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.
Quasiregular curves are Hölder continuous and have higher integrability.
The paper studies curves in Finsler-like spaces and their properties.
A classical result in Riemannian geometry states that the absolutely continuous curves into a (finite-dimensional) Riemannian manifold form an infinite-dimensional manifold. In the present paper this construction and related results are generalised to absolutely continuous curves with values in a strong Riemannian mani…
Study shows continuous evolution of curves in Fréchet distance.
Study of skateboard flips as continuous curves in group.
Regulated curves on Banach manifolds with continuous projections and regulated derivatives are studied.
The paper proves -convergence of discrete tangent-point energies to continuous energies and ropelength, with applications to biarc curves.
Maximal causal curves for Lipschitz metrics are either lightlike or timelike.
Continuous curves inscribe isosceles trapezoids in complex plane.
Continuous curve evolution depends on initial shape on sphere.
We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms the function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete …
New geometric transformations link discrete and continuous curve motions.
Paper studies geometric properties of nonlinear Lebesgue spaces.
Analytic plane curves determine unique conformal coordinates.
Extends curve functions to geodesic currents with a simple criterion.
It is well-known that the class of piecewise smooth curves together with a smooth Riemannian metric induces a metric space structure on a manifold. However, little is known about the minimal regularity needed to analyze curves and particularly to study length-minimizing curves where neither classical techniques such as…
We consider a continuous curve of linear elliptic formally self-adjoint differential operators of first order with smooth coefficients over a compact Riemannian manifold with boundary together with a continuous curve of global elliptic boundary value problems. We express the spectral flow of the resulting continuous fa…
The square root velocity framework is a method in shape analysis to define a distance between curves and functional data. Identifying two curves if they differ by a reparametrisation leads to the quotient space of unparametrised curves. In this paper we study analytical and topological aspects of this construction for …
The square root velocity function (SRVF), introduced by Srivastava et al, has proved to be an effective way to compare absolutely continuous curves in modulo reparametrization. Several computational papers have been published based on this method. In this paper, we carefully establish the theoretical foundations …
In this paper we consider the problem of transmitting a continuous alphabet discrete-time source over an AWGN channel. The design of good curves for this purpose relies on geometrical properties of spherical codes and projections of -dimensional lattices. We propose a constructive scheme based on a set of curves on …
Study on choosing points on cubic curves, answering some questions about their flexibility.
Study automorphisms of smooth curve graphs on surfaces.
Paper introduces hybrid curves moduli space and canonical measures.
Using convex integration we give a constructive proof of the well-known fact that every continuous curve in a contact -manifold can be approximated by a Legendrian curve.
Rectangular peg problem solved for many curves.
Researchers examine various causal structures for spacetimes with continuous metrics.
LoRA-Curve connects independent LoRA optima through continuous low-loss valleys, improving Bayesian model averaging.
In this manuscript we introduce a method to measure entanglement of curves in 3-space that extends the notion of knot and link polynomials to open curves. We define the bracket polynomial of curves in 3-space and show that it has real coefficients and is a continuous function of the chain coordinates. This is used to d…
Square-like quadrilaterals inscribed in space curves proven for finite total curvature.
Over a closed manifold, we consider the sectorial projection of an elliptic pseudo-differential operator A of positive order with two rays of minimal growth. We show that it depends continuously on A when the space of pseudo-differential operators is equipped with a certain topology which we explicitly describe. Our ma…
Paper develops methods to estimate derivative of dose-response curve for continuous treatments.
I show that every rectifiable simple closed curve in the plane can be continuously deformed into a convex curve in a motion which preserves arc length and does not decrease the Euclidean distance between any pair of points on the curve. This result is obtained by approximating the curve with polygons and invoking the r…
Defines Vassiliev complexity measures for open and closed curves in 3D space.
This paper constructs a continuous decomposition of the Sierpiński curve into acyclic continua one of which is an arc. This decomposition is then used to construct another continuous decomposition of the Sierpiński curve. The resulting decomposition space is homeomorphic to the continuum obtained from taking the Sierpi…
Every smooth cubic plane curve has 9 inflection points, 27 sextatic points, and 72 ``points of type nine". Motivated by these classical algebro-geometric constructions, we study the following topological question: Is it possible to continuously choose distinct unordered points on each smooth cubic plane curve for a…
We consider a continuous curve of self-adjoint Fredholm extensions of a curve of closed symmetric operators with fixed minimal domain and fixed {\it intermediate} domain . Our main example is a family of symmetric generalized operators of Dirac type on a compact manifold with boundary with varying well-posed…
Study evolutes of curves with varying smoothness.
Differential equations are derived for a continuous limit of iterated Schwarzian reflection of analytic curves, and solutions are interpreted as geodesics in an infinite-dimensional symmetric space geometry.
The paper explores continuous inverse ambiguous functions on various Lie groups.
Proposes VCNet for estimating ADRFs of continuous treatments.
Proves existence of curved surfaces in hyperbolic space.
We consider the class of affine LIBOR models with multiple curves, which is an analytically tractable class of discrete tenor models that easily accommodates positive or negative interest rates and positive spreads. By introducing an interpolating function, we extend the affine LIBOR models to a continuous tenor and de…
In this paper we prove a universal inequality describing the asymptotic behavior of support points for planar continuous curves. As corollaries we get an analogous result for tangent points of differentiable planar curves and some (partially known) assertions on the asymptotic of the mean value points for various class…
The Manhattan curve connects metrics of hyperbolic groups, showing rigidity.
We show that the definition of global hyperbolicity in terms of the compactness of the causal diamonds and non-total imprisonment can be extended to spacetimes with continuous metrics, while retaining all of the equivalences to other notions of global hyperbolicity. In fact, global hyperbolicity is equivalent to the co…
The systems of complex analytic second order ordinary differential equations whose solutions close up to become rational curves (after analytic continuation) are characterized by the vanishing of an explicit differential invariant, and turn out to provide an infinite dimensional family of integrable systems.
Continuing the program of math.SG/0012067 and math.SG/0310450, we introduce refinements of the Donaldson-Smith standard surface count which are designed to count nodal pseudoholomorphic curves and curves with a prescribed decomposition into reducible components. In cases where a corresponding analogue of the Gromov-Tau…
Counterexamples to continuity of optimal transportation on Riemannian manifolds with everywhere positive sectional curvature are provided. These examples show that the condition A3w of Ma, Trudinger, & Wang is not guaranteed by positivity of sectional curvature.