Related papers: I am the cat who walks by himself
In France, the first year of study at university is usually abbreviated L1 (for premiere annee de Licence). At Sorbonne Paris Nord University, we have been teaching an 18 hour introductory course in formal proofs to L1 students for 3 years.…
We consider the game with discrete units of resources for protection and destruction of some sites. In our model, Defender (DF) has locks and Attacker (AT) has bombs to allocate among sites, trying to destroy these sites. One or more bombs…
Levy walk is a fundamental model with applications ranging from quantum physics to paths of animal foraging. Taking animal foraging as an example, a natural idea that comes to one's mind is to introduce the multiple internal states for…
The current trend in technology shows that the robots will soon be seen interacting with humans and handling different tasks more efficiently in future. With advancement in artificial intelligence it can be foreseen that robots will…
LLM-generated stories are a popular use case, but they show very low variability. We sample 20,000 total stories from four current models using five prompts. We find that 11 words occur in 88.3% of generated stories, with little difference…
Cellular automata (CA) captivate researchers due to teh emergent, complex individualized behavior that simple global rules of interaction enact. Recent advances in the field have combined CA with convolutional neural networks to achieve…
We study the following question dating back to J.E. Littlewood (1885-1977): Can two lions catch a man in a bounded area with rectifiable lakes? The lions and the man are all assumed to be points moving with at most unit speed. That the…
The fourfold research proposal regards in particular: critical oriented percolation; random walk limit laws; neural networks with long-range connections; the ant in a labyrinth.
Emergence of hierarchies is investigated by Monte Carlo simulation in a timid society where all individuals are pacifist. The self-organiztion of hierarchies is shown to occur in two steps as the population is increased, i.e. there are…
Exploring the depths of Samuel Beckett's "Not I" through advanced natural language processing techniques, this research uncovers the intricate linguistic structures that underpin the text. By analyzing word frequency, detecting emotional…
The row projection (resp., column projection) of a two-dimensional language $L$ is the one-dimensional language consisting of all first rows (resp., first columns) of each two-dimensional word in $L$. The operation of row projection has…
As a large-scale instance of dramatic collective behaviour, the 2005 French riots started in a poor suburb of Paris, then spread in all of France, lasting about three weeks. Remarkably, although there were no displacements of rioters, the…
We show that the Euler walk on a Cayley tree exhibits two regimes (dynamic phases): a condensed phase and a low-density phase. In the condensed phase the self-organized area grows as a compact domain. In the low-density phase the proportion…
The paper introduces and publicly releases (Data download link available after acceptance) CAFE -- the first Code-switching dataset between Algerian dialect, French, and english languages. The CAFE speech data is unique for (a) its…
Aggression is a two-player game of troop placement and attack played on a map (modeled as a graph). Players take turns deploying troops on a territory (a vertex on the graph) until they run out. Once all troops are placed, players take…
A modified spatial prisoner's dilemma game with voluntary participation in Newman-Watts small-world networks is studied. Some reasonable ingredients are introduced to the game evolutionary dynamics: each agent in the network is a pure…
Interventions of central, top-down planning are serious limitations to the possibility of modelling the dynamics of cities. An example is the city of Paris (France), which during the 19th century experienced large modifications supervised…
We investigate a basic immigration process where colonies grow, during a random time, according to a general counting process until collapse. Upon collapse a random amount of individuals survive. These survivors try independently…
Hallucinations pose a critical challenge to the real-world deployment of large language models (LLMs) in high-stakes domains. In this paper, we present a framework for stress testing factual fidelity in LLMs in the presence of adversarial…
This chapter examines the geographical meaning of the Sahel, its fluid boundaries, and its spatial dynamics. Unlike other approaches that define the Sahel as a bioclimatic zone or as an ungoverned area, it shows that the Sahel is primarily…