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.
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.
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.
New method uses binary quadratic forms to classify Seifert surfaces in 4-ball.
Enhances power of covariance matrix tests for high-dimensional data.
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…
Novel link classification connects quadratic forms and knot theory.
Study quadratic one-forms on logarithmic Higgs bundles on pointed curves.
New quadratic forms expand and rotate linear endomorphisms in geometric theory.
Proves non-positivity of Hirzebruch form on stable weights and connects to flat logarithmic connections.
Hurwitz transformations are defined as specific automorphisms of a Cayley-Dickson algebra. These transformations generate quadratic and nonquadratic forms. We investigate here the Hurwitz transformations corresponding to Cayley-Dickson algebras of dimensions 2m = 2, 4 and 8. The Hurwitz transformations which lead to qu…
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…
Quadratic points of a surface in the projective 3-space are the points which can be exceptionally well approximated by a quadric. They are also singularities of a 3-web in the elliptic part and of a line field in the hyperbolic part of the surface. We show that generically the index of the 3-web at a quadratic point is…
Geometrically describes the linear and quadratic forms for rational links.
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.
We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a collection of proximal operators that share the same quadratic form, or if the qu…
The Samuelson condition is not satisfied by tangent lines of quadratic curves.
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.
We generalize Conway's approach to integral binary quadratic forms on Q to study integral binary hermitian forms on quadratic imaginary extensions of Q. In Conway's case, an indefinite form that doesn't represent 0 determines a line ("river") in the spine T associated with SL(2,Z) in the hyperbolic plane. In our genera…
Study connects curvature to graph theory and reveals differences.
Unified view of surfaces in R^n using Gauss map, caustics, and quadratic forms.
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…
We give sufficient conditions for a noncompact Riemannian manifold, which has quadratic curvature decay, to have finite topological type with ends that are cones over spherical space forms.
Introduces -framings for surfaces, generalizing quadratic forms.
Paper classifies conic submanifolds in control systems.
We investigate classification results for general quadratic functions on torsion abelian groups. Unlike the previously studied situations, general quadratic functions are allowed to be inhomogeneous or degenerate. We study the discriminant construction which assigns, to an integral lattice with a distinguished characte…
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…
New derivation shows spacetime interval is quadratic without light.
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.
Closed-form polynomial approximations replace MLPs in transformers, enabling new interpretability methods.
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 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^…
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…
Proposes QDF to improve multi-step time-series forecasting.
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are mostly not scalable. In this paper, we develop a method that transforms the quadra…
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…
New non-isotopic Seifert surfaces found in 4-ball.
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…
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…
Study of zero-divisors in sedenions via determinant factorization.
Inspired by complexity and diversity of biological neurons, our group proposed quadratic neurons by replacing the inner product in current artificial neurons with a quadratic operation on input data, thereby enhancing the capability of an individual neuron. Along this direction, we are motivated to evaluate the power o…
The study examines growth of quadratic forms under Anosov subgroups.
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 …
Study of quadratic form associated with surface automorphisms and its applications to singularity theory.
Study resolvent convergence for random matrices with general covariance profiles.
Unified methodology for statistical inference in least squares and PCA via randomized sketching.
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 …