Related papers: Survey on effective separability
We use the generalized concurrence approach to investigate the general multipartite separability problem. By extending the preconcurrence matrix formalism to arbitrary multipartite systems, we show that the separability problem can be…
In machine learning, the performance of a classifier depends on both the classifier model and the separability/complexity of datasets. To quantitatively measure the separability of datasets, we create an intrinsic measure -- the…
This research seeks to benefit the software engineering society by proposing comparative separation, a novel group fairness notion to evaluate the fairness of machine learning software on comparative judgment test data. Fairness issues have…
A basic question in the study of measure-once quantum finite automata is whether two distinct input words can be separated with certainty. The exact separation problem reduces to a trace-vanishing question in \(SU(2)\). The main difficulty…
A countable group is residually finite if every nontrivial element can act nontrivially on a finite set. When a group fails to be residually finite, we might want to measure how drastically it fails - it could be that only finitely many…
Clustering is a fundamental data mining tool that aims to divide data into groups of similar items. Generally, intuition about clustering reflects the ideal case -- exact data sets endowed with flawless dissimilarity between individual…
The separability problem for word languages of a class $\mathcal{C}$ by languages of a class $\mathcal{S}$ asks, for two given languages $I$ and $E$ from $\mathcal{C}$, whether there exists a language $S$ from $\mathcal{S}$ that includes…
The study of separating invariants is a recent trend in invariant theory. For a finite group acting linearly on a vector space, a separating set is a set of invariants whose elements separate the orbits of G. In some ways, separating sets…
We find explicit subdivision rules for all special cubulated groups. A subdivision rule for a group produces a sequence of tilings on a sphere which encode all quasi-isometric information for a group. We show how these tilings detect…
We investigate a famous decision problem in automata theory: separation. Given a class of language C, the separation problem for C takes as input two regular languages and asks whether there exists a third one which belongs to C, includes…
In cases of uncertainty, a multi-class classifier preferably returns a set of candidate classes instead of predicting a single class label with little guarantee. More precisely, the classifier should strive for an optimal balance between…
Linear second order recursive sequences with arbitrary initial conditions are studied. For sequences with the same parameters a ring and a group is attached, and isomorphisms and homomorphisms are established for related parameters. In the…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
We propose experimentally feasible separability criteria for bipartite systems based on local symmetric measurements. Through detailed examples, we demonstrate that our criteria can detect entanglement more effectively compared to existing…
Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider…
Unsupervised word segmentation in audio utterances is challenging as, in speech, there is typically no gap between words. In a preliminary experiment, we show that recent deep self-supervised features are very effective for word…
Community detection in networks is one of the most popular topics of modern network science. Communities, or clusters, are usually groups of vertices having higher probability of being connected to each other than to members of other…
It is known that there exists a first-order sentence that holds in a finite group if and only if the group is soluble. Here it is shown that the corresponding statements with 'solubility' replaced by 'nilpotence' and 'perfectness', among…
A permutoid is a set of partial permutations that contains the identity and is such that partial compositions, when defined, have at most one extension in the set. In 2004 Peter Cameron conjectured that there can exist no algorithm that…
We give a new, effective proof of the separability of cubically convex-cocompact subgroups of special groups. As a consequence, we show that if $G$ is a virtually compact special hyperbolic group, and $Q\leq G$ is a $K$-quasiconvex…