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A priorconditioned LSQR algorithm for linear ill-posed problems with edge-preserving regularizationAug 30 2013This article presents a method for solving large-scale linear inverse problems regular- ized with a nonlinear, edge-preserving penalty term such as the total variation or Perona-Malik. In the proposed scheme, the nonlinearity is handled with lagged diffusivity ... More

Optical tomography: forward and inverse problemsJul 15 2009This paper is a review of recent mathematical and computational advances in optical tomography. We discuss the physical foundations of forward models for light propagation on microscopic, mesoscopic and macroscopic scales. We also consider direct and ... More

Accelerated High-Resolution Photoacoustic Tomography via Compressed SensingApr 30 2016Sep 28 2016Current 3D photoacoustic tomography (PAT) systems offer either high image quality or high frame rates but are not able to deliver high spatial and temporal resolution simultaneously, which limits their ability to image dynamic processes in living tissue. ... More

Networks for Nonlinear Diffusion Problems in ImagingNov 29 2018A multitude of imaging and vision tasks have seen recently a major transformation by deep learning methods and in particular by the application of convolutional neural networks. These methods achieve impressive results, even for applications where it ... More

Expectation Propagation for Poisson DataOct 18 2018The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation propagation ... More

Expectation Propagation for Poisson DataOct 18 2018Apr 10 2019The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation propagation ... More

A pseudospectral method for solution of the radiative transport equationJan 19 2018Mar 18 2019The radiative transport equation accurately describes light transport in participating media such as biological tissues, though analytic solutions are known only for simple geometries. We present a pseudospectral technique to efficiently compute numerical ... More

Statistics on functional data and covariance operators in linear inverse problemsJun 11 2018We introduce a framework for the statistical analysis of functional data in a setting where these objects cannot be fully observed, but only indirect and noisy measurements are available, namely an inverse problem setting. The proposed methodology can ... More

A pseudospectral method for solution of the radiative transport equationJan 19 2018The Boltzmann transport equation accurately describes a number of physical phenomena, though analytic solutions are known only for simple geometries. We present a pseudospectral technique to efficiently compute numerical solutions to the time-domain transport ... More

Reconstruction-classification method for quantitative photoacoustic tomographyAug 04 2015We propose a combined reconstruction-classification method for simultaneously recovering absorption and scattering in turbid media from images of absorbed optical energy. This method exploits knowledge that optical parameters are determined by a limited ... More

Variational Gaussian Approximation for Poisson DataSep 18 2017The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the posterior distribution ... More

The Factorization method for three dimensional Electrical Impedance TomographyDec 05 2013Jan 29 2014The use of the Factorization method for Electrical Impedance Tomography has been proved to be very promising for applications in the case where one wants to find inhomogeneous inclusions in a known background. In many situations, the inspected domain ... More

Gradient-based quantitative image reconstruction in ultrasound-modulated optical tomography: first harmonic measurement type in a linearised diffusion formulationSep 06 2014Mar 20 2016Ultrasound-modulated optical tomography is an emerging biomedical imaging modality which uses the spatially localised acoustically-driven modulation of coherent light as a probe of the structure and optical properties of biological tissues. In this work ... More

Quantitative photoacoustic tomography using forward and adjoint Monte Carlo models of radianceAug 18 2016Forward and adjoint Monte Carlo (MC) models of radiance are proposed for use in model-based quantitative photoacoustic tomography. A 2D radiance MC model using a harmonic angular basis is introduced and validated against analytic solutions for the radiance ... More

A pseudospectral method for solution of the radiative transport equationJan 19 2018Mar 08 2018The radiative transport equation accurately describes light transport in participating media such as biological tissues, though analytic solutions are known only for simple geometries. We present a pseudospectral technique to efficiently compute numerical ... More

Enhancing Compressed Sensing Photoacoustic Tomography by Simultaneous Motion EstimationFeb 14 2018A crucial limitation of current high-resolution 3D photoacoustic tomography (PAT) devices that employ sequential scanning is their long acquisition time. In previous work, we demonstrated how to use compressed sensing techniques to improve upon this: ... More

Inference of Haemoglobin Concentration From Stereo RGBJul 11 2016Jun 22 2017Multispectral imaging (MSI) can provide information about tissue oxygenation, perfusion and potentially function during surgery. In this paper we present a novel, near real-time technique for intrinsic measurements of total haemoglobin (THb) and blood ... More

Fast Estimation of Haemoglobin Concentration in Tissue Via Wavelet DecompositionJun 22 2017Tissue oxygenation and perfusion can be an indicator for organ viability during minimally invasive surgery, for example allowing real-time assessment of tissue perfusion and oxygen saturation. Multispectral imaging is an optical modality that can inspect ... More

Enhancing Compressed Sensing 4D Photoacoustic Tomography by Simultaneous Motion EstimationFeb 14 2018Jun 15 2018A crucial limitation of current high-resolution 3D photoacoustic tomography (PAT) devices that employ sequential scanning is their long acquisition time. In previous work, we demonstrated how to use compressed sensing techniques to improve upon this: ... More

Real-time Cardiovascular MR with Spatio-temporal Artifact Suppression using Deep Learning - Proof of Concept in Congenital Heart DiseaseMar 14 2018Jun 14 2018PURPOSE: Real-time assessment of ventricular volumes requires high acceleration factors. Residual convolutional neural networks (CNN) have shown potential for removing artifacts caused by data undersampling. In this study we investigated the effect of ... More

Approximate Marginalization of Absorption and Scattering in Fluorescence Diffuse Optical TomographyJan 02 2015In fluorescence diffuse optical tomography (fDOT), the reconstruction of the fluorophore concentration inside the target body is usually carried out using a normalized Born approximation model where the measured fluorescent emission data is scaled by ... More

Approximate k-space models and Deep Learning for fast photoacoustic reconstructionJul 09 2018We present a framework for accelerated iterative reconstructions using a fast and approximate forward model that is based on k-space methods for photoacoustic tomography. The approximate model introduces aliasing artefacts in the gradient information ... More

Inference of Haemoglobin Concentration From Stereo RGBJul 11 2016Multispectral imaging (MSI) can provide information about tissue oxygenation, perfusion and potentially function during surgery. In this paper we present a novel, near real-time technique for intrinsic measurements of total haemoglobin (THb) and blood ... More

Model based learning for accelerated, limited-view 3D photoacoustic tomographyAug 31 2017Recent advances in deep learning for tomographic reconstructions have shown great potential to create accurate and high quality images with a considerable speed-up. In this work we present a deep neural network that is specifically designed to provide ... More

Numerical Methods for Coupled Reconstruction and Registration in Digital Breast TomosynthesisJul 23 2013Digital Breast Tomosynthesis (DBT) provides an insight into the fine details of normal fibroglandular tissues and abnormal lesions by reconstructing a pseudo-3D image of the breast. In this respect, DBT overcomes a major limitation of conventional X-ray ... More

On the Adjoint Operator in Photoacoustic TomographyFeb 05 2016Aug 01 2016Photoacoustic Tomography (PAT) is an emerging biomedical "imaging from coupled physics" technique, in which the image contrast is due to optical absorption, but the information is carried to the surface of the tissue as ultrasound pulses. Many algorithms ... More

Model based learning for accelerated, limited-view 3D photoacoustic tomographyAug 31 2017Mar 26 2018Recent advances in deep learning for tomographic reconstructions have shown great potential to create accurate and high quality images with a considerable speed-up. In this work we present a deep neural network that is specifically designed to provide ... More

Acoustic Wave Field Reconstruction from Compressed Measurements with Application in Photoacoustic TomographySep 09 2016We present a method for the recovery of compressively sensed acoustic fields using patterned, instead of point-by-point, detection. From a limited number of such compressed measurements, we propose to reconstruct the field on the sensor plane in each ... More

Deep De-Aliasing for Fast Compressive Sensing MRIMay 19 2017Fast Magnetic Resonance Imaging (MRI) is highly in demand for many clinical applications in order to reduce the scanning cost and improve the patient experience. This can also potentially increase the image quality by reducing the motion artefacts and ... More

A model of force balance in Saturn's magnetodiscSep 08 2009Oct 14 2009We present calculations of magnetic potential associated with the perturbation of Saturn's magnetic field by a rotating, equatorially-situated disc of plasma. Such structures are central to the dynamics of the rapidly rotating magnetospheres of Saturn ... More

Electric field variability and classifications of Titan's magnetoplasma environmentMay 12 2011The atmosphere of Saturn's largest moon Titan is driven by photochemistry, charged particle precipitation from Saturn's upstream magnetosphere, and presumably by the diffusion of the magnetospheric field into the outer ionosphere, amongst other processes. ... 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

On Estimating Many Means, Selection Bias, and the BootstrapNov 15 2013With recent advances in high throughput technology, researchers often find themselves running a large number of hypothesis tests (thousands+) and esti- mating a large number of effect-sizes. Generally there is particular interest in those effects estimated ... 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

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

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 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

A Note on the Expected Number of Interviews When Talent is Uniformly DistributedOct 26 2018Optimal stopping problems give rise to random distributions describing how many applicants the decision-maker will observe or interview before choosing one, a quantity sometimes referred to as the optimal stopping time. Despite the fact that is has important ... 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.

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

Calabi-Yau metrics on Kummer surfaces as a model glueing problemJul 23 2010This is an expository paper which aims to give a simple proof of the existence of Ricci-flat metrics on certain K3 surfaces, as an illustration of general "glueing" techniques.

Stability, birational transformations and the Kahler-Einstein problemJul 23 2010We define a new notion of "b-stability" for a polarised algebraic variety, adapted to the existence problem for Kahler-Einstein metrics on Fano manifolds.