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.
Let y''' = f(x, y, y', y'') be a 3rd order ODE. By Cartan equivalence method, we will study the local equivalence problem under the transformations group of time-fixed coordinates.
We answer to the question whether a system of the 3rd order ODEs describes geodesics of a conformal structure. We construct a functor from a category of conformal geometries to a category of Cartan geometries associated to the 3rd order ODEs systems. Explicit formulas which define the family of all equations on conform…
We provide five examples of conformal geometries which are naturally associated with ordinary differential equations (ODEs). The first example describes a one-to-one correspondence between the Wuenschmann class of 3rd order ODEs considered modulo contact transformations of variables and (local) 3-dimensional conformal …
Study of SO(3)-irreducible geometry in complex 5D and ternary Pauli exclusion principle.
problem Exploring SO(3)-irreducible geometry in complex 5D.
method Defined a ternary skew-symmetric tensor, split the 10D space into irreducible SO(3) subspaces, found invariants and defined geometric structures.
result Defined a SO(3)-irreducible geometric structure on a 5D complex Hermitian manifold.
We review the fundamentals of coupling constant metamorphosis (CCM) and the Stäckel transform, and apply them to map integrable and superintegrable systems of all orders into other such systems on different manifolds. In general, CCM does not preserve the order of constants of the motion or even take polynomials in the…
We construct differential invariants that vanish if and only if the geodesic flow of a 2-dimensional metric admits an integral of 3rd degree in momenta with a given Birkhoff-Kolokoltsov 3-codifferential.
This is an index to the papers that appear in the Proceedings of the 29th International Conference on Machine Learning (ICML-12). The conference was held in Edinburgh, Scotland, June 27th - July 3rd, 2012.
The aim of this paper is to show that Lawson's foliation on the 5-sphere admits a smooth leafwise symplectic structure. The main part of the construction is to show that the Fermat type cubic surface admits an end-periodic symplectic structure.
Paper studies second order symmetric parallel tensors in generalized f.pk-space forms.
problem Exploring properties of second order symmetric parallel tensors in generalized f.pk-space forms.
method Analyzes the properties of second order symmetric parallel tensors and deduces the existence or non-existence of certain tensors and hypersurfaces.
result There does not exist second order skew-symmetric parallel tensor in f.pk-space form. There is no parallel hypersurface in a generalized f.pk-space form but there is semi-parallel hypersurface.
This paper is an expansion of my lecture for David Epstein's birthday, which traced a logical progression from ideas of Euclid on subdividing polygons to some recent research on invariants of hyperbolic 3-manifolds. This `logical progression' makes a good story but distorts history a bit: the ultimate aims of the chara…
The integrability conditions for the existence of a conformal Killing-Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is…
The properties of a Killing-Yano tensor of order n-1 in an n-dimensional manifold are investigated. The integrability conditions are worked out and all metrics admitting a Killing-Yano tensor of order n-1 are found. It is pointed out a connection between such tensors and a generalization of the concept of angular momen…
Algorithm for exact partitioning of high-order models using convex tensor relaxation.
problem Exact partitioning of high-order models.
method Defining a general class of m-degree Homogeneous Polynomial Models, relaxing the high-order combinatorial problem to a convex conic form problem, defining the Carathéodory symmetric tensor cone, and constructing a primal-dual certificate.
result The solution of the convex relaxation is correct and provides a statistical upper bound for exact partitioning.
We construct new examples of algebraic curvature tensors so that the Jordan normal form of the higher order Jacobi operator is constant on the Grassmannian of subspaces of type (r,s) in a vector space of signature (p,q). We then use these examples to establish some results concerning higher order Osserman and highe…
Yasutaka Nakanishi asked in 1981 whether a 3-move is an unknotting operation. In Kirby's problem list, this question is called `The Montesinos-Nakanishi 3-move conjecture'. We define the n-th Burnside group of a link and use the 3rd Burnside group to answer Nakanishi's question; ie, we show that some links cannot be re…
Optimal low rank tensor recovery requires a minimum number of entries for accurate reconstruction.
problem Exact recovery of high order tensors of low rank from a subset of their entries.
method Riemannian optimization algorithm with initial value from a spectral method, leveraging tensor restricted isometry property and curvature of the manifold.
result Tensor of size nimesnimes⋯imesn of ranks (r,⋯,r) can be reconstructed with high probability from O((rd+dnr)log(d)) entries.
This paper deals with the problem of describing the vector spaces of divergence-free, natural tensors on a pseudo-Riemannian manifold that are second-order; i.e., that are defined using only second derivatives of the metric. The main result establishes isomorphisms between these spaces and certain spaces of tensors (at…