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.
Maximal index vanishes for certain spin manifolds with positive scalar curvature.
We discuss the relation between arc index, maximal Thurston--Bennequin number, and Khovanov homology for knots. As a consequence, we calculate the arc index and maximal Thurston--Bennequin number for all knots with at most 11 crossings. For some of these knots, the calculation requires a consideration of cables which a…
New index formula for hypoelliptic operators on manifolds.
The study characterizes maximal subgroups of a Thompson group and bounds the change in a knot invariant.
The paper proposes methods to directly optimize complex classification metrics.
Gini index needs auto-calibration for consistent decision-making.
Study quantisation of geometric operators on manifolds with group actions.
Researchers construct an index map for contact manifolds using K-theory.
We study the Cauchy data spaces of the strongly Callias-type operators using maximal domain on manifolds with non-compact boundary, with the aim of understanding the Atiyah-Patodi-Singer index and elliptic boundary value problems.
Classifies totally geodesic submanifolds in exceptional symmetric spaces.
The paper classifies complex Dirac structures on flag manifolds.
Let M be an irreducible Riemannian symmetric space. The index i(M) of M is the minimal codimension of a totally geodesic submanifold of M. In previous work the authors proved that i(M) is bounded from below by the rank rk(M) of M. In this paper we classify all irreducible Riemannian symmetric spaces M for which the equ…
We show that, on a complete and possibly non-compact Riemannian manifold of dimension at least 2 without close conjugate points at infinity, the existence of a closed geodesic with local homology in maximal degree and maximal index growth under iteration forces the existence of infinitely many closed geodesics. For clo…
Maximizes stock portfolio predictability using machine learning.
New RL algorithms learn Gittins indices for unknown Markovian states.
In this paper, we determine the maximally stable, rotationally invariant domains on the catenoids $\cC_a$ (minimal surfaces invariant by rotations) in the Heisenberg group with a left-invariant metric. We show that these catenoids have Morse index at least 3 and we bound the index from above in terms of the parameter $…
Defines an equivariant index for proper actions by .
We investigate a certain class of solvable metric Lie algebras. For this purpose a theory of twofold extensions associated to an orthogonal representation of an abelian Lie algebra is developed. Among other things, we obtain a classification scheme for indecomposable metric Lie algebras with maximal isotropic centre an…
Study of symmetries in 3D Lie groups, determining index and moduli space properties.
A blockchain protocol uses bandit algorithms to dynamically price transactions.
Maximizes probability of completing investment schedules with optimal portfolio weights.
Simplified account of Kubota's work on codimension 2 index obstructions.
New method optimizes policies without assuming known link functions between preferences and rewards.
In this paper, we present a new class of Markov decision processes (MDPs), called Tsallis MDPs, with Tsallis entropy maximization, which generalizes existing maximum entropy reinforcement learning (RL). A Tsallis MDP provides a unified framework for the original RL problem and RL with various types of entropy, includin…
The study proves how groups can be split with limited complexity.
We construct canonical frames and find all maximally symmetric models for a natural generic class of corank 2 distributions on manifolds of odd dimension greater or equal to 7. This class of distributions is characterized by the following two conditions: the pencil of 2-forms associated with the corresponding Pfaffian …
In this paper, the second of a series of two, we continue the study of higher index theory for expanders. We prove that if a sequence of graphs has girth tending to infinity, then the maximal coarse Baum-Connes assembly map is an isomorphism for the associated metric space . As discussed in the first paper in this s…
Higher index theorem for Dirac operators on finite-volume spaces.
We use the symbol calculus for foliations developed in our previous paper to derive a cohomological formula for the Connes-Chern character of the semi-finite spectral triple. The same proof works for the Type I spectral triple of Connes-Moscovici. The cohomology classes of the two Connes-Chern characters induce the sam…
Paper introduces a new measure combining entropy and Gini index.
We consider a curve of Fredholm pairs of Lagrangian subspaces in a fixed Banach space with continuously varying (weak) symplectic structures. Assuming vanishing index, we obtain intrinsically a continuously varying splitting of the total Banach space into pairs of symplectic subspaces. Using such decompositions we defi…
Study models weather index insurance pricing by insurers and farmers, finding flexible pricing kernels boost profits.
New index improves anomaly detection in correlated time series data.
We give a conceptual proof of the fact that if M is a complete submanifold of a space form, then the maximal integral manifolds of the nullity distribution of its second fundamental form through points of minimal index of nullity are complete.
We generalise the Atiyah-Segal-Singer fixed point theorem to noncompact manifolds. Using -theory, we extend the equivariant index to the noncompact setting, and obtain a fixed point formula for it. The fixed point formula is the explicit cohomological expression from Atiyah-Segal-Singer's result. In the noncompact …
In a previous paper, we showed nonvaninishing of the universal index elements in the K-theory of the maximal C*-algebras of the fundamental groups of enlargeable spin manifolds. The underlying notion of enlargeability was the one from the first relevant paper of Gromov and Lawson, involving contracting maps defined on …
A hyperbolic lattice is called \textit{-reflective} if the subgroup of its automorphism group generated by all - and -reflections is of finite index. The main result of this article is a complete classification of -reflective maximal anisotropic lattices of rank .
Study on indexability of restless multi-armed bandits and rollout policy performance.
In this paper we prove a strengthening of a theorem of Chang, Weinberger and Yu on obstructions to the existence of positive scalar curvature metrics on compact manifolds with boundary. They construct a relative index for the Dirac operator, which lives in a relative K-theory group, measuring the difference between the…
In 1987, Kalai proved that stacked spheres of dimension are characterised by the fact that they attain equality in Barnette's celebrated Lower Bound Theorem. This result does not extend to dimension . In this article, we give a characterisation of stacked -spheres using what we call the {\em separatio…
New bandit model for healthcare intervention planning.
The paper predicts survival functions using random survival trees and concordance maximization.
New spectral estimates for minimal surfaces with boundary conditions.
We construct and analyze minimal disc stackings with bounds on their Morse index.
Characterizes diagrams achieving Morton-Franks-Williams inequality for positive knots and links.
Let G be a connected compact Lie group acting on a manifold M and let D be a transversally elliptic operator on M. The multiplicity of the index of D is a function on the set of irreducible representations of G. Let T be a maximal torus of G with Lie algebra Lie(T). We construct a finite number of piecewise polynomial …
We prove a generalized version of the Morse index theorem for geodesics endowed with a non positive definite metric tensor (semi-Riemannian manifolds). We apply the result to obtain lower estimates on the number of geodesics joining two fixed non conjugate points in certain classes of manifolds. More specifically, we c…
Estimate relaxation times in nonextensive systems using gradient flow for Tsallis entropy maximization.