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.
Classifies star log symplectic structures on surfaces.
New counterexamples show the Kontsevich tetrahedral flows don't preserve Poisson bi-vectors.
The flow preserves Poisson bi-vectors if the monomials are balanced.
Graph complex acts on Poisson bi-vectors, producing universal cocycles.
Graph morphism maps Poisson cocycles to symmetries, revealing factorization through Jacobi identity.
Poisson and symplectic structures discussed in lecture notes.
Given a -form $\zw$ and a volume form $\zW$ on a -manifold one defines a bi-vector $\zL$ by setting $\zL(\za,\zb)={\frac {\za\zex\zb\zex\zw} {\zW}}$ for any -forms $\za,\zb$. In this way, locally, a Poisson pair, or bi-Hamiltonian structure, $(\zL,\zL_1 )$ is always represented by a couple of -forms…
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 …
Study shows Merton model limits to Poisson process with log-normal intensity, improving default portfolio prediction.
The paper explores obstructions for symplectic Lie algebroids on surfaces.
Establishes a microstructural foundation for a rough log-normal volatility model.
Defines log Floer cohomology for symplectic surfaces with a degenerate part.
New Lie groups found for Poisson diffeomorphisms.
This paper studies Poisson structures defined by divisor ideals.
We compute the Poisson cohomology of a class of Poisson manifolds that are symplectic away from a collection of hypersurfaces. These Poisson structures induce a generalization of symplectic and cosymplectic structures, which we call a k-cosymplectic structure, on the intersection of hypersurfaces in .
We describe the space of Poisson bivectors near a log-symplectic structure up to small diffeomorphisms.
Models predict soccer match outcomes with similar accuracy.
We look at Poisson geometry taking the viewpoint of singular foliations, understood as suitable submodules generated by Hamiltonian vector fields rather than partitions into (symplectic) leaves. The class of Poisson structures which behave best from this point of view, are those whose submodule generated by Hamiltonian…
We consider Lagrangian-like submanifolds in certain even-dimensional 'symplectic-like' Poisson manifolds. We show, under suitable transversality hypotheses, that the pair consisting of the ambient Poisson manifold and the submanifold has unobstructed deformations and that the deformations automatically preserve the Lag…
Flexible models cluster RNA sequencing data.
New insights into empirical Bayes and compound decision problems with improved regret bounds.
New Poisson structures defined from Lie algebroids, with conditions for existence.
The logistic regression model is known to converge to a Poisson point process model if the binary response tends to infinitely imbalanced. In this paper, it is shown that this phenomenon is universal in a wide class of link functions on binomial regression. The proof relies on the extreme value theory. For the logit, p…
Let X be a complex manifold with strongly pseudoconvex boundary M. If u is a defining function for M, then -log u is plurisubharmonic on a neighborhood of M in X, and the (real) 2-form s = i \del \delbar(-log u) is a symplectic structure on the complement of M in a neighborhood in X of M; it blows up along M. The Poiss…
Log-symplectic structures are Poisson structures on for which vanishes transversally. By viewing them as symplectic forms in a Lie algebroid, the -tangent bundle, we use symplectic techniques to obtain existence results for log-symplectic structures on total spaces of fibration-like maps…
Constructs curves in log-symplectic manifolds, classifying and obstructing certain structures.
Capital distribution curve is defined as log-log plot of normalized stock capitalizations ranked in descending order. The curve displays remarkable stability over periods of time. Theory of exchangeable distributions on set partitions, developed for purposes of mathematical genetics and recently applied in non-parametr…
Several new mutation-periodic quivers of period higher than 1 are introduced as well as the associated discrete dynamical systems. The reduction of these systems is developed using either a presymplectic or a Poisson approach. The presymplectic approach leads to a reduced system whose iteration map is symplectic with r…
The aim of this paper is to study the construction of prospective mortality tables from a low number of persons subjected to risk. The presented models are the Lee-Carter and log-Poisson methods respectively. The low number of people subjected to risk, particularly noticed for the persons who are getting on, implies th…
The paper constructs a Saito basis for a specific class of divisors and applies it to logarithmic Poisson geometry.
New model optimizes assortment and pricing with dynamic customer arrivals.
Develops data subsampling techniques for Poisson regression models.
Tree-based variational inference improves PLN model for hierarchical count data.
We give a generalization of toric symplectic geometry to Poisson manifolds which are symplectic away from a collection of hypersurfaces forming a normal crossing configuration. We introduce the tropical momentum map, which takes values in a generalization of affine space called a log affine manifold. Using this momentu…
Poisson Midpoint Method improves Langevin Dynamics for diffusion models.
Generalized R2R handles non-Gaussian noise for deep network training.
Proposes a method to handle sparse multiway count data with false zeros using zero-truncated Poisson regression.
We call a singularity of a presymplectic form removable in its graph if its graph extends to a smooth Dirac structure over the singularity. An example for this is the symplectic form of a magnetic monopole. A criterion for the removability of singularities is given in terms of regularizing functions for pure spinor…
New ZIPLN model accounts for zero-inflation in multivariate count data.
We extend the theory of matrix completion to the case where we make Poisson observations for a subset of entries of a low-rank matrix. We consider the (now) usual matrix recovery formulation through maximum likelihood with proper constraints on the matrix , and establish theoretical upper and lower bounds on the rec…
Poisson likelihood models have been prevalently used in imaging, social networks, and time series analysis. We propose fast, simple, theoretically-grounded, and versatile, optimization algorithms for Poisson likelihood modeling. The Poisson log-likelihood is concave but not Lipschitz-continuous. Since almost all gradie…
Generative model identifies temporal count data components with regime-dependent contributions.
Framework captures missing data in sparse data sets.
The paper analyzes convergence rates for stochastic approximation and reinforcement learning.
RPF improves recommendation by modeling user and item interactions over time.
A log symplectic manifold is a Poisson manifold which is generically nondegenerate. We develop two methods for constructing the symplectic groupoids of log symplectic manifolds. The first is a blow-up construction, corresponding to the notion of an elementary modification of a Lie algebroid along a subalgebroid. The se…
We extend the theory of low-rank matrix recovery and completion to the case when Poisson observations for a linear combination or a subset of the entries of a matrix are available, which arises in various applications with count data. We consider the usual matrix recovery formulation through maximum likelihood with pro…
This work tackles fitting Hawkes processes to interval-censored data.