A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
A new method for combining shapes in log-radius profiles.
Characterizes Coxeter groups with specific boundary shapes.
Defines a new method for combining curves and describes how certain properties behave.
Curve shortening flow shrinks curves to points.
Study shows unbounded Pontryagin numbers on curved manifolds.
The paper characterizes Legendre curves on trans-S-manifolds.
In the present paper, we handle the problem of finding a hypersurface family from a given asymptotic curve in R^4. Using the Frenet frame of the given asymptotic curve, we express the hypersurface as a linear combination of this frame and analyze the necessary and sufficient conditions for that curve to be asymptotic. …
A twisted curve in Euclidean 3-space E^3 can be considered as a curve whose position vector can be written as linear combination of its Frenet vectors. In the present study we study the twisted curves of constant ratio in E^3 and characterize such curves in terms of their curvature functions. Further, we obtain some re…
Let V be an open manifold with complete nonnegatively curved metric such that the normal sphere bundle to a soul has no section. We prove that the souls of nearby nonnegatively curved metrics on V are smoothly close. Combining this result with some topological properties of pseudoisotopies we show that for many V the s…
In this survey paper we give a proof of hyperbolicity of the complex of curves for a non-exceptional surface S of finite type combining ideas of Masur/Minsky and Bowditch. We also shortly discuss the relation between the geometry of the complex of curves and the geometry of Teichmueller space.
New method matches curves using varifolds and Sobolev metrics.
Paper explores folding patterns of curved creases preserving their geometric properties.
In this paper, we study the problem of finding a hypersurface family from a given spatial geodesic curve in R4. We obtain the parametric representation for a hypersurface family whose members have the same curve as a given geodesic curve. Using the Frenet frame of the given geodesic curve, we present the hypersurface a…
Combining the definition of Schwarzian derivative for conformal mappings between Riemannian manifolds given by Osgood and Stowe with that for parametrized curves in Euclidean space given by Ahlfors, we establish injectivity criteria for holomorphic curves . The result can be considered a ge…
Loewner inequality proven for curved surfaces.
We analyzed the problem of finding a surfaces family through an asymptotic curve with Cartan frame. We obtain the parametric representation for surfaces family whose members have the same as an asymptotic curve. By using the Cartan frame of the given null curve, we present the surface as a linear combination of this fr…
A robust machine learning approach forecasts U.S. Treasury yields, reducing risk for investors.
A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal su…
Study introduces D-type curves on surface pencils and their properties.
Study on curves in Heisenberg groups, proving fundamental theorem and curve classification.
A new method combines metrics for shape registration, inheriting advantages from both curve and surface approaches.
Generating realistic asset-class scenarios from time series and curves
Algorithm decides if curves on a surface are simple.
Complete conjecture on rational curves on K3 surfaces.
Proposes MCC-F1 curve for better binary classification evaluation.
In genus two and higher, the fundamental group of a closed surface acts naturally on the curve complex of the surface with one puncture. Combining ideas from previous work of Kent--Leininger--Schleimer and Mitra, we construct a universal Cannon--Thurston map from a subset of the circle at infinity for the closed surfac…
Study proves a criterion for curve diffusion flow blow-up.
Combines Bézier curves with Gaussian processes for better sequential data modeling.
We define a Fourier-Mukai transform for a triple consisting of two holomorphic vector bundles over an elliptic curve and a homomorphism between them. We prove that in some cases the transform preserves the natural stability condition for a triple. We also define a Nahm transform for solutions to natural gauge-theoretic…
Classifies real algebraic curves on a quadric ellipsoid of specific degree.
Suppose C is a singular curve in CP^2 and it is topologically an embedded surface of genus g; such curves are called cuspidal. The singularities of C are cones on knots K_i. We apply Heegaard Floer theory to find new constraints on the sets of knots {K_i} that can arise as the links of singularities of cuspidal curves.…
The main drawback of the Frenet frame is that it is undefined at those points where the curvature is zero. Further- more, in the case of planar curves, the Frenet frame does not agree with the standard framing of curves in the plane. The main drawback of the Bishop frame is that the principle normal vector N is not in …
In this paper, I shall demonstrate that sufficiently high-dimensional closed positively-curved Riemannian manifolds are either diffeomorphic to a spherical space form, or isometric to a locally compact rank one symmetric space. This surprising classification of positively-curved Riemannian manifolds results from combin…
New method for comparing curves with flexible matching constraints.
Deep learning models forecast multiple yield curves with improved accuracy.
We study the degree of polynomial representations of knots. We obtain the lexicographic degree for two-bridge torus knots and generalized twist knots. The proof uses the braid theoretical method developed by Orevkov to study real plane curves, combined with previous results from [KP10] and [BKP14]. We also give a sharp…
Paper develops methods for curve matching in medical imaging.
In this paper, we consider the intensity surface of a 2D image, we study the evolution of the symmetry sets (and medial axes) of 1-parameter families of iso-intensity curves. This extends the investigation done on 1-parameter families of smooth plane curves (Bruce and Giblin, Giblin and Kimia, etc.) to the general case…
Anosov surfaces with same length spectrum are isometric.
Study real algebraic curves on real del Pezzo surfaces using degeneration methods.
New latent variable model improves inflation forecasting accuracy.
Nearly spherical, positively curved surfaces are mapped from a sphere.
The paper introduces a new Markov chain sampler for knot diagrams.
Study on constraints of monodromy group for smooth plane curves.
In this paper we classify convex compact ancient solutions to the affine curve shortening flow: namely, any convex compact ancient solution to the affine curve shortening flow must be a shrinking ellipse. The method combines a rescaling argument inspired by \cite{Wang}, affine invariance of the equation and monotonicit…
Classifies Fano varieties with large pseudoindex and non-free rational curves.
Paper introduces hybrid curves moduli space and canonical measures.
Study of generalized Bishop frames on time-like curves in 4D Lorentz space.