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Information Directed Sampling and Bandits with Heteroscedastic NoiseJan 29 2018Apr 19 2018In the stochastic bandit problem, the goal is to maximize an unknown function via a sequence of noisy evaluations. Typically, the observation noise is assumed to be independent of the evaluation point and to satisfy a tail bound uniformly on the domain; ... More

Correlators with $s\ell_2$ Yangian symmetryAug 17 2016Aug 25 2016Correlators based on $s\ell_2$ Yangian symmetry and its quantum deformation are studied. Symmetric integral operators can be defined with such correlators as kernels. Yang-Baxter operators can be represented in this way. Particular Yangian symmetric correlators ... More

Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional SubspacesFeb 08 2019Bayesian optimization is known to be difficult to scale to high dimensions, because the acquisition step requires solving a non-convex optimization problem in the same search space. In order to scale the method and keep its benefits, we propose an algorithm ... More

Information-Directed Exploration for Deep Reinforcement LearningDec 18 2018Efficient exploration remains a major challenge for reinforcement learning. One reason is that the variability of the returns often depends on the current state and action, and is therefore heteroscedastic. Classical exploration strategies such as upper ... More

Effective Action for Multi-Regge Processes in QCDFeb 02 1994We construct the effective Lagrangian describing QCD in the multi-Regge kinematics. It is obtained from the original QCD Lagrangian by eliminating modes of gluon and quark fields not appearing in this underlying kinematics.

On the local isomorphism property for families of K3 surfacesOct 26 2018We construct two families of K3 surfaces over a complex manifold $S$ such that the families are pointwise isomorphic but not locally isomorphic over $S$. This answers a question of Wehler from 1977 in the negative and challenges a more recent result of ... More

Extendability of parallel sections in vector bundlesJul 07 2014Aug 26 2015We address the following question: Given a differentiable manifold $M$ what are the open subsets $U$ of $M$ such that, for all vector bundles $E$ over $M$ and all linear connections $\nabla$ on $E$, any $\nabla$-parallel section in $E$ defined on $U$ ... More

Uniform stability of linear evolution equations, with applications to parallel transportsFeb 12 2015I prove the bistability of linear evolution equations $x' = A(t)x$ in a Banach space $E$, where the operator-valued function $A$ is of the form $A(t) = f'(t)G(t,f(t))$ for a binary operator-valued function $G$ and a scalar function $f$. The constant that ... More

The role of electron confinement in Pd films for the oscillatory magnetic anisotropy in an adjacent Co layerAug 18 2016We demonstrate the interplay between quantum well states in Pd and the magnetic anisotropy in Pd/Co/Cu(001) by combined scanning tunneling spectroscopy (STS) and magneto optical Kerr effect (MOKE) measurements. Low temperature scanning tunneling spectroscopy ... More

On the variation of the Poisson structures of certain moduli spacesOct 29 1997Given a Lie group G whose Lie algebra is endowed with a nondegenerate invariant symmetric bilinear form, we construct a Poisson algebra of continuous functions on a certain open subspace R of the space of representations in G of the fundamental group ... More

Poisson geometry of flat connections for $\roman{SU}(2)$-bundles on surfacesDec 14 1993In earlier work we have shown that the moduli space $N$ of flat connections for the (trivial) $\roman{SU(2)}$-bundle on a closed surface of genus $\ell \geq 2$ inherits a structure of stratified symplectic space with two connected strata $N_Z$ and $N_{(T)}$ ... More

The Casson-Walker-Lescop Invariant and Link InvariantsJul 11 2000Formulas previously presented for the Casson-Walker invariant are generalized to Lescop's extension. These formulas in terms of linking numbers and surgery coefficients compute the change in Lescop's invariant under crossing changes in a framed link presenting ... More

Quantum Field Theories Coupled to Supergravity: AdS/CFT and Local CouplingsNov 03 2007Nov 25 2007This article is based on my PhD thesis and covers the following topics: Holographic meson spectra in a dilaton flow background, the mixed Coulomb-Higgs branch in terms of instantons on D7 branes, and a dual description of heavy-light mesons. Moreover, ... More

Algebraic independence of generalized Morita-Miller-Mumford classesOct 06 2009Mar 09 2010The generalized Morita-Miller-Mumford classes of a smooth oriented manifold bundle are defined as the image of the characteristic classes of the vertical tangent bundle under the Gysin homomorphism. We show that if the dimension of the manifold is even, ... More

Duality between Wilson Loops and Scattering AmplitudesOct 21 2008Oct 27 2008We summarise the status of an intriguing new duality between planar maximally helicity violating scattering amplitudes and light-like Wilson loops in N=4 super Yang-Mills. In particular, we focus on the role played by (dual) conformal symmetry, which ... More

A brief introduction to Luttinger liquidsMay 05 2000I give a brief introduction to Luttinger liquids. Luttinger liquids are paramagnetic one-dimensional metals without Landau quasi-particle excitations. The elementary excitations are collective charge and spin modes, leading to charge-spin separation. ... More

Charge-Spin Separation and the Spectral Properties of Luttinger LiquidsOct 21 1993Oct 25 1993We compute the spectral function rho(q,omega) of the one- dimensional Luttinger model. We discuss the distinct influences of charge-spin separation and of the anomalous dimensions of the fermion operators and their evolution with correlation strength. ... More

DWSB for heterotic flux compactificationsMar 14 2011We investigate the construction of non-supersymmetric vacua in compactifications of heterotic string theory with intrinsic torsion and background fluxes. We do this by using the technique of domain-wall supersymmetry breaking (DWSB) that was developed ... More

Dynamics of gene expression and the regulatory inference problemDec 21 2007Mar 05 2008From the response to external stimuli to cell division and death, the dynamics of living cells is based on the expression of specific genes at specific times. The decision when to express a gene is implemented by the binding and unbinding of transcription ... More

Processes, Roles and Their InteractionsFeb 21 2012Taking an interaction network oriented perspective in informatics raises the challenge to describe deterministic finite systems which take part in networks of nondeterministic interactions. The traditional approach to describe processes as stepwise executable ... More

Combined Data Structure for Previous- and Next-Smaller-ValuesFeb 02 2011Let $A$ be a static array storing $n$ elements from a totally ordered set. We present a data structure of optimal size at most $n\log_2(3+2\sqrt{2})+o(n)$ bits that allows us to answer the following queries on $A$ in constant time, without accessing $A$: ... More

Optimal Succinctness for Range Minimum QueriesDec 15 2008Dec 02 2009For a static array A of n ordered objects, a range minimum query asks for the position of the minimum between two specified array indices. We show how to preprocess A into a scheme of size 2n+o(n) bits that allows to answer range minimum queries on A ... More

Quasiparticle properties of strongly correlated electron systems with itinerant metamagnetic behaviorApr 18 2008Jul 22 2009A brief account of the zero temperature magnetic response of a system of strongly correlated electrons in strong magnetic field is given in terms of its quasiparticle properties. The scenario is based on the paramagnetic phase of the half-filled Hubbard ... More

Minimal free multi models for chain algebrasMay 10 2004Jan 21 2005Let R be a local ring and A a connected differential graded algebra over R which is free as a graded R-module. Using homological perturbation theory techniques, we construct a minimal free multi model for A having properties similar to that of an ordinary ... More

On the cohomology of the holomorph of a finite cyclic groupMar 02 2003Feb 11 2004The mod 2 cohomology algebra of the holomorph of any finite cyclic group whose order is a power of 2 is determined.

Group field theories generating polyhedral complexesJun 28 2015Group field theories are a generalization of matrix models which provide both a second quantized reformulation of loop quantum gravity as well as generating functions for spin foam models. While states in canonical loop quantum gravity, in the traditional ... More

A short proof that every finite graph has a tree-decomposition displaying its tanglesNov 09 2015May 31 2016We give a short proof that every finite graph (or matroid) has a tree-decomposition that displays all maximal tangles. This theorem for graphs is a central result of the graph minors project of Robertson and Seymour and the extension to matroids is due ... More

Moyal-Weyl deformations of $\mathrm{DGA}$ and $\mathrm{DGCA}$Feb 13 2015Jul 28 2015We consider a natural variant of the Moyal-Weyl product and show that it yields a functorial deformation of differential graded algebras and that we can deform coalgebras in a similar way. The Moyal-Weyl deformation of graded algebras has already been ... More

Some notes on Euler productsDec 21 2014We focus on a well-known convergence phenomenon, the fact that the $\zeta$ zeros are the universal singularities of certain Euler products.

The Local Semicircle Law for Random Matrices with a Fourfold SymmetryJun 15 2015Oct 06 2015We consider real symmetric and complex Hermitian random matrices with the additional symmetry $h_{xy}=h_{N-x,N-y}$. The matrix elements are independent (up to the fourfold symmetry) and not necessarily identically distributed. This ensemble naturally ... More

Generalizations of a result of Jarnik on simultaneous approximationOct 24 2014Nov 23 2016Consider a non-increasing function $\Psi$ from the positive reals to the positive reals with decay $o(1/x)$ as $x$ tends to infinity. Jarnik proved in 1930 that there exist real numbers $\zeta_{1},...,\zeta_{k}$ together with $1$ linearly independent ... More

Berkovich skeleta and birational geometrySep 18 2014We give a survey of joint work with Mircea Musta\c{t}\u{a} and Chenyang Xu on the connections between the geometry of Berkovich spaces over the field of Laurent series and the birational geometry of one-parameter degenerations of smooth projective varieties. ... More

Singular propagators in deformation quantization and Shoikhet-Tsygan formalityJan 06 2015Jan 29 2015This paper adds some details to the seminal approach to logarithmic formality \cite{AWRT} and interpolation formality \cite{WR} by Alekseev, Rossi, Torossian and Willwacher: We prove that the interpolation family of Kontsevich formality maps extends to ... More

Continuity Results and Estimates for the Lyapunov Exponent of Brownian Motion in Random PotentialApr 04 2014May 14 2014We collect some applications of the variational formula established by Schr\"oder (1988) and Rue\ss (2013) for the quenched Lyapunov exponent of Brownian motion in stationary and ergodic nonnegative potential. We show for example that the Lyapunov exponent ... More

Two limitations of our knowledge of qualitySep 19 2016This article develops a quality notion that is complementary to the system notion. As a major consequence, it becomes clear why quality can be measured only to a certain extend based on the issues of validity and incompleteness. First, there is an inherent ... More

Determination of some exponents of approximation for Sturmian continued fractionsMar 29 2016We determine the classical approximation constants $w_{3}(\zeta),w_{3}^{\ast}(\zeta),\lambda_{3}(\zeta)$ such as the uniform constants $\widehat{w}_{3}(\zeta),\widehat{w}_{3}^{\ast}(\zeta),\widehat{\lambda}_{3}(\zeta)$ associated to real numbers $\zeta$ ... More

The Cohen-Lenstra Heuristic: Methodology and ResultsDec 25 2009In number theory, great efforts have been undertaken to study the Cohen-Lenstra probability measure on the set of all finite abelian $p$-groups. On the other hand, group theorists have studied a probability measure on the set of all partitions induced ... More

Counting zeros of holomorphic functions of exponential growthOct 02 2009We consider the number of zeros of holomorphic functions in a bounded domain that depend on a small parameter and satisfy an exponential upper bound near the boundary of the domain and similar lower bounds at finitely many points along the boundary. Roughly ... More

Group Extended Markov Systems, Amenability, and the Perron-Frobenius OperatorMay 23 2012Jun 04 2013We characterise amenability of a countable group in terms of the spectral radius of the Perron-Frobenius operator associated to a group extension of a countable Markov shift and a H\"older continuous potential. This extends a result of Day for random ... More

Formal and rigid geometry: an intuitive introduction, and some applicationsJan 19 2007Mar 25 2009We give an informal introduction to formal and rigid geometry over complete discrete valuation rings, and we discuss some applications in algebraic and arithmetic geometry and singularity theory, with special emphasis on recent applications to the Milnor ... More

Relative homological algebra, equivariant de Rham theory, and Koszul dualityJan 14 2004Oct 02 2008Let G be a general (not necessarily finite dimensional compact) Lie group, let g be its Lie algebra, let Cg be the cone on g in the category of differential graded Lie algebras, and consider the functor which assigns to a chain complex V the V-valued ... More

Homological perturbations, equivariant cohomology, and Koszul dualityJan 14 2004Jul 31 2009Our main objective is to demonstrate how homological perturbation theory (HPT) results over the last 40 years immediately or with little extra work give some of the Koszul duality results that have appeared in the last decade. Higher homotopies typically ... More

Piecewise constant local martingales with bounded numbers of jumpsDec 23 2016A piecewise constant local martingale $M$ with boundedly many jumps is a uniformly integrable martingale if and only if $M_\infty^-$ is integrable.

The Uniform Integrability of Martingales. On a Question by Alexander ChernyJan 23 2015May 01 2015Let $X$ be a progressively measurable, almost surely right-continuous stochastic process such that $X_\tau \in L^1$ and $E[X_\tau] = E[X_0]$ for each finite stopping time $\tau$. In 2006, Cherny showed that $X$ is then a uniformly integrable martingale ... More

Stratified Kaehler structures on adjoint quotientsApr 06 2004Nov 02 2006Given a compact Lie group, endowed with a bi-invariant Riemannian metric, its complexification inherits a Kaehler structure having twice the kinetic energy of the metric as its potential, and Kaehler reduction with reference to the adjoint action yields ... More

Severi varieties and holomorphic nilpotent orbitsJun 14 2002Jan 29 2004Each of the four critical Severi varieties arises from a minimal holomorphic nilpotent orbit in a simple regular rank 3 hermitian Lie algebra and each such variety lies as singular locus in a cubic--the chordal variety--in the corresponding complex projective ... More

A new approach toward boundedness in a two-dimensional parabolic chemotaxis system with singular sensitivityJan 21 2015We consider the parabolic chemotaxis model \[ u_t=\Delta u - \chi \nabla\cdot(\frac uv \nabla v), \qquad\qquad v_t=\Delta v - v + u\] in a smooth, bounded, convex two-dimensional domain and show global existence and boundedness of solutions for $\chi\in(0,\chi_0)$ ... More

Locally bounded global solutions to a chemotaxis consumption model with singular sensitivity and nonlinear diffusionAug 18 2016We show the existence of locally bounded global solutions to the chemotaxis system \[ u_t = \nabla\cdot(D(u)\nabla u) - \nabla\cdot(\frac{u}{v} \nabla v) \] \[ v_t = \Delta v - uv \] with homogeneous Neumann boundary conditions and suitably regular positive ... More

Minimal number of points with bad reduction for elliptic curves over P^1Jul 25 2010Jul 22 2011In this work we use elementary methods to discuss the question of the minimal number of points with bad reduction over the projective line for elliptic curves E/k(T) which are non-constant resp. have non-constant j-invariant.

A characterization of the locally finite networks admitting non-constant harmonic functions of finite energyMay 10 2011We characterize the locally finite networks admitting non-constant harmonic functions of finite energy. Our characterization unifies the necessary existence criteria of Thomassen and of Lyons and Peres with the sufficient criterion of Soardi. We also ... More

Uniqueness and Non-Uniqueness for Spin-Glass Ground States on TreesDec 06 2018We consider a Spin Glass at temperature $T = 0$ where the underlying graph is a locally finite tree. We prove for a wide range of coupling distributions that uniqueness of ground states is equivalent to the maximal flow from any vertex to $\infty$ (where ... More

Finding the Maximizers of the Information Divergence from an Exponential FamilyDec 23 2009This paper investigates maximizers of the information divergence from an exponential family $E$. It is shown that the $rI$-projection of a maximizer $P$ to $E$ is a convex combination of $P$ and a probability measure $P_-$ with disjoint support and the ... More

A Lower Bound for the Exponent of Convergence of Normal Subgroups of Kleinian GroupsMar 14 2012Jun 04 2013We give a short new proof that for each non-elementary Kleinian group $\Gamma$, the exponent of convergence of an arbitrary non-trivial normal subgroup is bounded below by half of the exponent of convergence of $\Gamma$, and that strict inequality holds ... More

On intrinsic and extrinsic rational approximation to Cantor setsDec 27 2018Jan 25 2019We provide various new results on a problem proposed by K. Mahler in 1984 concerning rational approximation to fractal sets by rational numbers inside and outside the set in question, respectively. Thereby we complement and generalize recent results of ... More

Berikashvili's functor D and the deformation equationJun 05 1999Berikashvili's functor D defined in terms of twisting cochains is related to deformation theory, gauge theory, Chen's formal power series connections, and the master equation in physics. The idea is advertised that some unification and understanding of ... More

Twilled Lie-Rinehart algebras and differential Batalin-Vilkovisky algebrasNov 10 1998Twilled L(ie)-R(inehart) algebas generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an almost twilled pre-LR algebra, which is a true twilled LR-algebra iff the almost complex structure ... More

Differential Batalin-Vilkovisky algebras arising from twilled Lie-Rinehart algebrasMar 14 2013Twilled L(ie-)R(inehart)-algebras generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an "almost twilled pre-LR algebra", which is a true twilled LR-algebra iff the almost complex structure ... More

From Jantzen to Andersen Filtration via Tilting EquivalenceNov 08 2010Jan 20 2011The space of homomorphisms from a projective object to a Verma module in category O inherits an induced filtration from the Jantzen filtration on the Verma module. On the other hand there is the Andersen filtration on the space of homomorphisms from a ... More

Recurrence and pressure for group extensionsMay 21 2012Jun 04 2013We investigate the thermodynamic formalism for recurrent potentials on group extensions of countable Markov shifts. Our main result characterises recurrent potentials depending only on the base space, in terms of the existence of a conservative product ... More

Infinite time blow-up of many solutions to a general quasilinear parabolic-elliptic Keller-Segel systemOct 25 2017We consider a parabolic-elliptic chemotaxis system generalizing \[ \begin{cases}\begin{split} & u_t=\nabla\cdot((u+1)^{m-1}\nabla u)-\nabla \cdot(u(u+1)^{\sigma-1}\nabla v)\\ & 0 = \Delta v - v + u \end{split}\end{cases} \] in bounded smooth domains $\Omega\subset ... More

Next-to-leading gluonic reggeons in the high-energy effective actionDec 19 1997Apr 08 1998We study the next-to-leading gluon exchange in the high-energy scattering that contributes to the amplitude to order $s^0$ up to logarithmic corrections. Similar to the leading gluon exchange these contribution can be described in terms of reggeon exchanges. ... More

Effective Action for High-Energy Scattering in GravityDec 09 1994The multi-Regge effective action is derived directly from the linearized gravity action. After excluding the redundant field components we separate the fields into momentum modes and integrate over modes which correspond neither to the kinematics of scattering ... More

Resummation of small x contributions to hard-scattering amplitudesSep 24 2009The summation of the small x corrections to hard scattering QCD amplitudes by collinear factorisation method is reconsidered and the K-factor is derived in leading log x approximation. The corresponding expression by Catani and Hautmann (1994) has to ... More

Finite quotients of three-dimensional complex toriJan 17 2017May 06 2017We provide a characterization of quotients of three-dimensional complex tori by finite groups that act freely in codimension one via a vanishing condition on the first and second orbifold Chern class. We also treat the case of actions free in codimension ... More

Eigenvalue distribution for non-self-adjoint operators with small multiplicative random perturbationsFeb 25 2008Dec 02 2009In this work we continue the study of the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint (pseudo)differential operators with small random perturbations, by treating the case of multiplicative perturbations in arbitrary dimension. ... More

Standard and non-standard metarefraction with confocal lenslet arraysJan 21 2009A recent paper demonstrated that two lenslet arrays with focal lengths f_1 and f_2, separated by f_1 + f_2, change the direction of transmitted light rays approximately like the interface between isotropic media with refractive indices n_1 and n_2, where ... More

A perturbation theory for the Anderson modelFeb 26 2013Nov 17 2014Within the diagrammatic real time approach \cite{K\"onig96, Schoeller97}, the current across a quantum dot which is tunnel coupled to two leads at different chemical potentials is calculated by the use of two objects referred to as kernels. The stationary ... More

Poisson structures on certain moduli spaces for bundles on a surfaceNov 23 1994Let $\Sigma$ be a closed surface, $G$ a compact Lie group, with Lie algebra $g$, and $\xi \colon P \to \Sigma$ a principal $G$-bundle. In earlier work we have shown that the moduli space $N(\xi)$ of central Yang- Mills connections, for appropriate additional ... More

Smooth structures on certain moduli spaces for bundles on a surfaceNov 23 1994Let $\Sigma$ be a closed surface, $G$ a compact Lie group, with Lie algebra $g$, $\xi \colon P \to \Sigma$ a principal $G$-bundle, let $N(\xi)$ denote the moduli space of central Yang-Mills connections on $\xi$, for suitably chosen additional data, and ... More

The singularities of Yang-Mills connections for bundles on a surface. II. The stratificationNov 22 1994Let $\Sigma$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $\xi \colon P \to \Sigma$ be a principal $G$-bundle, and pick a Riemannian metric ... More

Symplectic and Poisson structures of certain moduli spacesDec 14 1993Symplectic and Poisson structures of certain moduli spaces/Huebschmann,J./ Abstract: Let $\pi$ be the fundamental group of a closed surface and $G$ a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction ... More

Topological Bragg Peaks And How They Characterise Point SetsSep 29 2013Bragg peaks in point set diffraction show up as eigenvalues of a dynamical system. Topological Bragg peaks arrise from topological eigenvalues and determine the torus parametrisation of the point set. We will discuss how qualitative properties of the ... More

Non Commutative Geometry of Tilings and Gap LabellingMar 17 1994Apr 22 1994To a given tiling a non commutative space and the corresponding C*-algebra are constructed. This includes the definition of a topology on the groupoid induced by translations of the tiling. The algebra is also the algebra of observables for discrete models ... More

Topological equivalence of tilingsSep 26 1996We introduce a notion of equivalence on tilings which is formulated in terms of their local structure. We compare it with the known concept of locally deriving one tiling from another and show that two tilings of finite type are topologically equivalent ... More

Constraining fast-roll inflationMay 25 2012Sep 10 2012We present constraints on how far single field inflation may depart from the familiar slow-roll paradigm. Considering a fast-roll regime while requiring a (near)-scale-invariant power spectrum introduces large self-interactions for the field and consequently ... More

Status of Polarized and Unpolarized Deep Inelastic ScatteringOct 16 2005The current status of deep inelastic scattering is briefly reviewed. We discuss future theoretical developments desired and measurements needed to further complete our understanding of the picture of nucleons at short distances.

Harmonic Sums and Mellin TransformsJun 24 1999The finite and infinite harmonic sums form the general basis for the Mellin transforms of all individual functions $f_i(x)$ describing inclusive quantities such as coefficient and splitting functions which emerge in massless field theories. We discuss ... More

${\cal O}(α^2 L^2)$ radiative corrections to deep inelastic $ep$ scattering for different kinematical variablesMar 22 1994The QED radiative corrections are calculated in the leading log approximation up to ${\cal O}(\alpha^2)$ for different definitions of the kinematical variables using jet measurement, the 'mixed' variables, the double angle method, and a measurement based ... More

Generalizations of a result of Jarnik on simultaneous approximationOct 24 2014Mar 08 2016Consider a non-increasing function $\Psi$ from the positive reals to the positive reals with decay $o(1/x)$ as $x$ tends to infinity. Jarnik proved in 1930 that there exist real numbers $\zeta_{1},...,\zeta_{k}$ together with $1$ linearly independent ... More

Slices for lifted tangent and cotangent actionsSep 02 2005Given a Lie group G, a G-manifold M, and a point b of M with compact stabilizer, we construct slices for the lifted tangent and cotangent actions at a pre-image of b in terms of a slice for the G-action on M at the point b. We interpret the slice for ... More

Deconvolution with unknown error distributionMay 23 2007Aug 21 2009We consider the problem of estimating a density $f_X$ using a sample $Y_1,...,Y_n$ from $f_Y=f_X\star f_{\epsilon}$, where $f_{\epsilon}$ is an unknown density. We assume that an additional sample $\epsilon_1,...,\epsilon_m$ from $f_{\epsilon}$ is observed. ... More

Inducing the LCP-ArrayJan 18 2011We show how to modify the linear-time construction algorithm for suffix arrays based on induced sorting (Nong et al., DCC'09) such that it computes the array of longest common prefixes (LCP-array) as well. Practical tests show that this outperforms recent ... More

The universal Hopf algebra associated with a Hopf-Lie-Rinehart algebraFeb 26 2008We introduce a notion of Hopf-Lie-Rinehart algebra and show that the universal algebra of a Hopf-Lie-Rinehart algebra acquires an ordinary Hopf algebra structure.

Exact sequences in the cohomology of a group extensionMar 13 2013Aug 15 2015In [J. of Alg. 369: 70-95, 2012], the authors constructed a seven term exact sequence in the cohomology of a group extension G of a normal subgroup N by a quotient group Q with coefficients in a G-module M. However, they were unable to establish the precise ... More

Geometric invariants for non-archimedean semialgebraic setsMar 29 2016This survey paper explains how one can attach geometric invariants to semialgebraic sets defined over non-archimedean fields, using the theory of motivic integration of Hrushovski and Kazhdan. It also discusses tropical methods to compute these invariants ... More

On canonical bases and induction of $W$-graphsNov 11 2014A canonical basis in the sense of Lusztig is a basis of a free module over a ring of Laurent polynomials that is invariant under a certain semilinear involution and is obtained from a fixed "standard basis" through base change matrix with polynomials ... More

On Consistent Kinetic and Derivative Interactions for GravitonsSep 26 2014Apr 20 2015The only known fully ghost-free and consistent Lorentz-invariant kinetic term for a graviton (or indeed for any spin-2 field) is the Einstein-Hilbert term. Here we propose and investigate a new family of candidate kinetic interactions and their extensions ... More

On the rate of accumulation of $αζ^{n}$ mod 1 to 0Jan 29 2014In this paper we study the distribution of the sequence $(\alpha \zeta^{n})_{n\geq 1}$ mod $1$, where $\alpha,\zeta$ are fixed positive real numbers, with special focus on the accumulation point $0$. For this purpose we introduce approximation constants ... More

On Approximation constants for Liouville numbersSep 04 2014Jan 08 2015We investigate some Diophantine approximation constants related to the simultaneous approximation of $(\zeta,\zeta^{2},\ldots,\zeta^{k})$ for Liouville numbers $\zeta$. For a certain class of Liouville numbers including the famous representative $\sum_{n\geq ... More

A statistical test for Nested Sampling algorithmsJul 21 2014Dec 02 2014Nested sampling is an iterative integration procedure that shrinks the prior volume towards higher likelihoods by removing a "live" point at a time. A replacement point is drawn uniformly from the prior above an ever-increasing likelihood threshold. Thus, ... More

Paradigm shifts. Part II. Reverse Transcriptase. Analysis of reference stability and word frequenciesDec 07 2014Dec 09 2014The reverse transcription paradigm shift in RNA tumor virus research marked by the discovery of the reverse transcriptase in 1970 was traced using co-citation and title word frequency analysis. It is shown that this event is associated with a break in ... More

On the C*-algebraic approach to topological phases for insulatorsSep 21 2015Dec 22 2015The notion of a topological phase of an insulator is based on the concept of homotopy between Hamiltonians. It therefore depends on the choice of a topological space to which the Hamiltonians belong. We advocate that this space should be the $C^*$-algebra ... More

Rust-Bio - a fast and safe bioinformatics librarySep 09 2015We present Rust-Bio, the first general purpose bioinformatics library for the innovative Rust programming language. Rust-Bio leverages the unique combination of speed, memory safety and high-level syntax offered by Rust to provide a fast and safe set ... More

Descent of algebraic cyclesJun 08 2015We characterize universally generalizing morphisms which satisfy descent of algebraic cycles integrally as those universally generalizing morphisms which are surjective with generically reduced fibres. In doing so, we introduce a naive pull-back of cycles ... More

Pionless Effective Field Theory in Few-Nucleon SystemsJun 01 2015Jun 02 2015A systematic description of low-energy observables in light nuclei is presented. The effective field theory formalism without pions is extended to: i) predictions with next-to-leading-order (non-perturbatively) accuracy for the 4-helium binding energy ... More

On self-adjointness of Poisson summationJan 04 2015Oct 14 2015We show that a combination of well-known operators, namely $\I{\tau}\circ{H}\circ\Ps$ is self-adjoint and {\em ad-hoc} related to the $\zeta$ function. Here ${\tau}$ is an involution appearing in Weil's positivity criteria needed for hermitrization, $H$ ... More

Statistical mechanics of the inverse Ising problem and the optimal objective functionNov 14 2016The inverse Ising problem seeks to reconstruct the parameters of an Ising Hamiltonian on the basis of spin configurations sampled from the Boltzmann measure. Recently, strategies to solve the inverse Ising problem based on convex optimisation have proven ... More

New Methods to Improve Large-Scale Microscopy Image Analysis with Prior Knowledge and UncertaintyAug 30 2016Multidimensional imaging techniques provide powerful ways to examine various kinds of scientific questions. The routinely produced datasets in the terabyte-range, however, can hardly be analyzed manually and require an extensive use of automated image ... More

The spectrogram expansion of Wigner functionsJul 01 2016Wigner functions generically attain negative values and hence are not probability densities. We prove an asymptotic expansion of Wigner functions in terms of Hermite spectrograms, which are probability densities. The expansion provides exact formulas ... More

Sections, Homotopy Rational Points and Reductions of CurvesJul 14 2015Sep 01 2016We study unramified sections of the fundamental group sequence of smooth projective curves of genus $\geq 2$ over $p$-adic fields together with an integral model. We are particularly interested in the induced specialized sections of the special fibre ... More