Statistical physics
Deep-layer distribution
The output distribution of a deep-layered machine with random logics exhibits a critical network depth, at which it is maximally biased.
TF
ArXivThe London Institute’s papers are the official record of our discoveries. They allow others to build on and apply our work. Each one is the result of many months of research, so we strive to make them clear, inspiring and beautiful, and publish them in leading journals.
Statistical physics
Deep learning simplicity
We give a theory for the output of deep-layered machines and show that, as the network depth increases, it is biased towards simple outputs.
TF
ArXiv
Statistical physics
Multiplicative loops
The dynamics of the Kauffman network can be expressed as a product of the dynamics of its disjoint loops, revealing a new algebraic structure.
TF
Physical Review Research
Combinatorics
In life, there are few rules
The bipartite nature of regulatory networks means gene-gene logics are composed, which severely restricts which ones can show up in life.
TFRH
SubmittedRHStatistical physics
Landau meets Kauffman
Insights from number theory suggest a new way to solve the critical Kauffman model, giving new bounds on the number and length of attractors.
FSTF
Journal of Physics ACombinatorics
Structure of genetic computation
The structural and functional building blocks of gene regulatory networks correspond, which tell us how genetic computation is organised.
TF
SubmittedNumber theory
Counting recursive divisors
Three new closed-form expressions give the number of recursive divisors and ordered factorisations, which were until now hard to compute.
TF
ArXivStatistical physics
Kauffman cracked
Surprisingly, the number of attractors in the critical Kauffman model with connectivity one grows exponentially with the size of the network.
TFFS
Physical Review LettersNumber theory
Recursively divisible numbers
Recursively divisible numbers are a new kind of number that are highly divisible, whose quotients are highly divisible, and so on, recursively.
TF
Journal of Number TheoryNumber theory
Recursive divisor properties
The recursive divisor function has a simple Dirichlet series that relates it to the divisor function and other standard arithmetic functions.
TF
ArXivNumber theory
Ample and pristine numbers
Parallels between the perfect and abundant numbers and their recursive analogs point to deeper structure in the recursive divisor function.
TF
ArXivEvolvability
Flowers of immortality
The eigenvalues of the mortality equation fall into two classes—the flower and the stem—but only the stem eigenvalues control the dynamics.
TFYH
ArXivEvolvability
I want to be forever young
The mortality equation governs the dynamics of an evolving population with a given maximum age, offering a theory for programmed ageing.
TF
ArXivTheory of innovation
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.
MRTFSLAL
Harvard Business ReviewTheory of innovation
Recursive structure of innovation
A theoretical model of recursive innovation suggests that new technologies are recursively built up from new combinations of existing ones.
TFIT
ArXivGeometry
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.
RFTF
Physical Review ETheory of innovation
The rate of innovation
The distribution of product complexity helps explain why some technology sectors tend to exhibit faster innovation rates than other sectors.
TFMR
Science AdvancesTheory of innovation
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.
TFMRPG
Strategy ScienceTheory of innovation
Serendipity and strategy
In systems of innovation, the relative usefulness of different components changes as the number of components we possess increases.
TFMRRFRP
Nature CommunicationsTheory of innovation
The secret structure of innovation
Firms can harness the shifting importance of component building blocks to build better products and services and hence increase their chances of sustained success.
MRTFRPJH
MIT Sloan Management ReviewDiscrete dynamics
Form and function in gene networks
The structural properties of a network motif predict its functional versatility and relate to gene regulatory networks.
TFSA
Interface FocusGraph theory
Eigenvalues of neutral networks
The principal eigenvalue of small neutral networks determines their robustness, and is bounded by the logarithm of the number of vertices.
TRRFJBAGTF
Discrete MathematicsNetwork theory
Easily repairable networks
When networks come under attack, a repairable architecture is superior to, and globally distinct from, an architecture that is robust.
RFTFJH
Physical Review LettersNetwork theory
The temperature of networks
A new concept, graph temperature, enables the prediction of distinct topological properties of real-world networks simultaneously.
TFGCDGSA
EntropyNetwork theory
Scales in weighted networks
Information theory fixes weighted networks’ degeneracy issues with a generalisation of binary graphs and an optimal scale of link intensities.
TFGCDGSA
Social InformaticsInformation theory
Assessing self-assembly
The information needed to self-assemble a structure quantifies its modularity and explains the prevalence of certain structures over others.
TFSAIJJDAL
Physical Review EDiscrete dynamics
Random cellular automata
Of the 256 elementary cellular automata, 28 of them exhibit random behavior over time, but spatio-temporal currents still lurk underneath.
TFJCSA
EPLStatistical physics
Single elimination competition
In single elimination competition the best indicator of success is a player's wealth: the accumulated wealth of all defeated players.
TFJCSA
EPL