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Approximately counting and sampling small witnesses using a colourful decision oracleJul 10 2019In this paper, we prove "black box" results for turning algorithms which decide whether or not a witness exists into algorithms to approximately count the number of witnesses, or to sample from the set of witnesses approximately uniformly, with essentially ... More

AND-compression of NP-complete problems: Streamlined proof and minor observationsMay 18 2014Sep 23 2014Drucker (2012) proved the following result: Unless the unlikely complexity-theoretic collapse coNP is in NP/poly occurs, there is no AND-compression for SAT. The result has implications for the compressibility and kernelizability of a whole range of NP-complete ... More

Note on "The Complexity of Counting Surjective Homomorphisms and Compactions"Oct 04 2017Focke, Goldberg, and \v{Z}ivn\'y (arXiv 2017) prove a complexity dichotomy for the problem of counting surjective homomorphisms from a large input graph G without loops to a fixed graph H that may have loops. In this note, we give a short proof of a weaker ... More

Kernelization of Packing ProblemsDec 07 2018Kernelization algorithms are polynomial-time reductions from a problem to itself that guarantee their output to have a size not exceeding some bound. For example, d-Set Matching for integers d>2 is the problem of finding a matching of size at least k ... More

Fine-grained reductions from approximate counting to decisionJul 14 2017Feb 07 2019In this paper, we introduce a general framework for fine-grained reductions of approximate counting problems to their decision versions. (Thus we use an oracle that decides whether any witness exists to multiplicatively approximate the number of witnesses ... More

Lovász Meets Weisfeiler and LemanFeb 24 2018May 22 2018In this paper, we relate a beautiful theory by Lov\'asz with a popular heuristic algorithm for the graph isomorphism problem, namely the color refinement algorithm and its k-dimensional generalization known as the Weisfeiler-Leman algorithm. We prove ... More

Homomorphisms Are a Good Basis for Counting Small SubgraphsMay 03 2017We introduce graph motif parameters, a class of graph parameters that depend only on the frequencies of constant-size induced subgraphs. Classical works by Lov\'asz show that many interesting quantities have this form, including, for fixed graphs $H$, ... More

Counting Answers to Existential QuestionsFeb 13 2019Conjunctive queries select and are expected to return certain tuples from a relational database. We study the potentially easier problem of counting all selected tuples, rather than enumerating them. In particular, we are interested in the problem's parameterized ... More

Fine-grained dichotomies for the Tutte plane and Boolean #CSPJun 21 2016Jaeger, Vertigan, and Welsh [15] proved a dichotomy for the complexity of evaluating the Tutte polynomial at fixed points: The evaluation is #P-hard almost everywhere, and the remaining points admit polynomial-time algorithms. Dell, Husfeldt, and Wahl\'en ... More

Extensor-CodingApr 25 2018We devise an algorithm that approximately computes the number of paths of length $k$ in a given directed graph with $n$ vertices up to a multiplicative error of $1 \pm \varepsilon$. Our algorithm runs in time $\varepsilon^{-2} 4^k(n+m) \operatorname{poly}(k)$. ... More

Counting edge-injective homomorphisms and matchings on restricted graph classesFeb 17 2017Jan 19 2018We consider the $\#\mathsf{W}[1]$-hard problem of counting all matchings with exactly $k$ edges in a given input graph $G$; we prove that it remains $\#\mathsf{W}[1]$-hard on graphs $G$ that are line graphs or bipartite graphs with degree $2$ on one side. ... More

Counting Answers to Existential QuestionsFeb 13 2019Apr 29 2019Conjunctive queries select and are expected to return certain tuples from a relational database. We study the potentially easier problem of counting all selected tuples, rather than enumerating them. In particular, we are interested in the problem's parameterized ... More

Limit theorems for empirical processes of cluster functionalsOct 02 2009Oct 19 2010Let $(X_{n,i})_{1\le i\le n,n\in\mathbb{N}}$ be a triangular array of row-wise stationary $\mathbb{R}^d$-valued random variables. We use a "blocks method" to define clusters of extreme values: the rows of $(X_{n,i})$ are divided into $m_n$ blocks $(Y_{n,j})$, ... More

Exponential Time Complexity of the Permanent and the Tutte PolynomialJun 08 2012We show conditional lower bounds for well-studied #P-hard problems: (a) The number of satisfying assignments of a 2-CNF formula with n variables cannot be counted in time exp(o(n)), and the same is true for computing the number of all independent sets ... More

Finding Detours is Fixed-parameter TractableJul 26 2016May 03 2017We consider the following natural "above guarantee" parameterization of the classical Longest Path problem: For given vertices s and t of a graph G, and an integer k, the problem Longest Detour asks for an (s,t)-path in G that is at least k longer than ... More

Finding Detours is Fixed-parameter TractableJul 26 2016We consider the following natural "above guarantee" parameterization of the classical Longest Path problem: For given vertices s and t of a graph G, and an integer k, the problem Longest Detour asks for an (s,t)-path in G that is at least k longer than ... More

More Consequences of Falsifying SETH and the Orthogonal Vectors ConjectureMay 22 2018The Strong Exponential Time Hypothesis and the OV-conjecture are two popular hardness assumptions used to prove a plethora of lower bounds, especially in the realm of polynomial-time algorithms. The OV-conjecture in moderate dimension states there is ... More

Correction note to "Limit Theorems for Empirical Processes of Cluster Functionals" [arXiv:0910.0343]Oct 29 2015We correct an error in a technical lemma of Drees and Rootz\'en (2010) [arXiv:0910.0343] and discuss consequences for applications.

Long-distance entanglement in Motzkin and Fredkin spin chainsApr 10 2019We derive some entanglement properties of the ground states of two classes of quantum spin chains described by the Fredkin model for half-integer spins and the Motzkin model for integer ones. Since the ground states of the two models are known analytically, ... More

Circulant and Toeplitz matrices in compressed sensingFeb 25 2009Compressed sensing seeks to recover a sparse vector from a small number of linear and non-adaptive measurements. While most work so far focuses on Gaussian or Bernoulli random measurements we investigate the use of partial random circulant and Toeplitz ... More

Wilsonian effective action for SU(2) Yang-Mills theory with Cho-Faddeev-Niemi-Shabanov decompositionFeb 06 2001Apr 18 2001The Cho-Faddeev-Niemi-Shabanov decomposition of the SU(2) Yang-Mills field is employed for the calculation of the corresponding Wilsonian effective action to one-loop order with covariant gauge fixing. The generation of a mass scale is observed, and the ... More

Multiple Quantization and the Concept of InformationFeb 24 1997The understanding of the meaning of quantization seems to be the main problem in understanding quantum structures. In this paper first the difference between quantized particle vs. radiation fields in the formalism of canonical quantization is discussed. ... More

The Principles of GaugingJan 11 2001The aim of this paper is twofold: First, to present an examination of the principles underlying gauge field theories. I shall argue that there are two principles directly connected to the two well-known theorems of Emmy Noether concerning global and local ... More

Testing Lorentz invariance by use of vacuum and matter filled cavity resonatorsDec 26 2004We consider tests of Lorentz invariance for the photon and fermion sector that use vacuum and matter-filled cavities. Assumptions on the wave-function of the electrons in crystals are eliminated from the underlying theory and accurate sensitivity coefficients ... More

Busy Beaver Scores and Alphabet SizeApr 27 2017We investigate the Busy Beaver Game introduced by Rado (1962) generalized to non-binary alphabets. Harland (2016) conjectured that activity (number of steps) and productivity (number of non-blank symbols) of candidate machines grow as the alphabet size ... More

A Note on Nested String ReplacementsJul 06 2016We investigate the number of nested string replacements required to reduce a string of identical characters to one character.

A Non-Oblivious Reduction of Counting Ones to MultiplicationJun 10 2015An algorithm counting the number of ones in a binary word is presented running in time $O(\log\log b)$ where $b$ is the number of ones. The operations available include bit-wise logical operations and multiplication.

Efficient Computation by Three Counter MachinesJan 09 2015We show that multiplication can be done in polynomial time on a three counter machine that receives its input as the contents of two counters. The technique is generalized to functions of two variables computable by deterministic Turing machines in linear ... More

A Note on Kolmogorov-Uspensky MachinesNov 23 2012Solving an open problem stated by Shvachko, it is shown that a language which is not real-time recognizable by some variants of pointer machines can be accepted by a Kolmogorov-Uspensky machine in real-time.

On K(1)-local SU-bordismJul 24 2009This paper works towards a K(1)-local multiplicative splitting of SU-bordism.

Random Sampling of Sparse Trigonometric PolynomialsDec 29 2005We study the problem of reconstructing a multivariate trigonometric polynomial having only few non-zero coefficients from few random samples. Inspired by recent work of Candes, Romberg and Tao we propose to recover the polynomial by Basis Pursuit, i.e., ... More

Coorbit Space Theory for Quasi-Banach SpacesJul 22 2005We generalize the classical coorbit space theory developed by Feichtinger and Gr"ochenig to quasi-Banach spaces. As a main result we provide atomic decompositions for coorbit spaces defined with respect to quasi-Banach spaces. These atomic decompositions ... More

The affine class group of a normal schemeSep 23 2002We study the property of a normal scheme, that the complement of every hypersurface is an affine scheme. To this end we introduce the affine class group. It is a factor group of the divisor class group and measures the deviation from this property. We ... More

p-adic L-functions of automorphic forms and exceptional zerosNov 24 2013Nov 29 2013Let F be a number field, p a prime number. We construct the (multi-variable) p-adic L-function of an automorphic representation of $GL_2(A_F)$ (with certain conditions at places above p and $\infty$), which interpolates the complex L-function at the central ... More

Equivariant Kasparov theory of finite groups via Mackey functorsMay 16 2011Let G be a finite group. We systematically exploit general homological methods in order to reduce the computation of G-equivariant KK-theory to topological equivariant K-theory. The key observation is that the functor assigning to a separable G-C*-algebra ... More

Localizing subcategories in the Bootstrap category of separable C*-algebrasFeb 28 2010Jul 06 2010Using the classical universal coefficient theorem of Rosenberg-Schochet, we prove a simple classification of all localizing subcategories of the Bootstrap category of separable complex C*-algebras. Namely, they are in bijective correspondence with subsets ... More

Scheduling With Inexact Job Sizes: The Merits of Shortest Processing Time FirstJul 10 2019It is well known that size-based scheduling policies, which take into account job size (i.e., the time it takes to run them), can perform very desirably in terms of both response time and fairness. Unfortunately, the requirement of knowing a priori the ... More

Strong laser fields as a probe for fundamental physicsDec 03 2008Upcoming high-intensity laser systems will be able to probe the quantum-induced nonlinear regime of electrodynamics. So far unobserved QED phenomena such as the discovery of a nonlinear response of the quantum vacuum to macroscopic electromagnetic fields ... More

On invariants and scalar chiral correlation functions in N=1 superconformal field theoriesOct 13 2010Jan 20 2011A general expression for the four-point function with vanishing total R-charge of anti-chiral and chiral superfields in N=1 superconformal theories is given. It is obtained by applying the exponential of a simple universal nilpotent differential operator ... More

The Power of Centralized PC Systems of Pushdown AutomataAug 06 2012Aug 13 2012Parallel communicating systems of pushdown automata (PCPA) were introduced in (Csuhaj-Varj{\'u} et. al. 2000) and in their centralized variants shown to be able to simulate nondeterministic one-way multi-head pushdown automata. A claimed converse simulation ... More

A Note on Pushdown Automata SystemsOct 01 2013Apr 04 2014In (Csuhaj-Varju et. al. 2000) Parallel Communicating Systems of Pushdown Automata (PCPA) were introduced and shown to be able to simulate nondeterministic one-way multi-head pushdown automata in returning mode, even if communication is restricted to ... More

Characteristic Polynomials of Sample Covariance MatricesJun 15 2009We investigate the second-order correlation function of the characteristic polynomial of a sample covariance matrix. Starting from an explicit formula for the generating function, we re-obtain several well-known kernels from random matrix theory.

Continuous solutions to algebraic forcing equationsAug 24 2006Aug 27 2006We ask for a given system of polynomials f_1,...,f_n and f over the complex numbers when there exist continuous functions q_1,...,q_n such that q_1 f_1+...+q_n f_n = f. This condition defines the continuous closure of an ideal. We give inclusion criteria ... More

Large sets of consecutive Maass forms and fluctuations in the Weyl remainderDec 13 2012We explore an algorithm which systematically finds all discrete eigenvalues of an analytic eigenvalue problem. The algorithm is more simple and elementary as could be expected before. It consists of Hejhal's identity, linearisation, and Turing bounds. ... More

Director Field Configurations around a Spherical Particle in a Nematic Liquid CrystalNov 16 1998We study the director field around a spherical particle immersed in a uniformly aligned nematic liquid crystal and assume that the molecules prefer a homeotropic orientation at the surface of the particle. Three structures are possible: a dipole, a Saturn-ring, ... More

Fast high--voltage amplifiers for driving electro-optic modulatorsJun 06 2005We describe five high-voltage (60 to 550V peak to peak), high-speed (1-300ns rise time; 1.3-300MHz bandwidth) linear amplifiers for driving capacitive or resistive loads such as electro-optic modulators. The amplifiers use bipolar transistors in various ... More

Characterizations of generalized Hermite and sieved ultraspherical polynomialsJun 06 1994A new characterization of the generalized Hermite polynomials and of the orthogonal polynomials with respect to the maesure $|x|^\g (1-x^2)^{\a-1/2}dx$ is derived which is based on a "reversing property" of the coefficients in the corresponding recurrence ... More

New bounds for Hahn and Krawichouk polynomialsJun 07 1994For the Hahn and Krawtchouk polynomials orthogonal on the set $\{0, \ldots,N\}$ new identities for the sum of squares are derived which generalize the trigonometric identity for the Chebyshev polynomials of the first and second kind. These results are ... More

Counting Ones Without Broadword OperationsNov 16 2015Jan 17 2016A lower time bound $\Omega(\min(\nu(x), n-\nu(x))$ for counting the number of ones in a binary input word $x$ of length $n$ is presented, where $\nu(x)$ is the number of ones. The operations available are increment, decrement, bit-wise logical operations, ... More

A Hilbert-Kunz criterion for solid closure in dimension two (characteristic zero)Mar 17 2004Let I denote a homogeneous R_+-primary ideal in a two-dimensional normal standard-graded domain over an algebraically closed field of characteristic zero. We show that a homogeneous element f belongs to the solid closure I^* if and only if e_{HK}(I) = ... More

Lifting chains of prime idealsSep 23 2002We give an elementary proof that for a ring homomorphism A -> B, satisfying the property that every ideal in A is contracted from B, the following property holds: for every chain of prime ideals p_0 \subset ... \subset p_r in A there exists a chain of ... More

A path algorithm for the Fused Lasso Signal ApproximatorOct 03 2009The Lasso is a very well known penalized regression model, which adds an $L_{1}$ penalty with parameter $\lambda_{1}$ on the coefficients to the squared error loss function. The Fused Lasso extends this model by also putting an $L_{1}$ penalty with parameter ... More

Renormalizability of gauge theories in extra dimensionsMay 23 2003We analyze the possibility of nonperturbative renormalizability of gauge theories in D > 4 dimensions. We develop a scenario, based on Weinberg's idea of asymptotic safety, that allows for renormalizability in extra dimensions owing to a non-Gaussian ... More

Running coupling in Yang-Mills theory - a flow equation study -Feb 28 2002May 08 2002The effective average action of Yang-Mills theory is analyzed in the framework of exact renormalization group flow equations. Employing the background-field method and using a cutoff that is adjusted to the spectral flow, the running of the gauge coupling ... More

LIKE Patterns and ComplexityMar 14 2019We investigate the expressive power and complexity questions for the LIKE operator in SQL.

Some Remarks on Real-Time Turing MachinesFeb 03 2019The power of real-time Turing machines using sublinear space is investigated. In contrast to a claim appearing in the literature, such machines can accept non-regular languages, even if working in deterministic mode. While maintaining a standard binary ... More

An NL-Complete PuzzleJul 09 2015We investigate the complexity of a puzzle that turns out to be NL-complete.

Some Remarks on Lower Bounds for Queue Machines (Preliminary Report)Oct 23 2013Mar 11 2018We first give an improved lower bound for the deterministic online simulation of tapes or pushdown stores by queues. Then we inspect some proofs in a classical work on queue machines in the area of Formal Languages and outline why a main argument in the ... More

A SWAR Approach to Counting OnesAug 18 2011Jul 01 2015We investigate the complexity of algorithms counting ones in different sets of operations. With addition and logical operations (but no shift) $O(\log^2(n))$ steps suffice to count ones. Parity can be computed with complexity $O(\log(n))$, which is the ... More

The Gromov-Witten invariants of symplectic manifoldsJun 21 2000We study the fix point components of the big torus action on the moduli space of stable maps into a smooth projective toric variety, and apply Graber and Pandharipande's localization formula for the virtual fundamental class to obtain an explicit formula ... More

Difference prophet inequalities for [0,1]-valued i.i.d. random variables with cost for observationsMar 25 2005Let X_1,X_2,... be a sequence of [0,1]-valued i.i.d. random variables, let c\geq 0 be a sampling cost for each observation and let Y_i=X_i-ic, i=1,2,.... For n=1,2,..., let M(Y_1,...,Y_n)=E(max_{1\leq i\leq n}Y_i) and V(Y_1,...,Y_n)=sup_{\tau \in C^n}E(Y_{\tau}), ... More

Approximating Novikov-Shubin numbers of virtually cyclic coveringsSep 03 2015Jan 26 2017We assign real numbers to finite sheeted coverings of compact CW complexes designed as finite counterparts to the Novikov-Shubin numbers. We prove an approximation theorem in the case of virtually cyclic fundamental groups employing methods from Diophantine ... More

Stability results for random sampling of sparse trigonometric polynomialsSep 22 2006Apr 06 2008Recently, it has been observed that a sparse trigonometric polynomial, i.e. having only a small number of non-zero coefficients, can be reconstructed exactly from a small number of random samples using Basis Pursuit (BP) or Orthogonal Matching Pursuit ... More

Total variation regularization with variable Lebesgue priorFeb 28 2017Mar 14 2017This work proposes the variable exponent Lebesgue modular as a replacement for the 1-norm in total variation (TV) regularization. It allows the exponent to vary with spatial location and thus enables users to locally select whether to preserve edges or ... More

The shrinkage type of knotsJul 13 2016Jan 26 2017We study spectral gaps of cellular differentials for finite cyclic coverings of knot complements. Their asymptotics can be expressed in terms of irrationality exponents associated with ratios of logarithms of algebraic numbers determined by the first ... More

Approximating Novikov-Shubin numbers of virtually cyclic coveringsSep 03 2015We assign real numbers to finite sheeted coverings of compact CW complexes designed as finite counterparts to the Novikov-Shubin numbers. We prove an approximation theorem in the case of virtually cyclic fundamental groups employing methods from Diophantine ... More

The Complexity of Some Combinatorial PuzzlesJul 30 2015We show that the decision versions of the puzzles Knossos and The Hour-Glass are complete for NP.

On Practical Regular ExpressionsAug 06 2014Jan 03 2015We report on simulation, hierarchy, and decidability results for Practical Regular Expressions (PRE), which may include back references in addition to the standard operations union, concatenation, and star. The following results are obtained: PRE can ... More

Bounded Counter LanguagesApr 03 2012We show that deterministic finite automata equipped with $k$ two-way heads are equivalent to deterministic machines with a single two-way input head and $k-1$ linearly bounded counters if the accepted language is strictly bounded, i.e., a subset of $a_1^*a_2^*... ... More

L^2-Betti numbers, isomorphism conjectures and noncommutative localizationMar 07 2003In this paper we discuss how the question about the rationality of L^2-Betti numbers is related to the Isomorphism Conjecture in algebraic K-theory and why in this context noncommutative localization appears as an important tool.

Bootstrapping Empirical Processes of Cluster Functionals with Application to ExtremogramsNov 02 2015In the extreme value analysis of time series, not only the tail behavior is of interest, but also the serial dependence plays a crucial role. Drees and Rootz\'en (2010) established limit theorems for a general class of empirical processes of so-called ... More

Extreme value analysis of actuarial risks: estimation and model validationMar 15 2011Nov 16 2011We give an overview of several aspects arising in the statistical analysis of extreme risks with actuarial applications in view. In particular it is demonstrated that empirical process theory is a very powerful tool, both for the asymptotic analysis of ... More

Rings of global sections in two-dimensional schemesSep 26 2002In this paper we study the ring of global sections of an open subset U=D(I) in Spec A, where A is a two-dimensional noetherian ring. The main concern is to give a geometric criterion when these rings are finitely generated, in order to correct an invalid ... More

Counting generic genus-0 curves on Hirzebruch surfacesSep 18 2000Hirzebruch surfaces provide an excellent example to underline the fact that in general symplectic manifolds, Gromov-Witten invariants might well count curves in the boundary components of the moduli space. We use this example to explain in detail that ... More

Multiple quantum products in toric varietiesJul 04 2001Jul 06 2001We generalize the author's formula for Gromov-Witten invariants of symplectic toric manifolds (see math.AG/0006156) to those needed to compute the quantum product of more than two classes directly, i.e. involving the pull-back of the Poincar\'e dual of ... More

On superheight conditions for the affineness of open subsetsSep 26 2002In this paper we consider the open complement U of a hypersurface Y=V(a) in an affine scheme X. We study the relations between the affineness of U, the intersection of Y with closed subschemes, the property that every closed surface in U is affine, the ... More

Non-uniqueness of phase shift in central scattering due to monodromyJul 16 2008Scattering at a central potential is completely characterized by the phase shifts which are the differences in phase between outgoing scattered and unscattered partial waves. In this letter it is shown that, for 2D scattering at a repulsive central potential, ... More

Complexity and Approximability of Parameterized MAX-CSPsNov 17 2015We study the optimization version of constraint satisfaction problems (Max-CSPs) in the framework of parameterized complexity; the goal is to compute the maximum fraction of constraints that can be satisfied simultaneously. In standard CSPs, we want to ... More

A Fixed-Parameter Perspective on #BISFeb 17 2017Oct 13 2017The problem of (approximately) counting the independent sets of a bipartite graph (#BIS) is the canonical approximate counting problem that is complete in the intermediate complexity class #RH\Pi_1. It is believed that #BIS does not have an efficient ... More

Complexity and Approximability of Parameterized MAX-CSPsNov 17 2015Jan 23 2017We study the optimization version of constraint satisfaction problems (Max-CSPs) in the framework of parameterized complexity; the goal is to compute the maximum fraction of constraints that can be satisfied simultaneously. In standard CSPs, we want to ... More

Even more spectra: tensor triangular comparison maps via graded commutative 2-ringsApr 10 2012We initiate the theory of graded commutative 2-rings, a categorification of graded commutative rings. The goal is to provide a systematic generalization of Paul Balmer's comparison maps between the spectrum of tensor-triangulated categories and the Zariski ... More

Tensor triangular geometry of non-commutative motivesApr 14 2011Dec 06 2011In this article we initiate the study of the tensor triangular geometry of the categories Mot(k)_a and Mot(k)_l of non-commutative motives (over a base ring k). Since the full computation of the spectrum of Mot(k)_a and Mot(k)_l seems completely out of ... More

Electrical resistivity near Pomeranchuk instability in two dimensionsNov 28 2006We analyze the DC charge transport in the quantum critical regime near a d-wave Pomeranchuk instability in two dimensions. The transport decay rate is linear in temperature everywhere on the Fermi surface except at cold spots on the Brillouin zone diagonal. ... More

Effective Schroedinger dynamics on $ ε$-thin Dirichlet waveguides via Quantum Graphs I: star-shaped graphsApr 27 2010Sep 16 2010We describe the boundary conditions at the vertex that one must choose to obtain a dynamical system that best describes the low-energy part of the evolution of a quantum system confined to a very small neighbourhood of a star-shaped metric graph.

Mackey algebras which are GorensteinSep 07 2017We complete the picture available in the literature by showing that the integral Mackey algebra is Gorenstein if and only if the group order is square-free, in which case it must have Gorenstein dimension one. We illustrate this result by looking in details ... More

A Quillen model for classical Morita theory and a tensor categorification of the Brauer groupNov 10 2012Let K be a commutative ring. In this article we construct a symmetric monoidal Quillen model structure on the category of small K-categories which enhances classical Morita theory. We then use it in order to obtain a natural tensor categorification of ... More

Topological property (T) for groupoidsNov 17 2018We introduce a notion of topological property (T) for \'etale groupoids. This simultaneously generalizes Kazhdan's property (T) for groups and geometric property (T) for coarse spaces. One main goal is to use this property (T) to prove the existence of ... More

Spreading of correlations in a quenched repulsive and attractive one dimensional lattice systemSep 23 2016We study the real time evolution of the correlation functions in a globally quenched interacting one dimensional lattice system by means of time adaptive density matrix renormalization group. We find a clear light-cone behavior quenching the repulsive ... More

A note on triangulated monads and categories of module spectraOct 26 2016Aug 01 2018Consider a monad on an idempotent complete triangulated category with the property that its Eilenberg-Moore category of modules inherits a triangulation. We show that any other triangulated adjunction realizing this monad is 'essentially monadic', i.e. ... More

Going-Down functors and the Künneth formula for crossed products by étale groupoidsOct 10 2018We study the connection between the Baum-Connes conjecture for an ample groupoid $G$ with coefficient $A$ and the K\"unneth formula for the K-theory of tensor products by the crossed product $A\rtimes_r G$. To do so we develop the machinery of Going-Down ... More

Triaxial Ellipsoidal Quantum BilliardsDec 04 1998The classical mechanics, exact quantum mechanics and semiclassical quantum mechanics of the billiard in the triaxial ellipsoid is investigated. The system is separable in ellipsoidal coordinates. A smooth description of the motion is given in terms of ... More

Combinatorial Identities from the Spectral Theory of Quantum GraphsMar 27 2000We present a few combinatorial identities which were encountered in our work on the spectral theory of quantum graphs. They establish a new connection between the theory of random matrix ensembles and combinatorics.

Vacuum Polarisation Tensors in Constant Electromagnetic Fields: Part IIIApr 08 2001The string-inspired technique is used for a first calculation of the one-loop axialvector vacuum polarisation in a general constant electromagnetic field. A compact result is reached for the difference between this tensor and the corresponding vector ... More

Nonlinear dynamics of a microswimmer in Poiseuille flowJan 03 2012We study the three-dimensional dynamics of a spherical microswimmer in cylindrical Poiseuille flow which can be mapped onto a Hamiltonian system. Swinging and tumbling trajectories are identified. In 2D they are equivalent to oscillating and circling ... More

Metachronal waves in a chain of rowers with hydrodynamic interactionsDec 01 2010Dec 15 2010Filaments on the surface of a microorganism such as Paramecium or Ophalina beat highly synchronized and form so-called metachronal waves that travel along the surfaces. In order to study under what principal conditions these waves form, we introduce a ... More

Geometrical Models of the Phase Space Structures Governing Reaction DynamicsJun 26 2009Hamiltonian dynamical systems possessing equilibria of ${saddle} \times {centre} \times...\times {centre}$ stability type display \emph{reaction-type dynamics} for energies close to the energy of such equilibria; entrance and exit from certain regions ... More

Fiber Bundle Gauge Theories and "Field's Dilemma"May 19 2000We propose a distinction between the physical and the mathematical parts of gauge field theories. The main problem we face is to uphold a strong and meaningful criterion of what is physical. We like to call it "Field's dilemma", referring to Hartry Field's ... More

Light fermions in quantum gravityApr 28 2011We study the impact of quantum gravity, formulated as a quantum field theory of the metric, on chiral symmetry in a fermionic matter sector. We specifically address the question as to whether metric fluctuations can induce chiral symmetry breaking and ... More

Correlation functions of one-dimensional Bose-Fermi mixturesJul 15 2005We calculate the asymptotic behaviour of correlation functions as a function of the microscopic parameters for a Bose-Fermi mixture with repulsive interaction in one dimension. For two cases, namely polarized and unpolarized fermions the singularities ... More

Randomly Evolving Idiotypic Networks: Modular Mean Field TheoryJan 17 2012We develop a modular mean field theory for a minimalistic model of the idiotypic network. The model comprises the random influx of new idiotypes and a deterministic selection. It describes the evolution of the idiotypic network towards complex modular ... More