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.
We interpret an open orbit in a 32-dimensional representation space of Spin(9,1) x SL(2,R) as a substitute for the non-existent group of invertible 2x2 matrices over the octonions and study various natural homogeneous subspaces. The approach is via twistor geometry in eight dimensions.
In this paper we show how generalized quaternions, including 2X2 matrices, can be used to find solutions of a non-commuting equation intimately connected with braid groups. These solutions can then be used to find polynomial invariants of virtual knots and links.
Using the representation of the isometries as 2x2 invertible matrices over the division algebra $\H$ of quaternions, we give an algebraic characterization of the dynamical types of the orientation-preserving isometries of the hyperbolic 5-space. We also determine the conjugacy classes and the conjugacy classes of centr…
It is known, since works of Burde and de Rham, that one can detect the roots of the Alexander polynomial of a knot by the study of the representations of the knot group into the group of the invertible upper triangular matrices. In this work, we propose to generalize this result by considering the representations…
The paper presents a new algebraic structure for planar surfaces.
The paper explores spinors and polyforms using quaternions and octonions.
An explicit solution found for maximizing/minimizing agreement in a 2x2 table.
The paper reduces the complexity of financial market correlation matrices to a 2x2 matrix.
We present a 2x2 Lax representation for discrete circular nets of constant negative Gauß curvature. It is tightly linked to the 4D consistency of the Lax representation of discrete K-nets (in asymptotic line parametrization). The description gives rise to Bäcklund transformations and an associated family. All the membe…
If a knot is represented by an m-strand braid, then HOMFLY polynomial in representation R is a sum over characters in all representations Q\in R^{\otimes m}. Coefficients in this sum are traces of products of quantum R-matrices along the braid, but these matrices act in the space of intertwiners, and their size is equa…
We introduce a new integrable system hierarchy which is a restriction of the AKNS nxn hierarchy coming from an unusual splitting of the loop algebra. This splitting comes from an automorphism of the loop algebra instead of an automorphism of SL(n,C). It is known that the 2x2 KdV is the standard KdV hierarchy.
Let G a be subgroup of SL(2,C), the group of 2x2 matrices of determinant 1 with complex entries. Let h map onto h(G) be a homomorphism. We call h a trace preserving homomorphism if tr(h(g))=tr(g) for all g in G,where tr(g) is the trace of g. We solve the question of when a trace invariant homomorphism is a conjugation …
Using geometrical approach exposed in arXiv:math/0304245 and arXiv:nlin/0511012, we explore the Camassa-Holm equation (both in its initial scalar form, and in the form of 2x2-system). We describe Hamiltonian and symplectic structures, recursion operators and infinite series of symmetries and conservation laws (local an…
The Kinetic Gas Theory like two-agent money exchange models, recently introduced in the Econophysics of Wealth distributions, are revisited. The emergence of Boltzmann-Gibbs like distribution of individual money to Pareto's law in the tail of the distribution is examined in terms of 2x2 Transition matrix with a general…
We develop a theory of bid and ask price dynamics where the two prices form due to interaction of buy and sell orders. In this model the two prices are represented by eigenvalues of a 2x2 price operator corresponding to "bid" and "ask" eigenstates. Matrix elements of price operator fluctuate in time which results in ph…
If a curve in R^3 is closed, then the curvature and the torsion are periodic functions satisfying some additional constraints. We show that these constraints can be naturally formulated in terms of the spectral problem for a 2x2 matrix differential operator. This operator arose in the theory of the self-focusing Nonlin…
We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of statistical independence between the microscopical variables of the system. Moreover, we e…
New kernels from neural networks show better performance than traditional methods.
No-regret learning fails to converge to Nash equilibria in mixed strategies.
Quantum theory explains price dynamics in financial markets, capturing bid-ask spread and ergodicity.
Participants enrolled into randomized controlled trials (RCTs) often do not reflect real-world populations. Previous research in how best to translate RCT results to target populations has focused on weighting RCT data to look like the target data. Simulation work, however, has suggested that an outcome model approach …
Study conullity two manifolds with constant scalar curvature.
We simplify matrix computations for block matrices, especially useful for covariance and correlation matrices.
Minimal submanifolds in matrix spaces proven for specific ranks.
The field of precision medicine aims to tailor treatment based on patient-specific factors in a reproducible way. To this end, estimating an optimal individualized treatment regime (ITR) that recommends treatment decisions based on patient characteristics to maximize the mean of a pre-specified outcome is of particular…
Computes isotropy subgroups of orthogonal matrices acting on Hermitian matrices.
Study on random matrices in deep neural networks using Gaussian data.
Study on random matrices in deep neural networks with IID entries.
Financial markets analyzed by reducing correlation matrix complexity.
Study isotropy groups for complex orthogonal and skew-symmetric matrices.
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…
By formulating N = 1, 2, 4, 8, D = 3, Yang-Mills with a single Lagrangian and single set of transformation rules, but with fields valued respectively in R,C,H,O, it was recently shown that tensoring left and right multiplets yields a Freudenthal-Rosenfeld-Tits magic square of D = 3 supergravities. This was subsequently…
Study of strictly accretive matrices using Finsler geometry.
Minimal spectral radii found for specific matrix types.
Researchers develop geodesics for a new metric on correlation matrices.
We find an upper bound for geodesic distances associated to monotone Riemannian metrics on positive definite matrices and density matrices.
New methods for sketching non-PSD matrices improve regression and optimization tasks.
Improved method for computing Fréchet means on SPD matrices.
Algorithm finds isotropy subgroups of orthogonal similarity on symmetric matrices.
We consider the problem of approximate joint triangularization of a set of noisy jointly diagonalizable real matrices. Approximate joint triangularizers are commonly used in the estimation of the joint eigenstructure of a set of matrices, with applications in signal processing, linear algebra, and tensor decomposition.…
Method estimates M-matrices in graphical models with improved accuracy.
Algorithm calculates Seifert matrices for colored links.
A framework estimates multiple precision matrices with shared structures.
In this paper we extend DDVV-type inequalities involving the Frobenius norm of commutators from real symmetric and skew-symmetric matrices to Hermitian and skew-Hermitian matrices.
Proposes a new Sliced-Wasserstein distance for covariance matrices in M/EEG signals.
Study extends bounds on sample covariance matrices with general dependence.
New -means method clusters radar image sequences using SPD matrices.
Kaleidoscope matrices improve model quality and inference speed.