Assessing agreement between instruments is fundamental in clinical and observational studies to evaluate how similarly two methods measure the same set of subjects. In this talk, we present two extensions of a widely used coefficient for assessing agreement between continuous variables. The first extension introduces a novel agreement coefficient for lattice sequences observed over the same areal units, motivated by the comparison of poverty measurement methodologies in Chile. The second extension proposes a new coefficient, denoted as ρ1, designed to measure agreement between continuous measurements obtained from two instruments observing the same experimental units. Unlike traditional approaches, ρ1 is based on L1 distances, providing robustness to outliers and avoiding dependence on nuisance parameters. Both proposals are supported by theoretical results, an inference framework, and simulation studies that illustrate their performance and practical relevance.
Comenzamos a estudiar la Teoría de Grandes Desvíos, la cual establece resultados que permiten estudiar el decaimiento (exponencial) de probabilidades. El estudio de estas tecnicas lleva a adquirir conocimientos no solo probabilísticos, sino que también del análisis. En particular, de análisis convexo.
El objetivo de estas sesiones es revisar los resultados clásicos de la teoría y ver sus aplicaciones en áreas de la probabilidad como la Mecánica Estadística.
En esta sesión comenzamos revisando la definición de un principio de grandes desvíos. Veremos una instancia particular del Teorema de Cramer y la noción abstracta de grandes desvíos.
The dynamics of a rain forest is extremely complex involving births, deaths and growth
of trees with complex interactions between trees, animals, climate, and environment. We
consider the patterns of recruits (new trees) and dead trees between rain forest censuses.
For a current census we specify regression models for the conditional intensity of recruits
and the conditional probabilities of death given the current trees and spatial covariates. We
estimate regression parameters using conditional composite likelihood functions that only
involve the conditional first order properties of the data. When constructing assumption
lean estimators of covariance matrices of parameter estimates we only need mild assumptions
of decaying conditional correlations in space while assumptions regarding correlations over
time are avoided by exploiting conditional centering of composite likelihood score functions.
Time series of point patterns from rain forest censuses are quite short while each point
pattern covers a fairly big spatial region. To obtain asymptotic results we therefore use a
central limit theorem for the fixed timespan - increasing spatial domain asymptotic setting.
This also allows us to handle the challenge of using stochastic covariates constructed from
past point patterns. Conveniently, it suffices to impose weak dependence assumptions on
the innovations of the space-time process. We investigate the proposed methodology by
simulation studies and an application to rain forest data.
We explore examples of Dirac operators on bounded domains exhibiting an interval of essential spectrum. In particular, we consider three-dimensional Dirac operators on Lipschitz domains with critical electrostatic and Lorentz scalar shell interactions supported on a compact smooth surface. Unlike typical bounded-domain settings where the spectrum is purely discrete, the criticality of these interactions can generate a nontrivial essential spectrum interval, whose position and length are explicitly controlled by the coupling constants and surface curvatures.
Based on joint work with J. Behrndt (TU Graz), M. Holzmann (TU Graz), and K. Pankrashkin (Univ. Oldenburg).
Torelli Theorem for K3 surfaces and its proof. Period map. Moduli of polarized K3 surfaces (the case of Kummer surfaces). Formulation of Torelli Theorem for IHS manifolds.
The goal of this seminar is to present the fundamental tools for formulating questions related to the study of specific geometric properties of K3 surfaces (e.g., such as automorphisms, elliptic fibrations, Shioda-Inose structures). Furthermore, it aims to explore the analogue of these tools in the context of higher-dimensional varieties, known as irreducible holomorphic symplectic (IHS) manifolds or Hyperkähler.
1. Hirzebruch-Jung continued fractions
1.1. Basics
1.2. Wahl chains
1.3. Zero continued fractions
2. Singular and nonsingular algebraic surfaces
2.1. Generalities on surfaces and singularities
2.2. Cyclic quotient singularities
2.3. T-singularities
3. Deformations
3.1. General basic theory for affine and proper varieties
3.2. Q-Gorenstein deformations
3.3. Kollár–Shepherd-Barron correspondence
4. W-surfaces
4.1. Picard group, class group, and topology
4.2. MMP for W-surfaces I
4.3. MMP for W-surfaces II
5. N-resolutions
5.1. Existence and uniqueness
5.2. Braid group action
6. Exceptional collections of Hacking bundles
6.1. Hacking exceptional bundles
6.2. Hacking exceptional collections
6.3. Exceptional collections and H.e.c.s
Wednesday, 5 March 2025, 17:15-19:00 (UTC+1)
A HIGH-TEMPERATURE PHASE TRANSITION FROM NUMBER THEORY Let S be the semidirect product of the multiplicative positive integers acting on the integers, with the operation (a,m)(b,n) = (ab,bm+n), where a and b are positive. In previous joint work with Astrid an Huef and Iain Raeburn, we studied the Toeplitz C*-algebra generated by the left regular representation of S on l^2(S), and showed that the extremal KMS equilibrium states with respect to the natural dynamics, for inverse temperatures above the critical value 1, are parametrized by the point masses on the unit circle. I will talk about what happens for inverse temperatures between 0 and 1. Surprisingly, the system has an unprecedented high-temperature phase transition with extremal KMS states parametrized by averages of point masses at roots of unity of the same primitive order together with Lebesgue measure. The quotients associated to these extremal states embed in the Bost-Connes algebra, and establish a link to the Bost-Connes phase transition with spontaneous symmetry breaking. This is current joint work with Tyler Schulz.https://uw-edu-pl.zoom.us/j/95105055663?pwd=TTIvVkxmMndhaHpqMFUrdm8xbzlHdz09Meeting ID: 951 0505 5663 Passcode: 924338
A HIGH-TEMPERATURE PHASE TRANSITION FROM NUMBER THEORY
Let S be the semidirect product of the multiplicative positive integers acting on the integers, with the operation (a,m)(b,n) = (ab,bm+n), where a and b are positive. In previous joint work with Astrid an Huef and Iain Raeburn, we studied the Toeplitz C*-algebra generated by the left regular representation of S on l^2(S), and showed that the extremal KMS equilibrium states with respect to the natural dynamics, for inverse temperatures above the critical value 1, are parametrized by the point masses on the unit circle. I will talk about what happens for inverse temperatures between 0 and 1. Surprisingly, the system has an unprecedented high-temperature phase transition with extremal KMS states parametrized by averages of point masses at roots of unity of the same primitive order together with Lebesgue measure. The quotients associated to these extremal states embed in the Bost-Connes algebra, and establish a link to the Bost-Connes phase transition with spontaneous symmetry breaking. This is current joint work with Tyler Schulz.https://uw-edu-pl.zoom.us/j/95105055663?pwd=TTIvVkxmMndhaHpqMFUrdm8xbzlHdz09Meeting ID: 951 0505 5663 Passcode: 924338
The Organizers:
Paul F. Baum, Francesco D'Andrea, Ludwik D?browski, Søren Eilers, Piotr M. Hajac, Frédéric Latrémolière, Tomasz Maszczyk, Ryszard Nest, Marc A. Rieffel, Andrzej Sitarz, Wojciech Szyma?ski, Adam Wegert