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.
Paper derives matrix formulae and proves skein relations for non-orientable surfaces in quasi-cluster algebras.
Matrix formulas for super Teichmüller spaces generalize previous work and yield super λ-lengths.
Formula for sectional curvatures on matrix groups.
Harer-Zagier formulas generalized to knot matrix models.
Derives adjoint formulas for matrix operations and applies them to specific cases.
We present a formula for the trace of any symmetric power of a matrix (with coefficients in a field) in terms of the ordinary powers of the matrix, an arbitrarily chosen linear function which vanishes on the identity matrix, and polynomial functions defined recursively.
This paper concerns cluster algebras with principal coefficients A(S,M) associated to bordered surfaces (S,M), and is a companion to a concurrent work of the authors with Schiffler [MSW2]. Given any (generalized) arc or loop in the surface -- with or without self-intersections -- we associate an element of (the fractio…
We obtain a family of matrix integrals which decompose to a product of Gamma-functions (they have some relations with S.G.Gindikin 'Beta', but generally speaking essentially differ from it). We obtain Plancherel formula for Berezin representations for all series of classical groups (for large values of parameters of re…
New Hessian estimates for heat equations on manifolds.
Proves a formula for Kontsevich-Witten tau-function using Schur Q-polynomials.
In this article we give an explicit description of the representation matrix of a Heisenberg type action constructed by Blanchet, Habegger, Masbaum and Vogel. We give the matrix in terms of a ribbon graph and its admissible colorings. We show that components of the representation matrix satisfies the {\it external edge…
We present two formulas for Chern classes of the tensor product of two vector bundles. In the first formula we consider a matrix containing Chern classes of the first bundle and we take a polynomial of this matrix with Chern classes of the second bundle as coefficients. The determinant of this expression equals the Che…
We study the heat kernel asymptotics for the Laplace type differential operators on vector bundles over Riemannian manifolds. In particular this includes the case of the Laplacians acting on differential p-forms. We extend our results obtained earlier for the scalar Laplacian and present closed formulas for all heat in…
Gradient descent solves rank-one matrix estimation problem with detailed time evolution analysis.
On a constraint manifold we give an explicit formula for the Hessian matrix of a cost function that involves the Hessian matrix of a prolonged function and the Hessian matrices of the constraint functions. We give an explicit formula for the case of the orthogonal group by using only Euclidean coordinates …
Simple matrix formulas for Grassmannian curvatures.
Paper finds formulas for mutual information and MMSE in matrix tensor product problems.
Many iterative and non-iterative methods have been developed for inverse problems associated with Ising models. Aiming to derive an accurate non-iterative method for the inverse problems, we employ the tree-reweighted approximation. Using the tree-reweighted approximation, we can optimize the rigorous lower bound of th…
This handbook simplifies Grassmann manifold geometry for matrix-based algorithms.
In this article we give a unified treatment of the construction of all possible Weitzenböck formulas for all irreducible, non--symmetric holonomy groups. The resulting classification is two--fold, we construct explicitly a basis of the space of Weitzenböck formulas on the one hand and characterize Weitzenböck formulas …
This paper sets fundamental limits for rank-one matrix estimation with varying noise levels.
In Part I (arXiv:1209.2045) we computed the Stokes data, though not the "connection matrix", for the smooth solutions of the tt*-Toda equations whose existence we established by p.d.e. methods. Here we give an alternative proof of the existence of some of these solutions by solving a Riemann-Hilbert problem. In the pro…
New proof for knot state-sum formula using bijection between states.
In this paper, we prove a mean value formula for bounded subharmonic Hermitian matrix valued function on a complete Riemannian manifold with nonnegative Ricci curvature. As its application, we obtain a Liouville type theorem for the complex Monge-Ampère equation on product manifolds.
Estimates the probability of a random symmetric tensor being close to rank-one.
A new method for efficiently computing derivatives of skew-symmetric matrix exponentials.
We derive an analytic formula for the dual Jacobian matrix of a generalised hyperbolic tetrahedron. Two cases are considered: a mildly truncated and a prism truncated tetrahedron. The Jacobian for the latter arises as an analytic continuation of the former, that falls in line with a similar behaviour of the correspondi…
Proves estimates for Kähler-Ricci flow solutions.
Abstract: Determinants and formulas for operators on various spaces.
This paper studies HOMFLY polynomials of specific and infinite classes of knots.
We prove an adiabatic decomposition formula of the zeta-determinant of the Laplace type operator with respect to Dirichlet boundary condition. We allow the non-invertible tangential operator. As a result, our adiabatic decomposition formula involves the scattering matrix over the manifold with cylindrical end. We also …
We show that integration over a -manifold can be reduced to integration over a minimal section with respect to an induced weighted measure and integration over a homogeneous space . We relate our formula to integration formulae for polar actions and calculate some weight functions. In case of a compact …
This talk is a report on joint work with A. Vaintrob [arXiv:math.CO/0109104 and math.GT/0111102]. It is organised as follows. We begin by recalling how the classical Matrix-Tree Theorem relates two different expressions for the lowest degree coefficient of the Alexander-Conway polynomial of a link. We then state our fo…
We derive the explicit formula for the joint Laplace transform of the Wishart process and its time integral which extends the original approach of Bru. We compare our methodology with the alternative results given by the variation of constants method, the linearization of the Matrix Riccati ODE's and the Runge-Kutta al…
Proves conjecture about integer sums of torus knot torsions.
The paper defines and calculates fourth fundamental form and i-th curvatures for hypersurfaces in 4D Euclidean space.
A1GM method improves efficiency in reconstructing missing data using KL divergence.
Paper derives local Plücker formulas for special orthogonal groups.
New formulas derived for Jones polynomial of rational links.
In the setting of polynomial jump-diffusion dynamics, we provide an explicit formula for computing correlators, namely, cross-moments of the process at different time points along its path. The formula appears as a linear combination of exponentials of the generator matrix, extending the well-known moment formula for p…
After defining convex near-polygons, a formula enumerating the number of triangulations of such configurations is derived in terms of edge-polynomials. The paper describes also a transfer-matrix approach for computing quantities related to triangulations.
New method improves covariance estimation for weighted samples.
We present in this work a new family of kernels to compare positive measures on arbitrary spaces $\Xcal$ endowed with a positive kernel , which translates naturally into kernels between histograms or clouds of points. We first cover the case where $\Xcal$ is Euclidian, and focus on kernels which take into account th…
Study on overlaps of singular vectors in Gaussian matrix submatrices.
In this paper, we define the eta cochain form and prove its regularity when the kernel of a family of Dirac operators is a vector bundle. We decompose the eta form as a pairing of the eta cochain form with the Chern character of an idempotent matrix and we also decompose the Chern character of the index bundle for a fi…
Paper derives a formula for the determinant of Dirichlet-to-Neumann operator on Riemann surfaces.
We solve principal component regression (PCR), up to a multiplicative accuracy , by reducing the problem to black-box calls of ridge regression. Therefore, our algorithm does not require any explicit construction of the top principal components, and is suitable for large-scale PCR instances. In…
Recently, a lot of effort has been paid to the efficient computation of Kriging predictors when observations are assimilated sequentially. In particular, Kriging update formulae enabling significant computational savings were derived in Barnes and Watson (1992), Gao et al. (1996), and Emery (2009). Taking advantage of …