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.
Interdisciplinary study linking potential theory and elliptic PDEs.
New proof of Penrose inequality using potential theory.
Alternative proof of flatness for Ricci-pinched 3-manifolds.
The paper applies potential theory to conformal geometry, proving theorems and dimension estimates.
Graph theory criterion for Hodge theory to match linearly.
We propose a geometric setup to study analytic aspects of a variant of the super symmetric two-dimensional nonlinear sigma model. This functional extends the functional of Dirac-harmonic maps by gravitino fields. The system of Euler--Lagrange equations of the two-dimensional nonlinear sigma model with gravitino is calc…
One has believed that low energy effective theories of the Higgs branch of gauged linear sigma models correspond to supersymmetric nonlinear sigma models, which have been already investigated by many works. In this paper we discuss a explicit derivation of supersymmetric nonlinear sigma models from gauged linear sigma …
Richberg technique adapted for nonlinear subequations.
We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of potential flat torsionless submanifolds. We show that all potential flat…
Paper proves anisotropic Minkowski inequality and related inequalities.
Set in Riemannian enviroment, the aim of this paper is to present and discuss some equivalent characterizations of the Liouville property relative to special operators, in some sense modeled after the p-Laplacian with potential. In particular, we discuss the equivalence between the Lioville property and the Khas'minski…
Paper analyzes multidimensional PIDEs for financial modeling, proving existence and uniqueness in Bessel spaces.
We prove several differential Harnack inequalities for positive solutions to nonlinear backward heat equations with different potentials coupled with the Ricci flow. We also derive an interpolated Harnack inequality for the nonlinear heat equation under the -Ricci flow on a closed surface. These new Harnac…
Spectral methods predict long-term signals from linear and nonlinear systems.
Optimistic estimate predicts best fitting performance of nonlinear models.
We introduce a class of potential submanifolds in pseudo-Euclidean spaces (each N-dimensional potential submanifold is a special flat torsionless submanifold in a 2N-dimensional pseudo-Euclidean space) and prove that each N-dimensional Frobenius manifold can be locally represented as an N-dimensional potential submanif…
We learn linear models from nonlinear systems using multiple trajectories and regularization.
Note on advancements in nonlinear elliptic equations' regularity theory.
We show that, locally, all geometric objects of Generalized Kahler Geometry can be derived from a function K, the "generalized Kahler potential''. The metric g and two-form B are determined as nonlinear functions of second derivatives of K. These nonlinearities are shown to arise via a quotient construction from an aux…
We study weak geodesics in the space of potentials for the deformed Hermitian-Yang-Mills equation. The geodesic equation can be formulated as a degenerate elliptic equation, allowing us to employ nonlinear Dirichlet duality theory, as developed by Harvey-Lawson. By exploiting the convexity of the level sets of the Lagr…
Paper extends ICA to ISA with auxiliary variables for better speech representation learning.
Kernel-based Bayesian filter for nonlinear systems using infinite-dimensional operators.
A new method clusters heterogeneous subgroups for accurate causal learning.
We identify linear models from nonlinear systems with initialization constraints.
We introduce a method for solving Calderón type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not…
Study of financial models using PIDEs with and without market liquidity.
Unravelling hidden patterns in datasets is a classical problem with many potential applications. In this paper, we present a challenge whose objective is to discover nonlinear relationships in noisy cloud of points. If a set of point satisfies a nonlinear relationship that is unlikely to be due to randomness, we will l…
The paper proposes a new method for creating interpretable models using convex optimization.
MMbeddings reduces categorical embeddings by treating them as latent effects, significantly decreasing parameters and mitigating overfitting.
In recent years, the study of the interplay between (fully) non-linear potential theory and geometry received important new impulse. The purpose of this work is to move a step further in this direction by investigating appropriate versions of parabolicity and maximum principles at infinity for large classes of non-line…
The paper tackles isotropy of symplectic forms using Hodge flows.
The Lax formulation of the hyper-Hermiticity condition in four dimensions is used to derive a potential that generalises Plebanski's second heavenly equation for hyper-Kahler 4-manifolds. A class of examples of hyper-Hermitian metrics which depend on two arbitrary functions of two complex variables is given. The twisto…
We discuss certain recent mathematical advances, mainly due to Perelman, in the theory of Ricci flows and their relevance for renormalization group (RG) flows. We consider nonlinear sigma models with closed target manifolds supporting a Riemannian metric, dilaton, and 2-form B-field. By generalizing recent mathematical…
Unified view of monotonicity formulas for inverse mean curvature flow and -capacitary potentials.
Quantum computing speeds up asset pricing models exponentially.
In this paper, we prove a new gradient estimate for minimal graphs defined on domains of a complete manifold with Ricci curvature bounded from below. In particular, we show that positive, entire minimal graphs on manifolds with non-negative Ricci curvature are constant, and that complete, parabolic manifolds with Ricci…
This paper deals with the conformal deformation of the standard metric in a domain on the sphere to a complete metric with the constant scalar curvature. The problem of description of domains allowing such deformation originates in the works of Loewner and Nirenberg, and Schoen and Yau concerned with the locally confor…
Unsupervised learning models can be indistinguishable without identifiability, leading to unreliable representations.
The new business paradigms originate a strong necessity to re-think the theory of the firm with the aim to get a better understanding on the organizational and functional principles of the firm, operating in the investment economies in the prosperous societies. In this connection, we make the innovative research to adv…
Panda predicts chaotic systems without retraining, showing emergent properties.
Identifying coordinate transformations that make strongly nonlinear dynamics approximately linear is a central challenge in modern dynamical systems. These transformations have the potential to enable prediction, estimation, and control of nonlinear systems using standard linear theory. The Koopman operator has emerged…
This research highlights the secrecy potential of nonlinear generative models and their all-or-nothing phase transition.
Solves geometric problems using fully nonlinear equations and Morse theory.
Researchers find a way to estimate potential functions for quaternionic metrics.
Let be an dimensional complete Riemannian manifold. In this paper we prove local Li-Yau type gradient estimates for all positive solutions to the following nonlinear parabolic equation \begin{equation*} (\partial_t - Δ_g + \mathcal{R}) u(x, t) = - a u(x, t) \log u(x, t) \end{equation*} along the generalised ge…
New algorithm speeds up IRT model fitting for large datasets.
In this paper we study asymptotic behavior of -superharmonic functions at isolated singularity using the Wolff potential and -capacity estimates in nonlinear potential theory. Our results are inspired by and extend those of Arsove-Huber and Taliaferro in 2 dimensions. To study -superharmonic functions we use a…
Develops a Barta theorem for p-Laplacian on manifolds.