Related papers: Open Problems, Questions, and Challenges in Finite…
In this paper, which corresponds to an updated version of the author's Habilitation lecture in Mathematics, we do an overview of several topics in elliptic problems. We review some old and new results regarding the Lane-Emden equation, both…
In contrast to finite arithmetic configurations, relatively little is known about which infinite patterns can be found in every set of natural numbers with positive density. Building on recent advances showing infinite sumsets can be found,…
Over the past two decades, biometric recognition has exploded into a plethora of different applications around the globe. This proliferation can be attributed to the high levels of authentication accuracy and user convenience that biometric…
This is a structured compilation of some of my favourite open problems.
The author discusses integrability of Hamiltonian dynamical systems in the aftermath of KdV. The author also discusses the role of integrable systems in certain numerical computations, particularly the computation of the eigenvalues of a…
The present review is devoted to the problems of finite-size scaling due to the presence of long-range interaction decaying at large distance as $1/r^{d+\sigma}$, where $d$ is the spatial dimension and the long-range parameter $\sigma>0$.…
This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…
In this survey we go through some of the recent results about the regularity of vectorial free boundary problems of Bernoulli type and free boundary systems. The aim is to illustrate the general methodologies as well as to outline a…
This volume contains a final and revised selection of papers presented at the Eighth Workshop on Intersection Types and Related Systems (ITRS 2016), held on June 26, 2016 in Porto, in affiliation with FSCD 2016.
Inclusion and accessibility in visualization research have gained increasing attention in recent years. However, many challenges still remain to be solved on the road toward a more inclusive, shared-experience-driven visualization design…
In this thesis I present most of the results obtained during my PhD, where I worked on different subjects regarding jamming in systems of frictionless spheres. In particular, I focused on microscopic properties of jammed packings, such as…
The declared goal of this paper is to fill this gap: "... cognitive systems research needs questions or challenges that define progress. The challenges are not (yet more) predictions of the future, but a guideline to what are the aims and…
We survey recent developments in the theory of achievement sets and present a substantial collection of open problems.
This monograph, written for educational purposes, serves as an introduction to the concept of integrability as it applies to systems of differential equations (both ordinary and partial) as well as to vector-valued fields. The general cases…
Talk presented at NATO Gran Finale Conference, Como, Italy, September 1993
This volume contains the papers presented at LINEARITY 2016, the Fourth International Workshop on Linearity, held on June 26, 2016 in Porto, Portugal. The workshop was a one-day satellite event of FSCD 2016, the first International…
The paper addresses the issue of reliability of complex embedded control systems in the safety-critical environment. In this paper, we propose a novel approach to design controller that (i) guarantees the safety of nonlinear physical…
The isoperimetric problem asks for the maximum area of a region of given perimeter. It is natural to consider other measurements of a region, such as the diameter and width, and ask for the extreme value of one when another is fixed. The…
Data is a precious resource in today's society, and is generated at an unprecedented and constantly growing pace. The need to store, analyze, and make data promptly available to a multitude of users introduces formidable challenges in…
This study is motivated by two key considerations: the significant benefits mobile applications offer individuals and businesses, and the limited empirical research on usability challenges. To address this gap, we conducted structured…