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Data-Driven Model Predictive Control with Stability and Robustness GuaranteesJun 11 2019We propose a robust data-driven model predictive control (MPC) scheme to control linear time-invariant (LTI) systems. The scheme uses an implicit model description based on behavioral systems theory and past measured trajectories. In particular, it does ... More

Linear robust adaptive model predictive control: Computational complexity and conservatismSep 04 2019In this paper, we present a robust adaptive model predictive control (MPC) scheme for linear systems subject to parametric uncertainty and additive disturbances. The proposed approach provides a computationally efficient formulation with theoretical guarantees ... More

Harmonic Oscillator Trap and the Phase-Shift ApproximationJan 14 2016The energy-spectrum of two point-like particles interacting in a 3-D isotropic Harmonic Oscillator (H.O.) trap is related to the free scattering phase-shifts $\delta$ of the particles by a formula first published by Busch et al. It is here used to find ... More

Low density Neutron Matter at Finite and Zero TemperaturesMar 20 2008This report concerns the energy of neutron-matter for densities below $0.15 fm^{-3}$ and temperatures at and below $10 MeV$. Separable NN-interactions are obtained by inverse scattering from the experimental phase-shifts with specified momentum cut-offs ... More

Learning an Approximate Model Predictive Controller with GuaranteesJun 11 2018A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of nonlinear systems. ... More

Transfer Learning with Human Corneal Tissues: An Analysis of Optimal Cut-Off LayerJun 19 2018Jun 22 2018Transfer learning is a powerful tool to adapt trained neural networks to new tasks. Depending on the similarity of the original task to the new task, the selection of the cut-off layer is critical. For medical applications like tissue classification, ... More

Learning from a Handful Volumes: MRI Resolution Enhancement with Volumetric Super-Resolution ForestsFeb 15 2018Magnetic resonance imaging (MRI) enables 3-D imaging of anatomical structures. However, the acquisition of MR volumes with high spatial resolution leads to long scan times. To this end, we propose volumetric super-resolution forests (VSRF) to enhance ... More

Optimal $RH_2$-- and $RH_\infty$--Approximation of Unstable Descriptor SystemsMar 27 2012Aug 01 2012Stability perserving is an important topic in approximation of systems, e.g.\ model reduction. If the original system is stable, we often want the approximation to be stable. But even if an algorithm preserves stability the resulting system could be unstable ... More

Glassy dynamics in mono-, di-, and tri-propylene glycol: From the alpha- to the fast beta-relaxationOct 29 2008We present a thorough characterization of the glassy dynamics of three propylene glycols (mono-, di- and trimer) by broadband dielectric spectroscopy. By covering a frequency range of more than 15 decades, we have access to the entire variety of dynamic ... More

Efficient charge separation in organic photovoltaics through incoherent hoppingNov 02 2016We demonstrate that efficient and nearly field-independent charge separation in organic planar heterojunction solar cells can be described by an incoherent hopping mechanism. We model the separation efficiency of electron-hole pairs created at donor-acceptor ... More

The Orbit of GG Tau AApr 12 2011Apr 27 2011We present a study of the orbit of the pre-main-sequence binary system GG Tau A and its relation to its circumbinary disk, in order to find an explanation for the sharp inner edge of the disk. Three new relative astrometric positions of the binary were ... More

2D nanoporous membrane for cation removal from water: effects of ionic valence, membrane hydrophobicity and pore sizeFeb 09 2018Using molecular dynamic simulations we show that single-layers of molybdenum disulfide (MoS$_2$) and graphene can effectively reject ions and allow high water permeability. Solutions of water and three cations with different valence (Na$^+$, Zn$^{2+}$ ... More

On uniform approximation to successive powers of a real numberMar 30 2016Apr 20 2016We establish new inequalities involving classical exponents of Diophantine approximation. This allows for improving on the work of Davenport, Schmidt and Laurent concerning the maximum value of the exponent $\hat{\lambda}_{n}(\zeta)$ among all real transcendental ... More

Duality for Lie-Rinehart algebras and the modular classFeb 08 1997Jan 29 2004We introduce a notion of duality for a Lie-Rinehart algebra giving certain bilinear pairings in its cohomology generalizing the usual notions of Poincar\'e duality in Lie algebra cohomology and de Rham cohomology. We show that the duality isomorphisms ... More

The singularities of Yang-Mills connections for bundles on a surface. I. The local modelNov 22 1994Let $\Sigma$ be a closed surface, $G$ a compact Lie group, not necessarily connected, with Lie algebra $g$, endowed with an adjoint action invariant scalar product, let $\xi \colon P \to \Sigma$ be a principal $G$-bundle, and pick a Riemannian metric ... More

Topological quantization of boundary forces and the integrated density of statesNov 08 2003For quantum systems described by Schr\"odinger operators on the half-space $\RR^{d-1}\times\RR^{leq 0}$ the boundary force per unit area and unit energy is topologically quantised provided the Fermi energy lies in a gap of the bulk spectrum. Under this ... More

On The Algebraic Characterization of Aperiodic Tilings Related To ADE-Root SystemsOct 14 1992Dec 30 1992\noindent The algebraic characterization of classes of locally isomorphic aperiodic tilings, being examples of quantum spaces, is conducted for a certain type of tilings in a manner proposed by A. Connes. These $2$-dimensional tilings are obtained by ... More

Comments on the distinction between color- and flavor-branes and new D3-D7 solutions with eight superchargesJul 07 2010We investigate the distinction between color- and flavor-branes, that is usually made in the context of gauge/string duality with backreacting flavors. Our remarks are based on a series of examples concerning the role of source terms in relatively simple ... More

Nonparametric estimation in functional linear models with second order stationary regressorsJan 27 2009We consider the problem of estimating the slope parameter in functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of second order stationary random functions X1,...,Xn. An orthogonal series estimator of the functional ... More

Reduction of Multiple Harmonic Sums and Harmonic PolylogarithmsFeb 18 2004May 03 2004The alternating and non-alternating harmonic sums and other algebraic objects of the same equivalence class are connected by algebraic relations which are induced by the product of these quantities and which depend on their index calss rather than on ... More

Discovery Potential of MSSM Higgs Bosons with ATLASDec 19 2005In this article the potential of the ATLAS experiment to discover MSSM Higgs bosons is discussed. Various Monte-Carlo studies for SM Higgs boson production and dedicated MSSM Higgs boson analyses are taken into account to investigate the discovery potential ... More

Results on searches for new physics at HERAMay 13 2003The H1 and ZEUS collaborations have searched for signals of physics beyond the Standard Model in ep collisions at a center-of-mass energy of 301-319 GeV. During the HERA I phase each experiment accumulated an integrated luminosity of about 110 pb^{-1} ... More

Mutual information in interacting spin systemsMar 18 2013This thesis uses a quantity that is defined and justified by information theory -- mutual information -- to examine models of condensed matter systems. More precisely, it studies models which are made up out of ferromagnetically interacting spins. Quantum ... More

Recent development in parton shower multijet mergingJul 07 2016Higher order calculations are necessary to predict and describe measurements in high energy collider physics. In recent years multiple approaches to combine multiple next-to-leading (NLO) order corrections with parton showers had been presented. We present ... More

Efficient Completion of Weighted AutomataSep 13 2016We consider directed graphs with edge labels from a semiring. We present an algorithm that allows efficient execution of queries for existence and weights of paths, and allows updates of the graph: adding nodes and edges, and changing weights of existing ... More

Some notes on the regular graph defined by Schmidt and Summerer and uniform approximationJan 05 2016Jan 12 2016Within the study of parametric geometry of numbers W. Schmidt and L. Summerer introduced so-called regular graphs. Roughly speaking the successive minima functions for the classical simultaneous Diophantine approximation problem have a very special pattern ... More

Secure Numerical and Logical Multi Party OperationsNov 12 2015Jan 31 2016We derive algorithms for efficient secure numerical and logical operations using a recently introduced scheme for secure multi-party computation~\cite{sch15} in the semi-honest model ensuring statistical or perfect security. To derive our algorithms for ... More

Discrete quantum geometries and their effective dimensionOct 29 2015In several approaches towards a quantum theory of gravity, such as group field theory and loop quantum gravity, quantum states and histories of the geometric degrees of freedom turn out to be based on discrete spacetime. The most pressing issue is then ... More

Describing the Heat Transport of Turbulent Rayleigh--Bénard Convection by POD methodsOct 23 2015Rayleigh--B\'enard convection, which is the buoyancy-induced motion of a fluid enclosed between two horizontal plates, is an idealised setup to study thermal convection. We analyse the modes that transport the most heat between the plates by computing ... More

G-bundles on the absolute Fargues-Fontaine curveJun 03 2016We prove that the category of vector bundles on the absolute Fargues-Fontaine curve is canonically equivalent to the category of isocrystals. We deduce a similar result for G-bundles for some arbitrary reductive group G over a p-adic local field.

Paradigm shifts. Part I. Collagen. Confirming and complementing the work of Henry SmallNov 27 2014Dec 07 2014The paradigm shift in collagen research during the early 1970s marked by the discovery of the collagen precursor molecule procollagen was traced using co-citation analysis and title word frequency determination, confirming previous work performed by Henry ... More

Change-point tests under local alternatives for long-range dependent processesJun 24 2015We consider the change-point problem for the marginal distribution of subordinated Gaussian processes that exhibit long-range dependence. The asymptotic distributions of Kolmogorov-Smirnov- and Cram\'er-von Mises type statistics are investigated. A special ... More

Normality of algebras over commutative rings, crossed pairs, and the Teichmueller classDec 22 2015Let S be a commutative unitary ring, Q a group that acts on S, and let R be the subring of S fixed under Q. A Q-normal S-algebra consists of a central S-algebra A and a homomorphism s from Q to the group Out(A) of outer automorphisms of A that lifts the ... More

Deformations of $Ξ(s)=Ξ(1-s)$ and the heat equationOct 13 2015This paper studies deformations of the well-known $\Xi(s)=\Xi(1-s)$ equation for the Riemann $\Xi$ function satisfied by $\Xi_\rho(s):=\int_{0}^\infty\frac{{\d}t}{t}{t^{\frac{s}{2}}}\Psi(t)e^{-\rho\ln^2(t)}$ where ${\Psi(t)=\sum_{n\in\mathbb{N}^+}e^{-\pi{n}^2t}}$. ... More

Matching effective few-nucleon theories to QCDSep 25 2015May 17 2016The emergence of complex macroscopic phenomena from a small set of parameters and microscopic concepts demonstrates the power and beauty of physical theories. A theory which relates the wealth of data and peculiarities found in nuclei to the small number ... More

The spinorial energy functional: solutions of the gradient flow on Berger spheresOct 16 2015We study the negative gradient flow of the spinorial energy functional (introduced by Ammann, Wei{\ss}, and Witt) on 3-dimensional Berger spheres. For a certain class of spinors we show that the Berger spheres collapse to a 2-dimensional sphere. Moreover, ... More

A General Multi-Party Protocol for Minimal Communication and Local ComputationAug 31 2015Jan 31 2016A client wishes to outsource computation on confidential data to a network of servers. He does not trust a server on its own, but believes that servers do not collude. To solve this problem we introduce a new scheme called \emph{JOS} for perfect security ... More

Drawing and Analyzing Causal DAGs with DAGittyAug 19 2015DAGitty is a software for drawing and analyzing causal diagrams, also known as directed acyclic graphs (DAGs). Functions include identification of minimal sufficient adjustment sets for estimating causal effects, diagnosis of insufficient or invalid adjustment ... More

Research at UNIS - The University Centre in Svalbard. A bibliometric studyMay 25 2014Jun 17 2014The scientific output 1994-2014 of the University Centre in Svalbard (UNIS) was bibliometrically analysed. It was found that the majority of the papers have been published as international cooperations and rank above world average. Analysis of the content ... More

Functional linear instrumental regression under second order stationarityMar 04 2016We consider the problem of estimating the slope parameter in functional linear instrumental regression, where in the presence of an instrument W, i.e., an exogenous random function, a scalar response Y is modeled in dependence of an endogenous random ... More

How Are Programs Found? Speculating About Language Ergonomics With Curry-HowardDec 02 2016Functional languages with strong static type systems have beneficial properties to help ensure program correctness and reliability. Surprisingly, their practical significance in applications is low relative to other languages lacking in those dimensions. ... More

The Weight in EnumerationDec 02 2016In our setting enumeration amounts to generate all solutions of a problem instance without duplicates. We address the problem of enumerating the models of B-formulae. A B-formula is a propositional formula whose connectives are taken from a fixed set ... More

Research performance of UNU - A bibliometric analysis of the United Nations UniversityDec 15 2016The scientific paper output of the United Nations University (UNU) was bibliometrically analysed.It was found that (i) a noticeable continous paper output starts in 1995, (ii) about 65% of the research papers have been published as international cooperations ... More

Embedding simply connected 2-complexes in 3-space -- II. Rotation systemsSep 14 2017We prove that 2-dimensional simplicial complexes whose first homology group is trivial have topological embeddings in 3-space if and only if there are embeddings of their link graphs in the plane that are compatible at the edges and they are simply connected. ... More

Collaborative Nested Sampling: Big Data vs. complex physical modelsJul 14 2017Oct 02 2018The data torrent unleashed by current and upcoming astronomical surveys demands scalable analysis methods. Many machine learning approaches scale well, but separating the instrument measurement from the physical effects of interest, dealing with variable ... More

BPS-like potential for compactifications of heterotic M-theory?Sep 09 2011Nov 07 2011We analyze the possibility to rewrite the action of Horava-Witten theory in a BPS-like form, which means that it is given as a sum of squares of the supersymmetry conditions. To this end we compactify the theory on a seven dimensional manifold of SU(3) ... More

The low-dimensional homotopy of the stable mapping class groupJul 06 2007Due to the deep work of Tillmann, Madsen, Weiss and Galatius, the cohomology of the stable mapping class group $\gaminf$ is known with rational or finite field coefficients. Little is known about the integral cohomology. In this paper, we study the first ... More

Measuring Object-Oriented Design PrinciplesFeb 23 2016The idea of automatizing the assessment of objectoriented design is not new. Different approaches define and apply their own quality models, which are composed of single metrics or combinations thereof, to operationalize software design. However, single ... More

Deformations of asymptotically cylindrical G_2 manifoldsMay 30 2007Mar 11 2009We prove that for a 7-dimensional manifold M with cylindrical ends the moduli space of exponentially asymptotically cylindrical torsion-free G_2 structures is a smooth manifold (if non-empty), and study some of its local properties. We also show that ... More

Eigenvalue distributions and Weyl laws for semi-classical non-self-adjoint operators in 2 dimensionsApr 25 2008In this note we compare two recent results about the distribution of eigenvalues for semi-classical pseudodifferential operators in two dimensions. For classes of analytic operators A. Melin and the author obtained a complex Bohr-Sommerfeld rule, showing ... More

A vanishing theorem for characteristic classes of odd-dimensional manifold bundlesFeb 27 2009Mar 09 2010We show how the Atiyah-Singer family index theorem for both, usual and self-adjoint elliptic operators fits naturally into the framework of the Madsen-Tillmann-Weiss spectra. Our main theorem concerns bundles of odd-dimensional manifolds. Using completely ... More

Ricci-flat deformations and special holonomyAug 03 2010Let G be one of the Ricci-flat holonomy groups SU(n), Sp(n), Spin(7) or G_2, and M a compact manifold of dimension 2n, 4n, 8 or 7, respectively. We prove that the natural map from the moduli space of torsion-free G-structures on M to the moduli space ... More

KMS states on the Toeplitz algebras of higher-rank graphsMay 23 2018The Toeplitz algebra $\mathcal{T}C^{*}(\Lambda)$ for a finite $k$-graph $\Lambda$ is equipped with a continuous one-parameter group $\alpha^{r}$ for each $ r\in \mathbb{R}^{k}$, obtained by composing the map $\mathbb{R} \ni t \to (e^{itr_{1}}, \dots , ... More

Equivariant cohomology over Lie groupoids and Lie-Rinehart algebrasJul 31 2009Using the language and terminology of relative homological algebra, in particular that of derived functors, we introduce equivariant cohomology over a general Lie-Rinehart algebra and equivariant de Rham cohomology over a locally trivial Lie groupoid ... More

On the spectrum of positive finite-rank operators with a partition of unity propertyMar 18 2014We characterize the spectrum of positive linear operators $T:X \to Y$, where $X$ and $Y$ are complex Banach function spaces with unit $1$, having finite rank and a partition of unity property. Then all the points in the spectrum are eigenvalues of $T$ ... More

A compactification of the moduli space of self-maps of $\mathbb{CP}^1$ using stable mapsApr 29 2016We present a new compactification $M(d,n)$ of the moduli space of self-maps of $\mathbb{CP}^1$ of degree $d$ with $n$ markings. It is constructed via GIT from the stable maps moduli space $\ ar M_{0,n}(\mathbb{CP}^1 \times \mathbb{CP}^1, (1,d))$. We show ... More

Resonances associated to a closed hyperbolic trajectory in dimension 2Sep 12 2002We consider resonances in the semi-classical limit, generated by a single closed hyperbolic orbit, for an operator on ${\bf R}^2$. We determine all such resonancess in a domain independent of the semi-classical parameter As an application we determine ... More

Next Event BacktrackingSep 02 2019In light transport simulation, challenging situations are caused by the variety of materials and the relative length of path segments. Path Tracing can handle many situations and scales well to parallel hardware. However, it is not able to produce paths ... More

On intrinsic and extrinsic rational approximation to Cantor setsDec 27 2018Sep 09 2019We establish various new results on a problem proposed by K. Mahler in 1984 concerning rational approximation to fractal sets by rational numbers inside and outside the set in question, respectively. Some of them provide a natural continuation and improvement ... More

Rational approximation to surfaces defined by polynomials in one variableJan 12 2016We study the rational approximation properties of special manifolds defined by a set of polynomials with rational coefficients. Mostly we will assume the case of all polynomials to depend on only one variable. In this case the manifold can be viewed as ... More

Jantzen sum formula for restricted Verma modules over affine Kac-Moody algebras at the critical levelDec 01 2012May 21 2013For a restricted Verma module of an affine Kac-Moody algebra at the critical level we describe the Jantzen filtration and give an alternating sum formula which corresponds to the Jantzen sum formula of a baby Verma module over a modular Lie algebra. This ... More

Auslander-Reiten triangles and Grothendieck groups of triangulated categoriesApr 04 2019We prove that if the Auslander-Reiten triangles generate the relations for the Grothendieck group of a Hom-finite Krull-Schmidt triangulated category with a cogenerator, then the category has only finitely many isomorphism classes of indecomposable objects ... More

On uniform approximation to successive powers of a real numberMar 30 2016Jan 11 2017We establish new inequalities involving classical exponents of Diophantine approximation. This allows for improving on the work of Davenport, Schmidt and Laurent concerning the maximum value of the exponent $\hat{\lambda}_{n}(\zeta)$ among all real transcendental ... More

Relaxation of Surface Profiles by Evaporation DynamicsJul 18 1997We present simulations of the relaxation towards equilibrium of one dimensional steps and sinusoidal grooves imprinted on a surface below its roughening transition. We use a generalization of the hypercube stacking model of Forrest and Tang, that allows ... More

Power Utility Maximization in Discrete-Time and Continuous-Time Exponential Levy ModelsMar 29 2011Apr 26 2012Consider power utility maximization of terminal wealth in a 1-dimensional continuous-time exponential Levy model with finite time horizon. We discretize the model by restricting portfolio adjustments to an equidistant discrete time grid. Under minimal ... More

Embedding simply connected 2-complexes in 3-space -- I. A Kuratowski-type characterisationSep 14 2017Sep 04 2019We characterise the embeddability of simply connected locally 3-connected 2-dimensional simplicial complexes in 3-space in a way analogous to Kuratowski's characterisation of graph planarity, by excluded minors. This answers questions of Lov\'asz, Pardon ... More

Thick subcategories of finite algebraic triangulated categoriesOct 01 2010We classify the thick subcategories of an algebraic triangulated standard category with finitely many indecomposable objects.

Barbasch-Sahi algebras and Dirac cohomologyAug 26 2016Sep 06 2016We define a class of algebras which are distinguished by a PBW property and an orthogonality condition, and which we call Hopf-Hecke algebras, since they generalize the Drinfeld Hecke algebras defined by Drinfeld. In the course of studying the orthogonality ... More

Index theory in spaces of noncompact manifolds I: Analytical foundationsAug 04 2016We develop elliptic regularity theory for Dirac operators in a very general framework: we consider Dirac operators linear over $C^*$-algebras, on noncompact manifolds, and in families which are not necessarily locally trivial fibre bundles.

A theoretical study of the dynamics of paramagnetic superrotors in external magnetic fieldsApr 13 2015Apr 20 2015We present a detailed theoretical study of oxygen molecules in high rotational states (molecular superrotors) interacting with an external magnetic field. The system shows rich dynamics, ranging from a spin-selective splitting of the angular distribution ... More

Extended moduli spaces and the Kan construction.II.Lattice gauge theoryJun 14 1995Let $Y$ be a CW-complex with a single 0-cell, $K$ its Kan group, a model for the loop space of $Y$, and let $G$ be a compact, connected Lie group. We give an explicit finite dimensional construction of generators of the equivariant cohomology of the geometric ... More

Symplectic and Poisson structures of certain moduli spaces. II. Projective representations of cocompact discrete planar groupsDec 21 1994Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary infinite orientation ... More

Extensions of Lie-Rinehart algebras and the Chern-Weil constructionJun 01 1997A Chern-Weil construction for extensions of Lie-Rinehart algebras is introduced. This generalizes the classical Chern-Weil construction in differential geometry and yields characteristic classes for arbitrary extensions of Lie-Rinehart algebras. Some ... More

The QCD Coupling and Parton Distributions at High PrecisionJul 29 2010Sep 10 2010A survey is given on the present status of the nucleon parton distributions and related precision calculations and precision measurements of the strong coupling constant $\alpha_s(M_Z^2)$. We also discuss the impact of these quantities on precision observables ... More

Structural Relations of Harmonic Sums and Mellin Transforms up to Weight w = 5Jan 20 2009Aug 26 2009We derive the structural relations between the Mellin transforms of weighted Nielsen integrals emerging in the calculation of massless or massive single--scale quantities in QED and QCD, such as anomalous dimensions and Wilson coefficients, and other ... More

Geometric limits to geometric optical imaging with infinite, planar, non-absorbing sheetsJan 23 2009May 25 2009New ray-optical elements allow generalized refraction of light rays, but geometry imposes limitations on possible mappings between the positions of an object and its geometric image. Here I study the case of an infinite, planar, non-absorbing sheet that ... More

Bayesian evidence for non-zero theta_13 and CP-violation in neutrino oscillationsMay 20 2012Aug 31 2012We present the Bayesian method for evaluating the evidence for a non-zero value of the leptonic mixing angle theta_13 and CP-violation in neutrino oscillation experiments. This is an application of the well-established method of Bayesian model selection, ... More

Trust, but verify: benefits and pitfalls of least-squares refitting in high dimensionsJun 01 2013Least-squares refitting is widely used in high dimensional regression to reduce the prediction bias of l1-penalized estimators (e.g., Lasso and Square-Root Lasso). We present theoretical and numerical results that provide new insights into the benefits ... More

Spectral properties of Luther-Emery systemsFeb 15 1996We calculate the spectral function of the Luther-Emery model which describes one-dimensional fermions with gapless charge and gapped spin degrees of freedom. We find a true singularity with interaction dependent exponents on the gapped spin dispersion ... More

Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant KMay 11 2017We consider systems A_\ell(t) y(q^\ell t) + ... + A_0(t) y(t) = b(t) of higher order q-recurrence equations with rational coefficients. We extend a method for finding a bound on the maximal power of t in the denominator of arbitrary rational solutions ... More

On a question of Schmidt and Summerer concerning $3$-systemsMay 11 2018Dec 27 2018Following a suggestion of W.M. Schmidt and L. Summerer, we construct a proper $3$-system $(P_{1},P_{2},P_{3})$ with the property $\overline{\varphi}_{3}=1$. In fact, our method generalizes to provide $n$-systems with $\overline{\varphi}_{n}=1$, for arbitrary ... More

Mesoscopic pairing without superconductivityJul 18 2017We discuss pairing signatures in mesoscopic nanowires with variable attractive pairing interaction. Depending on wire length, density, and interaction strength, these systems realize a simultaneous bulk-to-mesoscopic and BCS-BEC crossover, which we describe ... More

Symmetries of the KMS simplexOct 12 2017Aug 31 2018A continuous groupoid homomorphism $c$ on a locally compact second countable Hausdorff \'etale groupoid $\mathcal{G}$ gives rise to a $C^{*}$-dynamical system in which every $\beta$-KMS state can be associated to a $e^{-\beta c}$-quasi-invariant measure ... More

On the C*-algebraic approach to topological phases for insulatorsSep 21 2015Feb 17 2017The notion of a topological phase of an insulator is based on the concept of homotopy between Hamiltonians. It therefore depends on the choice of a topological space to which the Hamiltonians belong. We advocate that this space should be the $C^*$-algebra ... More

Transport and generation of macroscopically modulated waves in diatomic chainsMay 08 2011We derive and justify analytically the dynamics of a small macroscopically modulated amplitude of a single plane wave in a nonlinear diatomic chain with stabilizing on-site potentials including the case where a wave generates another wave via self-interaction. ... More

A Combinatorial Classification of Postcritically Fixed Newton MapsJan 05 2007We give a combinatorial classification for the class of postcritically fixed Newton maps of polynomials and indicate potential for extensions. As our main tool, we show that for a large class of Newton maps that includes all hyperbolic ones, every component ... More

Spectral properties of non-self-adjoint operatorsFeb 25 2010This text is a slightly expanded version of my 6 hour mini-course at the PDE-meeting in \'Evian-les-Bains in June 2009. The first part gives some old and recent results on non-self-adjoint differential operators. The second part is devoted to recent results ... More

A counterexample to Gouvêa's Dimension ConjectureMar 20 2012In this note we provide a counterexample to a conjecture due to F. Gouv\^ea, which says that the Krull dimension of the universal deformation ring - as defined by B. Mazur - associated to an absolutely irreducible residual representation could be expressed ... More

Local limit theorem for the maximum of a random walkMar 28 2014Mar 31 2014Consider a family of $\Delta$-latticed aperiodic random walks $\{S^{(a)},0\le a\le a_0\}$ with increments $X_i^{(a)}$ and non-positive drift $-a$. Suppose that $\sup_{a\le a_0}\mathbf{E}[(X^{(a)})^2]<\infty$ and $\sup_{a\le a_0}\mathbf{E}[\max\{0,X^{(a)}\}^{2+\varepsilon}]<\infty$ ... More

Integral powers of numbers in small intervals modulo $1$: The cardinality gap phenomenonJan 28 2015May 30 2016This paper deals with the distribution of $\alpha \zeta^{n} \bmod 1$, where $\alpha\neq 0,\zeta>1$ are fixed real numbers and $n$ runs through the positive integers. Denote by $\Vert.\Vert$ the distance to the nearest integer. We investigate the case ... More

Weyl law for semi-classical resonances with randomly perturbed potentialsNov 15 2011Dec 21 2013In this work we consider semi-classical Schr\"odinger operators with potentials supported in a bounded strictly convex subset ${\cal O}$ of ${\bf R}^n$ with smooth boundary. Letting $h$ denote the semi-classical parameter, we consider certain classes ... More

Non-equilibrium dynamics of gene expression and the Jarzynski equalityDec 03 2007In order to express specific genes at the right time, the transcription of genes is regulated by the presence and absence of transcription factor molecules. With transcription factor concentrations undergoing constant changes, gene transcription takes ... More

Statistical mechanics of random two-player gamesOct 22 1999Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate quantities ... More

The formal Kuranishi parametrization via the universal homological perturbation theory solution of the deformation equationJun 08 2018Using homological perturbation theory, we develop a formal version of the miniversal deformation associated with a deformation problem controlled by a differential graded Lie algebra over a field of characteristic zero. Our approach includes a formal ... More

Block bootstrap for the empirical process of long-range dependent dataJan 06 2016We consider long-range dependent data. It is shown that the bootstrapped empirical process of these data converges to a semi-degenerate limit. The random part of this limit is always Gaussian. Thus the bootstrap might fail when the original empirical ... More

Reductive group schemes over the Fargues-Fontaine curveMar 02 2017For an arbitrary non-archimedean local field we classify reductive group schemes over the corresponding Fargues-Fontaine curve by group schemes over the category of isocrystals. We then classify torsors under such reductive group schemes by a generalization ... More

On the construction of A-infinity structuresSep 27 2008We relate a construction of Kadeishvili's establishing an A-infinity-structure on the homology of a differential graded algebra or more generally of an A-infinity algebra with certain constructions of Chen and Gugenheim. Thereafter we establish the links ... More

The sh-Lie algebra perturbation LemmaOct 10 2007Feb 04 2010Let R be a commutative ring which contains the rationals as a subring and let g be a chain complex. Suppose given an sh-Lie algebra structure on g, that is, a coalgebra perturbation of the coalgebra differential on the cofree coaugmented differential ... More

Competing interactions and symmetry breaking in the Hubbard-Holstein modelJul 22 2009May 19 2010Competing interactions are often responsible for intriguing phase diagrams in correlated electron systems. Here we analyze the competition of instantaneous short range Coulomb interaction $U$ with the retarded electron-electron interaction induced by ... More

A spectral method for integral formulations of medium-frequency scattering problemsAug 26 2005A fast method for the computation of layer potentials that arise in acoustic scattering is introduced. The principal idea is to split the singular kernel into a smooth and a local part. The potential due to the smooth part is computed efficiently using ... More