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.
Geometric duality connects graph isomorphism and knot equivalence.
Geometric observables detect financial regime shifts with high accuracy.
Study shows observability for Schrödinger equations on product manifolds with specific conditions.
Geometric quantization shows compatibility of symmetries on coadjoint orbits and Kähler-Einstein manifolds.
We consider the wave equation on a closed Riemannian manifold. We observe the restriction of the solutions to a measurable subset along a time interval with . It is well known that, if is open and if the pair satisfies the Geometric Control Condition then an observability inequality is sat…
Survey on geometric foundations of data reduction methods.
Unified framework for observables in n-plectic geometry.
We characterize value functions in partially observable MDPs as semi-algebraic sets.
The notion of relativistic observer is confronted with Naveira's classification of (pseudo-)Riemannian almost-product structures on space-time manifolds. Some physical properties and their geometrical counterparts are shortly discussed.
Using geometric quantization procedure, the quantization of algebra of observables for physical system with Ricci-flat phase space is obtained. In the classical case the appointed physical system is reduced to harmonic oscillator when the one real parameter is vanished.
Since the discovery of differential calculus by Newton and Leibniz and the subsequent continuous growth of its applications to physics, mechanics, geometry, etc, it was observed that partial derivatives in the study of various natural problems are (self-)organized in certain structures usually called geometric. Tensors…
Study of a generalized geometric Brownian motion with varying entry and exit rates.
Study optimal policy regret in partially observable Markov games with adaptive opponents.
GD-VAEs learn dynamics from observations using geometric and topological information.
We observe that the comparison result of Barles-Biton-Ley for viscosity solutions of a class of nonlinear parabolic equations can be applied to a geometric fully nonlinear parabolic equation which arises from the graphic solutions for the Lagrangian mean curvature flow.
It is well-known that the LIE(Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of iso…
Paper constructs observables using multisymplectic geometry and algebraic methods.
The paper models financial order books using geometric shears and directional liquidity.
New method learns dynamics from sparse data using geometric constraints.
New algorithm learns HMM parameters on Riemannian manifolds.
The `observer space' of a Lorentzian spacetime is the space of future-timelike unit tangent vectors. Using Cartan geometry, we first study the structure a given spacetime induces on its observer space, then use this to define abstract observer space geometries for which no underlying spacetime is assumed. We propose ta…
Introduces optimization geometrodynamics for dynamic geometric optimization.
We discuss some aspects about the computation of kinematic, spectroscopic, Fermi and astrometric relative velocities that are geometrically defined in general relativity. Mainly, we state that kinematic and spectroscopic relative velocities only depend on the 4-velocities of the observer and the test particle, unlike F…
We survey some -vanishing results for solutions of Bochner or Simons type equations with refined Kato inequalities, under spectral assumptions on the relevant Schrödinger operators. New aspects are included in the picture. In particular, an abstract version of a structure theorem for stable minimal hypersurfaces…
Study finds GBM model accurately predicts stock prices on Ghana Stock Exchange.
Geometric Occam's Razor shapes deep learning solutions.
Profinite rigidity proven for many hyperbolic manifolds.
In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to define a dynamic-dependent metric tensor on the principal manifold, such that the…
Geometric model explains music perception combining neuroscience and acoustics.
Meta-learning performance is affected by how task diversity is allocated, not just overall variability.
Modified Gibbs-Helmholtz equation geometric models for thermodynamics.
In the present note we describe geometrically the homology classes in the total space of a surface bundle over a surface in terms of the holonomy map. We treat the cases where the base surface is closed or has one boundary component. We replace the wrong theorem of the previous version by some observations on the homol…
Study of normal and tangent maps to frontals.
SVarM uses varifold representations for shape classification and regression.
Introduces geometric formulation of EM algorithm for robust inference and various applications.
This paper tackles matching two complete graphs with correlated edge weights in geometric models.
In the present work, torsion energy is defined. Its law of conservation is given. It is shown that this type of energy gives rise to a repulsive force which can be used to interpret supernovae type Ia observations, and consequently the accelerating expansion of the Universe. This interpretation is a pure geometric one …
The problem of completing high-dimensional matrices from a limited set of observations arises in many big data applications, especially, recommender systems. Existing matrix completion models generally follow either a memory- or a model-based approach, whereas, geometric matrix completion models combine the best from b…
This informal technical report details the geometric illustration of decision boundaries for ReLU units in a three layer fully connected neural network. The network is designed and trained to predict pixel intensity from an (x, y) input location. The Geometric Illustration of Neural Networks (GINN) tool was built to vi…
Exponential families are a particular class of statistical manifolds which are particularly important in statistical inference, and which appear very frequently in statistics. For example, the set of normal distributions, with mean μ and deviation σ, form a 2-dimensional exponential family. In this paper, we show that …
New method recovers manifold distances from noisy data.
The paper explores symplectic foliations and their leaves on manifolds.
This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that when the stochastic processes satisfy a generalized Bernstein-type inequality, a u…
This paper solves a Bayes sequential impulse control problem for a diffusion, whose drift has an unobservable parameter with a change point. The partially-observed problem is reformulated into one with full observations, via a change of probability measure which removes the drift. The optimal impulse controls can be ex…
In this paper, we study both the continuous model and the discrete model of the Quantum Hall Effect (QHE) on the hyperbolic plane. The Hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of observables. We define a twisted analogue of the Kasparov map, which enables us to use…
New method speeds up Bayesian inverse problem solving with neural operators.
This paper presents a generalization of symplectic geometry to a principal bundle over the configuration space of a classical field. This bundle, the vertically adapted linear frame bundle, is obtained by breaking the symmetry of the full linear frame bundle of the field configuration space, and it inherits a generaliz…
Develops theory of Anosov representations for Fuchsian groups, showing stability and analytical properties.