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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.

Replica analysis of Bayesian data clustering

AMA. MozeikaTCT. Coolen Journal of Physics A

Replica clustering

We optimize Bayesian data clustering by mapping the problem to the statistical physics of a gas and calculating the lowest entropy state.

Exactly solvable random graph ensemble with extensively many short cycles

PBP. BaruccaFLMFAC Journal of Physics A: Mathematical and Theoretical

Exactly solvable random graph ensemble with extensively many short cycles

Controlling analytically second or higher-order properties of networks is a great mathematical challenge.

Spin systems on hypercubic Bethe lattices: a Bethe–Peierls approach

AMA. MozeikaAC Journal of Physics A

Spin systems on hypercubic Bethe lattices: a Bethe–Peierls approach

Hypercubic Bethe lattices retain many of the loops of the topology of realistic spin systems.

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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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4 Journal of Physics A

Entanglement typicality

We provide a measure of purity of an entanglement state.

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5 Journal of Physics A

Immune networks: multitasking capabilities near saturation

The immune system must simultaneously recall multiple defense strategies because many antigens can attack the host at the same time.

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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.