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.
Weak dual pairs defined in Dirac-Jacobi geometry, proving equivalence and leaf correspondence theorems.
Finite-time extinction and smoothing effects in fractional fast diffusion on manifolds.
Researchers solve porous medium equation on noncompact manifolds with Ricci curvature.
We consider a general path-dependent version of the hedging problem with price impact of Bouchard et al. (2019), in which a dual formulation for the super-hedging price is obtained by means of PDE arguments, in a Markovian setting and under strong regularity conditions. Using only probabilistic arguments, we prove, in …
Paper solves a complex equation for unbounded convex sets.
Study nonnegative solutions on Riemannian manifolds using fractional porous medium equation.
Proves existence and uniqueness of weak solutions for specific equations.
In this note, I discuss in some detail the dual version of the ribbon graph decomposition of the moduli spaces of Riemann surfaces with boundary and marked points, which I introduced in math.AG/0402015, and used in math.QA/0412149 to construct open-closed topological conformal field theories. This dual version of the r…
Paper proves uniqueness of weak solutions for Plateau flow.
In this paper we generalize the framework of the feasible descent method (FDM) to a randomized (R-FDM) and a coordinate-wise random feasible descent method (RC-FDM) framework. We show that the famous SDCA algorithm for optimizing the SVM dual problem, or the stochastic coordinate descent method for the LASSO problem, f…
Study finds weak solutions for complex map flows with optimal lifespan.
Paper tackles offline RL with weak assumptions on both function classes and data coverage.
Researchers prove uniqueness and continuity of solution to L_p dual Minkowski problem.
We present an invariant of connected and oriented closed 3-manifolds based on a coribbon Weak Hopf Algebra H with a suitable left-integral. Our invariant can be understood as the generalization to Weak Hopf Algebras of the Hennings-Kauffman-Radford evaluation of an unoriented framed link using a dual quantum-trace. Thi…
The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space, (2) the attainment of the supremum in the dual representation by order-continuous…
Unified Kantorovich duality for multimarginal optimal transport on Polish spaces.
Gradient estimates for solutions to a p-Laplacian equation on Riemannian manifolds.
The dual problem of optimal transportation in Lorentz-Finsler geometry is studied. It is shown that in general no solution exists even in the presence of an optimal coupling. Under natural assumptions dual solutions are established. It is further shown that the existence of a dual solution implies that the optimal tran…
In this note we prove that, under a weak condition, small deformations of a compact balanced manifold are also balanced. This condition is satisfied on the twistor space over a compact self-dual four manifold.
New algorithms solve weak optimal transport problems for nonlinear costs.
Solves a generalized dual Minkowski problem for specific values of q.
This paper solves the dual Minkowski problem for q-torsional rigidity.
Novel weak solutions for volume-preserving mean curvature flow established.
The purpose of this article is to prove existence of mass minimizing integral currents with prescribed possibly non-compact boundary in all dual Banach spaces and furthermore in certain spaces without linear structure, such as injective metric spaces and Hadamard spaces. We furthermore prove a weak-compactness theo…
We prove the smoothness of weak solutions to an elliptic complex Monge-Ampere equation, using the smoothing property of the corresponding parabolic flow.
We study the evolution of hypersurfaces in spacetime initial data sets by their null mean curvature. A theory of weak solutions is developed using the level-set approach. Starting from an arbitrary mean convex, outer untapped hypersurface , we show that there exists a weak solution to the null mean curvatu…
New varifold solutions for mean curvature flow converge and are unique.
Alternative proof of weak solutions to mean curvature flow using minimizing movements.
Paper solves dual Minkowski problem in 2D plane for specific curvature cases.
Smooth even solutions found for a generalized convex geometry problem.
New dual formulation reduces generalization error for ERM-fDR.
Segre quartic surfaces linked to minitwistor spaces with Einstein-Weyl structures.
The dual -Minkowski problem with is investigated in this paper. By proving a new existence result of solutions and constructing an example, we obtain the non-uniqueness of solutions to this problem.
Study constructs solutions for evolving hypersurfaces using inverse spacetime mean curvature.
We consider the task of training classifiers without labels. We propose a weakly supervised method---adversarial label learning---that trains classifiers to perform well against an adversary that chooses labels for training data. The weak supervision constrains what labels the adversary can choose. The method therefore…
Geometric analysis proves weak KAM solutions constant under specific conditions.
Previous studies on stochastic primal-dual algorithms for solving min-max problems with faster convergence heavily rely on the bilinear structure of the problem, which restricts their applicability to a narrowed range of problems. The main contribution of this paper is the design and analysis of new stochastic primal-d…
In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification. Previous theoretical results on randomized reduction methods hinge on strong assumptio…
The system of weak normality equations constitutes a part in the complete system of normality equations. Solutions of each of these two systems of equations are associated with some definite classes of Newtonian dynamical systems in Riemannian manifolds. In this paper for the case of simplest flat Riemannian manifold $…
The paper examines partial regularity of Lipschitz solutions to minimal surface system.
In this paper, the dual Orlicz curvature measure is proposed and its basic properties are provided. A variational formula for the dual Orlicz-quermassintegral is established in order to give a geometric interpretation of the dual Orlicz curvature measure. Based on the established variational formula, a solution to the …
New boundary condition for weak inverse mean curvature flow in bounded domains.
Dual optimization connects ERM-fDR to normalization function.
We propose a new Quantization algorithm for the approximation of inhomogeneous random walks, which are the key terms for the valuation of CDO-tranches in latent factor models. This approach is based on a dual quantization operator which posses an intrinsic stationarity and therefore automatically leads to a second orde…
We study weak solutions to degenerate quasilinear elliptic equations, involving first order terms, in unbounded tubular domains. In particular we show that, under suitable hypotheses, the weak comparison principle holds if the domain is narrow enough.
Study on fourth order Lamm-Riviere system for biharmonic mappings in 4D.
We prove the existence of weak solutions of complex Hessian equations on compact Hermitian manifolds for the nonnegative right hand side belonging to ( is the dimension of the manifold). For smooth, positive data the equation has been recently solved by Szekelyhidi and Zhang. We also give a stabilit…
Proves existence of proper solutions for inverse mean curvature flow.