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Spin dynamics in the optical cycle of single nitrogen-vacancy centres in diamondOct 06 2010We investigate spin-dependent decay and intersystem crossing in the optical cycle of single negatively-charged nitrogen-vacancy (NV) centres in diamond. We use spin control and pulsed optical excitation to extract both the spin-resolved lifetimes of the ... More

Control and coherence of the optical transition of single defect centers in diamondMay 24 2010We demonstrate coherent control of the optical transition of single Nitrogen-Vacancy defect centers in diamond. On applying short resonant laser pulses, we observe optical Rabi oscillations with a half-period as short as 1 nanosecond, an order of magnitude ... More

High-fidelity projective readout of a solid-state spin quantum registerJan 03 2013Initialization and readout of coupled quantum systems are essential ingredients for the implementation of quantum algorithms. If the state of a multi-qubit register can be read out in a single shot, this enables further key resources such as quantum error ... More

Two-photon quantum interference from separate nitrogen vacancy centers in diamondOct 14 2011Feb 20 2012We report on the observation of quantum interference of the emission from two separate nitrogen vacancy (NV) centers in diamond. Taking advantage of optically induced spin polarization in combination with polarization filtering, we isolate a single transition ... More

K->pipie+e- decays and chiral low-energy constantsOct 25 2000Mar 21 2001The branching ratios of the measured decay $K_L\to\pi^+\pi^-e^+e^-$ and of the still unmeasured decay $K^+\to\pi^+\pi^0e^+e^-$ are calculated to next-to-leading order in Chiral Perturbation Theory (CHPT). Recent experimental results are used to determine ... More

Inductive limits of semiprojective C*-algebrasApr 13 2018Feb 18 2019We prove closure properties for the class of C*-algebras that are inductive limits of semiprojective C*-algebras. Most importantly, we show that this class is closed under shape domination, and so in particular under shape and homotopy equivalence. It ... More

The topological dimension of type I C*-algebrasOct 16 2012Feb 05 2013While there is only one natural dimension concept for separable, metric spaces, the theory of dimension in noncommutative topology ramifies into different important concepts. To accommodate this, we introduce the abstract notion of a noncommutative dimension ... More

Inductive limits of projective C*-algebrasMay 10 2011Dec 14 2017We show that a separable C*-algebra is an inductive limits of projective C*-algebras if and only if it has trivial shape, that is, if it is shape equivalent to the zero C*-algebra. In particular, every contractible C*-algebra is an inductive limit of ... More

The generator rank for C*-algebrasOct 24 2012The invariant that assigns to a C*-algebra its minimal number of generators lacks natural permanence properties. In particular, it may increase when passing to ideals or inductive limits. It is therefore hard to compute this invariant directly. To obtain ... More

Preduals for spaces of operators involving Hilbert spaces and trace-class operatorsMar 03 2017Mar 27 2018Continuing the study of preduals of spaces $\mathcal{L}(H,Y)$ of bounded, linear maps, we consider the situation that $H$ is a Hilbert space. We establish a natural correspondence between isometric preduals of $\mathcal{L}(H,Y)$ and isometric preduals ... More

Demonstration of entanglement-by-measurement of solid state qubitsJun 10 2012Projective measurements are a powerful tool for manipulating quantum states. In particular, a set of qubits can be entangled by measurement of a joint property such as qubit parity. These joint measurements do not require a direct interaction between ... More

On the Hamilton-Jacobi Equation and Infimal Convolution in the Framework of Sobolev-functionsAug 20 2012We study the regularity properties of the Hamilton-Jacobi flow equation and infimal convolution in the case where initial datum function is continuous and lies in given Sobolev-space $W^{1,p}(\rn)$. We prove that under suitable assumptions it holds for ... More

Church's thesis is questioned by new calculation paradigmOct 07 2006Church's thesis claims that all effecticely calculable functions are recursive. A shortcoming of the various definitions of recursive functions lies in the fact that it is not a matter of a syntactical check to find out if an entity gives rise to a function. ... More

Fraud detection with statistics: A comment on "Evidential Value in ANOVA-Regression Results in Scientific Integrity Studies" (Klaassen, 2015)Jun 24 2015Jul 15 2015Klaassen in (Klaassen 2015) proposed a method for the detection of data manipulation given the means and standard deviations for the cells of a oneway ANOVA design. This comment critically reviews this method. In addition, inspired by this analysis, an ... More

On the uniqueness of quasihyperbolic geodesicsApr 08 2015In this work we solve a couple of well known open problems related to the quasihyperbolic metric. In the case of planar domains, our first main result states that quasihyperbolic geodesics are unique in simply connected domains. As the second main result, ... More

Hopf bifurcation and time periodic orbits in reaction-diffusion systems with pde2path - algorithms and applicationsApr 06 2016Aug 28 2017We describe the algorithms used in the Matlab continuation and bifurcation package pde2path for Hopf bifurcation and continuation of branches of periodic orbits in systems of PDEs in 1, 2, and 3 spatial dimensions, including the computation of Floquet ... More

kt - factorization and CCFM - the solution for describing the hadronic final states - everywhere ?Nov 20 2003Nov 25 2003The basic ideas of kt-factorization and CCFM parton evolution is discussed. The unintegrated gluon densities, obtained from CCFM fits to the proton structure function data at HERA are used to predict hadronic final state cross sections like jet production ... More

The variation of the maximal function of a radial functionFeb 02 2017We study the problem concerning the variation of the Hardy-Littlewood maximal function in higher dimensions. As the main result, we prove that the variation of the non-centered Hardy-Littlewood maximal function of a radial function is comparable to the ... More

Inductive limits of projective C*-algebrasMay 10 2011We show that a C*-algebra is an inductive limits of projective C*-algebras if and only if it has trivial shape, i.e., is shape equivalent to the zero C*-algebra. In particular, every contractible C*-algebra is an inductive limit of projectives, and one ... More

Three-Element Min-Sol and Conservative Min-Cost-HomDec 31 2012Sep 29 2013Thapper and Zivny [STOC'13] recently classified the complexity of VCSP for all finite-valued constraint languages. However, the complexity of VCSPs for constraint languages that are not finite-valued remains poorly understood. In this paper we study the ... More

Electromagnetic radiative corrections to pionic beta decay π^+ to π^0 e^+ ν_eSep 25 2002Pionic beta decay \pi^+ to \pi^0 e^+ \nu_e is analyzed in chiral perturbation theory with virtual photons and leptons. All electromagnetic corrections up to order e^2 p^2 are taken into account. Theoretical results are confronted with preliminary data ... More

Evaluation and selection of models for out-of-sample prediction when the sample size is small relative to the complexity of the data-generating processFeb 22 2008Oct 24 2008In regression with random design, we study the problem of selecting a model that performs well for out-of-sample prediction. We do not assume that any of the candidate models under consideration are correct. Our analysis is based on explicit finite-sample ... More

Semiprojectivity and semiinjectivity in different categoriesFeb 14 2018Projectivity and injectivity are fundamental notions in category theory. We consider natural weakenings termed semiprojectivity and semiinjectivity, and study these concepts in different categories. For example, in the category of metric spaces, (semi)injective ... More

Adapting Computer Vision Algorithms for Omnidirectional VideoJul 22 2019Omnidirectional (360{\deg}) video has got quite popular because it provides a highly immersive viewing experience. For computer vision algorithms, it poses several challenges, like the special (equirectangular) projection commonly employed and the huge ... More

Recent results from CCFM evolutionDec 04 2003Recent developments of the small $x$ CCFM evolution are described, including improvements of the splitting function. The resulting unintegrated gluon densities are used for predictions of hadronic final state measurements like jet production at HERA and ... More

Vector meson cross sections at HERAJan 13 2008Inelastic and elastic (exclusive) cross section measurements of vector meson production at HERA are discussed.

User guide on Hopf bifurcation and time periodic orbits with pde2pathAug 02 2019We explain the setup for using the pde2path libraries for Hopf bifurcation and continuation of branches of periodic orbits and give implementation details of the associated demo directories. See [Uecker, Comm. in Comp. Phys., 2019] for a description of ... More

The distribution of a linear predictor after model selection: Unconditional finite-sample distributions and asymptotic approximationsNov 07 2006We analyze the (unconditional) distribution of a linear predictor that is constructed after a data-driven model selection step in a linear regression model. First, we derive the exact finite-sample cumulative distribution function (cdf) of the linear ... More

On the Relative Expressiveness of Argumentation Frameworks, Normal Logic Programs and Abstract Dialectical FrameworksMay 05 2014We analyse the expressiveness of the two-valued semantics of abstract argumentation frameworks, normal logic programs and abstract dialectical frameworks. By expressiveness we mean the ability to encode a desired set of two-valued interpretations over ... More

Optimal harvesting and spatial patterns in a semi arid vegetation systemMay 22 2015Jan 11 2016We consider an infinite time horizon spatially distributed optimal harvesting problem for a vegetation and soil water reaction diffusion system, with rainfall as the main external parameter. By Pontryagin's maximum principle we derive the associated four ... More

On the differentiability of directionally differentiable functions and applicationsAug 20 2012May 10 2013In the first part of this paper we establish, in terms of so called k-tangential sets, a kind of optimal estimate for the size and structure of the set of non-differentiability of Lipshitz functions with one-sided directional derivatives. These results ... More

Semicircularity, Gaussianity and Monotonicity of EntropyDec 21 2005Mar 10 2006S. Artstein, K. Ball, F. Barthe, and A. Naor have shown that if (X_j) are i.i.d. random variables, then the entropy of n^{-1/2}(X_1+....+X_n) increases as n increases. The free analogue was recently proven by D. Shlyakhtenko. That is, if (x_j) are freely ... More

Probabilistic Software ModelingJun 23 2018Jun 26 2018Software Engineering and the implementation of software has become a challenging task as many tools, frameworks and languages must be orchestrated into one functioning piece. This complexity increases the need for testing and analysis methodologies that ... More

Parallel implementation of high-fidelity multi-qubit gates with neutral atomsAug 16 2019Aug 20 2019We report the implementation of universal two- and three-qubit entangling gates on neutral atom qubits encoded in long-lived hyperfine ground states. The gates are mediated by excitation to strongly interacting Rydberg states, and are implemented in parallel ... More

Large-Scale Uniform Optical Focus Array Generation with a Phase Spatial Light ModulatorMar 22 2019We report a new method to generate uniform large-scale optical focus arrays (LOFAs). By identifying and removing undesired phase rotation in the iterative Fourier-transform algorithm (IFTA), our approach rapidly produces computer-generated holograms of ... More

Hopf bifurcation and time periodic orbits in reaction-diffusion systems with pde2path -- a tutorial via reaction-diffusion systems and distributed optimal controlApr 06 2016Jun 06 2016We describe how to use the Matlab continuation and bifurcation package pde2path for Hopf bifurcations and the continuation of branches of periodic orbits, including the computation of Floquet multipliers, in systems of PDEs in 1, 2, and 3 spatial dimensions. ... More

The pde2path add-on toolbox p2pOC for solving infinite time-horizon spatially distributed optimal control problems - Quickstart Guide -Mar 18 2015May 22 2015p2pOC is an add-on toolbox to the Matlab package pde2path. It is aimed at the numerical solution of optimal control (OC) problems with an infinite time horizon for parabolic systems of PDE over 1D or 2D spatial domains. The basic idea is to treat the ... More

Computational Complexity of the Minimum Cost Homomorphism Problem on Three-Element DomainsAug 06 2013Sep 29 2013In this paper we study the computational complexity of the (extended) minimum cost homomorphism problem (Min-Cost-Hom) as a function of a constraint language, i.e. a set of constraint relations and cost functions that are allowed to appear in instances. ... More

On the conditional distributions of low-dimensional projections from high-dimensional dataApr 22 2013We study the conditional distribution of low-dimensional projections from high-dimensional data, where the conditioning is on other low-dimensional projections. To fix ideas, consider a random d-vector Z that has a Lebesgue density and that is standardized ... More

Pattern formation with pde2path -- a tutorialAug 02 2019We explain some pde2path setups for pattern formation in 1D, 2D and 3D. A focus is on new pde2path functions for branch switching at steady bifurcation points of higher multiplicity, typically due to discrete symmetries, but we also review general concepts ... More

Conditional predictive inference post model selectionAug 25 2009We give a finite-sample analysis of predictive inference procedures after model selection in regression with random design. The analysis is focused on a statistically challenging scenario where the number of potentially important explanatory variables ... More

Un-integrated PDFs in CCFMNov 22 2004The un-integrated parton distribution functions (uPDFs) obtained from a CCFM evolution are studied in terms of the intrinsic transverse momentum distribution at low scales. The uPDFs are studied for variations of the renormalization and factorization ... More

Parallel implementation of high-fidelity multi-qubit gates with neutral atomsAug 16 2019We report the implementation of universal two- and three-qubit entangling gates on neutral atom qubits encoded in long-lived hyperfine ground states. The gates are mediated by excitation to strongly interacting Rydberg states, and are implemented in parallel ... More

Probing many-body dynamics on a 51-atom quantum simulatorJul 13 2017Nov 30 2017Controllable, coherent many-body systems can provide insights into the fundamental properties of quantum matter, enable the realization of new quantum phases and could ultimately lead to computational systems that outperform existing computers based on ... More

Cold Matter Assembled Atom-by-AtomJul 11 2016The realization of large-scale fully controllable quantum systems is an exciting frontier in modern physical science. We use atom-by-atom assembly to implement a novel platform for the deterministic preparation of regular arrays of individually controlled ... More

Opening up the Quantum Three-Box Problem with Undetectable MeasurementsMay 11 2012One of the most striking features of quantum mechanics is the profound effect exerted by measurements alone. Sophisticated quantum control is now available in several experimental systems, exposing discrepancies between quantum and classical mechanics ... More

Quantum Kibble-Zurek mechanism and critical dynamics on a programmable Rydberg simulatorSep 14 2018Apr 01 2019Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics ... More

High-fidelity control and entanglement of Rydberg atom qubitsJun 12 2018Individual neutral atoms excited to Rydberg states are a promising platform for quantum simulation and quantum information processing. However, experimental progress to date has been limited by short coherence times and relatively low gate fidelities ... More

Nonanalytic quantum oscillator image of complete replica symmetry breakingMay 16 2011We describe the effect of replica symmetry breaking in the field distribution function P(h) of the T=0 SK-model as the difference between a split Gaussian and the first excited state $\psi_1$ of a weakly anharmonic oscillator with nonanalytic shift by ... More

NJL model of homogeneous neutral quark matter: Pseudoscalar diquark condensates revisitedDec 17 2009Apr 19 2010We use a Nambu-Jona Lasinio type model to investigate the phase diagram of dense quark matter under neutron star conditions in mean field approximation. The model contains selfconsistently determined quark masses and allows for diquark condensation in ... More

Lattice QCD Green's functions in maximally Abelian gauge: infrared Abelian dominance and the quark sectorApr 21 2015Nov 03 2015On lattice gauge field configurations with 2+1 dynamical quark flavors, we investigate the momentum space quark and gluon propagators in the combined maximally Abelian plus $U(1)_3\times U(1)_8$ Landau gauge. We extract the gluon fields from the lattice ... More

Gravitational Light Bending Prevents $γγ$ Absorption in Gravitational LensesSep 05 2016The magnification effect due to gravitational lensing enhances the chances of detecting moderate-redshift ($z \sim 1$) sources in very-high-energy (VHE; $E > 100$ GeV) $\gamma$-rays by ground-based Atmospheric Cherenkov Telescope facilities. It has been ... More

Admissibility of the usual confidence set for the mean of a univariate or bivariate normal population: The unknown-variance caseSep 20 2018Sep 21 2018In the Gaussian linear regression model (with unknown mean and variance), we show that the standard confidence set for one or two regression coefficients is admissible in the sense of Joshi (1969). This solves a long-standing open problem in mathematical ... More

Brown measure and iterates of the Aluthge transform for some operators arising from measurable actionsDec 09 2005Feb 05 2008We consider the Aluthge transform $|T|^{1/2}U|T|^{1/2}$ of a Hilbert space operator $T$, where $T=U|T|$ is the polar decomposition of $T$. We prove that the map that sends $T$ to its Aluthge transform is continuous with respect to the norm topology and ... More

Well-posedness of some initial-boundary-value problems for dynamo-generated poloidal magnetic fieldsDec 13 2012Given a bounded domain $G \subset \R^d$, $d\geq 3$, we study smooth solutions of a linear parabolic equation with non-constant coefficients in $G$, which at the boundary have to $C^1$-match with some harmonic function in $\R^d \setminus \ov{G}$ vanishing ... More

(Seemingly) Impossible Theorems in Constructive MathematicsApr 12 2019We prove some constructive results that on first and maybe even on second glance seem impossible.

Banach algebras generated by an invertible isometry of an $L^p$-spaceMay 22 2014Dec 18 2014We provide a complete description of those Banach algebras that are generated by an invertible isometry of an $L^p$-space together with its inverse. Examples include the algebra $PF_p(\mathbb{Z})$ of $p$-pseudofunctions on $\mathbb{Z}$, the commutative ... More

Optimal management and spatial patterns in a distributed shallow lake modelMar 18 2015Jun 10 2015We present a numerical framework to treat infinite time horizon spatially distributed optimal control problems via the associated canonical system derived by Pontryagin's Maximum Principle. The basic idea is to consider the canonical system in two steps. ... More

Saturation effects in final states due to CCFM with absorptive boundaryDec 22 2008Jan 26 2009We apply the absorptive boundary prescription to include saturation effects in CCFM evolution equation. We are in particular interested in saturation effects in exclusive processes which can be studied using Monte Carlo event generator CASCADE. We calculate ... More

On underwater sound reflection from layered ice sheetsApr 08 2016Reflection of sound from ice sheets floating on water is simulated using Thomson and Haskell's method of matrix propagation. The reflection coefficient is computed as a function of incidence angle and frequency for selected ice parameters of a uniform ... More

Advanced superconducting circuits and devicesFeb 27 2014Apr 02 2014Short review on advanced superconducting circuits and devices.

List and Probabilistic Unique Decoding of Folded Subspace CodesApr 21 2015A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding algorithm for this ... More

Coulomb, Landau and Maximally Abelian Gauge Fixing in Lattice QCD with Multi-GPUsDec 20 2012Apr 15 2013A lattice gauge theory framework for simulations on graphic processing units (GPUs) using NVIDIA's CUDA is presented. The code comprises template classes that take care of an optimal data pattern to ensure coalesced reading from device memory to achieve ... More

Multiple Kernel Learning: A Unifying Probabilistic ViewpointMar 04 2011Jun 07 2012We present a probabilistic viewpoint to multiple kernel learning unifying well-known regularised risk approaches and recent advances in approximate Bayesian inference relaxations. The framework proposes a general objective function suitable for regression, ... More

Photonic Quantum Circuits with Time DelaysOct 15 2015We study the dynamics of photonic quantum circuits consisting of nodes coupled by quantum channels. We are interested in the regime where time delay in communication between the nodes is significant. This includes the problem of quantum feedback, where ... More

Reversible Work Transiton State Theory: Application to Dissociative Adsorption of HydrogenNov 16 1994Nov 18 1994A practical method for finding free energy barriers for transitions in high-dimensional classical and quantum systems is presented and used to calculate the dissociative sticking probability of H2 on a metal surface within transition state theory (TST). ... More

Implementing Default and Autoepistemic Logics via the Logic of GKMay 05 2014The logic of knowledge and justified assumptions, also known as logic of grounded knowledge (GK), was proposed by Lin and Shoham as a general logic for nonmonotonic reasoning. To date, it has been used to embed in it default logic (propositional case), ... More

A Morse type uniqueness theorem for non-parametric minimizing hypersurfacesJul 02 2007A classical result about minimal geodesics on R^2 with Z^2 periodic metric that goes back to H.M. Morse asserts that a minimal geodesic that is asymptotic to a periodic minimal geodesic cannot intersect any periodic minimal geodesic of the same period. ... More

Invariant Subspaces for Operators in a General II_1-factorNov 09 2006It is shown that to every operator T in a general von Neumann factor M of type II_1 and to every Borel set B in the complex plane, one can associate a largest, closed, T-invariant subspace, K = K_T(B), affiliated with M, such that the Brown measure of ... More

Determination of transverse momentum dependent gluon density from HERA structure function measurementsJun 08 2012The transverse momentum dependent gluon density obtained with CCFM evolution is determined from a fit to the latest combined HERA structure function measurements.

Boundary value problems for the Lorentzian Dirac operatorApr 11 2017Jul 14 2017On a compact globally hyperbolic Lorentzian spin manifold with smooth spacelike Cauchy boundary the (hyperbolic) Dirac operator is known to be Fredholm when Atiyah-Patodi-Singer boundary conditions are imposed. In this paper we investigate to what extent ... More

Extending representations of Banach algebras to their bidualsMar 02 2017Mar 23 2018We show that a representation of a Banach algebra $A$ on a Banach space $X$ can be extended to a canonical representation of $A^{**}$ on $X$ if and only if certain orbit maps $A\to X$ are weakly compact. When this is the case, we show that the essential ... More

cuLGT: Lattice Gauge Fixing on GPUsDec 11 2014We adopt CUDA-capable Graphic Processing Units (GPUs) for Landau, Coulomb and maximally Abelian gauge fixing in 3+1 dimensional SU(3) and SU(2) lattice gauge field theories. A combination of simulated annealing and overrelaxation is used to aim for the ... More

Representations of $p$-convolution algebras on $L^q$-spacesSep 27 2016For a nontrivial locally compact group $G$, and $p\in [1,\infty)$, consider the Banach algebras of $p$-pseudofunctions, $p$-pseudomeasures, $p$-convolvers, and the full group $L^p$-operator algebra. We show that these Banach algebras are operator algebras ... More

Eigenvalue placement for regular matrix pencils with rank one perturbationsApr 12 2016A regular matrix pencil sE-A and its rank one perturbations are considered. We determine the sets in the extended complex plane which are the eigenvalues of the perturbed pencil. We show that the largest Jordan chains at each eigenvalue of sE-A may disappear ... More

Gauge fixing using overrelaxation and simulated annealing on GPUsSep 18 2012We adopt CUDA-capable Graphic Processing Units (GPUs) for Coulomb, Landau and maximally Abelian gauge fixing in 3+1 dimensional SU(3) lattice gauge field theories. The local overrelaxation algorithm is perfectly suited for highly parallel architectures. ... More

Role of two-flavor color superconductor pairing in a three-flavor Nambu--Jona-Lasinio model with axial anomalyJul 29 2010Oct 18 2010The phase diagram of strongly interacting matter is studied within a three-flavor Nambu--Jona-Lasinio model, which contains the coupling between chiral and diquark condensates through the axial anomaly. Our results show that it is essential to include ... More

Statistics for surface modes of nanoparticles with shape fluctuationsFeb 23 2010We develop a numerical method for approximating the surface modes of sphere-like nanoparticles in the quasi-static limit, based on an expansion of (the angular part of) the potentials into spherical harmonics. Comparisons of the results obtained in this ... More

Interdisciplinary patterns of a university: Investigating collaboration using co-publication network analysisMar 22 2010We investigate collaborative and interdisciplinary research features of University College Dublin, using methods from social network analysis to analyze and visualize (co-)publications covered by the Web of Science from 1998 through 2007. We account for ... More

Quantum Critical Dynamics Simulation of Dirty Boson SystemsSep 14 2011Nov 23 2011Recently the scaling result $z=d$ for the dynamic critical exponent at the Bose glass to superfluid quantum phase transition has been questioned both on theoretical and numerical grounds. This motivates a careful evaluation of the critical exponents in ... More

Robustness Against Outliers For Deep Neural Networks By Gradient Conjugate PriorsMay 21 2019We analyze a new robust method for the reconstruction of probability distributions of observed data in the presence of output outliers. It is based on a so-called gradient conjugate prior (GCP) network which outputs the parameters of a prior. By rigorously ... More

Pairing an arbitrary regressor with an artificial neural network estimating aleatoric uncertaintyJul 23 2017Sep 03 2018We suggest a general approach to quantification of different forms of aleatoric uncertainty in regression tasks performed by artificial neural networks. It is based on the simultaneous training of two neural networks with a joint loss function and a specific ... More

Quotients of Banach algebras acting on $L^p$-spacesDec 12 2014Mar 29 2016We show that the class of Banach algebras that can be isometrically represented on an $L^p$-space, for $p\neq 2$, is not closed under quotients. This answers a question asked by Le Merdy 20 years ago. Our methods are heavily reliant on our earlier study ... More

Density functional theory calculation and thermodynamic analysis of the bridgmanite surface structureOct 24 2018Nov 01 2018Bridgmanite, a high temperature and pressure form of $MgSiO_3$, is believed to be Earth's most abundant mineral and responsible for the observed seismic anisotropy in the mantle. Little is known about surfaces of bridgmanite but knowledge of the most ... More

Global weak solutions for an Newtonian Fluid interacting with a Koiter Type Shell under natural boundary conditionsJul 19 2018We consider an viscous, incompressible Newtonian fluid flowing through a thin elastic structure. The motion of the structure is described by the equations of a linearised Koiter shell, whose motion is restricted to transverse displacements. The fluid ... More

An integral boundary layer equation for film flow over inclined wavy bottomsNov 20 2008Aug 25 2009We study the flow of an incompressible liquid film down a wavy incline. Applying a Galerkin method with only one ansatz function to the Navier-Stokes equations we derive a second order weighted residual integral boundary layer equation, which in particular ... More

Brown Measures of Unbounded Operators Affiliated with a Finite von Neumann AlgebraMay 10 2006In this paper we generalize Brown's spectral distribution measure to a large class of unbounded operators affiliated with a finite von Neumann algebra. Moreover, we compute the Brown measure of all unbounded R-diagonal operators in this class. As a particular ... More

Shrinkage estimators for prediction out-of-sample: Conditional performanceSep 05 2012Nov 29 2013We find that, in a linear model, the James-Stein estimator, which dominates the maximum-likelihood estimator in terms of its in-sample prediction error, can perform poorly compared to the maximum-likelihood estimator in out-of-sample prediction. We give ... More

The Variation of the Fractional Maximal Function of a Radial FunctionOct 19 2017In this paper we study the regularity of the non-centered fractional maximal operator $M_{\beta}$. As the main result, we prove that there exists $C(n,\beta)$ such that if $q=n/(n-\beta)$ and $f$ is a radial function, then $\|DM_{\beta}f\|_{L^{q}(\mathbb{R}^n)}\leq ... More

Regularity for nonlinear stochastic gamesSep 24 2015Aug 11 2016We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for the corresponding ... More

Gradient walk and $p$-harmonic functionsMay 18 2016We consider a class of stochastic processes and establish its connection to $p$-harmonic functions. In particular, we obtain stochastic approximations that converge uniformly to a $p$-harmonic function, with an explicit convergence rate, and also obtain ... More

Functoriality of group algebras acting on $L^p$-spacesAug 24 2014We continue our study of group algebras acting on $L^p$-spaces, particularly of algebras of $p$-pseudofunctions of locally compact groups. We focus on the functoriality properties of these objects. We show that $p$-pseudofunctions are functorial with ... More

The ampsys tool of pde2pathJun 25 2019The computation of coefficients of amplitude systems for Turing bifurcations is a straightforward but sometimes elaborate task, in particular for 2D or 3D wave vector lattices. The Matlab tool ampsys automates such computations for two classes of problems, ... More

A feasible second order bundle algorithm for nonsmooth, nonconvex optimization problems with inequality constraints: I. Derivation and convergenceJun 26 2015This paper extends the SQP-approach of the well-known bundle-Newton method for nonsmooth unconstrained minimization to the nonlinearly constrained case. Instead of using a penalty function or a filter or an improvement function to deal with the presence ... More

Probing quantum critical dynamics on a programmable Rydberg simulatorSep 14 2018Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations. These fluctuations play a dominant role in the quantum critical region surrounding the transition point, where the dynamics ... More

Concentration of the spectral measure of large Wishart matrices with dependent entriesOct 15 2008We derive concentration inequalities for the spectral measure of large random matrices, allowing for certain forms of dependence. Our main focus is on empirical covariance (Wishart) matrices, but general symmetric random matrices are also considered.

On the Radiative Pion DecayJan 16 2008A reanalysis of the radiative pion decay together with the calculation of the radiative corrections within chiral perturbation theory (CHPT) is performed. The amplitude of this decay contains an inner Bremsstrahlung contribution and a structure-dependent ... More

Vibrational Coherences in Nano-Elastic TunnelingMay 18 2007Oct 25 2007Charging a nano-scale oscillator by single electron tunneling leads to an effective double-well potential due to image charges. We combine exact numerical diagonalizations with generalized Master equations and show that the resulting quantum tunneling ... More

Gradient conjugate priors and deep neural networksFeb 07 2018The paper deals with learning the probability distribution of the observed data by artificial neural networks. We suggest a so-called gradient conjugate prior (GCP) update appropriate for neural networks, which is a modification of the classical Bayesian ... More

Coupled Mode Equations and Gap Solitons for the 2D Gross-Pitaevskii equation with a non-separable periodic potentialOct 24 2008Aug 26 2010Gap solitons near a band edge of a spatially periodic nonlinear PDE can be formally approximated by solutions of Coupled Mode Equations (CMEs). Here we study this approximation for the case of the 2D Periodic Nonlinear Schr\"{o}dinger / Gross-Pitaevskii ... More