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 computes G-index for specific hyperbolic manifolds.
We introduce \textcolor{red}{general} new techniques for computing the geometric index of a link in the interior of a solid torus . These techniques simplify and unify previous ad hoc methods used to compute the geometric index in specific examples \textcolor{red}{ and allow the simple computation of geometric i…
Noise Sensitivity Exponent controls statistical-computational gaps in learning.
We compute the index of the real Cauchy-Riemann operator defined in FJRW theory in case of the smooth metric. For the cylindrical metric, we study the relation between the index of the linearized operator of Witten map and weights in weighted Sobolev space.
Develops obstruction theory for a specific 4-manifold index.
Paper calculates Morse index of Y-singular minimal surfaces.
New tools compute index of symmetry in homogeneous fibrations.
It is well known that quantifying uncertainty in the action-value estimates is crucial for efficient exploration in reinforcement learning. Ensemble sampling offers a relatively computationally tractable way of doing this using randomized value functions. However, it still requires a huge amount of computational resour…
Researchers compute the index of a specific operator on contact manifolds.
Formula calculates index for CR operators on surfaces with boundary punctures.
We define the "localized index" of longitudinal elliptic operators on Lie groupoids associated to Lie algebroid cohomology classes. We derive a topological expression for these numbers using the algebraic index theorem for Poisson manifolds on the dual of the Lie algebroid. Underlying the definition and computation of …
New index formula for hypoelliptic operators on manifolds.
Researchers develop a numerical method to compute the index of self-shrinkers, finding it to be 5 for the Angenent torus.
We find various lower and upper bounds for the index of Wente tori that contain a continuous family of planar principal curves. We then prove a result that gives an algorithm for computing the index sharply.
We prove a local index formula in conformal geometry by computing the Connes-Chern character for the conformal Dirac (twisted) spectral triple recently constructed by Connes-Moscovici. Following an observation of Moscovici, the computation reduces to the computation of the CM cocycle of an equivariant Dirac (ordinary) …
We compute the index of a Callias-type operator with APS boundary condition on a manifold with compact boundary in terms of combination of indexes of induced operators on a compact hypersurface. Our result generalizes the classical Callias-type index theorem to manifolds with compact boundary.
We compute lower bounds for the Morse index and nullity of constant mean curvature tori of revolution in the three-dimensional unit sphere. In particular, all such tori have index at least five, with index growing at least linearly with respect to the number of the surfaces' bulges, and the index of such tori can be ar…
Quantum computing tackles non-convex portfolio optimization with cardinality constraints.
The aim of this paper is to give an explicit formula in order to compute the Maslov index of the fundamental solution of a linear autonomous Hamiltonian system, in terms of the Conley-Zehnder index and the time one flow.
A new index rebalancing strategy reduces large constituent weights without undesirable effects.
The paper calculates the index and nullity of Fraser-Sargent surfaces and provides bounds.
We show how the index formula for manifolds with fibered boundaries can be used to compute the index of the Dirac operator on Taub-NUT space twisted by an anti-self-dual generic instanton connection.
Proves formula for 3D index change with Dehn filling.
An index theory for projective families of elliptic pseudodifferential operators is developed. The topological and the analytic index of such a family both take values in twisted K-theory of the parametrizing space, X. The main result is the equality of these two notions of index when the twisting class is in the torsi…
In this paper we introduce the notion of an unknotting index for virtual knots. We give some examples of computation by using writhe invariants, and discuss a relationship between the unknotting index and the virtual knot module. In particular, we show that for any non-negative integer there exists a virtual knot w…
Study hypoelliptic operators on Carnot manifolds, extending index theory results.
We investigate index theory in the context of Dirac operators coupled to superconnections. In particular, we prove a local index theorem for such operators, and for families of such operators. We investigate eta-invariants and prove an APS-theorem, and construct a geometric determinant line bundle for families of such …
The goal is to understand the index-theoretic aspects of the recent preprint of R. Nest and F. Radulescu, math.OA/9911042. The basic observation (due to E. Guenter/N. Higson) is that the index of the Toeplitz operator is equal to the index of an associated Callias type operator, i.e. a Dirac operator with potential, th…
Counterexample disproves key index computation in Gromov's conjecture paper.
We introduce a notion of cobordism of Callias-type operators over complete Riemannian manifolds and prove that the index is preserved by such a cobordism. As an application we prove a gluing formula for Callias-type index. In particular, a usual index of an elliptic operator on a compact manifold can be computed as a s…
In this note several computations of equivariant cohomology groups are performed. For the compactly supported equivariant cohomology, the notion of infinitesimal index developed in arXiv:1003.3525, allows to describe these groups in terms of certain spaces of distributions arising in the theory of splines. The new vers…
We consider the problem of pricing derivatives written on some industrial loss index via utility indifference pricing. The industrial loss index is modelled by a compound Poisson process and the insurer can adjust her portfolio by choosing the risk loading, which in turn determines the demand. We compute the price of a…
Minimal hypersurfaces in real projective spaces have at least n+2 Morse index.
Study links' arc index and Turaev genus, proving conjectures.
The Hype Index measures media attention to equities using NLP.
In this paper, we give proofs of the family index formula and the equivariant family index formula by the Greiner's approach to heat kernel asymptotics. We compute equivariant family JLO characters. We also define the equivariant eta form and give a proof of its regularity.
The paper proves index theorems for graph-based optimal control problems.
A recent anomaly computation of Horava and Witten is proved and generalized in the form of two index theorems in odd dimensions. Theorem A is a fixed point formula for orientation-reversing involutions. Theorem B is an index theorem for manifolds with boundary using local boundary conditions. Both hold for families of …
Study on indexability of restless multi-armed bandits and rollout policy performance.
New algorithm uses Whittle index to improve Q-learning for restless bandits.
Mathai, Melrose, and Singer introduced the notion of projective elliptic operators on manifolds equipped with an Azumaya bundle. In this note we compute the equivariant index of transversally elliptic operators that are the pullback of projective elliptic operators on the trivialization of the Azumaya bundle. It encomp…
The virtual dimensions of both framed and unframed SU(2) magnetic monopoles on asymptotically conic 3-manifolds are obtained by computing the index of a Fredholm extension of the associated deformation complex. The unframed dimension coincides with the one obtained by Braam for conformally compact 3-manifolds. The comp…
We develop a general method to compute the Morse index of branched Willmore spheres and show that the Morse index is equal to the index of certain matrix whose dimension is equal to the number of ends of the dual minimal surface. As a corollary, we find that for all immersed Willmore spheres $\vecΦ:S^2\rightarrow \math…
Researchers compute the index of meromorphic functions on tori.
New upper bounds on superbridge index for 49 knots, increasing known results to 49.
We determine all critical configurations for the Area function on polygons with vertices on a circle or an ellipse. For isolated critical points we compute their Morse index, resp index of the gradient vector field. We relate the computation at an isolated degenerate point to an eigenvalue question about combinations. …
This is an expository paper which gives a proof of the Atiyah-Singer index theorem for Dirac operators, presenting the theorem as a computation of the K-homology of a point. This paper and its follow up ("K-homology and index theory II: Elliptic Operators") was written to clear up basic points about index theory that a…
Constructs index for elliptic operators using rapidly decaying kernels.