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Distributed Nonlinear Observer with Robust Performance - A Circle Criterion ApproachApr 11 2016Apr 12 2016In this paper, we present a distributed version of the KYP-Lemma with the goal to express the strictly positive real-property for a class of physically interconnected systems by a set of local LMI-conditions. The resulting conditions are subsequently ... More

A Polyhedral Approximation Framework for Convex and Robust Distributed OptimizationMar 25 2013In this paper we consider a general problem set-up for a wide class of convex and robust distributed optimization problems in peer-to-peer networks. In this set-up convex constraint sets are distributed to the network processors who have to compute the ... More

Searching bifurcations in high-dimensional parameter space via a feedback loop breaking approachDec 01 2008Sep 22 2010Bifurcations leading to complex dynamical behaviour of non-linear systems are often encountered when the characteristics of feedback circuits in the system are varied. In systems with many unknown or varying parameters, it is an interesting, but difficult ... More

A trajectory-based framework for data-driven system analysis and controlMar 26 2019Sep 04 2019The vector space of all input-output trajectories of a discrete-time linear time-invariant (LTI) system is spanned by time-shifts of a single measured trajectory, given that the respective input signal is persistently exciting. This fact, which was proven ... More

Network-level dynamics of diffusively coupled cellsDec 18 2012We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular perturbation, which ... More

Structured Optimal Feedback in Multi-Agent Systems: A Static Output Feedback PerspectiveSep 02 2016In this paper we demonstrate how certain structured feedback gains necessarily emerge as the optimal controller gains in two linear optimal control formulations for multi-agent systems. We consider the cases of linear optimal synchronization and linear ... More

A trajectory-based framework for data-driven system analysis and controlMar 26 2019The vector space of all input-output trajectories of a discrete-time linear time-invariant (LTI) system is spanned by time-shifts of a single measured trajectory, given that the respective input signal is persistently exciting. This fact, which was proven ... More

Economic model predictive control for snake robot locomotionSep 02 2019In this work, the control of snake robot locomotion via economic model predictive control (MPC) is studied. Only very few examples of applications of MPC to snake robots exist and rigorous proofs for recursive feasibility and convergence are missing. ... More

Economic MPC using a Cyclic Horizon with Application to Networked Control SystemsFeb 21 2019Jun 04 2019In this paper, we analyze an economic model predictive control scheme with terminal region and cost, where the system is optimally operated in a certain subset of the state space. The predictive controller operates with a cyclic horizon, which means that ... More

Fekete points, formation control, and the balancing problemJun 27 2016We study formation control problems. Our approach is to let a group of systems maximize their pairwise distances whilst bringing them all to a given submanifold, determining the shape of the formation. The algorithm we propose allows to initialize the ... More

Cooperative Estimation for Synchronization of Heterogeneous Multi-Agent Systems Using Relative InformationDec 07 2015In this paper, we present a distributed estimation setup where local agents estimate their states from relative measurements received from their neighbours. In the case of heterogeneous multi-agent systems, where only relative measurements are available, ... More

Estimation of biochemical network parameter distributions in cell populationsMay 08 2009Sep 27 2009Populations of heterogeneous cells play an important role in many biological systems. In this paper we consider systems where each cell can be modelled by an ordinary differential equation. To account for heterogeneity, parameter values are different ... More

Economic MPC using a Cyclic Horizon with Application to Networked Control SystemsFeb 21 2019In this paper, we analyze an economic model predictive control scheme with terminal region and cost, where the system is optimally operated in a certain subset of the state space. The predictive controller operates with a cyclic horizon, which means that ... More

Nonlinear Dynamic Periodic Event-Triggered Control with Robustness to Packet Loss Based on Non-Monotonic Lyapunov FunctionsAug 30 2019This paper considers the stabilization of nonlinear continuous-time dynamical systems employing periodic event-triggered control (PETC). Assuming knowledge of a stabilizing feedback law for the continuous-time system with a certain convergence rate, a ... More

Bridging Time Scales in Cellular Decision Making with a Stochastic Bistable SwitchMay 10 2010Cellular transformations which involve a significant phenotypical change of the cell's state use bistable biochemical switches as underlying decision systems. In this work, we aim at linking cellular decisions taking place on a time scale of years to ... More

On the differential equation $\dotΘ=(Θ^{T}-Θ)Θ$ with $Θ\in{SO(n)}$Aug 30 2013In this note we consider the global convergence properties of the differential equation $\dot{\Theta}=(\Theta^{T}-\Theta)\Theta$ with $\Theta\in{SO(n)}$, which is a gradient flow of the function $f:SO(n)\rightarrow\mathbb{R},\Theta\mapsto{2n-2\tr{\Theta}}$. ... More

Duality and Network Theory in Passivity-based Cooperative ControlJan 16 2013Sep 02 2013This paper presents a class of passivity-based cooperative control problems that have an explicit connection to convex network optimization problems. The new notion of maximal equilibrium independent passivity is introduced and it is shown that networks ... More

Cooperative H-infinity Estimation for Large-Scale Interconnected Linear SystemsJul 02 2015In this paper, a synthesis method for distributed estimation is presented, which is suitable for dealing with large-scale interconnected linear systems with disturbance. The main feature of the proposed method is that local estimators only estimate a ... More

Fekete points, formation control, and the balancing problemJun 27 2016Oct 25 2016We study formation control problems. Our approach is to let a group of systems maximize their pairwise distances whilst bringing them all to a given submanifold, determining the shape of the formation. The algorithm we propose allows to initialize the ... More

Cooperative Control of Linear Multi-Agent Systems via Distributed Output Regulation and Transient SynchronizationMay 31 2014A wide range of multi-agent coordination problems including reference tracking and disturbance rejection requirements can be formulated as a cooperative output regulation problem. The general framework captures typical problems such as output synchronization, ... More

Global Sensitivity Analysis of Biochemical Reaction Networks via Semidefinite ProgrammingApr 29 2009We study the problem of computing outer bounds for the region of steady states of biochemical reaction networks modelled by ordinary differential equations, with respect to parameters that are allowed to vary within a predefined region. Using a relaxed ... More

Geometric stability considerations of the ribosome flow model with poolOct 13 2016In order to better understand the process of gene translation, the ribosome flow model (RFM) with pool was introduced recently. This model describes the movement of several ribosomes along an mRNA template and simultaneously captures the dynamics of the ... More

Optimal pricing control in distribution networks with time-varying supply and demandMar 27 2014This paper studies the problem of optimal flow control in dynamic inventory systems. A dynamic optimal distribution problem, including time-varying supply and demand, capacity constraints on the transportation lines, and convex flow cost functions of ... More

Model-Free Practical Cooperative Control for Diffusively Coupled SystemsJun 12 2019In this paper, we develop a data-based controller design framework for diffusively coupled systems with guaranteed convergence to an $\epsilon$-neighborhood of the desired formation. The controller is comprised of a fixed controller with an adjustable ... 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

Stochastic MPC with Offline Uncertainty SamplingJun 20 2016For discrete-time linear systems subject to parametric uncertainty described by random variables, we develop a sampling-based Stochastic Model Predictive Control algorithm. Unlike earlier results employing a scenario approximation, we propose an offline ... More

Constraint-Tightening and Stability in Stochastic Model Predictive ControlNov 11 2015May 12 2016Constraint tightening to non-conservatively guarantee recursive feasibility and stability in Stochastic Model Predictive Control is addressed. Stability and feasibility requirements are considered separately, highlighting the difference between existence ... More

Generalization of the construction method for multistability-equivalent gene regulatory networks to systems with multi-input multi-output loopbreakingDec 27 2013Jan 02 2014The problem of equivalence in terms of multistability properties between gene regulatory network models of different dimensionality has been recently addressed by Schittler et al. (2013). The authors in that work proposed construction rules for a high-dimensional ... More

A resource dependent protein synthesis model for evaluating synthetic circuitsOct 13 2016Reliable in-silico design of synthetic gene networks necessitates novel approaches to model the process of protein synthesis under the influence of limited resources. We present such a novel protein synthesis model which originates from the Ribosome Flow ... More

Structural requirements and discrimination of cell differentiation networksJul 05 2011Mathematical models of stem cell differentiation are commonly based upon the concept of subsequent cell fate decisions, each controlled by a gene regulatory network. These networks exhibit a multistable behavior and cause the system to switch between ... More

Model-Free Practical Cooperative Control for Diffusively Coupled SystemsJun 12 2019Jun 13 2019In this paper, we develop a data-based controller design framework for diffusively coupled systems with guaranteed convergence to an $\epsilon$-neighborhood of the desired formation. The controller is comprised of a fixed controller with an adjustable ... More

An Improved Constraint-Tightening Approach for Stochastic MPCSep 29 2014The problem of achieving a good trade-off in Stochastic Model Predictive Control between the competing goals of improving the average performance and reducing conservativeness, while still guaranteeing recursive feasibility and low computational complexity, ... More

Model-Free Practical Cooperative Control for Diffusively Coupled SystemsJun 12 2019Jun 14 2019In this paper, we develop a data-based controller design framework for diffusively coupled systems with guaranteed convergence to an $\epsilon$-neighborhood of the desired formation. The controller is comprised of a fixed controller with an adjustable ... More

Robust data-driven state-feedback designSep 10 2019We consider the problem of designing robust state-feedback controllers for discrete-time linear time-invariant systems, based directly on measured data. The proposed design procedures require no model knowledge, but only a single open-loop data trajectory, ... More

Distributed Filter Design for Cooperative H-Infinity-Type EstimationSep 20 2015In this paper, we consider the distributed robust filtering problem, where estimator design is based on a set of coupled linear matrix inequalities (LMIs). We separate the problem and show that the method of multipliers can be applied to obtain a solution ... More

Iterative learning extremum seeking tracking via Lie bracket approximationSep 07 2015In this paper, we develop an extremum seeking control method integrated with iterative learning control to track a time-varying optimizer within finite time. The behavior of the extremum seeking system is analyzed via an approximating system - the modified ... More

Iterative Learning and Extremum Seeking for Repetitive Time-Varying MappingsSep 07 2015Dec 16 2017In this paper, we develop an extremum seeking control method integrated with iterative learning control to track a time-varying optimizer within finite time. The behavior of the extremum seeking system is analyzed via an approximating system - the modified ... 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

Experimental observation of transient velocity-selective coherent population trapping in one dimensionJan 27 2005We report the observation of transient velocity-selective coherent population trapping (VSCPT) in a beam of metastable neon atoms. The atomic momentum distribution resulting from the interaction with counterpropagating sigma_+ and sigma_- radiation which ... More

Theory Vision, LHCP 2016Sep 22 2016I give my perspective on promising directions for high energy physics in coming years.

Hilbert C*-modules over monotone complete C*-algebrasAug 31 1994Jul 27 2010The aim of the present paper is to describe self-duality and C*- reflexivity of Hilbert {\bf A}-modules $\cal M$ over monotone complete C*-algebras {\bf A} by the completeness of the unit ball of $\cal M$ with respect to two types of convergence being ... More

Rotation Numbers and Instability SetsMar 24 2003Translation and rotation numbers have played an interesting and important role in the qualitative description of various dynamical systems. In this exposition we are especially interested in applications which lead to proofs of periodic motions in various ... More

On the one-sided exit problem for fractional Brownian motionJan 26 2011We consider the one-sided exit problem for fractional Brownian motion (FBM), which is equivalent to the question of the distribution of the lower tail of the maximum of FBM on the unit interval. We improve the bounds given by Molchan (1999) and shed some ... More

Market depth and price dynamics: A noteMar 30 2004This note explores the consequences of nonlinear price impact functions on price dynamics within the chartist-fundamentalist framework. Price impact functions may be nonlinear with respect to trading volume. As indicated by recent empirical studies, a ... More

Quantum theory of the real and the complexified projective lineSep 28 2005Quantum deformations of sets of points of the real and the complexified projective line are constructed. These deformations depend on the deformation parameter q and certain further parameters \lambda_{ij}. The deformations for which the subspace of polynomials ... More

A family of non-restricted $D=11$ geometric supersymmetriesJun 18 2014Sep 24 2015We construct a two parameter family of eleven-dimensional indecomposable Cahen-Wallach spaces with irreducible, non-flat, non-restricted geometric supersymmetry of fraction $\nu=\tfrac{3}{4}$. Its compactified moduli space can be parametrized by a compact ... More

The Torsion of Spinor Connections and Related StructuresNov 09 2006In this text we introduce the torsion of spinor connections. In terms of the torsion we give conditions on a spinor connection to produce Killing vector fields. We relate the Bianchi type identities for the torsion of spinor connections with Jacobi identities ... More

Grand Challenges in Planetary Nebulae Studies: Binary Evolution and MHDJun 23 2006We review work on the evolution of planetary nebulae and proto-planetaries via magneto-rotational mechanisms showing that a dynamo generated magnetic field can produce the energy and momentum needed to drive pPN and PNe outflows. Angular momentum considerations ... More

Where's the Disk?: LBV bubbles and Aspherical Fast WindsMay 02 1997Previous studies have explained the shapes of LBV nebulae, such as eta Car, by invoking the interaction of an isotropic fast wind with a previously deposited, slow aspherical wind (a "slow torus"). In this work I focus on the opposite scenario where an ... More

Physics Performance with the CMS Pixel DetectorDec 17 2014A large fraction of the results produced by the LHC experiments during the first run were made possible by precision vertexing detectors. The all-silicon tracking detector of the CMS experiment uses a pixel detector to do vertexing. This conference report ... More

First Alignment of the Complete CMS TrackerMar 12 2010This conference proceeding presents the first results of the full CMS Tracker alignment based on several million reconstructed tracks from the cosmic data taken during the commissioning runs with the detector in its final position and magnetic field present. ... More

Enlightenment, Knowledge, Ignorance, TemptationDec 14 2005Dec 17 2005I discuss the historical and conceptual roots of reasoning about the parameters of fundamental physics and cosmology based on selection effects. I argue concretely that such reasoning can and should be combined with arguments based on symmetry and dynamics; ... More

From "Not Wrong" to (Maybe) RightMar 24 2004This is a short, light spirited account of how some possibly important science actually happened. It very much conflicts with Popper's contention that the key to scientific progress is falsification.

Radical Conservatism and Nucleon DecayFeb 03 2000Feb 10 2000Unification of couplings, observation of neutrino masses in the expected range, and several other considerations confirm central implications of straightforward gauge unification based on SO(10) or a close relative and incorporating low-energy supersymmetry. ... More

Some Examples in the Realization of SymmetryOct 16 1997I briefly discuss three phenomena arising in recent work where the realization of symmetries in quantum mechanics is unusual. The first of these is, I believe, the very simplest realization of non-trivial confinement by a mechanism of charge-flux frustration. ... More

Asymptotic FreedomSep 11 1996I discuss how the basic phenomenon of asymptotic freedom in QCD can be understood in elementary physical terms. Similarly, I discuss how the long-predicted phenomenon of ``gluonization of the proton'' -- recently spectacularly confirmed at HERA -- is ... More

Superfluidity and Space-Time Translation Symmetry BreakingAug 27 2013I present a simple model that exhibits a temporal analogue of superconducting crystalline (LOFF) ordering. I sketch designs for minimally dissipative AC circuits, all based on time translation symmetry ($\tau$) invariant dynamics, exploiting weak links ... More

Introduction to {\it Quantum Matter}Sep 07 2011Nov 22 2011This paper records my opening remarks at Nobel Symposium 148, on Graphene and Quantum Matter, at Saltsj\"obaden, Sweden, in June 2010. After some broad comments on the quantum theory of matter as a frontier of physics, and some slightly more particular ... More

Anticipating a New Golden AgeAug 31 2007Oct 02 2007The standard model of fundamental interactions is remarkably successful, but it leaves an unfinished agenda. Several major questions seem ripe for exploration in the near future. I anticipate that the coming decade will be a Golden Age of discovery in ... More

Some Basic Aspects of Fractional Quantum NumbersJun 07 2002I review why and how physical states with fractional quantum numbers can occur, emphasizing basic mechanisms in simple contexts. The general mechanism of charge fractionalization is the passage from states created by local action of fields to states having ... More

Four Big Questions with Pretty Good AnswersJan 23 2002Feb 05 2002I discuss four big questions that can be importantly addressed using concepts from modern QCD. They concern the origin of mass, the feebleness of gravity, the uniqueness of physical laws, and the fate of matter when it is squeezed very hard.

The Future of Particle Physics as a Natural ScienceFeb 19 1997Feb 20 1997In the first part of the talk, I give a low-resolution overview of the current state of particle physics - the triumph of the Standard Model and its discontents. I review and re-endorse the remarkably direct and (to me) compelling argument that existing ... More

Beyond the Standard ModelApr 30 1993The standard model of particle physics is marvelously successful. However, it is obviously not a complete or final theory. I shall argue here that the structure of the standard model gives some quite concrete, compelling hints regarding what lies beyond. ... More

Detector Systems at CLICSep 15 2011The Compact Linear Collider CLIC is designed to deliver e+e- collisions at a center of mass energy of up to 3 TeV. The detector systems at this collider have to provide highly efficient tracking and excellent jet energy resolution and hermeticity for ... More

When teaching: Out with magnitudes, in with monochromatic luminosities!Jul 09 2008The goal of this document is to illustrate that teaching the concepts of magnitudes is a needless complication in introductory astronomy courses, and that use of monochromatic luminosities, rather than arbitrarily defined magnitudes, leads to a large ... More

X-rays from old star clustersJul 15 1999A brief overview is given of X-ray observations of old clusters. Most X-ray sources in old open clusters are interacting binaries, formed via evolution of a primordial binary, and emitting X-rays because of magnetic activity; however, a sizable fraction ... More

Observations of accretion disks in X-ray binariesSep 03 1998A brief overview is given of the observations of accretion disks in X-ray binaries, discussing their geometry, their effect on the rotation period of the accreting object, their optical and X-ray spectra, time variability, and radio emission and jets. ... More

Recent PHENIX Results on pi+, pi-, and eta Production in polarized pp Collisions at RHIC at sqrt(s) = 200 GeVAug 29 2008Measurements of double helicity asymmetries for inclusive hadron production in polarized proton-proton collisions are sensitive to spin-dependent parton distribution functions, in particular to the gluon distribution function. This study focuses on double ... More

Trace functions with applications in quantum physicsMay 08 2013Jul 02 2013We consider both known and not previously studied trace functions with applications in quantum physics. By using perspectives we obtain convexity statements for different notions of residual entropy, including the entropy gain of a quantum channel as ... More

Trace functions as Laplace transformsJul 01 2005Aug 02 2005We study trace functions on the form $ t\to\tr f(A+tB) $ where $ f $ is a real function defined on the positive half-line, and $ A $ and $ B $ are matrices such that $ A $ is positive definite and $ B $ is positive semi-definite. If $ f $ is non-negative ... More

Mechanical oscillations at the cellular scaleJun 21 2001Active phenomena which involve force generation and motion play a key role in a number of phenomena in living cells such as cell motility, muscle contraction and the active transport of material and organelles. Here we discuss mechanical oscillations ... More

Comparative Study of $Z'$ Searches in $e^+e^-$ and $e^-e^-$ ScatteringFeb 29 1996We consider indirect searches for additional neutral vector bosons in $e^+e^-$ and $e^-e^-$ collisions, and compare these two linear collider modes with similar analysis procedures and assumptions. Discovery limits and resolving power are discussed in ... More

Slepton Production in Polarized $γγ$ ScatteringSep 27 1995We study slepton pair-production in polarized $\gamma\gamma$ scattering. It turns out that the combined use of polarization and angular correlations greatly enhances the resolving power of this reaction.

Accelerating QDP++/Chroma on GPUsNov 23 2011Extensions to the C++ implementation of the QCD Data Parallel Interface are provided enabling acceleration of expression evaluation on NVIDIA GPUs. Single expressions are off-loaded to the device memory and execution domain leveraging the Portable Expression ... More

Noncommutative Spaces and GravityOct 21 2005This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative spaces. Then ... More

Uncertain for A Century: Quantum Mechanics and The Dilemma of InterpretationFeb 07 2016Quantum Mechanics, the physical theory describing the microworld, represents one of science's greatest triumphs. It lies at the root of all modern digital technologies and offers unparalleled correspondence between prediction and experiments. Remarkably, ... More

General isotropic flags are general (for Grassmannian Schubert calculus)Jan 17 2008Jul 21 2008We show that general isotropic flags for odd-orthogonal and symplectic groups are general for Schubert calculus on the classical Grassmannian in that Schubert cells defined by such flags meet transversally. This strengthens a result of Belkale and Kumar ... More

Enumerative geometry for real varietiesSep 12 1996We discuss the problem of whether a given problem in enumerative geometry can have all of its solutions be real. In particular, we describe an approach to problems of this type, and show how this can be used to show some enumerative problems involving ... More

Lepton Flavor Violation at the LHCOct 12 2007In supersymmetric scenarios, the seesaw mechanism involving heavy right-handed neutrinos implies sizable lepton flavor violation (LFV) in the slepton sector. We discuss the potential of detecting LFV processes at the LHC in mSUGRA+seesaw scenarios and ... More

The chemistry induced by mechanical loadMay 11 2016Results in the field of mechanochemistry are summarized. For example under mechanical load often a solvolysis is observed instead of a simple homolytic bond rupture. Also a mechanically induced redox reaction was reported experimentally and could be modelled ... More

Groups in simple theoriesApr 25 1997Groups definable in simple theories retain the chain conditions and decomposition properties known from stable groups, up to commensurability. In the small case, if a generic type of G is not foreign to some type q, there is a q-internal quotient. In ... More

Semidefinite programming bounds for error-correcting codesFeb 04 2019This chapter is written for the forthcoming book "A Concise Encyclopedia of Coding Theory" (CRC press), edited by W. Cary Huffman, Jon-Lark Kim, and Patrick Sol\'e. This book will collect short but foundational articles, emphasizing definitions, examples, ... More

Problems on homology manifoldsOct 17 2003Mar 18 2009A list of problems prepared for the proceedings of the Workshop on Exotic Homology Manifolds, Oberwolfach June 29-July 5 2003.

Composition of operator ideals and their regular hullsApr 24 1996Given two quasi-Banach ideals \oid{A}{}{} and \oid{B}{}{} we investigate the regular hull of their composition - $(\oid{A}{}{} \circ \oid{B}{}{})^{reg}$. In concrete situations this regular hull appears more often than the composition itself. As a first ... More

Computational Complexity Analysis of Multi-Objective Genetic ProgrammingMar 22 2012The computational complexity analysis of genetic programming (GP) has been started recently by analyzing simple (1+1) GP algorithms for the problems ORDER and MAJORITY. In this paper, we study how taking the complexity as an additional criteria influences ... More

The Time Structure of Hadronic Showers in Imaging Calorimeters with Scintillator and RPC ReadoutAug 29 2013The intrinsic time structure of hadronic showers has been studied to evaluate its influence on the timing capability and on the required integration time of highly granular hadronic calorimeters in future collider experiments. The experiments have been ... More

Coherent Control of Floquet-Mode Dressed Plasmon PolaritonsJun 07 2012Sep 15 2015We study the coherent properties of plasmon polaritons optically excited on periodic nanostructures. The gold grains are coupled to a single mode photonic waveguide which exhibits a dramatically reduced transmission originating from the derived quantum ... More

Quantum Criticality and Population Trapping of Fermions by Non-Equilibrium Lattice ModulationsSep 18 2011Mar 04 2016An ultracold gas of interacting fermionic atoms in a three-dimensional optical lattice is considered, where the lattice potential strength is periodically modulated. This non-equilibrium system is non-perturbatively described by means of a Keldysh-Floquet-Green's ... More

The eigencurve is proper at integral weightsFeb 15 2007We prove that the Coleman-Mazur eigencurve is proper (over weight space) at integral weights in the center of weight space.

Noncommutative complex analytic spacesJun 07 2006In this paper, we define NC complex spaces as complex spaces together with a structure sheaf of associative algebras in such a way that the abelization of the structure sheaf is the sheaf of holomorphic functions.

Notes on Chain Recurrence and Lyapunonv FunctionsApr 24 2017This short expository note provides an introduction to the concept of chain recurrence in topological dynamics and a proof of the existence complete Lyapunov functions for homeomorphisms of compact metric spaces due to Charles Conley. I have used it as ... More

Distortion in Groups of Circle and Surface DiffeomorphismsMay 28 2007In these lectures we consider how algebraic properties of discrete subgroups of Lie groups restrict the possible actions of those groups on surfaces. The results show a strong parallel between the possible actions of such a group on the circle $S^1$ and ... More

Mod p representations on elliptic curvesJun 11 2004Modular Galois representations into GL_2(F_p) with cyclotomic determinant arise from elliptic curves for p = 2,3,5. We show (by constructing explicit examples) that such elliptic curves cannot be chosen to have conductor as small as possible at all primes ... More

Natural TopologyOct 23 2012We give a theoretical and applicable framework for dealing with real-world phenomena. Joining pointwise and pointfree notions in BISH, natural topology gives a faithful idea of important concepts and results in intuitionism. Natural topology is well-suited ... More

Hilbert H*-modules and Hilbert modules over (non-self-adjoint) operator algebras -- a reference overview IIMay 07 1996The two reference lists contain 54/22 references of papers and preprints concerned with the theory and/or various applications of Hilbert modules over Hilbert $*$-algebras and over (non-self-adjoint) operator algebras. They are far from being complete, ... More

Markov chain Monte Carlo importance samplers for Bayesian models with intractable likelihoodsApr 11 2019We consider the efficient use of an approximation within Markov chain Monte Carlo (MCMC), with subsequent importance sampling (IS) correction of the Markov chain inexact output, leading to asymptotically exact inference. We detail convergence and central ... More

Pieri-type formulas for maximal isotropic Grassmannians via triple intersectionsAug 29 1997We give an elementary proof of the Pieri-type formula in the cohomology of a Grassmannian of maximal isotropic subspaces of an odd orthogonal or symplectic vector space. This proof proceeds by explicitly computing a triple intersection of Schubert varieties. ... More

The law of proportionate growth and its siblings: Applications in agent-based modeling of socio-economic systemsSep 02 2019The law of proportionate growth simply states that the time dependent change of a quantity $x$ is proportional to $x$. Its applicability to a wide range of dynamic phenomena is based on various assumptions for the proportionality factor, which can be ... More

Characters and Brauer trees of the covering group of $^2E_6(2)$Sep 08 2016Let $G$ be the finite simple Chevalley group of type $^2E_6(2)$. It has a Schur multiplier of type $C_2^2 \times C_3$. We determine the ordinary character tables of the central extensions $3.G$, $6.G$, $(2^2\times 3).G$ of $G$ and their extensions by ... More