arXiv research

The fundamental n-quandles of links are residually finite for n ≥ 2.

We study the structure of finite quandles in terms of subquandles. Every finite quandle $Q$ decomposes in a natural way as a union of disjoint $Q$-complemented subquandles; this decomposition coincides with the usual orbit decomposition of $Q$. Conversely, the structure of a finite quandle with a given orbit decomposit…

Classifies good involutions in conjugation subquandles and racks.

The study describes good involutions in quandles and Alexander quandles.

We study the quandle counting invariant for a certain family of finite quandles with trivial orbit subquandles. We show how these invariants determine the linking number of classical two-component links up to sign.

New polynomials defined for quandle structures, enhancing graph invariants.

We prove that the fundamental quandle of the trefoil knot is isomorphic to the projective primitive subquandle of transvections of the symplectic space $\Z \oplus \Z$. The last quandle can be identified with the Dehn quandle of the torus and the cord quandle on a 2-sphere with four punctures. We also show that the fund…

We give a formula of the connected component decomposition of the Alexander quandle: $\mathbb{Z}[t^{\pm1}]/(f_1(t),\ldots, f_k(t))=\bigsqcup^{a-1}_{i=0}\mathrm{Orb}(i)$, where $a=\gcd (f_1(1),\ldots, f_k(1))$. We show that the connected component $\mathrm{Orb}(i)$ is isomorphic to $\mathbb{Z}[t^{\pm1}]/J$ with an expli…

Study of profinite quandles with constructions and characterizations.

This paper constructs quandles with abelian inner automorphism groups from graphs, proving their homogeneity.

The paper studies quandles of hyperbolic 3-space isometries.

The study examines Hopfian properties of conjugation quandles and their underlying groups.

New graph types help identify complex relationships.

Neural networks can separate non-separable data using feature maps.

DSI measures dataset separability for neural networks.

Separates estimation and control in risk-sensitive investment problems with partial observation.

Deep learning approaches have recently achieved impressive performance on both audio source separation and sound classification. Most audio source separation approaches focus only on separating sources belonging to a restricted domain of source classes, such as speech and music. However, recent work has demonstrated th…

Bayesian approach uses generative models as priors for better source separation.

New examples show some convex-cocompact subgroups are separable.

Logarithmic separation profile in hyperbolic groups shows hierarchical structure.

New machine learning method detects quantum separability in large-scale systems.

The study shows subgroup separability conditions for specific groups.

The paper examines subgroup separability for surface and virtual braid groups.

We present a monophonic source separation system that is trained by only observing mixtures with no ground truth separation information. We use a deep clustering approach which trains on multi-channel mixtures and learns to project spectrogram bins to source clusters that correlate with various spatial features. We sho…

The study of random surfaces reveals asymptotic lengths of separating geodesics.

A new measure DCSI quantifies separability for density-based clustering.

A new NMF variant tackles underdetermined problems with sparse and separable assumptions.

This work examines a semi-blind single-channel source separation problem. Our specific aim is to separate one source whose local structure is approximately known, from another a priori unspecified background source, given only a single linear combination of the two sources. We propose a separation technique based on lo…

One approach to monitoring a dynamic system relies on decomposition of the system into weakly interacting subsystems. An earlier paper introduced a notion of weak interaction called separability, and showed that it leads to exact propagation of marginals for prediction. This paper addresses two questions left open by t…

Develops large-sample theory for non-stationary source separation.

Sound source separation has attracted attention from Music Information Retrieval(MIR) researchers, since it is related to many MIR tasks such as automatic lyric transcription, singer identification, and voice conversion. In this paper, we propose an intuitive spectrogram-based model for source separation by adapting U-…

Guiding the design of neural networks is of great importance to save enormous resources consumed on empirical decisions of architectural parameters. This paper constructs shallow sigmoid-type neural networks that achieve 100% accuracy in classification for datasets following a linear separability condition. The separab…

Criterion for subgroup separability in outer automorphism groups.

Study on hyperbolic groups, focusing on separability and splittings.

This paper proposes a new evaluation metric and boosting method for weight separability in neural network design. In contrast to general visual recognition methods designed to encourage both intra-class compactness and inter-class separability of latent features, we focus on estimating linear independence of column vec…

The paper solves optimal bounds for separating data points in high dimensions.

Suppose that all hyperbolic groups are residually finite. The following statements follow: In relatively hyperbolic groups with peripheral structures consisting of finitely generated nilpotent subgroups, quasiconvex subgroups are separable; Geometrically finite subgroups of non-uniform lattices in rank one symmetric sp…

Wavesplit separates speech from mixtures using clustering.

The paper introduces toric separable geometries and finds new extremal metrics.

Singing voice separation attempts to separate the vocal and instrumental parts of a music recording, which is a fundamental problem in music information retrieval. Recent work on singing voice separation has shown that the low-rank representation and informed separation approaches are both able to improve separation qu…

Separating an audio scene into isolated sources is a fundamental problem in computer audition, analogous to image segmentation in visual scene analysis. Source separation systems based on deep learning are currently the most successful approaches for solving the underdetermined separation problem, where there are more …

Adaptive algorithm reduces regret in causal bandits.

Study optimizes fairness in predictive models by balancing utility and separation.

Paper introduces a new time separation function for $C^0$ spacetimes.

A new neural network separates vocals from music accompaniment.

Improved mistake bound for group linear separable cases in online multiclass linear classification.

Study on diagonal and separating coordinates for symmetric spaces of rank 1.

A tensor field generates separation of variables for certain metrics.