Results for "Simon Dixon"

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Adversarial Semi-Supervised Audio Source Separation applied to Singing Voice ExtractionOct 31 2017The state of the art in music source separation employs neural networks trained in a supervised fashion on multi-track databases to estimate the sources from a given mixture. With only few datasets available, often extensive data augmentation is used ... More
Note Value Recognition for Piano Transcription Using Markov Random FieldsMar 23 2017Jul 07 2017This paper presents a statistical method for use in music transcription that can estimate score times of note onsets and offsets from polyphonic MIDI performance signals. Because performed note durations can deviate largely from score-indicated values, ... More
Similarity measures for vocal-based drum sample retrieval using deep convolutional auto-encodersFeb 14 2018The expressive nature of the voice provides a powerful medium for communicating sonic ideas, motivating recent research on methods for query by vocalisation. Meanwhile, deep learning methods have demonstrated state-of-the-art results for matching vocal ... More
Seeable matter; unseeable antimatterJul 16 2014The universe we see gives every sign of being composed of matter. This is considered a major unsolved problem in theoretical physics. Using the mathematical modeling based on the algebra ${\bf{T}} := {\bf{C}}\otimes{\bf{H}}\otimes{\bf{O}}$, an interpretation ... More
Regular ambitoric $4$-manifolds: from Riemannian Kerr to a complete classificationApr 11 2016Jun 22 2016We show that the conformal structure for the Riemannian analogues of Kerr black-hole metrics can be given an ambitoric structure. We then discuss the properties of the moment maps. In particular, we observe that the moment map image is not locally convex ... More
An End-to-End Neural Network for Polyphonic Piano Music TranscriptionAug 07 2015Feb 11 2016We present a supervised neural network model for polyphonic piano music transcription. The architecture of the proposed model is analogous to speech recognition systems and comprises an acoustic model and a music language model. The acoustic model is ... More
Sequential Complexity as a Descriptor for Musical SimilarityFeb 27 2014Sep 28 2014We propose string compressibility as a descriptor of temporal structure in audio, for the purpose of determining musical similarity. Our descriptors are based on computing track-wise compression rates of quantised audio features, using multiple temporal ... More
Identifying Cover Songs Using Information-Theoretic Measures of SimilarityJul 09 2014May 17 2015This paper investigates methods for quantifying similarity between audio signals, specifically for the task of of cover song detection. We consider an information-theoretic approach, where we compute pairwise measures of predictability between time series. ... More
Robust Joint Alignment of Multiple Versions of a Piece of MusicApr 28 2016Large music content libraries often comprise multiple versions of a piece of music. To establish a link between different versions, automatic music alignment methods map each position in one version to a corresponding position in another version. Due ... More
Classiffication-based Financial Markets Prediction using Deep Neural NetworksMar 29 2016Deep neural networks (DNNs) are powerful types of artificial neural networks (ANNs) that use several hidden layers. They have recently gained considerable attention in the speech transcription and image recognition community (Krizhevsky et al., 2012) ... More
Network Traffic Obfuscation and Automated Internet CensorshipMay 13 2016Internet censors seek ways to identify and block internet access to information they deem objectionable. Increasingly, censors deploy advanced networking tools such as deep-packet inspection (DPI) to identify such connections. In response, activists and ... More
The Far Ultraviolet Spectroscopic Explorer Survey of OVI Emission in the Milky WayMay 05 2006We present a survey of OVI 1032 emission in the Milky Way using data from the Far Ultraviolet Spectroscopic Explorer (FUSE) satellite. The observations span the period from launch in 1999 to July 2003. Our survey contains 112 sight lines, 23 of which ... More
A Hybrid Recurrent Neural Network For Music TranscriptionNov 06 2014We investigate the problem of incorporating higher-level symbolic score-like information into Automatic Music Transcription (AMT) systems to improve their performance. We use recurrent neural networks (RNNs) and their variants as music language models ... More
Bootstrapping a Five-Loop Amplitude from Steinmann RelationsSep 02 2016The analytic structure of scattering amplitudes is restricted by Steinmann relations, which enforce the vanishing of certain discontinuities of discontinuities. We show that these relations dramatically simplify the function space for the hexagon function ... More
Bootstrapping a Five-Loop Amplitude Using Steinmann RelationsSep 02 2016Nov 28 2016The analytic structure of scattering amplitudes is restricted by Steinmann relations, which enforce the vanishing of certain discontinuities of discontinuities. We show that these relations dramatically simplify the function space for the hexagon function ... More
Calculating Scattering Amplitudes EfficientlyJan 29 1996Dec 11 1996We review techniques for more efficient computation of perturbative scattering amplitudes in gauge theory, in particular tree and one-loop multi-parton amplitudes in QCD. We emphasize the advantages of (1) using color and helicity information to decompose ... More
Strings and Supersymmetry as Tools for Perturbative QCDJul 04 1995We review techniques simplifying the analytic calculation of one-loop QCD amplitudes with many external legs, for use in next-to-leading-order corrections to multi-jet processes. We explain how a supersymmetry-inspired organization works well in conjunction ... More
The SSM with Suppressed SUSY ChargeApr 21 2016May 18 2016An earlier paper showed that it is possible to write down new SUSY Actions in which it is not possible to define a Supersymmetry Charge. SUSY is defined in these new Actions by the fact that they satisfy Master Equations. The new SUSY Actions are very ... More
Detailed Calculations of the Mass Spectrum for the Leptons after Supersymmetry Breaking in the Supersymmetric Standard Model: Cybersusy IVAug 17 2008This is the fourth of a series of four papers introducing cybersusy, which is a new approach to supersymmetry breaking in the supersymmetric standard model. This paper contains a brief summary, and then goes on to the calculation of the propagators and ... More
Supersymmetry Anomalies, the Witten Index and the Standard ModelNov 17 1993The supersymmetric standard model (SSM) contains a wealth of potential supersymmetry anomalies, all of which occur in the renormalization of composite operators of the theory. The coefficients of the weak-E.M. superanomalies should be related to the Witten ... More
Some Composite Hadrons and Leptons which induce Supersymmetry Breaking in the Supersymmetric Standard Model: Cybersusy IIIAug 16 2008This is the third paper in a series of four papers which introduce cybersusy, which is a new mechanism for supersymmetry breaking in the supersymmetric standard model (SSM). In this paper we display some solutions to the constraint equations of BRS cohomology ... More
Composite Operators, Supersymmetry Anomalies and Supersymmetry Breaking in the Wess-Zumino ModelMar 17 2003The field equations of the auxiliary fields are nonlinear and free of derivatives. Hence, it is argued, a Legendre transform to generate the 1PI Generating Functionals is not correct for the auxiliary fields. A corrected formulation of the BRS symmetry ... More
BRS Cohomology, Composite Operators and the Supersymmetric Standard ModelJan 20 2006Jan 21 2006Supersymmetry might be broken, in the real world, by anomalies that affect composite operators, while leaving the action supersymmetric. New constraint equations that govern the composite operators and their anomalies are examined. It is shown that the ... More
A supersymmetric version of the quark model, and supersymmetry breaking for the Leptons, Baryons and Hadronic Mesons: Cybersusy VAug 27 2008Mar 14 2009Cybersusy is a new mechanism for supersymmetry breaking in the standard supersymmetric model (SSM). Here we note that the superpotential for the SSM has a set of thirteen invariances, five of which are well known, and eight of which are new. The eight ... More
Binary star influence on post-main-sequence multi-planet stabilityOct 17 2016Nearly every star known to host planets will become a white dwarf, and nearly 100 planet-hosts are now known to be accompanied by binary stellar companions. Here, we determine how a binary companion triggers instability in otherwise unconditionally stable ... 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
Cybersusy Solves the Cosmological Constant ProblemJun 11 2010Jun 15 2016Cybersusy is a new mechanism for SUSY breaking. When the auxiliary fields are integrated in any theory like the SSM, certain special new composite superfields arise. Spontaneous breaking of internal symmetry, like SU(2) X U(1) to U(1), gives rise to a ... More
Chiral SUSY Theories with a Suppressed SUSY ChargeApr 21 2016May 18 2016The well-known Chiral and Gauge SUSY Actions realize the SUSY charge in terms of transformations among the Fields. These transformations are included in the Master Equation by coupling them to Sources. Here we show that there are new local SUSY Actions ... More
Introduction to the BRS Cohomology of the Massless Wess Zumino Model: Cybersusy IIAug 16 2008This paper is the second paper in a series of four papers that introduce cybersusy, which is a new method for analyzing supersymmetry breaking in the standard supersymmetric model (SSM). The first paper was a summary of the results and the three next ... More
Supersymmetry Breaks when Gauge Symmetry Breaks: Cybersusy IAug 06 2008This paper summarizes a new approach to supersymmetry breaking in the supersymmetric standard model (SSM). The approach arises from some remarkable features of the BRS cohomology for composite operators in the SSM, and the behaviour of those operators ... More
A Resolution Prover for Coalition LogicApr 03 2014We present a prototype tool for automated reasoning for Coalition Logic, a non-normal modal logic that can be used for reasoning about cooperative agency. The theorem prover CLProver is based on recent work on a resolution-based calculus for Coalition ... 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
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
One way cuts in oriented graphsDec 28 2007Nov 19 2010This paper has been withdrawn by the author.
(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
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
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.
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
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
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
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.
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
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
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
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.
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.
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
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
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
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
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
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.
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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