arXiv subjects

Dario Borrelli

Publications and source records attributed to Dario Borrelli.

4 recordsLinked to original sources

arXiv2026

Largest connected component in duplication-divergence growing graphs with symmetric coupled divergence

The largest connected component in duplication-divergence growing graphs with symmetric coupled divergence is studied. Finite-size scaling reveals a phase transition occurring at a divergence rate $\delta_c$. The $\delta_c$ found stands near the locus of zero in Euler characteristic for finite-size graphs, known to be indicative of the largest connected component transition. The role of non-interacting vertices in shaping this transition with their presence ($d=0$) and absence ($d=1$) in duplication is also discussed, suggesting a particular transformation of the time variable considered, which yields a singularity locus in the natural logarithm of the absolute value of Euler characteristic in finite-size graphs near to that obtained with $d=1$ but from the model with $d=0$. The findings may suggest implications for bond percolation in these growing graph models.

cond-mat.stat-mech↗

arXiv2025

Duplication-divergence growing graph models

In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits that are not featured in traditional random graphs. In this respect, through a mean-field approach, this review tackles the statistical physics of graph models based on the interaction principle of duplication-divergence. Additional sophistications extending the duplication-divergence model are also reviewed as well as generalizations of other known models. Possible research gaps and related prior results are then discussed.

cond-mat.stat-mech↗

arXiv2024

Divergence asymmetry and connected components in a general duplication-divergence graph model

This Letter introduces a generalization of known duplication-divergence models for growing random graphs. This general duplication-divergence model includes a new coupled divergence asymmetry rate, which allows to obtain the structure of random growing networks by duplication-divergence in a continuous range of configurations between two known limit cases (i) complete asymmetric divergence, i.e., divergence rates affect only edges of either the original or the copy vertex, and (ii) symmetric divergence, i.e., divergence rates affect equiprobably both the original and the copy vertex. Multiple connected sub-graphs (of order greater than one) (of order greater than one) emerge as the divergence asymmetry rate slightly moves from the complete asymmetric divergence case. Mean-field results of priorly published models are nicely reproduced by this generalization. In special cases, the connected components size distribution $C_s$ suggests a power-law scaling of the form $C_s \sim s^{-\lambda}$ for $s>1$, e.g., with $\lambda \approx 5/3$ for divergence rate $\delta \approx 0.7$.

cond-mat.stat-mech↗

arXiv2021

A computational model implementing subjectivity with the 'Room Theory'. The case of detecting Emotion from Text

This work introduces a new method to consider subjectivity and general context dependency in text analysis and uses as example the detection of emotions conveyed in text. The proposed method takes into account subjectivity using a computational version of the Framework Theory by Marvin Minsky (1974) leveraging on the Word2Vec approach to text vectorization by Mikolov et al. (2013), used to generate distributed representation of words based on the context where they appear. Our approach is based on three components: 1. a framework/'room' representing the point of view; 2. a benchmark representing the criteria for the analysis - in this case the emotion classification, from a study of human emotions by Robert Plutchik (1980); and 3. the document to be analyzed. By using similarity measure between words, we are able to extract the relative relevance of the elements in the benchmark - intensities of emotions in our case study - for the document to be analyzed. Our method provides a measure that take into account the point of view of the entity reading the document. This method could be applied to all the cases where evaluating subjectivity is relevant to understand the relative value or meaning of a text. Subjectivity can be not limited to human reactions, but it could be used to provide a text with an interpretation related to a given domain ("room"). To evaluate our method, we used a test case in the political domain.

cs.CL↗