相关论文: Dynamics and Endogeny for recursive processes on t…

We argue that the stochastic dynamics of interacting agents which replicate, mutate and die constitutes a non-equilibrium physical process akin to aging in complex materials. Specifically, our study uses extensive computer simulations of…

Can sustained open-ended technological progress preserve natural resources in a finite planet? We address this question on the basis of a stylized model with genuine open-ended technological innovation, where an innovation event corresponds…

Random spanning trees are among the most prominent determinantal point processes. We give four examples of random spanning trees on ladder-like graphs whose rungs form stationary renewal processes or regenerative processes of order two,…

We calculate the density and expectation for the number of lineages in a reconstructed tree with $n$ extant species. This is done with conditioning on the age of the tree as well as with assuming a uniform prior for the age of the tree.

We define a novel quantitative strategy inspired by the ecological notion of nestedness to single out the scale at which innovation complexity emerges from the aggregation of specialized building blocks. Our analysis not only suggests that…

A fringe subtree of a rooted tree is a subtree induced by one of the vertices and all its descendants. We consider the problem of estimating the number of distinct fringe subtrees in two types of random trees: simply generated trees and…

Random processes with stationary increments and intrinsic random processes are two concepts commonly used to deal with non-stationary random processes. They are broader classes than stationary random processes and conceptually closely…

Bounded infinite graphs are defined on the basis of natural physical requirements. When specialized to trees this definition leads to a natural conjecture that the average connectivity dimension of bounded trees cannot exceed two. We verify…

Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…

We study systems of {\sigma}-algebras ordered by refinement and introduce the notion of an endogenous probability measure, invariant under admissible refinement transformations. We prove existence and structural properties of such measures…

We show that the action of two infinite commuting invariant rings of endomorphisms of a finite-dimensional virtually connected irreducible bi-module linearizes into a vector space over a definable field. The same holds if the action is…

Consider a uniformly sampled random $d$-regular graph on $n$ vertices. If $d$ is fixed and $n$ goes to $\infty$ then we can relate typical (large probability) properties of such random graph to a family of invariant random processes (called…

We expose a mechanism for the dynamical generation and control of light states with diverse topologies in spiraling guiding structures. Specifically, we show that spiraling shallow refractive index landscapes induce coupling and periodic…

Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…

We study a problem of damping a control system described by functional-differential equations of natural order $n$ and neutral type with non-smooth complex coefficients on an arbitrary tree with global delay. The latter means that the delay…

We propose a theoretical model for species that is focused on intrinsic organization and processes. Specifically, we regard species to be networks of organisms integrated by reproductive mechanisms (e.g., conjugation, meiosis, syngamy)…

Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations.…

A stochastic model of excitatory and inhibitory interactions which bears universality traits is introduced and studied. The endogenous component of noise, stemming from finite size corrections, drives robust inter-nodes correlations, that…

Natural systems are remarkably robust and resilient, maintaining essential functions despite variability, uncertainty, and hostile conditions. Understanding these nonlinear, dynamic behaviours is challenging because such systems involve…

Biodiversity widely observed in ecological systems is attributed to the dynamical balance among the competing species. The time-varying populations of the interacting species are often captured rather well by a set of deterministic…