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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

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

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

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

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

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

Classification using distance nearest neighboursApr 22 2010Jun 01 2010This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution of class labels is explicitly modelled using the distances between feature vectors. Intuitively, a class label should depend ... 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

Trigonometric Interpolation and Quadrature in Perturbed PointsDec 13 2016The trigonometric interpolants to a periodic function $f$ in equispaced points converge if $f$ is Dini-continuous, and the associated quadrature formula, the trapezoidal rule, converges if $f$ is continuous. What if the points are perturbed? With equispaced ... 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

The effect of a massive object on an expanding universeApr 22 2011May 22 2012A tetrad-based procedure is presented for solving Einstein's field equations for spherically-symmetric systems; this approach was first discussed by Lasenby et al. in the language of geometric algebra. The method is used to derive metrics describing a ... More

First-order adiabatic perturbations of a perfect fluid about a general FLRW background using the 1+3 covariant and gauge-invariant formalismSep 29 2009An analysis of adiabatic perturbations of a perfect fluid is performed to first-order about a general FLRW background using the 1+3 covariant and gauge-invariant formalism. The analog of the Mukhanov-Sasaki variable and the canonical variables needed ... More

SKYNET: an efficient and robust neural network training tool for machine learning in astronomySep 03 2013Jan 27 2014We present the first public release of our generic neural network training algorithm, called SkyNet. This efficient and robust machine learning tool is able to train large and deep feed-forward neural networks, including autoencoders, for use in a wide ... 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

Pointfree pointwise suprema in unital archimedean $\ell$-groupsNov 12 2014We generalize the concept of the pointwise supremum of real-valued functions to the pointfree setting. The concept itself admits a direct and intuitive formulation which makes no mention of points. But our aim here is to investigate pointwise suprema ... More

Cracking the Taub-NUTJul 09 2010We present further analysis of an anisotropic, non-singular early universe model that leads to the viable cosmology presented in Dechant et al (arXiv:0809.4335). Although this model (the DLH model) contains scalar field matter, it is reminiscent of the ... More

On certain functionals of the maximum of Brownian motion and their applicationsFeb 04 2015We consider a Brownian motion (BM) $x(\tau)$ and its maximal value $x_{\max} = \max_{0 \leq \tau \leq t} x(\tau)$ on a fixed time interval $[0,t]$. We study functionals of the maximum of the BM, of the form ${\cal O}_{\max}(t)=\int_0^t\, V(x_{\max} - ... 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

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

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 effect of an expanding universe on massive objectsApr 22 2011May 22 2012We present some astrophysical consequences of the metric for a point mass in an expanding universe derived in Nandra, Lasenby & Hobson, and of the associated invariant expression for the force required to keep a test particle at rest relative to the central ... More

An anisotropic, non-singular early universe model leading to a realistic cosmologySep 25 2008Feb 04 2009We present a novel cosmological model in which scalar field matter in a biaxial Bianchi IX geometry leads to a non-singular `pancaking' solution: the hypersurface volume goes to zero instantaneously at the `Big Bang', but all physical quantities, such ... More

uvbyCaHbeta CCD Photometry of Clusters. III. The Most Metal-Rich Open Cluster, NGC 6253Dec 12 2002CCD photometry on the intermediate-band uvbyCaH-beta system is presented for the old open cluster, NGC 6253. Despite a high level of field star contamination due to its location toward the galactic center, combination of the data from the multiple color ... 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

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

Metal to insulator transition in Conducting Polyaniline/Graphene Oxide compositesMar 19 2019Broadband Dielectric Spectroscopy (BDS) measurements of P{\omicron}lyaniline/Graphene oxide composites were conducted for an as-prepared and a thermally annealed specimen, respectively, from 15K to room temperature. Electrical conductivity values of the ... More

Constraining the shape of the CMB: a Peak-by-Peak analysisJul 12 2002Jan 09 2003The recent measurements of the power spectrum of Cosmic Microwave Background anisotropies are consistent with the simplest inflationary scenario and big bang nucleosynthesis constraints. However, these results rely on the assumption of a class of models ... 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

Is scientific literature subject to a sell-by-date? A general methodology to analyze the durability of scientific documentsJul 09 2009The study of the citation histories and ageing of documents are topics that have been addressed from several perspectives, especially in the analysis of documents with delayed recognition or sleeping beauties. However, there is no general methodology ... More

Static energetics in gravityNov 24 2018A stress-energy tensor for linear gravity adapted to the harmonic gauge was recently proposed by Butcher, Hobson and Lasenby. By removing gauge constraints and imposing full metrical GR, we find a natural generalisation to the pseudotensor of Einstein. ... More

Learning Shape and Texture Characteristics of CT Tree-in-Bud Opacities for CAD SystemsJun 26 2011Although radiologists can employ CAD systems to characterize malignancies, pulmonary fibrosis and other chronic diseases; the design of imaging techniques to quantify infectious diseases continue to lag behind. There exists a need to create more CAD systems ... More

Galaxy Cluster Assembly at z=0.37Mar 21 2005We present X-ray and spectroscopic confirmation of a cluster assembling from multiple, distinct galaxy groups at z=0.371. Initially detected in the Las Campanas Distant Cluster Survey, the structure contains at least four X-ray detected groups that lie ... 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

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

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

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

Acylindrical action on the hyperplanes of a CAT(0) cube complexOct 27 2016We prove that if a group acts essentially and acylindrically on the hyperplanes of a finite-dimensional CAT(0) cube complex then it is either acylindrically hyperbolic or virtually cyclic. An action on a CAT(0) cube complex is acylindrical on the hyperplanes ... More

Simulations of Core Collapse Supernovae In One and Two Dimemsions Using Multigroup Neutrino TransportApr 17 1997In one dimension, we present results from comparisons of stationary state multigroup flux-limited diffusion and Boltzmann neutrino transport, focusing on quantities central to the postbounce shock reheating. In two dimensions, we present results from ... More

Linear vertex-kernels for several dense ranking r-CSPsMar 16 2012Oct 25 2012A Ranking r-Constraint Satisfaction Problem (ranking r-CSP) consists of a ground set of vertices V, an arity r >= 2, a parameter k and a constraint system c, where c is a function which maps rankings of r-sized subsets of V to {0,1}. The objective is ... 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Optimal lower bounds on the maximal p-negative type of finite metric spacesJul 17 2008This article derives lower bounds on the supremal (strict) p-negative type of finite metric spaces using purely elementary techniques. The bounds depend only on the cardinality and the (scaled) diameter of the underlying finite metric space. Examples ... 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

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

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

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

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

The First Cohomology Group H^1(G,M)Oct 18 2003This paper characterizes the first cohomology group H^1(G,M) where M is a Banach space (with norm ||.||) that is also a left CG-module such that the elements of G act on M as continuous complex-linear transformations. Of particular interest is the topology ... More

Size-selective concentration of chondrules and other small particles in protoplanetary nebula turbulenceSep 13 2000Size-selective concentration of particles in a weakly turbulent protoplanetary nebula may be responsible for the initial collection of chondrules and other constituents into primitive body precursors. This paper presents the main elements of this process ... 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

Infinite Latin Squares: Neighbor Balance and OrthogonalityJul 23 2018Regarding neighbor balance, we consider natural generalizations of $D$-complete Latin squares and Vatican squares from the finite to the infinite. We show that if $G$ is an infinite abelian group with $|G|$-many square elements, then it is possible to ... 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

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

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

Mellin and Wiener-Hopf operators in a non-classical boundary value problem describing a Lévy processApr 28 2017Markov processes are well understood in the case when they take place in the whole Euclidean space. However, the situation becomes much more complicated if a Markov process is restricted to a domain with a boundary, and then a satisfactory theory only ... More

Welfare Maximization with Deferred Acceptance Auctions in Reallocation ProblemsJul 06 2015Sep 20 2015We design approximate weakly group strategy-proof mechanisms for resource reallocation problems using Milgrom and Segal's deferred acceptance auction framework: the radio spectrum and network bandwidth reallocation problems in the procurement auction ... 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

K^F-invariants in irreducible representations of G^F, when G=GL_nJul 24 2001Jan 25 2002Using a general result of Lusztig, we give explicit formulas for the dimensions of K^F-invariants in irreducible representations of G^F, when G=GL_n, F:G->G is a Frobenius map, and K is an F-stable subgroup of finite index in G^theta for some involution ... 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

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