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.
Study proves finiteness for distance functions on curved surfaces with controlled curvature.
3-manifolds study Hasse norm principle, akin to number fields.
Holographic principle matches deformed Liouville theory action.
We establish the proportionality principle between the Riemannian volume and locally finite simplicial volume for Q-rank 1 locally symmetric spaces covered by products of hyperbolic spaces, giving the first examples for manifolds whose cusp groups are not necessarily amenable. Also, we give a simple direct proof of the…
We propose a new objective function for finite-horizon episodic Markov decision processes that better captures Bellman's principle of optimality, and provide an expression for the gradient of the objective.
The principle result of this article is the determination of the possible finite subgroups of arithmetic lattices in U(2,1).
We extend Bony's propagation of support argument \cite{Bony} to solutions of the non-homogeneous sub-elliptic Laplacian associated to a system of smooth vector fields satisfying Hörmander's finite rank condition. As a consequence we prove a strong maximum principle and strong comparison principle that general…
In this paper we characterize the degenerate elliptic equations F(D^2u)=0 whose viscosity subsolutions, (F(D^2u) \geq 0), satisfy the strong maximum principle. We introduce an easily computed function f(t) for t > 0, determined by F, and we show that the strong maximum principle holds depending on whether the integral …
Establish C^{1,2} regularity of American value functions in Heston model
Derives time-averaged active inference from control principles.
Proof of genus formula for 3-manifolds using arithmetic topology.
On a multi-assets Black-Scholes economy, we introduce a class of barrier options. In this model we apply a generalized reflection principle in a context of the finite reflection group acting on a Euclidean space to give a valuation formula and the semi-static hedge.
In this paper, we develop several related finite dimensional variational principles for discrete optimal transport (DOT), Minkowski type problems for convex polytopes and discrete Monge-Ampere equation (DMAE). A link between the discrete optimal transport, discrete Monge-Ampere equation and the power diagram in computa…
Redundancy improves learning stability and generalization in structured systems.
An analytico-geometric reflection principle is established by means of normal deformations of analytic discs.
Study harmonic surfaces in 3D space, proving superposition principle.
Any Riemannian manifold has a canonical collection of valuations (finitely additive measures) attached to it, known as the intrinsic volumes or Lipschitz-Killing valuations. They date back to the remarkable discovery of H. Weyl that the coefficients of the tube volume polynomial are intrinsic invariants of the metric. …
Both analytic and geometric forms of an optimal monotone principle for -integral of the Green function of a simply-connected planar domain with rectifiable simple curve as boundary are established through a sharp one-dimensional power integral estimate of Riemann-Stieltjes type and the Huber analytic and geome…
The paper extends local h-principles to complex structures on Stein manifolds.
Study asymptotic behavior of Weingarten surfaces at infinity.
Study on discrepancy principle for learning algorithms in nonparametric regression.
The study proves a strong parametric h-principle for minimal surfaces.
The paper calculates prices for multi-step barrier options under the Black-Scholes model.
We study the Lipschitz simplicial volume, which is a metric version of the simplicial volume. We introduce the piecewise straightening procedure for singular chains, which allows us to generalize the proportionality principle and the product inequality to the case of complete Riemannian manifolds of finite volume with …
We establish large deviation principles for convolutional neural networks.
Classifies periodic points on regular and double n-gon surfaces.
The minimum description length (MDL) principle in supervised learning is studied. One of the most important theories for the MDL principle is Barron and Cover's theory (BC theory), which gives a mathematical justification of the MDL principle. The original BC theory, however, can be applied to supervised learning only …
Upper bounds on nullhomotopy volumes in nilpotent spaces are refined.
The aim of this work is to study how the asymptotic boundary of a minimal hypersurface in H^nxR determines the behavior of the hypersurface at finite points, in several geometric situations.
Extends Smale's principle to produce minimal graphs with singularities.
Periodic geodesics on Hilbert half-Lie groups exist whenever the fundamental group is nontrivial.
The uncertainty principle lemma for the Laplacian on Euclidean spaces shows the borderline-behavior of a potential for the following question : whether the Schrödinger operator has a finite or infinite number of the discrete pectrum. In this paper, we will give a generalization of this lemma on Euclidean spaces to that…
The paper extends the avoidance principle for mean curvature flows, proving new intersection dimension monotonicity results.
Computes a finite presentation for P(SL(2,Z)) from spin mapping class group.
New methods for estimating causal effects with limited overlap, using Stable Probability Weighting.
Gradient Ricci solitons can be extended to non-gradient Ricci solitons using energy function.
This paper improves a local-to-global principle for Morse quasigeodesics.
New proof of shrinking gradient Ricci soliton rigidity.
The paper establishes principles for initializing and designing GNNs with ReLU activations to avoid oversmoothing and correlation collapse.
Study controlled contagion with state-dependent killing, proving a comparison principle.
Rust library solves complex equations on abstract simplicial complexes.
The potential approach is a general and simple method for modelling interest rates, foreign exchange rates, and in principle other types of financial assets. This paper takes data on some liquid interest rate derivatives, and fits potential models using a small finite-state Markov chain as the base Markov process.
New boundary condition for Black-Scholes equations in strict local martingale models.
A new uncertainty principle helps traders better understand market activity.
In this paper, we show that Gromov-Thurston's principle works for hyperbolic 3-manifolds of infinite volume and with finitely generated fundamental group. As an application, we have a new proof of Ending Lamination Theorem. Our proof essentially relays only on Maximum Volume Law for hyperbolic 3-simplices.
Let H denote the standard one-point completion of a real Hilbert space. Given any non-trivial proper sub-set U of H one may define the so-called `Apollonian' metric d_U on U. When U \subset V \subset H are nested proper subsets we show that their associated Apollonian metrics satisfy the following uniform contraction p…
Let be a finite-dimensional local commutative algebra over , . In this work we consider compact manifolds over , and prove that the real part of an -differentiable function is constant. Also we find estimates for the dimensions of some spaces of 1-form.
In this paper we discuss the optimal liquidation over a finite time horizon until the exit time. The drift and diffusion terms of the asset price are general functions depending on all variables including control and market regime. There is also a local nonlinear transaction cost associated to the liquidation. The mode…