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Stem cells, through their ability to produce daughter stem cells and differentiate into specialized cells, are essential in the growth, maintenance, and repair of biological tissues. Understanding the dynamics of cell populations in the…
In this work we consider a mathematical model of the water treatment process and determine the effective characteristics of this model. At the microscopic length scale we describe our model in terms of a lattice random walk in a…
A new class of ``toy models'' for subaqueous bedform formation are proposed and examined. These models all show a similar mechanism of wavelength selection via bedform unification, and they may have applications to bedform stratigraphy. The…
We study the evolution of a passive scalar subject to molecular diffusion and advected by an incompressible velocity field on a 2D bounded domain. The velocity field is $u = \nabla^\perp H$, where H is an autonomous Hamiltonian whose level…
Flow-based generative models are composed of invertible transformations between two random variables of the same dimension. Therefore, flow-based models cannot be adequately trained if the dimension of the data distribution does not match…
Topological measurements are increasingly being accepted as an important tool for quantifying complex structures. In many applications, these structures can be expressed as nodal domains of real-valued functions and are obtained only…
The classical evolution equations of the Abelian Higgs model are studied at temperatures below the Ginsburg temperature of a phase transition which is assumed to be second order. It is shown that the initial thermal fluctuations provide a…
Understanding the decision-making processes of large language models is critical given their widespread applications. To achieve this, we aim to connect a formal mathematical framework - zigzag persistence from topological data analysis -…
We study the effect of learning dynamics on network topology. A network of discrete dynamical systems is considered for this purpose and the coupling strengths are made to evolve according to a temporal learning rule that is based on the…
We investigate through numerical simulations how a two-dimensional crystal yields and flows under an applied shear. We focus over a range that allows us to both address the response in the limit of an infinitesimal shear rate and describe…
We introduce Network Automata, a framework which couples the topological evolution of a network to its structure. It is useful for dealing with networks in which the topology evolves according to some specified microscopic rules and,…
This work presents a new modeling approach to macroscopic, polycrystalline elasto-plasticity starting from first principles and a few well-defined structural assumptions, incorporating the mildly rate-dependent (viscous) nature of plastic…
A recent paper by Zapletal arXiv:2404.10612 discusses permutation models of set theory which arise from dynamical ideals and highlights properties of the dynamical ideal which relate to fragments of choice in the permutation model. In this…
We propose a simple, self-consistent kinetic model for the evolution of a mixture of droplets and vapor expanding adiabatically in vacuum after rapid, almost isochoric heating. We study the evolution of the two-phase fluid at intermediate…
Previous symmetry-based database searches have already revealed ubiquitous band topology in nature, while the destiny of band topology under symmetry-breaking is yet to be studied comprehensively. Here we first develop a framework allowing…
The potential flow of two-dimensional ideal incompressible fluid with a free surface is studied. Using the theory of conformal mappings and Hamiltonian formalism allows us to derive exact equations of surface evolution. Simple form of the…
Hypothesis Understanding wetting behavior is of great importance for natural systems and technological applications. The traditional concept of contact angle, a purely geometrical measure related to curvature, is often used for…
We calculate the two-loop and one-loop/one-emission contributions required for soft gluon evolution at the next-to-leading order. The colour structures are expressed in the colour flow basis, and the kinematic dependence and loop integrals…
While a variety of fundamental differences are known to separate two-dimensional (2D) and three-dimensional (3D) fluid flows, it is not well understood how they are related. Conventionally, dimensional reduction is justified by an \emph{a…
The relation between thermodynamic phase transitions in classical systems and topology changes in their configuration space is discussed for a one-dimensional, analytically tractable solid-on-solid model. The topology of a certain family of…