Concept
Minkowski–Bouligand dimension
Related publications (66)
Fractal analysis in the quantification of medical imaging associated with multiple sclerosis pathology
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 PRESS2022Minkowski's Loop Fractal Antenna Dedicated to Sixth Generation (6G) Communication
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 ...
MDPI2022Finite Littlestone Dimension Implies Finite Information Complexity
Michael Christoph Gastpar, Aditya Pradeep, Ido Nachum
We prove that every online learnable class of functions of Littlestone dimension d admits a learning algorithm with finite information complexity. Towards this end, we use the notion of a globally stable algorithm. Generally, the information complexity of ...
2022A Unified Discretization Approach to Compute–Forward: From Discrete to Continuous Inputs
Michael Christoph Gastpar, Sung Hoon Lim, Adriano Pastore, Chen Feng
Compute–forward is a coding technique that enables receiver(s) in a network to directly decode one or more linear combinations of the transmitted codewords. Initial efforts focused on Gaussian channels and derived achievable rate regions via nested lattice ...
2022On the Characterisation of the Surface Roughness of 3d Object Scanned with Micro CT
This goal of this paper is the characterisation of surface roughness of 3D object scanned via micro CT. The idea is to extract the fractal dimension D of a 3D cloud of points. This project follows the work of a previous student project: Characterisation of ...
2021On the fractal structure of soil moisture fields
We study the spatial structure of soil moisture fields within savanna ecosystems, whose persistence is vital because it is the driver of the entire ecological structure and function. These include changes in the physical and biogeochemical conditions of th ...
ELSEVIER SCI LTD2021Additive and geometric transversality of fractal sets in the integers
By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...
2021Estimate on the Dimension of the Singular Set of the Supercritical Surface Quasigeostrophic Equation
Maria Carola Colombo, Silja Noëmi Aline Haffter
We consider the SQG equation with dissipation given by a fractional Laplacian of order α
2021Effects of spanwise confinement on stratified shear instabilities
François Gallaire, Yves-Marie François Ducimetière
We consider the influence of transverse confinement on the instability properties of velocity and density distributions reminiscent of those pertaining to exchange flows in stratified inclined ducts, such as the recent experiment of Lefauve et al. [J. Flui ...
2021Nearly-Tight and Oblivious Algorithms for Explainable Clustering
Ola Nils Anders Svensson, Adam Teodor Polak, Buddhima Ruwanmini Gamlath Gamlath Ralalage, Xinrui Jia
We study the problem of explainable clustering in the setting first formalized by Dasgupta, Frost, Moshkovitz, and Rashtchian (ICML 2020). A k-clustering is said to be explainable if it is given by a decision tree where each internal node splits data point ...
2021