total 9845took 0.24s

Graph-theoretic Simplification of Quantum Circuits with the ZX-calculusFeb 08 2019We present a new circuit-to-circuit optimisation routine based on an equational theory called the ZX-calculus. We first interpret quantum circuits as ZX-diagrams, a flexible, lower-level language for describing quantum computations graphically. Then, ... More

On Estimating Many Means, Selection Bias, and the BootstrapNov 15 2013With recent advances in high throughput technology, researchers often find themselves running a large number of hypothesis tests (thousands+) and esti- mating a large number of effect-sizes. Generally there is particular interest in those effects estimated ... More

The intrinsic torsion of SU(3) and G_2 structuresFeb 26 2002We analyse the relationship between the components of the intrinsic torsion of an SU(3) structure on a 6-manifold and a G_2 structure on a 7-manifold. Various examples illustrate the type of SU(3) structure that can arise as a reduction of a metric with ... More

Polymer Collapse on Fluctuating Random SurfacesSep 05 1994Jan 12 1995The conformations of interacting linear polymers on a dynamical planar random lattice are studied using a random two-matrix model. An exact expression for the partition function of self-avoiding chains subject to attractive contact interactions of relative ... More

On Loop Equations In KdV Exactly Solvable String TheoryNov 30 1991The non-perturbative behaviour of macroscopic loop amplitudes in the exactly solvable string theories based on the KdV hierarchies is considered. Loop equations are presented for the real non-perturbative solutions living on the spectral half-line, allowed ... More

Effective Theories for Circuits and AutomataJun 28 2011Feb 20 2012Abstracting an effective theory from a complicated process is central to the study of complexity. Even when the underlying mechanisms are understood, or at least measurable, the presence of dissipation and irreversibility in biological, computational ... More

Volatility Swap Under the SABR ModelMar 25 2013The SABR model is shortly presented and the volatility swap explained. The fair value for a volatility swap is then computed using the usual theory in financial mathematics. An analytical solution using confluent hypergeometric functions is found. The ... More

On the explanation for quantum statisticsNov 15 2005The concept of classical indistinguishability is analyzed and defended against a number of well-known criticisms, with particular attention to the Gibbs' paradox. Granted that it is as much at home in classical as in quantum statistical mechanics, the ... More

The Lattice Fermi SurfaceOct 08 2001The Nambu - Jona-Lasinio model in 2+1 dimensions is simulated for non-zero baryon chemical potential with a diquark source term. No evidence for a BCS condensate or gap is seen at high density; rather, critical behaviour with novel exponents is observed, ... More

Improving the Lattice QED ActionNov 24 1994Strongly coupled QED is a model whose physics is dominated by short-ranged effects. In order to assess which features of numerical simulations of the chiral phase transition are universal and which are not, we have formulated a quenched version of the ... More

Monte Carlo Study of the 3D Thirring ModelFeb 05 1997I review three different non-perturbative approaches to the three dimensional Thirring model: the 1/N_f expansion, Schwinger-Dyson equations, and Monte Carlo simulation. Simulation results are presented to support the existence of a non-perturbative fixed ... More

Towards a Systematic Development Process of Optimization MethodsFeb 29 2016Jul 18 2016The ultimate goal of all optimization methods is to solve real-world problems. For a successful project execution, knowledge about optimization and the application has to be pooled. As it is too inefficient to highly train one person in both fields, a ... More

Fourth Moment Theorems for complex Gaussian approximationNov 02 2015We prove a bound for the Wasserstein distance between vectors of smooth complex random variables and complex Gaussians in the framework of complex Markov diffusion generators. For the special case of chaotic eigenfunctions, this bound can be expressed ... More

Top quark mass measurements with the CMS experiment at the LHCJul 18 2016Measurements of the top quark mass are presented, obtained from CMS data collected in proton proton collisions at the LHC at centre-of-mass energies of 7 TeV and 8 TeV. The mass of the top quark is measured using several methods and channels, including ... More

Automating QCD amplitudes with on-shell methodsMay 07 2016We review some of the modern approaches to scattering amplitude computations in QCD and their application to precision LHC phenomenology. We emphasise the usefulness of momentum twistor variables in parameterising general amplitudes.

Up to and beyond ninth order in opacity: Radiative energy loss with GLVApr 29 2008A new examination of the GLV all-orders opacity result for radiative energy loss is presented. The opacity expansion is shown to be a Dyson expansion of a Schrodinger-like (or diffusion) equation, a form also found in BDMPS-Z-ASW, AMY and Higher Twist ... More

Nuts have no hairAug 18 1995We show that the Riemannian Kerr solutions are the only Riemannian, Ricci-flat and asymptotically flat ${\rm C}^{2}$-metrics $g_{\mu\nu}$ on a 4-dimensional complete manifold ${\cal M}$ of topology ${\rm R}^{2} \times {\rm S}^{2}$ which have (at least) ... More

Spreadsheet HellJan 21 2008This management paper looks at the real world issues faced by practitioners managing spreadsheets through the production phase of their life cycle. It draws on the commercial experience of several developers working with large corporations, either as ... More

A Galois-Connection between Cattell's and Szondi's Personality ProfilesMay 05 2014We propose a computable Galois-connection between, on the one hand, Cattell's 16-Personality-Factor (16PF) Profiles, one of the most comprehensive and widely-used personality measures for non-psychiatric populations and their containing PsychEval Personality ... More

NPPT Bound Entanglement ExistsAug 31 2006Every dXd bipartite system is shown to have a large family of undistillable states with nonpositive partial transpose (NPPT). This family subsumes the family of conjectured NPPT bound entangled Werner states. In particular, all one-copy undistillable ... More

A Relativistic Conical Function and its Whittaker LimitsNov 01 2011In previous work we introduced and studied a function $R(a_{+},a_{-},{\bf c};v,\hat{v})$ that is a generalization of the hypergeometric function ${}_2F_1$ and the Askey-Wilson polynomials. When the coupling vector ${\bf c}\in{\mathbb C}^4$ is specialized ... More

Controlling inclusive cross sections in parton shower + matrix element mergingNov 23 2012Dec 03 2012We propose an extension of matrix element plus parton shower merging at tree level to preserve inclusive cross sections obtained from the merged and showered sample. Implementing this constraint generates approximate next-to-leading order (NLO) contributions ... More

Natural Entanglement in Bose-Einstein CondensatesOct 18 2001Every Bose-Einstein condensate is in a highly entangled state, as a consequence of the fact that the particles in a condensate are distributed over space in a coherent way. It is proved that any two regions within a condensate of finite particle number ... More

Towards Critical Physics in 2+1d with U(2N)-Invariant FermionsOct 14 2016Interacting theories of N relativistic fermion flavors in reducible spinor representations in 2+1 spacetime dimensions are formulated on a lattice using domain wall fermions (DWF), for which a U(2N) global symmetry is recovered in the limit that the wall ... More

How to determine a K3 surface from a finite automorphismApr 29 2016In this article we pursue the question when an automorphism determines a (complex) K3 surface up to isomorphism. We prove that if the automorphism is finite non-symplectic and the transcendental lattice small, then the isomorphism class of the K3 surface ... More

Double-pass variants for multi-shift BiCGstab(ell)Oct 13 2010In analogy to Neuberger's double-pass algorithm for the Conjugate Gradient inversion with multi-shifts we introduce a double-pass variant for BiCGstab(ell). One possible application is the overlap operator of QCD at non-zero chemical potential, where ... More

Resolving the observer reference class problem in cosmologyJul 14 2017The assumption that we are typical observers plays a core role in attempts to make multiverse theories empirically testable. A widely shared worry about this assumption is that it suffers from systematic ambiguity concerning the reference class of observers ... More

Non-Gaussianities in a two-field generalization of Natural InflationNov 23 2017We describe a two-field model that generalizes Natural Inflation, in which the inflaton is the pseudo-Goldstone boson of an approximate symmetry that is spontaneously broken, and the radial mode is dynamical. We analyze how the dynamics fundamentally ... More

The Maser-Starburst connection in NGC253Nov 07 2017NGC253 is one of the closest starburst galaxies to the Milky Way and as such it has been studied in detail across the electromagnetic spectrum. Recent observations have detected the first extragalactic class I methanol masers at 36 and 44 GHz and the ... More

Kitaev MaterialsJan 24 2017In transition-metal compounds with partially filled $4d$ and $5d$ shells spin-orbit entanglement, electronic correlations, and crystal-field effects conspire to give rise to a variety of novel forms of topological quantum matter. This includes Kitaev ... More

Numerical study of the $2+1d$ Thirring model with U($2N$)-invariant fermionsAug 25 2017In 2+1 dimensions the global U($2N$) symmetry associated with massless Dirac fermions is broken to U($N)\otimes$U($N$) by a parity-invariant mass. I will show how to adapt the domain wall formulation to recover the U($2N$)-invariant limit in interacting ... More

The Spectral Gap of Sparse Random DigraphsAug 01 2017The second largest eigenvalue of a transition matrix $P$ has connections with many properties of the underlying Markov chain, and especially its convergence rate towards the stationary distribution. In this paper, we give an asymptotic upper bound for ... More

A remark on the group-completion theoremSep 07 2017Suppose that $M$ is a topological monoid satisfying $\pi_0M=\mathbb{N}$ to which the McDuff-Segal group-completion theorem applies. This implies that a certain map $f: \mathbb{M}_{\infty}\rightarrow \Omega BM$ defined on an infinite mapping telescope ... More

Query-driven Data Completeness Management (PhD Thesis)Nov 11 2014Apr 01 2015Knowledge about data completeness is essentially in data-supported decision making. In this thesis we present a framework for metadata-based assessment of database completeness. We discuss how to express information about data completeness and how to ... More

Global existence and convergence for a higher order flow in conformal geometryApr 22 2004We study a higher-order parabolic equation which generalizes the Ricci flow on two-dimensional surfaces. The metric is deformed conformally with a speed given by the Q-curvature of the metric. Under a condition on the Q-curvature of the initial metric ... More

JSJ decompositions of doubles of free groupsNov 04 2016Mar 21 2018We classify all possible JSJ decompositions of doubles of free groups of rank two and we then compute the Makanin-Razborov diagram of a particular double of a free group and deduce that in general limit groups are not freely subgroup separable.

Topological symmetry classes for non-Hermitian models and connections to the bosonic Bogoliubov-de Gennes equationJul 09 2018Aug 26 2018The Bernard-LeClair (BL) symmetry classes generalize the ten-fold way classes in the absence of Hermiticity. Within the BL scheme, time-reversal and particle-hole come in two flavors, and "pseudo-Hermiticity" generalizes Hermiticity. We propose that these ... More

Silicon Technologies for the CLIC Vertex DetectorJun 01 2017CLIC is a proposed linear e+e- collider designed to provide particle collisions at center-of-mass energies of up to 3 TeV. Precise measurements of the properties of the top quark and the Higgs boson, as well as searches for Beyond the Standard Model physics ... More

Some New Bounds on the Entropy Numbers of Diagonal OperatorsMar 01 2019Entropy numbers are an important tool for quantifying the compactness of operators. Besides establishing new upper bounds on the entropy numbers of diagonal operators $D_\sigma$ from $\ell_p$ to $\ell_q$, where $p\not=q$, we investigate the optimality ... More

Finding generically stable measuresSep 18 2010We discuss two constructions for obtaining generically stable Keisler measures in an NIP theory. First, we show how to symmetrize an arbitrary invariant measure to obtain a generically stable one from it. Next, we show that suitable sigma-additive probability ... More

Retrieving the three-dimensional matter power spectrum and galaxy biasing parameters from lensing tomographyFeb 09 2012Apr 16 2012With the availability of galaxy distance indicators in weak lensing surveys, lensing tomography can be harnessed to constrain the three-dimensional (3D) matter power spectrum over a range of redshift and physical scale. By combining galaxy-galaxy lensing ... More

On dp-minimal ordered structuresSep 23 2009We show some basic facts about dp-minimal ordered structures. The main results are : dp-minimal groups are abelian-by-finite-exponent, in a divisible ordered dp-minimal group, any infinite set has non-empty interior, and any theory of pure tree is dp-minimal. ... More

Extending the Stable Model Semantics with More Expressive RulesAug 06 1999The rules associated with propositional logic programs and the stable model semantics are not expressive enough to let one write concise programs. This problem is alleviated by introducing some new types of propositional rules. Together with a decision ... More

On the unimodality of power transformations of positive stable densitiesFeb 19 2010Nov 15 2013Let $Z_\alpha$ be a positive $\alpha-$stable random variable and $r\in{\bf R}.$ We show the existence of an unbounded open domain $D$ in $[1/2,1]\times{\bf R}$ with a cusp at $(1/2,-1/2)$, characterized by the complete monotonicity of the function $F_{\alpha, ... More

Automorphisms of Salem degree 22 on supersingular K3 surfaces of higher Artin invariant - a short noteSep 08 2016We give a short proof that every supersingular K3 surface in odd characteristic has an automorphism of Salem degree 22. The proof relies on the case $\sigma=1$ and the cone theorem.

(k+1)-sums versus k-sumsNov 19 2010Jun 08 2012A $k$-sum of a set $A\subseteq \mathbb{Z}$ is an integer that may be expressed as a sum of $k$ distinct elements of $A$. How large can the ratio of the number of $(k+1)$-sums to the number of $k$-sums be? Writing $k\wedge A$ for the set of $k$-sums of ... More

Bend conductance of crossed wires in the presence of Andreev scatteringApr 12 1994We study the 4-probe bend conductance $G_{14,32}$ of a mesoscopic crossed wire structure in the ballistic regime in the absence of a magnetic field, which for normal devices is usually negative. We predict that for sufficiently large devices and for small ... More

Summability of Superstring TheoryMar 11 1998Mar 20 1998Several arguments are given for the summability of the superstring perturbation series. Whereas the Schottky group coordinatization of moduli space may be used to provide refined estimates of large-order bosonic string amplitudes, the super-Schottky group ... More

Scalar Field Theory in Curved Space and the Definition of MomentumFeb 09 1997Dec 22 1997Some general remarks are made about the quantum theory of scalar fields and the definition of momentum in curved space. Special emphasis is given to field theory in anti-de Sitter space, as it represents a maximally symmetric space-time of constant curvature ... More

A Semiparametric Effect Size IndexFeb 19 2019Effect size indices are useful tools in study design and reporting because they are unitless measures of association strength that do not depend on sample size. Existing effect size indices are developed for particular parametric models or population ... More

A set of formulas for primesJan 03 2019Jan 18 2019A new set of formulas for primes is presented. These formulas are more efficient and grow much slower than the two known formulas of Mills and Wright.

Local asymptotic normality for shape and periodicity of a signal in the drift of a degenerate diffusion with internal variablesMar 08 2019Taking a multidimensional time-homogeneous dynamical system and adding a randomly perturbed time-dependent deterministic signal to some of its components gives rise to a high-dimensional system of stochastic differential equations which is driven by possibly ... More

Proceedings Sixth Workshop on Trends in Functional Programming in EducationMay 11 2018The Sixth International Workshops on Trends in Functional Programming in Education, TFPIE 2017, was held on 22 June 2017 at the University of Kent, in Canterbury, UK, and was co-located with TFP, the Symposium on Trends in Functional Programming. The ... More

On the Computation of the Shannon Capacity of a Discrete Channel with NoiseJan 30 2017Jan 31 2017Muroga [M52] showed how to express the Shannon channel capacity of a discrete channel with noise [S49] as an explicit function of the transition probabilities. His method accommodates channels with any finite number of input symbols, any finite number ... More

Repeated interaction processes in the continuous-time limit, applied to quadratic fermionic systemsMar 19 2019We study a class of Lindblad equation on finite-dimensional fermionic systems. The model is obtained as the continuous-time limit of a repeated interaction process between fermionic systems with quadratic Hamiltonians, a setup already used by Platini ... More

Tropical linear spaces and tropical convexityMay 08 2015In classical geometry, a linear space is a space that is closed under linear combinations. In tropical geometry, it has long been a consensus that tropical varieties defined by valuated matroids are the tropical analogue of linear spaces. It is not difficult ... More

Kähler-Einstein metrics and algebraic structures on limit spacesMar 28 2016This is an expository article, closely following the author's lecture at the 2014 Journal Differential Geometry conference.

Upper bounds for Maass forms on semisimple groupsMay 27 2014Dec 19 2017We prove a power saving over the local bound for the sup norm of Hecke-Maass forms on any quasi-split semisimple real group that is not isogenous to a product of odd special unitary groups.

Restrictions of SL_3 Maass forms to maximal flat subspacesAug 04 2013Aug 26 2014Let \psi be a Hecke-Maass form on a cubic division algebra over \Q. We apply arithmetic amplification to improve the local bound for the L^2 norm of \psi restricted to maximal flat subspaces.

Diophantine approximation and the solubility of the Schroedinger equationOct 22 2002Apr 29 2003We characterise the set of periods for which number theoretical obstructions prevent us from finding periodic solutions of the Schroedinger equation on a two dimensional torus as well as the asymptotic occurrence of possible resonances.

On the distribution of powers of real numbers modulo 1Nov 18 2014Given a strictly increasing sequence of positive real numbers tending to infinity $(q_{n})_{n=1}^{\infty}$, and an arbitrary sequence of real numbers $(r_{n})_{n=1}^{\infty}.$ We study the set of $\alpha\in(1,\infty)$ for which $\lim_{n\to\infty}\|\alpha^{q_{n}}-r_{n}\|= ... More

Exceptional digit frequencies and expansions in non-integer basesNov 28 2017In this paper we study the set of digit frequencies that are realised by elements of the set of $\beta$-expansions. The main result of this paper demonstrates that as $\beta$ approaches $1,$ the set of digit frequencies that occur amongst the set of $\beta$-expansions ... More

Some New Bounds on the Entropy Numbers of Diagonal OperatorsMar 01 2019May 27 2019Entropy numbers are an important tool for quantifying the compactness of operators. Besides establishing new upper bounds on the entropy numbers of diagonal operators $D_\sigma$ from $\ell_p$ to $\ell_q$, where $p\not=q$, we investigate the optimality ... More

Metric Diophantine approximation with respect to planar distance functionsJan 27 2004We outline a proof of an analogue of Khintchine's Theorem in R^2, where the ordinary height is replaced by a distance function satisfying an irrationality condition as well as certain decay and symmetry conditions.

Some integral curvature estimates for the Ricci flow in four dimensionsApr 10 2015We consider solutions (M,g(t)), 0 <= t <T, to Ricci flow on compact, four dimensional manifolds without boundary. We prove integral curvature estimates which are valid for any such solution. In the case that the scalar curvature is bounded and T is finite, ... More

Alternatives for optimization in systems and control: convex and non-convex approachesMay 01 2012In this presentation, we will develop a short overview of main trends of optimization in systems and control, and from there outline some new perspectives emerging today. More specifically, we will focus on the current situation, where it is clear that ... More

Brane Effective Actions, Kappa-Symmetry and ApplicationsOct 11 2011Nov 22 2011This is a review on brane effective actions, their symmetries and some of its applications. Its first part uncovers the Green-Schwarz formulation of single M- and D-brane effective actions focusing on kinematical aspects : the identification of their ... More

Extremal black holes, Holography & Coarse grainingJun 01 2011Jul 30 2011I review some of the concepts at the crossroads of gravitational thermodynamics, holography and quantum mechanics. First, the origin of gravitational thermodynamics due to coarse graining of quantum information is exemplified using the half-BPS sector ... More

The geometry of null rotation identificationsMar 21 2002Apr 16 2002The geometry of flat spacetime modded out by a null rotation (boost+rotation) is analysed. When embedding this quotient spacetime in String/M-theory, it still preserves one half of the original supersymmetries. Its connection with the BTZ black hole, ... More

Automorphisms as brane non-local transformationsOct 26 2000The relation among spacetime supersymmetry algebras and superbrane actions is further explored. It is proved that $SL(2,\bR)$ belongs to the automorphism group of the ${\cal N}=2$ D=10 type IIB SuperPoincar\'e algebra. Its SO(2) subgroup is identified ... More

Local smoothing results for the Ricci flow in dimensions two and threeSep 19 2012Jun 20 2013We present local estimates for solutions to the Ricci flow, without the assumption that the solution has bounded curvature. These estimates lead to a generalisation of one of the pseudolocality results of G.Perelman in dimension two.

A heteroclinic orbit connecting traveling waves pertaining to different nonlinearitiesJun 13 2017In this paper we consider a semilinear parabolic equation in an infinite cylinder. The spatially varying nonlinearity is such that it connects two (spatially independent) bistable nonlinearities in a compact set in space. We prove that, given such a setting, ... More

A multifractal zeta function for cookie cutter setsAug 13 2012Starting with the work of Lapidus and van Frankenhuysen a number of papers have introduced zeta functions as a way of capturing multifractal information. In this paper we propose a new multifractal zeta function and show that under certain conditions ... More

Constructive Gelfand duality for non-unital commutative C*-algebrasDec 05 2014Feb 03 2015We prove constructive versions of various usual results related to the Gelfand duality. Namely, that the constructive Gelfand duality extend to a duality between commutative nonunital C*-algebras and locally compact completely regular locales, that ideals ... More

Optimal Convergence Rates and One-Term Edgeworth Expansions for Multidimensional Functionals of Gaussian FieldsMay 28 2013Nov 11 2013We develop techniques for determining the exact asymptotic speed of convergence in the multidimensional normal approximation of smooth functions of Gaussian fields. As a by-product, our findings yield exact limits and often give rise to one-term generalized ... More

A counterexample to prism-hamiltonicity of 3-connected planar graphsJun 16 2019The prism over a graph $G$ is the Cartesian product of $G$ with the complete graph $K_2$. A graph $G$ is hamiltonian if there exists a spanning cycle in $G$, and $G$ is prism-hamiltonian if the prism over $G$ is hamiltonian. In [M.~Rosenfeld, D.~Barnette, ... More

Adiabatic limits of co-associative Kovalev-Lefschetz fibrationsMar 28 2016Apr 26 2016We study co-associative fibrations of G_{2}-manifolds. We propose that the adiabatic limit of this structure should be given locally by a maximal submanifold in a space of indefinite signature and set up global versions of the constructions.

Curves between Lipschitz and $C^1$ and their relation to geometric knot theoryFeb 29 2016In this article we investigate regular curves whose derivatives have vanishing mean oscillations. We show that smoothing these curves using a standard mollifier one gets regular curves again. We apply this result to solve a couple of open problems. We ... More

Local asymptotic normality for shape and periodicity of a signal in the drift of a degenerate diffusion with internal variablesMar 08 2019Aug 01 2019Taking a multidimensional time-homogeneous dynamical system and adding a randomly perturbed time-dependent deterministic signal to some of its components gives rise to a high-dimensional system of stochastic differential equations which is driven by possibly ... More

Meromorphic Szego functions and asymptotic series for Verblunsky coefficientsFeb 23 2005We prove that the Szeg\H{o} function, $D(z)$, of a measure on the unit circle is entire meromorphic if and only if the Verblunsky coefficients have an asymptotic expansion in exponentials. We relate the positions of the poles of $D(z)^{-1}$ to the exponential ... More

Green functions for the Dirac operator under local boundary conditions and applicationsMar 07 2007In this paper, we define the Green function for the Dirac operator under two local boundary conditions: the condition associated with a chirality operator (also called the chiral bag boundary condition) and the $\MIT$ bag boundary condition. Then we give ... More

A note on singularities in finite time for the constrained Willmore flowJul 05 2018This work investigates the formation of singularities under the steepest descent $L^2$-gradient flow of the functional $\mathcal W_{\lambda_1, \lambda_2}$, the sum of the Willmore energy, $\lambda_1$ times the area, and $\lambda_2$ times the signed volume ... More

Hyperplane Equipartitions Plus ConstraintsAug 01 2017Jul 22 2018While equivariant methods have seen many fruitful applications in geometric combinatorics, their inability to answer the now settled Topological Tverberg Conjecture has made apparent the need to move beyond the use of Borsuk--Ulam type theorems alone. ... More

Average-Value Tverberg Partitions via Finite Fourier AnalysisJan 19 2015Jul 25 2016The long-standing topological Tverberg conjecture claimed, for any continuous map from the boundary of an $N(q,d):=(q-1)(d+1)$-simplex to $d$-dimensional Euclidian space, the existence of $q$ pairwise disjoint subfaces whose images have non-empty $q$-fold ... More

A Dolbeault Isomorphism Theorem in Infinite DimensionsSep 27 2005For a large class of separable Banach spaces, we prove the real analytic Dolbeault Isomorphism Theorem for open subsets.

A theorem of Poincaré-Hopf typeMay 28 2009We compute (algebraically) the Euler characteristic of a complex of sheaves with constructible cohomology. A stratified Poincar\'e-Hopf formula is then a consequence of the smooth Poincar\'e-Hopf theorem and of additivity of the Euler-Poincar\'e characteristic ... More

Locality estimates for Fresnel-wave-propagation and stability of X-ray phase contrast imaging with finite detectorsMay 16 2018Nov 05 2018Coherent wave-propagation in the near-field Fresnel-regime is the underlying contrast-mechanism to (propagation-based) X-ray phase contrast imaging (XPCI), an emerging lensless technique that enables 2D- and 3D-imaging of biological soft tissues and other ... More

Mass Equidistribution for Automorphic Forms of Cohomological Type on GL_2Jun 16 2010Aug 13 2010We extend Holowinsky and Soundararajan's proof of quantum unique ergodicity for holomorphic Hecke modular forms on SL(2,Z), by establishing it for automorphic forms of cohomological type on GL_2 over an arbitrary number field which satisfy the Ramanujan ... More

Fonctions de Mittag-Leffler et processus de Lévy stables sans saut négatifApr 14 2009It is noticed that a certain transform of the Mittag-Leffler function Ea is completely monotone for a in [1,2]. Using the explicit expressions of its Bernstein density, an identity in law between suprema of completely asymmetric Levy a-stable processes. ... More

Bootstrapping the Mazur--Orlicz--König theoremDec 25 2015In this paper, we give some extensions of K\"onig's extension of the Mazur-Orlicz theorem. These extensions include generalizations of a surprising recent result of Sun Chuanfeng, and generalizations to the product of more than two spaces of the "Hahn-Banach-Lagrange" ... More

An almost-integral universal Vassiliev invariant of knotsMay 23 2001Sep 05 2002A `total Chern class' invariant of knots is defined. This is a universal Vassiliev invariant which is integral `on the level of Lie algebras' but it is not expressible as an integer sum of diagrams. The construction is motivated by similarities between ... More

Maximizing Riesz means of anisotropic harmonic oscillatorsDec 29 2017Oct 08 2018We consider problems related to the asymptotic minimization of eigenvalues of anisotropic harmonic oscillators in the plane. In particular we study Riesz means of the eigenvalues and the trace of the corresponding heat kernels. The eigenvalue minimization ... More

Front blocking versus propagation in the presence of a drift term in the direction of propagationMar 08 2018Oct 12 2018In this paper we derive quantitative conditions under which a compactly supported drift term depending on the direction of propagation blocks a traveling wave solution or lets it pass almost unchanged. We give explicit conditions on the drift term for ... More

Quasi-modularity of generalized sum-of-divisors functionsJun 16 2015Jul 24 2015In 1919, P. A. MacMahon studied generating functions for generalized divisor sums. In this paper, we provide a framework in which to view these generating functions in terms of Jacobi forms, and prove that they are quasi-modular forms.

Introduction to Modular FormsJul 04 2014We introduce the notion of modular forms, focusing primarily on the group PSL2Z. We further introduce quasi-modular forms, as wel as discuss their relation to physics and their applications in a variety of enumerative problems. These notes are based on ... More

A limit theorem for moments in space of the increments of Brownian local timeJun 24 2015Dec 01 2015We proof a limit theorem for moments in space of the increments of Brownian local time. As special cases for the second and third moments, previous results by Chen et al. (Ann. Prob. 38, 2010, no. 1) and Rosen (Stoch. Dyn. 11, 2011, no. 1), which were ... More

Positive Harris recurrence for degenerate diffusions with internal variables and randomly perturbed time-periodic inputJul 31 2019Aug 01 2019We consider a multidimensional time-homogeneous dynamical system and add a randomly perturbed time-dependent deterministic signal to some of its components, giving rise to a high-dimensional system of stochastic differential equations, which is driven ... More

The growth rate and dimension theory of beta-expansionsAug 30 2012Oct 15 2012In a recent paper of Feng and Sidorov they show that for $\beta\in(1,\frac{1+\sqrt{5}}{2})$ the set of $\beta$-expansions grows exponentially for every $x\in(0,\frac{1}{\beta-1})$. In this paper we study this growth rate further. We also consider the ... More

How to determine a K3 surface from a finite automorphismApr 29 2016Dec 13 2017In this article we pursue the question when an automorphism determines a (complex) K3 surface up to isomorphism. We prove that if the automorphism is finite non-symplectic and the transcendental lattice small, then the isomorphism class of the K3 surface ... More