arXiv subjects

Stefano Monni

Publications and source records attributed to Stefano Monni.

3 recordsLinked to original sources

arXiv2022

A Framework for Reconstructing COVID-19 Transmission Network to Inform Betweenness Centrality-Based Control Measures

In this paper, we propose a general framework for optimal control measures, which follows the evolution of COVID-19 infection counts collected by Surveillance Units on a country level. We employ an autoregressive model that allows to decompose the mean number of infections into three components that describe: intra-locality infections, inter-locality infections, and infections from other sources such as travelers arriving to a country from abroad. We identify the inter-locality term as a time-evolving network and when it drives the dynamics of the disease we focus on its properties. Tools from network analysis are then employed to get insight into its topology. Building on this, and particularly on the centrality of the nodes of the identified network, a strategy for intervention and disease control is devised.

physics.soc-ph↗

arXiv2020

An Orthogonally Equivariant Estimator of the Covariance Matrix in High Dimensions and for Small Sample Sizes

We introduce an estimation method of covariance matrices in a high-dimensional setting, i.e., when the dimension of the matrix, , is larger than the sample size . Specifically, we propose an orthogonally equivariant estimator. The eigenvectors of such estimator are the same as those of the sample covariance matrix. The eigenvalue estimates are obtained from an adjusted profile likelihood function derived by approximating the integral of the density function of the sample covariance matrix over its eigenvectors, which is a challenging problem in its own right. Exact solutions to the approximate likelihood equations are obtained and employed to construct estimates that involve a tuning parameter. Bootstrap and cross-validation based algorithms are proposed to choose this tuning parameter under various loss functions. Finally, comparisons with two well-known orthogonally equivariant estimators of the covariance matrix are given, which are based on Monte-Carlo risk estimates for simulated data and misclassification errors in real data analyses. In addition, Monte-Carlo risk estimates are also provided to compare our estimates of eigenvalues to those of a consistent estimator of population eigenvalues.

math.ST↗

arXiv2000

The Hurwitz Enumeration Problem of Branched Covers and Hodge Integrals

We use algebraic methods to compute the simple Hurwitz numbers for arbitrary source and target Riemann surfaces. For an elliptic curve target, we reproduce the results previously obtained by string theorists. Motivated by the Gromov-Witten potentials, we find a general generating function for the simple Hurwitz numbers in terms of the representation theory of the symmetric group S_n. We also find a generating function for Hodge integrals on the moduli space M_{g,2} of Riemann surfaces with two marked points, similar to that found by Faber and Pandharipande for the case of one marked point.

hep-th↗