Gauss Seminar Room (1st Floor)

The seminar will review and critically discuss the development of Multiple Frame (MF) surveys over more than six decades, from their first appearance in the sampling literature of the 1960s–1970s to the re-assessment of their role in today’s fast-evolving landscape of digital data sources and emerging data needs. An MF survey uses two or more sampling frames, usually with partial coverage and overlapping units, which together adequately cover the target population. MF surveys are especially useful when no single complete frame exists and no sufficient resources are available to construct one via record linkage. They can also be cost-effective even when a complete frame is available, which was, in fact, the practical motivation behind their initial introduction in the sampling statistics literature. Since then, MF surveys have undergone a significant and resilient evolution in their objectives, application areas, and estimation approaches. The initial cost-saving motivation has expanded to include applications to difficult-to-sample populations (e.g., undocumented immigrants), the handling of attrition in longitudinal studies, agricultural surveys combining satellite and field data, and MF-based strategies addressing long-standing challenges in sample surveys, such as rising costs and declining response rates. A parallel evolution in MF estimation has also occurred, mainly due to the inherent methodological difficulties associated with complex survey designs and notational cumbersomeness. This initially led to several seemingly disconnected estimation approaches, which can now be simplified and unified under the Multiplicity approach and the Generalized Multiplicity-Adjusted Horvitz–Thompson framework. The unprecedented availability of new digital and Big Data sources, together with the recent surge of interest in combining information from probability and non-probability samples to address budget constraints, the demand for timely estimates, and lack of respondent cooperation, calls for a re-assessment of MF practices and outlines directions for future research.

Día: 26 de mayo

Hora: 12:00

Aula: Seminario Gauss (1 planta)

Seminario GOYA

Conferenciante: Federico Nudo, Università Della Calabria

Título: Bivariate polynomial histopolation techniques

Abstract:

This work explores the reconstruction of a real-valued function $f$ defined over a domain $\Omega \subset \mathbb{R}^2$ using bivariate polynomials that satisfy triangular histopolation conditions. More precisely, we assume that only the averages of $f$ over a given triangulation $\mathcal{T}_N$ of $\Omega$ are available and seek a bivariate polynomial that approximates $f$ using a histopolation approach, potentially flanked by an additional regression technique. This methodology relies on the selection of a subset of triangles $\mathcal{T}_M \subset \mathcal{T}_N$ for histopolation, ensuring both the solvability and the well-conditioning of the problem. The remaining triangles can potentially be used to enhance the accuracy of the polynomial approximation through a simultaneous regression. We will introduce histopolation and combined histopolation-regression methods using the Padua points, discrete Leja sequences, and approximate Fekete nodes. The proposed algorithms are implemented and evaluated through numerical experiments that demonstrate their effectiveness in function approximation.

Conferencia: "A practical guide to using kernels and distance
functions for approximations: kernel functions and conic sections II"

Conferenciante: Martin Buhmann, Universidad Justus-Liebig, Giessen, Alemania

Lugar: Seminario Gauss, 1º Planta, IMAG

Fecha: 13 de mayo de 2026

Hora: 17:00

Resumen: After having described applications such as computations of
orbits of planets by Gauss, EEG data of the brain or pulmonary
hypertension in cardiology last week, we shall continue with
selections of kernels and distance functions. A particular emphasis
will be put on special convergence theorems and accuracy results for
applications in this talk.

The talk is independent of the previous one and a complete
introduction will be supplied for anybody who did not attend the
previous presentation.

Resumen: Two- or higher dimensional approximations are useful for
employing numerical methods such as quadrature rules or solving
partial differential equations in physics. Kernels methods are known
to be extremely versatile with respect to dimension and which
approximands are required. At the same time we must choose the right
distance functions or approaches to approximations when modelling data
even in simple instances like two dimensions. We shall show some
methods beginning with least-squares approximations on circles and
spheres to illustrate these points before we proceed to the general
and new cases of many types of kernel functions in any dimensions.

The least squares approximations on circles and spheres are chosen as
examples in order to honour Carl Friedrich Gauß from Göttingen whose
250th birthday is soon and who used least squares approximations on
circles and ellipses to approximate the positions of the planetoid
Ceres to extreme accuracy without employing a computer.

Abstract: Guiding Vector Fields (GVFs) are a powerful tool for path following in robotic systems, but their extension to rotational motion on SO(3) is nontrivial. In this seminar, I will first discuss the challenges associated with attitude representations and introduce the basic notions of geometric control on SO(3). I will then present my current work on GVF-based path following defined directly on SO(3), leading to a singularity-free formulation suitable for aerobatic flight. The seminar will conclude with several simulation examples, along with practical tips for implementing Lie group operations, not only in high-level simulations but also in real-time autopilot systems.

• Date: Friday September 18th to Friday November 20th.
• Time: 10:00h - 12:00h.
• Place: Gauss Seminar, IMAG, UGR.
• Area: Geometría diferencial y análisis geométrico.
• Language: Spanish.
• Speaker: Francisco Martín Serrano.
• Title: Superficies mínimas - Introducción a la teoría estructural de Colding y Minicozzi.
• Abstract: La teoría clásica de superficies mínimas constituye uno de los puntos de encuentro más fértiles entre geometría diferencial, cálculo de variaciones, teoría de ecuaciones elípticas y topología. En la últimas décadas, el estudio de superficies mínimas embebidas en variedades tridimensionales ha experimentado un avance decisivo gracias a la teoría estructural de Colding y Minicozzi. Sus estimaciones de curvatura, el análisis de gráficas multivaluadas y los teoremas de laminación permiten describir con gran precisión qué ocurre cuando una sucesión de superficies embebidas pierde control de curvatura. El curso propone una entrada gradual en esta teoría. Tras revisar los fundamentos analíticos y geométricos indispensables, se estudiará el paradigma del helicoide como doble escalera de caracol, la estimación unilateral de curvatura, la aparición de gráficas multivaluadas y la dicotomía entre regiones de tipo disco y regiones con cuellos. El objetivo no es reproducir todos los detalles técnicos de la serie original, sino proporcionar al estudiante un mapa conceptual riguroso, acceso a algunos argumentos fundamentales y la preparación necesaria para abordar la literatura especializada.