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Volumes of conditioned bipartite state spacesAug 15 2014Sep 17 2014We analyse the metric properties of $\textit{conditioned}$ quantum state spaces $\mathcal{M}^{(n\times m)}_{\eta}$. These spaces are the convex sets of $nm \times nm$ density matrices that, when partially traced over $m$ degrees of freedom, respectively ... More

Reconstructing open quantum system dynamics with limited controlOct 07 2016The dynamics of an open quantum system can be fully described and tomographically reconstructed if the experimenter has complete control over the system of interest. Most real-world experiments do not fulfill this assumption, and the amount of control ... More

An introduction to operational quantum dynamicsAug 02 2017In the summer of 2016, physicists gathered in Torun, Poland for the 48th annual Symposium on Mathematical Physics. This Symposium was special; it celebrated the 40th anniversary of the discovery of the Gorini-Kossakowski-Sudarshan-Lindblad master equation, ... More

Reconstructing open quantum system dynamics with limited controlOct 07 2016Jul 06 2018The dynamics of an open quantum system can be fully described and tomographically reconstructed if the experimenter has complete control over the system of interest. Most real-world experiments do not fulfill this assumption, and the amount of control ... More

The Structure of Quantum Stochastic Processes with Finite Markov OrderOct 25 2018Nov 10 2018Non-Markovian quantum processes exhibit different memory effects when measured in different ways; an unambiguous characterization of memory length requires accounting for the sequence of instruments applied to probe the system dynamics. This instrument-specific ... More

CP divisibility does not mean MarkovianityJan 16 2019In the classical domain, it is well-known that divisibility does not imply that a stochastic process is Markovian. However, for quantum processes, divisibility is often considered to be synonymous with Markovianity. We show that completely positive (CP) ... More

Points2Pix: 3D Point-Cloud to Image Translation using conditional Generative Adversarial NetworksJan 26 2019We present the first approach for 3D point-cloud to image translation based on conditional Generative Adversarial Networks (cGAN). The model handles multi-modal information sources from different domains, i.e. raw point-sets and images. The generator ... More

Non-Markovian quantum control as coherent stochastic trajectoriesFeb 09 2018Sep 19 2018We develop a notion of stochastic quantum trajectories. First, we construct a basis set of trajectories, called elementary trajectories, and go on to show that any quantum dynamical process, including those that are non-Markovian, can be expressed as ... More

Kolmogorov extension theorem for general (quantum) stochastic processesDec 07 2017In classical physics, the Kolmogorov extension theorem provides the foundation for the definition and investigation of stochastic processes. In its original form, it does not hold in quantum mechanics. More generally, it does not hold in any theory -- ... More

Non-Markovian quantum control as coherent stochastic trajectoriesFeb 09 2018Feb 12 2018We develop a notion of stochastic quantum trajectories. First, we construct a basis set of trajectories, called elementary trajectories, and go on to show that any quantum dynamical process, including those that are non-Markovian, can be expressed as ... More

The Structure of Quantum Stochastic Processes with Finite Markov OrderOct 25 2018Apr 10 2019Non-Markovian quantum processes exhibit different memory effects when measured in different ways; an unambiguous characterization of memory length requires accounting for the sequence of instruments applied to probe the system dynamics. This instrument-specific ... More

Kolmogorov extension theorem for (quantum) causal modelling and general probabilistic theoriesDec 07 2017Jul 07 2018In classical physics, the Kolmogorov extension theorem lays the foundation for the theory of stochastic processes. It has been known for a long time that, in its original form, this theorem does not hold in quantum mechanics. More generally, it does not ... More

Complex-YOLO: Real-time 3D Object Detection on Point CloudsMar 16 2018Sep 24 2018Lidar based 3D object detection is inevitable for autonomous driving, because it directly links to environmental understanding and therefore builds the base for prediction and motion planning. The capacity of inferencing highly sparse 3D data in real-time ... More

Quantum Markov OrderMay 29 2018Apr 10 2019We formally extend the notion of Markov order to open quantum processes by accounting for the instruments used to probe the system of interest at different times. Our description recovers the classical Markov order property in the appropriate limit: when ... More

Transverse profile and 3D spin canting of a Majorana state in carbon nanotubesDec 06 2018Apr 11 2019The full spatial 3D profile of Majorana bound states (MBS) in a nanowire-like setup featuring a semiconducting carbon nanotube (CNT) as the central element is discussed. By accurate tight-binding calculations we show that the chiral nature of the CNT ... More

Quantum Markov OrderMay 29 2018Nov 10 2018We formally extend the notion of Markov order to open quantum processes by accounting for the instruments used to probe the system of interest at different times. Our description recovers the classical Markov order property in the appropriate limit: when ... More

Entanglement, non-Markovianity, and causal non-separabilityNov 11 2017Quantum mechanics, in principle, allows for processes with indefinite causal order. However, most of these causal anomalies have not yet been detected experimentally. We show that every such process can be simulated experimentally by means of non-Markovian ... More

Efficient Semantic Segmentation for Visual Bird's-eye View InterpretationNov 29 2018The ability to perform semantic segmentation in real-time capable applications with limited hardware is of great importance. One such application is the interpretation of the visual bird's-eye view, which requires the semantic segmentation of the four ... More

Graphs with degree complete labelingJun 14 2017In 2006 Qian [J. Qian, Degree complete graphs; Discrete Mathematics 306 (2006), 533--537] introduced the concept of degree complete graphs for labeled graphs. He also gave a characterization of these graphs in terms of two forbidden subgraphs. Furthermore, ... More

Monocular Fisheye Camera Depth Estimation Using Sparse LiDAR SupervisionMar 16 2018Sep 24 2018Near field depth estimation around a self driving car is an important function that can be achieved by four wide angle fisheye cameras having a field of view of over 180. Depth estimation based on convolutional neural networks (CNNs) produce state of ... More

Complexer-YOLO: Real-Time 3D Object Detection and Tracking on Semantic Point CloudsApr 16 2019Accurate detection of 3D objects is a fundamental problem in computer vision and has an enormous impact on autonomous cars, augmented/virtual reality and many applications in robotics. In this work we present a novel fusion of neural network based state-of-the-art ... More

The resting microstate networks (RMN): cortical distributions, dynamics, and frequency specific information flowNov 07 2014Nov 15 2014A brain microstate is characterized by a unique, fixed spatial distribution of electrically active neurons with time varying amplitude. It is hypothesized that a microstate implements a functional/physiological state of the brain during which specific ... More

WoodScape: A multi-task, multi-camera fisheye dataset for autonomous drivingMay 04 2019Fisheye cameras are commonly employed for obtaining a large field of view in surveillance, augmented reality and in particular automotive applications. In spite of its prevalence, there are few public datasets for detailed evaluation of computer vision ... More

The intrinsic torsion of SU(3) and G_2 structuresFeb 26 2002We analyse the relationship between the components of the intrinsic torsion of an SU(3) structure on a 6-manifold and a G_2 structure on a 7-manifold. Various examples illustrate the type of SU(3) structure that can arise as a reduction of a metric with ... More

Realistic Ultrasonic Environment Simulation Using Conditional Generative Adversarial NetworksFeb 26 2019Recently, realistic data augmentation using neural networks especially generative neural networks (GAN) has achieved outstanding results. The communities main research focus is visual image processing. However, automotive cars and robots are equipped ... More

Book to the Future - a manifesto for book liberationJul 04 2015The Book Liberation Manifesto is an exploration of publishing outside of current corporate constraints and beyond the confines of book piracy. We believe that knowledge should be in free circulation to benefit humankind, which means an equitable and vibrant ... More

Particle Dark EnergyNov 11 2004Feb 23 2006We explore the physics of a gas of particles interacting with a condensate that spontaneously breaks Lorentz invariance. The equation of state of this gas varies from 1/3 to less than -1 and can lead to the observed cosmic acceleration. The particles ... More

Prediction of the Virgo axis anisotropy: CMB radiation illuminates the nature of thingsSep 25 2005Recent findings of the anisotropy in the Cosmic Microwave Background (CMB) radiation are confusing for standard cosmology. Remarkably, this fact has been predicted several years ago in the framework of our model of the physical world. Moreover, in exact ... More

Quantum entanglement analysis based on abstract interpretationJan 28 2008Entanglement is a non local property of quantum states which has no classical counterpart and plays a decisive role in quantum information theory. Several protocols, like the teleportation, are based on quantum entangled states. Moreover, any quantum ... More

The Evolution of Ellipticals, Spirals and Irregulars: Overcoming Selection BiasDec 07 2000The Hubble Deep Fields represent our best opportunity for probing galaxy evolution over a substantive look-back time. However as with any dataset the HDFs are prone to selection biases. These biases are extremely severe beyond z \~1.25 such that a meaningful ... More

Space-Time and ProbabilityDec 14 2001Special relativity is most naturally formulated as a theory of space-time geometry, but within the space-time framework probability apears to be at best an epistemic notion - a matter of what can be known, not of the status of events in themselves. However, ... More

What is Probability?Dec 24 2004Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics: it is argued that neither Bohr's Copenhagen interpretation, ... More

Derivation of the Born Rule from Operational AssumptionsNov 21 2002Nov 21 2002The Born rule is derived from operational assumptions, independent of the normalization of the state. Unlike Gleason's theorem, the argument applies even if probabilities are defined for only a single resolution of the identity, so it applies to all the ... More

Prospects for Precision Higgs Physics at Linear CollidersNov 30 2012A linear e+e- collider provides excellent possibilities for precision measurements of the properties of the Higgs boson. At energies close to the Z-Higgs threshold, the Higgs boson can be studied in recoil against a Z boson, to obtain not only a precision ... More

The sharp form of the strong Szego theoremFeb 06 2004Let $f$ be a function on the unit circle and $D_n(f)$ be the determinant of the $(n+1)\times (n+1)$ matrix with elements $\{c_{j-i}\}_{0\leq i,j\leq n}$ where $c_m =\hat f_m\equiv \int e^{-im\theta} f(\theta) \f{d\theta}{2\pi}$. The sharp form of the ... More

Sturm Oscillation and Comparison TheoremsNov 04 2003This is a celebratory and pedagogical discussion of Sturm oscillation theory. Included is the discussion of the difference equation case via determinants and a renormalized oscillation theorem of Gesztesy, Teschl, and the author.

Simulating Dense MatterMar 19 2007I review the Sign Problem hindering lattice QCD simulations of dense baryonic matter, focussing where possible on its physical relevance. The possibility of avoiding the Sign Problem via a duality transformation is also briefly considered. Finally, I ... More

Lattice MatterSep 28 2001I review recent developments in the study of strongly interacting field theories with non-zero chemical potential mu. In particular I focus on (a) the determination of the QCD critical endpoint in the (mu,T) plane; (b) superfluid condensates in Two Color ... More

The Phase Diagram of QCDMay 08 2001I use simple thermodynamic reasoning to argue that at temperatures of order a trillion kelvin, QCD, the theory which describes strongly interacting particles such as protons and neutrons under normal conditions, undergoes a phase transition to a plasma ... More

Cellular Automata on Group Sets and the Uniform Curtis-Hedlund-Lyndon TheoremMar 21 2016Jun 13 2016We introduce cellular automata whose cell spaces are left homogeneous spaces and prove a uniform as well as a topological variant of the Curtis-Hedlund-Lyndon theorem. Examples of left homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic ... More

A First Look at the Impact of NNNLO Theory Uncertainties on Top Mass Measurements at the ILCMar 15 2016Aug 22 2016A scan of the top production threshold at a future electron-positron collider provides the possibility for a precise measurement of the top quark mass in theoretically well-defined mass schemes. With statistical uncertainties of 20 MeV or below, systematics ... More

Static perfect fluids with Pant-Sah equations of stateJan 17 2008Mar 31 2008We analyze the 3-parameter family of exact, regular, static, spherically symmetric perfect fluid solutions of Einstein's equations (corresponding to a 2-parameter family of equations of state) due to Pant and Sah and "rediscovered" by Rosquist and the ... More

Criteria for (in)finite extent of static perfect fluidsApr 09 2002In Newton's and in Einstein's theory we give criteria on the equation of state of a barotropic perfect fluid which guarantee that the corresponding one-parameter family of static, spherically symmetric solutions has finite extent. These criteria are closely ... More

Conformal positive mass theoremsMar 29 2000We show the following two extensions of the standard positive mass theorem (one for either sign): Let (N,g) and (N,g') be asymptotically flat Riemannian 3-manifolds with compact interior and finite mass, such that g and g' are twice Hoelder differentiable ... More

ExSample -- A Library for Sampling Sudakov-Type DistributionsAug 31 2011Mar 19 2012Sudakov-type distributions are at the heart of generating radiation in parton showers as well as contemporary NLO matching algorithms along the lines of the POWHEG algorithm. In this paper, the C++ library ExSample is introduced, which implements adaptive ... More

Ricci Flow of regions with curvature bounded below in dimension threeJul 04 2014We consider smooth complete solutions to Ricci flow with bounded curvature on manifolds without boundary in dimension three. Assuming an open ball at time zero of radius one has curvature bounded from below by -1, then we prove estimates which show that ... More

Dynamics on supersingular K3 surfaces and automorphisms of Salem degree 22Jul 08 2015In this note we exhibit explicit automorphisms of maximal Salem degree 22 on the supersingular K3 surface of Artin invariant one for all primes p congruent 3 mod 4 in a systematic way. Automorphisms of Salem degree 22 do not lift to any characteristic ... More

Simulating the formation of massive seed black holes in the early Universe. I: An improved chemical modelJan 23 2015Jun 06 2015The direct collapse model for the formation of massive seed black holes in the early Universe attempts to explain the observed number density of supermassive black holes (SMBHs) at $z \sim 6$ by assuming that they grow from seeds with masses M > 10000 ... More

Logic of Negation-Complete Interactive Proofs (Formal Theory of Epistemic Deciders)Aug 29 2012May 29 2013We produce a decidable classical normal modal logic of internalised negation-complete and thus disjunctive non-monotonic interactive proofs (LDiiP) from an existing logical counterpart of non-monotonic or instant interactive proofs (LiiP). LDiiP internalises ... More

A Logic of Interactive Proofs (Formal Theory of Knowledge Transfer)Jan 17 2012Apr 05 2016We propose a logic of interactive proofs as a framework for an intuitionistic foundation for interactive computation, which we construct via an interactive analog of the Goedel-McKinsey-Tarski-Artemov definition of Intuitionistic Logic as embedded into ... More

Positive stable densities and the bell-shapeFeb 05 2013We show that positive stable densities are bell-shaped, that is their n-th derivatives vanish exactly n times on (0,+oo) and have an alternating sign sequence. This confirms the graphic predictions of Holt and Crow (1973) in the positive case.

Produit Beta-Gamma et régularité du signeJul 27 2012We study the total positivity of the multiplicative convolution kernel T associated with the independent product of two random variables $B(a,b)$ and $\Gamma(c).$ This kernel is totally positive of infinite order if $b$ or $d = a+b -c$ are integers. Otherwise ... More

Comment on "Separability of quantum states and the violation of Bell-type inequalities"Oct 05 2004The statement of E.R. Loubenets, Phys. Rev. A 69, 042102 (2004), that separable states can violate classical probabilistic constraints is based on a misleading definition of classicality, which is much narrower than Bell's concept of local hidden variables. ... More

The Foundations of Quantum Information and Feasible ExperimentsMar 12 2001This thesis consists of four parts. In the first part it is shown that optimal universal cloning of photons can be realized with the help of stimulated emission. Possible schemes based on three-level systems and on parametric down-conversion are analyzed ... More

Some remarks about equations defining coincident root lociAug 23 2011Consider the projective variety $X_\lambda$ of binary forms of degree $d$ whose linear factors are distributed according to the partition $\lambda$ of $d$. We determine minimal sets of local generators of the fiber product of $X_\lambda$ with its normalization, ... More

Refining Reasoning in Qualitative Probabilistic NetworksFeb 20 2013In recent years there has been a spate of papers describing systems for probabilisitic reasoning which do not use numerical probabilities. In some cases the simple set of values used by these systems make it impossible to predict how a probability will ... More

Hyperplane Equipartitions Plus ConstraintsAug 01 2017Oct 09 2017While equivariant methods have seen many fruitful applications in geometric combinatorics, their inability to answer the now settled Topological Tverberg Conjecture has made apparent the need to move beyond the use of Borsuk-Ulam type theorems alone. ... More

Topological phases in the non-Hermitian Su-Schrieffer-Heeger modelSep 12 2017Jan 02 2018We address the conditions required for a $\mathbb{Z}$ topological classification in the most general form of the non-Hermitian Su-Schrieffer-Heeger (SSH) model. Any chirally-symmetric SSH model will possess a "conjugated-pseudo-Hermiticity" which we show ... More

The Moore and the Myhill Property For Strongly Irreducible Subshifts Of Finite Type Over Group SetsJun 19 2017We prove the Moore and the Myhill property for strongly irreducible subshifts over right amenable and finitely right generated left homogeneous spaces with finite stabilisers. Both properties together mean that the global transition function of each big-cellular ... More

La théorie de Hodge des bimodules de Soergel (d'après Soergel et Elias-Williamson)Nov 07 2017Soergel bimodules are certain bimodules over polynomial algebras, associated with Coxeter groups, and introduced by Soergel in the 1990's while studying the category O of complex semisimple Lie algebras. Even though their definition is algebraic and rather ... More

Maximizing Riesz means of anisotropic harmonic oscillatorsDec 29 2017We consider problems related to the asymptotic minimization of eigenvalues of anisotropic harmonic oscillators in the plane. In particular we study Riesz means of the eigenvalues and the trace of the corresponding heat kernels. The eigenvalue minimization ... More

Regularized Newton methods for simultaneous Radon inversion and phase retrieval in phase contrast tomographyFeb 17 2015Promoted by the advent of coherent synchrotron light sources, phase contrast tomography allows to resolve three-dimensional variations of an unknown sample's complex refractive index from scattering intensities recorded at different incident angles of ... More

On the construction of solutions to the Yang-Mills equations in higher dimensionsFeb 10 2003Aug 13 2003We describe a glueing construction for the Yang-Mills equations in dimension $n > 4$. Our method is based on a construction of approximate solutions, and a detailed analysis of the linearized operator near an approximate solution.

On solutions to the Ginzburg-Landau equations in higher dimensionsFeb 06 2003Aug 13 2003We establish a glueing theorem for the Ginzburg-Landau equations in dimension $n > 2$. To this end, we consider a nondegenerate minimal submanifold of codimension 2, and construct a one-parameter family of solutions to the Ginzburg-Landau equations such ... More

Performance of a measurement-driven 'adiabatic-like' quantum 3-SAT solverSep 02 2015I describe one quantum approach to solving 3-satisfiability (3-SAT), the well known problem in computer science. The approach is based on repeatedly measuring the truth value of the clauses forming the 3-SAT proposition using a non-orthogonal basis. If ... More

Measure Equipartitions via Finite Fourier AnalysisMar 27 2014Jun 20 2015Applications of harmonic analysis on finite groups are introduced to measure partition problems, with equipartitions obtained as the vanishing of prescribed Fourier transforms. For elementary abelian groups $Z_p^k$, $p$ an odd prime, equipartitions are ... More

Equivariant Equipartitions: Ham Sandwich Theorems for Finite Subgroups of SpheresSep 04 2011Jun 19 2012Equivariant "Ham Sandwich" Theorems are obtained for the finite subgroups G of the unit spheres S(F) in the classical algebras F = R, C, and H. Given any n F-valued mass distributions on F^n, it is shown that there exists a G-equivariant decomposition ... More

Mass Partitions via Equivariant Sections of Stiefel BundlesNov 08 2010Aug 01 2017We consider a geometric combinatorial problem naturally associated to the geometric topology of certain spherical space forms. Given a collection of $m$ mass distributions on $\mathbb{R}^n$, the existence of $k$ affinely independent regular $q$-fans, ... More

Kahler metrics with cone singularities along a divisorFeb 06 2011Feb 14 2011We develop some foundations for the study of Kahler-Einstein metrics with cone singularities transverse to a divisor. The main goal is a treatment of the deformation of the cone angle.

Coupled Critical Models: Applications to Ising-Potts ModelsMay 28 1997We discuss the critical behaviour of 2D Ising and q-states Potts models coupled by their energy density. We found new tricritical points. The procedure employed is the renormalisation approach of the perturbations series around conformal field theories ... More

Rosenthal compacta and NIP formulasJul 22 2014Aug 07 2015We apply the work of Bourgain, Fremlin and Talagrand on compact subsets of the first Baire class to show new results about phi-types for phi NIP. In particular, we show that if M is a countable model, then an M-invariant phi-type is Borel definable. Also ... More

Coupled Minimal Models with and without DisorderOct 02 1997We analyse in this article the critical behavior of $M$ $q_1$-state Potts models coupled to $N$ $q_2$-state Potts models ($q_1,q_2\in [2..4]$) with and without disorder. The technics we use are based on perturbed conformal theories. Calculations have ... More

Zero repulsion in families of elliptic curve L-functions and an observation of S. J. MillerSep 01 2011Oct 20 2011We provide a theoretical explanation for an observation of S. J. Miller that if L(s,E) is an elliptic curve L-function for which L(1/2, E) is nonzero, then the lowest lying zero of L(s,E) exhibits a repulsion from the critical point which is not explained ... More

Numerical Root Finding via Cox RingsMar 28 2019We present a new eigenvalue method for solving a system of Laurent polynomial equations defining a zero-dimensional reduced subscheme of a toric compactification $X$ of $(\mathbb{C} \setminus \{0\})^n$. We homogenize the input equations to obtain a homogeneous ... More

The almost Daugavet property and translation-invariant subspacesJul 13 2013Let $G$ be a metrizable, compact abelian group and let $\Lambda$ be a subset of its dual group $\hat G$. We show that $C_\Lambda(G)$ has the almost Daugavet property if and only if $\Lambda$ is an infinite set, and that $L^1_\Lambda(G)$ has the almost ... More

Subspaces of almost Daugavet spacesJul 17 2010We study the almost Daugavet property, a generalization of the Daugavet property. It is analysed what kind of subspaces and sums of Banach spaces with the almost Daugavet property have this property as well. The main result of the paper is: if $Z$ is ... More

Approximations of generating functions and a few conjecturesNov 25 2009This is a collection of 1031 formulas that were generated by a computer program in 1992. The set is the database of integer sequences as of 1992 which contained 4568 sequences. These sequences were later published in the Encyclopedia of Integer Sequences ... More

Asymptotic shape optimization for Riesz means of the Dirichlet Laplacian over convex domainsNov 17 2016Aug 01 2018For $\Omega \subset \mathbb{R}^n$, a convex and bounded domain, we study the spectrum of $-\Delta_\Omega$ the Dirichlet Laplacian on $\Omega$. For $\Lambda\geq0$ and $\gamma \geq 0$ let $\Omega_{\Lambda, \gamma}(\mathcal{A})$ denote any extremal set of ... More

Technical Report: Modelling Multiple Cell Types with Partial Differential EquationsSep 28 2015Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly. However, in case ... More

Extending and Implementing the Stable Model SemanticsMay 08 2000An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of efficient implementation ... More

A metric theorem for restricted Diophantine approximation in positive characteristicJan 28 2004Oct 10 2005We calculate the measure and Hausdorff dimension of sets of matrices over fields of formal power series with good approximation properties for a restricted set of denominators.

Distal and non-distal NIP theoriesMar 11 2011Oct 27 2012We study one way in which stable phenomena can exist in an NIP theory. We start by defining a notion of 'pure instability' that we call 'distality' in which no such phenomenon occurs. O-minimal theories and the p-adics for example are distal. Next, we ... More

Hyperbolicity and Cubulability Are Preserved Under Elementary EquivalenceJan 29 2018The following properties are preserved under elementary equivalence, among finitely generated groups: being hyperbolic (possibly with torsion), being hyperbolic and cubulable, and being a subgroup of a hyperbolic group. In other words, if a finitely generated ... More

Minimum settling time control design through direct search optimizationSep 27 2011Dec 06 2011The aim of this work is to design controllers through explicit minimization of the settling time of a closed-loop response, by using a class of methods adequate for this objective. To the best of our knowledge, all the methods available in the literature ... More

Scanning Strategies at the Top Threshold at ILCFeb 19 2019A scan of the top quark pair production threshold at a future electron-positron collider provides the possibility for high-precision measurements of the top quark mass, and, when using two dimensional fits of the measured cross sections, also of other ... More

A detailed proof of Bourgain's Return Times TheoremJan 14 2019In this diploma thesis (written in German) we present a detailed proof of Bourgain's Return Times Theorem due to Bourgain, Furstenberg, Katznelson and Ornstein following their paper as well as the book by Assani. Moreover, we generalize the result to ... More

A Mayer-Vietoris Spectral Sequence for C*-Algebras and Coarse GeometryDec 29 2018Let $A$ be a C*-algebra that is the norm closure $A = \overline{\sum_{\beta \in \alpha} I_\beta}$ of an arbitrary sum of C*-ideals $I_\beta \subseteq A$. We construct a homological spectral sequence that takes as input the K-theory of $\bigcap_{j \in ... More

On the Critical Flavor Number in the 2+1$d$ Thirring ModelNov 12 2018Jan 30 2019The Thirring model in 2+1 spacetime dimensions, in which $N$ flavors of relativistic fermion interact via a contact interaction between conserved fermion currents, is studied using lattice field theory simulations employing domain wall fermions, which ... More

A contact camel theoremAug 16 2018We provide a contact analogue of the symplectic camel theorem that holds in $\mathbb{R}^{2n}\times S^1$, and indeed generalize the symplectic camel. Our proof is based on the generating function techniques introduced by Viterbo, extended to the contact ... More

FPGA implementation of a DCDS processorJul 13 2018An experimental digital correlated double sampler (DCDS) video processor has been implemented in a Xilinx Artix FPGA. It uses an Opal Kelly XEM7010-A50 module that comes with an integrated USB2 interface for easy interfac-ing to a data acquisition PC. ... More

On a theorem of Kac and GilbertMay 06 2004We prove a general operator theoretic result that asserts that many multiplicity two selfadjoint operators have simple singular spectrum.

The localic Istropy group of a toposJun 15 2017It has been shown by J.Funk, P.Hofstra and B.Steinberg that any Grothendieck topos T is endowed with a canonical group object, called its isotropy group, which acts functorially on every object of T. We show that this group is in fact the group of points ... More

Microlocal analysis of generalized pullbacks of Colombeau functionsJan 17 2007Feb 02 2007In distribution theory the pullback of a general distribution by a $C^{\infty}$-function is well-defined whenever the normal bundle of the $C^{\infty}$-function does not intersect the wavefront set of the distribution. However, the Colombeau theory of ... More

Splitting the Curvature of the Determinant Line BundleDec 21 1998It is shown that the determinant line bundle associated to a family of Dirac operators over a closed partitioned manifold has a canonical Hermitian metric with compatible connection whose curvature satisfies an additivity formula with contributions from ... More

An elliptic boundary value problem for $G_{2}$ structuresJan 05 2018Jan 22 2019We show that the $G_{2}$ holonomy equation on a manifold with boundary, with prescribed 3-form on the boundary, is elliptic. The main point is to set up a suitable linear elliptic boundary value problem. This result leads to a deformation theory. In particular ... More

Holomorphic horospherical duality "sphere-cone"Jan 02 2005We describe a construction of complex geometrical analysis which corresponds to the classical theory of spherical harmonics.

Splitting the K-Terminal ReliabilityApr 18 2011Let G=(V,E) be a graph and K a set of terminal vertices of G. Assume that the edges of G are failing independently with given probabilities. The K-terminal reliability R(G,K) is the probability that all vertices in K are mutually connected. In this article ... More

Geometric Hardy inequalities for the sub-elliptic Laplacian on convex domains in the Heisenberg groupMar 04 2016We prove geometric $L^p$ versions of Hardy's inequality for the sub-elliptic Laplacian on convex domains $\Omega$ in the Heisenberg group $\mathbb{H}^n$, where convex is meant in the Euclidean sense. When $p=2$ and $\Omega$ is the half-space given by ... More

Numerical Root Finding via Cox RingsMar 28 2019Mar 29 2019We present a new eigenvalue method for solving a system of Laurent polynomial equations defining a zero-dimensional reduced subscheme of a toric compactification $X$ of $(\mathbb{C} \setminus \{0\})^n$. We homogenize the input equations to obtain a homogeneous ... More

Hitting densities for spectrally positive stable processesFeb 08 2010A multiplicative identity in law connecting the hitting times of completely asymmetric $\alpha-$stable L\'evy processes in duality is established. In the spectrally positive case, this identity allows with an elementary argument to compute fractional ... More