Related papers: Region crossing change on surfaces
Changes in the extent of local concavity along with changes in surface roughness of binding sites of proteins have long been considered as useful markers to identify functional sites of proteins. However, an algorithm that describes the…
This is the first article of a series of two where we study the problem of bounded deviations for homeomorphisms of closed surfaces of genus $\ge 2$. This first part studies bounded deviations with respect to closed geodesics. As a…
Neural circuits comprise multiple interconnected regions, each with complex dynamics. The interplay between local and global activity is thought to underlie computational flexibility, yet the structure of multiregion neural activity and its…
We study the effect of heterogeneous load sharing in the fiber bundle models of fracture. The system is divided into two groups of fibers (fraction $p$ and $1-p$) in which one group follow the completely local load sharing mechanism and the…
Traditionally, alternating links are studied with alternating diagrams on $S^2$ in $S^3$. In this paper, we consider links which are alternating on higher genus surfaces $S_g$ in $S_g \times I$. We define what it means for such a link to be…
A natural generalization of a crossing change is a rational subtangle replacement (RSR). We characterize the fundamental situation of the rational tangles obtained from a given rational tangle via RSR, building on work of Berge and Gabai,…
In a range of scientific coauthorship networks, transitions emerge in degree distributions, correlations between degrees and local clustering coefficients, etc. The existence of those transitions could be regarded as a result of the…
The connection between the theory of permutation orbifolds, covering surfaces and uniformization is investigated, and the higher genus partition functions of an arbitrary permutation orbifold are expressed in terms of those of the original…
Modern deep neural networks display striking examples of rich internal computational structure. Uncovering principles governing the development of such structure is a priority for the science of deep learning. In this paper, we explore the…
The field theoretical approach to duality in the superconducting phase transition is reviewed. Emphasis is given to the scaling behavior, and recent results are discussed.
Given a surface with boundary and some points on its boundary, a polygon diagram is a way to connect those points as vertices of non-overlapping polygons on the surface. Such polygon diagrams represent non-crossing permutations on a surface…
Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…
We investigated domain growth in switching processes between the low-spin and high-spin phases in thermally induced hysteresis loops of spin-crossover (SC) solids. Elastic interactions among the molecules induce effective long-range…
We address the problem of message transfer in a communication network. The network consists of nodes and links, with the nodes lying on a two dimensional lattice. Each node has connections with its nearest neighbours, whereas some special…
A classification of spanning surfaces for alternating links is provided up to genus, orientability, and a new invariant that we call aggregate slope. That is, given an alternating link, we determine all possible combinations of genus,…
The labeling of point features on a map is a well-studied topic. In a static setting, the goal is to find a non-overlapping label placement for (a subset of) point features. In a dynamic setting, the set of point features and their…
We construct models of involution surface bundles over algebraic surfaces, degenerating over normal crossing divisors, and with controlled singularities of the total space.
Varying environmental conditions affect relations between interacting individuals in social dilemmas, thus affecting also the evolution of cooperation. Oftentimes these environmental variations are seasonal and can therefore be…
Using experimental techniques, we study properties of the "circumcenter map", which, upon $n$ iterations sends an $n$-gon to a scaled and rotated copy of itself. We also explore the topology of area-expanding and area-contracting regions…
We discuss self-crossing patterns of closed geodesics on a convex surface.