Related papers: The Rise-Contact involution on Tamari intervals
We examine the homological structure of the Barabasi-Albert model, focusing on the time evolution of $\Delta$-dimensional simplices and topological holes as functions of time $t$ and the attachment parameter $m$ (the number of edges added…
We numerically investigate the impact of scale evolution on double parton distributions, which are needed to compute multiple hard scattering processes. Assuming correlations between longitudinal and transverse variables or between the…
We introduce a simple bijection between Tamari intervals and the blossoming trees (Poulalhon and Schaeffer, 2006) encoding planar triangulations, using a new meandering representation of such trees. Its specializations to the families of…
We investigate the inflationary expansion of the universe induced by higher curvature corrections in M-theory. The inflationary evolution of the geometry is discussed in ref.[1], thus we succeed to analyse metric perturbations around the…
We present mathematical details of the construction of a topological invariant for periodically driven two-dimensional lattice systems with time-reversal symmetry and quasienergy gaps, which was proposed recently by some of us. The…
Highly nonlinear behavior of a system of discrete sites on a lattice is observed when a specific feedback loop is introduced into models employing coupled map lattices, quantum cellular automata, or the real-valued analogues of the latter.…
Proposed in this paper is a possible interaction which exists in nature - inertial interaction. It gives matter an inertia and inertial mass. The formula of inertial mass has been derived. It is possible that inertial interaction leads to…
We introduce extended fighting fish as branching surfaces that can also be seen as walks in the quarter plane defined by simple rewriting rules. The main result we present in the article is a direct bijection between extended fighting fish…
In this paper we are concerned with the two-stage contact process introduced in \cite{Krone1999} on a high-dimensional lattice. By comparing this process with an auxiliary model which is a linear system, we obtain two limit theorems for…
Maxwell lattices are characterized by an equal number of degrees of freedom and constraints. A subset of them, dubbed topological lattices, are capable of localizing stress and deformation on opposing edges, displaying a polarized…
Lattice models with non-hermitian, parity and time-reversal ($\mathcal{PT}$) symmetric Hamiltonians, realized most readily in coupled optical systems, have been intensely studied in the past few years. A $\mathcal{PT}$-symmetric dimer…
We explain a correspondence between some invariants in the dynamics of color exchange in a 2d coloring problem, which are polynomials of winding numbers, and linking numbers in 3d. One invariant is visualized as linking of lines on a…
The soliton resolution conjecture for evolution PDEs of dispersive type states (vaguely) that generic initial data of finite energy give rise asymptotically to a set of receding solitons and a decaying background radiation. In this letter,…
We consider the contact process on a dynamic graph defined as a random $d$-regular graph with a stationary edge-switching dynamics. In this graph dynamics, independently of the contact process state, each pair $\{e_1,e_2\}$ of edges of the…
Some classes of increment martingales, and the corresponding localized classes, are studied. An increment martingale is indexed by the real line and its increment processes are martingales. We focus primarily on the behavior as time goes to…
RHESSI observations of a solar flare showing continuous motions of double hard X-ray sources interpreted as footpoints of magnetic loops are presented. The temporal evolution shows many distinct emission peaks of duration of some tens of…
We focus on various dynamical invariants associated to toric correspondences, using algebraic geometry or arithmetic. We find a formula for the dynamical degrees, relate the exponential growth of the degree sequences with a strict…
This paper constructs two involutions on tip-augmented plane trees, as defined by Donaghey, that interchange two distinct types of leaves while preserving all other leaves. These two involutions provide bijective explanations addressing a…
As a classical object, the Tamari lattice has many generalizations, including $\nu$-Tamari lattices and parabolic Tamari lattices. In this article, we unify these generalizations in a bijective fashion. We first prove that parabolic Tamari…
Extending previous rigorous results, we prove existence of an ordering transition at finite temperature for a class of nematogenic lattice models, where spins are associated with a one- or two-dimensional lattice, and interact via…