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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

The Africa-Dummy: Gone with the Millennium?Mar 06 2019A fixed effects regression estimator is introduced that can directly identify and estimate the Africa-Dummy in one regression step so that its correct standard errors as well as correlations to other coefficients can easily be estimated. We can estimate ... 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

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

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

Variational bounds for the shear viscosity of gelling meltsFeb 26 2007May 03 2007We study shear stress relaxation for a gelling melt of randomly crosslinked, interacting monomers. We derive a lower bound for the static shear viscosity $\eta$, which implies that it diverges algebraically with a critical exponent $k\ge 2\nu-\beta$. ... 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

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

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

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

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

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.

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

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

Pattern equivariant functions and cohomologyNov 29 2002The cohomology of a tiling or a point pattern has originally been defined via the construction of the hull or the groupoid associated with the tiling or the pattern. Here we present a construction which is more direct and therefore easier accessible. ... 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

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

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

Even an infinite bureaucracy eventually makes a decisionApr 01 2014We show that the fact that a political decision filtered through a finite tree of committees gives a determined answer generalises in some sense to infinite trees. This implies a new special case of the Matroid Intersection Conjecture.

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

Pseudo Maurer-Cartan perturbation algebra and pseudo perturbation lemmaDec 14 2018We introduce the pseudo Maurer-Cartan perturbation algebra, establish a structural result and explore the structure of this algebra. That structural result entails, as a consequence, what we refer to as the pseudo perturbation lemma. This lemma, in turn, ... More

The Lie algebra perturbation lemmaAug 29 2007Oct 16 2007Let g be a differential graded Lie algebra and suppose given a contraction of chain complexes of g onto a general chain complex M. We show that the data determine an sh-Lie algebra structure on M, that is, a coalgebra perturbation of the coalgebra differential ... 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

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

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

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

Determination of hydrogen cluster velocities and comparison with numerical calculationsJul 05 2013Jan 06 2014The use of powerful hydrogen cluster jet targets in storage ring experiments led to the need of precise data on the mean cluster velocity as function of the stagnation temperature and pressure for the determination of the volume density of the target ... More

Multi-Frame Super-Resolution Reconstruction with Applications to Medical ImagingDec 21 2018The optical resolution of a digital camera is one of its most crucial parameters with broad relevance for consumer electronics, surveillance systems, remote sensing, or medical imaging. However, resolution is physically limited by the optics and sensor ... More

On the variation of the Poisson structures of certain moduli spacesOct 29 1997Given a Lie group G whose Lie algebra is endowed with a nondegenerate invariant symmetric bilinear form, we construct a Poisson algebra of continuous functions on a certain open subspace R of the space of representations in G of the fundamental group ... More

Poisson geometry of flat connections for $\roman{SU}(2)$-bundles on surfacesDec 14 1993In earlier work we have shown that the moduli space $N$ of flat connections for the (trivial) $\roman{SU(2)}$-bundle on a closed surface of genus $\ell \geq 2$ inherits a structure of stratified symplectic space with two connected strata $N_Z$ and $N_{(T)}$ ... More

The Casson-Walker-Lescop Invariant and Link InvariantsJul 11 2000Formulas previously presented for the Casson-Walker invariant are generalized to Lescop's extension. These formulas in terms of linking numbers and surgery coefficients compute the change in Lescop's invariant under crossing changes in a framed link presenting ... More

Why Precision?May 22 2012Jun 07 2012Precision measurements together with exact theoretical calculations have led to steady progress in fundamental physics. A brief survey is given on recent developments and current achievements in the field of perturbative precision calculations in the ... More

Structural Relations of Harmonic Sums and Mellin Transforms at Weight w=6Jan 07 2009We derive the structural relations between nested harmonic sums and the corresponding Mellin transforms of Nielsen integrals and harmonic polylogarithms at weight {\sf w = 6}. They emerge in the calculations of massless single--scale quantities in QED ... More

Status of Deeply Inelastic Parton DistributionsNov 12 2007A brief review on the status of unpolarized parton densities and the determination of the QCD scale $\Lambda_{\rm QCD}$ from deep-inelastic scattering data is presented.

On the Anomalous Dimension of the Transversity Distribution $h_1(x,Q^2)$Apr 10 2001May 15 2001We calculate the leading order anomalous dimension of the transversity structure function directly using three different methods, the local light-cone expansion in the forward case, the non-forward case, and the short-distance expansion of the forward ... More

Precision of electro--weak couplings of scalar leptoquarks at TESLASep 28 2000Nov 29 2000We investigate the potential to measure the electro-weak couplings of scalar leptoquarks $\Phi_s$ at TESLA for energies in the range of $\sqrt{s} \simeq 1 \TeV$ using the pair production process $e^+e^- \to \Phi_s \bar{\Phi}_s$.

The Status of the Polarized Parton DensitiesAug 10 2007Aug 13 2007A survey is given on the present knowledge of the polarized parton distribution functions. We give an outlook for further developments desired both on the theoretical as well on the experimental side to complete the understanding of the spin--structure ... More

Analytic Continuation of Mellin Transforms up to two-loop OrderMar 10 2000The analytic continuation of the Mellin transforms to complex values of N for the basic functions $g_i(x)$ of the momentum fraction x emerging in the quantities of massless QED and QCD up to two-loop order, as the unpolarized and polarized splitting functions, ... More

Small $x$ Contributions to the Structure Function $F_L(x,Q^2)$Aug 26 1994The gluon contributions to $F_L(x,Q^2)$ in ${\cal O}(\alpha_s)$ are calculated taking into account the transverse momentum of the initial state parton. In comparison with collinear factorization $F_L(x,Q^2)$, is not affected at large $x$ but takes smaller ... More

Quantum Field Theories Coupled to Supergravity: AdS/CFT and Local CouplingsNov 03 2007Nov 25 2007This article is based on my PhD thesis and covers the following topics: Holographic meson spectra in a dilaton flow background, the mixed Coulomb-Higgs branch in terms of instantons on D7 branes, and a dual description of heavy-light mesons. Moreover, ... More

Duality between Wilson Loops and Scattering AmplitudesOct 21 2008Oct 27 2008We summarise the status of an intriguing new duality between planar maximally helicity violating scattering amplitudes and light-like Wilson loops in N=4 super Yang-Mills. In particular, we focus on the role played by (dual) conformal symmetry, which ... More

A brief introduction to Luttinger liquidsMay 05 2000I give a brief introduction to Luttinger liquids. Luttinger liquids are paramagnetic one-dimensional metals without Landau quasi-particle excitations. The elementary excitations are collective charge and spin modes, leading to charge-spin separation. ... More

Charge-Spin Separation and the Spectral Properties of Luttinger LiquidsOct 21 1993Oct 25 1993We compute the spectral function rho(q,omega) of the one- dimensional Luttinger model. We discuss the distinct influences of charge-spin separation and of the anomalous dimensions of the fermion operators and their evolution with correlation strength. ... More

DWSB for heterotic flux compactificationsMar 14 2011We investigate the construction of non-supersymmetric vacua in compactifications of heterotic string theory with intrinsic torsion and background fluxes. We do this by using the technique of domain-wall supersymmetry breaking (DWSB) that was developed ... More

Processes, Roles and Their InteractionsFeb 21 2012Taking an interaction network oriented perspective in informatics raises the challenge to describe deterministic finite systems which take part in networks of nondeterministic interactions. The traditional approach to describe processes as stepwise executable ... More

Determination of some exponents of approximation for Sturmian continued fractionsMar 29 2016We determine the classical approximation constants $w_{3}(\zeta),w_{3}^{\ast}(\zeta),\lambda_{3}(\zeta)$ such as the uniform constants $\widehat{w}_{3}(\zeta),\widehat{w}_{3}^{\ast}(\zeta),\widehat{\lambda}_{3}(\zeta)$ associated to real numbers $\zeta$ ... More

Index theory in spaces of manifoldsAug 04 2016Jan 25 2019We formulate and prove a generalization of the Atiyah-Singer family index theorem in the context of the theory of spaces of manifolds \`a la Madsen, Tillmann, Weiss, Galatius and Randal-Williams. Our results are for Dirac-type operators linear over arbitrary ... More

Dynamics of gene expression and the regulatory inference problemDec 21 2007Mar 05 2008From the response to external stimuli to cell division and death, the dynamics of living cells is based on the expression of specific genes at specific times. The decision when to express a gene is implemented by the binding and unbinding of transcription ... More

A characterization of the locally finite networks admitting non-constant harmonic functions of finite energyMay 10 2011We characterize the locally finite networks admitting non-constant harmonic functions of finite energy. Our characterization unifies the necessary existence criteria of Thomassen and of Lyons and Peres with the sufficient criterion of Soardi. We also ... More

Quasiparticle properties of strongly correlated electron systems with itinerant metamagnetic behaviorApr 18 2008Jul 22 2009A brief account of the zero temperature magnetic response of a system of strongly correlated electrons in strong magnetic field is given in terms of its quasiparticle properties. The scenario is based on the paramagnetic phase of the half-filled Hubbard ... More

Minimal free multi models for chain algebrasMay 10 2004Jan 21 2005Let R be a local ring and A a connected differential graded algebra over R which is free as a graded R-module. Using homological perturbation theory techniques, we construct a minimal free multi model for A having properties similar to that of an ordinary ... More

On the cohomology of the holomorph of a finite cyclic groupMar 02 2003Feb 11 2004The mod 2 cohomology algebra of the holomorph of any finite cyclic group whose order is a power of 2 is determined.

The Local Semicircle Law for Random Matrices with a Fourfold SymmetryJun 15 2015Oct 06 2015We consider real symmetric and complex Hermitian random matrices with the additional symmetry $h_{xy}=h_{N-x,N-y}$. The matrix elements are independent (up to the fourfold symmetry) and not necessarily identically distributed. This ensemble naturally ... More

Counting zeros of holomorphic functions of exponential growthOct 02 2009We consider the number of zeros of holomorphic functions in a bounded domain that depend on a small parameter and satisfy an exponential upper bound near the boundary of the domain and similar lower bounds at finitely many points along the boundary. Roughly ... More

Formal and rigid geometry: an intuitive introduction, and some applicationsJan 19 2007Mar 25 2009We give an informal introduction to formal and rigid geometry over complete discrete valuation rings, and we discuss some applications in algebraic and arithmetic geometry and singularity theory, with special emphasis on recent applications to the Milnor ... More

Secret Sharing and Shared InformationJun 21 2017Nov 10 2017Secret sharing is a cryptographic discipline in which the goal is to distribute information about a secret over a set of participants in such a way that only specific authorized combinations of participants together can reconstruct the secret. Thus, secret ... More

Group Extended Markov Systems, Amenability, and the Perron-Frobenius OperatorMay 23 2012Jun 04 2013We characterise amenability of a countable group in terms of the spectral radius of the Perron-Frobenius operator associated to a group extension of a countable Markov shift and a H\"older continuous potential. This extends a result of Day for random ... More

Lie-Rinehart algebras, descent, and quantizationMar 02 2003A Lie-Rinehart algebra consists of a commutative algebra and a Lie algebra with additional structure which generalizes the mutual structure of interaction between the algebra of functions and the Lie algebra of smooth vector fields on a smooth manifold. ... More

Kaehler spaces, nilpotent orbits, and singular reductionApr 23 2001Aug 13 2002For a stratified symplectic space, a suitable concept of stratified Kaehler polarization, defined in terms of an appropriate Lie-Rinehart algebra, encapsulates Kaehler polarizations on the strata and the behaviour of the polarizations across the strata ... More

Stratified Kaehler structures on adjoint quotientsApr 06 2004Nov 02 2006Given a compact Lie group, endowed with a bi-invariant Riemannian metric, its complexification inherits a Kaehler structure having twice the kinetic energy of the metric as its potential, and Kaehler reduction with reference to the adjoint action yields ... More

Severi varieties and holomorphic nilpotent orbitsJun 14 2002Jan 29 2004Each of the four critical Severi varieties arises from a minimal holomorphic nilpotent orbit in a simple regular rank 3 hermitian Lie algebra and each such variety lies as singular locus in a cubic--the chordal variety--in the corresponding complex projective ... More

The Cohen-Lenstra Heuristic: Methodology and ResultsDec 25 2009In number theory, great efforts have been undertaken to study the Cohen-Lenstra probability measure on the set of all finite abelian $p$-groups. On the other hand, group theorists have studied a probability measure on the set of all partitions induced ... More

Homological perturbations, equivariant cohomology, and Koszul dualityJan 14 2004Jul 31 2009Our main objective is to demonstrate how homological perturbation theory (HPT) results over the last 40 years immediately or with little extra work give some of the Koszul duality results that have appeared in the last decade. Higher homotopies typically ... More

Line bundles on moduli and related spacesJul 30 2009Let G be a Lie goup, let M and N be smooth connected G-manifolds, let f be a smooth G-map from M to N, and let P denote the fiber of f. Given a closed and equivariantly closed relative 2-form for f with integral periods, we construct the principal G-circle ... More

Relative homological algebra, equivariant de Rham theory, and Koszul dualityJan 14 2004Oct 02 2008Let G be a general (not necessarily finite dimensional compact) Lie group, let g be its Lie algebra, let Cg be the cone on g in the category of differential graded Lie algebras, and consider the functor which assigns to a chain complex V the V-valued ... More

Finding the Maximizers of the Information Divergence from an Exponential FamilyDec 23 2009This paper investigates maximizers of the information divergence from an exponential family $E$. It is shown that the $rI$-projection of a maximizer $P$ to $E$ is a convex combination of $P$ and a probability measure $P_-$ with disjoint support and the ... More

Diophantine approximation in prescribed degreeJan 04 2017Dec 19 2017We investigate approximation to a given real number by algebraic numbers and algebraic integers of prescribed degree. We deal with both best and uniform approximation, and highlight the similarities and differences compared with the intensely studied ... More