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Evolved Art with Transparent, Overlapping, and Geometric ShapesApr 12 2019In this work, an evolutionary art project is presented where images are approximated by transparent, overlapping and geometric shapes of different types, e.g., polygons, circles, lines. Genotypes representing features and order of the geometric shapes ... More

Numerical upscaling of discrete network modelsOct 11 2018In this paper a numerical multiscale method for discrete networks is presented. The method gives an accurate coarse scale representation of the full network by solving sub-network problems. The method is used to solve problems with highly varying connectivity ... More

Perfect Skolem setsJun 08 2005A Skolem sequence is a sequence a_1,a_2,...,a_2n (where a_i \in A = {1,...,n }), each a_i occurs exactly twice in the sequence and the two occurrences are exactly a_i positions apart. A set A that can be used to construct Skolem sequences is called a ... More

Hadronic light-by-light scattering in the anomalous magnetic moment of the muonNov 20 2018Hadronic light-by-light scattering in the anomalous magnetic moment of the muon $a_\mu$ is one of two hadronic effects limiting the precision of the Standard Model prediction for this precision observable, and hence the new-physics discovery potential ... More

Carleman-Sobolev classes for small exponentsApr 11 2014Apr 17 2014This paper is devoted to the study of a generalization of Sobolev spaces for small $L^{p}$ exponents, i.e. $0<p<1$. We consider spaces defined as abstract completions of certain classes of smooth functions with respect to weighted quasi-norms, simultaneously ... More

Invariants of the special orthogonal group and an enhanced Brauer categoryDec 13 2016We first give a short intrinsic, diagrammatic proof of the First Fundamental Theorem of invariant theory (FFT) for the special orthogonal group $\text{SO}_m(\mathbb{C})$, given the FFT for $\text{O}_m(\mathbb{C})$. We then define, by means of a presentation ... More

The second fundamental theorem of invariant theory for the orthogonal groupFeb 16 2011Let $V=\C^n$ be endowed with an orthogonal form and $G=\Or(V)$ be the corresponding orthogonal group. Brauer showed in 1937 that there is a surjective homomorphism $\nu:B_r(n)\to\End_G(V^{\otimes r})$, where $B_r(n)$ is the $r$-string Brauer algebra with ... More

The resolution of the Nirenberg-Treves conjectureMar 17 2003In this paper we give a proof of the Nirenberg-Treves conjecture: that local solvability of principal type pseudo-differential operators is equivalent to condition ($\Psi$). This condition rules out certain sign changes of the imaginary part of the principal ... More

The Solvability and Subellipticity of Systems of Pseudodifferential OperatorsMay 24 2008Dec 28 2008The paper studies the local solvability and subellipticity for square systems of principal type. These are the systems for which the principal symbol vanishes of first order on its kernel. For systems of principal type having constant characteristics, ... More

An algebraic characterization of the Kronecker functionJun 13 2018Jan 22 2019We characterize the generating series of extended period polynomials of normalized Hecke eigenforms for $\operatorname{PSL}_2(\mathbb Z)$ studied by Zagier in terms of the period relations and existence of a suitable factorization. For this we prove a ... More

The meta-abelian elliptic KZB associator and periods of Eisenstein seriesAug 02 2016Nov 14 2017We compute the image of Enriquez' elliptic KZB associator in the (maximal) meta-abelian quotient of the fundamental Lie algebra of a once-punctured elliptic curve. Our main result is an explicit formula for this image in terms of Eichler integrals of ... More

The primitive solutions to x^3+y^9=z^2Oct 31 2003We determine the rational integers x,y,z such that x^3+y^9=z^2 and gcd(x,y,z)=1. First we determine a finite set of curves of genus 10 such that any primitive solution to x^3+y^9=z^2 corresponds to a rational point on one of those curves. We observe that ... More

Visualising Sha[2] in Abelian SurfacesSep 13 2002Given an elliptic curve E1 over a number field and an element s in its 2-Selmer group, we give two different ways to construct infinitely many Abelian surfaces A such that the homogeneous space representing s occurs as a fibre of A over another elliptic ... More

On the algebraic structure of iterated integrals of quasimodular formsAug 15 2017Oct 26 2017We study the algebra $\mathcal{I}^{QM}$ of iterated integrals of quasimodular forms for $\operatorname{SL}_2(\mathbb{Z})$, which is the smallest extension of the algebra $QM_{\ast}$ of quasimodular forms, which is closed under integration. We prove that ... More

An introduction to singular stochastic PDEs: Allen-Cahn equations, metastability and regularity structuresJan 22 2019These notes have been prepared for a series of lectures to be given at the Sarajevo Stochastic Analysis Winter School, from January 28 to February 1, 2019. There already exist several excellent lecture notes and reviews on the subject, such as (Hairer ... More

Noise-induced phase slips, log-periodic oscillations, and the Gumbel distributionMar 28 2014Oct 02 2014When two synchronised phase oscillators are perturbed by weak noise, they display occasional losses of synchrony, called phase slips. The slips can be characterised by their location in phase space and their duration. We show that when properly normalised, ... More

A scale-invariant model of marine population dynamicsMar 24 2010Sep 16 2010A striking feature of the marine ecosystem is the regularity in its size spectrum: the abundance of organisms as a function of their weight approximately follows a power law over almost ten orders of magnitude. We interpret this as evidence that the population ... More

The index bundle for Fredholm morphismsSep 03 2012We extend the index bundle construction for families of bounded Fredholm operators to morphisms between Banach bundles.

Explicit projective embeddings of standard opens of the Hilbert scheme of pointsMay 24 2016We describe explicitly how certain standard opens of the Hilbert scheme of points are embedded into Grassmannians. The standard opens of the Hilbert scheme that we consider are given as the intersection of a corresponding basic open affine of the Grassmannian ... More

FractalNet: Ultra-Deep Neural Networks without ResidualsMay 24 2016We introduce a design strategy for neural network macro-architecture based on self-similarity. Repeated application of a single expansion rule generates an extremely deep network whose structural layout is precisely a truncated fractal. Such a network ... More

Measuring thickness in thin NbN films for superconducting devicesDec 13 2018Jan 04 2019We present the use of a commercially available fixed-angle multi-wavelength ellipsometer for quickly measuring the thickness of NbN thin films for the fabrication and performance improvement of superconducting nanowire single photon detectors. The process ... More

Systemic Greeks: Measuring risk in financial networksOct 28 2018Since the latest financial crisis, the idea of systemic risk has received considerable interest. In particular, contagion effects arising from cross-holdings between interconnected financial firms have been studied extensively. Drawing inspiration from ... More

Interface dynamics of a metastable mass-conserving spatially extended diffusionAug 18 2015We study the metastable dynamics of a discretised version of the mass-conserving stochastic Allen-Cahn equation. Consider a periodic one-dimensional lattice with $N$ sites, and attach to each site a real-valued variable, which can be interpreted as a ... More

Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensionsApr 12 2015Jun 16 2015We prove local existence of solutions for a class of suitably renormalised coupled SPDE-ODE systems driven by space-time white noise, where the space dimension is equal to 2 or 3. This class includes in particular the FitzHugh-Nagumo system describing ... More

Erratum for "Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions"May 08 2018Lemma 4.8 in the article [Regularity structures and renormalisation of FitzHugh-Nagumo SPDEs in three space dimensions, Electronic J. Probability 21 (18):1-48 (2016), arXiv:1504.02953] contains a mistake, which implies a weaker regularity estimate than ... More

Stable shock formation for nearly simple outgoing plane symmetric wavesJan 06 2016Oct 03 2016In an influential 1964 article, P. Lax studied $2 \times 2$ genuinely nonlinear strictly hyperbolic PDE systems (in one spatial dimension). Using the method of Riemann invariants, he showed that a large set of smooth initial data lead to bounded solutions ... More

Hartogs' extension theorems on Stein spacesDec 17 2008Mar 24 2009We discuss various known generalizations of the classical Hartogs' extension theorem on Stein spaces with arbitrary singularities and present an analytic proof based on d-bar methods.

Nonmeromorphic operator product expansion and C_2-cofiniteness for a family of W-algebrasAug 08 2005Dec 05 2005We prove the existence and associativity of the nonmeromorphic operator product expansion for an infinite family of vertex operator algebras, the triplet W-algebras, using results from P(z)-tensor product theory. While doing this, we also show that all ... More

Uncertainty Estimates in the Heston Model via Fisher InformationOct 15 2016We address the information content of European option prices about volatility in terms of the Fisher information matrix. We assume that observed option prices are centred on the theoretical price provided by Heston's model disturbed by additive Gaussian ... More

On Ecalle's and Brown's polar solutions to the double shuffle equations modulo productsMay 24 2018Two explicit sets of solutions to the double shuffle equations modulo products were introduced by Ecalle and Brown respectively. We place the two solutions into the same algebraic framework and compare them. We find that they agree up to and including ... More

Arithmetic aspects of the Burkhardt quartic threefoldMay 25 2017May 29 2018We show that the Burkhardt quartic threefold is rational over any field of characteristic distinct from 3. We compute its zeta function over finite fields. We realize one of its moduli interpretations explicitly by determining a model for the universal ... More

On the noise-induced passage through an unstable periodic orbit II: General caseAug 13 2012Jul 24 2013Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the system's first exit ... More

Betti numbers for certain Cohen-Macaulay tangent conesMar 20 2018Oct 02 2018In this article, we compute Betti numbers for a Cohen-Macaulay tangent cone of a monomial curve in the affine $4$-space corresponding to a pseudo symmetric numerical semigroup. As a byproduct, we also show that for these semigroups, being of homogeneous ... More

The Mordell-Weil sieve: Proving non-existence of rational points on curvesJun 10 2009Nov 30 2009We discuss the Mordell-Weil sieve as a general technique for proving results concerning rational points on a given curve. In the special case of curves of genus 2, we describe quite explicitly how the relevant local information can be obtained if one ... More

The topology of arrangements of ideal typeJan 22 2018Oct 24 2018In 1962, Fadell and Neuwirth showed that the configuration space of the braid arrangement is aspherical. Having generalized this to many real reflection groups, Brieskorn conjectured this for all finite Coxeter groups. This in turn follows from Deligne's ... More

Reduction mod $\ell$ of Theta Series of Level $\ell^n$Jul 29 2008Oct 21 2008It is proved that the theta series of an even lattice whose level is a power of a prime $\ell$ is congruent modulo $\ell$ to an elliptic modular form of level~1. The proof uses arithmetic and algebraic properties of lattices rather than methods from the ... More

Median-Based Generation of Synthetic Speech Durations using a Non-Parametric ApproachAug 22 2016This paper proposes a new approach to duration modelling for statistical parametric speech synthesis in which a recurrent statistical model is trained to output a phone transition probability at each timestep (acoustic frame). Unlike conventional approaches ... More

Shock Formation in Small-Data Solutions to $3D$ Quasilinear Wave Equations: An OverviewJul 23 2014In his 2007 monograph, D. Christodoulou proved a remarkable result giving a detailed description of shock formation, for small $H^s$-initial conditions ($s$ sufficiently large), in solutions to the relativistic Euler equations in three space dimensions. ... More

Deep Encoder-Decoder Models for Unsupervised Learning of Controllable Speech SynthesisJul 30 2018Sep 09 2018Generating versatile and appropriate synthetic speech requires control over the output expression separate from the spoken text. Important non-textual speech variation is seldom annotated, in which case output control must be learned in an unsupervised ... More

Sheldon Spectrum and the Plankton Paradox: Two Sides of the Same Coin. A trait-based plankton size-spectrum modelJul 14 2016The Sheldon spectrum describes a remarkable regularity in aquatic ecosystems: the biomass density as a function of logarithmic body mass is approximately constant over many orders of magnitude. While size-spectrum models have explained this phenomenon ... More

Minimal models for rational functions in a dynamical settingApr 23 2012Oct 25 2012We present a practical algorithm to compute models of rational functions with minimal resultant under conjugation by fractional linear transformations. We also report on a search for rational functions of degrees 2 and 3 with rational coefficients that ... More

Spectral theory for random Poincaré mapsNov 15 2016Apr 21 2017We consider stochastic differential equations, obtained by adding weak Gaussian white noise to ordinary differential equations admitting $N$ asymptotically stable periodic orbits. We construct a discrete-time, continuous-space Markov chain, called a random ... More

Deciding existence of rational points on curves: an experimentApr 25 2006We consider all genus 2 curves over Q given by an equation y^2 = f(x) with f a squarefree polynomial of degree 5 or 6, with integral coefficients of absolute value at most 3. For each of these roughly 200000 isomorphism classes of curves, we decide if ... More

The Full-Color Two-Loop Four-Gluon Amplitude in $\mathcal{N} = 2$ Super-QCDApr 10 2019We present the fully integrated form of the two-loop four-gluon amplitude in $\mathcal{N} = 2$ supersymmetric quantum chromodynamics with gauge group SU$(N_c)$ and with $N_f$ massless supersymmetric quarks (hypermultiplets) in the fundamental representation. ... More

Realizing lateral wrap-gated nanowire FETs: Controlling gate length with chemistry rather than lithographyJan 18 2012An important consideration in miniaturizing transistors is maximizing the coupling between the gate and the semiconductor channel. A nanowire with a coaxial metal gate provides optimal gate-channel coupling, but has only been realized for vertically oriented ... More

Pencils and nets of small degree on curves on smooth, projective surfaces of Picard rank 1 and very ample generatorMay 12 2015Aug 18 2015Let S be a smooth, projective surface of Picard rank 1 and very ample generator embedding S into P^n. Let C be a smooth curve in O(m) for m \geq 5. We prove that any base-point free, complete g^r_d on C for r\in\{1,2\} and d small enough is cut out by ... More

A concentration phenomenon for semilinear elliptic equationsJun 14 2012Jun 18 2012For a domain $\Omega\subset\dR^N$ we consider the equation $ -\Delta u + V(x)u = Q_n(x)\abs{u}^{p-2}u$ with zero Dirichlet boundary conditions and $p\in(2,2^*)$. Here $V\ge 0$ and $Q_n$ are bounded functions that are positive in a region contained in ... More

The arithmetic of genus two curves with (4,4)-split JacobiansFeb 19 2009Apr 22 2011In this paper we study genus 2 curves whose Jacobians admit a polarized (4,4)-isogeny to a product of elliptic curves. We consider base fields of characteristic different from 2 and 3, which we do not assume to be algebraically closed. We obtain a full ... More

Automated Local Fourier Analysis (aLFA)Nov 05 2018Jan 23 2019Local Fourier analysis is a commonly used tool to assess the quality of geometric multigrid methods for translationally invariant operators. In this paper we completely automate the process of local Fourier analysis and generalize it to arbitrary, including ... More

Model Spaces of Regularity Structures for Space-Fractional SPDEsJan 11 2017Feb 26 2017We study model spaces, in the sense of Hairer, for stochastic partial differential equations involving the fractional Laplacian. We prove that the fractional Laplacian is a singular kernel suitable to apply the theory of regularity structures. Our main ... More

The International Linear Collider. A European PerspectiveJan 28 2019The International Linear Collider (ILC) being proposed in Japan is an electron-positron linear collider with an initial energy of 250 GeV. The ILC accelerator is based on the technology of superconducting radio-frequency cavities. This technology has ... More

Probing the neutron star interior and the Equation of State of cold dense matter with the SKADec 30 2014With an average density higher than the nuclear density, neutron stars (NS) provide a unique test-ground for nuclear physics, quantum chromodynamics (QCD), and nuclear superfluidity. Determination of the fundamental interactions that govern matter under ... More

Visualizing elements of Sha[3] in genus 2 jacobiansJan 29 2010Mazur proved that any element xi of order three in the Shafarevich-Tate group of an elliptic curve E over a number field k can be made visible in an abelian surface A in the sense that xi lies in the kernel of the natural homomorphism between the cohomology ... More

SL(2,Z)-Invariant Spaces Spanned by Modular UnitsApr 03 1997Sep 02 2005Characters of rational vertex operator algebras (RVOAs) arising in 2-dimensional conformal field theories often belong (after suitable normalization) to the (multiplicative) semigroup E^+ of modular units whose Fourier expansions are in 1+q Z_{>=0}[[q]], ... More

Homogenization of a Wilson-Cowan model for neural fieldsApr 29 2012Nov 09 2012Homogenization of Wilson-Cowan type of nonlocal neural field models is investigated. Motivated by the presence of a convolution terms in this type of models, we first prove some general convergence results related to convolution sequences. We then apply ... More

Maslov class rigidity for Lagrangian submanifolds via Hofer's geometryAug 10 2008In this work, we establish new rigidity results for the Maslov class of Lagrangian submanifolds in large classes of closed and convex symplectic manifolds. Our main result establishes upper bounds for the minimal Maslov number of displaceable Lagrangian ... More

On Quantum Lie Algebras and Quantum Root SystemsJun 22 1995Feb 06 1996As a natural generalization of ordinary Lie algebras we introduce the concept of quantum Lie algebras ${\cal L}_q(g)$. We define these in terms of certain adjoint submodules of quantized enveloping algebras $U_q(g)$ endowed with a quantum Lie bracket ... More

The effect of classical noise on a quantum two-level systemMay 07 2008We consider a quantum two-level system perturbed by classical noise. The noise is implemented as a stationary diffusion process in the off-diagonal matrix elements of the Hamiltonian, representing a transverse magnetic field. We determine the invariant ... More

Follow-the-Leader models can be viewed as a numerical approximation to the Lighthill-Whitham-Richards model for traffic flowFeb 06 2017Sep 21 2017We show how to view the standard Follow-the-Leader (FtL) model as a numerical method to compute numerically the solution of the Lighthill--Whitham--Richards (LWR) model for traffic flow. As a result we offer a simple proof that FtL models converge to ... More

Models for dense multilane vehicular trafficDec 04 2018We study vehicular traffic on a road with multiple lanes and dense, unidirectional traffic following the traditional Lighthill-Whitham-Richards model where the velocity in each lane depends only on the density in the same lane. The model assumes that ... More

Fast Dynamic ArraysNov 01 2017We present a highly optimized implementation of tiered vectors, a data structure for maintaining a sequence of $n$ elements supporting access in time $O(1)$ and insertion and deletion in time $O(n^\epsilon)$ for $\epsilon > 0$ while using $o(n)$ extra ... More

Tuning of the Rashba effect in Pb quantum well states via a variable Schottky barrierFeb 21 2013Spin-orbit interaction (SOI) in low-dimensional systems results in the fascinating property of spin-momentum locking. In a Rashba system the inversion symmetry normal to the plane of a two-dimensional (2D) electron gas is broken, generating a Fermi surface ... More

Competing edge structures of Sb and Bi bilayers by trivial and nontrivial band topologiesJun 12 2018One-dimensional (1D) edge states formed at the boundaries of 2D normal and topological insulators have shown intriguing quantum phases such as charge density wave and quantum spin Hall effect. Based on first-principles density-functional theory calculations ... More

AVRA: Automatic Visual Ratings of Atrophy from MRI images using Recurrent Convolutional Neural NetworksDec 23 2018Quantifying the degree of atrophy is done clinically by neuroradiologists following established visual rating scales. For these assessments to be reliable the rater requires substantial training and experience, and even then the rating agreement between ... More

Self-Supervised Relative Depth Learning for Urban Scene UnderstandingDec 13 2017Apr 02 2018As an agent moves through the world, the apparent motion of scene elements is (usually) inversely proportional to their depth. It is natural for a learning agent to associate image patterns with the magnitude of their displacement over time: as the agent ... More

Boundary clustered layers near the higher critical exponentsNov 11 2012We consider the supercritical problem {equation*} -\Delta u=|u| ^{p-2}u\text{\in}\Omega,\quad u=0\text{\on}\partial\Omega, {equation*} where $\Omega$ is a bounded smooth domain in $\mathbb{R}^{N}$ and $p$ smaller than the critical exponent $2_{N,k}^{\ast}:=\frac{2(N-k)}{N-k-2}$ ... More

On the existence of homoclinic type solutions of a class of inhomogenous second order Hamiltonian systemsOct 06 2018We show the existence of homoclinic type solutions of second order Hamiltonian systems with a potential satisfying a relaxed superquadratic growth condition and a forcing term that is sufficiently small in the space of square integrable functions. The ... More

On inductively free Restrictions of Reflection ArrangementsOct 07 2013Jul 21 2014Let W be a finite complex reflection group acting on the complex vector space V and let A(W) = (A(W), V) be the associated reflection arrangement. In an earlier paper by the last two authros, we classified all inductively free reflection arrangements ... More

Elliptic multiple zeta values and the elliptic double shuffle relationsMar 28 2017We study the algebra $\mathcal{E}$ of elliptic multiple zeta values, which is an elliptic analog of the algebra of multiple zeta values. We identify a set of generators of $\mathcal{E}$, which satisfy a double shuffle type family of algebraic relations, ... More

Higher-order Airy scaling in deformed Dyck pathsJun 22 2016Dec 03 2016We introduce a deformed version of Dyck paths (DDP), where additional to the steps allowed for Dyck paths, 'jumps' orthogonal to the preferred direction of the path are permitted. We consider the generating function of DDP, weighted with respect to their ... More

Critical behavior of weakly interacting bosons: A functional renormalization group approachSep 07 2004We present a detailed investigation of the momentum-dependent self-energy Sigma(k) at zero frequency of weakly interacting bosons at the critical temperature T_c of Bose-Einstein condensation in dimensions 3<=D<4. Applying the functional renormalization ... More

Descent via (3,3)-isogeny on Jacobians of genus 2 curvesJan 03 2014We give parametrisation of curves C of genus 2 with a maximal isotropic (ZZ/3)^2 in J[3], where J is the Jacobian variety of C, and develop the theory required to perform descent via (3,3)-isogeny. We apply this to several examples, where it can shown ... More

A Relativistic Interpretation of Bias in Newtonian SimulationsOct 25 2018Feb 25 2019Observables of cosmic structures are usually not the underlying matter field but biased tracers of matter, such as galaxies or halos. We show how the bias found in Newtonian N-body simulations can be interpreted in terms of the weak-field limit of General ... More

An Eyring-Kramers law for the stochastic Allen-Cahn equation in dimension twoApr 19 2016Jan 21 2017We study spectral Galerkin approximations of an Allen--Cahn equation over the two-dimensional torus perturbed by weak space-time white noise of strength $\sqrt{\varepsilon}$. We introduce a Wick renormalisation of the equation in order to have a system ... More

On Ladder Logic Bombs in Industrial Control SystemsFeb 17 2017In industrial control systems, devices such as Programmable Logic Controllers (PLCs) are commonly used to directly interact with sensors and actuators, and perform local automatic control. PLCs run software on two different layers: a) firmware (i.e. the ... More

Decoding of neural data using cohomological feature extractionNov 20 2017Sep 10 2018We introduce a novel data-driven approach to discover and decode features in the neural code coming from large population neural recordings with minimal assumptions, using cohomological feature extraction. We apply our approach to neural recordings of ... More

Multilinear processes in Banach spaceSep 05 2018A process $(X(t))_{t\geq 0}$ taking values in $\mathbb R^d$ is called a polynomial process if for every polynomial $p$ of degree $n$ on $\mathbb R^d$, there exists another polynomial $q$ of degree at most $n$ such that $E[p(X(t))|\mathcal F_s] = q(X(s))$ ... More

Joint state-parameter estimation of a nonlinear stochastic energy balance model from sparse noisy dataApr 10 2019While nonlinear stochastic partial differential equations arise naturally in spatiotemporal modeling, inference for such systems often faces two major challenges: sparse noisy data and ill-posedness of the inverse problem of parameter estimation. To overcome ... More

Numerical computation of endomorphism ringsJul 07 2018We give practical numerical methods to compute the period matrix of a plane algebraic curve (not necessarily smooth). We show how automorphisms and isomorphisms of such curves, as well as the decomposition of their Jacobians up to isogeny, can be calculated ... More

Restrictions of aspherical arrangementsMar 09 2018Sep 20 2018In this note we present examples of $K(\pi,1)$-arrangements which admit a restriction which fails to be $K(\pi,1)$. This shows that asphericity is not hereditary among hyperplane arrangements.

On the $K(π, 1)$-problem for restrictions of complex reflection arrangementsAug 17 2017Jan 01 2019Let $W\subset GL(V)$ be a complex reflection group, and ${\mathscr A}(W)$ the set of the mirrors of the complex reflections in $W$. It is known that the complement $X({\mathscr A}(W))$ of the reflection arrangement ${\mathscr A}(W)$ is a $K(\pi,1)$ space. ... More

Local dissipation limits the dynamics of impacting droplets on smooth and rough substratesNov 15 2016A droplet that impacts onto a solid substrate deforms in a complex dynamics. To extract the principal mechanisms that dominate this dynamics we deploy numerical simulations based on the phase field method. Direct comparison with experiments suggests that ... More

Universality in dynamic wetting dominated by contact line frictionNov 04 2011Mar 14 2012We report experiments on the rapid contact line motion present in the early stages of capillary driven spreading of drops on dry solid substrates. The spreading data fails to follow a conventional viscous or inertial scaling. By integrating experiments ... More

Bootstrap percolation in directed and inhomogeneous random graphsNov 25 2015Bootstrap percolation is a process that is used to model the spread of an infection on a given graph. In the model considered here each vertex is equipped with an individual threshold. As soon as the number of infected neighbors exceeds that threshold, ... More

Operator splitting for partial differential equations with Burgers nonlinearityFeb 21 2011We provide a new analytical approach to operator splitting for equations of the type $u_t=Au+u u_x$ where $A$ is a linear differential operator such that the equation is well-posed. Particular examples include the viscous Burgers' equation, the Korteweg-de ... More

Complex Valued Gated Auto-encoder for Video Frame PredictionMar 08 2019In recent years, complex valued artificial neural networks have gained increasing interest as they allow neural networks to learn richer representations while potentially incorporating less parameters. Especially in the domain of computer graphics, many ... More

Stochastic Volterra integral equations and a class of first order stochastic partial differential equationsMar 12 2019We investigate stochastic Volterra equations and their limiting laws. The stochastic Volterra equations we consider are driven by a Hilbert space valued \Levy noise and integration kernels may have non-linear dependence on the current state of the process. ... More

Probing the neutron skin thickness in collective modes of excitationJan 13 2014Nuclear collective motion provides valuable constraint on the size of neutron-skin thickness and the properties of nuclear matter symmetry energy. By employing relativistic nuclear energy density functional (RNEDF) and covariance analysis related to $\chi^2$ ... More

A scalable multi-photon coincidence detector based on superconducting nanowiresNov 28 2017Coincidence detection of single photons is crucial in numerous quantum technologies and usually requires multiple time-resolved single-photon detectors. However, the electronic readout becomes a major challenge when the measurement basis scales to large ... More

The intimate relation between the low T/W instability and the co-rotation pointSep 02 2014We study the low T/W instability associated with the f-mode of differentially rotating stars. Our stellar models are described by a polytropic equation of state and the rotation profile is given by the standard j-constant law. The properties of the relevant ... More

Jitter Characterization of a Dual-Readout SNSPDNov 05 2018Jan 18 2019To better understand the origins of the timing resolution, also known as jitter, of superconducting nanowire single-photon detectors (SNSPDs), we have performed timing characterizations of a niobium nitride SNSPD with a dual-ended readout. By simultaneously ... More

Convergence of a fully discrete finite difference scheme for the Korteweg-de Vries equationAug 31 2012We prove convergence of a fully discrete finite difference scheme for the Korteweg--de Vries equation. Both the decaying case on the full line and the periodic case are considered. If the initial data $u|_{t=0}=u_0$ is of high regularity, $u_0\in H^3(\R)$, ... More

From random Poincaré maps to stochastic mixed-mode-oscillation patternsDec 22 2013Nov 14 2014We quantify the effect of Gaussian white noise on fast--slow dynamical systems with one fast and two slow variables, which display mixed-mode oscillations owing to the presence of a folded-node singularity. The stochastic system can be described by a ... More

Fusion of Object Tracking and Dynamic Occupancy Grid MapApr 18 2019Environment modeling in autonomous driving is realized by two fundamental approaches, grid-based and feature-based approach. Both methods interpret the environment differently and show some situation-dependent beneficial realizations. In order to use ... More

Existence of martingale solutions and large-time behavior for a stochastic mean curvature flow of graphsMar 12 2019We are concerned with a stochastic mean curvature flow of graphs over a periodic domain of any space dimension. We establish existence of martingale solutions which are strong in the PDE sense and study their large-time behavior. Our analysis is based ... More

On formal groups and Tate cohomology in local fieldsDec 14 2016Let $L/K$ be a Galois extension of local fields of characteristic $0$ with Galois group $G$. If $\mathcal{F}$ is a formal group over the ring of integers in $K$, one can associate to $\mathcal F$ and each positive integer $n$ a $G$-module $F_L^n$ which ... More

Comparison of first-principles methods to extract magnetic parameters in ultra-thin films: Co/Pt(111)Apr 15 2019We compare three distinct computational approaches based on first-principles calculations within density functional theory to explore the magnetic exchange and the Dzyaloshinskii-Moriya interactions (DMI) of a Co monolayer on Pt(111), namely (i) the method ... More

An explicit finite difference scheme for the Camassa-Holm equationFeb 21 2008We put forward and analyze an explicit finite difference scheme for the Camassa-Holm shallow water equation that can handle general $H^1$ initial data and thus peakon-antipeakon interactions. Assuming a specified condition restricting the time step in ... More

Extending the scope of empirical likelihoodApr 20 2009This article extends the scope of empirical likelihood methodology in three directions: to allow for plug-in estimates of nuisance parameters in estimating equations, slower than $\sqrt{n}$-rates of convergence, and settings in which there are a relatively ... More

Fractal Dimension Invariant Filtering and Its CNN-based ImplementationMar 19 2016Mar 17 2017Fractal analysis has been widely used in computer vision, especially in texture image processing and texture analysis. The key concept of fractal-based image model is the fractal dimension, which is invariant to bi-Lipschitz transformation of image, and ... More