Publications associées à First passage sets of the 2D continuum Gaussian free field

Additive 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 ...

2024

Extensions of Peer Prediction Incentive Mechanisms

Adam Julian Richardson

As large, data-driven artificial intelligence models become ubiquitous, guaranteeing high data quality is imperative for constructing models. Crowdsourcing, community sensing, and data filtering have long been the standard approaches to guaranteeing or imp ...

EPFL2024

Stability of the Faber-Krahn inequality for the short-time Fourier transform

Joao Pedro Gonçalves Ramos

We prove a sharp quantitative version of the Faber–Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit which measures by how much the STFT of a function fails to be optimally concentrated on an arbitrary set of pos ...

Springer Heidelberg2024

Multiplicative chaos of the Brownian loop soup

Antoine Pierre François Jego, Titus Lupu

We construct a measure on the thick points of a Brownian loop soup in a bounded domain D

D

of the plane with given intensity theta>0

\theta >0

, which is formally obtained by exponentiating the square root of its occupation field. The measure is construct ...

WILEY2023

Fractal Analysis of Four Xerogels Based on TEGylated Phenothiazine and Chitosan

Maria-Alexandra Paun

The present article describes novel massive materials (in the solid phase) based on TEGylated phenothiazine and chitosan that possess great capability to recover mercury ions from constituent aqueous solutions. These were produced by chitosan hydrogelation ...

MDPI2023

Fractal Analysis in Pulmonary CT Images of COVID-19-Infected Patients

Maria-Alexandra Paun

In this paper, we propose to quantitatively compare the loss of human lung health under the influence of the illness with COVID-19, based on the fractal-analysis interpretation of the chest-pulmonary CT pictures, in the case of small datasets, which are us ...

MDPI2023

On a Finite-Size Neuronal Population Equation

Valentin Marc Schmutz, Tilo Schwalger, Eva Löcherbach

Population equations for infinitely large networks of spiking neurons have a long tradition in theoret-ical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form of a nonlinear ...

SIAM PUBLICATIONS2023

Appropriations and Uses of Travel Time

Ludy Juliana González Villamizar

Time has always been a central factor in understanding the challenges of daily mobility. For a long time, and still today, methods of economic evaluation of transport projects have monetized time savings so that they can be included in the cost–benefit ana ...

ISTE Wiley2023

Measurement of the 171Tm beta spectrum

Alexey Boyarsky, Lesya Shchutska

The beta spectrum of the main transition of the 171Tm was measured using a double focalizing spectrometer. The instrument was lately improved in order to reduce its low energy threshold to 34 keV. We used the spectrometer to measure the energy end-point of ...

2023

Impact of Redundancy on Resilience in Distributed Optimization and Learning

Shuo Liu, Nirupam Gupta

This paper considers the problem of resilient distributed optimization and stochastic learning in a server-based architecture. The system comprises a server and multiple agents, where each agent has its own local cost function. The agents collaborate with ...

Assoc Computing Machinery2023

Fifth-generation fractal antenna design based on the Koch Snowflake geometry. A fractal theory application

Maria-Alexandra Paun

The projection of fifth-generation (5G) fractal antennas and their advantageous geometry are examined. The fact that fractal-shaped antennas based on Koch Snowflake geometry are suitable for higher frequencies was shown above all. By the instrumentality of ...

WILEY2023

IMPROVED REGULARITY OF SECOND DERIVATIVES FOR SUBHARMONIC FUNCTIONS

Riccardo Tione, Xavier Fernandez-Real Girona

In this note, we prove that if a subharmonic function Delta u >= 0 has pure second derivatives partial derivative(ii)u that are signed measures, then their negative part (partial derivative(ii)u)- belongs to L-1 (in particular, it is not singular). We then ...

Amer Mathematical Soc2023

Well-posedness Issues For the Half-Wave Maps Equation With Hyperbolic And Spherical Targets

Yang Liu

This thesis is a study of the global well-posedness of the Cauchy problems for half-wave maps from the Minkowski space of dimension n+1 to the 2-dimensional sphere and the hyperbolic plane. The work is mainly based on the results from Krieger-Sire 17' in ...

EPFL2023

Single-shot Kramers-Kronig complex orbital angular momentum spectrum retrieval

Camille Sophie Brès, Jianqi Hu, Yujie Chen

Orbital angular momentum (OAM) spectrum diagnosis is a fundamental building block for diverse OAM-based systems. Among others, the simple on-axis interferometric measurement can retrieve the amplitude and phase information of complex OAM spectra in a few s ...

SPIE-SOC PHOTO-OPTICAL INSTRUMENTATION ENGINEERS2023

Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds

Le Chen, David Jean-Michel Candil, Cheuk Yin Lee

We consider nonlinear parabolic stochastic PDEs on a bounded Lipschitz domain driven by a Gaussian noise that is white in time and colored in space, with Dirichlet or Neumann boundary condition. We establish existence, uniqueness and moment bounds of the r ...

Springer2023

A Functional Perspective on Information Measures

Amedeo Roberto Esposito

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

EPFL2022

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

Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1

Maria Colombo

We prove non-uniqueness for a class of weak solutions to the Navier???Stokes equations which have bounded kinetic energy, integrable vorticity, and are smooth outside a fractal set of singular times with Hausdorff dimension strictly less than 1. ...

2022

Fractal Modeling of Polymer Plasma Laser Ablation, Plasma Plume Tsallis Entropy and Its q-Statistics Interpretation, Part I: Theory

Maria-Alexandra Paun

Polymer plasma produced by laser ablation is investigated in a theoretical manner. In relation to the fact that the charge carrier circulation is assumed to take place on fractal curves, the so-called fractality type, electrical charge transport can be res ...

MDPI2022

A Multifractal Vision of 5-Fluorouracil Release from Chitosan-Based Matrix

Maria-Alexandra Paun

A suite of four drug deliverance formulations grounded on 5-fluorouracil enclosed in a chitosan-founded intercellular substance was produced by 3,7-dimethyl-2,6-octadienal with in situ hydrogelation. The formulations have been examined from a morphological ...

MDPI2022