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Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…
We show that any pseudo-Anosov map that is a lift of pseudo-Anosov homeomorphism of a nonorientable surface has vanishing SAF invariant. We also provide a criterion to certify that a pseudo-Anosov map is not such a lift.
In this article, we briefly describe various tools and approaches that algebraic geometry has to offer to straighten bent objects. Throughout this article we will consider a specific example of a bent or curved piece of paper which in our…
We show that, for a closed non-orientable surface $F$, an automorphism of $H_1(F,\Z)$ is induced by a homeomorphism of $F$ if and only if it preserves the (mod 2) intersection pairing. We shall also prove the corresponding result for…
We present some algorithms that provide useful topological information about curves in surfaces. One of the main algorithms computes the geometric intersection number of two properly embedded 1-manifolds $C_1$ and $C_2$ in a compact…
Presentation attack is a challenging issue that persists in the security of automatic fingerprint recognition systems. This paper proposes a novel explainable residual slim network that detects the presentation attack by representing the…
Every pseudo-Anosov homeomorphism $f$ admits infinitely many Markov partitions. A \textit{geometric Markov partition} is a Markov partition $\mathcal{R}$ in which each rectangle is equipped with a vertical orientation. To each pair $(f,…
The attention that deep learning has garnered from the academic community and industry continues to grow year over year, and it has been said that we are in a new golden age of artificial intelligence research. However, neural networks are…
This paper presents the application of Kolmogorov-Arnold Networks (KAN) in classifying metal surface defects. Specifically, steel surfaces are analyzed to detect defects such as cracks, inclusions, patches, pitted surfaces, and scratches.…
In this paper we consider the numerical solution to the soft-margin support vector machine optimization problem. This problem is typically solved using the SMO algorithm, given the high computational complexity of traditional optimization…
Signature verification has been one of the major researched areas in the field of computer vision. Many financial and legal organizations use signature verification as access control and authentication. Signature images are not rich in…
Visual localization on standard-definition (SD) maps has emerged as a promising low-cost and scalable solution for autonomous driving. However, existing regression-based approaches often overlook inherent geometric priors, resulting in…
Partial differential equations (PDEs) on surfaces are fundamental to scientific computing and geometry processing. A popular approach to solving PDEs on surfaces is the finite element method (FEM), where the surface is divided into discrete…
Motivated by the enumeration of the BPS spectra of certain 3d $\mathcal{N}=2$ supersymmetric quantum field theories, obtained from the compactification of 6d superconformal field theories on three-manifolds, we study the homeomorphism…
Deep neural networks for 3D point cloud understanding have achieved remarkable success in object classification and recognition, yet recent work shows that these models remain highly vulnerable to adversarial perturbations. Existing 3D…
We present a characterisation of blenders based on mapping properties of certain sets of curves that can be rigorously verified by computer-assisted methods. We develop an algorithm to construct these sets of curves that requires only a…
We consider $f, h$ homeomorphims generating a faithful $BS(1,n)$-action on a closed surface $S$, that is, $h f h^{-1} = f^n$, for some $ n\geq 2$. According to \cite{GL}, after replacing $f$ by a suitable iterate if necessary, we can assume…
Among (isotopy classes of) automorphisms of handlebodies those called irreducible (or generic) are the most interesting, analogues of pseudo-Anosov automorphisms of surfaces. We consider the problem of isotoping an irreducible automorphism…
The dominant approach for surface defect detection is the use of hand-crafted feature-based methods. However, this falls short when conditions vary that affect extracted images. So, in this paper, we sought to determine how well several…
Existing deep learning algorithms for point cloud analysis mainly concern discovering semantic patterns from global configuration of local geometries in a supervised learning manner. However, very few explore geometric properties revealing…