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Towards autonomous ocean observing systems using Miniature Underwater Gliders with UAV deployment and recovery capabilitiesFeb 08 2019This paper presents preliminary results towards the development of an autonomous ocean observing system using Miniature Underwater Gliders (MUGs) that can operate with the support of Unmanned Aerial Vehicles (UAVs) and Unmanned Surface Vessels (USVs) ... More

On a Microscopic Representation of Space-Time IVDec 17 2015We summarize some previous work on SU(4) describing hadron representations and transformations as well as its noncompact 'counterpart' SU$*$(4) being the complex embedding of Sl(2,$\mathbb{H}$). So after having related the 16-dim Dirac algebra to SU$*$(4), ... More

Commuting varieties for nilpotent radicalsFeb 26 2018Jul 16 2018Let U be the unipotent radical of a Borel subgroup of a connected reductive algebraic group G, which is defined over an algebraically closed field k. In this paper, we extend work by Goodwin-R\"ohrle concerning the commuting variety of Lie(U) for char(k)=0 ... More

A Brunn-Minkowski theory for coconvex sets of finite volumeJun 12 2017Nov 07 2017Let $C$ be a closed convex cone in ${\mathbb R}^n$, pointed and with interior points. We consider sets of the form $A=C\setminus A^\bullet$, where $A^\bullet\subset C$ is a closed convex set. If $A$ has finite volume (Lebesgue measure), then $A$ is called ... More

SOLARPROP: Charge-sign Dependent Solar Modulation for EveryoneNov 24 2015Dec 11 2015We present SOLARPROP, a tool to compute the influence of charge-sign dependent solar modulation for cosmic ray spectra. SOLARPROP is able to use the output of popular tools like GALPROP or DRAGON and offers the possibility to embed new models for solar ... More

On a Microscopic Representation of Space-Time IVDec 17 2015May 06 2017We summarize some previous work on SU(4) describing hadron representations and transformations as well as its noncompact 'counterpart' SU$*$(4) being the complex embedding of SL(2,$\mathbb{H}$). So after having related the 16-dim Dirac algebra to SU$*$(4), ... More

Controlled Natural Language Processing as Answer Set Programming: an ExperimentJul 15 2014Most controlled natural languages (CNLs) are processed with the help of a pipeline architecture that relies on different software components. We investigate in this paper in an experimental way how well answer set programming (ASP) is suited as a unifying ... More

Weak Markov Processes as Linear SystemsJun 02 2012May 25 2015A noncommutative Fornasini-Marchesini system (a multi-variable version of a linear system) can be realized within a weak Markov process (a model for quantum evolution). For a discrete time parameter the resulting structure is worked out systematically ... More

Emergent spacetime and black hole probes from automorphic formsApr 29 2012Over the past few years the arithmetic Langlands program has found applications in two quite different problems that arise in string physics. The first of these is concerned with the fundamental problem of deriving the geometry of spacetime from the worldsheet ... More

Acoustic particle detection - from early ideas to future benefitsOct 15 2010Jan 14 2011The history of acoustic neutrino detection technology is shortly reviewed from first ideas 50 years ago to the detailed R&D programs of the last decade. The physics potential of ultra-high energy neutrino interaction studies is discussed for some examples. ... More

Polygons in hyperbolic geometry 2: Maximality of areaAug 23 2010This second part on polygons in the hyperbolic plane is based on the first part which deals with uniqueness and existence of cocyclic polygons with prescribed sidelengths. The topic here is the maximum question for the area of these polygons. It is shown ... More

Polygons in hyperbolic geometry 1: Rigidity and inversion of the n-inequalityAug 19 2010Certain topics on polygons are extended from Euclidean to hyperbolic geometry. This first part deals with uniqueness and existence of cocyclic polygons with prescribed sidelengths. The non-Euclidean versions are more difficult due to the existence of ... More

Purity of branch and critical locusMar 30 2010Jan 06 2013To a dominant morphism $X/S \to Y/S$ of N\oe therian integral $S$-schemes one has the inclusion $C_{X/Y}\subset B_{X/Y}$ of the critical locus in the branch locus of $X/Y$. Starting from the notion of locally complete intersection morphisms, we give conditions ... More

Rigorous solution of a Hubbard model extended by nearest-neighbor Coulomb and isotropic exchange interaction on a triangle and tetrahedronFeb 05 2009In the preprint cond-mat/0701060 we detected a factor two error in the coding of the Heisenberg term of the Hamiltonian. In the result the exchange term used in the paper was that of an anisotropic Heisenberg model with $J_x=J_y=J$ and $J_z=J/2$. Thus ... More

Sunspots: from small-scale inhomogeneities towards a global theoryNov 17 2008The penumbra of a sunspot is a fascinating phenomenon featuring complex velocity and magnetic fields. It challenges both our understanding of radiative magneto-convection and our means to measure and derive the actual geometry of the magnetic and velocity ... More

Scaling Behavior of Black Hole EntropyOct 29 2000It is shown that the entropy of fourdimensional black holes in string theory compactified on weighted Calabi-Yau hypersurfaces shows scaling behavior in a certain limit. This leads to non-monotonic functions on the moduli space.

Möbius invariants for pairs of spheresFeb 23 1999In this article we construct a complete system of M\"obius-geometric invariants for pairs $(S^m, S^l), l \leq m$, of spheres contained in the M\"obius space $S^n$. It consists of n-m generalised stationary angles. We interpret these invariants geometrically. ... More

Comparing different approaches to model the atomic structure of a ternary decagonal quasicrystalMar 04 1999It is shown that the covering approach with a single decagonal prototile can be transformed into a hexagon, boat and star tiling. Particularly, the atomic decoration recently proposed by Cockayne and Widom (Phys. Rev. Lett. 81, 598 (1998)) as a structure ... More

Two-dimensional Quantum GravityOct 05 1998This Ph.D. thesis pursues two goals: The study of the geometrical structure of two-dimensional quantum gravity and in particular its fractal nature. To address these questions we review the continuum formalism of quantum gravity with special focus on ... More

Controlling Functional UncertaintyAug 06 1996There have been two different methods for checking the satisfiability of feature descriptions that use the functional uncertainty device, namely~\cite{Kaplan:88CO} and \cite{Backofen:94JSC}. Although only the one in \cite{Backofen:94JSC} solves the satisfiability ... More

The Construction of Mirror SymmetrySep 06 1992The construction of mirror symmetry in the heterotic string is reviewed in the context of Calabi-Yau and Landau-Ginzburg compactifications. This framework has the virtue of providing a large subspace of the configuration space of the heterotic string, ... More

Scaling Behavior in String TheoryDec 09 1994Dec 11 1994In Calabi--Yau compactifications of the heterotic string there exist quantities which are universal in the sense that they are present in every Calabi--Yau string vacuum. It is shown that such universal characteristics provide numerical information, in ... More

D-modules with finite support are semi-simpleApr 18 2012Let $(R, \mf, k_R)$ be regular local $k$-algebra satisfying the weak Jacobian criterion, such that $k_R/k$ is an algebraic field extension. Let $D_R$ be the ring of $k$-linear differential operators of $R$. We give an explicit decomposition of the $D_R$-module ... More

D-modules and finite mapsNov 16 2018We study the preservation of semisimplicity for holonomic D-modules with respect to the direct and inverse image of mainly finite maps $\pi : X \to Y$ of smooth varieties. A natural filtration of the direct image $\pi_+({\mathcal O}_X)$ is defined by ... More

Intersection probabilities and kinematic formulas for polyhedral conesJun 12 2017For polyhedral convex cones in ${\mathbb R}^d$, we give a proof for the conic kinematic formula for conic curvature measures, which avoids the use of characterization theorems. For the random cones defined as typical cones of an isotropic random central ... More

The typical irregularity of virtual convex bodiesOct 25 2016The semigroup of convex bodies in ${\mathbb R}^n$ with Minkowski addition has a canonical embedding into an abelian group; its elements have been called virtual convex bodies. Geometric interpretations of such virtual convex bodies have been particularly ... More

Strongly confined fluids: Diverging time scales and slowing down of equilibrationJun 02 2016The Newtonian dynamics of strongly confined fluids exhibits a rich behavior. Its confined and unconfined degrees of freedom decouple for confinement length $L \to 0$. In that case and for a slit geometry the intermediate scattering functions $S_{\mu\nu}(q,t)$ ... More

Charge-sign dependent solar modulation for everyoneJan 12 2016We present a tool to compute the influence of charge-sign dependent solar modulation for cosmic ray spectra. The code is publicly available, easy to use and offers an extended view on solar modulation compared to the force-field approximation. We present ... More

On a Microscopic Representation of Space-Time VOct 05 2016In order to extend our approach based on SU$*$(4), we were led to (real) projective and (line) Complex geometry. So here we start from quadratic Complexe which yield naturally the 'light cone' $x_{1}^{2}+x_{2}^{2}+x_{3}^{2}-x_{0}^{2}=0$ when being related ... More

Stratifications of schemes using tangent vector fieldsDec 18 2012Apr 16 2018Let $X/k$ be a noetherian scheme over a field $k$ of characteristic 0, such that the residue field at its closed points are algebraic extensions of $k$. Let ${\mathfrak g}_{X/k}\subset T_{{X/k}}$ be an ${\mathcal O}_{X}$-submodule of the tangent sheaf ... More

On a microscopic representation of spacetimeJan 31 2011We start from a noncompact Lie algebra isomorphic to the Dirac algebra and relate this Lie algebra in a brief review to low energy hadron physics described by the compact group SU(4). This step permits an overall physical identification of the operator ... More

Purity of branch, critical and discriminant locusSep 11 2006Jun 27 2011To a dominant morphism $\pi:X/S \to Y/S$ of N{\oe}therian integral $S$-schemes one has the inclusion $C_\pi \subset B_\pi$ of the critical locus in the branch locus of $B_\pi$. Conditions on the relative differentials $\Omega_{X/Y}$, $\Omega_{X/S}$, and ... More

The Langlands Program and String Modular K3 SurfacesMar 29 2006A number theoretic approach to string compactification is developed for Calabi-Yau hypersurfaces in arbitrary dimensions. The motivic strategy involved is illustrated by showing that the Hecke eigenforms derived from Galois group orbits of the holomorphic ... More

Energy landscape properties studied by symbolic sequencesJan 04 2006We investigate a classical lattice system with $N$ particles. The potential energy $V$ of the scalar displacements is chosen as a $\phi ^4$ on-site potential plus interactions. Its stationary points are solutions of a coupled set of nonlinear equations. ... More

Alternative Detection Methods for Highest Energy NeutrinosNov 26 2004Several experimental techniques are currently under development, to measure the expected tiny fluxes of highest energy neutrinos above 10**18 eV. Projects in different stages of realisation are discussed here, which are based on optical and radio as well ... More

Round about Theta. Part I PrehistoryJul 29 2008There is a huge amount of work on different kinds of theta functions, the theta correspondence, cohomology classes coming from special Schwartz classes via theta distribution, and much more. The aim of this text is to try to find joint construction principles ... More

Decompositions of Beurling Type for E_0-SemigroupsDec 06 2004Feb 26 2009We define tensor product decompositions of $E_0$-semigroups with a structure analogous to a classical theorem of Beurling. Such decompositions can be characterized by adaptedness and exactness of unitary cocycles. For CCR-flows we show that such cocycles ... More

Adaptive finite element methods for partial differential equationsMay 01 2003The numerical simulation of complex physical processes requires the use of economical discrete models. This lecture presents a general paradigm of deriving a posteriori error estimates for the Galerkin finite element approximation of nonlinear problems. ... More

Spectroscopy and Charm Quark FragmentationOct 31 2003The large data sample accumulated at the KEKB storage ring allows for dedicated analysis in charm spectroscopy. This made the first observations of e.g. the broad D**resonances in B decays as well as other processes possible. The observation of the DsJ ... More

Theories of the Structural Glass TransitionMay 23 2003We review phenomenological and microscopic theories of the structural glass transition

Stratifications of schemes using tangent vector fieldsDec 18 2012Dec 28 2012Let $X/k$ be a noetherian scheme over a field $k$ of characteristic 0, such that the residue field at its closed points are algebraic extensions of $k$. Let ${\mathfrak g}_{X/k}\subset T_{{X/k}}$ be an ${\mathcal O}_{X}$-submodule of the tangent sheaf ... More

Spin-Flavour Symmetry and Contractions Towards Classical Space-Time SymmetryNov 27 1996A classification scheme of hadrons is proposed on the basis of the division algebra H of quaternions and an appropriate geometry. This scheme suggests strongly to understand flavour symmetry in another manner than from standard symmetry schemes. In our ... More

Is There Physics in Landau Poles ?Feb 03 1995Triviality and Landau poles are often greeted as harbingers of new physics at 1 TeV. After briefly reviewing the ideas behind this, a model of singular quantum mechanics is introduced. Its ultraviolet structure, as well as some features of its vacuum, ... More

Noncritical Dimensions for Critical String Theory: Life beyond the Calabi-Yau FrontierNov 02 1992A recently introduced framework for the compactification of supersymmetric string theory involving noncritical manifolds of complex dimension $2k+D_{crit}$, $k\geq 1$, is reviewed. These higher dimensional manifolds are spaces with quantized positive ... More

Mode dependent field renormalization and trivialityNov 06 1995We critically analyze the introduction of an independent zero momentum mode field renormalization for Phi4. It leads to an infrared divergent effective action. It does not achieve its purpose: triviality still gives massless particles in the broken phase ... More

Quark mass hierarchies in heterotic orbifold GUTsDec 20 2010We discuss how to calculate Yukawa couplings in string-derived orbifold GUTs. As an application we investigate the quark mass hierarchies in these models. An interplay of different mechanisms derived from string theory leads to an interesting pattern. ... More

Liftable derivations for generically separably algebraic morphisms of schemesApr 26 2006Jul 21 2007We consider dominant, generically algebraic, and tamely ramified (if the characteristic is positive) morphisms $\pi: X/S \to Y/S$, where Y,S are Noetherian and integral and X is a Krull scheme (e.g. normal Noetherian), and study the sheaf of tangent vector ... More

Arithmetic Spacetime Geometry from String TheoryOct 11 2005An arithmetic framework to string compactification is described. The approach is exemplified by formulating a strategy that allows to construct geometric compactifications from exactly solvable theories at $c=3$. It is shown that the conformal field theoretic ... More

Aspects of Conformal Field Theory from Calabi-Yau ArithmeticSep 13 2002This paper describes a framework in which techniques from arithmetic algebraic geometry are used to formulate a direct and intrinsic link between the geometry of Calabi-Yau manifolds and aspects of the underlying conformal field theory. As an application ... More

Arithmetic of Calabi-Yau Varieties and Rational Conformal Field TheoryNov 24 2001It is proposed that certain techniques from arithmetic algebraic geometry provide a framework which is useful to formulate a direct and intrinsic link between the geometry of Calabi-Yau manifolds and the underlying conformal field theory. Specifically ... More

Generating EPICS IOC Databases from a Relational Database - a Different ApproachNov 09 2001The EPICS based control system of the ISAC radioactive beam facility uses the CapFast schematic editor to construct the IOC function-block databases. This allows a self-documenting graphical representation of the IOC software using a hierarchical, object-like ... More

On a Microscopic Representation of Space-Time VII -- On SpinNov 18 2017We recall some basic aspects of line and line Complex representations, of symplectic symmetry emerging in bilinear point transformations as well as of Lie transfer of lines to spheres. Here, we identify SU(2) spin in terms of (classical) projective geometry ... More

Modular Inflation Observables and $j$-Inflation PhenomenologyDec 30 2016Jun 27 2017Modular inflation is the restriction to two fields of automorphic inflation, a general group based framework for multifield scalar field theories with curved target spaces, which can be parametrized by the comoving curvature perturbation ${\cal R}$ and ... More

Second moments related to Poisson hyperplane tessellationsApr 02 2015Sep 19 2015We consider the typical cell of a stationary Poisson hyperplane tessellation in d-dimensional Euclidean space. It is well known that the expected vertex number of the typical cell is independent of the directional distribution of the hyperplane process. ... More

Effects of liquid pore water on acoustic wave propagation in snow as a Biot-type porous materialFeb 04 2015A method to estimate phase velocity and attenuation of acoustic waves in the presence of liquid water in a snowpack is presented. The method is based on Biot's theory of wave propagation in porous materials. Empirical relations and a priori information ... More

Automorphic Black Hole EntropyDec 27 2013Over the past few years the understanding of the microscopic theory of black hole entropy has made important conceptual progress by recognizing that the degeneracies are encoded in partition functions which are determined by higher rank automorphic representations, ... More

String Automorphic Motives of nondiagonal VarietiesJan 11 2013Feb 11 2013In this paper automorphic motives are constructed and analyzed with a view toward the understanding of the geometry of compactification manifolds in string theory in terms of the modular structure of the worldsheet theory. The results described generalize ... More

Conic support measuresJul 10 2018The conic support measures localize the conic intrinsic volumes of closed convex cones in the same way as the support measures of convex bodies localize the intrinsic volumes of convex bodies. In this note, we extend the `Master Steiner formula' of McCoy ... More

Motivic L-Function Identities from CFT and Arithmetic Mirror SymmetryJan 10 2013Feb 19 2013Exactly solvable mirror pairs of Calabi-Yau threefolds of hypersurface type exist in the class of Gepner models that include nondiagonal affine invariants. Motivated by the string modular interpretation established previously for models in this class ... More

Representations of finite group schemes and morphisms of projective varietiesJan 31 2014Given a finite group scheme $\cG$ over an algebraically closed field $k$ of characteristic $\Char(k)=p>0$, we introduce new invariants for a $\cG$-module $M$ by associating certain morphisms $\deg^j_M : U_M \lra \Gr_d(M) \ \ (1\!\le\!j\!\le\! p\!-\!1)$ ... More

K-Rational D-Brane CrystalsMay 13 2012In this paper the problem of constructing spacetime from string theory is addressed in the context of D-brane physics. It is suggested that the knowledge of discrete configurations of D-branes is sufficient to reconstruct the motivic building blocks of ... More

Acoustic detection of ultra-high energetic neutrinos - a snap shotJan 04 2012Already more than 30 years ago the acoustic particle detection method has been considered to be one possibility to measure signals from ultra-high energetic neutrinos. The present status and problems of corresponding model predictions are discussed in ... More

Two extensions of Hilbert's finiteness theoremDec 19 2012Let $S^{\cdot}$ be a noetherian graded algebra over a commutative $k$-algebra $A$, where $k$ is a commutative ring, and assume it is a module over a Lie algebroid ${\mathfrak g}_{A/k}$. If $S^\cdot$ is semi-simple over ${\mathfrak g}_{A/k}$ we prove that ... More

Extensions of tame algebras and finite group schemes of domestic representation typeMay 08 2012Let k be an algebraically closed field. Given an extension A : B of finite-dimensional k- algebras, we establish criteria ensuring that the representation-theoretic notion of polynomial growth is preserved under ascent and descent. These results are then ... More

Categories of modules given by varieties of p-nilpotent operatorsOct 12 2011For a finite group scheme G over an algebraically closed field k of characteristic p>0 we study G-modules M, which are defined in terms of properties of their pull-backs along p-points of G. We show that the corresponding subcategories strongly depend ... More

Complexity, Periodicity and One-Parameter SubgroupsOct 08 2009We use the variety of one-parameter subgroups to define a numerical invariant for a representation of an infinitesimal group scheme. For an indecomposable module M of complexity 1, this number is related to the period of M.

Emergent spacetime from modular motivesDec 23 2008The program of constructing spacetime geometry from string theoretic modular forms is extended to Calabi-Yau varieties of dimensions two, three, and four, as well as higher rank motives. Modular forms on the worldsheet can be constructed from the geometry ... More

The Zariski-Lipman conjecture for complete intersectionsMar 22 2010Jul 12 2018The tangential ramification locus $B_{X/Y}^t\subset B_{X/Y}$ is the subset of points in the ramification locus where the sheaf of relative vector fields $T_{X/Y}$ fails to be locally free. It was conjectured by Zariski and Lipman that if $V/k$ is a variety ... More

Jordan Types for Indecomposable Modules of Finite Group SchemesOct 16 2009In this article we study the interplay between algebro-geometric notions related to $\pi$-points and structural features of the stable Auslander-Reiten quiver of a finite group scheme. We show that $\pi$-points give rise to a number of new invariants ... More

Non-Commutative Markov Chains and Multi-Analytic OperatorsFeb 19 2009We study a model of repeated interaction between quantum systems which can be thought of as a non-commutative Markov chain. It is shown that there exists an outgoing Cuntz scattering system associated to this model which induces an input-output formalism ... More

The Swampland Spectrum Conjecture in InflationOct 27 2018The quantum gravity conjectures that aim to separate the landscape from the swampland among the low energy theories were originally formulated in the context of scalar field spaces spanned by moduli. Because these conjectures have implications for cosmology ... More

Multifield Reheating after Modular $j$-InflationDec 28 2017Mar 22 2018In the inflationary framework of cosmology the initial phase of rapid expansion has to be followed by a reheating stage, which is envisioned to end in a radiation dominated big bang. Key parameters that characterize this big bang state are the temperature ... More

The middle hedgehog of a planar convex bodyJul 11 2016A convexity point of a convex body is a point with the property that the union of the body and its reflection in the point is convex. It is proved that in the plane a typical convex body (in the sense of Baire category) has infinitely many convexity points. ... More

On a Minimax Problem for OvalsJun 21 2016For a bounded metric space $ X $ one can consider the quantity $ \delta(X) := \text{inf\rule[-0.5ex]{0em}{1ex}}_{\,p\in X}\; \text{sup}_{q \in X} \; d(p,q) $. This purely metric invariant is known from approximation theory as the relative Chebyshev radius ... More

A General Framework of Automorphic InflationDec 30 2015Jul 10 2016Automorphic inflation is an application of the framework of automorphic scalar field theory, based on the theory of automorphic forms and representations. In this paper the general framework of automorphic and modular inflation is described in some detail, ... More

Status of space-based gamma-ray astronomyAug 31 2015Sep 16 2015Gamma-ray observations give us a direct view into the most extreme environments of the universe. They help us to study astronomical particle accelerators as supernovae remnants, pulsars, active galaxies or gamma-ray bursts and help us to understand the ... More

On a Microscopic Representation of Space-Time IIIAug 25 2015Jan 02 2019Using the Dirac (Clifford) algebra $\gamma^{\mu}$ as initial stage of our discussion, we summarize and extend previous work with respect to the isomorphic 15dimensional Lie algebra su$*$(4) as complex embedding of sl(2,$\mathbb{H}$), the relation to the ... More

Reflections of planar convex bodiesApr 02 2015It is proved that every convex body in the plane has a point such that the union of the body and its image under reflection in the point is convex. If the body is not centrally symmetric, then it has, in fact, three affinely independent points with this ... More

Automorphic inflationDec 30 2014Jun 23 2016A framework of inflation is formulated based on symmetry groups and their associated automorphic functions. In this setting the inflaton multiplet takes values in a curved target space constructed from a continuous group $G$ and a discrete subgroup $\Gamma$. ... More

Applied String TheoryOct 09 2008This is a review. Comments are welcome. The observation that the structure of string theory is rich enough to include the standard model in rough outline is an old one, starting with the early constructions of free field constructions, orbifold theories, ... More

A modularity test for elliptic mirror symmetryMay 16 2007In this note a prediction of an algebraic mirror construction is checked for elliptic curves of Brieskorn-Pham type via number theoretic methods. It is shown that the modular forms associated to the Hasse-Weil L-series of mirror pairs of such curves are ... More

Smooth Modules over Lie Algebroids IAug 26 1998A Lie algebroid on a variety X/k is an extension \alpha: g_X \to T_X of the tangent sheaf both as O_X-module and Lie algebra over the base field, with the obvious compatibilities; and given a Lie algebroid one has its associated ring of differential operators ... More

Critical Strings from Noncritical Dimensions: A Framework for Mirrors of Rigid VacauMar 11 1993The role in string theory of manifolds of complex dimension $D_{crit} + 2(Q-1)$ and positive first Chern class is described. In order to be useful for string theory, the first Chern class of these spaces has to satisfy a certain relation. Because of this ... More

Marginal Flows between Mirror Pairs of Landau-Ginzburg String Vacua: Thickening Moduli Space via c=0 TheoriesDec 09 1992A recently introduced method for constructing marginal singular flows between distinct Landau--Ginzburg theories at fixed central charge is reviewed. The flows are constructed in an enlarged moduli space obtained by adding theories with zero central charge. ... More

Specifying and Verbalising Answer Set Programs in Controlled Natural LanguageApr 28 2018We show how a bi-directional grammar can be used to specify and verbalise answer set programs in controlled natural language. We start from a program specification in controlled natural language and translate this specification automatically into an executable ... More

The Zariski-Lipman conjecture for complete intersectionsMar 22 2010Jan 25 2011The tangential branch locus $B_{X/Y}^t\subset B_{X/Y}$ is the subset of points in the branch locus where the sheaf of relative vector fields $T_{X/Y}$ fails to be locally free. It was conjectured by Zariski and Lipman that if $V/k$ is a variety over a ... More

On a Microscopic Representation of Space-Time IIIAug 25 2015Using the Dirac (Clifford) algebra $\gamma^{\mu}$ as initial stage of our discussion, we summarize and extend previous work with respect to the isomorphic 15dimensional Lie algebra su$*$(4) as complex embedding of sl(2,$\mathbb{H}$), the relation to the ... More

On Spin IIDec 09 2018Jan 02 2019Having previously identified the photon field with a (special) linear Complex, we give a brief account on identifications and reasoning so far. Then, in order to include spinorial degrees of freedom into the Lagrangean description, we discuss the mapping ... More

Small faces in stationary Poisson hyperplane tessellationsAug 16 2018We consider the tessellation induced by a stationary Poisson hyperplane process in $d$-dimensional Euclidean space. Under a suitable assumption on the directional distribution, and measuring the $k$-faces of the tessellation by a suitable size functional, ... More

Interaction of Poisson hyperplane processes and convex bodiesDec 20 2018Given a stationary and isotropic Poisson hyperplane process and a convex body $K$ in ${\mathbb R}^d$, we consider the random polytope defined by the intersection of all closed halfspaces containing $K$ that are bounded by hyperplanes of the process not ... More

Polyhedral Gauss-Bonnet theorems and valuationsAug 17 2017The Gauss-Bonnet theorem for a polyhedron (a union of finitely many compact convex polytopes) in $n$-dimensional Euclidean space expresses the Euler characteristic of the polyhedron as a sum of certain curvatures, which are different from zero only at ... More

The polytopes in a Poisson hyperplane tessellationApr 16 2018For a stationary Poisson hyperplane tessellation $X$ in ${\mathbb R}^d$, whose directional distribution satisfies some mild conditions (which hold in the isotropic case, for example), it was recently shown that with probability one every combinatorial ... More

Pitch and timbre discrimination at wave-to-spike transition in the cochleaNov 15 2017A new definition of musical pitch is proposed. A Finite-Difference Time Domain (FDTM) model of the cochlea is used to calculate spike trains caused by tone complexes and by a recorded classical guitar tone. All harmonic tone complexes, musical notes, ... More

A porosity-based Biot model for acoustic waves in snowFeb 04 2015Mar 06 2015Phase velocities and attenuation in snow can not be explained by the widely used elastic or viscoelastic models for acoustic wave propagation. Instead, Biot's model of wave propagation in porous materials should be used. However, the application of Biot's ... More

Black Hole Probes of Automorphic SpaceDec 24 2012Over the past few years the arithmetic Langlands program has proven useful in addressing physical problems. In this paper it is shown how Langlands' reciprocity conjecture for automorphic forms, in combination with a representation theoretic notion of ... More

Transfer Functions for Pairs of Wandering SubspacesFeb 27 2011Jun 04 2012To a pair of subspaces wandering with respect to a row isometry we associate a transfer function which in general is multi-Toeplitz and in interesting special cases is multi-analytic. Then we describe in an expository way how characteristic functions ... More

A computational theory for the classification of natural biosonar targets based on a spike codeAug 02 2002May 26 2003A computational theory for classification of natural biosonar targets is developed based on the properties of an example stimulus ensemble. An extensive set of echoes (84 800) from four different foliages was transcribed into a spike code using a parsimonious ... More

Scaling Behavior on the Space of Calabi-Yau ManifoldsDec 12 1996Dec 13 1996Recent work is reviewed which suggests that certain universal quantities, defined for all Calabi-Yau manifolds, exhibit a specific behavior which is not present for general K\"ahler manifolds. The variables in question, natural from a mathematical perspective, ... More

Relativistic SU(4) and QuaternionsJan 03 1996A classification of hadrons and their interactions at low energies according to SU(4) allows to identify combinations of the fifteen mesons $\pi$, $\omega$ and $\rho$ within the spin-isospin decomposition of the regular representation \rhdmulti{15}. Chirally ... More

Novel Flows beteen N=2 Landau-Ginzburg Theories: New Directions in Moduli Space via c=0 TheoriesNov 19 1992A new method for constructing flows between distinct Landau-Ginzburg theories at fixed central charge is presented. The essential ingredient of the construction is an enlarged moduli space obtained by adding theories with zero central charge. The flows ... More