Results for "Anthony N. Burkitt"

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General analytical solution to Linsker's application of Hebbian rules in neural networksMay 09 2018Previous work by Linsker revealed how simple cells can emerge in the absence of structured environmental input, via a selforganisation learning process. He empirically showed the development of spatial-opponent cells driven only by input noise, emerging ... More
Impact of axonal delay on structure development in a Linsker type networkMay 10 2018In his seminal, three paper series, Linsker provided a mechanism for how random activity in the visual pathway could give rise to many of the features observed experimentally in the early stages of visual processing. Owing to the complexity of multilayer ... More
On the Superradiance of Spin-1 Waves in an Equatorial Wedge around a Kerr HoleOct 21 1999Recently Van Putten has suggested that superradiance of magnetosonic waves in a toroidal magnetosphere around a Kerr black hole may play a role in the central engine of gamma-ray bursts. In this context, he computed (in the WKB approximation) the superradiant ... More
Corrigendum to `Orbit closures in the enhanced nilpotent cone', published in Adv. Math. 219 (2008)Aug 06 2010In this note, we point out an error in the proof of Theorem 4.7 of [P. Achar and A.~Henderson, `Orbit closures in the enhanced nilpotent cone', Adv. Math. 219 (2008), 27-62], a statement about the existence of affine pavings for fibres of a certain resolution ... More
Bayesian Indirect Inference Using a Parametric Auxiliary ModelMay 13 2015Indirect inference (II) is a methodology for estimating the parameters of an intractable (generative) model on the basis of an alternative parametric (auxiliary) model that is both analytically and computationally easier to deal with. Such an approach ... More
Orbit closures in the enhanced nilpotent coneDec 07 2007Aug 09 2010We study the orbits of $G=\mathrm{GL}(V)$ in the enhanced nilpotent cone $V\times\mathcal{N}$, where $\mathcal{N}$ is the variety of nilpotent endomorphisms of $V$. These orbits are parametrized by bipartitions of $n=\dim V$, and we prove that the closure ... More
Geometric Satake, Springer correspondence, and small representationsAug 25 2011Dec 03 2012For a simply-connected simple algebraic group $G$ over $\C$, we exhibit a subvariety of its affine Grassmannian that is closely related to the nilpotent cone of $G$, generalizing a well-known fact about $GL_n$. Using this variety, we construct a sheaf-theoretic ... More
A homotopic mapping between current-based and conductance-based synapses in a mesoscopic neural model of epilepsyOct 01 2015Dec 16 2018Changes in brain states, as found in many neurological diseases such as epilepsy, are often described as bifurcations in mesoscopic neural models. Nearly all of these models rely on a mathematically convenient, but biophysically inaccurate, description ... More
Are current-based synapses an accurate enough approximation? A homotopic mapping between current-based and conductance-based synapses in a neural field model of epilepsyOct 01 2015The overwhelming majority of neural field and mass models use current-based synapses [1] unlike spiking models which typically use conductance-based synapses [2]. Although neural field models that employ conductance-based synapses have been studied [3,9], ... More
Pressure-induced electro-switching of polymer/nano-graphene compositesMay 04 2019The pressure and temperature dependency of the electrical conductivity of poly(vinyl alcohol)/poly(vinyl pyrrolidone) (1/1, w/w) and poly(vinyl alcohol) and composites with dispersed nano-graphene platelets were studied. Above the critical platelet fraction ... More
Pieces of nilpotent cones for classical groupsJan 24 2010We compare orbits in the nilpotent cone of type $B_n$, that of type $C_n$, and Kato's exotic nilpotent cone. We prove that the number of $\F_q$-points in each nilpotent orbit of type $B_n$ or $C_n$ equals that in a corresponding union of orbits, called ... More
Geometric Satake, Springer correspondence, and small representations IIMay 23 2012Apr 23 2015For a split reductive group scheme $G$ over a commutative ring $k$ with Weyl group $W$, there is an important functor $Rep(G,k) \to Rep(W,k)$ defined by taking the zero weight space. We prove that the restriction of this functor to the subcategory of ... More
Unlensing Multiple Arcs in 0024+1654: Reconstruction of the Source ImageDec 19 1995A unique reconstruction of the image of a high redshift source galaxy responsible for multiple long arcs in the z = 0.4 cluster 0024+1654 is obtained by inverse lensing. Deep B and I imaging with the Hubble Space Telescope (Based on observations with ... More
Shaping Operations to Attack Robust Terror NetworksNov 04 2012Security organizations often attempt to disrupt terror or insurgent networks by targeting "high value targets" (HVT's). However, there have been numerous examples that illustrate how such networks are able to quickly re-generate leadership after such ... More
Modular generalized Springer correspondence: an overviewOct 30 2015Oct 07 2016This is an overview of our series of papers on the modular generalized Springer correspondence. It is an expansion of a lecture given by the second author in the Fifth Conference of the Tsinghua Sanya International Mathematics Forum, Sanya, December 2014, ... More
An alternative approach to modelling a cosmic void and its effect on the cosmic microwave backgroundApr 09 2018We apply our tetrad-based approach for constructing spherically-symmetric solutions in general relativity to modelling a void, and compare it with the standard Lema\^itre-Tolman-Bondi (LTB) formalism. In particular, we construct models for the void observed ... More
Normality of orbit closures in the enhanced nilpotent coneApr 22 2010We continue the study of the closures of $GL(V)$-orbits in the enhanced nilpotent cone $V\times\cN$ begun by the first two authors. We prove that each closure is an invariant-theoretic quotient of a suitably-defined enhanced quiver variety. We conjecture, ... More
Weyl group actions on the Springer sheafApr 09 2013Oct 03 2013We show that two Weyl group actions on the Springer sheaf with arbitrary coefficients, one defined by Fourier transform and one by restriction, agree up to a twist by the sign character. This generalizes a familiar result from the setting of l-adic cohomology, ... More
Modular generalized Springer correspondence II: classical groupsApr 03 2014Feb 02 2015We construct a modular generalized Springer correspondence for any classical group, by generalizing to the modular setting various results of Lusztig in the case of characteristic-$0$ coefficients. We determine the cuspidal pairs in all classical types, ... More
Ghost and tachyon free Poincaré gauge theories: a systematic approachDec 06 2018Apr 18 2019A systematic method is presented for determining the conditions on the parameters in the action of a parity-preserving gauge theory of gravity for it to contain no ghost or tachyon particles. The technique naturally accommodates critical cases in which ... More
Modular generalized Springer correspondence I: the general linear groupJul 10 2013Apr 24 2014We define a generalized Springer correspondence for the group GL(n) over any field. We also determine the cuspidal pairs, and compute the correspondence explicitly. Finally we define a stratification of the category of equivariant perverse sheaves on ... More
The Role of Data Analysis in Uncertainty Quantification: Case Studies for Materials ModelingDec 05 2017In computational materials science, mechanical properties are typically extracted from simulations by means of analysis routines that seek to mimic their experimental counterparts. However, simulated data often exhibit uncertainties that can propagate ... More
Modular generalized Springer correspondence III: exceptional groupsJul 02 2015Oct 07 2016We complete the construction of the modular generalized Springer correspondence for an arbitrary connected reductive group, with a uniform proof of the disjointness of induction series that avoids the case-by-case arguments for classical groups used in ... More
Rescattering effects in laser-assisted electron-atom bremsstrahlungJan 06 2015Feb 01 2015Rescattering effects in nonresonant spontaneous laser-assisted electron-atom bremsstrahlung (LABrS) are analyzed within the framework of time-dependent effective-range (TDER) theory. It is shown that high energy LABrS spectra exhibit rescattering plateau ... More
ABC model selection for spatial extremes models applied to South Australian maximum temperature dataOct 09 2017Aug 09 2018Max-stable processes are a common choice for modelling spatial extreme data as they arise naturally as the infinite-dimensional generalisation of multivariate extreme value theory. Statistical inference for such models is complicated by the intractability ... More
Diagram automorphisms of quiver varietiesSep 03 2013Sep 08 2014We show that the fixed-point subvariety of a Nakajima quiver variety under a diagram automorphism is a disconnected union of quiver varieties for the `split-quotient quiver' introduced by Reiten and Riedtmann. As a special case, quiver varieties of type ... More
Complex diffusion-weighted image estimation via matrix recovery under general noise modelsDec 14 2018We propose a patch-based singular value shrinkage method for diffusion magnetic resonance image estimation targeted at low signal to noise ratio and accelerated acquisitions. It operates on the complex data resulting from a sensitivity encoding reconstruction, ... More
Collapse of the charge ordering gap of Nd_{0.5}Sr_{0.5}MnO_{3} in an applied magnetic fieldMar 06 1999Mar 27 1999We report results of tunneling studies on the charge ordering compound Nd_{0.5}Sr_{0.5}MnO_{3} in a magnetic field up to 6T and for temperature down to 25K.We show that a gap (2\Delta_{CO} \approx 0.5eV opens up in the density of state (DOS) at the Fermilevel ... More
Low-temperature thermal expansion of rock-salt ZnOMar 09 2013Lattice parameter of metastable high-pressure phase of zinc oxide, rock-salt ZnO was measured in the 10-300 K temperature range using synchrotron X-ray powder diffraction. No phase transition was observed down to 10 K. The lattice parameter of rock-salt ... More
A geometrical triumvirate of real random matricesFeb 06 2012We present a five-step method for the calculation of eigenvalue correlation functions for various ensembles of real random matrices, based upon the method of (skew-) orthogonal polynomials. This scheme systematises existing methods and also involves some ... More
Exterior powers of the reflection representation in the cohomology of Springer fibresJan 18 2010Let $H^*(\calB_e)$ be the cohomology of the Springer fibre for the nilpotent element $e$ in a simple Lie algebra $\g$, on which the Weyl group $W$ acts by the Springer representation. Let $\Lambda^i V$ denote the $i$th exterior power of the reflection ... More
Induced characters of the projective general linear group over a finite fieldDec 13 2005Using a general result of Lusztig, we find the decomposition into irreducibles of certain induced characters of the projective general linear group over a finite field of odd characteristic.
Global Solutions of the Equations of 3D Compressible Magnetohydrodynamics with Zero ResistivityFeb 18 2012Nov 10 2014We prove the global-in-time existence of H^2 solutions of the equations of compressible magnetohydrodynamics with zero magnetic resistivity in three space dimensions. Initial data are taken to be small in H^2 modulo a constant state and initial densities ... More
Classical curves via one-vertex mapsJan 08 2012Jul 16 2012One-vertex maps (a type of dessin d'enfant) give a uniform characterization of certain well-known algebraic curves, including those of Klein, Wiman, Accola-Maclachlan and Kulkarni. The characterization depends on a new classification of one-vertex (dually, ... More
Global Solutions of the Navier-Stokes Equations for Isentropic Flow with Large External Potential ForceOct 01 2011Jul 10 2012We prove the global-in-time existence of weak solutions to the Navier-Stokes equations of compressible isentropic flow in three space dimensions with adiabatic exponent $\gamma\ge1$. Initial data and solutions are small in $L^2$ around a non-constant ... More
The geometry of two-valued subsets of $L_{p}$-spacesDec 29 2014Jul 13 2016Let $\mathcal{M}(\Omega, \mu)$ denote the algebra of all scalar-valued measurable functions on a measure space $(\Omega, \mu)$. Let $B \subset \mathcal{M}(\Omega, \mu)$ be a set of finitely supported measurable functions such that the essential range ... More
Experimental analysis of lattice walksDec 05 2017Feller's book An Introduction to Probability Theory and Its Application discusses statistics corresponding to sequences of coin tosses, with a dollar being won or lost depending on the outcome of each toss. This is equivalent to analyzing walks in the ... More
A Constructive Characterisation of Circuits in the Simple (2,2)-sparsity MatroidFeb 15 2012Jun 21 2013We provide a constructive characterisation of circuits in the simple (2,2)-sparsity matroid. A circuit is a simple graph G=(V,E) with |E|=2|V|-1 and the number of edges induced by any $X \subsetneq V$ is at most 2|X|-2. Insisting on simplicity results ... More
Exponents of diophantine approximation in dimension $2$ for numbers of Sturmian typeNov 21 2017We generalize the construction of Roy's Fibonacci type numbers to the case of a Sturmian recurrence and we determine the classical exponents of approximation $\omega_2(\xi)$, $\widehat{\omega}_2(\xi)$, $\lambda_2(\xi)$, $\widehat{\lambda}_2(\xi)$ associated ... More
Universality properties of Gelfand-Tsetlin patternsMay 06 2011Nov 12 2011A standard Gelfand-Tsetlin pattern of depth $n$ is a configuration of particles in $\{1,...,n\} \times \R$. For each $r \in \{1,...,n\}$, $\{r\} \times \R$ is referred to as the $r^\text{th}$ level of the pattern. A standard Gelfand-Tsetlin pattern has ... More
Trails, $S$-graphs and Identities in Demazure ModulesFeb 01 2017The Kashiwara crystal $B(\infty)$ parametrizes a basis for the Verma module of a Kac-Moody algebra. It has a deep combinatorial structure which one seeks to understand. For each sequence $J$ of reduced decompositions of elements of the Weyl group $W$, ... More
A preparation theorem for the kashiwara $b(\infty)$ crystalOct 21 2015The Kashiwara $B(\infty)$ crystal pertains to a Verma module for a Kac- Moody Lie algebra. Ostensibly it provides only a parametrisation of the global/canonical basis for the latter. Yet it is much more having a rich combinatorial structure from which ... More
Explicit expressions for the moments of the size of an (n, dn-1)-core partition with distinct partsFeb 18 2017Oct 15 2017In a previous paper (arXiv:1608.02262), we used computer-assisted methods to find explicit expressions for the moments of the size of a uniform random (n,n+1)-core partition with distinct parts. In particular, we conjectured that the distribution is asymptotically ... More
Rank-one isometries of CAT(0) cube complexes and their centralisersMay 01 2019If $G$ is a group acting geometrically on a CAT(0) cube complex $X$ and if $g \in G$ is an infinite-order element, we show that exactly one of the following situations occurs: (i) $g$ defines a rank-one isometry of $X$; (ii) the stable centraliser $SC_G(g)= ... More
Hyperplanes of Squier's cube complexesJul 07 2015To any semigroup presentation $\mathcal{P}= \langle \Sigma \mid \mathcal{R} \rangle$ and base word $w \in \Sigma^+$ may be associated a nonpositively curved cube complex $S(\mathcal{P},w)$, called a Squier complex, whose underlying graph consists of the ... More
A Remark on reverse Littlewood-Paley, restriction and KakeyaJul 09 2015We show that a certain conjectured optimal reverse Littlewood- Paley inequality would, if true, imply sharp results for the Kakeya maximal function, the Bochner-Riesz means and the Fourier restriction operator.
Cohomology Jumping Loci and Relative Malcev CompletionApr 25 2008Two standard invariants used to study the fundamental group G of the complement X of a hyperplane arrangement are the Malcev completion of G and the cohomology groups of X with coefficients in rank one local systems. In this paper, we develop a tool that ... More
An ignition key for atomic-scale enginesSep 06 2012A current-carrying resonant nanoscale device, simulated by non-adiabatic molecular dynamics, exhibits sharp activation of non-conservative current-induced forces with bias. The result, above the critical bias, is generalized rotational atomic motion with ... More
Scalable iterative methods for sampling from massive Gaussian random vectorsDec 05 2013Sampling from Gaussian Markov random fields (GMRFs), that is multivariate Gaussian ran- dom vectors that are parameterised by the inverse of their covariance matrix, is a fundamental problem in computational statistics. In this paper, we show how we can ... More
Influence of substitution on the optical properties of functionalized pentacene monomers and crystals: Experiment and theoryNov 14 2013The influence of solubilizing substitutional groups on the electronic and optical properties of functionalized pentacene molecules and crystals have been investigated. Density functional theory is used to calculate the electronic and optical properties ... More
Identifying dominant recombination mechanisms in perovskite solar cells by measuring the transient ideality factorApr 24 2018The ideality factor determined by measuring the open circuit voltage (VOC) as function of light intensity is often used as a means to identify the dominant recombination mechanism in solar cells. However, applying this Suns-VOC technique to perovskite ... More
Electric properties of carbon nano-onion/polyaniline composites: a combined electric modulus and ac conductivity studyApr 29 2017The complex electric modulus and the ac conductivity of carbon nanoonion/polyaniline composites were studied from 1 mHz to 1 MHz at isothermal conditions ranging from 15 K to room temperature. The temperature dependence of the electric modulus and the ... More
Learning compact q-space representations for multi-shell diffusion-weighted MRIJun 17 2018Oct 08 2018Diffusion-weighted MRI measures the direction and scale of the local diffusion process in every voxel through its spectrum in q-space, typically acquired in one or more shells. Recent developments in microstructure imaging and multi-tissue decomposition ... More
Detection of Interstellar HC$_5$O in TMC-1 with the Green Bank TelescopeJun 29 2017We report the detection of the carbon-chain radical HC$_5$O for the first time in the interstellar medium toward the dark cloud TMC-1 using the 100 m Green Bank Telescope. We observe four hyperfine components of this radical in the $J = 17/2 \rightarrow ... More
The logic of the future in quantum theorySep 02 2014May 02 2016According to quantum mechanics, statements about the future made by sentient beings like us are, in general, neither true nor false; they must satisfy a many-valued logic. I propose that the truth value of such a statement should be identified with the ... More
Entangling capacity and distinguishability of two-qubit unitary operatorsFeb 14 2005Sep 02 2005We prove that the entangling capacity of a two-qubit unitary operator without local ancillas, both with and without the restriction to initial product states, as quantified by the maximum attainable concurrence, is directly related to the distinguishability ... More
Distinguishability Measures and Ensemble OrderingsSep 27 2001Nov 01 2002It is shown that different distinguishability measures impose different orderings on ensembles of $N$ pure quantum states. This is demonstrated using ensembles of equally-probable, linearly independent, symmetrical pure states, with the maximum probabilities ... More
Top Production Properties at the TevatronNov 27 2000Nov 28 2000Following the confirmation of the top quark discovery at the Tevatron, the next step is to begin studying its properties. Because the scale of electroweak symmetry breaking is of the same order as the measured top mass, the top quark may be very sensitive ... More
John Bell and the great enterpriseAug 21 2018I outline Bell's vision of the "great enterprise" of science, and his view that conventional teachings about quantum mechanics constituted a betrayal of this enterprise. I describe a proposal of his to put the theory on a more satisfactory footing, and ... More
Polygonal equalities in Hilbert spacesSep 16 2012Sep 23 2014This work has been expanded and fully incorporated into arXiv:1203.5837. Cases of equality in the classical 2-negative type inequalities for Hilbert spaces are characterized in terms of balanced signed simplices. It follows that a metric subspace of a ... More
The numbers behind Plimpton 322Sep 17 2011Oct 02 2015A mathematically and culturally natural modification of Evart Bruins' explanation of the genesis of the numbers on the Old Babylonian tablet Plimpton 322 gives an economical accounting for the "missing pairs" in his reconstruction. When the new scheme ... More
Convexity properties of the canonical S-graphsJan 19 2017Let n be a positive integer and c an n-tuple of natural numbers. A convex set in Euclidean n-space given by a family of linear relations in the elements of c and depending on their natural order is defined. The extremal elements of this convex set are ... More
Zhelobenko Invariants, Bernstein-Gelfand-Gelfand operators and the analogue Kostant Clifford Algebra ConjectureSep 27 2011Let g be a complex simple Lie algebra and h a Cartan subalgebra. The Clifford algebra C(g) of g admits a Harish-Chandra map. Kostant conjectured (as communicated to Bazlov in about 1997) that the value of this map on a (suitably chosen) fundamental invariant ... More
On the Riemann zeta-function, Part I: OutlineMay 14 2007Results of a multipart work are outlined. Use is made therein of the conjunction of the Riemann hypothesis, RH, and hypotheses advanced by the author. Let z(n) be the nth nonreal zero of the Riemann zeta-function with positive imaginary part in order ... More
Negative curvature of automorphism groups of graph products with applications to right-angled Artin groupsJul 02 2018Oct 29 2018Given a (freely irreducible) product graph of groups $\Gamma \mathcal{G}$, we introduce and study its \emph{product graph} $P(\Gamma, \mathcal{G})$, defined as the graph whose vertices are the maximal product subgroups of $\Gamma \mathcal{G}$ and whose ... More
Minimal Surfaces from MonopolesMar 21 2002The geometry of minimal surfaces generated by charge 2 Bogomolny monopoles on 3-dimensional Euclidean space is described in terms of the moduli parameter k. We find that the distribution of Gaussian curvature on the surface reflects the monopole structure. ... More
On the Riemann zeta-function, Part IIMay 18 2007An odd meromorphic function f(s) is constructed from the Riemann zeta-function evaluated at one-half plus s. We determine the two-sided Laplace transform representation of f(s) on open vertical strips, V'(4w), disjoint from the (translated) critical strip. ... More
Explicit expressions for the moments of the size of an (s,s+1)-core partition with distinct partsAug 07 2016Nov 23 2016For fixed s, the size of an (s, s+1)-core partition with distinct parts can be seen as a random variable X_s. Using computer-assisted methods, we derive formulas for the expectation, variance, and higher moments of X_s. Our results give good evidence ... More
Hyperbolic diagram groups are freeMay 08 2015In this paper, we study the so-called diagram groups. Our main result is that diagram groups are free if and only if they do not contain any subgroup isomorphic to $\mathbb{Z}^2$. As an immediate corollary, we get that hyperbolic diagram groups are necessarily ... More
On the inadequacy of the projective structure with respect to the Univalence AxiomDec 06 2017Dec 12 2017In this article the author endows the functor category [B(Z2),Gpd] with the structure of a type-theoretic fibration category with a universe using the projective fibrations. It offers a new model of Martin-L\"of type theory with dependent sums, dependent ... More
Higher-order principal component analysis for the approximation of tensors in tree-based low-rank formatsMay 02 2017Apr 19 2018This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a product set equipped ... More
Coning-off CAT(0) cube complexesMar 21 2016In this paper, we study the geometry of cone-offs of CAT(0) cube complexes over a family of combinatorially convex subcomplexes, with an emphasis on their Gromov-hyperbolicity. A first application gives a direct cubical proof of the characterization of ... More
Time, chance and quantum theoryJan 19 2016I propose an understanding of Everett and Wheeler's relative-state interpretation of quantum mechanics, which restores the feature of indeterminism to the theory. This incorporates a theory of probability as truth values in a many-valued logic for future ... More
The Old and New Meanings of Cloud 'Belt' and 'Zone': A Study of Jovian and Saturnian Atmospheric BandingOct 13 2014Dec 24 2014The brightness of cloud bands on Jupiter and Saturn as a function of latitude is reported. Bright Jovian bands near the equator are located in regions of anti-cyclonic circulation of the atmosphere. By contrast, bright equatorial bands on Saturn are associated ... More
Single-world theory of the extended Wigner's world experimentAug 20 2016Frauchiger and Renner have recently claimed to prove that "Single-world interpretations of quantum theory cannot be self-consistent". This is contradicted by a construction due to Bell, inspired by Bohmian mechanics, which shows that any quantum system ... More
Unambiguous Discrimination Between Linearly-Independent Quantum StatesJul 08 1998The theory of generalised measurements is used to examine the problem of discriminating unambiguously between non-orthogonal pure quantum states. Measurements of this type never give erroneous results, although, in general, there will be a non-zero probability ... More
Topology and Non-Deterministic Polynomial Time Computation : Avoidance of The Misbehaviour of Hub-Free Diagrams and ConsequencesSep 05 2013To study groups with small Dehn's function, Olshanskii and Sapir developed a new invariant of bipartite chords diagrams and applied it to hub-free realization of S-machines. In this paper we consider this new invariant together with groups constructed ... More
A real quaternion spherical ensemble of random matricesSep 05 2012Sep 13 2012One can identify a tripartite classification of random matrix ensembles into geometrical universality classes corresponding to the plane, the sphere and the anti-sphere. The plane is identified with Ginibre-type (iid) matrices and the anti-sphere with ... More
Nonexistence of Self-Similar Singularities in the Ideal Viscoelastic FlowOct 01 2011Jun 27 2012We prove the nonexistence of finite time self-similar singularities in an ideal viscoelastic flow in $R^3$. We exclude the occurrence of Leray-type self-similar singularities under suitable integrability conditions on velocity and deformation tensor. ... More
Incompressible Magnetohydrodynamic Flow with Zero ResistivityJul 10 2012Nov 07 2014We prove the existence of both local and global smooth solutions to the Cauchy problem in $\R^3$ for the incompressible magnetohydrodynamics (MHD) system. We also prove that the solution to the incompressible MHD system can be obtained as the incompressible ... More
The Brouwer fixed point theorem and the Borsuk--Ulam theoremMay 21 2012These informal notes, not intended for publication, provide an approach to the Borsuk--Ulam theorem via Stokes' theorem, in a similar spirit to Lima's proof of the Brouwer fixed point theorem. They are intended to be accessible to anyone with a knowledge ... More
On the Riemann zeta-function, Part IIIMay 21 2007An odd meromorphic function f(s) is constructed from the Riemann zeta-function evaluated at one-half plus s. The partial fraction expansion, p(s), of f(s) is obtained using the conjunction of the Riemann hypothesis and hypotheses advanced by the author. ... More
Rational cohomology of the real Coxeter toric variety of type ANov 17 2010The toric variety corresponding to the Coxeter fan of type A can also be described as a De Concini-Procesi wonderful model. Using a general result of Rains which relates cohomology of real De Concini-Procesi models to poset homology, we give formulas ... More
OB Associations, Open Clusters, and the Luminosity Calibration of the Nearer StarsSep 29 2000In the context of the luminosity calibration of the nearer stars I discuss the Hipparcos results on distances to nearby OB associations and open clusters. The shortcomings and assumptions in the analyses used to derive these results are pointed out and ... More
Hilbert functions of Gorenstein algebras associated to a pencil of formsDec 18 2004Let R be a polynomial ring in r variables and D a dual ring upon which R acts as partial differential operators (classical apolarity). For a type two graded level Artinian algebras A=R/I, of socle degree j we consider the family of Artinian Gorenstein ... More
Strata of vector spaces of forms in k[x,y] and of rational curves in P^kJun 06 2013Mar 20 2015Consider the polynomial ring R=k[x,y] over an infinite field k and the subspace R_j of degree-j homogeneous polynomials. The Grassmanian G=Grass (R_j,d) parametrizes the vector spaces V in R_j having dimension d. The strata Grass_H(R_j,d) in G determined ... More
Representations of wreath products on cohomology of De Concini-Procesi compactificationsJul 30 2003The wreath product W(r,n) of the cyclic group of order r and the symmetric group S_n acts on the corresponding projective hyperplane complement, and on its wonderful compactification as defined by De Concini and Procesi. We give a formula for the characters ... More
Location of incenters and Fermat points in variable trianglesFeb 01 2000Dec 19 2001The orthocentroidal circle of a nonequilateral triangle has diameter GH, joining the centroid to the orthocenter. We show that the incenters of triangles with a given Euler line simply cover the interior of the orthocentroidal circle, and that their Fermat ... More
Cubical-like geometry of quasi-median graphs and applications to geometric group theoryDec 05 2017The class of quasi-median graphs is a generalisation of median graphs, or equivalently of CAT(0) cube complexes. The purpose of this thesis is to introduce these graphs in geometric group theory. In the first part of our work, we extend the definition ... More
Groups acting on quasi-median graphs. An introductionDec 05 2017Quasi-median graphs have been introduced by Mulder in 1980 as a generalisation of median graphs, known in geometric group theory to naturally coincide with the class of CAT(0) cube complexes. In his PhD thesis, the author showed that quasi-median graphs ... More
Embeddings into Thompson's groups from quasi-median geometrySep 12 2017The main result of this article is that any braided (resp. annular, planar) diagram group $D$ splits as a short exact sequence $1 \to R \to D \to S \to 1$ where $R$ is a subgroup of some right-angled Artin group and $S$ a subgroup of Thompson's group ... More
A cubical flat torus theorem and some of its applicationsFeb 13 2019Mar 15 2019The article is dedicated to the proof of the following cubical version of the flat torus theorem. Let $G$ be a group acting on a CAT(0) cube complex $X$ and $A \leq G$ a normal finitely generated abelian subgroup. Then there exists a median subalgebra ... More
Algebraic characterisations of negatively-curved special groups and applications to graph braid groupsSep 05 2017Nov 15 2018In this paper, we introduce a combinatorial formalism to study (virtually) special groups, introduced by Haglund and Wise. As a first application, we recover a result due to Caprace and Haglund: if the universal cover of a compact special cube complex ... More
Lamplighter groups, median spaces, and a-T-menabilityMay 02 2017This paper is dedicated to the proof of the following statement: the wreath product of two groups acting metrically properly on median spaces acts metrically properly on some median space we call space of wreaths. As a consequence of this construction, ... More
A note on torsion subgroups of groups acting on finite-dimensional CAT(0) cube complexesMay 01 2019In this article, we state and prove a general criterion which prevents some groups from acting properly on finite-dimensional CAT(0) cube complexes. As an application, we show that, for every non-trivial finite group $F$, the lamplighter group $F \wr ... More
On the geometry of van Kampen diagrams of graph products of groupsJan 14 2019Feb 11 2019In this article, we propose a geometric framework dedicated to the study of van Kampen diagrams of graph products of groups. As an application, we find information on the word and the conjugacy problems. The main new result of the paper deals with the ... More
Estimation of quadratic variation for two-parameter diffusionsJan 19 2008In this paper we give a central limit theorem for the weighted quadratic variations process of a two-parameter Brownian motion. As an application, we show that the discretized quadratic variations $\sum_{i=1}^{[n s]} \sum_{j=1}^{[n t]} | \Delta_{i,j} ... More
Determinism plus chance in random matrix theoryMay 18 1995We study Hamiltonians consisting of a deterministic term plus a random term. Using a daigrammatic approach and introducing the concept of "gluon connectedness," we calculate the density of energy levels for a wide class of probability distributions governing ... More
Effective field theoryFeb 13 1995I give a brief review of effective field theory, disscussing the contribution of Feza G\"ursey in particular and focusing on the literature I am most familiar with.
On lifting univalence to the equivariant settingDec 13 2015Apr 12 2016This PhD thesis deals with some new models of intensional type theory and the Univalence Axiom introduced by Vladimir Voevodsky. Our work takes place in the framework of the definitions of type-theoretic fibration categories (the notion of model under ... More