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Complex Molecules in the L1157 Molecular OutflowMay 16 2008We report the detection of complex organic molecules in the young protostellar outflow L1157. We identify lines from HCOOCH3, CH3CN, HCOOH and C2H5OH at the position of the B1 shock in the blueshifted lobe, making it the first time that complex species ... More

The chemical connection between 67P/C-G and IRAS 16293-2422Feb 08 2018The chemical evolution of a star- and planet-forming system begins in the prestellar phase and proceeds across the subsequent evolutionary phases. The chemical trail from cores to protoplanetary disks to planetary embryos can be studied by comparing distant ... More

The Mass Evolution of Protostellar Disks and Envelopes in the Perseus Molecular CloudFeb 15 2019In the standard picture for low-mass star formation, a dense molecular cloud undergoes gravitational collapse to form a protostellar system consisting of a new central star, a circumstellar disk, and a surrounding envelope of remaining material. The mass ... More

Probing strange stars and color superconductivity by r-mode instabilities in millisecond pulsarsDec 20 1999Jun 06 2000R-mode instabilities in rapidly rotating quark matter stars (strange stars) lead to specific signatures in the evolution of pulsars with periods below 2.5 msec, and may explain the apparent lack of very rapid pulsars. Existing data seem consistent with ... More

Interpolation and sampling in small Bergman spacesJun 20 2011Aug 16 2011Carleson measures and interpolating and sampling sequences for weighted Bergman spaces on the unit disk are described for weights that are radial and grow faster than the standard weights $(1-|z|)^{-\alpha}$, $0<\alpha<1$. These results make the Hardy ... More

Density theorems for sampling and interpolation in the Bargmann-Fock spaceApr 01 1992We give a complete description of sampling and interpolation in the Bargmann-Fock space, based on a density concept of Beurling. Roughly speaking, a discrete set is a set of sampling if and only if its density in every part of the plane is strictly larger ... More

Runge-Kutta methods for third order weak approximation of SDEs with multidimensional additive noiseOct 06 2009May 21 2010A new class of third order Runge-Kutta methods for stochastic differential equations with additive noise is introduced. In contrast to Platen's method, which to the knowledge of the author has been up to now the only known third order Runge-Kutta scheme ... More

Interplay between chemistry and dynamics in embedded protostellar disksSep 25 2013A fundamental part of the study of star formation is to place young stellar objects in an evolutionary sequence. Establishing a robust evolutionary classification scheme allows us not only to understand how the Sun was born but also to predict what kind ... More

Recent Advances in Cosmological Hydrogen ReionizationMar 22 2012I discuss recent advances in the study of hydrogen reionization, focusing on progress that was achieved during the years 2010-2011. First, I discuss recent measurements of the progress of reionization. Next, I discuss recent observational constraints ... More

A general solution to the Schrödinger-Poission equation for charged hard wall: Application to potential profile of an AlN/GaN barrier structureNov 08 2010A general, system-independent formulation of the parabolic Schr\"odinger-Poisson equation is presented for a charged hard wall in the limit of complete screening by the ground state. It is solved numerically using iteration and asymptotic-boundary conditions. ... More

A short review and primer on the use of human voice in human computer interaction applicationsSep 23 2016The application of psychophysiologicy in human-computer interaction is a growing field with significant potential for future smart personalised systems. Working in this emerging field requires comprehension of an array of physiological signals and analysis ... More

On some generalizations of skew-shifts on $\mathbb{T}^2$Oct 11 2016In this paper we investigate maps of the two-torus $\mathbb{T}^2$ of the form $T(x,y)=(x+\omega,g(x)+f(y))$ for Diophantine $\omega\in\mathbb{T}$ and for a class of maps $f,g:\mathbb{T}\to\mathbb{T}$, where each $g$ is strictly monotone and of degree ... More

Solving Stress and Compliance Constrained Volume Minimization using Anisotropic Mesh Adaptation, the Method of Moving Asymptotes and a Global p-normOct 28 2014Aug 04 2015The p-norm often used in stress constrained topology optimisation supposedly mimics a delta function and it is thus characterised by a small length scale and ideally one would also prefer to have the solid-void transition occur over a small length scale, ... More

A forward-backward splitting algorithm for the minimization of non-smooth convex functionals in Banach spaceJul 04 2008Oct 14 2008We consider the task of computing an approximate minimizer of the sum of a smooth and non-smooth convex functional, respectively, in Banach space. Motivated by the classical forward-backward splitting method for the subgradients in Hilbert space, we propose ... More

Zeros of functions in Hilbert spaces of Dirichlet seriesJun 13 2012Oct 11 2012The Dirichlet--Hardy space $\Ht$ consists of those Dirichlet series $\sum_n a_n n^{-s}$ for which $\sum_n |a_n|^2<\infty$. It is shown that the Blaschke condition in the half-plane $\operatorname{Re} s>1/2$ is a necessary and sufficient condition for ... More

A short review and primer on eye tracking in human computer interaction applicationsSep 23 2016The application of psychophysiologicy in human-computer interaction is a growing field with significant potential for future smart personalised systems. Working in this emerging field requires comprehension of an array of physiological signals and analysis ... More

The Interplay of Ultrahigh-Energy Cosmic Rays and Extra DimensionsMay 28 2004Regarding ultrahigh-energy cosmic rays (UHECRs) as a probe and extra dimensions as a possible ingredient of the fantastic ultrahigh-energy world, we discuss possible interplay between them. On the one hand small extra dimensions and Kaluza-Klein bursts ... More

Large-scale numerical simulations of star formation put to the test: Comparing synthetic images and actual observations for statistical samples of protostarsOct 27 2015Dec 14 2015(abridged) Context: Both observations and simulations of embedded protostars have progressed rapidly in recent years. Bringing them together is an important step in advancing our knowledge about the earliest phases of star formation. Aims: To compare ... More

Normally Regular DigraphsOct 30 2014A normally regular digraph with parameters $(v,k,\lambda,\mu)$ is a directed graph on $v$ vertices whose adjacency matrix $A$ satisfies the equation $AA^t=k I+\lambda (A+A^t)+\mu(J-I-A-A^t)$. This means that every vertex has out-degree $k$, a pair of ... More

Free energy of bubbles and droplets in the quark-hadron phase transitionJul 07 1998Aug 02 1999Using the MIT bag model, we calculate the free energy of droplets of quark-gluon plasma in a bulk hadronic medium, and of hadronic bubbles in a bulk quark-gluon plasma, under the assumption of vanishing chemical potentials. We investigate the validity ... More

Neutrino decoupling in the early UniverseJun 02 1995A calculation of neutrino decoupling in the early Universe, including full Fermi-Dirac statistics and electron mass dependence in the weak reaction rates, is presented. We find that after decoupling, the electron neutrinos contribute 0.83\% more to the ... More

A Cosmological Three Level Neutrino LaserFeb 14 1997We present a calculation of a neutrino decay scenario in the early Universe. The specific decay is \nu_{2} \to \nu_{1} + \phi, where \phi is a boson. If there is a neutrino mass hierarchy, m_{\nu_{e}} < m_{\nu_{\mu}} < m_{\nu_{\tau}}, we show that it ... More

Linking interstellar and cometary O$_2$: a deep search for $^{16}$O$^{18}$O in the solar-type protostar IRAS 16293--2422May 31 2018Recent measurements carried out at comet 67P/C-G with the ${\it Rosetta}$ probe revealed that molecular oxygen, O$_2$, is the fourth most abundant molecule in comets. Models show that O$_2$ is likely of primordial nature, coming from the interstellar ... More

A Way to the Dark Side of the Universe through Extra DimensionsSep 11 2002As indicated by Einstein's general relativity, matter and geometry are two faces of a single nature. In our point of view, extra dimensions, as a member of the {\em geometry face}, will be treated as a part of the {\em matter face} when they are beyond ... More

Viewpoint: Opportunities and challenges of two-dimensional magnetic van der Waals materials: magnetic graphene?Apr 29 2016There has been a huge increase of interests in two-dimensional van der Waals materials over the past ten years or so with the conspicuous absence of one particular class of materials: magnetic van der Waals systems. In this Viewpoint, we point it out ... More

Automatic Control over the Cosmological Constant through Non-minimal Phantom and QuintessenceJan 30 2008A mechanism to control the cosmological constant through a scalar field non-minimally coupled to gravity is proposed. By utilizing non-minimal phantom or quintessence, the cosmological constant, which may be large originally, can be automatically driven ... More

Oscillating QuintessenceNov 23 2007An oscillating scalar field as a quintessence model for dark energy is proposed. The case of a power-law potential is particularly intriguing and is the focus of the present article. In this model the equation of state w_{OQ} of dark energy is a constant ... More

Kaluza-Klein Burst: a New Mechanism for Generating Ultrahigh-Energy Cosmic RaysMay 28 2003Nov 10 2005By invoking small extra dimensions as a good energy bearer, a new scenario for understanding the origin of ultrahigh-energy cosmic rays (UHECRs), from both the bottom-up and the top-down viewpoints, is proposed. We explore the possibility of generating ... More

The homological content of the Jones representations at $q = -1$Feb 25 2014We generalize a discovery of Kasahara and show that the Jones representations of braid groups, when evaluated at $q = -1$, are related to the action on homology of a branched double cover of the underlying punctured disk. As an application, we prove for ... More

Minimal Tree-Level Seesaws with a Heavy Intermediate FermionMar 19 2013Jul 29 2013There exists a generic minimal tree-level diagram, with two external scalars and a heavy intermediate fermion, that can generate naturally small neutrino masses via a seesaw. This diagram has a mass insertion on the internal fermion line, and the set ... More

Structure and binding in crystals of cage-like molecules: hexamine and platonic hydrocarbonsOct 07 2010In this paper, we show that first-principle calculations using a van der Waals density functional (vdW-DF), [Phys. Rev. Lett. $\mathbf{92}$, 246401 (2004)] permits determination of molecular crystal structure. We study the crystal structures of hexamine ... More

Variety of power sums and divisors in the moduli space of cubic fourfoldsSep 07 2013Sep 19 2013We show that a cubic fourfold F that is apolar to a Veronese surface has the property that its variety of power sums VSP(F,10) is singular along a K3 surface of genus 20. We prove that these cubics form a divisor in the moduli space of cubic fourfolds ... More

On Asymptotic Global Error Estimation and Control of Finite Difference Solutions for Semilinear Parabolic EquationsNov 13 2009Dec 18 2014The aim of this paper is to extend the global error estimation and control addressed in Lang and Verwer [SIAM J. Sci. Comput. 29, 2007] for initial value problems to finite difference solutions of semilinear parabolic partial differential equations. The ... More

Bi-resolving graph homomorphisms and extensions of bi-closing codesApr 20 2009Jan 15 2010Given two graphs G and H, there is a bi-resolving (or bi-covering) graph homomorphism from G to H if and only if their adjacency matrices satisfy certain matrix relations. We investigate the bi-covering extensions of bi-resolving homomorphisms and give ... More

What classicality? Decoherence and Bohr's classical conceptsSep 21 2010Mar 12 2012Niels Bohr famously insisted on the indispensability of what he termed "classical concepts." In the context of the decoherence program, on the other hand, it has become fashionable to talk about the "dynamical emergence of classicality" from the quantum ... More

Probing Exotic Fermions from a Seesaw/Radiative Model at the LHCOct 02 2013Nov 29 2015There exist tree-level generalizations of the Type-I and Type-III seesaw mechanisms that realize neutrino mass via low-energy effective operators with d>5. However, these generalizations also give radiative masses that can dominate the seesaw masses in ... More

Efficient fourth order symplectic integrators for near-harmonic separable Hamiltonian systemsJan 18 2015Feb 09 2015Efficient fourth order symplectic integrators are proposed for numerical integration of separable Hamiltonian systems H(p,q)=T(p)+V(q). Symmetric splitting coefficients with five to nine stages are obtained by higher order decomposition of the simple ... More

Preferential sampling of helicity by isotropic helicoidsSep 16 2016We present a theoretical and numerical study on the motion of isotropic helicoids in complex flows. These are particles whose motion is invariant under rotations but not under mirror reflections of the particle. This is the simplest, yet unexplored, extension ... More

Helson's problem for sums of a random multiplicative functionNov 24 2014May 22 2015We consider the random functions $S_N(z):=\sum_{n=1}^N z(n) $, where $z(n)$ is the completely multiplicative random function generated by independent Steinhaus variables $z(p)$. It is shown that ${\Bbb E} |S_N|\gg \sqrt{N}(\log N)^{-0.05616}$ and that ... More

On quasi-linear PDAEs with convection: applications, indices, numerical solutionMar 17 2013For a class of partial differential algebraic equations (PDAEs) of quasi-linear type which include nonlinear terms of convection type a possibility to determine a time and spatial index is considered. As a typical example we investigate an application ... More

Diagonally drift-implicit Runge-Kutta methods of weak order one and two for Itô SDEs and stability analysisMar 20 2013May 08 2016The class of stochastic Runge-Kutta methods for stochastic differential equations due to R\"o{\ss}ler is considered. Coefficient families of diagonally drift-implicit stochastic Runge-Kutta (DDISRK) methods of weak order one and two are calculated. Their ... More

Classification of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential EquationsMar 19 2013In the present paper, a class of stochastic Runge-Kutta methods containing the second order stochastic Runge-Kutta scheme due to E. Platen for the weak approximation of It\^o stochastic differential equation systems with a multi-dimensional Wiener process ... More

Stochastic B-series analysis of iterated Taylor methodsMar 23 2010Jul 29 2010For stochastic implicit Taylor methods that use an iterative scheme to compute their numerical solution, stochastic B--series and corresponding growth functions are constructed. From these, convergence results based on the order of the underlying Taylor ... More

Composition of stochastic B-series with applications to implicit Taylor methodsMar 23 2010Sep 03 2010In this article, we construct a representation formula for stochastic B-series evaluated in a B-series. This formula is used to give for the first time the order conditions of implicit Taylor methods in terms of rooted trees. Finally, as an example we ... More

Light Neutrinos from a Mini-Seesaw Mechanism in Warped SpaceOct 13 2010Jan 08 2011The seesaw mechanism provides a simple explanation for the lightness of the known neutrinos. Under the standard assumption of a weak scale Dirac mass and a heavy sterile Majorana scale the neutrino mass is naturally suppressed below the weak scale. However, ... More

Warping the Universal Extra DimensionsMay 18 2009May 30 2009We develop the necessary ingredients for the construction of realistic models with warped universal extra dimensions. Our investigations are based on the seven dimensional (7D) spacetime AdS_5 x T^2 and we derive the Kaluza-Klein (KK) spectra for gravitons, ... More

Quark-Lepton Symmetry and Quartification in Five DimensionsJun 28 2007We outline some features of higher dimensional models possessing a Quark-Lepton (QL) symmetry. The QL symmetric model in five dimensions is discussed, with particular emphasis on the use of split fermions. An interesting fermionic geography which utilises ... More

Warping, Extra Dimensions and a Slice of AdS_dSep 29 2009Inspired by the Randall-Sundrum (RS) framework we consider a number of phenomenologically relevant model building questions on a slice of compactified AdS_d for d >5. Such spaces are interesting as they enable one to realize the weak scale via warping. ... More

Effective Potentials and the Vacuum Structure of Quantum Field TheoriesJul 12 2004I review some older work on the effective potentials of quantum field theories, in particular the use of anomalous symmetries to constrain the form of the effective potential, and the background field method for evaluating it perturbatively. Similar techniques ... More

Brane TilingsJun 12 2007We review and extend the progress made over the past few years in understanding the structure of toric quiver gauge theories; those which are induced on the world-volume of a stack of D3-branes placed at the tip of a toric Calabi-Yau cone, at an ``orbifold ... More

Algebraic Degree of Polynomial OptimizationFeb 09 2008Consider the polynomial optimization problem whose objective and constraints are all described by multivariate polynomials. Under some genericity assumptions, %% on these polynomials, we prove that the optimality conditions always hold on optimizers, ... More

Integral means and boundary limits of Dirichlet seriesDec 04 2007We study the boundary behavior of functions in the Hardy spaces HD^p for ordinary Dirichlet series. Our main result, answering a question of H. Hedenmalm, shows that the classical F. Carlson theorem on integral means does not extend to the imaginary axis ... More

Rotation numbers for quasiperiodically forced circle maps - Mode-locking vs strict monotonicityJul 24 2006We describe the relation between the dynamical properties of a quasiperiodically forced orientation-preserving circle homeomorphism and the behavior of the fibered rotation number with respect to strictly monotone perturbations. Despite the fact that ... More

Decay rates for approximation numbers of composition operatorsFeb 17 2013Dec 03 2013A general method for estimating the approximation numbers of composition operators on $\Ht$, using finite-dimensional model subspaces, is studied and applied in the case when the symbol of the operator maps the unit disc to a domain whose boundary meets ... More

Canonical curves and varieties of sums of powers of cubic polynomialsFeb 16 2001In this note we show that the apolar cubic forms associated to codimension two linear sections of canonical curves of genus at least eleven are special with respect to their presentation as sums of cubes.

On the Acceleration of the Multi-Level Monte Carlo MethodJan 31 2013Jun 04 2014The multi-level Monte Carlo method proposed by M. Giles (2008) approximates the expectation of some functionals applied to a stochastic process with optimal order of convergence for the mean-square error. In this paper, a modified multi-level Monte Carlo ... More

A study of the one dimensional total generalised variation regularisation problemSep 23 2013In this paper we study the one dimensional second order total generalised variation regularisation (TGV) problem with $L^{2}$ data fitting term. We examine some properties of this model and we calculate exact solutions using simple piecewise affine functions ... More

Blackhole evaporation model without information lossAug 23 2016A simple model of a blackhole evaporation without information loss is given. In this model, the blackhole is \textit{not} in a specific mass eigenstate as it evaporates but rather, is in a superposition of various mass eigenstates and is entangled with ... More

Calibration of the Mass-Temperature Relation for Clusters of Galaxies Using Weak Gravitational LensingMar 10 2006May 25 2007The main uncertainty in current determinations of the power spectrum normalization, sigma_8, from abundances of X-ray luminous galaxy clusters arises from the calibration of the mass-temperature relation. We use our weak lensing mass determinations of ... More

Domain Representable Spaces Defined by Strictly Positive InductionJun 29 2010Sep 02 2010Recursive domain equations have natural solutions. In particular there are domains defined by strictly positive induction. The class of countably based domains gives a computability theory for possibly non-countably based topological spaces. A $ qcb_{0} ... More

An extremal problem related to negative refractionJun 30 2005We solve an extremal problem that arises in the study of the refractive indices of passive metamaterials. The problem concerns Hermitian functions in $H^2$ of the upper half-plane, i.e., $H^2$ functions satisfying $f(-x)=\bar{f(x)}$. An additional requirement ... More

Homotopy theory of G-diagrams and equivariant excisionMar 24 2014Aug 31 2014Let $G$ be a finite group acting on a small category $I$. We study functors $X \colon I \to \mathscr{C}$ equipped with families of compatible natural transformations that give a kind of generalized $G$-action on $X$. Such objects are called $G$-diagrams. ... More

The quantum-to-classical transition: Bohr's doctrine of classical concepts, emergent classicality, and decoherenceApr 10 2008It is now widely accepted that environmental entanglement and the resulting decoherence processes play a crucial role in the quantum-to-classical transition and the emergence of "classicality" from quantum mechanics. To this extent, decoherence is often ... More

Full Restoration of Visual Encrypted Color ImagesNov 18 2011While strictly black and white images have been the basis for visual cryptography, there has been a lack of an easily implemented format for colour images. This paper establishes a simple, yet secure way of implementing visual cryptography with colour, ... More

GCD sums and complete sets of square-free numbersFeb 02 2014Oct 12 2014It is proved that \[ \sum_{k,{\ell}=1}^N\frac{\gcd(n_k,n_{\ell})}{\sqrt{n_k n_{\ell}}} \ll N\exp\left(C\sqrt{\frac{\log N \log\log\log N}{\log\log N}}\right) \] holds for arbitrary integers $1\le n_1<\cdots < n_N$. This bound is essentially better than ... More

Note on the resonance method for the Riemann zeta functionJan 18 2017We improve Montgomery's $\Omega$-results for $|\zeta(\sigma+it)|$ in the strip $1/2<\sigma<1$ and give in particular lower bounds for the maximum of $|\zeta(\sigma+it)|$ on $\sqrt{T}\le t \le T$ that are uniform in $\sigma$. We give similar lower bounds ... More

Simulating Viscous Fingering with a Timespace Method and Anisotropic Mesh AdaptationAug 17 2015We report findings related to a two dimensional viscous fingering problem solved with a timespace method and anisotropic elements. Timespace methods have attracted interest for solution of time dependent partial differential equations due to the implications ... More

String Theory and the Vacuum Structure of Confining Gauge TheoriesSep 25 2004We discuss recent progress in the understanding of the vacuum structure (effective superpotentials) of confining gauge theories with N=1 supersymmetry. Even for non-supersymmetric theories, appropriate perturbative calculations (e.g. using the background ... More

A Geometrical Construction of Rational Boundary States in Linear Sigma ModelsMar 28 2002Dec 12 2002Starting from the geometrical construction of special Lagrangian submanifolds of a toric variety, we identify a certain subclass of A-type D-branes in the linear sigma model for a Calabi-Yau manifold and its mirror with the A- and B-type Recknagel-Schomerus ... More

Niels Bohr as Philosopher of Experiment: Does Decoherence Theory Challenge Bohr's Doctrine of Classical Concepts?Feb 23 2015Niels Bohr's doctrine of the primacy of "classical concepts" is arguably his most criticized and misunderstood view. We present a new, careful historical analysis that makes clear that Bohr's doctrine was primarily an epistemological thesis, derived from ... More

Sommerfeld Enhancement from Multiple MediatorsMar 28 2012Mar 30 2013We study the Sommerfeld enhancement experienced by a scattering object that couples to a tower of mediators. This can occur in, e.g., models of secluded dark matter when the mediator scale is generated naturally by hidden-sector confinement. Specializing ... More

Sensitivity to temperature perturbations of the ageing states in a re-entrant ferromagnetSep 03 1998Dynamic magnetic properties and ageing phenomena of the re-entrant ferromagnet (Fe0.20Ni0.80)75P16B6Al3 are investigated by time dependent zero field cooled magnetic relaxation, m (t), measurements. The influence of a temperature cycling (perturbation), ... More

A statistical framework for fair predictive algorithmsOct 25 2016Predictive modeling is increasingly being employed to assist human decision-makers. One purported advantage of replacing human judgment with computer models in high stakes settings-- such as sentencing, hiring, policing, college admissions, and parole ... More

Creating massive entanglement of Bose condensed atomsApr 26 2001Apr 30 2001We propose a direct, coherent coupling scheme that can create massively entangled states of Bose-Einstein condensed atoms. Our idea is based on an effective interaction between two atoms from coherent Raman processes through a (two atom) molecular intermediate ... More

Approximation numbers of composition operators on the $H^2$ space of Dirichlet seriesFeb 17 2013Dec 09 2014By a theorem of Gordon and Hedenmalm, $\varphi$ generates a bounded composition operator on the Hilbert space $\mathscr{H}^2$ of Dirichlet series $\sum_n b_n n^{-s}$ with square-summable coefficients $b_n$ if and only if $\varphi(s)=c_0 s+\psi(s)$, where ... More

Conic bundles in projective fourspaceSep 27 1993P. Ellia and G.Sacchiero have shown that if $S$ is a smooth surface in $\Pn 4$ which is ruled in conics, then $S$ has degree 4 or 5. In this paper we give a proof of this result combining the ideas of Ellia and Sacchiero as they are used in the paper ... More

Addendum to "K3-surfaces of genus 8 and varieties of sums of powers of cubic fourfolds"Nov 17 2006In this note, which is an addendum to the e-print math.AG/9810121, we prove that the variety VSP(F,10) of presentations of a general cubic form F in 6 variables as a sum of 10 cubes is a smooth symplectic 4-fold, which is deformation equivalent to the ... More

K3-surfaces of genus 8 and varieties of sums of powers of cubic fourfoldsOct 19 1998Nov 17 2006The main outcome of this paper is that the variety VSP(F,10) of presentations of a general cubic form F in 6 variables as a sum of 10 cubes is a smooth symplectic 4-fold obtained a deformation of the Hilbert square of a K3 surface of genus 8. After publishing ... More

The Convex Hull of a VarietyApr 18 2010Jul 01 2010We present a characterization, in terms of projective biduality, for the hypersurfaces appearing in the boundary of the convex hull of a compact real algebraic variety.

Large GCD sums and extreme values of the Riemann zeta functionJul 21 2015Nov 23 2016It is shown that the maximum of $|\zeta(1/2+it)|$ on the interval $T^{1/2}\le t \le T$ is at least $\exp\left((1/\sqrt{2}+o(1)) \sqrt{\log T \log\log\log T/\log\log T}\right)$. Our proof uses Soundararajan's resonance method and a certain large GCD sum. ... More

Families of efficient second order Runge-Kutta methods for the weak approximation of Itô stochastic differential equationsMar 20 2013Recently, a new class of second order Runge-Kutta methods for It\^o stochastic differential equations with a multidimensional Wiener process was introduced by R\"o{\ss}ler. In contrast to second order methods earlier proposed by other authors, this class ... More

Continuous Weak Approximation for Stochastic Differential EquationsMar 18 2013A convergence theorem for the continuous weak approximation of the solution of stochastic differential equations by general one step methods is proved, which is an extension of a theorem due to Milstein. As an application, uniform second order conditions ... More

A micro/macro algorithm to accelerate Monte Carlo simulation of stochastic differential equationsSep 20 2010Nov 05 2011We present and analyze a micro/macro acceleration technique for the Monte Carlo simulation of stochastic differential equations (SDEs) in which there is a separation between the (fast) time-scale on which individual trajectories of the SDE need to be ... More

Convergence of Runge-Kutta Methods Applied to Linear Partial Differential-Algebraic EquationsMar 17 2013We apply Runge-Kutta methods to linear partial differential-algebraic equations of the form $Au_t(t,x) + B(u_{xx}(t,x)+ru_x(t,x))+Cu(t,x) = f(t,x)$, where $A,B,C\in\R^{n,n}$ and the matrix $A$ is singular. We prove that under certain conditions the temporal ... More

An optimal transport approach for solving dynamic inverse problems in spaces of measuresJan 29 2019In this paper we propose and study a novel optimal transport based regularization of linear dynamic inverse problems. The considered inverse problems aim at recovering a measure valued curve and are dynamic in the sense that (i) the measured data takes ... More

Mixed dark matter with low-mass bosonsJan 24 1996We calculate the linear power spectrum for a range of mixed dark matter (MDM) models assuming a massive (few eV) boson, $\phi$, instead of a neutrino as the hot component. We consider both the case where the hot dark matter (HDM) particle is a boson and ... More

Subarcsecond resolution observations of warm water towards three deeply embedded low-mass protostarsMar 22 2012Water is present during all stages of star formation: as ice in the cold outer parts of protostellar envelopes and dense inner regions of circumstellar disks, and as gas in the envelopes close to the protostars, in the upper layers of circumstellar disks ... More

Adaptable Radiative Transfer Innovations for Submillimeter Telescopes (ARTIST)Feb 23 2011Submillimeter observations are a key for answering many of the big questions in modern-day astrophysics, such as how stars and planets form, how galaxies evolve, and how material cycles through stars and the interstellar medium. With the upcoming large ... More

Cosmological Constant as a Manifestation of the HierarchyDec 14 2007Dec 20 2007There has been the suggestion that the cosmological constant as implied by the dark energy is related to the well-known hierarchy between the Planck scale, $M_{\rm Pl}$, and the Standard Model scale, $M_{\rm SM}$. Here we further propose that the same ... More

MIWAE: Deep Generative Modelling and Imputation of Incomplete DataDec 06 2018Feb 04 2019We consider the problem of handling missing data with deep latent variable models (DLVMs). First, we present a simple technique to train DLVMs when the training set contains missing-at-random data. Our approach, called MIWAE, is based on the importance-weighted ... More

Bayesian Logic ProgramsNov 23 2001Bayesian networks provide an elegant formalism for representing and reasoning about uncertainty using probability theory. Theyare a probabilistic extension of propositional logic and, hence, inherit some of the limitations of propositional logic, such ... More

Accurate Ground State Energies of Solids and Molecules from Time Dependent Density Functional TheoryMay 04 2014We demonstrate that ground state energies approaching chemical accuracy can be obtained by combining the adiabatic connection fluctuation-dissipation theorem (ACFDT) with time-dependent density functional theory (TDDFT). The key ingredient is a renormalization ... More

Static correlation beyond the random phase approximation: Dissociating H2 with the Bethe-Salpeter equation and time-dependent GWDec 19 2013May 04 2014We investigate various approximations to the correlation energy of a H$_2$ molecule in the dissociation limit, where the ground state is poorly described by a single Slater determinant. The correlation energies are derived from the density response function ... More

The random phase approximation applied to solids, molecules, and graphene-metal interfaces: From weak to strong binding regimesNov 29 2012Mar 01 2013The random phase approximation (RPA) is attracting renewed interest as a universal and accurate method for first-principles total energy calculations. The RPA naturally accounts for long-range dispersive forces without compromising accuracy for short ... More

Trapping of light pulses in ensembles of stationary Lambda atomsJan 18 2007We present a detailed theoretical description of the generation of stationary light pulses by standing wave electromagnetically induced transparency in media comprised of stationary atoms. We show that, contrary to thermal gas media, the achievable storage ... More

Harmonic measure and uniform densitiesMay 05 2003We study two problems concerning harmonic measure on "champagne subdomains" of the unit disk. These domains are obtained by removing from the unit disk little disks around sequences of points with a uniform distribution with respect to the pseudohyperbolic ... More

Conserving GW scheme for nonequilibrium quantum transport in molecular contactsOct 02 2007Apr 01 2008We give a detailed presentation of our recent scheme to include correlation effects in molecular transport calculations using the GW approximation within the non-equilibrium Keldysh formalism. We restrict the GW self-energy to the central region, and ... More

Warm water deuterium fractionation in IRAS 16293-2422 - The high-resolution ALMA and SMA viewNov 28 2012Measuring the water deuterium fractionation in the inner warm regions of low-mass protostars has so far been hampered by poor angular resolution obtainable with single-dish ground- and space-based telescopes. Observations of water isotopologues using ... More

Protostellar accretion traced with chemistry: Comparing synthetic C18O maps of embedded protostars to real observationsDec 01 2015Dec 19 2015Context: Understanding how protostars accrete their mass is a central question of star formation. One aspect of this is trying to understand whether the time evolution of accretion rates in deeply embedded objects is best characterised by a smooth decline ... More

Role of friction-induced torque in stick-slip motionJun 11 2010Dec 30 2010We present a minimal quasistatic 1D model describing the kinematics of the transition from static friction to stick-slip motion of a linear elastic block on a rigid plane. We show how the kinematics of both the precursors to frictional sliding and the ... More