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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

Convergence in Infinitary Term Graph Rewriting Systems is Simple (Extended Abstract)Feb 26 2013In this extended abstract, we present a simple approach to convergence on term graphs that allows us to unify term graph rewriting and infinitary term rewriting. This approach is based on a partial order and a metric on term graphs. These structures arise ... More

Partial Order Infinitary Term RewritingMar 22 2014Jun 02 2014We study an alternative model of infinitary term rewriting. Instead of a metric on terms, a partial order on partial terms is employed to formalise convergence of reductions. We consider both a weak and a strong notion of convergence and show that the ... 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

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

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

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

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

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

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

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

Modes of Convergence for Term Graph RewritingMay 02 2012May 31 2012Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However, this endeavour ... More

Infinitary Term Graph RewritingJul 04 2011Term graph rewriting provides a formalism for implementing term rewriting in an efficient manner by avoiding duplication. Infinitary term rewriting has been introduced to study infinite term reduction sequences. Such infinite reductions can be used to ... 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

A tunable ferroelectric based unreleased RF resonatorMay 15 2019This paper introduces the first tunable ferroelectric capacitor (FeCAP) based unreleased RF MEMS resonator, integrated seamlessly in Texas Instruments' 130nm Ferroelectric RAM (FeRAM) technology. An array of FeCAPs in this complementary metal-oxide-semiconductor ... More

Next generation of IACT arrays: scientific objectives versus energy domainsNov 04 2005Several key motivations and perspectives of ground based gamma-ray astronomy are discussed in the context of the specifics of detection techniques and scientific topics/objectives relevant to four major energy domains -- very-low or \textit{multi-GeV} ... More

Thermal emission in the prompt phase of gamma-ray burstsApr 25 2005I discuss the interpretation of the prompt phase in gamma-ray bursts as being dominated by quasi-thermal emission, rather than by synchrotron emission. Such an interpretation gives a more natural explanation of (i) the observed variety of spectral shape ... More

A Molecular Mass Gradient is the Key Parameter of the Genetc Code OrganizationJul 21 2009The structure of the genetic code is discussed in formal terms. A rectangular table of the code ("the code matrix"), whose properties reveal its arithmetical content tagged with the information symbols in several notations. New parameters used to analyze ... More

Studies of Neutrino Oscillations at ReactorsMay 09 2000Experiments with reactor neutrinos continue to shed light on our understanding of neutrino oscillations. We review some of the early decisive experiments. We then turn to the recent long baseline oscillation experiments at Palo Verde and Chooz which are ... More

A Z' Model for the CDF Dijet AnomalyApr 01 2011Apr 18 2011We adopt a bottom-up approach to constructing a new physics model to explain the CDF excess seen in dijets with an associated lepton and missing transverse energy. We find that the 145 GeV broad feature seen by CDF in the dijet invariant mass distribution ... More

Phenomenology of Enhanced Light Quark Yukawa Couplings and the $W^\pm h$ Charge AsymmetrySep 21 2016Feb 10 2017I 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

Di-jet resonances at future hadron colliders: A Snowmass whitepaperAug 05 2013I investigate the sensitivity of future hadron colliders to di-jet resonances arising from Z' or coloron models. The projected discovery potential and exclusion limits for these resonances is presented in the coupling vs. mass plane, which highlights ... More

Set-Monotonicity Implies Kelly-StrategyproofnessMay 26 2010Feb 05 2015This paper studies the strategic manipulation of set-valued social choice functions according to Kelly's preference extension, which prescribes that one set of alternatives is preferred to another if and only if all elements of the former are preferred ... More

Do You Like What I Like? Similarity Estimation in Proximity-based Mobile Social NetworksMay 19 2018While existing social networking services tend to connect people who know each other, people show a desire to also connect to yet unknown people in physical proximity. Existing research shows that people tend to connect to similar people. Utilizing technology ... More

Time Quasilattices in Dissipative Dynamical SystemsJul 28 2017May 28 2018We establish the existence of `time quasilattices' as stable trajectories in dissipative dynamical systems. These tilings of the time axis, with two unit cells of different durations, can be generated as cuts through a periodic lattice spanned by two ... More

Pell and Clapeyron Words as Stable Trajectories in Dynamical SystemsJul 28 2017Nov 30 2017We establish the existence of `time quasicrystals', tilings of the time axis with two unit cells of different duration. These aperiodic tilings can be constructed as slices through regular tilings of a space spanned by two orthogonal time directions. ... More

Graphs, Ultrafilters and ColourabilityMar 16 2018Let $\beta$ be the functor from Set to CHaus which maps each discrete set X to its Stone-Cech compactification, the set $\beta$ X of ultrafilters on X. Every graph G with vertex set V naturally gives rise to a graph $\beta G$ on the set $\beta V$ of ultrafilters ... More

Tadpole diagrams in constant electromagnetic fieldsSep 12 2017Oct 10 2017We show how all possible one-particle reducible tadpole diagrams in constant electromagnetic fields can be constructed from one-particle irreducible constant-field diagrams. The construction procedure is essentially algebraic and involves differentiations ... More

On the system of sets of lengths and the elasticity of submonoids of $\mathbb{N}^d$Jun 29 2018Let $H$ be an atomic monoid. For $x \in H$, let $\mathsf{L}(x)$ denote the set of all possible lengths of factorizations of $x$ into irreducibles. The system of sets of lengths of $H$ is the set $\mathcal{L}(H) = \{\mathsf{L}(x) \mid x \in H\}$. On the ... More

Positive Functionals Induced by Minimizers of Causal Variational PrinciplesAug 25 2017Feb 18 2018Considering second variations about a given minimizer of a causal variational principle, we derive positive functionals in space-time. It is shown that the strict positivity of these functionals ensures that the minimizer is nonlinearly stable within ... More

Supersymmetry in Quantum Theory Over a Galois FieldSep 26 2002As shown in our previous papers (hep-th/0209001 and reference therein), quantum theory based on a Galois field (GFQT) possesses a new symmetry between particles and antiparticles, which has no analog in the standard approach. In the present paper it is ... More

Elementary Particles in a Quantum Theory Over a Galois FieldAug 30 2002Oct 26 2008We consider elementary particles in a quantum theory based on a Galois field. In this approach infinities cannot exist, the cosmological constant problem does not arise and one irreducible representation of the symmetry algebra necessarily describes a ... More

Swap-invariant and exchangeable random measuresFeb 24 2016Jul 05 2016In this work we analyze the concept of swap-invariance, which is a weaker variant of exchangeability. A random vector $\xi$ in $\mathbb{R}^n$ is called swap-invariant if $\,{\mathbf E}\,\big| \!\sum_j u_j \xi_j \big|\,$ is invariant under all permutations ... More

Functional calculus estimates for Tadmor-Ritt operatorsJun 30 2015We show $H^{\infty}$-functional calculus estimates for Tadmor-Ritt operators (also known as Ritt operators), which generalize and improve results by Vitse. These estimates are in conformity with the best known power-bounds for Tadmor-Ritt operators in ... More

Spectral radius minus average degree: a better boundJul 16 2014Collatz and Sinogowitz had proposed to measure the departure of a graph $G$ from regularity by the difference of the (adjacency) spectral radius and the average degree: $\epsilon(G)=\rho(G)-\frac{2m}{n}$. We give here new lower bounds on this quantity, ... More

Modelling of transport phenomena in gases based on quantum scatteringMay 21 2018A quantum interatomic scattering is implemented in the direct simulation Monte Carlo (DSMC) method applied to transport phenomena in rarefied gases. In contrast to the traditional DSMC method based on the classical scattering, the proposed implementation ... More

Gromov-Witten theory of target curves and the tautological ringAug 28 2013In the Gromov-Witten theory of a target curve we consider descendent integrals against the virtual fundamental class relative to the forgetful morphism to the moduli space of curves. We show that cohomology classes obtained in this way lie in the tautological ... More

Structured, compactly supported Banach frame decompositions of decomposition spacesDec 27 2016$\newcommand{mc}[1]{\mathcal{#1}}$ $\newcommand{D}{\mc{D}(\mc{Q},L^p,\ell_w^q)}$ We present a framework for the construction of structured, possibly compactly supported Banach frames and atomic decompositions for decomposition spaces. Such a space $\D$ ... 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

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

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

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.

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

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

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

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

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

An Alternative View of the Universe Structure (on the invalidity of the four dimensional space-time concept)Nov 08 2007The model of the Universe in this paper uses equations of the unperturbed Keplerian motion. They have been updated, complementied and generalized when the solution of these equations is the characteristic function of a random value from the theory of ... 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

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

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

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

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

The Infrastructure of a Global Field of Arbitrary Unit RankSep 09 2008Oct 10 2010In this paper, we show a general way to interpret the infrastructure of a global field of arbitrary unit rank. This interpretation generalizes the prior concepts of the giant step operation and f-representations, and makes it possible to relate the infrastructure ... 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

Parametric Compositional Data TypesFeb 14 2012In previous work we have illustrated the benefits that compositional data types (CDTs) offer for implementing languages and in general for dealing with abstract syntax trees (ASTs). Based on Swierstra's data types \'a la carte, CDTs are implemented as ... 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

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

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

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 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

Causal Fermion Systems: Discrete Space-Times, Causation and Finite Propagation SpeedDec 01 2018The theory of causal fermion systems is a recent approach to fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. The dynamics is described by a ... More

Marked Groups with Isomorphic Cayley Graphs but Different Borel CombinatoricsOct 06 2018We construct pairs of marked groups with isomorphic Cayley graphs but different Borel chromatic numbers for the free parts of their shift graphs. This answers a question of Kechris and Marks. We also show that these graphs have different Baire measurable ... 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