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.
Method determines latent dimensionality in international trade flows.
Study one-dimensional topological theories with linear generating functions.
In their study of the representation theory of loop groups, Pressley and Segal introduced a determinant line bundle over an infinite dimensional Grassmann manifold. Mickelsson and Rajeev subsequently generalized the work of Pressley and Segal and in the process introduced for any p >=1 another infinite dimensional Gras…
Study on pseudo-Einstein 3-manifolds, calculating determinant changes under conformal transformations.
Unique hyperbolic manifolds identified by boundary pleating.
Researchers express spectral determinants on hyperbolic cones.
Study finds all 4D neutral manifolds.
This work generalizes a geometric Laplacian determinant description to higher dimensions.
We discuss the regularized determinant of elliptic boundary value problems on a line segment. Our framework is applicable for separated and non-separated boundary conditions.
We study three-dimensional generalized Ricci solitons, both in Riemannian and Lorentzian settings. We shall determine their homogeneous models, classifying left-invariant generalized Ricci solitons on three-dimensional Lie groups.
In the present paper, we determine the topologies of three-dimensional closed Alexandrov spaces which converge to lower dimensional spaces in the Gromov-Hausdorff topology.
This paper confirms volumes of geodesic balls can identify 4D space forms.
We study the geometry of determinant line bundles associated to Dirac operators on compact odd dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the commutator anomaly formula using a construction based on noncyclic trace extensions…
Paper shows string cobordism at 24 dims can be determined by elliptic genus.
This work presents a parametrized family of divergences, namely Alpha-Beta Log- Determinant (Log-Det) divergences, between positive definite unitized trace class operators on a Hilbert space. This is a generalization of the Alpha-Beta Log-Determinant divergences between symmetric, positive definite matrices to the infi…
We show that the four derivative terms in the effective action of three-dimensional N=8 Yang-Mills theory are determined by supersymmetry. These terms receive both perturbative and non-perturbative corrections. Using our technique for constraining the effective action, we are able to determine the exact form of the eig…
New algorithm selects relevant variables in high-dimensional graphical models.
We give a complete description of semi-symmetric algebraic curvature tensors on a four-dimensional Lorentzian vector space and we use this description to determine all four-dimensional homogeneous semi-symmetric Lorentzian manifolds.
We introduce and develop a novel approach to outlier detection based on adaptation of random subspace learning. Our proposed method handles both high-dimension low-sample size and traditional low-dimensional high-sample size datasets. Essentially, we avoid the computational bottleneck of techniques like minimum covaria…
The conformal anomalies and functional determinants of the Branson--GJMS operators, P_{2k}, on the d-dimensional sphere are evaluated in explicit terms for any d and k such that k < d/2+1 (if d is even). The determinants are given in terms of multiple gamma functions and a rational multiplicative anomaly, which vanishe…
In this paper we determine the at least -dimensional affine reductive homogeneous manifolds for an at most -dimensional simple Lie group or an at most -dimensional semi-simple Lie group. Those reductive spaces among them which admit a sharply transitive differentiable section yield local almost differentiable …
Two-dimensional Riemannian manifolds uniquely determined by boundary data.
We determine the automorphisms and the continuous endomorphisms of the Einstein gyrogroup in arbitrary dimension. This generalizes a recent result of Lajos Molnár and Dániel Virosztek, who have determined the continuous endomorphisms in the three-dimensional case.
We give an integral representaion of the zeta-reguralized determinant of Laplacians on three dimensional Heisenberg manifolds, and study a behaivior of the values when we deform the uniform discrete subgroups. Heiseberg manifolds are the total space of a fiber bundle with a torus as the base space and a circle as a typ…
A neural network method determines the latent dimensionality of NMF.
A marginally trapped surface in the four-dimensional Minkowski space is a spacelike surface whose mean curvature vector is lightlike at each point. We associate a geometrically determined moving frame field to such a surface and using the derivative formulas for this frame field we obtain seven invariant functions. Our…
The main purpose of this paper is to determine the admissible forms of the sectional curvature operator on a three-dimensional locally homogeneous Lorentzian manifolds.
Study of zero-divisors in sedenions via determinant factorization.
More analysis of operator determinants on homogeneous three dimensional lens spaces is presented with the emphasis on numerics so that Laplacians for massive fields can be dealt with. Polyhedral quotients are also briefly considered. Twisted fields, corresponding to flat connections, are looked at and examples of deter…
Let M,M' be smooth real hypersurfaces in N-dimensional space and assume that M is k-nondegenerate at a point p in M. We prove that holomorphic mappings that extend smoothly to M, sending a neighborhood of p in M diffeomorphically into M' are completely determined by their 2k-jet at p. As an application of this result, …
Study finds all 4D Lie groups with harmonic curvature.
Study identifies topologies of 3D spaces with boundary.
On base of three-dimensional flat metrics obtained with the help of solutions of the KdV-equation were constructed the examples of six-dimensional metrics, which are determined by the help of solutions of Krichever-Novikov and KdV. Their properties are discussed.
In the canonical framework, we propose an alternative approach for the multifractal analysis based on the detrending moving average method (MF-DMA). We define a canonical measure such that the multifractal mass exponent is related to the partition function and the multifractal spectrum can be directly det…
The aim of this paper is to determine left-invariant strictly almost Kähler structures on 4-dimensional Lie groups such that the Ricci tensor is -invariant.
In this paper we study homogeneous backgrounds of type IIB supergravity where the underlying geometry is that of a symmetric space. We determine which ten-dimensional lorentzian symmetric spaces (up to local isometry) admit such backgrounds and in about two thirds of the cases we determine fully their moduli space.
We determine the moduli space of metric 2-step nilpotent Lie algebras of dimension up to 6. This space is homeomorphic to a cone over a 4-dimensional contractible simplicial complex.
A numerical expression in the form of an integral is given for the determinant of the scalar GJMS operator on an odd--dimensional sphere. Manipulation yields a curious sum formula for the logdet in terms of the logdets of the ordinary conformal Laplacian for other dimensions. A few graphs are drawn.
Comment on a theorem about surface determination from map data.
Study determines a minimal surface in a Riemannian manifold from boundary data.
For a class of even dimensional conformally compact manifolds (X,g), we define a generalized Krein spectral function by applying a renormalized trace functional to the spectral measure of the Laplacian. We then show that this is the phase of the Kontsevich-Vishik determinant det S(s) of the scattering operator S(s) of …
Study invariant CKY 2-forms on 5D Lie groups, classifying and determining their properties.
In this paper we deal with symplectic Lie algebras. All symplectic structures are determined for dimension four and the corresponding Lie algebras are classified up to equivalence. Symplectic four dimensional Lie algebras are described either as solutions of the cotangent extension problem or as symplectic double exten…
The n-dimensional hypergeometric integrals associated with a hypersphere arrangement are formulated by the pairing of n-dimensional twisted cohomology and its dual. Under the condition of general position there are stated some results which concern an explicit representation of the standard form by a special (NBC) basi…
The Quillen-Bismut-Freed construction associates a determinant line bundle with connection to an infinite dimensional super vector bundle with a family of Dirac-type operators. We define the regularized first Chern form of the infinite dimensional bundle, and relate it to the curvature of the Bismut-Freed connection on…
In this paper we determine all Kobayashi-hyperbolic 2-dimensional complex manifolds for which the group of holomorphic automorphisms has dimension 3. This work concludes a recent series of papers by the author on the classification of hyperbolic -dimensional manifolds, with automorphism group of dimension at least $…
We classify connected sums of three-dimensional lens spaces which smoothly bound rational homology balls. We use this result to determine the order of each lens space in the group of rational homology 3-spheres up to rational homology cobordisms, and to determine the concordance order of each 2-bridge knot.
In this paper, we continue studying the 6-dimensional pseudo-Riemannian space V^6(g_{ij}) with signature [++--], which admits projective motions, i. e. continuous transformation groups preserving geodesics. In particular, we determine a necessary and sufficient condition that the 6-dimensional rigid h-spaces have const…