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.
Entropy corrections improve GBM's predictive accuracy for non-log-normal distributions.
We give a differential geometric construction of a connection in the bundle of quantum Hilbert spaces arising from half-form corrected geometric quantization of a prequantizable, symplectic manifold, endowed with a rigid, family of Kähler structures, all of which give vanishing first Dolbeault cohomology groups. In [An…
Corrected a false lemma in Cimasoni's work on linking theory.
Geometric approach finds correspondences between different conditions.
New technique tracks geometric properties to correct base algorithms' poor performance.
Study finds a small correction to Asian option volatility.
Geometrization theorem, fibered case: Every three-manifold that fibers over the circle admits a geometric decomposition. Double limit theorem: for any sequence of quasi-Fuchsian groups whose controlling pair of conformal structures tends toward a pair of projectively measured laminations that bind the surface, there is…
Geometric framework explains and controls implicit bias in machine learning.
Corrects a 1998 proof about free factors of free groups.
A lightweight framework improves convergence and stability of PINNs for complex PDEs.
We give geometric explanations and proofs of various mirror symmetry conjectures for -invariant Calabi-Yau manifolds when instanton corrections are absent. This uses fiberwise Fourier transformation together with base Legendre transformation. We discuss mirror transformations of (i) moduli spaces of complex stru…
We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of t…
Closed formulas for η-corrections in the once-punctured torus identified.
The paper refines classical covariance asymptotics using geometric information geometry.
A general, consistent and complete framework for geometrical formulation of mechanical systems is proposed, based on certain structures on affine bundles (affgebroids) that generalize Lie algebras and Lie algebroids. This scheme covers and unifies various geometrical approaches to mechanics in the Lagrangian and Hamilt…
Quantum codes on hyperbolic lattices outperform Euclidean ones with higher rates and lower overhead.
Financial contracts with options that allow the holder to extend the contract maturity by paying an additional fixed amount found many applications in finance. Closed-form solutions for the price of these options have appeared in the literature for the case when the contract underlying asset follows a geometric Brownia…
We critically review recent claims that financial crashes can be predicted using the idea of log-periodic oscillations or by other methods inspired by the physics of critical phenomena. In particular, the October 1997 `correction' does not appear to be the accumulation point of a geometric series of local minima.
Geometric formalism views optimization algorithms as discrete connections, revealing their algebraic curvature and flatness properties.
Geometrically refines Cramér-Rao bound using extrinsic manifold curvature.
Weaving knots are alternating knots with the same projection as torus knots, and were conjectured by X.-S. Lin to be among the maximum volume knots for fixed crossing number. We provide the first asymptotically correct volume bounds for weaving knots, and we prove that the infinite weave is their geometric limit.
A topological approach to stratification learning is developed for point cloud data drawn from a stratified space. Given such data, our objective is to infer which points belong to the same strata. First we define a multi-scale notion of a stratified space, giving a stratification for each radius level. We then use met…
We propose a geometric algorithm for topic learning and inference that is built on the convex geometry of topics arising from the Latent Dirichlet Allocation (LDA) model and its nonparametric extensions. To this end we study the optimization of a geometric loss function, which is a surrogate to the LDA's likelihood. Ou…
Study 3d N=1 vacua from M-theory compactification on Spin(7) space.
This is an almost self-contained monograph (containing some new results) on left-orderable groups which mostly rely on dynamical and probabilistic aspects, but also on geometric, combinatorial, analytic, and topological ones. This new version contains many improvements, corrections and updates, many of them suggested b…
This is the second part of the proof of the exact traiangles in Seiberg-Witten Floer theory. We analyse the splitting and gluing of flow lines of the Chern-Simons-Dirac functional when the underlying three-manifold splits along a torus. (two corrections added)
Geometric approach combines asset returns and investor views for better portfolio optimization.
We present a clear-cut example of the importance of the functorial approach of gauge-natural bundles and the general theory of Lie derivatives for classical field theory, where the sole correct geometrical formulation of Einstein (-Cartan) gravity coupled with Dirac fields gives rise to an unexpected indeterminacy in t…
We present a new, more elementary proof of the Freedman-Teichner result that the geometric classification techniques (surgery, s-cobordism, and pseudoisotopy) hold for topological 4-manifolds with groups of subexponential growth. In an appendix Freedman and Teichner give a correction to their original proof, and reform…
We show that using the family of adapted Kähler polarizations of the phase space of a compact, simply connected, Riemannian symmetric space of rank-1, the obtained field of quantum Hilbert spaces produced by geometric quantization including the half-form correction is flat if is the 3-dimensional sphere …
We construct a geometric structure on deformed supermanifolds as a certain subalgebra of the vector fields. In the classical limit we obtain a decoupling of the infinitesimal odd and even transformations, whereas in the semiclassical limit the result is a representation of the supersymmetry algebra. In the case of mass…
We prove that twisted correction terms in Heegaard Floer homology provide lower bounds on the Thurston norm of certain cohomology classes determined by the strong concordance class of a 2-component link in . We then specialise this procedure to knots in , and obtain a lower bound on their geomet…
Proposes CC-NMDF for analyzing manifold-valued data.
In this paper we introduce a projection method for the space of probability distributions based on the differential geometric approach to statistics. This method is based on a direct L2 metric as opposed to the usual Hellinger distance and the related Fisher Information metric. We explain how this apparatus can be used…
Unified geometric interpretation of statistical estimation inequalities.
We introduce a differential geometric framework for describing families of quantum error-correcting codes and for understanding quantum fault tolerance. This work unifies the notion of topological fault tolerance with fault tolerance in other kinds of quantum error-correcting codes. In particular, we use fibre bundles …
In 1978 Brakke introduced the mean curvature flow in the setting of geometric measure theory. There exist multiple variants of the original definition. Here we prove that most of them are indeed equal. One central point is to correct the proof of Brakke's §3.5, where he develops an estimate for the evolution of the mea…
We present a geometrical framework which incorporates higher derivative corrections to the action of N = 2 vector multiplets in terms of an enlarged scalar manifold which includes a complex deformation parameter. This enlarged space carries a deformed version of special Kahler geometry which we characterise. The holomo…
Geometric method improves uncertainty estimation in real-time.
Introduces a new spectral geometry framework with dissipative data.
We investigate geometric aspects of the the Bäcklund transform of principal contact element nets. A Bäcklund transform exists if and only if it the principal contact element net is of constant negative Gaussian curvature (a pseudosphere). We describe an elementary construction of the Bäcklund transform and prove its co…
Study of Lévy flights on Zoll surfaces, revealing geometric information.
When there is a family of complex structures on the phase space, parametrized by a set , the prequantum Hilbert spaces produced by geometric quantization, using the half-form correction, also depends on these parameters. This way we obtain a field of Hilbert spaces . We show that this field …
This article revisits an analysis on inaccuracies of time series averaging under dynamic time warping conducted by \cite{Niennattrakul2007}. The authors presented a correctness-criterion and introduced drift-outs of averages from clusters. They claimed that averages are inaccurate if they are incorrect or drift-outs. F…
The existing approaches to intrinsic dimension estimation usually are not reliable when the data are nonlinearly embedded in the high dimensional space. In this work, we show that the explicit accounting to geometric properties of unknown support leads to the polynomial correction to the standard maximum likelihood est…
Proposes a neural network method to correct residual distortions in coordinate transformations.
Upper bounds for second Robin eigenvalue on Riemannian surfaces.
Unified framework for geometric computation of minimum-area homotopy.