Elena Agliari
Last Update 20/07/2023
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    • Previous Courses >
      • Metodi Matematici e Informatici per la Biologia 15/16
      • Mathematics for AI (2017)
      • Metodi e Modelli Matematici per l'Ambiente 16/17
      • Metodi e Modelli Matematici per l'Ambiente 17/18
      • Metodi e Modelli Matematici per l'Ambiente 18/19
      • Machine Learning (Unbound Prometheus Program - Summer '19)
      • Modelli di Reti Neurali 19/20
      • Calcolo e Biostatistica 19/20
      • Modelli di Reti Neurali 20/21
      • Calcolo e Biostatistica 20/21
      • Metodi e Modelli Matematici e Informatici 21/22
    • Modelli di Reti Neurali 21/22
    • Calcolo e Biostatistica 22/23
    • Modelli di Reti Neurali 22/23
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Areas of Research:

Neural networks
Statistical Mechanics of Complex Systems and their Applications
Quantum Walks and quantum algorithms for searching problems
Random Walks in Inhomogeneous Topologies
Applications of Statistical Mechanics
Graph Theory and applications

Neural networks

Proof of the equivalence between formal "Hopfield networks" (i.e., the standard model for associative retrieval) and "Boltzmann machines" (i.e., the standard model for learning processes), and development of a comprehensive theory of the fluctuations of the order parameters to control analytically phase transitions in these models. Extension to more sophisticated multi-species Hopfield models toward a rational for deep learning.
In this field one of the most significant results is the introduction of the first attractor neural network able to process in parallel the information. Extension to non-trivial topologies and to high-storage regimes were also investigate.

Selected publications:
  • Non-convex multi-species Hopfield models ​ 
E Agliari, D Migliozzi, D Tantari 
to appear in Journal of Statistical Physics (2018)
  • Retrieving infinite numbers of patterns in a spin-glass model of immune networks
E Agliari, A Annibale, A Barra, ACC Coolen, D Tantari
Europhysics Letters 117, 28003 (2017)
  • Retrieval capabilities of hierarchical networks: From Dyson to Hopfield
E Agliari, A Barra, A Galluzzi, F Guerra, D Tantari, F Tavani
Physical Review Letters 114, 028103 (2015)
  • Hierarchical neural networks perform both serial and parallel processing
E Agliari, A Barra, A Galluzzi, F Guerra, D Tantari, F Tavani
Neural Networks 66, 22–35 (2015)
  • ​Parallel retrieval of correlated patterns: From Hopfield networks to Boltzmann machines
E Agliari, A Barra, A De Antoni, A Galluzzi
Neural Networks 38, 52-63 (2013)
  • Multitasking associative networks
E Agliari, A Barra, A Galluzzi, F Guerra, F Moauro
Physical Review Letters 109 (26), 268101 (2012
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Statistical Mechanics of Complex Systems and their Applications

Extension of techniques of analytical mechanics to solve complex problems (e.g., evaluation of the free energy of spin-glasses at low temperatures) in mean-field approximation (e.g., method of Hamilton-Jacobi, Noether invariants and Legendre transformations via Cole-Hopf transformation, Fourier methods). 
Analytical solution of non-mean-field models (e.g. embedded in hierarchical structures) and characterization of emerging metastable states.
Generalization of two-body problems to the case of many bodies (p-spin), in fully-connected structures as well as diluted structures; these problems were solved by extending classical methods of disordered systems (field cavities and stochastic stability).

Selected publications:
  • Metastable states in the hierarchical Dyson model drive parallel processing in the hierarchical Hopfield network
E Agliari, A Barra, A Galluzzi, F Guerra, D Tantari, F Tavani
Journal of Physics A: Mathematical and Theoretical 48 (1), 015001 (2015)
  •  Notes on the p-spin glass studied via Hamilton-Jacobi and smooth-cavity techniques
E Agliari, A Barra, R Burioni, A Di Biasio
Journal of Mathematical Physics 53 (6), 063304 (2012)
  • Notes on ferromagnetic diluted p-spin model
E Agliari, A Barra, F Camboni, 
Reports on Mathematical Physics 68, 1 (2011)
  • Criticality in diluted ferromagnets
E Agliari, A Barra, F Camboni
Journal of Statistical Mechanics: Theory and Experiment P10003 (2008)​
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Random Walks in Inhomogeneous Topologies

Rigorous solution of first-passage problems in low-dimension and/or non-exactly-decimable structures, possibly accounting for  memory effects and splitting between local and average phenomena.  
Extension of the mean-field techniques for the treatment of processes defined in restricted geometries where the mixing hypothesis does not hold. These results were used in two main areas: "search strategies" and "reaction diffusion".

Selected publications:
  • Scaling laws for diffusion on (trans)fractal scale-free networks
J Peng, E Agliari
Chaos 27, 083108 (2017)
  • Lévy flights with power-law absorption
L Cattivelli, E Agliari, F Sartori, D Cassi
Physical Review E 92, 042156 (2015)
  • Slow encounters of particle pairs in branched structures
E Agliari, A Blumen, D Cassi
Physical Review E 89 (5), 052147 (2014)
  • Exact calculations of first-passage quantities on recursive networks
B Meyer, E Agliari, O Bénichou, R Voituriez
Physical Review E 85 (2), 026113 (2012)
  • Exact mean first-passage time on the T-graph
E Agliari
Physical Review E 77 (1), 011128 (2008)​​
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Quantum walks and quantum algorithms for searching problems

Quantum walks were used to model the coherent motion of excitons in discretizable structures, possibly in the presence of reaction centers. 
Development of rigorous analytical techniques based on spectral theory and numerical methods based on the diagonalization of the Laplacian associated to the structure underlying the dynamic process. These results allowed us to show that, in the quantum computational theory, d = 4 is not an upper critical dimension.

Selected publications:​
  • Quantum-walk approach to searching on fractal structures
E Agliari, A Blumen, O Muelken
Physical Review A 82 (1), 012305 (2010)​
  • Continuous-time quantum walks and trapping
E Agliari, O Mülken, A Blumen
International Journal of Bifurcation and Chaos 20 (02), 271-279 (2010)​
  • Dynamics of continuous-time quantum walks in restricted geometries
E Agliari, A Blumen, O Mülken
Journal of Physics A: Mathematical and Theoretical 41 (44), 445301 (2008)
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Graph Theory and applications

Topological characterization of inhomogeneous structures through algebraic and spectral methods to probe local and average properties (e.g., transience, local dimension, connectivity, mixing time) [14].
The role of these properties on the behavior of random processes defined on the same topologies was also deepened in different contexts [22,28,29].

Selected publications:​
  • The exact Laplacian spectrum for the Dyson hierarchical network
 E Agliari, F Tavani 
Scientific Reports 7, 39962 (2017)
  • Percolation on correlated random networks, 
E Agliari, C Cioli, E Guadagnini
Physical Review E 84, 031120 (2011)
  • A Hebbian approach to complex-network generation
E Agliari, A Barra
Europhysics Letters 94 (1), 10002 (2011)
  • Metric characterization of cluster dynamics on the Sierpinski gasket
E Agliari, M Casartelli, E Vivo
Journal of Statistical Mechanics: Theory and Experiment P09002 (2010)
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Applications of Statistical Mechanics

From the analytical investigations described above, we developed several applications in many fields of research: theoretical immunology,  infectivology, chemical kinetics, quantitative sociology; the validity of our models was checked versus experimental data.

Selected publications:​
​
  • Organs on chip approach: a tool to evaluate cancer-immune cells interactions
E Biselli, E Agliari, A Barra, FR Bertani, A Gerardino et al. 
Scientific Reports 7, 12737 (2017)
  • Assessing the role of migration as trade-facilitator using the statistical mechanics of cooperative systems
A Barra, A Galluzzi, D Tantari, E Agliari, F Requena-Silvente
Palgrave Communications 2, 16021 (2016)
  • Complete integrability of information processing by biochemical reactions
E Agliari, A Barra, L Dello Schiavo, A Moro 
​Scientific Reports 6, 36314 (2016)
  • Notes on stochastic (bio)-logic gates: the role of allosteric cooperativity
E Agliari, M Altavilla, A Barra, L Dello Schiavo, E Katz
Scientific Reports 5, 9415 (2015)
  • Anergy in self-directed B lymphocytes: a statistical mechanics perspective
E Agliari, A Barra, G Del Ferraro, F Guerra, D Tantari
Journal of theoretical biology 375, 21-31 (2015)
  • Cancer-driven dynamics of immune cells in a microfluidic environment
E Agliari, E Biselli, A De Ninno, G Schiavoni, L Gabriele, A Gerardino, F Mattei, A Barra, L Businaro
Scientific Reports 4, 6639 (2014)
  • Application of a stochastic modeling to assess the evolution of tuberculous and non-tuberculous mycobacterial infection in patients treated with tumor necrosis factor inhibitors
E Agliari, L Asti, A Barra, R Scrivo, G Valesini, RS Wallis
PloS ONE 8 (1), e55017 (2013)​​
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