Related papers: Fighting Fish: enumerative properties
Sea urchin feeding fronts are a striking example of spatial pattern formation in an ecological system. If it is assumed that urchins are asocial, and that they move randomly, then the formation of these dense fronts is an apparent paradox.…
We study various combinatorial properties, and the implications between them, for filters generated by infinite-dimensional subspaces of a countable vector space. These properties are analogous to selectivity for ultrafilters on the natural…
We consider the tiling of an $n$-board (a board of size $n\times1$) with squares of unit width and $(1,1)$-fence tiles. A $(1,1)$-fence tile is composed of two unit-width square subtiles separated by a gap of unit width. We show that the…
This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and…
Quantifying interaction strength between species is of interest in food web studies for understanding population dynamics. Theory has run ahead of experiment in solving equations describing ecological systems (the Lotka-Volterra equations,…
When you think of fish, what comes to mind? Maybe you think of pet goldfish, movie characters like Dory or Nemo, or trout in a local river. One of the things that all of these fish have in common is patterns in their skin. Nemo sports black…
This paper is devoted to studying obstacle avoiding patterns and cohesiveness of fish school. First, we introduce a model of stochastic differential equations (SDEs) for describing the process of fish school's obstacle avoidance. Second, on…
We study a problem modelling segregation of an arbitrary number of competing species in planar domains. The solutions give rise to a well known free boundary problem with the domain partitioning itself into subdomains occupied by different…
Deep neural networks have been shown to suffer from a surprising weakness: their classification outputs can be changed by small, non-random perturbations of their inputs. This adversarial example phenomenon has been explained as originating…
We characterize winning strategies in various infinite games involving filters on the natural numbers in terms of combinatorics or structural properties of the given filter. These generalize several ultrafilter games of Galvin.
Amphiphiles are molecules which have both hydrophilic and hydrophobic parts. In water- and/or oil-like solvent, they self-assemble into extended sheet-like structures due to the hydrophobic effect. The free energy of an amphiphilic system…
Free gasses of spinless fermions moving on a lattice-symmetric geometric background are considered. Their topological properties at zero temperature can be used to classify their Fermi seas and associated boundaries. The flat orbifolds…
We classify flips of buildings arising from non-degenerate unitary spaces of dimension at least 4 over finite fields of odd characteristic in terms of their action on the underlying vector space. We also construct certain geometries related…
Let T be a weighted tree with n leaves. Let D_{i,j} be the distance between the leaves i and j. Let D_{i,j,k}= (D_{i,j} + D_{j,k} +D_{i,k})/2. We will call such numbers "triple weights" of the tree. In this paper, we give a…
Laman graphs naturally arise in structural mechanics and rigidity theory. Specifically, they characterize minimally rigid planar bar-and-joint systems which are frequently needed in robotics, as well as in molecular chemistry and polymer…
Knowing which parts of a complex system have identical roles simplifies computations and reveals patterns in its network structure. Group theory has been applied to study symmetries in unweighted networks. However, in real-world weighted…
In this work we give specific examples of competition models, with six and eight species, whose three-dimensional dynamics naturally leads to the formation of string networks with junctions, associated with regions that have a high…
A table is an object that captures structured and informative content within a document, and recognizing a table in an image is challenging due to the complexity and variety of table layouts. Many previous works typically adopt a two-stage…
In this paper, we introduce a prime factorization of open meanders, articulated through the framework of 2-colored operads. We demonstrate that each open meander can be canonically constructed from building blocks of two types: iterated…
There is an unproven duality theory hypothesizing that random discrete trees and their poissonized embeddings in continuous time share fundamental properties. We give additional evidence in favor of this theory by showing that several…