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.
Study finds symmetries in a special 3D space with a diagonal metric.
Study of symmetries in a 2D space with specific metric properties.
In integrable hydrodynamic systems, coordinates exist where generators and symmetries are simple.
We prove that certain dual pairs of Calabi-Yau manifolds have matching orbifold Euler characteristics.
The paper proves conditions for Darboux integrability in diagonal hydrodynamic systems.
Presented spherical symmetric teleparallel geometry frames and field equations.
Study on special symmetries in biwarped product 3-manifolds.
The horizon and geodesic structure of static configurations generated by anisotropic conformal transforms of the Schwarzschild metric is analyzed. We construct the maximal analytic extension of such off--diagonal vacuum metrics and conclude that for small deformations there are different classes of vacuum solutions of …
Extends method for solving certain hydrodynamic systems.
We construct new classes of exact solutions in metric--affine gravity (MAG) with string corrections by the antisymmetric --field. The solutions are parametrized by generic off--diagonal metrics possessing noncommutative symmetry associated to anholonomy framerelations and related nonlinear connection (N--connection)…
We propose a new framework for constructing geometric and physical models on nonholonomic manifolds provided both with Clifford -- Lie algebroid symmetry and nonlinear connection structure. Explicit parametrizations of generic off-diagonal metrics and linear and nonlinear connections define different types of Finsler, …
Ancient solutions to Ricci flow on torus bundles have additional symmetries.
New integrable systems constructed for non-diagonal Killing tensors.
Parallelizes DEC on curved meshes using group actions.
In this article we consider nonholonomic deformations of disk solutions in general relativity to generic off-diagonal metrics defining knew classes of exact solutions in 4D and 5D gravity. These solutions possess Lie algebroid symmetries and local anisotropy and define certain generalizations of manifolds with Killing …
Recently, there has been a trend to combine independent component analysis and canonical polyadic decomposition (ICA-CPD) for an enhanced robustness for the computation of CPD, and ICA-CPD could be further converted into CPD of a 5th-order partially symmetric tensor, by calculating the eigenmatrices of the 4th-order cu…
We provide an affirmative answer to a question posed by Tod \cite{Tod:1995b}, and construct all four-dimensional Kahler metrics with vanishing scalar curvature which are invariant under the conformal action of Bianchi V group. The construction is based on the combination of twistor theory and the isomonodromic problem …
A consistent theory of quantum gravity (QG) at Planck scale almost sure contains manifestations of Lorentz local symmetry violations (LV) which may be detected at observable scales. This can be effectively described and classified by models with nonlinear dispersions and related Finsler metrics and fundamental geometri…
Study of Khovanov homology for alternating virtual links, showing it's supported on specific diagonal lines.
The Darboux-Egoroff system of PDEs with any number of independent variables plays an essential role in the problems of describing -dimensional flat diagonal metrics of Egoroff type and Frobenius manifolds. We construct a recursion operator and its inverse for symmetries of the Darboux-Egoroff system and des…
We attempt to unveil the fine structure of volatility feedback effects in the context of general quadratic autoregressive (QARCH) models, which assume that today's volatility can be expressed as a general quadratic form of the past daily returns. The standard ARCH or GARCH framework is recovered when the quadratic kern…
The paper develops tensor learning methods exploiting symmetries of tensor functions.
An irreducible representation of the free group on two generators X,Y into SL(2,C) is determined up to conjugation by the traces of X,Y and XY. We study the diagonal slice of representations for which X,Y and XY have equal trace. Using the three-fold symmetry and Keen-Series pleating rays we locate those groups which a…
New method proves identifiability of deep generative models with algebraic contrast principles.
Noise balance theory explains SGD's behavior in neural networks.
Study on likelihood functions, associative equations, and Frobenius manifolds.
We present new classes of exact solutions with noncommutative symmetries constructed in vacuum Einstein gravity (in general, with nonzero cosmological constant), five dimensional (5D) gravity and (anti) de Sitter gauge gravity. Such solutions are generated by anholonomic frame transforms and parametrized by generic off…
We analyze the horizon and geodesic structure of a class of 4D off--diagonal metrics with deformed spherical symmetries, which are exact solutions of the vacuum Einstein equations with anholonomic variables. The maximal analytic extension of the ellipsoid type metrics are constructed and the Penrose diagrams are analyz…
Novel duality theory for operator Frobenius algebras solves long-standing hydrodynamic integrable systems problem.
New approach learns walk and trot gaits from simulated quadruped using strategic exploration.
In this paper we examine a new class of five dimensional (5D) exact solutions in extra dimension gravity possessing Lie algebroid symmetry. The constructions provide a motivation for the theory of Clifford nonholonomic algebroids elaborated in Ref. hep-th/0501217. Such Einstein-Dirac spacetimes are parametrized by gene…
A non-singular sesquilinear form is constructed that is preserved by the Lawrence-Krammer representation. It is shown that if the polynomial variables q and t of the Lawrence-Krammer representation are chosen to be appropriate algebraically independant unit complex numbers, then the form is negative-definite Hermitian.…
The paper explores equivariant means on topological spaces.
We provide a method to prepare covariance matrices for quantum datasets.
This paper solves matrix blind joint block diagonalization with noise.
Diagonalizes metrics of 3D Lorentzian manifolds.
Study Ricci vector fields on 2D space with diagonal metrics.
Develops a novel stochastic algorithm for diagonal estimation of large matrices.
Octagon map accelerates diagonal changes algorithm.
New diagonal knots found with non-torus structure.
We use mathematical induction to prove that the horizontal composition in the class of coherently diagonal complexes is indeed a binary operation. That is to say, the embedding of two coherently diagonal complexes in an alternating planar diagram produces a coherently diagonal complex.
With the developments of the last decade on complete constant mean curvature 1 (CMC 1) surfaces in the hyperbolic 3-space , many examples of such surfaces are now known. However, most of the known examples have regular ends. (An end is irregular, resp. regular, if the hyperbolic Gauss map of the surface has an ess…
Most known four-dimensional cohomogeneity-one Einstein metrics are diagonal in the basis defined by the left-invariant one-forms, though some essentially non-diagonal ones are known. We consider the problem of explicitly seeking non-diagonal Einstein metrics, and we find solutions which in some cases exhaust the possib…
Equal diagonal energies proven on Liouville surfaces.
Spin networks boost quantum algorithms solving SU(2) symmetric problems.
Diagonal linear networks converge to lasso regularization path during training.
We show that a basis of a semisimple Lie algebra of compact type, for which any diagonal left-invariant metric has a diagonal Ricci tensor, is characterized by the Lie algebraic condition of being "nice". Namely, the bracket of any two basis elements is a multiple of another basis element. This extends the work of Laur…
New diagonal move simplifies knots and links efficiently.