Related papers: Knot Dynamics
We consider a logic used to describe sets of configurations of distributed systems, whose network topologies can be changed at runtime, by reconfiguration programs. The logic uses inductive definitions to describe networks with an unbounded…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
We construct families of trivial $2$-knots $K_i$ in $\mathbb{R}^4$ such that the maximal complexity of $2$-knots in any isotopy connecting $K_i$ with the standard unknot grows faster than a tower of exponentials of any fixed height of the…
We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal (such as gravity or a magnetic field). We show that a maze of…
The advent of solid state nanodevices allows for interrogating the physico-chemical properties of a polyelectrolyte chain by electrophoretically driving it through a nanopore. Salient dynamical aspects of the translocation process have been…
Across all scales of the physical world, dynamical systems can often be usefully represented as abstract networks that encode the system's units and inter-unit interactions. Understanding how physical rules shape the topological structure…
Due to its non-crystalline nature, the glassy state has remained one the most exciting scientific challenges. To study such materials, Molecular Dynamics (MD) simulations have been extensively used because they provide a direct view into…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
The difficulty to simulate the dynamics of open quantum systems resides in their coupling to many-body reservoirs with exponentially large Hilbert space. Applying a tensor network approach in the time domain, we demonstrate that effective…
Few physical systems with topologies more complicated than simple gaussian linking have been explored in detail. Here we focus on examples with higher topologies in non-relativistic quantum mechanics and in QCD.
The interaction of distinct units in physical, social, biological and technological systems naturally gives rise to complex network structures. Networks have constantly been in the focus of research for the last decade, with considerable…
Physical systems ranging from elastic bodies to kinematic linkages are defined on high-dimensional configuration spaces, yet their typical low-energy configurations are concentrated on much lower-dimensional subspaces. This work addresses…
We develop a reinforcement learning pipeline for simplifying knot diagrams. A trained agent learns move proposals and a value heuristic for navigating Reidemeister moves. The pipeline applies to arbitrary knots and links; we test it on…
Many experiments have been done to determine the relative strength of different knots, and these show that the break in a knotted rope almost invariably occurs at a point just outside the `entrance' to the knot. The influence of knots on…
We investigate the dynamics of a quantum system subjected to a time-dependent and conditional resetting protocol. Namely, we ask: what happens when the unitary evolution of the system is repeatedly interrupted at random time instants with…
Vortex stretching is a common feature of many complex flows, including turbulence. Experiments and simulations of isolated vortex knots demonstrate that this behavior can also be seen in relatively simple systems, and appears to be…
Networked systems display complex patterns of interactions between a large number of components. In physical networks, these interactions often occur along structural connections that link components in a hard-wired connection topology,…
Contraction theory is a mathematical framework for studying the convergence, robustness, and modularity properties of dynamical systems and algorithms. In this opinion paper, we provide five main opinions on the virtues of contraction…
Neural networks (NNs) are now routinely implemented on systems that must operate in uncertain environments, but the tools for formally analyzing how this uncertainty propagates to NN outputs are not yet commonplace. Computing tight bounds…
The design of new devices and experiments in science and engineering has historically relied on the intuitions of human experts. This credo, however, has changed. In many disciplines, computer-inspired design processes, also known as…