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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

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

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

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

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

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

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

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

The number of ramified primes in number fields of small degreeAug 05 2014Sep 02 2016In this paper we investigate the distribution of the number of primes which ramify in number fields of degree d <= 5. In analogy with the classical Erdos-Kac theorem, we prove for S_d-extensions that the number of such primes is normally distributed with ... 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

Unexpected biases in the distribution of consecutive primesMar 11 2016May 30 2016While the sequence of primes is very well distributed in the reduced residue classes (mod $q$), the distribution of pairs of consecutive primes among the permissible $\phi(q)^2$ pairs of reduced residue classes (mod $q$) is surprisingly erratic. This ... 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

The distribution of consecutive prime biases and sums of sawtooth random variablesSep 18 2017In recent work, we considered the frequencies of patterns of consecutive primes $\pmod{q}$ and numerically found biases toward certain patterns and against others. We made a conjecture explaining these biases, the dominant factor in which permits an easy ... More

Propagation and dispersion of transverse wave trains in magnetic flux tubesFeb 18 2014The dispersion of small amplitude, impulsively excited wave trains propagating along a magnetic flux tube is investigated. The initial disturbance is a localized transverse displacement of the tube that excites a fast kink wave packet. The spatial and ... 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

Rank growth of elliptic curves in nonabelian extensionsOct 09 2018Given an elliptic curve $E/\mathbb{Q}$, it is a conjecture of Goldfeld that asymptotically half of its quadratic twists will have rank zero and half will have rank one. Nevertheless, higher rank twists do occur: subject to the parity conjecture, Gouv\^ea ... More

Propagation and dispersion of sausage wave trains in magnetic flux tubesFeb 04 2015A localized perturbation of a magnetic flux tube produces a pair of wave trains that propagate in opposite directions along the tube. These wave packets disperse as they propagate, where the extent of dispersion depends on the physical properties of the ... More

The distribution of 2-Selmer ranks of quadratic twists of elliptic curves with partial two-torsionJul 26 2013This paper presents a new result concerning the distribution of 2-Selmer ranks in the quadratic twist family of an elliptic curve over an arbitrary number field K with a single point of order two that does not have a cyclic 4-isogeny defined over its ... 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

Effective log-free zero density estimates for automorphic $L$-functions and the Sato-Tate conjectureMay 12 2015Nov 17 2016Let $K/\mathbb{Q}$ be a number field. Let $\pi$ and $\pi^\prime$ be cuspidal automorphic representations of $\mathrm{GL}_d(\mathbb{A}_K)$ and $\mathrm{GL}_{d^\prime}(\mathbb{A}_K)$, and suppose that either both $d$ and $d'$ are at most 2 or at least one ... More

Spatial Damping of Propagating Kink Waves in Prominence ThreadsSep 24 2010Transverse oscillations and propagating waves are frequently observed in threads of solar prominences/filaments and have been interpreted as kink magnetohydrodynamic (MHD) modes. We investigate the spatial damping of propagating kink MHD waves in transversely ... More

Propagation of nonadiabatic magnetoacoustic waves in a threaded prominence with mass flowsSep 29 2008High resolution observations of solar filaments suggest the presence of groups of prominence threads, i.e. the fine-structures of prominences, which oscillate coherently (in phase). In addition, mass flows along threads have been often observed. Here, ... More

The distribution of the Tamagawa ratio in the family of elliptic curves with a two-torsion pointJun 26 2014In recent work, Bhargava and Shankar have shown that the average size of the $2$-Selmer group of an elliptic curve over $\mathbb{Q}$ is exactly $3$, and Bhargava and Ho have shown that the average size of the $2$-Selmer group in the family of elliptic ... More

The no-boundary proposal in biaxial Bianchi IX minisuperspaceApr 25 2019We implement the no-boundary proposal for the wave function of the universe in an exactly solvable Bianchi IX minisuperspace model with two scale factors. We extend our earlier work (Phys. Rev. Lett. 121, 081302, 2018 / arXiv:1804.01102) to include the ... 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

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

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

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

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

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

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

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

A Stochastic Finite Element Model for the Dynamics of Globular MacromoleculesSep 21 2012We describe a novel coarse-grained simulation method for modelling the dynamics of globular macromolecules, such as proteins. The macromolecule is treated as a continuum that is subject to thermal fluctuations. The model includes a non-linear treatment ... 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 flowing prominence threads observed with HinodeMar 18 2008Apr 03 2008Recent observations with the Hinode Solar Optical Telescope display an active region prominence whose fine threads oscillate in the vertical direction as they move along a path parallel to the photosphere. A seismological analysis of this event is carried ... 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

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

Normal modes of transverse coronal loop oscillations from numerical simulations: I. Method and test caseFeb 01 2019Jun 13 2019The purpose of this work is to develop a procedure to obtain the normal modes of a coronal loop from time-dependent numerical simulations with the aim of better understanding observed transverse loop oscillations. To achieve this goal, in this paper we ... 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

Numerical Simulations of Magnetoacoustic-Gravity Waves in the Solar AtmosphereAug 29 2012We investigate the excitation of magnetoacoustic-gravity waves generated from localized pulses in the gas pressure as well as in vertical component of velocity. These pulses are initially launched at the top of the solar photosphere that is permeated ... 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

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

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

The Generalized Nagell-Ljunggren Problem: Powers with Repetitive RepresentationsJul 12 2017Jul 22 2017We consider a natural generalization of the Nagell-Ljunggren equation to the case where the qth power of an integer y, for q >= 2, has a base-b representation that consists of a length-l block of digits repeated n times, where n >= 2. Assuming the abc ... More

Dynamics of coronal rain and descending plasma blobs in solar prominences: II. partially ionized caseOct 28 2015Coronal rain clumps and prominence knots are dense condensations with chromospheric to transition region temperatures that fall down in the much hotter corona. Their typical speeds are in the range 30--150~km~s$^{-1}$ and of the order of 10--30~km~s$^{-1}$, ... More

Magnetic Rossby waves in the solar tachocline and Rieger-type periodicitiesNov 24 2009Apart from the 11-year solar cycle, another periodicity around 155-160 days was discovered during solar cycle 21 in high energy solar flares, and its presence in sunspot areas and strong magnetic flux has been also reported. This periodicity has an elusive ... 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

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

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

On the dynamics of planetesimals embedded in turbulent protoplanetary discs with dead zonesApr 20 2011Jun 22 2011(abridged) Accretion in protoplanetary discs is thought to be driven by [...] turbulence via the magnetorotational instability (MRI). Recent work has shown that a planetesimal swarm embedded in a fully turbulent disc is subject to strong excitation of ... More

Manifestly gauge invariant QEDMay 18 2005Nov 01 2005We uncover a method of calculation that proceeds at every step without fixing the gauge or specifying details of the regularisation scheme. Results are obtained by iterated use of integration by parts and gauge invariance identities. Calculations can ... 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

The spatial damping of magnetohydrodynamic waves in a flowing partially ionised prominence plasmaJan 27 2010Solar prominences are partially ionised plasmas displaying flows and oscillations. These oscillations show time and spatial damping and, commonly, have been explained in terms of magnetohydrodynamic (MHD) waves. We study the spatial damping of linear ... More

Reverse engineering of CAD models via clustering and approximate implicitizationOct 17 2018In applications like computer aided design, geometric models are often represented numerically as polynomial splines or NURBS, even when they originate from primitive geometry. For purposes such as redesign and isogeometric analysis, it is of interest ... 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

Three-isogeny Selmer groups and ranks of abelian varieties in quadratic twist families over a number fieldSep 28 2017Nov 30 2017For an abelian variety $A$ over a number field $F$, we prove that the average rank of the quadratic twists of $A$ is bounded, under the assumption that the multiplication-by-3 isogeny on $A$ factors as a composition of 3-isogenies over $F$. This is the ... More

Towards Schwinger production of magnetic monopoles in heavy-ion collisionsFeb 12 2019Magnetic monopoles may be produced by the Schwinger effect in the strong magnetic fields of peripheral heavy-ion collisions. We review the form of the electromagnetic fields in such collisions and calculate from first principles the cross section for ... 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

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

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

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

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

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

Rigidity of lattices and syndetic hulls in solvable Lie groupsNov 28 2013Dec 03 2013First let $G$ be a completely solvable Lie group. We recall the proof of the following result: Any closed subgroup of $G$ possesses a unique syndetic hull in $G$. As a consequence we conclude that any uniform subgroup $\Gamma$ of $G$ is strongly rigid ... 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

Improved bounds for the extremal number of subdivisionsSep 03 2018Let $H_t$ be the subdivision of $K_t$. Very recently, Conlon and Lee have proved that for any integer $t\geq 3$, there exists a constant $C$ such that $\text{ex}(n,H_t)\leq Cn^{3/2-1/6^t}$. In this paper, we prove that there exists a constant $C'$ such ... 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

The Dirac operator of a graphJun 10 2013We discuss some linear algebra related to the Dirac matrix D of a finite simple graph G=(V,E).

LeagueAI: Improving object detector performance and flexibility through automatically generated training data and domain randomizationMay 28 2019In this technical report I present my method for automatic synthetic dataset generation for object detection and demonstrate it on the video game League of Legends. This report furthermore serves as a handbook on how to automatically generate datasets ... More

On the index of a vector field tangent to a hypersurface with non-isolated zero in the embedding spaceApr 17 2002Dec 20 2002We give a generalization of an algebraic formula of Gomez-Mont for the index of a vector field with isolated zero in (C^n,0) and tangent to an isolated hypersurface singularity. We only assume that the vector field has an isolated zero on the singularity. ... 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

Some experiments in number theoryJun 20 2016We experiment with some topics in elementary number theory. For matrices defined by Gaussian primes we observe a circular spectral law for the eigenvalues. We look at matrices defined by Gaussian primes and look at the growth of the determinant, trace. ... 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

The representation theory of decoherence functionals in history quantum theoriesOct 25 1998In the first part of this paper the general perspective of history quantum theories is reviewed. History quantum theories provide a conceptual and mathematical framework for formulating quantum theories without a globally defined Hamiltonian time evolution ... More

An Elementary Dyadic Riemann HypothesisJan 15 2018The connection zeta function of a finite abstract simplicial complex G is defined as zeta_L(s)=sum_x 1/lambda_x^s, where lambda_x are the eigenvalues of the connection Laplacian L defined by L(x,y)=1 if x and y intersect and 0 else. (I) As a consequence ... 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

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

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

The deformations of flat affine structures on the two-torusDec 14 2011The group action which defines the moduli problem for the deformation space of flat affine structures on the two-torus is the action of the affine group $\Aff(2)$ on $\bbR^2$. Since this action has non-compact stabiliser $\GL(2,\bbR)$, the underlying ... 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

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

Entropy and a generalisation of `Poincare's Observation'Jan 29 2002Consider a sphere of radius root(n) in n dimensions, and consider X, a random variable uniformly distributed on its surface. Poincare's Observation states that for large n, the distribution of the first k coordinates of X is close in total variation distance ... 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

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

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

Higher algebraic structures in Hamiltonian Floer theory IOct 22 2013Aug 05 2016This is the first of two papers devoted to showing how the rich algebraic formalism of Eliashberg-Givental-Hofer's symplectic field theory (SFT) can be used to define higher algebraic structures on the symplectic cohomology of open symplectic manifolds. ... More

Obstruction bundles over moduli spaces with boundary and the action filtration in symplectic field theorySep 20 2007Mar 02 2010Branched covers of orbit cylinders are the basic examples of holomorphic curves studied in symplectic field theory. Since all curves with Fredholm index one can never be regular for any choice of cylindrical almost complex structure, we generalize the ... 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