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The random strategy in Maker-Breaker graph minor gamesJul 10 2019In a $(1:b)$ biased Maker-Breaker game, how good a strategy is for a player can be measured by the bias range for which its rival can win, choosing an appropriate counterstrategy. Bednarska and {\L}uczak proved that, in the $H$-subgraph game, the uniformly ... More

Finding unavoidable colorful patterns in multicolored graphsJul 08 2018Sep 11 2018Let $\chi$ be a coloring of the edges of a complete graph on $n$ vertices into $r$ colors. We call $\chi$ $\varepsilon$-balanced if all color classes have $\varepsilon$ fraction of the edges. Fix some graph $H$, together with an $r$-coloring of its edges. ... More

A Note on the Minimum Number of Edges in Hypergraphs with Property OMar 28 2017Sep 16 2018An oriented $k$-uniform hypergraph is said to have Property O if for every linear order of the vertex set, there is some edge oriented consistently with the linear order. Recently Duffus, Kay and R\"{o}dl investigate the minimum number $f(k)$ of edges ... More

A Note on the Minimum Number of Edges in Hypergraphs with Property OMar 28 2017May 28 2019An oriented $k$-uniform hypergraph is said to have Property O if for every linear order of the vertex set, there is some edge oriented consistently with the linear order. Recently Duffus, Kay and R\"{o}dl investigated the minimum number $f(k)$ of edges ... More

Upper density of monochromatic infinite pathsAug 09 2018Dec 24 2018We prove that in every $2$-colouring of the edges of $K_\mathbb{N}$ there exists a monochromatic infinite path $P$ such that $V(P)$ has upper density at least ${(12+\sqrt{8})}/{17} \approx 0.87226$ and further show that this is best possible. This settles ... More

A Note on the Minimum Number of Edges in Hypergraphs with Property OMar 28 2017Apr 30 2019An oriented $k$-uniform hypergraph is said to have Property O if for every linear order of the vertex set, there is some edge oriented consistently with the linear order. Recently Duffus, Kay and R\"{o}dl investigated the minimum number $f(k)$ of edges ... More

Square summability of variations and convergence of the transfer operatorDec 05 2006In this paper we study the one-sided shift operator on a state space defined by a finite alphabet. Using a scheme developed by Walters [13], we prove that the sequence of iterates of the transfer operator converges under square summability of variations ... More

Modeling Music Modality with a Key-Class Invariant Pitch Chroma CNNJun 17 2019This paper presents a convolutional neural network (CNN) that uses input from a polyphonic pitch estimation system to predict perceived minor/major modality in music audio. The pitch activation input is structured to allow the first CNN layer to compute ... More

Quantum mechanics as "space-time statistical mechanics"?Jan 24 2005In this paper we discuss and analyse the idea of trying to see (non-relativistic) quantum mechanics as a ``space-time statistical mechanics'', by using the classical statistical mechanical method on objective microscopic space-time configurations. It ... More

SUSY Flat Direction Decay - the prospect of particle production and preheating investigated in the unitary gaugeJan 04 2008Apr 22 2010We look at the possibility of non-perturbative particle production after inflation from SUSY flat directions produced by rotating eigenstates thereby avoiding the standard adiabaticity conditions. This might lead to preheating and prevent the delay of ... More

Local positivity of line bundles on smooth toric varieties and Cayley polytopesJul 11 2013For any non-negative integer $k$ the $k$-th osculating dimension at a given point $x$ of a variety $X$ embedded in projective space gives a measure of the local positivity of order $k$ at that point. In this paper we show that a smooth toric embedding ... More

First-passage percolation on Cartesian power graphsJun 29 2015We consider first-passage percolation with standard exponential edge weights on the class of "high-dimensional" graphs that can be written as an iterated Cartesian product $G\square G \square \dots \square G$ of some base graph $G$ as the number of factors ... More

Thermal state entanglement in harmonic latticesMar 07 2008Jun 18 2008We investigate the entanglement properties of thermal states of the harmonic lattice in one, two and three dimensions. We establish the value of the critical temperature for entanglement between neighbouring sites and give physical reasons. Further sites ... More

A classification of smooth convex 3-polytopes with at most 16 lattice pointsJun 21 2012We provide a complete classification up to isomorphism of all smooth convex lattice 3-polytopes with at most 16 lattice points. There exist in total 103 different polytopes meeting these criteria. Of these, 99 are strict Cayley polytopes and the remaining ... More

Completeness of the ring of polynomialsDec 19 2013Let $k$ be an uncountable field. We prove that the polynomial ring $R:=k[X_1,\dots,X_n]$ in $n\ge 2$ variables over $k$ is complete in its adic topology. In addition we prove that also the localization $R_{\goth m}$ at a maximal ideal $\goth m\subset ... More

Langevin molecular dynamics derived from Ehrenfest dynamicsDec 21 2007Mar 30 2011Stochastic Langevin molecular dynamics for nuclei is derived from the Ehrenfest Hamiltonian system (also called quantum classical molecular dynamics) in a Kac-Zwanzig setting, with the initial data for the electrons stochastically perturbed from the ground ... More

Algebra of Principal Fibre Bundles, and ConnectionsMay 12 2000We put together some of the efforts by several people of making aspects of fibre bundle theory into algebra. The initiator of these efforts was Charles Ehresmann, who put the notion of groupoid and groupoid action in the focus of fibre bundle theory in ... More

Comment on "Are financial crashes predictable?"May 13 2002May 15 2002Comment on "Are financial crashes predictable?", L. Laloux, M. Potters, R. Cont, J.P Aguilar and J.-P. Bouchaud, Europhys. Lett. 45, 1-5 (1999)

Origin of Crashes in 3 US stock markets: Shocks and BubblesJan 13 2004This paper presents an exclusive classification of the largest crashes in Dow Jones Industrial Average (DJIA), SP500 and NASDAQ in the past century. Crashes are objectively defined as the top-rank filtered drawdowns (loss from the last local maximum to ... More

Unoriented first-passage percolation on the n-cubeFeb 12 2014Jun 05 2014The $n$-dimensional binary hypercube is the graph whose vertices are the binary $n$-tuples $\{0, 1\}^n$ and where two vertices are connected by an edge if they differ at exactly one coordinate. We prove that if the edges are assigned independent mean ... More

Commutative monads as a theory of distributionsAug 30 2011The theory of commutative monads on cartesian closed categories provides a framework where aspects of the theory of distributions and other extensive quantities can be formulated and some results proved. We make explicit a link between our theory and ... More

A computation of Poisson kernels for some standard weighted biharmonic operators in the unit discJul 03 2007We compute Poisson kernels for integer weight parameter standard weighted biharmonic operators in the unit disc with Dirichlet boundary conditions. The computations performed extend the supply of explicit examples of such kernels and suggest similar formulas ... More

Non-commutative residue of projections in Boutet de Monvel's calculusSep 21 2007Using results by Melo, Nest, Schick, and Schrohe on the K-theory of Boutet de Monvel's calculus of boundary value problems, we show that the non-commutative residue introduced by Fedosov, Golse, Leichtnam, and Schrohe vanishes on projections in the calculus. ... More

A geometric theory of harmonic and semi-conformal mapsJun 12 2003We describe for any Riemannian manifold a certain infinitesimal neighbourhood of the diagonal. Semi-conformal maps are analyzed as those that preserve such neighbourhoods; harmonic maps are analyzed as those that preserve mirror image formation for pairs ... More

Partial Realization Theory and System Identification ReduxJun 17 2017Some twenty years ago we introduced a nonstandard matrix Riccati equation to solve the partial stochastic realization problem. In this paper we provide a new derivation of this equation in the context of system identification. This allows us to show that ... More

Polyphonic Pitch Tracking with Deep Layered LearningApr 09 2018Mar 18 2019This paper presents a polyphonic pitch tracking system able to extract both framewise and note-based estimates from audio. The system uses several artificial neural networks in a deep layered learning setup. First, cascading networks are applied to a ... More

Energetics of the brain and AIFeb 12 2016Does the energy requirements for the human brain give energy constraints that give reason to doubt the feasibility of artificial intelligence? This report will review some relevant estimates of brain bioenergetics and analyze some of the methods of estimating ... More

Chiral squaring and KLT relationsJan 12 2016Jan 29 2016We demonstrate that amplitudes based on matter supermultiplets can be combined to provide amplitudes of vector supermultiplets by means of KLT relations. In practice we do this by developing a procedure for removing supersymmetry supercharges from super ... More

Empirical Gaussian priors for cross-lingual transfer learningJan 09 2016Sequence model learning algorithms typically maximize log-likelihood minus the norm of the model (or minimize Hamming loss + norm). In cross-lingual part-of-speech (POS) tagging, our target language training data consists of sequences of sentences with ... More

Bundle functors and fibrationsMay 10 2015We give an account, in terms of fibered categories and their fibrewise duals, of aspects of the theory of bundle functors and star-bundle functors in differential geometry.

Entropy in the Kuramoto model and its implications for the stability of partially synchronized statesOct 10 2014Nov 04 2014We discuss the concept of entropy applied to the infinite-N Kuramoto model and derive an expression for its time derivative. The time derivative of the entropy functional is shown to depend on the synchronization order parameter in a very simple way and, ... More

Spectral zeta functionsJul 03 2019This paper discusses the simplest examples of spectral zeta functions, especially those associated with graphs, a subject which has not been much studied. The analogy and the similar structure of these functions, such as their parallel definition in terms ... More

Exploring light supersymmetry with GAMBITMay 24 2019I summarize a recent study by the GAMBIT Collaboration in which we investigated the combined collider constraints on the chargino and neutralino sector of the Minimal Supersymmetric Standard Model. Through a large fit using GAMBIT we found that current ... More

Elements of a metric spectral theoryApr 02 2019This paper discusses a general method for spectral type theorems using metric spaces instead of vector spaces. Advantages of this approach are that it applies to genuinely non-linear situations and also to random versions. Metric analogs of operator norm, ... More

The 2PI coupling expansion revisitedNov 01 2005Recently, out-of-equilibrium field theory has been studied using approximations based on truncations of the 2PI effective action. Although results are promising, the convergence of subsequent orders of the approximation is difficult to get a handle on, ... More

Efficient Representation of Computational MeshesMay 14 2012We present a simple yet general and efficient approach to representation of computational meshes. Meshes are represented as sets of mesh entities of different topological dimensions and their incidence relations. We discuss a straightforward and efficient ... More

Distributed Control of Positive SystemsFeb 29 2012May 14 2014A system is called positive if the set of non-negative states is left invariant by the dynamics. Stability analysis and controller optimization are greatly simplified for such systems. For example, linear Lyapunov functions and storage functions can be ... More

Automating the Finite Element MethodDec 02 2011The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations. However, the ... More

$ν$MSSM superpotential to 6th order - normalised and with no superfluous couplingsNov 30 2009Apr 28 2010We expand the superpotential of $\nu$MSSM to 6th order. This is the order at which all flat directions can be lifted. All 5179 couplings are independent ie. the superpotential cannot be zero for all fields, without all couplings being zero. Likewise, ... More

SUSY Flat Directions -- to get a VEV or not?Nov 13 2009We investigate the potential of SUSY flat directions (FDs). Large FD vacuum expectation values (VEVs) can delay thermalisation and solve the gravitino problem - if FDs decay perturbatively. This depends on how many and which directions get the VEVs. Recently ... More

Understanding the special theory of relativityJan 29 2009Feb 01 2009This paper constitutes a background to the paper 'Quantum mechanics as "space-time statistical mechanics"?', arXiv:quant-ph/0501133, presented previously by the author. But it is also a free-standing and self-contained paper. The purpose of this paper ... More

Polyphonic Pitch Tracking with Deep Layered LearningApr 09 2018Jan 10 2019This paper presents a polyphonic pitch tracking system able to extract both framewise and note-based estimates from audio. The system uses several artificial neural networks in a deep layered learning setup. First, cascading networks are applied to a ... More

The Role of Macros in Tractable PlanningJan 15 2014This paper presents several new tractability results for planning based on macros. We describe an algorithm that optimally solves planning problems in a class that we call inverted tree reducible, and is provably tractable for several subclasses of this ... More

Not served on a silver platter! Access to online mathematics information in AfricaMay 18 2009This paper argues that, contrary to the beliefs of many, the amount of mathematics information available for African researchers, including electronic scientific journals and databases, is indeed substantial. However, whereas information resources are ... More

Constant net-time headway as key mechanism behind pedestrian flow dynamicsAug 21 2009We show that keeping a constant lower limit on the net-time headway is the key mechanism behind the dynamics of pedestrian streams. There is a large variety in flow and speed as functions of density for empirical data of pedestrian streams, obtained from ... More

The role of magnetic fields for planetary formationMay 15 2009The role of magnetic fields for the formation of planets is reviewed. Protoplanetary disc turbulence driven by the magnetorotational instability has a huge influence on the early stages of planet formation. Small dust grains are transported both vertically ... More

Response time of internautsMar 01 2001A new experiment measuring the dynamical response of the Internet population to a ``point-like'' perturbation has been performed. The nature of the perturbation was that of an announcement, specifically a web-interview on stock market crashes, which contained ... More

The Dirichlet problem for p-harmonic functions on the topologist's combApr 05 2013In this paper we study the Perron method for solving the p-harmonic Dirichlet problem on the topologist's comb. For functions which are bounded and continuous at the accessible points, we obtain invariance of the Perron solutions under arbitrary perturbations ... More

Infinitesimal cubical structure, and higher connectionsMay 30 2007In the context of Synthetic Differential Geometry, we describe a notion of higher connection with values in a cubical groupoid. We do this by exploiting a certain structure of cubical complex derived from the first neighbourhood of the diagonal of a manifold. ... More

Multi-Adaptive Galerkin Methods for ODEs II: Implementation and ApplicationsMay 12 2012Continuing the discussion of the multi-adaptive Galerkin methods mcG(q) and mdG(q) presented in [A. Logg, SIAM J. Sci. Comput., 24 (2003), pp. 1879-1902], we present adaptive algorithms for global error control, iterative solution methods for the discrete ... More

Shotgun edge assembly of random jigsaw puzzlesMay 23 2016May 25 2016In recent work by Mossel and Ross, it was asked how large $q$ has to be for a random jigsaw puzzle with $q$ different shapes of "jigs" to have exactly one solution. The jigs are assumed symmetric in the sense that two jigs of the same type always fit ... More

Metric spaces and SDGOct 31 2016Feb 22 2017We explore how the synthetic theory of metric spaces (Busemann) can coexist with synthetic differential geometry in the sense based on nilpotent elements in the number line.

The dual fibration in elementary termsJan 08 2015We give an elementary construction of the dual fibration of a fibration. It does not use the non-elementary notion of (pseudo-) functor into the category of categories.

Let Δbe a Cohen-Macaulay complexNov 08 2014The concept of Cohen-Macaulay complexes emerged in the mid-1970s and swiftly became the focal point of an attractive and richly connected new area of mathematics, at the crossroads of combinatoics, commutative algebra and topology. As the main architect ... More

An improved energy argument for the Hegselmann-Krause modelJan 09 2015We show that the freezing time of the $d$-dimensional Hegselmann-Krause model is $O(n^4)$ where $n$ is the number of agents. This improves the best known upper bound whenever $d\geq 2$.

Duality for generic algebrasDec 20 2014We prove that double dualization into the generic algebra for an algebraic theory has some Gelfand- or Stone- duality properties

A Lipschitz metric for conservative solutions of the two-component Hunter--Saxton systemFeb 26 2015We establish the existence of conservative solutions of the initial value problem of the two-component Hunter--Saxton system on the line. Furthermore we investigate the stability of these solutions by constructing a Lipschitz metric.

Abstract Projective LinesDec 04 2009We describe a notion of (abstract) projective line over a field as a set equipped with a certain first order structure, and a projectivity between projective lines as a bijection preserving this structure. The structure in question is that of a groupoid, ... More

Geometric algebra of projective linesMar 10 2010The projective line over a field carries structure of a groupoid with a certain correspondence between objects and arrows. We discuss to what extent the field can be reconstructed from the groupoid.

Notes on risk theoryOct 12 2011The paper contains a basic course on classical Risk Theory for a compound Poisson process. It is based on probabilistic proofs using the method of the "Ballot Theorem" introduced by Tackas. This provides elegant and direct proofs. Also large deviation ... More

Spectral modeling of nebular-phase supernovaeDec 20 2011Massive stars live fast and die young. They shine furiously for a few million years, during which time they synthesize most of the heavy elements in the universe in their cores. They end by blowing themselves up in a powerful explosion known as a supernova. ... More

A complete and minimal catalogue of MSSM gauge invariant monomialsOct 02 2009Feb 16 2010We present a complete and minimal catalogue of MSSM gauge invariant monomials. That is, the catalogue of Gherghetta, Kolda and Martin is elaborated to include generational structure for all monomials. Any gauge invariant operator can be built as a linear ... More

Extraction of a_nn from pi- d -> n n gammaNov 03 2006I present a calculation of the pi- d -> n n gamma reaction to third order in chiral perturbation theory. The short-distance physics of this reaction can be constrained by relating it to several important low-energy weak reactions. The theoretical error ... More

Multi-pion production in the d d -> alpha X reactionNov 08 1999A simple model, based on two parallel and independent N N -> d pi processes, has recently been proposed for two-pion production in the d d -> alpha X reaction. It reproduces all observed features, including the sharp peak structure in momentum distributions ... More

Quantum field thermalization in expanding backgroundsJun 19 2008Mar 13 2009The 2PI effective action formalism for quantum fields out of equilibrium is set up in an expanding (Friedmann-Robertson-Walker) background. We write down and solve the evolution equations for a phi^4 model at NLO in a coupling expansion. We comment on ... More

Dynamics of Hilbert nonexpansive mapsFeb 19 2013In his work on the foundations of geometry, Hilbert observed that a formula which appeared in works by Beltrami, Cayley, and Klein, gives rise to a complete metric on any bounded convex domain. Some decades later, Garrett Birkhoff and Hans Samelson noted ... More

Yield and suppression of electrons from open heavy-flavor decays in heavy-ion collisionsDec 31 2011Measurements by the STAR and PHENIX collaborations indicate that a quark-gluon plasma, a hot and dense state of matter in which quarks and gluons are not confined inside hadrons, is formed in heavy-ion collisions at the Relativistic Heavy Ion Collider. ... More

Probing Human Response TimesMay 05 2003Jan 14 2004In a recent preprint \cite{eck}, the temporal dynamics of an e-mail network has been investigated by J.P. Eckmann, E. Moses and D. Sergi. Specifically, the time period between an e-mail message and its reply were recorded. It will be shown here that their ... More

On the distribution of angles between the N shortest vectors in a random latticeDec 15 2010We determine the joint distribution of the lengths of, and angles between, the N shortest lattice vectors in a random n-dimensional lattice as n tends to infinity. Moreover we interpret the result in terms of eigenvalues and eigenfunctions of the Laplacian ... More

On the Poisson distribution of lengths of lattice vectors in a random latticeJan 20 2010Sep 08 2010We prove that the volumes determined by the lengths of the non-zero vectors $\pm\vecx$ in a random lattice L of covolume 1 define a stochastic process that, as the dimension n tends to infinity, converges weakly to a Poisson process on the positive real ... More

A cell complex in number theoryJan 29 2011Let De_n be the simplicial complex of squarefree positive integers less than or equal to n ordered by divisibility. It is known that the asymptotic rate of growth of its Euler characteristic (the Mertens function) is closely related to deep properties ... More

Note: Random-to-front shuffles on treesJan 27 2009A Markov chain is considered whose states are orderings of an underlying fixed tree and whose transitions are local "random-to-front" reorderings, driven by a probability distribution on subsets of the leaves. The eigenvalues of the transition matrix ... More

Blueberry EarthJul 27 2018This paper explores the physics of the what-if question "what if the entire Earth was instantaneously replaced with an equal volume of closely packed, but uncompressed blueberries?" While the assumption may be absurd, the consequences can be explored ... More

Confounding caused by causal-effect covariabilityMay 15 2018Confounding seriously impairs our ability to learn about causal relations from observational data. Confounding can be defined as a statistical association between two variables due to inputs from a common source (the confounder). For example, if $Z\rightarrow ... More

Huygens' principle - a synthetic accountApr 16 2018We present an axiomatic/synthetic account of the Huygens Principle of wave fronts. The primitive notions are "touching", and (a weak notion of ) metric. The paper simplifies some of the exposition of the author's "Metric spaces and SDG", Theory and Appl. ... More

A species approach to Rota's twelvefold wayMar 27 2019An introduction to Joyal's theory of combinatorial species is given and through it an alternative view of Rota's twelvefold way emerges.

An entropy based clustering order parameter for finite ensembles of oscillatorsJul 20 2015Based on the entropy concept, we define a new clustering order parameter $c$ feasible for finite systems of interacting oscillators. Unlike the generalized synchronization order parameters of the Kuramoto type, this new order parameter singles out the ... More

New methods for old spaces: synthetic differential geometryOct 02 2016Sep 25 2017Survey talk on certain aspects of the subject, stressing the neighbor relation as a basic notion in differential geometry.

Affine combinations in affine schemesAug 18 2015We prove that finite sets of mutual neighbor points in an affine scheme admit affine combinations, preserved by any map. Furthermore, such combination has a value which is neighbor point of all the original points.

First-passage percolation on Cartesian power graphsJun 29 2015Apr 17 2017We consider first-passage percolation on the class of "high-dimensional" graphs that can be written as an iterated Cartesian product $G\square G \square \dots \square G$ of some base graph $G$ as the number of factors tends to infinity. We propose a natural ... More

Most edge-orderings of $K_n$ have maximal altitudeMay 23 2016Mar 08 2018Suppose the edges of the complete graph on $n$ vertices are assigned a uniformly chosen random ordering. Let $X$ denote the corresponding number of Hamiltonian paths that are increasing in this ordering. It was shown in a recent paper by Lavrov and Loh ... More

On the dynamics of isometriesDec 29 2005We provide an analysis of the dynamics of isometries and semicontractions of metric spaces. Certain subsets of the boundary at infinity play a fundamental role and are identified completely for the standard boundaries of CAT(0)-spaces, Gromov hyperbolic ... More

Selective self-excitation of higher vibrational modes of graphene nano-ribbons and carbon nanotubes through magnetomotive instabilityDec 05 2011We demonstrate theoretically the feasibility of selective self-excitation of higher-mode flexural vibrations of graphene nano-ribbons and carbon nanotubes by the means of magnetomotive instability. Apart from the mechanical resonator, the device consists ... More

Metric spaces and SDGOct 31 2016Nov 01 2016We explore how the synthetic theory of metric spaces (Busemann) can coexist with synthetic differential geometry in the sense based on nilpotent elements in the number line.

Selfoscillations of Suspended Carbon Nanotubes with a Deflection Sensitive Resistance under Voltage BiasJul 07 2010We theoretically investigate the electro-mechanics of a Suspended Carbon Nanotube with a Deflection Sensitive Resistance subjected to a homogeneous Magnetic Field and a constant Voltage Bias. We show that, (with the exception of a singular case), for ... More

Extracting the neutron-neutron scattering length -- recent developmentsApr 17 2009The experimental and theoretical issues and challenges for extracting the neutron-neutron scattering length are discussed. Particular emphasis is placed on recent results and their impact on the field. Comments are made regarding current experimental ... More

Estimating the Degree of Entanglement of Unknown Gaussian StatesOct 31 2006We give an introduction to Gaussian states and operations. A discussion of the entanglement properties of bipartite Gaussian states in terms of its covariance matrix follows. It is explained how entanglement can be witnessed using feasible measurements, ... More

The Ground State Energy of a Dilute Bose Gas in Dimension n >3Jan 23 2014Mar 24 2014We consider a Bose gas in spatial dimension $n>3$ with a repulsive, radially symmetric two-body potential $V$. In the limit of low density $\rho$, the ground state energy per particle in the thermodynamic limit is shown to be $(n-2)|\mathbb S^{n-1}|a^{n-2}\rho$, ... More

Theory of characteristics for first order partial differential equationsNov 25 2010We use the method of synthetic differential geometry to revisit the geometric reasoning employed by Lie, Klein and others in their study of partial differential equations.

On the invariants of the splitting algebraMay 23 2011For a given monic polynomial $p(t)$ of degree $n$ over a commutative ring $k$, the splitting algebra is the universal $k$-algebra in which $p(t)$ has $n$ roots, or, more precisely, over which $p(t)$ factors, $p(t)=(t-\xi_1)...(t-\xi_n)$. The symmetric ... More

A $q$-analogue of the FKG inequality and some applicationsJun 07 2009Aug 21 2009Let $L$ be a finite distributive lattice and $\mu : L \to {\mathbb R}^{+}$ a log-supermodular function. For functions $k: L \to {\mathbb R}^{+}$ let $$E_{\mu} (k; q) \defeq \sum_{x\in L} k(x) \mu (x) q^{{\mathrm rank}(x)} \in {\mathbb R}^{+}[q].$$ We ... More

Comment on A.-L. Barabasi, Nature 435 207-211 (2005)Feb 04 2006The purpose of this communication is twofold. First, it clarifies the origin of the power law obtained in the computer simulations presented in A.-L. Barabasi, Nature 435 207-211 (2005) as well as presenting a statistically more sound analysis of the ... More

Characterization of large price variations in financial marketsOct 25 2002Statistics of drawdowns (loss from the last local maximum to the next local minimum) plays an important role in risk assessment of investment strategies. As they incorporate higher ($>$ two) order correlations, they offer a better measure of real market ... More

Comment on recent claims by Sornette and ZhouFeb 07 2003Comment on recent claims by Sornette and Zhou: D. Sornette and W. Zhou, Quantitative Finance 2 (6), 468-481 (2002); Evidence of a Worldwide Stock Market Log-Periodic Anti-Bubble Since Mid-2000, cond-mat/0212010; Renormalization Group Analysis of the 2000-2002 ... More

Commutation StructuresNov 02 2005For a fixed object X in a monoidal category, an X-commutation structure on an object A is just a map from XA to AX. We study aspects of such structure in case A has a dual.

First neighbourhood of the diagonal, and geometric distributionsJun 07 2002We describe the geometric notion of distribution in synthetic terms, utilizing the notion of "first neighbourhood of the diagonal" from algebraic geometry. We characterize involutive distributions in combinatorial terms.

Pregroupoids and their enveloping groupoidsFeb 03 2005We prove that the forgetful functor from groupoids to pregroupoids has a left adjoint, with the front adjunction injective. Thus we get an enveloping groupoid for any pregroupoid. We prove that the category of torsors is equivalent to that of pregroupoids. ... More

Multi-Adaptive Galerkin Methods for ODEs IMay 12 2012We present multi-adaptive versions of the standard continuous and discontinuous Galerkin methods for ODEs. Taking adaptivity one step further, we allow for individual time-steps, order and quadrature, so that in particular each individual component has ... More

Calculus of extensive quantitiesMay 17 2011We show how a commutative monad gives rise to a theory of extensive quantities, including (under suitable further conditions) a differential calculus of such. The relationship to Schwartz distributions is dicussed. The paper is a companion to the author's ... More

Spikes as regularizersNov 18 2016We present a confidence-based single-layer feed-forward learning algorithm SPIRAL (Spike Regularized Adaptive Learning) relying on an encoding of activation spikes. We adaptively update a weight vector relying on confidence estimates and activation offsets ... More