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Complexity and Approximation of the Continuous Network Design ProblemJul 16 2013Nov 12 2013We revisit a classical problem in transportation, known as the continuous (bilevel) network design problem, CNDP for short. We are given a graph for which the latency of each edge depends on the ratio of the edge flow and the capacity installed. The goal ... More

Pricing in Resource Allocation Games Based on Duality GapsJul 03 2019Jul 09 2019We consider a basic resource allocation game, where the players' strategy spaces are subsets of $\mathbb{R}^m$ and cost/utility functions are parameterized by some common vector $u$ and, otherwise, only depend on the own strategy choice. A strategy of ... More

Pricing in Resource Allocation Games Based on Duality GapsJul 03 2019We consider a basic resource allocation game, where the players' strategy spaces are subsets of $\mathbb{R}^m$ and cost/utility functions are parameterized by some common vector $u$ and, otherwise, only depend on the own strategy choice. A strategy of ... More

Congestion Games with Variable DemandsDec 09 2010Dec 13 2010We initiate the study of congestion games with variable demands where the (variable) demand has to be assigned to exactly one subset of resources. The players' incentives to use higher demands are stimulated by non-decreasing and concave utility functions. ... More

Uniqueness of Equilibria in Atomic Splittable Polymatroid Congestion GamesDec 04 2015Mar 08 2016We study uniqueness of Nash equilibria in atomic splittable congestion games and derive a uniqueness result based on polymatroid theory: when the strategy space of every player is a bidirectional flow polymatroid, then equilibria are unique. Bidirectional ... More

Computing Equilibria in Atomic Splittable Polymatroid Congestion Games with Convex CostsAug 13 2018In this paper, we compute $\epsilon$-approximate Nash equilibria in atomic splittable polymatroid congestion games with convex Lipschitz continuous cost functions. The main approach relies on computing a pure Nash equilibrium for an associated integrally-splittable ... More

Dynamic Flows with Adaptive Route ChoiceNov 18 2018Nov 23 2018We study dynamic network flows and introduce a notion of instantaneous dynamic equilibrium (IDE) requiring that for any positive inflow into an edge, this edge must lie on a currently shortest path towards the respective sink. We measure current shortest ... More

Resource Buying GamesApr 18 2012In resource buying games a set of players jointly buys a subset of a finite resource set E (e.g., machines, edges, or nodes in a digraph). The cost of a resource e depends on the number (or load) of players using e, and has to be paid completely by the ... More

Capacity and Price Competition in Markets with Congestion EffectsMay 14 2019We study oligopolistic competition in service markets where firms offer a service to customers. The service quality of a firm (from a customer's perspective) depends on the level of congestion and the charged price. A firm can set a price for the service ... More

Equilibrium Computation in Atomic Splittable Singleton Congestion GamesDec 01 2016We devise the first polynomial time algorithm computing a pure Nash equilibrium for atomic splittable congestion games with singleton strategies and player-specific affine cost functions. Our algorithm is purely combinatorial and computes the exact equilibrium ... More

Robust Quantitative Comparative Statics for a Multimarket ParadoxJul 22 2013Dec 03 2015We introduce a quantitative approach to comparative statics that allows to bound the maximum effect of an exogenous parameter change on a system's equilibrium. The motivation for this approach is a well known paradox in multimarket Cournot competition, ... More

Dynamic Flows with Adaptive Route ChoiceNov 18 2018May 31 2019We study dynamic network flows and introduce a notion of instantaneous dynamic equilibrium (IDE) requiring that for any positive inflow into an edge, this edge must lie on a currently shortest path towards the respective sink. We measure current shortest ... More

Resource Competition on Integral PolymatroidsJul 29 2014We study competitive resource allocation problems in which players distribute their demands integrally on a set of resources subject to player-specific submodular capacity constraints. Each player has to pay for each unit of demand a cost that is a nondecreasing ... More

Sensitivity Analysis for Convex Separable Optimization over Integral PolymatroidsNov 16 2016We study the sensitivity of optimal solutions of convex separable optimization problems over an integral polymatroid base polytope with respect to parameters determining both the cost of each element and the polytope. Under convexity and a regularity ... More

Sensitivity Analysis for Convex Separable Optimization over Integral PolymatroidsNov 16 2016Dec 08 2016We study the sensitivity of optimal solutions of convex separable optimization problems over an integral polymatroid base polytope with respect to parameters determining both the cost of each element and the polytope. Under convexity and a regularity ... More

A Characterization of Undirected Graphs Admitting Optimal Cost SharesApr 06 2017Oct 04 2017In a seminal paper, Chen, Roughgarden and Valiant studied cost sharing protocols for network design with the objective to implement a low-cost Steiner forest as a Nash equilibrium of an induced cost-sharing game. One of the most intriguing open problems ... More

Strong Nash Equilibria in Games with the Lexicographical Improvement PropertySep 02 2009We introduce a class of finite strategic games with the property that every deviation of a coalition of players that is profitable to each of its members strictly decreases the lexicographical order of a certain function defined on the set of strategy ... More

Toll Caps in Privatized Road NetworksFeb 28 2018Feb 12 2019We consider a network pricing game on a parallel network with congestion effects in which link owners set tolls for travel so as to maximize profit. A central authority is able to regulate this competition by means of a (uniform) price cap. The first ... More

Routing Games with Progressive FillingAug 14 2013Jan 14 2014Max-min fairness (MMF) is a widely known approach to a fair allocation of bandwidth to each of the users in a network. This allocation can be computed by uniformly raising the bandwidths of all users without violating capacity constraints. We consider ... More

Efficient Black-Box Reductions for Separable Cost SharingFeb 28 2018In cost sharing games with delays, a set of agents jointly allocates a finite subset of resources. Each resource has a fixed cost that has to be shared by the players, and each agent has a nonshareable player-specific delay for each resource. A prominent ... More

Fare Evasion in Transit NetworksMay 12 2014Public transit systems in urban areas usually require large state subsidies, primarily due to high fare evasion rates. In this paper, we study new models for optimizing fare inspection strategies in transit networks based on bilevel programming. In the ... More

Matroids are Immune to Braess ParadoxApr 28 2015The famous Braess paradox describes the following phenomenon: It might happen that the improvement of resources, like building a new street within a congested network, may in fact lead to larger costs for the players in an equilibrium. In this paper we ... More

A Saw-tooth Scaling of Work Function in Hydrogenated GrapheneJul 25 2017The saw-tooth scaling investigations of work functions (WF) in hydrogenated graphene are theoretically performed by density functional theory. The positions of hydrogen atoms and the H/C ratios affect WF. With the comparison of different graphene structures ... More

Magnetic properties of quasi one-dimensional vanadium-benzene nanowire affected by gas molecules: a first-principle studyJul 24 2017Magnetic properties of quasi one-dimensional vanadium-benzene nanowires (VBNW) are investigated theoretically with the absorption of gas molecules-NO and NO2. With the increase adsorption of NO on VBNW, the phase transition from half metal to ferromagnetic ... More

The Reversible Spin Switch by External Control of Interval Distance of CuPc and C59N with the investigation of DFTJul 03 2017Jul 24 2017In this paper, we introduce a new kind of spin switch based on a joint system of copper phthalocyanine (CuPc) and C59N. Using density functional theory, we investigate the total magnetic moment of this system when gradually changing the interval distance ... More

Gaussian approximations for stochastic systems with delay: chemical Langevin equation and application to a Brusselator systemDec 10 2013Mar 25 2014We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics ... More

Cross ratios, translation lengths and maximal representationsAug 27 2009Jan 22 2011We define a family of four-point invariants for Shilov boundaries of bounded symmetric domains of tube type, which generalizes the classical four-point cross ratio on the unit circle. This generalization, which is based on a similar construction of Clerc ... More

Generating functionals and Gaussian approximations for interruptible delay reactionsMay 19 2015We develop a generating functional description of the dynamics of non-Markovian individual-based systems, in which delay reactions can be terminated before completion. This generalises previous work in which a path-integral approach was applied to dynamics ... More

How to Evaluate Controlled Natural LanguagesJul 07 2009This paper presents a general framework how controlled natural languages can be evaluated and compared on the basis of user experiments. The subjects are asked to classify given statements (in the language to be tested) as either true or false with respect ... More

AceWiki: Collaborative Ontology Management in Controlled Natural LanguageJul 29 2008AceWiki is a prototype that shows how a semantic wiki using controlled natural language - Attempto Controlled English (ACE) in our case - can make ontology management easy for everybody. Sentences in ACE can automatically be translated into first-order ... More

Lebesgue measure theory and integration theory on non-archimedean real closed fields with archimedean value groupSep 08 2014Feb 02 2016Given a non-archimedean real closed field with archimedean value group which contains the reals, we establish for the category of semialgebraic sets and functions a full Lebesgue measure and integration theory such that the main results from the classical ... More

Auslander-Reiten sequences, Brown-Comenetz duality, and the $K(n)$-local generating hypothesisMar 30 2016In this paper, we construct a version of Auslander-Reiten sequences for the $K(n)$-local stable homotopy category. In particular, the role of the Auslander-Reiten translation is played by the local Brown-Comenetz duality functor. As an application, we ... More

Decomposition of tensor products involving a Steinberg moduleJun 20 2016Jun 23 2016We study the decomposition of tensor products between a Steinberg module and a costandard module, both as a module for the algebraic group $G$ and when restricted to either a Frobenius kernel $G_r$ or a finite Chevalley group $G(\mathbb{F}_q)$. In all ... More

The Controlled Natural Language of Randall Munroe's Thing ExplainerMay 09 2016It is rare that texts or entire books written in a Controlled Natural Language (CNL) become very popular, but exactly this has happened with a book that has been published last year. Randall Munroe's Thing Explainer uses only the 1'000 most often used ... More

A Survey and Classification of Controlled Natural LanguagesJul 07 2015What is here called controlled natural language (CNL) has traditionally been given many different names. Especially during the last four decades, a wide variety of such languages have been designed. They are applied to improve communication among humans, ... More

Non-loose Legendrian spheres with trivial Contact Homology DGAFeb 16 2015Mar 14 2016Loose Legendrian n-submanifolds, for n at least 2, were introduced by Murphy and proved to be flexible in the h-principle sense: any two loose Legendrian submanifolds that are formally Legendrian isotopic are also actually Legendrian isotopic. Legendrian ... More

A Framework for Similarity Search with Space-Time Tradeoffs using Locality-Sensitive FilteringMay 09 2016We present a framework based on Locality-Sensitive Filtering (LSF) and apply it to show lower bounds and give improved upper bounds for the space-time tradeoff of solutions to the $(r, cr)$-near neighbor problem in high-dimensional spaces. Locality-sensitive ... More

A counterexample to conjecture 18.5 in "Geometric Etudes in Combinatorial Mathematics", second editionDec 31 2011A collection of sets $\Fscr$ has the $(p,q)$-property if out of every $p$ elements of $\Fscr$ there are $q$ that have a point in common. A transversal of a collection of sets $\Fscr$ is a set $A$ that intersects every member of $\Fscr$. Gr\"unbaum conjectured ... More

News on PenguinsNov 09 2011We summarize recent theoretical developments in the field of radiative and semileptonic penguin decays.

Two interacting electrons in a magnetic field: comparison of semiclassical, quantum, and variational solutionsSep 30 2010The quantum mechanical many-body problem is rarely analytically solvable. One notable exception is the case of two electrons interacting via a Coulomb potential in a uniform magnetic field. The motion is confined to a two-dimensional plane, which is commonly ... More

Inclusive Rare B DecaysJun 05 2001Jun 13 2001We review the present status of rare B decays, focusing on inclusive decay modes and their role in our search for new physics. We also briefly discuss direct CP violation in rare B decays and the rare kaon decays $K^+\to \pi^+\nu\bar{\nu}$ and $K_L \to ... More

Rare Decays as a Probe for New PhysicsDec 19 2006We discuss the indirect search for new degrees of freedom beyond the standard model, within flavour physics. In particular, we analyse the minimal flavour violation hypothesis and its phenomenological implications, especially the large-tan beta scenario ... More

New physics search in the LHCb eraSep 25 2008Dec 23 2008We present theoretical and experimental preparations for an indirect search for new physics using the rare decay $\bar B_d \to \bar K^* l^+ l^-$. We design new observables with very small theoretical uncertainties and good experimental resolution.

A short introduction to the telescope and chromatic splitting conjecturesFeb 13 2019In this note, we give a brief overview of the telescope conjecture and the chromatic splitting conjecture in stable homotopy theory. In particular, we provide a proof of the folklore result that Ravenel's telescope conjecture for all heights combined ... More

Feedback between interacting transport channelsMar 12 2015A model for autonomous feedback control of particle transport through a large number of channels is introduced. Interactions among the particles can lead to a strong suppression of fluctuations in the particle number statistics. Within a mean-field type ... More

Piecewise Weierstrass preparation and division for o-minimal holomorphic functionsJun 08 2016Oct 12 2016Given an o-minimal structure expanding the field of reals, we show a piecewise Weierstrass preparation theorem and a piecewise Weierstrass division theorem for definable holomorphic functions. In the semialgebraic setting and for the structure of globally ... More

Local Scattering Operators for P(φ)_2 Models and the Time-dependent Schrödinger EquationDec 29 2005We establish the existence of Bogoliubov's local scattering operators for P(\phi)_2 models of constructive quantum field theory in a nonperturbative way. To this end, we use the technique of evolution semigroups to prove a new result on wellposedness ... More

Global existence without decay for quadratic Klein-Gordon equationsSep 07 2012Sep 19 2012The Cauchy problem for quadratic Klein-Gordon systems is considered in two spatial dimensions and higher under a suitable non-resonance condition on the masses, including the main case of equal masses. A global well-posedness and scattering result is ... More

Resource convertibility and ordered commutative monoidsApr 14 2015Jul 02 2015Resources and their use and consumption form a central part of our life. Many branches of science and engineering are concerned with the question of which given resource objects can be converted into which target resource objects. For example, information ... More

Convex Spaces I: Definition and ExamplesMar 31 2009Oct 19 2015We propose an abstract definition of convex spaces as sets where one can take convex combinations in a consistent way. A priori, a convex space is an algebra over a finitary version of the Giry monad. We identify the corresponding Lawvere theory as the ... More

A presentation of the category of stochastic matricesFeb 16 2009Mar 31 2009This note gives generators and relations for the strict monoidal category of probabilistic maps on finite cardinals (i.e., stochastic matrices).

Velocity Polytopes of Periodic Graphs and a No-Go Theorem for Digital PhysicsSep 09 2011Jun 17 2013A periodic graph in dimension $d$ is a directed graph with a free action of $\Z^d$ with only finitely many orbits. It can conveniently be represented in terms of an associated finite graph with weights in $\Z^d$, corresponding to a $\Z^d$-bundle with ... More

Oddness of residually reducible Galois representationsNov 28 2016We show that suitable congruences between polarized automorphic forms over a CM field always produce elements in the Selmer group for exactly the +/--Asai (aka tensor induction) representation that is critical in the sense of Deligne. For this we relate ... More

Arithmetic properties of similitude theta lifts from orthogonal to symplectic groupsFeb 26 2009By adapting the work of Kudla and Millson we obtain a lifting of cuspidal cohomology classes for the symmetric space associated to GO(V) for an indefinite rational quadratic space V of even dimension to holomorphic Siegel modular forms on GSp_n(A). For ... More

Blow-up of weak solutions to a chemotaxis system under influence of an external chemoattractantOct 24 2015We study nonnnegative radially symmetric solutions of the parabolic-elliptic Keller-Segel whole space system \begin{align*} \left\{\begin{array}{c@{\,}l@{\quad}l@{\,}c} u_{t}&=\Delta u-\nabla\!\cdot(u\nabla v),\ &x\in\mathbb{R}^n,& t>0,\\ 0 &=\Delta v+u+f(x),\ ... More

Primitive finite nilpotent linear groups over number fieldsJun 02 2015Building upon the author's previous work on primitivity testing of finite nilpotent linear groups over fields of characteristic zero, we describe precisely those finite nilpotent groups which arise as primitive linear groups over a given number field. ... More

Cartier crystals and perverse constructible étale $p$-torsion sheavesMar 24 2016Feb 16 2018For an $F$-finite scheme $X$ separated over a perfect field $k$ of characteristic $p>0$ which admits an embedding into a smooth $k$-scheme, we establish an equivalence between the bounded derived categories of Cartier crystals on $X$ and constructible ... More

Computing topological zeta functions of groups, algebras, and modules, IISep 17 2014Building on our previous work (arXiv:1405.5711), we develop the first practical algorithm for computing topological zeta functions of nilpotent groups, non-associative algebras, and modules. While we previously depended upon non-degeneracy assumptions, ... More

Divisors on Projective Hibi VarietiesJun 08 2015We compute the divisor class group and the Picard group of projective varieties with Hibi rings as homogeneous coordinate rings. These varieties are precisely the toric varieties associated to order polytopes. We use tools from the theory of toric varieties ... More

Linear extensions of partial orders on Abelian groupsJun 20 2011Mar 12 2014Partially ordered groups, also known as po-groups, are groups with a compatible partial order. Results from M.I. Zajceva and H.-H. Teh are combined in order to provide a full characterisation of linear order extensions of a given order on a group. In ... More

Multi-Directional Flow as Touch-Stone to Assess Models of Pedestrian DynamicsDec 31 2012For simulation models of pedestrian dynamics there are always the issues of calibration and validation. These are usually done by comparing measured properties of the dynamics found in observation, experiments and simulation in certain scenarios. For ... More

Higgs-free Massive Nonabelian Gauge TheoriesNov 24 1995Sep 13 1996We analyze nonabelian massive Higgs-free theories in the causal Epstein-Glaser approach. Recently, there has been renewed interest in these models. In particular we consider the well-known Curci-Ferrari model and the nonabelian St\"uckelberg models. We ... More

A Note on Slavnov-Taylor Identities in the Causal Epstein-Glaser ApproachAug 27 1995An alternative approach to perturbative Yang-Mills theories in four (3+1) dimensional space-time based on the causal Epstein-Glaser method in QFT was recently proposed. In this short note we show that the set of identities between C-number distributions ... More

Matter waves from localized quantum sourcesSep 18 2003Matter waves originating from a localized region in space appear commonly in physics. Examples are photo-electrons, ballistic electrons in nanotechnology devices (scanning-tunneling microscopy, quantum Hall effect), or atoms released from a coherent source ... More

Combining Semantic Wikis and Controlled Natural LanguageOct 17 2008We demonstrate AceWiki that is a semantic wiki using the controlled natural language Attempto Controlled English (ACE). The goal is to enable easy creation and modification of ontologies through the web. Texts in ACE can automatically be translated into ... More

AceWiki: A Natural and Expressive Semantic WikiJul 29 2008We present AceWiki, a prototype of a new kind of semantic wiki using the controlled natural language Attempto Controlled English (ACE) for representing its content. ACE is a subset of English with a restricted grammar and a formal semantics. The use of ... More

Constraining the supersaturation density equation of state from core-collapse supernova simulations - Excluded volume extension of the baryonsApr 06 2016In this article the role of the supersaturation density equation of state (EOS) is explored in simulations of failed core-collapse supernova explosions. Therefore the nuclear EOS is extended via a one-parameter excluded volume description for baryons, ... More

A1-homotopy invariants of topological Fukaya categories of surfacesMay 26 2015Apr 25 2016We provide an explicit formula for localizing $A^1$-homotopy invariants of topological Fukaya categories of marked surfaces. Following a proposal of Kontsevich, this differential $\mathbb Z$-graded category is defined as global sections of a constructible ... More

Running Identical Threads in C-Slow Retiming based Designs for Functional Failure DetectionFeb 04 2015This paper shows the usage of C-Slow Retiming (CSR) in safety critical and low power applications. CSR generates C copies of a design by reusing the given logic resources in a time sliced fashion. When all C design copies are stimulated with the same ... More

Limits of End-to-End LearningApr 26 2017End-to-end learning refers to training a possibly complex learning system by applying gradient-based learning to the system as a whole. End-to-end learning system is specifically designed so that all modules are differentiable. In effect, not only a central ... More

Excited-State Quantum Phase Transitions in Dicke Superradiance ModelsJun 27 2013We derive analytical results for various quantities related to the excited-state quantum phase transitions in a class of Dicke superradiance models in the semiclassical limit. Based on a calculation of a partition sum restricted to Dicke states, we discuss ... More

An Introduction to Markov Chain Monte Carlo on Finite State SpacesMar 20 2019We elaborate the idea behind Markov chain Monte Carlo (MCMC) methods in a mathematically comprehensive way. Our focus is on simplicity. We give an elementary proof for the Perron-Frobenius theorem and a convergence theorem for Markov chains. Subsequently ... More

On the capacity of the dither-quantized Gaussian channelJan 27 2014Apr 25 2014This paper studies the capacity of the peak-and-average-power-limited Gaussian channel when its output is quantized using a dithered, infinite-level, uniform quantizer of step size $\Delta$. It is shown that the capacity of this channel tends to that ... More

Organic Computing as Chance for Interwoven SystemsAug 26 2018Systems are growing into more complex ones for developing and maintaining. Existing systems which do not have much in common on the first look are connected, due to the technical progress, even if it was never intended that way. It is an upcoming challenge ... More

Effective Unsupervised Author Disambiguation with Relative FrequenciesAug 10 2018This work addresses the problem of author name homonymy in the Web of Science. Aiming for an efficient, simple and straightforward solution, we introduce a novel probabilistic similarity measure for author name disambiguation based on feature overlap. ... More

Timing Driven C-Slow Retiming on RTL for MultiCores on FPGAsJul 14 2018In this paper C-Slow Retiming (CSR) on RTL is discussed. CSR multiplies the functionality of cores by adding the same number of registers into each path. The technique is ideal for FPGAs with their already existing registers. Previously publications are ... More

Mathematical models for magnetic particle imagingMar 05 2018Magnetic particle imaging (MPI) is a relatively new imaging modality. The nonlinear magnetization behavior of nanoparticles in an applied magnetic field is employed to reconstruct an image of the concentration of nanoparticles. Finding a sufficiently ... More

NLO Higgs+jet at large transverse momenta including top quark mass effectsFeb 08 2018We present a next-to-leading order calculation of H+jet in gluon fusion including the effect of a finite top quark mass $m_t$ at large transverse momenta. Using the recently published two-loop amplitudes in the high energy expansion and our previous setup ... More

RadioPropa - A Modular Raytracer for In-Matter Radio PropagationOct 03 2018Experiments for radio detection of UHE particles such as e.g. ARA/ARIANNA or NuMoon require detailed understanding of the propagation of radio waves in the surrounding matter. The index of refraction in e.g. polar ice or lunar rock may have a complex ... More

Hecke Operators for Period Functions for Congruence SubgroupsMar 23 2006This is basically a summary of [Mu]. The focus of the paper is the explicit computation of Hecke operators for period functions. In particular we compute the matrix representations of the 2nd Hecke operator on period functions for the full modular group ... More

Integrated Algorithms for HEX-Programs and Applications in Machine LearningMay 07 2019This paper summarizes my doctoral research on evaluation algorithms for HEX-programs, which extend Answer Set Programming with means for interfacing external computations. The focus is on integrating different subprocesses of HEX-evaluation, such as solving ... More

Denominators of Eisenstein cohomology classes for GL_2 over imaginary quadratic fieldsJun 21 2006Jan 05 2007We study the arithmetic of Eisenstein cohomology classes (in the sense of G. Harder) for symmetric spaces associated to GL_2 over imaginary quadratic fields. We prove in many cases a lower bound on their denominator in terms of a special L-value of a ... More

Regular homotopy and total curvatureOct 17 2003Mar 10 2009We consider properties of the total absolute geodesic curvature functional on circle immersions into a Riemann surface. In particular, we study its behavior under regular homotopies, its infima in regular homotopy classes, and the homotopy types of spaces ... More

Computing local zeta functions of groups, algebras, and modulesFeb 02 2016We develop a practical method for computing local zeta functions of groups, algebras, and modules in fortunate cases. Using our method, we obtain a complete classification of generic local representation zeta functions associated with unipotent algebraic ... More

Sublinear signal production in a two-dimensional Keller-Segel-Stokes systemFeb 01 2016We study the chemotaxis-fluid system \begin{align*} \left\{\begin{array}{r@{\,}l@{\quad}l@{\,}c} n_{t}&=\Delta n-\nabla\!\cdot(n\nabla c)-u\cdot\!\nabla n,\ &x\in\Omega,& t>0,\\ c_{t}&=\Delta c-c+f(n)-u\cdot\!\nabla c,\ &x\in\Omega,& t>0,\\ u_{t}&=\Delta ... More

The Riemann Mapping Theorem for semianalytic domains and o-minimalityMay 14 2007Jul 21 2008We consider the Riemann Mapping Theorem in the case of a bounded simply connected and semianalytic domain. We show that the germ at 0 of the Riemann map (i.e. biholomorphic map) from the upper half plane to such a domain can be realized in a certain quasianalytic ... More

A generalization of Strassen's PositivstellensatzOct 19 2018Jul 10 2019Strassen's Positivstellensatz is a powerful but little known theorem on preordered commutative semirings satisfying a boundedness condition similar to Archimedeanicity. It characterizes the relaxed preorder induced by all monotone homomorphisms to $\mathbb{R}_+$ ... More

Grothendieck duality for non-proper morphismsOct 14 2018We generalize the adjunction between the functors $Rf_*$ and $f^!$ of derived categories of quasi-coherent sheaves for proper morphisms $f\colon X \to Y$ of Noetherian schemes to the following situation: Let $f$ be a finite type morphism and let $Z' \subseteq ... More

Lebesgue measure theory and integration theory on non-archimedean real closed fields with archimedean value groupSep 08 2014Aug 08 2017Given a non-archimedean real closed field with archimedean value group which contains the reals, we establish for the category of semialgebraic sets and functions a full Lebesgue measure and integration theory such that the main results from the classical ... More

Rational Symplectic Field Theory over Z_2 for exact Lagrangian cobordismsDec 01 2006We construct a version of rational Symplectic Field Theory for pairs $(X,L)$, where $X$ is an exact symplectic manifold, where $L\subset X$ is an exact Lagrangian submanifold with components subdivided into $k$ subsets, and where both $X$ and $L$ have ... More

$R$-analytic functionsFeb 23 2015Apr 04 2016We introduce the notion of $R$-analytic functions. These are definable in an o-minimal expansion of a real closed field $R$ and are locally the restriction of a $K$-differentiable function (defined by Peterzil and Starchenko) where $K=R[\sqrt{-1}]$ is ... More

Computing topological zeta functions of groups, algebras, and modules, IMay 22 2014We develop techniques for computing zeta functions associated with nilpotent groups, not necessarily associative algebras, and modules, as well as Igusa-type zeta functions. At the heart of our method lies an explicit convex-geometric formula for a class ... More

Rapid mixing and Markov basesMay 12 2015Aug 20 2016The mixing behaviour of random walks on lattice points of polytopes using Markov bases is examined. It is shown that under a dilation of the underlying polytope, these random walks do not mix rapidly when a fixed Markov basis is used. We also show that ... More

Rational SFT, linearized Legendrian contact homology, and Lagrangian Floer cohomologyFeb 25 2009We relate the version of rational Symplectic Field Theory for exact Lagrangian cobordisms introduced in [5] with linearized Legendrian contact homology. More precisely, if $L\subset X$ is an exact Lagrangian submanifold of an exact symplectic manifold ... More

A Principled Approach to Grammars for Controlled Natural Languages and Predictive EditorsNov 15 2012Controlled natural languages (CNL) with a direct mapping to formal logic have been proposed to improve the usability of knowledge representation systems, query interfaces, and formal specifications. Predictive editors are a popular approach to solve the ... More

Codeco: A Grammar Notation for Controlled Natural Language in Predictive EditorsMar 29 2011Existing grammar frameworks do not work out particularly well for controlled natural languages (CNL), especially if they are to be used in predictive editors. I introduce in this paper a new grammar notation, called Codeco, which is designed specifically ... More

Status of SM calculations of b > s transitionsMar 21 2007May 22 2007We report recent progress in SM calculations of $b \to s$ transitions. We discuss the first NNLL prediction of the $\bar B \to X_s \gamma$ branching ratio, including important additional subtleties due to non-perturbative corrections and logarithmically-enhanced ... More

Equivariant spectral asymptotics for h-pseudodifferential operatorsNov 11 2013Dec 11 2014We prove equivariant spectral asymptotics for $ h$-pseudodifferential operators for compact orthogonal group actions generalizing results of El-Houakmi and Helffer (1991) and Cassanas (2006). Using recent results for certain oscillatory integrals with ... More

Quantum logic is undecidableJul 20 2016We investigate the first-order theory of closed subspaces of complex Hilbert spaces in the signature $(\lor,\perp,0)$, where `$\perp$' is orthogonality. Our main result is that already its purely implicational fragment is undecidable: there is no algorithm ... More

Nonabelian Gauge Symmetry in the Causal Epstein-Glaser ApproachNov 20 1995We present some generalizations of a recently proposed alternative approach to nonabelian gauge theories based on the causal Epstein-Glaser method in perturbative quantum field theory. Nonabelian gauge invariance is defined by a simple commutator relation ... More