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.
Develops Bilateral Gamma processes for financial market modeling.
This paper, sixth in a series of eight, uses the geometric calculus on manifolds developed in previous papers of the series to introduce through the concept of a metric extensor field g a metric structure for a smooth manifold M. The associated Christoffel operators, a notable decomposition of that object and the assoc…
The group Gamma of automorphisms of the polynomial kappa(x,y,z) = x^2 + y^2 + z^2 - xyz -2 is isomorphic to PGL(2,Z) semi-direct product with (Z/2+Z/2). For t in R, Gamma-action on ktR = kappa^{-1}(t) intersect R displays rich and varied dynamics. The action of Gamma preserves a Poisson structure defining a Gamma-invar…
New model for count data using gamma-Poisson construction.
The article introduces gamma-Psi-dimensions for margin multi-category classifiers.
While most Bayesian nonparametric models in machine learning have focused on the Dirichlet process, the beta process, or their variants, the gamma process has recently emerged as a useful nonparametric prior in its own right. Current inference schemes for models involving the gamma process are restricted to MCMC-based …
Let G be a connected semisimple Lie group such that the associated symmetric space X is Hermitian and let Gamma be the fundamental group of a compact orientable surface of genus at least 2. We survey the study of maximal representations, that is the subset of Hom(Gamma,G) which is a union of components characterized by…
A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a "multi-scoop" generalization of the beta-Bernoulli process. The BNB process is augmented into a beta-gamma-gamma-Poisson hierarchical structure, and applied as a nonparametric Bayesian prior for an infi…
LLMs detect market patterns through causal reasoning, not just temporal association.
Study pairs of subspaces with or without a common complement in Hilbert spaces.
Derives sub-Riemannian Ricci curvature for various manifolds.
A new model uses time-changed fractional Brownian motion to price financial options.
CNNs improve particle identification in ground-based gamma-ray astronomy.
PRGDS models count tensors with sparsity and burstiness.
PGBN infers multilayer representations of count vectors using Gibbs sampling.
New -structures found on symmetric spaces.
Bayesian variational models improve on ML for Gamma and inverse-Gamma mixture components in MRI analysis.
If Gamma is any finite graph, then the unlabelled configuration space of n points on Gamma, denoted UC^n(Gamma), is the space of n-element subsets of Gamma. The braid group of Gamma on n strands is the fundamental group of UC^n(Gamma). We apply a discrete version of Morse theory to these UC^n(Gamma), for any n and any …
Study on gamma-related OU processes with simulation methods.
New EPM models improve model shrinkage in edge partition models.
Introduces a new spectral geometry framework with dissipative data.
Let Gamma be a non-elementary Kleinian group acting on the closed n-dimensional unit ball and assume that its Poincare series converges at the exponent alpha. Let M_Gamma be the Gamma-quotient of the open unit ball. We consider certain families E = {E_1,...,E_p} of open subsets of M_Gamma such that M_Gamma minus the un…
We calculate the Heegaard Floer homologies$HF^+(M,s) for mapping tori M associated to certain surface diffeomorphisms, where s is any Spin^c structure on M whose first Chern class is non-torsion. Let gamma and delta be a pair of geometrically dual nonseparating curves on a genus g Riemann surface Sigma_g, and let sigma…
Efficient inference for nonparametric Hawkes processes using Pólya-Gamma augmentation.
We consider complex projective space P^{n} and a smooth closed curve gamma in P^{n}. Harvey and Lawson have defined the notion of the projective hull \hat{K} of a compact subset K in P^n. This concept is an analogue of the polynomial hull of compact subsets of C^{n}. In the present note we study the relation between th…
Develops Bayesian inference methods for gamma models.
Proposes a new model to better handle overdispersed count time series.
Develops a data augmentation method for models with gamma functions.
Let Gamma_k be the lower central series of a surface group Gamma of a compact surface S with one boundary component. A simple question to ponder is whether a mapping class of S can be determined to be pseudo-Anosov given only the data of its action on Gamma/Gamma_k for some k. In this paper, to each mapping class f whi…
Let P be a locally finite circle packing in the plane invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite, we construct an explicit Borel measure on the plane which describes the asymptotic distribution of small circles in P, assuming that either…
We consider discrete subgroups Gamma of the simply connected Lie group SU~(1,1), the universal cover of SU(1,1), of finite level, i.e. the subgroup intersects the centre of SU~(1,1) in a subgroup of finite index, this index is called the level of the group. The Killing form induces a Lorentzian metric of constant curva…
New calibration methods improve fitting of weak variance-alpha-gamma process.
Let G=SO(n,1) and Gamma a geometrically finite Zariski dense subgroup of G which is contained in an arithmetic subgroup of G. Denoting by Gamma(q) the principal congruence subgroup of Gamma of level q, and fixing a positive number λ_0 strictly smaller than (n-1)^2/4, we show that, as q tends to infinity along primes, t…
HCPF improves recommendation systems by decoupling sparsity and response models.
Let G be a finite group and let M be a G-manifold. We introduce the concept of generalized orbifold invariants of M/G associated to an arbitrary group Gamma, an arbitrary Gamma-set, and an arbitrary covering space of a connected manifold Sigma whose fundamental group is Gamma. Our orbifold invariants have a natural and…
A quick gamma approximation speeds up Bayesian inference.
There is an established bijection between finite-index subgroups Gamma of Gamma(2) and bipartite graphs on surfaces, or, equivalently, certain triples of permutations. We utilize this relationship to study both congruence and noncongruence subgroups in terms of the corresponding graphs. We show some elementary criteria…
New formulas derived for variance gamma model option pricing.
Researchers extend Gamma index theorem to non-compact spacetimes.
For i = 1,2, let Gamma_i be a lattice in a simply connected, solvable Lie group G_i, and let X_i be a connected Lie subgroup of G_i. The double cosets Gamma_igX_i provide a foliation F_i of the homogeneous space Gamma_i\G_i. Let f be a continuous map from Gamma_1\G_1 to Gamma_2\G_2 whose restriction to each leaf of F_1…
The article prices exchange options using variance gamma-like models.
Study shows variance gamma model outperforms Black-Scholes for USD-INR currency options.
Let Gamma be a finitely generated, amenable group. Using an idea of E Ghys, we prove that if Gamma has a nontrivial, orientation-preserving action on the real line, then Gamma has an infinite, cyclic quotient. (The converse is obvious.) This implies that if Gamma has a faithful action on the circle, then some finite-in…
The paper uses the variance-gamma model to price options and explain excess kurtosis.
The main result of this paper is a construction of fundamental domains for certain group actions on Lorentz manifolds of constant curvature. We consider the simply connected Lie group G~, the universal cover of the group SU(1,1) of orientation-preserving isometries of the hyperbolic plane. The Killing form on the Lie g…
The study examines how gamma positivity and PL homeomorphism types affect simplicial spheres.
We consider sequences of finitely generated discrete subgroups Gamma_i=rho_i(Gamma) of a rank 1 Lie group G, where the representations rho_i are not necessarily faithful. We show that, for algebraically convergent sequences (Gamma_i), unless Gamma_i's are (eventually) elementary or contain normal finite subgroups of ar…
The paper proposes a new model for financial order books without assuming prices or quantities.