Fernando (@FernandoL2006) profile picture

Fernando

@FernandoL2006

Professor at UFRGS, Brazil. Working on statistical physics of complex systems.

Joined August 2020
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Photo by Fernando (@FernandoL2006)Photo by Fernando (@FernandoL2006)Photo by Fernando (@FernandoL2006)Photo by Fernando (@FernandoL2006)Photo by Fernando (@FernandoL2006)Photo by Fernando (@FernandoL2006)Photo by Fernando (@FernandoL2006)Photo by Fernando (@FernandoL2006)Photo by Fernando (@FernandoL2006)Photo by Fernando (@FernandoL2006)
Our latest paper is out! iopscience.iop.org/article/1… We solve the zero-temperature dynamics of the Sompolinsky-Crisanti spherical model with asymmetric interactions. Slow dynamics does not survive, but the model, surprisingly enough, never reaches equilibrium! #StatisticalPhysics

Zero-temperature dynamics of the spherical model with non-reciprocal interactions

Zero-temperature dynamics of the spherical model with non-reciprocal interactions, Stariolo, Daniel A, Metz, Fernando L

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Happy to share our recent work on the SIS model on directed networks! #ComplexSystems journals.aps.org/pre/abstrac… We combine random matrices and spin-glass methods to compute the epidemic threshold and study disease localization within the QMF theory.

Epidemic threshold and localization of the SIS model on directed complex networks

We study the susceptible-infected-susceptible (SIS) model on directed complex networks within the quenched mean-field approximation. Combining results from random matrix theory with an analytic...

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Hubs are not as important as in unidirected networks. The epidemic threshold in directed networks is finite and independent of the degree distribution. The mechanism that sustains the endemic phase in this case remains open.
Phase diagram in terms of the mean degree and the standard deviation of pairwise infections rates (coupling strengths).

ALT Phase diagram in terms of the mean degree and the standard deviation of pairwise infections rates (coupling strengths).

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Proud to share my work on DMFT for dynamical systems on complex networks, selected as an Editors'Suggestion in PRL! @CompSysSoc @ifufrgs The paper presents a general solution for models of complex systems on sparse and directed networks. Check it out: journals.aps.org/prl/abstrac…
Dynamical Mean-Field Theory of Complex Systems on Sparse Directed Networks

Dynamical Mean-Field Theory of Complex Systems on Sparse Directed Networks

A generalized dynamical mean-field theory allows computation of the phase diagram of sparse and heterogeneous networks.

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I apply DMFT to derive the phase diagram of the Sompolinsky-Crisanti neural network model (1988) in the sparse regime. This model has shaped neural networks and spin glasses research for over 30 years. My work reveals how its phase diagram depends on network structure!
Vertical axis: mean degree. Horizontal axis: standard deviation of the coupling strengths. Phases I and II: fixed points. Phases III and IV: chaotic.

ALT Vertical axis: mean degree. Horizontal axis: standard deviation of the coupling strengths. Phases I and II: fixed points. Phases III and IV: chaotic.

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Beyond neural networks, the general solution for the path-probability applies to ecosystems, epidemic spreading, opinion dynamics and synchronization.
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Just out in @PhysRevE: journals.aps.org/pre/abstrac… Many thanks to coauthors @physicsidea and @FernandoL2006!

Effects of clustering heterogeneity on the spectral density of sparse networks

We derive exact equations for the spectral density of sparse networks with an arbitrary distribution of the number of single edges and triangles per node. These equations enable a systematic invest...

journals.aps.org
Thomas Peron (@thomas_peron) profile pictureThomas Peron@thomas_peron15 Apr 2024
New work with Tuan Minh Pham (@physicsidea) and Fernando Metz (@FernandoL2006)! "Effects of clustering heterogeneity on the spectral density of sparse networks" arxiv.org/abs/2404.08152
Image from Thomas Peron (@thomas_peron)
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I'm excited to share my new paper on DMFT! arxiv.org/abs/2406.06346 I derive an elegant solution for the dynamics of sparse and heterogeneous complex systems. Neural networks, epidemic spreading, Lotka-Volterra, all handled by a single equation! #ComplexSystems #NetworkScience
Time evolution of the standard deviation of microscopic variables for Lotka-Volterra (LV), neural networks (NN) and epidemic spreading (SIS model) on directed networks with average degree c=5, Poisson and geometric distributed degrees, and random couplings (Gaussian and uniform). Solid line: DMFT. Symbols: simulations.

ALT Time evolution of the standard deviation of microscopic variables for Lotka-Volterra (LV), neural networks (NN) and epidemic spreading (SIS model) on directed networks with average degree c=5, Poisson and geometric distributed degrees, and random couplings (Gaussian and uniform). Solid line: DMFT. Symbols: simulations.

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New work with Tuan Minh Pham (@physicsidea) and Fernando Metz (@FernandoL2006)! "Effects of clustering heterogeneity on the spectral density of sparse networks" arxiv.org/abs/2404.08152
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Consider a large number of pointlike sources of light and distribute them at random along a line. How the interference pattern depends on the distribution of sources? Check out our recent paper for an answer to this problem: journals.aps.org/pra/abstrac… #Optics #Physics @ifufrgs

Statistical properties of speckle patterns for a random number of scatterers and nonuniform phase...

The statistical properties of speckle patterns have important applications in optics, oceanography, and transport phenomena in disordered systems. Here we obtain closed-form analytic results for the...

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Our analytic expressions generalize classical results of the theory of light speckle patterns, including the Rayleigh distribution and K-statistics.
Amplitude distribution of the electromagnetic field. Each curve is for a different variance of the number of sources.

ALT Amplitude distribution of the electromagnetic field. Each curve is for a different variance of the number of sources.

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Still my favorite explanation of the scientific method.
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Our latest paper is out: journals.aps.org/pre/abstrac… The message is simple: details of the microscopic dynamics modify the critical behaviour of nonequilibrium systems on networks. We show this property for the Ising model.

Nonequilibrium dynamics of the Ising model on heterogeneous networks with an arbitrary distribution...

The Ising model on networks plays a fundamental role as a testing ground for understanding cooperative phenomena in complex systems. Here we solve the synchronous dynamics of the Ising model on...

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The critical exponent of the magnetization is determined by the tails of the distribution of the thermal noise.
Critical magnetization for different distributions of thermal noise.

ALT Critical magnetization for different distributions of thermal noise.

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Dynamical exponents governing the relaxation of the system are also affected by the details of the thermal noise. Other binary-state nonequilibrium models should also be sensitive to the details of the microscopic dynamics.
Critical dynamics of the magnetization for different distributions of thermal noise.

ALT Critical dynamics of the magnetization for different distributions of thermal noise.

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Our new preprint is out: arxiv.org/abs/2212.09424 We analytically solve the nonequilibrium dynamics of the Ising model on networks with large degrees. When detailed balance breaks down, the critical exponents surprisingly depend on the tails of the distribution of thermal noise.
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I'm delighted to share our new paper on JPhys:Complexity: iopscience.iop.org/article/1… We find an analytic, exact, and nontrivial solution of the resolvent equations that determine spectral and localization properties of networks!
Spectral density of the configuration model with large mean degree.

ALT Spectral density of the configuration model with large mean degree.

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We find an analytic solution for diverging mean degree that still depends on the shape of the degree distribution. The spectral density is not always given by the Wigner semicircle! The method is simple and it can be extended to graphs with triangles, for instance.
Distribution of the self-energy when the mean degree diverges. The function nu is the distribution of rescaled degrees.

ALT Distribution of the self-energy when the mean degree diverges. The function nu is the distribution of rescaled degrees.

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Among the consequences of our analytic solution, I like very much the beautiful expression for the distribution of the local density of states. Its power-law tail explains why the spectral density is singular.
Distribution of the local density of states, which captures the spatial fluctuations of the eigenvectors. The power-law tail leads to diverging moments.

ALT Distribution of the local density of states, which captures the spatial fluctuations of the eigenvectors. The power-law tail leads to diverging moments.

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