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.
Proves non-positivity of Hirzebruch form on stable weights and connects to flat logarithmic connections.
Enhances power of covariance matrix tests for high-dimensional data.
Proposes QDF to improve multi-step time-series forecasting.
This paper classifies quadratic form parameters over integers and computes their Witt groups.
The paper classifies biharmonic quadratic maps between spheres, proving their energy density properties.
New method uses binary quadratic forms to classify Seifert surfaces in 4-ball.
We introduce and study a canonical quadratic form, called the torsion quadratic form, of the determinant line of a flat vector bundle over a closed oriented odd-dimensional manifold. This quadratic form caries less information than the refined analytic torsion, introduced in our previous work, but is easier to construc…
New quadratic forms expand and rotate linear endomorphisms in geometric theory.
Novel link classification connects quadratic forms and knot theory.
A correspondence between different -type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of these quadratic forms.
In this paper, we compute the covolume of the group of units of the quadratic form f_d^n(x) = x_1^2 + x_2^2 + . . . + x_n^2 - d x_{n+1}^2 with d an odd, positive, square-free integer. Mcleod has determined the hyperbolic Coxeter fundamental domain of the reflection subgroup of the group of units of the quadratic form f…
We determine the center of a meta-nilpotent quotient of a mapping-torus group. As a corollary, we introduce two invariants, which are quadratic forms, of knots and of mapping classes.
An explicit (-1)^n-quadratic form over Z[Z^{2n}] representing the surgery problem E_8 x T^{2n} is obtained, for use in the Bryant-Ferry-Mio-Weinberger construction of 2n-dimensional exotic homology manifolds.
For a given lattice, we establish an equivalence involving a closed zone of the corresponding Voronoi polytope, a lamina hyperplane of the corresponding Delaunay partition and a quadratic form of rank 1 being an extreme ray of the corresponding L-type domain.
Unified view of surfaces in R^n using Gauss map, caustics, and quadratic forms.
Geometrically describes the linear and quadratic forms for rational links.
Introduces -framings for surfaces, generalizing quadratic forms.
We introduce a Bernstein-type inequality which serves to uniformly control quadratic forms of gaussian variables. The latter can for example be used to derive sharp model selection criteria for linear estimation in linear regression and linear inverse problems via penalization, and we do not exclude that its scope of a…
Given a smooth function f on R^n and a submanifold M, we prove that the set of diagonal quadratic forms q such that the restriction of f+q to M is Morse is a dense set (in the n-dimensional space of diagonal quadratic forms). The standard transversality argument seems not to work and we need a more refined approach.
We introduce a notion of doubly warped product of weighted graphs that is consistent with the doubly warped product in the Riemannian setting. We establish various discrete Bakry-Émery Ricci curvature-dimension bounds for such warped products in terms of the curvature of the constituent graphs. This requires deliberate…
Markov's theorem classifies the worst irrational numbers with respect to rational approximation and the indefinite binary quadratic forms whose values for integer arguments stay farthest away from zero. The main purpose of this paper is to present a new proof of Markov's theorem using hyperbolic geometry. The main ingr…
The main purpose of the paper is twofold: First, to extend a well known theorem of Ruh-Vilms in the Euclidean space to symmetric spaces and, secondly, to apply this result to extend Hoffman-Osserman-Schoen Theorem (HOS Theorem) to 3-dimensional symmetric spaces. Precisely, it is defined a Gauss map of a hypersurface M^…
There is considered the problem of describing up to linear conformal equivalence those harmonic cubic homogeneous polynomials for which the squared-norm of the Hessian is a nonzero multiple of the quadratic form defining the Euclidean metric. Solutions are constructed in all dimensions and solutions are classified in d…
This thesis is concerned with the residues modulo 4 and 8 of the signature of a 4k-dimensional oriented geometric Poincare complex. The Z_8-valued Brown-Kervaire invariant of Z_4-valued quadratic forms is used to prove that if the signature is divisible by 4, the divisibility by 8 is detected by the Arf invariant of a …
Unified framework for measuring concentration in weighted networks considering both weight distributions and network structure.
Study resolvent convergence for random matrices with general covariance profiles.
Unified methodology for statistical inference in least squares and PCA via randomized sketching.
Consider a closed connected hypersurface in with constant signature (k,l) of the second quadratic form, and approaching a quadratic cone at infinity. This hypersurface divides into two pieces. We prove that one of them contains a k-dimensional subspace, and another contains a l-dimensional…
A new test method improves goodness-of-fit tests for copulas.
In this paper, we present a unified study of the moduli space of tropical curves and Outer space which we link via period maps to the moduli space of tropical abelian varieties and the space of positive definite quadratic forms. Our work is a first step towards exhibiting Outer space and the space of positive definite …
The study examines growth of quadratic forms under Anosov subgroups.
New non-isotopic Seifert surfaces found in 4-ball.
The paper develops approximations for Pearson's chi-square statistic and applies them to confidence intervals.
We consider a quadratic form defined on the surfaces with parallel mean curvature vector of an any dimensional complex space form and prove that its -part is holomorphic. When the complex dimension of the ambient space is equal to we define a second quadratic form with the same property and then determine th…
Study of quadratic form associated with surface automorphisms and its applications to singularity theory.
We generalize Fujiki relation of Beauville-Bogomolov quadratic form on a projective symplectic variety. As an application, we study a fibre space structure of a projective symplectic variety.
Recurrent Neural Networks (RNNs) are rich models for the processing of sequential data. Recent work on advancing the state of the art has been focused on the optimization or modelling of RNNs, mostly motivated by adressing the problems of the vanishing and exploding gradients. The control of overfitting has seen consid…
Several important families of computational and statistical results in machine learning and randomized algorithms rely on uniform bounds on quadratic forms of random vectors or matrices. Such results include the Johnson-Lindenstrauss (J-L) Lemma, the Restricted Isometry Property (RIP), randomized sketching algorithms, …
Testing independence is of significant interest in many important areas of large-scale inference. Using extreme-value form statistics to test against sparse alternatives and using quadratic form statistics to test against dense alternatives are two important testing procedures for high-dimensional independence. However…
Research classifies quadratic forms over various fields.
The paper solves the existence problem of sphere packings in higher dimensions.
New derivation shows spacetime interval is quadratic without light.
The first part of this paper exposits a simple geometric description of the Kirby-Siebenmann invariant of a 4--manifold in terms of a quadratic refinement of its intersection form. This is the first in a sequence of higher-order intersection invariants of Whitney towers studied by the authors, particularly for the 4--b…
The paper establishes a Miyaoka-Yau type inequality for hyperplane arrangements in complex projective space.
For a non-orientable closed surface standardly embedded in the 4-sphere, a diffeomorphism over this surface is extendable if and only if this diffeomorphism preserves the Guillou-Marin quadratic form of this embedded surface.
Develops a foundational argument for Lorentzian or Euclidean spacetime geometry without light or electromagnetic phenomena.
The paper classifies Weyl tensors in Riemannian 4-manifolds via Lorentzian deformation.
Here I give a description of Alexandrov 4-point comparison via quadratic forms and then propose a natural 5-point condition which might have some future. Consider this note as a letter from me --- do not take it seriously.