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The chemical connection between 67P/C-G and IRAS 16293-2422Feb 08 2018The chemical evolution of a star- and planet-forming system begins in the prestellar phase and proceeds across the subsequent evolutionary phases. The chemical trail from cores to protoplanetary disks to planetary embryos can be studied by comparing distant ... More

Field structure and electron life times in the MEFISTO Electron Cyclotron Resonance Ion SourceFeb 01 2008The complex magnetic field of the permanent-magnet electron cyclotron resonance (ECR) ion source MEFISTO located at the University of Bern have been numerically simulated. For the first time the magnetized volume qualified for electron cyclotron resonance ... More

Molecular Oxygen in Oort Cloud Comet 1P/HalleyDec 05 2015Recently the ROSINA mass spectrometer suite on board the European Space Agency's Rosetta spacecraft discovered an abundant amount of molecular oxygen, O2, in the coma of Jupiter family comet 67P/Churyumov-Gerasimenko of O2/H2O = 3.80+/-0.85%. It could ... More

The ALMA-PILS survey: The sulphur connection between protostars and comets: IRAS 16293-2422 B and 67P/Churyumov-GerasimenkoFeb 08 2018The evolutionary past of our Solar System can be pieced together by comparing analogous low-mass protostars with remnants of our Protosolar Nebula - comets. Sulphur-bearing molecules may be unique tracers of the joint evolution of the volatile and refractory ... More

Identification of the ECR zone in the SWISSCASE ECR ion sourceJul 13 2008The magnetic field of the permanent magnet electron cyclotron resonance (ECR) ion source SWISSCASE located at the University of Bern has been numerically simulated and experimentally investigated. For the first time the magnetized volume qualified for ... More

Improved bounds for Fourier coefficients of Siegel modular formsMar 31 2016The goal of this paper is to improve existing bounds for Fourier coefficients of higher genus Siegel modular forms of small weight.

Optimal Shape of a Domain which minimizes the first Buckling EigenvalueDec 23 2015In this paper we prove the existence of an optimal domain which minimizes the buckling load of a clamped plate among all bounded domains with given measure. Instead of treating this variational problem with a volume constraint, we introduce a problem ... More

Sobolev index: A classification of Lévy processesMar 05 2012Apr 04 2012We classify L\'evy processes according to the solution spaces of the associated parabolic PIDEs. This classification reveals structural characteristics of the processes and is relevant for applications such as for solving PIDEs numerically for pricing ... More

The core in random hypergraphs and local weak convergenceNov 06 2015The degree of a vertex in a hypergraph is defined as the number of edges incident to it. In this paper we study the $k$-core, defined as the maximal induced subhypergraph of minimum degree $k$, of the random $r$-uniform hypergraph $H_r(n,p)$ for $r\geq ... More

Holomorphic projection for $\mathop{Sp}_2(\mathbb R)$ -- the case of weight $(4,4)$Feb 26 2016We define non-holomorphic Poincar\'e series of exponential type for symplectic groups $\mathop{Sp}_m(\mathbb R)$ and continue them analytically in case $m=2$ for the small weight $(4,4)$. For this we construct certain Casimir operators and study the spectral ... More

Feynman-Kac formula for Lévy processes with discontinuous killing rateFeb 26 2015Nov 04 2015The challenge to fruitfully merge state-of-the-art techniques from mathematical finance and numerical analysis has inspired researchers to develop fast deterministic option pricing methods. As a result, highly efficient algorithms to compute option prices ... More

Casimir operators for symplectic groupsNov 22 2010We give a full set of Casimir operators for the symplectic group of arbitrary genus in terms of a basis chosen such that the action on representations of known $K$-type becomes transparent. We give examples for the latter.

Asymptotics for rank partition functionsAug 05 2007In this paper, we obtain asymptotic formulas for an infinite class of rank generating functions. As an application, we solve a conjecture of Andrews and Lewis on inequalities between certain ranks.

On the explicit construction of higher deformations of partition statisticsJul 11 2007Dec 04 2007The modularity of the partition generating function has many important consequences, for example asymptotics and congruences for $p(n)$. In a series of papers the author and Ono \cite{BO1,BO2} connected the rank, a partition statistic introduced by Dyson, ... More

A generalisation of Zhang's local Gross-Zagier formulaMar 03 2010On the background of Zhang's local Gross-Zagier formulae for GL(2), we study some p-adic problems. The local Gross-Zagier formulae give identities of very special local geometric data (local linking numbers) with certain local Fourier coefficients of ... More

Sturm's operator for scalar weight in arbitrary genusSep 16 2016In contrast to the wellknown cases of large weights, Sturm's operator does not realize the holomorphic projection operator for lower weights. We prove its failure for arbitrary Siegel genus $m\geq 2$ and scalar weight $\kappa=m+1$. This generalizes a ... More

Polar harmonic Maass forms and their applicationsJun 02 2016In this survey, we present recent results of the authors about non-meromorphic modular objects known as polar harmonic Maass forms. These include the computation of Fourier coefficients of meromorphic modular forms and relations between inner products ... More

On a conjecture of Berndt and KimDec 20 2011We prove a recent conjecture of Berndt and Kim regarding the positivity of the coefficients in the asymptotic expansion of a class of partial theta functions. This generalizes results found in Ramanujan's second notebook, and recent work of Galway and ... More

The C*-algebra of SL(2,R)May 30 2016May 31 2016The $C^*$-algebra of the group $SL(2,{\mathbb R})$ is characterized using the operator valued Fourier transform. In particular, it is shown by explicit computations, that the Fourier transform of this $C^*$-algebra fulfills the norm controlled dual limit ... More

Overpartitions and class numbers of binary quadratic formsDec 04 2007We show that the Zagier-Eisenstein series shares its non-holomorphic part with certain weak Maass forms whose holomorphic parts are generating functions for overpartition rank differences. This has a number of consequences, including exact formulas, asymptotics, ... More

Inequalities for full rank differences of 2-marked Durfee symbolsFeb 09 2011Sep 27 2011In this paper, we obtain infinitely many non-trivial identities and inequalities between full rank differences for 2-marked Durfee symbols, a generalization of partitions introduced by Andrews. A certain strict inequality, which almost always holds, shows ... More

Schur's partition theorem and mixed mock modular formsJul 06 2013We study families of partitions with gap conditions that were introduced by Schur and Andrews, and describe their fundamental connections to combinatorial q-series and automorphic forms. In particular, we show that the generating functions for these families ... More

Translated points on hypertight contact manifoldsOct 02 2015A contact manifold admittting a supporting contact form without contractible Reeb orbits is called hypertight. In this paper we construct a Rabinowitz Floer homology associated to an arbitrary supporting contact form for a hypertight contact manifold, ... More

Embeddings of representationsJun 20 2014We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.

Non-embeddability of geometric lattices and buildingsNov 11 2012A fundamental question for simplicial complexes is to find the lowest dimensional Euclidean space in which they can be embedded. We investigate this question for order complexes of posets. We show that order complexes of thick geometric lattices as well ... More

Computational aspects of multigrid methods for optimization in shape spacesNov 16 2016We examine the interaction of multigrid methods and shape optimization in appropriate shape spaces. Our aim is a scalable algorithm for application on supercomputers, which can only be achieved by mesh-independent convergence. The impact of discrete approximations ... More

A Flexible Galerkin Scheme for Option Pricing in Lévy ModelsMar 27 2016One popular approach to option pricing in L\'evy models is through solving the related partial integro differential equation (PIDE). For the numerical solution of such equations powerful Galerkin methods have been put forward e.g. by Hilber et al. (2013). ... More

On the connectivity of manifold graphsJul 23 2012Oct 22 2013This paper is concerned with lower bounds for the connectivity of graphs (one-dimensional skeleta) of triangulations of compact manifolds. We introduce a structural invariant b_M for simplicial d-manifolds M taking values in the range 0 <= b_M <= d-1. ... More

Ramanujan and coefficients of meromorphic modular formsMar 23 2016The study of Fourier coefficients of meromorphic modular forms dates back to Ramanujan, who, together with Hardy, studied the reciprocal of the weight 6 Eisenstein series. Ramanujan conjectured a number of further identities for other meromorphic modular ... More

A problem of Petersson about weight 0 meromorphic modular formsMay 02 2015Mar 23 2016In this paper, we provide an explicit construction of weight $0$ meromorphic modular forms. Following work of Petersson, we build these via Poincar\'e series. There are two main aspects of our investigation which differ from his approach. Firstly, the ... More

Computational aspects of multigrid methods for optimization in shape spacesNov 16 2016Nov 18 2016We examine the interaction of multigrid methods and shape optimization in appropriate shape spaces. Our aim is a scalable algorithm for application on supercomputers, which can only be achieved by mesh-independent convergence. The impact of discrete approximations ... More

Optimality conditions for the buckling of a clamped plateAug 29 2014We prove the following uniqueness result for the buckling plate. Assume there exists a smooth domain which minimizes the first buckling eigenvalue for a plate among all smooth domains of given volume. Then the domain must be a ball. The proof uses the ... More

Multiplicative $q$-hypergeometric series arising from real quadratic fieldsDec 23 2008Andrews, Dyson, and Hickerson showed that 2 $q$-hypergeometric series, going back to Ramanujan, are related to real quadratic fields, which explains interesting properties of their Fourier coefficients. There is also an interesting relation of such series ... More

On the asymptotic behavior of unimodal rank generating functionsDec 23 2014In a recent paper, J. Lovejoy and the second author conjectured that ranks for four types of unimodal like sequences satisfy certain inequalities. In this paper, we prove these conjectures asymptotically. For this, we extend Wright's Circle Method and ... More

Pattern avoidance and the Bruhat order on involutionsNov 14 2007We show that the principal order ideal below an element w in the Bruhat order on involutions in a symmetric group is a Boolean lattice if and only if w avoids the patterns 4321, 45312 and 456123. Similar criteria for signed permutations are also stated. ... More

Simple Methods for Initializing the EM Algorithm for Gaussian Mixture ModelsDec 20 2013Aug 01 2016In this paper, we consider simple and fast approaches to initialize the Expectation-Maximization algorithm (EM) for multivariate Gaussian mixture models. We present new initialization methods based on the well-known $K$-means++ algorithm and the Gonzalez ... More

Phantom holomorphic projections arising from Sturm's formulaMay 06 2016We show the analytic continuation of certain Siegel Poincar\'e series to their critical point for weight three in genus two. We proof that this continuation posesses a nonhomomorphic part and describe it. We show that Sturm's operator also produces a ... More

Martingale Property in Terms of Semimartingale ProblemsMay 27 2016Jun 09 2016Starting from the seventies mathematicians face the question whether a non-negative local martingale is a true or a strict local martingale. In this article we answer this question from a semimartingale perspective. We connect the martingale property ... More

Ramanujan-like formulas for Fourier coefficients of all meromorphic cusp formsMar 30 2016Jul 11 2016In this paper, we investigate Fourier expansions of meromorphic modular forms. Over the years, a number of special cases of meromorphic modular forms were shown to have Fourier expansions closely resembling the expansion of the reciprocal of the weight ... More

Half-integral weight Eichler integrals and quantum modular formsSep 12 2014Aug 18 2015In analogy with the classical theory of Eichler integrals for integral weight modular forms, Lawrence and Zagier considered examples of Eichler integrals of certain half-integral weight modular forms. These served as early prototypes of a new type of ... More

Sums of class numbers and mixed mock modular formsMay 01 2013Nov 03 2013In this paper, we consider sums of class numbers of the type $\sum_{m\equiv a\pmod{p}} H(4n-m^2)$, where $p$ is an odd prime, $n\in \mathbb{N},$ and $a\in \mathbb{Z}$. By showing that these are coefficients of mixed mock modular forms, we obtain explicit ... More

Radial limits of mock theta functionsSep 12 2014Jul 25 2015Inspired by the original definition of mock theta functions by Ramanujan, a number of authors have considered the question of explicitly determining their behavior at the cusps. Moreover, these examples have been connected to important objects such as ... More

Asymptotic formulas for stacks and unimodal sequencesAug 30 2013We study enumeration functions for unimodal sequences of positive integers, where the size of a sequence is the sum of its terms. We survey known results for a number of natural variants of unimodal sequences, including Auluck's generalized Ferrer diagrams, ... More

Improved bounds on metastability thresholds and probabilities for generalized bootstrap percolationJan 12 2010Feb 26 2010We generalize and improve results of Andrews, Gravner, Holroyd, Liggett, and Romik on metastability thresholds for generalized two-dimensional bootstrap percolation models, and answer several of their open problems and conjectures. Specifically, we prove ... More

Dyson's Rank, overpartitions, and weak Maass formsAug 05 2007In a series of papers the first author and Ono connected the rank, a partition statistic introduced by Dyson, to weak Maass forms, a new class of functions which are related to modular forms. Naturally it is of wide interest to find other explicit examples ... More

A method for constructing random matrix models of disordered bosonsDec 17 2010Random matrix models of disordered bosons consist of matrices in the Lie algebra g=sp_n(R). Assuming dynamical stability, their eigenvalues are required to be purely imaginary. Here a method is proposed for constructing ensembles (E,P) of G-invariant ... More

From sheaves on P2 to a generalization of the Rademacher expansionJun 04 2010Oct 26 2011Moduli spaces of stable coherent sheaves on a surface are of much interest for both mathematics and physics. Yoshioka computed generating functions of Poincare polynomials of such moduli spaces if the surface is the projective plane P2 and the rank of ... More

On the Fourier expansion of Bloch-OkounkovDec 22 2014In this paper, we study algebraic and analytic properties of Fourier coefficients, expressed as $q$-series, of the so-called Bloch-Okounkov $n$-point function. We prove several results about these series and explain how they relate to Rogers' false theta ... More

Improved error bound for multivariate Chebyshev polynomial interpolationNov 26 2016Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For efficiency, ... More

On the positivity of black hole degeneracies in string theoryAug 16 2012Sep 14 2012Certain helicity trace indices of charged states in N=4 and N=8 superstring theory have been computed exactly using their explicit weakly coupled microscopic description. These indices are expected to count the exact quantum degeneracies of black holes ... More

A classification of harmonic Maass formsSep 22 2016We give a classification of the Harish-Chandra modules generated by the pullback to $\text{SL}_2(\mathbb R)$ of harmonic Maass forms for congruence subgroups of $\text{SL}_2(\mathbb Z)$ with exponential growth allowed at the cusps. We assume that the ... More

Rank-Crank type PDE's and non-holomorphic Jacobi formsJul 23 2008In this paper we show how Rank-Crank type PDE's (first found by Atkin and Garvan) occur naturally in the framework of non-holomorphic Jacobiforms and find an infinite family of such differential equations. As an application we show an infinite family ... More

Connectivity of chamber graphs of buildings and related complexesJul 02 2009Let \Delta be a finite building (or, more generally, a thick spherical and locally finite building). The chamber graph G(\Delta), whose edges are the pairs of adjacent chambers in \Delta, is known to be q-regular for a certain number q=q(\Delta). Our ... More

Hierarchical model reduction of nonlinear partial differential equations based on the adaptive empirical projection method and reduced basis techniquesJan 04 2014Jan 12 2016In this paper we extend the hierarchical model reduction framework based on reduced basis techniques for the application to nonlinear partial differential equations. The major new ingredient to accomplish this goal is the introduction of the adaptive ... More

Almost harmonic Maass forms and Kac-Wakimoto charactersDec 20 2011Mar 03 2013We resolve a question of Kac, and explain the automorphic properties of characters due to Kac-Wakimoto pertaining to sl(m|n)^ highest weight modules, for n \geq 1. We prove that the Kac-Wakimoto characters are essentially holomorphic parts of certain ... More

Polar harmonic Maass forms and their applicationsJun 02 2016Oct 30 2016In this survey, we present recent results of the authors about non-meromorphic modular objects known as polar harmonic Maass forms. These include the computation of Fourier coefficients of meromorphic modular forms and relations between inner products ... More

Modular local polynomialsMay 03 2014In this paper, we consider modular local polynomials. These functions satisfy modularity while they are locally defined as polynomials outside of an exceptional set. We prove an inequality for the dimension of the space of such forms when the exceptional ... More

Asymptotic formulas for coefficients of inverse theta functionsApr 26 2013Feb 05 2014We determine asymptotic formulas for the coefficients of a natural class of negative index and negative weight Jacobi forms. These coefficients can be viewed as a refinement of the numbers $p_k(n)$ of partitions of n into k colors. Part of the motivation ... More

Hecke duality relations of Jacobi formsNov 15 2007Dec 04 2007In this paper we introduce a new subspace of Jacobi forms of higher degree via certain relations among Fourier coefficients. We prove that this space can also be characterized by duality properties of certain distinguished embedded Hecke operators. We ... More

Approximation of skewed interfaces with tensor-based model reduction procedures: application to the reduced basis hierarchical model reduction approachJun 28 2014May 27 2016In this article we introduce a procedure, which allows to recover the potentially very good approximation properties of tensor-based model reduction procedures for the solution of partial differential equations in the presence of interfaces or strong ... More

Asymptotic inequalities for positive crank and rank momentsMay 10 2012Andrews, Chan, and Kim recently introduced a modified definition of crank and rank moments for integer partitions that allows the study of both even and odd moments. In this paper, we prove the asymptotic behavior of these moments in all cases, and our ... More

False theta functions and companions to Capparelli's identitiesApr 11 2014Jan 11 2015Capparelli conjectured two modular identities for partitions whose parts satisfy certain gap conditions, where were motivated by the calculation of characters for the standard modules of certain affine Lie algebras and by vertex operator theory. These ... More

On Dyson's crank conjecture and the uniform asymptotic behavior of certain inverse theta functionsNov 24 2013Jun 23 2014In this paper we prove a longstanding conjecture by Freeman Dyson concerning the limiting shape of the crank generating function. We fit this function in a more general family of inverse theta functions which play a key role in physics.

Using a model for telluric absorption in full-spectrum fitsDec 09 2013The typical approach for removing telluric absorption lines from a science spectrum is to divide it by the spectrum of a standard star of spectral type A or B observed close in time and airmass. We present a new method, where we use a model for the transmission ... More

Ricci Bounds for Euclidean and Spherical Cones (revised/extended version)Mar 01 2011We prove generalized lower Ricci bounds for Euclidean and spherical cones over complete Riemannian manifolds. These cones are regarded as complete metric measure spaces. In general, they will be neither manifolds nor Alexandrov spaces. We show that the ... More

A $\sim$32-70 K formation temperature range for the ice grains agglomerated by comet 67P/Churyumov-GerasimenkoApr 07 2015Grand Canonical Monte Carlo simulations are used to reproduce the N$_2$/CO ratio ranging between 1.7 $\times$ 10$^{-3}$ and 1.6 $\times$ 10$^{-2}$ observed {\it in situ} in the Jupiter family comet 67P/Churyumov-Gerasimenko by the ROSINA mass spectrometer ... More

On Symmetric Lepton Mixing MatricesNov 02 2006Nov 24 2006Contrary to the quark mixing matrix, the lepton mixing matrix could be symmetric. We study the phenomenological consequences of this possibility. In particular, we find that symmetry would imply that |U_{e3}| is larger than 0.16, i.e., above its current ... More

Low and High Energy Phenomenology of Quark-Lepton Complementarity ScenariosJul 10 2006Mar 16 2007We conduct a detailed analysis of the phenomenology of two predictive see-saw scenarios leading to Quark-Lepton Complementarity. In both cases we discuss the neutrino mixing observables and their correlations, neutrinoless double beta decay and lepton ... More

The C*-algebras of connected real two-step nilpotent Lie groupsSep 19 2014Using the operator valued Fourier transform, the C*-algebras of connected real two-step nilpotent Lie groups are characterized as algebras of operator fields defined over their spectra. In particular, it is shown by explicit computations, that the Fourier ... More

Effects of Axion-Photon Mixing on Gamma-Ray Spectra from Magnetized Astrophysical SourcesAug 08 2007Astrophysical gamma-ray sources come in a variety of sizes and magnetizations. We deduce general conditions under which gamma-ray spectra from such sources would be significantly affected by axion-photon mixing. We show that, depending on strength and ... More

Dynamic Hierarchical Reactive Controller SynthesisOct 25 2015Feb 15 2016In the formal approach to reactive controller synthesis, a symbolic controller for a possibly hybrid system is obtained by algorithmically computing a winning strategy in a two-player game. Such game-solving algorithms scale poorly as the size of the ... More

An exploratory study of Google ScholarJul 24 2007The paper discusses and analyzes the scientific search service Google Scholar (GS). The focus is on an exploratory study which investigates the coverage of scientific serials in GS. The study shows deficiencies in the coverage and up-to-dateness of the ... More

Localization and Tensorization Properties of the Curvature-Dimension Condition for Metric Measure SpacesMar 10 2010This paper is devoted to the analysis of metric measure spaces satisfying locally the curvature-dimension condition CD(K,N) introduced by the second author and also studied by Lott & Villani. We prove that the local version of CD(K,N) is equivalent to ... More

Ricci Bounds for Euclidean and Spherical ConesMar 10 2010We prove generalized lower Ricci bounds for Euclidean and spherical cones over compact Riemannian manifolds. These cones are regarded as complete metric measure spaces. We show that the Euclidean cone over an n-dimensional Riemannian manifold whose Ricci ... More

An algorithm for random signed 3-SAT with IntervalsMay 12 2011Aug 14 2013In signed k-SAT problems, one fixes a set M and a set $\mathcal S$ of subsets of M, and is given a formula consisting of a disjunction of m clauses, each of which is a conjunction of k literals. Each literal is of the form "$x \in S$", where $S \in \mathcal ... More

Nonautonomous control of stable and unstable manifolds in two-dimensional flowsAug 06 2013We outline a method for controlling the location of stable and unstable manifolds in the following sense. From a known location of the stable and unstable manifolds in a steady two-dimensional flow, the primary segments of the manifolds are to be moved ... More

A rough-and-ready cluster-based approach for extracting finite-time coherent sets from sparse and incomplete trajectory dataMay 18 2015Jun 23 2015We present a numerical method to identify regions of phase space that are approximately retained in a mobile compact neighbourhood over a finite time duration. Our approach is based on spatio-temporal clustering of trajectory data. The main advantages ... More

On the existence of infinitely many invariant Reeb orbitsNov 18 2014Nov 19 2014In this article we extend results of Grove and Tanaka on the existence of isometry-invariant geodesics to the setting of Reeb flows and strict contactomorphisms. Specifically, we prove that if M is a closed connected manifold with the property that the ... More

Tag Clusters as Information Retrieval InterfacesMar 04 2010The paper presents our design of a next generation information retrieval system based on tag co-occurrences and subsequent clustering. We help users getting access to digital data through information visualization in the form of tag clusters. Current ... More

Formulas for Jacobi forms and generalized Frobenius partitionsOct 05 2016Since their introduction by Andrews, generalized Frobenius partitions have interested a number of authors, many of whom have worked out explicit formulas for their generating functions in specific cases. This has uncovered interesting combinatorial structure ... More

Quasimodular forms and sl(m|m)^ charactersFeb 17 2013In this paper, we establish automorphic properties and asymptotic behaviors of characters due to Kac-Wakimoto pertaining to $s\ell(m|n)^\wedge$ highest weight modules in the case $m=n$, extending work of the first author and Ono \cite{BOKac} and the first ... More

Harmonic Maass-Jacobi forms with singularities and a theta-like decompositionJul 24 2012Mar 24 2014Real-analytic Jacobi forms play key roles in different areas of mathematics and physics, but a satisfactory theory of such Jacobi forms has been lacking. In this paper, we fill this gap by introducing a space of harmonic Maass-Jacobi forms with singularities ... More

Imaging the Earth's Interior: the Angular Distribution of Terrestrial NeutrinosMay 31 2004Decays of radionuclides throughout the Earth's interior produce geothermal heat, but also are a source of antineutrinos. The (angle-integrated) geoneutrino flux places an integral constraint on the terrestrial radionuclide distribution. In this paper, ... More

Clinical Validation of two Surface Imaging Systems for Patient Positioning in Percutaneous RadiotherapyFeb 11 2016Precise patient positioning and thus precise positioning of the planning target volume (PTV) is a prerequisite for effective treatment in percutaneous radiation therapy. Conventional imaging modalities used to ensure exact positioning for treatment typically ... More

Automorphic properties of generating functions for generalized rank moments and Durfee symbolsFeb 22 2008We define two-parameter generalizations of two combinatorial constructions of Andrews: the kth symmetrized rank moment and the k-marked Durfee symbol. We prove that three specializations of the associated generating functions are so-called quasimock theta ... More

Locally harmonic Maass forms and the kernel of the Shintani liftJun 06 2012Jan 22 2014In this paper we define a new type of modular object and construct explicit examples of such functions. Our functions are closely related to cusp forms constructed by Zagier which played an important role in the construction by Kohnen and Zagier of a ... More

Kohnen's limit process for real-analytic Siegel modular formsMay 27 2011Jun 08 2012Kohnen introduced a limit process for Siegel modular forms that produces Jacobi forms. He asked if there is a space of real-analytic Siegel modular forms such that skew-holomorphic Jacobi forms arise via this limit process. In this paper, we initiate ... More

Graphs and colorings for answer set programmingFeb 21 2005We investigate the usage of rule dependency graphs and their colorings for characterizing and computing answer sets of logic programs. This approach provides us with insights into the interplay between rules when inducing answer sets. We start with different ... More

Regularized inner products and errors of modularityMar 09 2016Sep 21 2016We develop a regularization for Petersson inner products of arbitrary weakly holomorphic modular forms, generalizing several known regularizations. As one application, we extend work of Duke, Imamoglu, and Toth on regularized inner products of weakly ... More

Analyticity of the Wiener-Hopf factors and valuation of exotic options in Lévy modelsNov 02 2009Oct 03 2010This paper considers the valuation of exotic path-dependent options in L\'evy models, in particular options on the supremum and the infimum of the asset price process. Using the Wiener--Hopf factorization, we derive expressions for the analytically extended ... More

A unified view of LIBOR modelsJan 06 2016Jul 10 2016We provide a unified framework for modeling LIBOR rates using general semimartingales as driving processes and generic functional forms to describe the evolution of the dynamics. We derive sufficient conditions for the model to be arbitrage-free which ... More

Magic points in finance: Empirical integration for parametric option pricingNov 03 2015Nov 04 2016We propose an offline-online procedure for Fourier transform based option pricing. The method supports the acceleration of such essential tasks of mathematical finance as model calibration, real-time pricing, and, more generally, risk assessment and parameter ... More

The cones of Hilbert functions of squarefree modulesJan 04 2012In this paper, we study different generalizations of the notion of squarefreeness for ideals to the more general case of modules. We describe the cones of Hilbert functions for squarefree modules in general and those generated in degree zero. We give ... More

Hard-Clustering with Gaussian Mixture ModelsMar 21 2016Training the parameters of statistical models to describe a given data set is a central task in the field of data mining and machine learning. A very popular and powerful way of parameter estimation is the method of maximum likelihood estimation (MLE). ... More

Identities for generalized Appell functions and the blow-up formulaOct 02 2015In this paper, we prove identities for a class of generalized Appell functions which are based on the $\operatorname{A}_2$ root lattice. The identities are reminiscent of periodicity relations for the classical Appell function, and are proven using only ... More

Automorphic properties of generating functions for generalized odd rank moments and odd Durfee symbolsAug 20 2010We define two-parameter generalizations of Andrews' $(k+1)$-marked odd Durfee symbols and $2k$th symmetrized odd rank moments, and study the automorphic properties of some of their generating functions. When $k=0$ we obtain families of modular forms and ... More

Maass-Jacobi Poincaré series and Mathieu MoonshineSep 15 2014Aug 18 2015Mathieu moonshine attaches a weak Jacobi form of weight zero and index one to each conjugacy class of the largest sporadic simple group of Mathieu. We introduce a modification of this assignment, whereby weak Jacobi forms are replaced by semi-holomorphic ... More

$p$-adic properties of modular shifted convolution Dirichlet seriesSep 02 2014Apr 15 2015Hoffstein and Hulse recently introduced the notion of shifted convolution Dirichlet series for pairs of modular forms $f_1$ and $f_2$. The second two authors investigated certain special values of symmetrized sums of such functions, numbers which are ... More

Formulas for Jacobi forms and generalized Frobenius partitionsOct 05 2016Oct 22 2016Since their introduction by Andrews, generalized Frobenius partitions have interested a number of authors, many of whom have worked out explicit formulas for their generating functions in specific cases. This has uncovered interesting combinatorial structure ... More

BREW: A Breakable Web Application for IT-Security Classroom UseJun 10 2015This paper presents BREW (Breakable Web Application), a tool for teaching IT Security. BREWs main teaching targets are identification and exploitation of vulnerabilities, using technologies and methodologies for software auditing and testing, and bug ... More