arXiv research

This paper considers aspects of 4-manifold topology from the point of view of the null cone of a neutral metric, a point of view we call neutral causal topology. In particular, we construct and investigate neutral 4-manifolds with null boundaries that arise from canonical 3- and 4-dimensional settings. A null hypersurf…

We study the neutral Kähler metric on the space of time-like lines in Lorentzian ${\Bbb{E}}^3_1$, which we identify with the total space of the tangent bundle to the hyperbolic plane. We find all of the infinitesimal isometries of this metric, as well as the geodesics, and interpret them in terms of the Lorentzian metr…

The paper introduces mortgage-rate-adjusted home prices to help buyers and adjust housing indices.

We study the geodesic flow on the normal line congruence of a minimal surface in ${\Bbb{R}}^3$ induced by the neutral Kähler metric on the space of oriented lines. The metric is lorentz with isolated degenerate points and the flow is shown to be completely integrable. In addition, we give a new holomorphic description …

We study the geodesic flow on the global holomorphic sections of the bundle $π:{TS}^2\to {S}^2$ induced by the neutral Kähler metric on the space of oriented lines of ${\Bbb{R}}^3$, which we identify with ${TS}^2$. This flow is shown to be completely integrable when the sections are symplectic and the behaviour of the …

Study predicts turbulent electric fields in fusion plasmas using deep learning.

The space ${\Bbb{L}}$ of oriented lines, or rays, in ${\Bbb{R}}^3$ is a 4-dimensional space with an abundance of natural geometric structure. In particular, it boasts a neutral Kähler metric which is closely related to the Euclidean metric on ${\Bbb{R}}^3$. In this paper we explore the relationship between the focal se…

We study surfaces in TN that are area-stationary with respect to a neutral Kaehler metric constructed on TN from a riemannian metric g on N. We show that holomorphic curves in TN are area-stationary, while lagrangian surfaces that are area-stationary are also holomorphic and hence totally null. However, in general, are…

Holomorphic discs converge to maximal surfaces under specific flows.

We study Lagrangian points on smooth holomorphic curves in T${\mathbb P}^1$ equipped with a natural neutral Kähler structure, and prove that they must form real curves. By virtue of the identification of T${\mathbb P}^1$ with the space ${\mathbb L}({\mathbb E}^3)$ of oriented affine lines in Euclidean 3-space ${\mathbb…

Characterizes neutral deformation modes of minimal surfaces.

Paper introduces benchmark-neutral pricing for long-term contracts.

The total space of the tangent bundle of a Kähler manifold admits a canonical Kähler structure. Parallel translation identifies the space ${\Bbb{T}}$ of oriented affine lines in ${\Bbb{R}}^3$ with the tangent bundle of $S^2$. Thus, the round metric on $S^2$ induces a Kähler structure on ${\Bbb{T}}$ which turns out to h…

The paper studies nilpotent structures in oriented neutral vector bundles and neutral hyperKähler structures.

Study finds all 4D neutral manifolds.

The purpose of this article is to review some recent results on the geometry of neutral signature metrics in dimension four and their twistor spaces. The following topics are considered: Neutral Kähler and hyperkähler surfaces, Walker metrics, Neutral anti-self-dual 4-manifolds and projective structures, Twistor spaces…

Currently, machine learning plays an important role in the lives and individual activities of numerous people. Accordingly, it has become necessary to design machine learning algorithms to ensure that discrimination, biased views, or unfair treatment do not result from decision making or predictions made via machine le…

A classical result attributed to Joachimsthal in 1846 states that if two surfaces intersect with constant angle along a line of curvature of one surface, then the curve of intersection is also a line of curvature of the other surface. In this note we prove a global analogue of this result, as follows. Suppose that two …

Optimizes risk-neutral probabilities for derivative pricing.

The paper explores almost paracomplex structures on 4-manifolds and their properties.

The paper shows how to calculate risk-neutral default probabilities from bid and ask CDS quotes.

Simulates risk-neutral markets using neural spline flows.

Generative model uses DDPMs for risk-neutral derivative pricing.

Trading strategy advantage based on information asymmetry.

A model for insider trading with past price dependencies.

Physics-informed ML models improve turbulence understanding in fusion plasmas.

The aim of this paper is to give examples of compact neutral 4-manifolds $(M,g)$ whose Ricci tensor $ρ$ satisfies the relation $\nabla_Xρ(X,X) =\frac13Xτg(X,X)$. We present also a family of new Einstein bi-Hermitian neutral metrics on ruled surfaces of genus $g>1$.

The paper shows that benchmark-neutral pricing minimizes option prices.

Project estimates risk-neutral dependence from option prices.

Paper studies pricing and hedging of nonreplicable insurance contracts using benchmark-neutral approach.

Minimal surfaces can be transformed into others with unchanged bending content.

Extends wealth tax neutrality framework to stochastic volatility and non-homothetic preferences.

We reformulate wealth taxation using Fokker-Planck equations to ensure tax neutrality.

Generative model prices options and extracts risk-neutral densities.

A curvature-type tensor invariant called para contact (pc) conformal curvature is defined on a paracontact manifold. It is shown that a paracontact manifold is locally paracontact conformal to the hyperbolic Heisenberg group or to a hyperquadric of neutral signature if and only if the pc conformal curvature vanishes. I…

AlphaZeroBeta uses deep reinforcement learning for market-neutral portfolios, outperforming traditional methods.

Study finds cryptocurrency market diversity patterns inconsistent with neutral models.

Deep Hedging learns risk-neutral vol dynamics for option pricing.

It is shown that if a compact four-dimensional manifold with metric of neutral signature is Jordan-Osserman, then it is either of constant sectional curvature or Ricci flat.

Wealth tax equivalent to government stake, affecting returns and portfolio choice.

Notation for spin coefficients for metrics of neutral signature in four dimensions is introduced. The utility and interpretation of spin coefficients is explored through themes in null geometry familiar from (complex) general relativity. Four-dimensional Walker geometry is exploited to provide examples and the generali…

Study extends wealth tax neutrality framework to heterogeneous investors.

Investment strategy for NYSE stocks minimizes market correlation.

We give the classification of constant mean curvature rotational surfaces of elliptic, hyperbolic, and parabolic type in the four-dimensional pseudo-Euclidean space with neutral metric.

The paper embeds CR manifolds into twistor spaces and constructs neutral hyperkähler metrics.

Proposes a method to construct risk-neutral marginals from arbitrage-free option prices.

In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the decorrelation. For a neutral vector variable, which is not multivariate Gaussian d…

We establish a connection between capillary floating in neutral equilibrium and the billiard ball problem. This allows us to reduce the question of floating in neutral equilibrium at any orientation with a prescribed contact angle for infinite homogeneous cylinders to a question about billiard caustics for their orthog…