arXiv research

Holomorphic Jacobi manifolds integrate to complex contact groupoids.

Lie group integrators improve global error estimates.

Discrete-time hidden Markov models are a broadly useful class of latent-variable models with applications in areas such as speech recognition, bioinformatics, and climate data analysis. It is common in practice to introduce temporal non-homogeneity into such models by making the transition probabilities dependent on ti…

Study splitting submanifolds in specific homogeneous spaces.

We give a new proof of the Jantzen sum formula for integral representations of Chevalley schemes over Spec Z. This is done by applying the fixed point formula of Lefschetz type in Arakelov geometry to generalized flag varieties. Our proof involves the computation of the equivariant Ray-Singer torsion for all equivarian…

New integrators preserve geometric structure in Hamiltonian systems.

The paper analyzes fixed step-size SA schemes on Riemannian manifolds.

Hopformer combines common trends with series-specific details for better time series forecasting.

Enhances Ponzi scheme detection on Ethereum using time-aware metapaths.

We review properties of so-called special conformal Killing tensors on a Riemannian manifold $(Q,g)$ and the way they give rise to a Poisson-Nijenhuis structure on the tangent bundle $TQ$. We then address the question of generalizing this concept to a Finsler space, where the metric tensor field comes from a regular La…

Method identifies IPS governing equations from particle data efficiently.

Adaptive importance sampling for estimating point process statistics.

Banks in the interbank network can not assess the true risks associated with lending to other banks in the network, unless they have full information on the riskiness of all the other banks. These risks can be estimated by using network metrics (for example DebtRank) of the interbank liability network which is availabl…

Adversarial reinforcement learning optimizes microswimmers' path-planning in turbulent flows.

The paper extends Hamiltonian Monte Carlo to Lie groups and constrained mechanics.

Inverse reinforcement learning (IRL) has become a useful tool for learning behavioral models from demonstration data. However, IRL remains mostly unexplored for multi-agent systems. In this paper, we show how the principle of IRL can be extended to homogeneous large-scale problems, inspired by the collective swarming b…

Starting from suitable tableaux over finite dimensional Lie algebras, we provide a scheme for producing involutive linear Pfaffian systems related to various classes of submanifolds in homogeneous spaces which constitute integrable systems. These include isothermic surfaces, Willmore surfaces, and other classical solit…

We introduce a criterion that a given bihamiltonian structure allows a local coordinate system where both brackets have constant coefficients. This criterion is applied to the bihamiltonian open Toda lattice in a generic point, which is shown to be locally isomorphic to a Kronecker odd-dimensional pair of brackets with…

We prove that the set of non-degenerate second order maximally superintegrable systems in the complex Euclidean plane carries a natural structure of a projective variety, equipped with a linear isometry group action. This is done by deriving the corresponding system of homogeneous algebraic equations. We then solve the…

Paper tackles efficient training of linear models on manycore processors.

Robust PDE method for path-dependent Asian-style options using MPDATA.

First proper learning algorithm for Gaussian halfspaces with matching sample and computational complexity.

Paper uses Mirror Descent for efficient risk budgeting portfolios.

Binomial tree methods (BTM) and explicit difference schemes (EDS) for the variational inequality model of American options with time dependent coefficients are studied. When volatility is time dependent, it is not reasonable to assume that the dynamics of the underlying asset's price forms a binomial tree if a partitio…

Unified analysis of federated learning with compression for various data distributions.

Introduces new types of homogeneous spaces and their properties.

The study finds homogeneous geodesics in homogeneous Kropina spaces.

Paper solves a max-min game for complex performance benchmarks.

Study finds six homogeneous surfaces with multiple invariant connections.

Introduces homogeneity supermanifolds for studying graded structures.

Solves a complex mathematical problem on curved surfaces.

Homogeneous three-spheres have only homogenous foliations.

Constant Proportion Portfolio Insurance (CPPI) is an investment strategy designed to give participation in the performance of a risky asset while protecting the invested capital. This protection is however not perfect and the gap risk must be quantified. CPPI strategies are path-dependent and may have American exercise…

In this paper, we study homogeneous geodesics in homogeneous Finsler spaces. We first give a simple criterion that characterizes geodesic vectors. We show that the geodesics on a Lie group, relative to a bi-invariant Finsler metric, are the cosets of the one-parameter subgroups. The existence of infinitely many homogen…

We prove that the Penrose limit of a spacetime along a homogeneous geodesic is a homogeneous plane wave spacetime and that the Penrose limit of a reductive homogeneous spacetime along a homogeneous geodesic is a Cahen--Wallach space. We then consider several homogenous examples to show that these results are indeed sha…

Improved sample complexity for learning halfspaces with malicious noise.

We prove that under some purely algebraic conditions every locally homogeneous structure modelled on some homogeneous space is induced by a locally homogeneous structure modelled on a different homogeneous space.

Develops methods to learn centre groupings from summary statistics in multi-centre studies.

Our purpose is to use a Darboux homogenous derivative to understand the harmonic maps with values in homogeneous space. We present a characterization of these harmonic maps from the geometry of homogeneous space. Furthermore, our work covers all type of invariant geometry in homogeneous space.

We show that a Lorentzian homogeneous space admitting a homogeneous structure of type T1 + T3 is either a (locally) symmetric space or a singular homogeneous plane wave.

In a recent paper, it was claimed that any homogeneous Finsler space of odd dimension admits a homogeneous geodesic through any point. For the proof, the algebraic method dealing with the reductive decomposition of the Lie algebra of the isometry group was used. However, the proof contains a serious gap. In the present…

The study verifies a conjecture about homogeneous quotients of manifolds with positive curvature.

In this article we study homogeneous warped product Einstein metrics and its connections with homogeneous Ricci solitons. We show that homogeneous $(λ,n+m)$-Einstein manifolds (which are the bases of homogeneous warped product Einstein metrics) are one-dimensional extensions of algebraic solitons. This answers a questi…

The Homogeneity Conjecture explores if constant displacement isometries imply homogeneous spaces.

In previous papers, a fundamental affine method for studying homogeneous geodesics was developed. Using this method and elementary differential topology it was proved that any homogeneous affine manifold and in particular any homogeneous pseudo-Riemannian manifold admits a homogeneous geodesic through arbitrary point. …

Survey of recent results on homogeneous finite-dimensional spaces.

Proposes a method for private aggregation in heterogeneous federated learning.

The paper extends two-step homogeneous geodesics to homogeneous Finsler spaces.