Related papers: Following Knots Down Their Energy Gradients
We present a computer simulation study of the compact self-avoiding loops as regards their length and topological state. We use a Hamiltonian closed path on the cubic-shaped segment of a 3D cubic lattice as a model of a compact polymer. The…
We demonstrate a novel method for measuring the discrete energy spectrum of a quantum dot connected very weakly to a single lead. A train of voltage pulses applied to a metal gate induces tunneling of electrons between the quantum dot and a…
The present chapter gives an overview on results for discrete knot energies. These discrete energies are designed to make swift numerical computations and thus open the field to computational methods. Additionally, they provide an…
The existence of stable links and knots is demonstrated in three-dimensional, bistable, chemical media. The reaction-diffusion medium segregates into regions of high and low concentration separated by sharp interfaces. The interfaces repel…
The last decade has shown a tremendous success in solving various computer vision problems with the help of deep learning techniques. Lately, many works have demonstrated that learning-based approaches with suitable network architectures…
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…
Energy correlators have recently come to the forefront of jet substructure studies at colliders due to their remarkable properties: they naturally separate physics at different scales, are robust to contamination from soft radiation, and…
Electrons and ions trapped with electromagnetic fields have long served as important high-precision metrological instruments, and more recently have also been proposed as a platform for quantum information processing. Here we point out that…
We explore free knot diagrams, which are projections of knots into the plane which don't record over/under data at crossings. We consider the combinatorial question of which free knot diagrams give which knots and with what probability.…
We consider countable linear orders and study the quasi-order of convex embeddability and its induced equivalence relation. We obtain both combinatorial and descriptive set-theoretic results, and further extend our research to the case of…
A well-known algorithm for unknotting knots involves traversing a knot diagram and changing each crossing that is first encountered from below. The minimal number of crossings changed in this way across all diagrams for a knot is called the…
This paper determines the minimal degree sequence for two compact rational knots, namely the trefoil and figure-eight knots. We find explicit projections with the minimal degree sequence of each knot. This is done by modifying a non-compact…
We discuss quantum information processing with trapped electrons. After recalling the operation principle of planar Penning traps we sketch the experimental conditions to load, cool and detect single electrons. Here we present a detailed…
Inspired by how certain proteins "sense" knots and entanglements in DNA molecules, here we ask if there exist local geometric features that may be used as a read-out of the underlying topology of generic polymers. We perform molecular…
We perform theoretical studies of stretching of 20 proteins with knots within a coarse grained model. The knot's ends are found to jump to well defined sequential locations that are associated with sharp turns whereas in homopolymers they…
During the last few years, there has been plenty of research for reducing energy consumption in telecommunication infrastructure. However, many of the proposals remain unim-plemented due to the lack of flexibility in legacy networks. In…
We introduce a method for calculating the extent to which chain non-crossing is important in the most efficient, optimal trajectories or pathways for a protein to fold. This involves recording all unphysical crossing events of a ghost…
We present a comprehensive theoretical study of the physical phenomena that determine the relative energies of the three of the lowest electronic states of each of the square-planar copper complexes $\cucl$, $\cunh$ and $\cuwater$, and…
Shallow, CNOT-efficient quantum circuits are crucial for performing accurate computational chemistry simulations on current noisy quantum hardware. Here, we explore the usefulness of non-iterative energy corrections, based on the method of…
We analyze a microscopic RNA model, which includes two widely used models as limiting cases, namely it contains terms for bond as well as for stacking energies. We numerically investigate possible changes in the qualitative and quantitative…