Related papers: Simple models for scaling in phylogenetic trees

Many physical systems share the property of scale invariance. Most of them show ordinary power-law scaling, where quantities can be expressed as a leading power law times a scaling function which depends on scaling-invariant ratios of the…

When training deep neural networks, a model's generalization error is often observed to follow a power scaling law dependent both on the model size and the data size. Perhaps the best known example of such scaling laws are for…

The population loss of trained deep neural networks often follows precise power-law scaling relations with either the size of the training dataset or the number of parameters in the network. We propose a theory that explains the origins of…

We study the asymptotic number of certain monotonically labeled increasing trees arising from a generalized evolution process. The main difference between the presented model and the classical model of binary increasing trees is that the…

Phylogenetics is now fundamental in life sciences, providing insights into the earliest branches of life and the origins and spread of epidemics. However, finding suitable phylogenies from the vast space of possible trees remains…

Random forests are classical ensemble algorithms that construct multiple randomized decision trees and aggregate their predictions using naive averaging. \citet{zhou2019deep} further propose a deep forest algorithm with multi-layer forests,…

Allometric scaling can reflect underlying mechanisms, dynamics and structures in complex systems; examples include typical scaling laws in biology, ecology and urban development. In this work, we study allometric scaling in scientific…

Recent studies on the phenomenology of ageing in certain many-particle systems which are at a critical point of their non-equilibrium steady-states, are reviewed. Examples include the contact process, the parity-conserving…

It has recently been discovered that many biological systems, when represented as graphs, exhibit a scale-free topology. One such system is the set of structural relationships among protein domains. The scale-free nature of this and other…

We extend classical results on simple varieties of trees (asymptotic enumeration, average behavior of tree parameters) to trees counted by their number of leaves. Motivated by genome comparison of related species, we then apply these…

Scale-free networks are prevalently observed in a great variety of complex systems, which triggers various researches relevant to networked models of such type. In this work, we propose a family of growth tree networks $\mathcal{T}_{t}$,…

We examine an interacting particle system on trees commonly referred to as the frog model. For its initial state, it begins with a single active particle at the root and i.i.d. $\mathrm{Poiss}(\lambda)$ many inactive particles at each…

In this article, we construct a generalization of the Blum-Fran\c{c}ois Beta-splitting model for evolutionary trees, which was itself inspired by Aldous' Beta-splitting model on cladograms. The novelty of our approach allows for asymmetric…

We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing…

The best-performing models in ML are not interpretable. If we can explain why they outperform, we may be able to replicate these mechanisms and obtain both interpretability and performance. One example are decision trees and their…

Phylogenetic trees constitute an interesting class of objects for stochastic processes due to the non-standard nature of the space they inhabit. In particular, many statistical applications require the construction of Markov processes on…

In this article we study the treewidth of the \emph{display graph}, an auxiliary graph structure obtained from the fusion of phylogenetic (i.e., evolutionary) trees at their leaves. Earlier work has shown that the treewidth of the display…

Phylogenetic networks are becoming of increasing interest to evolutionary biologists due to their ability to capture complex non-treelike evolutionary processes. From a combinatorial point of view, such networks are certain types of rooted…

Scaling laws describe how learning performance improves with data, compute, or training time, and have become a central theme in modern deep learning. We study this phenomenon in a canonical nonlinear model: phase retrieval with anisotropic…

Scaling behavior of scale-free evolving networks arising in communications, citations, collaborations, etc. areas is studied. We derive universal scaling relations describing properties of such networks and indicate limits of their…