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A Measurement Protocol for the Entanglement Spectrum of Cold AtomsMay 27 2016Entanglement plays a major role in characterizing many-body quantum systems. In particular, the entanglement spectrum holds a great promise to characterize essential physics of quantum many-body systems. While there has been a surge of theoretical works ... More

Quantum Spin Dimers from Chiral Dissipation in Cold-Atom ChainsAug 19 2014Dec 08 2014We consider the non-equilibrium dynamics of a driven dissipative spin chain with chiral coupling to a 1D bosonic bath, and its atomic implementation with a two-species mixture of cold quantum gases. The reservoir is represented by a spin-orbit coupled ... More

Non-Markovian Dynamics in Chiral Quantum Networks with Spins and PhotonsFeb 02 2016Jun 23 2016We study the dynamics of chiral quantum networks consisting of nodes coupled by unidirectional or asymmetric bidirectional quantum channels. In contrast to familiar photonic networks where driven two-level atoms exchange photons via 1D photonic nanostructures, ... 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

An entropy perspective on the thermal crossover in a fermionic Hubbard chainApr 19 2013We study the Renyi entropy in the finite temperature crossover regime of a Hubbard chain using quantum Monte Carlo. The ground state entropy has characteristic features such as a logarithmic divergence with block size and $2\kF$ oscillations that are ... More

On A Rapidly Converging Series For The Riemann Zeta FunctionJan 31 2012To evaluate Riemann's zeta function is important for many investigations related to the area of number theory, and to have quickly converging series at hand in particular. We investigate a class of summation formulae and find, as a special case, a new ... More

Spectral Risk Measures, With Adaptions For Stochastic OptimizationSep 17 2012Stochastic optimization problems often involve the expectation in its objective. When risk is incorporated in the problem description as well, then risk measures have to be involved in addition to quantify the acceptable risk, often in the objective. ... More

Inverse problems for Maxwell's equations in a slab with partial boundary dataJun 22 2018We consider two inverse boundary value problems for the time-harmonic Maxwell equations in an infinite slab. Assuming that tangential boundary data for the electric and magnetic fields at a fixed frequency is available either on subsets of one boundary ... More

Exploring Code Clones in Programmable Logic Controller SoftwareJun 13 2017The reuse of code fragments by copying and pasting is widely practiced in software development and results in code clones. Cloning is considered an anti-pattern as it negatively affects program correctness and increases maintenance efforts. Programmable ... More

Chiral quantum optics with V-level atoms and coherent quantum feedbackJun 23 2016Sep 20 2016We study the dissipative dynamics of an atom in a V-level configuration driven by lasers and coupled to a semi-infinite waveguide. The coupling to the waveguide is chiral, in that each transition interacts only with the modes propagating in a given direction, ... More

Periodic orbits, entanglement and quantum many-body scars in constrained models: matrix product state approachJul 04 2018Jan 30 2019We analyze quantum dynamics of strongly interacting, kinetically constrained many-body systems. Motivated by recent experiments demonstrating surprising long-lived, periodic revivals after quantum quenches in Rydberg atom arrays, we introduce a manifold ... More

Delayed Coherent Quantum Feedback from a Scattering Theory and a Matrix Product State PerspectiveJun 23 2017Sep 14 2017We study the scattering of photons propagating in a semi-infinite waveguide terminated by a mirror and interacting with a quantum emitter. This paradigm constitutes an example of coherent quantum feedback, where light emitted towards the mirror gets redirected ... More

Quantum State Transfer via Noisy Photonic and Phononic WaveguidesNov 30 2016Mar 28 2017We describe a quantum state transfer protocol, where a quantum state of photons stored in a first cavity can be faithfully transferred to a second distant cavity via an infinite 1D waveguide, while being immune to arbitrary noise (e.g. thermal noise) ... More

Measurement Protocol for the Entanglement Spectrum of Cold AtomsMay 27 2016Nov 22 2016Entanglement, and, in particular the entanglement spectrum, plays a major role in characterizing many-body quantum systems. While there has been a surge of theoretical works on the subject, no experimental measurement has been performed to date because ... More

Heating dynamics of bosonic atoms in a noisy optical latticeJan 13 2013Feb 28 2013We analyze the heating of interacting bosonic atoms in an optical lattice due to intensity fluctuations of the lasers forming the lattice. We focus in particular on fluctuations at low frequencies below the band gap frequency, such that the dynamics is ... More

Quantum Optics of Chiral Spin NetworksNov 11 2014Apr 15 2015We study the driven-dissipative dynamics of a network of spin-1/2 systems coupled to one or more chiral 1D bosonic waveguides within the framework of a Markovian master equation. We determine how the interplay between a coherent drive and collective decay ... More

Quantum Virtual CoolingDec 05 2018We propose a quantum information based scheme to reduce the temperature of quantum many-body systems, and access regimes beyond the current capability of conventional cooling techniques. We show that collective measurements on multiple copies of a system ... More

Quantum State Transfer via Noisy Photonic and Phononic WaveguidesNov 30 2016We describe a quantum state transfer protocol, where a quantum state of photons stored in a first cavity can be faithfully transferred to a second distant cavity via an infinite 1D waveguide, while being immune to arbitrary noise (e.g. thermal noise) ... More

Photonic tensor networks produced by a single quantum emitterFeb 07 2017We propose and analyze a protocol to generate two dimensional tensor network states using a single quantum system that sequentially interacts with a 1D string of qubits. This is accomplished by using parts of the string itself as a quantum queue memory. ... More

Generation and manipulation of Schrödinger cat states in Rydberg atom arraysMay 14 2019May 15 2019Quantum entanglement involving coherent superpositions of macroscopically distinct states is among the most striking features of quantum theory, but its realization is challenging, since such states are extremely fragile. Using a programmable quantum ... More

Entropy Based Risk MeasuresJan 22 2018Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is of particular ... 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

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

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

New bulk scalar field solutions in brane worldsOct 04 2004We use nonlinear perturbation theory to obtain new solutions for brane world models that incorporate a massive bulk scalar field. We then consider tensor perturbations and show that Newtonian gravity is recovered on the brane for both a light scalar field ... More

Uniqueness of Kusuoka RepresentationsOct 26 2012Feb 27 2013This paper addresses law invariant coherent risk measures and their Kusuoka representations. By elaborating the existence of a minimal representation we show that every Kusuoka representation can be reduced to its minimal representation. Uniqueness -- ... 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

On Banach spaces of vector-valued random variables and their duals motivated by risk measuresMar 30 2017Jun 16 2017We introduce Banach spaces of vector-valued random variables motivated from mathematical finance. So-called risk functionals are defined in a natural way on these Banach spaces and it is shown that these functionals are Lipschitz continuous. The risk ... More

Martingale Characterizations of Risk-Averse Stochastic Optimization ProblemsFeb 10 2018Feb 13 2018This paper addresses risk awareness of stochastic optimization problems. Nested risk measures appear naturally in this context, as they allow beneficial reformulations for algorithmic treatments. The reformulations presented extend usual Hamilton-Jacobi-Bellman ... 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

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

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

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

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

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

Dressed, noise- or disorder- resilient optical latticesMay 28 2012External noise is inherent in any quantum system, and can have especially strong effects for systems exhibiting sensitive many-body phenomena. We show how a dressed lattice scheme can provide control over certain types of noise for atomic quantum gases ... More

Computational complexity of the Rydberg blockade in two dimensionsSep 13 2018We discuss the computational complexity of finding the ground state of the two-dimensional array of quantum bits that interact via strong van der Waals interactions. Specifically, we focus on systems where the interaction strength between two spins depends ... More

Chiral Quantum OpticsAug 01 2016At the most fundamental level, the interaction between light and matter is manifested by the emission and absorption of single photons by single quantum emitters. Controlling light--matter interaction is the basis for diverse applications ranging from ... More

Quantum Optimization for Maximum Independent Set Using Rydberg Atom ArraysAug 31 2018We describe and analyze an architecture for quantum optimization to solve maximum independent set (MIS) problems using neutral atom arrays trapped in optical tweezers. Optimizing independent sets is one of the paradigmatic, NP-hard problems in computer ... More

Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term DevicesDec 03 2018The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical variational algorithm designed to tackle combinatorial optimization problems. Despite its promise for near-term quantum applications, not much is currently understood ... More

Quantum MetasurfacesApr 15 2019Metasurfaces mold the flow of classical light waves by engineering sub-wavelength patterns from dielectric or metallic thin films. We describe and analyze a method in which quantum operator-valued reflectivity can be used to control both spatio-temporal ... More

Public Goods Games on Adaptive Coevolutionary NetworksSep 18 2016Productive societies feature high levels of cooperation and strong connections between individuals. Public Goods Games (PGGs) are frequently used to study the development of social connections and cooperative behavior in model societies. In such games, ... More

Thermal vs. Entanglement Entropy: A Measurement Protocol for Fermionic Atoms with a Quantum Gas MicroscopeFeb 05 2013Jun 07 2013We show how to measure the order-two Renyi entropy of many-body states of spinful fermionic atoms in an optical lattice in equilibrium and non-equilibrium situations. The proposed scheme relies on the possibility to produce and couple two copies of the ... More

Numerical study of the chiral $\mathbb{Z}_3$ quantum phase transition in one spatial dimensionJun 05 2018Jul 16 2018Recent experiments on a one-dimensional chain of trapped alkali atoms [arXiv:1707.04344] have observed a quantum transition associated with the onset of period-3 ordering of pumped Rydberg states. This spontaneous $\mathbb{Z}_3$ symmetry breaking is described ... More

On the motion of a compact elastic bodyAug 07 2005Feb 02 2007We study the problem of motion of a relativistic, ideal elastic solid with free surface boundary by casting the equations in material form ("Lagrangian coordinates"). By applying a basic theorem due to Koch, we prove short-time existence and uniqueness ... 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

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

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

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

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

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

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.

Preduals and complementation of spaces of bounded linear operatorsSep 17 2016Mar 21 2018For Banach spaces X and Y, we establish a natural bijection between preduals of Y and preduals of L(X,Y) that respect the right L(X)-module structure. If X is reflexive, it follows that there is a unique predual making L(X) into a dual Banach algebra. ... 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

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

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

Quantum Hall Physics with Cold Atoms in Cylindrical Optical LatticesJun 30 2015Oct 15 2015We propose and study various realizations of a Hofstadter-Hubbard model on a cylinder geometry with fermionic cold atoms in optical lattices. The cylindrical optical lattice is created by copropagating Laguerre-Gauss beams, i.e.~light beams carrying orbital ... More

Searching for three-nucleon resonancesOct 09 1995We search for three-neutron resonances which were predicted from pion double charge exchange experiments on He-3. All partial waves up to J=5/2 are nonresonant except the J=3/2^+ one, where we find a state at E=14 MeV energy with 13 MeV width. The parameters ... More

Risk trading, network topology, and banking regulationSep 25 2003In the context of understanding the nature of the risk transformation process of the financial system we propose an iterative risk-trading game between several agents who build their trading strategies based on a general utility setting. The game is studied ... 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

Topological Quantum Optics in Two-Dimensional Atomic ArraysMar 15 2017Jul 17 2017We demonstrate that two-dimensional atomic emitter arrays with subwavelength spacing constitute topologically protected quantum optical systems where the photon propagation is robust against large imperfections while losses associated with free space ... More

Photonic Band Structure of Two-dimensional Atomic LatticesAug 11 2017Two-dimensional atomic arrays exhibit a number of intriguing quantum optical phenomena, including subradiance, nearly perfect reflection of radiation and long-lived topological edge states. Studies of emission and scattering of photons in such lattices ... More

Incorporating statistical model error into the calculation of acceptability prices of contingent claimsMar 16 2017Jan 30 2019The determination of acceptability prices of contingent claims requires the choice of a stochastic model for the underlying asset price dynamics. Given this model, optimal bid and ask prices can be found by stochastic optimization. However, the model ... 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

Leave-one-out prediction intervals in linear regression models with many variablesFeb 18 2016We study prediction intervals based on leave-one-out residuals in a linear regression model where the number of explanatory variables can be large compared to sample size. We establish uniform asymptotic validity (conditional on the training sample) of ... More

Prediction out-of-sample using block shrinkage estimators: model selection and predictive inferenceSep 12 2018In a linear regression model with random design, we consider a family of candidate models from which we want to select a `good' model for prediction out-of-sample. We fit the models using block shrinkage estimators, and we focus on the challenging situation ... More

Statistical inference with F-statistics when fitting simple models to high-dimensional dataFeb 12 2019We study linear subset regression in the context of the high-dimensional overall model $y = \vartheta+\theta' z + \epsilon$ with univariate response $y$ and a $d$-vector of random regressors $z$, independent of $\epsilon$. Here, "high-dimensional" means ... More

Monte Carlo Generators and the CCFM EquationJun 15 2000We discuss three implementations of the CCFM evolution equations in event generator programs. We find that some of them are able to describe observables such as forward jet rates in DIS at HERA, but only if the so-called consistency constraint is removed. ... More

Locally finite extensions and Gesztesy-Šeba realizations for the Dirac operator on a metric graphJun 11 2018We study extensions of direct sums of symmetric operators $S=\oplus_{n\in\mathbb{N}} S_n$. In general there is no natural boundary triplet for $S^*$ even if there is one for every $S_n^*$, $n\in\mathbb{N}$. We consider a subclass of extensions of $S$ ... More

A feasible second order bundle algorithm for nonsmooth nonconvex optimization problems with inequality constraints: II. Implementation and numerical resultsJun 26 2015This paper presents a concrete implementation of the feasible second order bundle algorithm for nonsmooth, nonconvex optimization problems with inequality constraints \cite{HannesPaperB}. It computes the search direction by solving a convex quadratically ... More

Eigenvalue placement for regular matrix pencils with rank one perturbationsApr 12 2016Jan 05 2017A 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

General and Fractional Hypertree Decompositions: Hard and Easy CasesNov 03 2016Hypertree decompositions, the more powerful generalized hypertree decompositions (GHDs), and the yet more general fractional hypertree decompositions (FHD) are hypergraph decomposition methods successfully used for answering conjunctive queries and for ... More

Distributed Information-Theoretic BiclusteringFeb 15 2016Apr 07 2016We study a novel multi-terminal source coding setup motivated by the biclustering problem. Two separate encoders observe two stationary, memoryless sources $X^n$ and $Z^n$, respectively. The goal is to find rate-limited encodings $f(x^n)$ and $g(z^n)$ ... More

General and Fractional Hypertree Decompositions: Hard and Easy CasesNov 03 2016Nov 29 2016Hypertree decompositions, the more powerful generalized hypertree decompositions (GHDs), and the yet more general fractional hypertree decompositions (FHD) are hypergraph decomposition methods successfully used for answering conjunctive queries and for ... More

A nonconforming Trefftz virtual element method for the Helmholtz problemMay 15 2018Oct 25 2018We introduce a novel virtual element method (VEM) for the two dimensional Helmholtz problem endowed with impedance boundary conditions. Local approximation spaces consist of Trefftz functions, i.e., functions belonging to the kernel of the Helmholtz operator. ... More

Non-conforming harmonic virtual element method: $h$- and $p$-versionsJan 02 2018Jul 27 2018We study the $h$- and $p$-versions of non-conforming harmonic virtual element methods (VEM) for the approximation of the Dirichlet-Laplace problem on a 2D polygonal domain, providing quasi-optimal error bounds. Harmonic VEM do not make use of internal ... 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

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

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

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

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

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

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

Preduals and complementation of spaces of bounded linear operatorsSep 17 2016For Banach spaces X and Y, we establish a natural bijection between preduals of Y and preduals of L(X,Y) that respect the right L(X)-module structure. If X is reflexive, it follows that there is a unique predual making L(X) into a dual Banach algebra. ... More

On the Ambiguity of Interaction and Nonlinear Main Effects in a Regime of Dependent CovariatesDec 09 2015Frequently the analysis of large experimental datasets reveals significant interactions that are difficult to interpret within the theoretical framework guiding the research. Some of these interactions are actually spurious artifacts arising from the ... More

Density functional theory calculations and thermodynamic analysis of the forsterite $Mg_{2}SiO_{4}$(010) surfaceAug 30 2018Sep 13 2018The stability of possible termination structures for the (010) surface of forsterite, $ Mg_2SiO_4 $, is studied using a density functional theory (DFT) based thermodynamic approach. The DFT calculations are used to estimate the surface Gibbs free energy ... More

Towards precision determination of uPDFsJul 29 2007The unintegrated Parton Density Function of the gluon is obtained from a fit to dijet production in DIS as measured at HERA. Reasonable descriptions of the measurements are obtained, and a first attempt to constrain the intrinsic transverse momentum distribution ... More

Small-x Physics and Forward Jet Production at THERAMay 14 2001We discuss some aspects of forward jet production as a signature for small $x$ physics at THERA energies.

Need for fully unintegrated parton densitiesAug 27 2005Associated with the use of conventional integrated parton densities are kinematic approximations on parton momenta which result in unphysical differential distributions for final-state particles. We argue that it is important to reformulate perturbative ... More

The generator problem for Z-stable C*-algebrasJan 18 2012The generator problem was posed by Kadison in 1967, and it remains open until today. We provide a solution for the class of C*-algebras absorbing the Jiang-Su algebra Z tensorially. More precisely, we show that every unital, separable, Z-stable C*-algebras ... More

Bifurcation of Nonlinear Bloch Waves from the Spectrum in the Gross-Pitaevskii EquationSep 15 2014Dec 14 2015We rigorously analyze the bifurcation of stationary so called nonlinear Bloch waves (NLBs) from the spectrum in the Gross-Pitaevskii (GP) equation with a periodic potential, in arbitrary space dimensions. These are solutions which can be expressed as ... More

Necessary subspace concentration conditions for the even dual Minkowski problemMar 30 2017We prove tight subspace concentration inequalities for the dual curvature measures $\widetilde{\mathrm{C}}_q(K,\cdot)$ of an $n$-dimensional origin-symmetric convex body for $q\geq n+1$. This supplements former results obtained in the range $q\leq n$. ... More