Related papers: Following Knots Down Their Energy Gradients
This article surveys the use of configuration space integrals in the study of the topology of knot and link spaces. The main focus is the exposition of how these integrals produce finite type invariants of classical knots and links. More…
Understanding the biological function of knots in proteins and their folding process is an open and challenging question in biology. Recent studies classify the topology and geometry of knotted proteins by analysing the distribution of a…
There are well-known protocols for performing CNOT quantum logic with qubits coupled by particular high-symmetry (Ising or Heisenberg) interactions. However, many architectures being considered for quantum computation involve qubits or…
Knots are deeply entangled with every branch of science. One of the biggest open challenges in knot theory is to formalise a knot invariant that can unambiguously and efficiently distinguish any two knotted curves. Additionally, the…
This work presents KnotDLO, a method for one-handed Deformable Linear Object (DLO) knot tying that is robust to occlusion, repeatable for varying rope initial configurations, interpretable for generating motion policies, and requires no…
The altenating knots, links and twists projected on the S_2 sphere are identified with the phase Space of a Hamiltonian dynamic system of one degree of freedom. The saddles of the system correspond to the crossing points, the edges, to the…
Due to the energy transition, today's electrical networks include synchronous machines and inverter-based resources interfacing renewable energies such as wind turbines, solar panels, and Battery Energy Storage Systems to the grid. In such…
We study RNA foldings and investigate their topology using a combination of knot theory and embedded rigid vertex graphs. Knot theory has been helpful in modeling biomolecules, but classical knots place emphasis on a biomolecule's…
Random cost simulations were introduced as a method to investigate optimization problems in systems with conflicting constraints. Here I study the approach in connection with the training of a feed-forward multilayer perceptron, as used in…
The magnetic relaxation processes in disordered two-dimensional ensembles of dipole-coupled magnetic nanoparticles are theoretically investigated by performing numerical simulations. The energy landscape of the system is explored by…
The inelastic scattering of electrons is one route to study the vibrational and electronic properties of materials. Such experiments, also called electron energy-loss spectroscopy, are particularly useful for the investigation of the…
This is a short expository article on alternating knots and is to appear in the Concise Encyclopedia of Knot Theory.
We define some physical variables associated with the traversing sequences of electrons along the orbit which is a 2D projection of 8$_{18}$-knot. The configuration is regular but the resulting contributions, which are related to the…
In physical networks trained using supervised learning, physical parameters are adjusted to produce desired responses to inputs. An example is electrical contrastive local learning networks of nodes connected by edges that are resistors…
In models with large additional dimensions, the GUT scale can be lowered to values accessible by future colliders. Due to modification of the loop corrections from particles propagating into the extra dimensions, the logarithmic running of…
This paper focuses on the graphs in the Petersen family, the set of minor minimal intrinsically linked graphs. We prove there is a relationship between algebraic linking of an embedding and knotting in an embedding. We also present a more…
Knots, links and entangled filaments appear in many physical systems of interest in biology and engineering. Classifying knots and measuring entanglement is of interest both for advancing knot theory, as well as for analyzing large data…
Topological entanglements are abundant, and often detrimental, in polymeric systems in biology and materials science. Here we theoretically investigate the topological simplification of knots by diffusing slip-links (SLs), which may…
Knots are familiar entities that appear at a captivating nexus of art, technology, mathematics, and science. As topologically stable objects within field theories, they have been speculatively proposed as explanations for diverse persistent…
Proteins can sometimes be knotted, and for many reasons the study of knotted proteins is rapidly becoming very important. For example, it has been proposed that a knot increases the stability of a protein. Knots may also alter enzymatic…