Claire David

Antoine Amarilli, Claire David, Nadime Francis et al.

We give the first two algorithms to enumerate all binary words of $\{0,1\}^\ell$ (like Gray codes) while ensuring that the delay and the auxiliary space is independent from $\ell$, i.e., constant time for each word, and constant memory in addition to the $\ell$ bits storing the current word. Our algorithms are given in two new computational models: tape machines and deque machines. We also study more restricted models, queue machines and stack machines, and show that they cannot enumerate all binary words with constant auxiliary space, even with unrestricted delay. A tape machine is a Turing machine that stores the current binary word on a single working tape of length $\ell$ (which never increases), using no other tape. The machine has a single head and must edit its tape to reach all possible words of $\{0,1\}^\ell$, and output them (in unit time, by entering special output states), with no duplicates. Hence a tape machine uses constant auxiliary space by definition (up to the head position). We construct a tape machine that achieves this task with constant delay between consecutive outputs, so that the machine implements a so-called skew-tolerant quasi-Gray code. We then construct a more involved tape machine that implements a Gray code. A deque machine stores the current binary word on a double-ended queue of length $\ell$, and stores a constant-size internal state. It works as a tape machine, except that it modifies the content of the deque by performing push and pop operations on the endpoints. Hence again a deque machine uses constant auxiliary space by definition. We construct deque machines that enumerate all words of $\{0,1\}^\ell$ with constant-delay. The main technical challenge in this model is to correctly detect when enumeration has finished.

Nizare Riane, Claire David

In the sequel, we extend our previous work on the Minkowski Curve to Sierpiński simplices (Gasket and Tetrahedron), in the case of the heat equation. First, we build the finite difference scheme. Then, we give a theoretical study of the error, compute the scheme error, give stability conditions, and prove the convergence of the scheme. Contrary to existing work, we do not call for approximations of the eigenvalues.

Nizare Riane, Claire David

In this work, we describe how to approximate solutions of some partial differential equations using the finite difference method defined on the Minkowski self-similar curve.

Claire David

Artificial Intelligence (AI) and Machine Learning (ML) have been prevalent in particle physics for over three decades, shaping many aspects of High Energy Physics (HEP) analyses. As AI's influence grows, it is essential for physicists $\unicode{x2013}$ as both researchers and informed citizens $\unicode{x2013}$ to critically examine its foundations, misconceptions, and impact. This paper explores AI definitions, examines how ML differs from traditional programming, and provides a brief review of AI/ML applications in HEP, highlighting promising trends such as Simulation-Based Inference, uncertainty-aware machine learning, and Fast ML for anomaly detection. Beyond physics, it also addresses the broader societal harms of AI systems, underscoring the need for responsible engagement. Finally, it stresses the importance of adapting research practices to an evolving AI landscape, ensuring that physicists not only benefit from the latest tools but also remain at the forefront of innovation.

Kim Albertsson, Piero Altoe, Dustin Anderson et al.

Machine learning has been applied to several problems in particle physics research, beginning with applications to high-level physics analysis in the 1990s and 2000s, followed by an explosion of applications in particle and event identification and reconstruction in the 2010s. In this document we discuss promising future research and development areas for machine learning in particle physics. We detail a roadmap for their implementation, software and hardware resource requirements, collaborative initiatives with the data science community, academia and industry, and training the particle physics community in data science. The main objective of the document is to connect and motivate these areas of research and development with the physics drivers of the High-Luminosity Large Hadron Collider and future neutrino experiments and identify the resource needs for their implementation. Additionally we identify areas where collaboration with external communities will be of great benefit.

Emma Hoarau, Claire David, Pierre Sagaut et al.

Differential equations arising in fluid mechanics are usually derived from the intrinsic properties of mechanical systems, in the form of conservation laws, and bear symmetries, which are not generally preserved by a finite difference approximation, and leading to inaccurate numerical results. This paper proposes a method that enables us to build a scheme that preserves some of those symmetries.

Emma Hoarau, Claire David

A Mathematica based program has been elaborated in order to determine the symmetry group of a finite difference equation, by means of its differential representation. The package provides functions which enable us to solve the determining equations of the related Lie group