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.
The paper examines conditions for linearity in a conditional mean estimator under vector Poisson noise.
Transformers solve Poisson means estimation via empirical Bayes.
Introduces Poisson double algebroids and their relation to Lie 2-bialgebras.
Poisson-NIjenhuis structures for an arbitrary Lie agebroid are defined and studied by means of tangent lifts of tensor fields.
The paper establishes a Poisson integral formula for bounded pluriharmonic functions on Teichmüller space.
Multivariate Poisson approximation of the length spectrum of random surfaces is studied by means of the Chen-Stein method. This approach delivers simple and explicit error bounds in Poisson limit theorems. They are used to prove that Poisson approximation applies to curves of length up to order with …
We characterize Poisson and Jacobi structures by means of complete lifts of the corresponding tensors: the lifts have to be related to canonical structures by morphisms of corresponding vector bundles. Similar results hold for generalized Poisson and Jacobi structures (canonical structures) associated with Lie algebroi…
A new sequential method estimates Poisson means in streaming data, achieving optimality and efficiency.
We give a geometric description of the Poisson boundaries of certain extensions of free and hyperbolic groups. In particular, we get a full description of the Poisson boundaries of free-by-cyclic groups. We rely upon the description of Poisson boundaries by means of a topological compactification as developed by Kaiman…
Paper establishes sufficient condition for comparing linear combinations of infinite-mean risks.
We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random variable whose mean is a sparse linear superposition of known patterns. Unlike many co…
Gaussian surrogates improve Poisson imaging performance at low doses.
Deforms Poisson quasi-Nijenhuis manifolds using closed 2-forms.
The paper starts with an interpretation of the complete lift of a Poisson structure from a manifold M to its tangent bundle TM by means of the Schouten- Nijenhuis bracket of covariant symmetric tensor fields defined by the co- tangent Lie algebroid of M. Then, we discuss Poisson structures of TM which have a graded res…
Paper designs Poisson integrators using machine learning.
We previously extended the Marsden-Ratiu reduction theorem in Poisson geometry by means of graded geometry (see Part I of Arxiv:1009.0948) . In this note we provide the background material about graded geometry necessary for the proof. Further, we provide an alternative algebraic proof.
We prove that an arbitrary Poisson structure omega^{ij}(u) and an arbitrary closed 3-form T_{ijk}(u) generate the local Poisson structure A^{ij}(u,u_x) = M^i_s(u,u_x)omega^{sj}(u), where M^i_s(u,u_x)(delta^s_j + omega^{sp}(u)T_{pjk}(u)u^k_x) = delta^i_j, on the corresponding loop space. We obtain also a special graded …
V1 cortex reconstructs images as Poisson equation solutions with varying weights.
We introduce and study a new spectral sequence associated with a Poisson group action on a Poisson manifold and an equivariant momentum mapping. This spectral sequence is a Poisson analog of the Leray spectral sequence of a fibration. The spectral sequence converges to the Poisson cohomology of the manifold and has the…
We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying Poisson process is equal to that of the beta process. We use this underlying re…
Mack's estimator improves chain ladder prediction for large exposure insurance models.
We study the transverse Poisson structure to adjoint orbits in a complex semi-simple Lie algebra. The problem is first reduced to the case of nilpotent orbits. We prove then that in suitably chosen quasi-homogeneous coordinates the quasi-degree of the transverse Poisson structure is -2. In the particular case of {\emph…
The paper introduces transposed Poisson superalgebras and their properties.
We provide an alternative method for obtaining of compatible Poisson structures on Lie groups by means of the adjoint representations of Lie algebras. In this way, we calculate some compatible Poisson structures on four dimensional and nilpotent six dimensional symplectic real Lie groups. Then using Magri-Morosi's theo…
Arnlind, Hoppe and Huisken showed how to express the Gauss and mean curvature of a surface embedded in a Riemannian manifold in terms of Poisson brackets of the embedding coordinates. We generalize these expressions to the pseudo-Riemannian setting and derive explicit formulas for the case of surfaces embedded in $\R^m…
Let Q denote a smooth manifold acted upon smoothly by a Lie group G. The G-action lifts to an action on the total space T of the cotangent bundle of Q and hence on the standard symplectic Poisson algebra of smooth functions on T. The Poisson algebra of G-invariant functions on T yields a Poisson structure on the space …
Let be a Poisson algebra, a vector space and an epimorphism of vector spaces with . The global extension problem asks for the classification of all Poisson algebra structures that can be defined on such that becomes a morphism of Poisson algebras. From a geometri…
We investigate connections between information-theoretic and estimation-theoretic quantities in vector Poisson channel models. In particular, we generalize the gradient of mutual information with respect to key system parameters from the scalar to the vector Poisson channel model. We also propose, as another contributi…
We propose an extension of n-ary Nambu-Poisson bracket to superspace R^{n|m} and construct by means of superdeterminant a family of Nambu-Poisson algebras of even degree functions, where the parameter of this family is an invertible transformation of Grassmann coordinates in superspace R^{n|m}. We prove in the case of …
A general approach to proving that the length spectrum of a compact Riemannian manifold is an invariant of the Laplace spectrum comes from considering the wave trace, a spectrally determined tempered distribution. The Poisson relation states that the singularities of the wave trace can only occur at lengths of closed g…
Investigates RI strategies for life insurers with LRD mortality rates.
Despite the fundamental nature of the inhomogeneous Poisson process in the theory and application of stochastic processes, and its attractive generalizations (e.g. Cox process), few tractable nonparametric modeling approaches of intensity functions exist, especially when observed points lie in a high-dimensional space.…
The Poisson equation is commonly encountered in engineering, for instance in computational fluid dynamics (CFD) where it is needed to compute corrections to the pressure field to ensure the incompressibility of the velocity field. In the present work, we propose a novel fully convolutional neural network (CNN) architec…
Study on length distribution of random multicurves on large genus surfaces converging to Poisson-Dirichlet distribution.
New insights into empirical Bayes and compound decision problems with improved regret bounds.
We look at generalized complex structures from the point of view of Poisson and Dirac geometry and we remark that the puzzling equations underlying the notion of generalized complex structure have miraculously simple meaning when passing to Lie algebroids/groupoids.
Kontsevich's formula for a deformation quantization of Poisson structures involves a Feynman series of graphs, with the weights given by some complicated integrals (using certain pullbacks of the standard angle form on a circe). We explain the geometric meaning of this series as degrees of maps of some grand configurat…
Ridge regression linked to Poisson resetting in statistical physics.
The Mishchenko-Fomenko conjecture says that for each real or complex finite-dimensional Lie algebra $\goth g$ there exists a complete set of commuting polynomials on its dual space $\goth g^*$. In terms of the theory of integrable Hamiltonian systems this means that the dual space $\goth g^*$ endowed with the standard …
In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distributio…
Speeding up Markov Chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention. A pseudo-marginal MCMC method is proposed that estimates the likelihood by data subsampling using a block-Poisson estimator. The estimator is a product of Poisson estimators,…
New tree-structured Markov fields with Poisson marginals for counting variables.
New sampling method uses gradient-free IPS with RKHS velocity field.
The Brownian bridge serves as a physics-informed prior for solving the Poisson equation.
Contractions of Leibniz algebras and Courant algebroids by means of (1,1)-tensors are introduced and studied. An appropriate version of Nijenhuis tensors leads to natural deformations of Dirac structures and Lie bialgebroids. One recovers presymplectic-Nijenhuis structures, Poisson-Nijenhuis structures, and triangular …
The telegraph process models a random motion with finite velocity and it is usually proposed as an alternative to diffusion models. The process describes the position of a particle moving on the real line, alternatively with constant velocity or . The changes of direction are governed by an homogeneous Poisso…
This work constructs groupoids from flat bundles over surfaces.
Random translation surfaces converge to a Poisson plane as genus grows.