arXiv subjects

Marina Bertolini

Publications and source records attributed to Marina Bertolini.

12 recordsLinked to original sources

arXiv2025

The effect of a new power interconnector on energy prices volatility: the case of Sicily

Integrating energy islands into the European electricity market is a key challenge for the energy transition. This study investigates the impact of the Sorgente-Rizziconi interconnector on electricity price volatility in Sicily. Before its commissioning on 28 May 2016, the Sicilian electricity market zone was poorly interconnected with the Italian mainland. Using daily data from 2015 to 2018, the analysis applies a semi-parametric GARCH model with a logistic intervention function to estimate changes in conditional price variance. A fully non-parametric additive model is employed as a robustness check, allowing the data to shape volatility dynamics without imposing a predefined structure. The results reveal that the new interconnector significantly increased price volatility in Sicily, without reducing average price levels. No significant effects were observed in other Italian market zones. These findings highlight the context-dependent nature of infrastructure impacts and suggest that physical integration alone does not guarantee price stability. The results have important implications for energy policy, investment planning, and risk management in electricity markets.

stat.AP↗

arXiv2024

Accounting carbon emissions from electricity generation: a review and comparison of emission factor-based methods

Accurate estimation of greenhouse gas (GHG) is essential to meet carbon neutrality targets, particularly through the calculation of direct CO2 emissions from electricity generation. This work reviews and compares emission factor-based methods for accounting direct carbon emissions from electricity generation. The emission factor approach is commonly worldwide used. Empirical comparisons are based on emission factors computed using data from the Italian electricity market. The analyses reveal significant differences in the CO2 estimates according to different methods. This, in turn, highlights the need to select an appropriate method for reliable emissions, which could support effective regulatory compliance and informed policy-making. As concerns, in particular, the market zones of the Italian electricity market, the results underscore the importance of tailoring emission factors to accurately capture regional fuel variations.

stat.AP↗

arXiv2024

Birational geometry of critical loci in Algebraic Vision

In Algebraic Vision, the projective reconstruction of the position of each camera and scene point from the knowledge of many enough corresponding points in the views is called the structure from motion problem. It is known that the reconstruction is ambiguous if the scene points are contained in particular algebraic varieties, called critical loci. To be more precise, from the definition of criticality, for the same reconstruction problem, two critical loci arise in a natural way. In the present paper, we investigate the relations between these two critical loci, and we prove that, under some mild smoothness hypotheses, (some of) their irreducible components are birational. To this end, we introduce a unified critical locus that restores the symmetry between the two critical loci, and a natural commutative diagram relating the unified critical locus and the two single critical loci. For technical reasons, but of interest in its own, we also consider how a critical locus change when one increases the number of views.

math.AG↗

arXiv2024

Problems and related results in Algebraic Vision and Multiview Geometry

The article presents a survey of results in algebraic vision and multiview geometry. The starting points is the study of projective algebraic varieties critical for scene reconstruction. Initially studied for reconstructing static scenes in three-dimensional spaces, these critical loci are later investigated for dynamic and segmented scenes in higher-dimensional projective spaces. The formal analysis of the ideals of critical loci employs Grassmann tensors, introduced as crucial tools for determining these ideals and aiding the reconstruction process away from critical loci. A long-term goal of the authors with other co-authors involves two main aspects: firstly studying properties of Grassmann tensors, as rank, multi-rank and core, along with the varieties that parameterize these tensors; concurrently conducting an analysis of families of critical loci in various scenarios.

math.AG↗

arXiv2023

The Multilinear Rank and Core of Trifocal Grassmann Tensors

Closed formulas for the multilinear rank of trifocal Grassmann tensors are obtained. An alternative process to the standard HOSVD is introduced for the computation of the core of trifocal Grassmann tensors. Both of these results are obtained, under natural genericity conditions, leveraging the canonical form for these tensors, obtained by the same authors in a previous work. A gallery of explicit examples is also included.

math.AG↗

arXiv2022

The Varieties of Bifocal Grassmann Tensors

Grassmann tensors arise from classical problems of scene reconstruction in computer vision. In particular, bifocal Grassmann tensors, related to a pair of projections from a projective space onto view-spaces of varying dimensions, generalise the classical notion of fundamental matrices. In this paper we study in full generality the variety of bifocal Grassmann tensors focusing on its birational geometry. To carry out this analysis, every object of multi-view geometry is declined both from an algebraic and geometric point of view, e.g., the duality between the view spaces and the space of rays is explicitly described via polarity. Next, we deal with the moduli of bifocal Grassmann tensors, thus showing that this variety is both birational to a suitable homogeneous space and endowed with a dominant rational map to a Grassmannian.

math.AG↗

arXiv2021

Impact of Local Energy Markets on the Distribution Systems: A Comprehensive Review

In recent years extensive research has been conducted on the development of different models that enable energy trading between prosumers and consumers due to expected high integration of distributed energy resources. Some of the most researched mechanisms include Peer-to-Peer energy trading, Community Self-Consumption and Transactive Energy Models. Here, we present an exhaustive review of existing research around Local Energy Market integration into distribution systems, in particular benefits and challenges that the power grid can expect from integrating these models. We also present a detailed overview of methods that are used to integrate physical network constraints into the market mechanisms, their advantages, drawbacks, and scaling potential. We find that financial energy transactions do not directly reflect the physical energy flows imposed by the constraints of the installed electrical infrastructure. Therefore, ensuring the stable and reliable delivery of electricity, it is vital to understand the impact of these transactions on the grid infrastructure, e.g., impacts on the control, operation, and planning of electricity distribution systems.

eess.SY↗

arXiv2021

Smooth determinantal varieties and critical loci in Multiview Geometry

Linear projections from P^k to P^h appear in computer vision as models of images of dynamic or segmented scenes. Given multiple projections of the same scene, the identification of many enough correspondences between the images allows, in principle, to reconstruct the position of the projected objects. A critical locus for the reconstruction problem is a variety in P^k containing the set of points for which the reconstruction fails. Critical loci turn out to be determinantal varieties. In this paper we determine and classify all the smooth critical loci, showing that they are classical projective varieties.

math.AG↗

arXiv2019

The Rank of Trifocal Grassmann Tensors

Grassmann tensors arise from classical problems of scene reconstruction in computer vision. Trifocal Grassmann tensors, related to three projections from a projective space of dimension k onto view-spaces of varying dimensions are studied in this work. A canonical form for the combined projection matrices is obtained. When the centers of projections satisfy a natural generality assumption, such canonical form gives a closed formula for the rank of the trifocal Grassmann tensors. The same approach is also applied to the case of two projections, confirming a previous result obtained with different methods in [6]. The rank of sequences of tensors converging to tensors associated with degenerate configurations of projection centers is also considered, giving concrete examples of a wide spectrum of phenomena that can happen.

math.AG↗

arXiv2019

Matrices dropping rank in codimension one and critical loci in computer vision

Critical loci for projective reconstruction from three views in four dimensional projective space are defined by an ideal generated by maximal minors of suitable $4 \times 3$ matrices, $N,$ of linear forms. Such loci are classified in this paper, in the case in which $N$ drops rank in codimension one, giving rise to reducible varieties. This leads to a complete classification of matrices of size $(n+1) \times n$ for $n \le 3,$ which drop rank in codimension one. Instability of reconstruction near non-linear components of critical loci is explored experimentally.

math.AG↗

arXiv1997

Numerical Criteria for vey Ampleness of Divisors on Projective Bundles over an elliptic curve

In Butler, J.Differential Geom. 39 (1):1--34,1994, the author gives a sufficient condition for a line bundle associated with a divisor D to be normally generated on $X=P(E)$ where E is a vector bundle over a smooth curve C. A line bundle which is ample and normally generated is automatically very ample. Therefore the condition found in Butler's work, together with Miyaoka's well known ampleness criterion, give a sufficient condition for the very ampleness of D on X. This work is devoted to the study of numerical criteria for very ampleness of divisors D which do not satisfy the above criterion, in the case of C elliptic. Numerical conditions for the very ampleness of D are proved,improving existing results. In some cases a complete numerical characterization is found.

alg-geom↗

arXiv1993

Classification of smooth congruences with a fundamental curve

We give a classification and a construction of all smooth $(n-1)$-dimensional varieties of lines in ${\bf P}\sp n$ verifying that all their lines meet a curve. This also gives a complete classification of $(n-1)$-scrolls over a curve contained in $G(1,n)$.

alg-geom↗