arXiv subjects

Sara Sommariva

Publications and source records attributed to Sara Sommariva.

14 recordsLinked to original sources

arXiv2026

Testing for a common subspace in compositional datasets with structural zeros

In this paper, we consider the problem of testing for a common principal subspace in compositional datasets with structural zeros. In particular, we address the problem in the general setting in which two groups are compared, each characterized by its own pattern of structural zeros. This situation prevents the direct use of standard logratio-based principal subspace comparison methods, since the two groups cannot be represented in a common logratio coordinate system in the usual way. We thus define a test for the presence of a common subspace that is fully compatible with the Aitchison geometry and logratio analysis. The proposed construction allows the principal subspaces associated with the two groups to be compared despite the different patterns of structural zeros. Under logratio-normality, we derive an analytical approximation to the null distribution of the test statistic. Alongside this parametric version, we also introduce a nonparametric bootstrap procedure that does not rely on distributional assumptions. The finite-sample behaviour of the test is investigated through simulations. The method is finally illustrated on a reproducible microbiome dataset available through Bioconductor.

stat.ME↗

arXiv2026

A neighbour selection approach for identifying differential networks in conditional functional graphical models

Estimating how different brain regions communicate with each other using EEG data is valuable both for medical research and clinical diagnosis. This involves quantifying the statistical dependencies among the activities of different brain areas, captured by the time-varying electric field recorded by scalp sensors. These dependencies can vary within and across individuals also in relationship with external factors such as age, mental state, or disease severity. Motivated by this problem, we propose a novel neighbor selection approach based on Gaussian functional graphical models and functional-on-functional regression to identify which brain regions interact and how interaction strength changes with individual features or covariates (e.g., age or clinical status). Our approach is fully automated and data-driven, and, in principle, can handle any number of continuous and categorical covariates simultaneously. Unlike existing approaches, it also produces results that are easy to interpret: one can directly assess whether the strength of each estimated interaction increases or decreases as the value of a given covariate varies. We evaluate our method through extensive simulation experiments and an application to real EEG data. The results demonstrate clear advantages over existing approaches, including more accurate estimation of brain connections and reduced computational cost, especially in high-dimensional settings involving a large number of brain regions and large sample sizes.

stat.ME↗

arXiv2025

When algebra twinks system biology: a conjecture on the structure of Gröbner bases in complex chemical reaction networks

We address the challenge of identifying all real positive steady states in chemical reaction networks (CRNs) governed by mass-action kinetics. Traditional numerical methods often require specific initial guesses and may fail to find all the solutions in systems exhibiting multistability. Gröbner bases offer an algebraic framework that systematically transforms polynomial equations into simpler forms, facilitating comprehensive solution enumeration. In this work, we propose a conjecture that CRNs with at most pairwise interactions yield Gröbner bases possessing a near-"triangular" structure, under appropriate assumptions. We illustrate this phenomenon using examples from a gene regulatory network and the Wnt signaling pathway, where the Gröbner basis approach reliably captures all real positive solutions. Our computational experiments reveal the potential of Gröbner bases to overcome limitations of local numerical methods for finding the steady states of complex biological systems, making them a powerful tool for understanding dynamical processes across diverse biochemical models.

q-bio.MN↗

arXiv2025

AI-based modular warning machine for risk identification in proximity healthcare

"DHEAL-COM - Digital Health Solutions in Community Medicine" is a research and technology project funded by the Italian Department of Health for the development of digital solutions of interest in proximity healthcare. The activity within the DHEAL-COM framework allows scientists to gather a notable amount of multi-modal data whose interpretation can be performed by means of machine learning algorithms. The present study illustrates a general automated pipeline made of numerous unsupervised and supervised methods that can ingest such data, provide predictive results, and facilitate model interpretations via feature identification.

cs.LG↗

arXiv2024

Sparse optimization for estimating the cross-power spectrum in linear inverse models : from theory to the application in brain connectivity

In this work we present a computationally efficient linear optimization approach for estimating the cross--power spectrum of an hidden multivariate stochastic process from that of another observed process. Sparsity in the resulting estimator of the cross--power is induced through $\ell_1$ regularization and the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) is used for computing such an estimator. With respect to a standard implementation, we prove that a proper initialization step is sufficient to guarantee the required symmetric and antisymmetric properties of the involved quantities. Further, we show how structural properties of the forward operator can be exploited within the FISTA update in order to make our approach adequate also for large--scale problems such as those arising in context of brain functional connectivity. The effectiveness of the proposed approach is shown in a practical scenario where we aim at quantifying the statistical relationships between brain regions in the context of non-invasive electromagnetic field recordings. Our results show that our method provide results with an higher specificity that classical approaches based on a two--step procedure where first the hidden process describing the brain activity is estimated through a linear optimization step and then the cortical cross--power spectrum is computed from the estimated time--series.

stat.ME↗

arXiv2022

A fast and convergent combined Newton and gradient descent method for computing steady states of chemical reaction networks

In this work we present a fast, globally convergent, iterative algorithm for computing the asymptotically stable states of nonlinear large--scale systems of quadratic autonomous Ordinary Differential Equations (ODEs) modeling, e.g., the dynamic of complex chemical reaction networks. Towards this aim, we reformulate the problem as a box--constrained optimization problem where the roots of a set of nonlinear equations need to be determined. Then, we propose to use a projected Newton's approach combined with a gradient descent algorithm so that every limit point of the sequence generated by the overall algorithm is a stationary point. More importantly, we suggest replacing the standard orthogonal projector with a novel operator that ensures the final solution to satisfy the box constraints while lowering the probability that the intermediate points reached at each iteration belong to the boundary of the box where the Jacobian of the objective function may be singular. The effectiveness of the proposed approach is shown in a practical scenario concerning a chemical reaction network modeling the signaling network of colorectal cancer cells. Specifically, in this scenario the proposed algorithm is proven to be faster and more accurate than a classical dynamical approach where the asymptotically stable states are computed as the limit points of the flux of the Cauchy problem associated with the ODEs system.

math.NA↗

arXiv2020

The role of spectral complexity in connectivity estimation

The study of functional connectivity from magnetoecenphalographic (MEG) data consists in quantifying the statistical dependencies among time series describing the activity of different neural sources from the magnetic field recorded outside the scalp. This problem can be addressed by utilizing connectivity measures whose computation in the frequency domain often relies on the evaluation of the cross-power spectrum of the neural time-series estimated by solving the MEG inverse problem. Recent studies have focused on the optimal determination of the cross-power spectrum in the framework of regularization theory for ill-posed inverse problems, providing indications that, rather surprisingly, the regularization process that leads to the optimal estimate of the neural activity does not lead to the optimal estimate of the corresponding functional connectivity. Along these lines, the present paper utilizes synthetic time series simulating the neural activity recorded by an MEG device to show that the regularization of the cross-power spectrum is significantly correlated with the signal-to-noise ratio of the measurements and that, as a consequence, this regularization correspondingly depends on the spectral complexity of the neural activity.

math.NA↗

arXiv2020

Gain and Loss of Function mutations in biological chemical reaction networks: a mathematical model with application to colorectal cancer cells

This paper studies a system of Ordinary Differential Equations modeling a chemical reaction network and derives from it a simulation tool mimicking Loss of Function and Gain of Function mutations found in cancer cells. More specifically, from a theoretical perspective, our approach focuses on the determination of moiety conservation laws for the system and their relation with the corresponding stoichiometric surfaces. Then we show that Loss of Function mutations can be implemented in the model via modification of the initial conditions in the system, while Gain of Function mutations can be implemented by eliminating specific reactions. Finally, the model is utilized to examine in detail the G1-S phase of a colorectal cancer cell.

q-bio.MN↗

arXiv2020

Mathematical modelling of nuclear medicine data

Positron Emission Tomography using 2-[18F]-2deoxy-D-glucose as radiotracer (FDG-PET) is currently one of the most frequently applied functional imaging methods in clinical applications. The interpretation of FDG-PET data requires sophisticated mathematical approaches able to exploit the dynamical information contained in this kind of data. Most of these approaches are formulated within the framework of compartmental analysis, which connects the experimental nuclear data with unknown tracer coefficients measuring the effectiveness of the tracer metabolism by means of Cauchy systems of ordinary differential equations. This paper provides a coincise overview of linear compartmental methods, focusing on the analytical solution of the forward compartmental problem and on the specific issues concerning the corresponding compartmental inverse problem.

q-bio.TO↗

arXiv2019

On the two-step estimation of the cross--power spectrum for dynamical inverse problems

We consider the problem of reconstructing the cross--power spectrum of an unobservable multivariate stochatic process from indirect measurements of a second multivariate stochastic process, related to the first one through a linear operator. In the two--step approach, one would first compute a regularized reconstruction of the unobservable signal, and then compute an estimate of its cross--power spectrum from the regularized solution. We investigate whether the optimal regularization parameter for reconstruction of the signal also gives the best estimate of the cross--power spectrum. We show that the answer depends on the regularization method, and specifically we prove that, under a white Gaussian assumption: (i) when regularizing with truncated SVD the optimal parameter is the same; (ii) when regularizing with the Tikhonov method, the optimal parameter for the cross--power spectrum is lower than half the optimal parameter for the signal. We also provide evidence that a one--step approach would likely have better mathematical properties of the two--step approach. Our results apply particularly to the brain connectivity estimation from magneto/electro-encephalographic recordings and provide a formal interpretation of recent empirical results.

math.NA↗

arXiv2018

Bayesian Multi--Dipole Modeling in the Frequency Domain

Background: Magneto- and Electro-encephalography record the electromagnetic field generated by neural currents with high temporal frequency and good spatial resolution, and are therefore well suited for source localization in the time and in the frequency domain. In particular, localization of the generators of neural oscillations is very important in the study of cognitive processes in the healthy and in the pathological brain. New method: We introduce the use of a Bayesian multi-dipole localization method in the frequency domain. Given the Fourier Transform of the data at one or multiple frequencies and/or trials, the algorithm approximates numerically the posterior distribution with Monte Carlo techniques. Results: We use synthetic data to show that the proposed method behaves well under a wide range of experimental conditions, including low signal-to-noise ratios and correlated sources. We use dipole clusters to mimic the effect of extended sources. In addition, we test the algorithm on real MEG data to confirm its feasibility. Comparison with existing method(s): Throughout the whole study, DICS (Dynamic Imaging of Coherent Sources) is used systematically as a benchmark. The two methods provide similar general pictures; the posterior distributions of the Bayesian approach contain much richer information at the price of a higher computational cost. Conclusions: The Bayesian method described in this paper represents a reliable approach for localization of multiple dipoles in the frequency domain.

q-bio.QM↗

arXiv2017

A comparative study of the robustness of frequency--domain connectivity measures to finite data length

In this work we use numerical simulation to investigate how the temporal length of the data affects the reliability of the estimates of brain connectivity from EEG time--series. We assume that the neural sources follow a stable MultiVariate AutoRegressive model, and consider three connectivity metrics: Imaginary part of Coherency (IC), generalized Partial Directed Coherence (gPDC) and frequency--domain Granger Causality (fGC). In order to assess the statistical significance of the estimated values, we use the surrogate data test by generating phase--randomized and autoregressive surrogate data. We first consider the ideal case where we know the source time courses exactly. Here we show how, expectedly, even exact knowledge of the source time courses is not sufficient to provide reliable estimates of the connectivity when the number of samples gets small; however, while gPDC and fGC tend to provide a larger number of false positives, the IC becomes less sensitive to the presence of connectivity. Then we proceed with more realistic simulations, where the source time courses are estimated using eLORETA, and the EEG signal is affected by biological noise of increasing intensity. Using the ideal case as a reference, we show that the impact of biological noise on IC estimates is qualitatively different from the impact on gPDC and fGC.

q-bio.QM↗

arXiv2017

Bayesian multi--dipole localization and uncertainty quantification from simultaneous EEG and MEG recordings

We deal with estimation of multiple dipoles from combined MEG and EEG time--series. We use a sequential Monte Carlo algorithm to characterize the posterior distribution of the number of dipoles and their locations. By considering three test cases, we show that using the combined data the method can localize sources that are not easily (or not at all) visible with either of the two individual data alone. In addition, the posterior distribution from combined data exhibits a lower variance, i.e. lower uncertainty, than the posterior from single device.

q-bio.QM↗

arXiv2014

Sequential Monte Carlo samplers for semilinear inverse problems and application to magnetoencephalography

We discuss the use of a recent class of sequential Monte Carlo methods for solving inverse problems characterized by a semi-linear structure, i.e. where the data depend linearly on a subset of variables and nonlinearly on the remaining ones. In this type of problems, under proper Gaussian assumptions one can marginalize the linear variables. This means that the Monte Carlo procedure needs only to be applied to the nonlinear variables, while the linear ones can be treated analytically; as a result, the Monte Carlo variance and/or the computational cost decrease. We use this approach to solve the inverse problem of magnetoencephalography, with a multi-dipole model for the sources. Here, data depend nonlinearly on the number of sources and their locations, and depend linearly on their current vectors. The semi-analytic approach enables us to estimate the number of dipoles and their location from a whole time-series, rather than a single time point, while keeping a low computational cost.

stat.AP↗