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 derives formulas for moments of a Student t distribution and applies them to quantify -quantiles.
We discuss various aspects of moment map geometry in symplectic and hyperKähler geometry. In particular, we classify complete hyperKähler manifolds of dimension with a tri-Hamiltonian action of a torus of dimension , without any assumption on the finiteness of the Betti numbers. As a result we find that the hyp…
Paper reviews and proves the uniqueness of multipole moments for stationary spacetimes.
New method unfolds distribution moments directly from data without binning.
New rigidity results for complex and quaternionic moment-angle manifolds.
For geometries with a closed three-form we briefly overview the notion of multi-moment maps. We then give concrete examples of multi-moment maps for homogeneous hypercomplex and nearly Kaehler manifolds. A special role in the theory is played by Lie algebras with second and third Betti numbers equal to zero. These we c…
Moment-angle manifolds provide a wide class of examples of non-Kaehler compact complex manifolds. A complex moment-angle manifold Z is constructed via certain combinatorial data, called a complete simplicial fan. In the case of rational fans, the manifold Z is the total space of a holomorphic bundle over a toric variet…
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…
We consider symplectic manifolds with Hamiltonian torus actions which are "almost but not quite completely integrable": the dimension of the torus is one less than half the dimension of the manifold. We provide a complete set of invariants for such spaces when they are "centered" and the moment map is proper. In partic…
We study torus actions on symplectic manifolds with proper moment maps in the case that each reduced space is two-dimensional. We provide a complete set of invariants for such spaces. Our proof uses sheaves of groupoids of Hamiltonian spaces.
Classification of SL(n) covariant valuations on Orlicz spaces.
The moment-angle complex Z_K is cell complex with a torus action constructed from a finite simplicial complex K. When this construction is applied to a triangulated sphere K or, in particular, to the boundary of a simplicial polytope, the result is a manifold. Moment-angle manifolds and complexes are central objects in…
Completely random measures (CRM) represent the key building block of a wide variety of popular stochastic models and play a pivotal role in modern Bayesian Nonparametrics. A popular representation of CRMs as a random series with decreasing jumps is due to Ferguson and Klass (1972). This can immediately be turned into a…
We present a semi-supervised learning algorithm for learning discrete factor analysis models with arbitrary structure on the latent variables. Our algorithm assumes that every latent variable has an "anchor", an observed variable with only that latent variable as its parent. Given such anchors, we show that it is possi…
Classifies SL(n) covariant matrix-valued valuations on Lp-spaces.
Study of stochastic differential equations on non-compact manifolds, solving open problem on strong completeness.
We describe the basic cohomology ring of the canonical holomorphic foliation on a moment-angle manifold, LVMB-manifold or any complex manifold with a maximal holomorphic torus action. Namely, we show that the basic cohomology has a description similar to the cohomology ring of a complete simplicial toric variety due to…
A new filter reduces density fitting to a linear solve, improving performance on nonlinear systems.
The paper tackles matrix completion in ultra-sparse sampling, improving imputation accuracy.
We show that the cone associated with a moment map for an action of a torus on a contact compact connected manifold is a convex polyhedral cone and that the moment map has connected fibers provided the dimension of the torus is bigger than 2 and that no orbit is tangent to the contact distribution. This may be consider…
Let be a compact Kähler manifold and a subvariety of with higher co-dimension. The aim is to study complete constant scalar curvature Kähler metrics on non-compact Kähler manifold with Poincaré--Mok--Yau asymptotic property (see Definition \ref{def}). In this paper, the methods of Calabi's ansatz and …
Analysis of Vlasov plasma dynamics using matched pair Lie-Poisson formulation.
Study shows submanifolds can't be immersed in certain spaces.
The ability of many powerful machine learning algorithms to deal with large data sets without compromise is often hampered by computationally expensive linear algebra tasks, of which calculating the log determinant is a canonical example. In this paper we demonstrate the optimality of Maximum Entropy methods in approxi…
We study the problem of learning a distribution from samples, when the underlying distribution is a mixture of product distributions over discrete domains. This problem is motivated by several practical applications such as crowd-sourcing, recommendation systems, and learning Boolean functions. The existing solutions e…
A note proves the binary perceptron's capacity is less than 0.847.
This paper presents sampling-based speech parameter generation using moment-matching networks for Deep Neural Network (DNN)-based speech synthesis. Although people never produce exactly the same speech even if we try to express the same linguistic and para-linguistic information, typical statistical speech synthesis pr…
We consider a connected compact Lie group K acting on a symplectic manifold M such that a moment map m exists. A pull-back function via m Poisson commutes with all K-invariants. Guillemin-Sternberg raised the problem to find a converse. In this paper, we solve this problem by determining the Poisson commutant of the al…
In the classical theory of toric manifolds polytopes appear in two guises -- as Newton polytopes of line bundles on the complex, and as moment polytopes on the symplectic side, the link between the two being established by the prequantizability condition on the cohomology class of the symplectic form. Here we give a co…
Up to symmetries, the orbits of three equal masses under an inverse cube force with zero angular momentum and constant moment of inertia can be reparametrized as the geodesics of a complete, negatively curved metric on a pair of pants. The ends of the pants represent binary collisions. Here we will examine the visibili…
The purpose of this note is to give a simple description of a (complete) family of functions in involution on certain hermitian symmetric spaces. This family, obtained via bi-hamiltonian approach using the Bruhat Poisson structure, is especially simple for the projective spaces, where the formulas in terms of the momen…
A new method calculates fractional moments using the moment-generating function.
New model detects gradual changes in processes more accurately.
Study compares weak and homotopy moment maps in multisymplectic geometry.
Management of a portfolio that includes an illiquid asset is an important problem of modern mathematical finance. One of the ways to model illiquidity among others is to build an optimization problem and assume that one of the assets in a portfolio can not be sold until a certain finite, infinite or random moment of ti…
Study of symplectic Monge-Ampère equations using moment maps and contact structures.
Exact simulation of correlated binary outcomes using PMF constraints and linear programming.
Paper introduces Lambda EVaR, a new risk measure.
For a GJR-GARCH specification with a generic innovation distribution we derive analytic expressions for the first four conditional moments of the forward and aggregated returns and variances. Moment for the most commonly used GARCH models are stated as special cases. We also the limits of these moments as the time hori…
This paper identifies and bounds ICE central moments using PO marginal central moments.
We tackle causal inference under conditional moment restrictions using importance weighting.
Revisits Lee's Moment Formula, relaxing moment assumptions for implied volatility.
This paper analyzes the skewness of momentum trading strategies.
Enhanced Adam uses higher-order moments for better performance.
Developed moment estimators for affine stochastic volatility models.
Stiefel-Whitney classes of moment-angle manifolds are trivial.
A new method for estimating causal parameters from observables reduces the need for finite moment conditions.
Develops a Gaussian-based message-passing algorithm for noisy matrix completion.