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Pathwise Derivatives Beyond the Reparameterization TrickJun 05 2018Jul 05 2018We observe that gradients computed via the reparameterization trick are in direct correspondence with solutions of the transport equation in the formalism of optimal transport. We use this perspective to compute (approximate) pathwise gradients for probability ... More

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

Multi-Agent Deployment for Visibility Coverage in Polygonal Environments with HolesAug 30 2010Dec 02 2010This article presents a distributed algorithm for a group of robotic agents with omnidirectional vision to deploy into nonconvex polygonal environments with holes. Agents begin deployment from a common point, possess no prior knowledge of the environment, ... More

Tensor Variable Elimination for Plated Factor GraphsFeb 08 2019May 17 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

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

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

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

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

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

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

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

A synthetic approach to Markov kernels, conditional independence, and theorems on sufficient statisticsAug 19 2019We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning and disintegration; ... More

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

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

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.

Curious properties of free hypergraph C*-algebrasAug 28 2018Jul 09 2019A finite hypergraph $H$ consists of a finite set of vertices $V(H)$ and a collection of subsets $E(H) \subseteq 2^{V(H)}$ which we consider as partition of unity relations between projection operators. These partition of unity relations freely generate ... 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

Direct Uncertainty Prediction for Medical Second OpinionsJul 04 2018Jan 07 2019The issue of disagreements amongst human experts is a ubiquitous one in both machine learning and medicine. In this work, we show that machine learning models can be successfully trained to give uncertainty scores to data instances that result in high ... 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

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

Quantum analogues of Hardy's nonlocality paradoxJun 12 2010Apr 01 2018Hardy'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

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

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

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

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

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).

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

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

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

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

Generalized automorphic sheaves and the proportionality principle of Hirzebruch-MumfordMar 14 2016Jun 05 2019We axiomatize the algebraic properties of toroidal compactifications of (mixed) Shimura varieties and their automorphic vector bundles. A notion of generalized automorphic sheaf is proposed which includes sheaves of (meromorphic) sections of automorphic ... 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

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

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

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

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

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

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

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

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

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

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

The Algorithmic Automation Problem: Prediction, Triage, and Human EffortMar 28 2019In a wide array of areas, algorithms are matching and surpassing the performance of human experts, leading to consideration of the roles of human judgment and algorithmic prediction in these domains. The discussion around these developments, however, ... 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

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

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

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

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

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

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

A Borg-Type Theorem Associated with Orthogonal Polynomials on the Unit CircleJan 14 2005We prove a general Borg-type result for reflectionless unitary Cantero-Moral-Velazquez (CMV) operators U associated with orthogonal polynomials on the unit circle. The spectrum of U is assumed to be a connected arc on the unit circle. This extends a recent ... More

The universal property of infinite direct sums in C$^*$-categories and W$^*$-categoriesJul 10 2019When formulating universal properties for objects in a dagger category, one usually expects a universal property to characterize the universal object up to unique unitary isomorphism. We observe that this is automatically the case in the important special ... More

NN Correlations and Relativistic Hartree Fock in Finite NucleiSep 28 1993Two different approximation schemes for the self-consistent solution of the relativistic Brueckner-Hartree-Fock equation for finite nuclei are discussed using realistic One-Boson-Exchange potentials. In a first scheme, the effects of correlations are ... More

Lyapunov exponents for random continuous-time switched systems and stabilizabilityNov 20 2015For linear systems in continuous time with random switching, the Lyapunov exponents are characterized using the Multiplicative Ergodic Theorem for an associated system in discrete time. An application to control systems shows that here a controllability ... More

Renormalized oscillation theory for Hamiltonian systemsAug 06 2016We extend a result on renormalized oscillation theory, originally derived for Sturm-Liouville and Dirac-type operators on arbitrary intervals in the context of scalar coefficients, to the case of general Hamiltonian systems with block matrix coefficients. ... More

(Almost) C*-algebras as sheaves with self-actionDec 05 2015Sep 08 2016Via Gelfand duality, a unital C*-algebra $A$ induces a functor from compact Hausdorff spaces to sets, $\mathsf{CHaus}\to\mathsf{Set}$. We show how this functor encodes standard functional calculus in $A$ as well as its multivariate generalization. Certain ... More

Simplified End-to-End MMI Training and Voting for ASRMar 30 2017Jul 16 2017A simplified speech recognition system that uses the maximum mutual information (MMI) criterion is considered. End-to-end training using gradient descent is suggested, similarly to the training of connectionist temporal classification (CTC). We use an ... More

Tutorial on Answering Questions about Images with Deep LearningOct 04 2016Together with the development of more accurate methods in Computer Vision and Natural Language Understanding, holistic architectures that answer on questions about the content of real-world images have emerged. In this tutorial, we build a neural-based ... More

The antiferromagnetic Ising model on the swedenborgite latticeJun 05 2014Geometrical frustration in spin systems often results in a large number of degenerate ground states. In this work we study the antiferromagnetic Ising model on the three dimensional swedenborgite lattice which is a specific stacking of Kagom\'e and triangular ... More

Mid-infrared frequency comb spanning an octave based on an Er fiber laser and difference-frequency generationFeb 27 2012Mar 22 2012We describe a coherent mid-infrared continuum source with 700 cm-1 usable bandwidth, readily tuned within 600 - 2500 cm-1 (4 - 17 \mum) and thus covering much of the infrared "fingerprint" molecular vibration region. It is based on nonlinear frequency ... More

The Physics of Kondo Impurities in GrapheneAug 15 2012Feb 15 2013This article summarizes our understanding of the Kondo effect in graphene, primarily from a theoretical perspective. We shall describe different ways to create magnetic moments in graphene, either by adatom deposition or via defects. For dilute moments, ... More

An entropic approach to local realism and noncontextualityJan 16 2012Jan 30 2012For any Bell locality scenario (or Kochen-Specker noncontextuality scenario), the joint Shannon entropies of local (or noncontextual) models define a convex cone for which the non-trivial facets are tight entropic Bell (or contextuality) inequalities. ... More

Quantum chaos and effective thermalizationOct 06 2011Mar 21 2012We demonstrate effective equilibration for unitary quantum dynamics under conditions of classical chaos. Focusing on the paradigmatic example of the Dicke model, we show how a constructive description of the thermalization process is facilitated by the ... More

On Self-adjoint and J-self-adjoint Dirac-type Operators: A Case StudyNov 15 2005Nov 30 2005We provide a comparative treatment of some aspects of spectral theory for self-adjoint and non-self-adjoint (but J-self-adjoint) Dirac-type operators connected with the defocusing and focusing nonlinear Schr\"odinger equation, of relevance to nonlinear ... More

On subgroup conjugacy separability in the class of virtually free groupsDec 22 2010A group G is called subgroup conjugacy separable (abbreviated as SCS), if any two finitely generated and non-conjugate subgroups of G remain non-conjugate in some finite quotient of G. We prove that the free groups and the fundamental groups of finite ... More

Weak Convergence of Spectral Shift Functions for One-Dimensional Schrödinger OperatorsNov 01 2011Nov 08 2011We study the manner in which spectral shift functions associated with self-adjoint one-dimensional Schr\"odinger operators on the finite interval $(0,R)$ converge in the infinite volume limit $R\to\infty$ to the half-line spectral shift function. Relying ... More

Bimonoidal Structure of Probability MonadsApr 10 2018Aug 22 2018We give a conceptual treatment of the notion of joints, marginals, and independence in the setting of categorical probability. This is achieved by endowing the usual probability monads (like the Giry monad) with a monoidal and an opmonoidal structure, ... More

On the spectrum of Schrödinger operators with quasi-periodic algebro-geometric KdV potentialsDec 10 2003We characterize the spectrum of one-dimensional Schr\"odinger operators H=-d^2/dx^2+V with quasi-periodic complex-valued algebro-geometric potentials V (i.e., potentials V which satisfy one (and hence infinitely many) equation(s) of the stationary Korteweg-de ... More

On traces and modified Fredholm determinants for half-line Schrödinger operators with purely discrete spectraApr 18 2018Jul 21 2018After recalling a fundamental identity relating traces and modified Fredholm determinants, we apply it to a class of half-line Schr\"odinger operators $(- d^2/dx^2) + q$ on $(0,\infty)$ with purely discrete spectra. Roughly speaking, the class considered ... More

Stochastic order on metric spaces and the ordered Kantorovich monadAug 29 2018In earlier work, we had introduced the Kantorovich probability monad on complete metric spaces, extending a construction due to van Breugel. Here we extend the Kantorovich monad further to a certain class of ordered metric spaces, by endowing the spaces ... More

Some Remarks on the Spectral Problem Underlying the Camassa-Holm HierarchyMar 22 2013We consider left-definite eigenvalue problems $A \psi = \lambda B \psi$, with $A \geq \varepsilon I$ for some $\varepsilon > 0$ and $B$ self-adjoint, but $B$ not necessarily positive or negative definite, applicable, in particular, to the eigenvalue problem ... More

Decay rates for stabilization of linear continuous-time systems with random switchingNov 20 2015Mar 21 2018For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative Ergodic Theorem applied ... More

Renormalized oscillation theory for Hamiltonian systemsAug 06 2016Apr 15 2017We extend a result on renormalized oscillation theory, originally derived for Sturm-Liouville and Dirac-type operators on arbitrary intervals in the context of scalar coefficients, to the case of general Hamiltonian systems with block matrix coefficients. ... More

Some applications of almost analytic extensions to operator bounds in trace idealsFeb 04 2015Feb 03 2016Using the Davies-Helffer-Sj\"ostrand functional calculus based on almost analytic extensions, we address the following problem: Given self-adjoint operators $S_j$, $j=1,2$, in $\mathcal{H}$, and functions $f$ in an appropriate class, for instance, $f ... 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

Compositories and GleavesAug 29 2013Oct 20 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

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

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

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

Bayesian inference for stationary data on finite state spacesOct 04 2017Oct 23 2017In this work the issue of Bayesian inference for stationary data is addressed. Therefor a parametrization of a statistically suitable subspace of the the shift-ergodic probability measures on a Cartesian product of some finite state space is given using ... 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 inverse approach to Dirac-type systems based on the $A$-function conceptMar 02 2019The principal objective in this paper is a new inverse approach to general Dirac-type systems modeled after B. Simon's 1999 inverse approach to half-line Schr\"odinger operators. In particular, we derive the so-called A-equation associated to Dirac-type ... More

English and Spanish Translation of Zwicky's (1933) The Redshift of Extragalactic NebulaeNov 06 2017English and Spanish translations are provided for Fritz Zwicky's seminal article on "The Redshift of Extragalactic Nebulae", published in German in Helvetica Physica Acta in 1933 <https://www.e-periodica.ch/digbib/view?pid=hpa-001:1933:6#112>. This paper ... More

Causal Classical Physics in Time Symmetric Quantum MechanicsFeb 06 2018The letter submitted is an executive summary of our previous paper. To solve the Einstein Podolsky Rosen 'paradox' the two boundary quantum mechanics is taken as self consistent interpretation of quantum dynamics. The difficulty with this interpretation ... More

On the axiomatization of convex subsets of Banach spacesMay 06 2011Oct 20 2015We prove that any convex-like structure in the sense of Nate Brown is affinely and isometrically isomorphic to a closed convex subset of a Banach space. This answers an open question of Brown. As an intermediate step, we identify Brown's algebraic axioms ... More

Level statistics in arithmetical and pseudo-arithmetical chaosJan 19 2010Feb 01 2010We resolve a long-standing riddle in quantum chaos, posed by certain fully chaotic billiards with constant negative curvature whose periodic orbits are highly degenerate in length. Depending on the boundary conditions for the quantum wave functions, the ... More

de Haas-van Alphen oscillations for non-relativistic fermions coupled to an emergent U(1) gauge fieldOct 26 2009We investigate magento-oscillations in the specific heat of non-relativistic fermions with a Fermi surface minimally coupled to a fluctuating U(1) gauge field. Our study is motivated by the recent observation of quantum oscillations in the underdoped ... More

Quantum measurements without macroscopic superpositionsNov 06 2007May 22 2008We study a class of quantum measurement models. A microscopic object is entangled with a macroscopic pointer such that each eigenvalue of the measured object observable is tied up with a specific pointer deflection. Different pointer positions mutually ... More

How do clarinet players adjust the resonances of their vocal tracts for different playing effectsMay 27 2005Jul 27 2005In a simple model, the reed of the clarinet is mechanically loaded by the series combination of the acoustical impedances of the instrument itself and of the player's vocal tract. Here we measure the complex impedance spectrum of players' tracts using ... More

Kondo screening in unconventional superconductors: The role of anomalous propagatorsMay 25 2005Dec 21 2005The Kondo effect in superconductors is frequently investigated using the local quasiparticle density of states as sole bath characteristics, i.e., the presence of anomalous propagators is ignored. Here we point out that this treatment is exact for a number ... More

Noncommutative spherically symmetric spacetimes at semiclassical orderNov 15 2016Working within the recent formalism of Poisson-Riemannian geometry, we completely solve the case of generic spherically symmetric metric and spherically symmetric Poisson-bracket to find a unique answer for the quantum differential calculus, quantum metric ... More

Time Symmetric Quantum Mechanics and Causal Classical PhysicsApr 14 2016Jan 22 2017A 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

Kernel Methods for Linear Discrete-Time EquationsJul 11 2015Aug 10 2015Methods from learning theory are used in the state space of linear dynamical and control systems in order to estimate the system matrices. An application to stabilization via algebraic Riccati equations is included. The approach is illustrated via a series ... More