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.
NKI integrates obfuscated datasets using nonlinear kernels for improved data collaboration.
The nonlinear equations describing all the nonsingular pencils of metrics of constant Riemannian curvature are derived and the integrability of these nonlinear equations by the method of inverse scattering problem is proved. It is proved that all the nonsingular pairs of compatible metrics of constant Riemannian curvat…
The paper establishes Harnack inequalities for solutions of nonlinear parabolic equations on manifolds with integral Ricci curvature bounds.
The paper studies frequency monotonicity for solutions of nonlinear equations under Ricci flow.
We present a probabilistic framework for nonlinearities, based on doubly truncated Gaussian distributions. By setting the truncation points appropriately, we are able to generate various types of nonlinearities within a unified framework, including sigmoid, tanh and ReLU, the most commonly used nonlinearities in neural…
Study on smoothness of solutions to nonlinear equations on Riemannian manifolds.
We solve the problem of description for nonsingular pairs of compatible flat metrics in the general N-component case. The integrable nonlinear partial differential equations describing all nonsingular pairs of compatible flat metrics (or, in other words, nonsingular flat pencils of metrics) are found and integrated. Th…
CDSSL improves representation quality by integrating linear and nonlinear dependencies.
The paper derives new gradient estimates for nonlinear elliptic equations under integral Ricci curvature bounds.
This article studies the financial integration between the six main Latin American markets and the US market in a nonlinear framework. Using the threshold cointegration techniques of Hansen and Seo (2002), we show significant threshold stock market linkages between Mexico, Chile and the US. Thus, the dynamics of these …
New methods integrate nonlinear, sparse, and multi-view aspects for high-dimensional data analysis.
D2PCCA integrates deep learning and probabilistic modeling for nonlinear dynamical systems.
We introduce GP-FNARX: a new model for nonlinear system identification based on a nonlinear autoregressive exogenous model (NARX) with filtered regressors (F) where the nonlinear regression problem is tackled using sparse Gaussian processes (GP). We integrate data pre-processing with system identification into a fully …
Constructs differential characters on nonlinear Graßmannians.
Study decay and compact support of solutions to certain nonlinear PDEs.
DGPFM uses deep Gaussian processes to map functions accurately and quantify uncertainty.
Two discretizations, linear and nonlinear, of basic notions of the complex analysis are considered. The underlying lattice is an arbitrary quasicrystallic rhombic tiling of a plane. The linear theory is based on the discrete Cauchy-Riemann equations, the nonlinear one is based on the notion of circle patterns. We clari…
Paper extends ICA to ISA with auxiliary variables for better speech representation learning.
Proposes an INLA-based method for state and parameter estimation in nonlinear systems.
Connections between integration along hypersufaces, Radon transforms, and neural networks are exploited to highlight an integral geometric mathematical interpretation of neural networks. By analyzing the properties of neural networks as operators on probability distributions for observed data, we show that the distribu…
In this paper, we study the formal solution space of a nonlinear PDE in a fiber bundle. To this end, we start with foundational material and introduce the notion of a pfd structure to build up a new concept of profinite dimensional manifolds. We show that the infinite jet space of the fiber bundle is a profinite dimens…
We show that Plebanski's second heavenly equation, when written as a first-order nonlinear evolutionary system, admits multi-Hamiltonian structure. Therefore by Magri's theorem it is a completely integrable system. Thus it is an example of a completely integrable system in four dimensions.
We give an explicit formula, as a formal differential operator, for quantum microformal morphisms of (super)manifolds that we introduced earlier. Such quantum microformal morphisms are essentially oscillatory integral operators or Fourier integral operators of a particular kind. They act on oscillatory wave functions, …
Improved stability analysis of neural network systems using Zames-Falb multipliers.
We study several optimal stopping problems that arise from trading a mean-reverting price spread over a finite horizon. Modeling the spread by the Ornstein-Uhlenbeck process, we analyze three different trading strategies: (i) the long-short strategy; (ii) the short-long strategy, and (iii) the chooser strategy, i.e. th…
This paper tackles Bayesian system identification with probabilistic numerical methods.
Bayesian quadrature improves integration on Riemannian manifolds.
In this paper we develop some group theoretical methods which are shown to be very useful for a better understanding of the properties of the Riccati equation and we discuss some of its integrability conditions from a group theoretical perspective. The nonlinear superposition principle also arises in a simple way.
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.
A general nonlinear logistic equation has been proposed to model long-time saturation in industrial growth. An integral solution of this equation has been derived for any arbitrary degree of nonlinearity. A time scale for the onset of nonlinear saturation in industrial growth can be estimated from an equipartition cond…
Develops AMITE for analyzing neural network nonlinearities.
We find explicitly all bi-umbilical foliated semi-symmetric hypersurfaces in the four-dimensional Euclidean space.
Enhances learning of structured distributions using nonlinear denoising score matching.
Motion of curves and surfaces in lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through geometric and gauge symmetric connections/equivalence. Here we point out the fact that…
Paper quantifies neural operators' efficiency for solving nonlinear parabolic PDEs.
Paper solves a complex portfolio selection problem with time-inconsistent preferences.
Neural ARFIMA model improves exchange rate forecasting for BRIC economies.
We introduce the truncated Gaussian graphical model (TGGM) as a novel framework for designing statistical models for nonlinear learning. A TGGM is a Gaussian graphical model (GGM) with a subset of variables truncated to be nonnegative. The truncated variables are assumed latent and integrated out to induce a marginal m…
We study the existence of a metric with zero scalar curvature maximizing the isoperimetric ratio among all zero scalar curvature metrics in a fixed conformal class of metrics on a compact manifold with boundary. The question may be reduced to an extremal problem for the harmonic extension of functions and the related n…
In this paper we investigate compatible overdetermined systems of PDEs on the plane with one common characteristic. Lie's theorem states that its integration is equivalent to a system of ODEs, and we relate this to the geometry of rank 2 distributions. We find a criterion for integration in quadratures and in closed fo…
Rediscovered by a systematic search, a forgotten class of integrable surfaces is shown to disprove the Finkel-Wu conjecture. The associated integrable nonlinear partial differential equation possesses a zero curvature representation, a third-order symmetry, and a nonlocal transformatio…
Proposes CoDEAL for estimating heterogeneous treatment effects in panel data models.
The paper tackles data-driven optimal control of unknown nonlinear systems using RKHS.
We prove that second-order hyperbolic Monge-Ampere equations for one function of two variables are connected to the wave equation by a Backlund transformation if and only if they are integrable by the method of Darboux at second order. One direction of proof, proving Darboux integrability, follows the implications of t…
Based on conservation laws for surface layer integrals for critical points of causal variational principles, it is shown how jet spaces can be endowed with an almost-complex structure. We analyze under which conditions the almost-complex structure can be integrated to a canonical complex structure. Combined with the sc…
Gradient descent and SGD solve nonlinear inverse problems efficiently.
Kernel-spectral embedding learns low-dim. structures from noisy data.
Transformer-based method for causal discovery with prior knowledge integration.