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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 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

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

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

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

Correlators with $s\ell_2$ Yangian symmetryAug 17 2016Nov 11 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

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

Information-Directed Exploration for Deep Reinforcement LearningDec 18 2018Mar 25 2019Efficient 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

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

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

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

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

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

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

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

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.

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

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

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

Comment on "Under-reported data analysis with INAR-hidden Markov chains"Dec 17 2018In Fernandez-Fontelo et al (Statis. Med. 2016, DOI 10.1002/sim.7026) hidden integer-valued autoregressive (INAR) processes are used to estimate reporting probabilities for various diseases. In this comment it is demonstrated that the Poisson INAR(1) model ... 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

Index theory in spaces of manifoldsAug 04 2016Jan 25 2019We formulate and prove a generalization of the Atiyah-Singer family index theorem in the context of the theory of spaces of manifolds \`a la Madsen, Tillmann, Weiss, Galatius and Randal-Williams. Our results are for Dirac-type operators linear over arbitrary ... 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

Oblivious Sorting and QueuesDec 10 2016We present a deterministic oblivious LIFO (Stack), FIFO, double-ended and double-ended priority queue as well as an oblivious mergesort and quicksort algorithm. Our techniques and ideas include concatenating queues end-to-end, size balancing of multiple ... 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

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

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

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

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

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

Diophantine approximation in prescribed degreeJan 04 2017Dec 19 2017We investigate approximation to a given real number by algebraic numbers and algebraic integers of prescribed degree. We deal with both best and uniform approximation, and highlight the similarities and differences compared with the intensely studied ... More

On the discrepancy between best and uniform approximationJan 04 2017Dec 19 2017For $\zeta$ a transcendental real number, we consider the classical Diophantine exponents $w_{n}(\zeta)$ and $\widehat{w}_{n}(\zeta)$. They measure how small $| P(\zeta)|$ can be for an integer polynomial $P$ of degree at most $n$ and naive height bounded ... 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

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

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

Lie-Rinehart algebras, descent, and quantizationMar 02 2003A Lie-Rinehart algebra consists of a commutative algebra and a Lie algebra with additional structure which generalizes the mutual structure of interaction between the algebra of functions and the Lie algebra of smooth vector fields on a smooth manifold. ... More

Kaehler spaces, nilpotent orbits, and singular reductionApr 23 2001Aug 13 2002For a stratified symplectic space, a suitable concept of stratified Kaehler polarization, defined in terms of an appropriate Lie-Rinehart algebra, encapsulates Kaehler polarizations on the strata and the behaviour of the polarizations across the strata ... 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

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

Line bundles on moduli and related spacesJul 30 2009Let G be a Lie goup, let M and N be smooth connected G-manifolds, let f be a smooth G-map from M to N, and let P denote the fiber of f. Given a closed and equivariantly closed relative 2-form for f with integral periods, we construct the principal G-circle ... 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.

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.

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

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

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

Secret Sharing and Shared InformationJun 21 2017Nov 10 2017Secret sharing is a cryptographic discipline in which the goal is to distribute information about a secret over a set of participants in such a way that only specific authorized combinations of participants together can reconstruct the secret. Thus, secret ... 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

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

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

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

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

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

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

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

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

Quarkonium Spectroscopy: Beyond One-Gluon ExchangeJul 09 2007In this work an improved potential model for quarkonium spectra (charmonium, bottomonium) is constructed. Beside the one-gluon exchange and a linear confinement potential, the model includes systematically effects from two-gluon exchange and the induced ... More

On uniform approximation to successive powers of a real numberMar 30 2016Apr 20 2016We establish new inequalities involving classical exponents of Diophantine approximation. This allows for improving on the work of Davenport, Schmidt and Laurent concerning the maximum value of the exponent $\hat{\lambda}_{n}(\zeta)$ among all real transcendental ... More

Duality for Lie-Rinehart algebras and the modular classFeb 08 1997Jan 29 2004We introduce a notion of duality for a Lie-Rinehart algebra giving certain bilinear pairings in its cohomology generalizing the usual notions of Poincar\'e duality in Lie algebra cohomology and de Rham cohomology. We show that the duality isomorphisms ... More

The singularities of Yang-Mills connections for bundles on a surface. I. The local modelNov 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

Topological quantization of boundary forces and the integrated density of statesNov 08 2003For quantum systems described by Schr\"odinger operators on the half-space $\RR^{d-1}\times\RR^{leq 0}$ the boundary force per unit area and unit energy is topologically quantised provided the Fermi energy lies in a gap of the bulk spectrum. Under this ... More

On The Algebraic Characterization of Aperiodic Tilings Related To ADE-Root SystemsOct 14 1992Dec 30 1992\noindent The algebraic characterization of classes of locally isomorphic aperiodic tilings, being examples of quantum spaces, is conducted for a certain type of tilings in a manner proposed by A. Connes. These $2$-dimensional tilings are obtained by ... More

Comments on the distinction between color- and flavor-branes and new D3-D7 solutions with eight superchargesJul 07 2010We investigate the distinction between color- and flavor-branes, that is usually made in the context of gauge/string duality with backreacting flavors. Our remarks are based on a series of examples concerning the role of source terms in relatively simple ... More

Nonparametric estimation in functional linear models with second order stationary regressorsJan 27 2009We consider the problem of estimating the slope parameter in functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of second order stationary random functions X1,...,Xn. An orthogonal series estimator of the functional ... More

Deformations of asymptotically cylindrical G_2 manifoldsMay 30 2007Mar 11 2009We prove that for a 7-dimensional manifold M with cylindrical ends the moduli space of exponentially asymptotically cylindrical torsion-free G_2 structures is a smooth manifold (if non-empty), and study some of its local properties. We also show that ... More

Discovery Potential of MSSM Higgs Bosons with ATLASDec 19 2005In this article the potential of the ATLAS experiment to discover MSSM Higgs bosons is discussed. Various Monte-Carlo studies for SM Higgs boson production and dedicated MSSM Higgs boson analyses are taken into account to investigate the discovery potential ... More

Results on searches for new physics at HERAMay 13 2003The H1 and ZEUS collaborations have searched for signals of physics beyond the Standard Model in ep collisions at a center-of-mass energy of 301-319 GeV. During the HERA I phase each experiment accumulated an integrated luminosity of about 110 pb^{-1} ... More

BPS-like potential for compactifications of heterotic M-theory?Sep 09 2011Nov 07 2011We analyze the possibility to rewrite the action of Horava-Witten theory in a BPS-like form, which means that it is given as a sum of squares of the supersymmetry conditions. To this end we compactify the theory on a seven dimensional manifold of SU(3) ... More

Mutual information in interacting spin systemsMar 18 2013This thesis uses a quantity that is defined and justified by information theory -- mutual information -- to examine models of condensed matter systems. More precisely, it studies models which are made up out of ferromagnetically interacting spins. Quantum ... More

Recent development in parton shower multijet mergingJul 07 2016Higher order calculations are necessary to predict and describe measurements in high energy collider physics. In recent years multiple approaches to combine multiple next-to-leading (NLO) order corrections with parton showers had been presented. We present ... More

Efficient Completion of Weighted AutomataSep 13 2016We consider directed graphs with edge labels from a semiring. We present an algorithm that allows efficient execution of queries for existence and weights of paths, and allows updates of the graph: adding nodes and edges, and changing weights of existing ... More

Some notes on the regular graph defined by Schmidt and Summerer and uniform approximationJan 05 2016Jan 12 2016Within the study of parametric geometry of numbers W. Schmidt and L. Summerer introduced so-called regular graphs. Roughly speaking the successive minima functions for the classical simultaneous Diophantine approximation problem have a very special pattern ... More

Secure Numerical and Logical Multi Party OperationsNov 12 2015Jan 31 2016We derive algorithms for efficient secure numerical and logical operations using a recently introduced scheme for secure multi-party computation~\cite{sch15} in the semi-honest model ensuring statistical or perfect security. To derive our algorithms for ... More

Discrete quantum geometries and their effective dimensionOct 29 2015In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then ... More

Describing the Heat Transport of Turbulent Rayleigh--Bénard Convection by POD methodsOct 23 2015Rayleigh--B\'enard convection, which is the buoyancy-induced motion of a fluid enclosed between two horizontal plates, is an idealised setup to study thermal convection. We analyse the modes that transport the most heat between the plates by computing ... More

G-bundles on the absolute Fargues-Fontaine curveJun 03 2016We prove that the category of vector bundles on the absolute Fargues-Fontaine curve is canonically equivalent to the category of isocrystals. We deduce a similar result for G-bundles for some arbitrary reductive group G over a p-adic local field.

Measuring Object-Oriented Design PrinciplesFeb 23 2016The idea of automatizing the assessment of objectoriented design is not new. Different approaches define and apply their own quality models, which are composed of single metrics or combinations thereof, to operationalize software design. However, single ... More

Paradigm shifts. Part I. Collagen. Confirming and complementing the work of Henry SmallNov 27 2014Dec 07 2014The paradigm shift in collagen research during the early 1970s marked by the discovery of the collagen precursor molecule procollagen was traced using co-citation analysis and title word frequency determination, confirming previous work performed by Henry ... More

Change-point tests under local alternatives for long-range dependent processesJun 24 2015We consider the change-point problem for the marginal distribution of subordinated Gaussian processes that exhibit long-range dependence. The asymptotic distributions of Kolmogorov-Smirnov- and Cram\'er-von Mises type statistics are investigated. A special ... More

Normality of algebras over commutative rings, crossed pairs, and the Teichmueller classDec 22 2015Let S be a commutative unitary ring, Q a group that acts on S, and let R be the subring of S fixed under Q. A Q-normal S-algebra consists of a central S-algebra A and a homomorphism s from Q to the group Out(A) of outer automorphisms of A that lifts the ... More

Deformations of $Ξ(s)=Ξ(1-s)$ and the heat equationOct 13 2015This paper studies deformations of the well-known $\Xi(s)=\Xi(1-s)$ equation for the Riemann $\Xi$ function satisfied by $\Xi_\rho(s):=\int_{0}^\infty\frac{{\d}t}{t}{t^{\frac{s}{2}}}\Psi(t)e^{-\rho\ln^2(t)}$ where ${\Psi(t)=\sum_{n\in\mathbb{N}^+}e^{-\pi{n}^2t}}$. ... More

Matching effective few-nucleon theories to QCDSep 25 2015May 17 2016The emergence of complex macroscopic phenomena from a small set of parameters and microscopic concepts demonstrates the power and beauty of physical theories. A theory which relates the wealth of data and peculiarities found in nuclei to the small number ... More

The spinorial energy functional: solutions of the gradient flow on Berger spheresOct 16 2015We study the negative gradient flow of the spinorial energy functional (introduced by Ammann, Wei{\ss}, and Witt) on 3-dimensional Berger spheres. For a certain class of spinors we show that the Berger spheres collapse to a 2-dimensional sphere. Moreover, ... More

A General Multi-Party Protocol for Minimal Communication and Local ComputationAug 31 2015Jan 31 2016A client wishes to outsource computation on confidential data to a network of servers. He does not trust a server on its own, but believes that servers do not collude. To solve this problem we introduce a new scheme called \emph{JOS} for perfect security ... More

Drawing and Analyzing Causal DAGs with DAGittyAug 19 2015DAGitty is a software for drawing and analyzing causal diagrams, also known as directed acyclic graphs (DAGs). Functions include identification of minimal sufficient adjustment sets for estimating causal effects, diagnosis of insufficient or invalid adjustment ... More

Research at UNIS - The University Centre in Svalbard. A bibliometric studyMay 25 2014Jun 17 2014The scientific output 1994-2014 of the University Centre in Svalbard (UNIS) was bibliometrically analysed. It was found that the majority of the papers have been published as international cooperations and rank above world average. Analysis of the content ... More

Functional linear instrumental regression under second order stationarityMar 04 2016We consider the problem of estimating the slope parameter in functional linear instrumental regression, where in the presence of an instrument W, i.e., an exogenous random function, a scalar response Y is modeled in dependence of an endogenous random ... More

The Weight in EnumerationDec 02 2016In our setting enumeration amounts to generate all solutions of a problem instance without duplicates. We address the problem of enumerating the models of B-formulae. A B-formula is a propositional formula whose connectives are taken from a fixed set ... More