Related papers: A Recurrent Rotor-Router Configuration in Z^3
We propose a simple mathematical model that describes the time evolution of a self-propelled object on a liquid surface using such variables as the object location, the surface concentration of active molecules and the hydrodynamic surface…
We study frequently recurrent unilateral and bilateral backward shift operators on Fr\'echet sequence spaces. We prove that if a backward shift admits a non-zero frequently recurrent vector, then it supports a dense set of such vectors, so…
Sequential recommendation requires the recommender to capture the evolving behavior characteristics from logged user behavior data for accurate recommendations. However, user behavior sequences are viewed as a script with multiple ongoing…
We consider reachability in dynamical systems with discrete linear updates, but with fixed digital precision, i.e., such that values of the system are rounded at each step. Given a matrix $M \in \mathbb{Q}^{d \times d}$, an initial vector…
The rotor-router model is a deterministic process analogous to a simple random walk on a graph. This paper is concerned with a generalized model, functional-router model, which imitates a Markov chain possibly containing irrational…
We study the dynamics of multidimensional contracted rotations and address a problem posed by Y. Bugeaud and J-P. Conze in \textit{Acta Arithmetica} in 1999. More precisely, we show that if $A$ is an invertible linear contraction of…
Glass networks are piecewise linear ODE systems that models an interactive system where there are 'switching points': the underlying dynamic changes qualitatively when a certain variable pass over a threshold. One of the most well-studied…
Given an integer m>1 we consider Zm-equivariant and orientation preserving homeomorphisms in the plane with an asymptotically stable fixed point at the origin. We present examples without periodic points and having some complicated…
Connections between nodes in optical networks are realized by lightpaths. Due to the decay of the signal, a regenerator has to be placed on every lightpath after at most $d$ hops, for some given positive integer $d$. A regenerator can serve…
We study the routing policy choice problems in a stochastic time-dependent (STD) network. A routing policy is defined as a decision rule applied at the end of each link that maps the realized traffic condition to the decision on the link to…
Recurrence properties of systems and associated sets of integers that suffice for recurrence are classical objects in topological dynamics. We describe relations between recurrence in different sorts of systems, study ways to formulate…
A product of Moore machines with feedback published in 1962 by Juris Hartmanis and a class of primitive recursive functions on finite sequences published in a textbook by Roza Peter originally in 1950 are keys to a method for working with…
A one-parameter family of time-reversible systems on $\mathbb{T}^3$ is considered. It is shown that the dynamics is not conservative, namely the attractor and repeller intersect but not coincide. We explain this as the manifestation of the…
Recently, a new type of second-order topological insulator has been theoretically proposed by introducing an in-plane Zeeman field into the Kane-Mele model in the two-dimensional honeycomb lattice. A pair of topological corner states arise…
We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…
Linear recurrent neural networks, such as State Space Models (SSMs) and Linear Recurrent Units (LRUs), have recently shown state-of-the-art performance on long sequence modelling benchmarks. Despite their success, their empirical…
Changes in air transport networks over time may be induced by competition among carriers, changes in regulations on airline industry, and socioeconomic events such as terrorist attacks and epidemic outbreaks. Such network changes may…
The development of multi-core processor systems is a demanded branch of science and technology. The appearance of processors with dozens and hundreds of cores poses to the developers the question of choosing the optimal topology capable to…
In this work we present a novel recurrent neural network architecture designed to model systems characterized by multiple characteristic timescales in their dynamics. The proposed network is composed by several recurrent groups of neurons…
Motivated by what is required for real-time path planning, the paper starts out by presenting sRMPD, a new recursive "local" planner founded on the key notion that, unless made necessary by an obstacle, there must be no deviation from the…