total 3918took 0.12s

Geometric and analytic structures on the higher adèlesOct 19 2015Oct 09 2017The ad\`eles of a scheme have local components - these are topological higher local fields. The topology plays a large role since Yekutieli showed in 1992 that there can be an abundance of inequivalent topologies on a higher local field and no canonical ... More

On the local residue symbol in the style of Tate and BeilinsonMar 31 2014Sep 15 2016Tate gave a famous construction of the residue symbol on curves by using some non-commutative operator algebra in the context of algebraic geometry. We explain Beilinson's multidimensional generalization, which is not so well-documented in the literature. ... More

On the relative K-group in the ETNCJun 28 2018We consider the Burns-Flach formulation of the equivariant Tamagawa number conjecture (ETNC). In their setup, a Tamagawa number is an element of a relative K-group. We show that this relative group agrees with an ordinary K-group, namely of the category ... More

An alternative construction of equivariant Tamagawa numbersJun 11 2019We propose a new formulation of the equivariant Tamagawa number conjecture (ETNC) for non-commutative coefficients. We remove Picard groupoids, determinant functors, virtual objects and relative K-groups. Our Tamagawa numbers lie in an idele group instead ... More

On the relative K-group in the ETNC, Part IINov 07 2018In a previous paper we showed, under some assumptions, that the relative K-group in the Burns-Flach formulation of the equivariant Tamagawa number conjecture (ETNC) is canonically isomorphic to a K-group of locally compact equivariant modules. This viewpoint, ... More

Torsion homology growth beyond asymptoticsFeb 21 2017We show that (under mild assumptions) the generating function of log homology torsion of a knot exterior has a meromorphic continuation to the entire complex plane. As corollaries, this gives new proofs of (a) the Silver-Williams asymptotic, (b) Fried's ... More

K-theory of locally compact modules over rings of integersOct 30 2017We generalize a recent result of Clausen: For a number field with integers O, we compute the K-theory of locally compact O-modules. For the rational integers this recovers Clausen's result as a special case. Our method of proof is quite different: Instead ... More

Multiplicative zeta function and logarithmic point counting over finite fieldsMay 02 2017The zeta function of a motive over a finite field is multiplicative with respect to the direct sum of motives. It has beautiful analytic properties, as were predicted by the Weil conjectures. There is also a multiplicative zeta function, which instead ... More

Adele residue symbol and Tate's central extension for multiloop Lie algebrasJun 10 2012Feb 05 2014We generalize the linear algebra setting of Tate's central extension to arbitrary dimension. In general, one obtains a Lie (n+1)-cocycle. We compute it explicitly. The construction is based on a Lie algebra variant of Beilinson's adelic multidimensional ... More

K-theory of semi-linear endomorphisms via the Riemann-Hilbert correspondenceOct 03 2016Oct 12 2016Grayson, developing ideas of Quillen, has made computations of the K-theory of "semi-linear endomorphisms". In the present text we develop a technique to compute these groups in the case of Frobenius semi-linear actions. The main idea is to interpret ... More

On the homology of Lie algebras like $\mathfrak{gl}(\infty,R)$Dec 05 2017We revisit a recent paper of Fialowski and Iohara. They compute the homology of the Lie algebra $\mathfrak{gl}(\infty,R)$ for $R$ an associative unital algebra over a field of characteristic zero. We explain how to obtain essentially the same results ... More

Two-dimensional Idèles with Cycle Module CoefficientsJan 02 2011Mar 20 2014We give a theory of id\`eles with coefficients for smooth surfaces over a field. It is an analogue of Beilinson/Huber's theory of higher ad\`eles, but handling cycle module sheaves instead of quasi-coherent ones. We prove that they give a flasque resolution ... More

Volume of line bundles via valuation vectors (different from Okounkov bodies)Mar 11 2019Up to a factor 1/n!, the volume of a big line bundle agrees with the Euclidean volume of its Okounkov body. The latter is the convex hull of top rank valuation vectors of sections, all with respect to a single flag. In this text we give a different volume ... More

Automorphisms of OT manifolds and ray class numbersJul 30 2018We compute the automorphism group of OT manifolds of simple type. We show that the graded pieces under a natural filtration are related to a certain ray class group of the underlying number field. This does not solve the open question whether the geometry ... More

Hochschild coniveau spectral sequence and the Beilinson residueJul 26 2016We develop the Hochschild analogue of the coniveau spectral sequence and the Gersten complex. Since Hochschild homology does not have devissage or A^1-invariance, this is a little different from the K-theory story. In fact, the rows of our spectral sequence ... More

On the automorphic side of the K-theoretic Artin symbolMar 01 2018Clausen has constructed a homotopical enrichment of the Artin reciprocity symbol in class field theory. On the Galois side, Selmer K-homology replaces the abelianized Galois group, while on the automorphic side the K-theory of locally compact vector spaces ... More

Geometric and analytic structures on the higher adèlesOct 19 2015The ad\`eles of a scheme have local components - these are topological higher local fields. The topology plays a large role since Yekutieli showed in 1992 that there can be an abundance of inequivalent topologies on a higher local field and no canonical ... More

Relative Tate Objects and Boundary Maps in the K-Theory of Coherent SheavesNov 18 2015We investigate the properties of relative analogues of admissible Ind, Pro, and elementary Tate objects for pairs of exact categories, and give criteria for those categories to be abelian. A relative index map is introduced, and as an application we deduce ... More

Tate Objects in Exact Categories (with appendix by Jan \vS\vtov\'ı\vcek and Jan Trlifaj)Feb 20 2014Oct 06 2014We study elementary Tate objects in an exact category. We characterize the category of elementary Tate objects as the smallest sub-category of admissible Ind-Pro objects which contains the categories of admissible Ind-objects and admissible Pro-objects, ... More

The Index Map in Algebraic K-TheoryOct 06 2014Nov 18 2015For a ring $R$, we construct a universal $K_R$-torsor $\mathcal{T}_R\to K_{Tate(R)}$ on the $K$-theory space of Tate $R$-modules. This torsor is closely related to canonical central extensions of loop groups. Just like classical loop group theory has ... More

Operator ideals in Tate objectsAug 31 2015Tate's central extension originates from 1968 and has since found many applications to curves. In the 80s Beilinson found an n-dimensional generalization: cubically decomposed algebras, based on ideals of bounded and discrete operators in ind-pro limits ... More

The $A_\infty$-structure of the index mapJun 22 2018Let $F$ be a local field with residue field $k$. The classifying space of $GL_n(F)$ comes canonically equipped with a map to the delooping of the $K$-theory space of $k$. Passing to loop spaces, such a map abstractly encodes a homotopy coherently associative ... More

The Index Map in Algebraic K-TheoryOct 06 2014Jun 22 2018For a ring $R$, we construct a universal $K_R$-torsor $\mathcal{T}_R\to K_{Tate(R)}$ on the $K$-theory space of Tate $R$-modules. This torsor is closely related to canonical central extensions of loop groups. Just like classical loop group theory has ... More

A Generalized Contou-Carrère Symbol and its Reciprocity Laws in Higher DimensionsOct 13 2014Jul 24 2015We generalize the theory of Contou-Carr\`ere symbols to higher dimensions. To an $(n+1)$-tuple $f_0,\dots,f_n \in A((t_1))\cdots((t_n))^{\times}$, where $A$ denotes a commutative algebra over a field $k$, we associate an element $(f_0,\dots,f_n) \in A^{\times}$, ... More

On the normally ordered tensor product and duality for Tate objectsSep 22 2017This paper generalizes the normally ordered tensor product from Tate vector spaces to Tate objects over arbitrary exact categories. We show how to lift bi-right exact monoidal structures, duality functors, and construct external Homs. We list some applications: ... More

Oeljeklaus-Toma manifolds and arithmetic invariantsMar 07 2015Oeljeklaus-Toma (OT) manifolds are certain compact complex manifolds built from number fields. Conversely, we show that the fundamental group often pins down the number field uniquely. We relate the first homology to some interesting ideal. OT manifolds ... More

Explicit Wodzicki excision in cyclic homologyNov 17 2013Oct 21 2014Assuming local one-sided units exist, I give an elementary proof of Wodzicki excision for cyclic homology. The proof is also constructive and provides an explicit inverse excision map. As far as I know, the latter is new.

Closed strings as single-valued open strings: A genus-zero derivationAug 02 2018Oct 11 2018Based on general mathematical assumptions we give an independent, elementary derivation of a theorem by Francis Brown and Cl\'ement Dupont which states that tree-level amplitudes of closed and open strings are related through the single-valued map `sv'. ... More

Consistent Histories and Operational Quantum PhysicsDec 22 1995Jun 07 1996In this work a generalization of the consistent histories approach to quantum mechanics is presented. We first critically review the consistent histories approach to nonrelativistic quantum mechanics in a mathematically rigorous way and give some general ... More

Sum-over-histories representation for the causal Green function of free scalar field theoryNov 03 1993A set of Green functions ${\cal G}_{\alpha}(x-y), \alpha \in [0, 2 \pi [$, for free scalar field theory is introduced, varying between the Hadamard Green function $\Delta_1(x-y) \equiv \linebreak[2] \lsta{0} \hspace{-0.1cm} \{ \varphi(x), \varphi(y) \} ... More

The representation theory of decoherence functionals in history quantum theoriesOct 25 1998In the first part of this paper the general perspective of history quantum theories is reviewed. History quantum theories provide a conceptual and mathematical framework for formulating quantum theories without a globally defined Hamiltonian time evolution ... More

An axisymmetric evolution code for the Einstein equations on hyperboloidal slicesOct 01 2009Jan 12 2010We present the first stable dynamical numerical evolutions of the Einstein equations in terms of a conformally rescaled metric on hyperboloidal hypersurfaces extending to future null infinity. Axisymmetry is imposed in order to reduce the computational ... More

On Klein's Icosahedral Solution of the QuinticAug 05 2013We present an exposition of the icosahedral solution of the quintic equation first described in Klein's classic work "Lectures on the icosahedron and the solution of equations of the fifth degree". Although we are heavily influenced by Klein we follow ... More

Twisted Injectivity in PEPS and the Classification of Quantum PhasesJul 29 2013We introduce a class of projected entangled pair states (PEPS) which is based on a group symmetry twisted by a 3-cocycle of the group. This twisted symmetry gives rise to a new standard form for PEPS from which we construct a family of local Hamiltonians ... More

On the complete classification of the unitary N=2 minimal superconformal field theoriesDec 07 2008Nov 25 2011Aiming at a complete classification of unitary N=2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each modular invariant candidate of a partition function for such a theory is indeed the partition ... More

Metastability for the Ising Model on the hypercubeAug 31 2015We consider Glauber dynamics for the low-temperature, ferromagnetic Ising Model set on the n-dimensional hypercube. We derive precise asymptotic results for the crossover time (the time it takes for the dynamics to go from the configuration with a "-1" ... More

Fast Computation on Semirings Isomorphic to $(\times, \max)$ on $\mathbb{R}_+$Nov 18 2015Jun 17 2016Important problems across multiple disciplines involve computations on the semiring $(\times, \max)$ (or its equivalents, the negated version $(\times, \min)$), the log-transformed version $(+, \max)$, or the negated log-transformed version $(+, \min)$): ... More

A discrete log-Sobolev inequality under a Bakry-Emery type conditionJul 22 2015Jul 06 2016We consider probability mass functions $V$ supported on the positive integers using arguments introduced by Caputo, Dai Pra and Posta, based on a Bakry--\'{E}mery condition for a Markov birth and death operator with invariant measure $V$. Under this condition, ... More

A de Bruijn identity for symmetric stable lawsOct 08 2013We show how some attractive information--theoretic properties of Gaussians pass over to more general families of stable densities. We define a new score function for symmetric stable laws, and use it to give a stable version of the heat equation. Using ... More

Collisionless Dynamics and the Cosmic WebDec 16 2014I review the nature of three-dimensional collapse in the Zeldovich approximation, how it relates to the underlying nature of the three-dimensional Lagrangian manifold and naturally gives rise to a hierarchical structure formation scenario that progresses ... More

Seiberg-Witten Invariants, Alexander Polynomials, and Fibred ClassesFeb 15 2015Mar 11 2015Since their introduction in 1994, the Seiberg-Witten invariants have become one of the main tools used in 4-manifold theory. In this thesis, we will use these invariants to identify sufficient conditions for a 3-manifold to fibre over a circle. Additionally, ... More

Clues on the Majorana scale from scalar resonances at the LHCJul 01 2016In order to address the observation of the neutrino oscillations and the metastability of the Standard Model, we extend the fermion sector with two right-handed (i.e. sterile) neutrinos, and the scalar sector of the SM with a real scalar, the Hill field. ... More

The k-core and branching processesNov 03 2005Feb 12 2007The k-core of a graph G is the maximal subgraph of G having minimum degree at least k. In 1996, Pittel, Spencer and Wormald found the threshold $\lambda_c$ for the emergence of a non-trivial k-core in the random graph $G(n,\lambda/n)$, and the asymptotic ... More

Quantifying nonorthogonalityJul 30 1999An exploratory approach to the possibility of analyzing nonorthogonality as a quantifiable property is presented. Three different measures for the nonorthogonality of pure states are introduced, and one of these measures is extended to single-particle ... More

Galaxy populations from Deep ISO SurveysJun 19 2001I discuss some of the main extra-galactic field surveys which have been undertaken by the Infrared Space Observatory (ISO). I review the findings from the source counts analysies and then examine some of the more recent detailed investigations into the ... More

The European Large Area ISO Survey: ELAISApr 09 1996I describe a European collaborative project to survey \sim 20 square degrees of the sky at 15\micron and 90\micron with ISO. This is the largest open time project being undertaken by ISO. The depth and areal coverage were designed to complement the various ... More

An invariant for minimum triangle-free graphsAug 26 2016Sep 24 2016We study the number of edges, $e(G)$, in triangle-free graphs with a prescribed number of vertices, $n(G)$, independence number, $\alpha(G)$, and number of cycles of length four, $\operatorname{N}(C_4;G)$. We in particular show that $$3e(G) - 17n(G) + ... More

K-theory, LQEL manifolds and Severi varietiesAug 05 2013Aug 24 2013We use topological K-theory to study non-singular varieties with quadratic entry locus. We thus obtain a new proof of Russo's Divisibility Property for locally quadratic entry locus manifolds. In particular we obtain a K-theoretic proof of Zak's theorem ... More

Arnold conjecture and nonlinear Schrodinger equationsJul 02 2015Under natural restrictions it is known that a nonlinear Schrodinger equation is a Hamiltonian PDE which defines a symplectic flow on a symplectic Hilbert space preserving the Hilbert norm. When the potential is one-periodic in time and after passing to ... More

Graphical functions and single-valued multiple polylogarithmsFeb 26 2013Nov 11 2014Graphical functions are single-valued complex functions which arise from Feynman amplitudes. We study their properties and use their connection to multiple polylogarithms to calculate Feynman periods. For the zig-zag and two more families of phi^4 periods ... More

Infinite-dimensional symplectic non-squeezing using non-standard analysisJan 23 2015Jun 16 2018We prove a non-squeezing result for infinite-dimensional Hamiltonian flows using non-standard model theory. For this we prove the existence of a corresponding family of pseudoholomorphic spheres and characterize the maximal time in terms of a limiting ... More

The Cohomology for Wu CharacteristicsMar 19 2018While Euler characteristic X(G)=sum_x w(x) super counts simplices, Wu characteristics w_k(G) = sum_(x_1,x_2,...,x_k) w(x_1)...w(x_k) super counts simultaneously pairwise interacting k-tuples of simplices in a finite abstract simplicial complex G. More ... More

Improved bounds for the extremal number of subdivisionsSep 03 2018Let $H_t$ be the subdivision of $K_t$. Very recently, Conlon and Lee have proved that for any integer $t\geq 3$, there exists a constant $C$ such that $\text{ex}(n,H_t)\leq Cn^{3/2-1/6^t}$. In this paper, we prove that there exists a constant $C'$ such ... More

Chiral logs in twisted mass lattice QCD with large isospin breakingAug 04 2010Nov 17 2010The pion masses and the pion decay constant are calculated to 1-loop order in twisted mass Wilson chiral perturbation theory, assuming a large pion mass splitting and tuning to maximal twist. Taking the large mass splitting at leading order in the chiral ... More

Higher algebraic structures in Hamiltonian Floer theory IOct 22 2013Aug 05 2016This is the first of two papers devoted to showing how the rich algebraic formalism of Eliashberg-Givental-Hofer's symplectic field theory (SFT) can be used to define higher algebraic structures on the symplectic cohomology of open symplectic manifolds. ... More

On Atiyah-Singer and Atiyah-Bott for finite abstract simplicial complexesAug 21 2017A linear or multi-linear valuation on a finite abstract simplicial complex can be expressed as an analytic index dim(ker(D)) -dim(ker(D^*)) of a differential complex D:E -> F. In the discrete, a complex D can be called elliptic if a McKean-Singer spectral ... More

LeagueAI: Improving object detector performance and flexibility through automatically generated training data and domain randomizationMay 28 2019In this technical report I present my method for automatic synthetic dataset generation for object detection and demonstrate it on the video game League of Legends. This report furthermore serves as a handbook on how to automatically generate datasets ... More

Prehomogeneous Affine Representations and Flat Pseudo-Riemannian ManifoldsSep 04 2008The theory of flat Pseudo-Riemannian manifolds and flat affine manifolds is closely connected to the topic of prehomogeneous affine representations of Lie groups. In this article, we exhibit several aspects of this correspondence. At the heart of our ... More

On higher order estimates in quantum electrodynamicsDec 31 2009We propose a new method to derive certain higher order estimates in quantum electrodynamics. Our method is particularly convenient in the application to the non-local semi-relativistic models of quantum electrodynamics as it avoids the use of iterated ... More

The Dirac operator of a graphJun 10 2013We discuss some linear algebra related to the Dirac matrix D of a finite simple graph G=(V,E).

Obstruction bundles over moduli spaces with boundary and the action filtration in symplectic field theorySep 20 2007Mar 02 2010Branched covers of orbit cylinders are the basic examples of holomorphic curves studied in symplectic field theory. Since all curves with Fredholm index one can never be regular for any choice of cylindrical almost complex structure, we generalize the ... More

An Elementary Dyadic Riemann HypothesisJan 15 2018The connection zeta function of a finite abstract simplicial complex G is defined as zeta_L(s)=sum_x 1/lambda_x^s, where lambda_x are the eigenvalues of the connection Laplacian L defined by L(x,y)=1 if x and y intersect and 0 else. (I) As a consequence ... More

Exact Ramsey Theory: Green-Tao numbers and SATApr 05 2010Apr 24 2010We consider the links between Ramsey theory in the integers, based on van der Waerden's theorem, and (boolean, CNF) SAT solving. We aim at using the problems from exact Ramsey theory, concerned with computing Ramsey-type numbers, as a rich source of test ... More

Invariant differential operators and central Fourier multipliers on exponential Lie groupsFeb 22 2012Let $G$ be an exponential solvable Lie group. By definition $G$ is $\ast$-regular if $ker_{L^1(G)}\pi$ is dense in $ker_{C^\ast(G)}\pi$ for all unitary representations $\pi$ of $G$. Boidol characterized the $\ast$-regular exponential Lie groups by a purely ... More

One can hear the Euler characteristic of a simplicial complexNov 27 2017We prove that that the number p of positive eigenvalues of the connection Laplacian L of a finite abstract simplicial complex G matches the number b of even dimensional simplices in G and that the number n of negative eigenvalues matches the number f ... More

The strong ring of simplicial complexesAug 05 2017We define a ring R of geometric objects G generated by finite abstract simplicial complexes. To every G belongs Hodge Laplacian H as the square of the Dirac operator determining its cohomology and a unimodular connection matrix L). The sum of the matrix ... More

Solving primal plasticity increment problems in the time of a single predictor-corrector iterationJul 12 2017Oct 18 2017The Truncated Nonsmooth Newton Multigrid (TNNMG) method is a well-established method for the solution of strictly convex block-separably nondifferentiable minimization problems. It achieves multigrid-like performance even for non-smooth nonlinear problems, ... More

The deformations of flat affine structures on the two-torusDec 14 2011The group action which defines the moduli problem for the deformation space of flat affine structures on the two-torus is the action of the affine group $\Aff(2)$ on $\bbR^2$. Since this action has non-compact stabiliser $\GL(2,\bbR)$, the underlying ... More

Rigidity of lattices and syndetic hulls in solvable Lie groupsNov 28 2013Dec 03 2013First let $G$ be a completely solvable Lie group. We recall the proof of the following result: Any closed subgroup of $G$ possesses a unique syndetic hull in $G$. As a consequence we conclude that any uniform subgroup $\Gamma$ of $G$ is strongly rigid ... More

Long cycles in random subgraphs of graphs with large minimum degreeAug 14 2013May 24 2014Let $G$ be any graph of minimum degree at least $k$, and let $G_p$ be the random subgraph of $G$ obtained by keeping each edge independently with probability $p$. Recently, Krivelevich, Lee and Sudakov showed that if $pk\to\infty$ then with probability ... More

Selfsimilarity in the Birkhoff sum of the cotangent functionJun 24 2012We prove that the Birkhoff sum S(n)/n = (1/n) sum_(k=1)^(n-1) g(k A) with g(x) = cot(Pi x) and golden ratio A converges in the sense that the sequence of functions s(x) = S([ x q(2n)])/q(2n) with Fibonacci numbers q(n) converges to a self similar limiting ... More

Some experiments in number theoryJun 20 2016We experiment with some topics in elementary number theory. For matrices defined by Gaussian primes we observe a circular spectral law for the eigenvalues. We look at matrices defined by Gaussian primes and look at the growth of the determinant, trace. ... More

Entropy and a generalisation of `Poincare's Observation'Jan 29 2002Consider a sphere of radius root(n) in n dimensions, and consider X, a random variable uniformly distributed on its surface. Poincare's Observation states that for large n, the distribution of the first k coordinates of X is close in total variation distance ... More

The Jordan-Brouwer theorem for graphsJun 22 2015We prove a discrete Jordan-Brouwer-Schoenflies separation theorem telling that a (d-1)-sphere H embedded in a d-sphere G defines two different connected graphs A,B in G such a way that the intersection of A and B is H and the union is G and such that ... More

Coloring graphs using topologyDec 22 2014Higher dimensional graphs can be used to colour two-dimensional geometric graphs. If G the boundary of a three dimensional graph H for example, we can refine the interior until it is colourable with 4 colours. The later goal is achieved if all interior ... More

On the index of a vector field tangent to a hypersurface with non-isolated zero in the embedding spaceApr 17 2002Dec 20 2002We give a generalization of an algebraic formula of Gomez-Mont for the index of a vector field with isolated zero in (C^n,0) and tangent to an isolated hypersurface singularity. We only assume that the vector field has an isolated zero on the singularity. ... More

Dynamically generated NetworksNov 18 2013Simple algebraic rules can produce complex networks with rich structures. These graphs are obtained when looking at a monoid operating on a ring. There are relations to dynamical systems theory and number theory. This document illustrates this class of ... More

On index expectation and curvature for networksFeb 21 2012We prove that the expectation value of the index function i(x) over a probability space of injective function f on any finite simple graph G=(V,E) is equal to the curvature K(x) at the vertex x. This result complements and links Gauss-Bonnet sum K(x) ... More

Natural orbital networksNov 26 2013Given a finite set T of maps on a finite ring R, we look at the finite simple graph G=(V,E) with vertex set V=R and edge set E={(a,b) | exists t in T, b=t(a), b not equal to a}. An example is when R=Z_n and T consists of a finite set of quadratic maps ... More

A discrete Gauss-Bonnet type theoremSep 13 2010We prove a prototype curvature theorem for subgraphs G of the flat triangular tesselation which play the analogue of "domains" in two dimensional Euclidean space: The Pusieux curvature K(p) = 2|S1(p)| - |S2(p)| is equal to 12 times the Euler characteristic ... More

A separability criterion for density operatorsFeb 09 2000We give a necessary and sufficient condition for a mixed quantum mechanical state to be separable. The criterion is formulated as a boundedness condition in terms of the greatest cross norm on the tensor product of trace class operators.

On the Classification of Decoherence FunctionalsAug 28 1996Dec 19 1996The basic ingredients of the consistent histories approach to quantum mechanics are the space of histories and the space of decoherence functionals. In this work we extend the classification theorem for decoherence functionals proven by Isham, Linden ... More

Explicit solution of the linearized Einstein equations in TT gauge for all multipolesSep 10 2008Dec 28 2008We write out the explicit form of the metric for a linearized gravitational wave in the transverse-traceless gauge for any multipole, thus generalizing the well-known quadrupole solution of Teukolsky. The solution is derived using the generalized Regge-Wheeler-Zerilli ... More

Astronomical Tests of the Einstein Equivalence PrincipleMay 22 2003The Einstein equivalence principle is certainly a key element in the development of new enhanced theories of gravity. Although being an important building block in Einstein's general relativity, theoretically predicted violations of its validity are a ... More

Unsupervised K-Nearest Neighbor RegressionJul 19 2011Sep 26 2011In many scientific disciplines structures in high-dimensional data have to be found, e.g., in stellar spectra, in genome data, or in face recognition tasks. In this work we present a novel approach to non-linear dimensionality reduction. It is based on ... More

Amplitude relations in heterotic string theory and Einstein-Yang-MillsJul 30 2016Nov 19 2016We present all-multiplicity evidence that the tree-level S-matrix of gluons and gravitons in heterotic string theory can be reduced to color-ordered single-trace amplitudes of the gauge multiplet. Explicit amplitude relations are derived for up to three ... More

Entropy and thinning of discrete random variablesOct 19 2015Jun 07 2016We describe five types of results concerning information and concentration of discrete random variables, and relationships between them, motivated by their counterparts in the continuous case. The results we consider are information theoretic approaches ... More

Strong converses for group testing in the finite blocklength regimeSep 21 2015We prove new strong converse results in a variety of group testing settings, generalizing a result of Baldassini, Johnson and Aldridge. These results are proved by two distinct approaches, corresponding to the non-adaptive and adaptive cases. In the non-adaptive ... More

Infinite-dimensional symplectic non-squeezing using non-standard analysisJan 23 2015Jul 17 2016Believing in the axiom of choice, we show how to deduce symplectic non-squeezing in infinite dimensions from the corresponding result of Gromov for all finite dimensions using pseudoholomorphic curves. For this we use that every separable symplectic Hilbert ... More

Formation and decay of Einstein-Yang-Mills black holesSep 22 2014Jan 05 2015We study various aspects of black holes and gravitational collapse in Einstein-Yang-Mills theory under the assumption of spherical symmetry. Numerical evolution on hyperboloidal surfaces extending to future null infinity is used. We begin by constructing ... More

Non-Hermitian Polynomial Hybrid Monte CarloSep 05 2008We report on a new variant of the hybrid Monte Carlo algorithm employing a polynomial approximation of the inverse of the non-Hermitian Dirac-Wilson operator. Our approximation relies on simple and stable recurrence relations of complex Chebyshev polynomials. ... More

A Field-length based refinement criterion for adaptive mesh simulations of the interstellar mediumFeb 02 2009Adequate modelling of the multiphase interstellar medium requires optically thin radiative cooling, comprising an inherent thermal instability. The size of the occurring condensation and evaporation interfaces is determined by the so-called Field-length, ... More

Randomized Dynamical Decoupling Strategies and Improved One-Way Key Rates for Quantum CryptographyJun 15 2009Jun 16 2009The present thesis deals with various methods of quantum error correction. It is divided into two parts. In the first part, dynamical decoupling methods are considered which have the task of suppressing the influence of residual imperfections in a quantum ... More

Counterfactual entanglement and nonlocal correlations in separable statesJul 30 1999It is shown that the outcomes of measurements on systems in separable mixed states can be partitioned, via subsequent measurements on a disentangled extraneous system, into subensembles that display the statistics of entangled states. This motivates the ... More

FIRST Extra-Galactic Surveys: Practical ConsiderationsJun 19 2001We discuss some of the practical considerations that need to be made in the design of extra-galactic field surveys using FIRST. We investigate the various limitations that confusion noise imposes on possible FIRST surveys and the benefits of super resolution ... More

The European Large Area ISO Survey: ELAISJan 20 1999The European Large Area ISO Survey (ELAIS) has surveyed ~12 square degrees of the sky at 15mu and 90mu and subsets of this area at 6.75mu and 175mu using the Infrared Space Observatory (ISO). This project was the largest single open time programme executed ... More

Zeta Functions on Arithmetic SurfacesNov 27 2013Mar 02 2015We use a form of lifted harmonic analysis to develop a two-dimensional adelic integral representation of the zeta functions of simple arithmetic surfaces. Manipulations of this integral then lead to an adelic interpretation of the so-called mean-periodicity ... More

Adaptive scanning - a proposal how to scan theoretical predictions over a multi-dimensional parameter space efficientlyJul 29 2004A method is presented to exploit adaptive integration algorithms using importance sampling, like VEGAS, for the task of scanning theoretical predictions depending on a multi-dimensional parameter space. Usually, a parameter scan is performed with emphasis ... More

A Modular and Flexible Architecture for an Integrated Corpus Query SystemAug 02 1994The paper describes the architecture of an integrated and extensible corpus query system developed at the University of Stuttgart and gives examples of some of the modules realized within this architecture. The modules form the core of a corpus workbench. ... More

Random cliques in random graphsFeb 06 2018We show that for each $r\ge 4$, in a density range extending up to, and slightly beyond, the threshold for a $K_r$-factor, the copies of $K_r$ in the random graph $G(n,p)$ are randomly distributed, in the (one-sided) sense that the hypergraph that they ... More