Lecture 1. Populations, Ecosystems, and their fluctuations: a network approach

03/10/2024, 11:00-13:00 (Aula2, San Francesco complex). 

Also online at http://imt.lu/aula2.

Abstract: Natural ecosystems consist of a myriad of different types of organisms that, through their interactions, process the energy and matter flowing and cycling on Earth. A world without networks of ecological interactions would simply not function. Ecosystem networks, however, are much more challenging to measure and model than other types of networks such as computer ones, or financial and social ones. Even the identity of the nodes or what they represent, or the nature of the links connecting the nodes is extremely complex to define and ultimately model, which is sometimes also a major interdisciplinary barrier. There are, indeed, different types of network models that apply to ecosystems, from food webs to bipartite mutualistic networks, or combinations of different types of interactions and nodes in multilayers and multiplexes. In this seminar, I will pitch some key questions around some applications of network models in ecology with a focus on network nodes as species and network links as trophic links or “service links” (e.g. pollination/resource exchange). I will consider cases in which node size models population size to highlight how network models can be used to predict fluctuations in natural populations. I will specifically concentrate on the relationship between theory and experiments, and how network theory can guide experimental measurements necessary to test ecological theories around the stability and resilience of ecosystems facing perturbations.

Lecture 2. Network science and microbiomes: challenges and opportunities

27/11/2024, 16:30-17:00 (Cappella Guinigi, San Francesco complex). 

Also online at http://imt.lu/guinigi.

Abstract: The study of environmental microbiomes, such as assemblages of prokaryotes and fungi in soil and plant roots, is becoming central to the understanding of how ecosystems are structured and function. Network science offers the tools to describe the structure of these complex associations, the processes that form them, and also their response to perturbations. In this talk, I will introduce these complex communities for a diverse range of systems, such as the rhizosphere of cereals like wheat and barley, that of different species in grasslands, or soil. I will offer examples of the application of maximum entropy network models applied to these ecological assemblages and metrics that help characterize their complexity, including fluctuations of network configurations, stability, and responses to perturbations.

Lecture 3. Entropy in ecological networks: bridging theory and experiments

07/05/2025, 15:00-17:00 (Conference Room, San Ponziano complex). 

Also online at http://imt.lu/conference.

Abstract: Maximum entropy network models have become a major tool in the analysis of complex systems, including ecological ones. In these models, entropy is a fundamental concept related to ideas borrowed from statistical mechanics and information theory. In particular, network entropy relates both to the configurations the system can take and the uncertainty in the probability distribution describing those configurations. As for the latter one, the key idea is that the probability distribution needs be chosen such to maximize the entropy and so ensure maximal randomness, apart from the imposed constraints. Here, I will mostly focus on the configurational aspect, and whether the metric of entropy itself could measure aspects of the complexity of the network that may help understand its structure and dynamics. In the case of the microcanonical ensemble, for binary configuration models with hard constraints on the degree sequence, one obtains the uniform distribution and a simple interpretation of the entropy, that is the count of the number of allowed configurations (all equally likely). In most applications, however, we have no access to that number, neither are hard constraints reasonable. The soft constraints case is much more reasonable for ecological datasets, and in principle all configurations are possible but not equally probable, with the observed one assumed to be the average one, and the averaged one also assumed to be the most probable one. This allows a new point of view: the system configurations can now be seen as fluctuations around the most typical configuration, the average one. As a concept, this vision suits ecological system at equilibrium very well and, in principle, it allows measuring other properties that can be predicted through the constraints, including their statistical fluctuations. In the seminar, I will push this idea to the limit to propose experimental research lines on systems such as food webs and mutualistic networks around concepts such as stability vs. entropy, fluctuations vs. induced variance (perturbations), and realistic vs. null network models. 

Lecture 1. 

04/03/2025, 09:00-11:00 (Sagrestia, San Francesco complex). 

Also online at http://imt.lu/sagrestia.

Lecture 2. 

05/03/2025, 11:00-13:00 (Aula 2, San Francesco complex). 

Also online at http://imt.lu/aula2.

Block 1. Deterministic dynamical systems: tools and methods

14/04/2023, 11:00-13:00 (Sagrestia, San Francesco complex) and 14:00-16:00 (Sagrestia, San Francesco complex). 

Also online at http://imt.lu/seminar.

The first block is devoted to the description of the basic mathematical tools, needed to study determinisitic dynamical systems. As applications we discuss how to characterize the dynamics by statistical methods (symbolic representation, etc) and by its spectrum of Lyapunov exponents, making use of analytical and numerical techniques. Topics include:

• An introduction to dynamical systems: fluxes and maps;

• Mathematical ingredients: singular points, manifolds, Poincarè section, chaotic scenarios;

• Dissipative and conservative dynamical systems;

• Stability analysis: Lyapunov spectra (covariant definition).

Block 2. Dynamical evolutions in spatially extended systems

28/04/2023, 11:00-13:00 (Sagrestia, San Francesco complex) and 14:00-16:00 (Sagrestia, San Francesco complex).

Also online at http://imt.lu/seminar.

The second block deals with deterministic dynamical systems made of many degrees of freedom, organized on lattices and networks. Applications will be focused on the relation of hydrodynamics with the Lyapunov spectrum in conservative systems, on the spectral method for solving transport problems in disordered harmonic chains and on suitable methods (stable chaos, heterogeneous mean-field) for models of neural networks. Topics include:

• Dynamics in systems with many degrees of freedom;

• Dynamics and disorder: transport in harmonic chains;

• Coupled maps, networks and stable chaos.

Block 3. Stochastic dynamics: basic ingredients

12/05/2023, 11:00-13:00 (Sagrestia, San Francesco complex) and 14:00-16:00 (Conference Room, San Ponziano complex). 

Also online at http://imt.lu/seminar.

The third block provides an introduction to stochastic processes in discrete-time (Markov chains) and continuous time (Langevin, Fokker-Planck). For what concerns applications we focus on simple examples of Markov processes (random walker on a ring, Monte-Carlo algorithms) and on models of anomalous diffusion. Topics include:

• Markov Chains  and their spectral properties (ergodicity);

• Stochastic dynamics: Langevin and Fokker-Planck;

• Anomalous diffusion.

Block 4. Stochastic processes, reversibility and fluctuation relations

26/05/2023, 11:00-13:00 (Sagrestia, San Francesco complex) and 14:00-16:00 (Sagrestia, San Francesco complex). 

Also online at http://imt.lu/seminar.

The fourth block deals with the problem of “irreversibility” in stochastic processes in the framework of the Chapman Kolmogorov equation and on the basic aspects of fluctuation-dissipation relations. Applications are devoted to outline the general approach to solve “first passage problems” and also to describe Jarzinsky, Crooks and Gallavotti-Cohen relations, associated with fluctuating thermodynamics. The final comments will be about linear response theory and coupled transport. Topics include:

• Chapman-Kolmogorov equations (first-passage problem);

• Fluctuation-dissipation and stochastic thermodynamics;

• Linear response theory and transport.

Workshop 1. Network coarse-graining

27/11/2019, 9:00-13:00 (Aula 2, San Francesco complex)

Network coarse-graining refers to the reduction of a larger network to a smaller version of it, by keeping certain properties preserved. This procedure is needed in a diverse range of disciplines, especially when the original network is too big to be dealt with mathematically, computationally or experimentally. The mini-workshop aims at exposing different techniques that have been proposed across disciplines (most prominently mathematics, physics and computer science), and to highlight the open challenges that require a multidisciplinary approach.

Program:

• 09:00 Luca Avena: "Renormalisation for graphs and signals on graphs via random walk kernels"

• 10:30 Mirco Tribastone: "Automatic simplification of large-scale reaction networks"

• 11:00 Coffee break

• 11:30 Margherita Lalli: "Spectral coarse graining of complex networks"

• 12:00 Diego Garlaschelli: "Multiscale network renormalization: scale-invariance without geometry"

• 12:30 Matteo Serafino: "Scale-free networks revealed from finite-size scaling"

• 13:00 Lunch

Workshop 2. Brain networks and metastability

27/11/2019, 9:00-13:00 (Aula 2, San Francesco complex)

Metastability is the property of systems that, before eventually reaching a completely stable state, visit a number of intermediate states that are temporarily and transiently stable. This workshop aims at introducing some mathematical aspects of metastability and discussing the potential applications to the empirical analysis of brain networks, especially in relation to the presence of possible transient neural states and/or modular functional structures.

Program: 

• 09:00 Luca Avena: "Mesoscopic explorations of graphs through random rooted forests"

• 10:30 Tommaso Gili: "Functional brain networks dynamics: from time series to metastability"

• 11:00 Coffee break

• 11:30 Rossana Mastrandrea: "Functional brain networks in schizophrenic patients and healthy individuals"

• 12:00 Virginia Gurioli: "Reconstruction of functional connectivity brain network in healthy subjects and schizophrenic patients"

• 12:15 Adrian Ioan Onicaș: "Detecting task events in fMRI time series based on the topological structure of visibility graphs"

• 12:30 Francesca Santucci: "Statistical inference for brain network construction"

• 12:45 Diego Garlaschelli: "Communities from brain correlation matrices: functional modules without functional networks"

• 13:00 Lunch