相关论文: Some Ropelength-Critical Clasps
We produce embeddings of knots in thin position that admit compressible thin levels. We also find the bridge number of tangle sums where each tangle is high distance.
We consider the distribution of cycles in two models of random permutations, that are related to one another. In the first model, cycles receive a weight that depends on their length. The second model deals with permutations of points in…
We present a new proof of a recent $\epsilon$ regularity of G. Tian and J.Viaclovsky. Moreover, our idea also also works with a kind of $L^p, p<\dim M/2$ assumptions on the curvature.
We study Kauffman's model of folded ribbon knots: knots made of a thin strip of paper folded flat in the plane. The ribbonlength is the length to width ratio of such a folded ribbon knot. We show for any knot or link type that there exist…
We study dynamics of a Rouse polymer chain, which diffuses in a three-dimensional space under the constraint that one of its ends, referred to as the slip-link, may move only along a one-dimensional line containing randomly placed,…
We show that near any given minimizing sequence of paths for the mountain pass lemma, there exists a critical point whose polarization is also a critical point. This is motivated by the fact that if any polarization of a critical point is…
When a ribbon or tube is twisted far enough it forms buckles and wrinkles. Its new geometry can be strikingly ordered, or hopelessly disordered. Here we study this process in a tube with hybrid boundary conditions: one end a cylinder, and…
We calculate the ground-state compressibility of a deformable spin-1/2 Heisenberg-Ising chain with Dzyaloshinskii-Moriya interaction to discuss how a quantum critical point inherent in this spin system may manifest itself in the elastic…
A trapping mechanism is observed and proposed as the origin of the anomalous behavior recently discovered in transport properties of overdamped ratchets subject to external oscillatory drive in the presence of quenched noise. In particular,…
We study bond percolation for a family of infinite hyperbolic graphs. We relate percolation to the appearance of homology in finite versions of these graphs. As a consequence, we derive an upper bound on the critical probabilities of the…
A statistical study of crumpled paper is allowed by a minimal 1D model: a self-avoiding line bent at sharp angles -- in which resides the elastic energy -- put in a confining potential. Many independent equilibrium configurations are…
Many mechanical structures, both engineered and biological, combine heavy rigid elements such as bones and beams with lightweight flexible ones such as cables and membranes. These are referred to as tensegrities, reflecting that cables can…
Robotic manipulation of deformable, one-dimensional objects (DOOs) like ropes or cables has important potential applications in manufacturing, agriculture, and surgery. In such environments, the task may involve threading through or…
Skew braces are intensively studied owing to their wide ranging connections and applications. We generalize the definition of a skew brace to give a new algebraic object, which we term a skew bracoid. Our construction involves two groups…
Cages ($r$-regular graphs of girth $g$ and minimum order) and their variants have been studied for over seventy years. Here we propose a new variant, "weighted cages". We characterize their existence; for cases $g=3,4$ we determine their…
Grasp learning has become an exciting and important topic in robotics. Just a few years ago, the problem of grasping novel objects from unstructured piles of clutter was considered a serious research challenge. Now, it is a capability that…
In this note, we try to analyze and clarify the intriguing interplay between some counting problems related to specific thermalized weighted graphs and random walks consistent with such graphs.
This paper provides a systematic treatment of Gorenstein homological aspects for cleft extensions of rings. In particular, we investigate Goresnteinness, Gorenstein projective modules and singularity categories in the context of cleft…
This paper presents the following results on sets that are complete for NP. 1. If there is a problem in NP that requires exponential time at almost all lengths, then every many-one NP-complete set is complete under length-increasing…
The problem of homological stability helps us to catch the structure of group homology. We calculate homological stability of special orthogonal groups, and we also calculate the stability of orthogonal groups with determinant-twisted…