Results for "Oliver J. Hulme"

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Ergodicity-breaking reveals time optimal economic behavior in humansJun 11 2019Jun 19 2019Ergodicity describes an equivalence between the expectation value and the time average of observables. Applied to human behaviour, ergodic theory reveals how individuals should tolerate risk in different environments. To optimise wealth over time, agents ... More
Long time $L^\infty(L^2)$ a posteriori error estimates for fully discrete parabolic problemsMar 08 2018Computable estimates for the error of finite element discretisations of parabolic problems in the $L^\infty(0,T; L^2)$ norm are developed, which exhibit constant effectivities (the ratio of the estimated error to the true error) with respect to the simulation ... More
A New General-Purpose Method to Multiply 3x3 Matrices Using Only 23 MultiplicationsAug 14 2011Aug 19 2011One of the most famous conjectures in computer algebra is that matrix multiplication might be feasible in not much more than quadratic time. The best known exponent is 2.376, due to Coppersmith and Winograd. Many attempts to solve this problems in the ... More
Sequential disruption of the shortest path in critical percolationJun 22 2019We investigate the effect of sequentiallydisrupting the shortest path of percolation clusters at criticality by comparing it with the shortest alternative path. We measure the difference in length and the enclosed area between the two paths. The sequential ... More
Wilsonian Renormalization of Noncommutative Scalar Field TheoryFeb 27 2009Jul 22 2009Drawing on analogies with the commutative case, the Wilsonian picture of renormalization is developed for noncommutative scalar field theory. The dimensionful noncommutativity parameter, theta, induces several new features. Fixed-points are replaced by ... More
Can power corrections be reliably computed in models with extra dimensions?Feb 11 2003We critically revisit the issue of power-law running in models with extra dimensions. The analysis is carried out in the context of a higher-dimensional extension of QED, with the extra dimensions compactified on a torus. It is shown that a naive $\beta$ ... More
The role of Rayleigh-Taylor instabilities in filament threadsMar 20 2012Many solar filaments and prominences show short-lived horizontal threads lying parallel to the photosphere. In this work the possible link between Rayleigh-Taylor instabilities and thread lifetimes is investigated. This is done by calculating the eigenmodes ... More
Why Are Neutrinos Light? -- An AlternativeSep 23 2004We review the recent proposal that neutrinos are light because their masses are proportional to a low scale, f, of lepton flavor symmetry breaking. This mechanism is testable because the resulting pseudo-Goldstone bosons, of mass m_G, couple strongly ... More
Power corrections in models with extra dimensionsOct 07 2003We critically revisit the issue of power-law running in models with extra dimensions. The general conclusion is that, in the absence of any additional physical principle, the power-corrections tend to depend strongly on the details of the underlying theory. ... More
B Physics and Extra DimensionsSep 03 2002We compute the dominant new physics contributions to the processes Z -> b b and B - B in the context of two representative models with extra dimensions. The main thrust of the calculations focuses on how to control the effects of the infinite tower of ... More
Bounds on models with one latticized extra dimensionJun 30 2003We study an extension of the standard model with one latticized extra dimension accessible to all fields. The model is characterized by the size of the extra dimension and the number of sites, and contains a tower of massive particles. At energies lower ... More
Universal extra dimensions and Z->b bar-bDec 30 2002We study, at the one loop level, the dominant contributions from a single universal extra dimension to the process (Z\to b\bar{b}). By resorting to the gaugeless limit of the theory we explain why the result is expected to display a strong dependence ... More
Extensions of endomorphisms of C(X)Oct 01 2004For a compact space X we consider extending endomorphisms of the algebra C(X) to be endomorphisms of Arens-Hoffman and Cole extensions of C(X). Given a non-linear, monic polynomial p in C(X)[t], with C(X)[t]/pC(X)[t] semi-simple, we show that if an endomorphism ... More
Note on new interesting baryon channels to measure the photon polarization in b -> s gammaJul 21 2010Nov 11 2010At LHC a large number of b-flavored baryons will be produced. In this note we propose new baryon modes to determine the photon helicity of the penguin transition $b \to s \gamma$. The decay $\Lambda_b \to \Lambda \gamma$ has the drawback that the $\Lambda$, ... More
Quasifree martingalesMar 30 2012A noncommutative Kunita-Watanabe-type representation theorem is established for the martingales of quasifree states of CCR algebras. To this end the basic theory of quasifree stochastic integrals is developed using the abstract It\^o integral in symmetric ... More
Time damping of non-adiabatic magnetohydrodynamic waves in a partially ionized prominence plasma: Effect of heliumOct 15 2009Prominences are partially ionized, magnetized plasmas embedded in the solar corona. Damped oscillations and propagating waves are commonly observed. These oscillations have been interpreted in terms of magnetohydrodynamic (MHD) waves. Ion-neutral collisions ... More
Ergodicity-breaking reveals time optimal economic behavior in humansJun 11 2019Jun 12 2019Ergodicity describes an equivalence between the expectation value and the time average of observables. Applied to human behaviour, ergodic theory reveals how individuals should tolerate risk in different environments. To optimise wealth over time, agents ... More
Investigating bounds on decoherence in quantum mechanics via B and D-mixingAug 01 2014Oct 01 2014We investigate bounds on decoherence in quantum mechanics by studying $B$ and $D$-mixing observables, making use of many precise new measurements, particularly from the LHC and B factories. In that respect we show that the stringent bounds obtained by ... More
Homogeneous decoherence functionals in standard and history quantum mechanicsJul 23 1998General history quantum theories are quantum theories without a globally defined notion of time. Decoherence functionals represent the states in the history approach and are defined as certain bivariate complex-valued functionals on the space of all histories. ... More
A practical illustration of the importance of realistic individualized treatment rules in causal inferenceDec 05 2007The effect of vigorous physical activity on mortality in the elderly is difficult to estimate using conventional approaches to causal inference that define this effect by comparing the mortality risks corresponding to hypothetical scenarios in which all ... More
Pretentiously detecting power cancellationNov 08 2011Granville and Soundararajan have recently introduced the notion of pretentiousness in the study of multiplicative functions of modulus bounded by 1, essentially the idea that two functions which are similar in a precise sense should exhibit similar behavior. ... More
Quasi-normal modes of black holes in Horndeski gravityApr 24 2018We study the perturbations to General Relativistic black holes (i.e. those without scalar hair) in Horndeski scalar-tensor gravity. First, we derive the equations of odd and even parity perturbations of both the metric and scalar field in the case of ... More
Oscillatory Modes of a Prominence-PCTR-Corona Slab ModelOct 16 2007Oscillations of magnetic structures in the solar corona have often been interpreted in terms of magnetohydrodynamic waves. We study the adiabatic magnetoacoustic modes of a prominence plasma slab with a uniform longitudinal magnetic field, surrounded ... More
Non-adiabatic magnetohydrodynamic waves in a cylindrical prominence thread with mass flowMar 18 2008May 21 2008High-resolution observations show that oscillations and waves in prominence threads are common and that they are attenuated in a few periods. In addition, observers have also reported the presence of material flows in such prominence fine-structures. ... More
The effect of the solar corona on the attenuation of small-amplitude prominence oscillations. I. Longitudinal magnetic fieldApr 12 2007Jun 12 2007Context. One of the typical features shown by observations of solar prominence oscillations is that they are damped in time and that the values of the damping times are usually between one and three times the corresponding oscillatory period. However, ... More
Magnetohydrodynamic Waves in a Partially Ionized Filament ThreadApr 20 2009May 06 2009Oscillations and propagating waves are commonly seen in high-resolution observations of filament threads, i.e., the fine-structures of solar filaments/prominences. Since the temperature of prominences is typically of the order of 10^4 K, the prominence ... More
Ergodicity-breaking reveals time optimal economic behavior in humansJun 11 2019Ergodicity describes an equivalence between the expectation value and the time average of observables. Applied to human behaviour, ergodic theory reveals how individuals should tolerate risk in different environments. To optimise wealth over time, agents ... More
Choosing Collaboration Partners. How Scientific Success in Physics Depends on Network PositionsAug 10 2016Physics is one of the most successful endeavors in science. Being a prototypic big science it also reflects the growing tendency for scientific collaborations. Utilizing 250,000 papers from ArXiv.org a prepublishing platform prevalent in Physics we construct ... More
Localization to delocalization transition in a driven nonlinear cavity arraySep 07 2017We study nonlinear cavity arrays where the particle relaxation rate in each cavity increases with the excitation number. We show that coherent parametric inputs can drive such arrays into states with commensurate filling that form non-equilibrium analogs ... More
Forecasts for Low Spin Black Hole Spectroscopy in Horndeski GravityApr 10 2019Jun 17 2019We investigate the prospect of using black hole spectroscopy to constrain the parameters of Horndeski gravity through observations of gravitational waves from perturbed black holes. We study the gravitational waves emitted during ringdown from black holes ... More
Resonantly Damped Kink Magnetohydrodynamic Waves in a Partially Ionized Filament ThreadSep 19 2009Transverse oscillations of solar filament and prominence threads have been frequently reported. These oscillations have the common features of being of short period (2-10 min) and being damped after a few periods. Kink magnetohydrodynamic (MHD) wave modes ... More
Attenuation of small-amplitude oscillations in a prominence-corona model with a transverse magnetic fieldJan 24 2008Aug 14 2008Small-amplitude prominence oscillations are usually damped after a few periods. We study the attenuation of non-adiabatic magnetoacoustic waves in a slab prominence embedded in the coronal medium. We assume an equilibrium configuration with a transverse ... More
Evolving Dark Energy with w Deviating from -1Mar 31 2005Theories of evolving quintessence are constructed that generically lead to deviations from the w = -1 prediction of non-evolving dark energy. The small mass scale that governs evolution, m_\phi \approx 10^{-33} eV, is radiatively stable, and the ``Why ... More
CMB Signals of Neutrino Mass GenerationDec 18 2003We propose signals in the cosmic microwave background to probe the type and spectrum of neutrino masses. In theories that have spontaneous breaking of approximate lepton flavor symmetries at or below the weak scale, light pseudo-Goldstone bosons recouple ... More
Explicit Supersymmetry Breaking on Boundaries of Warped Extra DimensionsFeb 25 2003Oct 28 2003Explicit supersymmetry breaking is studied in higher dimensional theories by having boundaries respect only a subgroup of the bulk symmetry. If the boundary symmetry is the maximal subgroup allowed by the boundary conditions imposed on the fields, then ... More
Transverse oscillations of systems of coronal loopsSep 24 2008We study the collective kinklike normal modes of a system of several cylindrical loops using the T-matrix theory. Loops that have similar kink frequencies oscillate collectively with a frequency which is slightly different from that of the individual ... More
Resonantly damped surface and body MHD waves in a solar coronal slab with oblique propagationAug 28 2007The theory of magnetohydrodynamic (MHD) waves in solar coronal slabs in a zero-$\beta$ configuration and for parallel propagation of waves does not allow the existence of surface waves. When oblique propagation of perturbations is considered both surface ... More
On the support of neutrals against gravity in solar prominencesMar 18 2015Cool and dense prominences found in the solar atmosphere are known to be partially ionized because of their relative low temperature. In this Letter, we address the long-standing problem of how the neutral component of the plasma in prominences is supported ... More
Transverse oscillations of two coronal loopsJul 05 2007Dec 11 2007We study transverse fast magnetohydrodynamic waves in a system of two coronal loops modeled as smoothed, dense plasma cylinders in a uniform magnetic field. The collective oscillatory properties of the system due to the interaction between the individual ... More
The statistical significance of the N-S asymmetry of solar activity revisitedSep 12 2007The main aim of this study is to point out the difficulties found when trying to assess the statistical significance of the North-South asymmetry (hereafter SSNSA) of the most usually considered time series of solar activity. First of all, we distinguish ... More
Stochastic transport in the presence of spatial disorder: fluctuation-induced corrections to homogenizationJun 17 2016Aug 21 2016Motivated by uncertainty quantification in natural transport systems, we investigate an individual-based transport process involving particles undergoing a random walk along a line of point sinks whose strengths are themselves independent random variables. ... More
Spectral line width decrease in the solar corona: resonant energy conversion from Alfv{é}n to acoustic wavesMar 13 2007Observations reveal an increase with height of the line width of several coronal spectral lines probably caused by outwardly propagating Alfv{\'e}n waves. However, the spectral line width sometimes shows a sudden decrease at a height 0.1-0.2 R, where ... More
Solving and Verifying the boolean Pythagorean Triples problem via Cube-and-ConquerMay 03 2016The boolean Pythagorean Triples problem has been a longstanding open problem in Ramsey Theory: Can the set N = $\{1, 2, ...\}$ of natural numbers be divided into two parts, such that no part contains a triple $(a,b,c)$ with $a^2 + b^2 = c^2$ ? A prize ... More
A covariant approach to parameterised cosmological perturbationsJun 30 2017Sep 12 2017We present a covariant formulation for constructing general quadratic actions for cosmological perturbations, invariant under a given set of gauge symmetries for a given field content. This approach allows us to analyse scalar, vector and tensor perturbations ... More
Transverse oscillations of a multi-stranded loopDec 22 2009May 10 2010We investigate the transverse oscillations of a line-tied multi-stranded coronal loop composed of several parallel cylindrical strands. First, the collective fast normal modes of the loop are found with the T-matrix theory. There is a huge quantity of ... More
Gauge Invariant Regularization in the AdS/CFT Correspondence and Ghost D-branesJan 17 2006Mar 29 2006A field theoretic understanding of how the radial direction in the AdS/CFT Correspondence plays the role of a gauge invariant measure of energy scale has long been missing. In SU(N) Yang-Mills, a realization of a gauge invariant cutoff has been achieved ... More
Global hydromagnetic simulations of a planet embedded in a dead zone: gap opening, gas accretion and formation of a protoplanetary jetSep 11 2013Oct 17 2013We present global hydrodynamic and magnetohydrodynamic (MHD) simulations with mesh refinement of accreting planets embedded in protoplanetary disks (PPDs). The magnetized disk includes Ohmic resistivity that depends on the overlying mass column, leading ... More
A posteriori error estimates for the virtual element methodMar 18 2016Apr 24 2017An posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residual-type and applies on very general polygonal/polyhedral meshes. The estimator is fully computable ... More
The Properties of Long-Period Variables in the Large Magellanic Cloud from MACHOAug 12 2008We present a new analysis of the long-period variables in the Large Magellanic Cloud (LMC) from the MACHO Variable Star Catalog. Three-quarters of our sample of evolved, variable stars have periodic light curves. We characterize the stars in our sample ... More
Elements of given order in Tate-Shafarevich groups of abelian varieties in quadratic twist familiesMar 29 2019Let $A$ be an abelian variety over a number field $F$ and let $p$ be a prime. Cohen-Lenstra-Delaunay-style heuristics predict that the Tate-Shafarevich group of $A_s$ should contain an element of order $p$ for a positive proportion of quadratic twists ... More
ViTa-SLAM: Biologically-Inspired Visuo-Tactile SLAMApr 11 2019May 14 2019In this work, we propose a novel, bio-inspired multi-sensory SLAM approach called ViTa-SLAM. Compared to other multisensory SLAM variants, this approach allows for a seamless multi-sensory information fusion whilst naturally interacting with the environment. ... More
Characterising dark matter searches at colliders and direct detection experiments: Vector mediatorsJul 31 2014Jan 16 2015We introduce a Minimal Simplified Dark Matter (MSDM) framework to quantitatively characterise dark matter (DM) searches at the LHC. We study two MSDM models where the DM is a Dirac fermion which interacts with a vector and axial-vector mediator. The models ... More
Global shallow water magnetohydrodynamic waves in the solar tachoclineOct 23 2008Dec 05 2008We derive analytical solutions and dispersion relations of global magnetic Poincar\'e (magneto-gravity) and magnetic Rossby waves in the approximation of shallow water magnetohydrodynamics. The solutions are obtained in a rotating spherical coordinate ... More
Damping of filament thread oscillations: effect of the slow continuumFeb 03 2009Mar 19 2009Transverse oscillations of small amplitude are commonly seen in high-resolution observations of filament threads, i.e. the fine-structures of solar filaments/prominences, and are typically damped in a few periods. Kink wave modes supported by the thread ... More
Bound on the curvature of the Isgur-Wise function of the baryon semileptonic decay Lambda_b -> Lambda_c + l + nuAug 21 2008Dec 03 2008In the heavy quark limit of QCD, using the Operator Product Expansion, the formalism of Falk for hadrons or arbitrary spin, and the non-forward amplitude, as proposed by Uraltsev, we formulate sum rules involving the Isgur-Wise function $\xi_{\Lambda} ... More
Exact Duality and Bjorken Sum Rule in Heavy Quark Models à la Bakamjian-ThomasMar 12 1996The heavy mass limit of quark models based on the Bakamjian-Thomas cons\-truction reveals remarkable features. In addition to previously demonstrated properties of covariance and Isgur-Wise scaling, exact duality, leading to the Bjorken-Isgur-Wise sum ... More
Dirac Neutrinos and Hybrid Inflation from String TheoryMay 16 2005Jun 15 2005We consider a possible scenario for the generation of Dirac neutrino masses motivated by Type I string theory. The smallness of the neutrino Yukawa couplings is explained by an anisotropic compactification with one compactification radius larger than ... More
Efficient, adaptive cross-validation for tuning and comparing models, with application to drug discoveryFeb 29 2012Cross-validation (CV) is widely used for tuning a model with respect to user-selected parameters and for selecting a "best" model. For example, the method of $k$-nearest neighbors requires the user to choose $k$, the number of neighbors, and a neural ... More
Speed of gravitational waves and black hole hairFeb 23 2018Apr 10 2018The recent detection of GRB 170817A and GW170817 constrains the speed of gravity waves $c_T$ to be that of light, which severely restricts the landscape of modified gravity theories that impact the cosmological evolution of the universe. In this work, ... More
General theories of linear gravitational perturbations to a Schwarzschild Black HoleNov 06 2017Feb 20 2018We use the covariant formulation proposed in Tattersall et al (2017) to analyse the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasi-normal modes of perturbed ... More
Quasi-biennial oscillations in the solar tachocline caused by magnetic Rossby wave instabilitiesNov 05 2010Quasi-biennial oscillations (QBO) are frequently observed in the solar activity indices. However, no clear physical mechanism for the observed variations has been suggested so far. Here we study the stability of magnetic Rossby waves in the solar tachocline ... More
Investigating the Late Stages of Stellar Evolution with Long Period Variables from MACHO and 2MASSSep 19 2005Sep 21 2005We are re-analyzing the MACHO variable star database to explore the relationships between pulsation, evolution, and mass loss in evolved stars. We will analyze the multi-periodic properties of long period variable (LPV) stars, 50% of which could not be ... More
On functorial (co)localization of algebras and modules over operadsDec 04 2018Motivated by calculations of motivic homotopy groups, we give widely attained conditions under which operadic algebras and modules thereof are preserved under (co)localization functors
Braking Index of Isolated Pulsars II: A novel two-dipole model of pulsar magnetismAug 03 2016The magnetic dipole radiation (MDR) model is currently the best approach we have to explain pulsar radiation. However a most characteristic parameter of the observed radiation, the braking index n$_{\rm obs}$ shows deviations for all the eight best studied ... More
Motivic slices and colored operadsDec 15 2010Apr 13 2012Colored operads were introduced in the 1970's for the purpose of studying homotopy invariant algebraic structures on topological spaces. In this paper we introduce colored operads in motivic stable homotopy theory. Our main motivation is to uncover hitherto ... More
The effects of magnetic-field geometry on longitudinal oscillations of solar prominences: Cross-sectional area variation for thin tubesJul 11 2016Solar prominences are subject to both field-aligned (longitudinal) and transverse oscillatory motions, as evidenced by an increasing number of observations. Large-amplitude longitudinal motions provide valuable information on the geometry of the filament-channel ... More
Resonant absorption in complicated plasma configurations: applications to multi-stranded coronal loop oscillationsFeb 05 2008We study the excitation and damping of transverse oscillations in a multi-stranded model of a straight line-tied coronal loop. The transverse geometry of our equilibrium configuration is quite irregular and more realistic than the usual cylindrical loop ... More
MHD waves in two-dimensional prominences embedded in coronal arcadesSep 19 2013Solar prominence models used so far in the analysis of MHD waves in such structures are quite elementary. In this work, we calculate numerically magnetohydrostatic models in two-dimensional configurations under the presence of gravity. Our interest is ... More
Conditions for observing emergent SU(4) symmetry in a double quantum dotMar 17 2016We analyze conditions for the observation of a low energy SU(4) fixed point in capacitively coupled quantum dots. One problem, due to dots with different couplings to their baths, has been considered by Tosi, Roura-Bas and Aligia (2015). They showed how ... More
Prominence seismologyJan 22 2012Given the difficulty in directly determining prominence physical parameters from observations, prominence seismology stands as an alternative method to probe the nature of these structures. We show recent examples of the application of magnetohydrodynamic ... More
Wave Leakage and Resonant Absorption in a Loop Embedded in a Coronal ArcadeJan 19 2012We investigate the temporal evolution of impulsively generated perturbations in a potential coronal arcade with an embedded loop. As the initial configuration we consider a coronal loop, represented by a density enhancement, which is unbounded in the ... More
Radiative Electroweak Symmetry Breaking from a Quasi-Localized Top QuarkAug 15 2002May 17 2003We consider 5D supersymmetric SU(3) x SU(2) x U(1) theories compactified at the TeV scale on S^1/Z_2 with supersymmetry broken by boundary conditions. Localizing the top quark at a boundary of a fifth dimension by a bulk mass term M_t, reduces the strength ... More
Consistent Histories and Operational Quantum PhysicsDec 22 1995Jun 07 1996In this work a generalization of the consistent histories approach to quantum mechanics is presented. We first critically review the consistent histories approach to nonrelativistic quantum mechanics in a mathematically rigorous way and give some general ... More
Sum-over-histories representation for the causal Green function of free scalar field theoryNov 03 1993A set of Green functions ${\cal G}_{\alpha}(x-y), \alpha \in [0, 2 \pi [$, for free scalar field theory is introduced, varying between the Hadamard Green function $\Delta_1(x-y) \equiv \linebreak[2] \lsta{0} \hspace{-0.1cm} \{ \varphi(x), \varphi(y) \} ... More
Chiral logs in twisted mass lattice QCD with large isospin breakingAug 04 2010Nov 17 2010The pion masses and the pion decay constant are calculated to 1-loop order in twisted mass Wilson chiral perturbation theory, assuming a large pion mass splitting and tuning to maximal twist. Taking the large mass splitting at leading order in the chiral ... More
$Nπ$-excited state contamination in nucleon 3-point functions using ChPTJul 07 2019The $N\pi$-state contribution to nucleon 3-pt functions involving the pseudoscalar density $P(x)$ and the time component $A_4(x)$ of the axial vector current are computed to LO in ChPT. In case of the latter the $N\pi$ contribution is O($M_N$) enhanced ... More
K-theory of semi-linear endomorphisms via the Riemann-Hilbert correspondenceOct 03 2016Oct 12 2016Grayson, developing ideas of Quillen, has made computations of the K-theory of "semi-linear endomorphisms". In the present text we develop a technique to compute these groups in the case of Frobenius semi-linear actions. The main idea is to interpret ... More
Volume of line bundles via valuation vectors (different from Okounkov bodies)Mar 11 2019Up to a factor 1/n!, the volume of a big line bundle agrees with the Euclidean volume of its Okounkov body. The latter is the convex hull of top rank valuation vectors of sections, all with respect to a single flag. In this text we give a different volume ... More
Long cycles in random subgraphs of graphs with large minimum degreeAug 14 2013May 24 2014Let $G$ be any graph of minimum degree at least $k$, and let $G_p$ be the random subgraph of $G$ obtained by keeping each edge independently with probability $p$. Recently, Krivelevich, Lee and Sudakov showed that if $pk\to\infty$ then with probability ... More
Dynamically generated NetworksNov 18 2013Simple algebraic rules can produce complex networks with rich structures. These graphs are obtained when looking at a monoid operating on a ring. There are relations to dynamical systems theory and number theory. This document illustrates this class of ... More
Natural orbital networksNov 26 2013Given a finite set T of maps on a finite ring R, we look at the finite simple graph G=(V,E) with vertex set V=R and edge set E={(a,b) | exists t in T, b=t(a), b not equal to a}. An example is when R=Z_n and T consists of a finite set of quadratic maps ... More
Coloring graphs using topologyDec 22 2014Higher dimensional graphs can be used to colour two-dimensional geometric graphs. If G the boundary of a three dimensional graph H for example, we can refine the interior until it is colourable with 4 colours. The later goal is achieved if all interior ... More
Exact Ramsey Theory: Green-Tao numbers and SATApr 05 2010Apr 24 2010We consider the links between Ramsey theory in the integers, based on van der Waerden's theorem, and (boolean, CNF) SAT solving. We aim at using the problems from exact Ramsey theory, concerned with computing Ramsey-type numbers, as a rich source of test ... More
Invariant differential operators and central Fourier multipliers on exponential Lie groupsFeb 22 2012Let $G$ be an exponential solvable Lie group. By definition $G$ is $\ast$-regular if $ker_{L^1(G)}\pi$ is dense in $ker_{C^\ast(G)}\pi$ for all unitary representations $\pi$ of $G$. Boidol characterized the $\ast$-regular exponential Lie groups by a purely ... More
A computerised classification of some almost minimal triangle-free Ramsey graphsOct 18 2017A graph $G$ is called a $(3,j;n)$-minimal Ramsey graph if it has the least amount of edges, $e(3,j;n)$, given that $G$ is triangle-free, the independence number $\alpha(G) < j$ and that $G$ has $n$ vertices. Triangle-free graphs $G$ with $\alpha(G) < ... More
Solving primal plasticity increment problems in the time of a single predictor-corrector iterationJul 12 2017Oct 18 2017The Truncated Nonsmooth Newton Multigrid (TNNMG) method is a well-established method for the solution of strictly convex block-separably nondifferentiable minimization problems. It achieves multigrid-like performance even for non-smooth nonlinear problems, ... More
On the relative K-group in the ETNC, Part IINov 07 2018Jul 01 2019In a previous paper we showed, under some assumptions, that the relative K-group in the Burns-Flach formulation of the equivariant Tamagawa number conjecture (ETNC) is canonically isomorphic to a K-group of locally compact equivariant modules. This viewpoint, ... More
The Jordan-Brouwer theorem for graphsJun 22 2015We prove a discrete Jordan-Brouwer-Schoenflies separation theorem telling that a (d-1)-sphere H embedded in a d-sphere G defines two different connected graphs A,B in G such a way that the intersection of A and B is H and the union is G and such that ... More
Cyclic Sieving of Increasing Tableaux and small Schröder PathsSep 06 2012Apr 04 2014An increasing tableau is a semistandard tableau with strictly increasing rows and columns. It is well known that the Catalan numbers enumerate both rectangular standard Young tableaux of two rows and also Dyck paths. We generalize this to a bijection ... More
On the homology of Lie algebras like $\mathfrak{gl}(\infty,R)$Dec 05 2017We revisit a recent paper of Fialowski and Iohara. They compute the homology of the Lie algebra $\mathfrak{gl}(\infty,R)$ for $R$ an associative unital algebra over a field of characteristic zero. We explain how to obtain essentially the same results ... More
First-Order Quantifiers and the Syntactic Monoid of Height Fragments of Picture LanguagesApr 19 2012Apr 22 2012We investigate the expressive power of first-order quantifications in the context of monadic second-order logic over pictures. We show that k+1 set quantifier alternations allow to define a picture language that cannot be defined using k set quantifier ... More
Two-dimensional Idèles with Cycle Module CoefficientsJan 02 2011Mar 20 2014We give a theory of id\`eles with coefficients for smooth surfaces over a field. It is an analogue of Beilinson/Huber's theory of higher ad\`eles, but handling cycle module sheaves instead of quasi-coherent ones. We prove that they give a flasque resolution ... More
Prehomogeneous Affine Representations and Flat Pseudo-Riemannian ManifoldsSep 04 2008The theory of flat Pseudo-Riemannian manifolds and flat affine manifolds is closely connected to the topic of prehomogeneous affine representations of Lie groups. In this article, we exhibit several aspects of this correspondence. At the heart of our ... More
The energy of a simplicial complexJul 07 2019A finite abstract simplicial complex G defines a matrix L, where L(x,y)=1 if two simplicies x,y in G intersect and where L(x,y)=0 if they don't. This matrix is always unimodular so that the inverse g of L has integer entries g(x,y). In analogy to Laplacians ... More
K-theory, LQEL manifolds and Severi varietiesAug 05 2013Aug 24 2013We use topological K-theory to study non-singular varieties with quadratic entry locus. We thus obtain a new proof of Russo's Divisibility Property for locally quadratic entry locus manifolds. In particular we obtain a K-theoretic proof of Zak's theorem ... More
Selfsimilarity in the Birkhoff sum of the cotangent functionJun 24 2012We prove that the Birkhoff sum S(n)/n = (1/n) sum_(k=1)^(n-1) g(k A) with g(x) = cot(Pi x) and golden ratio A converges in the sense that the sequence of functions s(x) = S([ x q(2n)])/q(2n) with Fibonacci numbers q(n) converges to a self similar limiting ... More
On index expectation and curvature for networksFeb 21 2012We prove that the expectation value of the index function i(x) over a probability space of injective function f on any finite simple graph G=(V,E) is equal to the curvature K(x) at the vertex x. This result complements and links Gauss-Bonnet sum K(x) ... More
Adele residue symbol and Tate's central extension for multiloop Lie algebrasJun 10 2012Feb 05 2014We generalize the linear algebra setting of Tate's central extension to arbitrary dimension. In general, one obtains a Lie (n+1)-cocycle. We compute it explicitly. The construction is based on a Lie algebra variant of Beilinson's adelic multidimensional ... More
One can hear the Euler characteristic of a simplicial complexNov 27 2017We prove that that the number p of positive eigenvalues of the connection Laplacian L of a finite abstract simplicial complex G matches the number b of even dimensional simplices in G and that the number n of negative eigenvalues matches the number f ... More
The strong ring of simplicial complexesAug 05 2017We define a ring R of geometric objects G generated by finite abstract simplicial complexes. To every G belongs Hodge Laplacian H as the square of the Dirac operator determining its cohomology and a unimodular connection matrix L). The sum of the matrix ... More