1 Contributo su Rivista

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Network renormalization

The renormalization group (RG) is a powerful theoretical framework. It is used on systems with many degrees of freedom to transform the description of their configurations, along with the associated model parameters and coupling constants, across different levels of resolution. The RG also provides a way to identify critical points of phase transitions and study the system’s behaviour around them. In traditional physical applications, the RG largely builds on the notions of homogeneity, symme...

Introduction to correlation networks: Interdisciplinary approaches beyond thresholding

Many empirical networks originate from correlational data, arising in domains as diverse as psychology, neuroscience, genomics, microbiology, finance, and climate science. Specialized algorithms and theory have been developed in different application domains for working with such networks, as well as in statistics, network science, and computer science, often with limited communication between practitioners in different fields. This leaves significant room for cross-pollination across discipl...

Testing maximum entropy models with e-values

E-values have recently emerged as a robust and flexible alternative to p-values for hypothesis testing, especially under optional continuation, i.e., when additional data from further experiments are collected. In this work we define optimal e-values for testing between maximum entropy models, in both the microcanonical (hard constraints) and canonical (soft constraints) settings. We show that, when testing between two hypotheses that are both microcanonical, the so-called growth-rate optimal...

Inhomogeneous random graphs with infinite-mean fitness variables

We consider an inhomogeneous Erdős–Rényi random graph ensemble with exponentially decaying random disconnection probabilities determined by an independent and identically distributed field of variables with heavy tails and infinite mean associated with the vertices of the graph. This model was recently investigated in the physics literature (Garuccio, Lalli, and Garlaschelli 2023) as a scale-invariant random graph within the context of network renormalization. From a mathematical perspective,...

Interbank network reconstruction enforcing density and reciprocity

Networks of financial exposures are the key propagators of risk and distress among banks, but their empirical structure is not publicly available because of confidentiality. This limitation has triggered the development of methods of network reconstruction from partial, aggregate information. Unfortunately, even the best methods available fail in replicating the number of directed cycles, which on the other hand play a crucial role in determining graph spectra and hence the degree of network ...

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