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Results for "Lukas Giner"

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Store-to-Leak Forwarding: Leaking Data on Meltdown-resistant CPUsMay 14 2019Meltdown and Spectre exploit microarchitectural changes the CPU makes during transient out-of-order execution. Using side-channel techniques, these attacks enable leaking arbitrary data from memory. As state-of-the-art software mitigations for Meltdown ... More
An efficient implementation of Slater-Condon rulesNov 25 2013Slater-Condon rules are at the heart of any quantum chemistry method as they allow to simplify $3N$-dimensional integrals as sums of 3- or 6-dimensional integrals. In this paper, we propose an efficient implementation of those rules in order to identify ... More
statmod: Probability Calculations for the Inverse Gaussian DistributionMar 22 2016Jul 28 2016The inverse Gaussian distribution (IGD) is a well known and often used probability distribution for which fully reliable numerical algorithms have not been available. Our aim in this article is to develop software for this distribution for the R programming ... More
One-dimension cubic-quintic Gross-Pitaevskii equation in Bose-Einstein condensates in a trap potentialAug 11 2012By means of new general variational method we report a direct solution for the quintic self-focusing nonlinearity and cubic-quintic 1D Gross Pitaeskii equation (GPE) in a harmonic confined potential. We explore the influence of the 3D transversal motion ... More
Content Translation: Computer-assisted translation tool for Wikipedia articlesJun 05 2015The quality and quantity of articles in each Wikipedia language varies greatly. Translating from another Wikipedia is a natural way to add more content, but the translation process is not properly supported in the software used by Wikipedia. Past computer-assisted ... More
Electric field and exciton structure in CdSe nanocrystalsMay 30 2004Quantum Stark effect in semiconductor nanocrystals is theoretically investigated, using the effective mass formalism within a $4\times 4$ Baldereschi-Lipari Hamiltonian model for the hole states. General expressions are reported for the hole eigenfunctions ... More
Parallel Transport of Higher Flat Gerbes as an Extended Homotopy Quantum Field TheoryFeb 28 2018We prove that the parallel transport of a flat (higher) gerbe on any given target space gives rise to an extended homotopy quantum field theory. In case the target space is the classifying space of a finite group, we provide explicit formulae for this ... More
The Little Bundles OperadJan 15 2019Feb 10 2019Hurwitz spaces are homotopy quotients of the braid group action on the moduli space of principal bundles over a punctured plane. By considering a certain model for this homotopy quotient we build an aspherical topological operad that we call the little ... More
Equivariant Higher Hochschild Homology and Topological Field TheoriesSep 18 2018We present a version of higher Hochschild homology for spaces equipped with principal bundles for a structure group $G$. As coefficients, we allow $E_\infty$-algebras with $G$-action. For this homology theory, we establish an equivariant version of excision ... More
Fixed-Node Diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctionsAug 15 2014The potential energy curve of the F$_2$ molecule is calculated with Fixed-Node Diffusion Monte Carlo (FN-DMC) using Configuration Interaction (CI)-type trial wavefunctions. To keep the number of determinants reasonable (the first and second derivatives ... More
Electron-acoustic-phonon interaction in core/shell Ge/Si and Si/Ge nanowiresJul 05 2016Jul 07 2016General expressions for the electron- and hole-acoustical-phonon deformation potential Hamiltonian (H_{E-DP}) are derived for the case of Ge/Si and Si/Ge core/shell nanowire structures (NWs) with circular cross section. Based on the short-range elastic ... More
Exciton and confinement potential effects on the resonant Raman scattering in quantum dotsAug 06 1998Resonant Raman scattering in semiconductor quantum dots with spherical shape is theoretically investigated. The Frohlich-like interaction between electronic states and optical vibrations has been considered. The Raman profiles are studied for the following ... More
Bose-Einstein condensates in optical lattices: mathematical analysis and analytical approximate formulaeJul 14 2011We show that the Gross-Pitaevskii equation with cubic nonlinearity, as a model to describe the one dimensional Bose-Einstein condensates loaded into a harmonically confined optical lattice, presents a set of ground states which is orbitally stable for ... More
Sets in Almost General PositionJan 26 2016Erd\H{o}s asked the following question: given $n$ points in the plane in almost general position (no 4 collinear), how large a set can we guarantee to find that is in general position (no 3 collinear)? F\"uredi constructed a set of $n$ points in almost ... More
Lepton flavor violation in supersymmetric low-scale seesaw modelsDec 04 2013The minimal supersymmetric standard model with a low scale see-saw mechanism is presented. Within this framework, the lepton flavour violation in the charged lepton sector is thoroughly studied. Special attention is paid to the individual loop contributions ... More
An improved upper bound for the grid Ramsey problemSep 25 2018For a positive integer $r$, let $G(r)$ be the smallest $N$ such that, whenever the edges of the Cartesian product $K_N \times K_N$ are $r$-coloured, then there is a rectangle in which both pairs of opposite edges receive the same colour. In this paper, ... More
Covering complete graphs by monochromatically bounded setsMay 25 2017Given a $k$-colouring of the edges of the complete graph $K_n$, are there $k-1$ monochromatic components that cover its vertices? This important special case of the well-known Lov\'asz-Ryser conjecture is still open. In this paper we consider a strengthening ... More
Dynamical description of Tychonian UniverseApr 26 2013Mar 16 2015Using Mach's principle, we will show that the observed diurnal and annual motion of the Earth can just as well be accounted as the diurnal rotation and annual revolution of the Universe around the fixed and centered Earth. This can be performed by postulating ... More
The Intersection Problem for Finite SemigroupsJun 13 2018We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We introduce compressibility ... More
A comparison of semi-Lagrangian discontinuous Galerkin and spline based Vlasov solvers in four dimensionsMar 06 2018The purpose of the present paper is to compare two semi-Lagrangian methods in the context of the four-dimensional Vlasov--Poisson equation. More specifically, our goal is to compare the performance of the more recently developed semi-Lagrangian discontinuous ... More
A GPU accelerated and error-controlled solver for the unbounded Poisson equation in three dimensionsDec 06 2016An efficient solver for the three dimensional free-space Poisson equation is presented. The underlying numerical method is based on finite Fourier series approximation. While the error of all involved approximations can be fully controlled, the overall ... More
An adaptive step size controller for iterative implicit methodsSep 29 2017Jun 09 2018The automatic selection of an appropriate time step size has been considered extensively in the literature. However, most of the strategies developed operate under the assumption that the computational cost (per time step) is independent of the step size. ... More
Frequency Based Index Estimating the Subclusters' Connection StrengthOct 19 2017Oct 25 2017In this paper, a frequency coefficient based on the Sen-Shorrocks-Thon (SST) poverty index notion is proposed. The clustering SST index can be used as the method for determination of the connection between similar neighbor sub-clusters. Consequently, ... More
Radiation Damping of a Polarizable ParticleAug 20 2017A polarizable body moving in an external electromagnetic field will slow down. This effect is referred to as radiation damping and is analogous to Doppler cooling in atomic physics. Using the principles of special relativity we derive an expression for ... More
Pseudorandomness of the Ostrowski sum-of-digits functionNov 09 2016For an irrational $\alpha\in(0,1)$, we investigate the Ostrowski sum-of-digits function $\sigma_\alpha$. For $\alpha$ having bounded partial quotients and $\vartheta\in\mathbb R\setminus\mathbb Z$, we prove that the function $g:n\mapsto \mathrm e(\vartheta ... More
A Dynamical Bogomolov PropertyMar 07 2011A field F is said to have the Bogomolov Property related to a height function h, if h(a) is either zero or bounded from below by a positive constant for all a in F. In this paper we prove that the maximal algebraic extension of a number field K, which ... More
Small totally $p$-adic algebraic numbersFeb 16 2018Jan 10 2019The purpose of this note is to give a short and elementary proof of the fact, that the absolute logarithmic Weil-height is bounded from below by a positive constant for all totally p-adic numbers which are neither zero nor a root of unity. The proof is ... More
Invariant Hochschild cohomology of smooth functionsAug 24 2018Mar 14 2019Given an action of a Lie group on a smooth manifold, we discuss the induced action on the Hochschild cohomology of smooth functions, and notions of invariance on this space. Depending on whether one considers invariance of cochains or invariance of cohomology ... More
The Linear Ordering Polytope via RepresentationsSep 23 2011Oct 25 2011Let $P_n$ denote the $n$-th linear ordering polytope. We define projections from $P_n$ to the $n$-th permutahedron and to the $(n-1)$-st linear ordering polytope. Both projections are equivariant with respect to the natural $\Sn$-action and they project ... More
Heights and totally $p$-adic numbersApr 20 2015Oct 28 2015We study the behavior of canonical height functions $\widehat{h}_f$, associated to rational maps $f$, on totally $p$-adic fields. In particular, we prove that there is a gap between zero and the next smallest value of $\widehat{h}_f$ on the maximal totally ... More
Approaching Cusick's conjecture on the sum-of-digits functionApr 18 2019Cusick's conjecture on the binary sum of digits $s(n)$ of a nonnegative integer $n$ states the following: for all nonnegative integers $t$ we have \[ c_t=\lim_{N\rightarrow\infty}\frac 1N\left\lvert\{n<N:s(n+t)\geq s(n)\}\right\rvert>1/2. \] We prove ... More
Linearity in minimal resolutions of monomial idealsFeb 24 2017Mar 24 2017Let $S = k[x_1, \dotsc, x_n]$ be a polynomial ring over a field $k$ and let $M$ be a graded $S$-module with minimal free resolution $\mathbb{F}_\bullet$. Its linear part $lin(\mathbb{F}_\bullet)$ is obtained by deleting all non-linear entries from the ... More
A response-matrix-centred approach to presenting cross-section measurementsMar 15 2019Mar 21 2019The current canonical approach to publishing cross-section data is to unfold the reconstructed distributions. Detector effects like efficiency and smearing are undone mathematically, yielding distributions in true event properties. This is an ill-posed ... More
Generalized Monotone Triangles: an extended Combinatorial Reciprocity TheoremJul 18 2012In a recent work, the combinatorial interpretation of the polynomial alpha(n;k1,k2,...,kn) counting the number of Monotone Triangles with bottom row k1 < k2 < ... < kn was extended to weakly decreasing sequences k1 >= k2 >= ... >= kn. In this case the ... More
Stanley depth and simplicial spanning treesOct 14 2014Mar 09 2015We show that for proving the Stanley conjecture, it is sufficient to consider a very special class of monomial ideals. These ideals (or rather their lcm lattices) are in bijection with the simplicial spanning trees of skeletons of a simplex. We apply ... More
Completing the classification of representations of $\mathrm{SL}_n$ with complete intersection invariant ringDec 05 2018We present a full list of all representations of the special linear group $\mathrm{SL}_n$ over the complex numbers with complete intersection invariant ring, completing the classification of Shmelkin. For this task, we combine three techniques. Firstly, ... More
A non-Golod ring with a trivial product on its Koszul homologyNov 16 2015We present a monomial ideal $\mathfrak{a} \subset S$ such that $S/\mathfrak{a}$ is not Golod, even though the product on its Koszul homology is trivial. This constitutes a counterexample to a well-known theorem by Berglund and J\"ollenbeck (the error ... More
Wormhole Effects on Yang-Mills TheoryJul 25 1994In this paper wormhole effects on $SO(3)$ YM theory are examined. The wormhole wave functions for the scalar, the vector and the tensor expansion modes are computed assuming a small gauge coupling which leads to an effective decoupling of gravity and ... More
sl3-foam homology calculationsDec 11 2012Feb 20 2013We exhibit a certain infinite family of three-stranded quasi-alternating pretzel knots which are counterexamples to Lobb's conjecture that the sl_3-knot concordance invariant s_3 (suitably normalised) should be equal to the Rasmussen invariant s_2. For ... More
Structure preserving numerical methods for the Vlasov equationApr 09 2016To preserve a number of physically relevant invariants is a major concern when considering long time integration of the Vlasov equation. In the present work we consider the semi-Lagrangian discontinuous Galerkin method for the Vlasov-Poisson system. We ... More
A study on conserving invariants of the Vlasov equation in semi-Lagrangian computer simulationsJan 10 2016Mar 07 2017The semi-Lagrangian discontinuous Galerkin method, coupled with a splitting approach in time, has recently been introduced for the Vlasov--Poisson equation. Since these methods are conservative, local in space, and able to limit numerical diffusion, they ... More
A modern resistive magnetohydrodynamics solver using C++ and the Boost libraryJul 11 2014In this paper we describe the implementation of our C++ resistive magnetohydrodynamics solver. The framework developed facilitates the separation of the code implementing the specific numerical method and the physical model, on the one hand, from the ... More
A low-rank algorithm for weakly compressible flowApr 12 2018In this paper, we propose a numerical method for solving weakly compressible fluid flow based on a dynamical low-rank projector splitting. The low-rank splitting scheme is applied to the Boltzmann equation with BGK collision term, which results in a set ... More
A note on friezes of type $Λ_4$ and $Λ_6$Feb 22 2018We point out a certain connection between Conway-Coxeter friezes of triangulations and $p$-angulated generalisation of frieze patterns recently introduced by Holm and J{\o}rgensen: the friezes of type $\Lambda_p$ coincide with Conway-Coxeter friezes of ... More
The relative effects of dimensionality and multiplicity of hypotheses on the F-test in linear regressionNov 19 2015Nov 07 2016Recently, several authors have re-examined the power of the classical F-test in linear regression in a `large-p, large-n' framework (cf. Zhong and Chen (2011), Wang and Cui (2013)). They highlight the loss of power as the number of regressors p increases ... More
Piatetski-Shapiro sequences via Beatty sequencesJul 17 2017Integer sequences of the form $\lfloor n^c\rfloor$, where $1<c<2$, can be locally approximated by sequences of the form $\lfloor n\alpha+\beta\rfloor$ in a very good way. Following this approach, we are led to an estimate of the difference \[\sum_{n\leq ... More
A digit reversal property for an analogue of Stern's sequenceSep 17 2017We consider a variant of Stern's diatomic sequence, studied recently by Northshield. We prove that this sequence $b$ is invariant under \emph{digit reversal} in base $3$, that is, $b_n=b_{n^R}$, where $n^R$ is obtained by reversing the base-$3$ expansion ... More
A note on extensions of $\mathbb{Q}^{tr}$Aug 27 2014In this note we investigate the behaviour of the absolute logarithmic Weil-height h on extensions of the field $\mathbb{Q}^{tr}$ of totally real numbers. It is known that there is a gap between zero and the next smallest value of h on $\mathbb{Q}^{tr}$, ... More
Discrepancy results for the Van der Corput sequenceOct 04 2017Let $d_N=ND_N(\omega)$ be the discrepancy of the Van der Corput sequence in base $2$. We improve on the known bounds for the number of indices $N$ such that $d_N\leq \log N/100$. Moreover, we show that the summatory function of $d_N$ satisfies an exact ... More
A digit reversal property for Stern polynomialsOct 01 2016Nov 15 2017We consider the following polynomial generalization of Stern's diatomic series: let $s_1(x,y)=1$, and for $n\geq 1$ set $s_{2n}(x,y)=s_n(x,y)$ and $s_{2n+1}(x,y)=x\,s_n(x,y)+y\,s_{n+1}(x,y)$. The coefficient $[x^iy^j]s_n(x,y)$ is the number of hyperbinary ... More
A magnetostatic energy formula arising from the $L^2$-orthogonal decomposition of the stray fieldNov 07 2016A formula for the magnetostatic energy of a finite magnet is proven. In contrast to common approaches, the new energy identity does not rely on evaluation of a nonlocal boundary integral inside the magnet or the solution of an equivalent Dirichlet problem. ... More
A topological classification of molecules and chemical reactions with a perplectic structureDec 20 2018In this paper, a topological classification of molecules and their chemical reactions on a single particle level is proposed. We consider 0-dimensional electronic Hamiltonians in a real-space tight-binding basis with spinless time-reversal symmetry and ... More
TraX: The visual Tracking eXchange Protocol and LibraryMay 12 2017In this paper we address the problem of developing on-line visual tracking algorithms. We present a specialized communication protocol that serves as a bridge between a tracker implementation and utilizing application. It decouples development of algorithms ... More
Commuting Contractive FamiliesJan 26 2016A family $f_1,...,f_n$ of operators on a complete metric space $X$ is called contractive if there exists a positive $\lambda < 1$ such that for any $x,y$ in $X$ we have $d(f_i(x),f_i(y)) \leq \lambda d(x,y)$ for some $i$. Austin conjectured that any commuting ... More
Time-dependent CP violation in $B$ decays at BelleDec 18 2013Using the full data sample collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider, we present three recent measurements of time-dependent CP violation in $B$ decays, and a measurement of branching fraction of the $B^0\to\rho^0\rho^0$ ... More
Falsifying Baryogenesis with Neutrinoless Double Beta DecayMay 03 2016We discuss the relation between lepton number violation at high and low energies, particularly, the constraints on baryogenesis models, which would be implied by an observation of neutrinoless double beta decay. The primordial baryon asymmetry can be ... More
About a theorem of Wiener on the Bessel-Kingman HypergroupFeb 19 2016A theorem of Wiener on the circle group was strengthened and extended by Fournier in [2] to locally compact abelian groups and extended further to the Bessel-Kingman hypergroup with parameter {\alpha} = 1 / 2 by Bloom/Fournier/Leinert in [1]. We further ... More
On the Complexity of the Cayley Semigroup Membership ProblemFeb 02 2018Apr 14 2018We investigate the complexity of deciding, given a multiplication table representing a semigroup S, a subset X of S and an element t of S, whether t can be expressed as a product of elements of X. It is well-known that this problem is NL-complete and ... More
Path-by-path uniqueness of infinite-dimensional stochastic differential equationsJun 23 2017Consider the stochastic differential equation $\mathrm dX_t = -A X_t \,\mathrm dt + f(t, X_t) \,\mathrm dt + \mathrm dB_t$ in a (possibly infinite-dimensional) separable Hilbert space, where $B$ is a cylindrical Brownian motion and $f$ is a just measurable, ... More
Measurement of neutrino interactions in gaseous argon with T2KOct 03 2016The T2K near-detector, ND280, employs three large argon gas TPCs (Time Projection Chambers) for particle tracking and identification. The gas inside the TPCs can be used as an active target to study the neutrino interactions in great detail. The low density ... More
On the Hilbert series of the GrassmannianDec 15 2017We compute the Hilbert series of the complex Grassmannian using invariant theoretic methods and show that its h-polynomial coincides with the k-Narayana polynomial. We give a simplified formula for the h-polynomial of Schubert varieties. Finally, we use ... More
Linearizability of Saturated PolynomialsJul 09 2015Mar 11 2019Brjuno and R\"ussmann proved that every irrationally indifferent fixed point of an analytic function with a Brjuno rotation number is linearizable, and Yoccoz proved that this is sharp for quadratic polynomials. Douady conjectured that this is sharp for ... More
Smooth Siegel disks without number theory: A remark on a proof by Buff and CheritatOct 26 2005X. Buff and A. Cheritat proved that there are quadratic polynomials having Siegel disks with smooth boundaries. Based on a simplification of A. Avila, we give yet another simplification of their proof. The main tool used is a harmonic function introduced ... More
On Temple--Kato like inequalities and applicationsNov 16 2005May 16 2007We give both lower and upper estimates for eigenvalues of unbounded positive definite operators in an arbitrary Hilbert space. We show scaling robust relative eigenvalue estimates for these operators in analogy to such estimates of current interest in ... More
The Golod property for Stanley-Reisner rings in varying characteristicApr 20 2015Jan 19 2016We show that the Golod property of a Stanley-Reisner ring can depend on the characteristic of the base field. More precisely, for every finite set $T$ of prime numbers we construct simplicial complexes $\Delta$ and $\Gamma$, such that $\mathbb{K}[\Delta]$ ... More
On the exceptional set in a conditional theorem of LittlewoodApr 03 2014Sep 11 2014In 1952, Littlewood stated a conjecture about the average growth of spherical derivatives of polynomials, and showed that it would imply that for entire function of finite order, "most" preimages of almost all points are concentrated in a small subset ... More
The level of distribution of the Thue--Morse sequenceMar 05 2018The level of distribution of a complex valued sequence $b$ measures "how well $b$ behaves" on arithmetic progressions $nd+a$. Determining whether $\theta$ is a level of distribution for $b$ involves summing a certain error over $d\leq D$, where $D$ depends ... More
Normality of the Thue--Morse sequence along Piatetski-Shapiro sequencesJul 17 2017We prove that for $1<c<4/3$ the subsequence of the Thue--Morse sequence $\mathbf t$ indexed by $\lfloor n^c\rfloor$ defines a normal sequence, that is, each finite sequence $(\varepsilon_0,\ldots,\varepsilon_{T-1})\in \{0,1\}^T$ occurs as a contiguous ... More
On homology spheres with few minimal non facesJan 24 2011Apr 13 2011Let \Delta be a (d-1)-dimensional homology sphere on n vertices with m minimal non-faces. We consider the invariant \alpha := m - (n-d) and prove that for a given value of \alpha, there are only finitely many homology spheres that cannot be obtained through ... More
An optimization approach for dynamical Tucker tensor approximationSep 28 2017Feb 07 2018An optimization-based approach for the Tucker tensor approximation of parameter-dependent data tensors and solutions of tensor differential equations with low Tucker rank is presented. The problem of updating the tensor decomposition is reformulated as ... More
Evaluation of the Intel Xeon Phi and NVIDIA K80 as accelerators for two-dimensional panel codesNov 06 2015To predict the properties of fluid flow over a solid geometry is an important engineering problem. In many applications so-called panel methods (or boundary element methods) have become the standard approach to solve the corresponding partial differential ... More
Moving Five-Branes and CosmologyOct 03 2002We discuss low-energy heterotic M-theory with five-branes in four and five dimensions and its application to moving brane cosmology.
The No-Boundary Wave Function and the Duration of the Inflationary PeriodSep 07 1994For the simplest minisuperspace model based on a homogeneous, isotropic metric and a minimally coupled scalar field we derive analytic expressions for the caustic which separates Euklidean and Minkowskian region and its breakdown value $\p_*$. This value ... More
Spontaneous breaking of Lorentz symmetry in (2+1)-dimensional QEDApr 21 2016Jul 21 2016The phase diagram of massless quantum electrodynamics in three space-time dimensions as a function of fermion flavor number $N$ exhibits two well-known phases: at large $N > N_c^{conf}$ the system is in a conformal gapless state, while for small $N < ... More
The structure of DGA resolutions of monomial idealsOct 20 2016Let $I \subset k[x_1, \dotsc, x_n]$ be a squarefree monomial ideal a polynomial ring. In this paper we study multiplications on the minimal free resolution $\mathbb{F}$ of $S/I$. In particular, we characterize the possible vectors of total Betti numbers ... More
Motion planning in high-dimensional spacesJun 19 2018Jul 19 2018Motion planning is a key tool that allows robots to navigate through an environment without collisions. The problem of robot motion planning has been studied in great detail over the last several decades, with researchers initially focusing on systems ... More
Small Sets with Large Difference SetsMay 24 2017For every $\epsilon > 0$ and $k \in \mathbb{N}$, Haight constructed a set $A \subset \mathbb{Z}_N$ ($\mathbb{Z}_N$ stands for the integers modulo $N$) for a suitable $N$, such that $A-A = \mathbb{Z}_N$ and $|kA| < \epsilon N$. Recently, Nathanson posed ... More
Newton-Machian analysis of Neo-tychonian model of planetary motionsJan 25 2013Feb 06 2013The calculation of the trajectories in the Sun-Earth-Mars system will be performed in two different models, both in the framework of Newtonian mechanics. First model is well-known Copernican system, which assumes the Sun is at rest and all the planets ... More
Relative convergence estimates for the spectral asymptotic in the Large Coupling LimitFeb 13 2009We prove optimal convergence estimates for eigenvalues and eigenvectors of a class of singular/stiff perturbed problems. Our profs are constructive in nature and use (elementary) techniques which are of current interest in computational Linear Algebra ... More
High performance computing aspects of a dimension independent semi-Lagrangian discontinuous Galerkin codeJan 22 2015The recently developed semi-Lagrangian discontinuous Galerkin approach is used to discretize hyperbolic partial differential equations (usually first order equations). Since these methods are conservative, local in space, and able to limit numerical diffusion, ... More
Homomorphisms of Gray-categories as pseudo algebrasAug 15 2014Given Gray-categories $P$ and $L$, there is a Gray-category $\mathrm{Tricat}_{\mathrm{ls}}(P,L)$ of locally strict trihomomorphisms with domain $P$ and codomain $L$, tritransformations, trimodifications, and perturbations. If the domain $P$ is small and ... More
Evaluation of the Intel Xeon Phi 7120 and NVIDIA K80 as accelerators for two-dimensional panel codesNov 06 2015Mar 28 2018To optimize the geometry of airfoils for a specific application is an important engineering problem. In this context genetic algorithms have enjoyed some success as they are able to explore the search space without getting stuck in local optima. However, ... More
Spontaneous breaking of Lorentz symmetry in $(2+ε)$-dimensional QEDApr 21 2016Nov 15 2016The phase diagram of massless quantum electrodynamics in three space-time dimensions as a function of fermion flavor number $N$ exhibits two well-known phases: at large $N > N_c^{conf}$ the system is in a conformal gapless state, while for small $N < ... More
Betti posets and the Stanley depthSep 28 2015Feb 05 2016Let $S$ be a polynomial ring and let $I \subseteq S$ be a monomial ideal. In this short note, we propose the conjecture that the Betti poset of $I$ determines the Stanley projective dimension of $S/I$ or $I$. Our main result is that this conjecture implies ... More
Linearizability of Saturated PolynomialsJul 09 2015Jul 14 2015Brjuno and R\"ussmann proved that every irrationally indifferent fixed point of an analytic function with a Brjuno rotation number is linearizable, and Yoccoz proved that this is sharp for quadratic polynomials. Douady conjectured that this is sharp for ... More
Invariant Hochschild cohomology of smooth functionsAug 24 2018Sep 26 2018Given an action of a Lie group on a smooth manifold, we discuss the induced action on the Hochschild cohomology of smooth functions, and notions of invariance on this space. Depending on whether one considers invariance of cochains or invariance of cohomology ... More
Heights of points with bounded ramificationJan 16 2012Nov 18 2013Let $E$ be an elliptic curve defined over a number field $K$ with fixed non-archimedean absolute value $v$ of split-multiplicative reduction, and let $f$ be an associated Latt\`es map. Baker proved in 2003 that the N\'eron-Tate height on $E$ is either ... More
Rasmussen's spectral sequences and the sl(N)-concordance invariantsOct 11 2013Jul 18 2014Combining known spectral sequences with a new spectral sequence relating reduced and unreduced sl(N)-homology yields a relationship between the Homflypt-homology of a knot and its sl(N)-concordance invariants. As an application, some of the sl(N)-concordance ... More
Polytopal affine semigroups with holes deep insideOct 16 2012Mar 20 2013Given a non-negative integer k, we construct a lattice 3-simplex P with the following property: The affine semigroup Q_P associated to P is not normal, and every element $q \in \sat{Q}_P \setminus Q_P$ has lattice distance at least k above every facet ... More
Algebraic Multilevel Methods for Markov ChainsNov 12 2017Dec 30 2017A new algebraic multilevel algorithm for computing the second eigenvector of a column-stochastic matrix is presented. The method is based on a deflation approach in a multilevel aggregation framework. In particular a square and stretch approach, first ... More
Sharp bounds for the valence of certain harmonic polynomialsOct 25 2005D. Khavinson and G. Swiatek proved that harmonic polynomials p(z)+q(z), where p is holomorphic, q is antiholomorphic, and deg p = n > 1 = deg q, can have at most 3n-2 complex zeros. We show that this bound is sharp for all n by proving a conjecture of ... More
The structure of DGA resolutions of monomial idealsOct 20 2016Jun 20 2018Let $I \subset k[x_1, \dotsc, x_n]$ be a squarefree monomial ideal a polynomial ring. In this paper we study multiplications on the minimal free resolution $\mathbb{F}$ of $k[x_1, \dotsc, x_n]/I$. In particular, we characterize the possible vectors of ... More
Boundary algebra of a GL$_m$-dimerApr 19 2018We consider GL$_m$-dimers of triangulations of regular convex $n$-gons, which give rise to a dimer model with boundary $Q$ and a dimer algebra $\Lambda_Q$. Let $e_b$ be the sum of the idempotents of all the boundary vertices, and $\mathcal{B}_Q:= e_b ... More
A magnetostatic energy formula arising from the $L^2$-orthogonal decomposition of the stray fieldNov 07 2016Jul 23 2018A formula for the magnetostatic energy of a finite magnet is proven. In contrast to common approaches, the new energy identity does not rely on evaluation of a nonlocal boundary integral inside the magnet or the solution of an equivalent Dirichlet problem. ... More
Spectral inequalities for Jacobi operators and related sharp Lieb-Thirring inequalities on the continuumOct 14 2013In this paper we approximate a Schr\"odinger operator on $L^2(\R)$ by Jacobi operators on $\ell^2(\Z)$ to provide new proofs of sharp Lieb-Thirring inequalities for the powers $\gamma=1/2$ and $\gamma=3/2$. To this end we first investigate spectral inequalities ... More
Gorensteinness and iteration of Cox rings for Fano type varietiesMar 19 2019We show that finitely generated Cox rings are Gorenstein. This leads to a refined characterization of varieties of Fano type: they are exactly those projective varieties with Gorenstein canonical quasicone Cox ring. We then show that for varieties of ... More
Contractive Families on Compact SpacesDec 02 2013A family f_1,...,f_n of operators on a complete metric space X is called contractive if there exists lambda < 1 such that for any x,y in X we have d(f_i(x),f_i(y)) leq lambda d(x,y) for some i. Stein conjectured that for any contractive family there is ... More
Classification theorem for strong triangle blocking arrangementsSep 23 2018A strong triangle blocking arrangement is a geometric arrangement of some line segments in a triangle with certain intersection properties. It turns out that they are closely related to blocking sets. Our aim in this paper is to prove a classification ... More
Long-Range Superharmonic Josephson CurrentJan 27 2011Jul 23 2011We consider a long superconductor-ferromagnet-superconductor junction with one spin-active region. It is shown that an \textit{odd} number of Cooper pairs cannot have a long-range propagation when there is \textit{only one} spin-active region. When temperature ... More
Polynomial bound for partition rank in terms of analytic rankFeb 26 2019Let $G_1, \dots, G_k$ be vector spaces over a finite field $\mathbb{F} = \mathbb{F}_q$ with a non-trivial additive character $\chi$. The analytic rank of a multilinear form $\alpha \colon G_1 \times \dots \times G_k \to \mathbb{F}$ is defined as $\operatorname{arank}(\alpha) ... More