Related papers: The geometry of learning
This study develops a comprehensive theoretical and computational framework for Random Nonlinear Iterated Function Systems (RNIFS), a generalization of classical IFS models that incorporates both nonlinearity and stochasticity. We establish…
This study introduces a physics-based machine learning framework for modeling both brittle and ductile fractures. Unlike physics-informed neural networks, which solve partial differential equations by embedding physical laws as soft…
We check the robustness of a recently proposed dynamical model of associative Pavlovian learning that extends the Rescorla-Wagner (RW) model in a natural way and predicts progressively damped oscillations in the response of the subjects.…
This paper proposes a new method to analyze the spatial structure of urban systems using ideas from fractals. Regarding a system of cities as a set of "particles" distributed randomly on a triangular lattice, we construct a spatial…
A frequently encountered situation in the study of delay systems is that the length of the delay time changes with time, which is of relevance in many fields such as optics, mechanical machining, biology or physiology. A characteristic…
In this article, we have employed fractal formalism to calculate the Fracture Functions of the Leading neutron produced in \textit{ep} collisions. The fractal concept describes the self-similar behavior of the proton structure at Leading…
Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…
We study novel three-dimensional gapped quantum phases of matter which support quasiparticles with restricted mobility, including immobile "fracton" excitations. So far, most existing fracton models may be instructively viewed as…
For a Borel measure on the unit interval and a sequence of scales that tend to zero, we define a one-parameter family of zeta functions called multifractal zeta functions. These functions are a first attempt to associate a zeta function to…
The metriplectic formalism couples Poisson brackets of the Hamiltonian description with metric brackets for describing systems with both Hamiltonian and dissipative components. The construction builds in asymptotic convergence to a…
Fractal behavior is found on the topographies of pericellular brushes on the surfaces of model healthy and cancerous cells, using dissipative particle dynamics models and simulations. The influence of brush composition, chain stiffness and…
In chaotic reaction-diffusion systems with two degrees of freedom, the modes governing the exponential relaxation to the thermodynamic equilibrium present a fractal structure which can be characterized by a Hausdorff dimension. For long…
This paper investigates fractal dimension of linear combination of fractal continuous functions with the same or different fractal dimensions. It has been proved that: (1) $BV_{I}$ all fractal continuous functions with bounded variation is…
As well known, Hebb's learning traces its origin in Pavlov's Classical Conditioning, however, while the former has been extensively modelled in the past decades (e.g., by Hopfield model and countless variations on theme), as for the latter…
In this paper I discuss the formation of topological defects in quantum field theory and the relation between fractals and coherent states. The study of defect formation is particularly useful in the understanding of the same mathematical…
We describe the fractal solid by a special continuous medium model. We propose to describe the fractal solid by a fractional continuous model, where all characteristics and fields are defined everywhere in the volume but they follow some…
Fractal behaviour, i.e. scale invariance in spatio-temporal dynamics, have been found to describe and model many systems in nature, in particular fluid mechanics and geophysical related geometrical objects, like the convective boundary…
We focus on mesoscopic dislocation patterning via a continuum dislocation dynamics theory (CDD) in three dimensions (3D). We study three distinct physically motivated dynamics which consistently lead to fractal formation in 3D with rather…
The fractal dimension of a surface allows its degree of roughness to be characterized quantitatively. However, limited effort is attempted to calculate the fractal dimension of surfaces computed from precisely known atomic coordinates from…
Clouds in observations are fractals: they show self-similarity across scales ranging from one to 1000 km. This includes individual storms and large-scale cloud structures typical of organised convection. It is not known whether global…