Related papers: The Ant on a Rubber Rope Paradox
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…
Condensed active matter is exemplary for its capacity to morph and exhibit internal flows despite remaining cohered. To facilitate understanding of this ability, we investigate the cause of finger-like protrusions that emerge from…
The ribbonlength of a link is a geometric invariant defined as the infimum of the ratio of the length to the width of a folded ribbon realization of the link. In this paper, we prove that if an alternating link admits an alternating diagram…
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.
Consider a growing system of random walks on the 3,2-alternating tree, where generations of nodes alternate between having two and three children. Any time a particle lands on a node which has not been visited previously, a new particle is…
It appears paradoxical that science is producing outstanding new results and theories at a rapid rate at the same time that researchers are identifying serious problems in the practice of science that cause many reports to be irreproducible…
Suppose that $k$ runners having different constant speeds run laps on a circular track of unit length. The Lonely Runner Conjecture states that, sooner or later, any given runner will be at distance at least $1/k$ from all the other…
Using elementary distributed computing techniques we suggest an explanation for two unexplained phenomena in regards to ant colonies, (a) a substantial amount of ants in an ant colony are idle, and (b) the observed low survivability of new…
We develop techniques to obtain rigorous bounds on the behaviour of random walks on combs. Using these bounds we calculate exactly the spectral dimension of random combs with infinite teeth at random positions or teeth with random but…
We consider the longest common subsequence problem in the context of subsequences with gap constraints. In particular, following Day et al. 2022, we consider the setting when the distance (i. e., the gap) between two consecutive symbols of…
In this paper, we consider pursuit-evasion and probabilistic consequences of some geometric notions for bounded and suitably regular domains in Euclidean space that are CAT(kappa) for some kappa > 0. These geometric notions are useful for…
We obtain new average results on the conjectures of Lang-Trotter and Sato-Tate about elliptic curves.
Relativistic rigid motion suggests a new version for the so-called `twin paradox', comparing the ages of two astronauts on a very long spaceship. Although there is always an instantaneous inertial frame in which the whole spaceship, being…
A new general equation to explain bending of arbitrary rods (from arbitrary materials, cross sections, densities, strengthnesses, bending angles, etc) was proposed. This equation can solve several problems found in classical equations,…
Recent advances on the glass problem motivate reexamining classical models of percolation. Here, we consider the displacement of an ant in a labyrinth near the percolation threshold on cubic lattices both below and above the upper critical…
We consider the problem of extracting accurate average ant trajectories from many (possibly inaccurate) input trajectories contributed by citizen scientists. Although there are many generic software tools for motion tracking and specific…
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
We consider transient nearest neighbor random walks on the positive part of the real line. We give criteria for the finiteness of the number of cutpoints and strong cutpoints. Examples and open problems are presented.
The problem of a random walk on a finite triangular lattice with a single interior source point and zig-zag absorbing boundaries is solved exactly. This problem has been previously considered intractable.
We consider two varieties of labeled rooted trees, and the probability that a vertex chosen from all vertices of all trees of a given size uniformly at random has a given rank. We prove that this probability converges to a limit as the tree…