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.
Examines the linear independence of curvature tensors and pseudotensors in non-symmetric affine connection spaces.
problem Determining the linear independence of curvature tensors and pseudotensors in non-symmetric affine connection spaces.
method Analyzes the number of covariant derivatives and curvature tensors/pseudotensors required for a complete study, and examines their linear independence.
result Identifies the number of curvature tensors and pseudotensors that are linearly independent in non-symmetric affine connection spaces.
A method to generalize results from Riemannian Geometry to Finsler geometry is presented. We use the method to generalize several results that involve only metric conditions. Between them we show that the topology induced by the Finsler structure is equivalent to the manifold topology, we provide a new proof of the Hop…
Let F be Cayley's ruled cubic surface in a projective three-space over any commutative field K. We determine all collineations fixing F, as a set, and all cubic forms defining F. For both problems the cases ∣K∣=2,3 turn out to be exceptional. On the other hand, if ∣K∣≥4 then the set of simple points of …
Paper finds conditions for different norms to produce same billiard paths.
problem Conditions for different norms to define the same billiard reflection law.
method Extending previous works by Milena Radnović and Serge Tabachnikov, the paper establishes conditions for two different non-symmetric norms to define the same billiard reflection law.
result Conditions for two different norms to define the same billiard reflection law.
In this work, we are interested in a non symmetric homogeneous space, namely SO(2m)/Sp(m). We show that this space admits a structure of Z22-symmetric space. We describe all the non degenerated metrics and classify the Riemannian and Lorentzian ones.
This paper proves a curvature entropy inequality for non-symmetric convex bodies.
problem Proving a curvature entropy inequality for non-symmetric convex bodies.
method Demonstrated the log-Minkowski inequality of curvature entropy for general convex bodies in 2D.
result Equivalence of cone-volume measure uniqueness, log-Minkowski volume inequality, and curvature entropy inequality for general convex bodies in 2D.
Connections with (skew-symmetric) torsion on non-symmetric Riemannian manifold satisfying the Einstein metricity condition (NGT with torsion) are considered. It is shown that an almost Hermitian manifold is an NGT with torsion if and only if it is a Nearly Kähler manifold. In the case of an almost contact metric manifo…
Bayesian networks are simplified for categorical variables using staged trees and asymmetry-labeled DAGs.
problem Representing non-symmetric conditional independences in Bayesian networks.
method Formalized relationship between Bayesian networks and staged trees, introduced asymmetry-labeled DAGs, and developed an algorithm to learn staged trees.
result A novel algorithm for learning staged trees that captures non-symmetric independences.
Non-symmetric rectangular correlation matrices occur in many problems in economics. We test the method of extracting statistically meaningful correlations between input and output variables of large dimensionality and build a toy model for artificially included correlations in large random time series.The results are t…
It is well-known that sigma-models with symmetric target spaces are classically integrable. At the example of the model with target space the flag manifold U(3)/U(1)^3 -- a non-symmetric space -- we show that the introduction of torsion allows to cast the equations of motion in the form of a zero-curvature condition fo…
Adapting the method of Andrews-Clutterbuck we prove an eigenvalue gap theorem for a class of non symmetric second order linear elliptic operators on a convex domain in euclidean space. The class of operators includes the Bakry-Emery laplacian with potential and any operator with second order term the laplacian whose fi…
We obtain new examples of non-symmetric Einstein solvmanifolds by combining two techniques. In \cite{T2}, H. Tamaru constructs new {\em attached} solvmanifolds, which are submanifolds of the solvmanifolds corresponding to noncompact symmetric spaces, endowed with a natural metric. Extending this construction, we apply …
We discuss fibered commensurability of fibrations on a hyperbolic 3-manifold, a notion introduced by Calegari, Sun and Wang. We construct manifolds with non-symmetric but commensurable fibrations on the same fibered face. We also prove that if a given manifold M does not have any hidden symmetries, then M does not admi…
A generalized positive energy theorem for spaces with asymptotic SUSY compactification involving non-symmetric data is proved. This work is motivated by the work of Dai [D1][D2], Hertog-Horowitz-Maeda [HHM], and Zhang [Z].
We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson correlation matrices to the realm of complex eigenvalues. We employ some recent random…
We prove that all generalised symmetric spaces of compact simple Lie groups are formal in the sense of Sullivan. Nevertheless, many of them, including all the non-symmetric flag manifolds, do not admit Riemannian metrics for which all products of harmonic forms are harmonic.
Recently, the old notion of causal boundary for a spacetime V has been redefined in a consistent way. The computation of this boundary ∂V for a standard conformally stationary spacetime V = R x M, suggests a natural compactification MB associated to any Riemannian metric on M or, more generally, to any Fin…
The paper solves curvature flow problems to prove sphere convergence and dual Minkowski solutions.
problem Proving sphere convergence and dual Minkowski solutions for curvature flow problems.
method A contracting flow of closed, convex hypersurfaces with speed frαK where K is the Gauss curvature, r is the distance from the hypersurface to the origin, and f is a positive and smooth function.
result The flow exists for all time and converges smoothly to a soliton, which is a sphere centred at the origin if f≡1.
We generalize reduction theorems for classical connections to operators with values in k-th order natural bundles. Using the first reduction theorem in order two we classify all (0,2)-tensor fields on the cotangent bundle of a manifold with a linear (non-symmetric) connection.
New estimates show all stable Einstein manifolds are linear stable with respect to Perelman's ν-entropy.
problem Estimating the smallest eigenvalue of Laplace-Beltrami operator for stable Einstein manifolds.
method Estimating the smallest positive eigenvalue λ1 of the Laplace-Beltrami operator for standard Einstein manifolds (G/H,gst) and proving λ1>2E for all but 7 exceptions.
result All stable Einstein manifolds found by Schwahn are linear stable with respect to Perelman's ν-entropy.