Related papers: Loewner Theory in annulus I: evolution families an…
In the present work we analyze the problem of adaptation and evolution of RNA virus populations, by defining the basic stochastic model as a multivariate branching process in close relation with the branching process advanced by Demetrius,…
In the first part of our paper we analyze bisolutions and inverses of (non-autonomous) evolution equations. We are mostly interested in pseudo-unitary evolutions on Krein spaces, which naturally arise in linear Quantum Field Theory. We…
We formulate the notion of continuous evolution algebra in terms of differentiable matrix-valued functions, to then study those such algebras arising as solutions of ODE problems. Given their dependence on natural bases, matrix Lie groups…
Growth fronts of slime molds are characterized through a direct geometric analysis based on Loewner evolutions, using experimentally acquired time-resolved images. The associated Loewner driving functions reconstructed from expanding…
This paper invokes a new mechanism for reducing a coupled system of fields (including Einstein's equations without a cosmological constant) to equations that possess solutions exhibiting characteristics of immediate relevance to current…
The Loewner framework is one of the most successful data-driven model order reduction techniques. If $N$ is the cardinality of a given data set, the so-called Loewner and shifted Loewner matrices $\mathbb{L}\in\mathbb{C}^{N\times N}$ and…
We use the Springer correspondence to give a partial characterization of the irreducible representations which appear in the Tymoczko dot-action of the Weyl group on the cohomology ring of a regular semisimple Hessenberg variety. In type A,…
Assuming the existence of a general nonuniform dichotomy for the evolution operator of a non-autonomous ordinary linear differential equation in a Banach space, we establish the existence of invariant stable manifolds for the semiflow…
In 1994, P.-G. Becker and W. Bergweiler listed all the differentially algebraic solutions of three famous functional equations: the Schr{\"o}der's, B{\"o}ttcher's and Abel's equations. The proof of this theorem combines various domains of…
A tendency in biological theorizing is to formulate principles above or equal to Evolution by Variation and Selection of Darwin and Wallace. In this letter I analyze one such recent proposal which did so for the developmental ascendency. I…
We provide explicit formulas of non-recursive type for the linearizing transformations of a non-resonant analytic germ of diffeomorphism at a fixed point or a non-resonant analytic germ of vector field at a singular point, in any complex…
Cooperation is a widespread natural phenomenon yet current evolutionary thinking is dominated by the paradigm of selfish competition. Recent advanced in many fronts of Biology and Non-linear Physics are helping to bring cooperation to its…
This chapter is an overview of foundational results in the mathematical theory of replicator systems. Its primary aim is to provide a unified framework for the mathematical formalisation of evolutionary processes in the spirit of…
We propose a generalization of Schramm-Loewner evolution (SLE) that has internal degrees of freedom described by an affine Lie superalgebra. We give a general formulation of SLE corresponding to representation theory of an affine Lie…
Our understanding of past evolutionary change is often based on reconstructions based on incomplete data, raising fundamental questions about the degree to which we can make reliable inferences about past evolutionary processes. This was…
We show that the standard discrete update rule of transformer layers can be naturally interpreted as a forward Euler discretization of a continuous dynamical system. Our Transformer Flow Approximation Theorem demonstrates that, under…
Recently there have been several attempts to provide a whole set of generators of the ideal of the algebraic variety associated to a phylogenetic tree evolving under an algebraic model. These algebraic varieties have been proven to be…
The fundamental lemma by Jan C. Willems and co-workers, which is deeply rooted in behavioral systems theory, has become one of the supporting pillars of the recent progress on data-driven control and system analysis. This tutorial-style…
By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on…
It is discussed how stochastic evolutions may be linked to logarithmic conformal field theory. This introduces an extension of the stochastic Loewner evolutions. Based on the existence of a logarithmic null vector in an indecomposable…