Related papers: A Recurrent Rotor-Router Configuration in Z^3
Global routing has been a historically challenging problem in electronic circuit design, where the challenge is to connect a large and arbitrary number of circuit components with wires without violating the design rules for the printed…
This work studies existence and regularity questions for attracting invariant tori in three dimensional dissipative systems of ordinary differential equations. Our main result is a constructive method of computer assisted proof which…
Synchronous computation models simplify the design and the verification of fault-tolerant distributed systems. For efficiency reasons such systems are designed and implemented using an asynchronous semantics. In this paper, we bridge the…
Methods for specifying Moore type state machines (transducers) abstractly via primitive recursive functions and for defining parallel composition via simultaneous primitive recursion are discussed. The method is mostly of interest as a…
The problem of classifying linear systems of conics in projective planes dates back at least to Jordan, who classified pencils (one-dimensional systems) of conics over $\mathbb{C}$ and $\mathbb{R}$ in 1906--1907. The analogous problem for…
Switched server systems are mathematical models of manufacturing, traffic and queueing systems that have being studied since the early 1990s. In particular, it is known that typically the dynamics of such systems is asymptotically periodic:…
The authors study the spectral theory of self-adjoint operators that are subject to certain types of perturbations. An iterative introduction of infinitely many randomly coupled rank-one perturbations is one of our settings. Spectral…
We study fourfold rotation invariant gapped topological systems with time-reversal symmetry in two and three dimensions ($d=2,3$). We show that in both cases nontrivial topology is manifested by the presence of the $(d-2)$-dimensional edge…
We consider a billiard in the plane with periodic configuration of convex scatterers. This system is recurrent, in the sense that almost every orbit comes back arbitrarily close to the initial point. In this paper we study the time needed…
The verification of topological superconductivity has become a major experimental challenge. Apart from the very few spin-triplet superconductors with p-wave pairing symmetry, another candidate system is a conventional, two-dimensional (2D)…
We obtain a complete characterization of all orbits of a quadratic Collatz-type recursion called the divide-or-choose-2 rule. Each orbit either ends in a cycle whose period depends on the initial value or it goes to infinity. We specify…
A reservoir computer is a complex nonlinear dynamical system that has been shown to be useful for solving certain problems, such as prediction of chaotic signals, speech recognition or control of robotic systems. Typically a reservoir…
Traditional approaches to replication require client requests to be ordered before making them durable by copying them to replicas. As a result, clients must wait for two round-trip times (RTTs) before updates complete. In this paper, we…
For lattice modular self-reconfigurable robots (MSRRs), maintaining stable connections during reconfiguration is crucial for physical feasibility and deployability. This letter presents a novel self-reconfiguration planning algorithm for…
We present a new Ginzburg-Landau theory for superconductivity in UPt$_3$, based upon a multicomponent order parameter transforming under an irreducible space group representation; the phase is staggered in real space. Our model can explain…
The frog model is a growing system of random walks where a particle is added whenever a new site is visited. A longstanding open question is how often the root is visited on the infinite $d$-ary tree. We prove the model undergoes a phase…
We study Latent Recurrent Transformer (LRT), a lightweight augmentation of autoregressive transformers that reuses a high-level source-layer hidden state from the previous token as recurrent memory for the next token. Because this source…
The contribution of this paper is the application of compound state-triggered constraints (STCs) to real-time quad-rotor path planning. Originally developed for rocket landing applications, STCs are made up of a trigger condition and a…
Let $Z^2$ denote the standard lattice in the plane $R^2$. We prove that given a finite subset $S\subset R^2$ and $\eps>0$, then for all sufficiently large dilations $t>0$ there exists a rotation $\rho\colon R^2\to R^2$ around the origin…
We prove that the acyclic reorientation poset of a directed acyclic graph $D$ is a lattice if and only if the transitive reduction of any induced subgraph of $D$ is a forest. We then show that the acyclic reorientation lattice is always…