Related papers: Detecting unknots via equational reasoning, I: Exp…

We address the problem of sequentially selecting and observing processes from a given set to find the anomalies among them. The decision-maker observes one process at a time and obtains a noisy binary indicator of whether or not the…

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…

A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…

In this paper, we study knot diagrams for which the underlying graph has treewidth two. We give a linear time algorithm for the following problem: given a knot diagram of treewidth two, does it represent the unknot? We also show that for a…

The fundamental problem of knot theory is to know whether two knots are equivalent or not. As a tool to prove that two knots are different, mathematicians have developed various invariants. Knots invariants are just functions that can be…

We introduce an experimental procedure for the detection of quantum entanglement of an unknown quantum state with as few measurements as possible. The method requires neither a priori knowledge of the state nor a shared reference frame…

When neural networks are employed for high-stakes decision-making, it is desirable that they provide explanations for their prediction in order for us to understand the features that have contributed to the decision. At the same time, it is…

Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will…

A fundamental problem in the analysis of network data is the detection of network communities, groups of densely interconnected nodes, which may be overlapping or disjoint. Here we describe a method for finding overlapping communities based…

Despite their unprecedented performance in various domains, utilization of Deep Neural Networks (DNNs) in safety-critical environments is severely limited in the presence of even small adversarial perturbations. The present work develops a…

In this paper we develop an approach for detecting entanglement, which is based on measuring quantum correlations and constructing a correlation matrix. The correlation matrix is then used for defining a family of parameters, named…

We look into computational aspects of two classical knot invariants. We look for ways of simplifying the computation of the coloring invariant and of the Alexander module. We support our ideas with explicit computations on pretzel knots.

The complexity of modern electro-mechanical systems require the development of sophisticated diagnostic methods like anomaly detection capable of detecting deviations. Conventional anomaly detection approaches like signal processing and…

A kernel based procedure for correcting experimental data for distortions due to the finite resolution and limited detector acceptance is presented. The unfolding problem is known to be an ill-posed problem that can not be solved without…

Recently Iltgen, Lewark and Marino introduced the concept of a proper rational tangle replacement and the corresponding notion of the proper rational unknotting number. In this note we derive a version of the Montesinos trick for proper…

We use Heegaard Floer homology to give obstructions to unknotting a knot with a single crossing change. These restrictions are particularly useful in the case where the knot in question is alternating. As an example, we use them to classify…

We consider the problem of inferring the topology of a network using the measurements available at the end nodes, without cooperation from the internal nodes. To this end, we provide a simple method to obtain path interference which…

We consider knot theories possessing a {\em parity}: each crossing is decreed {\em odd} or {\em even} according to some universal rule. If this rule satisfies some simple axioms concerning the behaviour under Reidemeister moves, this leads…

Anomaly detection algorithms have been proved to be useful in the search of new physics beyond the Standard Model. However, a prerequisite for using an anomaly detection algorithm is that the signal to be sought is indeed anomalous. This…

This paper presents a theory of non-linear integer/real arithmetic and algorithms for reasoning about this theory. The theory can be conceived as an extension of linear integer/real arithmetic with a weakly-axiomatized multiplication…