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.
Common positive stabilisation found for isotopic contact structures.
New open books defy positive factorisation in genus one.
New method for learning with non-Euclidean data using decomposable kernels.
Paper solves open question about non-positive kernels by decomposing them into PD kernels.
The study proves manifolds with positive scalar curvature can be decomposed into spherical and toroidal pieces.
Study grid homology of diagonal knots, finding key terms related to prime factors and decompositions.
Given a 3-holed sphere decomposition of an orientable closed surface, it is shown that each orientation preserving homeomorphism of the surface is isotopic to a composition AB where A is a product of positive Dehn twists and B is a product of negative Dehn twists on the decomposition curves.
Let k be a knot in S3. In [8], H.N. Howards and J. Schultens introduced a method to construct a manifold decomposition of double branched cover of (S3, k) from a thin position of k. In this article, we will prove that if a thin position of k induces a thin decomposition of double branched cover of (S3,k) by Howards and…
Article generalizes open book construction for 5D contact pairs.
It is known by A. Loi and R. Piergallini that a closed, oriented, smooth 3-manifold is Stein fillable if and only if it has a positive open book decomposition. In the present paper we will show that for every link L in a Stein fillable 3-manifold there exists an additional knot L' to L such that the union of the links …
Study elliptic isometries on a matrix manifold with specific metrics.
Study of 3-manifolds in 5-sphere using bridge decompositions.
We show that any non-minimal bridge decomposition of a torus knot is stabilized and that -bridge decompositions of a torus knot are unique for any integer . This implies that a knot in a bridge position is a torus knot if and only if there exists a torus containing the knot such that it intersects the bridge sphe…
New proof of Giroux Correspondence for tight contact 3-manifolds.
New analysis of crushing surfaces of positive genus impacts triangulation complexity.
Paper breaks down risk contribution into inherent and correlation risk components.
We present an elementary treatment of the Optional Decomposition Theorem for continuous semimartingales and general filtrations. This treatment does not assume the existence of equivalent local martingale measure(s), only that of strictly positive local martingale deflator(s).
The paper explores totally geodesic submanifolds in SPD matrices and their properties.
In this paper, we determine the canonical polyhedral decomposition of every hyperbolic once-punctured torus bundle over the circle. In fact, we show that the only ideal polyhedral decomposition that is straight in the hyperbolic structure and that is invariant under a certain involution is the ideal triangulation defin…
We show that the eigenspaces of the Laplacian on -forms on a compact Kähler manifold carry Hodge and Lefschetz decompositions. Among other consequences, we show that the positive part of the spectrum of lies in the spectrum of .
For Einstein four-manifolds with positive scalar curvature, we derive relations among various positivity conditions on the curvature tensor, some of which are of great importance in the study of the Ricci flow. These relations suggest possible new ideas to study the well-known rigidity conjecture for positively curved …
This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition technique yields consistent parameter estimates from low-order observable moments, wit…
We develop the structure theory of full isometry groups of locally compact non-positively curved metric spaces. Amongst the discussed themes are de Rham decompositions, normal subgroup structure and characterising properties of symmetric spaces and Bruhat--Tits buildings. Applications to discrete groups and further dev…
We introduce Clique Matrices as an alternative representation of undirected graphs, being a generalisation of the incidence matrix representation. Here we use clique matrices to decompose a graph into a set of possibly overlapping clusters, de ned as well-connected subsets of vertices. The decomposition is based on a s…
We present a new Riemannian metric, termed Log-Cholesky metric, on the manifold of symmetric positive definite (SPD) matrices via Cholesky decomposition. We first construct a Lie group structure and a bi-invariant metric on Cholesky space, the collection of lower triangular matrices whose diagonal elements are all posi…
The paper shows knots can have zero support genus in certain spaces.
Study shows knots surgered elliptic surfaces admit handle decompositions without 1- and 3-handles.
New matrix approximation method using RBF components for better memory efficiency.
New geometric framework for positive semidefinite matrices of fixed rank.
We study diffeomorphisms of compact, oriented surfaces, developing methods of distinguishing those which have positive factorizations into Dehn twists from those which satisfy the weaker condition of right veering. We use these to construct open book decompositions of Stein-fillable 3-manifolds whose monodromies have n…
We provide a complete set of two moves that suffice to relate any two open book decompositions of a given 3-manifold. One of the moves is the usual plumbing with a positive or negative Hopf band, while the other one is a special local version of Harer's twisting, which is presented in two different (but stably equivale…
A real 3-manifold is a smooth 3-manifold together with an orientation preserving smooth involution, called a real structure. In this article we study open book decompositions on smooth real 3-manifolds that are compatible with the real structure. We call them real open book decompositions. We show that each real open b…
Denise learns a function to quickly decompose covariance matrices robustly.
Counterexample disproves log canonical Beauville--Bogomolov decomposition.
Paper tackles tensor decomposition for unaligned observations using RKHS and novel loss functions.
In the present paper, we study deformations of polar weighted homogeneous polynomials which are also polar weighted homogeneous polynomials. We describe a round handle decomposition of the Milnor fibration of a deformation of a polar weighted homogeneous polynomial concretely and give the number of round handles by the…
Paper defines new stability and metrics for complex spaces.
Study of strictly accretive matrices using Finsler geometry.
We prove that Stein surfaces with boundary coincide up to orientation preserving diffeomorphisms with simple branched coverings of $\B^4$ whose branch set is a positive braided surface. As a consequence, we have that a smooth oriented 3-manifold is Stein fillable iff it has a positive open-book decomposition.
3D contact forms have supporting decompositions, leading to entropy results.
New -vectors reveal geometric Lefschetz-like decompositions of flag spheres.
The study shows conditions for elliptic surfaces without 1-handles.
We find a canonical decomposition of a geodesic current on a surface of finite type arising from a topological decomposition of the surface along special geodesics. We show that each component either is associated to a measured lamination or has positive systole. For a current with positive systole, we show that the in…
The study proves properties of 4D projective manifolds and builds non-hyperbolic examples.
We prove that any mapping class on a compact oriented surface with nonempty boundary can be made pseudo-Anosov and right-veering after a sequence of positive stabilizations.
Characterizes Legendrian knots in lens spaces.
We break down transformer embeddings into interpretable components revealing hidden geometric structures.
Traders in a stock market exchange stock shares and form a stock trading network. Trades at different positions of the stock trading network may contain different information. We construct stock trading networks based on the limit order book data and classify traders into classes using the -shell decomposition m…