Related papers: Self-Organizing Height-Arrow Model: Numerical and …
Recent experimental results for covalent glasses suggest the existence of an intermediate phase attributed to the self-organization of the glass network resulting from the tendency to minimize its internal stress. However, the exact nature…
Many topological data analysis (TDA) pipelines compute large collections of persistence diagrams, yet vectorizations and kernel methods discard the rank-induced implication relations among persistence intervals that are essential for…
We show how to construct a complete set of eigenstates of the hamiltonian of the one-dimensional Hubbard model on a lattice of even length $L$. This is done by using the nested Bethe Ansatz {\it and} the $SO(4)$ symmetry of the model. We…
The major uncertainties in studies of the multi-scale structure of the Universe arise not from observational errors but from the variety of legitimate definitions and detection methods for individual structures. To facilitate the study of…
Distributivity is a well-established and extensively studied notion in lattice theory. In the context of data analysis, particularly within Formal Concept Analysis (FCA), lattices are often observed to exhibit a high degree of…
We study several probability distributions relevant to the avalanche dynamics of elastic interfaces driven on a random substrate: The distribution of size, duration, lateral extension or area, as well as velocities. Results from the…
The Abelian Manna model of self-organized criticality is studied on various three-dimensional and fractal lattices. The exponents for avalanche size, duration and area distribution of the model are obtained by using a high-accuracy moment…
We study the Bak-Sneppen model in the probabilistic framework of the Run Time Statistics (RTS). This model has attracted a large interest for its simplicity being a prototype for the whole class of models showing Self-Organized Criticality.…
The avalanche properties of models that exhibit 'self-organized criticality' (SOC) are still mostly awaiting theoretical explanations. A recent mapping (Europhys. Lett.~53, 569) of many sandpile models to interface depinning is presented…
We develop and discuss the properties of a new class of lattice-based avalanche models of solar flares. These models are readily amenable to a relatively unambiguous physical interpretation in terms of slow twisting of a coronal loop. They…
Uniform spherical beads were used to explore the behavior of a granular system near its critical angle of repose on a conical bead pile. We found two tuning parameters that could take the system to a critical point where a simple power-law…
Building height estimation is important in many applications such as 3D city reconstruction, urban planning, and navigation. Recently, a new building height estimation method using street scene images and 2D maps was proposed. This method…
We propose a new jump-diffusion process, the Heston-Queue-Hawkes (HQH) model, combining the well-known Heston model and the recently introduced Queue-Hawkes (Q-Hawkes) jump process. Like the Hawkes process, the HQH model can capture the…
This paper deals with a clustering algorithm for histogram data based on a Self-Organizing Map (SOM) learning. It combines a dimension reduction by SOM and the clustering of the data in a reduced space. Related to the kind of data, a…
Bootstrap percolation transition may be first order or second order, or it may have a mixed character where a first order drop in the order parameter is preceded by critical fluctuations. Recent studies have indicated that the mixed…
The evaluation of robustness and reliability of realistic structures in the presence of uncertainty involves costly numerical simulations with a very high number of evaluations. This motivates model order reduction techniques like the…
We test different implementations of the halo occupation distribution (HOD) model to reconstruct the spatial distribution of galaxies as predicted by a publicly available semi-analytical model (SAM). We compare the measured two-point…
The free energy and local height probabilities of the dilute A models with broken $\Integer_2$ symmetry are calculated analytically using inversion and corner transfer matrix methods. These models possess four critical branches. The first…
We introduce a simple model for the size distribution of avalanches based on the idea that the front of an avalanche can be described by a directed random walk. The model captures some of the qualitative features of earthquakes, avalanches…
A modeling of the soil structure and surface roughness by means of the concepts of the fractal growth is presented. Two parameters are used to control the model: the fragmentation dimension, $D_f$, and the maximum mass of the deposited…