Results for "Simon Watkins"

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Bounding the distinguishing number of infinite graphsFeb 18 2013A group of permutations G of a set V is k-distinguishable if there exists a partition of V into k parts such that only the identity permutation in G fixes setwise all of the cells of the partition. The least cardinal number k such that (G,V) is k-distinguishable ... More
Relative Entropy Minimization over Hilbert Spaces via Robbins-MonroJun 30 2015Feb 26 2019One way of getting insight into non-Gaussian measures, posed on infinite dimensional Hilbert spaces, is to first obtain best fit Gaussian approximations, which are more amenable to numerical approximation. These Gaussians can then be used to accelerate ... More
Distinguishability of infinite groups and graphsJun 23 2011The {\em distinguishing number} of a group $G$ acting faithfully on a set $V$ is the least number of colors needed to color the elements of $V$ so that no non-identity element of the group preserves the coloring. The {\em distinguishing number} of a graph ... More
Growth of Face-Homogeneous TessellationsJul 11 2017A tessellation of the plane is face-homogeneous if for some integer $k\geq3$ there exists a cyclic sequence $\sigma=[p_0,p_1,\ldots,p_{k-1}]$ of integers $\geq3$ such that, for every face $f$ of the tessellation, the valences of the vertices incident ... More
Non-local Corrections to Collisional Transport in Magnetised PlasmasApr 10 2019Apr 26 2019In modern inertial fusion experiments there is a complex interplay between non-locality and magnetisation that can greatly influence transport. In this work we use a matrix recursion method to include higher-order corrections beyond the diffusion approximation ... More
Hierarchical Text Generation using an OutlineOct 20 2018Many challenges in natural language processing require generating text, including language translation, dialogue generation, and speech recognition. For all of these problems, text generation becomes more difficult as the text becomes longer. Current ... More
Bees with attitude: the effect of gusts on flight dynamicsFeb 10 2018Flight is a complicated task at small scales in part due to the ubiquitous unsteady air which contains it. Flying organisms deal with these difficulties using active and passive control mechanisms to steer their body motion. Body attitudes of flapping ... More
High-Resolution, Three-Dimensional Reconstruction of the Outflow Tract Demonstrates Segmental Differences in Cleared EyesOct 28 2017Purpose: The rate of conventional aqueous humor outflow is the highest nasally. We hypothesized that this is reflected in regionally different outflow structures and analyzed the entire limbus by high-resolution, full-thickness ribbon-scanning confocal ... More
Infinite Motion and 2-Distinguishability of Graphs and GroupsApr 23 2013May 08 2013A group A acting faithfully on a set X is 2-distinguishable if there is a 2-coloring of X that is not preserved by any nonidentity element of A, equivalently, if there is a proper subset of X with trivial setwise stabilizer. The motion of an element a ... More
Scaling collapse and structure functions: Identifying self-affinity in finite length time seriesApr 04 2005Jul 11 2005Empirical determination of the scaling properties and exponents of time series presents a formidable challenge in testing, and developing, a theoretical understanding of turbulence and other out-of-equilibrium phenomena. We discuss the special case of ... More
Explicit lower bounds on the modular degree of an elliptic curveAug 10 2004We derive an explicit zero-free region for symmetric square L-functions of elliptic curves, and use this to derive an explicit lower bound for the modular degree of rational elliptic curves. The techniques are similar to those used in the classical derivation ... More
Rhythm and Randomness in Human ContactSep 21 2010There is substantial interest in the effect of human mobility patterns on opportunistic communications. Inspired by recent work revisiting some of the early evidence for a L\'evy flight foraging strategy in animals, we analyse datasets on human contact ... More
The application of computational mechanics to the analysis of geomagnetic dataOct 11 2001We discuss how the ideal formalism of Computational Mechanics can be adapted to apply to a non-infinite series of corrupted and correlated data, that is typical of most observed natural time series. Specifically, a simple filter that removes the corruption ... More
The Higher Rank Rigidity Theorem for Manifolds With No Focal PointsNov 23 2011Jun 04 2012We say that a Riemannian manifold M has rank at least k if every geodesic in M admits at least k parallel Jacobi fields. The Rank Rigidity Theorem of Ballmann and Burns-Spatzier, later generalized by Eberlein-Heber, states that a complete, irreducible, ... More
The RMS Peculiar Velocity of ClustersOct 15 1997We study the rms peculiar velocity of clusters as a convenient statistic to put constraints on cosmological models. This statistic is easy to compute theoretically given a model for the power spectrum; we show that with some assumptions it can be directly ... More
Some remarks on Heegner point computationsJun 16 2005Apr 05 2006We explain how to find a rational point on a rational elliptic curve of rank 1 using Heegner points. We give some examples, and list new algorithms that are due to Cremona and Delaunay. These are notes from a short course given at the Institut Henri Poincare ... More
What can we infer about the underlying physics from burst distributions observed in an RMHD simulation ?Nov 20 2000Jun 12 2001We determine that the sizes of bursts in mean-square current density in a reduced magnetohydrodynamic (RMHD)simulation follow power-law probability density function (PDF). The PDFs for burst durations and waiting time between bursts are clearly not exponential ... More
Layer dependent role of collagen recruitment during loading of the rat bladder wallMay 09 2017In this work, we reevaluated long standing conjectures as to the source of the exceptionally large compliance of the bladder wall. Whereas, these conjectures were based on indirect measures of loading mechanisms, in this work we take advantage of advances ... More
Learn to segment single cells with deep distance estimator and deep cell detectorMar 28 2018Single cell segmentation is critical and challenging in live cell imaging data analysis. Traditional image processing methods and tools require time-consuming and labor-intensive efforts of manually fine-tuning parameters. Slight variations of image setting ... More
The intrinsic torsion of SU(3) and G_2 structuresFeb 26 2002We analyse the relationship between the components of the intrinsic torsion of an SU(3) structure on a 6-manifold and a G_2 structure on a 7-manifold. Various examples illustrate the type of SU(3) structure that can arise as a reduction of a metric with ... More
On Estimating Many Means, Selection Bias, and the BootstrapNov 15 2013With recent advances in high throughput technology, researchers often find themselves running a large number of hypothesis tests (thousands+) and esti- mating a large number of effect-sizes. Generally there is particular interest in those effects estimated ... More
Longitudinal spin-relaxation of donor-bound electrons in direct bandgap semiconductorsMay 19 2016We measure the donor-bound electron longitudinal spin-relaxation time ($T_1$) as a function of magnetic field ($B$) in three high-purity direct-bandgap semiconductors: GaAs, InP, and CdTe, observing a maximum $T_1$ of $1.4~\text{ms}$, $0.4~\text{ms}$ ... More
Bound States Can Stabilize Electroweak StringsNov 20 1992Nov 23 1992We show that the electroweak $Z-$string can be stabilized by the presence of bound states of a complex scalar field. We argue that fermions coupled to the scalar field of the string can also make the string stable and discuss the physical case where the ... More
Modular Parametrizations of Neumann-Setzer Elliptic CurvesApr 19 2004Suppose $p$ is a prime of the form $u^2+64$ for some integer $u$, which we take to be 3 mod 4. Then there are two Neumann--Setzer elliptic curves $E_0$ and $E_1$ of prime conductor $p$, and both have Mordell--Weil group $\Z/2\Z$. There is a surjective ... More
Relative Entropy Minimization over Hilbert Spaces via Robbins-MonroJun 30 2015Jun 27 2017One way of getting insight into non-Gaussian measures, posed on infinite dimensional Hilbert spaces, is to first obtain best fit Gaussian approximations, which are more amenable to numerical approximation. These Gaussians can then be used to accelerate ... More
Mandelbrot's 1/f fractional renewal models of 1963-67: The non-ergodic missing link between change points and long range dependenceFeb 29 2016The problem of 1/f noise has been with us for about a century. Because it is so often framed in Fourier spectral language, the most famous solutions have tended to be the stationary long range dependent (LRD) models such as Mandelbrot's fractional Gaussian ... More
Galactic substructure traced by RR Lyraes in SDSS Stripe 82Nov 18 2011Using a sample of 407 RR Lyrae stars extracted from SDSS Stripe 82, we study the degree of substructure in the Galactic halo. We identify overdensities associated with the known substructures of the Hercules-Aquila Cloud and the Sagittarius Stream, and ... More
Relative Entropy Minimization over Hilbert Spaces via Robbins-MonroJun 30 2015Jul 07 2016One way of getting insight into non-Gaussian measures, posed on infinite dimensional Hilbert spaces, is to first obtain best fit Gaussian approximations, which are more amenable to numerical approximation. These Gaussians can then be used to accelerate ... More
Studies on optimizing potential energy functions for maximal intrinsic hyperpolarizabilityApr 13 2007We use numerical optimization to study the properties of (1) the class of one-dimensional potential energy functions and (2) systems of point charges in two-dimensions that yield the largest hyperpolarizabilities, which we find to be within 30% of the ... More
Vortices In Circumstellar DisksJan 12 1995We discuss the physics of vortices in the circumstellar disks associated with young stellar objects. We elucidate the basic physical properties of these localized storm systems. In particular, we consider point vortices, linear vortices, the effects of ... More
Symmetric powers of elliptic curve L-functionsApr 05 2006Apr 17 2006The conjectures of Deligne, Be\u\i linson, and Bloch-Kato assert that there should be relations between the arithmetic of algebro-geometric objects and the special values of their $L$-functions. We make a numerical study for symmetric power $L$-functions ... More
An evolutionary model that satisfies detailed balanceFeb 27 2019We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is removed according ... More
Avalanching and Self Organised Criticality, a paradigm for geomagnetic activity?Jul 07 2000Oct 20 2000The characterization of global energy storage and release in the coupled solar wind-magnetosphere system remains one of the fundamental problems of space physics.Recently, it has been realised that a new paradigm in physics, that of Self Organised Criticality ... More
Scaling in long term data sets of geomagnetic indices and solar wind epsilon as seen by WIND spacecraftOct 14 2003We study scaling in fluctuations of the geomagnetic indices (AE, AU, and AL) that provide a measure of magnetospheric activity and of the epsilon parameter which is a measure of the solar wind driver. Generalized structure function (GSF) analysis shows ... More
Book to the Future - a manifesto for book liberationJul 04 2015The Book Liberation Manifesto is an exploration of publishing outside of current corporate constraints and beyond the confines of book piracy. We believe that knowledge should be in free circulation to benefit humankind, which means an equitable and vibrant ... More
Particle Dark EnergyNov 11 2004Feb 23 2006We explore the physics of a gas of particles interacting with a condensate that spontaneously breaks Lorentz invariance. The equation of state of this gas varies from 1/3 to less than -1 and can lead to the observed cosmic acceleration. The particles ... More
Quantum entanglement analysis based on abstract interpretationJan 28 2008Entanglement is a non local property of quantum states which has no classical counterpart and plays a decisive role in quantum information theory. Several protocols, like the teleportation, are based on quantum entangled states. Moreover, any quantum ... More
The Evolution of Ellipticals, Spirals and Irregulars: Overcoming Selection BiasDec 07 2000The Hubble Deep Fields represent our best opportunity for probing galaxy evolution over a substantive look-back time. However as with any dataset the HDFs are prone to selection biases. These biases are extremely severe beyond z \~1.25 such that a meaningful ... More
Prospects for Precision Higgs Physics at Linear CollidersNov 30 2012A linear e+e- collider provides excellent possibilities for precision measurements of the properties of the Higgs boson. At energies close to the Z-Higgs threshold, the Higgs boson can be studied in recoil against a Z boson, to obtain not only a precision ... More
The sharp form of the strong Szego theoremFeb 06 2004Let $f$ be a function on the unit circle and $D_n(f)$ be the determinant of the $(n+1)\times (n+1)$ matrix with elements $\{c_{j-i}\}_{0\leq i,j\leq n}$ where $c_m =\hat f_m\equiv \int e^{-im\theta} f(\theta) \f{d\theta}{2\pi}$. The sharp form of the ... More
Sturm Oscillation and Comparison TheoremsNov 04 2003This is a celebratory and pedagogical discussion of Sturm oscillation theory. Included is the discussion of the difference equation case via determinants and a renormalized oscillation theorem of Gesztesy, Teschl, and the author.
Simulating Dense MatterMar 19 2007I review the Sign Problem hindering lattice QCD simulations of dense baryonic matter, focussing where possible on its physical relevance. The possibility of avoiding the Sign Problem via a duality transformation is also briefly considered. Finally, I ... More
Lattice MatterSep 28 2001I review recent developments in the study of strongly interacting field theories with non-zero chemical potential mu. In particular I focus on (a) the determination of the QCD critical endpoint in the (mu,T) plane; (b) superfluid condensates in Two Color ... More
The Phase Diagram of QCDMay 08 2001I use simple thermodynamic reasoning to argue that at temperatures of order a trillion kelvin, QCD, the theory which describes strongly interacting particles such as protons and neutrons under normal conditions, undergoes a phase transition to a plasma ... More
Cellular Automata on Group Sets and the Uniform Curtis-Hedlund-Lyndon TheoremMar 21 2016Jun 13 2016We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic ... More
A First Look at the Impact of NNNLO Theory Uncertainties on Top Mass Measurements at the ILCMar 15 2016Aug 22 2016A scan of the top production threshold at a future electron-positron collider provides the possibility for a precise measurement of the top quark mass in theoretically well-defined mass schemes. With statistical uncertainties of 20 MeV or below, systematics ... More
Static perfect fluids with Pant-Sah equations of stateJan 17 2008Mar 31 2008We analyze the 3-parameter family of exact, regular, static, spherically symmetric perfect fluid solutions of Einstein's equations (corresponding to a 2-parameter family of equations of state) due to Pant and Sah and "rediscovered" by Rosquist and the ... More
Criteria for (in)finite extent of static perfect fluidsApr 09 2002In Newton's and in Einstein's theory we give criteria on the equation of state of a barotropic perfect fluid which guarantee that the corresponding one-parameter family of static, spherically symmetric solutions has finite extent. These criteria are closely ... More
Conformal positive mass theoremsMar 29 2000We show the following two extensions of the standard positive mass theorem (one for either sign): Let (N,g) and (N,g') be asymptotically flat Riemannian 3-manifolds with compact interior and finite mass, such that g and g' are twice Hoelder differentiable ... More
ExSample -- A Library for Sampling Sudakov-Type DistributionsAug 31 2011Mar 19 2012Sudakov-type distributions are at the heart of generating radiation in parton showers as well as contemporary NLO matching algorithms along the lines of the POWHEG algorithm. In this paper, the C++ library ExSample is introduced, which implements adaptive ... More
Ricci Flow of regions with curvature bounded below in dimension threeJul 04 2014We consider smooth complete solutions to Ricci flow with bounded curvature on manifolds without boundary in dimension three. Assuming an open ball at time zero of radius one has curvature bounded from below by -1, then we prove estimates which show that ... More
Dynamics on supersingular K3 surfaces and automorphisms of Salem degree 22Jul 08 2015In this note we exhibit explicit automorphisms of maximal Salem degree 22 on the supersingular K3 surface of Artin invariant one for all primes p congruent 3 mod 4 in a systematic way. Automorphisms of Salem degree 22 do not lift to any characteristic ... More
Some remarks about equations defining coincident root lociAug 23 2011Consider the projective variety $X_\lambda$ of binary forms of degree $d$ whose linear factors are distributed according to the partition $\lambda$ of $d$. We determine minimal sets of local generators of the fiber product of $X_\lambda$ with its normalization, ... More
Refining Reasoning in Qualitative Probabilistic NetworksFeb 20 2013In recent years there has been a spate of papers describing systems for probabilisitic reasoning which do not use numerical probabilities. In some cases the simple set of values used by these systems make it impossible to predict how a probability will ... More
Regularized Newton methods for simultaneous Radon inversion and phase retrieval in phase contrast tomographyFeb 17 2015Promoted by the advent of coherent synchrotron light sources, phase contrast tomography allows to resolve three-dimensional variations of an unknown sample's complex refractive index from scattering intensities recorded at different incident angles of ... More
On the construction of solutions to the Yang-Mills equations in higher dimensionsFeb 10 2003Aug 13 2003We describe a glueing construction for the Yang-Mills equations in dimension $n > 4$. Our method is based on a construction of approximate solutions, and a detailed analysis of the linearized operator near an approximate solution.
On solutions to the Ginzburg-Landau equations in higher dimensionsFeb 06 2003Aug 13 2003We establish a glueing theorem for the Ginzburg-Landau equations in dimension $n > 2$. To this end, we consider a nondegenerate minimal submanifold of codimension 2, and construct a one-parameter family of solutions to the Ginzburg-Landau equations such ... More
Measure Equipartitions via Finite Fourier AnalysisMar 27 2014Jun 20 2015Applications of harmonic analysis on finite groups are introduced to measure partition problems, with equipartitions obtained as the vanishing of prescribed Fourier transforms. For elementary abelian groups $Z_p^k$, $p$ an odd prime, equipartitions are ... More
Equivariant Equipartitions: Ham Sandwich Theorems for Finite Subgroups of SpheresSep 04 2011Jun 19 2012Equivariant "Ham Sandwich" Theorems are obtained for the finite subgroups G of the unit spheres S(F) in the classical algebras F = R, C, and H. Given any n F-valued mass distributions on F^n, it is shown that there exists a G-equivariant decomposition ... More
Mass Partitions via Equivariant Sections of Stiefel BundlesNov 08 2010Aug 01 2017We consider a geometric combinatorial problem naturally associated to the geometric topology of certain spherical space forms. Given a collection of $m$ mass distributions on $\mathbb{R}^n$, the existence of $k$ affinely independent regular $q$-fans, ... More
Coupled Critical Models: Applications to Ising-Potts ModelsMay 28 1997We discuss the critical behaviour of 2D Ising and q-states Potts models coupled by their energy density. We found new tricritical points. The procedure employed is the renormalisation approach of the perturbations series around conformal field theories ... More
Rosenthal compacta and NIP formulasJul 22 2014Aug 07 2015We apply the work of Bourgain, Fremlin and Talagrand on compact subsets of the first Baire class to show new results about phi-types for phi NIP. In particular, we show that if M is a countable model, then an M-invariant phi-type is Borel definable. Also ... More
Coupled Minimal Models with and without DisorderOct 02 1997We analyse in this article the critical behavior of $M$ $q_1$-state Potts models coupled to $N$ $q_2$-state Potts models ($q_1,q_2\in [2..4]$) with and without disorder. The technics we use are based on perturbed conformal theories. Calculations have ... More
Zero repulsion in families of elliptic curve L-functions and an observation of S. J. MillerSep 01 2011Oct 20 2011We provide a theoretical explanation for an observation of S. J. Miller that if L(s,E) is an elliptic curve L-function for which L(1/2, E) is nonzero, then the lowest lying zero of L(s,E) exhibits a repulsion from the critical point which is not explained ... More
Numerical Root Finding via Cox RingsMar 28 2019We present a new eigenvalue method for solving a system of Laurent polynomial equations defining a zero-dimensional reduced subscheme of a toric compactification $X$ of $(\mathbb{C} \setminus \{0\})^n$. We homogenize the input equations to obtain a homogeneous ... More
The almost Daugavet property and translation-invariant subspacesJul 13 2013Let $G$ be a metrizable, compact abelian group and let $\Lambda$ be a subset of its dual group $\hat G$. We show that $C_\Lambda(G)$ has the almost Daugavet property if and only if $\Lambda$ is an infinite set, and that $L^1_\Lambda(G)$ has the almost ... More
Subspaces of almost Daugavet spacesJul 17 2010We study the almost Daugavet property, a generalization of the Daugavet property. It is analysed what kind of subspaces and sums of Banach spaces with the almost Daugavet property have this property as well. The main result of the paper is: if $Z$ is ... More
Approximations of generating functions and a few conjecturesNov 25 2009This is a collection of 1031 formulas that were generated by a computer program in 1992. The set is the database of integer sequences as of 1992 which contained 4568 sequences. These sequences were later published in the Encyclopedia of Integer Sequences ... More
Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domainsNov 17 2016Aug 01 2018For $\Omega \subset \mathbb{R}^n$, a convex and bounded domain, we study the spectrum of $-\Delta_\Omega$ the Dirichlet Laplacian on $\Omega$. For $\Lambda\geq0$ and $\gamma \geq 0$ let $\Omega_{\Lambda, \gamma}(\mathcal{A})$ denote any extremal set of ... More
Technical Report: Modelling Multiple Cell Types with Partial Differential EquationsSep 28 2015Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly. However, in case ... More
Extending and Implementing the Stable Model SemanticsMay 08 2000An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of efficient implementation ... More
A metric theorem for restricted Diophantine approximation in positive characteristicJan 28 2004Oct 10 2005We calculate the measure and Hausdorff dimension of sets of matrices over fields of formal power series with good approximation properties for a restricted set of denominators.
Hyperbolicity and Cubulability Are Preserved Under Elementary EquivalenceJan 29 2018The following properties are preserved under elementary equivalence, among finitely generated groups: being hyperbolic (possibly with torsion), being hyperbolic and cubulable, and being a subgroup of a hyperbolic group. In other words, if a finitely generated ... More
Minimum settling time control design through direct search optimizationSep 27 2011Dec 06 2011The aim of this work is to design controllers through explicit minimization of the settling time of a closed-loop response, by using a class of methods adequate for this objective. To the best of our knowledge, all the methods available in the literature ... More
Scanning Strategies at the Top Threshold at ILCFeb 19 2019A scan of the top quark pair production threshold at a future electron-positron collider provides the possibility for high-precision measurements of the top quark mass, and, when using two dimensional fits of the measured cross sections, also of other ... More
A detailed proof of Bourgain's Return Times TheoremJan 14 2019In this diploma thesis (written in German) we present a detailed proof of Bourgain's Return Times Theorem due to Bourgain, Furstenberg, Katznelson and Ornstein following their paper as well as the book by Assani. Moreover, we generalize the result to ... More
A Mayer-Vietoris Spectral Sequence for C*-Algebras and Coarse GeometryDec 29 2018Let $A$ be a C*-algebra that is the norm closure $A = \overline{\sum_{\beta \in \alpha} I_\beta}$ of an arbitrary sum of C*-ideals $I_\beta \subseteq A$. We construct a homological spectral sequence that takes as input the K-theory of $\bigcap_{j \in ... More
On the Critical Flavor Number in the 2+1$d$ Thirring ModelNov 12 2018Jan 30 2019The Thirring model in 2+1 spacetime dimensions, in which $N$ flavors of relativistic fermion interact via a contact interaction between conserved fermion currents, is studied using lattice field theory simulations employing domain wall fermions, which ... More
A contact camel theoremAug 16 2018We provide a contact analogue of the symplectic camel theorem that holds in $\mathbb{R}^{2n}\times S^1$, and indeed generalize the symplectic camel. Our proof is based on the generating function techniques introduced by Viterbo, extended to the contact ... More
FPGA implementation of a DCDS processorJul 13 2018An experimental digital correlated double sampler (DCDS) video processor has been implemented in a Xilinx Artix FPGA. It uses an Opal Kelly XEM7010-A50 module that comes with an integrated USB2 interface for easy interfac-ing to a data acquisition PC. ... More
The localic Istropy group of a toposJun 15 2017It has been shown by J.Funk, P.Hofstra and B.Steinberg that any Grothendieck topos T is endowed with a canonical group object, called its isotropy group, which acts functorially on every object of T. We show that this group is in fact the group of points ... More
A Note on the Expected Number of Interviews When Talent is Uniformly DistributedOct 26 2018Optimal stopping problems give rise to random distributions describing how many applicants the decision-maker will observe or interview before choosing one, a quantity sometimes referred to as the optimal stopping time. Despite the fact that is has important ... More
Microlocal analysis of generalized pullbacks of Colombeau functionsJan 17 2007Feb 02 2007In distribution theory the pullback of a general distribution by a $C^{\infty}$-function is well-defined whenever the normal bundle of the $C^{\infty}$-function does not intersect the wavefront set of the distribution. However, the Colombeau theory of ... More
Splitting the Curvature of the Determinant Line BundleDec 21 1998It is shown that the determinant line bundle associated to a family of Dirac operators over a closed partitioned manifold has a canonical Hermitian metric with compatible connection whose curvature satisfies an additivity formula with contributions from ... More
Holomorphic horospherical duality "sphere-cone"Jan 02 2005We describe a construction of complex geometrical analysis which corresponds to the classical theory of spherical harmonics.
Approximation properties of $β$-expansions IIJun 25 2015Given $\beta\in(1,2)$ and $x\in[0,\frac{1}{\beta-1}]$, a sequence $(\epsilon_{i})_{i=1}^{\infty}\in\{0,1\}^{\mathbb{N}}$ is called a $\beta$-expansion for $x$ if $$x=\sum_{i=1}^{\infty}\frac{\epsilon_{i}}{\beta^{i}}.$$ In a recent article the author studied ... More
Splitting the K-Terminal ReliabilityApr 18 2011Let G=(V,E) be a graph and K a set of terminal vertices of G. Assume that the edges of G are failing independently with given probabilities. The K-terminal reliability R(G,K) is the probability that all vertices in K are mutually connected. In this article ... More
Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domains in the Heisenberg groupMar 04 2016We prove geometric $L^p$ versions of Hardy's inequality for the sub-elliptic Laplacian on convex domains $\Omega$ in the Heisenberg group $\mathbb{H}^n$, where convex is meant in the Euclidean sense. When $p=2$ and $\Omega$ is the half-space given by ... More
Hitting densities for spectrally positive stable processesFeb 08 2010A multiplicative identity in law connecting the hitting times of completely asymmetric $\alpha-$stable L\'evy processes in duality is established. In the spectrally positive case, this identity allows with an elementary argument to compute fractional ... More
Quantum Walk Sampling by Growing Seed SetsApr 25 2019This work describes a new algorithm for creating a superposition over the edge set of a graph, encoding a quantum sample of the random walk stationary distribution. The algorithm requires a number of quantum walk steps scaling as $\widetilde{O}(m^{1/3} ... More
A uniqueness result for propagation-based phase contrast imaging from a single measurementSep 16 2014Apr 27 2015Phase contrast imaging seeks to reconstruct the complex refractive index of an unknown sample from scattering intensities, measured for example under illumination with coherent X-rays. By incorporating refraction, this method yields improved contrast ... More
Asymptotically tight bounds on subset sumsMay 31 2008For a subset A of a finite abelian group G we define Sigma(A)={sum_{a\in B}a:B\subset A}. In the case that Sigma(A) has trivial stabiliser, one may deduce that the size of Sigma(A) is at least quadratic in |A|; the bound |Sigma(A)|>= |A|^{2}/64 has recently ... More
Weak model categories in classical and constructive mathematicsJul 07 2018We introduce a notion of "weak model category". It is a weakening of the classical notion of Quillen model category, still sufficient to define a homotopy category, Quillen adjunction, Quillen equivalence and most of the usual categorical homotopy theory ... More
Strongly Asymptotically Optimal Schemes for the Strong Approximation of Non-Lipschitzian Stochastic Differential Equations with respect to the Supremum ErrorJan 18 2019Our subject of study is strong approximation of systems of stochastic differential equations (SDEs) with respect to the supremum error criterion, and we seek approximations that perform strongly asymptotically optimal. In this context, we focus on two ... More
Jost functions and Jost solutions for Jacobi matrices, III. Asymptotic series for decay and meromorphicityMar 18 2005We show that the parameters $a_n, b_n$ of a Jacobi matrix have a complete asymptotic series $ a_n^2 -1 &= \sum_{k=1}^{K(R)} p_k(n) \mu_k^{-2n} + O(R^{-2n}) b_n &= \sum_{k=1}^{K(R)} p_k(n) \mu_k^{-2n+1} + O(R^{-2n}) $ where $1 < |\mu_j| < R$ for $j\leq ... More
Endoscopy and cohomology growth on U(3)Jan 30 2013We apply the endoscopic classification of automorphic forms on U(3) to prove a case of a conjecture of Sarnak and Xue on cohomology growth.
On the Closing Lemma problem for vector fields of bounded type on the torusNov 07 2008We investigate the open Closing Lemma problem for vector fields on the 2-dimensional torus. Under the assumption of bounded type rotation number, the $C^r$ Closing Lemma is verified for smooth vector fields that are area-preserving at all saddle points. ... More
Rank one perturbations and the zeros of paraorthogonal polynomials on the unit circleJun 01 2006We prove several results about zeros of paraorthogonal polynomials using the theory of rank one perturbations of unitary operators. In particular, we obtain new details on the interlacing of zeros for successive POPUC.
Combinatorics of tropical Hurwitz cyclesJul 15 2014Jun 25 2015We study properties of the tropical double Hurwitz loci defined by Bertram, Cavalieri and Markwig. We show that all such loci are connected in codimension one. If we mark preimages of simple ramification points, then for a generic choice of such points ... More
Geodesic restrictions of arithmetic eigenfunctionsApr 03 2012Aug 17 2013Let X be an arithmetic hyperbolic surface, \psi a Hecke-Maass form, and l a geodesic segment on X. We obtain a power saving over the local bound of Burq-G\'erard-Tzvetkov for the L^2 norm of \psi restricted to l, by extending the technique of arithmetic ... More