Related papers: Loewner Theory in annulus II: Loewner chains
Stellar astrophysicists are increasingly taking into account the effects of orbiting companions on stellar evolution. New discoveries, many thanks to systematic time-domain surveys, have underlined the role of binary star interactions in a…
Self-consistent account of the most simple non-gauge vector fields leads to a broad spectrum of regular scenarios of temporal evolution of the Universe completely within the frames of the Einstein's General relativity. The longitudinal…
A stretched DNA molecule which is also under- or overwound, undergoes a buckling transition forming intertwined looped domains called plectonemes. Here we develop a simple theory that extends the two-phase model of stretched supercoiled…
Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…
The probability distributions for bending angles in double helical DNA obtained in all-atom molecular dynamics simulations are compared with theoretical predictions. The computed distributions remarkably agree with the worm-like chain…
Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…
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…
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…
This paper studies the dynamics and integrability of a variable-length coupled pendulum system. The complexity of the model is presented by joining various numerical methods, such as the Poincar\'e cross-sections, phase-parametric diagrams,…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
A category of Brauer diagrams, analogous to Turaev's tangle category, is introduced, and a presentation of the category is given; specifically, we prove that seven relations among its four generating homomorphisms suffice to deduce all…
We present a systematic approach for the semiclassical treatment of many-body dynamics of interacting, open spin systems. Our approach overcomes some of the shortcomings of the recently developed discrete truncated Wigner approximation…
A crucial step in the history of General Relativity was Einstein's adoption of the principle of general covariance which demands a coordinate independent formulation for our spacetime theories. General covariance helps us to disentangle a…
A novel framework for the analysis of observation statistics on time discrete linear evolutions in Banach space is presented. The model differs from traditional models for stochastic processes and, in particular, clearly distinguishes…
We present the first complete confirmation of Granovetter's theory of social networks using a massive dataset. For this purpose, we study a scientific collaboration network, which is considered one of the most important examples that…
In this paper, we interpret Deep Neural Networks with Complex Network Theory. Complex Network Theory (CNT) represents Deep Neural Networks (DNNs) as directed weighted graphs to study them as dynamical systems. We efficiently adapt CNT…
We present an alternative domain concerning mathematics to investigate universal evolution mechanisms by focusing on large cycles theory (LCT) - a simplified version of well-known hamiltonian graph theory. LCT joins together a number of…
The two-parameter Macdonald polynomials are a central object of algebraic combinatorics and representation theory. We give a Markov chain on partitions of k with eigenfunctions the coefficients of the Macdonald polynomials when expanded in…
This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion…
Invariants for complicated objects such as those arising in phylogenetics, whether they are invariants as matrices, polynomials, or other mathematical structures, are important tools for distinguishing and working with such objects. In this…