Browsing 2017 by Title

Now showing items 8-27 of 36

    • Detecting Ineffective Features for Pattern Recognition 

      [OWP-2017-26] Györfi, László; Walk, Harro (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-17)
      For a binary classification problem, the hypothesis testing is studied, that a component of the observation vector is not effective, i.e., that component carries no information for the classification. We introduce nearest ...

    • Exact Rate of Convergence of k-Nearest-Neighbor Classification Rule 

      [OWP-2017-25] Györfi, László; Döring, Maik; Walk, Harro (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-16)
      A binary classification problem is considered. The excess error probability of the k-nearest neighbor classification rule according to the error probability of the Bayes decision is revisited by a decomposition of the ...

    • Experimenting with Zariski Dense Subgroups 

      [OWP-2017-31] Detinko, Alla; Flannery, Dane; Hulpke, Alexander (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-28)
      We give a method to describe all congruence images of a finitely generated Zariski dense group $H\leq SL(n, \mathbb{R})$. The method is applied to obtain efficient algorithms for solving this problem in odd prime degree ...

    • An Extension Problem and Trace Hardy Inequality for the Sublaplacian on H-Type Groups 

      [OWP-2017-20] Roncal, Luz; Thangavelu, Sundaram (Mathematisches Forschungsinstitut Oberwolfach, 2017-07-24)
      In this paper we study the extension problem for the sublaplacian on a H-type group and use the solutions to prove trace Hardy and Hardy inequalities for fractional powers of the sublaplacian.

    • Freeness of Multi-Reflection Arrangements via Primitive Vector Fields 

      [OWP-2017-10] Hoge, Torsten; Mano, Toshiyuki; Röhrle, Gerhard; Stump, Christian (Mathematisches Forschungsinstitut Oberwolfach, 2017-04-20)
      In 2002, Terao showed that every reflection multi-arrangement of a real reflection group with constant multiplicity is free by providing a basis of the module of derivations. We first generalize Terao's result to ...

    • GAP Functionality for Zariski Dense Groups 

      [OWP-2017-22] Detinko, Alla; Flannery, Dane; Hulpke, Alexander (Mathematisches Forschungsinstitut Oberwolfach, 2017-09-14)
      In this document we describe the functionality of GAP [4] routines for Zariski dense or arithmetic groups that are developed in [1, 2, 3]. The research underlying the software was supported through the programme "Research ...

    • Geometry of Free Loci and Factorization of Noncommutative Polynomials 

      [OWP-2017-23] Helton, J. William; Klep, Igor; Volčič, Jurij; Helton, J. William (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-02)
      The free singularity locus of a noncommutative polynomial f is defined to be the sequence $Z_n(f)=\{X\in M_n^g : \det f(X)=0\}$ of hypersurfaces. The main theorem of this article shows that f is irreducible if and only if ...

    • Gradient Canyons, Concentration of Curvature, and Lipschitz Invariants 

      [OWP-2017-35] Paunescu, Laurentiu; Tibăr, Mihai-Marius (Mathematisches Forschungsinstitut Oberwolfach, 2017-12-13)
      We find new bi-Lipschitz invariants of holomorphic functions of two variables by using the gradient canyons and by combining analytic and geometric viewpoints on the concentration of curvature.

    • Holonomy Groups of $G_2^*$-Manifolds 

      [OWP-2017-07] Fino, Anna; Kath, Ines (Mathematisches Forschungsinstitut Oberwolfach, 2017-03-07)
      We classify the holonomy algebras of manifolds admitting an indecomposable torsion free $G_2^*$-structure, i.e. for which the holonomy representation does not leave invariant any proper non-degenerate subspace. We realize ...

    • The Index of Singular Zeros of Harmonic Mappings of Anti-Analytic Degree One 

      [OWP-2017-03] Luce, Robert; Sète, Olivier (Mathematisches Forschungsinstitut Oberwolfach, 2017-02-02)
      We study harmonic mappings of the form $f(z) = h(z) - \overline{z}$, where $h$ is an analytic function. In particular we are interested in the index (a generalized multiplicity) of the zeros of such functions. Outside the ...

    • Inductive Freeness of Ziegler’s Canonical Multiderivations for Reflection Arrangements 

      [OWP-2017-14] Hoge, Torsten; Röhrle, Gerhard (Mathematisches Forschungsinstitut Oberwolfach, 2017-04-30)
      Let $A$ be a free hyperplane arrangement. In 1989, Ziegler showed that the restriction $A''$ of $A$ to any hyperplane endowed with the natural multiplicity is then a free multiarrangement. We initiate a study of the stronger ...

    • Linear Syzygies, Hyperbolic Coxeter Groups and Regularity 

      [OWP-2017-15] Constantinescu, Alexandru; Kahle, Thomas; Varbaro, Matteo (Mathematisches Forschungsinstitut Oberwolfach, 2017-05-24)
      We build a new bridge between geometric group theory and commutative algebra by showing that the virtual cohomological dimension of a Coxeter group is essentially the regularity of the Stanley–Reisner ring of its nerve. ...

    • Locally Compact Abelian p-Groups Revisited 

      [OWP-2017-06] Herfort, Wolfgang; Hofmann, Karl Heinrich; Kramer, Linus (Mathematisches Forschungsinstitut Oberwolfach, 2017-03-03)
      Even though the structure of locally compact abelian groups is generally considered to be rather thoroughly known through a wealth of publications, one keeps encountering corners that are not elucidated in up-to-date ...

    • Looking Back on Inverse Scattering Theory 

      [OWP-2017-24] Colton, David; Kress, Rainer (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-05)
      We present an essay on the mathematical development of inverse scattering theory for time-harmonic waves during the past fifty years together with some personal memories of our participation in these events.

    • Matrix Elements of Irreducible Representations of SU(n+1) x SU(n+1) and Multivariable Matrix-Valued Orthogonal Polynomials 

      [OWP-2017-16] Koelink, Erik; van Pruijssen, Maarten; Román, Pablo Manuel (Mathematisches Forschungsinstitut Oberwolfach, 2017-06-14)
      In Part 1 we study the spherical functions on compact symmetric pairs of arbitrary rank under a suitable multiplicity freeness assumption and additional conditions on the branching rules. The spherical functions are ...

    • The Minimal Resolution Conjecture on a general quartic surface in $\mathbb P^3$ 

      [OWP-2017-21] Boij, Mats; Migliore, Juan; Miró-Roig, Rosa M.; Nagel, Uwe (Mathematisches Forschungsinstitut Oberwolfach, 2017-07-27)
      Mustaţă has given a conjecture for the graded Betti numbers in the minimal free resolution of the ideal of a general set of points on an irreducible projective algebraic variety. For surfaces in $\mathbb P^3$ this conjecture ...

    • Non-Extendability of Holomorphic Functions with Bounded or Continuously Extendable Derivatives 

      [OWP-2017-30] Moschonas, Dionysios; Nestoridis, Vassili (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-21)
      We consider the spaces $H_{F}^{\infty}(\Omega)$ and $\mathcal{A}_{F}(\Omega)$ containing all holomorphic functions $f$ on an open set $\Omega \subseteq \mathbb{C}$, such that all derivatives $f^{(l)}$, $l\in F \subseteq ...

    • Numerical Invariants and Moduli Spaces for Line Arrangements 

      [OWP-2017-02] Dimca, Alexandru; Ibadula, Denis; Măcinic, Daniela Anca (Mathematisches Forschungsinstitut Oberwolfach, 2017-02-01)
      Using several numerical invariants, we study a partition of the space of line arrangements in the complex projective plane, given by the intersection lattice types. We offer also a new characterization of the free plane ...

    • On an Effective Variation of Kronecker’s Approximation Theorem Avoiding Algebraic Sets 

      [OWP-2017-28] Fukshansky, Lenny; German, Oleg; Moshchevitin, Nikolay (Mathematisches Forschungsinstitut Oberwolfach, 2017-10-19)
      Let $\Lambda \subset \mathbb R^n$ be an algebraic lattice, coming from a projective module over the ring of integers of a number field $K$. Let $\mathcal Z \subset \mathbb R^n$ be the zero locus of a finite collection of ...

    • On the Markov inequality in the $L_2$-norm with the Gegenbauer weight 

      [OWP-2017-05] Nikolov, Geno P.; Shadrin, Alexei (Mathematisches Forschungsinstitut Oberwolfach, 2017-02-22)
      Let $w_{\lambda}(t) := (1-t^2)^{\lambda-1/2}$, where ${\lambda} > -\frac{1}{2}$, be the Gegenbauer weight function, let $\|\cdot\|_{w_{\lambda}}$ be the associated $L_2$-norm, $$ |f\|_{w_{\lambda}} = \left\{\int_{-1}^1 ...