Source author record

Carmen Rovi

Carmen Rovi appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record

math.AT math.GT math.CT Machine Learning math.GR math.KT math.ST

Catalog footprint

What is connected

5works

7topics

4close collaborators

Actions

Connect this record

Open graph Browse works

Inspect adjacent papers, topics, institutions and collaborators without losing the researcher page.

Building this map preview

BZPEER is loading the nearby papers, people, topics and institutions for this page.

preprint2026arXiv

A Stable Distance Persistence Homology for Dynamic Bayesian Network Clustering

Dynamic Bayesian networks (DBNs) are a widely used framework for modeling systems whose probabilistic structure evolves over time. Standard inference methods focus on local conditional distributions and can miss larger-scale patterns in how dependencies between variables organize and change over time. We introduce a topological approach to this problem. To each DBN we associate a time-varying graph, called a Dynamic Bayesian Graph (DBG), by assigning to each edge a strength that measures variation in its conditional dependence across parent configurations, and retaining edges whose strength exceeds a chosen threshold. We show that this construction fits within the dynamic graph framework of Kim and Mémoli, enabling the use of tools from topological data analysis. Applying persistent homology to a DBG produces a barcode, which records the merging and disappearance of connected groups of strongly dependent variables over time. We prove that this barcode is stable: small perturbations in the conditional probability tables of the DBN lead to small changes in the resulting barcode. This yields a principled and noise-resistant summary of how dependency structure evolves in a dynamic Bayesian network.

preprint2023arXiv

Chain duality for categories over complexes

We show that the additive category of chain complexes parametrized by a finite simplicial complex $K$ forms a category with chain duality. This fact, never fully proven in the original reference, is fundamental for Ranicki's algebraic formulation of the surgery exact sequence of Sullivan and Wall, and his interpretation of the surgery obstruction map as the passage from local Poincaré duality to global Poincaré duality. Our paper also gives a new, conceptual, and geometric treatment of chain duality on $K$-based chain complexes.

preprint2020arXiv

Signature Cocycles on the Mapping Class Group and Symplectic Groups

Werner Meyer constructed a cocycle in $H^2(Sp(2g, \mathbb{Z}); \mathbb{Z})$ which computes the signature of a closed oriented surface bundle over a surface, with fibre a surface of genus g. By studying properties of this cocycle, he also showed that the signature of such a surface bundle is a multiple of 4. In this paper, we study the signature cocycles both from the geometric and algebraic points of view. We present geometric constructions which are relevant to the signature cocycle and provide an alternative to Meyer's decomposition of a surface bundle. Furthermore, we discuss the precise relation between the Meyer and Wall-Maslov index. The main theorem of the paper, Theorem 6.6, provides the necessary group cohomology results to analyze the signature of a surface bundle modulo any integer N. Using these results, we are able to give a complete answer for N = 2, 4 and 8, and based on a theorem of Deligne, we show that this is the best we can hope for using this method.

preprint2015arXiv

The signature modulo 8 of fibre bundles

This thesis is concerned with the residues modulo 4 and 8 of the signature of a 4k-dimensional oriented geometric Poincare complex. The Z_8-valued Brown-Kervaire invariant of Z_4-valued quadratic forms is used to prove that if the signature is divisible by 4, the divisibility by 8 is detected by the Arf invariant of a Z_2-valued quadratic form. This result is applied to a fibration of geometric Poincare complexes with the total space 4k-dimensional. It is known that the signature is multiplicative modulo 4, and that there are examples of non-multiplicativity modulo 8. We identify the obstruction to multiplicativity modulo 8 with the Arf invariant of the Z_2-valued quadratic form defined on an appropriate Z_2-cohomology vector space by dividing the Z_4-valued Pontryagin square by 2. The obstruction is then shown to vanish under certain assumptions.

preprint2014arXiv

Orbispaces and their Mapping Spaces via Groupoids: A Categorical Approach

In this paper, we give an accessible introduction to the theory of orbispaces via groupoids. We define a certain class of topological groupoids, which we call orbigroupoids. Each orbigroupoid represents an orbispace, but just as with orbifolds and Lie groupoids, this representation is not unique: orbispaces are Morita equivalence classes of orbigroupoids. We show how to formalize this equivalence by defining the category of orbispaces as a bicatecory of fractions from the category of orbigroupoids. We focus particularly on laying the groundwork for future work in creating mapping objects for orbispaces which are themselves orbispaces, and providing a concrete description of how this mapping space construction will get its orbispace structure. Throughout this paper, we illustrate our definitions and results with numerous examples which we hope will be useful in seeing how the categorical point of view is used to study these spaces.