we investigate the relation between double points and complex points of immersed surfaces in almost-complex 4-manifolds and show how estimates for the minimal genus of embedded surfaces lead to inequalities between the number of double points ... More
Auxiliary matrices for the six-vertex model at roots of 1 and a geometric interpretation of its symmetriesFeb 03 2003Apr 24 2003The construction of auxiliary matrices for the six-vertex model at a root of unity is investigated from a quantum group theoretic point of view. Employing the concept of intertwiners associated with the quantum loop algebra $U_q(\tilde{sl}_2)$ at $q^N=1$ ... More
Colours associated to non simply-laced Lie algebras and exact S-matricesOct 31 2000Jan 02 2001A new set of exact scattering matrices in 1+1 dimensions is proposed by solving the bootstrap equations. Extending earlier constructions of colour valued scattering matrices this new set has its colour structure associated to non simply-laced Lie algebras. ... More
PT Symmetry of the non-Hermitian XX Spin-Chain: Non-local Bulk Interaction from Complex Boundary FieldsMar 31 2008The XX spin-chain with non-Hermitian diagonal boundary conditions is shown to be quasi-Hermitian for special values of the boundary parameters. This is proved by explicit construction of a new inner product employing a "quasi-fermion" algebra in momentum ... More
Turning the Quantum Group Invariant XXZ Spin-Chain Hermitian: A Conjecture on the Invariant ProductSep 24 2007This is a continuation of a previous joint work with Robert Weston on the quantum group invariant XXZ spin-chain (math-ph/0703085). The previous results on quasi-Hermiticity of this integrable model are briefly reviewed and then connected with a new construction ... More
Solving Baxter's TQ-equation via representation theoryNov 09 2004Nov 23 2004Baxter's TQ-equation is solved for the six-vertex model using the representation theory of quantum groups at roots of unity. A novel simplified construction of the Q-operator is given depending on a new free parameter. Specializing this general construction ... More
On the logarithm of the characteristic polynomial of the Ginibre ensembleJul 30 2015We prove a slightly sharper version of a result of Rider and Vir\'ag who proved that after centering, the logarithm of the absolute value of the characteristic polynomial of the Ginibre ensemble converges in law to the Gaussian Free Field on the unit ... More
Maximum Matching in Turnstile StreamsMay 06 2015We consider the unweighted bipartite maximum matching problem in the one-pass turnstile streaming model where the input stream consists of edge insertions and deletions. In the insertion-only model, a one-pass $2$-approximation streaming algorithm can ... More
Hamiltonians with Riesz Bases of Generalised Eigenvectors and Riccati EquationsMay 28 2010An algebraic Riccati equation for linear operators is studied, which arises in systems theory. For the case that all involved operators are unbounded, the existence of infinitely many selfadjoint solutions is shown. To this end, invariant graph subspaces ... More
Spin squeezing, entanglement and quantum metrology with Bose-Einstein condensatesMar 23 2012Squeezed states, a special kind of entangled states, are known as a useful resource for quantum metrology. In interferometric sensors they allow to overcome the "classical" projection noise limit stemming from the independent nature of the individual ... More
Cosmology and gravitational waves in the Nordstrom-Vlasov system, a laboratory for Dark EnergyJan 24 2013We discuss a cosmological solution of the system which was originally introduced by Calogero and is today popularly known as "Nordstrom-Vlasov system". Although the model is un-physical, its cosmological solution results interesting for the same reasons ... More
Effective temperature for black holesJul 26 2011Jul 28 2011The physical interpretation of black hole's quasinormal modes is fundamental for realizing unitary quantum gravity theory as black holes are considered theoretical laboratories for testing models of such an ultimate theory and their quasinormal modes ... More
A precise response function for the magnetic component of Gravitational Waves in Scalar-Tensor GravityFeb 03 2011Feb 04 2011The important issue of the magnetic component of gravitational waves (GWs) has been considered in various papers in the literature. From such analyses, it resulted that such a magnetic component becomes particularly important in the high frequency portion ... More
Information on the inflaton field from the spectrum of relic gravitational wavesSep 23 2009Nov 18 2009After a review of a traditional analysis, it is shown a variation of a more recent treatment on the spectrum of relic gravitational waves (GWs). Then, a connection between the two different treatments will be analysed. Such a connection permits to obtain ... More
A longitudinal component in massive gravitational waves arising from a bimetric theory of gravityNov 06 2008After a brief review of the work of de Paula, Miranda and Marinho on massive gravitational waves arising from a bimetric theory of gravity, in this paper it is shown that the presence of the mass generates a longi- tudinal component in a particular polarization ... More
Analysis of the transverse effect of Einstein's gravitational wavesJul 13 2007The investigation of the transverse effect of gravitational waves (GWs) could constitute a further tool to discriminate among several relativistic theories of gravity on the ground. After a review of the TT gauge, the transverse effect of GWs arising ... More
Interpretation of Mössbauer experiment in a rotating system: a new proof for general relativityFeb 14 2015A historical experiment by K\"undig on the transverse Doppler shift in a rotating system measured with the M\"ossbauer effect has been recently first re-analyzed and then replied [1,2]. The results have shown that a correct re-processing of K\"undig's ... More
Black hole quantum spectrumOct 26 2012Nov 19 2013Introducing a black hole (BH) effective temperature, which takes into account both the non-strictly thermal character of Hawking radiation and the countable behavior of emissions of subsequent Hawking quanta, we recently re-analysed BH quasi-normal modes ... More
Massive relic gravitational waves from f(R) theories of gravity: production and potential detectionJul 23 2010The production of a stochastic background of relic gravitational waves is well known in various works in the literature, where, by using the so called adiabatically-amplified zero-point fluctuations process, it has been shown how the standard inflationary ... More
A review of the stochastic background of gravitational waves in f(R) gravity with WMAP constrainsJan 09 2009Jan 15 2009This paper is a review of previous works on the stochastic background of gravitational waves (SBGWs) which has been discussed in various peer-reviewed journals and international conferences. The SBGWs is analyzed with the aid of the Wilkinson Microwave ... More
A non-geodesic motion in the R^-1 theory of gravity tuned with observationsJan 01 2008Jan 11 2008In the general picture of high order theories of gravity, recently, the R^-1 theory has been analyzed in two different frameworks. In this letter a third context is added, considering an explicit coupling between the R^-1 function of the Ricci scalar ... More
The production of matter from curvature in a particular linearized high order theory of gravity and the longitudinal response function of interferometersMar 26 2007The strict analogy between scalar-tensor theories of gravity and high order gravity is well known in literature. In this paper it is shown that, from a particular high order gravity theory known in literature, it is possible to produce, in the linearized ... More
Beta Beams Implementation at CERNSep 09 2011Beta Beam,the concept of generating a pure and intense (anti) neutrino beam by letting accelerated radioactive ions beta decay in a storage ring, called Decay Ring (DR), is the base of one of the proposed next generation neutrino oscillation facilities, ... More
Recursive Numerical Evaluation of the Cumulative Bivariate Normal DistributionApr 21 2010We propose an algorithm for evaluation of the cumulative bivariate normal distribution, building upon Marsaglia's ideas for evaluation of the cumulative univariate normal distribution. The algorithm is mathematically transparent, delivers competitive ... More
Random matrices and Riemann hypothesisSep 22 2011The curious connection between the spacings of the eigenvalues of random matrices and the corresponding spacings of the non trivial zeros of the Riemann zeta function is analyzed on the basis of the geometric dynamical global program of Langlands whose ... More
When is the underlying space of an orbifold a manifold with boundary?Sep 22 2015We answer the question of when the underlying space of an orbifold is a manifold with boundary in several categories.
A survey of the Schrödinger problem and some of its connections with optimal transportAug 01 2013This article is aimed at presenting the Schr\"odinger problem and some of its connections with optimal transport. We hope that it can be used as a basic user's guide to Schr\"odinger problem. We also give a survey of the related literature. In addition, ... More
Entropic Projections and Dominating PointsNov 01 2007Sep 07 2010Generalized entropic projections and dominating points are solutions to convex minimization problems related to conditional laws of large numbers. They appear in many areas of applied mathematics such as statistical physics, information theory, mathematical ... More
Convex minimization problems with weak constraint qualificationsOct 08 2007One revisits the standard saddle-point method based on conjugate duality for solving convex minimization problems. Our aim is to reduce or remove unnecessary topological restrictions on the constraint set. Dual equalities and characterizations of the ... More
Some properties of path measuresAug 01 2013We call any measure on a path space, a path measure. Some notions about path measures which appear naturally when solving the Schr\"odinger problem are presented and worked out in detail.
Characterization of the optimal plans for the Monge-Kantorovich transport problemJul 24 2006We present a general method, based on conjugate duality, for solving a convex minimization problem without assuming unnecessary topological restrictions on the constraint set. It leads to dual equalities and characterizations of the minimizers without ... More
Factorial growth rates for the number of hyperbolic 3-manifolds of a given volumeSep 05 2012Nov 05 2013The work of J{\o}rgensen and Thurston shows that there is a finite number N(v) of orientable hyperbolic 3-manifolds with any given volume v. In this paper, we construct examples showing that the number of hyperbolic knot complements with a given volume ... More
q,t-Fuss-Catalan numbers for complex reflection groupsJun 18 2008In type A, the q,t-Fuss -Catalan numbers can be defined as a bigraded Hilbert series of a module associated to the symmetric group S_n. We generalize this construction to (finite) complex reflection groups and exhibit some nice conjectured algebraic and ... More
Efficient Gluing of Numerical Continuation and a Multiple Solution Method for Elliptic PDEsJun 26 2014Oct 18 2014Numerical continuation calculations for ordinary differential equations (ODEs) are, by now, an established tool for bifurcation analysis in dynamical systems theory as well as across almost all natural and engineering sciences. Although several excellent ... More
Time-Scale and Noise Optimality in Self-Organized Critical Adaptive NetworksOct 25 2011Dec 23 2011Recent studies have shown that adaptive networks driven by simple local rules can organize into "critical" global steady states, providing another framework for self-organized criticality (SOC). We focus on the important convergence to criticality and ... More
A Remark on Geometric Desingularization of a Non-Hyperbolic Point using Hyperbolic SpaceMar 15 2014A steady state (or equilibrium point) of a dynamical system is hyperbolic if the Jacobian at the steady state has no eigenvalues with zero real parts. In this case, the linearized system does qualitatively capture the dynamics in a small neighborhood ... More
On highly regular strongly regular graphsApr 30 2014Oct 19 2016In this paper we unify many existing regularity conditions for graphs, including strong regularity, $k$-isoregularity, and the $t$-vertex condition. We develop an algebraic composition/decomposition theory of regularity conditions. Using our theoretical ... More
Exponentials form a basis of discrete holomorphic functionsOct 08 2002We show that discrete exponentials form a basis of discrete holomorphic functions. On a convex, the discrete polynomials form a basis as well.
On the signatures of even 4-manifoldsFeb 18 2000Nov 13 2000In this paper, we prove a number of inequalities between the signature and the Betti numbers of a 4-manifold with even intersection form. Furthermore, we introduce a new geometric group invariant and discuss some of its properties.
The rationality of the moduli space of curves of genus 3 after P. KatsyloApr 09 2008This article is a survey of P. Katsylo's proof that the moduli space of smooth projective complex curves of genus 3 is rational. We hope to make the argument more comprehensible and transparent by emphasizing the underlying geometry in the proof and its ... More
New bounds for the prime counting function π(x)Sep 05 2014Jan 12 2016In this paper we establish a number of new estimates concerning the prime counting function \pi(x), which improve the estimates proved in the literature. As an application, we deduce a new result concerning the existence of prime numbers in small intervals. ... More
Scattering theory for Klein-Gordon equations with non-positive energyJan 11 2011Sep 09 2011We study the scattering theory for charged Klein-Gordon equations: \[\{{array}{l} (\p_{t}- \i v(x))^{2}\phi(t,x) \epsilon^{2}(x, D_{x})\phi(t,x)=0,[2mm] \phi(0, x)= f_{0}, [2mm] \i^{-1} \p_{t}\phi(0, x)= f_{1}, {array}. \] where: \[\epsilon^{2}(x, D_{x})= ... More
Spectral and scattering theory of charged $P(\varphi)_2$ modelsJun 30 2009We consider in this paper space-cutoff charged $P(\varphi)_{2}$ models arising from the quantization of the non-linear charged Klein-Gordon equation: \[ (\p_{t}+\i V(x))^{2}\phi(t, x)+ (-\Delta_{x}+ m^{2})\phi(t,x)+ g(x)\p_{\overline{z}}P(\phi(t,x), \overline{\phi}(t,x))=0, ... More
Strangeness at high temperaturesOct 11 2013We use up to fourth order cumulants of net strangeness fluctuations and their correlations with net baryon number fluctuations to extract information on the strange meson and baryon contribution to the low temperature hadron resonance gas, the dissolution ... More
Conserved charge fluctuations with HISQ fermionsJan 28 2013We calculate cumulants of fluctuations of net-baryon number, net-electric charge and net-strangeness, in the framework of lattice regularized QCD. We use a highly improved staggered quark (HISQ) action on lattices with temporal extent of N_tau=6,8 and ... More
QCD bulk thermodynamics and conserved charge fluctuations with HISQ fermionsDec 18 2012After briefly reviewing recent progress by the HotQCD collaboration in studying the 2+1 flavor QCD equation of state, we will focus on results on fluctuations of conserved charges by the BNL-Bielefeld and HotQCD collaborations. Higher order cumulants ... More
On the base locus of the linear system of generalized theta functionsJul 23 2007Apr 14 2008Let $\cM_r$ denote the moduli space of semi-stable rank-$r$ vector bundles with trivial determinant over a smooth projective curve $C$ of genus $g$. In this paper we study the base locus $\cB_r \subset \cM_r$ of the linear system of the determinant line ... More
On the Structure of Physical Measures in Gauge TheoriesJul 23 2001It is indicated that the definition of physical measures via ``exponential of minus the action times kinematical measure'' contradicts properties of certain physical models. In particular, theories describing confinement typically cannot be gained this ... More
k-Means Clustering Is Matrix FactorizationDec 23 2015We show that the objective function of conventional k-means clustering can be expressed as the Frobenius norm of the difference of a data matrix and a low rank approximation of that data matrix. In short, we show that k-means clustering is a matrix factorization ... More
Getting Started with Isabelle/jEditAug 07 2012Jan 31 2013We give a beginner-oriented introduction to Isabelle/jEdit, providing motivation for using it as well as pointing at some differences to the traditional Proof General interface and current limitations.
The Canonical Map and Horikawa Surfaces in Positive CharacteristicApr 10 2010Dec 20 2011We extend fundamental inequalities related to the canonical map of surfaces of general type to positive characteristic. Next, we classify surfaces on the Noether lines, i.e., even and odd Horikawa surfaces, in positive characteristic. We describe their ... More
Uniruled Surfaces of General TypeAug 24 2006Nov 06 2006We give a systematic construction of uniruled surfaces in positive characteristic. Using this construction, we find surfaces of general type with non-trivial vector fields, surfaces with arbitrarily non-reduced Picard schemes as well as surfaces with ... More
Non-classical Godeaux SurfacesApr 21 2008Aug 25 2008A non-classical Godeaux surface is a minimal surface of general type with $\chi=K^2=1$ but with $h^{01}\neq0$. We prove that such surfaces fulfill $h^{01}=1$ and they can exist only over fields of positive characteristic at most 5. Like non-classical ... More
Algebraic Surfaces of General Type with Small c_1^2 in Positive CharacteristicFeb 19 2007Oct 26 2007We establish Noether's inequality for surfaces of general type in positive characteristic.Then we extend Enriques' and Horikawa's classification of surfaces on the Noether line, the so-called Horikawa surfaces. We construct examples for all possible numerical ... More
A Combinatorial Derivation of the Racah-Speiser Algorithm for Gromov-Witten invariantsOct 18 2009Using a finite-dimensional Clifford algebra a new combinatorial product formula for the small quantum cohomology ring of the complex Grassmannian is presented. In particular, Gromov-Witten invariants can be expressed through certain elements in the Clifford ... More
Units of ring spectra and their traces in algebraic K-theoryMay 05 2004Let GL_1(R) be the units of a commutative ring spectrum R. In this paper we identify the composition BGL_1(R)->K(R)->THH(R)->\Omega^{\infty}(R), where K(R) is the algebraic K-theory and THH(R) the topological Hochschild homology of R. As a corollary we ... More
The Saxl Conjecture and the Dominance OrderOct 24 2014May 05 2015In 2012 Jan Saxl conjectured that all irreducible representations of the symmetric group occur in the decomposition of the tensor square of the irreducible representation corresponding to the staircase partition. We make progress on this conjecture by ... More
Higher algebraic K-theories related to the global program of LanglandsSep 14 2010The paper revisits concretely the algebraic K-theory in the light of the global program of Langlands by taking into account the new algebraic interpretation of homotopy viewed as deformation(s) of Galois representations given by compactified algebraic ... More
Galilean IsometriesMar 09 2009We introduce three nested Lie algebras of infinitesimal `isometries' of a Galilei space-time structure which play the r\^ole of the algebra of Killing vector fields of a relativistic Lorentz space-time. Non trivial extensions of these Lie algebras arise ... More
Recent progress constraining the nuclear equation of state from astrophysics and heavy ion reactionsJun 01 2007The quest for the nuclear equation of state (EoS) at high densities and/or extreme isospin is one of the longstanding problems of nuclear physics. Ab initio calculations for the nuclear many-body problem make predictions for the density and isospin dependence ... More
More Compact Oracles for Approximate Distances in Planar GraphsSep 12 2011Oct 28 2011Distance oracles are data structures that provide fast (possibly approximate) answers to shortest-path and distance queries in graphs. The tradeoff between the space requirements and the query time of distance oracles is of particular interest and the ... More
Heat and Gravitation. II. StabilityApr 02 2009In this second article of a series we propose to base criteria of stability on the hamiltonian functional that is provided by the variational principle, to replace the reliance that has often been placed on {\it ad hoc} definitions of the "energy". We ... More
Generalization and Exact Deformations of Quantum GroupsJun 25 1996A large family of "standard" coboundary Hopf algebras is investigated. The existence of a universal R-matrix is demonstrated for the case when the parameters are in general position. Algebraic surfaces in parameter space are characterized by the appearance ... More
Universal T-matrix for Twisted Quantum gl(N)May 16 1995The Universal T-matrix is the capstone of the structure that consists of a quantum group and its dual, and the central object from which spring the T-matrices (monodromies) of all the associated integrable models. A closed expression is obtained for the ... More