Classifies shapes of yield curves in the Svensson family.
problem Classifying shapes of yield curves in the Svensson family.
method Complete classification of shapes using mathematical analysis.
result Certain complex shapes cannot appear after a deterministic time horizon.
Study connects flow dynamics to 3D geometry via surface intersections.
problem Relating flow dynamics to geometric properties of 3-manifolds.
method Relates pseudo-Anosov flow dynamics to hyperbolic geometry via curve graphs.
result Established a link between flow invariants and geometric features of 3-manifolds.
We study a class of nonlocal, energy-driven dynamical models that govern the motion of closed, embedded curves from both an energetic and dynamical perspective. Our energetic results provide a variety of ways to understand physically motivated energetic models in terms of more classical, combinatorial measures of compl…
Study homeomorphisms on fine curve graph of surfaces, revealing new types of dynamics.
problem Understanding dynamics of homeomorphisms on fine curve graphs of surfaces.
method Analyzing the action of homeomorphisms on the fine curve graph and relating to classical curve graphs.
result Homeomorphisms induce parabolic isometries, and all positive reals are realized as asymptotic translation lengths.
Construct intrinsic Langevin dynamics for rigid inclusions on curved surfaces.
problem Stochastic dynamics of rigid inclusions on curved surfaces.
method Cartan's method of moving frames, Hamiltonian equations, intrinsic Langevin equations, Fokker-Planck equation.
result Extracted overdamped equations for accurate simulations of diffusion processes.
Study on curve shortening flow in 3D space curves, showing convexity preservation and avoidance principle.
problem Analyzing the behavior of space curves under curve shortening flow in R3. method Analysis of properties of space curves evolved by the curve shortening flow, including convexity preservation and avoidance principle.
result Orthogonal projections of space curves remain convex, and the Avoidance principle is shown for spherical curves.
We derive an equation of motion for interest-rate yield curves by applying a minimum Fisher information variational approach to the implied probability density. By construction, solutions to the equation of motion recover observed bond prices. More significantly, the form of the resulting equation explains the success …
Generic model for commodity derivatives pricing.
problem Modeling forward curves in commodity derivatives.
method Theoretical demonstration of multiple components driving commodity prices; empirical validation.
result Model accurately prices commodity derivatives, close to market prices.
Study on dynamic curves with elastic energy and spontaneous curvature.
problem Modeling and analyzing dynamic planar curves with elastic energy.
method Gradient flow of inclination angle, nonlocal quasilinear system, local well-posedness, global existence, convergence.
result Local well-posedness, global existence, convergence of the flow for weak regularity initial data.
We consider the Frenet-Serret geometry of null curves in a three and a four-dimensional Minkowski background. We develop a theory of deformations adapted to the Frenet-Serret frame. We exploit it to provide a Lagrangian description of the dynamics of geometric models for null curves.
The paper extends the Manhattan curve concept to complex dynamics and studies its relation to multiplier spectra.
problem Understanding the growth rate of lengths of closed geodesics in complex dynamics.
method Defining and studying the Manhattan curve for holomorphic endomorphisms of CPk and relating it to multiplier spectra. result The Manhattan curve for two holomorphic endomorphisms is related to the correlation number of their multiplier spectra.
Study the geometry and dynamics of skew evolutes and involutes, related to bicycle kinematics.
problem Understanding the geometry and dynamics of skew evolutes and involutes.
method Investigate the skew evolute and involute maps, comparing them to bicycle kinematics.
result The skew evolute and involute maps have properties analogous to bicycle kinematics.
This paper describes how to define and work with differential equations in the abstract setting of tangent categories. The key notion is that of a curve object which is, for differential geometry, the structural analogue of a natural number object. A curve object is a preinitial object for dynamical systems; dynamical …
Study shows invariant curves in tubular origami dynamics, revealing geometric barriers to folding transitions.
problem Understanding the dynamics and geometric barriers in tubular origami structures.
method Kolmogorov--Arnold--Moser (KAM) theory and numerical simulations.
result Invariant curves persist in large module limits, providing phase-space interpretation of folding modes.
Paper introduces k-DTW for robust curve comparison.
problem Robust dissimilarity measure for polygonal curves.
method Introduces k-Dynamic Time Warping (k-DTW) as a novel dissimilarity measure.
result k-DTW is more robust to outliers and has stronger metric properties than DTW.
The paper shows that energy futures yield curves have an affine geometry.
problem Estimating dynamic behavior of yield curves from data while avoiding arbitrage.
method Finite dimensional models for yield curves, diffusion coefficients, and compatibility conditions.
result The compatibility of yield curves with diffusion coefficients forces an affine geometry.
A new model explains relative spreads between economies using dynamic Nelson-Siegel and functional regression.
problem Analyzing and predicting relative spreads between economies in fixed income markets.
method State-space functional regression model incorporating dynamic Nelson-Siegel model and kernel PCA.
result The new model outperforms the dynamic Nelson-Siegel model in explaining relative spreads.
Enhances patient failure prediction using dynamic survival models.
problem Lack of precise individual level prediction in conventional models.
method Developed counterfactual dynamic survival model (CDSM).
result Inflection point of estimated survival curves predicts patient failure time.
We express invariants of Finsler manifolds in a geometrical way by means of using moving planes and their associated Jacobi curves, which are curves in a fixed homogeneous Grassmann manifold. Some applications are given.
ResNets learn the geodesic curve in Wasserstein space.
problem Characterize the dynamics of deep residual networks during training.
method Modeling ResNet dynamics using continuity equations and optimal transport.
result ResNets learn the geodesic curve in the Wasserstein space.
We present a HJM approach to the projection of multiple yield curves developed to capture the volatility content of historical term structures for risk management purposes. Since we observe the empirical data at daily frequency and only for a finite number of time-to-maturity buckets, we propose a modelling framework w…
A robust machine learning approach forecasts U.S. Treasury yields, reducing risk for investors.
problem Noisy and uncertain U.S. Treasury yields pose risk to forecast users.
method Formulates yield curve forecasting as a distributionally robust problem, combining factor models and machine learning.
result Robust forecast combinations improve out-of-sample performance across different maturity periods.
The study examines dynamics on SU(2)-representation varieties for surfaces and non-orientable surfaces.
problem Dynamics of group actions on SU(2)-representation varieties of surfaces and non-orientable surfaces.
method Description and analysis of group actions generated by Dehn twists on SU(2)-representation varieties.
result Explicit invariant rational functions on SU(2)-representation varieties for specific cases of surfaces and non-orientable surfaces.
Abstract: Deltoid map connects complex dynamics and algebra.
problem Understanding complex dynamics through a specific map.
method Analyzing the geometry and algebra of the deltoid map.
result Illustrates Julia set and iterated monodromy group.
A new model captures forward curve dynamics with stochastic volatility.
problem Modeling continuous-time evolution of forward curves in financial markets.
method Affine stochastic volatility model with modulated dynamics.
result Model allows for maturity-specific risk and volatility clustering.
New dynamic curves improve cryptocurrency exchange liquidity.
problem Low liquidity and arbitrage opportunities in existing AMMs.
method Dynamic curves adjust AMM function based on market prices.
result Maintains liquidity and total LP value over wide market price ranges.
For a long time interest-rate models were built on a single yield curve used both for discounting and forwarding. However, the crisis that has affected financial markets in the last years led market players to revise this assumption and accommodate basis-swap spreads, whose remarkable widening can no longer be neglecte…
The Weinstein conjecture is extended to a new class of manifolds.
problem Existence of Reeb 2-curves in locally conformally symplectic manifolds.
method Extended Gromov-Witten theory and elliptic curve counts.
result Partial verification of the conjecture in higher dimensions.
Geometric analysis of nonlinear dynamics applied to financial time series.
problem Understanding dynamic properties of financial time series.
method Nonparametric filtering method to estimate vector fields and their derivatives from nonlinear oscillation models.
result Vector fields and their derivatives provide insights into the dynamic properties of financial time series.
This paper focuses on the interplay between the intersection theory and the Teichmueller dynamics on the moduli space of curves. As applications, we study the cycle class of strata of the Hodge bundle, present an algebraic method to calculate the class of the divisor parameterizing abelian differentials with a non-simp…
In this article we investigate the dynamics of special solutions to the surface diffusion flow of idealised ribbons. This equation reduces to studying the curve diffusion flow for the profile curve of the ribbon. We provide: (1) a complete classification of stationary solutions; (2) qualitative results on shrinkers, tr…
Study of normal and tangent maps to frontals.
problem Understanding geometric and dynamical properties of frontals.
method Geometrical and dynamical analysis of normal and tangent maps.
result Parallels of the tangent map to a frontal curve are right equivalent to the tangent map of a frontal curve under certain conditions.
The paper explores how complex models can improve system identification beyond traditional limits.
problem Balancing model richness and spurious learning in system identification.
method Investigates the double-descent phenomenon in the context of dynamic systems.
result Complex models can improve system identification performance beyond the point of interpolation.
Curves can bound only finitely many developable surfaces.
problem Bounding developable surfaces with nonvanishing mean curvature.
method Proof of finiteness for developable surfaces with prescribed boundary curves.
result Generic curves bound only finitely many developable surfaces.
Investment strategies derived from commodity futures curves exploit dynamics in price movements.
problem Modeling and predicting the term structure of commodity futures prices.
method Employed the Nelson-Siegel framework to model term structure, and developed investment strategies based on changes in slope and curvature parameters.
result Significant profits generated from systematic strategies based on the change in slope, unrelated to risk factors and robust to transaction costs.
In this paper we study the (asymptotic and exponential) stability of the m-fold circle as a solution of the p-curve shortening flow (p≥1 an integer).
A new algorithm computes elastic shape distances between curves efficiently.
problem Computing elastic shape distances between curves in high dimensions.
method Dynamic Programming for optimal diffeomorphisms and Kabsch-Umeyama algorithm for optimal rotation matrices.
result Efficient computation of elastic shape distances with improved efficiency for closed curves.
In 1872 G. Darboux defined a family of curves on surfaces of R^3 which are preserved by the action of the Mobius group and share many properties with geodesics. Here we characterize these curves under the view point of Lorentz geometry and prove some general properties and make them explicit them on simple surfaces, re…
This is an introduction to the algebraic aspect of Teichmüller dynamics, with a focus on its interplay with the geometry of moduli spaces of curves as well as recent advances in the field.
The so-called inverse problem of dynamics is about constructing a potential for a given family of curves. We observe that there is a more general way of posing the problem by making use of ideas of another inverse problem, namely the inverse problem of the calculus of variations. We critically review and clarify differ…
We prove that a closed immersed plane curve with total curvature 2πm has entropy at least m times the entropy of the embedded circle, as long as it generates a type I singularity under the curve shortening flow (CSF). We construct closed immersed plane curves of total curvature 2πm whose entropy is less than m …
Two methods forecast functional time series, offering competitive results.
problem Forecasting functional time series with model-free approaches.
method Two nonparametric methods: k-nearest neighbors adaptation and curve envelope selection.
result Competitive results with and often superior to benchmarks.
Study of phase separation and geometry on a closed elastic curve, including dynamics and free energy minimization.
problem Free energy and dynamics of a closed elastic filament coupled to a scalar concentration field.
method Analytical and numerical simulations of coupled Willmore flow and Cahn--Hilliard gradient flow on differential geometry.
result Qualitative changes in free energy landscape due to closure constraint, leading to metastable and stable multi-domain morphologies.
Estimates the number of closed curves on surfaces with power-saving error terms.
problem Counting closed curves on surfaces with given properties.
method Effective dynamics of mapping class group on Teichmüller space and space of closed curves, introducing novel methods.
result Proves estimates with power-saving error terms for filling closed curves and curves with respect to a current.
Study predicts success of crypto-tokens on Pump.fun platform.
problem Identify factors affecting the success of new crypto-tokens.
method Build predictive models using bonding curve mechanism and structural/behavioral variables.
result Conditional variables significantly improve the predictive power of token success.
We introduce a dynamical-systems approach for the study of the Sard problem in sub-Riemannian Carnot groups. We show that singular curves can be obtained by concatenating trajectories of suitable dynamical systems. As an applications, we positively answer the Sard problem in some classes of Carnot groups.
Study characterizes bladder motion using dynamic MRI and statistical analysis.
problem Limited volume coverage in dynamic MRI sequences hinders 3D shape reconstruction.
method 3D dense velocity measurements, LDDMM framework, statistical characterization, mean curvature changes, surface deformation analysis.
result Stable shape descriptor for characterizing bladder surface dynamics.
The local induction equation, or the binormal flow on space curves is a well-known model of deformation of space curves as it describes the dynamics of vortex filaments, and the complex curvature is governed by the nonlinear Schrödinger equation. In this paper, we present its discrete analogue, namely, a model of defor…