Related papers: Langton's Ant from the Ant's referential

We consider braids with repeating patterns inside arbitrary knots which provides a multi-parametric family of knots, depending on the "evolution" parameter, which controls the number of repetitions. The dependence of knot (super)polynomials…

We propose and test an algorithm to simulate a lattice system of interacting fermions in two spatial dimensions. The approach is an extension of the entanglement renormalization technique [Phys. Rev. Lett. 99, 220405 (2007)] and the related…

The motion of social insects is often used a paradigmatic example of complex adaptive dynamics arising from decentralized individual behavior. In this paper we revisit the topic of the ruling laws behind burst of activity in ants. The…

We study branching random walks in random i.i.d. environment in $\Z^d, d \geq 1$. For this model, the population size cannot decrease, and a natural definition of recurrence is introduced. We prove a dichotomy for recurrence/transience,…

For a partial lattice L the so-called two-point extension is defined in order to extend L to a lattice. We are motivated by the fact that the one-point extension broadly used for partial algebras does not work in this case, i.e. the…

We introduce a simple model for DNA evolution. Using the method of Peng et al.$^1$, we investigate the fractal properties of the system. For small chains and chains of intermediate size we find a fractal exponent that indicates the…

We discuss two possible ways of representing tolerances: first, as a homomorphic image of some congruence; second, as the relational composition of some compatible relation with its converse. The second way is independent from the variety…

This is an informal paper presenting historical results around the recent paper of the author about Lang's Conjecture and torsion of elliptic curves. This paper also discusses a few aspects of the proof.

In this paper, we study the "free exploration" of individual ants of the species Atta insularis, i.e., their motion on a featureless flat, horizontal surface. Two basic preliminary results emerge from our work (a) the free exploration is…

We analyze a trapping reaction with a single penetrable trap, in a one dimensional lattice, where both species (particles and trap) are mobile and have a drift velocity. We obtain the density as seen from a reference system attached to the…

Lattice-based cryptography has recently emerged as a prominent candidate for secure communication in the quantum age. Its security relies on the hardness of certain lattice problems, and the inability of known lattice algorithms, such as…

The expansion of a population into new habitat is a transient process that leaves its footprints in the genetic composition of the expanding population. How the structure of the environment shapes the population front and the evolutionary…

Latent space is rapidly emerging as a native substrate for language-based models. While modern systems are still commonly understood through explicit token-level generation, an increasing body of work shows that many critical internal…

The ants process is a stochastic process introduced by Kious, Mailler and Schapira as a model for the phenomenon of ants finding shortest paths between their nest and a source of food (seen as two marked nodes in a finite graph), with no…

Many organisms exhibit branching morphologies that twist around each other and become entangled. Entanglement occurs when different objects interlock, creating complex and often irreversible configurations. This physical phenomenon is…

We introduce a formula for translating any upper bound on the percolation threshold of a lattice \g into a lower bound on the exponential growth rate of lattice animals $a(G)$ and vice-versa. We exploit this to improve on the best known…

Dense prediction tasks typically employ encoder-decoder architectures, but the prevalent convolutions in the decoder are not image-adaptive and can lead to boundary artifacts. Different generalized convolution operations have been…

The Santa Fe Ant model problem has been extensively used to investigate, test and evaluate Evolutionary Computing systems and methods over the past two decades. There is however no literature on its program structures that are…

Environmental heterogeneity can drive genetic heterogeneity in expanding populations; mutant strains may emerge that trade overall growth rate for an improved ability to survive in patches that are hostile to the wild type. This…

We study the range of a planar random walk on a randomly oriented lattice, already known to be transient. We prove that the expectation of the range grows linearly, in both the quenched (for a.e. orientation) and annealed ("averaged")…