Results for "Felix Bahr"

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Extraction of bare Form Factors for $\mathrm B_\mathrm s \to \mathrm K \ell ν$ Decays in non-perturbative HQETMar 14 2019We discuss the extraction of the ground state $\langle \mathrm{K} ({\bf p})|V_\mu(0)|\mathrm{B} ({\bf 0})\rangle$ matrix elements from Euclidean lattice correlation functions. The emphasis is on the elimination of excited state contributions. Two typical ... More
Operator Spin Foams: holonomy formulation and coarse grainingDec 15 2011A dual holonomy version of operator spin foam models is presented, which is particularly adapted to the notion of coarse graining. We discuss how this leads to a natural way of comparing models on different discretization scales, and a notion of renormalization ... More
Breaking and restoring of diffeomorphism symmetry in discrete gravitySep 30 2009We discuss the fate of diffeomorphism symmetry in discrete gravity. Diffeomorphism symmetry is typically broken by the discretization. This has repercussions for the observable content and the canonical formulation of the theory. It might however be possible ... More
Automorphisms in Loop Quantum GravityNov 02 2007We investigate a certain distributional extension of the group of spatial diffeomorphisms in Loop Quantum Gravity. This extension, which is given by the automorphisms Aut(P) of the path groupoid P, was proposed by Velhinho and is inspired by category ... More
Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groupsSep 28 2007This is the second paper concerning gauge-invariant coherent states for Loop Quantum Gravity. Here, we deal with the gauge group SU(2), this being a significant complication compared to the abelian U(1) case encountered in the previous article. We study ... More
Discretisations, Constraints and Diffeomorphisms in Quantum GravityNov 08 2011Jan 08 2012In this review we discuss the interplay between discretization, constraint implementation, and diffeomorphism symmetry in Loop Quantum Gravity and Spin Foam models. To this end we review the Consistent Discretizations approach, which is an application ... More
B $\to$ $π$ form factor with 2 flavours of $O(a)$ improved Wilson quarksOct 12 2012The determinations of $|V_{\rm ub}|$ from the exclusive branching ratios of $B\to \tau \nu$ and $B \to \pi l \nu$ tend to show a tension at the level of $3\sigma$ \cite{Beringer:1900zz}. On the theoretical side they depend on the lattice computation of ... More
Continuum limit of the leading order HQET form factor in $B_s \to K\ellν$ decaysJan 17 2016Jun 02 2016We discuss the computation of form factors for semi-leptonic decays of $\rm B$-, $\rm B_s$- mesons in lattice QCD. Considering in particular the example of the static $\rm B_s$ form factors we demonstrate that after non-perturbative renormalization the ... More
Form factors for $\mathrm B_\mathrm s \to \mathrm K \ell ν$ decays in Lattice QCDNov 14 2014We present the current status of the computation of the form factor $f_+ (q^2)$ for the semi-leptonic decay $\mathrm B_\mathrm s \to \mathrm K \ell \nu$ by the ALPHA collaboration. We use gauge configurations which were generated as part of the Coordinated ... More
Non-convex 4d polytopes in Spin Foam ModelsDec 26 2018In this article we consider non-convex $4d$ polytopes in $\mathbb{R}^4$. The paper consist of two parts: Firstly, we extend the proof of the formula for the $4d$ volume in terms of $2d$ face bivectors and boundary graph crossings from convex to non-convex ... More
Strict Ideal Completions of the Lambda CalculusMay 17 2018The infinitary lambda calculi pioneered by Kennaway et al. extend the basic lambda calculus by metric completion to infinite terms and reductions. Depending on the chosen metric, the resulting infinitary calculi exhibit different notions of strictness. ... More
On background-independent renormalization of spin foam modelsJul 29 2014Sep 09 2014In this article we discuss an implementation of renormalization group ideas to spin foam models, where there is no a priori length scale with which to define the flow. In the context of the continuum limit of these models, we show how the notion of cylindrical ... More
On knottings in the physical Hilbert space of LQG as given by the EPRL modelJun 03 2010We consider the EPRL spin foam amplitude for arbitrary embedded two-complexes. Choosing a definition of the face- and edge amplitudes which lead to spin foam amplitudes invariant under trivial subdivisions, we investigate invariance properties of the ... More
Volume of 4-polytopes from bivectorsAug 29 2018In this article we prove a formula for the volume of 4-dimensional polytopes, in terms of their face bivectors, and the crossings within their boundary graph. This proves that the volume is an invariant of bivector-coloured graphs in $S^3$.
The Hot Bang state of massless fermionsApr 25 2005In 2002, a method has been proposed by Buchholz et al. in the context of Local Quantum Physics, to characterize states that are locally in thermodynamic equilibrium. It could be shown for the model of massless bosons that these states exhibit quite interesting ... More
Soft interactions in Herwig++May 28 2009We describe the recent developments to extend the multi-parton interaction model of underlying events in Herwig++ into the soft, non-perturbative, regime. This allows the program to describe also minimum bias collisions in which there is no hard interaction, ... More
Numerical evidence for a phase transition in 4d spin foam quantum gravityMay 24 2016Oct 12 2016Building on recent advances in defining Wilsonian RG flows, and in particular the notion of scales, for background-independent theories, we present a first investigation of the renormalization of the 4d spin foam path integral for quantum gravity, both ... More
Investigation of the Spinfoam Path integral with Quantum Cuboid IntertwinersAug 31 2015May 17 2016In this work, we investigate the 4d path integral for Euclidean quantum gravity on a hypercubic lattice, as given by the Spin Foam model by Engle, Pereira, Rovelli, Livine, Freidel and Krasnov (EPRL-FK). To tackle the problem, we restrict to a set of ... More
Subrings of $\mathbb{C}$ Generated by AnglesJan 02 2016Consider the following inductively defined set. Given a collection $U$ of unit magnitude complex numbers, and a set initially containing just 0 and 1, through each point in the set, draw lines whose angles with the real axis are in $U$. Add every intersection ... More
Active double emulsionsOct 16 2018Jan 08 2019The capability to produce controllable, active microcapsules would present a leap forward in the development of artificial cells, microreactors, and microsensors. One example of inactive microcapsules are double emulsions, or droplets-in-droplets, which ... More
(Broken) Gauge Symmetries and Constraints in Regge CalculusMay 11 2009We will examine the issue of diffeomorphism symmetry in simplicial models of (quantum) gravity, in particular for Regge calculus. We find that for a solution with curvature there do not exist exact gauge symmetries on the discrete level. Furthermore we ... More
Approximating the physical inner product of Loop Quantum CosmologyJul 19 2006In this article, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: Firstly, we compute it analytically ... More
Definition of the Dirac Sea in the Presence of External FieldsMay 02 1997Jan 06 2009It is shown that the Dirac sea can be uniquely defined for the Dirac equation with general interaction, if we impose a causality condition on the Dirac sea. We derive an explicit formula for the Dirac sea in terms of a power series in the bosonic potentials. ... More
Dynamical phase transitions in glasses induced by the ruggedness of the free energy landscapeNov 10 1999We propose damage spreading (DS) as a tool to investigate the topological features related to the ruggedness of the free energy landscape. We argue that DS measures the positiveness of the largest Lyapunov exponent associated to the basins of attraction ... More
Cross-over in scaling laws: A simple example from micromagneticsMay 01 2003Scaling laws for characteristic length scales (in time or in the model parameters) are both experimentally robust and accessible for rigorous analysis. In multiscale situations cross--overs between different scaling laws are observed. We give a simple ... More
Circular velocity profiles of dark matter haloesMar 03 2004Dec 19 2005We use a high-resolution simulation of a galaxy-sized dark matter halo, published simulated data as well as four cluster-sized haloes from Fukushige, Kawai & Makino to study the inner halo structure in a Lambda cold dark matter cosmology. We find that ... More
Reactor Neutrino Physics -- An UpdateJun 18 1999We review the status and the results of reactor neutrino experiments. Long baseline oscillation experiments at Palo Verde and Chooz have provided limits for the oscillation parameters while the recently proposed Kamland experiment at a baseline of more ... More
Relative entropies and their use in quantum information theoryNov 27 2016This dissertation investigates relative entropies, also called generalized divergences, and how they can be used to characterize information-theoretic tasks in quantum information theory. The main goal is to further refine characterizations of the optimal ... More
Phenomenology of Enhanced Light Quark Yukawa Couplings and the $W^\pm h$ Charge AsymmetrySep 21 2016I propose the measurement of the $W^\pm h$ charge asymmetry as a consistency test for the Standard Model (SM) Higgs, which is sensitive to enhanced Yukawa couplings of the first and second generation quarks. I present a collider analysis for the charge ... More
Causal Fermion Systems -- An OverviewMay 19 2015Jul 28 2015The theory of causal fermion systems is an approach to describe fundamental physics. We here introduce the mathematical framework and give an overview of the objectives and current results.
Quantum Ergodicity and the Analysis of Semiclassical Pseudodifferential OperatorsOct 11 2014This undergraduate thesis is concerned with developing the tools of differential geometry and semiclassical analysis needed to understand the the quantum ergodicity theorem of Schnirelman (1974), Zelditch (1987), and Colin de Verdi\`ere (1985) and the ... More
Affine differential geometry and smoothness maximization as tools for identifying geometric movement primitivesSep 02 2014Jan 27 2016Neuroscientific studies of drawing-like movements usually analyze neural representation of either geometric (eg. direction, shape) or temporal (eg. speed) features of trajectories rather than trajectory's representation as a whole. This work is about ... More
Automating Political Bias PredictionAug 07 2016Every day media generate large amounts of text. An unbiased view on media reports requires an understanding of the political bias of media content. Assistive technology for estimating the political bias of texts can be helpful in this context. This study ... More
Quadratic Equations in Three Variables over Gaussian IntegersJul 25 2016We develop an algebraic method of studying of Diophantine quadratic equations in three variables over the ring of Gaussian integers.
Photon propagation in slowly varying electromagnetic fieldsJul 06 2016We study the effective theory of soft photons in slowly varying electromagnetic background fields at one-loop order in QED. This is of relevance for the study of all-optical signatures of quantum vacuum nonlinearity in realistic electromagnetic background ... More
Fermat's Last Theorem: Algebra and Number TheoryMay 02 2016Jul 03 2016In our work we give the examples using Fermat's Last Theorem for solving some problems from algebra and number theory.
The Continuum Limit of Causal Fermion SystemsMay 16 2016Aug 21 2016This monograph introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting cases and is ... More
Independence and Matching Number in Graphs with Maximum Degree 4Dec 02 2013We prove that $\frac{7}{4}\alpha(G)+\beta(G)\geq n(G)$ and $\alpha(G)+\frac{3}{2}\beta(G)\geq n(G)$ for every triangle-free graph $G$ with maximum degree at most $4$, where $\alpha(G)$ is the independence number and $\beta(G)$ is the matching number of ... More
A Universal Quaternary Quadratic Form over Gaussian IntegersOct 23 2013May 08 2014In this article we show that the form $x^2 + iy^2 + z^2 + iw^2$ represents all gaussian integers. The main tools used in this proof are Fermat's little theorem (over finite field extensions), the Mordell-Niven theorem (representation of some gaussians), ... More
Perturbative Quantum Field Theory in the Framework of the Fermionic ProjectorOct 15 2013Apr 16 2014We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the ... More
Set theory and topology. An introduction to the foundations of analysis. Part II: Topology - Fundamental notionsJun 28 2013We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as well as their ... More
Diophantine Inequalities with Primes, Auxiliary Inequalities, Evaluations of the Difference between Consecutive PrimesOct 07 2015The goal of the present paper is to present a method of proving of Diophantine inequalities with primes through the use of auxiliary inequalities and available evaluations of the difference between consecutive primes. We study the Legendre - Ingham's ... More
Rational formality of mapping spacesMar 29 2010Let X and Y be finite nilpotent CW complexes with dimension of X less than the connectivity of Y. Generalizing results of Vigu\'e-Poirrier and Yamaguchi, we prove that the mapping space Map(X,Y) is rationally formal if and only if Y has the rational homotopy ... More
Anatomizing Exotic Production of the Higgs BosonApr 10 2014We discuss exotic production modes of the Higgs boson and how their phenomenology can be probed in current Higgs analyses. We highlight the importance of differential distributions in disentangling standard production mechanisms from exotic modes. We ... More
Uniqueness of compact tangent flows in Mean Curvature FlowJul 22 2011Oct 11 2011We show, for mean curvature flows in Euclidean space, that if one of the tangent flows at a given space-time point consists of a closed, multiplicity-one, smoothly embedded self-similar shrinker, then it is the unique tangent flow at that point. That ... More
Evolution of area-decreasing maps between two-dimensional Euclidean spacesAug 18 2016We consider the mean curvature flow of the graph of a smooth map $f:\mathbb{R}^2\to\mathbb{R}^2$ between two-dimensional Euclidean spaces. If $f$ satisfies an area-decreasing property, the solution exists for all times and the evolving submanifold stays ... More
Volume preserving embeddings of open subsets of $R^n$ into manifoldsDec 23 2001We consider a connected smooth $n$-dimensional manifold $M$ endowed with a volume form $\Omega$, and we show that an open subset $U$ of $R^n$ of Lebesgue measure $\Vol (U)$ embeds into $M$ by a smooth volume preserving embedding whenever the volume condition ... More
A spectral bound for graph irregularityAug 18 2013The imbalance of an edge $e=\{u,v\}$ in a graph is defined as $i(e)=|d(u)-d(v)|$, where $d(\cdot)$ is the vertex degree. The irregularity $I(G)$ of $G$ is then defined as the sum of imbalances over all edges of $G$. This concept was introduced by Albertson ... More
Vacuum birefringence in the head-on collision of XFEL and optical high-intensity laser pulsesJul 09 2018The focus of this article is on providing compact analytical expressions for the differential number of polarization flipped signal photons constituting the signal of vacuum birefringence in the head-on collision of x-ray free electron (XFEL) and optical ... More
A general version of Price's theoremOct 10 2017Assume that $X_{\Sigma}\in\mathbb{R}^{n}$ is a random vector following a multivariate normal distribution with zero mean and positive definite covariance matrix $\Sigma$. Let $g:\mathbb{R}^{n}\to\mathbb{C}$ be measurable and of moderate growth, e.g., ... More
Efficient Tree Solver for Hines Matrices on the GPUOct 30 2018Nov 06 2018The human brain consists of a large number of interconnected neurons communicating via exchange of electrical spikes. Simulations play an important role in better understanding electrical activity in the brain and offers a way to to compare measured data ... More
Evolution of Contractions between Non-Compact ManifoldsMay 29 2018Let $N$ be a complete manifold with bounded geometry, such that $\sec_N\le -\sigma < 0$ for some positive constant $\sigma$. We investigate the mean curvature flow of the graphs of smooth length-decreasing maps $f:\mathbb{R}^m\to N$. In this case, the ... More
Convergence theorems for graph sequencesApr 03 2013Jan 13 2015In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We examine their ... More
Measurements of the properties of Lambda_c(2595), Lambda_c(2625), Sigma_c(2455), and Sigma_c(2520) baryonsMay 30 2011Jul 28 2011We report measurements of the resonance properties of Lambda_c(2595)+ and Lambda_c(2625)+ baryons in their decays to Lambda_c+ pi+ pi- as well as Sigma_c(2455)++,0 and Sigma_c(2520)++,0 baryons in their decays to Lambda_c+ pi+/- final states. These measurements ... More
Light-Cone Expansion of the Dirac Sea with Light Cone IntegralsJul 13 1997The Dirac sea is calculated in an expansion around the light cone. The method is to analyze the perturbation expansion for the Dirac sea in position space. This leads to integrals over expressions containing distributions which are singular on the light ... More
Derivation of Local Gauge Freedom from a Measurement PrincipleJan 06 1997Apr 07 1999We define operator manifolds as manifolds on which a spectral measure on a Hilbert space is given as additional structure. The spectral measure mathematically describes space as a quantum mechanical observable. We show that the vectors of the Hilbert ... More
The maximum number of intersections of two polygonsJul 04 2012Feb 10 2015We investigate the maximum number of intersections between two polygons with p and q vertices, respectively, in the plane. The cases where p or q is even or the polygons do not have to be simple are quite easy and already known, but when p and q are both ... More
Chaos in short-range spin glassesJul 29 1993The nature of static chaos in Ising spin glasses is studied. For the problem of chaos with magnetic field, scaling relations in the case of the SK model and short-range models are presented. Our results also suggest that if there is de Almeida-Thouless ... More
Solvable dynamics in a system of interacting random topsMay 21 1997In this letter a new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops with random precession frequencies. The model allows for an explicit study of orientational effects in synchronized phenomena. ... More
An extension theorem in symplectic geometryDec 31 2001We extend the ``Extension after Restriction Principle'' for symplectic embeddings of bounded starlike domains to a large class of symplectic embeddings of unbounded starlike domains.
Galactic Sources of High Energy NeutrinosFeb 26 2007The undisputed galactic origin of cosmic rays at energies below the so-called knee implies an existence of a nonthemal population of galactic objects which effectively accelerate protons and nuclei to TeV-PeV energies. The distinct signatures of these ... More
The Cooling Behavior of Thermal Pulses in Gamma-Ray BurstsJun 30 2004Nov 09 2004We discuss gamma-ray bursts that have very hard spectra, consistent with black-body radiation, throughout their duration. We find that the temperature decay during a pulse can be well described by a broken power-law in time, with an initially constant ... More
Quartic Equations with Trivial Solutions over Gaussian IntegersJul 28 2016In our work we study the equations of the form $aX^4+bX^2 Y^2+cY^4=dZ^2$ over Gaussian integers by a method of the resolvents. We study as a new equations $X^4+6X^2 Y^2+Y^4=Z^2$ (Mordell's equation over $\mathbb{Z}[i]$), $X^4+6(1+i)X^2Y^2+2iY^4=Z^2$ and ... More
Fermat's Last Theorem: Algebra, Geometry, and Number TheoryJul 16 2016In our work we give the examples using Fermat's Last Theorem for solving some problems from algebra, geometry and number theory
Fast Gibbs sampling for high-dimensional Bayesian inversionFeb 27 2016Jul 05 2016Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to explore and ... More
Instability and InformationNov 11 2015Many complex systems exhibit extreme events far more often than expected for a normal distribution. This work examines how self-similar bursts of activity across several orders of magnitude can emerge from first principles in systems that adapt to information. ... More
On the Difference between Consecutive Primes and Estimates of the Number of Primes in the Interval $(n, 2n)$Jul 24 2015Using evaluations of the difference between consecutive primes we develop another way of estimating of the number of primes in the interval $(n, 2n)$. We also discuss the ultra Cramer conjecture, $p_{n+1} - p_n = O(log^{1+\epsilon}p_n)$ where $\epsilon ... More
Linear idempotents in Matsuo algebrasJun 26 2015Matsuo algebras are an algebraic incarnation of 3-transposition groups with a parameter $\alpha$, where idempotents takes the role of the transpositions. We show that a large class of idempotents in Matsuo algebras satisfy the Seress property, making ... More
Induced Matchings in Graphs of Maximum Degree 4Jul 31 2014For a graph $G$, let $\nu_s(G)$ be the induced matching number of $G$. We prove the sharp bound $\nu_s(G)\geq \frac{n(G)}{9}$ for every graph $G$ of maximum degree at most $4$ and without isolated vertices that does not contain a certain blown up $5$-cycle ... More
Fusion rules from root systems I: case ${\rm A}_n$Mar 13 2014Axial algebras are commutative algebras generated by idempotents; they generalise associative algebras by allowing the idempotents to have additional eigenvectors, controlled by fusion rules. If the fusion rules are $\mathbb{Z}/2$-graded, axial algebras ... More
Review of LHC Dark Matter SearchesFeb 08 2017Mar 06 2017This review discusses both experimental and theoretical aspects of searches for dark matter at the LHC. An overview of the various experimental search channels is given, followed by a summary of the different theoretical approaches for predicting dark ... More
New results on eigenvalues and degree deviationMar 11 2014Let $G$ be a graph. In a famous paper Collatz and Sinogowitz had proposed to measure its deviation from regularity by the difference of the (adjacency) spectral radius and the average degree: $\epsilon(G)=\rho(G)-\frac{2m}{n}$. We obtain here a new upper ... More
On the LHC sensitivity for non-thermalised hidden sectorsJan 23 2018We show under rather general assumptions that hidden sectors that never reach thermal equilibrium in the early Universe are also inaccessible for the LHC. In other words, any particle that can be produced at the LHC must either have been in thermal equilibrium ... More
Stability Conditions and Lagrangian CobordismsDec 06 2017Jul 17 2018In this paper we study the interplay between Lagrangian cobordisms and stability conditions. We show that any stability condition on the derived Fukaya category $D\mathcal{F}uk(M)$ of a symplectic manifold $(M,\omega)$ induces a stability condition on ... More
Causal Fermion Systems: A Primer for Lorentzian GeometersSep 13 2017Feb 20 2018We give a brief introduction to causal fermion systems with a focus on the geometric structures in space-time.
Pressure induced magnetism in rotated graphene bilayersNov 10 2018Using ab initio methods based on the density functional theory we show that rotated graphene bilayers at angles different from the magic ones can have an electronic spectrum similar to those by applying moderate external pressures. We find that for an ... More
Spectral Aspects of the Evolution of Gamma-Ray BurstsOct 12 1999A review on the spectral and temporal properties of gamma-ray bursts is given. Special attention is paid to the spectral evolution of their continuum emission and its connection to the time evolution of the intensity. Efforts on systematizing these observations ... More
Smoothly Broken Power Law Spectra of Gamma-Ray BurstsNov 30 1998A five-parameter expression for a smoothly broken power law is presented. It is used to fit Gamma-Ray Burst (GRB) spectra observed by BATSE. The function is compared to previously used four-parameter functions, such as a sharply broken power law and the ... More
A primer on information theory, with applications to neuroscienceApr 08 2013Oct 07 2013Given the constant rise in quantity and quality of data obtained from neural systems on many scales ranging from molecular to systems', information-theoretic analyses became increasingly necessary during the past few decades in the neurosciences. Such ... More
Propensity score matching in SPSSJan 30 2012Propensity score matching is a tool for causal inference in non-randomized studies that allows for conditioning on large sets of covariates. The use of propensity scores in the social sciences is currently experiencing a tremendous increase; however it ... More
Glassiness in a model without energy barriersApr 20 1995Apr 22 1995We propose a microscopic model without energy barriers in order to explain some generic features observed in structural glasses. The statics can be exactly solved while the dynamics has been clarified using Monte Carlo calculations. Although the model ... More
Static chaos and scaling behaviour in the spin-glass phaseApr 09 1994We discuss the problem of static chaos in spin glasses. In the case of magnetic field perturbations, we propose a scaling theory for the spin-glass phase. Using the mean-field approach we argue that some pure states are suppressed by the magnetic field ... More
On a question of Dusa McDuffJan 01 2002Consider the $2n$-dimensional closed ball $B$ of radius 1 in the $2n$-dimensional symplectic cylinder $Z = D \times R^{2n-2}$ over the closed disc $D$ of radius 1. We construct for each $\epsilon >0$ a Hamiltonian deformation $\phi$ of $B$ in $Z$ of energy ... More
MicroLux: high-precision timing of high-speed photometric observationsJul 03 2008MicroLux is a GPS-based high precision and high speed timing add-on to the Calar Alto Lucky Imaging camera AstraLux. It allows timestamping of individual CCD exposures at frame rates of more than 1 kHz with an accuracy better than one microsecond with ... More
Results on Charm Baryon Spectroscopy from TevatronMay 03 2011Due to an excellent mass resolution and a large amount of available data, the CDF experiment, located at the Tevatron proton-antiproton accelerator, allows the precise measurement of spectroscopic properties, like mass and decay width, of a variety of ... More
Bounds on the Automata Size for Presburger ArithmeticJun 02 2005Automata provide a decision procedure for Presburger arithmetic. However, until now only crude lower and upper bounds were known on the sizes of the automata produced by this approach. In this paper, we prove an upper bound on the the number of states ... More
Set theory and topology. An introduction to the foundations of analysis. Part I: Sets, relations, numbersMay 29 2013We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of number systems. ... More
Increasing Positive Monoids of Ordered Fields Are FF-monoidsOct 27 2016Given an ambient ordered field $K$, a positive monoid is a countably generated additive submonoid of the nonnegative cone of $K$. In this paper, we first generalize a few atomic features exhibited by Puiseux monoids of the field of rational numbers to ... More
Explicit Methods for Radical Function Fields over Finite FieldsNov 30 2009We develop explicit formulas and algorithms for arithmetic in radical function fields K/k(x) over finite constant fields. First, we classify which places of k(x) whose local integral bases have an easy monogenic form, and give explicit formulas for these ... More
Isometry groups of Lorentzian manifolds of finite volume and The local geometry of compact homogeneous Lorentz spacesJun 27 2011Oct 06 2011Based on the work of Adams and Stuck as well as on the work of Zeghib, we classify the Lie groups which can act isometrically and locally effectively on Lorentzian manifolds of finite volume. In the case that the corresponding Lie algebra contains a direct ... More
Embeddings of decomposition spacesMay 31 2016Feb 15 2018Many smoothness spaces in harmonic analysis are decomposition spaces. In this paper we ask: Given two decomposition spaces, is there an embedding between the two? A decomposition space $\mathcal{D}(\mathcal{Q}, L^p, Y)$ can be described using : a covering ... More
On monotonicity-preserving perturbations of $M$-matricesAug 04 2013We obtain an explicit analytical sufficient condition on $E$ that ensures the monotonicity of the matrix $M+E$, where $M$ is an $M$-matrix.
Chip-firing may be much faster than you thinkNov 06 2014Nov 24 2014A new bound (Theorem \ref{thm:main}) for the duration of the chip-firing game with $N$ chips on a $n$-vertex graph is obtained, by a careful analysis of the pseudo-inverse of the discrete Laplacian matrix of the graph. This new bound is expressed in terms ... More
Tautological relations in moduli spaces of weighted pointed curvesJun 27 2013Sep 29 2015Pandharipande-Pixton have used the geometry of the moduli space of stable quotients to produce relations between tautological Chow classes on the moduli space $M_g$ of smooth genus g curves. We study a natural extension of their methods to the boundary ... More
Finite temperature coupled cluster theories for extended systemsJul 24 2018Nov 20 2018At zero temperature coupled cluster theory is widely used to predict total energies, ground state expectation values and even excited states for molecules and extended systems. Generalizations to finite temperature exist, however, they are in practice ... More
Positroids Induced by Rational Dyck PathsJun 29 2017A rational Dyck path of type $(m,d)$ is an increasing unit-step lattice path from $(0,0)$ to $(m,d) \in \mathbb{Z}^2$ that never goes above the diagonal line $y = (d/m)x$. On the other hand, a positroid of rank $d$ on the ground set $[d+m]$ is a special ... More
The Causal Action in Minkowski Space and Surface Layer IntegralsNov 19 2017The Lagrangian of the causal action principle is computed in Minkowski space for Dirac wave functions interacting with classical electromagnetism and linearized gravity in the limiting case when the ultraviolet cutoff is removed. Various surface layer ... More
Hopf invariants and differential formsNov 13 2017Dec 11 2018Let $f,g:M \rightarrow N$ be two maps between simply-connected smooth manifolds $M$ and $N$, such that $M$ is compact and $N$ is of finite $\mathbb{R}$-type. The goal of this paper is to use integration of certain differential forms to obtain a complete ... More
The Heisenberg-Euler effective action in slowly varying electric field inhomogeneities of Lorentzian shapeMar 23 2017Apr 23 2017We use a locally constant field approximation (LCFA) to study the one-loop Heisenberg-Euler effective action in a particular class of slowly varying inhomogeneous electric fields of Lorentzian shape with $0\leq d\leq 4$ inhomogeneous directions. We show ... More
$E_n$-Hopf invariantsSep 21 2018The classical Hopf invariant is an invariant of homotopy classes of maps from $S^{4n-1} $ to $S^{2n}$, and is an important invariant in homotopy theory. The goal of this paper is to use the Koszul duality theory for $E_n$-operads to define a generalization ... More