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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

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

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

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

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 relative K-group in the ETNC, Part IINov 07 2018Jul 01 2019In 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$Nπ$-excited state contamination in nucleon 3-point functions using ChPTJul 07 2019The $N\pi$-state contribution to nucleon 3-pt functions involving the pseudoscalar density $P(x)$ and the time component $A_4(x)$ of the axial vector current are computed to LO in ChPT. In case of the latter the $N\pi$ contribution is O($M_N$) enhanced ... 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

A computerised classification of some almost minimal triangle-free Ramsey graphsOct 18 2017A graph $G$ is called a $(3,j;n)$-minimal Ramsey graph if it has the least amount of edges, $e(3,j;n)$, given that $G$ is triangle-free, the independence number $\alpha(G) < j$ and that $G$ has $n$ vertices. Triangle-free graphs $G$ with $\alpha(G) < ... More

Cyclic Sieving of Increasing Tableaux and small Schröder PathsSep 06 2012Apr 04 2014An increasing tableau is a semistandard tableau with strictly increasing rows and columns. It is well known that the Catalan numbers enumerate both rectangular standard Young tableaux of two rows and also Dyck paths. We generalize this to a bijection ... More

First-Order Quantifiers and the Syntactic Monoid of Height Fragments of Picture LanguagesApr 19 2012Apr 22 2012We investigate the expressive power of first-order quantifications in the context of monadic second-order logic over pictures. We show that k+1 set quantifier alternations allow to define a picture language that cannot be defined using k set quantifier ... 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

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

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

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

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

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

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

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

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).

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

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

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

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

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

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

Energized simplicial complexesAug 19 2019For a simplicial complex with n sets, let W^-(x) be the set of sets in G contained in x and W^+(x) the set of sets in G containing x. An integer-valued function h on G defines for every A subset G an energy E[A]=sum_x in A h(x). The function energizes ... More

The energy of a simplicial complexJul 07 2019A finite abstract simplicial complex G defines a matrix L, where L(x,y)=1 if two simplicies x,y in G intersect and where L(x,y)=0 if they don't. This matrix is always unimodular so that the inverse g of L has integer entries g(x,y). In analogy to Laplacians ... More

The counting matrix of a simplicial complexJul 22 2019For a finite abstract simplicial complex G with n sets, define the n x n matrix K(x,y) which is the number of subsimplices in the intersection of x and y. We call it the counting matrix of G. Similarly as the connection matrix L which is L(x,y)=1 if x ... 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 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

A note on "A Matrix Realignment Method for Recognizing Entanglement," quant-ph/0205017 v1May 10 2002In quant-ph/0205017 v1 Chen, Wu and Yang formulated a necessary separability criterion based on a realignment method for matrices. This note is to point out that this criterion is identical to the necessary cross norm criterion previously put forward ... More

Further results on the cross norm criterion for separabilityFeb 21 2002In the present paper the cross norm criterion for separability of density matrices is studied. In the first part of the paper we determine the value of the greatest cross norm for Werner states, for isotropic states and for Bell diagonal states. In the ... More

Axisymmetric Numerical RelativityJan 17 2006Dec 05 2013This thesis is concerned with formulations of the Einstein equations in axisymmetric spacetimes which are suitable for numerical evolutions. We develop two evolution systems based on the (2+1)+1 formalism. The first is a (partially) constrained scheme ... More

Calculating B-meson decay constants using domain-wall light quarks and nonperturbatively tuned relativistic b-quarksNov 14 2012Nov 28 2012We calculate B-physics quantities using the RBC/UKQCD 2+1 flavor domain-wall plus Iwasaki lattices and the relativistic heavy quark action developed by Christ, Li and Lin. After tuning these parameters nonperturbatively, we present our preliminary results ... More

Supernova-driven Turbulence and Magnetic Field Amplification in Disk GalaxiesJan 28 2010Supernovae are known to be the dominant energy source for driving turbulence in the interstellar medium. Yet, their effect on magnetic field amplification in spiral galaxies is still poorly understood. Analytical models based on the uncorrelated-ensemble ... More

Braking index of isolated pulsars: open questions and ways forwardMar 31 2015Isolated pulsars are rotating neutron stars with accurately measured angular velocities $\Omega$, and their time derivatives which show unambiguously that the pulsars are slowing down. Although the exact mechanism of the spin-down is a question of debate, ... More

A fast numerical method for max-convolution and the application to efficient max-product inference in Bayesian networksJan 12 2015Sep 02 2015Observations depending on sums of random variables are common throughout many fields; however, no efficient solution is currently known for performing max-product inference on these sums of general discrete distributions (max-product inference can be ... More

Scheme theoretic tropicalizationAug 31 2015Oct 26 2016In this paper, we introduce ordered blueprints and ordered blue schemes, which serve as a common language for the different approaches to tropicalizations and which enhances tropical varieties with a schematic structure. As an abstract concept, we consider ... More

Sensitive Phase Gratings for X-ray Phase Contrast - a Simulation-based ComparisonMar 12 2016Mar 21 2016Medical differential phase contrast x-ray imaging (DPCI) promises improved soft-tissue contrast at lower x-ray dose. The dose strongly depends on both the angular sensitivity and on the visibility of a grating-based Talbot-Lau interferometer. Using a ... More

Tameness of fusion systems of sporadic simple groupsApr 19 2016Apr 20 2016We prove here that with a very small number of exceptions, when $G$ is a sporadic simple group and $p$ is a prime such that the $p$-fusion system of $G$ is simple, then $Out(G)$ is isomorphic to the outer automorphism groups of the fusion and linking ... More

Chiral perturbation theory at non-zero lattice spacingSep 19 2004Oct 18 2004A review of chiral perturbation theory for lattice QCD at non-zero lattice spacing is given.

On the $η$-inverted sphereFeb 29 2016It is shown that the first and second homotopy groups of the $\eta$-inverted sphere spectrum over a field of characteristic not two are zero. A cell presentation of higher Witt theory is given as well, at least over the complex numbers.

Numbers and Functions in Quantum Field TheoryJun 28 2016We review recent results in the theory of numbers and single-valued functions on the complex plane which arise in quantum field theory.

Evaluation of the period of a family of triangle and box ladder graphsOct 19 2012We prove that the period of a family of $n$ loop graphs with triangle and box ladders evaluates to $\frac{4}{n}\binom{2n-2}{n-1}\zeta(2n-3)$

Polynomial bound for the partition rank vs the analytic rank of tensorsFeb 26 2019A tensor defined over a finite field $\mathbb{F}$ has low analytic rank if the distribution of its values differs significantly from the uniform distribution. An order $d$ tensor has partition rank 1 if it can be written as a product of two tensors of ... More

Classical mathematical structures within topological graph theoryFeb 10 2014Finite simple graphs are a playground for classical areas of mathematics. We illustrate this by looking at some theorems. These are slightly enhanced preparation notes for a talk given at the joint AMS meeting of January 16, 2014 in Baltimore.

Maximal correlation and the rate of Fisher information convergence in the Central Limit TheoremMay 28 2019We consider the behaviour of the Fisher information of scaled sums of independent and identically distributed random variables in the Central Limit Theorem regime. We show how this behaviour can be related to the second-largest non-trivial eigenvalue ... More

Continuity properties of the semi-group and its integral kernel in non-relativistic QEDDec 14 2015Employing recent results on stochastic differential equations associated with the standard model of non-relativistic quantum electrodynamics by B. G\"uneysu, J.S. M{\o}ller, and the present author, we study the continuity of the corresponding semi-group ... More