Related papers: A neural network approach to predicting and comput…
Although artificial neural networks have occasionally been used for Quantitative Structure-Activity/Property Relationship (QSAR/QSPR) studies in the past, the literature has of late been dominated by other machine learning techniques such…
In this paper we describe what should perhaps be called a `type-2' Vassiliev invariant of knots S^2 -> S^4. We give a formula for an invariant of 2-knots, taking values in Z_2 that can be computed in terms of the double-point diagram of the…
Deep neural networks have been applied in many applications exhibiting extraordinary abilities in the field of computer vision. However, complex network architectures challenge efficient real-time deployment and require significant…
Deep neural networks have achieved impressive performance in many applications but their large number of parameters lead to significant computational and storage overheads. Several recent works attempt to mitigate these overheads by…
We extend knot contact homology to a theory over the ring $\mathbb{Z}[\lambda^{\pm 1},\mu^{\pm 1}]$, with the invariant given topologically and combinatorially. The improved invariant, which is defined for framed knots in $S^3$ and can be…
Algorithm of construction of all knots, links with given number of crosses on diagram of knot, link is offered. This algorithm is based on simple proposition, that there is a representation of knot (link) as closure of braid with n threads…
We perform a massive evaluation of neural networks with architectures corresponding to random graphs of various types. We investigate various structural and numerical properties of the graphs in relation to neural network test accuracy. We…
Frequently, knots are enumerated by their crossing number. However, the number of knots with crossing number $c$ grows exponentially with $c$, and to date computer-assisted proofs can only classify diagrams up to around twenty crossings.…
Virtual knot theory is a generalization (discovered by the author in 1996) of knot theory to the study of all oriented Gauss codes. (Classical knot theory is a study of planar Gauss codes.) Graph theory studies non-planar graphs via…
In topologically-protected quantum computation, quantum gates can be carried out by adiabatically braiding two-dimensional quasiparticles, reminiscent of entangled world lines. Bonesteel et al. [Phys. Rev. Lett. 95, 140503 (2005)], as well…
Physical knot classification is a challenging fine-grained recognition task in which the intended discriminative cue is rope crossing structure; however, high closed-set accuracy may still arise from low-level appearance shortcuts rather…
We show that any of the new knot invariants obtained from Chern-Simons theory based on an arbitrary non-abelian gauge group do not distinguish isotopically inequivalent mutant knots and links. In an attempt to distinguish these knots and…
An important problem in network analysis is predicting a node attribute using both network covariates, such as graph embedding coordinates or local subgraph counts, and conventional node covariates, such as demographic characteristics.…
We introduce a pruning algorithm that provably sparsifies the parameters of a trained model in a way that approximately preserves the model's predictive accuracy. Our algorithm uses a small batch of input points to construct a data-informed…
Quantum networks illustrate the use of connected nodes of quantum systems as the backbone of distributed quantum information processing. When the network nodes are entangled in graph states, such a quantum platform is indispensable to…
The purpose of the paper is two-fold: to introduce a multivariable creative telescoping method, and to apply it in a problem of Quantum Topology: namely the computation of the non-commutative $A$-polynomial of twist knots. Our multivariable…
In this paper, we consider the knot matching problem arising in computational forestry. The knot matching problem is an important problem that needs to be solved to advance the state of the art in automatic strength prediction of lumber. We…
We construct two distinct yet related M-theory models that provide suitable frameworks for the study of knot invariants. We then focus on the four-dimensional gauge theory that follows from appropriately compactifying one of these M-theory…
We show experimentally that the accuracy of a trained neural network can be predicted surprisingly well by looking only at its weights, without evaluating it on input data. We motivate this task and introduce a formal setting for it. Even…
Ito-Takimura recently defined a splice-unknotting number $u^-(D)$ for knot diagrams. They proved that this number provides an upper bound for the crosscap number of any prime knot, asking whether equality holds in the alternating case. We…