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.
The paper provides estimates for higher-order Ricci curvature along Kähler-Ricci flows.
Existence of translating solutions shown for curve diffusion flow.
Paper proves higher-order flow matching preserves optimality in generative modeling.
Comprehending complex systems by simplifying and highlighting important dynamical patterns requires modeling and mapping higher-order network flows. However, complex systems come in many forms and demand a range of representations, including memory and multilayer networks, which in turn call for versatile community-det…
The paper defines and analyzes higher-order Yang-Mills-Higgs functionals and their gradient flows.
We show that solutions to certain higher-order intrinsic geometric flows on a compact manifold, including some flows generated by the ambient obstruction tensor, are unique. With the goal of providing a complete self-contained proof, details surrounding map covariant derivatives and a careful application of the DeTurck…
The paper studies geometric Airy curve flows on R^n and their properties.
We establish short-time existence and regularity for higher-order flows generated by a class of polynomial natural tensors that, after an adjustment by the Lie derivative of the metric with respect to a suitable vector field, have strongly parabolic linearizations. We apply this theorem to flows by powers of the Laplac…
We demonstrate that the uniqueness of solutions to a broad class of parabolic geometric evolution equations can be proven via a direct and essentially classical energy argument which avoids the DeTurck trick entirely. Previously, we have used a variation of this technique to give an alternative proof and slight extensi…
Paper studies Laplace operator estimates in harmonic map heat flows.
The paper introduces a geometric flow for Lagrangian submanifolds that preserves Hamiltonian isotopy.
We consider the local solution to the Calabi flow for C^αinitial metric. We also prove that the Calabi flow on compact Kaehler surfaces can be extended once the metrics along the flow are bounded in L^\infty sense. This can be viewed as obtaining higher order derivative estimates from second order derivatives for a fou…
The paper proves existence and classification of translating solitons in warped product manifolds.
The biharmonic flow and Willmore flow are studied in higher dimensions using geometric evolution equations.
We define functionals generalising the Seiberg-Witten functional on closed manifolds, involving higher order derivatives of the curvature form and spinor field. We then consider their associated gradient flows and, using a gauge fixing technique, are able to prove short time existence for the flows. We then pr…
We study a higher-order parabolic equation which generalizes the Ricci flow on two-dimensional surfaces. The metric is deformed conformally with a speed given by the Q-curvature of the metric. Under a condition on the Q-curvature of the initial metric we show that the soluton exists for all time and converges to a metr…
Mean curvature flow of clusters of n-dimensional surfaces in R^{n+k} that meet in triples at equal angles along smooth edges and higher order junctions on lower dimensional faces is a natural extension of classical mean curvature flow. We call such a flow a mean curvature flow with triple edges. We show that if a smoot…
Paper introduces Tensor Gauge Flow Models for better data encoding.
In this note we review some results regarding higher order elliptic differential operators on manifolds without boundary.
In this article, we study the higher-order regularity of the Kähler-Ricci flow on compact Kähler manifolds with semi-ample canonical line bundle. We proved, using a parabolic analogue of Hein-Tosatti's work on collapsing Calabi-Yau metrics, that when the generic fibers of the Iitaka fibration are biholomorphic to each …
Submodular functions can be exactly minimized in polynomial time, and the special case that graph cuts solve with max flow \cite{KZ:PAMI04} has had significant impact in computer vision \cite{BVZ:PAMI01,Kwatra:SIGGRAPH03,Rother:GrabCut04}. In this paper we address the important class of sum-of-submodular (SoS) function…
We recover the higher order terms for the acoustic wave equation from measurements of the modulus of the solution. The recovery of these coefficients is reduced to a question of stability for inverting a Hamiltonian flow transform, not the geodesic X-ray transform encountered in other inverse boundary problems like the…
A model simulates how different types of traders react to macroeconomic news.
We introduce a regularization method for mean curvature flow of a submanifold of arbitrary codimension in the Euclidean space, through higher order equations. We prove that the regularized problems converge to the mean curvature flow for all times before the first singularity.
We analyse second order (in Riemann curvature) geometric flows (un-normalised) on locally homogeneous three manifolds and look for specific features through the solutions (analytic whereever possible, otherwise numerical) of the evolution equations. Several novelties appear in the context of scale factor evolution, fix…
Analyzes Willmore flow for graphs with boundary data, proving existence and convergence.
Higher-order ODE solvers improve deep learning performance.
Paper transforms a complex equation into simpler forms for analysis.
New flow for Yang-Mills-Higgs theory avoids singularities.
Higher Gauge Flow Models integrate higher geometry and symmetries into Generative Flow Models.
This paper extends 3D results to higher dimensions, proving compactness for PIC1 pinched manifolds.
The quantum field theory of two-dimensional sigma models with bulk and boundary couplings provides a natural framework to realize and unite different species of geometric flows that are of current interest in mathematics. In particular, the bulk renormalization group equation gives rise to the Ricci flow of target spac…
In this paper, we continue to study the generalized Ricci flow. We give a criterion on steady gradient Ricci soliton on complete and noncompact Riemannian manifolds that is Ricci-flat, and then introduce a natural flow whose stable points are Ricci-flat metrics. Modifying the argument used by Shi and List, we prove the…
The study finds translators for higher order mean curvature flows in Euclidean and hyperbolic spaces.
We define a family of functionals generalizing the Yang-Mills functional. We study the corresponding gradient flows and prove long-time existence and convergence results for subcritical dimensions as well as a bubbling criterion for the critical dimensions. Consequently, we have an alternate proof of the convergence of…
We give a simple, direct proof of the backward uniqueness of solutions to a class of second-order geometric evolution equations including the Ricci and cross-curvature flows. The proof, based on a classical argument of Agmon-Nirenberg, uses the logarithmic convexity of a certain energy quantity in the place of Carleman…
AMM finds optimal contract for LPs to maximize order flow.
Derivative estimates for pluriclosed flow control curvature and torsion.
Tseytlin has recently proposed that an action functional exists whose gradient generates to all orders in perturbation theory the Renormalization Group (RG) flow of the target space metric in the worldsheet sigma model. The gradient is defined with respect to a metric on the space of coupling constants which is explici…
Study curves evolving on hypersurfaces with free boundaries, preserving length.
We study the local geometry of irreducible parabolic geometries admitting strongly essential flows; these are flows by local automorphisms with higher-order fixed points. We prove several new rigidity results, and recover some old ones for projective and conformal structures, which show that in many cases the existence…
We investigate reductions of the two-dimensional Dirac equation imposed by the requirement of the existence of a differential operator of order mapping its eigenfunctions to adjoint eigenfunctions. For first order operators these reductions (and multi-component analogs thereof) lead to the Lame equations desc…
This is a survey of some of the recent developments on the geometric and analytic aspects of the Anomaly flow. It is a flow of -forms on a -fold which was originally motivated by string theory and the need to preserve the conformally balanced property of a Hermitian metric in the absence of a $\partial\bar\pa…
For a continuous curve of families of Dirac type operators we define a higher spectral flow as a -group element. We show that this higher spectral flow can be computed analytically by $\heta$-forms, and is related to the family index in the same way as the spectral flow is related to the index. We introduce a notion…
The study examines order flow in financial markets using fractional Lévy stable motion.
Paper tackles stochastic control with mean and higher-order moments, finding Nash equilibria.
OP-GFNs sample candidates in order-preserving proportion to a learned reward function.
Higher-dimensional Ricci flows are shown to have unique and stable solutions.