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Polarization-driven spin precession of mesospheric sodium atomsSep 11 2018We report experimental results on the first on-sky observation of atomic spin precession of mesospheric sodium driven by polarization modulation of a continuous-wave laser. The magnetic resonance was remotely detected from the ground by observing the ... More

Remote sensing of geomagnetic fields and atomic collisions in the mesosphereFeb 09 2018Magnetic-field sensing has contributed to the formulation of the plate-tectonics theory, the discovery and mapping of underground structures on Earth, and the study of magnetism in other planets. Filling the gap between space-based and near-Earth observation, ... More

Magnetometry with Mesospheric SodiumDec 22 2009Measurement of magnetic fields on the few-hundred-kilometer length scale is significant for a variety of geophysical applications including mapping of crustal magnetism and ocean-circulation measurements, yet available techniques for such measurements ... More

Modeling of pulsed laser guide stars for the Thirty Meter Telescope projectMar 27 2012Jun 19 2012The Thirty Meter Telescope (TMT) has been designed to include an adaptive optics system and associated laser guide star (LGS) facility to correct for the image distortion due to Earth's atmospheric turbulence and achieve diffraction-limited imaging. We ... More

The blowup formula for Donaldson invariantsMay 09 1994Jul 07 1994In this paper we present a formula which relates the Donaldson invariants of a 4-manifold X with the Donaldson invariants of its blowup X#-CP(2). This blow-up formula is independent of X and involves sigma-functions associated to a naturally arising elliptic ... More

Rational Blowdowns of Smooth 4-ManifoldsMay 17 1995In this paper we introduce a surgical procedure, called a rational blowdown, for a smooth 4-manifold X and determine how this procedure affects both the Donaldson and Seiberg-Witten invariants of X.

A note on evolutionary stochastic portfolio optimization and probabilistic constraintsJan 29 2010In this note, we extend an evolutionary stochastic portfolio optimization framework to include probabilistic constraints. Both the stochastic programming-based modeling environment as well as the evolutionary optimization environment are ideally suited ... More

Contact process with mobile disorderMay 03 2009I study the absorbing-state phase transition in the one-dimensional contact process with mobile disorder. In this model the dilution sites, though permanently inactive, diffuse freely, exchanging positions with the other sites, which host a basic contact ... More

Nonequilibrium Phase Transitions in Epidemics and SandpilesOct 01 2001Nonequilibrium phase transitions between an active and an absorbing state are found in models of populations, epidemics, autocatalysis, and chemical reactions on a surface. While absorbing-state phase transitions fall generically in the DP universality ... More

Reweighting in nonequilibrium simulationsFeb 22 1999A simple reweighting scheme is proposed for Monte Carlo simulations of interacting particle systems, permitting one to study various parameter values in a single study, and improving efficiency by an order of magnitude. Unlike earlier reweighting schemes, ... More

Are the Dirac particles of the Standard Model dynamically confined states in a higher-dimensional flat space?Apr 02 1999Some time ago Rubakov and Shaposhnikov (RS) suggested that elementary particles might be excitations trapped on a soliton in a flat higher dimensional space. They gave as an example phi-4 theory in five dimensions with a bosonic excitation on a domain ... More

The matrix element for radiative Bhabha scattering in the forward directionAug 23 1993We present an approximation to the matrix element for the process e+e- --> e+e-gamma, appropriate to the situation where one or both of the fermions are scattered over very small angles. The leading terms in the situation where all scattering angles are ... More

Optimal packing of polydisperse hard-sphere fluids IIApr 27 2000We consider the consequences of keeping the total surface fixed for a polydisperse system of $N$ hard spheres. In contrast with a similar model (J. Zhang {\it et al.}, J. Chem. Phys. {\bf 110}, 5318 (1999)), the Percus-Yevick and Mansoori equations of ... More

Computing trading strategies based on financial sentiment data using evolutionary optimizationApr 12 2015In this paper we apply evolutionary optimization techniques to compute optimal rule-based trading strategies based on financial sentiment data. The sentiment data was extracted from the social media service StockTwits to accommodate the level of bullishness ... More

Exact sequences of fibrations of crossed complexes, homotopy classification of maps, and nonabelian extensions of groupsFeb 29 2008Jun 25 2008The classifying space of a crossed complex generalises the construction of Eilenberg-Mac Lane spaces. We show how the theory of fibrations of crossed complexes allows the analysis of homotopy classes of maps from a free crossed complex to such a classifying ... More

A topologically induced 2-in/2-out operation on loop cohomologyAug 29 2011May 16 2012We apply the Transfer Algorithm introduced in arXiv:1106.5090 to transfer an A_\infty-algebra structure that cannot be computed using the classical Basic Perturbation Lemma. We construct a space X whose (base pointed) loop cohomology H = H^*(\Omega X; ... More

Combinations and Mixtures of Optimal Policies in Unichain Markov Decision Processes are OptimalAug 17 2005We show that combinations of optimal (stationary) policies in unichain Markov decision processes are optimal. That is, let M be a unichain Markov decision process with state space S, action space A and policies \pi_j^*: S -> A (1\leq j\leq n) with optimal ... More

`Double modules', double categories and groupoids, and a new homotopical double groupoidMar 15 2009Mar 21 2009We give a rather general construction of double categories and so, under further conditions, double groupoids, from a structure we call a `double module'. We also give a homotopical construction of a double groupoid from a triad consisting of a space, ... More

A Short Note on Stationary Distributions of Unichain Markov Decision ProcessesApr 20 2006Dealing with unichain MDPs, we consider stationary distributions of policies that coincide in all but $n$ states. In these states each policy chooses one of two possible actions. We show that the stationary distributions of n+1 such policies uniquely ... More

Tori in symplectic 4-manifoldsNov 19 2003Sep 29 2004We study the question of how many embedded symplectic or Lagrangian tori can represent the same homology class in a simply connected symplectic 4-manifold.

Double node neighborhoods and families of simply connected 4-manifolds with b^+=1Dec 07 2004Jan 18 2005We introduce a new technique that is used to show that the complex projective plane blown up at 6, 7, or 8 points has infinitely many distinct smooth structures. None of these smooth structures admit smoothly embedded spheres with self-intersection -1, ... More

Symplectic surfaces in a fixed homology classFeb 04 1999Oct 08 1999The purpose of this paper is to investigate the following problem: For a fixed 2-dimensional homology class K in a simply connected symplectic 4-manifold, up to smooth isotopy, how many connected smoothly embedded symplectic submanifolds represent K? ... More

Covering morphisms of groupoids, derived modules and a 1-dimensional Relative Hurewicz TheoremDec 13 2010Jan 08 2011We fill a lacuna in the literature by giving a version in dimension 1 of the Relative Hurewicz Theorem, and relate this to abelianisations of groupoids, covering spaces and covering morphisms of groupoids, and Crowell's notion of derived modules.

Modelling and Computing Homotopy Types: IOct 24 2016The aim of this article is to explain a philosophy for applying higher dimensional Seifert-van Kampen Theorems, and how the use of groupoids and strict higher groupoids resolves some foundational anomalies in algebraic topology at the border between homology ... More

Rain, power laws, and advectionOct 15 2002Localized rain events have been found to follow power-law size and duration distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws are generated ... More

Supernova Detection in IceCube: Status and FutureFeb 08 2013The IceCube detector, located at the South Pole, is discussed as a detector for core collapse supernovae. The large flux of $\bar{\nu}_{e}$ from a Galactic supernova gives rise to Cherenkov light from positrons and electrons created in neutrino interactions ... More

Three themes in the work of Charles Ehresmann: Local-to-global; Groupoids; Higher dimensionsFeb 22 2006Mar 04 2006This paper illustrates the themes of the title in terms of: van Kampen type theorems for the fundamental groupoid; holonomy and monodromy groupoids; and higher homotopy groupoids. Interaction with work of the writer is explored.

Upper Bounds on the Number of Vertices of Weight <=k in Particular Arrangements of PseudocirclesJun 06 2007Jun 13 2008In arrangements of pseudocircles (Jordan curves) the weight of a vertex (intersection point) is the number of pseudocircles that contain the vertex in its interior. We give improved upper bounds on the number of vertices of weight <=k in certain arrangements ... More

Covering morphisms of groupoids, derived modules and a 1-dimensional Relative Hurewicz TheoremDec 13 2010Mar 19 2017We fill a lacuna in the literature by giving a version in dimension 1 of the Relative Hurewicz Theorem, and relate this to abelianisations of groupoids, covering spaces and covering morphisms of groupoids, and Crowell's notion of derived modules.

Comment: Fisher Lecture: Dimension Reduction in RegressionAug 28 2007Comment: Fisher Lecture: Dimension Reduction in Regression [arXiv:0708.3774]

Moore hyperrectangles on a space form a strict cubical omega-categorySep 11 2009Sep 21 2009A question of Jack Morava is answered by generalising the notion of Moore paths to that of Moore hyperrectangles, so obtaining a strict cubical omega-category. This also has the structure of connections in the sense of Brown and Higgins, but cancellation ... More

Modelling and Computing Homotopy Types: IOct 24 2016Feb 03 2017The aim of this article is to explain a philosophy for applying higher dimensional Seifert-van Kampen Theorems, and how the use of groupoids and strict higher groupoids resolves some foundational anomalies in algebraic topology at the border between homology ... More

Duality theory for Markov processes: Part 1Feb 11 2010This is the first part of a possible monograph on the duality of Markov processes. It contains a proof of Fitzsimmons' existence theorem of a moderate Markov dual process relative to an excessive measure, m, together with the necessary preliminary material. ... More

Resonant Interactions Along the Critical Line of the Riemann Zeta FunctionSep 18 2013Nov 11 2013We have studied some properties of the special Gram points of the Riemann zeta function which lie on contour lines ${\bf Im}(\zeta ( s )) = 0$ which do not contain zeroes of $\zeta ( s )$. We find that certain functions of these points, which all lie ... More

Computing Homotopy Types Using Crossed N-Cubes of GroupsSep 14 2001Aug 13 2006The aim of this paper is to explain how, through the work of a number of people, some algebraic structures related to groupoids have yielded algebraic descriptions of homotopy n-types. Further, these descriptions are explicit, and in some cases completely ... More

Crossed modules and the homotopy 2-type of a free loop spaceMar 29 2010May 23 2010The question was asked by Niranjan Ramachandran: how to describe the fundamental groupoid of LX, the free loop space of a space X? We give an answer by assuming X to be the classifying space of a crossed module over a group, and then describe completely ... More

Possible connections between whiskered categories and groupoids, many object Leibniz algebras, automorphism structures and local-to-global questionsAug 13 2007Jul 28 2010We define the notion of whiskered categories and groupoids, showing that whiskered groupoids have a commutator theory. So also do whiskered $R$-categories, thus answering questions of what might be `commutative versions' of these theories. We relate these ... More

Ising Meets Ornstein and Zernike, Debye and Huckel, Widom and Rowlinson, and OthersDec 06 2000The name Ising has come to stand not only for a specific model, but for an entire universality class - arguably the most important such class - in the theory of critical phenomena. I review several examples, both in and out of equilibrium, in which Ising ... More

Nonuniversality and critical point shift in systems with infinitely many absorbing configurationsSep 23 1999A detailed study of critical spreading in the one-dimensional pair contact process is performed using a recently devised reweighting method. The results confirm the validity of a generalized hyperscaling relation among the (nonuniversal) spreading exponents, ... More

First- and second-order phase transitions in a driven lattice gas with nearest-neighbor exclusionSep 21 2000Oct 31 2000A lattice gas with infinite repulsion between particles separated by $\leq 1$ lattice spacing, and nearest-neighbor hopping dynamics, is subject to a drive favoring movement along one axis of the square lattice. The equilibrium (zero drive) transition ... More

Exact analytic expression for a subset of fourth virial coefficients of polydisperse hard sphere mixturesDec 07 1998We derive an exact, analytic expression for the fourth virial coefficient of a system of polydisperse spheres under the constraint that the smallest sphere has a radius smaller than a given function of the radii of the three remaining particles.

Regret Bounds for Reinforcement Learning via Markov Chain ConcentrationAug 06 2018Jan 19 2019We give a simple optimistic algorithm for which it is easy to derive regret bounds of $\tilde{O}(\sqrt{t_{\rm mix} SAT})$ after $T$ steps in uniformly ergodic Markov decision processes with $S$ states, $A$ actions, and mixing time parameter $t_{\rm mix}$. ... More

Measurement-to-Track Association and Finite-Set StatisticsJan 05 2017Multi-hypothesis trackers (MHT's), which are based on the measurement-to-track association (MTA) concept, have long been asserted to be "Bayes-optimal." Recently, rather bolder claims have come to the fore: "The right model of the multitarget state is ... More

Muon Collider: Plans, Progress and ChallengesApr 16 2012We in the physics community expect the LHC to uncover new physics in the next few years. The character and energy scale of the new physics remain unclear, but it is likely that data from the LHC will need to be complemented by information from a lepton ... More

Phase coexistence far from equilibriumFeb 10 2016Investigation of simple far-from-equilibrium systems exhibiting phase separation leads to the conclusion that phase coexistence is not well defined in this context. This is because the properties of the coexisting nonequilibrium systems depend on how ... More

Failure of steady state thermodynamics in lattice gases under nonuniform driveJul 29 2014To be useful, steady state thermodynamics (SST) must be self-consistent and have predictive value. Although consistency of SST was recently verified for driven lattice gases under global weak exchange, I show here that it does not predict the coexisting ... More

Modeling multi-stage decision optimization problemsApr 23 2014Multi-stage optimization under uncertainty techniques can be used to solve long-term management problems. Although many optimization modeling language extensions as well as computational environments have been proposed, the acceptance of this technique ... More

Evolutionary Optimization for Decision Making under UncertaintyJan 19 2014Optimizing decision problems under uncertainty can be done using a variety of solution methods. Soft computing and heuristic approaches tend to be powerful for solving such problems. In this overview article, we survey Evolutionary Optimization techniques ... More

Evidence of Long Range Order in the Riemann Zeta FunctionOct 14 2012We have done a statistical analysis of some properties of the contour lines Im$(\zeta (s))$ = 0 of the Riemann zeta function. We find that this function is broken up into strips whose average width on the critical line does not appear to vary with height. ... More

Nonabelian Algebraic TopologyJul 15 2004Jul 27 2004This talk gave a sketch of the contents and background to a book with the title `Nonabelian algebraic topology' being written under support of a Leverhulme Emeritus Fellowship (2002-2004) by the speaker and Rafael Sivera (Valencia). The aim is to give ... More

Towards non commutative algebraic topologyMay 12 2003This is a slightly edited version of the transparencies for a seminar at UCL, May 7, 2003. It is intended to give a quick view of background, ideas, and some calculations, in the applicatioon of some non commutative methods to algebraic topology.

A note on percolation in cocycle measuresAug 09 2006We describe infinite clusters which arise in nearest-neighbour percolation for so-called cocycle measures on the square lattice. These measures arise naturally in the study of random transformations. We show that infinite clusters have a very specific ... More

Spin goups of super metrics and a Theorem of RogersFeb 15 2016We derive the canonical forms of super Riemannian metrics and the local isometry groups of such metrics. For certain super metrics we also compute the simply connected covering groups of the local isometry groups and interpret these as local spin groups ... More

A new higher homotopy groupoid: the fundamental globular omega-groupoid of a filtered spaceFeb 22 2007We use the n-globe with its skeletal filtration to define the fundamental globular omega--groupoid of a filtered space; the proofs use an analogous fundamental cubical omega--groupoid due to the author and Philip Higgins. This method also relates the ... More

J. L. Doob: Foundations of stochastic processes and probabilistic potential theorySep 23 2009During the three decades from 1930 to 1960 J. L. Doob was, with the possible exception of Kolmogorov, the man most responsible for the transformation of the study of probability to a mathematical discipline. His accomplishments were recognized by both ... More

Geometry of Thin FilmsNov 23 2015Jan 12 2016We study ray optics in the context of double mirror systems, in the limit as the two mirrors approach one another (thin films). This leads to a novel set of differential equations on a mirror surface which have interesting structure as seen from the perspective ... More

Double groupoids, matched pairs and then matched triplesApr 08 2011In this note we show that the known relation between double groupoids and matched pairs of groups may be extended, or seems to extend, to the triple case. The references give some other occurrences of double groupoids.

Knots, Links, and 4-ManifoldsDec 18 1996Jan 10 1997In this paper we investigate the relationship between isotopy classes of knots and links in S^3 and the diffeomorphism types of homeomorphic smooth 4-manifolds. As a corollary of this initial investigation, we begin to uncover the surprisingly rich structure ... More

Nondiffeomorphic symplectic 4-manifolds with the same Seiberg-Witten invariantsNov 04 1998Nov 17 1999The goal of this paper is to demonstrate that, at least for nonsimply connected 4-manifolds, the Seiberg-Witten invariant alone does not determine diffeomorphism type within the same homeomorphism type.

Invariants for Lagrangian toriApr 25 2003Jul 09 2004We define an simple invariant of an embedded nullhomologous Lagrangian torus and use this invariant to show that many symplectic 4-manifolds have infinitely many pairwise symplectically inequivalent nullhomologous Lagrangian tori. We further show that ... More

Pinwheels and nullhomologous surgery on 4-manifolds with b^+ = 1Apr 18 2010Apr 13 2011We present a method for finding embedded nullhomologous tori in standard 4-manifolds which can be utilized to change their smooth structure. As an application, we show how to obtain infinite families of simply connected smooth 4-manifolds with b^+ = 1 ... More

Six Lectures on Four 4-ManifoldsOct 23 2006Jan 03 2007Despite spectacular advances in defining invariants for simply connected smooth and symplectic 4-dimensional manifolds and the discovery of effective surgical techniques, we still have been unable to classify simply connected smooth manifolds up to diffeomorphism. ... More

Surfaces in 4-ManifoldsMay 29 1997In this paper we introduce a technique, called rim surgery, which can change a smooth embedding of an orientable surface of positive genus and nonnegative self-intersection in a smooth 4-manifold while leaving the topological embedding unchanged.

Surfaces in 4-manifolds: AddendumNov 29 2005In this note we fill a gap in the proof of the main theorem (Theorem 1.2) of our paper 'Surfaces in 4-manifolds', Math. Res. Letters 4 (1997), 907-914.

Surgery on Nullhomologous ToriNov 18 2011Nov 28 2011By studying the example of smooth structures on CP^2#3(-CP^2) we illustrate how surgery on a single embedded nullhomologous torus can be utilized to change the symplectic structure, the Seiberg-Witten invariant, and hence the smooth structure on a 4-manifold. ... More

Constructions of Smooth 4-ManifoldsJul 27 1999We describe a collection of constructions which illustrate a panoply of ``exotic'' smooth 4-manifolds.

Evolutionary multi-stage financial scenario tree generationDec 08 2009Jan 18 2010Multi-stage financial decision optimization under uncertainty depends on a careful numerical approximation of the underlying stochastic process, which describes the future returns of the selected assets or asset categories. Various approaches towards ... More

On point processes in multitarget trackingMar 08 2016The finite-set statistics (FISST) approach to multitarget tracking was introduced in the mid-1990s. Its current extended form dates from 2001. In 2008, an "elementary" alternative to FISST was proposed, based on "finite point processes" rather than RFS's. ... More

Absorbing-state phase transitions: exact solutions of small systemsSep 24 2007I derive precise results for absorbing-state phase transitions using exact (numerically determined) quasistationary probability distributions for small systems. Analysis of the contact process on rings of 23 or fewer sites yields critical properties (control ... More

Fractal rain distributions and chaotic advectionNov 17 2003Localized rain events have been found to follow power-law distributions over several decades, suggesting parallels between precipitation and seismic activity [O. Peters et al., PRL 88, 018701 (2002)]. Similar power laws can be generated by treating raindrops ... More

Generic slow relaxation in a stochastic sandpileSep 25 2002Simulations of a stochastic fixed-energy sandpile in one and two dimensions reveal slow relaxation of the order parameter, even far from the critical point. The decay of the activity is best described by a stretched-exponential form. The persistence probability ... More

Numerical analysis of the master equationOct 26 2001Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta, become inefficient when the rates associated with various transitions differ by several orders of magnitude. We introduce an integration scheme that remains ... More

Restricted sandpile revisitedJan 18 2006I report large-scale Monte Carlo studies of a one-dimensional height-restricted stochastic sandpile using the quasistationary simulation method. Results for systems of up to 50 000 sites yield estimates for critical exponents that differ significantly ... More

Nonuniversal Critical Spreading in Two DimensionsOct 18 1995Continuous phase transitions are studied in a two dimensional nonequilibrium model with an infinite number of absorbing configurations. Spreading from a localized source is characterized by nonuniversal critical exponents, which vary continuously with ... More

Modelling and Computing Homotopy Types: IOct 24 2016Nov 01 2016The aim of this article is to explain a philosophy for applying higher dimensional Seifert-van Kampen Theorems, and how the use of groupoids and strict higher groupoids resolves some foundational anomalies in algebraic topology at the border between homology ... More

Discontinuous phase transition in a dimer lattice gasMay 27 2012I study a dimer model on the square lattice with nearest-neighbor exclusion as the only interaction. Detailed simulations using tomographic entropic sampling show that as the chemical potential is varied, there is a strongly discontinuous phase transition, ... More

Scaling Behavior in the 3D Random Field $XY$ ModelJan 05 2018May 07 2018We have performed studies of the 3D random field $XY$ model on $L \times L \times L$ simple cubic lattices with periodic boundary conditions, with a random field strength of $h_r$ = 1.875, for $L = 64$ and $L = 96$, using a parallelized Monte Carlo algorithm. ... More

The Deformation Complex For DG Hopf AlgebrasJun 29 2001Sep 11 2002Let H be a differential graded Hopf algebra over a field k. This paper gives an explicit construction of a triple cochain complex that defines the Hochschild-Cartier cohomology of H. A certain truncation of this complex is the appropriate setting for ... More

Local behaviour of first passage probabilitiesJun 28 2010Suppose that S is an asymptotically stable random walk with norming sequence c_{n} and that T_{x} is the time that S first enters (x,\inf), where x\ge 0. The asymptotic behaviour of P(T_0=n) has been described in a recent paper of Vatutin and Wachtel, ... More

Stochastic energetics of a Brownian motor and refrigerator driven by non-uniform temperatureJul 05 2009Jun 02 2014The energetics of a Brownian heat engine and heat pump driven by position dependent temperature, known as the B\"uttiker-Landauer heat engine and heat pump, is investigated by numerical simulations of the inertial Langevin equation. We identify parameter ... More

N-Site approximations and CAM analysis for a stochastic sandpileApr 29 2002I develop n-site cluster approximations for a stochastic sandpile in one dimension. A height restriction is imposed to limit the number of states: each site can harbor at most two particles (height z_i \leq 2). (This yields a considerable simplification ... More

Numerical Study of a Field Theory for Directed PercolationJul 12 1994A numerical method is devised for study of stochastic partial differential equations describing directed percolation, the contact process, and other models with a continuous transition to an absorbing state. Owing to the heightened sensitivity to fluctuationsattending ... More

On point processes in multitarget trackingMar 08 2016Mar 02 2018The finite-set statistics (FISST) approach to multitarget tracking was introduced in the mid-1990s. Its current extended form dates from 2001. In 2008, an "elementary" alternative to FISST was proposed, based on "finite point processes" rather than RFS's. ... More

An Evolutionary Optimization Approach to Risk Parity Portfolio SelectionNov 27 2014Jan 19 2015In this paper we present an evolutionary optimization approach to solve the risk parity portfolio selection problem. While there exist convex optimization approaches to solve this problem when long-only portfolios are considered, the optimization problem ... More

Beyond the Imry-Ma Length: Scaling Behavior in the 3D Random Field $XY$ ModelDec 13 2018We have performed studies of the 3D random field $XY$ model on $L \times L \times L$ simple cubic lattices with periodic boundary conditions, with a random field strength of $h_r$ = 1.875, for $L =$ 64, 96 and 128, using a parallelized Monte Carlo algorithm. ... More

Continuously variable spreading exponents in the absorbing Nagel-Schreckenberg modelJun 19 2018I study the critical behavior of a traffic model with an absorbing state. The model is a variant of the Nagel-Schreckenberg (NS) model, in which drivers do not decelerate if their speed is smaller than their headway, the number of empty sites between ... More

Percentile rank scores are congruous indicators of relative performance, or aren't they?Aug 09 2011Percentile ranks and the I3 indicator were introduced by Bornmann, Leydesdorff, Mutz and Opthof. These two notions are based on the concept of percentiles (or quantiles) for discrete data. As several definitions for these notions exist we propose one ... More

Groupoids, the Phragmen-Brouwer Property and the Jordan Curve TheoremJul 09 2006We publicise a proof of the Jordan Curve Theorem which relates it to the Phragmen-Brouwer Property, and whose proof uses the van Kampen theorem for the fundamental groupoid on a set of base points.

Embeddability of Arrangements of Pseudocircles into the SphereAug 17 2005An arrangement of pseudocircles is a finite set of oriented closed Jordan curves each two of which cross each other in exactly two points. To describe the combinatorial structure of arrangements on closed orientable surfaces, in (Linhart, Ortner 2004) ... More

Structure Relations in Special A_\infty-bialgebrasJun 22 2005Jun 22 2005We compute the structure relations in special A_\infty-bialgebras whose operations are limited to those defining the underlying A_\infty-(co)algebra substructure. Such bialgebras appear as the homology of certain loop spaces. Whereas structure relations ... More

Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional local-to-global problemsDec 19 2002Oct 10 2008We outline the main features of the definitions and applications of crossed complexes and cubical $\omega$-groupoids with connections. These give forms of higher homotopy groupoids, and new views of basic algebraic topology and the cohomology of groups, ... More

Surgery on nullhomologous tori and simply connected 4-manifolds with b^+=1Jan 01 2007For 5 <= k <= 8 we show that the infinite family of exotic smooth structures on CP^2# k(-CP^2) can be achieved by 1/n - surgeries on a single embedded nullhomologous torus in a manifold R_k which is homeomorphic to CP^2# k(-CP^2).

Nonsymplectic 4-Manifolds with One Basic ClassJul 27 1999It is the purpose of this paper to construct families of examples of nonsymplectic 4-manifolds which (up to sign) have just one Seiberg-Witten basic class.

Families of Simply Connected 4-Manifolds with the Same Seiberg-Witten InvariantsOct 14 2002This article presents the constructions of new infinite families of smooth 4-manifolds with the property that any two manifolds in the same family are homeomorphic and, from their construction, seem to be quite different, but cannot be distinguished by ... More

Rational surfaces and symplectic 4-manifolds with one basic classFeb 19 2002May 26 2002We present constructions of simply connected symplectic 4-manifolds which have (up to sign) one basic class and which fill up the geographical region between the half-Noether and Noether lines.

Exotic group actions on simply connected smooth 4-manifoldsFeb 05 2009Sep 17 2009We produce infinite families of exotic actions of finite cyclic groups on simply connected smooth 4-manifolds with nontrivial Seiberg-Witten invariants.

Bounds on the Number of Longest Common SubsequencesJan 28 2003Aug 06 2003This paper performs the analysis necessary to bound the running time of known, efficient algorithms for generating all longest common subsequences. That is, we bound the running time as a function of input size for algorithms with time essentially proportional ... More

Quantum spin pumping with adiabatically modulated magnetic barrier'sMar 29 2003Dec 09 2003A quantum pump device involving magnetic barriers produced by the deposition of ferro magnetic stripes on hetero-structure's is investigated. The device for dc- transport does not provide spin-polarized currents, but in the adiabatic regime, when one ... More

Approximation using scattered shifts of a multivariate functionFeb 18 2008The approximation of a general $d$-variate function $f$ by the shifts $\phi(\cdot-\xi)$, $\xi\in\Xi\subset \Rd$, of a fixed function $\phi$ occurs in many applications such as data fitting, neural networks, and learning theory. When $\Xi=h\Z^d$ is a dilate ... More

Distribution of dust and stars in the GalaxyAug 20 2000Using far-infrared 240 micron and near-infrared K band data from the COBE/DIRBE instrument, we model the Galactic stellar and dust distribution. Making the assumption that the Galaxy is transparent in the 240 micron band, the dust emission is modeled ... More