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The modality of a Borel subgroup in a simple algebraic group of type $E_8$Feb 09 2018Let $G$ be a simple algebraic group over an algebraically closed field $k$, where $\mathrm{char}\, k$ is either 0 or a good prime for $G$. We consider the modality $\mathrm{mod}(B : \mathfrak u)$ of the action of a Borel subgroup $B$ of $G$ on the Lie ... More

On the coadjoint orbits of maximal unipotent subgroups of reductive groupsSep 16 2014Jan 26 2015Let G be a simple algebraic group defined over an algebraically closed field of characteristic 0 or a good prime for G. Let U be a maximal unipotent subgroup of G and \u its Lie algebra. We prove the separability of orbit maps and the connectedness of ... More

Calculating conjugacy classes in Sylow p-subgroups of finite Chevalley groups of rank six and sevenFeb 27 2013Let G(q) be a finite Chevalley group, where q is a power of a good prime p, and let U(q) be a Sylow p-subgroup of G(q). Then a generalized version of a conjecture of Higman asserts that the number k(U(q)) of conjugacy classes in U(q) is given by a polynomial ... More

Aspects of workDec 08 2015Various approaches of defining and determining work performed on a quantum system are compared. Any operational definition of work, however, must allow for two facts, first, that work characterizes a process rather than an instantaneous state of a system, ... More

Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence (2010)May 11 2012Aug 28 2014This is the Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence, which was held on Catalina Island, CA, July 8 - 11 2010.

Phi, Omega and Rho production from deconfined matter in relativistic heavy ion collisions at CERN SPSSep 29 1999We investigate the production of the Phi meson and the Omega baryon which interact weakly with hot hadronic matter, and thus their spectra reflect the early stage of the heavy ion collisions. Our analysis shows that the hadronization temperature, T_had, ... More

Regret and Jeffreys Integrals in Exp. FamiliesMar 31 2009The problem of whether minimax redundancy, minimax regret and Jeffreys integrals are finite or infinite are discussed.

General Solutions for Multispin Two-Time Correlation and Response Functions in the Glauber-Ising ChainJul 09 2003The kinetic Glauber-Ising spin chain is one of the very few exactly solvable models of non-equilibrium statistical mechanics. Nevertheless, existing solutions do not yield tractable expressions for two-time correlation and response functions of observables ... More

Changing gears: Isospectrality via eigenderivative transplantationSep 11 2015We introduce a new method for constructing isospectral quantum graphs that is based on transplanting derivatives of eigenfunctions. We also present simple digraphs with the same reversing zeta function, which generalizes the Bartholdi zeta function to ... More

A spatial model for selection and cooperationMar 02 2016Nov 02 2016We study the evolution of cooperation in an interacting particle system with two types. The model we investigate is an extension of a two-type biased voter model. One type (called defector) has a (positive) bias $\alpha$ with respect to the other type ... More

A spatial model for selection and cooperationMar 02 2016Oct 11 2016We study the evolution of cooperation in an interacting particle system with two types. The model we investigate is an extension of a two-type biased voter model. One type (called defector) has a (positive) bias $\alpha$ with respect to the other type ... More

Structural Intervention Distance (SID) for Evaluating Causal GraphsJun 05 2013Apr 07 2014Causal inference relies on the structure of a graph, often a directed acyclic graph (DAG). Different graphs may result in different causal inference statements and different intervention distributions. To quantify such differences, we propose a (pre-) ... More

Spectral asymptotics of the Laplacian on supercritical bond-percolation graphsJun 21 2005Jul 03 2007We investigate Laplacians on supercritical bond-percolation graphs with different boundary conditions at cluster borders. The integrated density of states of the Dirichlet Laplacian is found to exhibit a Lifshits tail at the lower spectral edge, while ... More

Statistical Cosmology with Quadratic Density FieldsAug 15 2002Primordial fluctuations in the cosmic density are usually assumed to take the form of a Gaussian random field that evolves under the action of gravitational instability. In the early stages, while they have low amplitude, the fluctuations grow linearly. ... More

Galaxy-galaxy-galaxy lensing: Third-order correlations between the galaxy and mass distributions in the UniverseFeb 25 2005Galaxy-galaxy lensing (GGL) measures the 2-point cross-correlation between galaxies and mass in the Universe. In this work we seek to generalise this effect by considering the third-order correlations between galaxies and mass: galaxy-galaxy-galaxy lensing. ... More

Percolation HamiltoniansFeb 26 2010Jan 09 2011There has been quite some activity and progress concerning spectral asymptotics of random operators that are defined on percolation subgraphs of different types of graphs. In this short survey we record some of these results and explain the necessary ... More

Identifiability of Gaussian structural equation models with equal error variancesMay 11 2012Aug 28 2013We consider structural equation models in which variables can be written as a function of their parents and noise terms, which are assumed to be jointly independent. Corresponding to each structural equation model, there is a directed acyclic graph describing ... More

Open system trajectories specify fluctuating work but not heatMay 24 2016Aug 26 2016Based on the explicit knowledge of a Hamiltonian of mean force, the classical statistical mechanics and equilibrium thermodynamics of open systems in contact with a thermal environment at arbitrary interaction strength can be formulated. Even though the ... More

Aging in One-Dimensional Coagulation-Diffusion Processes and the Fredrickson-Andersen ModelFeb 26 2007We analyse the aging dynamics of the one-dimensional Fredrickson-Andersen (FA) model in the nonequilibrium regime following a low temperature quench. Relaxation then effectively proceeds via diffusion limited pair coagulation (DLPC) of mobility excitations. ... More

Observable Dependent Quasi-Equilibrium in Slow DynamicsMay 31 2004Apr 18 2005We present examples demonstrating that quasi-equilibrium fluctuation-dissipation behavior at short time differences is not a generic feature of systems with slow non-equilibrium dynamics. We analyze in detail the non-equilibrium fluctuation-dissipation ... More

Some limit results for Markov chains indexed by treesJun 14 2014We consider a sequence of Markov chains $(\mathcal X^n)_{n=1,2,...}$ with $\mathcal X^n = (X^n_\sigma)_{\sigma\in\mathcal T}$, indexed by the full binary tree $\mathcal T = \mathcal T_0 \cup \mathcal T_1 \cup ...$, where $\mathcal T_k$ is the $k$th generation ... More

A spatial model for selection and cooperationMar 02 2016We study the evolution of cooperation in an interacting particle system with two types. The model we investigate is an extension of a two-type biased voter model. One type (called defector) has a (positive) bias $\alpha$ with respect to the other type ... More

The Tasaki-Crooks quantum fluctuation theoremMay 09 2007Starting out from the recently established quantum correlation function expression of the characteristic function for the work performed by a force protocol on the system [cond-mat/0703213] the quantum version of the Crooks fluctuation theorem is shown ... More

Studying Attractor Symmetries by Means of Cross Correlation SumsMay 02 1996We use the cross correlation sum introduced recently by H. Kantz to study symmetry properties of chaotic attractors. In particular, we apply it to a system of six coupled nonlinear oscillators which was shown by Kroon et al. to have attractors with several ... More

The generalized Catalan equation in positive characteristicOct 20 2016Let $K = \mathbb{F}_p(z_1, \ldots, z_r)$ be a finitely generated field over $\mathbb{F}_p$. In this article we study the generalized Catalan equation $ax^m + by^n = 1$ in $x, y \in K$ and integers $m, n > 1$ coprime with $p$. Our main result shows that ... More

Plasticity-rigidity cycles: A general adaptation mechanismNov 04 2015Nov 06 2015Successful adaptation helped the emergence of complexity. Alternating plastic- and rigid-like states were recurrently considered to play a role in adaptive processes. However, this extensive knowledge remained fragmented. In this paper I describe plasticity-rigidity ... More

Elementary construction of Lusztig's canonical basisFeb 16 2016Jun 06 2016In this largely expository article we present an elementary construction of Lusztig's canonical basis in type ADE. The method, which is essentially Lusztig's original approach, is to use the braid group to reduce to rank two calculations. Some of the ... More

Quantum circuits of T-depth oneOct 03 2012Apr 03 2013We give a Clifford+T representation of the Toffoli gate of T-depth 1, using four ancillas. More generally, we describe a class of circuits whose T-depth can be reduced to 1 by using sufficiently many ancillas. We show that the cost of adding an additional ... More

Generators and relations for n-qubit Clifford operatorsOct 25 2013Jun 18 2015We define a normal form for Clifford circuits, and we prove that every Clifford operator has a unique normal form. Moreover, we present a rewrite system by which any Clifford circuit can be reduced to normal form. This yields a presentation of Clifford ... More

Killip-Simon problem and Jacobi flow on GMP matricesMay 05 2015One of the first theorems in perturbation theory claims that for an arbitrary self-adjoint operator A there exists a perturbation B of Hilbert-Schmidt class, which destroys completely the absolutely continuous spectrum of A (von Neumann). However, if ... More

The Length Scales of Dynamic Heterogeneity: Results from Molecular Dynamics SimulationsSep 29 2010Over times shorter than that required for relaxation of enthalpy, a liquid can exhibit striking heterogeneities. The picture of these heterogeneities is complex with transient patches of rigidity, irregular yet persistent, intersected by tendrils of mobile ... More

Cross-intersecting integer sequencesDec 31 2012Jan 17 2014We call $(a_1, \dots, a_n)$ an \emph{$r$-partial sequence} if exactly $r$ of its entries are positive integers and the rest are all zero. For ${\bf c} = (c_1, \dots, c_n)$ with $1 \leq c_1 \leq \dots \leq c_n$, let $S_{\bf c}^{(r)}$ be the set of $r$-partial ... More

Compatible sequences and a slow Winkler percolationNov 01 2000Jan 18 2003Two infinite 0-1 sequences are called compatible when it is possible to cast out 0's from both in such a way that they become complementary to each other. Answering a question of Peter Winkler, we show that if the two 0-1-sequences are random i.i.d. and ... More

Electronic transport in strongly anisotropic disordered systems: model for the random matrix theory with non-integer betaSep 17 2000Jan 18 2002We study numerically an electronic transport in strongly anisotropic weakly disorderd two-dimensional systems. We find that the conductance distribution is gaussian but the conductance fluctuations increase when anisotropy becomes stronger. We interpret ... More

Sufficiency on the Stock MarketJan 27 2016It is well-known that there are a number of relations between theoretical finance theory and information theory. Some of these relations are exact and some are approximate. In this paper we will explore some of these relations and determine under which ... More

Correction to the 2005 paper: "Digit Selection for SRT Division and Square Root"Nov 24 2014It has been pointed out by counterexamples in a 2013 paper in the IEEE Transactions on Computers [1], that there is an error in the previously ibid.\ in 2005 published paper [2] on the construction of valid digit selection tables for SRT type division ... More

A Review of the Instability of Hot Electroweak Theory and its Bounds on $m_h$ and $m_t$Dec 22 1992[Talk presented at the International Seminar Quarks `92, Zvenigorod, Russia, May 11-17, 1992.] The electroweak vacuum need not be absolutely stable. For certain top and Higgs masses in the Minimal Standard Model, it is instead metastable with a lifetime ... More

An Overview of the $ε$ Expansion and the Electroweak Phase TransitionJul 18 1994Talk presented at the NATO Advanced Workshop on Electroweak Physics and the Early Universe: Sintra, Portugal, 1994. I summarize work done with Larry Yaffe on applying $\epsilon$ expansion techniques to the electroweak phase transition.

Several Dirac Operator in parabolic geometryAug 09 2007In this thesis, we show the existence of a sequence of differential operators starting with with the Dirac operator in k Clifford variables, $D=(D_1,..., D_k)$, where $D_i=\sum_j e_j\cdot \partial_{ij}: C^\infty((\R^n)^k,\S)\to C^\infty((\R^n)^k,\S)$ ... More

Uniqueness in the Characteristic Cauchy Problem of the Klein-Gordon Equation and Tame Restrictions of Generalized FunctionsAug 12 2004We show that every tempered distribution, which is a solution of the (homogenous) Klein-Gordon equation, admits a ``tame'' restriction to the characteristic (hyper)surface $\{x^0+x^n=0\}$ in $(1+n)$-dimensional Minkowski space and is uniquely determined ... More

Energy Spectrum of Quasi-Geostrophic TurbulenceJul 24 2002We consider the energy spectrum of a quasi-geostrophic model of forced, rotating turbulent flow. We provide a rigorous a priori bound E(k) <= Ck^{-2} valid for wave numbers that are smaller than a wave number associated to the forcing injection scale. ... More

Versal embeddings of compact, regular 3-pseudoconcave CR submanifoldsSep 24 2001We prove that for an induced CR structure on a compact, generic, regular 3-pseudoconcave CR submanifold ${\bold M}\subset{\bold G}$, of a complex manifold ${\bold G}$, satisfying condition $\dim H^1({\bold M}, T^{\prime}({\bold G})|_{\bold M})=0$ all ... More

A note on pseudo-Anosov maps with small growth rateSep 25 2003We present an explicit sequence of pseudo-Anosov maps $\phi_k: S_{2k}\to S_{2k}$ of surfaces of genus $2k$ whose growth rates converge to one.

Morita base change in quantum groupoidsApr 29 2002Let $L$ be a quantum semigroupoid, more precisely a $\times_R$-bialgebra in the sense of Takeuchi. We describe a procedure replacing the algebra $R$ by any Morita equivalent, or in fact more generally any $\sqrt{\text{Morita}}$ equivalent (in the sense ... More

Spin Correlations in Monte Carlo SimulationsOct 08 2001We show that the algorithm originally proposed by Collins and Knowles for spin correlations in the QCD parton shower can be used in order to include spin correlations between the production and decay of heavy particles in Monte Carlo event generators. ... More

Maximizing the spin correlation of top quark pairs produced at the LHCDec 07 2004The measurement of top quark spin correlation is an important tool for precise studies of top quark interactions. In this letter I construct a quantization axis maximizing the spin correlation at the LHC within the Standard Model. Using this axis a spin ... More

Signal transport in and conductance of correlated nanostructuresJul 16 2013Here we report on our project concerning the application of time dependent DMRG to strongly correlated systems. We show that a previously reported simulation of the spin charge separation in a one-dimensional Hubbard system exceeds a relative error of ... More

The dark side of DFT based transport calculationsFeb 13 2013We compare the conductance of an interacting ring of six lattice sites threaded by flux $\pi$ in a two terminal setup with the conductance of the corresponding Kohn-Sham particles. Based on symmetry considerations we can show that even within (lattice) ... More

Calculating Green Functions from Finite SystemsJan 15 2010In calculating Green functions for interacting quantum systems numerically one often has to resort to finite systems which introduces a finite size level spacing. In order to describe the limit of system size going to infinity correctly, one has to introduce ... More

Photon-induced Reactions in Stars and in the Laboratory: A Critical ComparisonMay 28 2004Photon-induced reactions during the astrophysical p- (or gamma-) process occur at typical temperatures of 1.8 < T9 < 3.3. Experimental data of (gamma,n), (gamma,p), or (gamma,alpha) reactions - if available in the relevant energy region - cannot be used ... More

Unexpected properties of the $^{33}$S($α$,p)$^{36}$Cl reaction cross section at low energiesApr 24 2014Apr 26 2014New experimental data for the $^{33}$S($\alpha$,p)$^{36}$Cl reaction show a very unusual energy dependence. Contrary to common findings for many other $\alpha$-induced reactions, statistical model calculations underestimate the measured cross sections ... More

Total reaction cross section $σ_{\rm{reac}}$ of $α$-induced reactions from elastic scattering: the example $^{140}$Ce($α$,$α$)$^{140}$CeMar 06 2013Angular distributions of elastic $^{140}$Ce($\alpha$,$\alpha$)$^{140}$Ce scattering are analyzed in the framework of the optical model from low energies around the Coulomb barrier up to about 40\,MeV. From the local fits the total reaction cross section ... More

A reintroduction of dynamical SU(2) gauge fields in Hubbard modelsJul 02 2012Jul 10 2012This is a preprint from 1990, in which it is explained how non-Abelian gauge magnets originate as effective dynamics in models of hopping particles. In particular, an explicit model is discussed in which both link and plaquette terms appear. The motivation ... More

Local Holomorphic Isometries of a Modified Projective Space into a Standard Projective Space; Rational Conformal FactorsJul 28 2014We consider local modifications $\omega_n+f^*\omega_d$ of the Fubini-Study metric (with associated $(1,1)$-form $\omega_n$) on an open subset $\Omega\subset \bC\bP^n$ induced by a local holomorphic mapping $f\colon \Omega\to \bP^d$. Our main result is ... More

Partial rigidity of degenerate CR embeddings into spheresAug 14 2012Aug 15 2012In this paper, we study degenerate CR embeddings $f$ of a strictly pseudoconvex hypersurface $M\subset \bC^{n+1}$ into a sphere $\bS$ in a higher dimensional complex space $\bC^{N+1}$. The degeneracy of the mapping $f$ will be characterized in terms of ... More

On the unicity of types in special linear groupsNov 02 2015Oct 24 2016Let $F$ be a non-archimedean local field. We show that any representation of a maximal compact subgroup of $\mathbf{SL}_N(F)$ which is typical for an essentially tame supercuspidal representation must be induced from a Bushnell--Kutzko maximal simple ... More

Central hadron production in crossing of dedicated hadronic beamsMay 04 2004The original aim of this work, was to give a {\it brief} review of gluonic mesons, to be searched for in an experiment dedicated to central production of a relatively low mass hadronic system, whereby rapidity gaps are possible to impose, requiring initial ... More

Mass Generation in QCD -- Oscillating Quarks and GluonsApr 20 2014The present lecture is devoted to embedding the approximate genuine harmonic oscillator structure of valence q qbar mesons and in more detail the q q q configurations for up,down,strange - flavored baryons in Q C D for three light flavors of quark.

A quantum of historySep 21 2014With reference to primary sources it is shown that key claims made regarding the history of the pilot wave theory in Quantum Theory at the Crossroads are not supported by the historical record. It is also argued that the association of de Broglie with ... More

Symmetries and conservation laws in the Lagrangian picture of quantum hydrodynamicsNov 05 2012Quantum hydrodynamics represents quantum mechanics through two complementary models: the Eulerian picture, a direct transcription of wave mechanics, and the Lagrangian picture, in which the quantum state is represented by the collective motion of a continuum ... More

Spin-like current from phase space distributionsJan 04 2009The spin 0 generalized phase space approach provides a general expression for local current which depends on the choice of distribution function and generally deviates from the Schrodinger current. It is shown that the continuity equation restricts the ... More

What's wrong with Einstein's 1927 hidden-variable interpretation of quantum mechanics?Jan 05 2004Einstein's unpublished 1927 deterministic trajectory interpretation of quantum mechanics is critically examined, in particular with regard to the reason given by Einstein for rejecting his theory. It is shown that the aspect Einstein found objectionable ... More

Uniqueness of conserved currents in quantum mechanicsMay 29 2003It is proved by a functional method that the conventional expression for the Dirac current is the only conserved 4-vector implied by the Dirac equation that is a function of just the quantum state. The demonstration is extended to derive the unique conserved ... More

Quantum potential energy as concealed motionOct 01 2014Nov 13 2014It is known that the Schroedinger equation may be derived from a hydrodynamic model in which the Lagrangian position coordinates of a continuum of particles represent the quantum state. Using Routh\s method of ignorable coordinates it is shown that the ... More

The roads not taken: empty waves, wavefunction collapse and protective measurement in quantum theorySep 19 2014Within the class of ontological interpretations of quantum theory where a physical system comprises a particle and a field (wavefunction) guiding it, an empty wave is a segment of the wavefunction not containing the particle. We examine the impact of ... More

Hydrodynamics, particle relabelling and relativityMay 18 2011Using the wave equation as an example, it is shown how to extend the hydrodynamic Lagrangian-picture method of constructing field evolution using a continuum of trajectories to second-order theories. The wave equation is represented through Eulerian-picture ... More

Schrodinger dynamics as a two-phase conserved flow: an alternative trajectory construction of quantum propagationJul 28 2008Dec 16 2008It is shown that the Schrodinger equation can be cast in the form of two coupled real conservation equations, in Euclidean spacetime in the free case and in a five-dimensional Eisenhart geometry in the presence of an external potential. This implies a ... More

An estimate about multiple stochastic integrals with respect to a normalized empirical measureOct 20 2003Let a sequence of iid. random variables $\xi_1,...,\xi_n$ be given on a measurable space $(X,\cal X)$ with distribution $\mu$ together with a function $f(x_1,...,x_k)$ on the product space $(X^k,{\cal X}^k)$. Let $\mu_n$ denote the empirical measure defined ... More

Testing a new mesh refinement code in the evolution of a spherically symmetric Klein-Gordon fieldMay 04 2005Sep 22 2005Numerical evolution of the spherically symmetric, massive Klein-Gordon field is presented using a new adaptive mesh refinement (AMR) code with fourth order discretization in space and time, along with compactification in space. The system is non-interacting ... More

Generalised space-time and dualityJun 04 2010Aug 03 2010In this paper we consider the previously proposed generalised space-time and investigate the structure of the field theory upon which it is based. In particular, we derive a SO(D,D) formulation of the bosonic string as a non-linear realisation at lowest ... More

Brane dynamics, central charges and E_{11}Dec 31 2004We consider a theory in which supersymmetry is partially spontaneously broken and show that the dynamical fields in the same supersymmetric multiplet as the Goldstino are Goldstone bosons whose corresponding generators are central charges in the underlying ... More

Cosmological Applications of Gravitational LensingDec 08 1995The last decade has seen an enormous increase of activity in the field of gravitational lensing, mainly driven by improvements of observational capabilities. I will review the basics of gravitational lens theory, just enough to understand the rest of ... More

Generalized shear-ratio tests: A new relation between cosmological distances, and a diagnostic for a redshift-dependent multiplicative bias in shear measurementsMar 14 2016We derive a new relation between cosological distances, valid in any (statistically) isotropic space-time and independent of cosmological parameters or even the validity of the field equation of General Relativity. In particular, this relation yields ... More

Lattice Investigations of the Running CouplingNov 13 1995A review of investigations of running couplings using lattice techniques is given. This includes i) studies of the running of particular non-perturbatively defined renormalized couplings in pure gauge theories over a range of energies, and ii) how estimates ... More

Formalism for dilepton production via virtual photon bremsstrahlung in hadronic reactionsDec 01 1998We derive a set of new formulas for various distributions in dilepton production via virtual photon bremsstrahlung from pseudoscalar mesons and unpolarized spin-one-half fermions. These formulas correspond to the leading and sub-leading terms in the Low-Burnett-Kroll ... More

Some implications of meson dominance in weak interactionsFeb 15 1997The hypothesis is scrutinized that the weak interaction of hadronic systems at low energies is dominated by the coupling of the pseudoscalar, vector, and axial-vector mesons to the weak gauge bosons. The strength of the weak coupling of the rho(770) meson ... More

Meson dominance implications for the bottomness preserving decays of the B_c^+ mesonAug 31 2013Sep 03 2013Encouraged by a recent observation of the B_c^+ -> B_s^0 + pi^+ decay by the LHCb collaboration we present the meson dominance predictions for other weak decays of the B_c^+ into B_s^0 or B^0 in the form of branching ratios to the observed decay.

About one long-range contribution to K+ -> pi+ l+ l- decaysApr 07 1999We investigate the mechanism of K+ -> pi+ l+ l- (l= e, mu) decays in which a virtual photon is emitted either from the incoming K+ or the outgoing pi+. We point out some inconsistencies with and between two previous calculations, discuss the possible ... More

Non-autonomous dynamics of holomorphic mappings in projective spaceJan 16 2004We study the dynamics of compositions of a sequence of holomorphic mappings in projective space. We define ergodicity and mixing for non-autonomous dynamical systems, and we construct totally invariant measures for which our sequence satisfies these properties. ... More

On Lyubeznik's invariants and endomorphisms of local cohomology modulesApr 16 2007May 07 2009Let $(R, \mathfrak m)$ denote an $n$-dimensional Gorenstein ring. For an ideal $I \subset R$ of height $c$ we are interested in the endomorphism ring $B = \Hom_R(H^c_I(R), H^c_I(R)).$ It turns out that $B$ is a commutative ring. In the case of $(R,\mathfrak ... More

Matrix Representation of Operators Using FramesOct 07 2005Nov 23 2006In this paper it is investigated how to find a matrix representation of operators on a Hilbert space with Bessel sequences, frames and Riesz bases. In many applications these sequences are often preferable to orthonormal bases (ONBs). Therefore it is ... More

Testing Goodness-of-Fit via Rate DistortionMar 31 2009A framework is developed using techniques from rate distortion theory in statistical testing. The idea is first to do optimal compression according to a certain distortion function and then use information divergence from the compressed empirical distribution ... More

On Arbitrary Phases in Quantum Amplitude AmplificationJun 07 2000We consider the use of arbitrary phases in quantum amplitude amplification which is a generalization of quantum searching. We prove that the phase condition in amplitude amplification is given by $\tan(\varphi/2) = \tan(\phi/2)(1-2a)$, where $\phi$ and ... More

The hybrid spectral testJun 13 2013The starting point of this paper is the interplay between the construction principle of a sequence and the characters of the compact abelian group that underlies the construction. In case of the Halton sequence in base $\mathbf b=(b_1, \ldots, b_s)$ in ... More

Existence of Spontaneous Pair CreationJun 25 2005May 17 2006A prove of the existence of spontaneous pair creation as an external field problem in second quantized Dirac theory. PHD Thesis

Frames and Finite Dimensionality: Frame Transformation, Classification and AlgorithmsAug 11 2006Oct 25 2006In this paper we will look at the connection of frames and finite dimensionality. A main focus is to present simple algorithms and make them available online. The main result is a way to 'switch' between different frames, giving an algorithm to calculate ... More

Some quasitensor autoequivalences of Drinfeld doubles of finite groupsFeb 10 2015We report on two classes of autoequivalences of the category of Yetter-Drinfeld modules over a finite group, or, equivalently the Drinfeld center of the category of representations of a finite group. Both operations are related to the $r$-th power operation, ... More

Why should one expect to find long runs of (non)-Ramanujan primes ?Jan 18 2012Sondow et al have studied Ramanujan primes (RPs) and observed numerically that, while half of all primes are RPs asymptotically, one obtains runs of consecutives RPs (resp. non-RPs) which are statistically significantly longer than one would expect if ... More

Separated Lie models and the homotopy Lie algebraJun 21 2004May 07 2007A simply connected topological space X has homotopy Lie algebra $\pi_*(\Omega X) \tensor \Q$. Following Quillen, there is a connected differential graded free Lie algebra (dgL) called a Lie model, which determines the rational homotopy type of X, and ... More

Heavy quark production and non-linear gluon evolution at the LHCJun 26 2006We investigate the importance of unitarity corrections to parton evolution in heavy flavor production at the LHC. The gluon distribution is determined with a fit to HERA data applying a unified BFKL-DGLAP approach, in which the non-linear evolution is ... More

Projective Limit Random Probabilities on Polish SpacesJan 24 2011Oct 19 2011A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be constructed from their ... More

Recent Developments in the Bethe-Salpeter Description of Light MesonsNov 02 2004Results for the light meson mass spectrum from a Bethe-Salpeter approach are presented. The results obtained in the standard framework are Poincar\'{e} covariant and compare favourably with lattice results. Using a more sophisticated scheme, the pseudoscalar, ... More

Hubbard Models with Superconducting Quantum SymmetryJan 16 1997We discuss classical and quantum symmetries of extended Hubbard models. The quantum symmetries are shown to be related to the known superconducting SU(2) symmetry of the original Hubbard model at half filling via generalized Lang-Firsov transformations ... More

From Quantum Planes to Quantum Groups and back; Cartan CalculusDec 10 1993A Cartan Calculus of Lie derivatives, differential forms, and inner derivations, based on an undeformed Cartan identity, is constructed. We attempt a classification of various types of quantum Lie algebras and present a fairly general example for their ... More

Santa and the moonNov 23 2011Nov 29 2011Happy end-of-the-year evening and night events provide good opportunities to explain the phases of the moon. The need for such moon phase education is once again demonstrated, through an investigation of illustrations on Santa Claus and Christmas gift ... More

Herschel and Galaxies/AGNNov 24 2004Herschel will represent a breakthrough in the study of nearby gas-rich and gas-poor galaxies, as it will for the first time permit imaging photometric and spectroscopic observations of their ISM in the FIR-submm wavelength range. The unprecedented sensitivity ... More

The twistor geometry of three-qubit entanglementMar 08 2004A geometrical description of three qubit entanglement is given. A part of the transformations corresponding to stochastic local operations and classical communication on the qubits is regarded as a gauge degree of freedom. Entangled states can be represented ... More

Quantum torsors and Hopf-Galois objectsAug 06 2002We prove that every faithfully flat Hopf-Galois object is a quantum torsor in the sense of Grunspan.

Quantum Speedup and Categorical DistributivityMar 12 2013This paper studies one of the best known quantum algorithms - Shor's factorisation algorithm - via categorical distributivity. A key aim of the paper is to provide a minimal set of categorical requirements for key parts of the algorithm, in order to establish ... More

Girard's $!()$ as a reversible fixed-point operatorSep 02 2013We give a categorical description of the treatment of the !() exponential in the Geometry of Interaction system, with particular emphasis on the fact that the GoI interpretation 'forgets types'. We demonstrate that it may be thought of as a fixed-point ... More