Related papers: I am the cat who walks by himself
A diffusing lion pursues a diffusing lamb when both of them are allowed to get back to their homes intermittently. Identifying the system with a pair of vicious random walkers, we study their dynamics under Poissonian and sharp resetting.…
We study the escape behavior of a lamb to safe haven pursued by a hungry lion. Identifying the system with a pair of vicious Brownian walkers we evaluate the probability density function for the vicious pair and from there we estimate the…
We consider a variant of a pursuit and evasion game studied independently by Britnell and Wildon as well as Haslegrave. In their game, a cat has to catch an invisible mouse that moves along the edges of some graph $G$. In our version, the…
It has generally been assumed that geopolitical bias in language models originates from the training data used during the pre-training phase. We tested seven open-weight LLM pairs consisting of the base model (pre-training only) and the…
The revolution and Civil War in Syria has led to substantial death and suffering, a massive refugee crisis, and growth of ISIS extremism and its terror attacks globally. Conflict between disparate groups is ongoing. Complex ethnic geography…
We present the first--ever example of a macroscopic system in a quantum superposition. The system in question is a Siamese cat known as Lola; however, on a time scale of about 12 hours it oscillates into a different state that we refer to…
Motivated by the "tug-of-war" game studied in [12], we consider a "non-local" version of the game which goes as follows: at every step two players pick respectively a direction and then, instead of flipping a coin in order to decide which…
Autonomous explorative robots frequently encounter scenarios where multiple future trajectories can be pursued. Often these are cases with multiple paths around an obstacle or trajectory options towards various frontiers. Humans in such…
The dynamics of ``vicious'', continuously growing civilizations (domains), which engage in ``war'' whenever two domains meet, is investigated. In the war event, the smaller domain is annihilated, while the larger domain is reduced in size…
This is an update of my problem list.
Contemporary literature on the dynamics of economic activities in growing cities mainly focused on a few years or decades time frames. Using a new geo-historical database constructed from historical directories with about 1 million entries,…
This is a fairy tale taking place in Chessland, located in the Bermuda triangle. The chess pieces survey their land and trap enemy pieces. Behind the story, there is fascinating mathematics on how to optimize surveying and trapping. The…
This paper proposes a strategy for a group of deaf and dumb robots, carrying clocks from different countries, to meet at a geographical location which is not fixed in advanced. The robots act independently. They can observe others, compute…
We introduce a toy model of the "rat race" in which individuals try to better themselves relative to the rest of the population. An individual is characterized by a real-valued fitness and each advances at a constant rate by an amount that…
Petit is an educational programming language for learning compilers. Students embark on the journey of learning compilers through a series of six tutorials, progressing from topics like lexical analysis and syntactic analysis to semantic…
This habilitation memoir (in French, submitted in May 2014) is made up of five chapters, each being an introduction to work of the author between 2006 and 2014. The core of the memoir consists of the first three chapters, pertaining to…
Let $X=(V\!X,E\!X)$ be an infinite, locally finite, connected graph without loops or multiple edges. We consider the edges to be oriented, and $E\!X$ is equipped with an involution which inverts the orientation. Each oriented edge is…
We give an example of automated geometry reasoning for an imaginary classroom project by using the free software package GeoGebra Discovery. The project is motivated by a publicly available toy, a rocking camel, installed at a medical…
A generic property of biological, social and economical networks is their ability to evolve in time, creating and suppressing interactions. We approach this issue within the framework of an adaptive network of agents playing a Prisoner's…
A few of ant robots are dropped to a labirynth, formed by a square lattice with a small number of nodes removed. Ants move according to a deterministic algorithm designed to explore all corridors. Each ant remembers the shape of corridors…