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Scaling Nonparametric Bayesian Inference via Subsample-AnnealingFeb 22 2014We describe an adaptation of the simulated annealing algorithm to nonparametric clustering and related probabilistic models. This new algorithm learns nonparametric latent structure over a growing and constantly churning subsample of training data, where ... More

Towards Mott design by $δ$-doping of strongly correlated titanatesNov 06 2014Apr 08 2015Doping the distorted-perovskite Mott insulators LaTiO$_3$ and GdTiO$_3$ with a single SrO layer along the [001] direction gives rise to a rich correlated electronic structure. A realistic superlattice study by means of the charge self-consistent combination ... More

Billiard knots in a cylinderNov 02 1998We define cylinder knots as billiard knots in a cylinder. We present a necessary condition for cylinder knots: after dividing cylinder knots by possible rotational symmetries we obtain ribbon knots. We obtain an upper bound for the number of cylinder ... More

Tensor Variable Elimination for Plated Factor GraphsFeb 08 2019A wide class of machine learning algorithms can be reduced to variable elimination on factor graphs. While factor graphs provide a unifying notation for these algorithms, they do not provide a compact way to express repeated structure when compared to ... More

Thresholds in choice behaviour and the size of travel time savingsFeb 14 2014Sep 02 2015Travel time savings are usually the most substantial economic benefit of transport infrastructure projects. However, questions surround whether small time savings are as valuable per unit as larger savings. Thresholds in individual choice behaviour are ... More

Asynchronous Distributed Searchlight SchedulingJan 11 2007Aug 10 2007This paper develops and compares two simple asynchronous distributed searchlight scheduling algorithms for multiple robotic agents in nonconvex polygonal environments. A searchlight is a ray emitted by an agent which cannot penetrate the boundary of the ... More

Joint Mapping and Calibration via Differentiable Sensor FusionNov 21 2018Dec 20 2018We leverage automatic differentiation (AD) and probabilistic programming to develop an end-to-end optimization algorithm for batch triangulation of a large number of unknown objects. Given noisy detections extracted from noisily geo-located street level ... More

Short-term Mortality Prediction for Elderly Patients Using Medicare Claims DataDec 02 2017Risk prediction is central to both clinical medicine and public health. While many machine learning models have been developed to predict mortality, they are rarely applied in the clinical literature, where classification tasks typically rely on logistic ... More

Quantum analogues of Hardy's nonlocality paradoxJun 12 2010Apr 04 2011Hardy's nonlocality is a "nonlocality proof without inequalities": it exemplifies that quantum correlations can be qualitatively stronger than classical correlations. This paper introduces variants of Hardy's nonlocality in the CHSH scenario which are ... More

Quantum correlations in the temporal CHSH scenarioMay 19 2010Mar 26 2014We consider a temporal version of the CHSH scenario using projective measurements on a single quantum system. It is known that quantum correlations in this scenario are fundamentally more general than correlations obtainable with the assumptions of macroscopic ... More

On the existence of quantum representations for two dichotomic measurementsAug 18 2009Feb 16 2010Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum system with trivial ... More

Long Baseline Neutrino Physics: From Fermilab to KamiokaMar 03 2002We have investigated the physics potential of very long baseline experiments designed to measure nu_mu to nu_e oscillation probabilities. The principles of our design are to tune the beam spectrum to the resonance energy for the matter effect, and to ... More

From Sazonov's Non-Dcpo Natural Domains to Closed Directed-Lub Partial OrdersMay 06 2016Normann proved that the domains of the game model of PCF (the domains of sequential functionals) need not be dcpos. Sazonov has defined natural domains for a theory of such incomplete domains. This paper further develops that theory. It defines lub-rules ... More

Full Abstraction for a Recursively Typed Lambda Calculus with Parallel ConditionalJun 11 2008We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a restricted ... More

On infinite-dimensional state spacesFeb 16 2012Apr 26 2013It is well-known that the canonical commutation relation $[x,p]=i$ can be realized only on an infinite-dimensional Hilbert space. While any finite set of experimental data can also be explained in terms of a finite-dimensional Hilbert space by approximating ... More

Quantum logic is undecidableJul 20 2016Nov 04 2016We investigate the first-order theory of closed subspaces of complex Hilbert spaces in the signature $(\lor,\perp,0,1)$, where `$\perp$' is the orthogonality relation. Our main result is that already its purely implicational fragment is undecidable: there ... More

Polyhedral duality in Bell scenarios with two binary observablesFeb 01 2012Jun 18 2012For the Bell scenario with two parties and two binary observables per party, it is known that the no-signaling polytope is the polyhedral dual (polar) of the Bell polytope. Computational evidence suggests that this duality also holds for three parties. ... More

Antisymmetry of the stochastic order on all ordered metric spacesOct 16 2018In this short note, we prove that the stochastic order of Radon probability measures on any metric space is antisymmetric.

Transition probabilities and measurement statistics of postselected ensemblesMar 23 2010Jul 20 2010It is well-known that a quantum measurement can enhance the transition probability between two quantum states. Such a measurement operates after preparation of the initial state and before postselecting for the final state. Here we analyze this kind of ... More

Fibered Multiderivators and (co)homological descentMay 05 2015Nov 24 2015The theory of derivators enhances and simplifies the theory of triangulated categories. In this article a notion of fibered (multi-)derivator is developed, which similarly enhances fibrations of (monoidal) triangulated categories. We present a theory ... More

Nonlocality with less ComplementarityJun 20 2011Feb 01 2012In quantum mechanics, nonlocality (a violation of a Bell inequality) is intimately linked to complementarity, by which we mean that consistently assigning values to different observables at the same time is not possible. Nonlocality can only occur when ... More

Beyond Bell's Theorem: Correlation ScenariosJun 22 2012Sep 02 2012Bell's Theorem witnesses that the predictions of quantum theory cannot be reproduced by theories of local hidden variables in which observers can choose their measurements independently of the source. Working out an idea of Branciard, Rosset, Gisin and ... More

Laser Cooling of TeV MuonsJul 20 2000We show that Compton scattering can be used to cool TeV-scale muon beams, and we derive analytical expressions for the equilibrium transverse angular spread, longitudinal energy spread, and power requirements. We find that a factor of a few thousand reduction ... More

Towards a Re-definition of the Second Based on Optical Atomic ClocksJan 09 2015Jan 28 2015The rapid increase in accuracy and stability of optical atomic clocks compared to the caesium atomic clock as primary standard of time and frequency asks for a future re-definition of the second in the International System of Units (SI). The status of ... More

Intensional Constructed Numbers: Towards Formalizing the Notion of AlgorithmSep 25 2017This work is meant to be a step towards the formal definition of the notion of algorithm, in the sense of an equivalence class of programs working "in a similar way". But instead of defining equivalence transformations directly on programs, we look at ... More

B+ and B0 Mean Lifetime MeasurementsSep 19 1994We review $B^+$ and $B^0$ mean lifetime measurements, including direct measurements and determination of the lifetime ratio via measurements of the ratio of branching ratios. We present world averages.

$B$ Physics with the CDF Run II UpgradeDec 21 1995We summarize Run I results relevant to an analysis of the CP asymmetry in $B\to J/\psi K_s$, the CDF upgrade plans for Run II, and some of the main $B$ physics goals related to the exploration of the origin of CP violation.

Quantum-Critical transport at a semimetal-to-insulator transition on the honeycomb latticeDec 01 2010Jan 25 2012In this paper we study transport properties of electrons on the two-dimensional honeycomb lattice. We consider a half-filled system in the vicinity of a symmetry-breaking transition from a semimetallic phase towards an insulating phase with either charge ... More

On the computation of harmonic maps by unconstrained algorithms based on totally geodesic embeddingsOct 17 2016In this paper, we present an algorithm for the computation of harmonic maps, and respectively, of the harmonic map heat flow between two closed Riemannian manifolds. Our approach is based on the totally geodesic embedding of the target manifold into $\mathbb{R}^N$ ... More

Tsirelson's problem and Kirchberg's conjectureAug 06 2010May 04 2012Tsirelson's problem asks whether the set of nonlocal quantum correlations with a tensor product structure for the Hilbert space coincides with the one where only commutativity between observables located at different sites is assumed. Here it is shown ... More

Descent for coherent sheaves along formal/open coveringsMar 07 2016For a regular noetherian scheme $X$ with a divisor with strict normal crossings $D$ we prove that coherent sheaves satisfy descent w.r.t. the 'covering' consisting of the open parts in the various completions of $X$ along the components of $D$ and their ... More

Generalized automorphic sheaves and the proportionality principle of Hirzebruch-MumfordMar 14 2016We axiomatize the algebraic structure of toroidal compactifications of Shimura varieties and their automorphic vector bundles. We propose a notion of generalized automorphic sheaf which includes the sheaves of sections of automorphic vector bundles with ... More

Inverse spectral theory as influenced by Barry SimonFeb 02 2010We survey Barry Simon's principal contributions to the field of inverse spectral theory in connection with one-dimensional Schrodinger and Jacobi operators.

Pyro: Deep Universal Probabilistic ProgrammingOct 18 2018Pyro is a probabilistic programming language built on Python as a platform for developing advanced probabilistic models in AI research. To scale to large datasets and high-dimensional models, Pyro uses stochastic variational inference algorithms and probability ... More

Unconventional Ideas for Axion and Dark Matter ExperimentsSep 26 2015In this contribution an entirely different way compared to conventional approaches for axion, hidden photon and dark matter (DM) detection is proposed for discussion. The idea is to use living plants which are known to be very sensitive to all kind of ... More

Distance Measurements and Stellar Population Properties via Surface Brightness FluctuationsMay 07 2012Surface Brightness Fluctuations (SBFs) are one of the most powerful techniques to measure the distance and to constrain the unresolved stellar content of extragalactic systems. For a given bandpass, the absolute SBF magnitude \bar{M} depends on the properties ... More

Integrable Systems in the Infinite Genus LimitJul 07 1999We provide an elementary approach to integrable systems associated with hyperelliptic curves of infinite genus. In particular, we explore the extent to which the classical Burchnall-Chaundy theory generalizes in the infinite genus limit, and systematically ... More

Curious properties of hypergraph C*-algebrasAug 28 2018Oct 17 2018Given a finite hypergraph $H$, the associated hypergraph C*-algebra $C^*(H)$ is finitely presented by one projection for each vertex of $H$, such that each hyperedge forms a partition of unity. General hypergraph C*-algebras were first studied in the ... More

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

Differentiable equivalence of fractional linear mapsAug 10 2006A Moebius system is an ergodic fibred system $(B,T)$ (see \citer5) defined on an interval $B=[a,b]$ with partition $(J_k),k\in I,#I\geq 2$ such that $Tx=\frac{c_k+d_kx}{a_k+b_kx}$, $x\in J_k$ and $T|_{J_k}$ is a bijective map from $J_k$ onto $B$. It is ... More

Six Functor Formalisms and Fibered MultiderivatorsMar 07 2016Feb 28 2017We develop the theory of (op)fibrations of 2-multicategories and use it to define abstract six-functor-formalisms. We also give axioms for Wirthm\"uller and Grothendieck formalisms (where either $f^!=f^*$ or $f_!=f_*$) or intermediate formalisms where ... More

Derivator Six-Functor-Formalisms - Construction IIFeb 10 2019Starting from very simple and obviously necessary axioms on a (derivator enhanced) four-functor-formalism, we construct derivator six-functor-formalisms using compactifications. This works, for example, for various contexts over topological spaces and ... More

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

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

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

Six Functor Formalisms and Fibered MultiderivatorsMar 07 2016We define abstract six-functor-formalisms using the theory of (op)fibrations of 2-multicategories. We also give axioms for a Wirthm\"uller and Grothendieck formalism (where either $f_!=f_*$ or $f^!=f^*$) or intermediate formalisms (where we have e.g. ... More

Beyond Bell's Theorem II: Scenarios with arbitrary causal structureApr 18 2014Aug 10 2015It has recently been found that Bell scenarios are only a small subclass of interesting setups for studying the non-classical features of quantum theory within spacetime. We find that it is possible to talk about classical correlations, quantum correlations ... More

The dynamics of a charged particleApr 29 2008Using physical arguments, I derive the physically correct equations of motion for a classical charged particle from the Lorentz-Abraham-Dirac equations (LAD) which are well known to be physically incorrect. Since a charged particle can classically not ... More

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

Operator system structures on the unital direct sum of C*-algebrasNov 04 2010Feb 09 2012This work is motivated by Radulescu's result on the comparison of C*-tensor norms on C*(F_n) x C*(F_n). For unital C*-algebras A and B, there are natural inclusions of A and B into their unital free product, their maximal tensor product and their minimal ... More

On Berry's conjectures about the stable order in PCFAug 02 2011Oct 11 2012PCF is a sequential simply typed lambda calculus language. There is a unique order-extensional fully abstract cpo model of PCF, built up from equivalence classes of terms. In 1979, G\'erard Berry defined the stable order in this model and proved that ... More

Categories of Fractions RevisitedMar 18 2008Sep 16 2011The theory of categories of fractions as originally developed by Gabriel and Zisman is reviewed in a pedagogical manner giving detailed proofs of all statements. A weakening of the category of fractions axioms used by Higson is discussed and shown to ... More

The geometric and arithmetic volume of Shimura varieties of orthogonal typeMay 26 2011We apply the theory of Borcherds products to calculate arithmetic volumes (heights) of Shimura varieties of orthogonal type up to contributions from very bad primes. The approach is analogous to the well-known computation of their geometric volume by ... More

Invariance entropy, quasi-stationary measures and control setsMay 24 2017Nov 27 2017For control systems in discrete time, this paper discusses measure-theoretic invariance entropy for a subset Q of the state space with respect to a quasi-stationary measure obtained by endowing the control range with a probability measure. The main results ... More

A unified construction of semiring-homomorphic graph invariantsJan 04 2019Jan 22 2019It has recently been observed by Zuiddam that finite graphs form a preordered commutative semiring under the graph homomorphism preorder together with join and disjunctive product as addition and multiplication, respectively. This led to a new characterization ... More

A generalization of Strassen's Positivstellensatz and its application to large deviation theoryOct 19 2018Jan 04 2019Strassen's Positivstellensatz is a powerful but little known theorem on preordered commutative semirings satisfying a boundedness condition similar to Archimedeanicity. It characterizes the relaxed preorder induced by all monotone homomorphisms to $\mathbb{R}_+$ ... More

On recursive properties of certain p-adic Whittaker functionsOct 05 2010We investigate recursive properties of certain p-adic Whittaker functions (of which representation densities of quadratic forms are special values). The proven relations can be used to compute them explicitly in arbitrary dimensions, provided that enough ... More

Notes on Triangulated CategoriesJul 14 2014Jul 16 2014We give an elementary introduction to the theory of triangulated categories covering their axioms, homological algebra in triangulated categories, triangulated subcategories, and Verdier localization. We try to use a minimal set of axioms for triangulated ... More

Enlargement of (fibered) derivatorsJun 29 2017We show that the theory of derivators (or, more generally, of fibered multiderivators) on all small categories is equivalent to this theory on partially ordered sets, in the following sense: Every derivator (more generally, every fibered multiderivator) ... More

Derivator Six Functor Formalisms --- Definition and Construction IJan 09 2017Jul 17 2017A theory of a derivator version of six-functor-formalisms is developed, using an extension of the notion of fibered multiderivator due to the author. Using the language of (op)fibrations of 2-multicategories this has (like a usual fibered multiderivator) ... More

A Probabilistic Model of Cardiac Physiology and ElectrocardiogramsDec 01 2018An electrocardiogram (EKG) is a common, non-invasive test that measures the electrical activity of a patient's heart. EKGs contain useful diagnostic information about patient health that may be absent from other electronic health record (EHR) data. As ... More

Compositories and GleavesAug 29 2013Oct 17 2016Sheaves are objects of a local nature: a global section is determined by how it looks locally. Hence, a sheaf cannot describe mathematical structures which contain global or nonlocal geometric information. To fill this gap, we introduce the theory of ... More

Time Symmetric Quantum Mechanics and Causal Classical PhysicsApr 14 2016May 23 2016A two boundary quantum mechanics without time ordered causal structure is advocated as consistent theory. The apparent causal structure of usual "near future" macroscopic phenomena is attributed to a cosmological asymmetry and to rules governing the transition ... More

Equilibration and macroscopic quantum fluctuations in the Dicke modelJan 31 2012We discuss the unitary quantum dynamics of the Dicke model (spin and oscillator coupled). A suitable quasiprobabilty representing the quantum state turns out to obey a Fokker-Planck equation, with drift terms representing the underlying classical Hamiltonian ... More

Local Conservation Laws and the Hamiltonian Formalism for the Toda Hierarchy RevisitedAug 16 2006We revisit an elementary recursive approach to local conservation laws and the Hamiltonian formalism for the Toda hierarchy.

Baryon Transport in Dual Models and the Possibility of a Backward Peak in DiffractionJul 20 2000We begin to briefly survey the experimental and conceptual side of baryon transfers in particle scattering. A discussion of baryon transfers in heavy ion scattering follows. It shortly reviews existing string model concepts, which were found to be consistent ... More

Algebro-Geometric Solutions of the Camassa--Holm hierarchyMay 08 2001May 21 2001We provide a detailed treatment of the Camassa--Holm (CH) hierarchy with special emphasis on its algebro-geometric solutions. In analogy to other completely integrable hierarchies of soliton equations such as the KdV or AKNS hierarchies, the CH hierarchy ... More

The Cole-Hopf and Miura transformations revisitedDec 21 1998An elementary yet remarkable similarity between the Cole-Hopf transformation relating the Burgers and heat equation and Miura's transformation connecting the KdV and mKdV equations is studied in detail.

Interaction dominated transport and Coulomb drag in bilayer grapheneOct 22 2012We investigate interaction effects in transport phenomena in bilayer graphene (BLG). For the minimal conductivity in pristine BLG, we find that the conductivity assumes a constant value in the limit $T\to 0$, with the first correction being $\propto \sqrt{T}$. ... More

Kinetic theory of Coulomb drag in two monolayers of graphene: from the Dirac point to the Fermi liquid regimeJun 22 2012We theoretically investigate Coulomb drag in a system of two parallel monolayers of graphene. Using a Boltzmann equation approach we study a variety of limits ranging from the non-degenerate interaction dominated limit close to charge neutrality all the ... More

Genetic Algorithm Based Robust and Optimal Path Planning for Sample-Return Mission from an Asteroid on an Earth Fly-By TrajectoryAug 19 2015In this study, an interplanetary space flight mission design is established to obtain the minimum \(\Delta V\) required for a rendezvous and sample return mission from an asteroid. Given the initial (observed) conditions of an asteroid, a (robust) genetic ... More

Elliptic Algebro-Geometric Solutions of the KdV and AKNS Hierarchies - An Analytic ApproachAug 31 1998We provide an overview of elliptic algebro-geometric solutions of the KdV and AKNS hierarchies, with special emphasis on Floquet theoretic and spectral theoretic methods. Our treatment includes an effective characterization of all stationary elliptic ... More

Heuristic Derivation of Blackbody Radiation Laws using Principles of Dimensional AnalysisJan 15 2008Mar 22 2008A generalized form of Wien's displacement law and the blackbody radiation laws of (a) Rayleigh and Jeans, (b) Rayleigh, (c) Wien and Paschen, (d) Thiesen and (e) Planck are derived using principles of dimensional analysis. This kind of scaling is expressed ... More

Standard State Space Models of Unawareness (Extended Abstract)Jun 24 2016The impossibility theorem of Dekel, Lipman and Rustichini has been thought to demonstrate that standard state-space models cannot be used to represent unawareness. We first show that Dekel, Lipman and Rustichini do not establish this claim. We then distinguish ... More

Hardy's Non-locality Paradox and Possibilistic Conditions for Non-localityMay 09 2011Hardy's non-locality paradox is a proof without inequalities showing that certain non-local correlations violate local realism. It is `possibilistic' in the sense that one only distinguishes between possible outcomes (positive probability) and impossible ... More

A Bi-Directional Big Bang / Crunch Universe within a Two-State-Vector Quantum Mechanics?Jul 13 2018A two boundary quantum mechanics incorporating a big bang / big crunch universe is carefully considered. After a short motivation of the concept we address the central question how a proposed a-causal quantum universe can be consistent with what is known ... More

A Probability Monad as the Colimit of Spaces of Finite SamplesDec 14 2017Mar 12 2019We define and study a probability monad on the category of complete metric spaces and short maps. It assigns to each space the space of Radon probability measures on it with finite first moment, equipped with the Kantorovich-Wasserstein distance. This ... More

Monads, partial evaluations, and rewritingOct 14 2018Mar 08 2019Monads can be interpreted as encoding formal expressions, or formal operations in the sense of universal algebra. We give a construction which formalizes the idea of "evaluating an expression partially": for example, "2+3" can be obtained as a partial ... More

Generalized Robin Boundary Conditions, Robin-to-Dirichlet Maps, and Krein-Type Resolvent Formulas for Schrödinger Operators on Bounded Lipschitz DomainsMar 21 2008May 15 2008We study generalized Robin boundary conditions, Robin-to-Dirichlet maps, and Krein-type resolvent formulas for Schr\"odinger operators on bounded Lipschitz domains in $\bbR^n$, $n\ge 2$. We also discuss the case of bounded $C^{1,r}$-domains, $(1/2)<r<1$. ... More

The Concept of an Emergent Cosmographic VacuumJul 10 2009Mar 12 2010The argument for an "Emergent Cosmographic Vacuum" state which generates fermion and weak boson masses is outlined. Its limitations and its consequences are discussed. Predictions for LHC are presented.

Central Baryons in Dual Models and the Possibility of a Backward Peak in DiffractionFeb 17 2000Mar 09 2000Two distinct interactions of Pomerons should occur in dense multi-string events. Besides the usual triple Pomeron processes transitions to membraned cylinders can be expected to contribute in a significant way. They offer an efficient mechanism for central ... More

Baryon Transport in Dual Models and the Possibility of a Backward Peak in DiffractionJan 17 2001Dual string models contain significant baryon transfers and seem essentially consistent with the available data. We here turn to a careful consideration of the relevant topological structures. The baryon transfer is associated with one of two possible ... More

Linear Representations of the Automorphism Group of a Free GroupJun 08 2006Let $F_n$ be the free group on $n\ge 2$ elements and $\A(F_n)$ its group of automorphisms. In this paper we present a rich collection of linear representations of $\A(F_n)$ arising through the action of finite index subgroups of it on relation modules ... More

Quadratic sequences of powers and Mohanty's ConjectureOct 17 2016We prove under the Bombieri-Lang conjecture for surfaces that there is an absolute bound on the length of sequences of integer squares with constant second differences, for sequences which are not formed by the squares of integers in arithmetic progression. ... More

Generating Optimal Plans in Highly-Dynamic DomainsMay 09 2012Generating optimal plans in highly dynamic environments is challenging. Plans are predicated on an assumed initial state, but this state can change unexpectedly during plan generation, potentially invalidating the planning effort. In this paper we make ... More

Weyl-Titchmarsh M-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac OperatorsFeb 06 2001We explicitly determine the high-energy asymptotics for Weyl-Titchmarsh matrices associated with general Dirac-type operators on half-lines and on $\bbR$. We also prove new local uniqueness results for Dirac-type operators in terms of exponentially small ... More

Derivation of the Leroux system as the hydrodynamic limit of a two-component lattice gasApr 29 2003May 13 2003The long time behavior of a couple of interacting asymmetric exclusion processes of opposite velocities is investigated in one space dimension. We do not allow two particles at the same site, and a collision effect (exchange) takes place when particles ... More

A Multi-World Approach to Question Answering about Real-World Scenes based on Uncertain InputOct 01 2014May 05 2015We propose a method for automatically answering questions about images by bringing together recent advances from natural language processing and computer vision. We combine discrete reasoning with uncertain predictions by a multi-world approach that represents ... More

Monads, partial evaluations, and rewritingOct 14 2018Monads can be interpreted as encoding formal expressions, or formal operations in the sense of universal algebra. We give a construction which formalizes the idea of "evaluating an expression partially": for example, "2+3" can be obtained as a partial ... More

A Probability Monad as the Colimit of Finite PowersDec 14 2017Nov 27 2018We define and study a probability monad on the category of complete metric spaces and short maps. It assigns to each space the space of Radon probability measures on it with finite first moment, equipped with the Kantorovich-Wasserstein distance. This ... More

Spin-liquid phase and order-by-disorder of classical Heisenberg spins on the swedenborgite latticeApr 07 2014Frustration refers to the inability to satisfy competing interactions simultaneously, often leading to a large number of degenerate ground states. This can suppress ordering tendencies, sometimes resulting in a spin liquid phase. An intrinsic effect lifting ... More

Modification of the Lifshitz-Kosevich formula for anomalous quantum oscillations in inverted insulatorsApr 21 2017It is generally believed that quantum oscillations are a hallmark of a Fermi surface and the oscillations constitute the ringing of it. Recently, it was understood that in order to have well defined quantum oscillations you do not only not need well defined ... More

Self-averaging characteristics of spectral fluctuationsOct 20 2014The spectral form factor as well as the two-point correlator of the density of (quasi-)energy levels of individual quantum dynamics are not self-averaging. Only suitable smoothing turns them into useful characteristics of spectra. We present numerical ... More

Factorizations and Hardy-Rellich-Type InequalitiesJan 31 2017Apr 14 2017The principal aim of this note is to illustrate how factorizations of singular, even-order partial differential operators yield an elementary approach to classical inequalities of Hardy-Rellich-type. More precisly, introducing the two-parameter $n$-dimensional ... More

On (conditional) positive semidefiniteness in a matrix-valued contextFeb 01 2016Jan 23 2017In a nutshell, we intend to extend Schoenberg's classical theorem connecting conditionally positive semidefinite functions $F\colon \mathbb{R}^n \to \mathbb{C}$, $n \in \mathbb{N}$, and their positive semidefinite exponentials $\exp(tF)$, $t > 0$, to ... More

An Abstract Approach to Weak Convergence of Spectral Shift Functions and Applications to Multi-Dimensional Schrödinger OperatorsNov 01 2011We study the manner in which a sequence of spectral shift functions $\xi(\cdot;H_j,H_{0,j})$ associated with abstract pairs of self-adjoint operators $(H_j, H_{0,j})$ in Hilbert spaces $\cH_j$, $j\in\bbN$, converge to a limiting spectral shift function ... More

Spectral Properties of a Class of Reflectionless Schrödinger OperatorsMar 03 2006We prove that one-dimensional reflectionless Schr\"odinger operators with spectrum a homogeneous set in the sense of Carleson, belonging to the class introduced by Sodin and Yuditskii, have purely absolutely continuous spectra. This class includes all ... More

A Jost-Pais-type reduction of (modified) Fredholm determinants for semi-separable operators in infinite dimensionsApr 03 2014Aug 29 2014We study the analog of semi-separable integral kernels in $\mathcal{H}$ of the type $$ K(x,x')=\begin{cases} F_1(x)G_1(x'), & a<x'< x< b, \\ F_2(x)G_2(x'), & a<x<x'<b, \end{cases} $$ where $-\infty\leq a<b\leq \infty$, and for a.e.\ $x \in (a,b)$, $F_j ... More

Nonlocal Robin Laplacians and some remarks on a paper by Filonov on eigenvalue inequalitiesDec 10 2008Feb 03 2010The aim of this paper is twofold: First, we characterize an essentially optimal class of boundary operators $\Theta$ which give rise to self-adjoint Laplacians $-\Delta_{\Theta, \Omega}$ in $L^2(\Omega; d^n x)$ with (nonlocal and local) Robin-type boundary ... More

On Spectral Theory for Schrödinger Operators with Strongly Singular PotentialsMay 06 2005Jul 27 2010We examine two kinds of spectral theoretic situations: First, we recall the case of self-adjoint half-line Schr\"odinger operators on [a,\infty), a\in\bbR, with a regular finite end point a and the case of Schr\"odinger operators on the real line with ... More