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Diophantine approximation and the solubility of the Schroedinger equationOct 22 2002Apr 29 2003We characterise the set of periods for which number theoretical obstructions prevent us from finding periodic solutions of the Schroedinger equation on a two dimensional torus as well as the asymptotic occurrence of possible resonances.

Irrationality and transcendence of continued fractions with algebraic integersFeb 12 2019We extend a result of Han\v{c}l, Kolouch and Nair on the irrationality and transcendence of continued fractions. We show that for a sequence $\{\alpha_n\}$ of algebraic integers of bounded degree, each attaining the maximum absolute value among their ... More

Metric Diophantine approximation with respect to planar distance functionsJan 27 2004We outline a proof of an analogue of Khintchine's Theorem in R^2, where the ordinary height is replaced by a distance function satisfying an irrationality condition as well as certain decay and symmetry conditions.

Badly approximable systems of linear forms over a field of formal seriesJun 26 2003Aug 05 2004We prove that the Hausdorff dimension of the set of badly approximable systems of m linear forms in n variables over the field of Laurent series with coefficients from a finite field is maximal. This is a analogue of Schmidt's multi-dimensional generalisation ... 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.

Metrical theorems on systems of small inhomogeneous linear formsJun 16 2014In this paper we establish complete Khintchine--Groshev and Schmidt type theorems for inhomogeneous small linear forms in the so-called doubly metric case, in which the inhomogeneous parameter is not fixed.

Metrical results on systems of small linear formsDec 20 2011In this paper the metric theory of Diophantine approximation associated with the small linear forms is investigated. Khintchine-Groshev theorems are established along with Hausdorff measure generalization without the monotonic assumption on the approximating ... More

Metrical irrationality results related to values of the Riemann $ζ$-functionFeb 12 2018We introduce a one-parameter family of series associated to the Riemann $\zeta$-function and prove that the values of the elements of this family at integers are linearly independent over the rationals for almost all values of the parameter, where almost ... More

Diophantine exponents for mildly restricted approximationSep 06 2007We are studying the Diophantine exponent \mu_{n,l}$ defined for integers 1 \leq l < n and a vector \alpha \in \mathbb{R}^n by letting \mu_{n,l} = \sup{\mu \geq 0: 0 < ||x \cdot \alpha|| < H(x)^{-\mu} for infinitely many x \in C_{n,l} \cap \mathbb{Z}^n}, ... More

Badly approximable systems of linear forms in absolute valueNov 25 2011In this paper we show that the set of mixed type badly approximable simultaneously small linear forms is of maximal dimension. As a consequence of this theorem we settle a conjecture of the first author.

Arithmetic properties of series of reciprocals of algebraic integersJul 12 2018Dec 18 2018We obtain results bounding the degree of the series $\sum_{n=1}^{\infty} 1/\alpha_n$, where $\{\alpha_n\}$ is a sequence of algebraic integers satisfying certain algebraic conditions and growth conditions. Our results extend results of Erd\H{o}s, Han\v{c}l ... More

Hausdorff Dimension and Diophantine ApproximationMay 28 2003Jun 12 2003We begin with a brief treatment of Hausdorff measure and Hausdorff dimension. We then explain some of the principal results in Diophantine approximation and the Hausdorff dimension of related sets, originating in the pioneering work of Vojtech Jarnik. ... More

A problem in non-linear Diophantine approximationMay 22 2015In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is also associated with a class of linear inhomogeneous partial differential equations ... More

Diophantine approximation and badly approximable setsMay 24 2004Apr 13 2005Let (X,d) be a metric space and (\Omega, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of \Omega. Loosely speaking, these consist of points in \Omega which `stay clear' ... More

Metrical musings on Littlewood and friendsApr 04 2012We prove a metrical result on a family of conjectures related to the Littlewood conjecture, namely the original Littlewood conjecture, the mixed Littlewood conjecture of de Mathan and Teuli\'e and a hybrid between a conjecture of Cassels and the Littlewood ... More

A problem in non-linear Diophantine approximationMay 22 2015Apr 19 2018In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential equations whose ... More

Metrical theorems on systems of small Affine formsJun 16 2014Oct 01 2018In this paper we discuss metric theory associated with the inhomogeneous linear forms in the so called doubly metric settings within the classical and the absolute value settings. We prove the Khintchine--Groshev and Jarn\'ik type theorems for absolute ... More

Some remarks on Mahler's classification in higher dimensionJun 20 2016We prove a number of results on the metric and non-metric theory of Diophantine approximation for Yu's multidimensional variant of Mahler's classification of transcendental numbers. Our results arise as applications of well known results in Diophantine ... More

A converse to linear independence criteria, valid almost everywhereFeb 08 2013We prove a weighted analogue of the Khintchine-Groshev Theorem, where the distance to the nearest integer is replaced by the absolute value. This is subsequently applied to proving the optimality of several linear independence criteria over the field ... More

On shrinking targets for Z^m actions on toriJul 24 2008Dec 08 2008Let A be an n by m matrix with real entries. Consider the set Bad_A of x \in [0,1)^n for which there exists a constant c(x)>0 such that for any q \in Z^m the distance between x and the point {Aq} is at least c(x) |q|^{-m/n}. It is shown that the intersection ... More

Managing Communication Latency-Hiding at Runtime for Parallel Programming Languages and LibrariesJan 18 2012This work introduces a runtime model for managing communication with support for latency-hiding. The model enables non-computer science researchers to exploit communication latency-hiding techniques seamlessly. For compiled languages, it is often possible ... More

Evolution of CO lines in time-dependent models of protostellar disk formationApr 18 2013(Abridged) Star and planet formation theories predict an evolution in the density, temperature, and velocity structure as the envelope collapses and forms an accretion disk. The aim of this work is to model the evolution of the molecular excitation, line ... More

cphVB: A System for Automated Runtime Optimization and Parallelization of Vectorized ApplicationsOct 26 2012Mar 25 2013Modern processor architectures, in addition to having still more cores, also require still more consideration to memory-layout in order to run at full capacity. The usefulness of most languages is deprecating as their abstractions, structures or objects ... More

Fusion of Array Operations at RuntimeJan 20 2016Jan 21 2016We address the problem of fusing array operations based on criteria such as shape compatibility, data reusability, and communication. We formulate the problem as a graph partition problem that is general enough to handle loop fusion, combinator fusion, ... More

Three-dimensional integral equation approach to light scattering, extinction cross sections, local density of states and quasinormal modesMay 22 2013We present a numerical formalism for solving the Lippmann-Schwinger equation for the electric field in three dimensions. The formalism may be applied to scatterers of different shapes and embedded in different background media, and we develop it in detail ... More

How to find MH370?Nov 22 2018May 06 2019The disappearance of flight MH370 is possibly the greatest mystery in aviation history. A large zone in the Southern Indian Ocean was searched unsuccessfully leaving an open case and an unacceptable situation for the family members. We discuss the scientific ... More

Regularity of minimizers of autonomous convex variational integralsOct 16 2013We establish local higher integrability and differentiability results for minimizers of variational integrals $$ \mathfrak{F}(v,\Omega) = \int_{\Omega} /! F(Dv(x)) \, dx $$ over $W^{1,p}$--Sobolev mappings $u \colon \Omega \subset {\mathbb R}^n \to {\mathbb ... More

Calculation, normalization and perturbation of quasinormal modes in coupled cavity-waveguide systemsAug 04 2014We show how one can use a non-local boundary condition, which is compatible with standard frequency domain methods, for numerical calculation of quasinormal modes in optical cavities coupled to waveguides. In addition, we extend the definition of the ... More

Solving Dynamic Discrete Choice Models Using Smoothing and Sieve MethodsApr 10 2019We propose to combine smoothing, simulations and sieve approximations to solve for either the integrated or expected value function in a general class of dynamic discrete choice (DDC) models. We use importance sampling to approximate the Bellman operators ... More

Oxygen budget in low-mass protostars: the NGC1333-IRAS4A R1 shock observed in [OI] at 63 um with SOFIA-GREATApr 25 2017In molecular outflows from forming low-mass protostars, most oxygen is expected to be locked up in water. However, Herschel observations have shown that typically an order of magnitude or more of the oxygen is still unaccounted for. To test if the oxygen ... More

How to find MH370?Nov 22 2018The disappearance of flight MH370 is possibly the greatest mystery in aviation history. A large zone in the Southern Indian Ocean was searched unsuccessfully leaving an open case and an unacceptable situation for the family members. We discuss the scientific ... More

Reply to "Comment on "Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators" " by E. A. Muljarov and W. LangbeinMay 16 2016We refute all claims of the "Comment on "Normalization of quasinormal modes in leaky optical cavities and plasmonic resonators" " by E. A. Muljarov and W. Langbein (arXiv:1602.07278v1). Based entirely on information already contained in our original article ... More

Diophantine approximation with perfect squares and the solvability of an inhomogeneous wave equationDec 29 2005The Hausdorff dimension of an exceptional set of periods for which convergence of a formal solution to an inhomogeneous wave equation in n spatial and one temporal dimension is problematic, is determined along with conditions which the periods must satisfy ... More

Ultracold-atom collisions in atomic waveguides : A two-channel analysisDec 16 2014Apr 16 2015Low dimensional behavior of two ultra-cold atoms trapped in two-and one-dimensional waveguides is investigated in the vicinity of a magnetic Feshbach resonance. A quantitative two-channel model for the Feshbach mechanism is used allowing an exhaustive ... 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

High-fidelity conditional two-qubit swapping gate using tunable ancillasSep 24 2018Oct 16 2018Scalable quantum computing relies crucially on high-fidelity entangling operations. Here we demonstrate that four coupled qubits can operate as a high-fidelity two-qubit entangling gate that swaps two target qubits and adds a relative sign on the $\lvert ... More

Sobolev regularity for Symmetric-Convex FunctionalsOct 26 2016We study Sobolev regularity results for minimisers of autonomous, convex variational of linear growth which depend on the symmetric gradient rather than the full gradient. This extends the results available in the literature for the BV-setting to the ... More

Bias dependent subband edges and the 0.7 conductance anomalyNov 07 2001The 0.7 2e^2/h conductance anomaly is studied in strongly confined, etched GaAs/GaAlAs quantum point contacts by measuring the differential conductance G as a function of source-drain bias V_sd and gate-source bias V_gs as well as a function of temperature. ... More

Evidence for a single hydrogen molecule connected by an atomic chainDec 29 2006Stable, single-molecule conducting-bridge configurations are typically identified from peak structures in a conductance histogram. In previous work on Pt with H$_2$ at cryogenic temperatures it has been shown that a peak near 1 $G{_0}$ identifies a single ... More

Semi-analytical quasi-normal mode theory for the local density of states in coupled photonic crystal cavity-waveguide structuresSep 29 2015We present and validate a semi-analytical quasi-normal mode (QNM) theory for the local density of states (LDOS) in coupled photonic crystal (PhC) cavity-waveguide structures. By means of an expansion of the Green's function on one or a few QNMs, a closed-form ... More

On the theory of coupled modes in optical cavity-waveguide structuresJan 11 2017Light propagation in systems of optical cavities coupled to waveguides can be conveniently described by a general rate equation model known as (temporal) coupled mode theory (CMT). We present an alternative derivation of the CMT for optical cavity-waveguide ... More

Regularity for higher order quasiconvex problems with linear growth from belowMar 19 2019We announce new existence and $\varepsilon$-regularity results for minimisers of the relaxation of strongly quasiconvex integrals that on smooth maps $u\colon\Omega\subset\mathbb{R}^{n}\to\mathbb{R}^{N}$ are defined by $$u\mapsto \int_{\Omega}F(\nabla^{k}u)dx.$$ ... More

One-dimensional ultracold atomic gases: Impact of the effective range on integrabilityJun 12 2015Mar 24 2016Three identical bosons or fermions are considered in the limit of zero-range interactions and finite effective range. By using a two channel model, we show that these systems are not integrable and that the wave function verifies specific continuity conditions ... More

Partial Regularity for BV MinimizersMar 26 2018We establish an $\varepsilon$-regularity result for the derivative of a map of bounded variation that minimizes a strongly quasiconvex variational integral of linear growth, and, as a consequence, the partial regularity of such BV minimizers. This result ... More

Lower semicontinuity for an integral functional in BVDec 17 2015We prove a lower semicontinuity result for a functional of linear growth initially defined by \[ \int_{\Omega}F\left(\frac{dDu}{d\mu}\right)\,d\mu \] for $u\in BV(\Omega;\mathbb{R}^N)$ with $Du\ll \mu$. The positive Radon measure $\mu$ is only assumed ... More

On Rank-One Convex Functions that are homogeneous of Degree OneMay 18 2015We show that positively $1$--homogeneous rank one convex functions are convex at $0$ and at matrices of rank one. The result is a special case of an abstract convexity result that we establish for positively $1$--homogeneous directionally convex functions ... More

Piecewise affine approximations for functions of bounded variationNov 08 2012Jul 22 2015BV functions cannot be approximated well by piecewise constant functions, but this work will show that a good approximation is still possible with (countably) piecewise affine functions. In particular, this approximation is area-strictly close to the ... More

Wrong side of the tracks: Big Data and Protected CategoriesDec 15 2014Jun 24 2016When we use machine learning for public policy, we find that many useful variables are associated with others on which it would be ethically problematic to base decisions. This problem becomes particularly acute in the Big Data era, when predictions are ... More

Further solvable analogues of the Baer-Suzuki theorem and generation of nonsolvable groupsDec 11 2010Dec 14 2010Let $G$ be an almost simple group. We prove that if $x \in G$ has prime order $p \ge 5$, then there exists an involution $y$ such that $<x,y>$ is not solvable. Also, if $x$ is an involution then there exist three conjugates of $x$ that generate a nonsolvable ... More

Towards a Theory of GlueDec 17 2012We propose and study the notions of behaviour type and composition operator making a first step towards the definition of a formal framework for studying behaviour composition in a setting sufficiently general to provide insight into how the component-based ... More

Population genetics models of local ancestryFeb 22 2012Apr 25 2012Migrations have played an important role in shaping the genetic diversity of human populations. Understanding genomic data thus requires careful modeling of historical gene flow. Here we consider the effect of relatively recent population structure and ... More

Euler characteristics and compact p-adic Lie groupsSep 21 2009Oct 08 2009We discuss Euler characteristics for finitely generated modules over Iwasawa algebras. We show that the Euler characteristic of a module is well-defined whenever the 0th homology group is finite if and only if the relevant compact p-adic Lie group is ... More

The hadronization of partonsOct 23 2008Oct 07 2010We review the description of inclusive single unpolarized light hadron production using fragmentation functions in the framework of the factorization theorem. We summarize the factorization of quantities into perturbatively calculable quantities and these ... More

Perturbative description of inclusive single hadron production at HERAAug 07 2008Light charged hadron production data in the current fragmentation region at HERA are calculated using next-to-leading order perturbative calculations and fragmentation functions obtained from similar data from e+ e- reactions. General good agreement is ... More

On the remainder term of the Berezin inequality on a convex domainSep 22 2015Jan 02 2016We study the Dirichlet eigenvalues of the Laplacian on a convex domain in $\mathbb{R}^n$, with $n\geq 2$. In particular, we generalize and improve upper bounds for the Riesz means of order $\sigma\geq 3/2$ established in an article by Geisinger, Laptev ... More

Masers : High resolution probes of massive star formationSep 26 2003Astrophysical masers are one of the most readily detected signposts of high-mass star formation. Their presence indicates special conditions, probably indicative of a specific evolutionary phase. Masers also represent the ultimate high-resolution probe ... More

Quasi-random oriented graphsJan 28 2011Aug 10 2011We show that a number of conditions on oriented graphs, all of which are satisfied with high probability by randomly oriented graphs, are equivalent. These equivalences are similar to those given by Chung, Graham and Wilson in the case of unoriented graphs, ... More

Detector Systems at CLICSep 15 2011The Compact Linear Collider CLIC is designed to deliver e+e- collisions at a center of mass energy of up to 3 TeV. The detector systems at this collider have to provide highly efficient tracking and excellent jet energy resolution and hermeticity for ... More

Domain Wall Fermions for Planar PhysicsJul 28 2015Aug 22 2015In 2+1 dimensions, Dirac fermions in reducible, i.e. four-component representations of the spinor algebra form the basis of many interesting model field theories and effective descriptions of condensed matter phenomena. This paper explores lattice formulations ... More

High Density Effective Theory Confronts the Fermi LiquidOct 07 2003Nov 20 2003The high density effective theory recently introduced by Hong and Hsu to describe ultradense relativistic fermionic matter is used to calculate the tree-level forward scattering amplitude between two particles at the Fermi surface. While the direct term ... More

Fixed Point Four-Fermi TheoriesJun 24 1997I review dynamical chiral symmetry breaking in four-fermi models, including results of Monte Carlo simulations with dynamical fermions. For 2<d<4, where the phase transition defines an ultraviolet fixed point of the renormalisation group, the continuum ... More

Bounds on area and charge for marginally trapped surfaces with cosmological constantSep 28 2011May 03 2012We sharpen the known inequalities $A \Lambda \le 4\pi (1-g)$ and $A\ge 4\pi Q^2$ between the area $A$ and the electric charge $Q$ of a stable marginally outer trapped surface (MOTS) of genus g in the presence of a cosmological constant $\Lambda$. In particular, ... More

A Mass Partition Problem Related to Equivariant Sections of Stiefel BundlesNov 08 2010Jun 19 2012We consider a geometric combinatorial problem naturally associated to the geometric topology of certain spherical space forms. Given a collection of m mass distributions on R^n, the existence of k linearly independent regular q-fans, each of which equipartitions ... More

IndistinguishabilitySep 18 2016This is a systematic review of the concept of indistinguishability in both classical and quantum mechanics, with particular attention to Gibbs' paradox. Section 1 is on the Gibbs paradox; section 2 is a defense of the concept of classical indistinguishability, ... More

Summing Large-N Towers in Colour Flow EvolutionDec 09 2013We consider soft gluon evolution in the colour flow basis. We give explicit expressions for the colour structure of the (one-loop) soft anomalous dimension matrix for an arbitrary number of partons, and show how the successive exponentiation of classes ... More

Almost Parallel StructuresJul 20 2001A discussion of torsion of Riemannian G-structures leads to a survey of contributions of Alfred Gray and others on almost Hermitian manifolds, G_2-manifolds, curvature identities, volume expansions, plotting geodesics, and the geometry of nilmanifolds. ... More

EuSpRIG 2006 Commercial Spreadsheet ReviewFeb 29 2008This management summary provides an outline of a commercial spreadsheet review process. The aim of this process is to ensure remedial or enhancement work can safely be undertaken on a spreadsheet with a commercially acceptable level of risk of introducing ... More

Physical Mechanism of the d->d+is TransitionJun 02 2000We discuss the basic physical mechanism of the d->d+is transition, which is the currently accepted explanation for the results of tunneling experiments into $ab$ planes. Using the first-order perturbation theory, we show that the zero-bias states drive ... More

A Galois-Connection between Myers-Briggs' Type Indicators and Szondi's Personality ProfilesMar 08 2014We propose a computable Galois-connection between Myers-Briggs' Type Indicators (MBTIs), the most widely-used personality measure for non-psychiatric populations (based on C.G. Jung's personality types), and Szondi's personality profiles (SPPs), a less ... More

Total positivity in stable semigroupsNov 29 2014We characterize the total positivity in space-time of real strictly stable semigroups. In the positive case, this solves a problem which had been raised by Karlin. In the drifted Cauchy case, this concludes a study which we had initiated in a previous ... More

Quasidense monotone multifunctionsDec 08 2016In this paper, we discuss quasidense multifunctions from a Banach space into its dual, and use the two sum theorems proved in a previous paper to give various characterizations of quasidensity. We prove that, for closed monotone multifunctions, quasidensity ... More

Improving three-dimensional mass mapping with weak gravitational lensing using galaxy clusteringMar 28 2012Nov 01 2013The weak gravitational lensing distortion of distant galaxy images (defined as sources) probes the projected large-scale matter distribution in the Universe. To improve quality in the 3D mass mapping using 3D-lensing, we combine the lensing information ... More

Extending four dimensional Ricci flows with bounded scalar curvatureApr 11 2015We consider smooth solutions (M,g(t)), 0 <= t <T, to Ricci flow on compact, connected, four dimensional manifolds without boundary. We assume that the scalar curvature is bounded uniformly, and that T is finite. In this case, we show that the metric space ... More

Ricci flow of non-collapsed 3-manifolds whose Ricci curvature is bounded from belowMar 12 2009Dec 01 2009We consider complete (possibly non-compact) three dimensional Riemannian manifolds (M,g) such that: a) (M,g) is non-collapsed, b) the Ricci curvature of (M,g) is bounded from below, c) the geometry of (M,g) at infinity is not too extreme. Given such initial ... More

Hydrodynamic limit for the velocity flip modelJun 11 2012Feb 20 2013We study the diffusive scaling limit for a chain of $N$ coupled oscillators. In order to provide the system with good ergodic properties, we perturb the Hamiltonian dynamics with random flips of velocities, so that the energy is locally conserved. We ... More

A Formula for the Reliability of a $d$-dimensional Consecutive-$k$-out-of-$n$:F SystemJun 11 2015Aug 14 2015We derive a formula for the reliability of a $d$-dimensional consecutive-$k$-out-of-$n$:F system. That is, a formula for the probability that an $n_1 \times \ldots \times n_d$ array whose entries are (independently of each other) $0$ with probability ... More

Measure Partitions via Fourier Analysis II: Center Transversality in the $L^2$-norm for Complex HyperplanesJun 22 2015Sep 13 2015Applications of harmonic analysis on finite groups were recently introduced to measure partition problems, with a variety of equipartition types by convex fundamental domains obtained as the vanishing of prescribed Fourier transforms. Considering the ... More

A Ham Sandwich Analogue for Quaternionic Measures and Finite Subgroups of S^3Sep 29 2010Sep 03 2011A "ham sandwich" theorem is established for n quaternionic Borel measures on quaternionic space H^n. For each finite subgroup G of S^3, it is shown that there is a quaternionic hyperplane H and a corresponding tiling of H^n into |G| fundamental regions ... More

From the Ham Sandwich to the Pizza Pie: A Simultaneous Z_m Equipartition of Complex MeasuresJun 23 2010Sep 03 2011A "ham sandwich" theorem is derived for n complex Borel measures on C^n. For each integer m>=2, it shown that there exists a regular m-fan centered about a complex hyperplane, satisfying the condition that for each complex measure, the "Z_m rotational ... More

A method for obtaining the algebraic generating function from a seriesDec 01 2009We describe here an experimental method that permits to compute a good candidate for the closed form of a generating function if we know the first few terms of a series. The method is based on integer relations algorithms and uses either two programs ... More

Fine structure of the zeros of orthogonal polynomials, III. Periodic recursion coefficientsDec 16 2004We discuss asymptotics of the zeros of orthogonal polynomials on the real line and on the unit circle when the recursion coefficients are periodic. The zeros on or near the absolutely continuous spectrum have a clock structure with spacings inverse to ... More

Symmetric Powers of Symmetric Bilinear Forms, Homogeneous Orthogonal Polynomials on the Sphere and an Application to Compact Hyperkähler ManifoldsJul 01 2015Jan 18 2016The Beauville-Fujiki relation for a compact Hyperk\"ahler manifold $X$ of dimension $2k$ allows to equip the symmetric power $\text{Sym}^kH^2(X)$ with a symmetric bilinear form induced by the Beauville-Bogomolov form. We study some of its properties and ... More

Overlapping iterated function systems from the perspective of Metric Number TheoryJan 23 2019In this paper we develop a new approach for studying overlapping iterated function systems. This approach is inspired by a famous result due to Khintchine from Diophantine approximation. This result shows that for a family of limsup sets, their Lebesgue ... More

Technologies for Future Vertex and Tracking Detectors at CLICDec 06 2018CLIC is a proposed linear $e^{+}e^{-}$ collider with center-of-mass energies of up to $3\,\textrm{TeV}$. Its main objectives are precise top quark and Higgs boson measurements, as well as searches for Beyond Standard Model physics. To meet the physics ... More

Persistence Characterisation of teledyne H2RG detectorsJul 13 2018Image persistence is a major problem in infrared detectors, potentially seriously limiting data quality in many observational regimes. The problem manifests itself as remnant images that can persist for several days after a deep exposure. In this study, ... More

Orthogonal polynomials with exponentially decaying recursion coefficientsMar 03 2006We review recent results on necessary and sufficient conditions for measures on $\mathbb{R}$ and $\partial\mathbb{D}$ to yield exponential decay of the recursion coefficients of the corresponding orthogonal polynomials. We include results on the relation ... More

Complex horospherical transform on real sphereJan 02 2005We define a new integral transform on the real sphere which is invariant relative to the orthogonal group and similar to the horospherical Radon transform for the hyperbolic space. This transform involves complex geometry associated with the sphere.

Horospherical Cauchy-Radon transform on compact symmetric spacesJan 02 2005Harmonic analysis on noncompact Riemannian symmetric spaces is in a sense equivalent to the theory of the horospherical transform. There are no horospheres on compact symmetric spaces, but we define a complex version of horospherical transform which plays ... More

Small Black holes vs horizonless solutions in AdSOct 16 2009Nov 20 2009It is argued that the appropriate macroscopic description of half-BPS mesonic chiral operators in generic $d=4$ ${\cal N}=1$ toric gauge theories is in terms of the geometric quantization of smooth horizonless configurations. The relevance of different ... More

Visible Points On Exponential CurvesOct 16 2017We provide two new bounds on the number of visible points on exponential curves modulo a prime for all choices of primes. We also provide one new bound on the number of visible points on exponential curves modulo a prime for almost all primes.

On toposes generated by cardinal finite objectsMay 19 2015Apr 05 2016We give a characterizations of toposes which admit a generating family of objects which are internally cardinal finite (i.e. Kuratowski finite and decidable) in terms of "topological" conditions. The central result is that, constructively, a hyperconnected ... More

Counting points on hyperelliptic curves with explicit real multiplication in arbitrary genusOct 25 2018We present a probabilistic Las Vegas algorithm for computing the local zeta function of a genus-$g$ hyperelliptic curve defined over $\mathbb F_q$ with explicit real multiplication (RM) by an order $\Z[\eta]$ in a degree-$g$ totally real number field. ... More

Low frequency dispersive estimates for the wave equation in higher dimensionsApr 26 2007Sep 17 2007We prove dispersive estimates at low frequency in dimensions n greater or equal to 4 for the wave equation for a very large class of real-valued potentials, provided the zero is neither an eigenvalue nor a resonance.

Decomposition of subsets in finite fieldsMar 29 2018We extend a bound of Roche-Newton, Shparlinski and Winterhof which says any subset of a finite field can be decomposed into two disjoint subset $\cU$ and $\cV$ of which the additive energy of $\cU$ and $f(\cV)$ are small, for suitably chosen rational ... More

Characters and invariant random subgroups of the finitary symmetric groupDec 06 2018We will describe the relationship between the indecomposable characters of the finitary symmetric group and its ergodic invariant random subgroups; and we will interpret each Thoma character as an asymptotic limit of a naturally associated sequence of ... More

Incidence Results and Bounds of Trilinear and Quadrilinear Exponential SumsJul 26 2017Aug 31 2017We give a new bound on the number of collinear triples for two arbitrary subsets of a finite field. This improves on existing results which rely on the Cauchy inequality. We then us this to provide a new bound on trilinear and quadrilinear exponential ... More

The Quantum Cosmological Wavefunction at Very Early Times for a Quadratic Gravity TheoryMay 28 2003The quantum cosmological wavefunction for a quadratic gravity theory derived from the heterotic string effective action is obtained near the inflationary epoch and during the initial Planck era. Neglecting derivatives with respect to the scalar field, ... More

Divergences in the Moduli Space Integral and Accumulating Handles in the Infinite-Genus LimitOct 24 1994The symmetries associated with the closed bosonic string partition function are examined so that the integration region in Teichmuller space can be determined. The conditions on the period matrix defining the fundamental region can be translated to relations ... More

Endoscopy and cohomology of a quasi-split U(4)Aug 31 2014Sep 18 2016We prove asymptotic upper bounds for the $L^2$ Betti numbers of the locally symmetric spaces associated to a quasi-split $U(4)$. These manifolds are 8-dimensional, and we prove bounds in degrees 2 and 3, with the behaviour in the other degrees being well ... More

An abstract elementary class non-axiomatizable in $L_{(\infty,κ)}$Dec 03 2018We show that for any uncountable cardinal $\lambda$, the category of sets of cardinality at least $\lambda$ and monomorphisms between them cannot appear as the category of point of a topos, in particular is not the category of models of a $L_{(\infty,\omega)}$-theory. ... More