DSpace Collection:https://hdl.handle.net/10316/155442024-03-29T09:39:39Z2024-03-29T09:39:39ZSubstitution Principle and semidirect productsBorlido, CéliaGehrke, Maihttps://hdl.handle.net/10316/1144732024-03-28T09:19:52Z2023-01-01T00:00:00ZTitle: Substitution Principle and semidirect products
Authors: Borlido, Célia; Gehrke, Mai
Abstract: In the classical theory of regular languages the concept of recognition by profinite monoids
is an important tool. Beyond regularity, Boolean spaces with internal monoids (BiMs) were
recently proposed as a generalization. On the other hand, fragments of logic defining regular
languages can be studied inductively via the so-called “Substitution Principle”. In this paper
we make the logical underpinnings of this principle explicit and extend it to arbitrary languages
using Stone duality. Subsequently we show how it can be used to obtain topo-algebraic recognizers
for classes of languages defined by a wide class of first-order logic fragments. This naturally
leads to a notion of semidirect product of BiMs extending the classical such construction for
profinite monoids. Our main result is a generalization of Almeida and Weil’s Decomposition
Theorem for semidirect products from the profinite setting to that of BiMs. This is a crucial
step in a program to extend the profinite methods of regular language theory to the setting of
complexity theory.2023-01-01T00:00:00ZNonparametric inference about increasing odds rate distributionsLando, TommasoArab, IdirOliveira, Paulo Eduardohttps://hdl.handle.net/10316/1144212024-03-27T11:52:58Z2023-01-01T00:00:00ZTitle: Nonparametric inference about increasing odds rate distributions
Authors: Lando, Tommaso; Arab, Idir; Oliveira, Paulo Eduardo
Abstract: To improve nonparametric estimates of lifetime distributions, we
propose using the increasing odds rate (IOR) model as an alternative
to other popular, but more restrictive, ‘adverse ageing’ models,
such as the increasing hazard rate one. This extends the scope of
applicability of some methods for statistical inference under order
restrictions, since the IOR model is compatible with heavy-tailed
and bathtub distributions. We study a strongly uniformly consistent
estimator of the cumulative distribution function of interest under
the IOR constraint. Numerical evidence shows that this estimator
often outperforms the classic empirical distribution function when
the underlying model does belong to the IOR family. We also study
two different tests to detect deviations from the IOR property and
establish their consistency. The performance of these tests is also
evaluated through simulations.2023-01-01T00:00:00ZOverdamped dynamics of a falling inextensible network: Existence of solutionsTelciyan, AykVorotnikov, Dmitryhttps://hdl.handle.net/10316/1142622024-03-26T13:39:21Z2023-01-01T00:00:00ZTitle: Overdamped dynamics of a falling inextensible network: Existence of solutions
Authors: Telciyan, Ayk; Vorotnikov, Dmitry
Abstract: We study the equations of overdamped motion of an inextensible triod with three fixed
ends and a free junction under the action of gravity. The problem can be expressed as a system of
PDEs that involves unknown Lagrange multipliers and non-standard boundary conditions related to
the freely moving junction. It can also be formally interpreted as a gradient flow of the potential
energy on a certain submanifold of the Otto–Wasserstein space of probability measures. We prove
global existence of generalized solutions to this problem.2023-01-01T00:00:00ZDegenerations of Poisson algebrasAbdelwahab, HaniOuaridi, Amir FernándezGonzález, Cándido Martínhttps://hdl.handle.net/10316/1141842024-03-26T10:13:31Z2023-01-01T00:00:00ZTitle: Degenerations of Poisson algebras
Authors: Abdelwahab, Hani; Ouaridi, Amir Fernández; González, Cándido Martín
Abstract: We construct a method to obtain the algebraic classification of Poisson algebras defined on a commutative associative alge bra, and we apply it to obtain the classification of the 3-dimensional Poisson algebras. In addition, we study the geometric classification,
the graph of degenerations and the closures of the orbits of the variety of 3-dimensional Poisson algebras. Finally, we also study the
algebraic classification of the Poisson algebras defined on a commutative associative null-filiform or filiform algebra and, to enrich this
classification, we study the degenerations between these particular Poisson algebras.2023-01-01T00:00:00Z