相关论文: Recent advances on the non-coherent band surgery m…

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…

In this paper we study how randomly generated knots occupy a volume of space using topological methods. To this end, we consider the evolution of the first homology of an immersed metric neighbourhood of a knot's embedding for growing…

Coherent structures emerge from the dynamics of many kinds of dissipative, externally driven, nonlinear systems, and continue to provoke new questions that challenge our physical and mathematical understanding. In one specific sub-class of…

We extend the quandle cocycle invariant to the context of stuck links. More precisely, we define an invariant of stuck links by assigning Boltzmann weights at both classical and stuck crossings. As an application, we define a…

Let M be a closed oriented 3-manifold with first Betti number one. Its equivariant linking pairing may be seen as a two-dimensional cohomology class in an appropriate infinite cyclic covering of the space of ordered pairs of distinct points…

We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unknotted, capable of being continuously deformed without self-intersection so that it lies in a plane. We show that this problem, {\sc…

A spin-charge recombination route to superconductivity, proposed earlier (1992)], is examined using the Schwinger boson representation of the t-J model. The representation is known to work well at half-filling. It was shown in the earlier…

We study some comparison between a bilinear cohomology pairing in local coefficients and the Blanchfield pairing of a knot. We show that the former pairing is an $S$-equivalent invariant, and give a criterion to a relation between the two…

We consider knots equipped with a representation of their knot groups onto a dihedral group D_{2n} (where n is odd). To each such knot there corresponds a closed 3-manifold, the (irregular) dihedral branched covering space, with the…

Harmonization improves data consistency and is central to effective integration of diverse imaging data acquired across multiple sites. Recent deep learning techniques for harmonization are predominantly supervised in nature and hence…

DNA regulation and repair processes require direct interactions between proteins and DNA at specific sites. Local fluctuations of the sugar-phosphate backbones and bases of DNA (a form of DNA "breathing") play a central role in such…

Though the problem of sequence-reversed protein folding is largely unexplored, one might speculate that reversed native protein sequences should be significantly more foldable than purely random heteropolymer sequences. In this article, we…

We derive exact formulae for the allele frequency spectrum under the coalescent with mutation, conditioned on allele counts at some fixed time in the past. We consider unlinked biallelic markers mutating according to a finite sites, or…

We present a simple two-dimensional model of the indirect dissociative recombination process. The model has one electronic and one nuclear degree of freedom and it can be solved to high precision, without making any physically motivated…

Biological systems are driven by intricate interactions among the complex array of molecules that comprise the cell. Many methods have been developed to reconstruct network models of those interactions. These methods often draw on large…

Biological networks provide insight into the complex organization of biological processes in a cell at the system level. They are an effective tool for understanding the comprehensive map of functional interactions, finding the functional…

We provide three 3-dimensional characterizations of the Z-slice genus of a knot, the minimal genus of a locally-flat surface in 4-space cobounding the knot whose complement has cyclic fundamental group: in terms of balanced algebraic…

While the thermodynamics of DNA hybridization is well understood, much less is known about the kinetics of this classic system. Filling this gap in our understanding has new urgency because DNA nanotechnology often depends critically on…

Non-invertible symmetries have by now seen numerous constructions in higher dimensional Quantum Field Theories (QFT). In this paper we provide an in depth study of gauging 0-form symmetries in the presence of non-invertible symmetries. The…

Residue-residue interactions that fold a protein into a unique three-dimensional structure and make it play a specific function impose structural and functional constraints on each residue site. Selective constraints on residue sites are…