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.
Extends moment map concept to locally conformally Kähler manifolds.
We consider a stochastic volatility model where the moment generating function of the logarithmic price is finite only on part of the real line. Using a new Tauberian result obtained in [1] and [2], we show that the knowledge of the moment generating function near its critical moment gives a sharp asymptotic expansion …
The paper trivializes moment maps for various geometric structures.
New rigidity results for complex and quaternionic moment-angle manifolds.
This study proves the local existence of a symplectic gradient flow on a flat torus.
In decision under risk, the primal moments of mean and variance play a central role to define the local index of absolute risk aversion. In this paper, we show that in canonical non-EU models dual moments have to be used instead of, or on par with, their primal counterparts to obtain an equivalent index of absolute ris…
We present a proof due to Duistermaat that the gradient flow of the norm squared of the moment map defines a deformation retract of the appropriate piece of the manifold onto the zero level set of the moment map. Duistermaat's proof is an adaptation of Lojasiewicz's argument for analytic functions to functions which ar…
Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of the unknown data generating density. This paper contributes to the mathematical understanding of this phenomenon and helps define better justified sampling algorithms for deep learning based on auto-encoder v…
The sectional curvature of a compact Riemannian manifold M can be seen as a random variable on the Grassmann bundle of 2-planes in TM endowed with the Fubini-Study volume density. In this article we calculate the moments of this random variable by integrating suitable local Riemannian invariants and discuss the distrib…
For a finite-dimensional (but possibly noncompact) symplectic manifold with a compact group acting with a proper moment map, we show that the square of the moment map is an equivariantly perfect Morse function in the sense of Kirwan, and that the set of critical points of the square of the moment map is a countable dis…
We define a moment map associated to a smooth torus action on a smooth manifold, without a two-form. We define cobordisms of such structures, allowing non compact manifolds as long as the moment maps are proper. We prove that a compact manifold with a torus action and a moment map is cobordant to the disjoint union of …
New real algebraic maps with prescribed images and compositions are constructed locally like moment maps.
This study shows the moment-SOS hierarchy converges in polynomial optimization over product of spheres.
FedIV uses federated GMM for IV analysis in non-i.i.d. data.
Tropical curves match to special Lagrangian shapes.
Study local perturbations of vector bundles with polynomial curvature solutions.
Optimizes mixture models without parametrizing distributions using tensor decomposition.
We prove a localization formula for group-valued equivariant de Rham cohomology of a compact G-manifold. This formula is a non-trivial generalization of the localization formula of Berline-Vergne and Atiyah-Bott for the usual equivariant de Rham cohomology. As an application, we obtain a version of the Duistermaat-Heck…
Study nearly parallel G2-structures with torus symmetry using multi-moment maps.
MuML models predict molecular dipole moments using atomic partial charges and dipoles.
The paper examines Nash equilibrium in GANs for stationary Gaussian processes.
The latest generation of volatility derivatives goes beyond variance and volatility swaps and probes our ability to price realized variance and sojourn times along bridges for the underlying stock price process. In this paper, we give an operator algebraic treatment of this problem based on Dyson expansions and moment …
Polynomial Duistermaat-Heckman measure on symplectic groupoid quotients.
New method uses machine learning to improve statistical inference.
We investigate special lcs and twisted Hamiltonian torus actions on strict lcs manifolds and characterize them geometrically in terms of the minimal presentation. We prove a convexity theorem for the corresponding twisted moment map, establishing thus an analog of the symplectic convexity theorem of Atiyah and Guillemi…
We propose -graph embedding for robustly learning feature vectors from data vectors and noisy link weights. A newly introduced empirical moment -score reduces the influence of contamination and robustly measures the difference between the underlying correct expected weights of links and the specified generative m…
Study local expansions of continuous-time processes using Ito signature properties.
We show that the conformal structure for the Riemannian analogues of Kerr black-hole metrics can be given an ambitoric structure. We then discuss the properties of the moment maps. In particular, we observe that the moment map image is not locally convex near the singularity corresponding to the ring singularity in the…
New method approximates MMD using pseudo-differential operators and singular values.
Study finds the minimum number of finite Gaussian mixtures for best approximation.
Motivated by the prediction of cell loads in cellular networks, we formulate the following new, fundamental problem of statistical learning of geometric marks of point processes: An unknown marking function, depending on the geometry of point patterns, produces characteristics (marks) of the points. One aims at learnin…
Researchers study metrics with maximal Ricci curvature on homogeneous spaces.
Let K be a connected Lie group and M a Hamiltonian K-manifold. In this paper, we introduce the notion of convexity of M. It implies that the momentum image is convex, the moment map has connected fibers, and the total moment map is open onto its image. Conversely, the three properties above imply convexity. We show tha…
We apply a local differential geometric framework from Kähler toric geometry to (re)construct Calabi's extremal Kähler metrics on $\bbC\bbP^n$ blown-up at a point from data on the moment polytope.
New method uses geometric moments for accurate machine learning potentials.
We prove that higher moment maps on area measures of a euclidean vector space are injective, while the kernel of the centroid map equals the image of the first variation map. Based on this, we introduce the space of smooth dual area measures on a finite-dimensional euclidean vector space and prove that it admits a natu…
We prove an analogue of the Atiyah-Bott-Berline-Vergne localization formula in the setting of equivariant basic cohomology of -contact manifolds. As a consequence, we deduce analogues of Witten's nonabelian localization and the Jeffrey-Kirwan residue formula, which relate equivariant basic integrals on a contact man…
Nous considérons un espace topologique qui est localement isomorphe au quotient de R^k par l'action d'un groupe discret et nous l'appelons quasi-variété de dimension k. Les quasi-variétés généralisent les variétés et les V-variétés et représentent le cadre naturel pour la réduction symplectique par rapport à l'action i…
Samplets and multiwavelets constructed from scattered data converge to specific densities in the limit.
AdamNX improves Adam's stability by adjusting its learning rate.
Develops a contraction framework for MCMC mixing rates.
Develops a new method for estimating models with conditional moment restrictions.
The paper optimizes estimating high-dimensional Gaussian mixtures without separation conditions.
RELTA-SGLD stabilizes nonconvex SGLD updates with a lighter taming scheme.
We prove a computable version of de Finetti's theorem on exchangeable sequences of real random variables. As a consequence, exchangeable stochastic processes expressed in probabilistic functional programming languages can be automatically rewritten as procedures that do not modify non-local state. Along the way, we pro…
A new method calculates fractional moments using the moment-generating function.
Study compares weak and homotopy moment maps in multisymplectic geometry.
New method estimates log-determinant using trace powers, avoiding classical limitations.