Results for "Matthias Franz"

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Koszul duality and equivariant cohomology for toriJan 09 2003Let T be a torus. We show that Koszul duality can be used to compute the equivariant cohomology of topological T-spaces as well as the cohomology of pull backs of the universal T-bundle. The new features are that no further assumptions about the spaces ... More
Homotopy Gerstenhaber formality of Davis-Januszkiewicz spacesJul 10 2019A homotopy Gerstenhaber structure on a differential graded algebra is essentially a family of operations defining a multiplication on its bar construction. We prove that the normalized singular cochain algebra of a Davis-Januszkiewicz space is formal ... More
The cohomology rings of homogeneous spacesJul 10 2019Let $G$ be a compact connected Lie group and $K$ a closed connected subgroup. Assume that the order of any torsion element in the integral cohomology of $G$ and $K$ is invertible in a given principal ideal domain $k$. It is known that in this case the ... More
On the integral cohomology of smooth toric varietiesAug 27 2003Let $X_\Sigma$ be a smooth, not necessarily compact toric variety. We show that a certain complex, defined in terms of the fan $\Sigma$, computes the integral cohomology of $X_\Sigma$, including the module structure over the homology of the torus. In ... More
Syzygies in equivariant cohomology for non-abelian Lie groupsSep 02 2014Sep 22 2015We extend the work of Allday-Franz-Puppe on syzygies in equivariant cohomology from tori to arbitrary compact connected Lie groups G. In particular, we show that for a compact orientable G-manifold X the analogue of the Chang-Skjelbred sequence is exact ... More
The syzygy order of big polygon spacesApr 01 2019Big polygon spaces are compact orientable manifolds with a torus action whose equivariant cohomology can be torsion-free or reflexive without being free as a module over $H^*(BT)$. We determine the exact syzygy order of the equivariant cohomology of a ... More
Freeness of equivariant cohomology and mutants of compactified representationsOct 11 2007Oct 16 2007We survey generalisations of the Chang-Skjelbred Lemma for integral coefficients. Moreover, we construct examples of manifolds with actions of tori of rank > 2 whose equivariant cohomology is torsion-free, but not free. This answers a question of Allday's. ... More
Testing multivariate uniformity based on random geometric graphsDec 20 2018We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\mathbb{R}^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the null hypothesis ... More
A recursive distribution equation for the stable treeDec 20 2018We provide a new characterisation of Duquesne and Le Gall's $\alpha$-stable tree, $\alpha\in(1,2]$, as the solution of a recursive distribution equation (RDE) of the form $\mathcal{T}\overset{d}{=}g(\xi,\mathcal{T}_i, i\geq0)$, where $g$ is a concatenation ... More
Symmetric products of equivariantly formal spacesApr 28 2016Let X be a CW complex with a continuous action of a topological group G, and let F be a field. We show that if X is equivariantly formal for singular cohomology with coefficients in F, then so are all symmetric products of X and in fact all its Gamma-products. ... More
The cohomology rings of smooth toric varieties and quotients of moment-angle complexesJul 10 2019Partial quotients of moment-angle complexes are topological analogues of smooth, not necessarily compact toric varieties. In 1998, Buchstaber and Panov proposed a formula for the cohomology ring of such a partial quotient in terms of a torsion product ... More
Homotopy Gerstenhaber algebras are strongly homotopy commutativeJul 10 2019We show that any homotopy Gerstenhaber algebra is canonically a strongly homotopy commutative (shc) algebra in the sense of Stasheff-Halperin with a homotopy associative structure map. In the presence of certain additional operations corresponding to ... More
Tensor products of homotopy Gerstenhaber algebrasSep 06 2010Sep 26 2010On the tensor product of two homotopy Gerstenhaber algebras we construct a Hirsch algebra structure which extends the canonical dg algebra structure. Our result applies more generally to tensor products of "level 3 Hirsch algebras" and also to the Mayer-Vietoris ... More
A quotient criterion for syzygies in equivariant cohomologyMay 20 2012Nov 22 2018Let X be a manifold with an action of a torus T such that all isotropy groups are connected and satisfying some other mild hypotheses. We provide a necessary and sufficient criterion for the T-equivariant cohomology of X with real coefficients to be a ... More
Symmetric products of equivariantly formal spacesApr 28 2016May 04 2017Let X be a CW complex with a continuous action of a topological group G. We show that if X is equivariantly formal for singular cohomology with coefficients in a field, then so are all symmetric products of X and in fact all its Gamma-products. In particular, ... More
CO Tip Functionalization Inverts Atomic Force Microscopy Contrast via Short-Range Electrostatic ForcesFeb 21 2014We investigated insulating Cu$_2$N islands grown on Cu(100) by means of combined scanning tunneling microscopy and atomic force microscopy with two vastly different tips: a bare metal tip and a CO-terminated tip. We use scanning tunneling microscopy data ... More
Is every toric variety an M-variety?Oct 11 2005A complex algebraic variety X defined over the real numbers is called an M-variety if the sum of its Betti numbers (for homology with closed supports and coefficients in Z/2) coincides with the corresponding sum for the real part of X. It has been known ... More
A quotient criterion for syzygies in equivariant cohomologyMay 20 2012Feb 11 2016Let X a manifold with an action of a torus T such that all isotropy groups are connected and satisfying some other mild hypotheses. We provide a necessary and sufficient criterion for the T-equivariant cohomology of X with real coefficients to be a certain ... More
Describing toric varieties and their equivariant cohomologySep 01 2009Mar 25 2010Topologically, compact toric varieties can be constructed as identification spaces: they are quotients of the product of a compact torus and the order complex of the fan. We give a detailed proof of this fact, extend it to the non-compact case and draw ... More
Big polygon spacesMar 18 2014Apr 07 2015We study a new class of compact orientable manifolds, called big polygon spaces. They are intersections of real quadrics and related to polygon spaces, which appear as their fixed point set under a canonical torus action. What makes big polygon spaces ... More
Koszul duality and equivariant cohomologyJul 09 2003Nov 28 2003Let G be a topological group such that its homology H(G) with coefficients in a principal ideal domain R is an exterior algebra, generated in odd degrees. We show that the singular cochain functor carries the duality between G-spaces and spaces over BG ... More
Adaptive mixed norm optical flow estimationNov 03 2016The pel-recursive computation of 2-D optical flow has been extensively studied in computer vision to estimate motion from image sequences, but it still raises a wealth of issues, such as the treatment of outliers, motion discontinuities and occlusion. ... More
Graph equivariant cohomological rigidity for GKM-graphsOct 23 2017Sep 10 2018We formulate the notion of an isomorphism of GKM graphs. We then show that two GKM graphs have isomorphic graph equivariant cohomology algebras if and only if the graphs are isomorphic.
NMR Studies on the Temperature-Dependent Dynamics of Confined WaterJul 16 2014We use $^2$H NMR to study the rotational motion of supercooled water in silica pores of various diameters, specifically, in the MCM-41 materials C10, C12, and C14. Combination of spin-lattice relaxation, line-shape, and stimulated-echo analyses allows ... More
A binary embedding of the stable line-breaking constructionNov 07 2016We embed Duquesne and Le Gall's stable tree into a binary compact continuum random tree (CRT) in a way that solves an open problem posed by Goldschmidt and Haas. This CRT can be obtained by applying a recursive construction method of compact CRTs as presented ... More
Weights in cohomology and the Eilenberg-Moore spectral sequenceMay 31 2004Nov 23 2004We show that in the category of complex algebraic varieties, the Eilenberg--Moore spectral sequence can be endowed with a weight filtration. This implies that it degenerates if all involved spaces have pure cohomology. As application, we compute the rational ... More
Steenrod squares on conjugation spacesOct 07 2005We prove that the coefficients of the so-called conjugation equation for conjugation spaces in the sense of Hausmann-Holm-Puppe are completely determined by Steenrod squares. This generalises a result of V.A. Krasnov for certain complex algebraic varieties. ... More
Recursive construction of continuum random treesJul 18 2016We introduce a general recursive method to construct continuum random trees (CRTs) from independent copies of a random string of beads, that is, any random interval equipped with a random discrete probability measure, and from related structures. We prove ... More
Exact sequences for equivariantly formal spacesJul 09 2003May 06 2010Let T be a torus. We present an exact sequence relating the relative equivariant cohomologies of the skeletons of an equivariantly formal T-space. This sequence, which goes back to Atiyah and Bredon, generalizes the so-called Chang-Skjelbred lemma. As ... More
Exact cohomology sequences with integral coefficients for torus actionsMay 27 2005Sep 10 2006Using methods applied by Atiyah in equivariant K-theory, Bredon obtained exact sequences for the relative cohomologies (with rational coefficients) of the equivariant skeletons of (sufficiently nice) T-spaces, T=(S^1)^n, with free equivariant cohomology ... More
Machine Learning in Falls Prediction; A cognition-based predictor of falls for the acute neurological in-patient populationJul 05 2016Background Information: Falls are associated with high direct and indirect costs, and significant morbidity and mortality for patients. Pathological falls are usually a result of a compromised motor system, and/or cognition. Very little research has been ... More
Maximum Gain Round Trips with Cost ConstraintsMay 04 2011May 05 2011Searching for optimal ways in a network is an important task in multiple application areas such as social networks, co-citation graphs or road networks. In the majority of applications, each edge in a network is associated with a certain cost and an optimal ... More
Equivariant Poincaré-Alexander-Lefschetz duality and the Cohen-Macaulay propertyMar 05 2013Sep 15 2013We prove a Poincare-Alexander-Lefschetz duality theorem for rational torus-equivariant cohomology and rational homology manifolds. We allow non-compact and non-orientable spaces. We use this to deduce certain short exact sequences in equivariant cohomology, ... More
The random connection model and functions of edge-marked Poisson processes: second order properties and normal approximationAug 03 2018The random connection model is a random graph whose vertices are given by the points of a Poisson process and whose edges are obtained by randomly connecting pairs of Poisson points in a position dependent but independent way. We study first and second ... More
Rational Quartic Reciprocity IIOct 24 2013We continue investigating rational quartic reciprocity laws and, at the suggestion of the editor of AA, provide details of a proof of a remark in the first article with this title.
Higher Descent on Pell Conics III. The First 2-DescentNov 18 2003In this articel we describe the first 2-descent on Pell conics, and compute the associated 2-part of the Tate-Shafarevich group.
Unramified Quaternion Extensions of Quadratic Number FieldsOct 24 2013We show how to construct unramified qoaternion extensions of quadratic number fields.
Harbingers of Artin's Reciprocity Law. IV. Bernstein's Reciprocity LawFeb 26 2012In the last article of this series we will first explain how Artin's reciprocity law for unramified abelian extensions can be formulated with the help of power residue symbols, and then show that, in this case, Artin's reciprocity law was already stated ... More
MLD Relations of Pisot Substitution TilingsJan 15 2010We consider 1-dimensional, unimodular Pisot substitution tilings with three intervals, and discuss conditions under which pairs of such tilings are locally isomorhphic (LI), or mutually locally derivable (MDL). For this purpose, we regard the substitutions ... More
Two classes of nonlocal Evolution Equations related by a shared Traveling Wave ProblemMar 17 2017We consider reaction-diffusion equations and Korteweg-de Vries-Burgers (KdVB) equations, i.e. scalar conservation laws with diffusive-dispersive regularization. We review the existence of traveling wave solutions for these two classes of evolution equations. ... More
Equivariant cohomology, syzygies and orbit structureNov 03 2011Mar 06 2013Let X be a "nice" space with an action of a torus T. We consider the Atiyah-Bredon sequence of equivariant cohomology modules arising from the filtration of X by orbit dimension. We show that a front piece of this sequence is exact if and only if the ... More
Deep Learning Parametrization for B-Spline Curve ApproximationJul 22 2018In this paper we present a method using deep learning to compute parametrizations for B-spline curve approximation. Existing methods consider the computation of parametric values and a knot vector as separate problems. We propose to train interdependent ... More
Essential spectra of tensor product Hilbert complexes, and the $\overline\partial$-Neumann problem on product manifoldsJul 16 2015We investigate tensor products of Hilbert complexes, in particular the (essential) spectrum of their Laplacians. It is shown that the essential spectrum of the Laplacian associated to the tensor product complex is computable in terms of the spectra of ... More
Monotone and Boolean Convolutions for Non-compactly Supported Probability MeasuresMar 14 2007Jul 03 2009The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the multiplicative boolean ... More
Weighted projective spaces and iterated Thom spacesSep 11 2011For any (n+1)-dimensional weight vector {\chi} of positive integers, the weighted projective space P(\chi) is a projective toric variety, and has orbifold singularities in every case other than CP^n. We study the algebraic topology of P(\chi), paying ... More
The equivariant cohomology of weighted projective spaceAug 11 2007May 18 2008We describe the integral equivariant cohomology ring of a weighted projective space in terms of piecewise polynomials, and thence by generators and relations. We deduce that the ring is a perfect invariant, and prove a Chern class formula for weighted ... More
Boolean convolution of probability measures on the unit circleMar 15 2004Dec 13 2006We introduce the boolean convolution for probability measures on the unit circle. Roughly speaking, it describes the distribution of the product of two boolean independent unitary random variables. We find an analogue of the characteristic function and ... More
Parametrizing Algebraic CurvesAug 31 2011We present the technique of parametrization of plane algebraic curves from a number theorist's point of view and present Kapferer's simple and beautiful (but little known) proof that nonsingular curves of degree > 2 cannot be parametrized by rational ... More
Quantifying Residual Finiteness of Linear GroupsFeb 15 2016Feb 27 2016Normal residual finiteness growth measures how well a finitely generated group is approximated by its finite quotients. We show that any linear group $\Gamma \leq \mathrm{GL}_d(K)$ has normal residual finiteness growth asymptotically bounded above by ... More
Zeros of polynomials orthogonal on several intervalsMar 28 2002Apr 30 2002First a formula for the number of zeros of the orthogonal polynomial in the intervals is presented. Then a criteria about the appearance of a zero in a gap is given. Finally a necessary and sufficient condition is derived such that the zeros of the orthogonal ... More
Cumulants in Noncommutative Probability Theory IV. De Finetti's Theorem and $L^p$-InequalitiesSep 02 2004Dec 19 2013In this paper we collect a few results about exchangeability systems in which crossing cumulants vanish, which we call noncrossing exchangeability systems. The main result is a free version of De Finetti's theorem, characterising amalgamated free products ... More
What is Stochastic Independence?Jun 03 2002The notion of a tensor product with projections or with inclusions is defined. It is shown that the definition of stochastic independence relies on such a structure and that independence can be defined in an arbitrary category with a tensor product with ... More
The Balian-Low theorem and noncommutative toriJul 03 2015Feb 01 2018We point out a link between the theorem of Balian and Low on the non-existence of well-localized Gabor-Riesz bases and a constant curvature connection on projective modules over noncommutative tori.
Substitution rules and topological properties of the Robinson tilingsOct 24 2012A relatively simple substitution for the Robinson tilings is presented, which requires only 56 tiles up to translation. In this substitution, due to Joan M. Taylor, neighboring tiles are substituted by partially overlapping patches of tiles. We show that ... More
Uniform Error Estimation for Convection-Diffusion ProblemsMar 03 2014Let us consider the singularly perturbed model problem $Lu:=-\varepsilon\Delta u-bu_x+c u =f$ with homogeneous Dirichlet boundary conditions on $\Gamma=\partial\Omega$ $u|_\Gamma =0$ on the unit-square $\Omega=(0,1)^2$. Assuming that $b>0$ is of order ... More
The site frequency spectrum of dispensable genesJul 09 2014The differences between DNA-sequences within a population are the basis to infer the ancestral relationship of the individuals. Within the classical infinitely many sites model, it is possible to estimate the mutation rate based on the site frequency ... More
Multiplicative monotone convolutionsMar 25 2005Recently, Bercovici has introduced multiplicative convolutions based on Muraki's monotone independence and shown that these convolution of probability measures correspond to the composition of some function of their Cauchy transforms. We provide a new ... More
Ideal class groups of cyclotomic number fields IIFeb 26 2012We first study some families of maximal real subfields of cyclotomic fields with even class number, and then explore the implications of large plus class numbers of cyclotomic fields. We also discuss capitulation of the minus part and the behaviour of ... More
On the surface structure of sunspotsNov 28 2012A precise knowledge of the surface structure of sunspots is essential to construct adequate input models for helioseismic inversion tools. We summarize our recent findings about the velocity and magnetic field in and around sunspots using HINODE observation. ... More
Superconvergence Using Pointwise Interpolation in Convection-Diffusion ProblemsApr 28 2013Considering a singularly perturbed convection-diffusion problem, we present an analysis for a superconvergence result using pointwise interpolation of Gau{\ss}-Lobatto type for higher-order streamline diffusion FEM. We show a useful connection between ... More
SPHERES, Jülich's High-Flux Neutron Backscattering Spectrometer at FRM IIApr 16 2012Aug 13 2012SPHERES (SPectrometer with High Energy RESolution) is a third-generation neutron backscattering spectrometer, located at the 20 MW German neutron source FRM II and operated by the Juelich Centre for Neutron Science. It offers an energy resolution (fwhm) ... More
The classification of weighted projective spacesAug 09 2011Dec 03 2012We obtain two classifications of weighted projective spaces; up to homeomorphism and up to homotopy equivalence. We show that the former coincides with Al Amrani's classification up to isomorphism of algebraic varieties, and deduce the latter by proving ... More
Image Inpainting for High-Resolution Textures using CNN Texture SynthesisDec 08 2017Feb 12 2018Deep neural networks have been successfully applied to problems such as image segmentation, image super-resolution, coloration and image inpainting. In this work we propose the use of convolutional neural networks (CNN) for image inpainting of large regions ... More
Mutants of compactified representations revisitedNov 03 2015We show that the mutants of compactified representations constructed by Franz and Puppe can be written as intersections of real quadrics involving division algebras and as generalizations of polygon spaces. We also show that these manifolds are connected ... More
A Reduction System for Optimal 1-Planar GraphsFeb 20 2016A graph with n vertices is 1-planar if it can be drawn in the plane such that each edge is crossed at most once, and is optimal if it has the maximum of 4n-8 edges. There is a two-rule graph reduction system that reduces every optimal 1-planar graph to ... More
Direct Hopf Bifurcation in Parametric Resonance of Hybridized WavesJun 04 1996We study parametric resonance of interacting waves having the same wave vector and frequency. In addition to the well-known period-doubling instability we show that under certain conditions the instability is caused by a Hopf bifurcation leading to quasiperiodic ... More
Gravitation in 4D Euclidean Space-Time GeometryOct 10 2007Jan 01 2011The Euclidean interpretation of special relativity which has been suggested by the author is a formulation of special relativity in ordinary 4D Euclidean space-time geometry. The natural and geometrically intuitive generalization of this view involves ... More
On ergodic properties of convolution operators associated with compact quantum groupsFeb 09 2008Feb 12 2008Recent results of M.Junge and Q.Xu on the ergodic properties of the averages of kernels in noncommutative L^p-spaces are applied to the analysis of the almost uniform convergence of operators induced by the convolutions on compact quantum groups.
Valuation theoretic and model theoretic aspects of local uniformizationMar 29 2010This paper gives a survey on a valuation theoretical approach to local uniformization in positive characteristic, the model theory of valued fields in positive characteristic, and their connection with the valuation theoretical phenomenon of defect.
Approximation of elements in henselizationsMar 29 2010For valued fields $K$ of rank higher than 1, we describe how elements in the henselization $K^h$ of $K$ can be approximated from within $K$; our result is a handy generalization of the well-known fact that in rank 1, all of these elements lie in the completion ... More
The algebra and model theory of tame valued fieldsMar 31 2013Jul 14 2014A henselian valued field $K$ is called a tame field if its algebraic closure $\tilde{K}$ is a tame extension, that is, the ramification field of the normal extension $\tilde{K}|K$ is algebraically closed. Every algebraically maximal Kaplansky field is ... More
On the sharpness of Green's function estimates for a convection-diffusion problemFeb 22 2011May 31 2011Linear singularly perturbed convection-diffusion problems with characteristic layers are considered in three dimensions. We demonstrate the sharpness of our recently obtained upper bounds for the associated Green's function and its derivatives in the ... More
Full analysis of the Green's function for a singularly perturbed convection-diffusion problem in three dimensionsMar 15 2011May 31 2011A linear singularly perturbed convection-diffusion problem with characteristic layers is considered in three dimensions. Sharp bounds for the associated Green's function and its derivatives are established in the $L_1$ norm. The dependence of these bounds ... More
Arithmetic of Pell surfacesAug 31 2011We define a group stucture on the primitive integer points (A,B,C) of the algebraic variety Q_0(B,C)=A^n, where Q_0 is the principal binary quadratic form of fundamental discriminant \Delta and n is a fixed integer greater than 1. A surjective homomorphism ... More
Pair correlations of aperiodic inflation rules via renormalisation: Some interesting examplesNov 03 2015This article presents, in an illustrative fashion, a first step towards an extension of the spectral theory of constant length substitutions. Our starting point is the general observation that the symbolic picture (as defined by the substitution rule) ... More
Modulation Spaces as a Smooth Structure in Noncommutative GeometrySep 28 2018Jun 05 2019We demonstrate that a class of modulation spaces are examples of a smooth structure on the noncommutative 2-torus in the sense of recent developments in KK-theory. In addition, we prove that this class of modulation spaces can be represented as corners ... More
Magnetic spectra in the tridiminished-icosahedron \{Fe$_9$\} nano-cluster by inelastic neutron scatteringJun 03 2014Inelastic neutron scattering (INS) experiments under applied magnetic field at low temperatures show detailed low lying magnetic excitations in the so called tridiminshed iron icosahedron magnetic molecule. The magnetic molecule consists of nine iron ... More
Surface Tension in Kac Glass ModelsDec 14 2009Feb 15 2010In this paper we study a distance-dependent surface tension, defined as the free-energy cost to put metastable states at a given distance. This will be done in the framework of a disordered microscopic model with Kac interactions that can be solved in ... More
Resolvent estimates and numerical implementation for the homogenisation of one-dimensional periodic mixed type problemsNov 23 2017We study a homogenisation problem for problems of mixed type in the framework of evolutionary equations. The change of type is highly oscillatory. The numerical treatment is done by a discontinuous Galerkin method in time and a continuous Galerkin method ... More
Homogenisation of parabolic/hyperbolic mediaOct 02 2018We consider an evolutionary problem with rapidly oscillating coefficients. This causes the problem to change frequently between a parabolic and an hyperbolic state. We prove convergence of the homogenisation process in the unit square and present a numerical ... More
Volume inequalities and additive maps of convex bodiesJul 31 2012Analogues of the classical inequalities from the Brunn-Minkowski theory for rotation intertwining additive maps of convex bodies are developed. Analogues are also proved of inequalities from the dual Brunn-Minkowski theory for intertwining additive maps ... More
Differentiability of the stable norm in codimension oneMar 15 2004Dec 03 2004The real homology of a compact, n-dimensional Riemannian manifold M is naturally endowed with the stable norm. The stable norm of a homology class is the minimal Riemannian volume of its representatives. If M is orientable the stable norm on H_{n-1}(M,R) ... More
The infinitely many genes model with horizontal gene transferJan 28 2013Nov 20 2014The genome of bacterial species is much more flexible than that of eukaryotes. Moreover, the distributed genome hypothesis for bacteria states that the total number of genes present in a bacterial population is greater than the genome of every single ... More
Fano schemes of generic intersections and machine learningJan 14 2013We investigate Fano schemes of conditionally generic intersections, i.e. of hypersurfaces in projective space chosen generically up to additional conditions. Via a correspondence between generic properties of algebraic varieties and events in probability ... More
Convolutions for Berezin quantization and Berezin-Lieb inequalitiesMay 16 2017Dec 14 2017Notions and results from quantum harmonic analysis, such as the convolution between functions and operators or between two operators, is identified as the appropriate setting for Berezin quantization and Berezin-Lieb inequalities. Based on this insight ... More
Non-Equilibrium relation between mobility and diffusivity of interacting Brownian particles under shearNov 09 2009We investigate the relation between mobility and diffusivity for Brownian particles under steady shear near the glass transition, using mode coupling approximations. For the two directions perpendicular to the shear direction, the particle motion is diffusive ... More
Poisson--Voronoi approximationJun 23 2009Let $X$ be a Poisson point process and $K\subset\mathbb{R}^d$ a measurable set. Construct the Voronoi cells of all points $x\in X$ with respect to $X$, and denote by $v_X(K)$ the union of all Voronoi cells with nucleus in $K$. For $K$ a compact convex ... More
Topological Insulators on the Lieb and Perovskite LatticesApr 29 2010Electrons hopping on the sites of a two-dimensional Lieb lattice and three-dimensional edge centered cubic (perovskite) lattice are shown to form topologically non-trivial insulating phases when spin-orbit coupling is introduced. These simple models on ... More
Rapid Exact Signal Scanning with Deep Convolutional Neural NetworksAug 27 2015Mar 23 2016We introduce and analyze a rigorous formulation of the dynamics of a signal processing scheme aimed at exact dense signal scanning. Related methods proposed in the recent past lack a satisfactory analysis whether they actually fulfill any exactness constraints. ... More
Probing quasi-equilibrium behavior during aging in the bi-dimensional Edwards-Anderson modelJan 14 2003Jul 10 2003This paper has been withdrawn due to new simulations that modify some of the results.
A Combinatorial Algebraic Approach for the Identifiability of Low-Rank Matrix CompletionJun 27 2012In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of arbitrary rank ... More
Towards the full N=4 conformal supergravity actionOct 16 2015Nov 29 2015Based on the known non-linear transformation rules of the Weyl multiplet fields, the action of $N=4$ conformal supergravity is constructed up to terms quadratic in the fermion fields. The bosonic sector corrects a recent result in the literature.
Automatic Clustering of a Network Protocol with Weakly-Supervised ClusteringJun 04 2018Abstraction is a fundamental part when learning behavioral models of systems. Usually the process of abstraction is manually defined by domain experts. This paper presents a method to perform automatic abstraction for network protocols. In particular ... More
On the Finiteness of the Number of Eigenvalues of Jacobi Operators below the Essential SpectrumSep 26 2001Feb 09 2014We present a new oscillation criterion to determine whether the number of eigenvalues below the essential spectrum of a given Jacobi operator is finite or not. As an application we show that Kenser's criterion for Jacobi operators follows as a special ... More
The velocity field of sunspot penumbrae II. Return flow and magnetic fields of opposite polarityDec 19 2012Jan 10 2013Aims: We search for penumbral magnetic fields of opposite polarity and for their correspondence with downflows. Methods: We used spectropolarimetric HINODE data of a spot very close to disk center to suppress the horizontal velocity components as much ... More
Tricritical Ising phase transition in two-ladder Majorana fermion latticeFeb 26 2016We introduce a two-ladder lattice model with interacting Majorana fermions that could be realized on the surfaces of a topological insulator film. We study this model by a combination of analytical and numerical techniques and find a phase diagram that ... More
Quasiparticle spectroscopy as a probe of the topological phase in graphene with heavy adatomsFeb 26 2014May 30 2014Electrons in graphene with heavy adatoms (such as In or Tl) have been predicted to form a 2D topological insulator phase with a substantial spectral gap potentially suitable for future practical applications. In order to facilitate the ongoing experimental ... More
Simplest Cubic Number FieldsFeb 27 2012In this paper we intend to show that certain integers do not occur as the norms of principal ideals in a family of cubic fields studied by Cohn, Shanks, and Ennola. These results will simplify the construction of certain unramified quadratic extensions ... More
Elimination of Ramification I: The Generalized Stability TheoremMar 29 2010We prove a general version of the "Stability Theorem": if $K$ is a valued field such that the ramification theoretical defect is trivial for all of its finite extensions, and if $F|K$ is a finitely generated (transcendental) extension of valued fields ... More
Correction and notes to the paper "A classification of Artin-Schreier defect extensions and characterizations of defectless fields"Dec 05 2018We correct a mistake in a lemma in the paper cited in the title and show that it did not affect any of the other results of the paper. To this end we prove results on linearly disjoint field extensions that do not seem to be commonly known. We give an ... More