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Replica analysis of overfitting in generalized linear models

TCT. CoolenAMA. MozeikaFAF. AntenucciMSFA Sub. to Journal of Physics A

A fix for overfitting

Statistical methods that normally fail for very high-dimensional data can be rescued via mathematical tools from statistical physics.

The space of functions computed by deep layered machines

AMA. MozeikaBLDS Physical Review Letters

Deep layered machines

The ability of deep neural networks to generalize can be unraveled using path integral methods to compute their typical Boolean functions.

Bayesian networks analysis of malocclusion data

GCG. CaldarelliMSPALF Scientific Reports

Bayesian orthodontics

Bayesian networks describe the evolution of orthodontic features on patients receiving treatment versus no treatment for malocclusion.

Quantum generalisation of feedforward neural networks

ODO. DahlstenKWHKRGMK Nature Quantum Information

Quantum neural networks

We generalise neural networks into a quantum framework, demonstrating the possibility of quantum auto-encoders and teleportation.

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1 International Journal of Parallel, Emergent and Distributed Systems

Memristive networks

Memristive networks preserve memory and have the ability to learn according to analysis of the network’s internal memory dynamics.

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3 Physical Review E

Dynamics of memristors

Exact equations of motion provide an analytical description of the evolution and relaxation properties of complex memristive circuits.

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3 EPL

From memory to scale-free

A local model of preferential attachment with short-term memory generates scale-free networks, which can be readily computed by memristors.

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4 PLOS ONE

How the taxonomy of products drives the economic development of countries

A less developed country has to learn simple capabilities in order to start a stable industrialization and development process.

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2 ESAIM: Proceedings and surveys

Random graph ensembles with many short loops

Short loops (cycles) in real networks are a theoretical challenge for modeling.

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2 Journal of Physics A

Entropies of tailored random graph ensembles: bipartite graphs, generalized degrees, and node neighbourhoods

Ensembles of tailored random graphs allow us to reason quantitatively about the complexity of system.

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5 Journal of Physics A

Immune networks: multi-tasking capabilities at medium load

An intriguing analogy exists between neural networks and immune networks.

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3 Journal of Physics A

Tailored graph ensembles as proxies or null models for real networks II: results on directed graphs

Our approach gives a rigorous quantitative method for prioritising network properties.