Related papers: Knotting probabilities after a local strand passag…
The statistical properties of random lattice knots, the topology of which is determined by the algebraic topological Jones-Kauffman invariants was studied by analytical and numerical methods. The Kauffman polynomial invariant of a random…
We present a non-algebraic, locality-preserving framework for triangle detection in worst-case sparse graphs. Our algorithm processes the graph in $O(\log n)$ independent layers and partitions incident edges into prefix-based classes where…
The work addresses the analogy between trivial knotting and excluded volume in looped polymer chains of moderate length, $N<N_0$, where the effects of knotting are small. A simple expression for the swelling seen in trivially knotted loops…
We study random digraphs on sequences of expanders with bounded average degree {which converge locally in probability}. We prove that the threshold for the existence of a giant strongly connected component, as well as the asymptotic…
The unknotting number of a positive braid with n strands and k intersections is known to be equal to (k-n+1)/2. We consider Lorenz knots (which are positive braids) and, using a different method, find their unknotting numbers in terms of…
In this paper, we consider Bernoulli percolation on a locally finite, transitive and infinite graph (e.g. the hypercubic lattice $\mathbb{Z}^d$). We prove the following estimate, where $\theta_n(p)$ is the probability that there is a path…
We study rooted self avoiding polygons and self avoiding walks on deterministic fractal lattices of finite ramification index. Different sites on such lattices are not equivalent, and the number of rooted open walks W_n(S), and rooted…
The pseudogap phase occurring in cuprate and organic superconductors is analyzed based on the dynamical cluster approximation (DCA) approach to the Hubbard model. A cluster embedded in a self-consistent bath is studied. With increasing…
The contact process is a simple model for the spread of an infection in a structured population. We investigate the case when the underlying structure evolves dynamically as a degree-dependent dynamical percolation model. Starting with a…
Self-avoiding walks are studied on the 3-simplex fractal lattice as a model of linear polymer conformations in a dilute, non-homogeneous solution. A model is supplemented with bending energies and attractive-interaction energies between…
A special type of geometric situation in ensembles of non-intersecting paths occurs when the non-intersecting trajectories are required to be nonnegative so that the limit shape becomes tangential to the hard-edge $0$. The local fluctuation…
A two-dimensional square-lattice model for the formation of secondary structures in proteins, the hydrogen-bonding model, is extended to include the effects of solvent quality. This is achieved by allowing configuration-dependent…
We consider the variation of von Neumann entropy of subsystem reduced states of general many- body lattice spin systems due to local quantum quenches. We obtain Lieb-Robinson-like bounds that are independent of the subsystem volume. The…
We study a variant of bootstrap percolation in which growth is restricted to a single active cluster. Initially there is a single active site at the origin, while other sites of Z^2 are independently occupied with small probability p,…
A simple braid is a positive braid that can be drawn so that any two strands cross at most once. We prove that as $n \to \infty$, the proportion of simple braids on $n$ strands that have positive topological entropy tends toward $100\%$.…
The presence of slipknots in configurations of proteins and DNA has been shown to affect their functionality, or alter it entirely. Historically, polymers are modeled as polygonal chains in space. As an alternative to space curves, we…
Semiflexible polymers are widely used as a paradigm for understanding structural phases in biomolecules including folding of proteins. Here, we compare bead-spring and bead-stick variants of coarse-grained semiflexible polymer models that…
The square lattice with central-force springs on nearest-neighbor bonds is isostatic. It has a zero mode for each row and column, and it does not support shear. Using the Coherent Potential Approximation (CPA), we study how the random…
An implementation of BFACF-style algorithms on knotted polygons in the simple cubic, face centered cubic and body centered cubic lattice is used to estimate the statistics and writhe of minimal length knotted polygons in each of the…
Generalizing unknotting number, $n$-adjacent knots have $n$ crossings such that changing any non-empty subset of them results in the unknot. In this paper, we determine the 2-adjacent knots through 12 crossings. Using Heegaard Floer…