arXiv research

Proposes MCC-F1 curve for better binary classification evaluation.

Comparison of decision curve analysis and cost curves for model evaluation.

Study theta-curves on torus in 3-sphere, classifying them.

Simplified proof classifies surfaces using normal curves.

We consider the global symplectic classification problem of plane curves. First we give the exact classification result under symplectomorphisms, for the case of generic plane curves, namely immersions with transverse self-intersections. Then the set of symplectic classes form the symplectic moduli space which we compl…

Classification of curves up to affine transformation in a finite dimensional space was studied by some different methods. In this paper, we achieve the exact formulas of affine invariants via the equivalence problem and in the view of Cartan's lemma and then, state a necessary and sufficient condition for classificatio…

Study on triharmonic curves in 3D spaces, proving their existence and classification.

We classify curves in the moduli space of curves that are both Shimura- and Teichmueller curves: Except for the moduli space of genus one curves there is only a single such curve. We start with a Hodge-theoretic description of Shimura curves and of Teichmueller curves that reveals similarities and differences of the tw…

A directed curve is a possibly singular curve with well-defined tangent lines along the curve. Then the tangent surface to a directed curve is naturally defined as the ruled surface by tangent geodesics to the curve, whenever any affine connection is endowed with the ambient space. In this paper the local diffeomorphis…

The paper characterizes Legendre curves on trans-S-manifolds.

It is given the diffeomorphism classification on generic singularities of tangent varieties to curves with arbitrary codimension in a projective space. The generic classifications are performed in terms of certain geometric structures and differential systems on flag manifolds, via several techniques in differentiable …

We show that the topological classification and the smooth classification are generically the same for certain families of plane curves in a semi-local case(the double local case). Especially we give the normal form of transversely jointed two families of plane curves with second order contact at the envelope.

We present a local classification of smooth projective surfaces in 3-space via projective transformations in accordance with singularity types of central projections up to codimension 4. We also discuss relations between our classification of Monge forms and bifurcations of parabolic curves and flecnodal curves.

Machine learning predicts arithmetic curve invariants with high accuracy.

This paper is motivated by the real symplectic isotopy problem : does there exists a nonsingular real pseudoholomorphic curve not isotopic in the projective plane to any real algebraic curve of the same degree? Here, we focus our study on symmetric real curves on the projective plane. We give a classification of real s…

In this paper we provide a classification of fundamental group elements representing simple closed curves on the punctured Klein bottle, Similar to the Birman-Series classification of curves on the punctured torus[1]. In the process, an explicit description of the mapping class group is given. We then apply this to giv…

Survey on rational curves on complex surfaces, highlighting different approaches.

Classifies manifolds with quasipositive curvature.

New method uses contours of segmented images for X-ray classification.

The paper classifies different types of cusps on plane curves.

This paper is devoted to the classification of the infinite families of Teichmuller curves generated by Prym eigenforms of genus 3 having a single zero. These curves were discovered by McMullen. The main invariants of our classification is the discriminant D of the corresponding quadratic order, and the generators of t…

Classification of torus homeomorphisms on fine curve graph completed.

Paper estimates optimal ROC curve arc length and AUC, improving classification performance.

Classifies ancient convex curves in convex domains.

Study proves existence and properties of shrinkers in area-preserving curve-shortening flow.

Optimal cutoff interval for risk scores improves binary classification accuracy.

We study the horizontally regular curves in the Heisenberg groups $H_n$. We show the fundamental theorem of curves in $H_n$ $(n\geq 2)$ and define the concept of the orders for horizontally regular curves. We also show that the curve $γ$ is of order $k$ if and only if $γ$ lies in $H_k$ but not in $H_{k-1}$ up to a Heis…

New optimization method improves AUC for binary classification and changepoint detection.

Proposes a new tree-based algorithm for class-imbalanced data.

In this paper, we classify the class of constant weighted curvature curves in the plane with a log-linear density, or in other words, classify all traveling curved fronts with a constant forcing term in $\Bbb R^2.$ The classification gives some interesting phenomena and consequences including: the family of curves conv…

Proposes FunNoL for better curve classification and reconstruction in multivariate functional data.

Classifies hexagonal circular 3-webs with cubic polar curves.

New hexagonal circular 3-webs with reducible curves classified.

Classifies curved bidifferential operators on manifolds.

Classifies real rational knots and curves in a specific quadric space.

This paper introduces a novel mixture model-based approach for simultaneous clustering and optimal segmentation of functional data which are curves presenting regime changes. The proposed model consists in a finite mixture of piecewise polynomial regression models. Each piecewise polynomial regression model is associat…

Algorithm to determine if two curves are of the same type.

The Large Synoptic Survey Telescope will complete its survey in 2022 and produce terabytes of imaging data each night. To work with this massive onset of data, automated algorithms to classify astronomical light curves are crucial. Here, we present a method for automated classification of photometric light curves for a…

Classifies Fano varieties with large pseudoindex and non-free rational curves.

Study geodesic curves on Heisenberg group, classify them, and compute first step of quadrature.

We give a classification of all self-similar solutions to the curve shortening flow in the plane.

We classify pro-$p$ Poincaré duality pairs in dimension two. We then use this classification to build a pro-$p$ analogue of the curve complex and establish its basic properties. We conclude with some statements concerning separability properties of the mapping class group.

New algebraic theory classifies symplectic curves in complex projective space.

Geometric arguments show simplicial arrangements with few double points can't have an irreducible cubic curve dual.

Modified AUC improves CNN training by considering model confidence.

In this paper, we study helices and the Bertrand curves. We obtain some of the classification results of these curves with respect to the modified orthogonal frame in Euclidean 3-spaces.

A good classification method should yield more accurate results than simple heuristics. But there are classification problems, especially high-dimensional ones like the ones based on image/video data, for which simple heuristics can work quite accurately; the structure of the data in such problems is easy to uncover wi…

This work is a contribution to the classification of Teichmüller curves in the moduli space $\M_2$ of Riemann surfaces of genus 2. While the classification of primitive Teichmüller curves in $\M_2$ is complete, the classification of the imprimitive curves, which is related to branched torus covers and square-tiled surf…