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Anti-de Sitter massless scalar field spacetimes in arbitrary dimensionsMar 21 2012Jun 07 2012We consider $d$-dimensional static spacetimes in Einstein gravity with a cosmological constant in the presence of a minimally coupled massless scalar field. The spacetimes have a $(d-2)$-dimensional base manifold given by an Einstein space and the massless ... More

A multipole-expanded effective field theory for vortex ring-sound interactionsSep 06 2017Feb 14 2018The low-energy dynamics of a zero temperature superfluid or of the compressional modes of an ordinary fluid can be described by a simple effective theory for a scalar field---the superfluid 'phase'. However, when vortex lines are present, to describe ... More

Flattened non-Gaussianities from the effective field theory of inflation with imaginary speed of soundMay 31 2018Nov 06 2018Inflationary perturbations in multi-field theories can exhibit a transient tachyonic instability as a consequence of their non-trivial motion in the internal field space. When an effective single-field description is applicable, the resulting theory is ... More

Consistent deformations of free massive field theories in the Stueckelberg formulationJun 12 2018Jul 11 2018Cohomological techniques within the Batalin-Vilkovisky (BV) extension of the Becchi-Rouet-Stora-Tyutin (BRST) formalism have proved invaluable for classifying consistent deformations of gauge theories. In this work we investigate the application of this ... More

Supersymmetric Partially Massless Fields and Non-Unitary Superconformal RepresentationsOct 03 2018We find and classify the ${\cal N}=1$ SUSY multiplets on AdS$_4$ which contain partially massless fields. We do this by studying the non-unitary representations of the $d=3$ superconformal algebra of the boundary. The simplest super-multiplet which contains ... More

Hyper non-Gaussianities in inflation with strongly non-geodesic motionFeb 08 2019Several recent proposals to embed inflation into high-energy physics rely on inflationary dynamics characterized by a strongly non-geodesic motion in negatively curved field space. This naturally leads to a transient instability of perturbations on sub-Hubble ... More

Asymmetry and spin-orbit coupling of light scattered from subwavelength particlesDec 17 2018Light scattering and spin-orbit angular momentum coupling phenomena from subwavelength objects, with electric and magnetic dipolar responses, are receiving an increasing interest. Under illumination by circularly polarized light, spin-orbit coupling effects ... More

Transition from Diffusive to Localized Regimes in Surface Corrugated Optical WaveguidesJan 30 1998Exact calculations of the transmittance of surface corrugated optical waveguides are presented. The elastic scattering of diffuse light or other electromagnetic waves from a rough surface induces a diffusive transport along the waveguide axis. As the ... More

Intensity Distribution of Modes in Surface Corrugated WaveguidesMay 20 1998Exact calculations of transmission and reflection coefficients in surface randomly corrugated optical waveguides are presented. As the length of the corrugated part of the waveguide increases, there is a strong preference to forward coupling through the ... More

First Sound in Holographic Superfluids at Zero TemperatureJun 09 2016Aug 18 2016Within the context of AdS/CFT, the gravity dual of an s-wave superfluid is given by scalar QED on an asymptotically AdS spacetime. While this conclusion is vastly supported by numerical arguments, here we provide an analytical proof that this is indeed ... More

A non-linear extension of the spin-2 partially massless symmetryOct 31 2014We investigate the possibility of extending the "partially massless" symmetry of a spin-2 field in de Sitter to nonlinear order. To do so, we impose a closure condition on the symmetry transformations. This requirement imposes strong constraints on the ... More

The KPZ Universality Class and Related TopicsApr 05 2019These notes are based on a talk given at the 2018 Arizona School of Analysis and Mathematical Physics. We give a comprehensive introduction to the KPZ universality class, a conjectured class of stochastic process with local interactions related to random ... More

A general class of holographic superconductorsJun 05 2009Sep 11 2009We introduce a simple generalization of the basic holographic superconductor model in which the spontaneous breaking of a global U(1) symmetry occurs via the Stueckelberg mechanism. This more general setting allows tuning features such as the order of ... More

A microfluidic platform for high-throughput multiplexed protein quantitationOct 20 2014We present a high-throughput microfluidic platform capable of quantitating up to 384 biomarkers in 4 distinct samples by immunoassay. The microfluidic device contains 384 unit cells, which can be individually programmed with pairs of capture and detection ... More

Primordial fluctuations and non-Gaussianities in sidetracked inflationApr 30 2018Jul 27 2018Heavy scalar fields can undergo an instability during inflation as a result of their kinetic couplings with the inflaton. This is known as the geometrical destabilization of inflation, as it relies on the effect of the negative curvature of the field-space ... More

Black Hole PulsarAug 23 2018Apr 15 2019In anticipation of a LIGO detection of a black hole/neutron star merger, we expand on the intriguing possibility of an electromagnetic counterpart. Black hole/Neutron star mergers could be disappointingly dark since most black holes will be large enough ... More

Black Hole PulsarAug 23 2018Dec 16 2018In anticipation of a LIGO detection of a black hole/neutron star merger, we expand on the intriguing possibility of an electromagnetic counterpart. Black hole/Neutron star mergers could be disappointingly dark since most black holes will be large enough ... More

Gravitino Dark Matter and Neutrino Masses in Partial Split SupersymmetryJun 01 2011Sep 25 2011Partial Split Supersymmetry with bilinear R-parity violation allows to reproduce all neutrino mass and mixing parameters. The viable dark matter candidate in this model is the gravitino. We study the hypothesis that both possibilities are true: Partial ... More

Bordered magic squares: elements for a comprehensive approachMay 19 2003Oct 20 2003General methods for the construction of magic squares of any order have been searched for centuries. There have been several standard strategies for this purpose, such as the knight movement, or the construction of bordered magic squares, which played ... More

Strong magnetic response of submicron Silicon particles in the infraredMay 29 2010High-permittivity dielectric particles with resonant magnetic properties are being explored as constitutive elements of new metamaterials and devices in the microwave regime. Magnetic properties of low-loss dielectric nanoparticles in the visible or infrared ... More

Exact theoretical description of two ultracold atoms in a single site of a 3D optical lattice using realistic interatomic interaction potentialsApr 16 2009May 12 2009A theoretical approach was developed for an exact numerical description of a pair of ultracold atoms interacting via a central potential that are trapped in a three-dimensional optical lattice. The coupling of center-of-mass and relative-motion coordinates ... More

On Net Maps: Examples and Nonexistence ResultsJul 04 2015A Thurston map is called nearly Euclidean if its local degree at each critical point is 2 and it has exactly four postcritical points. Nearly Euclidean Thurston (NET) maps are simple generalizations of rational Lattes maps. We investigate when such a ... More

Antiproton and proton collisions with the alkali metal atoms Li, Na, and KJan 02 2008Single-electron ionization and excitation cross sections as well as cross sections for excitation into the first excited p state of the alkali metal atoms Li(2s), Na(3s) and K(4s) colliding with antiprotons and protons were calculated using a time-dependent ... More

Proceedings of the first workshop on Flavor Symmetries and consequences in Accelerators and Cosmology (FLASY2011)Jan 26 2012The main goals of the first "Workshop on FLAvor SYmmetries and consequences in accelerators and cosmology" (FLASY) was to summarize the theoretical status of flavor symmetries, bringing together young researchers in the field to stimulate discussions ... More

A Structural Analysis of Field/Circuit Coupled Problems Based on a Generalised Circuit ElementJan 22 2018Mar 05 2018In some applications there arises the need of a spatially distributed description of a physical quantity inside a device coupled to a circuit. Then, the in-space discretised system of partial differential equations is coupled to the system of equations ... More

Break-down of the single-active-electron approximation for one-photon ionization of the B $^1Σ_u^+$ state of H$_2$ exposed to intense laser fieldsJan 27 2010Ionization, excitation, and de-excitation to the ground state is studied theoretically for the first excited singlet state B $^1\Sigma_u^+$ of H$_2$ exposed to intense laser fields with photon energies in between about 3 eV and 13 eV. A parallel orientation ... More

Influence of a tight isotropic harmonic trap on photoassociation in ultracold homonuclear alkali gasesSep 19 2006The influence of a tight isotropic harmonic trap on photoassociation of two ultracold alkali atoms forming a homonuclear diatomic is investigated using realistic atomic interaction potentials. Confinement of the initial atom pair due to the trap leads ... More

Collisions of antiprotons with hydrogen molecular ionsJun 30 2009Time-dependent close-coupling calculations of the ionization and excitation cross section for antiproton collisions with molecular hydrogen ions are performed in an impact-energy range from 0.5 keV to 10 MeV. The Born-Oppenheimer and Franck-Condon approximations ... More

Stopping power of antiprotons in H, H2, and He targetsDec 30 2008Mar 16 2009The stopping power of antiprotons in atomic and molecular hydrogen as well as helium was calculated in an impact-energy range from 1 keV to 6.4 MeV. In the case of H2 and He the targets were described with a single-active electron model centered on the ... More

Antiproton collisions with molecular hydrogenJul 08 2008Aug 25 2008Theoretical antiproton and proton cross sections for ionization and excitation of hydrogen molecules as well as energy spectra of the ionized electrons were calculated in the impact-energy range from 8 to 4000 keV. The cross sections were computed with ... More

Computing Koszul Homology for Monomial IdealsMay 12 2006The Koszul homology of modules of the polynomial ring $R$ is a central object in commutative algebra.It is strongly related with the minimal free resolution of these modules, and thus with regularity, Hilbert functions, etc. Here we consider the case ... More

Combinatorial Koszul Homology: Computations and ApplicationsMar 04 2008With a particular focus on explicit computations and applications of the Koszul homology and Betti numbers of monomial ideals, the main goals of this thesis are the following: Analyze the Koszul homology of monomial ideals and apply it to describe the ... More

Photodissociation of the {HeH$^+$} molecular ionMar 31 2009The photodissociation cross section of the molecular ion HeH$^+$ was calculated within the Born-Oppenheimer approximation for a parallel, a perpendicular, and an isotropic orientation of the molecular axis with respect to the field, considering also different ... More

Collisions of low-energy antiprotons with molecular hydrogen: ionization, excitation and stopping powerOct 31 2008A time-dependent coupled-channel approach was used to calculate ionization, excitation, and energy-loss cross sections as well as energy spectra for antiproton and proton collisions with molecular hydrogen for impact energies 8 keV < E < 4000 keV.

Reduced Order Modelling for the Simulation of Quenches in Superconducting MagnetsOct 13 2017This contributions discusses the simulation of magnetothermal effects in superconducting magnets as used in particle accelerators. An iterative coupling scheme using reduced order models between a magnetothermal partial differential model and an electrical ... More

Systems of Differential Algebraic Equations in Computational ElectromagneticsFeb 19 2018Nov 02 2018Starting from space-discretisation of Maxwell's equations, various classical formulations are proposed for the simulation of electromagnetic fields. They differ in the phenomena considered as well as in the variables chosen for discretisation. This contribution ... More

Axial field induced chiral channels in an acoustic Weyl systemJun 25 2018Condensed-matter and other engineered systems, such as cold atoms, photonic, or phononic metamaterials, have proven to be versatile platforms for the observation of low-energy counterparts of elementary particles from relativistic field theories. These ... More

Alignment-Dependent Ionization of Molecular Hydrogen in Intense Laser FieldsSep 24 2009The alignment dependence of the ionization behavior of H$_2$ exposed to intense ultrashort laser pulses is investigated on the basis of solutions of the full time-dependent Schr\"odinger equation within the fixed-nuclei and dipole approximation. The total ... More

No-go for Partially Massless Spin-2 Yang-MillsNov 10 2015Feb 11 2016There are various no-go results forbidding self-interactions for a single partially massless spin-2 field. Given the photon-like structure of the linear partially massless field, it is natural to ask whether a multiplet of such fields can interact under ... More

Theoretical description of two ultracold atoms in finite 3D optical lattices using realistic interatomic interaction potentialsJul 14 2011Aug 24 2011A theoretical approach is described for an exact numerical treatment of a pair of ultracold atoms interacting via a central potential that are trapped in a finite three-dimensional optical lattice. The coupling of center-of-mass and relative-motion coordinates ... More

Non-perturbative theoretical description of two atoms in an optical lattice with time-dependent perturbationsSep 02 2012A theoretical approach for a non-perturbative dynamical description of two interacting atoms in an optical lattice potential is introduced. The approach builds upon the stationary eigenstates found by a procedure described in Grishkevich et al. [Phys. ... More

Application of the Waveform Relaxation Technique to the Co-Simulation of Power Converter Controller and Electrical Circuit ModelsApr 10 2017In this paper we present the co-simulation of a PID class power converter controller and an electrical circuit by means of the waveform relaxation technique. The simulation of the controller model is characterized by a fixed-time stepping scheme reflecting ... More

Robust Gaussian Filtering using a Pseudo MeasurementSep 14 2015May 30 2016Many sensors, such as range, sonar, radar, GPS and visual devices, produce measurements which are contaminated by outliers. This problem can be addressed by using fat-tailed sensor models, which account for the possibility of outliers. Unfortunately, ... More

Optimized Field/Circuit Coupling for the Simulation of Quenches in Superconducting MagnetsFeb 03 2017Jul 06 2017In this paper, we propose an optimized field/circuit coupling approach for the simulation of magnetothermal transients in superconducting magnets. The approach improves the convergence of the iterative coupling scheme between a magnetothermal partial ... More

Painlevé equations, topological type property and reconstruction by the topological recursionJan 11 2016Oct 09 2017In this article we prove that Lax pairs associated with $\hbar$-dependent six Painlev\'e equations satisfy the topological type property proposed by Berg\`ere, Borot and Eynard for any generic choice of the monodromy parameters. Consequently we show that ... More

The RHIC Zero Degree CalorimeterAug 08 2000High Energy collisions of nuclei usually lead to the emission of evaporation neutrons from both ``beam'' and ``target'' nuclei. At the RHIC heavy ion collider with 100GeV/u beam energy, evaporation neutrons diverge by less than $~2$ milliradians from ... More

Size-Resolved Photoelectron Anisotropy of Gas Phase Water Clusters and Predictions for Liquid WaterDec 07 2016We report the first measurement of size-resolved photoelectron angular distributions for the valence orbitals of water clusters with up to 20 molecules. A systematic decrease of the photoelectron anisotropy is found for clusters with up to 5-6 molecules, ... More

Anomalous decoupling dynamics in glycerol and its nanocolloid with silver nanoparticlesOct 04 2014Orientational and translational decouplings in ultraviscous glass forming glycerol and its nanocolloid based on Ag nanoparticles, as the function of temperature and pressure up to challenging P more than 1.5 GPa, are discussed. The analysis is focused ... More

Frustrated collisions and unconventional pairing on a quantum superlatticeApr 26 2010May 20 2010We solve the problem of scattering and binding of two spin-1/2 fermions on a one-dimensional superlattice with a period of twice the lattice spacing analytically. We find the exact bound states and the scattering states, consisting of a generalized Bethe ... More

Ab-initio determination of Bose-Hubbard parameters for two ultracold atoms in an optical lattice using a three-well potentialMar 18 2009May 12 2009We calculate numerically the exact energy spectrum of the six dimensional problem of two interacting Bosons in a three-well optical lattice. The particles interact via a full Born-Oppenheimer potential which can be adapted to model the behavior of the ... More

Electronic Transmission Through Metallic Nanowires: Generalized Scattering Matrix ApproachDec 14 2000An easy to implement and powerful method for the solution of 3D scattering problems that can be well described by Helmholtz equation is presented. The matrix algebra used provides excellent stability versus the number of junctions as well as great computational ... More

Interaction of antiprotons with Rb atoms and a comparison of antiproton stopping powers of the atoms H, Li, Na, K, and RbOct 31 2008Ionization and excitation cross sections as well as electron-energy spectra and stopping powers of the alkali metal atoms Li, Na, K, and Rb colliding with antiprotons were calculated using a time-dependent channel-coupling approach. An impact-energy range ... More

A simple parameter-free one-center model potential for an effective one-electron description of molecular hydrogenAug 22 2008Oct 10 2008For the description of an H2 molecule an effective one-electron model potential is proposed which is fully determined by the exact ionization potential of the H2 molecule. In order to test the model potential and examine its properties it is employed ... More

(n-1)-st Koszul homology and the structure of monomial idealsNov 06 2008Koszul homology of monomial ideals provides a description of the structure of such ideals, not only from a homological point of view (free resolutions, Betti numbers, Hilbert series) but also from an algebraic viewpoint. In this paper we show that, in ... More

The completeness of the Bethe ansatz for the periodic ASEPNov 12 2015Dec 03 2017The asymmetric simple exclusion process (ASEP) for N particles on a ring with L sites may be analyzed using the Bethe ansatz. In this paper, we provide a rigorous proof that the Bethe ansatz is complete for the periodic ASEP. More precisely, we show that ... More

Universal Conductance Distributions in the Crossover between Diffusive and Localization RegimesJul 19 2001The full distribution of the conductance $P(G)$ in quasi-one-dimensional wires with rough surfaces is analyzed from the diffusive to the localization regime. In the crossover region, where the statistics is dominated by only one or two eigenchannels, ... More

Observation of a phononic quadrupole topological insulatorAug 16 2017The modern theory of charge polarization in solids is based on a generalization of Berry's phase. Its quantization lies at the heart of our understanding of all systems with topological band structures that were discovered over the last decades. These ... More

Fractional Debye-Stokes-Einstein behaviour in an ultraviscous nanocolloid: glycerol and silver nanoparticlesNov 12 2015One of hallmark features of glass forming ultraviscous liquids is the decoupling between translational and orientational dynamics. This report presents studies of this phenomenon in glycerol, a canonical molecular glass former, heading for the impact ... More

A 2-D Finite-Element Model for Electro-Thermal Transients in Accelerator MagnetsOct 03 2017Dec 05 2017Superconducting accelerator magnets require sophisticated monitoring and means of protection due to the large energy stored in the magnetic field. Numerical simulations play a crucial role in understanding transient phenomena occurring within the magnet, ... More

Mimicking multi-channel scattering with single-channel approachesSep 24 2009The collision of two atoms is an intrinsic multi-channel (MC) problem as becomes especially obvious in the presence of Feshbach resonances. Due to its complexity, however, single-channel (SC) approximations, which reproduce the long-range behavior of ... More

Imaging of the umbrella motion and tunneling in the ammonia molecule by strong-field ionizationAug 05 2016The geometry-dependent ionization behavior of the ammonia molecule is investigated. Different theoretical approaches for obtaining the ionization yield are compared, all of them showing a strong dependence of the ionization yield on the inversion coordinate ... More

Efficient multicut enumeration of k-out-of-n:F and consecutive k-out-of-n:F systemsDec 21 2017We study multiple simultaneous cut events for k-out-of-n:F and linear consecutive k-out-of-n:F systems in which each component has a constant failure probability. We list the multicuts of these systems and describe the structural differences between them. ... More

What produces the extended LINER-type emission in the NUGA galaxy NGC 5850?Aug 15 2013(Abridged) The role of low ionization nuclear emission region (LINER) galaxies within the picture of active galactic nuclei (AGN) has been controversial. It is still not clear whether they host an AGN in a low accretion mode, or whether they are not active ... More

Controlling absorption resonances from sub-wavelength cylinder arraysJun 14 2006The absorption and extinction spectra of sub-wavelength cylinder arrays are shown to present two different kind of resonances. Close to the Rayleigh anomalies, the diffractive coupling with the lattice periodicity leads to sharp peaks in the extinction ... More

Dimensionality-Reduction of Climate Data using Deep AutoencodersAug 27 2018We explore the use of deep neural networks for nonlinear dimensionality reduction in climate applications. We train convolutional autoencoders (CAEs) to encode two temperature field datasets from pre-industrial control runs in the CMIP5 first ensemble, ... More

Water Molecules in Ultrashort Intense Laser FieldsDec 12 2011Ionization and excitation of water molecules in intense laser pulses is studied theoretically by solving the three-dimensional time-dependent electronic Schr\"odinger equation within the single-active-electron approximation. The possibility to image orbital ... More

A scalar field governed cosmological model from noncompact Kaluza-Klein theoryNov 15 2004This paper is a review of a recently introduced cosmological model from a noncompact Kaluza-Klein theory for a single scalar field minimally coupled to gravity. We obtain that the 4D scalar potential has a geometrical origin and assume different representations ... More

Helicity dipolar beams reveal an oscillatory duality symmetryApr 14 2019The perfect optical vortex arising at backscattering when the duality symmetry is satisfied is often discussed from the scattering of high refractive index (HRI) nano-particles. In this Letter, we extend these results to arbitrary dielectric spheres, ... More

Systematic study of outflows in the Local Universe using CALIFA: I. Sample selection and main propertiesNov 03 2018Nov 07 2018We present a sample of 17 objects from the CALIFA survey where we find initial evidence of galactic winds based on their off-axis ionization properties. We identify the presence of outflows using various optical diagnostic diagrams (e.g., EW(H$\alpha$), ... More

Coupling of Magneto-Thermal and Mechanical Superconducting Magnet Models by Means of Mesh-Based InterpolationDec 29 2017In this paper we present an algorithm for the coupling of magneto-thermal and mechanical finite element models representing superconducting accelerator magnets. The mechanical models are used during the design of the mechanical structure as well as the ... More

STEAM: A Hierarchical Co-Simulation Framework for Superconducting Accelerator Magnet CircuitsJan 26 2018Simulating the transient effects occurring in superconducting accelerator magnet circuits requires including the mutual electro-thermo-dynamic interaction among the circuit elements, such as power converters, magnets, and protection systems. Nevertheless, ... More

Electromagnetic surface states in structured perfect-conductor surfacesJun 03 2005Surface-bound modes in metamaterials forged by drilling periodic hole arrays in perfect-conductor surfaces are investigated by means of both analytical techniques and rigorous numerical solution of Maxwell's equations. It is shown that these metamaterials ... More

Excitation of surface plasmon polariton modes with multiple nitrogen vacancy centers in single nanodiamondsSep 15 2016Nitrogen-vacancy (NV) centers in diamonds are interesting due to their remarkable characteristics that are well suited to applications in quantum-information processing and magnetic field sensing, as well as representing stable fluorescent sources. Multiple ... More

XPath Node Selection over Grammar-Compressed TreesNov 21 2013XML document markup is highly repetitive and therefore well compressible using grammar-based compression. Downward, navigational XPath can be executed over grammar-compressed trees in PTIME: the query is translated into an automaton which is executed ... More

LHCb anomalies from a natural perspectiveNov 10 2016Mar 29 2017Tension between the Standard Model (SM) and data concerning $b \rightarrow s$ processes has become apparent. Most notoriously, concerning the $R_K$ ratio, which probes lepton non-universality in $b$ decays, and measurements involving the decays $B \rightarrow ... More

Demonstration of zero optical backscattering from single nanoparticlesDec 12 2012We present the first experimental demonstration of zero backscattering from nanoparticles at op- tical frequencies as originally discussed by Kerker et. al. [M. Kerker, D. Wang, and C. Giles, J. Opt. Soc. A 73, 765 (1983)]. GaAs pillars were fabricated ... More

Infrared excesses in stars with and without planets using revised ${\it WISE}$ photometryJul 13 2017We present an analysis on the potential prevalence of mid infrared excesses in stars with and without planetary companions. Based on an extended database of stars detected with the ${\it WISE}$ satellite, we studied two stellar samples: one with 236 planet ... More

A Deterministic Approach to the Synchronization of Cellular AutomataMar 10 2011In this work we introduce a deterministic scheme of synchronization of linear and nonlinear cellular automata (CA) with complex behavior, connected through a master-slave coupling. By using a definition of Boolean derivative, we use the linear approximation ... More

On an analogue of a Brauer theorem for fusion categoriesMar 16 2015In this paper we prove an analogue of Brauer's theorem for faithful objects in fusion categories. Other notions, such as the order and the index associated to faithful objects of fusion categories are also discussed. We show that the index of a faithful ... More

Resolutions for unit groups of ordersSep 28 2016We present a general algorithm for constructing a free resolution for unit groups of orders in semisimple rational algebras. The approach is based on computing a contractible $G$-complex employing the theory of minimal classes of quadratic forms and Opgenorth's ... More

Equivalence Problems for Tree Transducers: A Brief SurveyMay 22 2014The decidability of equivalence for three important classes of tree transducers is discussed. Each class can be obtained as a natural restriction of deterministic macro tree transducers (MTTs): (1) no context parameters, i.e., top-down tree transducers, ... More

Continuity of discrete homomorphisms of diffeomorphism groupsJul 16 2013Jul 15 2016Let $M$ and $N$ be two closed $C^{\infty}$ manifolds and let $\text{Diff}_c(M)$ denote the group of $C^{\infty}$ diffeomorphisms isotopic to the identity. We prove that any (discrete) group homomorphism between $\text{Diff}_c(M)$ and $\text{Diff}_c(N)$ ... More

Machine learning-assisted discovery of GPCR bioactive ligandsDec 16 2018While G-protein coupled receptors (GPCRs) constitute the largest class of membrane proteins, structures and endogenous ligands of a large portion of GPCRs remain unknown. Due to the involvement of GPCRs in various signaling pathways and physiological ... More

Model Evaluation, Model Selection, and Algorithm Selection in Machine LearningNov 13 2018Dec 03 2018The correct use of model evaluation, model selection, and algorithm selection techniques is vital in academic machine learning research as well as in many industrial settings. This article reviews different techniques that can be used for each of these ... More

Feature Learning for Meta-Paths in Knowledge GraphsSep 07 2018In this thesis, we study the problem of feature learning on heterogeneous knowledge graphs. These features can be used to perform tasks such as link prediction, classification and clustering on graphs. Knowledge graphs provide rich semantics encoded in ... More

Black Hole Evaporation: Sparsity in Analogue and General Relativistic Space-TimesJan 17 2019Our understanding of black holes changed drastically, when Stephen Hawking discovered their evaporation due to quantum mechanical processes. One core feature of this effect is both its similarity and simultaneous dissimilarity to classical black body ... More

Automated discovery of GPCR bioactive ligandsDec 16 2018Mar 28 2019While G-protein coupled receptors (GPCRs) constitute the largest class of membrane proteins, structures and endogenous ligands of a large portion of GPCRs remain unknown. Due to the involvement of GPCRs in various signaling pathways and physiological ... More

High order surface radiation conditions for time-harmonic waves in exterior domainsFeb 23 2017We formulate a new family of high order on-surface radiation conditions to approximate the outgoing solution to the Helmholtz equation in exterior domains. Motivated by the pseudo-differential expansion of the Dirichlet-to-Neumann operator developed by ... More

A spectral curve approach to Lawson symmetric CMC surfaces of genus 2Sep 14 2012Apr 11 2013Minimal and CMC surfaces in $S^3$ can be treated via their associated family of flat $\SL(2,\C)$-connections. In this the paper we parametrize the moduli space of flat $\SL(2,\C)$-connections on the Lawson minimal surface of genus 2 which are equivariant ... More

Hölder-Zygmund Estimates for Degenerate Parabolic SystemsJul 19 2013We consider energy solutions of the inhomogeneous parabolic $p$-Laplacien system $\partial_t u-\text{div}(|D u|^{p-2}D u)=-\text{div} g$. We show in the case $p\geq 2$ that if the right hand side $g$ is locally in $L^\infty(\text{BMO})$, then $u$ is locally ... More

Totally geodesic submanifolds of the exceptional Riemannian symmetric spaces of rank 2Sep 08 2008The present article is the final part of a series on the classification of the totally geodesic submanifolds of the irreducible Riemannian symmetric spaces of rank 2. After this problem has been solved for the 2-Grassmannians in my previous papers cited ... More

Conformally Flat Circle Bundles over SurfacesFeb 26 2009We classify conformally flat Riemannian $3-$manifolds which possesses a free isometric $S^1-$action.

For which positive $p$ is the integral Menger curvature $\mathcal{M}_{p}$ finite for all simple polygons?Feb 02 2012In this brief note we show that the integral Menger curvature $\mathcal{M}_{p}$ is finite for all simple polygons if and only if $p\in (0,3)$. For the intermediate energies $\mathcal{I}_{p}$ and $\mathcal{U}_{p}$ we obtain the analogous result for $p\in ... More

Recovery of the absorption coefficient in radiative transport from a single measurementAug 21 2013Feb 14 2015In this paper, we investigate the recovery of the absorption coefficient from boundary data assuming that the region of interest is illuminated at an initial time. We consider a sufficiently strong and isotropic, but otherwise unknown initial state of ... More

An Automatic Speedup Theorem for Distributed ProblemsFeb 26 2019Recently, Brandt et al. [STOC'16] proved a lower bound for the distributed Lov\'asz Local Lemma, which has been conjectured to be tight for sufficiently relaxed LLL criteria by Chang and Pettie [FOCS'17]. At the heart of their result lies a speedup technique ... More

Scalar Curvature Estimates by Parallel Alternating TorsionSep 28 2007We generalize Llarull's scalar curvature comparison to Riemannian manifolds admitting metric connections with parallel and alternating torsion and having a nonnegative curvature operator on 2-vectors. As a byproduct, we show that Euler number and signature ... More

Discrete knot energiesMar 08 2016The present chapter gives an overview on results for discrete knot energies. These discrete energies are designed to make swift numerical computations and thus open the field to computational methods. Additionally, they provide an independent, geometrically ... More

Properties of the Dirac spectrum on three dimensional lens spacesApr 13 2015Aug 14 2015We present a spectral rigidity result for the Dirac operator on lens spaces. More specifically, we show that each homogeneous lens space and each three dimensional lens space $L(q;p)$ with $q$ prime is completely characterized by its Dirac spectrum in ... More

Group theoretical independence of $\ell$-adic Galois representationsJan 17 2017Let $K/\mathbb{Q}$ be a finitely generated field of characteristic zero and $X/K$ a smooth projective variety. Fix $q\in\mathbb{N}$. For every prime number $\ell$ let $\rho_\ell$ be the representation of $\mathrm{Gal}(K)$ on the \'etale cohomology group ... More

Conjugacy classes and centralizers for pivotal fusion categoriesApr 03 2019A criterion for M\"uger centralizer of a fusion subcategory of a braided non-degenerate fusion category is given. Along the way we extend some identities on the space of class functions of a fusion category introduced by Shimizu in \cite{scalg}. We also ... More