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Additive and geometric transversality of fractal sets in the integers

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Relative, local and global dimension in complex networks

Alexis Arnaudon

Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and distorted by inhomogenei ...

Nature Portfolio2022

Fractal analysis in the quantification of medical imaging associated with multiple sclerosis pathology

Maria-Alexandra Paun

Backgrounds: Multiple sclerosis (MS) is an inveterate phlogistic situation characterized by focal and vaguely diffusive de-myelination and neurodegeneration, in the sphere of central nervous system (CNS). The brain's chronic inflammatory reaction includes ...

IMR PRESS2022

Fractal Analysis and Time Series Application in ZY-4 SEM Micro Fractographies Evaluation

Maria-Alexandra Paun

SEM microfractographies of Zircaloy-4 are studied by fractal analysis and the time-series method. We first develop a computer application that associates the fractal dimension and lacunarity to each SEM micrograph picture, and produce a nonlinear analysis ...

MDPI2022

Fourier non-uniqueness sets from totally real number fields

Martin Peter Stoller

Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...

EUROPEAN MATHEMATICAL SOC-EMS2022

The exploration process of critical Boltzmann planar maps decorated by a triangular O(n) loop model

Aleksandra Korzhenkova

In this paper we investigate pointed (q, g, n)-Boltzmann loop-decorated maps with loops traversing only inner triangular faces. Using peeling exploration Budd (2018) modified to this setting we show that its law in the non-generic critical phase can be cod ...

IMPA2022

Minkowski's Loop Fractal Antenna Dedicated to Sixth Generation (6G) Communication

Maria-Alexandra Paun

In this study, we will discuss the engineering construction of a special sixth generation (6G) antenna, based on the fractal called Minkowski's loop. The antenna has the shape of this known fractal, set at four iterations, to obtain maximum performance. Th ...

MDPI2022

Biocompatible Chitosan-Based Hydrogels for Bioabsorbable Wound Dressings

Maria-Alexandra Paun

Supramolecular hydrogels based on chitosan and monoaldehydes are biomaterials with high potential for a multitude of bioapplications. This is due to the proper choice of the monoaldehyde that can tune the hydrogel properties for specific practices. In this ...

MDPI2022

Spatial Series and Fractal Analysis Associated with Fracture Behaviour of UO2 Ceramic Material

Maria-Alexandra Paun

SEM micrographs of the fracture surface for UO2 ceramic materials have been analysed. In this paper, we introduce some algorithms and develop a computer application based on the time-series method. Utilizing the embedding technique of phase space, the attr ...

MDPI2022

Geometrical Treatise on the Modelling of 3D Particulate Inclusion-Matrix Microstructures with an Application to Historical Stone Masonry Walls

Mahmoud S. M. Shaqfa

As historical stone masonry structures are vulnerable and prone to damage in earthquakes, investigating their structural integrity is important to reduce injuries and casualties while preserving their historical value. Stone masonry is a composite material ...

EPFL2022

HIERARCHICAL MARKOV CHAIN MONTE CARLO METHODS FOR BAYESIAN INVERSE PROBLEMS

Juan Pablo Madrigal Cianci

This thesis is devoted to the construction, analysis, and implementation of two types of hierarchical Markov Chain Monte Carlo (MCMC) methods for the solution of large-scale Bayesian Inverse Problems (BIP). The first hierarchical method we present is base ...

EPFL2022

Geometric Percolation of Spherically Symmetric Fractal Aggregates

Claudio Grimaldi

The connectedness percolation threshold (phi(c)) for spherically symmetric, randomly distributed fractal aggregates is investigated as a function of the fractal dimension (d(F)) of the aggregates through a mean-field approach. A pair of aggregates (each of ...

SPRINGER2022