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.
Condition for generic sliced spaces to be globally hyperbolic.
Lapse-supported life insurance exacerbates adverse selection risks.
Study rigidifies geometry of electrostatic systems with specific tensor properties.
Paper predicts embryo implantation probability from IVF time-lapse imaging.
In this article, existence results concerning temporal functions with additional properties on a globally hyperbolic manifold are obtained. These properties are certain bounds on geometric quantities as lapse and shift. The results are linked to completeness properties and the existence of closed isometric embeddings i…
New theorem proves uniqueness of Schwarzschild-de Sitter spacetime.
We consider four-dimensional vacuum spacetimes which admit a nonvanishing spacelike Killing field. The quotient with respect to the Killing action is a three-dimensional quotient spacetime . We establish several results regarding maximal hypersurfaces (spacelike hypersurfaces of zero mean curvature) in such quot…
Multi-StyleGAN simulates live cell microscopy imagery.
Given an d-dimensional manifold with two commuting Killing vectors, together with an d - 1 dimensional submanifold in which one of the Killing vectors lies, then the lapse and shift of the second Killing vector, relative to this slice, remain constant along the orbits of the `surface' Killing vector. Alternatively, the…
Lapse improves parameter servers by dynamically allocating parameters, achieving near-linear scaling.
The classification of solutions of the static vacuum Einstein equations, on a given closed manifold or an asymptotically flat one, is a long-standing and much-studied problem. Solutions are characterized by a complete Riemannian -manifold and a positive function , called the lapse. We study this problem o…
Electrostatic systems with specific tensors are locally conformally flat.
We characterize those spacetimes which admit a isometric (or conformal) embedding in some Lorentz-Minkowski space L^N. In particular, any globally hyperbolic spacetime can be isometrically embedded in L^N. This is proven by a result of its own interest: the construction of a smooth time function whose gradient is bound…
New topological quantum gravity theories linked to Ricci flow.
Let $\M_*=\cup_{t\in [t_0, t_*)} Σ_t$ be a part of vacuum globally hyperbolic space-time $(\bM, \bg)$, foliated by constant mean curvature hypersurfaces with . We show that the foliation can be extended beyond if the second fundamental form and the lapse function satisfy $$ \int_{t_0}^{t_…
We analyze (the harmonic map representation of) static solutions of the Einstein Equations in dimension three from the point of view of comparison geometry. We find simple monotonic quantities capturing sharply the influence of the Lapse function on the focussing of geodesics. This allows, in particular, a sharp estima…
We use an idea of Wang and Yau to give a new definition of quasi-local mass for a topological sphere in an initial date set. The new definition modifies Brown-York's definition by using certain spinor norm as lapse function. And it requires mean curvature of the topological sphere satisfies apparent horizon conditions,…
Study compares non-parametric models for predicting medical insurance reimbursement delays.
New option type preserves fungibility by amortizing payments over time.
In this paper we extend the local scalar curvature rigidity result in [6] to a small domain on general vacuum static spaces, which confirms the interesting dichotomy of local surjectivity and local rigidity about the scalar curvature in general in the light of the paper [10]. We obtain the local scalar curvature rigidi…
Model evaluates insurance risk using thermodynamic principles.
We present a new geometric approach to the study of static isolated general relativistic systems for which we suggest the name geometrostatics. After describing the setup, we introduce localized formulas for the ADM-mass and ADM/CMC-center of mass of geometrostatic systems. We then explain the pseudo-Newtonian characte…
The paper explores stable surfaces in Einstein-Maxwell theory, proving mass bounds and nonexistence results.
We establish a black hole uniqueness theorem for Schwarzschild-de Sitter spacetime, also called Kottler spacetime, which satisfies Einstein's field equations of general relativity with positive cosmological constant. Our result concerns the class of static vacuum spacetimes with compact spacelike slices and regular max…
In 1993, Bartnik introduced a quasi-spherical construction of metrics of prescribed scalar curvature on 3-manifolds. Under quasi-spherical ansatz, the problem is converted into the initial value problem for a semi-linear parabolic equation of the lapse function. The original ansatz of Bartnik started with a background …
We show that local deformations, near closed subsets, of solutions to open partial differential relations can be extended to global deformations, provided all but the highest derivatives stay constant along the subset. The applicability of this general result is illustrated by a number of examples, dealing with convex …
The celebrated uniqueness's theorem of the Schwarzschild solution by Israel, Robinson et al, and Bunting/Masood-ul-Alam, asserts that the only asymptotically flat static solution of the vacuum Einstein equations with compact but non-necessarily connected horizon is Schwarzschild. Between this article and its sequel we …
We consider static spacetimes whose spatial part admits foliations with the extrinsic curvature tensor K_{ab}=0. There are two complementary cases when the gradient of the lapse function points 1) to the direction of foliation or 2) orthogonally to it. Case 1) gives generalization of metrics like Bertotti-Robinson or N…
Introduces a new tensor for electrostatic systems in arbitrary dimensions.
Proposes a model to update industrial data predictions based on temporal changes.
The conformal method is a technique for finding Cauchy data in general relativity solving the Einstein constraint equations, and its parameters include a conformal class, a conformal momentum (as measured by a densitized lapse), and a mean curvature. Although the conformal method is successful in generating constant me…
The paper classifies electrovacuum spaces in higher dimensions, proving several key results.
Generative adversarial networks (GANs) are pow- erful generative models based on providing feed- back to a generative network via a discriminator network. However, the discriminator usually as- sesses individual samples. This prevents the dis- criminator from accessing global distributional statistics of generated samp…
Study on the geometry of Cotton gravity field equations.
We establish a uniform estimate for the injectivity radius of the past null cone of a point in a general Lorentzian manifold foliated by spacelike hypersurfaces and satisfying an upper curvature bound. Precisely, our main assumptions are, on one hand, upper bounds on the null curvature of the spacetime and the lapse fu…
Develops a unified framework for valuing insurance products with guarantees.
New relation found between ADM mass and generalized Komar energy for dynamical spacetimes.
Develops workflow for synthetic insurance datasets.
Revisits life insurance surplus models with new technical bases.
The guaranteed minimum withdrawal benefit (GMWB) rider, as an add on to a variable annuity (VA), guarantees the return of premiums in the form of peri- odic withdrawals while allowing policyholders to participate fully in any market gains. GMWB riders represent an embedded option on the account value with a fee structu…
Study of Ricci flow equations in topological quantum gravity.
Perelman's Ricci flow emerges in quantum gravity, linking math and physics.
We investigate the set of spacetime general coordinate transformations (G.C.T.) which leave the line element of a generic Bianchi Type Geometry, quasi-form invariant; i.e. preserve manifest spatial Homogeneity. We find that these G.C.T.'s, induce special time-dependent automorphic changes, on the spatial scale factor m…
Solves Einstein vacuum equations gluing problem for close Minkowski data.
This paper modifies the Ait-Sahalia model to better describe interest rate behaviors.
This paper addresses the problem of learning the concept of "propagation" in the pretopology theoretical formalism. Our proposal is first to define the pseudo-closure operator (modeling the propagation concept) as a logical combination of neighborhoods. We show that learning such an operator lapses into the Multiple In…
A new tontine design aims to protect longevity risk with non-indexed investments.
We consider generic static spacetimes with Killing horizons and study properties of curvature tensors in the horizon limit. It is determined that the Weyl, Ricci, Riemann and Einstein tensors are algebraically special and mutually aligned on the horizon. It is also pointed out that results obtained in the tetrad adjust…