arXiv research

This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in a compact, accessible manner, and to show how to use it for computational purpo…

Algorithm determines spatial graph isomorphism with vertex, edge colorings and orientations.

The paper classifies vehicle shapes and colors using deep neural networks.

Adversarial perturbations are more effective in Y-channel of YCbCr color space.

Deep convolutional neural networks (CNNs) based approaches are the state-of-the-art in various computer vision tasks, including face recognition. Considerable research effort is currently being directed towards further improving deep CNNs by focusing on more powerful model architectures and better learning techniques. …

Computer graphics techniques improve art pricing by measuring painting effort.

Pruning of redundant or irrelevant instances of data is a key to every successful solution for pattern recognition. In this paper, we present a novel ranking-selection framework for low-length but highly correlated instances. Instead of working in the low-dimensional instance space, we learn a supervised projection to …

VCML learns concepts and metaconcepts from images and questions.

Our research focuses on analysing human activities according to a known behaviorist scenario, in case of noisy and high dimensional collected data. The data come from the monitoring of patients with dementia diseases by wearable cameras. We define a structural model of video recordings based on a Hidden Markov Model. N…

Convolutional neural networks (CNN) have recently achieved state-of-the-art results in various applications. In the case of image recognition, an ideal model has to learn independently of the training data, both local dependencies between the three components (R,G,B) of a pixel, and the global relations describing edge…

Unified tensor model disentangles object appearance factors.

The paper uses VGG-19 for plant species classification from leaf images.

The paper shows links can be colored with fewer colors than previously thought.

Study finds minimal coloring numbers for torus links using rack colorings.

For a link with zero determinants, a Z-coloring is defined as a generalization of Fox coloring. We call a link having a diagram which admits a non-trivial Z-coloring a Z-colorable link. The minimal coloring number of a Z-colorable link is the minimal number of colors for non-trivial Z-colorings on diagrams of the link.…

Study on knots using 17 colors, finding specific color assignments.

It was shown that any $\mathbb{Z}$-colorable link has a diagram which admits a non-trivial $\mathbb{Z}$-coloring with at most four colors. In this paper, we consider minimal numbers of colors for non-trivial $\mathbb{Z}$-colorings on minimal diagrams of $\mathbb{Z}$-colorable links. We show, for any positive integer $N…

Aicardi's invariant $F(L)$ is extended to colored singular links using graphical calculus.

The paper finds minimum Dehn colors for knots and defines useful graphs for coloring.

K. Ichihara and E. Matsudo introduced the notions of $\mathbb{Z}$-colorable links and the minimal coloring number for $\mathbb{Z}$-colorable links, which is one of invariants for links. They proved that the lower bound of minimal coloring number of a non-splittable $\mathbb{Z}$-colorable link is 4. In this paper, we sh…

Factor complexity $b_φ(n)$ for a vertex coloring $φ$ of a regular tree is the number of colored $n$-balls up to color-preserving automorphisms. Sturmian colorings are colorings of minimal unbounded factor complexity $b_φ(n) = n+2$. In this article, we prove an induction algorithm for Sturmian colorings using colored ba…

While several approaches to face emotion recognition task are proposed in literature, none of them reports on power consumption nor inference time required to run the system in an embedded environment. Without adequate knowledge about these factors it is not clear whether we are actually able to provide accurate face e…

We prove that any $11$-colorable knot is presented by an $11$-colored diagram where exactly five colors of eleven are assigned to the arcs. The number five is the minimum for all non-trivially $11$-colored diagrams of the knot. We also prove a similar result for any $11$-colorable ribbon $2$-knot.

This survey article discusses three aspects of knot colorings. Fox colorings are assignments of labels to arcs, Dehn colorings are assignments of labels to regions, and Alexander-Briggs colorings assign labels to vertices. The labels are found among the integers modulo n. The choice of n depends upon the knot. Each typ…

The study characterizes torus links' coloring quivers using dihedral quandles.

For each odd prime p, and for each non-split link admitting non-trivial p-colorings, we prove that the maximum number of Fox colors is p. We also prove that we can assemble a non-trivial p-coloring with any number of colors, from the minimum to the maximum number of colors. Furthermore, for any rational link, we prove …

Paper describes a state sum formula for a graph coloring polynomial.

The minimal coloring number of a $\mathbb{Z}$-colorable link is the minimal number of colors for non-trivial $\mathbb{Z}$-colorings on diagrams of the link. In this paper, we show that the minimal coloring number of any non-splittable $\mathbb{Z}$-colorable links is four. As an example, we consider the link obtained by…

Convolutional neural networks (CNNs) achieve state-of-the-art performance in a wide variety of tasks in computer vision. However, interpreting CNNs still remains a challenge. This is mainly due to the large number of parameters in these networks. Here, we investigate the role of compression and particularly pruning fil…

The paper discusses knot colorings and their invariants using Goeritz matrices.

For any link and for any modulus $m$ we introduce an equivalence relation on the set of non-trivial m-colorings of the link (an m-coloring has values in Z/mZ). Given a diagram of the link, the equivalence class of a non-trivial m-coloring is formed by each assignment of colors to the arcs of the diagram that is obtaine…

Introduced coloring-allowed invariants of planar knotoids with the coloring number.

Study of quandle coloring quivers with dihedral quandles.

In this article we present the following new fact for prime p=11. For knots 6_2 and 7_2, mincol_{11} 6_2 = 5 = mincol_{11} 7_2, along with the following feature. There is a pair of diagrams, one for 6_2 and the other one for 7_2, each of them admitting only non-trivial 11-colorings using 5 colors, but neither of them a…

New TQFT homologies help color graphs, potentially solving the four color theorem.

The ability to characterize the color content of natural imagery is an important application of image processing. The pixel by pixel coloring of images may be viewed naturally as points in color space, and the inherent structure and distribution of these points affords a quantization, through clustering, of the color i…

In this article we show that if a knot diagram admits a non-trivial coloring modulo 13 then there is an equivalent diagram which can be colored with 5 colors. Leaning on known results, this implies that the minimum number of colors modulo 13 is 5.

Study shows colored Jones invariants limit to link volumes.

The paper finds 3-colorings of 2-sphere triangulations.

Study on quandle coloring quivers for (p, 2)-torus knots and links.

Gradient descent with error feedback performs better than vanilla when features are rare.

Paper extends Enami-Ozeki-Yamaguchi's work on planar quadrangulations.

New colored link invariants using multi-quandles.

Classifies colored links and spatial graphs up to colored link-homotopy.

New colored knot Floer homology defined using infinite full twists.

We define a Khovanov homotopy type for $sl_2(\mathbb{C})$ colored links and quantum spin networks and derive some of its basic properties. In the case of $n$-colored B-adequate links, we show a stabilization of the homotopy types as the coloring $n\rightarrow\infty$, generalizing the tail behavior of the colored Jones …

We introduce three spectral sequences which give some expressions of colored Jones polynomials. Each spectral sequence contains a Khovanov-type homology groups. Two of them are derived from a bicomplex of the colored Jones polynomial. The other is the spectral sequence that deduces a colored Rasmussen invariant of link…

New knot homology invariant grows exponentially with color.