Some exact results for the statistical physics problem of high-dimensional linear regression

AMA. Mozeika F F. AntenucciACA. CoolenFA M Arxiv

Exact linear regression

Exact methods supersede approximations used in high-dimensional linear regression to find correlations in statistical physics problems.

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.

Recursively abundant and recursively perfect numbers

TFT. Fink Arxiv

Ample & pristine numbers

Parallels between the perfect and abundant numbers and their recursive analogs point to deeper structure in the recursive divisor function.

Replica analysis of overfitting in generalized linear models

ACA. CoolenAMA. MozeikaFAF. AntenucciMSFA Journal of Physics A

Replica analysis of overfitting

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


7 Mathematical Finance

Network valuation in financial systems

Consistent valuation of interbank claims within an interconnected financial system can be found with a recursive update of banks' equities.


4 Harvard Business Review

Taming complexity

Insights from biology, physics and business shed light on the nature and costs of complexity and how to manage it in business organizations.


1 Arxiv

Recursively divisible numbers

Recursively divisible numbers are a new kind of number that are highly divisible, whose quotients are highly divisible, and so on.


2 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.


2 Arxiv

The mathematical structure of innovation

A theoretical model of recursive innovation suggests that new technologies are recursively built up from new combinations of existing ones.


2 Journal of Economic Interaction and Coordination

Bursting dynamic networks

A mathematical model captures the temporal and steady state behaviour of networks whose two sets of nodes either generate or destroy links.


2 Physical Review E

Geometry of discrete space

A phase transition creates the geometry of the continuum from discrete space, but it needs disorder if it is to have the right metric.


4 Scientific Reports

Energy harvesting with AI

Machine learning techniques enhance the efficiency of energy harvesters by implementing reversible energy-conserving operations.

2 Sub. to Physical Review D

Scale of non-locality

The number of particles in a higher derivative theory of gravity relates to its effective mass scale, which signals the theory’s viability.

2 Science Advances

The rate of innovation

The distribution of product complexity helps explain why some technology sectors tend to exhibit faster innovation rates than others.


Memristive networks

A simple solvable model of memristive networks suggests a correspondence between the asymptotic states of memristors and the Ising model.

6 Nature Reviews Physics

Physics of networks

Statistical physics harnesses links between maximum entropy and information theory to capture null model and real-world network features.

3 Foundations of Physics

A Hamiltonian recipe

An explicit recipe for defining the Hamiltonian in general probabilistic theories, which have the potential to generalise quantum theory.

4 Physical Review Materials

Grain shape inference

The distributions of size and shape of a material’s grains can be constructed from a 2D slice of the material and electron diffraction data.

2 European Physical Journal B

Exactly solvable model of memristive circuits: Lyapunov functional and mean field theory

In this paper we sketch a general methodology for studying the phase diagram of memristive circuits.

3 Journal of Statistical Physics

Information asymmetry

Network users who have access to the network’s most informative node, as quantified by a novel index, the InfoRank, have a competitive edge.

4 Physical Review E

One-shot statistic

One-shot analogs of fluctuation-theorem results help unify these two approaches for small-scale, nonequilibrium statistical physics.

3 European Journal of Combinatorics

Hypercube eigenvalues

Hamming balls, subgraphs of the hypercube, maximise the graph’s largest eigenvalue exactly when the dimension of the cube is large enough.

4 ACM Transactions on Modeling and Computer Simulation

Volunteer clouds

A novel approach to volunteer clouds outperforms traditional distributed task scheduling algorithms in the presence of intensive workloads.

4 Journal of Statistical Physics

From ecology to finance

Bipartite networks model the structures of ecological and economic real-world systems, enabling hypothesis testing and crisis forecasting.

7 Technological Forecasting and Social Change

How well do experience curves predict technological progress? A method for making distributional forecasts

We presented a method to test the accuracy and validity of experience curve forecasts.


Resolution of ranking hierarchies in directed networks

Identifying ranking hierarchies in complex networks is of paramount importance in many disciplines and applications

2 Computational Management Science

The interbank network

The large-scale structure of the interbank network changes drastically in times of crisis due to the effect of measures from central banks.

4 Journal of Physics A

Exactly solvable random graph

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

3 Strategy Science

The science of strategy

The usefulness of components and the complexity of products inform the best strategy for innovation at different stages of the process.

4 Nature Communications

Serendipity and strategy

In systems of innovation, the relative usefulness of different components changes as the number of components we possess increases.

3 Journal of Computational Social Science

Network models of financial systemic risk: a review

Stylized balance sheet of a bank

4 Scientific Reports

Bayesian analysis of medical data

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

4 Physical Review B

Dirac cones in 2D borane

Theoretical searches propose 2D borane as a new graphene-like material which is stable and semi-metallic with Dirac cone structure.

5 Nature Quantum Information

Quantum neural networks

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

3 Physical Review E

Enhanced capital-asset pricing model for bipartite financial networks reconstruction

The challenge of statistical reconstruction is using the limited available information to predict stock holdings.

3 Physical Review E

Bipartite trade network

A new algorithm unveils complicated structures in the bipartite mapping between countries and products of the international trade network.

4 Proceedings of the Royal Society A

Quantum thermodynamics

Spectroscopy experiments show that energy shifts due to photon emission from individual molecules satisfy a fundamental quantum relation.


Debunking in a world of tribes

When people operate in echo chambers, they focus on information adhering to their system of beliefs. Debunking them is harder than it seems

3 Mineralogical Magazine

3d grains from 2d slices

Moment-based methods provide a simple way to describe a population of spherical particles and extract 3d information from 2d measurements.

1 Physical Review E

Spectral partitioning

The spectral density of graph ensembles provides an exact solution to the graph partitioning problem and helps detect community structure.

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.

6 New Journal of Physics

Entropic equality for worst-case work at any protocol speed

A battery from which work is taken or given to a single heat bath.

4 MIT Sloan Management Review

Harnessing the secret structure of innovation

Firms can harness the shifting importance of component building blocks to build better products and services.

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.

4 Nature Communications

Pathways towards instability

Processes believed to stabilize financial markets can drive them towards instability by creating cyclical structures that amplify distress.

4 Journal of Statistical Mechanics: Theory and Experiment

Disentangling group and link persistence in Dynamic Stochastic Block models

We present a new way of finding communities in networks that change over time.

2 Physical Review E

Optimal heat exchange networks

Compact heat exchangers can be designed to run at low power if the exchange is concentrated in a crumpled surface fed by a fractal network.

4 Physical Review E

Optimal growth rates

An extension of the Kelly criterion maximises the growth rate of multiplicative stochastic processes when limited resources are available.

5 Proceedings of the National Academy of Sciences

The price of complexity

Increasing the complexity of the network of contracts between financial institutions decreases the accuracy of estimating systemic risk.

2 Physical Review Letters

Tunnelling interpreted

In quantum tunnelling, a particle tunnels through a barrier that it classically could not surmount.

2 Royal Society

Form and function in gene regulatory networks

The structure of network motifs determines fundamental properties of their dynamical state space.

4 Physica D Nonlinear Phenomena

Cascades in flow networks

Coupled distribution grids are more vulnerable to a cascading systemic failure but they have larger safe regions within their networks.


Bounds on transient instability for complex ecosystems

Pseudospectrum of a random community matrix with S = 50, C = 0.1, μ = 1 and σ = 0.3, which is asymptotically stable.

3 Journal of Statistical Mechanics: Theory and Experiment

Emergence of strongly connected components in continuum disk-spin percolation

Single realization of random positions and orientations of 100 disks with an external field pointing in the direction of the red arrow.

2 Research Policy

How predictable is technological progress?

Predicting the evolution of technology allow us to make better investments and policies.

2 Classical and Quantum Gravity

Geometric phases and cyclic isotropic cosmologies

Does a scalar field maintain a quantum memory from previous bounces?

5 Discrete Mathematics

Eigenvalues of neutral networks: Interpolating between hypercubes

The first 16 ‘‘bricklayer’s graphs’’ and the principal eigenvalue of their adjacency matrices.

6 Physical Review Letters

Photonic Maxwell’s demon

By analogy with Maxwell’s original thought experiment, the setup uses energy extracted from a thermal system.


Coupling news sentiment with web browsing data improves prediction of intra-day price dynamics

Complementary of the cumulative distribution function of the number of clicks a news receives for the ten assets.

4 Transactions of the American Mathematical Society

Subcritical U-Bootstrap percolation models have non-trivial phase transitions

Our results re-open the study of critical probabilities in bootstrap percolation on infinite lattices.

3 Physical Review E

Communities in networks

A new tool derived from information theory quantitatively identifies trees, hierarchies and community structures within complex networks.


The effects of Twitter sentiment on stock price returns

Distribution of sentiment polarity for the 260 detected Twitter peaks

3 Physical Review E

Democracy in networks

Analysis of the hyperbolicity of real-world networks distinguishes between those which are aristocratic and those which are democratic.

3 Journal of the Royal Society Interface

Quantifying noise in mass spectrometry and yeast two-hybrid protein interaction detection experiments

Protein detection experiments seek to measure for each pair of protein species whether they interact in any complex.

3 Forum of Mathematics, Sigma

Transference for the Erdős-Ko-Rado theorem

Two constructions for an intersecting family of r-sets.


Twitter-based analysis of the dynamics of collective attention to political parties

Daily tweet volume for each party around elections

4 New Journal of Physics

A measure of majorization emerging from single-shot statistical mechanics

Abstract depiction of the set of states, including the initial state ρ and final state σ . Each state is associated wi

2 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.


DebtRank: a microscopic foundation for shock propagation

The DebtRank algorithm was introduced to account for the build-up of distress in the markets, before the occurrence of defaults.

1 Journal of Economic Dynamics and Control

Self-organization of knowledge economies

Simulations for 106 periods, using different social networks.

2 Physical Review B

Structures and stability of calcium and magnesium carbonates at mantle pressures

Predicting stable structures of calcium and magnesium carbonate is crucial for understanding the Earth's deep carbon cycle.

3 Network Theory of Finance

How the interbank market becomes systemically dangerous: an agent-based network model of financial distress propagation

We assess the fragility of the interbank lending market from 2004 to 2013


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.


The heterogeneous dynamics of economic complexity

The growth dynamics of countries in the fitness-income plane exhibits a high degree of heterogeneity.

2 SIAM Journal on Discrete Mathematics

Maximum percolation time in two-dimensional bootstrap percolation

What is the maximum percolation time in a two-dimensional grid?


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.

2 ESAIM: Proceedings and surveys

Random graph ensembles with many short loops

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

1 Journal of Chemical Physics

Simple heuristic for the viscosity of polydisperse hard spheres

Spheres crowd around each other in a manner that depends on their size distribution. We give a simple way to estimate the packing fraction.

3 Scientific Reports

Credit default swaps networks and systemic risk

CDS spreads over time for the selected institutions

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.

3 Physical Review Letters

Easily repairable networks

When networks come under attack, a repairable architecture is superior to, and globally distinct from, an architecture that is robust.

4 Journal of Physics A

Entanglement typicality

We provide a measure of purity of an entanglement state.

2 Physical Review B

Predicting interface structures: from SrTiO 3 to graphene

Graphene grain boundary structures between armchair and zigzag regions.

4 Electronic Journal of Probability

Bootstrap percolation on Galton–Watson trees

In bootstrap percolation, a node is infected when a sufficient number of neighbours are infected.

5 Scientific Reports

Memory effects in stock price dynamics: evidences of technical trading

Price dynamics incorporates the strategies of traders and investors in the market.


Self-healing networks: redundancy and structure

Infrastructure networks are very well engineered systems characterized by fluxes of commodities, from electric power to drinking water.

3 Physical Review E

Structural imperfections

Fractal structures need very little mass to support a load; but for current designs, this makes them vulnerable to manufacturing errors.

5 Scientific Reports

Default cascades in complex networks: topology and systemic risk

Frontier of large cascades evolution of the e-MID market in the period between January 1999 and January 2011.

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.

1 Powder Technology

Random close packing fractions of lognormal distributions of hard spheres

Lognormal distributions (and mixtures of same) are a useful model for the size distribution in emulsions and sediments.

5 Journal of Economic Dynamics and Control

Economic complexity: conceptual grounding of a new metrics for global competitiveness

We introduce a novel method to define a self-consistent and non-monetary metrics for the competitiveness of countries.


Measuring the intangibles: a metric for the economic complexity of countries and products

We present a framework to define a data-driven metrics to assess the level of competitiveness of a country.

4 Entropy

Low-temperature behaviour of social and economic networks

We define a generalized ensemble of graphs by introducing the concept of graph temperature.

5 Journal of Physics A

Immune networks: multi-tasking capabilities at medium load

An intriguing analogy exists between neural networks and immune networks.

3 Physics World

Towers of strength

The Eiffel Tower was never intended to be a permanent feature of the Parisian landscape.

3 Physical Review E

Hierarchical structures

We show that self-similar fractal structures exhibit new strength-to-mass scaling relations, offering unprecedented mechanical efficiency.

6 Scientific Reports

Evolution of controllability in interbank networks

External inputs allow us to control the state of the interbank lending network.

5 Nature Physics

Reconstructing a credit network

New mathematical tools can help infer financial networks from partial data to understand the propagation of distress through the network.

5 Nature Physics

Complex derivatives

Network-based metrics to assess systemic risk and the importance of financial institutions can help tame the financial derivatives market.

5 Journal of Statistical Physics

Bootstrapping topology and systemic risk of complex network using the fitness model

Vulnerability and systemicity do not depend only on GDP but also on the complex network of financial relations.

4 Physical Review E

Weighted network evolution

A statistical procedure identifies dominant edges within weighted networks to determine whether a network has reached its steady state.

3 Physical Review Letters

Ultralight fractal structures from hollow tubes

A material’s architecture can be controlled over an ever increasing set of length scales.


A network analysis of countries’ export flows: firm grounds for the building blocks of the economy

The network of countries and products and the two possible projections.

5 Scientific Reports

A new metric for countries’ fitness and products’ complexity

A snapshot of the bipartite network for the most important countries; size of vertices is the fitness and the complexity


Web search queries can predict stock market volumes

Graphical illustration of the analysis presented in this paper.

2 Physical Review E

Unbiased randomization

Unbiased randomisation processes generate sophisticated synthetic networks for modelling and testing the properties of real-world networks.


Clustering inverted

Edge multiplicity—the number of triangles attached to edges—is a powerful analytic tool to understand and generalize network properties.


Random cellular automata

Of the 256 elementary cellular automata, 28 of them exhibit random behavior over time, but spatio-temporal currents still lurk underneath.

2 Interface Focus

What you see is not what you get: how sampling affects macroscopic features of biological networks

It is vital that we understand in detail how the topological characteristics of a real network relate to those of a finite random network.

4 Food Biophysics

Shear elastic deformation and particle packing in plant cell dispersions

Schematic of the disruption of close-packed polyhedral cells in tomato tissue into individual cells.

2 Philosophical Magazine

Transfer operator analysis of the parallel dynamics of disordered Ising chains

The dynamics of one-dimensional Ising chains is of interest in the context of ageing phenomena.

1 Mathematics and Computers in Simulation

Diffusional Monte Carlo model of liquid-phase sintering

Our Monte Carlo model sheds light on the Ostwald ripening, namely the growth of big particles at the expense of the small ones.

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.

5 Physical Review E

Assessing self-assembly

The information needed to self-assemble a structure quantifies its modularity and explains the prevalence of certain structures over others.

2 Physical Review E

Ever-shrinking spheres

Techniques from random sphere packing predict the dimension of the Apollonian gasket, a fractal made up of non-overlapping hyperspheres.

2 Physica A

Tie knots, random walks and topology

The thirteen canonical knot classes and the corresponding most aesthetic knots.


Strategy for conkers

In single elimination competition the best indicator of success is a player's wealth: the accumulated wealth of all defeated players.


Microstructural coarsening

Rapid temperature cycling from one extreme to another affects the rate at which the mean particle size in solid or liquid solutions changes.