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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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

A Note on Space Tiling ZonotopesFeb 04 2004In 1908 Voronoi conjectured that every convex polytope which tiles space face-to-face by translations is affinely equivalent to the Dirichlet-Voronoi polytope of some lattice. In 1999 Erdahl proved this conjecture for the special case of zonotopes. A ... More

Laborexperimente zur Entstehung und Wirkung kosmischer MagnetfelderMar 10 2014Magnetic fields of cosmic bodies are generated by the hydromagnetic dynamo effect in moving electrically conducting fluids, such as liquid metals or plasmas. Once produced, cosmic magnetic fields are able to act back on moving fluids. This back-reaction ... More

Isomorphisms of Hilbert C*-Modules and $*$-Isomorphisms of Related Operator C*-AlgebrasMay 09 1995Let $\cal M$ be a Banach C*-module over a C*-algebra $A$ carrying two $A$-valued inner products $< .,. >_1$, $<.,. >_2$ which induce equivalent to the given one norms on $\cal M$. Then the appropriate unital C*-algebras of adjointable bounded $A$-linear ... More

Categorical characterizations of operator-valued measuresDec 30 2014The most general type of measurement in quantum physics is modeled by a positive operator-valued measure (POVM). Mathematically, a POVM is a generalization of a measure, whose values are not real numbers, but positive operators on a Hilbert space. POVMs ... More

Even Galois Representations and the Fontaine--Mazur conjecture IIDec 21 2010Sep 29 2011We prove, under mild hypotheses, that there are no irreducible two-dimensional_even_ Galois representations of $\Gal(\Qbar/\Q)$ which are de Rham with distinct Hodge--Tate weights. This removes the "ordinary" hypothesis required in previous work of the ... More

Semistable abelian varieties over Z[1/6] and Z[1/10]Mar 03 2001Continuing on from recent results of Brumer-Kramer and of Schoof, we show that there exist non-zero semistable Abelian varieties over Z[1/N], with N squarefree, if and only if N is not in the set {1,2,3,5,6,7,10,13}. Our results are contingent on the ... More

On the symmetrical Kullback-Leibler Jeffreys centroidsMar 29 2013Jan 22 2014Due to the success of the bag-of-word modeling paradigm, clustering histograms has become an important ingredient of modern information processing. Clustering histograms can be performed using the celebrated $k$-means centroid-based algorithm. From the ... More

Cramer-Rao Lower Bound and Information GeometryJan 16 2013Jan 24 2013This article focuses on an important piece of work of the world renowned Indian statistician, Calyampudi Radhakrishna Rao. In 1945, C. R. Rao (25 years old then) published a pathbreaking paper, which had a profound impact on subsequent statistical research. ... More

A sharp regularization error estimate for bang-bang solutions for an iterative Bregman regularization method for optimal control problemsJun 06 2016In the present work, we present numerical results for an iterative method for solving an optimal control problem with inequality contraints. The method is based on generalized Bregman distances. Under a combination of a source condition and a regularity ... More

YSO Jets and Molecular Outflows: Tracing the History of Star FormationApr 29 1998Collimated outflows from Young Stellar Objects (YSOs) can be seen as tracers of the accretion powered systems which drive them. In this paper I review some theoretical and observational aspects of YSO outflows through the prism of questions relating to ... More

Origins of MassJun 29 2012Aug 22 2012Newtonian mechanics posited mass as a primary quality of matter, incapable of further elucidation. We now see Newtonian mass as an emergent property. Most of the mass of standard matter, by far, arises dynamically, from back-reaction of the color gluon ... More

Prelude to Compressed Baryonic MatterJan 15 2010This is intended to appear as the introduction to "The CBM Physics Book: compressed baryonic matter in laboratory experiments" (ed. B. Friman, C. H\"ohne, S. Leupold, J. Knoll, J. Randrup, R. Rapp, P. Senger), to be published by Springer. At the end there ... More

Asymptotic Freedom: From Paradox to ParadigmFeb 11 2005Feb 15 2005Asymptotic freedom was developed as a response to two paradoxes: the weirdness of quarks, and in particular their failure to radiate copiously when struck; and the coexistence of special relativity and quantum theory, despite the apparent singularity ... More

A Model of Anthropic Reasoning, Addressing the Dark to Ordinary Matter CoincidenceAug 14 2004Sep 17 2004If inflation occurs after the breaking of Peccei-Quinn symmetry then large values of the breaking scale $F$, which are forbidden in conventional axion cosmology, are permitted, provided that we inhabit a region of the Multiverse where the initial misalignment ... More

A Constructive Critique of the Three Standard SystemsJan 17 2004This is a broad and in part unconventional review of our current knowledge of fundamental physics, emphasizing the potential for advances the LHC will open up.

Beyond The Standard Model: An Answer and Twenty QuestionsFeb 23 1998These are the essence of two lectures given at the Ettore Majorana Summer School, 1997, and the discussion sections which followed them. The title indicates their content: some reasoned expectations for physics beyond the Standard Model, and an annotated ... More

Fundamental ConstantsAug 31 2007The notion of ``fundamental constant'' is heavily theory-laden. A natural, fairly precise formulation is possible in the context of the standard model (here defined to include gravity). Some fundamental constants have profound geometric meaning. The ordinary ... More

QCD and Natural PhilosophyDec 05 2002Dec 12 2002QCD sheds considerable light on several of the most basic features of the natural world including the origin of mass, the feebleness of gravity, the extent to which the properties of matter can be determined conceptually, the possible utility of the anthropic ... More

Future SummaryJan 17 2001We are emerging from a period of consolidation in particle physics. Its great, historic achievement was to establish the Theory of Matter. This Theory will serve as our description of ordinary matter under ordinary conditions -- allowing for an extremely ... More

Quantum Field TheoryMar 09 1998May 19 1998I discuss the general principles underlying quantum field theory, and attempt to identify its most profound consequences. The deepest of these consequences result from the infinite number of degrees of freedom invoked to implement locality. I mention ... More

Particle Physics for CosmologyAug 09 1996I discuss some central issues in particle physics which are potentially relevant to cosmology. I first briefly review the present (glorious) experimental status of the Standard Model, emphasizing that it provides a firm foundation both for early Universe ... More

From the Standard Model to Dark MatterJan 19 1995The 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

WYD-like skew information measuresJul 18 2012Following recent advances in the theory of operator monotone functions we introduce new classes of WYD-like skew information measures.

Characterization of symmetric monotone metrics on the state space of quantum systemsJan 26 2006Mar 29 2006The quantum Fisher information is a Riemannian metric, defined on the state space of a quantum system, which is symmetric and decreasing under stochastic mappings. Contrary to the classical case such a metric is not unique. We complete the characterization, ... More

Binary evolution and neutron stars in globular clustersOct 02 2002Improved observations of globular clusters are uncovering a large number of radio pulsars and of X-ray sources. The latter include binaries in which a neutron star or a white dwarf accretes matter from a companion, recycled pulsars, and magnetically active ... More

Analyzing biosignals using the R freeware (open source) toolMar 16 2011Jul 08 2014For researchers in electromyography (EMG), and similar biosginals, signal processing is naturally an essential topic. There are a number of excellent tools available. To these one may add the freely available open source statistical software package R, ... More

Double Helicity Asymmetry and Cross Section for eta Production in Polarized pp Collisions at PHENIXDec 13 2006Measurements 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, Delta g. This study presents the ... More

Tropical InterpolationJan 11 2005Feb 05 2005This short article, which appeared in the MSRI Fall 2004 newletter, is intended for a general mathematical audience. It describes some mathematical themes from the Winter 2004 program at MSRI in topological aspects of real algebraic geometry in the context ... More

Cohomology of effect algebrasFeb 01 2016We will define two ways to assign cohomology groups to effect algebras, which occur in the algebraic study of quantum logic. The first way is based on Connes' cyclic cohomology. The resulting cohomology groups are related to the state space of the effect ... More

Leptoquark Production in $e^-e^-$ ScatteringOct 30 1995Mar 13 1996We consider the production of scalar and vector leptoquarks in $e^-e^-$ collisions. Although this reaction is not competitive with {\em e.g.} $e^-\gamma$ scattering for discovering these heavy states, it is the main process susceptible of differentiating ... More

Nuclear motion is classicalMay 23 2016The notion from ab-initio molecular dynamics simulations that nuclear motion is best described by classical Newton dynamics instead of the time-dependent Schr{\"o}dinger equation is substantiated. In principle a single experiment should bring clarity. ... More

Recent results in four-dimensional non-perturbative string theoryOct 25 2007We review recent progress in understanding non-perturbative instanton corrections to the hypermultiplet moduli space in type II string compactifications on Calabi-Yau threefolds.

New Results on Deeply Virtual Compton Scattering at H1, ZEUS and HERMESOct 29 2004The process of deeply virtual Compton scattering will be shortly introduced, and the latest results from measurements at the HERA ep-collider at DESY will be given. In particular, the cross section has been measured with increased statistics at the collider ... More

An experimental Study using ACSL and Frama-C to formulate and verify Low-Level Requirements from a DO-178C compliant Avionics ProjectAug 17 2015Safety critical avionics software is a natural application area for formal verification. This is reflected in the formal method's inclusion into the certification guideline DO-178C and its formal methods supplement DO-333. Airbus and Dassault-Aviation, ... More

Bubbles of congruent primesJan 25 2012Shiu proved that if a and q are arbitrary coprime integers, then there exist arbitrarily long strings of consecutive primes which are all congruent to a modulo q. We generalize Shiu's theorem to imaginary quadratic fields, where we prove the existence ... More

Computation of Kazhdan-Lusztig polynomials and some applications to finite groupsOct 22 2016We discuss a practical algorithm to compute parabolic Kazhdan-Lusztig polynomials. As an application we compute Kazhdan-Lusztig polynomials which are needed to evaluate a character formula for reductive groups due to Lusztig. Some coefficients of these ... More

A simplified disproof of Beck's three permutations conjecture and an application to root-mean-squared discrepancyNov 02 2018Nov 27 2018A $k$-permutation family on $n$ vertices is a set system consisting of the intervals of $k$ permutations of the integers $1$ through $n$. The discrepancy of a set system is the minimum over all red-blue vertex colorings of the maximum difference between ... More

On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract meansApr 08 2019The Jensen-Shannon divergence is a renown bounded symmetrization of the unbounded Kullback-Leibler divergence which measures the total Kullback-Leibler divergence to the average mixture distribution. However the Jensen-Shannon divergence between Gaussian ... More

Fractions in elementary educationNov 10 2013This paper is one of a series in which elementary-education practice is analyzed by comparison with the history of mathematics, mathematical structure, modern practice, and (occasionally) cognitive neuroscience. The primary concerns are: Why do so many ... More

Hyperelementary assembly for K-theory of virtually abelian groupsSep 13 2005Feb 16 2006Controlled $K$-theory is used to show that algebraic $K$-theory of virtually abelian groups is described by an assembly map defined using possibly-infinite hyperelementary subgroups. The Farrell-Jones summand (coming from infinite subgroups) is parameterized ... More

The first cohomology of separably rationally connected varietiesMar 09 2013Apr 21 2014In this short note we prove that if X is a separably rationally connected variety over an algebraically closed field of positive characteristic, then H^1(X, O_X)=0.

Dual 2-complexes in 4-manifoldsSep 27 2000Concerns decompositions of smooth 4-manifolds as the union of two handlebodies, each with handles of index <=2 (``Heegard'' decompositions).Sample result: Two 2-complexes are (up to 2-deformation) dual spines of a Heegard decomposition of the 4-sphere ... More

Pascal's Theorem and Quantum DeformationSep 28 2005By a transfer principle Pascal's Theorem is equivalent to a theorem about point pairs on the real line. It appears that Pascal's Theorem is equivalent to the vanishing of a common invariant of six quadratic forms. Using the q-deformed invariant theory ... More

Bad GroupsMar 06 2017There is no bad group of Morley rank 2n+1 with an abelian Borel subgroup of Morley rank n. In particular, there is no bad group of Morley rank 3 (O. Fr{\'e}con).

Deformation of singularities via $L_\infty$-algebrasJul 22 2004This is an addendum to the paper ``Deformation of $L_\infty$-Algebras'' of the same author. We explain in which way the deformation theory of $L_\infty$-algebras extends the deformation theory of singularities. We show that the construction of semi-universal ... More

On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract meansApr 08 2019Apr 30 2019The Jensen-Shannon divergence is a renown bounded symmetrization of the unbounded Kullback-Leibler divergence which measures the total Kullback-Leibler divergence to the average mixture distribution. However the Jensen-Shannon divergence between Gaussian ... More

Sur les Theoremes I et II de PainleveMar 02 2004We lecture on fundamental Painleve's early Theorems on first order ordinary differential equations with many examples. We end-up with two conjectures about the global analytic continuation of holonomy maps locally defined by Theorem II.

Versal deformation of the analytic saddle-nodeMar 03 2004We derive simple forms for saddle-node singular points of analytic foliations in the real or complex plane just by gluing foliated complex manifolds. We give the versal analytic deformation of the simplest model. We also derive a unique analytic form ... More

SUSY structures on deformed supermanifoldsJul 24 2007Mar 05 2008We construct a geometric structure on deformed supermanifolds as a certain subalgebra of the vector fields. In the classical limit we obtain a decoupling of the infinitesimal odd and even transformations, whereas in the semiclassical limit the result ... More

In orbifolds, small isoperimetric regions are small ballsDec 23 2006Jun 28 2008In a compact orbifold, for small prescribed volume, an isoperimetric region is close to a small metric ball; in a Euclidean orbifold, it is a small metric ball.

Regularity of area-minimizing surfaces in 3D polytopes and of invariant hypersurfaces in R^nApr 27 2004In (the surface of) a convex polytope P^3 in R^4, an area-minimizing surface avoids the vertices of P and crosses the edges orthogonally. In a smooth Riemannian manifold M with a group of isometries G, an area-minimizing G-invariant oriented hypersurface ... More

Real Rational Curves in GrassmanniansApr 29 1999Fulton asked how many solutions to a problem of enumerative geometry can be real, when that problem is one of counting geometric figures of some kind having specified position with respect to some general fixed figures. For the problem of plane conics ... More

Pieri's rule for flag manifolds and Schubert polynomialsMay 02 1995We establish the formula for multiplication by the class of a special Schubert variety in the integral cohomology ring of the flag manifold. This formula also describes the multiplication of a Schubert polynomial by either an elementary symmetric polynomial ... More

Homology manifolds and 4-dimensional surgeryApr 12 2005May 09 2005Withdrawn May 2005. There is an error in the even-dimensional case of the proof in the April 2005 version. The hoped-for 4-dimensional applications are unlikely to survive the repairs.

Symmetry in semidefinite programsJun 28 2007Jul 30 2008This paper is a tutorial in a general and explicit procedure to simplify semidefinite programs which are invariant under the action of a symmetry group. The procedure is based on basic notions of representation theory of finite groups. As an example we ... More

The Stable Homology of Congruence SubgroupsNov 20 2013Jan 30 2015In a previous paper, the author (together with Matthew Emerton) proved that the completed cohomology groups of SL_N(Z) are stable in fixed degree as N goes to infinity (Z may be replaced by the ring O_F of integers of any number field). In this paper, ... More

Existence of Least-perimeter PartitionsNov 27 2007Feb 19 2008We prove the existence of a perimeter-minimizing partition of R^n into regions of unit volume. We conclude with a short tribute to the late Manuel A. Fortes.

Three deformation functors for associative algebrasSep 27 2005Nov 29 2005We show that three deformation functors (deformations of the product, flat deformations and deformations of the relations) assigned to an associative algebra are naturally isomorphic.

Zhang Neural Networks for Fast and Accurate Computations of the Field of ValuesApr 23 2019In this paper a new and different neural network, called Zhang Neural Network (ZNN) is appropriated from discrete time-varying matrix problems and applied to the angle parameter-varying matrix field of values (FoV) problem. This problem acts as a test ... More

Applying Lepskij-Balancing in PracticeAug 03 2010In a stochastic noise setting the Lepskij balancing principle for choosing the regularization parameter in the regularization of inverse problems is depending on a parameter $\tau$ which in the currently known proofs is depending on the unknown noise ... More

Path regularity of Gaussian processes via small deviationsMay 20 2009We study the a.s. sample path regularity of Gaussian processes. To this end we relate the path regularity directly to the theory of small deviations. In particular, we show that if the process is $n$-times differentiable then the exponential rate of decay ... More

A q-product tutorial for a q-series MAPLE packageDec 16 1998This is a tutorial for using a new q-series Maple package. The package includes facilities for conversion between q-series and q-products and finding algebraic relations between q-series. Andrews found an algorithm for converting a q-series into a product. ... More

Frontiers of Reality in Schubert CalculusJul 10 2009Aug 06 2009The theorem of Mukhin, Tarasov, and Varchenko (formerly the Shapiro conjecture for Grassmannians) asserts that all (a priori complex) solutions to certain geometric problems in the Schubert calculus are actually real. Their proof is quite remarkable, ... More

Untersuchungen zur SprechtraktakustikFeb 07 2013May 10 2015This thesis investigates acoustic properties of the vocal tract. Starting from a historical background (to name a few: Galen, Ibn Sina/Avicenna, Mersenne, Hooke, Euler, Kempelen, Abbe Mical, Kratzenstein, Wheatstone, Helmholtz, Riesz, Dudley, Dunn, Kelly, ... More

Shintani's zeta function is not a finite sum of Euler productsDec 06 2011Nov 09 2012We prove that the Shintani zeta function associated to the space of binary cubic forms cannot be written as a finite sum of Euler products. Our proof also extends to several closely related Dirichlet series. This answers a question of Wright in the negative. ... More