arXiv research

New privacy-preserving method for conformal prediction without splitting data.

Study describes splitting and filtration of Hodge bundle on quadratic differentials.

DiPriMe forests use private medians to create balanced tree splits for privacy-protected data.

Differential K-theory gets a $λ$-ring structure.

A new method speeds up option pricing under Heston's stochastic volatility model.

This paper generalizes Batchelor's theorem in $C^\infty$-superschemes.

Differentially private conformal prediction improves statistical efficiency.

Study shows splitting schemes can approximate WFR flows faster than the exact flow.

Introduces nonlinear splittings on fibre bundles for generalizing connections.

Low regularity spacetimes split into simpler structures.

This paper deals with the efficient numerical solution of the two-dimensional partial integro-differential complementarity problem (PIDCP) that holds for the value of American-style options under the two-asset Merton jump-diffusion model. We consider the adaptation of various operator splitting schemes of both the impl…

High order splitting schemes with complex timesteps are applied to Kolmogorov backward equations stemming from stochastic differential equations in Stratonovich form. In the setting of weighted spaces, the necessary analyticity of the split semigroups can be easily proved. A numerical example from interest rate theory,…

New estimator for digital options using path splitting and MLMC.

This paper deals with the numerical approximation of American-style option values governed by partial differential complementarity problems. For a variety of one- and two-asset American options we investigate by ample numerical experiments the temporal convergence behaviour of three modern splitting methods: the explic…

In classical field theory, the composite fibred manifolds Y -> Z -> X provides the adequate mathematical formulation of gauge models with broken symmetries, e.g., the gauge gravitation theory. This work is devoted to connections on composite fibred manifolds. In particular, we get the horizontal splitting of the vertic…

Very few results are known about the topology of the strata of the moduli space of quadratic differentials. In this paper, we prove that any connected component of such strata has only one topological end. A typical flat surface in a neighborhood of the boundary is naturally split by a collection of parallel short sadd…

Study splitting submanifolds in specific homogeneous spaces.

Paper introduces a new cosmological volume function and its properties.

We construct normed spaces of real-valued functions with controlled growth on possibly infinite-dimensional state spaces such that semigroups of positive, bounded operators $(P_t)_{t\ge 0}$ thereon with $\lim_{t\to 0+}P_t f(x)=f(x)$ are in fact strongly continuous. This result applies to prove optimal rates of converge…

Boosting as gradient descent algorithms is one popular method in machine learning. In this paper a novel Boosting-type algorithm is proposed based on restricted gradient descent with structural sparsity control whose underlying dynamics are governed by differential inclusions. In particular, we present an iterative reg…

Sobolev maps on product spaces are split or approximately split.

In this paper, we construct a homotopy Poisson algebra of degree 3 associated to a split Lie 2-algebroid, by which we give a new approach to characterize a split Lie 2-bialgebroid. We develop the differential calculus associated to a split Lie 2-algebroid and establish the Manin triple theory for split Lie 2-algebroids…

The usual Gromoll-Meyer's generalized Morse lemma near degenerate critical points on Hilbert spaces, so called splitting lemma, is stated for at least $C^2$-smooth functionals. In this paper we establish a splitting theorem and a shifting theorem for a class of continuously directional differentiable functionals (lower…

We study the geometry of type II supergravity compactifications in terms of an oriented vector bundle $E$, endowed with a bundle metric of split signature and further datum. The geometric structure is associated with a so-called generalised $G$-structure and characterised by an $E$-spinor $ρ$, which we can regard as a …

In work the internal structure of de Rham cohomology is considered. As examples the phase flows in $\mathbb {R}^3$ admitting the Nambu Poisson structure are studied.

It is shown that the determinant line bundle associated to a family of Dirac operators over a closed partitioned manifold has a canonical Hermitian metric with compatible connection whose curvature satisfies an additivity formula with contributions from the families of Dirac operators over the two halves. This curvatur…

We propose a new, unified approach to solving jump-diffusion partial integro-differential equations (PIDEs) that often appear in mathematical finance. Our method consists of the following steps. First, a second-order operator splitting on financial processes (diffusion and jumps) is applied to these PIDEs. To solve the…

We associate a flow $φ$ to a solution of the vortex equations on a closed oriented Riemannian 2-manifold $(M,g)$ of negative Euler characteristic and investigate its properties. We show that $φ$ always admits a dominated splitting and identify special cases in which $φ$ is Anosov. In particular, starting from holomorph…

We introduce multiplicative differential forms on Lie groupoids with values in VB-groupoids. Our main result gives a complete description of these objects in terms of infinitesimal data. By considering split VB-groupoids, we are able to present a Lie theory for differential forms on Lie groupoids with values in 2-term …

Study on Wasserstein distance for numerical approximations of stochastic differential equations.

We generalize the Bartsch-Li's splitting lemma at infinity for $C^2$-functionals in [2] and some later variants of it to a class of continuously directional differentiable functionals on Hilbert spaces. Different from the previous flow methods our proof is to combine the ideas of the Morse-Palais lemma due to Duc-Hung-…

The paper introduces a privacy-preserving method for estimating treatment effects that maintains accuracy.

Financial derivatives pricing aims to find the fair value of a financial contract on an underlying asset. Here we consider option pricing in the partial differential equations framework. The contemporary models lead to one-dimensional or multidimensional parabolic problems of the convection-diffusion type and generaliz…

Split learning preserves privacy in 1D CNN models for detecting heart abnormalities.

Study shows special Kähler geometry on base of holomorphic Lagrangian fibrations implies projective space.

In this paper we introduce flat grafting as a deformation of quadratic differentials on a surface of finite type that is analogous to the grafting map on hyperbolic surfaces. Flat grafting maps are generic in the strata structure and preserve parallel measured foliations. We use flat grafting to construct paths connect…

Despite the impressive performance of random forests (RF), its theoretical properties have not been thoroughly understood. In this paper, we propose a novel RF framework, dubbed multinomial random forest (MRF), to analyze the \emph{consistency} and \emph{privacy-preservation}. Instead of deterministic greedy split rule…

The abstract generalizes a construction for splitting supermanifolds and studies Lie supergroup cases.

Paper learns dictionaries for sparse signal recovery using automatic differentiation.

Let G be a Lie group acting by diffeomorphisms on a manifold M and consider the image of T[1]G and T[1]M, of G and M respectively, in the category of differential graded manifolds. We show that the obstruction to lift the action of T[1]G on T[1]M to an action on a R[n]-bundle over T[1]M is measured by the G equivariant…

This paper deals with the notion of quadratic differential in spherical CR geometry (or more generally on strictly pseudoconvex CR manifolds). We get to this notion by studying a splitting of Rumin complex and discuss its first features such as trajectories and length. We also define several differential operators on q…

A deep learning method solves nonlinear filtering problems efficiently.

A new method identifies class-specific covariates in multi-class prediction tasks.

Study numerical methods for singular FBSDEs with degenerate forward component.

The paper efficiently solves a complex option valuation equation for two assets.

We study geometric structures of $\mathcal{W}_4$-type in the sense of A. Gray on a Riemannian manifold. If the structure group $\mathrm{G} \subset \SO(n)$ preserves a spinor or a non-degenerate differential form, its intrinsic torsion $Γ$ is a closed 1-form (Proposition \ref{dGamma} and Theorem \ref{Fixspinor}). Using …

We present a detailed analysis and implementation of a splitting strategy to identify simultaneously the local-volatility surface and the jump-size distribution from quoted European prices. The underlying model consists of a jump-diffusion driven asset with time and price dependent volatility. Our approach uses a forwa…

A novel gradient-based method optimizes decision trees for complex tasks.